From b34b60bcc821e09a08bcb1f08cb3f214a8117a5b Mon Sep 17 00:00:00 2001 From: Joerg Sonnenberger Date: Tue, 26 Jul 2005 21:15:20 +0000 Subject: [PATCH] FreeBSD and NetBSD both use derivates of Sun's math library. On FreeBSD, it's been put into lib/msun, on NetBSD it is under lib/libm. Since DragonFly misses a lot of the changes which went into both and I consider the NetBSD version cleaner, switch to that. Biggest difference to NetBSD is the omission of wrappers for non-IEEE757 floating point support. There's no point in supporting anything but IEEE 757 and that saves at least a function call per math entry point. Addtionally, important the fpclassify, isinf, isnan and signbit functions into libc as required for C99. Remove the support for non-POSIX operation. matherr is pointless and wasn't really supported anyway. --- Makefile.inc1 | 4 +- gnu/usr.bin/groff/src/libs/libgroff/Makefile | 4 +- include/Makefile | 4 +- include/math.h | 400 ++++++++++ lib/Makefile | 5 +- lib/libc/gen/Makefile.inc | 23 +- lib/libc/gen/fpclassify.3 | 90 +++ lib/libc/gen/fpclassifyd.c | 67 ++ lib/libc/gen/fpclassifyf.c | 67 ++ lib/libc/gen/infinity.c | 16 + lib/libc/gen/infinityf.c | 16 + lib/libc/gen/infinityl_dbl.c | 22 + lib/libc/gen/isfinite.3 | 77 ++ lib/libc/gen/isfinited.c | 58 ++ lib/libc/gen/isfinitef.c | 58 ++ lib/libc/gen/isinf.3 | 74 +- lib/libc/{i386/gen/isinf.c => gen/isinfd.c} | 54 +- lib/libc/{i386/gen/isinf.c => gen/isinff.c} | 54 +- lib/libc/gen/{isinf.3 => isnan.3} | 75 +- lib/libc/{i386/gen/isinf.c => gen/isnand.c} | 54 +- lib/libc/{i386/gen/isinf.c => gen/isnanf.c} | 54 +- lib/libc/gen/signbit.3 | 77 ++ lib/libc/gen/signbitd.c | 55 ++ lib/libc/gen/signbitf.c | 55 ++ lib/libc/i386/gen/Makefile.inc | 9 +- lib/libc/i386/gen/flt_rounds.S | 33 + lib/libc/i386/gen/fpclassifyl.c | 70 ++ lib/libc/i386/gen/fpgetmask.S | 23 + lib/libc/i386/gen/fpgetround.S | 23 + lib/libc/i386/gen/fpgetsticky.S | 21 + lib/libc/i386/gen/fpsetmask.S | 34 + lib/libc/i386/gen/fpsetround.S | 35 + lib/libc/i386/gen/fpsetsticky.S | 33 + lib/libc/i386/gen/infinity.c | 10 - lib/libc/i386/gen/infinityl.c | 12 + lib/libc/i386/gen/isfinitel.c | 61 ++ lib/libc/i386/gen/{isinf.c => isinfl.c} | 55 +- lib/libc/i386/gen/{isinf.c => isnanl.c} | 55 +- lib/libc/i386/gen/nanf.c | 9 + lib/libc/i386/gen/signbitl.c | 55 ++ lib/libm/Makefile | 12 + lib/libm/arch/i386/Makefile.inc | 12 + lib/libm/arch/i386/abi.h | 74 ++ lib/libm/arch/i386/e_acos.S | 25 + lib/libm/arch/i386/e_asin.S | 24 + lib/libm/arch/i386/e_atan2.S | 19 + lib/libm/arch/i386/e_atan2f.S | 19 + lib/libm/arch/i386/e_exp.S | 131 ++++ lib/libm/arch/i386/e_expf.S | 29 + lib/libm/arch/i386/e_fmod.S | 23 + lib/libm/arch/i386/e_log.S | 19 + lib/libm/arch/i386/e_log10.S | 19 + lib/libm/arch/i386/e_log10f.S | 19 + lib/libm/arch/i386/e_logf.S | 19 + lib/libm/arch/i386/e_remainder.S | 23 + lib/libm/arch/i386/e_remainderf.S | 23 + lib/libm/arch/i386/e_scalb.S | 20 + lib/libm/arch/i386/e_scalbf.S | 19 + lib/libm/arch/i386/e_sqrt.S | 18 + lib/libm/arch/i386/e_sqrtf.S | 18 + lib/libm/arch/i386/lrint.S | 24 + lib/libm/arch/i386/s_atan.S | 19 + lib/libm/arch/i386/s_atanf.S | 19 + lib/libm/arch/i386/s_ceil.S | 46 ++ lib/libm/arch/i386/s_ceilf.S | 44 ++ lib/libm/arch/i386/s_copysign.S | 54 ++ lib/libm/arch/i386/s_copysignf.S | 54 ++ lib/libm/arch/i386/s_cos.S | 32 + lib/libm/arch/i386/s_cosf.S | 19 + lib/libm/arch/i386/s_finite.S | 27 + lib/libm/arch/i386/s_finitef.S | 26 + lib/libm/arch/i386/s_floor.S | 44 ++ lib/libm/arch/i386/s_floorf.S | 44 ++ lib/libm/arch/i386/s_ilogb.S | 33 + lib/libm/arch/i386/s_ilogbf.S | 33 + lib/libm/arch/i386/s_log1p.S | 77 ++ lib/libm/arch/i386/s_log1pf.S | 77 ++ lib/libm/arch/i386/s_logb.S | 19 + lib/libm/arch/i386/s_logbf.S | 19 + lib/libm/arch/i386/s_rint.S | 18 + lib/libm/arch/i386/s_rintf.S | 18 + lib/libm/arch/i386/s_scalbn.S | 20 + lib/libm/arch/i386/s_scalbnf.S | 20 + lib/libm/arch/i386/s_significand.S | 19 + lib/libm/arch/i386/s_significandf.S | 19 + lib/libm/arch/i386/s_sin.S | 32 + lib/libm/arch/i386/s_sinf.S | 19 + lib/libm/arch/i386/s_tan.S | 34 + lib/libm/arch/i386/s_tanf.S | 20 + lib/libm/man/Makefile.inc | 28 + lib/{libc/gen/isinf.3 => libm/man/acos.3} | 98 +-- lib/{libc/gen/isinf.3 => libm/man/acosh.3} | 90 ++- lib/{libc/gen/isinf.3 => libm/man/asin.3} | 100 +-- lib/{libc/gen/isinf.3 => libm/man/asinh.3} | 86 +-- lib/{libc/gen/isinf.3 => libm/man/atan.3} | 92 ++- lib/libm/man/atan2.3 | 193 +++++ lib/{libc/gen/isinf.3 => libm/man/atanh.3} | 90 ++- lib/{libc/gen/isinf.3 => libm/man/ceil.3} | 80 +- lib/{libc/gen/isinf.3 => libm/man/cos.3} | 92 ++- lib/{libc/gen/isinf.3 => libm/man/cosh.3} | 96 +-- lib/{libc/gen/isinf.3 => libm/man/erf.3} | 98 +-- lib/libm/man/exp.3 | 307 ++++++++ lib/{libc/gen/isinf.3 => libm/man/fabs.3} | 84 +-- lib/{libc/gen/isinf.3 => libm/man/floor.3} | 80 +- lib/{libc/gen/isinf.3 => libm/man/fmod.3} | 90 ++- lib/libm/man/hypot.3 | 137 ++++ lib/libm/man/ieee.3 | 169 +++++ .../gen/isinf.3 => libm/man/ieee_test.3} | 111 +-- lib/libm/man/j0.3 | 154 ++++ lib/libm/man/lgamma.3 | 124 ++++ lib/libm/man/math.3 | 681 ++++++++++++++++++ lib/{libc/gen/isinf.3 => libm/man/rint.3} | 79 +- lib/{libc/gen/isinf.3 => libm/man/round.3} | 92 ++- lib/{libc/gen/isinf.3 => libm/man/sin.3} | 88 +-- lib/{libc/gen/isinf.3 => libm/man/sinh.3} | 91 ++- lib/{libc/gen/isinf.3 => libm/man/sqrt.3} | 100 +-- lib/{libc/gen/isinf.3 => libm/man/tan.3} | 92 ++- lib/{libc/gen/isinf.3 => libm/man/tanh.3} | 89 ++- lib/libm/src/Makefile.inc | 37 + lib/libm/src/e_acos.c | 102 +++ lib/libm/src/e_acosf.c | 80 ++ lib/libm/src/e_acosh.c | 61 ++ lib/libm/src/e_acoshf.c | 48 ++ lib/libm/src/e_asin.c | 113 +++ lib/libm/src/e_asinf.c | 85 +++ lib/libm/src/e_atan2.c | 121 ++++ lib/libm/src/e_atan2f.c | 96 +++ lib/libm/src/e_atanh.c | 61 ++ lib/libm/src/e_atanhf.c | 45 ++ lib/libm/src/e_cosh.c | 84 +++ lib/libm/src/e_coshf.c | 63 ++ lib/libm/src/e_exp.c | 160 ++++ lib/libm/src/e_expf.c | 97 +++ lib/libm/src/e_fmod.c | 131 ++++ lib/libm/src/e_fmodf.c | 104 +++ lib/libm/src/e_hypot.c | 123 ++++ lib/libm/src/e_hypotf.c | 82 +++ lib/libm/src/e_j0.c | 386 ++++++++++ lib/libm/src/e_j0f.c | 343 +++++++++ lib/libm/src/e_j1.c | 381 ++++++++++ lib/libm/src/e_j1f.c | 339 +++++++++ lib/libm/src/e_jn.c | 266 +++++++ lib/libm/src/e_jnf.c | 197 +++++ lib/libm/src/e_lgamma_r.c | 296 ++++++++ lib/libm/src/e_lgammaf_r.c | 232 ++++++ lib/libm/src/e_log.c | 134 ++++ lib/libm/src/e_log10.c | 85 +++ lib/libm/src/e_log10f.c | 54 ++ lib/libm/src/e_logf.c | 85 +++ lib/libm/src/e_pow.c | 300 ++++++++ lib/libm/src/e_powf.c | 244 +++++++ lib/libm/src/e_rem_pio2.c | 167 +++++ lib/libm/src/e_rem_pio2f.c | 179 +++++ lib/libm/src/e_remainder.c | 71 ++ lib/libm/src/e_remainderf.c | 64 ++ lib/libm/src/e_scalb.c | 46 ++ lib/libm/src/e_scalbf.c | 43 ++ lib/libm/src/e_sinh.c | 77 ++ lib/libm/src/e_sinhf.c | 59 ++ lib/libm/src/e_sqrt.c | 444 ++++++++++++ lib/libm/src/e_sqrtf.c | 88 +++ lib/libm/src/k_cos.c | 87 +++ lib/libm/src/k_cosf.c | 55 ++ lib/libm/src/k_rem_pio2.c | 303 ++++++++ lib/libm/src/k_rem_pio2f.c | 196 +++++ lib/libm/src/k_sin.c | 70 ++ lib/libm/src/k_sinf.c | 45 ++ lib/libm/src/k_tan.c | 154 ++++ lib/libm/src/k_tanf.c | 92 +++ lib/libm/src/llrint.c | 14 + lib/libm/src/llrintf.c | 14 + lib/libm/src/llround.c | 14 + lib/libm/src/llroundf.c | 14 + lib/libm/src/lrint.c | 93 +++ lib/libm/src/lrintf.c | 88 +++ lib/libm/src/lround.c | 86 +++ lib/libm/src/lroundf.c | 81 +++ lib/libm/src/math_private.h | 181 +++++ lib/libm/src/s_asinh.c | 56 ++ lib/libm/src/s_asinhf.c | 48 ++ lib/libm/src/s_atan.c | 118 +++ lib/libm/src/s_atanf.c | 98 +++ lib/libm/src/s_cbrt.c | 80 ++ lib/libm/src/s_cbrtf.c | 70 ++ lib/libm/src/s_ceil.c | 71 ++ lib/libm/src/s_ceilf.c | 52 ++ lib/libm/src/s_copysign.c | 33 + lib/libm/src/s_copysignf.c | 36 + lib/libm/src/s_cos.c | 77 ++ lib/libm/src/s_cosf.c | 48 ++ lib/libm/src/s_erf.c | 301 ++++++++ lib/libm/src/s_erff.c | 210 ++++++ lib/libm/src/s_expm1.c | 221 ++++++ lib/libm/src/s_expm1f.c | 126 ++++ lib/libm/src/s_fabsf.c | 33 + lib/libm/src/s_finite.c | 30 + lib/libm/src/s_finitef.c | 33 + lib/libm/src/s_floor.c | 72 ++ lib/libm/src/s_floorf.c | 61 ++ lib/libm/src/s_frexpf.c | 43 ++ lib/libm/src/s_ilogb.c | 46 ++ lib/libm/src/s_ilogbf.c | 38 + lib/libm/src/s_ldexpf.c | 30 + lib/libm/src/s_log1p.c | 163 +++++ lib/libm/src/s_log1pf.c | 102 +++ lib/libm/src/s_logb.c | 37 + lib/libm/src/s_logbf.c | 34 + lib/libm/src/s_modff.c | 55 ++ lib/libm/src/s_nextafter.c | 74 ++ lib/libm/src/s_nextafterf.c | 65 ++ lib/libm/src/s_rint.c | 77 ++ lib/libm/src/s_rintf.c | 62 ++ lib/libm/src/s_round.c | 54 ++ lib/libm/src/s_roundf.c | 54 ++ lib/libm/src/s_scalbn.c | 58 ++ lib/libm/src/s_scalbnf.c | 54 ++ lib/libm/src/s_signgam.c | 7 + lib/libm/src/s_significand.c | 29 + lib/libm/src/s_significandf.c | 26 + lib/libm/src/s_sin.c | 77 ++ lib/libm/src/s_sinf.c | 48 ++ lib/libm/src/s_tan.c | 71 ++ lib/libm/src/s_tanf.c | 43 ++ lib/libm/src/s_tanh.c | 77 ++ lib/libm/src/s_tanhf.c | 55 ++ lib/libm/src/w_cabs.c | 18 + lib/libm/src/w_cabsf.c | 18 + lib/libm/src/w_drem.c | 17 + lib/libm/src/w_dremf.c | 18 + lib/libm/src/w_gamma.c | 29 + lib/libm/src/w_gamma_r.c | 27 + lib/libm/src/w_gammaf.c | 26 + lib/libm/src/w_gammaf_r.c | 30 + lib/libm/src/w_lgamma.c | 28 + lib/libm/src/w_lgammaf.c | 26 + sys/cpu/i386/include/math.h | 5 + sys/i386/include/math.h | 5 + 237 files changed, 17369 insertions(+), 1297 deletions(-) create mode 100644 include/math.h create mode 100644 lib/libc/gen/fpclassify.3 create mode 100644 lib/libc/gen/fpclassifyd.c create mode 100644 lib/libc/gen/fpclassifyf.c create mode 100644 lib/libc/gen/infinity.c create mode 100644 lib/libc/gen/infinityf.c create mode 100644 lib/libc/gen/infinityl_dbl.c create mode 100644 lib/libc/gen/isfinite.3 create mode 100644 lib/libc/gen/isfinited.c create mode 100644 lib/libc/gen/isfinitef.c copy lib/libc/{i386/gen/isinf.c => gen/isinfd.c} (62%) copy lib/libc/{i386/gen/isinf.c => gen/isinff.c} (62%) copy lib/libc/gen/{isinf.3 => isnan.3} (62%) copy lib/libc/{i386/gen/isinf.c => gen/isnand.c} (62%) copy lib/libc/{i386/gen/isinf.c => gen/isnanf.c} (62%) create mode 100644 lib/libc/gen/signbit.3 create mode 100644 lib/libc/gen/signbitd.c create mode 100644 lib/libc/gen/signbitf.c create mode 100644 lib/libc/i386/gen/flt_rounds.S create mode 100644 lib/libc/i386/gen/fpclassifyl.c create mode 100644 lib/libc/i386/gen/fpgetmask.S create mode 100644 lib/libc/i386/gen/fpgetround.S create mode 100644 lib/libc/i386/gen/fpgetsticky.S create mode 100644 lib/libc/i386/gen/fpsetmask.S create mode 100644 lib/libc/i386/gen/fpsetround.S create mode 100644 lib/libc/i386/gen/fpsetsticky.S delete mode 100644 lib/libc/i386/gen/infinity.c create mode 100644 lib/libc/i386/gen/infinityl.c create mode 100644 lib/libc/i386/gen/isfinitel.c copy lib/libc/i386/gen/{isinf.c => isinfl.c} (62%) rename lib/libc/i386/gen/{isinf.c => isnanl.c} (62%) create mode 100644 lib/libc/i386/gen/nanf.c create mode 100644 lib/libc/i386/gen/signbitl.c create mode 100644 lib/libm/Makefile create mode 100644 lib/libm/arch/i386/Makefile.inc create mode 100644 lib/libm/arch/i386/abi.h create mode 100644 lib/libm/arch/i386/e_acos.S create mode 100644 lib/libm/arch/i386/e_asin.S create mode 100644 lib/libm/arch/i386/e_atan2.S create mode 100644 lib/libm/arch/i386/e_atan2f.S create mode 100644 lib/libm/arch/i386/e_exp.S create mode 100644 lib/libm/arch/i386/e_expf.S create mode 100644 lib/libm/arch/i386/e_fmod.S create mode 100644 lib/libm/arch/i386/e_log.S create mode 100644 lib/libm/arch/i386/e_log10.S create mode 100644 lib/libm/arch/i386/e_log10f.S create mode 100644 lib/libm/arch/i386/e_logf.S create mode 100644 lib/libm/arch/i386/e_remainder.S create mode 100644 lib/libm/arch/i386/e_remainderf.S create mode 100644 lib/libm/arch/i386/e_scalb.S create mode 100644 lib/libm/arch/i386/e_scalbf.S create mode 100644 lib/libm/arch/i386/e_sqrt.S create mode 100644 lib/libm/arch/i386/e_sqrtf.S create mode 100644 lib/libm/arch/i386/lrint.S create mode 100644 lib/libm/arch/i386/s_atan.S create mode 100644 lib/libm/arch/i386/s_atanf.S create mode 100644 lib/libm/arch/i386/s_ceil.S create mode 100644 lib/libm/arch/i386/s_ceilf.S create mode 100644 lib/libm/arch/i386/s_copysign.S create mode 100644 lib/libm/arch/i386/s_copysignf.S create mode 100644 lib/libm/arch/i386/s_cos.S create mode 100644 lib/libm/arch/i386/s_cosf.S create mode 100644 lib/libm/arch/i386/s_finite.S create mode 100644 lib/libm/arch/i386/s_finitef.S create mode 100644 lib/libm/arch/i386/s_floor.S create mode 100644 lib/libm/arch/i386/s_floorf.S create mode 100644 lib/libm/arch/i386/s_ilogb.S create mode 100644 lib/libm/arch/i386/s_ilogbf.S create mode 100644 lib/libm/arch/i386/s_log1p.S create mode 100644 lib/libm/arch/i386/s_log1pf.S create mode 100644 lib/libm/arch/i386/s_logb.S create mode 100644 lib/libm/arch/i386/s_logbf.S create mode 100644 lib/libm/arch/i386/s_rint.S create mode 100644 lib/libm/arch/i386/s_rintf.S create mode 100644 lib/libm/arch/i386/s_scalbn.S create mode 100644 lib/libm/arch/i386/s_scalbnf.S create mode 100644 lib/libm/arch/i386/s_significand.S create mode 100644 lib/libm/arch/i386/s_significandf.S create mode 100644 lib/libm/arch/i386/s_sin.S create mode 100644 lib/libm/arch/i386/s_sinf.S create mode 100644 lib/libm/arch/i386/s_tan.S create mode 100644 lib/libm/arch/i386/s_tanf.S create mode 100644 lib/libm/man/Makefile.inc copy lib/{libc/gen/isinf.3 => libm/man/acos.3} (54%) copy lib/{libc/gen/isinf.3 => libm/man/acosh.3} (55%) copy lib/{libc/gen/isinf.3 => libm/man/asin.3} (54%) copy lib/{libc/gen/isinf.3 => libm/man/asinh.3} (55%) copy lib/{libc/gen/isinf.3 => libm/man/atan.3} (54%) create mode 100644 lib/libm/man/atan2.3 copy lib/{libc/gen/isinf.3 => libm/man/atanh.3} (55%) copy lib/{libc/gen/isinf.3 => libm/man/ceil.3} (54%) copy lib/{libc/gen/isinf.3 => libm/man/cos.3} (54%) copy lib/{libc/gen/isinf.3 => libm/man/cosh.3} (54%) copy lib/{libc/gen/isinf.3 => libm/man/erf.3} (55%) create mode 100644 lib/libm/man/exp.3 copy lib/{libc/gen/isinf.3 => libm/man/fabs.3} (54%) copy lib/{libc/gen/isinf.3 => libm/man/floor.3} (54%) copy lib/{libc/gen/isinf.3 => libm/man/fmod.3} (55%) create mode 100644 lib/libm/man/hypot.3 create mode 100644 lib/libm/man/ieee.3 copy lib/{libc/gen/isinf.3 => libm/man/ieee_test.3} (53%) create mode 100644 lib/libm/man/j0.3 create mode 100644 lib/libm/man/lgamma.3 create mode 100644 lib/libm/man/math.3 copy lib/{libc/gen/isinf.3 => libm/man/rint.3} (55%) copy lib/{libc/gen/isinf.3 => libm/man/round.3} (50%) copy lib/{libc/gen/isinf.3 => libm/man/sin.3} (54%) copy lib/{libc/gen/isinf.3 => libm/man/sinh.3} (54%) copy lib/{libc/gen/isinf.3 => libm/man/sqrt.3} (55%) copy lib/{libc/gen/isinf.3 => libm/man/tan.3} (54%) copy lib/{libc/gen/isinf.3 => libm/man/tanh.3} (54%) create mode 100644 lib/libm/src/Makefile.inc create mode 100644 lib/libm/src/e_acos.c create mode 100644 lib/libm/src/e_acosf.c create mode 100644 lib/libm/src/e_acosh.c create mode 100644 lib/libm/src/e_acoshf.c create mode 100644 lib/libm/src/e_asin.c create mode 100644 lib/libm/src/e_asinf.c create mode 100644 lib/libm/src/e_atan2.c create mode 100644 lib/libm/src/e_atan2f.c create mode 100644 lib/libm/src/e_atanh.c create mode 100644 lib/libm/src/e_atanhf.c create mode 100644 lib/libm/src/e_cosh.c create mode 100644 lib/libm/src/e_coshf.c create mode 100644 lib/libm/src/e_exp.c create mode 100644 lib/libm/src/e_expf.c create mode 100644 lib/libm/src/e_fmod.c create mode 100644 lib/libm/src/e_fmodf.c create mode 100644 lib/libm/src/e_hypot.c create mode 100644 lib/libm/src/e_hypotf.c create mode 100644 lib/libm/src/e_j0.c create mode 100644 lib/libm/src/e_j0f.c create mode 100644 lib/libm/src/e_j1.c create mode 100644 lib/libm/src/e_j1f.c create mode 100644 lib/libm/src/e_jn.c create mode 100644 lib/libm/src/e_jnf.c create mode 100644 lib/libm/src/e_lgamma_r.c create mode 100644 lib/libm/src/e_lgammaf_r.c create mode 100644 lib/libm/src/e_log.c create mode 100644 lib/libm/src/e_log10.c create mode 100644 lib/libm/src/e_log10f.c create mode 100644 lib/libm/src/e_logf.c create mode 100644 lib/libm/src/e_pow.c create mode 100644 lib/libm/src/e_powf.c create mode 100644 lib/libm/src/e_rem_pio2.c create mode 100644 lib/libm/src/e_rem_pio2f.c create mode 100644 lib/libm/src/e_remainder.c create mode 100644 lib/libm/src/e_remainderf.c create mode 100644 lib/libm/src/e_scalb.c create mode 100644 lib/libm/src/e_scalbf.c create mode 100644 lib/libm/src/e_sinh.c create mode 100644 lib/libm/src/e_sinhf.c create mode 100644 lib/libm/src/e_sqrt.c create mode 100644 lib/libm/src/e_sqrtf.c create mode 100644 lib/libm/src/k_cos.c create mode 100644 lib/libm/src/k_cosf.c create mode 100644 lib/libm/src/k_rem_pio2.c create mode 100644 lib/libm/src/k_rem_pio2f.c create mode 100644 lib/libm/src/k_sin.c create mode 100644 lib/libm/src/k_sinf.c create mode 100644 lib/libm/src/k_tan.c create mode 100644 lib/libm/src/k_tanf.c create mode 100644 lib/libm/src/llrint.c create mode 100644 lib/libm/src/llrintf.c create mode 100644 lib/libm/src/llround.c create mode 100644 lib/libm/src/llroundf.c create mode 100644 lib/libm/src/lrint.c create mode 100644 lib/libm/src/lrintf.c create mode 100644 lib/libm/src/lround.c create mode 100644 lib/libm/src/lroundf.c create mode 100644 lib/libm/src/math_private.h create mode 100644 lib/libm/src/s_asinh.c create mode 100644 lib/libm/src/s_asinhf.c create mode 100644 lib/libm/src/s_atan.c create mode 100644 lib/libm/src/s_atanf.c create mode 100644 lib/libm/src/s_cbrt.c create mode 100644 lib/libm/src/s_cbrtf.c create mode 100644 lib/libm/src/s_ceil.c create mode 100644 lib/libm/src/s_ceilf.c create mode 100644 lib/libm/src/s_copysign.c create mode 100644 lib/libm/src/s_copysignf.c create mode 100644 lib/libm/src/s_cos.c create mode 100644 lib/libm/src/s_cosf.c create mode 100644 lib/libm/src/s_erf.c create mode 100644 lib/libm/src/s_erff.c create mode 100644 lib/libm/src/s_expm1.c create mode 100644 lib/libm/src/s_expm1f.c create mode 100644 lib/libm/src/s_fabsf.c create mode 100644 lib/libm/src/s_finite.c create mode 100644 lib/libm/src/s_finitef.c create mode 100644 lib/libm/src/s_floor.c create mode 100644 lib/libm/src/s_floorf.c create mode 100644 lib/libm/src/s_frexpf.c create mode 100644 lib/libm/src/s_ilogb.c create mode 100644 lib/libm/src/s_ilogbf.c create mode 100644 lib/libm/src/s_ldexpf.c create mode 100644 lib/libm/src/s_log1p.c create mode 100644 lib/libm/src/s_log1pf.c create mode 100644 lib/libm/src/s_logb.c create mode 100644 lib/libm/src/s_logbf.c create mode 100644 lib/libm/src/s_modff.c create mode 100644 lib/libm/src/s_nextafter.c create mode 100644 lib/libm/src/s_nextafterf.c create mode 100644 lib/libm/src/s_rint.c create mode 100644 lib/libm/src/s_rintf.c create mode 100644 lib/libm/src/s_round.c create mode 100644 lib/libm/src/s_roundf.c create mode 100644 lib/libm/src/s_scalbn.c create mode 100644 lib/libm/src/s_scalbnf.c create mode 100644 lib/libm/src/s_signgam.c create mode 100644 lib/libm/src/s_significand.c create mode 100644 lib/libm/src/s_significandf.c create mode 100644 lib/libm/src/s_sin.c create mode 100644 lib/libm/src/s_sinf.c create mode 100644 lib/libm/src/s_tan.c create mode 100644 lib/libm/src/s_tanf.c create mode 100644 lib/libm/src/s_tanh.c create mode 100644 lib/libm/src/s_tanhf.c create mode 100644 lib/libm/src/w_cabs.c create mode 100644 lib/libm/src/w_cabsf.c create mode 100644 lib/libm/src/w_drem.c create mode 100644 lib/libm/src/w_dremf.c create mode 100644 lib/libm/src/w_gamma.c create mode 100644 lib/libm/src/w_gamma_r.c create mode 100644 lib/libm/src/w_gammaf.c create mode 100644 lib/libm/src/w_gammaf_r.c create mode 100644 lib/libm/src/w_lgamma.c create mode 100644 lib/libm/src/w_lgammaf.c create mode 100644 sys/cpu/i386/include/math.h create mode 100644 sys/i386/include/math.h diff --git a/Makefile.inc1 b/Makefile.inc1 index 681ee645b4..a9cbaa622a 100644 --- a/Makefile.inc1 +++ b/Makefile.inc1 @@ -1,6 +1,6 @@ # # $FreeBSD: src/Makefile.inc1,v 1.141.2.62 2003/04/06 19:54:00 dwmalone Exp $ -# $DragonFly: src/Makefile.inc1,v 1.74 2005/07/14 18:02:33 joerg Exp $ +# $DragonFly: src/Makefile.inc1,v 1.75 2005/07/26 21:15:19 joerg Exp $ # # Make command line options: # -DMAKE_KERBEROS5 to build Kerberos5 @@ -909,7 +909,7 @@ _generic_libs+= kerberos5/lib _prebuild_libs+= lib/libcom_err lib/libcrypt lib/libmd \ lib/libncurses/libncurses lib/libopie lib/libradius \ - lib/libskey lib/libtacplus lib/libz lib/msun lib/libpam + lib/libskey lib/libtacplus lib/libz lib/libm lib/libpam lib/libopie__L lib/libradius__L lib/libtacplus__L: lib/libmd__L lib/libskey__L: lib/libcrypt__L lib/libmd__L diff --git a/gnu/usr.bin/groff/src/libs/libgroff/Makefile b/gnu/usr.bin/groff/src/libs/libgroff/Makefile index 55aea36f4a..b70db18b86 100644 --- a/gnu/usr.bin/groff/src/libs/libgroff/Makefile +++ b/gnu/usr.bin/groff/src/libs/libgroff/Makefile @@ -1,5 +1,5 @@ # $FreeBSD: src/gnu/usr.bin/groff/src/libs/libgroff/Makefile,v 1.1.2.4 2003/02/14 15:22:14 ru Exp $ -# $DragonFly: src/gnu/usr.bin/groff/src/libs/libgroff/Makefile,v 1.2 2003/06/17 04:25:46 dillon Exp $ +# $DragonFly: src/gnu/usr.bin/groff/src/libs/libgroff/Makefile,v 1.3 2005/07/26 21:15:19 joerg Exp $ LIB= groff INTERNALLIB= YES @@ -9,7 +9,7 @@ SRCS= assert.cc change_lf.cc cmap.cc color.cc cset.cc device.cc errarg.cc\ maxfilename.cc mksdir.cc nametoindex.cc new.cc paper.cc prime.cc\ progname.cc ptable.cc searchpath.cc string.cc strsave.cc\ tmpfile.cc tmpname.cc version.cc -SRCS+= getopt.c getopt1.c iftoa.c itoa.c matherr.c +SRCS+= getopt.c getopt1.c iftoa.c itoa.c CLEANFILES= version.cc .include diff --git a/include/Makefile b/include/Makefile index 36b7f092a2..d7bffd2598 100644 --- a/include/Makefile +++ b/include/Makefile @@ -1,6 +1,6 @@ # @(#)Makefile 8.2 (Berkeley) 1/4/94 # $FreeBSD: src/include/Makefile,v 1.109.2.27 2003/01/24 05:12:29 sam Exp $ -# $DragonFly: src/include/Makefile,v 1.25 2005/07/07 11:49:55 corecode Exp $ +# $DragonFly: src/include/Makefile,v 1.26 2005/07/26 21:15:19 joerg Exp $ # # Doing a make install builds /usr/include # @@ -14,7 +14,7 @@ INCS= a.out.h ar.h assert.h bitstring.h complex.h cpio.h ctype.h db.h \ dlfcn.h elf.h elf-hints.h err.h fnmatch.h fstab.h \ fts.h getopt.h glob.h grp.h histedit.h iconv.h ieeefp.h ifaddrs.h \ iso646.h inttypes.h \ - langinfo.h libgen.h limits.h link.h locale.h malloc.h memory.h \ + langinfo.h libgen.h limits.h link.h locale.h malloc.h math.h memory.h \ mpool.h ndbm.h netdb.h nl_types.h nlist.h objformat.h \ paths.h pthread.h pthread_np.h pwd.h \ ranlib.h readpassphrase.h regex.h regexp.h resolv.h re_comp.h rmd160.h \ diff --git a/include/math.h b/include/math.h new file mode 100644 index 0000000000..2c319c757d --- /dev/null +++ b/include/math.h @@ -0,0 +1,400 @@ +/* $NetBSD: math.h,v 1.40 2005/02/03 04:39:32 perry Exp $ */ + +/* + * ==================================================== + * Copyright (C) 1993 by Sun Microsystems, Inc. All rights reserved. + * + * Developed at SunPro, a Sun Microsystems, Inc. business. + * Permission to use, copy, modify, and distribute this + * software is freely granted, provided that this notice + * is preserved. + * ==================================================== + * + * $NetBSD: math.h,v 1.40 2005/02/03 04:39:32 perry Exp $ + * $DragonFly: src/include/math.h,v 1.5 2005/07/26 21:15:19 joerg Exp $ + */ + +/* + * @(#)fdlibm.h 5.1 93/09/24 + */ + +#ifndef _MATH_H_ +#define _MATH_H_ + +#include + +union __float_u { + unsigned char __dummy[sizeof(float)]; + float __val; +}; + +union __double_u { + unsigned char __dummy[sizeof(double)]; + double __val; +}; + +union __long_double_u { + unsigned char __dummy[sizeof(long double)]; + long double __val; +}; + +#include + +#ifdef __HAVE_LONG_DOUBLE +#define __fpmacro_unary_floating(__name, __arg0) \ + /* LINTED */ \ + ((sizeof (__arg0) == sizeof (float)) \ + ? __ ## __name ## f (__arg0) \ + : (sizeof (__arg0) == sizeof (double)) \ + ? __ ## __name ## d (__arg0) \ + : __ ## __name ## l (__arg0)) +#else +#define __fpmacro_unary_floating(__name, __arg0) \ + /* LINTED */ \ + ((sizeof (__arg0) == sizeof (float)) \ + ? __ ## __name ## f (__arg0) \ + : __ ## __name ## d (__arg0)) +#endif /* __HAVE_LONG_DOUBLE */ + +/* + * ANSI/POSIX + */ +/* 7.12#3 HUGE_VAL, HUGELF, HUGE_VALL */ +extern __const union __double_u __infinity; +#define HUGE_VAL __infinity.__val + +/* + * ISO C99 + */ +#if __ISO_C_VISIBLE >= 1999 +/* 7.12#3 HUGE_VAL, HUGELF, HUGE_VALL */ +extern __const union __float_u __infinityf; +#define HUGE_VALF __infinityf.__val + +extern __const union __long_double_u __infinityl; +#define HUGE_VALL __infinityl.__val + +/* 7.12#4 INFINITY */ +#ifdef __INFINITY +#define INFINITY __INFINITY /* float constant which overflows */ +#else +#define INFINITY HUGE_VALF /* positive infinity */ +#endif /* __INFINITY */ + +/* 7.12#5 NAN: a quiet NaN, if supported */ +#ifdef __HAVE_NANF +extern __const union __float_u __nanf; +#define NAN __nanf.__val +#endif /* __HAVE_NANF */ + +/* 7.12#6 number classification macros */ +#define FP_INFINITE 0x00 +#define FP_NAN 0x01 +#define FP_NORMAL 0x02 +#define FP_SUBNORMAL 0x03 +#define FP_ZERO 0x04 +/* NetBSD extensions */ +#define _FP_LOMD 0x80 /* range for machine-specific classes */ +#define _FP_HIMD 0xff + +#endif /* ISO C99 */ + +/* + * XOPEN/SVID + */ +#if __XSI_VISIBLE > 0 +#define M_E 2.7182818284590452354 /* e */ +#define M_LOG2E 1.4426950408889634074 /* log 2e */ +#define M_LOG10E 0.43429448190325182765 /* log 10e */ +#define M_LN2 0.69314718055994530942 /* log e2 */ +#define M_LN10 2.30258509299404568402 /* log e10 */ +#define M_PI 3.14159265358979323846 /* pi */ +#define M_PI_2 1.57079632679489661923 /* pi/2 */ +#define M_PI_4 0.78539816339744830962 /* pi/4 */ +#define M_1_PI 0.31830988618379067154 /* 1/pi */ +#define M_2_PI 0.63661977236758134308 /* 2/pi */ +#define M_2_SQRTPI 1.12837916709551257390 /* 2/sqrt(pi) */ +#define M_SQRT2 1.41421356237309504880 /* sqrt(2) */ +#define M_SQRT1_2 0.70710678118654752440 /* 1/sqrt(2) */ + +#define MAXFLOAT ((float)3.40282346638528860e+38) +extern int signgam; +#endif /* _XSI_VISIBLE */ + +#if __DF_VISIBLE +#define HUGE MAXFLOAT + +/* + * set X_TLOSS = pi*2**52, which is possibly defined in + * (one may replace the following line by "#include ") + */ + +#define X_TLOSS 1.41484755040568800000e+16 + +#define DOMAIN 1 +#define SING 2 +#define OVERFLOW 3 +#define UNDERFLOW 4 +#define TLOSS 5 +#define PLOSS 6 + +#endif /* __DF_VISIBLE */ + +__BEGIN_DECLS +/* + * ANSI/POSIX + */ +double acos(double); +double asin(double); +double atan(double); +double atan2(double, double); +double cos(double); +double sin(double); +double tan(double); + +double cosh(double); +double sinh(double); +double tanh(double); + +double exp(double); +double frexp(double, int *); +double ldexp(double, int); +double log(double); +double log10(double); +double modf(double, double *); + +double pow(double, double); +double sqrt(double); + +double ceil(double); +double fabs(double); +double floor(double); +double fmod(double, double); + +#if __XSI_VISIBLE > 0 +double erf(double); +double erfc(double); +double gamma(double); +double hypot(double, double); +int finite(double); +double j0(double); +double j1(double); +double jn(int, double); +double lgamma(double); +double y0(double); +double y1(double); +double yn(int, double); +#endif /* __XSI_VISIBLE */ + +#if __XSI_VISIBLE >= 500 +double acosh(double); +double asinh(double); +double atanh(double); +double cbrt(double); +double expm1(double); +int ilogb(double); +double log1p(double); +double logb(double); +double nextafter(double, double); +double remainder(double, double); +double rint(double); +double scalb(double, double); +#endif /* __XSI_VISIBLE >= 500 */ + +/* + * ISO C99 + */ +#if __ISO_C_VISIBLE >= 1999 +/* 7.12.3.1 int fpclassify(real-floating x) */ +#define fpclassify(__x) __fpmacro_unary_floating(fpclassify, __x) + +/* 7.12.3.2 int isfinite(real-floating x) */ +#define isfinite(__x) __fpmacro_unary_floating(isfinite, __x) + +/* 7.12.3.5 int isnormal(real-floating x) */ +#define isnormal(__x) (fpclassify(__x) == FP_NORMAL) + +/* 7.12.3.6 int signbit(real-floating x) */ +#define signbit(__x) __fpmacro_unary_floating(signbit, __x) + +/* 7.12.4 trigonometric */ + +float acosf(float); +float asinf(float); +float atanf(float); +float atan2f(float, float); +float cosf(float); +float sinf(float); +float tanf(float); + +/* 7.12.5 hyperbolic */ + +float acoshf(float); +float asinhf(float); +float atanhf(float); +float coshf(float); +float sinhf(float); +float tanhf(float); + +/* 7.12.6 exp / log */ + +float expf(float); +float expm1f(float); +float frexpf(float, int *); +int ilogbf(float); +float ldexpf(float, int); +float logf(float); +float log10f(float); +float log1pf(float); +float logbf(float); +float modff(float, float *); +float scalbnf(float, int); + +/* 7.12.7 power / absolute */ + +float cbrtf(float); +float fabsf(float); +float hypotf(float, float); +float powf(float, float); +float sqrtf(float); + +/* 7.12.8 error / gamma */ + +float erff(float); +float erfcf(float); +float lgammaf(float); + +/* 7.12.9 nearest integer */ + +float ceilf(float); +float floorf(float); +float rintf(float); +double round(double); +float roundf(float); +long int lrint(double); +long int lrintf(float); +/* LONGLONG */ +long long int llrint(double); +/* LONGLONG */ +long long int llrintf(float); +long int lround(double); +long int lroundf(float); +/* LONGLONG */ +long long int llround(double); +/* LONGLONG */ +long long int llroundf(float); + +/* 7.12.10 remainder */ + +float fmodf(float, float); +float remainderf(float, float); + +/* 7.2.11 manipulation */ + +float copysignf(float, float); +float nextafterf(float, float); + +#endif /* __ISO_C_VISIBLE >= 1999 */ + +#if __ISO_C_VISIBLE >= 1999 +/* 7.12.3.3 int isinf(real-floating x) */ +#ifdef __isinf +#define isinf(__x) __isinf(__x) +#else +#define isinf(__x) __fpmacro_unary_floating(isinf, __x) +#endif + +/* 7.12.3.4 int isnan(real-floating x) */ +#ifdef __isnan +#define isnan(__x) __isnan(__x) +#else +#define isnan(__x) __fpmacro_unary_floating(isnan, __x) +#endif +#endif /* __ISO_C_VISIBLE >= 1999 */ + +#if __DF_VISIBLE +/* + * IEEE Test Vector + */ +double significand(double); + +/* + * Functions callable from C, intended to support IEEE arithmetic. + */ +double copysign(double, double); +double scalbn(double, int); + +/* + * BSD math library entry points + */ +double drem(double, double); + +/* + * Reentrant version of gamma & lgamma; passes signgam back by reference + * as the second argument; user must allocate space for signgam. + */ +double gamma_r(double, int *); +double lgamma_r(double, int *); +#endif /* __DF_VISIBLE */ + + +#if __DF_VISIBLE + +/* float versions of ANSI/POSIX functions */ + +float gammaf(float); +int isinff(float); +int isnanf(float); +int finitef(float); +float j0f(float); +float j1f(float); +float jnf(int, float); +float y0f(float); +float y1f(float); +float ynf(int, float); + +float scalbf(float, float); + +/* + * float version of IEEE Test Vector + */ +float significandf(float); + +/* + * float versions of BSD math library entry points + */ +float dremf(float, float); + +/* + * Float versions of reentrant version of gamma & lgamma; passes + * signgam back by reference as the second argument; user must + * allocate space for signgam. + */ +float gammaf_r(float, int *); +float lgammaf_r(float, int *); +#endif /* __DF_VISIBLE */ + +/* + * Library implementation + */ +int __fpclassifyf(float); +int __fpclassifyd(double); +int __isfinitef(float); +int __isfinited(double); +int __isinff(float); +int __isinfd(double); +int __isnanf(float); +int __isnand(double); +int __signbitf(float); +int __signbitd(double); + +#ifdef __HAVE_LONG_DOUBLE +int __fpclassifyl(long double); +int __isfinitel(long double); +int __isinfl(long double); +int __isnanl(long double); +int __signbitl(long double); +#endif +__END_DECLS + +#endif /* _MATH_H_ */ diff --git a/lib/Makefile b/lib/Makefile index 3e11c5dd87..6347fcdd61 100644 --- a/lib/Makefile +++ b/lib/Makefile @@ -1,6 +1,6 @@ # @(#)Makefile 8.1 (Berkeley) 6/4/93 # $FreeBSD: src/lib/Makefile,v 1.107.2.16 2002/10/10 19:24:35 kbyanc Exp $ -# $DragonFly: src/lib/Makefile,v 1.23 2005/07/15 18:14:53 eirikn Exp $ +# $DragonFly: src/lib/Makefile,v 1.24 2005/07/26 21:15:19 joerg Exp $ # To satisfy shared library or ELF linkage when only the libraries being # built are visible: @@ -8,7 +8,6 @@ # csu must be built before all shared libaries for ELF. # libcom_err must be built before libkrb and libpam. # libcrypt must be built before libkrb, libpam and libskey. -# msun must be built before libg++ and libstdc++. # libmd must be built before libatm, libopie, libradius, libskey, and # libtacplus. # libncurses must be built before libdialog, libedit and libreadline. @@ -20,7 +19,7 @@ # # Otherwise, the SUBDIR list should be in alphabetical order. -SUBDIR= ${_csu} csu/common libarchive libcom_err libcrypt msun libmd \ +SUBDIR= ${_csu} csu/common libarchive libcom_err libcrypt libm libmd \ libncurses libradius libskey libtacplus libutil libsbuf \ libalias libatm ${_libbind} libbz2 libc ${_libc_r} libcalendar \ libcam libcompat libdevstat libdisk libedit libfetch libftpio \ diff --git a/lib/libc/gen/Makefile.inc b/lib/libc/gen/Makefile.inc index fb0d655b2e..0be218f705 100644 --- a/lib/libc/gen/Makefile.inc +++ b/lib/libc/gen/Makefile.inc @@ -1,6 +1,6 @@ # @(#)Makefile.inc 8.6 (Berkeley) 5/4/95 # $FreeBSD: src/lib/libc/gen/Makefile.inc,v 1.62.2.19 2003/02/21 13:46:16 phantom Exp $ -# $DragonFly: src/lib/libc/gen/Makefile.inc,v 1.13 2005/05/03 07:29:04 joerg Exp $ +# $DragonFly: src/lib/libc/gen/Makefile.inc,v 1.14 2005/07/26 21:15:19 joerg Exp $ # machine-independent gen sources .PATH: ${.CURDIR}/../libc/${MACHINE_ARCH}/gen ${.CURDIR}/../libc/gen @@ -10,13 +10,16 @@ SRCS+= _pthread_stubs.c _rand48.c _spinlock_stub.c _thread_init.c \ clock.c closedir.c confstr.c \ ctermid.c ctype.c daemon.c devname.c dirname.c disklabel.c \ dlfcn.c drand48.c erand48.c err.c errlst.c \ - exec.c fmtcheck.c fnmatch.c fstab.c ftok.c fts.c getbootfile.c getbsize.c \ + exec.c fmtcheck.c fnmatch.c fpclassifyd.c fpclassifyf.c fstab.c \ + ftok.c fts.c getbootfile.c getbsize.c \ getcap.c getcwd.c getdomainname.c getgrent.c getgrouplist.c \ gethostname.c getloadavg.c getlogin.c getmntinfo.c getnetgrent.c \ getobjformat.c getosreldate.c getpagesize.c \ getpeereid.c getprogname.c getpwent.c getttyent.c \ getusershell.c getvfsbyname.c getvfsent.c glob.c \ - initgroups.c isascii.c isatty.c isctype.c jrand48.c lcong48.c \ + infinity.c infinityf.c initgroups.c isascii.c \ + isatty.c isctype.c isfinited.c isfinitef.c isinfd.c isinff.c \ + isnand.c isnanf.c jrand48.c lcong48.c \ lockf.c lrand48.c mrand48.c msgctl.c \ msgget.c msgrcv.c msgsnd.c nice.c \ nlist.c nrand48.c ntp_gettime.c opendir.c \ @@ -26,10 +29,10 @@ SRCS+= _pthread_stubs.c _rand48.c _spinlock_stub.c _thread_init.c \ setdomainname.c sethostname.c setjmperr.c setmode.c setprogname.c \ setproctitle.c \ shmat.c shmctl.c shmdt.c shmget.c siginterrupt.c siglist.c signal.c \ - sigsetops.c sigwait.c sleep.c srand48.c stringlist.c strtofflags.c \ - sysconf.c sysctl.c sysctlbyname.c sysctlnametomib.c \ - syslog.c telldir.c termios.c time.c times.c timezone.c \ - tolower.c toupper.c ttyname.c ttyslot.c ualarm.c ulimit.c \ + signbitd.c signbitf.c sigsetops.c sigwait.c sleep.c srand48.c \ + stringlist.c strtofflags.c sysconf.c sysctl.c sysctlbyname.c \ + sysctlnametomib.c syslog.c telldir.c termios.c time.c times.c \ + timezone.c tolower.c toupper.c ttyname.c ttyslot.c ualarm.c ulimit.c \ uname.c unvis.c usleep.c utime.c valloc.c vis.c \ wait.c wait3.c waitpid.c @@ -46,7 +49,7 @@ MAN+= alarm.3 arc4random.3 clock.3 \ confstr.3 ctermid.3 ctype.3 daemon.3 \ devname.3 directory.3 dirname.3 \ dladdr.3 dlinfo.3 dlopen.3 \ - err.3 exec.3 fmtcheck.3 fnmatch.3 frexp.3 ftok.3 fts.3 \ + err.3 exec.3 fmtcheck.3 fnmatch.3 fpclassify.3 frexp.3 ftok.3 fts.3 \ getbootfile.3 getbsize.3 getcap.3 getcwd.3 \ getdiskbyname.3 getdomainname.3 getfsent.3 \ getgrent.3 getgrouplist.3 gethostname.3 getloadavg.3 \ @@ -55,12 +58,12 @@ MAN+= alarm.3 arc4random.3 clock.3 \ getttyent.3 getusershell.3 getvfsbyname.3 getvfsent.3 \ glob.3 initgroups.3 isalnum.3 isalpha.3 isascii.3 isblank.3 \ iscntrl.3 isdigit.3 isgraph.3 islower.3 isprint.3 ispunct.3 \ - isspace.3 isupper.3 isxdigit.3 isinf.3 \ + isspace.3 isupper.3 isxdigit.3 isinf.3 isfinite.3 isnan.3 \ ldexp.3 lockf.3 modf.3 msgctl.3 msgget.3 msgrcv.3 msgsnd.3 \ nice.3 nlist.3 pause.3 popen.3 psignal.3 pwcache.3 \ raise.3 rand48.3 readpassphrase.3 rfork_thread.3 \ scandir.3 setjmp.3 setmode.3 setproctitle.3 shm_open.3 \ - siginterrupt.3 signal.3 sigsetops.3 sleep.3 stringlist.3 \ + siginterrupt.3 signal.3 signbit.3 sigsetops.3 sleep.3 stringlist.3 \ strtofflags.3 sysconf.3 sysctl.3 syslog.3 tcgetpgrp.3 \ tcsendbreak.3 tcsetattr.3 tcsetpgrp.3 time.3 times.3 timezone.3 \ toascii.3 tolower.3 toupper.3 ttyname.3 tzset.3 ualarm.3 \ diff --git a/lib/libc/gen/fpclassify.3 b/lib/libc/gen/fpclassify.3 new file mode 100644 index 0000000000..40980853ab --- /dev/null +++ b/lib/libc/gen/fpclassify.3 @@ -0,0 +1,90 @@ +.\" $NetBSD: fpclassify.3,v 1.2 2004/01/15 19:43:45 kleink Exp $ +.\" $DragonFly: src/lib/libc/gen/fpclassify.3,v 1.1 2005/07/26 21:15:19 joerg Exp $ +.\" +.\" Copyright (c) 2003 The NetBSD Foundation, Inc. +.\" All rights reserved. +.\" +.\" This code is derived from software contributed to The NetBSD Foundation +.\" by Klaus Klein. +.\" +.\" Redistribution and use in source and binary forms, with or without +.\" modification, are permitted provided that the following conditions +.\" are met: +.\" 1. Redistributions of source code must retain the above copyright +.\" notice, this list of conditions and the following disclaimer. +.\" 2. Redistributions in binary form must reproduce the above copyright +.\" notice, this list of conditions and the following disclaimer in the +.\" documentation and/or other materials provided with the distribution. +.\" 3. All advertising materials mentioning features or use of this software +.\" must display the following acknowledgement: +.\" This product includes software developed by the NetBSD +.\" Foundation, Inc. and its contributors. +.\" 4. Neither the name of The NetBSD Foundation nor the names of its +.\" contributors may be used to endorse or promote products derived +.\" from this software without specific prior written permission. +.\" +.\" THIS SOFTWARE IS PROVIDED BY THE NETBSD FOUNDATION, INC. AND CONTRIBUTORS +.\" ``AS IS'' AND ANY EXPRESS OR IMPLIED WARRANTIES, INCLUDING, BUT NOT LIMITED +.\" TO, THE IMPLIED WARRANTIES OF MERCHANTABILITY AND FITNESS FOR A PARTICULAR +.\" PURPOSE ARE DISCLAIMED. IN NO EVENT SHALL THE FOUNDATION OR CONTRIBUTORS +.\" BE LIABLE FOR ANY DIRECT, INDIRECT, INCIDENTAL, SPECIAL, EXEMPLARY, OR +.\" CONSEQUENTIAL DAMAGES (INCLUDING, BUT NOT LIMITED TO, PROCUREMENT OF +.\" SUBSTITUTE GOODS OR SERVICES; LOSS OF USE, DATA, OR PROFITS; OR BUSINESS +.\" INTERRUPTION) HOWEVER CAUSED AND ON ANY THEORY OF LIABILITY, WHETHER IN +.\" CONTRACT, STRICT LIABILITY, OR TORT (INCLUDING NEGLIGENCE OR OTHERWISE) +.\" ARISING IN ANY WAY OUT OF THE USE OF THIS SOFTWARE, EVEN IF ADVISED OF THE +.\" POSSIBILITY OF SUCH DAMAGE. +.\" +.Dd January 14, 2004 +.Dt FPCLASSIFY 3 +.Os +.Sh NAME +.Nm fpclassify +.Nd classify real floating type +.Sh LIBRARY +.Lb libc +.Sh SYNOPSIS +.In math.h +.Ft int +.Fn fpclassify "real-floating x" +.Sh DESCRIPTION +The +.Fn fpclassify +macro performs classification of its argument +.Fa x . +An argument represented in a format wider than its semantic type is +converted to its semantic type first. +The classification is then based on the type of the argument. +.Ss IEEE 754 +.Bl -tag -width "FP_SUBNORMALXXX" -compact -offset indent +.It Dv FP_INFINITE +infinity, either positive or negative +.It Dv FP_NAN +not-a-number +.Pq Dq NaN +.It Dv FP_NORMAL +normal +.It Dv FP_SUBNORMAL +subnormal +.It Dv FP_ZERO +zero +.El +.Sh RETURN VALUES +The +.Fn fpclassify +macro returns the value of the number classification macro appropriate +to its argument +.Fa x +as described above. +.Sh ERRORS +No errors are defined. +.Sh SEE ALSO +.Xr isfinite 3 , +.Xr isnormal 3 , +.Xr math 3 , +.Xr signbit 3 +.Sh STANDARDS +The +.Fn fpclassify +macro conforms to +.St -isoC-99 . diff --git a/lib/libc/gen/fpclassifyd.c b/lib/libc/gen/fpclassifyd.c new file mode 100644 index 0000000000..50f0841873 --- /dev/null +++ b/lib/libc/gen/fpclassifyd.c @@ -0,0 +1,67 @@ +/* $NetBSD: fpclassifyd_ieee754.c,v 1.1 2003/10/28 22:50:42 kleink Exp $ */ +/* $DragonFly: src/lib/libc/gen/fpclassifyd.c,v 1.1 2005/07/26 21:15:19 joerg Exp $ */ + +/*- + * Copyright (c) 2003 The NetBSD Foundation, Inc. + * All rights reserved. + * + * This code is derived from software contributed to The NetBSD Foundation + * by Klaus Klein. + * + * Redistribution and use in source and binary forms, with or without + * modification, are permitted provided that the following conditions + * are met: + * 1. Redistributions of source code must retain the above copyright + * notice, this list of conditions and the following disclaimer. + * 2. Redistributions in binary form must reproduce the above copyright + * notice, this list of conditions and the following disclaimer in the + * documentation and/or other materials provided with the distribution. + * 3. All advertising materials mentioning features or use of this software + * must display the following acknowledgement: + * This product includes software developed by the NetBSD + * Foundation, Inc. and its contributors. + * 4. Neither the name of The NetBSD Foundation nor the names of its + * contributors may be used to endorse or promote products derived + * from this software without specific prior written permission. + * + * THIS SOFTWARE IS PROVIDED BY THE NETBSD FOUNDATION, INC. AND CONTRIBUTORS + * ``AS IS'' AND ANY EXPRESS OR IMPLIED WARRANTIES, INCLUDING, BUT NOT LIMITED + * TO, THE IMPLIED WARRANTIES OF MERCHANTABILITY AND FITNESS FOR A PARTICULAR + * PURPOSE ARE DISCLAIMED. IN NO EVENT SHALL THE FOUNDATION OR CONTRIBUTORS + * BE LIABLE FOR ANY DIRECT, INDIRECT, INCIDENTAL, SPECIAL, EXEMPLARY, OR + * CONSEQUENTIAL DAMAGES (INCLUDING, BUT NOT LIMITED TO, PROCUREMENT OF + * SUBSTITUTE GOODS OR SERVICES; LOSS OF USE, DATA, OR PROFITS; OR BUSINESS + * INTERRUPTION) HOWEVER CAUSED AND ON ANY THEORY OF LIABILITY, WHETHER IN + * CONTRACT, STRICT LIABILITY, OR TORT (INCLUDING NEGLIGENCE OR OTHERWISE) + * ARISING IN ANY WAY OUT OF THE USE OF THIS SOFTWARE, EVEN IF ADVISED OF THE + * POSSIBILITY OF SUCH DAMAGE. + */ + +#include +#include + +/* + * 7.12.3.1 fpclassify - classify real floating type + * IEEE 754 double-precision version + */ +int +__fpclassifyd(double x) +{ + union ieee_double_u u; + + u.dblu_d = x; + + if (u.dblu_dbl.dbl_exp == 0) { + if (u.dblu_dbl.dbl_frach == 0 && u.dblu_dbl.dbl_fracl == 0) + return FP_ZERO; + else + return FP_SUBNORMAL; + } else if (u.dblu_dbl.dbl_exp == DBL_EXP_INFNAN) { + if (u.dblu_dbl.dbl_frach == 0 && u.dblu_dbl.dbl_fracl == 0) + return FP_INFINITE; + else + return FP_NAN; + } + + return FP_NORMAL; +} diff --git a/lib/libc/gen/fpclassifyf.c b/lib/libc/gen/fpclassifyf.c new file mode 100644 index 0000000000..948da0e714 --- /dev/null +++ b/lib/libc/gen/fpclassifyf.c @@ -0,0 +1,67 @@ +/* $NetBSD: fpclassifyf_ieee754.c,v 1.2 2003/10/29 19:34:11 kleink Exp $ */ +/* $DragonFly: src/lib/libc/gen/fpclassifyf.c,v 1.1 2005/07/26 21:15:19 joerg Exp $ */ + +/*- + * Copyright (c) 2003 The NetBSD Foundation, Inc. + * All rights reserved. + * + * This code is derived from software contributed to The NetBSD Foundation + * by Klaus Klein. + * + * Redistribution and use in source and binary forms, with or without + * modification, are permitted provided that the following conditions + * are met: + * 1. Redistributions of source code must retain the above copyright + * notice, this list of conditions and the following disclaimer. + * 2. Redistributions in binary form must reproduce the above copyright + * notice, this list of conditions and the following disclaimer in the + * documentation and/or other materials provided with the distribution. + * 3. All advertising materials mentioning features or use of this software + * must display the following acknowledgement: + * This product includes software developed by the NetBSD + * Foundation, Inc. and its contributors. + * 4. Neither the name of The NetBSD Foundation nor the names of its + * contributors may be used to endorse or promote products derived + * from this software without specific prior written permission. + * + * THIS SOFTWARE IS PROVIDED BY THE NETBSD FOUNDATION, INC. AND CONTRIBUTORS + * ``AS IS'' AND ANY EXPRESS OR IMPLIED WARRANTIES, INCLUDING, BUT NOT LIMITED + * TO, THE IMPLIED WARRANTIES OF MERCHANTABILITY AND FITNESS FOR A PARTICULAR + * PURPOSE ARE DISCLAIMED. IN NO EVENT SHALL THE FOUNDATION OR CONTRIBUTORS + * BE LIABLE FOR ANY DIRECT, INDIRECT, INCIDENTAL, SPECIAL, EXEMPLARY, OR + * CONSEQUENTIAL DAMAGES (INCLUDING, BUT NOT LIMITED TO, PROCUREMENT OF + * SUBSTITUTE GOODS OR SERVICES; LOSS OF USE, DATA, OR PROFITS; OR BUSINESS + * INTERRUPTION) HOWEVER CAUSED AND ON ANY THEORY OF LIABILITY, WHETHER IN + * CONTRACT, STRICT LIABILITY, OR TORT (INCLUDING NEGLIGENCE OR OTHERWISE) + * ARISING IN ANY WAY OUT OF THE USE OF THIS SOFTWARE, EVEN IF ADVISED OF THE + * POSSIBILITY OF SUCH DAMAGE. + */ + +#include +#include + +/* + * 7.12.3.1 fpclassify - classify real floating type + * IEEE 754 single-precision version + */ +int +__fpclassifyf(float x) +{ + union ieee_single_u u; + + u.sngu_f = x; + + if (u.sngu_sng.sng_exp == 0) { + if (u.sngu_sng.sng_frac == 0) + return FP_ZERO; + else + return FP_SUBNORMAL; + } else if (u.sngu_sng.sng_exp == SNG_EXP_INFNAN) { + if (u.sngu_sng.sng_frac == 0) + return FP_INFINITE; + else + return FP_NAN; + } + + return FP_NORMAL; +} diff --git a/lib/libc/gen/infinity.c b/lib/libc/gen/infinity.c new file mode 100644 index 0000000000..9700101928 --- /dev/null +++ b/lib/libc/gen/infinity.c @@ -0,0 +1,16 @@ +/* $NetBSD: infinity_ieee754.c,v 1.3 2005/06/12 05:21:27 lukem Exp $ */ +/* $DragonFly: src/lib/libc/gen/infinity.c,v 1.1 2005/07/26 21:15:19 joerg Exp $ */ + +/* + * IEEE-compatible infinity.c -- public domain. + */ + +#include +#include + +const union __double_u __infinity = +#if BYTE_ORDER == BIG_ENDIAN + { { 0x7f, 0xf0, 0, 0, 0, 0, 0, 0 } }; +#else + { { 0, 0, 0, 0, 0, 0, 0xf0, 0x7f } }; +#endif diff --git a/lib/libc/gen/infinityf.c b/lib/libc/gen/infinityf.c new file mode 100644 index 0000000000..f95f3f9ed3 --- /dev/null +++ b/lib/libc/gen/infinityf.c @@ -0,0 +1,16 @@ +/* $NetBSD: infinityf_ieee754.c,v 1.2 2005/06/12 05:21:27 lukem Exp $ */ +/* $DragonFly: src/lib/libc/gen/infinityf.c,v 1.1 2005/07/26 21:15:19 joerg Exp $ */ + +/* + * IEEE-compatible infinityf.c -- public domain. + */ + +#include +#include + +const union __float_u __infinityf = +#if BYTE_ORDER == BIG_ENDIAN + { { 0x7f, 0x80, 0, 0 } }; +#else + { { 0, 0, 0x80, 0x7f } }; +#endif diff --git a/lib/libc/gen/infinityl_dbl.c b/lib/libc/gen/infinityl_dbl.c new file mode 100644 index 0000000000..6122b58554 --- /dev/null +++ b/lib/libc/gen/infinityl_dbl.c @@ -0,0 +1,22 @@ +/* $NetBSD: infinityl_dbl_ieee754.c,v 1.1 2003/10/25 22:31:20 kleink Exp $ */ +/* $DragonFly: src/lib/libc/gen/infinityl_dbl.c,v 1.1 2005/07/26 21:15:19 joerg Exp $ */ + +/* + * IEEE-compatible infinityl.c -- public domain. + * For platforms where long double == double. + */ + +#include +#include +#include + +#if LDBL_MANT_DIG != DBL_MANT_DIG +#error double / long double mismatch +#endif + +const union __long_double_u __infinityl = +#if BYTE_ORDER == BIG_ENDIAN + { { 0x7f, 0xf0, 0, 0, 0, 0, 0, 0 } }; +#else + { { 0, 0, 0, 0, 0, 0, 0xf0, 0x7f } }; +#endif diff --git a/lib/libc/gen/isfinite.3 b/lib/libc/gen/isfinite.3 new file mode 100644 index 0000000000..7e43f5c903 --- /dev/null +++ b/lib/libc/gen/isfinite.3 @@ -0,0 +1,77 @@ +.\" $NetBSD: isfinite.3,v 1.2 2004/01/15 19:43:45 kleink Exp $ +.\" $DragonFly: src/lib/libc/gen/isfinite.3,v 1.1 2005/07/26 21:15:19 joerg Exp $ +.\" +.\" Copyright (c) 2003 The NetBSD Foundation, Inc. +.\" All rights reserved. +.\" +.\" This code is derived from software contributed to The NetBSD Foundation +.\" by Klaus Klein. +.\" +.\" Redistribution and use in source and binary forms, with or without +.\" modification, are permitted provided that the following conditions +.\" are met: +.\" 1. Redistributions of source code must retain the above copyright +.\" notice, this list of conditions and the following disclaimer. +.\" 2. Redistributions in binary form must reproduce the above copyright +.\" notice, this list of conditions and the following disclaimer in the +.\" documentation and/or other materials provided with the distribution. +.\" 3. All advertising materials mentioning features or use of this software +.\" must display the following acknowledgement: +.\" This product includes software developed by the NetBSD +.\" Foundation, Inc. and its contributors. +.\" 4. Neither the name of The NetBSD Foundation nor the names of its +.\" contributors may be used to endorse or promote products derived +.\" from this software without specific prior written permission. +.\" +.\" THIS SOFTWARE IS PROVIDED BY THE NETBSD FOUNDATION, INC. AND CONTRIBUTORS +.\" ``AS IS'' AND ANY EXPRESS OR IMPLIED WARRANTIES, INCLUDING, BUT NOT LIMITED +.\" TO, THE IMPLIED WARRANTIES OF MERCHANTABILITY AND FITNESS FOR A PARTICULAR +.\" PURPOSE ARE DISCLAIMED. IN NO EVENT SHALL THE FOUNDATION OR CONTRIBUTORS +.\" BE LIABLE FOR ANY DIRECT, INDIRECT, INCIDENTAL, SPECIAL, EXEMPLARY, OR +.\" CONSEQUENTIAL DAMAGES (INCLUDING, BUT NOT LIMITED TO, PROCUREMENT OF +.\" SUBSTITUTE GOODS OR SERVICES; LOSS OF USE, DATA, OR PROFITS; OR BUSINESS +.\" INTERRUPTION) HOWEVER CAUSED AND ON ANY THEORY OF LIABILITY, WHETHER IN +.\" CONTRACT, STRICT LIABILITY, OR TORT (INCLUDING NEGLIGENCE OR OTHERWISE) +.\" ARISING IN ANY WAY OUT OF THE USE OF THIS SOFTWARE, EVEN IF ADVISED OF THE +.\" POSSIBILITY OF SUCH DAMAGE. +.\" +.Dd October 29, 2003 +.Dt ISFINITE 3 +.Os +.Sh NAME +.Nm isfinite +.Nd test for finite value +.Sh LIBRARY +.Lb libc +.Sh SYNOPSIS +.In math.h +.Ft int +.Fn isfinite "real-floating x" +.Sh DESCRIPTION +The +.Fn isfinite +determines whether its argument +.Fa x +has a finite value. +An argument represented in a format wider than its semantic type is +converted to its semantic type first. +The determination is then based on the type of the argument. +.Sh RETURN VALUES +The +.Fn isfinite +macro returns a non-zero value if the value of +.Fa x +is finite. +Otherwise 0 is returned. +.Sh ERRORS +No errors are defined. +.Sh SEE ALSO +.Xr fpclassify 3 , +.Xr isnormal 3 , +.Xr math 3 , +.Xr signbit 3 +.Sh STANDARDS +The +.Fn isfinite +macro conforms to +.St -isoC-99 . diff --git a/lib/libc/gen/isfinited.c b/lib/libc/gen/isfinited.c new file mode 100644 index 0000000000..6cfacd7281 --- /dev/null +++ b/lib/libc/gen/isfinited.c @@ -0,0 +1,58 @@ +/* $NetBSD: isfinited_ieee754.c,v 1.1 2003/10/29 20:03:51 kleink Exp $ */ +/* $DragonFly: src/lib/libc/gen/isfinited.c,v 1.1 2005/07/26 21:15:19 joerg Exp $ */ + +/*- + * Copyright (c) 2003 The NetBSD Foundation, Inc. + * All rights reserved. + * + * This code is derived from software contributed to The NetBSD Foundation + * by Klaus Klein. + * + * Redistribution and use in source and binary forms, with or without + * modification, are permitted provided that the following conditions + * are met: + * 1. Redistributions of source code must retain the above copyright + * notice, this list of conditions and the following disclaimer. + * 2. Redistributions in binary form must reproduce the above copyright + * notice, this list of conditions and the following disclaimer in the + * documentation and/or other materials provided with the distribution. + * 3. All advertising materials mentioning features or use of this software + * must display the following acknowledgement: + * This product includes software developed by the NetBSD + * Foundation, Inc. and its contributors. + * 4. Neither the name of The NetBSD Foundation nor the names of its + * contributors may be used to endorse or promote products derived + * from this software without specific prior written permission. + * + * THIS SOFTWARE IS PROVIDED BY THE NETBSD FOUNDATION, INC. AND CONTRIBUTORS + * ``AS IS'' AND ANY EXPRESS OR IMPLIED WARRANTIES, INCLUDING, BUT NOT LIMITED + * TO, THE IMPLIED WARRANTIES OF MERCHANTABILITY AND FITNESS FOR A PARTICULAR + * PURPOSE ARE DISCLAIMED. IN NO EVENT SHALL THE FOUNDATION OR CONTRIBUTORS + * BE LIABLE FOR ANY DIRECT, INDIRECT, INCIDENTAL, SPECIAL, EXEMPLARY, OR + * CONSEQUENTIAL DAMAGES (INCLUDING, BUT NOT LIMITED TO, PROCUREMENT OF + * SUBSTITUTE GOODS OR SERVICES; LOSS OF USE, DATA, OR PROFITS; OR BUSINESS + * INTERRUPTION) HOWEVER CAUSED AND ON ANY THEORY OF LIABILITY, WHETHER IN + * CONTRACT, STRICT LIABILITY, OR TORT (INCLUDING NEGLIGENCE OR OTHERWISE) + * ARISING IN ANY WAY OUT OF THE USE OF THIS SOFTWARE, EVEN IF ADVISED OF THE + * POSSIBILITY OF SUCH DAMAGE. + */ + +#include +#include + +/* + * 7.12.3.2 isfinite - determine whether an argument has finite value + * IEEE 754 double-precision version + */ +int +__isfinited(double x) +{ + union ieee_double_u u; + + u.dblu_d = x; + + if (u.dblu_dbl.dbl_exp == DBL_EXP_INFNAN) + return 0; + + return 1; +} diff --git a/lib/libc/gen/isfinitef.c b/lib/libc/gen/isfinitef.c new file mode 100644 index 0000000000..6bbbb9e147 --- /dev/null +++ b/lib/libc/gen/isfinitef.c @@ -0,0 +1,58 @@ +/* $NetBSD: isfinitef_ieee754.c,v 1.1 2003/10/29 20:03:51 kleink Exp $ */ +/* $DragonFly: src/lib/libc/gen/isfinitef.c,v 1.1 2005/07/26 21:15:19 joerg Exp $ */ + +/*- + * Copyright (c) 2003 The NetBSD Foundation, Inc. + * All rights reserved. + * + * This code is derived from software contributed to The NetBSD Foundation + * by Klaus Klein. + * + * Redistribution and use in source and binary forms, with or without + * modification, are permitted provided that the following conditions + * are met: + * 1. Redistributions of source code must retain the above copyright + * notice, this list of conditions and the following disclaimer. + * 2. Redistributions in binary form must reproduce the above copyright + * notice, this list of conditions and the following disclaimer in the + * documentation and/or other materials provided with the distribution. + * 3. All advertising materials mentioning features or use of this software + * must display the following acknowledgement: + * This product includes software developed by the NetBSD + * Foundation, Inc. and its contributors. + * 4. Neither the name of The NetBSD Foundation nor the names of its + * contributors may be used to endorse or promote products derived + * from this software without specific prior written permission. + * + * THIS SOFTWARE IS PROVIDED BY THE NETBSD FOUNDATION, INC. AND CONTRIBUTORS + * ``AS IS'' AND ANY EXPRESS OR IMPLIED WARRANTIES, INCLUDING, BUT NOT LIMITED + * TO, THE IMPLIED WARRANTIES OF MERCHANTABILITY AND FITNESS FOR A PARTICULAR + * PURPOSE ARE DISCLAIMED. IN NO EVENT SHALL THE FOUNDATION OR CONTRIBUTORS + * BE LIABLE FOR ANY DIRECT, INDIRECT, INCIDENTAL, SPECIAL, EXEMPLARY, OR + * CONSEQUENTIAL DAMAGES (INCLUDING, BUT NOT LIMITED TO, PROCUREMENT OF + * SUBSTITUTE GOODS OR SERVICES; LOSS OF USE, DATA, OR PROFITS; OR BUSINESS + * INTERRUPTION) HOWEVER CAUSED AND ON ANY THEORY OF LIABILITY, WHETHER IN + * CONTRACT, STRICT LIABILITY, OR TORT (INCLUDING NEGLIGENCE OR OTHERWISE) + * ARISING IN ANY WAY OUT OF THE USE OF THIS SOFTWARE, EVEN IF ADVISED OF THE + * POSSIBILITY OF SUCH DAMAGE. + */ + +#include +#include + +/* + * 7.12.3.2 isfinite - determine whether an argument has finite value + * IEEE 754 single-precision version + */ +int +__isfinitef(float x) +{ + union ieee_single_u u; + + u.sngu_f = x; + + if (u.sngu_sng.sng_exp == SNG_EXP_INFNAN) + return 0; + + return 1; +} diff --git a/lib/libc/gen/isinf.3 b/lib/libc/gen/isinf.3 index cf68a79e5d..d58b3b4f4f 100644 --- a/lib/libc/gen/isinf.3 +++ b/lib/libc/gen/isinf.3 @@ -9,11 +9,7 @@ .\" 2. Redistributions in binary form must reproduce the above copyright .\" notice, this list of conditions and the following disclaimer in the .\" documentation and/or other materials provided with the distribution. -.\" 3. All advertising materials mentioning features or use of this software -.\" must display the following acknowledgement: -.\" This product includes software developed by the University of -.\" California, Berkeley and its contributors. -.\" 4. Neither the name of the University nor the names of its contributors +.\" 3. Neither the name of the University nor the names of its contributors .\" may be used to endorse or promote products derived from this software .\" without specific prior written permission. .\" @@ -30,53 +26,59 @@ .\" SUCH DAMAGE. .\" .\" @(#)isinf.3 8.2 (Berkeley) 1/29/94 -.\" $FreeBSD: src/lib/libc/gen/isinf.3,v 1.5.2.3 2003/05/04 22:25:22 murray Exp $ -.\" $DragonFly: src/lib/libc/gen/isinf.3,v 1.2 2003/06/17 04:26:42 dillon Exp $ +.\" $NetBSD: isinf.3,v 1.12 2004/03/04 23:47:56 wiz Exp $ +.\" $DragonFly: src/lib/libc/gen/isinf.3,v 1.3 2005/07/26 21:15:19 joerg Exp $ .\" -.Dd January 29, 1994 +.Dd March 5, 2004 .Dt ISINF 3 .Os .Sh NAME -.Nm isinf , -.Nm isnan , -.Nm isnanf -.Nd test for infinity or not-a-number +.Nm isinf +.Nd test for infinity .Sh LIBRARY .Lb libc .Sh SYNOPSIS .In math.h .Ft int -.Fn isinf double -.Ft int -.Fn isnan double -.Ft int -.Fn isnanf float +.Fn isinf "real-floating x" .Sh DESCRIPTION The .Fn isinf -function -returns 1 if the number is -.Dq \\*(If , -otherwise 0. -.Pp +macro determines whether its argument +.Fa x +is an infinity (positive or negative). +An argument represented in a format wider than its semantic type is +converted to its semantic type first. +The determination is then based on the type of the argument. +.Ss IEEE 754 +It is determined whether the value of +.Fa x +is an infinity. +.Ss VAX +Infinities are not supported. +.Sh RETURN VALUES The -.Fn isnan -and -.Fn isnanf -functions -return 1 if the double or float (respectively) is -.Dq not-a-number , -otherwise 0. +.Fn isinf +macro returns a non-zero value if the value of +.Fa x +is an infinity. +Otherwise 0 is returned. .Sh SEE ALSO -.Xr math 3 +.Xr fpclassify 3 , +.Xr isfinite 3 , +.Xr isinff 3 , +.Xr isnan 3 , +.Xr isnanf 3 , +.Xr isnormal 3 , +.Xr math 3 , +.Xr signbit 3 .Rs .%T "IEEE Standard for Binary Floating-Point Arithmetic" .%Q ANSI .%R Std 754-1985 .Re -.Sh BUGS -Neither the -.Tn VAX -nor the Tahoe floating point have distinguished values -for either infinity or not-a-number. -These routines always return 0 on those architectures. +.Sh STANDARDS +The +.Fn isinf +macro conforms to +.St -isoC-99 . diff --git a/lib/libc/i386/gen/isinf.c b/lib/libc/gen/isinfd.c similarity index 62% copy from lib/libc/i386/gen/isinf.c copy to lib/libc/gen/isinfd.c index 30c1366d15..be01f0b6ba 100644 --- a/lib/libc/i386/gen/isinf.c +++ b/lib/libc/gen/isinfd.c @@ -1,7 +1,14 @@ -/*- - * Copyright (c) 1991, 1993 +/* $NetBSD: isinfd_ieee754.c,v 1.1 2004/03/04 23:42:39 kleink Exp $ */ +/* $DragonFly: src/lib/libc/gen/isinfd.c,v 1.1 2005/07/26 21:15:19 joerg Exp $ */ + +/* + * Copyright (c) 1992, 1993 * The Regents of the University of California. All rights reserved. * + * This software was developed by the Computer Systems Engineering group + * at Lawrence Berkeley Laboratory under DARPA contract BG 91-66 and + * contributed to Berkeley. + * * Redistribution and use in source and binary forms, with or without * modification, are permitted provided that the following conditions * are met: @@ -10,11 +17,7 @@ * 2. Redistributions in binary form must reproduce the above copyright * notice, this list of conditions and the following disclaimer in the * documentation and/or other materials provided with the distribution. - * 3. All advertising materials mentioning features or use of this software - * must display the following acknowledgement: - * This product includes software developed by the University of - * California, Berkeley and its contributors. - * 4. Neither the name of the University nor the names of its contributors + * 3. Neither the name of the University nor the names of its contributors * may be used to endorse or promote products derived from this software * without specific prior written permission. * @@ -30,36 +33,23 @@ * OUT OF THE USE OF THIS SOFTWARE, EVEN IF ADVISED OF THE POSSIBILITY OF * SUCH DAMAGE. * - * $FreeBSD: src/lib/libc/i386/gen/isinf.c,v 1.6 1999/08/27 23:59:21 peter Exp $ - * $DragonFly: src/lib/libc/i386/gen/Attic/isinf.c,v 1.4 2004/10/25 19:38:01 drhodus Exp $ + * from: Header: isinf.c,v 1.1 91/07/08 19:03:34 torek Exp */ -#include +#include +#include +/* + * 7.12.3.3 isinf - test for infinity + * IEEE 754 double-precision version + */ int -isnan(d) - double d; +__isinfd(double x) { - struct IEEEdp { - u_int manl : 32; - u_int manh : 20; - u_int exp : 11; - u_int sign : 1; - } *p = (struct IEEEdp *)&d; + union ieee_double_u u; - return(p->exp == 2047 && (p->manh || p->manl)); -} - -int -isinf(d) - double d; -{ - struct IEEEdp { - u_int manl : 32; - u_int manh : 20; - u_int exp : 11; - u_int sign : 1; - } *p = (struct IEEEdp *)&d; + u.dblu_d = x; - return(p->exp == 2047 && !p->manh && !p->manl); + return (u.dblu_dbl.dbl_exp == DBL_EXP_INFNAN && + (u.dblu_dbl.dbl_frach == 0 && u.dblu_dbl.dbl_fracl == 0)); } diff --git a/lib/libc/i386/gen/isinf.c b/lib/libc/gen/isinff.c similarity index 62% copy from lib/libc/i386/gen/isinf.c copy to lib/libc/gen/isinff.c index 30c1366d15..871cefb614 100644 --- a/lib/libc/i386/gen/isinf.c +++ b/lib/libc/gen/isinff.c @@ -1,7 +1,14 @@ -/*- - * Copyright (c) 1991, 1993 +/* $NetBSD: isinff_ieee754.c,v 1.1 2004/03/04 23:42:39 kleink Exp $ */ +/* $DragonFly: src/lib/libc/gen/isinff.c,v 1.1 2005/07/26 21:15:19 joerg Exp $ */ + +/* + * Copyright (c) 1992, 1993 * The Regents of the University of California. All rights reserved. * + * This software was developed by the Computer Systems Engineering group + * at Lawrence Berkeley Laboratory under DARPA contract BG 91-66 and + * contributed to Berkeley. + * * Redistribution and use in source and binary forms, with or without * modification, are permitted provided that the following conditions * are met: @@ -10,11 +17,7 @@ * 2. Redistributions in binary form must reproduce the above copyright * notice, this list of conditions and the following disclaimer in the * documentation and/or other materials provided with the distribution. - * 3. All advertising materials mentioning features or use of this software - * must display the following acknowledgement: - * This product includes software developed by the University of - * California, Berkeley and its contributors. - * 4. Neither the name of the University nor the names of its contributors + * 3. Neither the name of the University nor the names of its contributors * may be used to endorse or promote products derived from this software * without specific prior written permission. * @@ -30,36 +33,23 @@ * OUT OF THE USE OF THIS SOFTWARE, EVEN IF ADVISED OF THE POSSIBILITY OF * SUCH DAMAGE. * - * $FreeBSD: src/lib/libc/i386/gen/isinf.c,v 1.6 1999/08/27 23:59:21 peter Exp $ - * $DragonFly: src/lib/libc/i386/gen/Attic/isinf.c,v 1.4 2004/10/25 19:38:01 drhodus Exp $ + * from: Header: isinf.c,v 1.1 91/07/08 19:03:34 torek Exp */ -#include +#include +#include +/* + * 7.12.3.3 isinf - test for infinity + * IEEE 754 single-precision version + */ int -isnan(d) - double d; +__isinff(float x) { - struct IEEEdp { - u_int manl : 32; - u_int manh : 20; - u_int exp : 11; - u_int sign : 1; - } *p = (struct IEEEdp *)&d; + union ieee_single_u u; - return(p->exp == 2047 && (p->manh || p->manl)); -} - -int -isinf(d) - double d; -{ - struct IEEEdp { - u_int manl : 32; - u_int manh : 20; - u_int exp : 11; - u_int sign : 1; - } *p = (struct IEEEdp *)&d; + u.sngu_f = x; - return(p->exp == 2047 && !p->manh && !p->manl); + return (u.sngu_sng.sng_exp == SNG_EXP_INFNAN && + u.sngu_sng.sng_frac == 0); } diff --git a/lib/libc/gen/isinf.3 b/lib/libc/gen/isnan.3 similarity index 62% copy from lib/libc/gen/isinf.3 copy to lib/libc/gen/isnan.3 index cf68a79e5d..c4982ba2b6 100644 --- a/lib/libc/gen/isinf.3 +++ b/lib/libc/gen/isnan.3 @@ -1,3 +1,6 @@ +.\" $NetBSD: isnan.3,v 1.2 2004/03/04 23:49:31 wiz Exp $ +.\" $DragonFly: src/lib/libc/gen/isnan.3,v 1.1 2005/07/26 21:15:19 joerg Exp $ +.\" .\" Copyright (c) 1991, 1993 .\" The Regents of the University of California. All rights reserved. .\" @@ -9,11 +12,7 @@ .\" 2. Redistributions in binary form must reproduce the above copyright .\" notice, this list of conditions and the following disclaimer in the .\" documentation and/or other materials provided with the distribution. -.\" 3. All advertising materials mentioning features or use of this software -.\" must display the following acknowledgement: -.\" This product includes software developed by the University of -.\" California, Berkeley and its contributors. -.\" 4. Neither the name of the University nor the names of its contributors +.\" 3. Neither the name of the University nor the names of its contributors .\" may be used to endorse or promote products derived from this software .\" without specific prior written permission. .\" @@ -29,54 +28,54 @@ .\" OUT OF THE USE OF THIS SOFTWARE, EVEN IF ADVISED OF THE POSSIBILITY OF .\" SUCH DAMAGE. .\" -.\" @(#)isinf.3 8.2 (Berkeley) 1/29/94 -.\" $FreeBSD: src/lib/libc/gen/isinf.3,v 1.5.2.3 2003/05/04 22:25:22 murray Exp $ -.\" $DragonFly: src/lib/libc/gen/isinf.3,v 1.2 2003/06/17 04:26:42 dillon Exp $ +.\" From: @(#)isinf.3 8.2 (Berkeley) 1/29/94 +.\" from: NetBSD: isinf.3,v 1.10 2003/08/07 16:42:52 agc Exp .\" -.Dd January 29, 1994 -.Dt ISINF 3 +.Dd March 5, 2004 +.Dt ISNAN 3 .Os .Sh NAME -.Nm isinf , -.Nm isnan , -.Nm isnanf -.Nd test for infinity or not-a-number +.Nm isnan +.Nd test for not-a-number .Sh LIBRARY .Lb libc .Sh SYNOPSIS .In math.h .Ft int -.Fn isinf double -.Ft int -.Fn isnan double -.Ft int -.Fn isnanf float +.Fn isnan "real-floating x" .Sh DESCRIPTION The -.Fn isinf -function -returns 1 if the number is -.Dq \\*(If , -otherwise 0. -.Pp +.Fn isnan +macro determines whether its argument +.Fa x +is not-a-number +.Pq Dq NaN . +An argument represented in a format wider than its semantic type is +converted to its semantic type first. +The determination is then based on the type of the argument. +.Sh RETURN VALUES The .Fn isnan -and -.Fn isnanf -functions -return 1 if the double or float (respectively) is -.Dq not-a-number , -otherwise 0. +macro returns a non-zero value if the value of +.Fa x +is a NaN. +Otherwise 0 is returned. .Sh SEE ALSO -.Xr math 3 +.Xr fpclassify 3 , +.Xr isfinite 3 , +.Xr isinf 3 , +.Xr isinff 3 , +.Xr isnanf 3 , +.Xr isnormal 3 , +.Xr math 3 , +.Xr signbit 3 .Rs .%T "IEEE Standard for Binary Floating-Point Arithmetic" .%Q ANSI .%R Std 754-1985 .Re -.Sh BUGS -Neither the -.Tn VAX -nor the Tahoe floating point have distinguished values -for either infinity or not-a-number. -These routines always return 0 on those architectures. +.Sh STANDARDS +The +.Fn isnan +macro conforms to +.St -isoC-99 . diff --git a/lib/libc/i386/gen/isinf.c b/lib/libc/gen/isnand.c similarity index 62% copy from lib/libc/i386/gen/isinf.c copy to lib/libc/gen/isnand.c index 30c1366d15..f5b7db7185 100644 --- a/lib/libc/i386/gen/isinf.c +++ b/lib/libc/gen/isnand.c @@ -1,7 +1,14 @@ -/*- - * Copyright (c) 1991, 1993 +/* $NetBSD: isnand_ieee754.c,v 1.1 2004/03/04 23:42:39 kleink Exp $ */ +/* $DragonFly: src/lib/libc/gen/isnand.c,v 1.1 2005/07/26 21:15:19 joerg Exp $ */ + +/* + * Copyright (c) 1992, 1993 * The Regents of the University of California. All rights reserved. * + * This software was developed by the Computer Systems Engineering group + * at Lawrence Berkeley Laboratory under DARPA contract BG 91-66 and + * contributed to Berkeley. + * * Redistribution and use in source and binary forms, with or without * modification, are permitted provided that the following conditions * are met: @@ -10,11 +17,7 @@ * 2. Redistributions in binary form must reproduce the above copyright * notice, this list of conditions and the following disclaimer in the * documentation and/or other materials provided with the distribution. - * 3. All advertising materials mentioning features or use of this software - * must display the following acknowledgement: - * This product includes software developed by the University of - * California, Berkeley and its contributors. - * 4. Neither the name of the University nor the names of its contributors + * 3. Neither the name of the University nor the names of its contributors * may be used to endorse or promote products derived from this software * without specific prior written permission. * @@ -30,36 +33,23 @@ * OUT OF THE USE OF THIS SOFTWARE, EVEN IF ADVISED OF THE POSSIBILITY OF * SUCH DAMAGE. * - * $FreeBSD: src/lib/libc/i386/gen/isinf.c,v 1.6 1999/08/27 23:59:21 peter Exp $ - * $DragonFly: src/lib/libc/i386/gen/Attic/isinf.c,v 1.4 2004/10/25 19:38:01 drhodus Exp $ + * from: Header: isinf.c,v 1.1 91/07/08 19:03:34 torek Exp */ -#include +#include +#include +/* + * 7.12.3.4 isnan - test for a NaN + * IEEE 754 double-precision version + */ int -isnan(d) - double d; +__isnand(double x) { - struct IEEEdp { - u_int manl : 32; - u_int manh : 20; - u_int exp : 11; - u_int sign : 1; - } *p = (struct IEEEdp *)&d; + union ieee_double_u u; - return(p->exp == 2047 && (p->manh || p->manl)); -} - -int -isinf(d) - double d; -{ - struct IEEEdp { - u_int manl : 32; - u_int manh : 20; - u_int exp : 11; - u_int sign : 1; - } *p = (struct IEEEdp *)&d; + u.dblu_d = x; - return(p->exp == 2047 && !p->manh && !p->manl); + return (u.dblu_dbl.dbl_exp == DBL_EXP_INFNAN && + (u.dblu_dbl.dbl_frach != 0 || u.dblu_dbl.dbl_fracl != 0)); } diff --git a/lib/libc/i386/gen/isinf.c b/lib/libc/gen/isnanf.c similarity index 62% copy from lib/libc/i386/gen/isinf.c copy to lib/libc/gen/isnanf.c index 30c1366d15..d34d456411 100644 --- a/lib/libc/i386/gen/isinf.c +++ b/lib/libc/gen/isnanf.c @@ -1,7 +1,14 @@ -/*- - * Copyright (c) 1991, 1993 +/* $NetBSD: isnanf_ieee754.c,v 1.1 2004/03/04 23:42:39 kleink Exp $ */ +/* $DragonFly: src/lib/libc/gen/isnanf.c,v 1.1 2005/07/26 21:15:19 joerg Exp $ */ + +/* + * Copyright (c) 1992, 1993 * The Regents of the University of California. All rights reserved. * + * This software was developed by the Computer Systems Engineering group + * at Lawrence Berkeley Laboratory under DARPA contract BG 91-66 and + * contributed to Berkeley. + * * Redistribution and use in source and binary forms, with or without * modification, are permitted provided that the following conditions * are met: @@ -10,11 +17,7 @@ * 2. Redistributions in binary form must reproduce the above copyright * notice, this list of conditions and the following disclaimer in the * documentation and/or other materials provided with the distribution. - * 3. All advertising materials mentioning features or use of this software - * must display the following acknowledgement: - * This product includes software developed by the University of - * California, Berkeley and its contributors. - * 4. Neither the name of the University nor the names of its contributors + * 3. Neither the name of the University nor the names of its contributors * may be used to endorse or promote products derived from this software * without specific prior written permission. * @@ -30,36 +33,23 @@ * OUT OF THE USE OF THIS SOFTWARE, EVEN IF ADVISED OF THE POSSIBILITY OF * SUCH DAMAGE. * - * $FreeBSD: src/lib/libc/i386/gen/isinf.c,v 1.6 1999/08/27 23:59:21 peter Exp $ - * $DragonFly: src/lib/libc/i386/gen/Attic/isinf.c,v 1.4 2004/10/25 19:38:01 drhodus Exp $ + * from: Header: isinf.c,v 1.1 91/07/08 19:03:34 torek Exp */ -#include +#include +#include +/* + * 7.12.3.4 isnan - test for a NaN + * IEEE 754 single-precision version + */ int -isnan(d) - double d; +__isnanf(float x) { - struct IEEEdp { - u_int manl : 32; - u_int manh : 20; - u_int exp : 11; - u_int sign : 1; - } *p = (struct IEEEdp *)&d; + union ieee_single_u u; - return(p->exp == 2047 && (p->manh || p->manl)); -} - -int -isinf(d) - double d; -{ - struct IEEEdp { - u_int manl : 32; - u_int manh : 20; - u_int exp : 11; - u_int sign : 1; - } *p = (struct IEEEdp *)&d; + u.sngu_f = x; - return(p->exp == 2047 && !p->manh && !p->manl); + return (u.sngu_sng.sng_exp == SNG_EXP_INFNAN && + u.sngu_sng.sng_frac != 0); } diff --git a/lib/libc/gen/signbit.3 b/lib/libc/gen/signbit.3 new file mode 100644 index 0000000000..a8ecf93a2d --- /dev/null +++ b/lib/libc/gen/signbit.3 @@ -0,0 +1,77 @@ +.\" $NetBSD: signbit.3,v 1.2 2004/01/15 20:31:40 wiz Exp $ +.\" $DragonFly: src/lib/libc/gen/signbit.3,v 1.1 2005/07/26 21:15:19 joerg Exp $ +.\" +.\" Copyright (c) 2003 The NetBSD Foundation, Inc. +.\" All rights reserved. +.\" +.\" This code is derived from software contributed to The NetBSD Foundation +.\" by Klaus Klein. +.\" +.\" Redistribution and use in source and binary forms, with or without +.\" modification, are permitted provided that the following conditions +.\" are met: +.\" 1. Redistributions of source code must retain the above copyright +.\" notice, this list of conditions and the following disclaimer. +.\" 2. Redistributions in binary form must reproduce the above copyright +.\" notice, this list of conditions and the following disclaimer in the +.\" documentation and/or other materials provided with the distribution. +.\" 3. All advertising materials mentioning features or use of this software +.\" must display the following acknowledgement: +.\" This product includes software developed by the NetBSD +.\" Foundation, Inc. and its contributors. +.\" 4. Neither the name of The NetBSD Foundation nor the names of its +.\" contributors may be used to endorse or promote products derived +.\" from this software without specific prior written permission. +.\" +.\" THIS SOFTWARE IS PROVIDED BY THE NETBSD FOUNDATION, INC. AND CONTRIBUTORS +.\" ``AS IS'' AND ANY EXPRESS OR IMPLIED WARRANTIES, INCLUDING, BUT NOT LIMITED +.\" TO, THE IMPLIED WARRANTIES OF MERCHANTABILITY AND FITNESS FOR A PARTICULAR +.\" PURPOSE ARE DISCLAIMED. IN NO EVENT SHALL THE FOUNDATION OR CONTRIBUTORS +.\" BE LIABLE FOR ANY DIRECT, INDIRECT, INCIDENTAL, SPECIAL, EXEMPLARY, OR +.\" CONSEQUENTIAL DAMAGES (INCLUDING, BUT NOT LIMITED TO, PROCUREMENT OF +.\" SUBSTITUTE GOODS OR SERVICES; LOSS OF USE, DATA, OR PROFITS; OR BUSINESS +.\" INTERRUPTION) HOWEVER CAUSED AND ON ANY THEORY OF LIABILITY, WHETHER IN +.\" CONTRACT, STRICT LIABILITY, OR TORT (INCLUDING NEGLIGENCE OR OTHERWISE) +.\" ARISING IN ANY WAY OUT OF THE USE OF THIS SOFTWARE, EVEN IF ADVISED OF THE +.\" POSSIBILITY OF SUCH DAMAGE. +.\" +.Dd October 29, 2003 +.Dt SIGNBIT 3 +.Os +.Sh NAME +.Nm signbit +.Nd test sign +.Sh LIBRARY +.Lb libc +.Sh SYNOPSIS +.In math.h +.Ft int +.Fn signbit "real-floating x" +.Sh DESCRIPTION +The +.Fn signbit +macro determines whether the sign of its argument value +.Fa x +is negative. +An argument represented in a format wider than its semantic type is +converted to its semantic type first. +The determination is then based on the type of the argument. +.Sh RETURN VALUES +The +.Fn signbit +macro returns a non-zero value if the sign of its value +.Fa x +is negative. +Otherwise 0 is returned. +.Sh ERRORS +No errors are defined. +.Sh SEE ALSO +.Xr fpclassify 3 , +.Xr isfinite 3 , +.Xr isnormal 3 , +.Xr math 3 +.Sh STANDARDS +The +.Fn signbit +macro conforms to +.St -isoC-99 . diff --git a/lib/libc/gen/signbitd.c b/lib/libc/gen/signbitd.c new file mode 100644 index 0000000000..9110a65382 --- /dev/null +++ b/lib/libc/gen/signbitd.c @@ -0,0 +1,55 @@ +/*- + * Copyright (c) 2003 The NetBSD Foundation, Inc. + * All rights reserved. + * + * This code is derived from software contributed to The NetBSD Foundation + * by Klaus Klein. + * + * Redistribution and use in source and binary forms, with or without + * modification, are permitted provided that the following conditions + * are met: + * 1. Redistributions of source code must retain the above copyright + * notice, this list of conditions and the following disclaimer. + * 2. Redistributions in binary form must reproduce the above copyright + * notice, this list of conditions and the following disclaimer in the + * documentation and/or other materials provided with the distribution. + * 3. All advertising materials mentioning features or use of this software + * must display the following acknowledgement: + * This product includes software developed by the NetBSD + * Foundation, Inc. and its contributors. + * 4. Neither the name of The NetBSD Foundation nor the names of its + * contributors may be used to endorse or promote products derived + * from this software without specific prior written permission. + * + * THIS SOFTWARE IS PROVIDED BY THE NETBSD FOUNDATION, INC. AND CONTRIBUTORS + * ``AS IS'' AND ANY EXPRESS OR IMPLIED WARRANTIES, INCLUDING, BUT NOT LIMITED + * TO, THE IMPLIED WARRANTIES OF MERCHANTABILITY AND FITNESS FOR A PARTICULAR + * PURPOSE ARE DISCLAIMED. IN NO EVENT SHALL THE FOUNDATION OR CONTRIBUTORS + * BE LIABLE FOR ANY DIRECT, INDIRECT, INCIDENTAL, SPECIAL, EXEMPLARY, OR + * CONSEQUENTIAL DAMAGES (INCLUDING, BUT NOT LIMITED TO, PROCUREMENT OF + * SUBSTITUTE GOODS OR SERVICES; LOSS OF USE, DATA, OR PROFITS; OR BUSINESS + * INTERRUPTION) HOWEVER CAUSED AND ON ANY THEORY OF LIABILITY, WHETHER IN + * CONTRACT, STRICT LIABILITY, OR TORT (INCLUDING NEGLIGENCE OR OTHERWISE) + * ARISING IN ANY WAY OUT OF THE USE OF THIS SOFTWARE, EVEN IF ADVISED OF THE + * POSSIBILITY OF SUCH DAMAGE. + * + * $NetBSD: signbitd_ieee754.c,v 1.1 2004/01/15 19:43:45 kleink Exp $ + * $DragonFly: src/lib/libc/gen/signbitd.c,v 1.1 2005/07/26 21:15:19 joerg Exp $ + */ + +#include +#include + +/* + * 7.12.3.6 signbit - determine whether the sign of an argument is negative + * IEEE 754 double-precision version + */ +int +__signbitd(double x) +{ + union ieee_double_u u; + + u.dblu_d = x; + + return (u.dblu_dbl.dbl_sign == 1); +} diff --git a/lib/libc/gen/signbitf.c b/lib/libc/gen/signbitf.c new file mode 100644 index 0000000000..4f8b69e258 --- /dev/null +++ b/lib/libc/gen/signbitf.c @@ -0,0 +1,55 @@ +/*- + * Copyright (c) 2003 The NetBSD Foundation, Inc. + * All rights reserved. + * + * This code is derived from software contributed to The NetBSD Foundation + * by Klaus Klein. + * + * Redistribution and use in source and binary forms, with or without + * modification, are permitted provided that the following conditions + * are met: + * 1. Redistributions of source code must retain the above copyright + * notice, this list of conditions and the following disclaimer. + * 2. Redistributions in binary form must reproduce the above copyright + * notice, this list of conditions and the following disclaimer in the + * documentation and/or other materials provided with the distribution. + * 3. All advertising materials mentioning features or use of this software + * must display the following acknowledgement: + * This product includes software developed by the NetBSD + * Foundation, Inc. and its contributors. + * 4. Neither the name of The NetBSD Foundation nor the names of its + * contributors may be used to endorse or promote products derived + * from this software without specific prior written permission. + * + * THIS SOFTWARE IS PROVIDED BY THE NETBSD FOUNDATION, INC. AND CONTRIBUTORS + * ``AS IS'' AND ANY EXPRESS OR IMPLIED WARRANTIES, INCLUDING, BUT NOT LIMITED + * TO, THE IMPLIED WARRANTIES OF MERCHANTABILITY AND FITNESS FOR A PARTICULAR + * PURPOSE ARE DISCLAIMED. IN NO EVENT SHALL THE FOUNDATION OR CONTRIBUTORS + * BE LIABLE FOR ANY DIRECT, INDIRECT, INCIDENTAL, SPECIAL, EXEMPLARY, OR + * CONSEQUENTIAL DAMAGES (INCLUDING, BUT NOT LIMITED TO, PROCUREMENT OF + * SUBSTITUTE GOODS OR SERVICES; LOSS OF USE, DATA, OR PROFITS; OR BUSINESS + * INTERRUPTION) HOWEVER CAUSED AND ON ANY THEORY OF LIABILITY, WHETHER IN + * CONTRACT, STRICT LIABILITY, OR TORT (INCLUDING NEGLIGENCE OR OTHERWISE) + * ARISING IN ANY WAY OUT OF THE USE OF THIS SOFTWARE, EVEN IF ADVISED OF THE + * POSSIBILITY OF SUCH DAMAGE. + * + * $NetBSD: signbitf_ieee754.c,v 1.1 2004/01/15 19:43:45 kleink Exp $ + * $DragonFly: src/lib/libc/gen/signbitf.c,v 1.1 2005/07/26 21:15:19 joerg Exp $ + */ + +#include +#include + +/* + * 7.12.3.6 signbit - determine whether the sign of an argument is negative + * IEEE 754 single-precision version + */ +int +__signbitf(float x) +{ + union ieee_single_u u; + + u.sngu_f = x; + + return (u.sngu_sng.sng_sign == 1); +} diff --git a/lib/libc/i386/gen/Makefile.inc b/lib/libc/i386/gen/Makefile.inc index 2a212f471b..e087e9e460 100644 --- a/lib/libc/i386/gen/Makefile.inc +++ b/lib/libc/i386/gen/Makefile.inc @@ -1,6 +1,9 @@ # @(#)Makefile.inc 8.1 (Berkeley) 6/4/93 # $FreeBSD: src/lib/libc/i386/gen/Makefile.inc,v 1.10.2.1 2001/02/07 00:12:45 peter Exp $ -# $DragonFly: src/lib/libc/i386/gen/Makefile.inc,v 1.4 2005/03/29 19:26:19 joerg Exp $ +# $DragonFly: src/lib/libc/i386/gen/Makefile.inc,v 1.5 2005/07/26 21:15:19 joerg Exp $ -SRCS+= _setjmp.S alloca.S fabs.S frexp.c infinity.c isinf.c \ - ldexp.c modf.S rfork_thread.S setjmp.S sigsetjmp.S +SRCS+= fpclassifyl.c frexp.c infinityl.c isfinitel.c isinfl.c isnanl.c \ + ldexp.c nanf.c signbitl.c \ + _setjmp.S alloca.S fabs.S flt_rounds.S fpgetmask.S fpgetround.S \ + fpgetsticky.S fpsetmask.S fpsetround.S fpsetsticky.S modf.S \ + rfork_thread.S setjmp.S sigsetjmp.S diff --git a/lib/libc/i386/gen/flt_rounds.S b/lib/libc/i386/gen/flt_rounds.S new file mode 100644 index 0000000000..4f49c3e370 --- /dev/null +++ b/lib/libc/i386/gen/flt_rounds.S @@ -0,0 +1,33 @@ +/* + * Written by J.T. Conklin, Apr 4, 1995 + * Public domain. + * + * $NetBSD: flt_rounds.S,v 1.6 1999/08/23 08:45:09 kleink Exp $ + * $DragonFly: src/lib/libc/i386/gen/flt_rounds.S,v 1.1 2005/07/26 21:15:19 joerg Exp $ + */ + +#include + +_START_ENTRY +_map: + .byte 1 /* round to nearest */ + .byte 3 /* round to negative infinity */ + .byte 2 /* round to positive infinity */ + .byte 0 /* round to zero */ + +ENTRY(__flt_rounds) + subl $4,%esp + fnstcw (%esp) + movl (%esp),%eax + shrl $10,%eax + andl $3,%eax +#ifdef PIC + PIC_PROLOGUE + leal PIC_GOTOFF(_map),%ecx + PIC_EPILOGUE + movb (%ecx,%eax,1),%al +#else + movb _map(,%eax,1),%al +#endif + addl $4,%esp + ret diff --git a/lib/libc/i386/gen/fpclassifyl.c b/lib/libc/i386/gen/fpclassifyl.c new file mode 100644 index 0000000000..c39106ca3f --- /dev/null +++ b/lib/libc/i386/gen/fpclassifyl.c @@ -0,0 +1,70 @@ +/* $NetBSD: fpclassifyl.c,v 1.1 2003/10/28 22:05:37 kleink Exp $ */ +/* $DragonFly: src/lib/libc/i386/gen/fpclassifyl.c,v 1.1 2005/07/26 21:15:19 joerg Exp $ */ + +/*- + * Copyright (c) 2003 The NetBSD Foundation, Inc. + * All rights reserved. + * + * This code is derived from software contributed to The NetBSD Foundation + * by Klaus Klein. + * + * Redistribution and use in source and binary forms, with or without + * modification, are permitted provided that the following conditions + * are met: + * 1. Redistributions of source code must retain the above copyright + * notice, this list of conditions and the following disclaimer. + * 2. Redistributions in binary form must reproduce the above copyright + * notice, this list of conditions and the following disclaimer in the + * documentation and/or other materials provided with the distribution. + * 3. All advertising materials mentioning features or use of this software + * must display the following acknowledgement: + * This product includes software developed by the NetBSD + * Foundation, Inc. and its contributors. + * 4. Neither the name of The NetBSD Foundation nor the names of its + * contributors may be used to endorse or promote products derived + * from this software without specific prior written permission. + * + * THIS SOFTWARE IS PROVIDED BY THE NETBSD FOUNDATION, INC. AND CONTRIBUTORS + * ``AS IS'' AND ANY EXPRESS OR IMPLIED WARRANTIES, INCLUDING, BUT NOT LIMITED + * TO, THE IMPLIED WARRANTIES OF MERCHANTABILITY AND FITNESS FOR A PARTICULAR + * PURPOSE ARE DISCLAIMED. IN NO EVENT SHALL THE FOUNDATION OR CONTRIBUTORS + * BE LIABLE FOR ANY DIRECT, INDIRECT, INCIDENTAL, SPECIAL, EXEMPLARY, OR + * CONSEQUENTIAL DAMAGES (INCLUDING, BUT NOT LIMITED TO, PROCUREMENT OF + * SUBSTITUTE GOODS OR SERVICES; LOSS OF USE, DATA, OR PROFITS; OR BUSINESS + * INTERRUPTION) HOWEVER CAUSED AND ON ANY THEORY OF LIABILITY, WHETHER IN + * CONTRACT, STRICT LIABILITY, OR TORT (INCLUDING NEGLIGENCE OR OTHERWISE) + * ARISING IN ANY WAY OUT OF THE USE OF THIS SOFTWARE, EVEN IF ADVISED OF THE + * POSSIBILITY OF SUCH DAMAGE. + */ + +#include +#include +#include + +/* + * 7.12.3.1 fpclassify - classify real floating type + * IEEE 754 compatible 80-bit extended-precision Intel 386 version + */ +int +__fpclassifyl(long double x) +{ + union ieee_ext_u u; + + u.extu_ld = x; + + _DIAGASSERT(u.extu_ext.ext_exp == 0 || u.extu_ext.ext_int == 1); + + if (u.extu_ext.ext_exp == 0) { + if (u.extu_ext.ext_frach == 0 && u.extu_ext.ext_fracl == 0) + return FP_ZERO; + else + return FP_SUBNORMAL; + } else if (u.extu_ext.ext_exp == EXT_EXP_INFNAN) { + if (u.extu_ext.ext_frach == 0 && u.extu_ext.ext_fracl == 0) + return FP_INFINITE; + else + return FP_NAN; + } + + return FP_NORMAL; +} diff --git a/lib/libc/i386/gen/fpgetmask.S b/lib/libc/i386/gen/fpgetmask.S new file mode 100644 index 0000000000..aa9c432c0a --- /dev/null +++ b/lib/libc/i386/gen/fpgetmask.S @@ -0,0 +1,23 @@ +/* + * Written by J.T. Conklin, Apr 4, 1995 + * Public domain. + * + * $NetBSD: fpgetmask.S,v 1.4 2002/01/13 21:45:42 thorpej Exp $ + * $DragonFly: src/lib/libc/i386/gen/fpgetmask.S,v 1.1 2005/07/26 21:15:19 joerg Exp $ + */ + +#include + +#ifdef WEAK_ALIAS +WEAK_ALIAS(fpgetmask, _fpgetmask) +ENTRY(_fpgetmask) +#else +ENTRY(fpgetmask) +#endif + subl $4,%esp + fnstcw (%esp) + movl (%esp),%eax + notl %eax + andl $63,%eax + addl $4,%esp + ret diff --git a/lib/libc/i386/gen/fpgetround.S b/lib/libc/i386/gen/fpgetround.S new file mode 100644 index 0000000000..3a7f9a7a98 --- /dev/null +++ b/lib/libc/i386/gen/fpgetround.S @@ -0,0 +1,23 @@ +/* + * Written by J.T. Conklin, Apr 4, 1995 + * Public domain. + * + * $NetBSD: fpgetround.S,v 1.5 2002/01/13 21:45:43 thorpej Exp $ + * $DragonFly: src/lib/libc/i386/gen/fpgetround.S,v 1.1 2005/07/26 21:15:19 joerg Exp $ + */ + +#include + +#ifdef WEAK_ALIAS +WEAK_ALIAS(fpgetround, _fpgetround) +ENTRY(_fpgetround) +#else +ENTRY(fpgetround) +#endif + subl $4,%esp + fnstcw (%esp) + movl (%esp),%eax + rorl $10,%eax + andl $3,%eax + addl $4,%esp + ret diff --git a/lib/libc/i386/gen/fpgetsticky.S b/lib/libc/i386/gen/fpgetsticky.S new file mode 100644 index 0000000000..a6285dc0ae --- /dev/null +++ b/lib/libc/i386/gen/fpgetsticky.S @@ -0,0 +1,21 @@ +/* + * Written by J.T. Conklin, Apr 4, 1995 + * Public domain. + * $NetBSD: fpgetsticky.S,v 1.6 2002/01/13 21:45:43 thorpej Exp $ + * $DragonFly: src/lib/libc/i386/gen/fpgetsticky.S,v 1.1 2005/07/26 21:15:19 joerg Exp $ + */ + +#include + +#ifdef WEAK_ALIAS +WEAK_ALIAS(fpgetsticky, _fpgetsticky) +ENTRY(_fpgetsticky) +#else +ENTRY(fpgetsticky) +#endif + subl $4,%esp + fnstsw (%esp) + movl (%esp),%eax + andl $63,%eax + addl $4,%esp + ret diff --git a/lib/libc/i386/gen/fpsetmask.S b/lib/libc/i386/gen/fpsetmask.S new file mode 100644 index 0000000000..ad8278c1f0 --- /dev/null +++ b/lib/libc/i386/gen/fpsetmask.S @@ -0,0 +1,34 @@ +/* + * Written by Charles M. Hannum, Apr 9, 1995 + * Public domain. + * + * $NetBSD: fpsetmask.S,v 1.4 2002/01/13 21:45:43 thorpej Exp $ + * $DragonFly: src/lib/libc/i386/gen/fpsetmask.S,v 1.1 2005/07/26 21:15:19 joerg Exp $ + */ + +#include + +#ifdef WEAK_ALIAS +WEAK_ALIAS(fpsetmask, _fpsetmask) +ENTRY(_fpsetmask) +#else +ENTRY(fpsetmask) +#endif + subl $4,%esp + + fnstcw (%esp) + movl (%esp),%eax + movl %eax,%edx + + notl %eax + andl $63,%eax + + addl %eax,%edx + movl 8(%esp),%ecx + andl $63,%ecx + subl %ecx,%edx + movl %edx,(%esp) + fldcw (%esp) + + addl $4,%esp + ret diff --git a/lib/libc/i386/gen/fpsetround.S b/lib/libc/i386/gen/fpsetround.S new file mode 100644 index 0000000000..24f63d807d --- /dev/null +++ b/lib/libc/i386/gen/fpsetround.S @@ -0,0 +1,35 @@ +/* + * Written by Charles M. Hannum, Apr 9, 1995 + * Public domain. + * + * $NetBSD: fpsetround.S,v 1.3 2002/01/13 21:45:43 thorpej Exp $ + * $DragonFly: src/lib/libc/i386/gen/fpsetround.S,v 1.1 2005/07/26 21:15:19 joerg Exp $ + */ + +#include + +#ifdef WEAK_ALIAS +WEAK_ALIAS(fpsetround, _fpsetround) +ENTRY(_fpsetround) +#else +ENTRY(fpsetround) +#endif + subl $4,%esp + + fnstcw (%esp) + movl (%esp),%eax + + rorl $10,%eax + movl %eax,%edx + andl $3,%eax + + subl %eax,%edx + movl 8(%esp),%ecx + andl $3,%ecx + orl %ecx,%edx + roll $10,%edx + movl %edx,(%esp) + fldcw (%esp) + + addl $4,%esp + ret diff --git a/lib/libc/i386/gen/fpsetsticky.S b/lib/libc/i386/gen/fpsetsticky.S new file mode 100644 index 0000000000..58b7b7ecff --- /dev/null +++ b/lib/libc/i386/gen/fpsetsticky.S @@ -0,0 +1,33 @@ +/* + * Written by Charles M. Hannum, Apr 9, 1995 + * Public domain. + * + * $NetBSD: fpsetsticky.S,v 1.6 2002/01/13 21:45:43 thorpej Exp $ + * $DragonFly: src/lib/libc/i386/gen/fpsetsticky.S,v 1.1 2005/07/26 21:15:19 joerg Exp $ + */ + +#include + +#ifdef WEAK_ALIAS +WEAK_ALIAS(fpsetsticky, _fpsetsticky) +ENTRY(_fpsetsticky) +#else +ENTRY(fpsetsticky) +#endif + subl $28,%esp + + fnstenv (%esp) + movl 4(%esp),%eax + movl %eax,%edx + + andl $63,%eax + + subl %eax,%edx + movl 32(%esp),%ecx + andl $63,%ecx + addl %ecx,%edx + movl %edx,4(%esp) + fldenv (%esp) + + addl $28,%esp + ret diff --git a/lib/libc/i386/gen/infinity.c b/lib/libc/i386/gen/infinity.c deleted file mode 100644 index 6cad64697e..0000000000 --- a/lib/libc/i386/gen/infinity.c +++ /dev/null @@ -1,10 +0,0 @@ -/* - * infinity.c - * $FreeBSD: src/lib/libc/i386/gen/infinity.c,v 1.5 1999/08/27 23:59:21 peter Exp $ - * $DragonFly: src/lib/libc/i386/gen/Attic/infinity.c,v 1.2 2003/06/17 04:26:43 dillon Exp $ - */ - -#include - -/* bytes for +Infinity on a 387 */ -char __infinity[] = { 0, 0, 0, 0, 0, 0, 0xf0, 0x7f }; diff --git a/lib/libc/i386/gen/infinityl.c b/lib/libc/i386/gen/infinityl.c new file mode 100644 index 0000000000..08b868bf94 --- /dev/null +++ b/lib/libc/i386/gen/infinityl.c @@ -0,0 +1,12 @@ +/* $NetBSD: infinityl.c,v 1.2 2005/06/12 05:21:26 lukem Exp $ */ +/* $DragonFly: src/lib/libc/i386/gen/infinityl.c,v 1.1 2005/07/26 21:15:19 joerg Exp $ */ + +/* + * IEEE-compatible infinityl.c for little-endian 80-bit format -- public domain. + * Note that the representation includes 16 bits of tail padding per i386 ABI. + */ + +#include + +const union __long_double_u __infinityl = + { { 0, 0, 0, 0, 0, 0, 0, 0x80, 0xff, 0x7f, 0, 0 } }; diff --git a/lib/libc/i386/gen/isfinitel.c b/lib/libc/i386/gen/isfinitel.c new file mode 100644 index 0000000000..a6c09a065f --- /dev/null +++ b/lib/libc/i386/gen/isfinitel.c @@ -0,0 +1,61 @@ +/* $NetBSD: isfinitel.c,v 1.1 2003/10/29 20:03:51 kleink Exp $ */ +/* $DragonFly: src/lib/libc/i386/gen/isfinitel.c,v 1.1 2005/07/26 21:15:19 joerg Exp $ */ + +/*- + * Copyright (c) 2003 The NetBSD Foundation, Inc. + * All rights reserved. + * + * This code is derived from software contributed to The NetBSD Foundation + * by Klaus Klein. + * + * Redistribution and use in source and binary forms, with or without + * modification, are permitted provided that the following conditions + * are met: + * 1. Redistributions of source code must retain the above copyright + * notice, this list of conditions and the following disclaimer. + * 2. Redistributions in binary form must reproduce the above copyright + * notice, this list of conditions and the following disclaimer in the + * documentation and/or other materials provided with the distribution. + * 3. All advertising materials mentioning features or use of this software + * must display the following acknowledgement: + * This product includes software developed by the NetBSD + * Foundation, Inc. and its contributors. + * 4. Neither the name of The NetBSD Foundation nor the names of its + * contributors may be used to endorse or promote products derived + * from this software without specific prior written permission. + * + * THIS SOFTWARE IS PROVIDED BY THE NETBSD FOUNDATION, INC. AND CONTRIBUTORS + * ``AS IS'' AND ANY EXPRESS OR IMPLIED WARRANTIES, INCLUDING, BUT NOT LIMITED + * TO, THE IMPLIED WARRANTIES OF MERCHANTABILITY AND FITNESS FOR A PARTICULAR + * PURPOSE ARE DISCLAIMED. IN NO EVENT SHALL THE FOUNDATION OR CONTRIBUTORS + * BE LIABLE FOR ANY DIRECT, INDIRECT, INCIDENTAL, SPECIAL, EXEMPLARY, OR + * CONSEQUENTIAL DAMAGES (INCLUDING, BUT NOT LIMITED TO, PROCUREMENT OF + * SUBSTITUTE GOODS OR SERVICES; LOSS OF USE, DATA, OR PROFITS; OR BUSINESS + * INTERRUPTION) HOWEVER CAUSED AND ON ANY THEORY OF LIABILITY, WHETHER IN + * CONTRACT, STRICT LIABILITY, OR TORT (INCLUDING NEGLIGENCE OR OTHERWISE) + * ARISING IN ANY WAY OUT OF THE USE OF THIS SOFTWARE, EVEN IF ADVISED OF THE + * POSSIBILITY OF SUCH DAMAGE. + */ + +#include +#include +#include + +/* + * 7.12.3.2 isfinite - determine whether an argument has finite value + * IEEE 754 compatible 80-bit extended-precision Intel 386 version + */ +int +__isfinitel(long double x) +{ + union ieee_ext_u u; + + u.extu_ld = x; + + _DIAGASSERT(u.extu_ext.ext_exp == 0 || u.extu_ext.ext_int == 1); + + if (u.extu_ext.ext_exp == EXT_EXP_INFNAN) + return 0; + + return 1; +} diff --git a/lib/libc/i386/gen/isinf.c b/lib/libc/i386/gen/isinfl.c similarity index 62% copy from lib/libc/i386/gen/isinf.c copy to lib/libc/i386/gen/isinfl.c index 30c1366d15..4482c45a01 100644 --- a/lib/libc/i386/gen/isinf.c +++ b/lib/libc/i386/gen/isinfl.c @@ -1,7 +1,14 @@ -/*- - * Copyright (c) 1991, 1993 +/* $NetBSD: isinfl.c,v 1.5 2004/03/04 23:42:38 kleink Exp $ */ +/* $DragonFly: src/lib/libc/i386/gen/isinfl.c,v 1.1 2005/07/26 21:15:19 joerg Exp $ */ + +/* + * Copyright (c) 1992, 1993 * The Regents of the University of California. All rights reserved. * + * This software was developed by the Computer Systems Engineering group + * at Lawrence Berkeley Laboratory under DARPA contract BG 91-66 and + * contributed to Berkeley. + * * Redistribution and use in source and binary forms, with or without * modification, are permitted provided that the following conditions * are met: @@ -10,11 +17,7 @@ * 2. Redistributions in binary form must reproduce the above copyright * notice, this list of conditions and the following disclaimer in the * documentation and/or other materials provided with the distribution. - * 3. All advertising materials mentioning features or use of this software - * must display the following acknowledgement: - * This product includes software developed by the University of - * California, Berkeley and its contributors. - * 4. Neither the name of the University nor the names of its contributors + * 3. Neither the name of the University nor the names of its contributors * may be used to endorse or promote products derived from this software * without specific prior written permission. * @@ -30,36 +33,24 @@ * OUT OF THE USE OF THIS SOFTWARE, EVEN IF ADVISED OF THE POSSIBILITY OF * SUCH DAMAGE. * - * $FreeBSD: src/lib/libc/i386/gen/isinf.c,v 1.6 1999/08/27 23:59:21 peter Exp $ - * $DragonFly: src/lib/libc/i386/gen/Attic/isinf.c,v 1.4 2004/10/25 19:38:01 drhodus Exp $ + * from: Header: isinf.c,v 1.1 91/07/08 19:03:34 torek Exp */ -#include +#include +#include +/* + * 7.12.3.3 isinf - test for infinity + * IEEE 754 compatible 80-bit extended-precision Intel 386 version + */ int -isnan(d) - double d; +__isinfl(long double x) { - struct IEEEdp { - u_int manl : 32; - u_int manh : 20; - u_int exp : 11; - u_int sign : 1; - } *p = (struct IEEEdp *)&d; + union ieee_ext_u u; - return(p->exp == 2047 && (p->manh || p->manl)); -} - -int -isinf(d) - double d; -{ - struct IEEEdp { - u_int manl : 32; - u_int manh : 20; - u_int exp : 11; - u_int sign : 1; - } *p = (struct IEEEdp *)&d; + u.extu_ld = x; - return(p->exp == 2047 && !p->manh && !p->manl); + return (u.extu_ext.ext_exp == EXT_EXP_INFNAN && + (u.extu_ext.ext_int == 1 && + u.extu_ext.ext_frach == 0 && u.extu_ext.ext_fracl == 0)); } diff --git a/lib/libc/i386/gen/isinf.c b/lib/libc/i386/gen/isnanl.c similarity index 62% rename from lib/libc/i386/gen/isinf.c rename to lib/libc/i386/gen/isnanl.c index 30c1366d15..ca5e9300b4 100644 --- a/lib/libc/i386/gen/isinf.c +++ b/lib/libc/i386/gen/isnanl.c @@ -1,7 +1,14 @@ -/*- - * Copyright (c) 1991, 1993 +/* $NetBSD: isnanl.c,v 1.5 2004/03/04 23:42:38 kleink Exp $ */ +/* $DragonFly: src/lib/libc/i386/gen/isnanl.c,v 1.1 2005/07/26 21:15:19 joerg Exp $ */ + +/* + * Copyright (c) 1992, 1993 * The Regents of the University of California. All rights reserved. * + * This software was developed by the Computer Systems Engineering group + * at Lawrence Berkeley Laboratory under DARPA contract BG 91-66 and + * contributed to Berkeley. + * * Redistribution and use in source and binary forms, with or without * modification, are permitted provided that the following conditions * are met: @@ -10,11 +17,7 @@ * 2. Redistributions in binary form must reproduce the above copyright * notice, this list of conditions and the following disclaimer in the * documentation and/or other materials provided with the distribution. - * 3. All advertising materials mentioning features or use of this software - * must display the following acknowledgement: - * This product includes software developed by the University of - * California, Berkeley and its contributors. - * 4. Neither the name of the University nor the names of its contributors + * 3. Neither the name of the University nor the names of its contributors * may be used to endorse or promote products derived from this software * without specific prior written permission. * @@ -30,36 +33,24 @@ * OUT OF THE USE OF THIS SOFTWARE, EVEN IF ADVISED OF THE POSSIBILITY OF * SUCH DAMAGE. * - * $FreeBSD: src/lib/libc/i386/gen/isinf.c,v 1.6 1999/08/27 23:59:21 peter Exp $ - * $DragonFly: src/lib/libc/i386/gen/Attic/isinf.c,v 1.4 2004/10/25 19:38:01 drhodus Exp $ + * from: Header: isinf.c,v 1.1 91/07/08 19:03:34 torek Exp */ -#include +#include +#include +/* + * 7.12.3.4 isnan - test for a NaN + * IEEE 754 compatible 80-bit extended-precision Intel 386 version + */ int -isnan(d) - double d; +__isnanl(long double x) { - struct IEEEdp { - u_int manl : 32; - u_int manh : 20; - u_int exp : 11; - u_int sign : 1; - } *p = (struct IEEEdp *)&d; + union ieee_ext_u u; - return(p->exp == 2047 && (p->manh || p->manl)); -} - -int -isinf(d) - double d; -{ - struct IEEEdp { - u_int manl : 32; - u_int manh : 20; - u_int exp : 11; - u_int sign : 1; - } *p = (struct IEEEdp *)&d; + u.extu_ld = x; - return(p->exp == 2047 && !p->manh && !p->manl); + return (u.extu_ext.ext_exp == EXT_EXP_INFNAN && + u.extu_ext.ext_int == 1 && + (u.extu_ext.ext_frach != 0 || u.extu_ext.ext_fracl != 0)); } diff --git a/lib/libc/i386/gen/nanf.c b/lib/libc/i386/gen/nanf.c new file mode 100644 index 0000000000..730b6d95e6 --- /dev/null +++ b/lib/libc/i386/gen/nanf.c @@ -0,0 +1,9 @@ +/* $NetBSD: nanf.c,v 1.3 2005/04/15 22:39:11 kleink Exp $ */ +/* $DragonFly: src/lib/libc/i386/gen/nanf.c,v 1.1 2005/07/26 21:15:19 joerg Exp $ */ + +#include +#include + +/* bytes for quiet NaN (IEEE single precision) */ +const union __float_u __nanf = + { { 0, 0, 0xc0, 0x7f } }; diff --git a/lib/libc/i386/gen/signbitl.c b/lib/libc/i386/gen/signbitl.c new file mode 100644 index 0000000000..ba5ede6c31 --- /dev/null +++ b/lib/libc/i386/gen/signbitl.c @@ -0,0 +1,55 @@ +/* $NetBSD: signbitl.c,v 1.1 2004/01/15 19:43:45 kleink Exp $ */ +/* $DragonFly: src/lib/libc/i386/gen/signbitl.c,v 1.1 2005/07/26 21:15:19 joerg Exp $ */ + +/*- + * Copyright (c) 2003 The NetBSD Foundation, Inc. + * All rights reserved. + * + * This code is derived from software contributed to The NetBSD Foundation + * by Klaus Klein. + * + * Redistribution and use in source and binary forms, with or without + * modification, are permitted provided that the following conditions + * are met: + * 1. Redistributions of source code must retain the above copyright + * notice, this list of conditions and the following disclaimer. + * 2. Redistributions in binary form must reproduce the above copyright + * notice, this list of conditions and the following disclaimer in the + * documentation and/or other materials provided with the distribution. + * 3. All advertising materials mentioning features or use of this software + * must display the following acknowledgement: + * This product includes software developed by the NetBSD + * Foundation, Inc. and its contributors. + * 4. Neither the name of The NetBSD Foundation nor the names of its + * contributors may be used to endorse or promote products derived + * from this software without specific prior written permission. + * + * THIS SOFTWARE IS PROVIDED BY THE NETBSD FOUNDATION, INC. AND CONTRIBUTORS + * ``AS IS'' AND ANY EXPRESS OR IMPLIED WARRANTIES, INCLUDING, BUT NOT LIMITED + * TO, THE IMPLIED WARRANTIES OF MERCHANTABILITY AND FITNESS FOR A PARTICULAR + * PURPOSE ARE DISCLAIMED. IN NO EVENT SHALL THE FOUNDATION OR CONTRIBUTORS + * BE LIABLE FOR ANY DIRECT, INDIRECT, INCIDENTAL, SPECIAL, EXEMPLARY, OR + * CONSEQUENTIAL DAMAGES (INCLUDING, BUT NOT LIMITED TO, PROCUREMENT OF + * SUBSTITUTE GOODS OR SERVICES; LOSS OF USE, DATA, OR PROFITS; OR BUSINESS + * INTERRUPTION) HOWEVER CAUSED AND ON ANY THEORY OF LIABILITY, WHETHER IN + * CONTRACT, STRICT LIABILITY, OR TORT (INCLUDING NEGLIGENCE OR OTHERWISE) + * ARISING IN ANY WAY OUT OF THE USE OF THIS SOFTWARE, EVEN IF ADVISED OF THE + * POSSIBILITY OF SUCH DAMAGE. + */ + +#include +#include + +/* + * 7.12.3.6 signbit - determine whether the sign of an argument is negative + * IEEE 754 compatible 80-bit extended-precision Intel 386 version + */ +int +__signbitl(long double x) +{ + union ieee_ext_u u; + + u.extu_ld = x; + + return (u.extu_ext.ext_sign == 1); +} diff --git a/lib/libm/Makefile b/lib/libm/Makefile new file mode 100644 index 0000000000..54ddc00213 --- /dev/null +++ b/lib/libm/Makefile @@ -0,0 +1,12 @@ +# $DragonFly: src/lib/libm/Makefile,v 1.5 2005/07/26 21:15:19 joerg Exp $ + +LIB= m +SHLIB_MAJOR= 3 +WARNS?= 6 + +# Don't MD fragment must be included before MI fragment. +.include "arch/${MACHINE_ARCH}/Makefile.inc" +.include "man/Makefile.inc" +.include "src/Makefile.inc" + +.include diff --git a/lib/libm/arch/i386/Makefile.inc b/lib/libm/arch/i386/Makefile.inc new file mode 100644 index 0000000000..e832ea87ab --- /dev/null +++ b/lib/libm/arch/i386/Makefile.inc @@ -0,0 +1,12 @@ +# $DragonFly: src/lib/libm/arch/i386/Makefile.inc,v 1.1 2005/07/26 21:15:19 joerg Exp $ + +.PATH: ${.CURDIR}/arch/i386 + +SRCS+= e_acos.S e_asin.S e_atan2.S e_atan2f.S e_exp.S e_expf.S e_fmod.S \ + e_log.S e_log10.S e_log10f.S e_logf.S e_remainder.S e_remainderf.S \ + e_scalb.S e_scalbf.S e_sqrt.S e_sqrtf.S lrint.S s_atan.S s_atanf.S \ + s_ceil.S s_ceilf.S s_copysign.S s_copysignf.S s_cos.S s_cosf.S \ + s_finite.S s_finitef.S s_floor.S s_floorf.S s_ilogb.S s_ilogbf.S \ + s_log1p.S s_log1pf.S s_logb.S s_logbf.S s_rint.S s_rintf.S \ + s_scalbn.S s_scalbnf.S s_significand.S s_significandf.S s_sin.S \ + s_sinf.S s_tan.S s_tanf.S diff --git a/lib/libm/arch/i386/abi.h b/lib/libm/arch/i386/abi.h new file mode 100644 index 0000000000..3d45ba0d12 --- /dev/null +++ b/lib/libm/arch/i386/abi.h @@ -0,0 +1,74 @@ +/* + * Written by Frank van der Linden (fvdl@wasabisystems.com) + * + * $NetBSD: abi.h,v 1.3 2004/03/22 13:41:09 wiz Exp $ + * $DragonFly: src/lib/libm/arch/i386/abi.h,v 1.1 2005/07/26 21:15:19 joerg Exp $ + */ + +/* + * The x86-64 ABI specifies that float, double and long double + * arguments are passed in SSE2 (xmm) registers. Unfortunately, + * there is no way to push those on to the FP stack, which is + * where the fancier instructions get their arguments from. + * + * Define some prologues and epilogues to store and retrieve + * xmm regs to local variables. + */ + +#ifdef __x86_64__ + +#define ARG_DOUBLE_ONE -8(%rsp) +#define ARG_DOUBLE_TWO -16(%rsp) +#define ARG_FLOAT_ONE -4(%rsp) +#define ARG_FLOAT_TWO -8(%rsp) + +#define XMM_ONE_ARG_DOUBLE_PROLOGUE \ + movsd %xmm0, ARG_DOUBLE_ONE + +#define XMM_TWO_ARG_DOUBLE_PROLOGUE \ + movsd %xmm0, ARG_DOUBLE_ONE ; \ + movsd %xmm1, ARG_DOUBLE_TWO + +#define XMM_ONE_ARG_FLOAT_PROLOGUE \ + movss %xmm0, ARG_FLOAT_ONE + +#define XMM_TWO_ARG_FLOAT_PROLOGUE \ + movss %xmm0, ARG_FLOAT_ONE ; \ + movss %xmm1, ARG_FLOAT_TWO + +#define XMM_DOUBLE_EPILOGUE \ + fstpl ARG_DOUBLE_ONE ; \ + movsd ARG_DOUBLE_ONE, %xmm0 + +#define XMM_FLOAT_EPILOGUE \ + fstps ARG_FLOAT_ONE ; \ + movss ARG_FLOAT_ONE, %xmm0 + +#define FLDL_VAR(x) fldl x(%rip) + +#else + +#define ARG_DOUBLE_ONE 4(%esp) +#define ARG_DOUBLE_TWO 12(%esp) +#define ARG_FLOAT_ONE 4(%esp) +#define ARG_FLOAT_TWO 8(%esp) + +#define XMM_ONE_ARG_DOUBLE_PROLOGUE +#define XMM_TWO_ARG_DOUBLE_PROLOGUE +#define XMM_ONE_ARG_FLOAT_PROLOGUE +#define XMM_TWO_ARG_FLOAT_PROLOGUE + +#define XMM_DOUBLE_EPILOGUE +#define XMM_FLOAT_EPILOGUE + +#ifdef PIC +#define FLDL_VAR(x) \ + PIC_PROLOGUE ; \ + fldl PIC_GOTOFF(x) ; \ + PIC_EPILOGUE +#else +#define FLDL_VAR(x) \ + fldl x + +#endif +#endif diff --git a/lib/libm/arch/i386/e_acos.S b/lib/libm/arch/i386/e_acos.S new file mode 100644 index 0000000000..ab1d7444cd --- /dev/null +++ b/lib/libm/arch/i386/e_acos.S @@ -0,0 +1,25 @@ +/* + * Written by J.T. Conklin . + * Public domain. + * + * $NetBSD: e_acos.S,v 1.8 2003/07/26 19:24:57 salo Exp $ + * $DragonFly: src/lib/libm/arch/i386/e_acos.S,v 1.1 2005/07/26 21:15:19 joerg Exp $ + */ + +#include + +#include "abi.h" + +/* acos = atan (sqrt(1 - x^2) / x) */ +ENTRY(acos) + XMM_ONE_ARG_DOUBLE_PROLOGUE + fldl ARG_DOUBLE_ONE /* x */ + fld %st(0) + fmul %st(0) /* x^2 */ + fld1 + fsubp /* 1 - x^2 */ + fsqrt /* sqrt (1 - x^2) */ + fxch %st(1) + fpatan + XMM_DOUBLE_EPILOGUE + ret diff --git a/lib/libm/arch/i386/e_asin.S b/lib/libm/arch/i386/e_asin.S new file mode 100644 index 0000000000..ba91b31d9d --- /dev/null +++ b/lib/libm/arch/i386/e_asin.S @@ -0,0 +1,24 @@ +/* + * Written by J.T. Conklin . + * Public domain. + * + * $NetBSD: e_asin.S,v 1.7 2003/07/26 19:24:58 salo Exp $ + * $DragonFly: src/lib/libm/arch/i386/e_asin.S,v 1.1 2005/07/26 21:15:19 joerg Exp $ + */ + +#include + +#include "abi.h" + +/* asin = atan (x / sqrt(1 - x^2)) */ +ENTRY(asin) + XMM_ONE_ARG_DOUBLE_PROLOGUE + fldl ARG_DOUBLE_ONE /* x */ + fld %st(0) + fmul %st(0) /* x^2 */ + fld1 + fsubp /* 1 - x^2 */ + fsqrt /* sqrt (1 - x^2) */ + fpatan + XMM_DOUBLE_EPILOGUE + ret diff --git a/lib/libm/arch/i386/e_atan2.S b/lib/libm/arch/i386/e_atan2.S new file mode 100644 index 0000000000..e444ec62dc --- /dev/null +++ b/lib/libm/arch/i386/e_atan2.S @@ -0,0 +1,19 @@ +/* + * Written by J.T. Conklin . + * Public domain. + * + * $NetBSD: e_atan2.S,v 1.6 2003/07/26 19:24:58 salo Exp $ + * $DragonFly: src/lib/libm/arch/i386/e_atan2.S,v 1.1 2005/07/26 21:15:19 joerg Exp $ + */ + +#include + +#include "abi.h" + +ENTRY(atan2) + XMM_TWO_ARG_DOUBLE_PROLOGUE + fldl ARG_DOUBLE_ONE + fldl ARG_DOUBLE_TWO + fpatan + XMM_DOUBLE_EPILOGUE + ret diff --git a/lib/libm/arch/i386/e_atan2f.S b/lib/libm/arch/i386/e_atan2f.S new file mode 100644 index 0000000000..a8d7daa8c7 --- /dev/null +++ b/lib/libm/arch/i386/e_atan2f.S @@ -0,0 +1,19 @@ +/* + * Written by J.T. Conklin . + * Public domain. + * + * $NetBSD: e_atan2f.S,v 1.3 2003/07/26 19:24:58 salo Exp $ + * $DragonFly: src/lib/libm/arch/i386/e_atan2f.S,v 1.1 2005/07/26 21:15:19 joerg Exp $ + */ + +#include + +#include "abi.h" + +ENTRY(atan2f) + XMM_TWO_ARG_FLOAT_PROLOGUE + flds ARG_FLOAT_ONE + flds ARG_FLOAT_TWO + fpatan + XMM_FLOAT_EPILOGUE + ret diff --git a/lib/libm/arch/i386/e_exp.S b/lib/libm/arch/i386/e_exp.S new file mode 100644 index 0000000000..02b30c7d30 --- /dev/null +++ b/lib/libm/arch/i386/e_exp.S @@ -0,0 +1,131 @@ +/* + * Copyright (c) 1993,94 Winning Strategies, Inc. + * All rights reserved. + * + * Redistribution and use in source and binary forms, with or without + * modification, are permitted provided that the following conditions + * are met: + * 1. Redistributions of source code must retain the above copyright + * notice, this list of conditions and the following disclaimer. + * 2. Redistributions in binary form must reproduce the above copyright + * notice, this list of conditions and the following disclaimer in the + * documentation and/or other materials provided with the distribution. + * 3. All advertising materials mentioning features or use of this software + * must display the following acknowledgement: + * This product includes software developed by Winning Strategies, Inc. + * 4. The name of the author may not be used to endorse or promote products + * derived from this software without specific prior written permission. + * + * THIS SOFTWARE IS PROVIDED BY THE AUTHOR ``AS IS'' AND ANY EXPRESS OR + * IMPLIED WARRANTIES, INCLUDING, BUT NOT LIMITED TO, THE IMPLIED WARRANTIES + * OF MERCHANTABILITY AND FITNESS FOR A PARTICULAR PURPOSE ARE DISCLAIMED. + * IN NO EVENT SHALL THE AUTHOR BE LIABLE FOR ANY DIRECT, INDIRECT, + * INCIDENTAL, SPECIAL, EXEMPLARY, OR CONSEQUENTIAL DAMAGES (INCLUDING, BUT + * NOT LIMITED TO, PROCUREMENT OF SUBSTITUTE GOODS OR SERVICES; LOSS OF USE, + * DATA, OR PROFITS; OR BUSINESS INTERRUPTION) HOWEVER CAUSED AND ON ANY + * THEORY OF LIABILITY, WHETHER IN CONTRACT, STRICT LIABILITY, OR TORT + * (INCLUDING NEGLIGENCE OR OTHERWISE) ARISING IN ANY WAY OUT OF THE USE OF + * THIS SOFTWARE, EVEN IF ADVISED OF THE POSSIBILITY OF SUCH DAMAGE. + * + * $NetBSD: e_exp.S,v 1.12 2002/02/27 16:32:46 christos Exp $ + * $FreeBSD: src/lib/msun/i387/e_exp.S,v 1.8.2.1 2000/07/10 09:16:28 obrien Exp $ + * $DragonFly: src/lib/libm/arch/i386/e_exp.S,v 1.1 2005/07/26 21:15:19 joerg Exp $ + */ + +/* + * Written by: + * J.T. Conklin (jtc@wimsey.com), Winning Strategies, Inc. + */ + +#include + +#include "abi.h" + + +/* e^x = 2^(x * log2(e)) */ +ENTRY(exp) +#ifndef __i386__ + /* + * XXX: This code is broken and needs to be merged with the i386 case. + */ + fstcw -12(%rsp) + movw -12(%rsp),%dx + orw $0x0180,%dx + movw %dx,-16(%rsp) + fldcw -16(%rsp) + movsd %xmm0,-8(%rsp) + fldl -8(%rsp) + + fldl2e + fmulp /* x * log2(e) */ + fld %st(0) + frndint /* int(x * log2(e)) */ + fxch %st(1) + fsub %st(1),%st /* fract(x * log2(e)) */ + f2xm1 /* 2^(fract(x * log2(e))) - 1 */ + fld1 + faddp /* 2^(fract(x * log2(e))) */ + fscale /* e^x */ + fstp %st(1) + + fstpl -8(%rsp) + movsd -8(%rsp),%xmm0 + fldcw -12(%rsp) + ret +#else + /* + * If x is +-Inf, then the subtraction would give Inf-Inf = NaN. + * Avoid this. Also avoid it if x is NaN for convenience. + */ + movl 8(%esp),%eax + andl $0x7fffffff,%eax + cmpl $0x7ff00000,%eax + jae x_Inf_or_NaN + + fldl 4(%esp) + + /* + * Ensure that the rounding mode is to nearest (to give the smallest + * possible fraction) and that the precision is as high as possible. + * We may as well mask interrupts if we switch the mode. + */ + fstcw 4(%esp) + movl 4(%esp),%eax + andl $0x0300,%eax + cmpl $0x0300,%eax /* RC == 0 && PC == 3? */ + je 1f /* jump if mode is good */ + movl $0x137f,8(%esp) + fldcw 8(%esp) +1: + fldl2e + fmulp /* x * log2(e) */ + fst %st(1) + frndint /* int(x * log2(e)) */ + fst %st(2) + fsubrp /* fract(x * log2(e)) */ + f2xm1 /* 2^(fract(x * log2(e))) - 1 */ + fld1 + faddp /* 2^(fract(x * log2(e))) */ + fscale /* e^x */ + fstp %st(1) + je 1f + fldcw 4(%esp) +1: + ret + +x_Inf_or_NaN: + /* + * Return 0 if x is -Inf. Otherwise just return x, although the + * C version would return (x + x) (Real Indefinite) if x is a NaN. + */ + cmpl $0xfff00000,8(%esp) + jne x_not_minus_Inf + cmpl $0,4(%esp) + jne x_not_minus_Inf + fldz + ret + +x_not_minus_Inf: + fldl 4(%esp) + ret +#endif diff --git a/lib/libm/arch/i386/e_expf.S b/lib/libm/arch/i386/e_expf.S new file mode 100644 index 0000000000..af11c13421 --- /dev/null +++ b/lib/libm/arch/i386/e_expf.S @@ -0,0 +1,29 @@ +/* + * Written by J.T. Conklin . + * Public domain. + * + * $NetBSD: e_expf.S,v 1.5 2003/07/26 19:24:58 salo Exp $ + * $DragonFly: src/lib/libm/arch/i386/e_expf.S,v 1.1 2005/07/26 21:15:19 joerg Exp $ + */ + +#include + +#include "abi.h" + +/* e^x = 2^(x * log2(e)) */ +ENTRY(expf) + XMM_ONE_ARG_FLOAT_PROLOGUE + flds ARG_FLOAT_ONE + fldl2e + fmulp /* x * log2(e) */ + fld %st(0) + frndint /* int(x * log2(e)) */ + fsubr %st(0),%st(1) /* fract(x * log2(e)) */ + fxch + f2xm1 /* 2^(fract(x * log2(e))) - 1 */ + fld1 + faddp /* 2^(fract(x * log2(e))) */ + fscale /* e^x */ + fstp %st(1) + XMM_FLOAT_EPILOGUE + ret diff --git a/lib/libm/arch/i386/e_fmod.S b/lib/libm/arch/i386/e_fmod.S new file mode 100644 index 0000000000..8f45112c22 --- /dev/null +++ b/lib/libm/arch/i386/e_fmod.S @@ -0,0 +1,23 @@ +/* + * Written by J.T. Conklin . + * Public domain. + * + * $NetBSD: e_fmod.S,v 1.7 2003/07/26 19:24:58 salo Exp $ + * $DragonFly: src/lib/libm/arch/i386/e_fmod.S,v 1.1 2005/07/26 21:15:19 joerg Exp $ + */ + +#include + +#include "abi.h" + +ENTRY(fmod) + XMM_TWO_ARG_DOUBLE_PROLOGUE + fldl ARG_DOUBLE_TWO + fldl ARG_DOUBLE_ONE +1: fprem + fstsw %ax + btw $10,%ax + jc 1b + fstp %st(1) + XMM_DOUBLE_EPILOGUE + ret diff --git a/lib/libm/arch/i386/e_log.S b/lib/libm/arch/i386/e_log.S new file mode 100644 index 0000000000..89255eb050 --- /dev/null +++ b/lib/libm/arch/i386/e_log.S @@ -0,0 +1,19 @@ +/* + * Written by J.T. Conklin . + * Public domain. + * + * $NetBSD: e_log.S,v 1.6 2003/07/26 19:24:58 salo Exp $ + * $DragonFly: src/lib/libm/arch/i386/e_log.S,v 1.1 2005/07/26 21:15:19 joerg Exp $ + */ + +#include + +#include "abi.h" + +ENTRY(log) + XMM_ONE_ARG_DOUBLE_PROLOGUE + fldln2 + fldl ARG_DOUBLE_ONE + fyl2x + XMM_DOUBLE_EPILOGUE + ret diff --git a/lib/libm/arch/i386/e_log10.S b/lib/libm/arch/i386/e_log10.S new file mode 100644 index 0000000000..ed3a95c976 --- /dev/null +++ b/lib/libm/arch/i386/e_log10.S @@ -0,0 +1,19 @@ +/* + * Written by J.T. Conklin . + * Public domain. + * + * $NetBSD: e_log10.S,v 1.6 2003/07/26 19:24:59 salo Exp $ + * $DragonFly: src/lib/libm/arch/i386/e_log10.S,v 1.1 2005/07/26 21:15:19 joerg Exp $ + */ + +#include + +#include "abi.h" + +ENTRY(log10) + XMM_ONE_ARG_DOUBLE_PROLOGUE + fldlg2 + fldl ARG_DOUBLE_ONE + fyl2x + XMM_DOUBLE_EPILOGUE + ret diff --git a/lib/libm/arch/i386/e_log10f.S b/lib/libm/arch/i386/e_log10f.S new file mode 100644 index 0000000000..0921f848d9 --- /dev/null +++ b/lib/libm/arch/i386/e_log10f.S @@ -0,0 +1,19 @@ +/* + * Written by J.T. Conklin . + * Public domain. + * + * $NetBSD: e_log10f.S,v 1.3 2003/07/26 19:24:59 salo Exp $ + * $DragonFly: src/lib/libm/arch/i386/e_log10f.S,v 1.1 2005/07/26 21:15:19 joerg Exp $ + */ + +#include + +#include "abi.h" + +ENTRY(log10f) + XMM_ONE_ARG_FLOAT_PROLOGUE + fldlg2 + flds ARG_FLOAT_ONE + fyl2x + XMM_FLOAT_EPILOGUE + ret diff --git a/lib/libm/arch/i386/e_logf.S b/lib/libm/arch/i386/e_logf.S new file mode 100644 index 0000000000..6b9656ba8d --- /dev/null +++ b/lib/libm/arch/i386/e_logf.S @@ -0,0 +1,19 @@ +/* + * Written by J.T. Conklin . + * Public domain. + * + * $NetBSD: e_logf.S,v 1.4 2003/07/26 19:24:59 salo Exp $ + * $DragonFly: src/lib/libm/arch/i386/e_logf.S,v 1.1 2005/07/26 21:15:19 joerg Exp $ + */ + +#include + +#include "abi.h" + +ENTRY(logf) + XMM_ONE_ARG_FLOAT_PROLOGUE + fldln2 + flds ARG_FLOAT_ONE + fyl2x + XMM_FLOAT_EPILOGUE + ret diff --git a/lib/libm/arch/i386/e_remainder.S b/lib/libm/arch/i386/e_remainder.S new file mode 100644 index 0000000000..d1fbc9df54 --- /dev/null +++ b/lib/libm/arch/i386/e_remainder.S @@ -0,0 +1,23 @@ +/* + * Written by J.T. Conklin . + * Public domain. + * + * $NetBSD: e_remainder.S,v 1.7 2003/07/26 19:24:59 salo Exp $ + * $DragonFly: src/lib/libm/arch/i386/e_remainder.S,v 1.1 2005/07/26 21:15:19 joerg Exp $ + */ + +#include + +#include "abi.h" + +ENTRY(remainder) + XMM_TWO_ARG_DOUBLE_PROLOGUE + fldl ARG_DOUBLE_TWO + fldl ARG_DOUBLE_ONE +1: fprem1 + fstsw %ax + btw $10,%ax + jc 1b + fstp %st(1) + XMM_DOUBLE_EPILOGUE + ret diff --git a/lib/libm/arch/i386/e_remainderf.S b/lib/libm/arch/i386/e_remainderf.S new file mode 100644 index 0000000000..d0273e04e5 --- /dev/null +++ b/lib/libm/arch/i386/e_remainderf.S @@ -0,0 +1,23 @@ +/* + * Written by J.T. Conklin . + * Public domain. + * + * $NetBSD: e_remainderf.S,v 1.5 2003/07/26 19:24:59 salo Exp $ + * $DragonFly: src/lib/libm/arch/i386/e_remainderf.S,v 1.1 2005/07/26 21:15:19 joerg Exp $ + */ + +#include + +#include "abi.h" + +ENTRY(remainderf) + XMM_TWO_ARG_FLOAT_PROLOGUE + flds ARG_FLOAT_TWO + flds ARG_FLOAT_ONE +1: fprem1 + fstsw %ax + btw $10,%ax + jc 1b + fstp %st(1) + XMM_FLOAT_EPILOGUE + ret diff --git a/lib/libm/arch/i386/e_scalb.S b/lib/libm/arch/i386/e_scalb.S new file mode 100644 index 0000000000..2e0848b94f --- /dev/null +++ b/lib/libm/arch/i386/e_scalb.S @@ -0,0 +1,20 @@ +/* + * Written by J.T. Conklin . + * Public domain. + * + * $NetBSD: e_scalb.S,v 1.7 2003/07/26 19:25:00 salo Exp $ + * $DragonFly: src/lib/libm/arch/i386/e_scalb.S,v 1.1 2005/07/26 21:15:19 joerg Exp $ + */ + +#include + +#include "abi.h" + +ENTRY(scalb) + XMM_TWO_ARG_DOUBLE_PROLOGUE + fldl ARG_DOUBLE_TWO + fldl ARG_DOUBLE_ONE + fscale + fstp %st(1) /* bug fix for fp stack overflow */ + XMM_DOUBLE_EPILOGUE + ret diff --git a/lib/libm/arch/i386/e_scalbf.S b/lib/libm/arch/i386/e_scalbf.S new file mode 100644 index 0000000000..34890812e6 --- /dev/null +++ b/lib/libm/arch/i386/e_scalbf.S @@ -0,0 +1,19 @@ +/* + * Written by J.T. Conklin . + * Public domain. + * + * $NetBSD: e_scalbf.S,v 1.3 2003/07/26 19:25:00 salo Exp $ + * $DragonFly: src/lib/libm/arch/i386/e_scalbf.S,v 1.1 2005/07/26 21:15:19 joerg Exp $ + */ + +#include + +#include "abi.h" + +ENTRY(scalbf) + XMM_TWO_ARG_FLOAT_PROLOGUE + flds ARG_FLOAT_TWO + flds ARG_FLOAT_ONE + fscale + XMM_FLOAT_EPILOGUE + ret diff --git a/lib/libm/arch/i386/e_sqrt.S b/lib/libm/arch/i386/e_sqrt.S new file mode 100644 index 0000000000..02be103768 --- /dev/null +++ b/lib/libm/arch/i386/e_sqrt.S @@ -0,0 +1,18 @@ +/* + * Written by J.T. Conklin . + * Public domain. + * + * $NetBSD: e_sqrt.S,v 1.6 2003/07/26 19:25:00 salo Exp $ + * $DragonFly: src/lib/libm/arch/i386/e_sqrt.S,v 1.1 2005/07/26 21:15:19 joerg Exp $ + */ + +#include + +ENTRY(sqrt) +#ifdef __i386__ + fldl 4(%esp) + fsqrt +#else + sqrtsd %xmm0,%xmm0 +#endif + ret diff --git a/lib/libm/arch/i386/e_sqrtf.S b/lib/libm/arch/i386/e_sqrtf.S new file mode 100644 index 0000000000..b11010d765 --- /dev/null +++ b/lib/libm/arch/i386/e_sqrtf.S @@ -0,0 +1,18 @@ +/* + * Written by J.T. Conklin . + * Public domain. + * + * $NetBSD: e_sqrtf.S,v 1.4 2003/07/26 19:25:00 salo Exp $ + * $DragonFly: src/lib/libm/arch/i386/e_sqrtf.S,v 1.1 2005/07/26 21:15:19 joerg Exp $ + */ + +#include + +ENTRY(sqrtf) +#ifdef __i386__ + flds 4(%esp) + fsqrt +#else + sqrtss %xmm0,%xmm0 +#endif + ret diff --git a/lib/libm/arch/i386/lrint.S b/lib/libm/arch/i386/lrint.S new file mode 100644 index 0000000000..6318ad88a7 --- /dev/null +++ b/lib/libm/arch/i386/lrint.S @@ -0,0 +1,24 @@ +/* + * Written by Matthias Drochner . + * Public domain. + * + * $NetBSD: lrint.S,v 1.2 2004/10/13 15:18:32 drochner Exp $ + * $DragonFly: src/lib/libm/arch/i386/lrint.S,v 1.1 2005/07/26 21:15:19 joerg Exp $ + */ + +#include + +ENTRY(lrint) +#ifdef __i386__ + pushl %ebp + movl %esp,%ebp + subl $4,%esp + fldl 8(%ebp) + fistpl (%esp) + movl (%esp),%eax + leave + ret +#else + cvtsd2siq %xmm0,%rax + ret +#endif diff --git a/lib/libm/arch/i386/s_atan.S b/lib/libm/arch/i386/s_atan.S new file mode 100644 index 0000000000..a60dc3c1a9 --- /dev/null +++ b/lib/libm/arch/i386/s_atan.S @@ -0,0 +1,19 @@ +/* + * Written by J.T. Conklin . + * Public domain. + * + * $NetBSD: s_atan.S,v 1.6 2003/07/26 19:25:00 salo Exp $ + * $DragonFly: src/lib/libm/arch/i386/s_atan.S,v 1.1 2005/07/26 21:15:19 joerg Exp $ + */ + +#include + +#include "abi.h" + +ENTRY(atan) + XMM_ONE_ARG_DOUBLE_PROLOGUE + fldl ARG_DOUBLE_ONE + fld1 + fpatan + XMM_DOUBLE_EPILOGUE + ret diff --git a/lib/libm/arch/i386/s_atanf.S b/lib/libm/arch/i386/s_atanf.S new file mode 100644 index 0000000000..cf2aefc668 --- /dev/null +++ b/lib/libm/arch/i386/s_atanf.S @@ -0,0 +1,19 @@ +/* + * Written by J.T. Conklin . + * Public domain. + * + * $NetBSD: s_atanf.S,v 1.5 2003/07/26 19:25:00 salo Exp $ + * $DragonFly: src/lib/libm/arch/i386/s_atanf.S,v 1.1 2005/07/26 21:15:19 joerg Exp $ + */ + +#include + +#include "abi.h" + +ENTRY(atanf) + XMM_ONE_ARG_FLOAT_PROLOGUE + flds ARG_FLOAT_ONE + fld1 + fpatan + XMM_FLOAT_EPILOGUE + ret diff --git a/lib/libm/arch/i386/s_ceil.S b/lib/libm/arch/i386/s_ceil.S new file mode 100644 index 0000000000..ea3e7be76a --- /dev/null +++ b/lib/libm/arch/i386/s_ceil.S @@ -0,0 +1,46 @@ +/* + * Written by J.T. Conklin . + * Public domain. + * + * $NetBSD: s_ceil.S,v 1.7 2003/07/26 19:25:00 salo Exp $ + * $DragonFly: src/lib/libm/arch/i386/s_ceil.S,v 1.1 2005/07/26 21:15:19 joerg Exp $ + */ + +#include + +#include "abi.h" + +ENTRY(ceil) +#ifdef __i386__ + pushl %ebp + movl %esp,%ebp + subl $8,%esp + + fstcw -4(%ebp) /* store fpu control word */ + movw -4(%ebp),%dx + orw $0x0800,%dx /* round towards +oo */ + andw $0xfbff,%dx + movw %dx,-8(%ebp) + fldcw -8(%ebp) /* load modfied control word */ + + fldl 8(%ebp); /* round */ + frndint + + fldcw -4(%ebp) /* restore original control word */ + + leave +#else + fstcw -12(%rsp) + movw -12(%rsp),%dx + orw $0x0800,%dx + andw $0xfbff,%dx + movw %dx,-16(%rsp) + fldcw -16(%rsp) + movsd %xmm0,-8(%rsp) + fldl -8(%rsp) + frndint + fldcw -12(%rsp) + fstpl -8(%rsp) + movsd -8(%rsp),%xmm0 +#endif + ret diff --git a/lib/libm/arch/i386/s_ceilf.S b/lib/libm/arch/i386/s_ceilf.S new file mode 100644 index 0000000000..d6aa3308af --- /dev/null +++ b/lib/libm/arch/i386/s_ceilf.S @@ -0,0 +1,44 @@ +/* + * Written by J.T. Conklin . + * Public domain. + * + * $NetBSD: s_ceilf.S,v 1.8 2004/07/16 18:40:24 drochner Exp $ + * $DragonFly: src/lib/libm/arch/i386/s_ceilf.S,v 1.1 2005/07/26 21:15:19 joerg Exp $ + */ + +#include + +ENTRY(ceilf) +#ifdef __i386__ + pushl %ebp + movl %esp,%ebp + subl $8,%esp + + fstcw -4(%ebp) /* store fpu control word */ + movw -4(%ebp),%dx + orw $0x0800,%dx /* round towards +oo */ + andw $0xfbff,%dx + movw %dx,-8(%ebp) + fldcw -8(%ebp) /* load modfied control word */ + + flds 8(%ebp); /* round */ + frndint + + fldcw -4(%ebp) /* restore original control word */ + + leave +#else + fstcw -8(%rsp) + movw -8(%rsp),%dx + orw $0x0800,%dx + andw $0xfbff,%dx + movw %dx,-12(%rsp) + fldcw -12(%rsp) + movss %xmm0,-4(%rsp) + flds -4(%rsp) + frndint + fldcw -8(%rsp) + fstps -4(%rsp) + movss -4(%rsp),%xmm0 +#endif + ret diff --git a/lib/libm/arch/i386/s_copysign.S b/lib/libm/arch/i386/s_copysign.S new file mode 100644 index 0000000000..6a256bbc1a --- /dev/null +++ b/lib/libm/arch/i386/s_copysign.S @@ -0,0 +1,54 @@ +/* + * Written by J.T. Conklin . + * Public domain. + * + * $NetBSD: s_copysign.S,v 1.6 2003/07/26 19:25:01 salo Exp $ + * $DragonFly: src/lib/libm/arch/i386/s_copysign.S,v 1.1 2005/07/26 21:15:19 joerg Exp $ + */ + +/* + * XXXfvdl might as well split this file. + */ + +#include + +#ifdef __x86_64__ +.Lpos: + .quad 0x8000000000000000 +.Lneg: + .quad 0x7fffffffffffffff +#endif + + +ENTRY(copysign) +#ifdef __i386__ + movl 16(%esp),%edx + andl $0x80000000,%edx + movl 8(%esp),%eax + andl $0x7fffffff,%eax + orl %edx,%eax + movl %eax,8(%esp) + fldl 4(%esp) +#else +#if 0 + /* + * XXXfvdl gas doesn't grok this yet. + */ + movq .Lpos(%rip),%xmm2 + movq .Lneg(%rip),%xmm3 + pand %xmm2,%xmm1 + pand %xmm3,%xmm0 + por %xmm1,%xmm0 +#else + movsd %xmm0,-8(%rsp) + movsd %xmm1,-16(%rsp) + movl -12(%rsp),%edx + andl $0x80000000,%edx + movl -4(%rsp),%eax + andl $0x7fffffff,%eax + orl %edx,%eax + movl %eax,-4(%rsp) + movsd -8(%rsp),%xmm0 +#endif +#endif + ret diff --git a/lib/libm/arch/i386/s_copysignf.S b/lib/libm/arch/i386/s_copysignf.S new file mode 100644 index 0000000000..4198854056 --- /dev/null +++ b/lib/libm/arch/i386/s_copysignf.S @@ -0,0 +1,54 @@ +/* + * Written by J.T. Conklin . + * Public domain. + * + * $NetBSD: s_copysignf.S,v 1.5 2003/07/26 19:25:01 salo Exp $ + * $DragonFly: src/lib/libm/arch/i386/s_copysignf.S,v 1.1 2005/07/26 21:15:19 joerg Exp $ + */ + +#include + +/* + * XXXfvdl split this file. + */ + +#ifdef __x86_64__ +.Lneg: + .long 0x7fffffff +.Lpos: + .long 0x80000000 +#endif + +ENTRY(copysignf) +#ifdef __i386__ + movl 8(%esp),%edx + andl $0x80000000,%edx + movl 4(%esp),%eax + andl $0x7fffffff,%eax + orl %edx,%eax + movl %eax,4(%esp) + flds 4(%esp) +#else +#if 0 + /* + * XXXfvdl gas doesn't grok this. + * but it's legal according to the p4 manual. + */ + movss .Lpos(%rip),%xmm2 + movss .Lneg(%rip),%xmm3 + pandq %xmm2,%xmm1 + pandq %xmm3,%xmm0 + porq %xmm1,%xmm0 +#else + movss %xmm0,-4(%rsp) + movss %xmm1,-8(%rsp) + movl -8(%rsp),%edx + andl $0x80000000,%edx + movl -4(%rsp),%eax + andl $0x7fffffff,%eax + orl %edx,%eax + movl %eax,-4(%rsp) + movss -4(%rsp),%xmm0 +#endif +#endif + ret diff --git a/lib/libm/arch/i386/s_cos.S b/lib/libm/arch/i386/s_cos.S new file mode 100644 index 0000000000..733560933b --- /dev/null +++ b/lib/libm/arch/i386/s_cos.S @@ -0,0 +1,32 @@ +/* + * Written by J.T. Conklin . + * Public domain. + * + * $NetBSD: s_cos.S,v 1.8 2003/07/26 19:25:01 salo Exp $ + * $DragonFly: src/lib/libm/arch/i386/s_cos.S,v 1.1 2005/07/26 21:15:19 joerg Exp $ + */ + +#include + +#include "abi.h" + +ENTRY(cos) + XMM_ONE_ARG_DOUBLE_PROLOGUE + fldl ARG_DOUBLE_ONE + fcos + fnstsw %ax + andw $0x400,%ax + jnz 1f + XMM_DOUBLE_EPILOGUE + ret +1: fldpi + fadd %st(0) + fxch %st(1) +2: fprem1 + fnstsw %ax + andw $0x400,%ax + jnz 2b + fstp %st(1) + fcos + XMM_DOUBLE_EPILOGUE + ret diff --git a/lib/libm/arch/i386/s_cosf.S b/lib/libm/arch/i386/s_cosf.S new file mode 100644 index 0000000000..fcd5d1736e --- /dev/null +++ b/lib/libm/arch/i386/s_cosf.S @@ -0,0 +1,19 @@ +/* + * Written by J.T. Conklin . + * Public domain. + * + * $NetBSD: s_cosf.S,v 1.6 2003/07/26 19:25:01 salo Exp $ + * $DragonFly: src/lib/libm/arch/i386/s_cosf.S,v 1.1 2005/07/26 21:15:19 joerg Exp $ + */ + +#include + +#include "abi.h" + +/* A float's domain isn't large enough to require argument reduction. */ +ENTRY(cosf) + XMM_ONE_ARG_FLOAT_PROLOGUE + flds ARG_FLOAT_ONE + fcos + XMM_FLOAT_EPILOGUE + ret diff --git a/lib/libm/arch/i386/s_finite.S b/lib/libm/arch/i386/s_finite.S new file mode 100644 index 0000000000..9c3a34f1d1 --- /dev/null +++ b/lib/libm/arch/i386/s_finite.S @@ -0,0 +1,27 @@ +/* + * Written by J.T. Conklin . + * Public domain. + * + * $NetBSD: s_finite.S,v 1.7 2003/07/26 19:25:01 salo Exp $ + * $DragonFly: src/lib/libm/arch/i386/s_finite.S,v 1.1 2005/07/26 21:15:19 joerg Exp $ + */ + +#include + +ENTRY(finite) +#ifdef __i386__ + movl 8(%esp),%eax + andl $0x7ff00000, %eax + cmpl $0x7ff00000, %eax + setne %al + andl $0x000000ff, %eax +#else + xorl %eax,%eax + movq $0x7ff0000000000000,%rsi + movq %rsi,%rdi + movsd %xmm0,-8(%rsp) + andq -8(%rsp),%rsi + cmpq %rdi,%rsi + setne %al +#endif + ret diff --git a/lib/libm/arch/i386/s_finitef.S b/lib/libm/arch/i386/s_finitef.S new file mode 100644 index 0000000000..1cc58d5d40 --- /dev/null +++ b/lib/libm/arch/i386/s_finitef.S @@ -0,0 +1,26 @@ +/* + * Written by J.T. Conklin . + * Public domain. + * + * $NetBSD: s_finitef.S,v 1.6 2003/07/26 19:25:01 salo Exp $ + * $DragonFly: src/lib/libm/arch/i386/s_finitef.S,v 1.1 2005/07/26 21:15:19 joerg Exp $ + */ + +#include + +ENTRY(finitef) +#ifdef __i386__ + movl 4(%esp),%eax + andl $0x7f800000, %eax + cmpl $0x7f800000, %eax + setne %al + andl $0x000000ff, %eax +#else + xorl %eax,%eax + movl $0x7ff00000,%esi + movss %xmm0,-4(%rsp) + andl -4(%rsp),%esi + cmpl $0x7ff00000,%esi + setne %al +#endif + ret diff --git a/lib/libm/arch/i386/s_floor.S b/lib/libm/arch/i386/s_floor.S new file mode 100644 index 0000000000..e29780129a --- /dev/null +++ b/lib/libm/arch/i386/s_floor.S @@ -0,0 +1,44 @@ +/* + * Written by J.T. Conklin . + * Public domain. + * + * $NetBSD: s_floor.S,v 1.8 2003/07/26 19:25:02 salo Exp $ + * $DragonFly: src/lib/libm/arch/i386/s_floor.S,v 1.1 2005/07/26 21:15:19 joerg Exp $ + */ + +#include + +ENTRY(floor) +#ifdef __i386__ + pushl %ebp + movl %esp,%ebp + subl $8,%esp + + fstcw -4(%ebp) /* store fpu control word */ + movw -4(%ebp),%dx + orw $0x0400,%dx /* round towards -oo */ + andw $0xf7ff,%dx + movw %dx,-8(%ebp) + fldcw -8(%ebp) /* load modfied control word */ + + fldl 8(%ebp); /* round */ + frndint + + fldcw -4(%ebp) /* restore original control word */ + + leave +#else + movsd %xmm0, -8(%rsp) + fstcw -12(%rsp) + movw -12(%rsp),%dx + orw $0x0400,%dx + andw $0xf7ff,%dx + movw %dx,-16(%rsp) + fldcw -16(%rsp) + fldl -8(%rsp) + frndint + fldcw -12(%rsp) + fstpl -8(%rsp) + movsd -8(%rsp),%xmm0 +#endif + ret diff --git a/lib/libm/arch/i386/s_floorf.S b/lib/libm/arch/i386/s_floorf.S new file mode 100644 index 0000000000..930734170f --- /dev/null +++ b/lib/libm/arch/i386/s_floorf.S @@ -0,0 +1,44 @@ +/* + * Written by J.T. Conklin . + * Public domain. + * + * $NetBSD: s_floorf.S,v 1.7 2004/07/16 18:40:24 drochner Exp $ + * $DragonFly: src/lib/libm/arch/i386/s_floorf.S,v 1.1 2005/07/26 21:15:19 joerg Exp $ + */ + +#include + +ENTRY(floorf) +#ifdef __i386__ + pushl %ebp + movl %esp,%ebp + subl $8,%esp + + fstcw -4(%ebp) /* store fpu control word */ + movw -4(%ebp),%dx + orw $0x0400,%dx /* round towards -oo */ + andw $0xf7ff,%dx + movw %dx,-8(%ebp) + fldcw -8(%ebp) /* load modfied control word */ + + flds 8(%ebp); /* round */ + frndint + + fldcw -4(%ebp) /* restore original control word */ + + leave +#else + movss %xmm0, -4(%rsp) + fstcw -8(%rsp) + movw -8(%rsp),%dx + orw $0x0400,%dx + andw $0xf7ff,%dx + movw %dx,-12(%rsp) + fldcw -12(%rsp) + flds -4(%rsp) + frndint + fldcw -8(%rsp) + fstps -4(%rsp) + movss -4(%rsp),%xmm0 +#endif + ret diff --git a/lib/libm/arch/i386/s_ilogb.S b/lib/libm/arch/i386/s_ilogb.S new file mode 100644 index 0000000000..e53419ec29 --- /dev/null +++ b/lib/libm/arch/i386/s_ilogb.S @@ -0,0 +1,33 @@ +/* + * Written by J.T. Conklin . + * Public domain. + * + * $NetBSD: s_ilogb.S,v 1.7 2003/07/26 19:25:02 salo Exp $ + * $DragonFly: src/lib/libm/arch/i386/s_ilogb.S,v 1.1 2005/07/26 21:15:19 joerg Exp $ + */ + +#include + +ENTRY(ilogb) +#ifdef __i386__ + pushl %ebp + movl %esp,%ebp + subl $4,%esp + + fldl 8(%ebp) + fxtract + fstp %st + + fistpl -4(%ebp) + movl -4(%ebp),%eax + + leave +#else + movsd %xmm0,-8(%rsp) + fldl -8(%rsp) + fxtract + fstp %st + fistpl -8(%rsp) + movl -8(%rsp),%eax +#endif + ret diff --git a/lib/libm/arch/i386/s_ilogbf.S b/lib/libm/arch/i386/s_ilogbf.S new file mode 100644 index 0000000000..8791e5e846 --- /dev/null +++ b/lib/libm/arch/i386/s_ilogbf.S @@ -0,0 +1,33 @@ +/* + * Written by J.T. Conklin . + * Public domain. + * + * $NetBSD: s_ilogbf.S,v 1.6 2003/07/26 19:25:02 salo Exp $ + * $DragonFly: src/lib/libm/arch/i386/s_ilogbf.S,v 1.1 2005/07/26 21:15:19 joerg Exp $ + */ + +#include + +ENTRY(ilogbf) +#ifdef __i386__ + pushl %ebp + movl %esp,%ebp + subl $4,%esp + + flds 8(%ebp) + fxtract + fstp %st + + fistpl -4(%ebp) + movl -4(%ebp),%eax + + leave +#else + movss %xmm0,-4(%rsp) + flds -4(%rsp) + fxtract + fstp %st + fistpl -4(%rsp) + movl -4(%rsp),%eax +#endif + ret diff --git a/lib/libm/arch/i386/s_log1p.S b/lib/libm/arch/i386/s_log1p.S new file mode 100644 index 0000000000..5397debec3 --- /dev/null +++ b/lib/libm/arch/i386/s_log1p.S @@ -0,0 +1,77 @@ +/* + * Written by J.T. Conklin . + * Public domain. + * + * $NetBSD: s_log1p.S,v 1.13 2003/09/16 18:17:11 wennmach Exp $ + * $DragonFly: src/lib/libm/arch/i386/s_log1p.S,v 1.1 2005/07/26 21:15:19 joerg Exp $ + */ + +/* + * Modified by Lex Wennmacher + * Still public domain. + */ + +#include + +#include "abi.h" + +/* + * The log1p() function is provided to compute an accurate value of + * log(1 + x), even for tiny values of x. The i387 FPU provides the + * fyl2xp1 instruction for this purpose. However, the range of this + * instruction is limited to: + * -(1 - (sqrt(2) / 2)) <= x <= sqrt(2) - 1 + * -0.292893 <= x <= 0.414214 + * at least on older processor versions. + * + * log1p() is implemented by testing the range of the argument. + * If it is appropriate for fyl2xp1, this instruction is used. + * Else, we compute log1p(x) = ln(2)*ld(1 + x) the traditional way + * (using fyl2x). + * + * The range testing costs speed, but as the rationale for the very + * existence of this function is accuracy, we accept that. + * + * In order to reduce the cost for testing the range, we check if + * the argument is in the range + * -0.25 <= x <= 0.25 + * which can be done with just one conditional branch. If x is + * inside this range, we use fyl2xp1. Outside of this range, + * the use of fyl2x is accurate enough. + * + */ + +.text + .align 4 +ENTRY(log1p) + XMM_ONE_ARG_DOUBLE_PROLOGUE + fldl ARG_DOUBLE_ONE + fabs + fld1 /* ... x 1 */ + fadd %st(0) /* ... x 2 */ + fadd %st(0) /* ... x 4 */ + fld1 /* ... 4 1 */ + fdivp /* ... x 0.25 */ + fcompp + fnstsw %ax + andb $69,%ah + jne use_fyl2x + jmp use_fyl2xp1 + + .align 4 +use_fyl2x: + fldln2 + fldl ARG_DOUBLE_ONE + fld1 + faddp + fyl2x + XMM_DOUBLE_EPILOGUE + ret + + .align 4 +use_fyl2xp1: + fldln2 + fldl ARG_DOUBLE_ONE + fyl2xp1 + XMM_DOUBLE_EPILOGUE + ret diff --git a/lib/libm/arch/i386/s_log1pf.S b/lib/libm/arch/i386/s_log1pf.S new file mode 100644 index 0000000000..7a20816e75 --- /dev/null +++ b/lib/libm/arch/i386/s_log1pf.S @@ -0,0 +1,77 @@ +/* + * Written by J.T. Conklin . + * Public domain. + * + * $NetBSD: s_log1pf.S,v 1.10 2003/09/16 18:17:11 wennmach Exp $ + * $DragonFly: src/lib/libm/arch/i386/s_log1pf.S,v 1.1 2005/07/26 21:15:19 joerg Exp $ + */ + +/* + * Modified by Lex Wennmacher + * Still public domain. + */ + +#include + +#include "abi.h" + +/* + * The log1pf() function is provided to compute an accurate value of + * log(1 + x), even for tiny values of x. The i387 FPU provides the + * fyl2xp1 instruction for this purpose. However, the range of this + * instruction is limited to: + * -(1 - (sqrt(2) / 2)) <= x <= sqrt(2) - 1 + * -0.292893 <= x <= 0.414214 + * at least on older processor versions. + * + * log1pf() is implemented by testing the range of the argument. + * If it is appropriate for fyl2xp1, this instruction is used. + * Else, we compute log1pf(x) = ln(2)*ld(1 + x) the traditional way + * (using fyl2x). + * + * The range testing costs speed, but as the rationale for the very + * existence of this function is accuracy, we accept that. + * + * In order to reduce the cost for testing the range, we check if + * the argument is in the range + * -0.25 <= x <= 0.25 + * which can be done with just one conditional branch. If x is + * inside this range, we use fyl2xp1. Outside of this range, + * the use of fyl2x is accurate enough. + * + */ + +.text + .align 4 +ENTRY(log1pf) + XMM_ONE_ARG_FLOAT_PROLOGUE + flds ARG_FLOAT_ONE + fabs + fld1 /* ... x 1 */ + fadd %st(0) /* ... x 2 */ + fadd %st(0) /* ... x 4 */ + fld1 /* ... 4 1 */ + fdivp /* ... x 0.25 */ + fcompp + fnstsw %ax + andb $69,%ah + jne use_fyl2x + jmp use_fyl2xp1 + + .align 4 +use_fyl2x: + fldln2 + flds ARG_FLOAT_ONE + fld1 + faddp + fyl2x + XMM_FLOAT_EPILOGUE + ret + + .align 4 +use_fyl2xp1: + fldln2 + flds ARG_FLOAT_ONE + fyl2xp1 + XMM_FLOAT_EPILOGUE + ret diff --git a/lib/libm/arch/i386/s_logb.S b/lib/libm/arch/i386/s_logb.S new file mode 100644 index 0000000000..aad0f926db --- /dev/null +++ b/lib/libm/arch/i386/s_logb.S @@ -0,0 +1,19 @@ +/* + * Written by J.T. Conklin . + * Public domain. + * + * $NetBSD: s_logb.S,v 1.6 2003/07/26 19:25:02 salo Exp $ + * $DragonFly: src/lib/libm/arch/i386/s_logb.S,v 1.1 2005/07/26 21:15:19 joerg Exp $ + */ + +#include + +#include "abi.h" + +ENTRY(logb) + XMM_ONE_ARG_DOUBLE_PROLOGUE + fldl ARG_DOUBLE_ONE + fxtract + fstp %st + XMM_DOUBLE_EPILOGUE + ret diff --git a/lib/libm/arch/i386/s_logbf.S b/lib/libm/arch/i386/s_logbf.S new file mode 100644 index 0000000000..ec66ed4b81 --- /dev/null +++ b/lib/libm/arch/i386/s_logbf.S @@ -0,0 +1,19 @@ +/* + * Written by J.T. Conklin . + * Public domain. + * + * $NetBSD: s_logbf.S,v 1.5 2003/07/26 19:25:02 salo Exp $ + * $DragonFly: src/lib/libm/arch/i386/s_logbf.S,v 1.1 2005/07/26 21:15:19 joerg Exp $ + */ + +#include + +#include "abi.h" + +ENTRY(logbf) + XMM_ONE_ARG_FLOAT_PROLOGUE + flds ARG_FLOAT_ONE + fxtract + fstp %st + XMM_FLOAT_EPILOGUE + ret diff --git a/lib/libm/arch/i386/s_rint.S b/lib/libm/arch/i386/s_rint.S new file mode 100644 index 0000000000..2f3d72da67 --- /dev/null +++ b/lib/libm/arch/i386/s_rint.S @@ -0,0 +1,18 @@ +/* + * Written by J.T. Conklin . + * Public domain. + * + * $NetBSD: s_rint.S,v 1.6 2003/07/26 19:25:03 salo Exp $ + * $DragonFly: src/lib/libm/arch/i386/s_rint.S,v 1.1 2005/07/26 21:15:19 joerg Exp $ + */ + +#include + +#include "abi.h" + +ENTRY(rint) + XMM_ONE_ARG_DOUBLE_PROLOGUE + fldl ARG_DOUBLE_ONE + frndint + XMM_DOUBLE_EPILOGUE + ret diff --git a/lib/libm/arch/i386/s_rintf.S b/lib/libm/arch/i386/s_rintf.S new file mode 100644 index 0000000000..893d3b9e3f --- /dev/null +++ b/lib/libm/arch/i386/s_rintf.S @@ -0,0 +1,18 @@ +/* + * Written by J.T. Conklin . + * Public domain. + * + * $NetBSD: s_rintf.S,v 1.5 2003/07/26 19:25:03 salo Exp $ + * $DragonFly: src/lib/libm/arch/i386/s_rintf.S,v 1.1 2005/07/26 21:15:19 joerg Exp $ + */ + +#include + +#include "abi.h" + +ENTRY(rintf) + XMM_ONE_ARG_FLOAT_PROLOGUE + flds ARG_FLOAT_ONE + frndint + XMM_FLOAT_EPILOGUE + ret diff --git a/lib/libm/arch/i386/s_scalbn.S b/lib/libm/arch/i386/s_scalbn.S new file mode 100644 index 0000000000..e8b9c22825 --- /dev/null +++ b/lib/libm/arch/i386/s_scalbn.S @@ -0,0 +1,20 @@ +/* + * Written by J.T. Conklin . + * Public domain. + * + * $NetBSD: s_scalbn.S,v 1.7 2003/07/26 19:25:03 salo Exp $ + * $DragonFly: src/lib/libm/arch/i386/s_scalbn.S,v 1.1 2005/07/26 21:15:19 joerg Exp $ + */ + +#include + +#include "abi.h" + +ENTRY(scalbn) + XMM_TWO_ARG_DOUBLE_PROLOGUE + fildl ARG_DOUBLE_TWO + fldl ARG_DOUBLE_ONE + fscale + fstp %st(1) /* bug fix for fp stack overflow */ + XMM_DOUBLE_EPILOGUE + ret diff --git a/lib/libm/arch/i386/s_scalbnf.S b/lib/libm/arch/i386/s_scalbnf.S new file mode 100644 index 0000000000..421960d1cc --- /dev/null +++ b/lib/libm/arch/i386/s_scalbnf.S @@ -0,0 +1,20 @@ +/* + * Written by J.T. Conklin . + * Public domain. + * + * $NetBSD: s_scalbnf.S,v 1.6 2003/07/26 19:25:03 salo Exp $ + * $DragonFly: src/lib/libm/arch/i386/s_scalbnf.S,v 1.1 2005/07/26 21:15:19 joerg Exp $ + */ + +#include + +#include "abi.h" + +ENTRY(scalbnf) + XMM_TWO_ARG_FLOAT_PROLOGUE + fildl ARG_FLOAT_TWO + flds ARG_FLOAT_ONE + fscale + fstp %st(1) /* bug fix for fp stack overflow */ + XMM_FLOAT_EPILOGUE + ret diff --git a/lib/libm/arch/i386/s_significand.S b/lib/libm/arch/i386/s_significand.S new file mode 100644 index 0000000000..7b62ce2a66 --- /dev/null +++ b/lib/libm/arch/i386/s_significand.S @@ -0,0 +1,19 @@ +/* + * Written by J.T. Conklin . + * Public domain. + * + * $NetBSD: s_significand.S,v 1.6 2003/07/26 19:25:03 salo Exp $ + * $DragonFly: src/lib/libm/arch/i386/s_significand.S,v 1.1 2005/07/26 21:15:19 joerg Exp $ + */ + +#include + +#include "abi.h" + +ENTRY(significand) + XMM_ONE_ARG_DOUBLE_PROLOGUE + fldl ARG_DOUBLE_ONE + fxtract + fstp %st(1) + XMM_DOUBLE_EPILOGUE + ret diff --git a/lib/libm/arch/i386/s_significandf.S b/lib/libm/arch/i386/s_significandf.S new file mode 100644 index 0000000000..57a4cd2b79 --- /dev/null +++ b/lib/libm/arch/i386/s_significandf.S @@ -0,0 +1,19 @@ +/* + * Written by J.T. Conklin . + * Public domain. + * + * $NetBSD: s_significandf.S,v 1.5 2003/07/26 19:25:03 salo Exp $ + * $DragonFly: src/lib/libm/arch/i386/s_significandf.S,v 1.1 2005/07/26 21:15:19 joerg Exp $ + */ + +#include + +#include "abi.h" + +ENTRY(significandf) + XMM_ONE_ARG_FLOAT_PROLOGUE + flds ARG_FLOAT_ONE + fxtract + fstp %st(1) + XMM_FLOAT_EPILOGUE + ret diff --git a/lib/libm/arch/i386/s_sin.S b/lib/libm/arch/i386/s_sin.S new file mode 100644 index 0000000000..26eaa09fad --- /dev/null +++ b/lib/libm/arch/i386/s_sin.S @@ -0,0 +1,32 @@ +/* + * Written by J.T. Conklin . + * Public domain. + * + * $NetBSD: s_sin.S,v 1.7 2003/07/26 19:25:03 salo Exp $ + * $DragonFly: src/lib/libm/arch/i386/s_sin.S,v 1.1 2005/07/26 21:15:19 joerg Exp $ + */ + +#include + +#include "abi.h" + +ENTRY(sin) + XMM_ONE_ARG_DOUBLE_PROLOGUE + fldl ARG_DOUBLE_ONE + fsin + fnstsw %ax + andw $0x400,%ax + jnz 1f + XMM_DOUBLE_EPILOGUE + ret +1: fldpi + fadd %st(0) + fxch %st(1) +2: fprem1 + fnstsw %ax + andw $0x400,%ax + jnz 2b + fstp %st(1) + fsin + XMM_DOUBLE_EPILOGUE + ret diff --git a/lib/libm/arch/i386/s_sinf.S b/lib/libm/arch/i386/s_sinf.S new file mode 100644 index 0000000000..4f39f62feb --- /dev/null +++ b/lib/libm/arch/i386/s_sinf.S @@ -0,0 +1,19 @@ +/* + * Written by J.T. Conklin . + * Public domain. + * + * $NetBSD: s_sinf.S,v 1.5 2003/07/26 19:25:04 salo Exp $ + * $DragonFly: src/lib/libm/arch/i386/s_sinf.S,v 1.1 2005/07/26 21:15:19 joerg Exp $ + */ + +#include + +#include "abi.h" + +/* A float's domain isn't large enough to require argument reduction. */ +ENTRY(sinf) + XMM_ONE_ARG_FLOAT_PROLOGUE + flds ARG_FLOAT_ONE + fsin + XMM_FLOAT_EPILOGUE + ret diff --git a/lib/libm/arch/i386/s_tan.S b/lib/libm/arch/i386/s_tan.S new file mode 100644 index 0000000000..9fd47e6174 --- /dev/null +++ b/lib/libm/arch/i386/s_tan.S @@ -0,0 +1,34 @@ +/* + * Written by J.T. Conklin . + * Public domain. + * + * $NetBSD: s_tan.S,v 1.7 2003/07/26 19:25:04 salo Exp $ + * $DragonFly: src/lib/libm/arch/i386/s_tan.S,v 1.1 2005/07/26 21:15:19 joerg Exp $ + */ + +#include + +#include "abi.h" + +ENTRY(tan) + XMM_ONE_ARG_DOUBLE_PROLOGUE + fldl ARG_DOUBLE_ONE + fptan + fnstsw %ax + andw $0x400,%ax + jnz 1f + fstp %st(0) + XMM_DOUBLE_EPILOGUE + ret +1: fldpi + fadd %st(0) + fxch %st(1) +2: fprem1 + fstsw %ax + andw $0x400,%ax + jnz 2b + fstp %st(1) + fptan + fstp %st(0) + XMM_DOUBLE_EPILOGUE + ret diff --git a/lib/libm/arch/i386/s_tanf.S b/lib/libm/arch/i386/s_tanf.S new file mode 100644 index 0000000000..87535c7b9a --- /dev/null +++ b/lib/libm/arch/i386/s_tanf.S @@ -0,0 +1,20 @@ +/* + * Written by J.T. Conklin . + * Public domain. + * + * $NetBSD: s_tanf.S,v 1.5 2003/07/26 19:25:04 salo Exp $ + * $DragonFly: src/lib/libm/arch/i386/s_tanf.S,v 1.1 2005/07/26 21:15:19 joerg Exp $ + */ + +#include + +#include "abi.h" + +/* A float's domain isn't large enough to require argument reduction. */ +ENTRY(tanf) + XMM_ONE_ARG_FLOAT_PROLOGUE + flds ARG_FLOAT_ONE + fptan + fstp %st(0) + XMM_FLOAT_EPILOGUE + ret diff --git a/lib/libm/man/Makefile.inc b/lib/libm/man/Makefile.inc new file mode 100644 index 0000000000..cef57362c7 --- /dev/null +++ b/lib/libm/man/Makefile.inc @@ -0,0 +1,28 @@ +# $DragonFly: src/lib/libm/man/Makefile.inc,v 1.1 2005/07/26 21:15:20 joerg Exp $ + +.PATH: ${.CURDIR}/man + +MAN+= acos.3 acosh.3 asin.3 asinh.3 atan.3 atan2.3 atanh.3 ceil.3 \ + cos.3 cosh.3 erf.3 exp.3 fabs.3 floor.3 fmod.3 hypot.3 ieee.3 \ + ieee_test.3 j0.3 lgamma.3 math.3 rint.3 round.3 sin.3 \ + sinh.3 sqrt.3 tan.3 tanh.3 +MLINKS+= \ + acos.3 acosf.3 acosh.3 acoshf.3 asin.3 asinf.3 asinh.3 asinhf.3 \ + atan.3 atanf.3 atan2.3 atan2f.3 atanh.3 atanhf.3 ceil.3 ceilf.3 \ + cos.3 cosf.3 cosh.3 coshf.3 erf.3 erff.3 erf.3 erfc.3 erf.3 erfcf.3 \ + exp.3 expf.3 exp.3 expm1.3 exp.3 expm1f.3 exp.3 log.3 exp.3 logf.3 \ + exp.3 log10.3 exp.3 log10f.3 exp.3 log1p.3 exp.3 pow.3 exp.3 powf.3 \ + fabs.3 fabsf.3 floor.3 floorf.3 fmod.3 fmodf.3 hypot.3 hypotf.3 \ + hypot.3 cabs.3 bypot.3 cabsf.3 ieee.3 copysign.3 ieee.3 copysignf.3 \ + ieee.3 finite,3 ieee.3 finitef.3 ieee.3 ilogb.3 ieee.3 ilogbf.3 \ + ieee.3 nextafter.3 ieee.3 nextafterf.3 ieee.3 remainder.3 \ + ieee.3 remainderf.3 ieee.3 scalbn.3 ieee.3 scalbnf.3 \ + ieee_test.3 logb.3 ieee_test.3 logbf.3 ieee_test.3 scalb.3 \ + ieee_test.3 scalbf.3 ieee_test.3 significand.3 \ + ieee_test.3 significandf.3 j0.3 j0f.3 j0.3 j1.3 j0.3 j1f.3 j0.3 jn.3 \ + j0.3 jnf.3 j0.3 y0.3 j0.3 y0f.3 j0.3 y1.3 j0.3 y1f.3 j0.3 \ + yn.3 j0.3 ynf.3 lgamma.3 lgammaf.3 lgamma.3 lgamma_r.3 \ + lgamma.3 lgammaf_r.3 lgamma.3 gamma.3 lgamma.3 gammaf.3 \ + lgamma.3 gamma_r.3 lgamma.3 gammaf_r.3 rint.3 rintf.3 \ + round.3 roundf.3 sin.3 sinf.3 sinh.3 sinhf.3 sqrt.3 cbrt.3 \ + sqrt.3 cbrtf.3 sqrt.3 sqrtf.3 tan.3 tanf.3 tanh.3 tanhf.3 diff --git a/lib/libc/gen/isinf.3 b/lib/libm/man/acos.3 similarity index 54% copy from lib/libc/gen/isinf.3 copy to lib/libm/man/acos.3 index cf68a79e5d..c59a2f22c4 100644 --- a/lib/libc/gen/isinf.3 +++ b/lib/libm/man/acos.3 @@ -1,5 +1,5 @@ -.\" Copyright (c) 1991, 1993 -.\" The Regents of the University of California. All rights reserved. +.\" Copyright (c) 1991 The Regents of the University of California. +.\" All rights reserved. .\" .\" Redistribution and use in source and binary forms, with or without .\" modification, are permitted provided that the following conditions @@ -9,11 +9,7 @@ .\" 2. Redistributions in binary form must reproduce the above copyright .\" notice, this list of conditions and the following disclaimer in the .\" documentation and/or other materials provided with the distribution. -.\" 3. All advertising materials mentioning features or use of this software -.\" must display the following acknowledgement: -.\" This product includes software developed by the University of -.\" California, Berkeley and its contributors. -.\" 4. Neither the name of the University nor the names of its contributors +.\" 3. Neither the name of the University nor the names of its contributors .\" may be used to endorse or promote products derived from this software .\" without specific prior written permission. .\" @@ -29,54 +25,60 @@ .\" OUT OF THE USE OF THIS SOFTWARE, EVEN IF ADVISED OF THE POSSIBILITY OF .\" SUCH DAMAGE. .\" -.\" @(#)isinf.3 8.2 (Berkeley) 1/29/94 -.\" $FreeBSD: src/lib/libc/gen/isinf.3,v 1.5.2.3 2003/05/04 22:25:22 murray Exp $ -.\" $DragonFly: src/lib/libc/gen/isinf.3,v 1.2 2003/06/17 04:26:42 dillon Exp $ +.\" from: @(#)acos.3 5.1 (Berkeley) 5/2/91 +.\" $NetBSD: acos.3,v 1.16 2003/08/07 16:44:46 agc Exp $ +.\" $DragonFly: src/lib/libm/man/acos.3,v 1.1 2005/07/26 21:15:20 joerg Exp $ .\" -.Dd January 29, 1994 -.Dt ISINF 3 +.Dd May 2, 1991 +.Dt ACOS 3 .Os .Sh NAME -.Nm isinf , -.Nm isnan , -.Nm isnanf -.Nd test for infinity or not-a-number +.Nm acos , +.Nm acosf +.Nd arc cosine function .Sh LIBRARY -.Lb libc +.Lb libm .Sh SYNOPSIS .In math.h -.Ft int -.Fn isinf double -.Ft int -.Fn isnan double -.Ft int -.Fn isnanf float +.Ft double +.Fn acos "double x" +.Ft float +.Fn acosf "float x" .Sh DESCRIPTION The -.Fn isinf -function -returns 1 if the number is -.Dq \\*(If , -otherwise 0. -.Pp -The -.Fn isnan +.Fn acos +and +.Fn acosf +functions compute the principal value of the arc cosine of +.Fa x +in the range +.Bq 0 , \*(Pi . +.Sh RETURN VALUES +If |x|\*[Gt]1, +.Fn acos "x" and -.Fn isnanf -functions -return 1 if the double or float (respectively) is -.Dq not-a-number , -otherwise 0. +.Fn acosf "x" +.\" POSIX_MODE +set the global variable +.Va errno +to EDOM. +.\" SYSV_MODE +.\" call +.\" .Xr matherr 3 . .Sh SEE ALSO -.Xr math 3 -.Rs -.%T "IEEE Standard for Binary Floating-Point Arithmetic" -.%Q ANSI -.%R Std 754-1985 -.Re -.Sh BUGS -Neither the -.Tn VAX -nor the Tahoe floating point have distinguished values -for either infinity or not-a-number. -These routines always return 0 on those architectures. +.Xr asin 3 , +.Xr atan 3 , +.Xr atan2 3 , +.Xr cos 3 , +.Xr cosh 3 , +.Xr math 3 , +.Xr sin 3 , +.Xr sinh 3 , +.Xr tan 3 , +.Xr tanh 3 +.\" .Xr matherr 3 +.Sh STANDARDS +The +.Fn acos +function conforms to +.St -ansiC . diff --git a/lib/libc/gen/isinf.3 b/lib/libm/man/acosh.3 similarity index 55% copy from lib/libc/gen/isinf.3 copy to lib/libm/man/acosh.3 index cf68a79e5d..39274d85ea 100644 --- a/lib/libc/gen/isinf.3 +++ b/lib/libm/man/acosh.3 @@ -1,5 +1,5 @@ -.\" Copyright (c) 1991, 1993 -.\" The Regents of the University of California. All rights reserved. +.\" Copyright (c) 1991 Regents of the University of California. +.\" All rights reserved. .\" .\" Redistribution and use in source and binary forms, with or without .\" modification, are permitted provided that the following conditions @@ -9,11 +9,7 @@ .\" 2. Redistributions in binary form must reproduce the above copyright .\" notice, this list of conditions and the following disclaimer in the .\" documentation and/or other materials provided with the distribution. -.\" 3. All advertising materials mentioning features or use of this software -.\" must display the following acknowledgement: -.\" This product includes software developed by the University of -.\" California, Berkeley and its contributors. -.\" 4. Neither the name of the University nor the names of its contributors +.\" 3. Neither the name of the University nor the names of its contributors .\" may be used to endorse or promote products derived from this software .\" without specific prior written permission. .\" @@ -29,54 +25,54 @@ .\" OUT OF THE USE OF THIS SOFTWARE, EVEN IF ADVISED OF THE POSSIBILITY OF .\" SUCH DAMAGE. .\" -.\" @(#)isinf.3 8.2 (Berkeley) 1/29/94 -.\" $FreeBSD: src/lib/libc/gen/isinf.3,v 1.5.2.3 2003/05/04 22:25:22 murray Exp $ -.\" $DragonFly: src/lib/libc/gen/isinf.3,v 1.2 2003/06/17 04:26:42 dillon Exp $ +.\" from: @(#)acosh.3 5.2 (Berkeley) 5/6/91 +.\" $NetBSD: acosh.3,v 1.15 2003/08/07 16:44:46 agc Exp $ +.\" $DragonFly: src/lib/libm/man/acosh.3,v 1.1 2005/07/26 21:15:20 joerg Exp $ .\" -.Dd January 29, 1994 -.Dt ISINF 3 +.Dd May 6, 1991 +.Dt ACOSH 3 .Os .Sh NAME -.Nm isinf , -.Nm isnan , -.Nm isnanf -.Nd test for infinity or not-a-number +.Nm acosh , +.Nm acoshf +.Nd inverse hyperbolic cosine function .Sh LIBRARY -.Lb libc +.Lb libm .Sh SYNOPSIS .In math.h -.Ft int -.Fn isinf double -.Ft int -.Fn isnan double -.Ft int -.Fn isnanf float +.Ft double +.Fn acosh "double x" +.Ft float +.Fn acoshf "float x" .Sh DESCRIPTION The -.Fn isinf -function -returns 1 if the number is -.Dq \\*(If , -otherwise 0. -.Pp -The -.Fn isnan +.Fn acosh +and +.Fn acoshf +functions compute the inverse hyperbolic cosine +of the real +argument +.Ar x . +.Sh RETURN VALUES +.\" POSIX_MODE +If x is less than one, +.Fn acosh "x" and -.Fn isnanf -functions -return 1 if the double or float (respectively) is -.Dq not-a-number , -otherwise 0. +.Fn acoshf "x" +return NaN and set the global variable +.Va errno +to EDOM. +.\" SVR4_MODE +.\" call +.\" .Xr matherr 3 . .Sh SEE ALSO +.Xr asinh 3 , +.Xr atanh 3 , +.Xr exp 3 , .Xr math 3 -.Rs -.%T "IEEE Standard for Binary Floating-Point Arithmetic" -.%Q ANSI -.%R Std 754-1985 -.Re -.Sh BUGS -Neither the -.Tn VAX -nor the Tahoe floating point have distinguished values -for either infinity or not-a-number. -These routines always return 0 on those architectures. +.\" .Xr matherr 3 +.Sh HISTORY +The +.Fn acosh +function appeared in +.Bx 4.3 . diff --git a/lib/libc/gen/isinf.3 b/lib/libm/man/asin.3 similarity index 54% copy from lib/libc/gen/isinf.3 copy to lib/libm/man/asin.3 index cf68a79e5d..49ab906844 100644 --- a/lib/libc/gen/isinf.3 +++ b/lib/libm/man/asin.3 @@ -1,5 +1,5 @@ -.\" Copyright (c) 1991, 1993 -.\" The Regents of the University of California. All rights reserved. +.\" Copyright (c) 1991 The Regents of the University of California. +.\" All rights reserved. .\" .\" Redistribution and use in source and binary forms, with or without .\" modification, are permitted provided that the following conditions @@ -9,11 +9,7 @@ .\" 2. Redistributions in binary form must reproduce the above copyright .\" notice, this list of conditions and the following disclaimer in the .\" documentation and/or other materials provided with the distribution. -.\" 3. All advertising materials mentioning features or use of this software -.\" must display the following acknowledgement: -.\" This product includes software developed by the University of -.\" California, Berkeley and its contributors. -.\" 4. Neither the name of the University nor the names of its contributors +.\" 3. Neither the name of the University nor the names of its contributors .\" may be used to endorse or promote products derived from this software .\" without specific prior written permission. .\" @@ -29,54 +25,62 @@ .\" OUT OF THE USE OF THIS SOFTWARE, EVEN IF ADVISED OF THE POSSIBILITY OF .\" SUCH DAMAGE. .\" -.\" @(#)isinf.3 8.2 (Berkeley) 1/29/94 -.\" $FreeBSD: src/lib/libc/gen/isinf.3,v 1.5.2.3 2003/05/04 22:25:22 murray Exp $ -.\" $DragonFly: src/lib/libc/gen/isinf.3,v 1.2 2003/06/17 04:26:42 dillon Exp $ +.\" from: @(#)asin.3 5.1 (Berkeley) 5/2/91 +.\" $NetBSD: asin.3,v 1.16 2003/08/07 16:44:46 agc Exp $ +.\" $DragonFly: src/lib/libm/man/asin.3,v 1.1 2005/07/26 21:15:20 joerg Exp $ .\" -.Dd January 29, 1994 -.Dt ISINF 3 +.Dd May 2, 1991 +.Dt ASIN 3 .Os .Sh NAME -.Nm isinf , -.Nm isnan , -.Nm isnanf -.Nd test for infinity or not-a-number +.Nm asin , +.Nm asinf +.Nd arc sine function .Sh LIBRARY -.Lb libc +.Lb libm .Sh SYNOPSIS .In math.h -.Ft int -.Fn isinf double -.Ft int -.Fn isnan double -.Ft int -.Fn isnanf float +.Ft double +.Fn asin "double x" +.Ft float +.Fn asinf "float x" .Sh DESCRIPTION The -.Fn isinf -function -returns 1 if the number is -.Dq \\*(If , -otherwise 0. -.Pp -The -.Fn isnan +.Fn asin +and +.Fn asinf +functions compute the principal value of the arc sine of +.Fa x +in the range +.Bk -words +.Bq -\*(Pi/2, +\*(Pi/2 . +.Ek +.Sh RETURN VALUES +.\" POSIX_MODE +If |x|\*[Gt]1, +.Fn asin "x" and -.Fn isnanf -functions -return 1 if the double or float (respectively) is -.Dq not-a-number , -otherwise 0. +.Fn asinf "x" +return NaN and set the global variable +.Va errno +to EDOM. +.\" SYSV_MODE +.\" call +.\" .Xr matherr 3 . .Sh SEE ALSO -.Xr math 3 -.Rs -.%T "IEEE Standard for Binary Floating-Point Arithmetic" -.%Q ANSI -.%R Std 754-1985 -.Re -.Sh BUGS -Neither the -.Tn VAX -nor the Tahoe floating point have distinguished values -for either infinity or not-a-number. -These routines always return 0 on those architectures. +.Xr acos 3 , +.Xr atan 3 , +.Xr atan2 3 , +.Xr cos 3 , +.Xr cosh 3 , +.Xr math 3 , +.Xr sin 3 , +.Xr sinh 3 , +.Xr tan 3 , +.Xr tanh 3 +.\" .Xr matherr 3 +.Sh STANDARDS +The +.Fn asin +function conforms to +.St -ansiC . diff --git a/lib/libc/gen/isinf.3 b/lib/libm/man/asinh.3 similarity index 55% copy from lib/libc/gen/isinf.3 copy to lib/libm/man/asinh.3 index cf68a79e5d..9d8dcb14d8 100644 --- a/lib/libc/gen/isinf.3 +++ b/lib/libm/man/asinh.3 @@ -1,5 +1,5 @@ -.\" Copyright (c) 1991, 1993 -.\" The Regents of the University of California. All rights reserved. +.\" Copyright (c) 1985, 1991 Regents of the University of California. +.\" All rights reserved. .\" .\" Redistribution and use in source and binary forms, with or without .\" modification, are permitted provided that the following conditions @@ -9,11 +9,7 @@ .\" 2. Redistributions in binary form must reproduce the above copyright .\" notice, this list of conditions and the following disclaimer in the .\" documentation and/or other materials provided with the distribution. -.\" 3. All advertising materials mentioning features or use of this software -.\" must display the following acknowledgement: -.\" This product includes software developed by the University of -.\" California, Berkeley and its contributors. -.\" 4. Neither the name of the University nor the names of its contributors +.\" 3. Neither the name of the University nor the names of its contributors .\" may be used to endorse or promote products derived from this software .\" without specific prior written permission. .\" @@ -29,54 +25,52 @@ .\" OUT OF THE USE OF THIS SOFTWARE, EVEN IF ADVISED OF THE POSSIBILITY OF .\" SUCH DAMAGE. .\" -.\" @(#)isinf.3 8.2 (Berkeley) 1/29/94 -.\" $FreeBSD: src/lib/libc/gen/isinf.3,v 1.5.2.3 2003/05/04 22:25:22 murray Exp $ -.\" $DragonFly: src/lib/libc/gen/isinf.3,v 1.2 2003/06/17 04:26:42 dillon Exp $ +.\" from: @(#)asinh.3 6.4 (Berkeley) 5/6/91 +.\" $NetBSD: asinh.3,v 1.15 2003/08/07 16:44:46 agc Exp $ +.\" $DragonFly: src/lib/libm/man/asinh.3,v 1.1 2005/07/26 21:15:20 joerg Exp $ .\" -.Dd January 29, 1994 -.Dt ISINF 3 +.Dd May 6, 1991 +.Dt ASINH 3 .Os .Sh NAME -.Nm isinf , -.Nm isnan , -.Nm isnanf -.Nd test for infinity or not-a-number +.Nm asinh , +.Nm asinhf +.Nd inverse hyperbolic sine function .Sh LIBRARY -.Lb libc +.Lb libm .Sh SYNOPSIS .In math.h -.Ft int -.Fn isinf double -.Ft int -.Fn isnan double -.Ft int -.Fn isnanf float +.Ft double +.Fn asinh "double x" +.Ft float +.Fn asinhf "float x" .Sh DESCRIPTION The -.Fn isinf -function -returns 1 if the number is -.Dq \\*(If , -otherwise 0. -.Pp +.Fn asinh +and +.Fn asinhf +functions compute the inverse hyperbolic sine +of the real +argument +.Sh RETURN VALUES The -.Fn isnan +.Fn asinh and -.Fn isnanf -functions -return 1 if the double or float (respectively) is -.Dq not-a-number , -otherwise 0. +.Fn asinhf +functions return the inverse hyperbolic sine of +.Ar x . +.\" SYSV_MODE +.\" .Sh RETURN VALUES +.\" Exceptional cases are handled by +.\" .Xr matherr 3 . .Sh SEE ALSO +.Xr acosh 3 , +.Xr atanh 3 , +.Xr exp 3 , .Xr math 3 -.Rs -.%T "IEEE Standard for Binary Floating-Point Arithmetic" -.%Q ANSI -.%R Std 754-1985 -.Re -.Sh BUGS -Neither the -.Tn VAX -nor the Tahoe floating point have distinguished values -for either infinity or not-a-number. -These routines always return 0 on those architectures. +.\" .Xr matherr 3 +.Sh HISTORY +The +.Fn asinh +function appeared in +.Bx 4.3 . diff --git a/lib/libc/gen/isinf.3 b/lib/libm/man/atan.3 similarity index 54% copy from lib/libc/gen/isinf.3 copy to lib/libm/man/atan.3 index cf68a79e5d..144e106547 100644 --- a/lib/libc/gen/isinf.3 +++ b/lib/libm/man/atan.3 @@ -1,5 +1,5 @@ -.\" Copyright (c) 1991, 1993 -.\" The Regents of the University of California. All rights reserved. +.\" Copyright (c) 1991 The Regents of the University of California. +.\" All rights reserved. .\" .\" Redistribution and use in source and binary forms, with or without .\" modification, are permitted provided that the following conditions @@ -9,11 +9,7 @@ .\" 2. Redistributions in binary form must reproduce the above copyright .\" notice, this list of conditions and the following disclaimer in the .\" documentation and/or other materials provided with the distribution. -.\" 3. All advertising materials mentioning features or use of this software -.\" must display the following acknowledgement: -.\" This product includes software developed by the University of -.\" California, Berkeley and its contributors. -.\" 4. Neither the name of the University nor the names of its contributors +.\" 3. Neither the name of the University nor the names of its contributors .\" may be used to endorse or promote products derived from this software .\" without specific prior written permission. .\" @@ -29,54 +25,54 @@ .\" OUT OF THE USE OF THIS SOFTWARE, EVEN IF ADVISED OF THE POSSIBILITY OF .\" SUCH DAMAGE. .\" -.\" @(#)isinf.3 8.2 (Berkeley) 1/29/94 -.\" $FreeBSD: src/lib/libc/gen/isinf.3,v 1.5.2.3 2003/05/04 22:25:22 murray Exp $ -.\" $DragonFly: src/lib/libc/gen/isinf.3,v 1.2 2003/06/17 04:26:42 dillon Exp $ +.\" from: @(#)atan.3 5.1 (Berkeley) 5/2/91 +.\" $NetBSD: atan.3,v 1.16 2003/08/07 16:44:46 agc Exp $ +.\" $DragonFly: src/lib/libm/man/atan.3,v 1.1 2005/07/26 21:15:20 joerg Exp $ .\" -.Dd January 29, 1994 -.Dt ISINF 3 +.Dd May 2, 1991 +.Dt ATAN 3 .Os .Sh NAME -.Nm isinf , -.Nm isnan , -.Nm isnanf -.Nd test for infinity or not-a-number +.Nm atan , +.Nm atanf +.Nd arc tangent function of one variable .Sh LIBRARY -.Lb libc +.Lb libm .Sh SYNOPSIS .In math.h -.Ft int -.Fn isinf double -.Ft int -.Fn isnan double -.Ft int -.Fn isnanf float +.Ft double +.Fn atan "double x" +.Ft float +.Fn atanf "float x" .Sh DESCRIPTION The -.Fn isinf -function -returns 1 if the number is -.Dq \\*(If , -otherwise 0. -.Pp -The -.Fn isnan +.Fn atan and -.Fn isnanf -functions -return 1 if the double or float (respectively) is -.Dq not-a-number , -otherwise 0. +.Fn atanf +functions compute the principal value of the arc tangent of +.Fa x +in the range +.Bk -words +.Bq -\*(Pi/2 , +\*(Pi/2 . +.Ek +.\" SYSV_MODE +.\" .Sh RETURN VALUES +.\" Exceptional cases are handled by +.\" .Xr matherr 3 . .Sh SEE ALSO -.Xr math 3 -.Rs -.%T "IEEE Standard for Binary Floating-Point Arithmetic" -.%Q ANSI -.%R Std 754-1985 -.Re -.Sh BUGS -Neither the -.Tn VAX -nor the Tahoe floating point have distinguished values -for either infinity or not-a-number. -These routines always return 0 on those architectures. +.Xr acos 3 , +.Xr asin 3 , +.Xr atan2 3 , +.Xr cos 3 , +.Xr cosh 3 , +.Xr math 3 , +.Xr sin 3 , +.Xr sinh 3 , +.Xr tan 3 , +.Xr tanh 3 +.\" .Xr matherr 3 +.Sh STANDARDS +The +.Fn atan +functions conforms to +.St -ansiC . diff --git a/lib/libm/man/atan2.3 b/lib/libm/man/atan2.3 new file mode 100644 index 0000000000..b98484185d --- /dev/null +++ b/lib/libm/man/atan2.3 @@ -0,0 +1,193 @@ +.\" Copyright (c) 1991 The Regents of the University of California. +.\" All rights reserved. +.\" +.\" Redistribution and use in source and binary forms, with or without +.\" modification, are permitted provided that the following conditions +.\" are met: +.\" 1. Redistributions of source code must retain the above copyright +.\" notice, this list of conditions and the following disclaimer. +.\" 2. Redistributions in binary form must reproduce the above copyright +.\" notice, this list of conditions and the following disclaimer in the +.\" documentation and/or other materials provided with the distribution. +.\" 3. Neither the name of the University nor the names of its contributors +.\" may be used to endorse or promote products derived from this software +.\" without specific prior written permission. +.\" +.\" THIS SOFTWARE IS PROVIDED BY THE REGENTS AND CONTRIBUTORS ``AS IS'' AND +.\" ANY EXPRESS OR IMPLIED WARRANTIES, INCLUDING, BUT NOT LIMITED TO, THE +.\" IMPLIED WARRANTIES OF MERCHANTABILITY AND FITNESS FOR A PARTICULAR PURPOSE +.\" ARE DISCLAIMED. IN NO EVENT SHALL THE REGENTS OR CONTRIBUTORS BE LIABLE +.\" FOR ANY DIRECT, INDIRECT, INCIDENTAL, SPECIAL, EXEMPLARY, OR CONSEQUENTIAL +.\" DAMAGES (INCLUDING, BUT NOT LIMITED TO, PROCUREMENT OF SUBSTITUTE GOODS +.\" OR SERVICES; LOSS OF USE, DATA, OR PROFITS; OR BUSINESS INTERRUPTION) +.\" HOWEVER CAUSED AND ON ANY THEORY OF LIABILITY, WHETHER IN CONTRACT, STRICT +.\" LIABILITY, OR TORT (INCLUDING NEGLIGENCE OR OTHERWISE) ARISING IN ANY WAY +.\" OUT OF THE USE OF THIS SOFTWARE, EVEN IF ADVISED OF THE POSSIBILITY OF +.\" SUCH DAMAGE. +.\" +.\" from: @(#)atan2.3 5.1 (Berkeley) 5/2/91 +.\" $NetBSD: atan2.3,v 1.16 2003/08/07 16:44:46 agc Exp $ +.\" $DragonFly: src/lib/libm/man/atan2.3,v 1.1 2005/07/26 21:15:20 joerg Exp $ +.\" +.Dd May 2, 1991 +.Dt ATAN2 3 +.Os +.Sh NAME +.Nm atan2 , +.Nm atan2f +.Nd arc tangent function of two variables +.Sh LIBRARY +.Lb libm +.Sh SYNOPSIS +.In math.h +.Ft double +.Fn atan2 "double y" "double x" +.Ft float +.Fn atan2f "float y" "float x" +.Sh DESCRIPTION +The +.Fn atan2 +and +.Fn atan2f +functions compute the principal value of the arc tangent of +.Ar y/ Ns Ar x , +using the signs of both arguments to determine the quadrant of +the return value. +.Sh RETURN VALUES +The +.Fn atan2 +function, if successful, +returns the arc tangent of +.Ar y/ Ns Ar x +in the range +.Bk -words +.Bq \&- Ns \*(Pi , \&+ Ns \*(Pi +.Ek +radians. +If both +.Ar x +and +.Ar y +are zero, the global variable +.Va errno +is set to +.Er EDOM . +On the +.Tn VAX : +.Bl -column atan_(y,x)_:=____ sign(y)_(Pi_atan2(Xy_xX))___ +.It Fn atan2 y x No := Ta +.Fn atan y/x Ta +if +.Ar x +\*[Gt] 0, +.It Ta sign( Ns Ar y Ns )*(\*(Pi - +.Fn atan "\\*(Bay/x\\*(Ba" ) Ta +if +.Ar x +\*[Lt] 0, +.It Ta +.No 0 Ta +if x = y = 0, or +.It Ta +.Pf sign( Ar y Ns )*\\*(Pi/2 Ta +if +.Ar x += 0 \*(!= +.Ar y . +.El +.Sh NOTES +The function +.Fn atan2 +defines "if x \*[Gt] 0," +.Fn atan2 0 0 += 0 on a +.Tn VAX +despite that previously +.Fn atan2 0 0 +may have generated an error message. +The reasons for assigning a value to +.Fn atan2 0 0 +are these: +.Bl -enum -offset indent +.It +Programs that test arguments to avoid computing +.Fn atan2 0 0 +must be indifferent to its value. +Programs that require it to be invalid are vulnerable +to diverse reactions to that invalidity on diverse computer systems. +.It +The +.Fn atan2 +function is used mostly to convert from rectangular (x,y) +to polar +.if n\ +(r,theta) +.if t\ +(r,\(*h) +coordinates that must satisfy x = +.if n\ +r\(**cos theta +.if t\ +r\(**cos\(*h +and y = +.if n\ +r\(**sin theta. +.if t\ +r\(**sin\(*h. +These equations are satisfied when (x=0,y=0) +is mapped to +.if n \ +(r=0,theta=0) +.if t \ +(r=0,\(*h=0) +on a VAX. +In general, conversions to polar coordinates should be computed thus: +.Bd -unfilled -offset indent +.if n \{\ +r := hypot(x,y); ... := sqrt(x\(**x+y\(**y) +theta := atan2(y,x). +.\} +.if t \{\ +r := hypot(x,y); ... := \(sr(x\u\s82\s10\d+y\u\s82\s10\d) +\(*h := atan2(y,x). +.\} +.Ed +.It +The foregoing formulas need not be altered to cope in a +reasonable way with signed zeros and infinities +on a machine that conforms to +.Tn IEEE 754 ; +the versions of +.Xr hypot 3 +and +.Fn atan2 +provided for +such a machine are designed to handle all cases. +That is why +.Fn atan2 \(+-0 \-0 += \(+-\*(Pi +for instance. +In general the formulas above are equivalent to these: +.Bd -unfilled -offset indent +.if n \ +r := sqrt(x\(**x+y\(**y); if r = 0 then x := copysign(1,x); +.if t \ +r := \(sr(x\(**x+y\(**y);\0\0if r = 0 then x := copysign(1,x); +.Ed +.El +.Sh SEE ALSO +.Xr acos 3 , +.Xr asin 3 , +.Xr atan 3 , +.Xr cos 3 , +.Xr cosh 3 , +.Xr math 3 , +.Xr sin 3 , +.Xr sinh 3 , +.Xr tan 3 , +.Xr tanh 3 +.Sh STANDARDS +The +.Fn atan2 +function conforms to +.St -ansiC . diff --git a/lib/libc/gen/isinf.3 b/lib/libm/man/atanh.3 similarity index 55% copy from lib/libc/gen/isinf.3 copy to lib/libm/man/atanh.3 index cf68a79e5d..6ce7a6e76e 100644 --- a/lib/libc/gen/isinf.3 +++ b/lib/libm/man/atanh.3 @@ -1,5 +1,5 @@ -.\" Copyright (c) 1991, 1993 -.\" The Regents of the University of California. All rights reserved. +.\" Copyright (c) 1985, 1991 Regents of the University of California. +.\" All rights reserved. .\" .\" Redistribution and use in source and binary forms, with or without .\" modification, are permitted provided that the following conditions @@ -9,11 +9,7 @@ .\" 2. Redistributions in binary form must reproduce the above copyright .\" notice, this list of conditions and the following disclaimer in the .\" documentation and/or other materials provided with the distribution. -.\" 3. All advertising materials mentioning features or use of this software -.\" must display the following acknowledgement: -.\" This product includes software developed by the University of -.\" California, Berkeley and its contributors. -.\" 4. Neither the name of the University nor the names of its contributors +.\" 3. Neither the name of the University nor the names of its contributors .\" may be used to endorse or promote products derived from this software .\" without specific prior written permission. .\" @@ -29,54 +25,54 @@ .\" OUT OF THE USE OF THIS SOFTWARE, EVEN IF ADVISED OF THE POSSIBILITY OF .\" SUCH DAMAGE. .\" -.\" @(#)isinf.3 8.2 (Berkeley) 1/29/94 -.\" $FreeBSD: src/lib/libc/gen/isinf.3,v 1.5.2.3 2003/05/04 22:25:22 murray Exp $ -.\" $DragonFly: src/lib/libc/gen/isinf.3,v 1.2 2003/06/17 04:26:42 dillon Exp $ +.\" from: @(#)atanh.3 5.2 (Berkeley) 5/6/91 +.\" $NetBSD: atanh.3,v 1.15 2003/08/07 16:44:46 agc Exp $ +.\" $DragonFly: src/lib/libm/man/atanh.3,v 1.1 2005/07/26 21:15:20 joerg Exp $ .\" -.Dd January 29, 1994 -.Dt ISINF 3 +.Dd May 6, 1991 +.Dt ATANH 3 .Os .Sh NAME -.Nm isinf , -.Nm isnan , -.Nm isnanf -.Nd test for infinity or not-a-number +.Nm atanh , +.Nm atanhf +.Nd inverse hyperbolic tangent function .Sh LIBRARY -.Lb libc +.Lb libm .Sh SYNOPSIS .In math.h -.Ft int -.Fn isinf double -.Ft int -.Fn isnan double -.Ft int -.Fn isnanf float +.Ft double +.Fn atanh "double x" +.Ft float +.Fn atanhf "float x" .Sh DESCRIPTION The -.Fn isinf -function -returns 1 if the number is -.Dq \\*(If , -otherwise 0. -.Pp -The -.Fn isnan +.Fn atanh +and +.Fn atanhf +functions compute the inverse hyperbolic tangent +of the real +argument +.Ar x . +.Sh RETURN VALUES +If |x|\*[Ge]1, +.Fn atanh "x" and -.Fn isnanf -functions -return 1 if the double or float (respectively) is -.Dq not-a-number , -otherwise 0. +.Fn atanhf "x" +.\" POSIX_MODE +return +inf, -inf or NaN, and sets the global variable +.Va errno +to EDOM. +.\" SYSV_MODE +.\" call +.\" .Xr matherr 3 . .Sh SEE ALSO +.Xr acosh 3 , +.Xr asinh 3 , +.Xr exp 3 , .Xr math 3 -.Rs -.%T "IEEE Standard for Binary Floating-Point Arithmetic" -.%Q ANSI -.%R Std 754-1985 -.Re -.Sh BUGS -Neither the -.Tn VAX -nor the Tahoe floating point have distinguished values -for either infinity or not-a-number. -These routines always return 0 on those architectures. +.\" .Xr matherr 3 +.Sh HISTORY +The +.Fn atanh +function appeared in +.Bx 4.3 . diff --git a/lib/libc/gen/isinf.3 b/lib/libm/man/ceil.3 similarity index 54% copy from lib/libc/gen/isinf.3 copy to lib/libm/man/ceil.3 index cf68a79e5d..fa8ccc0721 100644 --- a/lib/libc/gen/isinf.3 +++ b/lib/libm/man/ceil.3 @@ -1,5 +1,5 @@ -.\" Copyright (c) 1991, 1993 -.\" The Regents of the University of California. All rights reserved. +.\" Copyright (c) 1991 The Regents of the University of California. +.\" All rights reserved. .\" .\" Redistribution and use in source and binary forms, with or without .\" modification, are permitted provided that the following conditions @@ -9,11 +9,7 @@ .\" 2. Redistributions in binary form must reproduce the above copyright .\" notice, this list of conditions and the following disclaimer in the .\" documentation and/or other materials provided with the distribution. -.\" 3. All advertising materials mentioning features or use of this software -.\" must display the following acknowledgement: -.\" This product includes software developed by the University of -.\" California, Berkeley and its contributors. -.\" 4. Neither the name of the University nor the names of its contributors +.\" 3. Neither the name of the University nor the names of its contributors .\" may be used to endorse or promote products derived from this software .\" without specific prior written permission. .\" @@ -29,54 +25,42 @@ .\" OUT OF THE USE OF THIS SOFTWARE, EVEN IF ADVISED OF THE POSSIBILITY OF .\" SUCH DAMAGE. .\" -.\" @(#)isinf.3 8.2 (Berkeley) 1/29/94 -.\" $FreeBSD: src/lib/libc/gen/isinf.3,v 1.5.2.3 2003/05/04 22:25:22 murray Exp $ -.\" $DragonFly: src/lib/libc/gen/isinf.3,v 1.2 2003/06/17 04:26:42 dillon Exp $ +.\" from: @(#)ceil.3 5.1 (Berkeley) 5/2/91 +.\" $NetBSD: ceil.3,v 1.17 2003/08/07 16:44:47 agc Exp $ +.\" $DragonFly: src/lib/libm/man/ceil.3,v 1.1 2005/07/26 21:15:20 joerg Exp $ .\" -.Dd January 29, 1994 -.Dt ISINF 3 +.Dd March 10, 1994 +.Dt CEIL 3 .Os .Sh NAME -.Nm isinf , -.Nm isnan , -.Nm isnanf -.Nd test for infinity or not-a-number +.Nm ceil , +.Nm ceilf +.Nd "round to smallest integral value greater than or equal to x" .Sh LIBRARY -.Lb libc +.Lb libm .Sh SYNOPSIS .In math.h -.Ft int -.Fn isinf double -.Ft int -.Fn isnan double -.Ft int -.Fn isnanf float +.Ft double +.Fn ceil "double x" +.Ft float +.Fn ceilf "float x" .Sh DESCRIPTION The -.Fn isinf -function -returns 1 if the number is -.Dq \\*(If , -otherwise 0. -.Pp -The -.Fn isnan +.Fn ceil and -.Fn isnanf -functions -return 1 if the double or float (respectively) is -.Dq not-a-number , -otherwise 0. +.Fn ceilf +functions return the smallest integral value +greater than or equal to +.Fa x . .Sh SEE ALSO -.Xr math 3 -.Rs -.%T "IEEE Standard for Binary Floating-Point Arithmetic" -.%Q ANSI -.%R Std 754-1985 -.Re -.Sh BUGS -Neither the -.Tn VAX -nor the Tahoe floating point have distinguished values -for either infinity or not-a-number. -These routines always return 0 on those architectures. +.Xr abs 3 , +.Xr fabs 3 , +.Xr floor 3 , +.Xr ieee 3 , +.Xr math 3 , +.Xr rint 3 +.Sh STANDARDS +The +.Fn ceil +function conforms to +.St -ansiC . diff --git a/lib/libc/gen/isinf.3 b/lib/libm/man/cos.3 similarity index 54% copy from lib/libc/gen/isinf.3 copy to lib/libm/man/cos.3 index cf68a79e5d..41fd88fa1c 100644 --- a/lib/libc/gen/isinf.3 +++ b/lib/libm/man/cos.3 @@ -1,5 +1,5 @@ -.\" Copyright (c) 1991, 1993 -.\" The Regents of the University of California. All rights reserved. +.\" Copyright (c) 1991 The Regents of the University of California. +.\" All rights reserved. .\" .\" Redistribution and use in source and binary forms, with or without .\" modification, are permitted provided that the following conditions @@ -9,11 +9,7 @@ .\" 2. Redistributions in binary form must reproduce the above copyright .\" notice, this list of conditions and the following disclaimer in the .\" documentation and/or other materials provided with the distribution. -.\" 3. All advertising materials mentioning features or use of this software -.\" must display the following acknowledgement: -.\" This product includes software developed by the University of -.\" California, Berkeley and its contributors. -.\" 4. Neither the name of the University nor the names of its contributors +.\" 3. Neither the name of the University nor the names of its contributors .\" may be used to endorse or promote products derived from this software .\" without specific prior written permission. .\" @@ -29,54 +25,54 @@ .\" OUT OF THE USE OF THIS SOFTWARE, EVEN IF ADVISED OF THE POSSIBILITY OF .\" SUCH DAMAGE. .\" -.\" @(#)isinf.3 8.2 (Berkeley) 1/29/94 -.\" $FreeBSD: src/lib/libc/gen/isinf.3,v 1.5.2.3 2003/05/04 22:25:22 murray Exp $ -.\" $DragonFly: src/lib/libc/gen/isinf.3,v 1.2 2003/06/17 04:26:42 dillon Exp $ +.\" from: @(#)cos.3 5.1 (Berkeley) 5/2/91 +.\" $NetBSD: cos.3,v 1.15 2003/08/07 16:44:47 agc Exp $ +.\" $DragonFly: src/lib/libm/man/cos.3,v 1.1 2005/07/26 21:15:20 joerg Exp $ .\" -.Dd January 29, 1994 -.Dt ISINF 3 +.Dd May 2, 1991 +.Dt COS 3 .Os .Sh NAME -.Nm isinf , -.Nm isnan , -.Nm isnanf -.Nd test for infinity or not-a-number +.Nm cos , +.Nm cosf +.Nd cosine function .Sh LIBRARY -.Lb libc +.Lb libm .Sh SYNOPSIS .In math.h -.Ft int -.Fn isinf double -.Ft int -.Fn isnan double -.Ft int -.Fn isnanf float +.Ft double +.Fn cos "double x" +.Ft float +.Fn cosf "float x" .Sh DESCRIPTION The -.Fn isinf -function -returns 1 if the number is -.Dq \\*(If , -otherwise 0. -.Pp -The -.Fn isnan +.Fn cos and -.Fn isnanf -functions -return 1 if the double or float (respectively) is -.Dq not-a-number , -otherwise 0. +.Fn cosf +functions compute the cosine of +.Fa x +(measured in radians). +A large magnitude argument may yield a result with little or no +significance. +For a discussion of error due to roundoff, see +.Xr math 3 . +.Sh RETURN VALUES +The +.Fn cos +function returns the cosine value. .Sh SEE ALSO -.Xr math 3 -.Rs -.%T "IEEE Standard for Binary Floating-Point Arithmetic" -.%Q ANSI -.%R Std 754-1985 -.Re -.Sh BUGS -Neither the -.Tn VAX -nor the Tahoe floating point have distinguished values -for either infinity or not-a-number. -These routines always return 0 on those architectures. +.Xr acos 3 , +.Xr asin 3 , +.Xr atan 3 , +.Xr atan2 3 , +.Xr cosh 3 , +.Xr math 3 , +.Xr sin 3 , +.Xr sinh 3 , +.Xr tan 3 , +.Xr tanh 3 +.Sh STANDARDS +The +.Fn cos +function conforms to +.St -ansiC . diff --git a/lib/libc/gen/isinf.3 b/lib/libm/man/cosh.3 similarity index 54% copy from lib/libc/gen/isinf.3 copy to lib/libm/man/cosh.3 index cf68a79e5d..804c0ed5bd 100644 --- a/lib/libc/gen/isinf.3 +++ b/lib/libm/man/cosh.3 @@ -1,5 +1,5 @@ -.\" Copyright (c) 1991, 1993 -.\" The Regents of the University of California. All rights reserved. +.\" Copyright (c) 1989, 1991 The Regents of the University of California. +.\" All rights reserved. .\" .\" Redistribution and use in source and binary forms, with or without .\" modification, are permitted provided that the following conditions @@ -9,11 +9,7 @@ .\" 2. Redistributions in binary form must reproduce the above copyright .\" notice, this list of conditions and the following disclaimer in the .\" documentation and/or other materials provided with the distribution. -.\" 3. All advertising materials mentioning features or use of this software -.\" must display the following acknowledgement: -.\" This product includes software developed by the University of -.\" California, Berkeley and its contributors. -.\" 4. Neither the name of the University nor the names of its contributors +.\" 3. Neither the name of the University nor the names of its contributors .\" may be used to endorse or promote products derived from this software .\" without specific prior written permission. .\" @@ -29,54 +25,58 @@ .\" OUT OF THE USE OF THIS SOFTWARE, EVEN IF ADVISED OF THE POSSIBILITY OF .\" SUCH DAMAGE. .\" -.\" @(#)isinf.3 8.2 (Berkeley) 1/29/94 -.\" $FreeBSD: src/lib/libc/gen/isinf.3,v 1.5.2.3 2003/05/04 22:25:22 murray Exp $ -.\" $DragonFly: src/lib/libc/gen/isinf.3,v 1.2 2003/06/17 04:26:42 dillon Exp $ +.\" from: @(#)cosh.3 5.1 (Berkeley) 5/2/91 +.\" $NetBSD: cosh.3,v 1.15 2003/08/07 16:44:47 agc Exp $ +.\" $DragonFly: src/lib/libm/man/cosh.3,v 1.1 2005/07/26 21:15:20 joerg Exp $ .\" -.Dd January 29, 1994 -.Dt ISINF 3 +.Dd May 2, 1991 +.Dt COSH 3 .Os .Sh NAME -.Nm isinf , -.Nm isnan , -.Nm isnanf -.Nd test for infinity or not-a-number +.Nm cosh , +.Nm coshf +.Nd hyperbolic cosine function .Sh LIBRARY -.Lb libc +.Lb libm .Sh SYNOPSIS .In math.h -.Ft int -.Fn isinf double -.Ft int -.Fn isnan double -.Ft int -.Fn isnanf float +.Ft double +.Fn cosh "double x" +.Ft float +.Fn coshf "float x" .Sh DESCRIPTION The -.Fn isinf -function -returns 1 if the number is -.Dq \\*(If , -otherwise 0. -.Pp -The -.Fn isnan +.Fn cosh +and +.Fn coshf +functions compute the hyperbolic cosine of +.Fa x . +.Sh RETURN VALUES +If the magnitude of x is too large, +.Fn cosh "x" and -.Fn isnanf -functions -return 1 if the double or float (respectively) is -.Dq not-a-number , -otherwise 0. +.Fn coshf "x" +.\" POSIX_MODE +return Inf and sets the global variable +.Va errno +to ERANGE. +.\" SYSV_MODE +.\" call +.\" .Xr matherr 3 . .Sh SEE ALSO -.Xr math 3 -.Rs -.%T "IEEE Standard for Binary Floating-Point Arithmetic" -.%Q ANSI -.%R Std 754-1985 -.Re -.Sh BUGS -Neither the -.Tn VAX -nor the Tahoe floating point have distinguished values -for either infinity or not-a-number. -These routines always return 0 on those architectures. +.Xr acos 3 , +.Xr asin 3 , +.Xr atan 3 , +.Xr atan2 3 , +.Xr cos 3 , +.Xr math 3 , +.Xr sin 3 , +.Xr sinh 3 , +.Xr tan 3 , +.Xr tanh 3 +.\" .Xr matherr 3 +.Sh STANDARDS +The +.Fn cosh +function conforms to +.St -ansiC . diff --git a/lib/libc/gen/isinf.3 b/lib/libm/man/erf.3 similarity index 55% copy from lib/libc/gen/isinf.3 copy to lib/libm/man/erf.3 index cf68a79e5d..f0283d532a 100644 --- a/lib/libc/gen/isinf.3 +++ b/lib/libm/man/erf.3 @@ -1,5 +1,5 @@ -.\" Copyright (c) 1991, 1993 -.\" The Regents of the University of California. All rights reserved. +.\" Copyright (c) 1985, 1991 Regents of the University of California. +.\" All rights reserved. .\" .\" Redistribution and use in source and binary forms, with or without .\" modification, are permitted provided that the following conditions @@ -9,11 +9,7 @@ .\" 2. Redistributions in binary form must reproduce the above copyright .\" notice, this list of conditions and the following disclaimer in the .\" documentation and/or other materials provided with the distribution. -.\" 3. All advertising materials mentioning features or use of this software -.\" must display the following acknowledgement: -.\" This product includes software developed by the University of -.\" California, Berkeley and its contributors. -.\" 4. Neither the name of the University nor the names of its contributors +.\" 3. Neither the name of the University nor the names of its contributors .\" may be used to endorse or promote products derived from this software .\" without specific prior written permission. .\" @@ -29,54 +25,64 @@ .\" OUT OF THE USE OF THIS SOFTWARE, EVEN IF ADVISED OF THE POSSIBILITY OF .\" SUCH DAMAGE. .\" -.\" @(#)isinf.3 8.2 (Berkeley) 1/29/94 -.\" $FreeBSD: src/lib/libc/gen/isinf.3,v 1.5.2.3 2003/05/04 22:25:22 murray Exp $ -.\" $DragonFly: src/lib/libc/gen/isinf.3,v 1.2 2003/06/17 04:26:42 dillon Exp $ +.\" from: @(#)erf.3 6.4 (Berkeley) 4/20/91 +.\" $NetBSD: erf.3,v 1.12 2003/08/07 16:44:47 agc Exp $ +.\" $DragonFly: src/lib/libm/man/erf.3,v 1.1 2005/07/26 21:15:20 joerg Exp $ .\" -.Dd January 29, 1994 -.Dt ISINF 3 +.Dd April 20, 1991 +.Dt ERF 3 .Os .Sh NAME -.Nm isinf , -.Nm isnan , -.Nm isnanf -.Nd test for infinity or not-a-number +.Nm erf , +.Nm erff , +.Nm erfc , +.Nm erfcf +.Nd error function operators .Sh LIBRARY -.Lb libc +.Lb libm .Sh SYNOPSIS .In math.h -.Ft int -.Fn isinf double -.Ft int -.Fn isnan double -.Ft int -.Fn isnanf float +.Ft double +.Fn erf "double x" +.Ft float +.Fn erff "float x" +.Ft double +.Fn erfc "double x" +.Ft float +.Fn erfcf "float x" .Sh DESCRIPTION +These functions calculate the error function of +.Fa x . +.Pp The -.Fn isinf -function -returns 1 if the number is -.Dq \\*(If , -otherwise 0. +.Fn erf +calculates the error function of x; where +.Bd -filled -offset indent +.if n \{\ +erf(x) = 2/sqrt(pi)\(**\|integral from 0 to x of exp(\-t\(**t) dt. \} +.if t \{\ +erf\|(x) := +(2/\(sr\(*p)\|\(is\d\s8\z0\s10\u\u\s8x\s10\d\|exp(\-t\u\s82\s10\d)\|dt. \} +.Ed .Pp The -.Fn isnan -and -.Fn isnanf -functions -return 1 if the double or float (respectively) is -.Dq not-a-number , -otherwise 0. +.Fn erfc +function calculates the complementary error function of +.Fa x ; +that is +.Fn erfc +subtracts the result of the error function +.Fn erf x +from 1.0. +This is useful, since for large +.Fa x +places disappear. .Sh SEE ALSO .Xr math 3 -.Rs -.%T "IEEE Standard for Binary Floating-Point Arithmetic" -.%Q ANSI -.%R Std 754-1985 -.Re -.Sh BUGS -Neither the -.Tn VAX -nor the Tahoe floating point have distinguished values -for either infinity or not-a-number. -These routines always return 0 on those architectures. +.Sh HISTORY +The +.Fn erf +and +.Fn erfc +functions appeared in +.Bx 4.3 . diff --git a/lib/libm/man/exp.3 b/lib/libm/man/exp.3 new file mode 100644 index 0000000000..ad5a2971a0 --- /dev/null +++ b/lib/libm/man/exp.3 @@ -0,0 +1,307 @@ +.\" Copyright (c) 1985, 1991 Regents of the University of California. +.\" All rights reserved. +.\" +.\" Redistribution and use in source and binary forms, with or without +.\" modification, are permitted provided that the following conditions +.\" are met: +.\" 1. Redistributions of source code must retain the above copyright +.\" notice, this list of conditions and the following disclaimer. +.\" 2. Redistributions in binary form must reproduce the above copyright +.\" notice, this list of conditions and the following disclaimer in the +.\" documentation and/or other materials provided with the distribution. +.\" 3. Neither the name of the University nor the names of its contributors +.\" may be used to endorse or promote products derived from this software +.\" without specific prior written permission. +.\" +.\" THIS SOFTWARE IS PROVIDED BY THE REGENTS AND CONTRIBUTORS ``AS IS'' AND +.\" ANY EXPRESS OR IMPLIED WARRANTIES, INCLUDING, BUT NOT LIMITED TO, THE +.\" IMPLIED WARRANTIES OF MERCHANTABILITY AND FITNESS FOR A PARTICULAR PURPOSE +.\" ARE DISCLAIMED. IN NO EVENT SHALL THE REGENTS OR CONTRIBUTORS BE LIABLE +.\" FOR ANY DIRECT, INDIRECT, INCIDENTAL, SPECIAL, EXEMPLARY, OR CONSEQUENTIAL +.\" DAMAGES (INCLUDING, BUT NOT LIMITED TO, PROCUREMENT OF SUBSTITUTE GOODS +.\" OR SERVICES; LOSS OF USE, DATA, OR PROFITS; OR BUSINESS INTERRUPTION) +.\" HOWEVER CAUSED AND ON ANY THEORY OF LIABILITY, WHETHER IN CONTRACT, STRICT +.\" LIABILITY, OR TORT (INCLUDING NEGLIGENCE OR OTHERWISE) ARISING IN ANY WAY +.\" OUT OF THE USE OF THIS SOFTWARE, EVEN IF ADVISED OF THE POSSIBILITY OF +.\" SUCH DAMAGE. +.\" +.\" from: @(#)exp.3 6.12 (Berkeley) 7/31/91 +.\" $NetBSD: exp.3,v 1.21 2003/08/07 16:44:47 agc Exp $ +.\" $DragonFly: src/lib/libm/man/exp.3,v 1.1 2005/07/26 21:15:20 joerg Exp $ +.\" +.Dd July 31, 1991 +.Dt EXP 3 +.Os +.Sh NAME +.Nm exp , +.Nm expf , +.Nm expm1 , +.Nm expm1f , +.Nm log , +.Nm logf , +.Nm log10 , +.Nm log10f , +.Nm log1p , +.Nm log1pf , +.Nm pow , +.Nm powf +.Nd exponential, logarithm, power functions +.Sh LIBRARY +.Lb libm +.Sh SYNOPSIS +.In math.h +.Ft double +.Fn exp "double x" +.Ft float +.Fn expf "float x" +.Ft double +.Fn expm1 "double x" +.Ft float +.Fn expm1f "float x" +.Ft double +.Fn log "double x" +.Ft float +.Fn logf "float x" +.Ft double +.Fn log10 "double x" +.Ft float +.Fn log10f "float x" +.Ft double +.Fn log1p "double x" +.Ft float +.Fn log1pf "float x" +.Ft double +.Fn pow "double x" "double y" +.Ft float +.Fn powf "float x" "float y" +.Sh DESCRIPTION +The +.Fn exp +function computes the exponential value of the given argument +.Fa x . +.Pp +The +.Fn expm1 +function computes the value exp(x)\-1 accurately even for tiny argument +.Fa x . +.Pp +The +.Fn log +function computes the value of the natural logarithm of argument +.Fa x . +.Pp +The +.Fn log10 +function computes the value of the logarithm of argument +.Fa x +to base 10. +.Pp +The +.Fn log1p +function computes +the value of log(1+x) accurately even for tiny argument +.Fa x . +.Pp +The +.Fn pow +computes the value +of +.Ar x +to the exponent +.Ar y . +.Sh RETURN VALUES +These functions will return the appropriate computation unless an error +occurs or an argument is out of range. +The functions +.Fn exp , +.Fn expm1 +and +.Fn pow +detect if the computed value will overflow, +set the global variable +.Va errno +to +.Er ERANGE +and cause a reserved operand fault on a +.Tn VAX . +The function +.Fn pow x y +checks to see if +.Fa x +\*[Lt] 0 and +.Fa y +is not an integer, in the event this is true, +the global variable +.Va errno +is set to +.Er EDOM +and on the +.Tn VAX +generate a reserved operand fault. +On a +.Tn VAX , +.Va errno +is set to +.Er EDOM +and the reserved operand is returned +by log unless +.Fa x +\*[Gt] 0, by +.Fn log1p +unless +.Fa x +\*[Gt] \-1. +.Sh ERRORS +exp(x), log(x), expm1(x) and log1p(x) are accurate to within +an +.Em ulp , +and log10(x) to within about 2 +.Em ulps ; +an +.Em ulp +is one +.Em Unit +in the +.Em Last +.Em Place . +The error in +.Fn pow x y +is below about 2 +.Em ulps +when its +magnitude is moderate, but increases as +.Fn pow x y +approaches +the over/underflow thresholds until almost as many bits could be +lost as are occupied by the floating\-point format's exponent +field; that is 8 bits for +.Tn "VAX D" +and 11 bits for IEEE 754 Double. +No such drastic loss has been exposed by testing; the worst +errors observed have been below 20 +.Em ulps +for +.Tn "VAX D" , +300 +.Em ulps +for +.Tn IEEE +754 Double. +Moderate values of +.Fn pow +are accurate enough that +.Fn pow integer integer +is exact until it is bigger than 2**56 on a +.Tn VAX , +2**53 for +.Tn IEEE +754. +.Sh NOTES +The functions exp(x)\-1 and log(1+x) are called +expm1 and logp1 in +.Tn BASIC +on the Hewlett\-Packard +.Tn HP Ns \-71B +and +.Tn APPLE +Macintosh, +.Tn EXP1 +and +.Tn LN1 +in Pascal, exp1 and log1 in C +on +.Tn APPLE +Macintoshes, where they have been provided to make +sure financial calculations of ((1+x)**n\-1)/x, namely +expm1(n\(**log1p(x))/x, will be accurate when x is tiny. +They also provide accurate inverse hyperbolic functions. +.Pp +The function +.Fn pow x 0 +returns x**0 = 1 for all x including x = 0, +.if n \ +Infinity +.if t \ +\(if +(not found on a +.Tn VAX ) , +and +.Em NaN +(the reserved +operand on a +.Tn VAX ) . +Previous implementations of pow may +have defined x**0 to be undefined in some or all of these +cases. +Here are reasons for returning x**0 = 1 always: +.Bl -enum -width indent +.It +Any program that already tests whether x is zero (or +infinite or \*(Na) before computing x**0 cannot care +whether 0**0 = 1 or not. +Any program that depends +upon 0**0 to be invalid is dubious anyway since that +expression's meaning and, if invalid, its consequences +vary from one computer system to another. +.It +Some Algebra texts (e.g. Sigler's) define x**0 = 1 for +all x, including x = 0. +This is compatible with the convention that accepts a[0] +as the value of polynomial +.Bd -literal -offset indent +p(x) = a[0]\(**x**0 + a[1]\(**x**1 + a[2]\(**x**2 +...+ a[n]\(**x**n +.Ed +.Pp +at x = 0 rather than reject a[0]\(**0**0 as invalid. +.It +Analysts will accept 0**0 = 1 despite that x**y can +approach anything or nothing as x and y approach 0 +independently. +The reason for setting 0**0 = 1 anyway is this: +.Bd -filled -offset indent +If x(z) and y(z) are +.Em any +functions analytic (expandable +in power series) in z around z = 0, and if there +x(0) = y(0) = 0, then x(z)**y(z) \(-\*[Gt] 1 as z \(-\*[Gt] 0. +.Ed +.It +If 0**0 = 1, then +.if n \ +infinity**0 = 1/0**0 = 1 too; and +.if t \ +\(if**0 = 1/0**0 = 1 too; and +then \*(Na**0 = 1 too because x**0 = 1 for all finite +and infinite x, i.e., independently of x. +.El +.Sh SEE ALSO +.Xr math 3 +.Sh STANDARDS +The +.Fn exp , +.Fn log , +.Fn log10 +and +.Fn pow +functions conform to +.St -ansiC . +.Sh HISTORY +A +.Fn exp , +.Fn log +and +.Fn pow +functions +appeared in +.At v6 . +A +.Fn log10 +function +appeared in +.At v7 . +The +.Fn log1p +and +.Fn expm1 +functions appeared in +.Bx 4.3 . diff --git a/lib/libc/gen/isinf.3 b/lib/libm/man/fabs.3 similarity index 54% copy from lib/libc/gen/isinf.3 copy to lib/libm/man/fabs.3 index cf68a79e5d..ae464839b4 100644 --- a/lib/libc/gen/isinf.3 +++ b/lib/libm/man/fabs.3 @@ -1,5 +1,5 @@ -.\" Copyright (c) 1991, 1993 -.\" The Regents of the University of California. All rights reserved. +.\" Copyright (c) 1991 The Regents of the University of California. +.\" All rights reserved. .\" .\" Redistribution and use in source and binary forms, with or without .\" modification, are permitted provided that the following conditions @@ -9,11 +9,7 @@ .\" 2. Redistributions in binary form must reproduce the above copyright .\" notice, this list of conditions and the following disclaimer in the .\" documentation and/or other materials provided with the distribution. -.\" 3. All advertising materials mentioning features or use of this software -.\" must display the following acknowledgement: -.\" This product includes software developed by the University of -.\" California, Berkeley and its contributors. -.\" 4. Neither the name of the University nor the names of its contributors +.\" 3. Neither the name of the University nor the names of its contributors .\" may be used to endorse or promote products derived from this software .\" without specific prior written permission. .\" @@ -29,54 +25,46 @@ .\" OUT OF THE USE OF THIS SOFTWARE, EVEN IF ADVISED OF THE POSSIBILITY OF .\" SUCH DAMAGE. .\" -.\" @(#)isinf.3 8.2 (Berkeley) 1/29/94 -.\" $FreeBSD: src/lib/libc/gen/isinf.3,v 1.5.2.3 2003/05/04 22:25:22 murray Exp $ -.\" $DragonFly: src/lib/libc/gen/isinf.3,v 1.2 2003/06/17 04:26:42 dillon Exp $ +.\" from: @(#)fabs.3 5.1 (Berkeley) 5/2/91 +.\" $NetBSD: fabs.3,v 1.14 2003/08/07 16:44:47 agc Exp $ +.\" $DragonFly: src/lib/libm/man/fabs.3,v 1.1 2005/07/26 21:15:20 joerg Exp $ .\" -.Dd January 29, 1994 -.Dt ISINF 3 +.Dd May 2, 1991 +.Dt FABS 3 .Os .Sh NAME -.Nm isinf , -.Nm isnan , -.Nm isnanf -.Nd test for infinity or not-a-number +.Nm fabs , +.Nm fabsf +.Nd floating-point absolute value function .Sh LIBRARY -.Lb libc +.Lb libm .Sh SYNOPSIS .In math.h -.Ft int -.Fn isinf double -.Ft int -.Fn isnan double -.Ft int -.Fn isnanf float +.Ft double +.Fn fabs "double x" +.Ft float +.Fn fabsf "float x" .Sh DESCRIPTION The -.Fn isinf -function -returns 1 if the number is -.Dq \\*(If , -otherwise 0. -.Pp -The -.Fn isnan +.Fn fabs and -.Fn isnanf -functions -return 1 if the double or float (respectively) is -.Dq not-a-number , -otherwise 0. +.Fn fabsf +functions compute the absolute value of a floating-point number +.Fa x . +.Sh RETURN VALUES +The +.Fn fabs +function returns the absolute value of +.Fa x . .Sh SEE ALSO -.Xr math 3 -.Rs -.%T "IEEE Standard for Binary Floating-Point Arithmetic" -.%Q ANSI -.%R Std 754-1985 -.Re -.Sh BUGS -Neither the -.Tn VAX -nor the Tahoe floating point have distinguished values -for either infinity or not-a-number. -These routines always return 0 on those architectures. +.Xr abs 3 , +.Xr ceil 3 , +.Xr floor 3 , +.Xr ieee 3 , +.Xr math 3 , +.Xr rint 3 +.Sh STANDARDS +The +.Fn fabs +function conforms to +.St -ansiC . diff --git a/lib/libc/gen/isinf.3 b/lib/libm/man/floor.3 similarity index 54% copy from lib/libc/gen/isinf.3 copy to lib/libm/man/floor.3 index cf68a79e5d..ada22a0044 100644 --- a/lib/libc/gen/isinf.3 +++ b/lib/libm/man/floor.3 @@ -1,5 +1,5 @@ -.\" Copyright (c) 1991, 1993 -.\" The Regents of the University of California. All rights reserved. +.\" Copyright (c) 1985, 1991 The Regents of the University of California. +.\" All rights reserved. .\" .\" Redistribution and use in source and binary forms, with or without .\" modification, are permitted provided that the following conditions @@ -9,11 +9,7 @@ .\" 2. Redistributions in binary form must reproduce the above copyright .\" notice, this list of conditions and the following disclaimer in the .\" documentation and/or other materials provided with the distribution. -.\" 3. All advertising materials mentioning features or use of this software -.\" must display the following acknowledgement: -.\" This product includes software developed by the University of -.\" California, Berkeley and its contributors. -.\" 4. Neither the name of the University nor the names of its contributors +.\" 3. Neither the name of the University nor the names of its contributors .\" may be used to endorse or promote products derived from this software .\" without specific prior written permission. .\" @@ -29,54 +25,42 @@ .\" OUT OF THE USE OF THIS SOFTWARE, EVEN IF ADVISED OF THE POSSIBILITY OF .\" SUCH DAMAGE. .\" -.\" @(#)isinf.3 8.2 (Berkeley) 1/29/94 -.\" $FreeBSD: src/lib/libc/gen/isinf.3,v 1.5.2.3 2003/05/04 22:25:22 murray Exp $ -.\" $DragonFly: src/lib/libc/gen/isinf.3,v 1.2 2003/06/17 04:26:42 dillon Exp $ +.\" from: @(#)floor.3 6.5 (Berkeley) 4/19/91 +.\" $NetBSD: floor.3,v 1.14 2003/08/07 16:44:47 agc Exp $ +.\" $DragonFly: src/lib/libm/man/floor.3,v 1.1 2005/07/26 21:15:20 joerg Exp $ .\" -.Dd January 29, 1994 -.Dt ISINF 3 +.Dd March 10, 1994 +.Dt FLOOR 3 .Os .Sh NAME -.Nm isinf , -.Nm isnan , -.Nm isnanf -.Nd test for infinity or not-a-number +.Nm floor , +.Nm floorf +.Nd round to largest integral value not greater than x .Sh LIBRARY -.Lb libc +.Lb libm .Sh SYNOPSIS .In math.h -.Ft int -.Fn isinf double -.Ft int -.Fn isnan double -.Ft int -.Fn isnanf float +.Ft double +.Fn floor "double x" +.Ft float +.Fn floorf "float x" .Sh DESCRIPTION The -.Fn isinf -function -returns 1 if the number is -.Dq \\*(If , -otherwise 0. -.Pp -The -.Fn isnan +.Fn floor and -.Fn isnanf -functions -return 1 if the double or float (respectively) is -.Dq not-a-number , -otherwise 0. +.Fn floorf +functions return the largest integral value +less than or equal to +.Fa x . .Sh SEE ALSO -.Xr math 3 -.Rs -.%T "IEEE Standard for Binary Floating-Point Arithmetic" -.%Q ANSI -.%R Std 754-1985 -.Re -.Sh BUGS -Neither the -.Tn VAX -nor the Tahoe floating point have distinguished values -for either infinity or not-a-number. -These routines always return 0 on those architectures. +.Xr abs 3 , +.Xr ceil 3 , +.Xr fabs 3 , +.Xr ieee 3 , +.Xr math 3 , +.Xr rint 3 +.Sh STANDARDS +The +.Fn floor +function conforms to +.St -ansiC . diff --git a/lib/libc/gen/isinf.3 b/lib/libm/man/fmod.3 similarity index 55% copy from lib/libc/gen/isinf.3 copy to lib/libm/man/fmod.3 index cf68a79e5d..0a592d0306 100644 --- a/lib/libc/gen/isinf.3 +++ b/lib/libm/man/fmod.3 @@ -1,5 +1,5 @@ -.\" Copyright (c) 1991, 1993 -.\" The Regents of the University of California. All rights reserved. +.\" Copyright (c) 1991 The Regents of the University of California. +.\" All rights reserved. .\" .\" Redistribution and use in source and binary forms, with or without .\" modification, are permitted provided that the following conditions @@ -9,11 +9,7 @@ .\" 2. Redistributions in binary form must reproduce the above copyright .\" notice, this list of conditions and the following disclaimer in the .\" documentation and/or other materials provided with the distribution. -.\" 3. All advertising materials mentioning features or use of this software -.\" must display the following acknowledgement: -.\" This product includes software developed by the University of -.\" California, Berkeley and its contributors. -.\" 4. Neither the name of the University nor the names of its contributors +.\" 3. Neither the name of the University nor the names of its contributors .\" may be used to endorse or promote products derived from this software .\" without specific prior written permission. .\" @@ -29,54 +25,56 @@ .\" OUT OF THE USE OF THIS SOFTWARE, EVEN IF ADVISED OF THE POSSIBILITY OF .\" SUCH DAMAGE. .\" -.\" @(#)isinf.3 8.2 (Berkeley) 1/29/94 -.\" $FreeBSD: src/lib/libc/gen/isinf.3,v 1.5.2.3 2003/05/04 22:25:22 murray Exp $ -.\" $DragonFly: src/lib/libc/gen/isinf.3,v 1.2 2003/06/17 04:26:42 dillon Exp $ +.\" from: @(#)fmod.3 5.1 (Berkeley) 5/2/91 +.\" $NetBSD: fmod.3,v 1.11 2003/08/07 16:44:47 agc Exp $ +.\" $DragonFly: src/lib/libm/man/fmod.3,v 1.1 2005/07/26 21:15:20 joerg Exp $ .\" -.Dd January 29, 1994 -.Dt ISINF 3 +.Dd May 2, 1991 +.Dt FMOD 3 .Os .Sh NAME -.Nm isinf , -.Nm isnan , -.Nm isnanf -.Nd test for infinity or not-a-number +.Nm fmod , +.Nm fmodf +.Nd floating-point remainder function .Sh LIBRARY -.Lb libc +.Lb libm .Sh SYNOPSIS .In math.h -.Ft int -.Fn isinf double -.Ft int -.Fn isnan double -.Ft int -.Fn isnanf float +.Ft double +.Fn fmod "double x" "double y" +.Ft float +.Fn fmodf "float x" "float y" .Sh DESCRIPTION The -.Fn isinf -function -returns 1 if the number is -.Dq \\*(If , -otherwise 0. -.Pp +.Fn fmod +function computes the floating-point remainder of +.Fa x Ns / Fa y . +.Sh RETURN VALUES The -.Fn isnan +.Fn fmod and -.Fn isnanf -functions -return 1 if the double or float (respectively) is -.Dq not-a-number , -otherwise 0. +.Fn fmodf +functions return the value +.Sm off +.Fa x - Em i * Fa y , +.Sm on +for some integer +.Em i +such that, if +.Fa y +is non-zero, the result has the same sign as +.Fa x +and magnitude less than the magnitude of +.Fa y . +If +.Fa y +is zero, whether a domain error occurs or the +.Fn fmod +function returns zero is implementation-defined. .Sh SEE ALSO .Xr math 3 -.Rs -.%T "IEEE Standard for Binary Floating-Point Arithmetic" -.%Q ANSI -.%R Std 754-1985 -.Re -.Sh BUGS -Neither the -.Tn VAX -nor the Tahoe floating point have distinguished values -for either infinity or not-a-number. -These routines always return 0 on those architectures. +.Sh STANDARDS +The +.Fn fmod +function conforms to +.St -ansiC . diff --git a/lib/libm/man/hypot.3 b/lib/libm/man/hypot.3 new file mode 100644 index 0000000000..bc56ea820a --- /dev/null +++ b/lib/libm/man/hypot.3 @@ -0,0 +1,137 @@ +.\" Copyright (c) 1985, 1991 Regents of the University of California. +.\" All rights reserved. +.\" +.\" Redistribution and use in source and binary forms, with or without +.\" modification, are permitted provided that the following conditions +.\" are met: +.\" 1. Redistributions of source code must retain the above copyright +.\" notice, this list of conditions and the following disclaimer. +.\" 2. Redistributions in binary form must reproduce the above copyright +.\" notice, this list of conditions and the following disclaimer in the +.\" documentation and/or other materials provided with the distribution. +.\" 3. Neither the name of the University nor the names of its contributors +.\" may be used to endorse or promote products derived from this software +.\" without specific prior written permission. +.\" +.\" THIS SOFTWARE IS PROVIDED BY THE REGENTS AND CONTRIBUTORS ``AS IS'' AND +.\" ANY EXPRESS OR IMPLIED WARRANTIES, INCLUDING, BUT NOT LIMITED TO, THE +.\" IMPLIED WARRANTIES OF MERCHANTABILITY AND FITNESS FOR A PARTICULAR PURPOSE +.\" ARE DISCLAIMED. IN NO EVENT SHALL THE REGENTS OR CONTRIBUTORS BE LIABLE +.\" FOR ANY DIRECT, INDIRECT, INCIDENTAL, SPECIAL, EXEMPLARY, OR CONSEQUENTIAL +.\" DAMAGES (INCLUDING, BUT NOT LIMITED TO, PROCUREMENT OF SUBSTITUTE GOODS +.\" OR SERVICES; LOSS OF USE, DATA, OR PROFITS; OR BUSINESS INTERRUPTION) +.\" HOWEVER CAUSED AND ON ANY THEORY OF LIABILITY, WHETHER IN CONTRACT, STRICT +.\" LIABILITY, OR TORT (INCLUDING NEGLIGENCE OR OTHERWISE) ARISING IN ANY WAY +.\" OUT OF THE USE OF THIS SOFTWARE, EVEN IF ADVISED OF THE POSSIBILITY OF +.\" SUCH DAMAGE. +.\" +.\" from: @(#)hypot.3 6.7 (Berkeley) 5/6/91 +.\" $NetBSD: hypot.3,v 1.16 2003/11/02 11:17:16 wiz Exp $ +.\" $DragonFly: src/lib/libm/man/hypot.3,v 1.1 2005/07/26 21:15:20 joerg Exp $ +.\" +.Dd May 6, 1991 +.Dt HYPOT 3 +.Os +.Sh NAME +.Nm hypot , +.Nm hypotf , +.Nm cabs , +.Nm cabsf +.Nd Euclidean distance and complex absolute value functions +.Sh LIBRARY +.Lb libm +.Sh SYNOPSIS +.In math.h +.Ft double +.Fn hypot "double x" "double y" +.Ft float +.Fn hypotf "float x" "float y" +.Ft double +.Fn cabs "struct complex { double x; double y; } z" +.Ft float +.Fn cabsf "struct complex { float x; float y; } z" +.Sh DESCRIPTION +The +.Fn hypot +and +.Fn cabs +functions +compute the +sqrt(x*x+y*y) +in such a way that underflow will not happen, and overflow +occurs only if the final result deserves it. +.Pp +.Fn hypot "\*(If" "v" += +.Fn hypot "v" "\*(If" += +\*(If for all +.Ar v , +including \*(Na. +.Sh ERRORS +Below 0.97 +.Em ulps . +Consequently +.Fn hypot "5.0" "12.0" += 13.0 +exactly; +in general, hypot and cabs return an integer whenever an +integer might be expected. +.Pp +The same cannot be said for the shorter and faster version of hypot +and cabs that is provided in the comments in cabs.c; its error can +exceed 1.2 +.Em ulps . +.Sh NOTES +As might be expected, +.Fn hypot "v" "\*(Na" +and +.Fn hypot "\*(Na" "v" +are \*(Na for all +.Em finite +.Ar v ; +with "reserved operand" in place of "\*(Na", the +same is true on a +.Tn VAX . +But programmers on machines other than a +.Tn VAX +(it has no \*(If) +might be surprised at first to discover that +.Fn hypot "\(+-\*(If" "\*(Na" += +\*(If. +This is intentional; it happens because +.Fn hypot "\*(If" "v" += +\*(If +for +.Em all +.Ar v , +finite or infinite. +Hence +.Fn hypot "\*(If" "v" +is independent of +.Ar v . +Unlike the reserved operand fault on a +.Tn VAX , +the +.Tn IEEE +\*(Na is designed to +disappear when it turns out to be irrelevant, as it does in +.Fn hypot "\*(If" "\*(Na" . +.Sh SEE ALSO +.Xr math 3 , +.Xr sqrt 3 +.Sh HISTORY +Both a +.Fn hypot +function and a +.Fn cabs +function +appeared in +.At v7 . +.Sh BUGS +The +.Fn cabs +and +.Fn cabsf +functions use structures that are not defined in any header and need to +be defined by the user. +As such they cannot be prototyped properly. diff --git a/lib/libm/man/ieee.3 b/lib/libm/man/ieee.3 new file mode 100644 index 0000000000..9876790bbd --- /dev/null +++ b/lib/libm/man/ieee.3 @@ -0,0 +1,169 @@ +.\" Copyright (c) 1985, 1991 Regents of the University of California. +.\" All rights reserved. +.\" +.\" Redistribution and use in source and binary forms, with or without +.\" modification, are permitted provided that the following conditions +.\" are met: +.\" 1. Redistributions of source code must retain the above copyright +.\" notice, this list of conditions and the following disclaimer. +.\" 2. Redistributions in binary form must reproduce the above copyright +.\" notice, this list of conditions and the following disclaimer in the +.\" documentation and/or other materials provided with the distribution. +.\" 3. Neither the name of the University nor the names of its contributors +.\" may be used to endorse or promote products derived from this software +.\" without specific prior written permission. +.\" +.\" THIS SOFTWARE IS PROVIDED BY THE REGENTS AND CONTRIBUTORS ``AS IS'' AND +.\" ANY EXPRESS OR IMPLIED WARRANTIES, INCLUDING, BUT NOT LIMITED TO, THE +.\" IMPLIED WARRANTIES OF MERCHANTABILITY AND FITNESS FOR A PARTICULAR PURPOSE +.\" ARE DISCLAIMED. IN NO EVENT SHALL THE REGENTS OR CONTRIBUTORS BE LIABLE +.\" FOR ANY DIRECT, INDIRECT, INCIDENTAL, SPECIAL, EXEMPLARY, OR CONSEQUENTIAL +.\" DAMAGES (INCLUDING, BUT NOT LIMITED TO, PROCUREMENT OF SUBSTITUTE GOODS +.\" OR SERVICES; LOSS OF USE, DATA, OR PROFITS; OR BUSINESS INTERRUPTION) +.\" HOWEVER CAUSED AND ON ANY THEORY OF LIABILITY, WHETHER IN CONTRACT, STRICT +.\" LIABILITY, OR TORT (INCLUDING NEGLIGENCE OR OTHERWISE) ARISING IN ANY WAY +.\" OUT OF THE USE OF THIS SOFTWARE, EVEN IF ADVISED OF THE POSSIBILITY OF +.\" SUCH DAMAGE. +.\" +.\" from: @(#)ieee.3 6.4 (Berkeley) 5/6/91 +.\" $NetBSD: ieee.3,v 1.19 2003/08/07 16:44:48 agc Exp $ +.\" $DragonFly: src/lib/libm/man/ieee.3,v 1.1 2005/07/26 21:15:20 joerg Exp $ +.\" +.Dd February 25, 1994 +.Dt IEEE 3 +.Os +.Sh NAME +.Nm copysign , +.Nm copysignf , +.Nm finite , +.Nm finitef , +.Nm ilogb , +.Nm ilogbf , +.Nm nextafter , +.Nm nextafterf , +.Nm remainder , +.Nm remainderf , +.Nm scalbn , +.Nm scalbnf +.Nd functions for IEEE arithmetic +.Sh LIBRARY +.Lb libm +.Sh SYNOPSIS +.In math.h +.Ft double +.Fn copysign "double x" "double y" +.Ft float +.Fn copysignf "float x" "float y" +.Ft int +.Fn finite "double x" +.Ft int +.Fn finitef "float x" +.Ft int +.Fn ilogb "double x" +.Ft int +.Fn ilogbf "float x" +.Ft double +.Fn nextafter "double x" "double y" +.Ft float +.Fn nextafterf "float x" "float y" +.Ft double +.Fn remainder "double x" "double y" +.Ft float +.Fn remainderf "float x" "float y" +.Ft double +.Fn scalbn "double x" "int n" +.Ft float +.Fn scalbnf "float x" "int n" +.Sh DESCRIPTION +These functions are required or recommended by +.St -ieee754 . +.Pp +.Fn copysign +returns +.Fa x +with its sign changed to +.Fa y Ns 's . +.Pp +.Fn finite +returns the value 1 just when +\-\*(If \*(Lt +.Fa x +\*(Lt +\*(If; +otherwise a +zero is returned +(when +.Pf \\*(Ba Ns Fa x Ns \\*(Ba += \*(If or +.Fa x +is \*(Na). +.Pp +.Fn ilogb +returns +.Fa x Ns 's exponent +.Fa n , +in integer format. +.Fn ilogb \*(Pm\*(If +returns +.Dv INT_MAX +and +.Fn ilogb 0 +returns +.Dv INT_MIN . +.Pp +.Fn nextafter +returns the next machine representable number from +.Fa x +in direction +.Fa y . +.Pp +.Fn remainder +returns the remainder +.Fa r +:= +.Fa x +\- +.Fa n\(**y +where +.Fa n +is the integer nearest the exact value of +.Bk -words +.Fa x Ns / Ns Fa y ; +.Ek +moreover if +.Pf \\*(Ba Fa n +\- +.Sm off +.Fa x No / Fa y No \\*(Ba +.Sm on += +1/2 +then +.Fa n +is even. +Consequently the remainder is computed exactly and +.Sm off +.Pf \\*(Ba Fa r No \\*(Ba +.Sm on +\*(Le +.Sm off +.Pf \\*(Ba Fa y No \\*(Ba/2 . +.Sm on +But +.Fn remainder x 0 +and +.Fn remainder \*(If 0 +are invalid operations that produce a \*(Na. +.Pp +.Fn scalbn +returns +.Fa x Ns \(**(2** Ns Fa n ) +computed by exponent manipulation. +.Sh SEE ALSO +.Xr math 3 +.Sh STANDARDS +.St -ieee754 +.Sh HISTORY +The +.Nm ieee +functions appeared in +.Bx 4.3 . diff --git a/lib/libc/gen/isinf.3 b/lib/libm/man/ieee_test.3 similarity index 53% copy from lib/libc/gen/isinf.3 copy to lib/libm/man/ieee_test.3 index cf68a79e5d..6e49d46b0e 100644 --- a/lib/libc/gen/isinf.3 +++ b/lib/libm/man/ieee_test.3 @@ -1,5 +1,5 @@ -.\" Copyright (c) 1991, 1993 -.\" The Regents of the University of California. All rights reserved. +.\" Copyright (c) 1985, 1991 Regents of the University of California. +.\" All rights reserved. .\" .\" Redistribution and use in source and binary forms, with or without .\" modification, are permitted provided that the following conditions @@ -9,11 +9,7 @@ .\" 2. Redistributions in binary form must reproduce the above copyright .\" notice, this list of conditions and the following disclaimer in the .\" documentation and/or other materials provided with the distribution. -.\" 3. All advertising materials mentioning features or use of this software -.\" must display the following acknowledgement: -.\" This product includes software developed by the University of -.\" California, Berkeley and its contributors. -.\" 4. Neither the name of the University nor the names of its contributors +.\" 3. Neither the name of the University nor the names of its contributors .\" may be used to endorse or promote products derived from this software .\" without specific prior written permission. .\" @@ -29,54 +25,73 @@ .\" OUT OF THE USE OF THIS SOFTWARE, EVEN IF ADVISED OF THE POSSIBILITY OF .\" SUCH DAMAGE. .\" -.\" @(#)isinf.3 8.2 (Berkeley) 1/29/94 -.\" $FreeBSD: src/lib/libc/gen/isinf.3,v 1.5.2.3 2003/05/04 22:25:22 murray Exp $ -.\" $DragonFly: src/lib/libc/gen/isinf.3,v 1.2 2003/06/17 04:26:42 dillon Exp $ +.\" from: @(#)ieee.3 6.4 (Berkeley) 5/6/91 +.\" $NetBSD: ieee_test.3,v 1.10 2003/08/07 16:44:48 agc Exp $ +.\" $DragonFly: src/lib/libm/man/ieee_test.3,v 1.1 2005/07/26 21:15:20 joerg Exp $ .\" -.Dd January 29, 1994 -.Dt ISINF 3 +.Dd March 10, 1994 +.Dt IEEE_TEST 3 .Os .Sh NAME -.Nm isinf , -.Nm isnan , -.Nm isnanf -.Nd test for infinity or not-a-number +.Nm logb , +.Nm logbf , +.Nm scalb , +.Nm scalbf , +.Nm significand , +.Nm significandf +.Nd IEEE test functions .Sh LIBRARY -.Lb libc +.Lb libm .Sh SYNOPSIS .In math.h -.Ft int -.Fn isinf double -.Ft int -.Fn isnan double -.Ft int -.Fn isnanf float +.Ft double +.Fn logb "double x" +.Ft float +.Fn logbf "float x" +.Ft double +.Fn scalb "double x" "double n" +.Ft float +.Fn scalbf "float x" "float n" +.Ft double +.Fn significand "double x" +.Ft float +.Fn significandf "float x" .Sh DESCRIPTION -The -.Fn isinf -function -returns 1 if the number is -.Dq \\*(If , -otherwise 0. +These functions allow users to test conformance to +.St -ieee754 . +Their use is not otherwise recommended. .Pp -The -.Fn isnan -and -.Fn isnanf -functions -return 1 if the double or float (respectively) is -.Dq not-a-number , -otherwise 0. +.Fn logb x +returns +.Fa x Ns 's exponent +.Fa n , +a signed integer converted to double\-precision floating\-point. +.Fn logb \*(Pm\*(If += +\*(If; +.Fn logb 0 += -\*(If with a division by zero exception. +.Pp +.Fn scalbn x n +returns +.Fa x Ns \(**(2** Ns Fa n ) +computed by exponent manipulation. +.Pp +.Fn significand x +returns +.Fa sig , +where +.Fa x +:= +.Fa sig No \(** 2** Ns Fa n +with 1 \*[Le] +.Fa sig +\*[Lt] 2. +.Fn significand x +is not defined when +.Fa x +is 0, \*(Pm\*(If, or \*(Na. .Sh SEE ALSO +.Xr ieee 3 , .Xr math 3 -.Rs -.%T "IEEE Standard for Binary Floating-Point Arithmetic" -.%Q ANSI -.%R Std 754-1985 -.Re -.Sh BUGS -Neither the -.Tn VAX -nor the Tahoe floating point have distinguished values -for either infinity or not-a-number. -These routines always return 0 on those architectures. +.Sh STANDARDS +.St -ieee754 diff --git a/lib/libm/man/j0.3 b/lib/libm/man/j0.3 new file mode 100644 index 0000000000..1dd591b781 --- /dev/null +++ b/lib/libm/man/j0.3 @@ -0,0 +1,154 @@ +.\" Copyright (c) 1985, 1991 Regents of the University of California. +.\" All rights reserved. +.\" +.\" Redistribution and use in source and binary forms, with or without +.\" modification, are permitted provided that the following conditions +.\" are met: +.\" 1. Redistributions of source code must retain the above copyright +.\" notice, this list of conditions and the following disclaimer. +.\" 2. Redistributions in binary form must reproduce the above copyright +.\" notice, this list of conditions and the following disclaimer in the +.\" documentation and/or other materials provided with the distribution. +.\" 3. Neither the name of the University nor the names of its contributors +.\" may be used to endorse or promote products derived from this software +.\" without specific prior written permission. +.\" +.\" THIS SOFTWARE IS PROVIDED BY THE REGENTS AND CONTRIBUTORS ``AS IS'' AND +.\" ANY EXPRESS OR IMPLIED WARRANTIES, INCLUDING, BUT NOT LIMITED TO, THE +.\" IMPLIED WARRANTIES OF MERCHANTABILITY AND FITNESS FOR A PARTICULAR PURPOSE +.\" ARE DISCLAIMED. IN NO EVENT SHALL THE REGENTS OR CONTRIBUTORS BE LIABLE +.\" FOR ANY DIRECT, INDIRECT, INCIDENTAL, SPECIAL, EXEMPLARY, OR CONSEQUENTIAL +.\" DAMAGES (INCLUDING, BUT NOT LIMITED TO, PROCUREMENT OF SUBSTITUTE GOODS +.\" OR SERVICES; LOSS OF USE, DATA, OR PROFITS; OR BUSINESS INTERRUPTION) +.\" HOWEVER CAUSED AND ON ANY THEORY OF LIABILITY, WHETHER IN CONTRACT, STRICT +.\" LIABILITY, OR TORT (INCLUDING NEGLIGENCE OR OTHERWISE) ARISING IN ANY WAY +.\" OUT OF THE USE OF THIS SOFTWARE, EVEN IF ADVISED OF THE POSSIBILITY OF +.\" SUCH DAMAGE. +.\" +.\" from: @(#)j0.3 6.7 (Berkeley) 4/19/91 +.\" $NetBSD: j0.3,v 1.16 2003/08/07 16:44:48 agc Exp $ +.\" $DragonFly: src/lib/libm/man/j0.3,v 1.1 2005/07/26 21:15:20 joerg Exp $ +.\" +.Dd April 19, 1991 +.Dt J0 3 +.Os +.Sh NAME +.Nm j0 , +.Nm j0f , +.Nm j1 , +.Nm j1f , +.Nm jn , +.Nm jnf , +.Nm y0 , +.Nm y0f , +.Nm y1 , +.Nm y1f , +.Nm yn , +.Nm ynf +.Nd Bessel functions of first and second kind +.Sh LIBRARY +.Lb libm +.Sh SYNOPSIS +.In math.h +.Ft double +.Fn j0 "double x" +.Ft float +.Fn j0f "float x" +.Ft double +.Fn j1 "double x" +.Ft float +.Fn j1f "float x" +.Ft double +.Fn jn "int n" "double x" +.Ft float +.Fn jnf "int n" "float x" +.Ft double +.Fn y0 "double x" +.Ft float +.Fn y0f "float x" +.Ft double +.Fn y1 "double x" +.Ft float +.Fn y1f "float x" +.Ft double +.Fn yn "int n" "double x" +.Ft float +.Fn ynf "int n" "float x" +.Sh DESCRIPTION +The functions +.Fn j0 , +.Fn j0f , +.Fn j1 +and +.Fn j1f +compute the +.Em Bessel function of the first kind of the order +0 and the +.Em order +1, respectively, +for the +real value +.Fa x ; +the functions +.Fn jn +and +.Fn jnf +compute the +.Em Bessel function of the first kind of the integer order +.Fa n +for the real value +.Fa x . +.Pp +The functions +.Fn y0 , +.Fn y0f , +.Fn y1 +and +.Fn y1f +compute the linearly independent +.Em Bessel function of the second kind of the order +0 and the +.Em order +1, respectively, +for the +positive +.Em integer +value +.Fa x +(expressed as a double); +the functions +.Fn yn +and +.Fn ynf +compute the +.Em Bessel function of the second kind for the integer order +.Fa n +for the positive +.Em integer +value +.Fa x +(expressed as a double). +.Sh RETURN VALUES +If these functions are successful, +the computed value is returned, otherwise +the global +variable +.Va errno +is set to +.Er EDOM +and a reserve operand fault is generated. +.\" On the +.\" .Tn VAX +.\" and +.\" .Tn Tahoe +.\" architectures, a negative +.\" .Fa x +.\" value +.\" results in an error. +.Sh SEE ALSO +.Xr math 3 +.\" .Xr matherr 3 +.Sh HISTORY +This set of functions +appeared in +.At v7 . diff --git a/lib/libm/man/lgamma.3 b/lib/libm/man/lgamma.3 new file mode 100644 index 0000000000..b26f74462d --- /dev/null +++ b/lib/libm/man/lgamma.3 @@ -0,0 +1,124 @@ +.\" Copyright (c) 1985, 1991 Regents of the University of California. +.\" All rights reserved. +.\" +.\" Redistribution and use in source and binary forms, with or without +.\" modification, are permitted provided that the following conditions +.\" are met: +.\" 1. Redistributions of source code must retain the above copyright +.\" notice, this list of conditions and the following disclaimer. +.\" 2. Redistributions in binary form must reproduce the above copyright +.\" notice, this list of conditions and the following disclaimer in the +.\" documentation and/or other materials provided with the distribution. +.\" 3. Neither the name of the University nor the names of its contributors +.\" may be used to endorse or promote products derived from this software +.\" without specific prior written permission. +.\" +.\" THIS SOFTWARE IS PROVIDED BY THE REGENTS AND CONTRIBUTORS ``AS IS'' AND +.\" ANY EXPRESS OR IMPLIED WARRANTIES, INCLUDING, BUT NOT LIMITED TO, THE +.\" IMPLIED WARRANTIES OF MERCHANTABILITY AND FITNESS FOR A PARTICULAR PURPOSE +.\" ARE DISCLAIMED. IN NO EVENT SHALL THE REGENTS OR CONTRIBUTORS BE LIABLE +.\" FOR ANY DIRECT, INDIRECT, INCIDENTAL, SPECIAL, EXEMPLARY, OR CONSEQUENTIAL +.\" DAMAGES (INCLUDING, BUT NOT LIMITED TO, PROCUREMENT OF SUBSTITUTE GOODS +.\" OR SERVICES; LOSS OF USE, DATA, OR PROFITS; OR BUSINESS INTERRUPTION) +.\" HOWEVER CAUSED AND ON ANY THEORY OF LIABILITY, WHETHER IN CONTRACT, STRICT +.\" LIABILITY, OR TORT (INCLUDING NEGLIGENCE OR OTHERWISE) ARISING IN ANY WAY +.\" OUT OF THE USE OF THIS SOFTWARE, EVEN IF ADVISED OF THE POSSIBILITY OF +.\" SUCH DAMAGE. +.\" +.\" from: @(#)lgamma.3 6.6 (Berkeley) 12/3/92 +.\" $NetBSD: lgamma.3,v 1.21 2003/08/07 16:44:48 agc Exp $ +.\" $DragonFly: src/lib/libm/man/lgamma.3,v 1.1 2005/07/26 21:15:20 joerg Exp $ +.\" +.Dd December 3, 1992 +.Dt LGAMMA 3 +.Os +.Sh NAME +.Nm lgamma , +.Nm lgammaf , +.Nm lgamma_r , +.Nm lgammaf_r , +.Nm gamma , +.Nm gammaf , +.Nm gamma_r , +.Nm gammaf_r +.Nd log gamma function +.Sh LIBRARY +.Lb libm +.Sh SYNOPSIS +.In math.h +.Ft extern int +.Fa signgam ; +.sp +.Ft double +.Fn lgamma "double x" +.Ft float +.Fn lgammaf "float x" +.Ft double +.Fn lgamma_r "double x" "int *sign" +.Ft float +.Fn lgammaf_r "float x" "int *sign" +.Ft double +.Fn gamma "double x" +.Ft float +.Fn gammaf "float x" +.Ft double +.Fn gamma_r "double x" "int *sign" +.Ft float +.Fn gammaf_r "float x" "int *sign" +.Sh DESCRIPTION +.Fn lgamma x +.if t \{\ +returns ln\||\(*G(x)| where +.Bd -unfilled -offset indent +\(*G(x) = \(is\d\s8\z0\s10\u\u\s8\(if\s10\d t\u\s8x\-1\s10\d e\u\s8\-t\s10\d dt for x \*[Gt] 0 and +.br +\(*G(x) = \(*p/(\(*G(1\-x)\|sin(\(*px)) for x \*[Lt] 1. +.Ed +.\} +.if n \ +returns ln\||\(*G(x)|. +.Pp +The external integer +.Fa signgam +returns the sign of \(*G(x). +.Pp +.Fn lgamma_r +is a reentrant interface that performs identically to +.Fn lgamma , +differing in that the sign of \(*G(x) is stored in the location +pointed to by the +.Fa sign +argument and +.Fa signgam +is not modified. +.Sh IDIOSYNCRASIES +Do not use the expression +.Dq Li signgam\(**exp(lgamma(x)) +to compute g := \(*G(x). +Instead use a program like this (in C): +.Bd -literal -offset indent +lg = lgamma(x); g = signgam\(**exp(lg); +.Ed +.Pp +Only after +.Fn lgamma +has returned can signgam be correct. +.Sh RETURN VALUES +.Fn lgamma +returns appropriate values unless an argument is out of range. +Overflow will occur for sufficiently large positive values, and +non-positive integers. +On the +.Tn VAX , +the reserved operator is returned, +and +.Va errno +is set to +.Er ERANGE . +.Sh SEE ALSO +.Xr math 3 +.Sh HISTORY +The +.Nm lgamma +function appeared in +.Bx 4.3 . diff --git a/lib/libm/man/math.3 b/lib/libm/man/math.3 new file mode 100644 index 0000000000..3256e443d1 --- /dev/null +++ b/lib/libm/man/math.3 @@ -0,0 +1,681 @@ +.\" Copyright (c) 1985 Regents of the University of California. +.\" All rights reserved. +.\" +.\" Redistribution and use in source and binary forms, with or without +.\" modification, are permitted provided that the following conditions +.\" are met: +.\" 1. Redistributions of source code must retain the above copyright +.\" notice, this list of conditions and the following disclaimer. +.\" 2. Redistributions in binary form must reproduce the above copyright +.\" notice, this list of conditions and the following disclaimer in the +.\" documentation and/or other materials provided with the distribution. +.\" 3. Neither the name of the University nor the names of its contributors +.\" may be used to endorse or promote products derived from this software +.\" without specific prior written permission. +.\" +.\" THIS SOFTWARE IS PROVIDED BY THE REGENTS AND CONTRIBUTORS ``AS IS'' AND +.\" ANY EXPRESS OR IMPLIED WARRANTIES, INCLUDING, BUT NOT LIMITED TO, THE +.\" IMPLIED WARRANTIES OF MERCHANTABILITY AND FITNESS FOR A PARTICULAR PURPOSE +.\" ARE DISCLAIMED. IN NO EVENT SHALL THE REGENTS OR CONTRIBUTORS BE LIABLE +.\" FOR ANY DIRECT, INDIRECT, INCIDENTAL, SPECIAL, EXEMPLARY, OR CONSEQUENTIAL +.\" DAMAGES (INCLUDING, BUT NOT LIMITED TO, PROCUREMENT OF SUBSTITUTE GOODS +.\" OR SERVICES; LOSS OF USE, DATA, OR PROFITS; OR BUSINESS INTERRUPTION) +.\" HOWEVER CAUSED AND ON ANY THEORY OF LIABILITY, WHETHER IN CONTRACT, STRICT +.\" LIABILITY, OR TORT (INCLUDING NEGLIGENCE OR OTHERWISE) ARISING IN ANY WAY +.\" OUT OF THE USE OF THIS SOFTWARE, EVEN IF ADVISED OF THE POSSIBILITY OF +.\" SUCH DAMAGE. +.\" +.\" from: @(#)math.3 6.10 (Berkeley) 5/6/91 +.\" $NetBSD: math.3,v 1.18 2003/12/03 23:31:21 jschauma Exp $ +.\" $DragonFly: src/lib/libm/man/math.3,v 1.1 2005/07/26 21:15:20 joerg Exp $ +.\" +.TH MATH 3 "Dec 3, 2003" +.UC 4 +.ds up \fIulp\fR +.ds nn \fINaN\fR +.de If +.if n \\ +\\$1Infinity\\$2 +.if t \\ +\\$1\\(if\\$2 +.. +.SH NAME +math \- introduction to mathematical library functions +.SH DESCRIPTION +These functions constitute the C math library, +.I libm. +The link editor searches this library under the \*(lq\-lm\*(rq option. +Declarations for these functions may be obtained from the include file +.RI \*[Lt] math.h \*[Gt]. +.\" The Fortran math library is described in ``man 3f intro''. +.SH "LIST OF FUNCTIONS" +.sp 2 +.nf +.ta \w'copysign'u+2n +\w'lgamma.3'u+10n +\w'inverse trigonometric func'u +\fIName\fP \fIAppears on Page\fP \fIDescription\fP \fIError Bound (ULPs)\fP +.ta \w'copysign'u+4n +\w'lgamma.3'u+4n +\w'inverse trigonometric function'u+6nC +.sp 5p +acos acos.3 inverse trigonometric function 3 +acosh acosh.3 inverse hyperbolic function 3 +asin asin.3 inverse trigonometric function 3 +asinh asinh.3 inverse hyperbolic function 3 +atan atan.3 inverse trigonometric function 1 +atanh atanh.3 inverse hyperbolic function 3 +atan2 atan2.3 inverse trigonometric function 2 +cabs hypot.3 complex absolute value 1 +cbrt sqrt.3 cube root 1 +ceil ceil.3 integer no less than 0 +copysign ieee.3 copy sign bit 0 +cos cos.3 trigonometric function 1 +cosh cosh.3 hyperbolic function 3 +erf erf.3 error function ??? +erfc erf.3 complementary error function ??? +exp exp.3 exponential 1 +expm1 exp.3 exp(x)\-1 1 +fabs fabs.3 absolute value 0 +finite ieee.3 test for finity 0 +floor floor.3 integer no greater than 0 +fmod fmod.3 remainder ??? +hypot hypot.3 Euclidean distance 1 +ilogb ieee.3 exponent extraction 0 +isinf isinf.3 test for infinity 0 +isnan isnan.3 test for not-a-number 0 +j0 j0.3 Bessel function ??? +j1 j0.3 Bessel function ??? +jn j0.3 Bessel function ??? +lgamma lgamma.3 log gamma function ??? +log exp.3 natural logarithm 1 +log10 exp.3 logarithm to base 10 3 +log1p exp.3 log(1+x) 1 +nextafter ieee.3 next representable number 0 +pow exp.3 exponential x**y 60\-500 +remainder ieee.3 remainder 0 +rint rint.3 round to nearest integer 0 +scalbn ieee.3 exponent adjustment 0 +sin sin.3 trigonometric function 1 +sinh sinh.3 hyperbolic function 3 +sqrt sqrt.3 square root 1 +tan tan.3 trigonometric function 3 +tanh tanh.3 hyperbolic function 3 +y0 j0.3 Bessel function ??? +y1 j0.3 Bessel function ??? +yn j0.3 Bessel function ??? +.ta +.fi +.SH "LIST OF DEFINED VALUES" +.sp 2 +.nf +.ta \w'M_2_SQRTPI'u+2n +\w'1.12837916709551257390'u+4n +\w'2/sqrt(pi)'u+6nC +\fIName\fP \fIValue\fP \fIDescription\fP +.ta \w'M_2_SQRTPI'u+2n +\w'1.12837916709551257390'u+4n +\w'2/sqrt(pi)'u+6nC +.sp 3p +M_E 2.7182818284590452354 e +M_LOG2E 1.4426950408889634074 log 2e +M_LOG10E 0.43429448190325182765 log 10e +M_LN2 0.69314718055994530942 log e2 +M_LN10 2.30258509299404568402 log e10 +M_PI 3.14159265358979323846 pi +M_PI_2 1.57079632679489661923 pi/2 +M_PI_4 0.78539816339744830962 pi/4 +M_1_PI 0.31830988618379067154 1/pi +M_2_PI 0.63661977236758134308 2/pi +M_2_SQRTPI 1.12837916709551257390 2/sqrt(pi) +M_SQRT2 1.41421356237309504880 sqrt(2) +M_SQRT1_2 0.70710678118654752440 1/sqrt(2) +.ta +.fi +.SH NOTES +In 4.3 BSD, distributed from the University of California +in late 1985, most of the foregoing functions come in two +versions, one for the double\-precision "D" format in the +DEC VAX\-11 family of computers, another for double\-precision +arithmetic conforming to the IEEE Standard 754 for Binary +Floating\-Point Arithmetic. +The two versions behave very +similarly, as should be expected from programs more accurate +and robust than was the norm when UNIX was born. +For instance, the programs are accurate to within the numbers +of \*(ups tabulated above; an \*(up is one \fIU\fRnit in the \fIL\fRast +\fIP\fRlace. +And the programs have been cured of anomalies that +afflicted the older math library \fIlibm\fR in which incidents like +the following had been reported: +.RS +sqrt(\-1.0) = 0.0 and log(\-1.0) = \-1.7e38. +.br +cos(1.0e\-11) \*[Gt] cos(0.0) \*[Gt] 1.0. +.br +pow(x,1.0) +.if n \ +!= +.if t \ +\(!= +x when x = 2.0, 3.0, 4.0, ..., 9.0. +.br +pow(\-1.0,1.0e10) trapped on Integer Overflow. +.br +sqrt(1.0e30) and sqrt(1.0e\-30) were very slow. +.RE +However the two versions do differ in ways that have to be +explained, to which end the following notes are provided. +.PP +\fBDEC VAX\-11 D_floating\-point:\fR +.PP +This is the format for which the original math library \fIlibm\fR +was developed, and to which this manual is still principally dedicated. +It is \fIthe\fR double\-precision format for the PDP\-11 +and the earlier VAX\-11 machines; VAX\-11s after 1983 were +provided with an optional "G" format closer to the IEEE +double\-precision format. +The earlier DEC MicroVAXs have no D format, only G double\-precision. +(Why? +Why not?) +.PP +Properties of D_floating\-point: +.RS +Wordsize: 64 bits, 8 bytes. +Radix: Binary. +.br +Precision: 56 +.if n \ +sig. +.if t \ +significant +bits, roughly like 17 +.if n \ +sig. +.if t \ +significant +decimals. +.RS +If x and x' are consecutive positive D_floating\-point +numbers (they differ by 1 \*(up), then +.br +1.3e\-17 \*[Lt] 0.5**56 \*[Lt] (x'\-x)/x \*[Le] 0.5**55 \*[Lt] 2.8e\-17. +.RE +.nf +.ta \w'Range:'u+1n +\w'Underflow threshold'u+1n +\w'= 2.0**127'u+1n +Range: Overflow threshold = 2.0**127 = 1.7e38. + Underflow threshold = 0.5**128 = 2.9e\-39. + NOTE: THIS RANGE IS COMPARATIVELY NARROW. +.ta +.fi +.RS +Overflow customarily stops computation. +.br +Underflow is customarily flushed quietly to zero. +.br +CAUTION: +.RS +It is possible to have x +.if n \ +!= +.if t \ +\(!= +y and yet +x\-y = 0 because of underflow. +Similarly x \*[Gt] y \*[Gt] 0 cannot prevent either x\(**y = 0 +or y/x = 0 from happening without warning. +.RE +.RE +Zero is represented ambiguously. +.RS +Although 2**55 different representations of zero are accepted by +the hardware, only the obvious representation is ever produced. +There is no \-0 on a VAX. +.RE +.If +is not part of the VAX architecture. +.br +Reserved operands: +.RS +of the 2**55 that the hardware +recognizes, only one of them is ever produced. +Any floating\-point operation upon a reserved +operand, even a MOVF or MOVD, customarily stops +computation, so they are not much used. +.RE +Exceptions: +.RS +Divisions by zero and operations that +overflow are invalid operations that customarily +stop computation or, in earlier machines, produce +reserved operands that will stop computation. +.RE +Rounding: +.RS +Every rational operation (+, \-, \(**, /) on a +VAX (but not necessarily on a PDP\-11), if not an +over/underflow nor division by zero, is rounded to +within half an \*(up, and when the rounding error is +exactly half an \*(up then rounding is away from 0. +.RE +.RE +.PP +Except for its narrow range, D_floating\-point is one of the +better computer arithmetics designed in the 1960's. +Its properties are reflected fairly faithfully in the elementary +functions for a VAX distributed in 4.3 BSD. +They over/underflow only if their results have to lie out of range +or very nearly so, and then they behave much as any rational +arithmetic operation that over/underflowed would behave. +Similarly, expressions like log(0) and atanh(1) behave +like 1/0; and sqrt(\-3) and acos(3) behave like 0/0; +they all produce reserved operands and/or stop computation! +The situation is described in more detail in manual pages. +.RS +.ll -0.5i +\fIThis response seems excessively punitive, so it is destined +to be replaced at some time in the foreseeable future by a +more flexible but still uniform scheme being developed to +handle all floating\-point arithmetic exceptions neatly.\fR +.ll +0.5i +.RE +.PP +How do the functions in 4.3 BSD's new \fIlibm\fR for UNIX +compare with their counterparts in DEC's VAX/VMS library? +Some of the VMS functions are a little faster, some are +a little more accurate, some are more puritanical about +exceptions (like pow(0.0,0.0) and atan2(0.0,0.0)), +and most occupy much more memory than their counterparts in +\fIlibm\fR. +The VMS codes interpolate in large table to achieve +speed and accuracy; the \fIlibm\fR codes use tricky formulas +compact enough that all of them may some day fit into a ROM. +.PP +More important, DEC regards the VMS codes as proprietary +and guards them zealously against unauthorized use. +But the \fIlibm\fR codes in 4.3 BSD are intended for the public domain; +they may be copied freely provided their provenance is always +acknowledged, and provided users assist the authors in their +researches by reporting experience with the codes. +Therefore no user of UNIX on a machine whose arithmetic resembles +VAX D_floating\-point need use anything worse than the new \fIlibm\fR. +.PP +\fBIEEE STANDARD 754 Floating\-Point Arithmetic:\fR +.PP +This standard is on its way to becoming more widely adopted +than any other design for computer arithmetic. +VLSI chips that conform to some version of that standard have been +produced by a host of manufacturers, among them ... +.nf +.ta 0.5i +\w'Intel i8070, i80287'u+6n + Intel i8087, i80287 National Semiconductor 32081 + Motorola 68881 Weitek WTL-1032, ... , -1165 + Zilog Z8070 Western Electric (AT\*[Am]T) WE32106. +.ta +.fi +Other implementations range from software, done thoroughly +in the Apple Macintosh, through VLSI in the Hewlett\-Packard +9000 series, to the ELXSI 6400 running ECL at 3 Megaflops. +Several other companies have adopted the formats +of IEEE 754 without, alas, adhering to the standard's way +of handling rounding and exceptions like over/underflow. +The DEC VAX G_floating\-point format is very similar to the IEEE +754 Double format, so similar that the C programs for the +IEEE versions of most of the elementary functions listed +above could easily be converted to run on a MicroVAX, though +nobody has volunteered to do that yet. +.PP +The codes in 4.3 BSD's \fIlibm\fR for machines that conform to +IEEE 754 are intended primarily for the National Semi. 32081 +and WTL 1164/65. +To use these codes with the Intel or Zilog +chips, or with the Apple Macintosh or ELXSI 6400, is to +forego the use of better codes provided (perhaps freely) by +those companies and designed by some of the authors of the +codes above. +Except for \fIatan\fR, \fIcabs\fR, \fIcbrt\fR, \fIerf\fR, +\fIerfc\fR, \fIhypot\fR, \fIj0\-jn\fR, \fIlgamma\fR, \fIpow\fR +and \fIy0\-yn\fR, +the Motorola 68881 has all the functions in \fIlibm\fR on chip, +and faster and more accurate; +it, Apple, the i8087, Z8070 and WE32106 all use 64 +.if n \ +sig. +.if t \ +significant +bits. +The main virtue of 4.3 BSD's +\fIlibm\fR codes is that they are intended for the public domain; +they may be copied freely provided their provenance is always +acknowledged, and provided users assist the authors in their +researches by reporting experience with the codes. +Therefore no user of UNIX on a machine that conforms to +IEEE 754 need use anything worse than the new \fIlibm\fR. +.PP +Properties of IEEE 754 Double\-Precision: +.RS +Wordsize: 64 bits, 8 bytes. +Radix: Binary. +.br +Precision: 53 +.if n \ +sig. +.if t \ +significant +bits, roughly like 16 +.if n \ +sig. +.if t \ +significant +decimals. +.RS +If x and x' are consecutive positive Double\-Precision +numbers (they differ by 1 \*(up), then +.br +1.1e\-16 \*[Lt] 0.5**53 \*[Lt] (x'\-x)/x \*[Le] 0.5**52 \*[Lt] 2.3e\-16. +.RE +.nf +.ta \w'Range:'u+1n +\w'Underflow threshold'u+1n +\w'= 2.0**1024'u+1n +Range: Overflow threshold = 2.0**1024 = 1.8e308 + Underflow threshold = 0.5**1022 = 2.2e\-308 +.ta +.fi +.RS +Overflow goes by default to a signed +.If "" . +.br +Underflow is \fIGradual,\fR rounding to the nearest +integer multiple of 0.5**1074 = 4.9e\-324. +.RE +Zero is represented ambiguously as +0 or \-0. +.RS +Its sign transforms correctly through multiplication or +division, and is preserved by addition of zeros +with like signs; but x\-x yields +0 for every +finite x. +The only operations that reveal zero's +sign are division by zero and copysign(x,\(+-0). +In particular, comparison (x \*[Gt] y, x \*[Ge] y, etc.) +cannot be affected by the sign of zero; but if +finite x = y then +.If +\&= 1/(x\-y) +.if n \ +!= +.if t \ +\(!= +\-1/(y\-x) = +.If \- . +.RE +.If +is signed. +.RS +it persists when added to itself +or to any finite number. +Its sign transforms +correctly through multiplication and division, and +.If (finite)/\(+- \0=\0\(+-0 +(nonzero)/0 = +.If \(+- . +But +.if n \ +Infinity\-Infinity, Infinity\(**0 and Infinity/Infinity +.if t \ +\(if\-\(if, \(if\(**0 and \(if/\(if +are, like 0/0 and sqrt(\-3), +invalid operations that produce \*(nn. ... +.RE +Reserved operands: +.RS +there are 2**53\-2 of them, all +called \*(nn (\fIN\fRot \fIa N\fRumber). +Some, called Signaling \*(nns, trap any floating\-point operation +performed upon them; they are used to mark missing +or uninitialized values, or nonexistent elements of arrays. +The rest are Quiet \*(nns; they are +the default results of Invalid Operations, and +propagate through subsequent arithmetic operations. +If x +.if n \ +!= +.if t \ +\(!= +x then x is \*(nn; every other predicate +(x \*[Gt] y, x = y, x \*[Lt] y, ...) is FALSE if \*(nn is involved. +.br +NOTE: Trichotomy is violated by \*(nn. +.RS +Besides being FALSE, predicates that entail ordered +comparison, rather than mere (in)equality, +signal Invalid Operation when \*(nn is involved. +.RE +.RE +Rounding: +.RS +Every algebraic operation (+, \-, \(**, /, +.if n \ +sqrt) +.if t \ +\(sr) +is rounded by default to within half an \*(up, and +when the rounding error is exactly half an \*(up then +the rounded value's least significant bit is zero. +This kind of rounding is usually the best kind, +sometimes provably so; for instance, for every +x = 1.0, 2.0, 3.0, 4.0, ..., 2.0**52, we find +(x/3.0)\(**3.0 == x and (x/10.0)\(**10.0 == x and ... +despite that both the quotients and the products +have been rounded. +Only rounding like IEEE 754 can do that. +But no single kind of rounding can be +proved best for every circumstance, so IEEE 754 +provides rounding towards zero or towards +.If + +or towards +.If \- +at the programmer's option. +And the same kinds of rounding are specified for +Binary\-Decimal Conversions, at least for magnitudes +between roughly 1.0e\-10 and 1.0e37. +.RE +Exceptions: +.RS +IEEE 754 recognizes five kinds of floating\-point exceptions, +listed below in declining order of probable importance. +.RS +.nf +.ta \w'Invalid Operation'u+6n +\w'Gradual Underflow'u+2n +Exception Default Result +.tc \(ru + +.tc +Invalid Operation \*(nn, or FALSE +.if n \{\ +Overflow \(+-Infinity +Divide by Zero \(+-Infinity \} +.if t \{\ +Overflow \(+-\(if +Divide by Zero \(+-\(if \} +Underflow Gradual Underflow +Inexact Rounded value +.ta +.fi +.RE +NOTE: An Exception is not an Error unless handled badly. +What makes a class of exceptions exceptional +is that no single default response can be satisfactory +in every instance. +On the other hand, if a default +response will serve most instances satisfactorily, +the unsatisfactory instances cannot justify aborting +computation every time the exception occurs. +.RE +.PP +For each kind of floating\-point exception, IEEE 754 +provides a Flag that is raised each time its exception +is signaled, and stays raised until the program resets it. +Programs may also test, save and restore a flag. +Thus, IEEE 754 provides three ways by which programs +may cope with exceptions for which the default result +might be unsatisfactory: +.IP 1) \w'\0\0\0\0'u +Test for a condition that might cause an exception +later, and branch to avoid the exception. +.IP 2) \w'\0\0\0\0'u +Test a flag to see whether an exception has occurred +since the program last reset its flag. +.IP 3) \w'\0\0\0\0'u +Test a result to see whether it is a value that only +an exception could have produced. +.RS +CAUTION: The only reliable ways to discover +whether Underflow has occurred are to test whether +products or quotients lie closer to zero than the +underflow threshold, or to test the Underflow flag. +(Sums and differences cannot underflow in +IEEE 754; if x +.if n \ +!= +.if t \ +\(!= +y then x\-y is correct to +full precision and certainly nonzero regardless of +how tiny it may be.) +Products and quotients that +underflow gradually can lose accuracy gradually +without vanishing, so comparing them with zero +(as one might on a VAX) will not reveal the loss. +Fortunately, if a gradually underflowed value is +destined to be added to something bigger than the +underflow threshold, as is almost always the case, +digits lost to gradual underflow will not be missed +because they would have been rounded off anyway. +So gradual underflows are usually \fIprovably\fR ignorable. +The same cannot be said of underflows flushed to 0. +.RE +.PP +At the option of an implementor conforming to IEEE 754, +other ways to cope with exceptions may be provided: +.IP 4) \w'\0\0\0\0'u +ABORT. +This mechanism classifies an exception in +advance as an incident to be handled by means +traditionally associated with error\-handling +statements like "ON ERROR GO TO ...". +Different languages offer different forms of this statement, +but most share the following characteristics: +.IP \(em \w'\0\0\0\0'u +No means is provided to substitute a value for +the offending operation's result and resume +computation from what may be the middle of an expression. +An exceptional result is abandoned. +.IP \(em \w'\0\0\0\0'u +In a subprogram that lacks an error\-handling +statement, an exception causes the subprogram to +abort within whatever program called it, and so +on back up the chain of calling subprograms until +an error\-handling statement is encountered or the +whole task is aborted and memory is dumped. +.IP 5) \w'\0\0\0\0'u +STOP. +This mechanism, requiring an interactive +debugging environment, is more for the programmer +than the program. +It classifies an exception in +advance as a symptom of a programmer's error; the +exception suspends execution as near as it can to +the offending operation so that the programmer can +look around to see how it happened. +Quite often +the first several exceptions turn out to be quite +unexceptionable, so the programmer ought ideally +to be able to resume execution after each one as if +execution had not been stopped. +.IP 6) \w'\0\0\0\0'u +\&... Other ways lie beyond the scope of this document. +.RE +.PP +The crucial problem for exception handling is the problem of +Scope, and the problem's solution is understood, but not +enough manpower was available to implement it fully in time +to be distributed in 4.3 BSD's \fIlibm\fR. +Ideally, each elementary function should act +as if it were indivisible, or atomic, in the sense that ... +.IP i) \w'iii)'u+2n +No exception should be signaled that is not deserved by +the data supplied to that function. +.IP ii) \w'iii)'u+2n +Any exception signaled should be identified with that +function rather than with one of its subroutines. +.IP iii) \w'iii)'u+2n +The internal behavior of an atomic function should not +be disrupted when a calling program changes from +one to another of the five or so ways of handling +exceptions listed above, although the definition +of the function may be correlated intentionally +with exception handling. +.PP +Ideally, every programmer should be able \fIconveniently\fR to +turn a debugged subprogram into one that appears atomic to +its users. +But simulating all three characteristics of an +atomic function is still a tedious affair, entailing hosts +of tests and saves\-restores; work is under way to ameliorate +the inconvenience. +.PP +Meanwhile, the functions in \fIlibm\fR are only approximately atomic. +They signal no inappropriate exception except possibly ... +.RS +Over/Underflow +.RS +when a result, if properly computed, might have lain barely within range, and +.RE +Inexact in \fIcabs\fR, \fIcbrt\fR, \fIhypot\fR, \fIlog10\fR and \fIpow\fR +.RS +when it happens to be exact, thanks to fortuitous cancellation of errors. +.RE +.RE +Otherwise, ... +.RS +Invalid Operation is signaled only when +.RS +any result but \*(nn would probably be misleading. +.RE +Overflow is signaled only when +.RS +the exact result would be finite but beyond the overflow threshold. +.RE +Divide\-by\-Zero is signaled only when +.RS +a function takes exactly infinite values at finite operands. +.RE +Underflow is signaled only when +.RS +the exact result would be nonzero but tinier than the underflow threshold. +.RE +Inexact is signaled only when +.RS +greater range or precision would be needed to represent the exact result. +.RE +.RE +.\" .Sh FILES +.\" .Bl -tag -width /usr/lib/libm_p.a -compact +.\" .It Pa /usr/lib/libm.a +.\" the static math library +.\" .It Pa /usr/lib/libm.so +.\" the dynamic math library +.\" .It Pa /usr/lib/libm_p.a +.\" the static math library compiled for profiling +.\" .El +.SH SEE ALSO +An explanation of IEEE 754 and its proposed extension p854 +was published in the IEEE magazine MICRO in August 1984 under +the title "A Proposed Radix\- and Word\-length\-independent +Standard for Floating\-point Arithmetic" by W. J. Cody et al. +The manuals for Pascal, C and BASIC on the Apple Macintosh +document the features of IEEE 754 pretty well. +Articles in the IEEE magazine COMPUTER vol. 14 no. 3 (Mar. 1981), +and in the ACM SIGNUM Newsletter Special Issue of +Oct. 1979, may be helpful although they pertain to +superseded drafts of the standard. +.SH BUGS +When signals are appropriate, they are emitted by certain +operations within the codes, so a subroutine\-trace may be +needed to identify the function with its signal in case +method 5) above is in use. +And the codes all take the +IEEE 754 defaults for granted; this means that a decision to +trap all divisions by zero could disrupt a code that would +otherwise get correct results despite division by zero. diff --git a/lib/libc/gen/isinf.3 b/lib/libm/man/rint.3 similarity index 55% copy from lib/libc/gen/isinf.3 copy to lib/libm/man/rint.3 index cf68a79e5d..91c6ba817f 100644 --- a/lib/libc/gen/isinf.3 +++ b/lib/libm/man/rint.3 @@ -1,5 +1,5 @@ -.\" Copyright (c) 1991, 1993 -.\" The Regents of the University of California. All rights reserved. +.\" Copyright (c) 1985, 1991 Regents of the University of California. +.\" All rights reserved. .\" .\" Redistribution and use in source and binary forms, with or without .\" modification, are permitted provided that the following conditions @@ -9,11 +9,7 @@ .\" 2. Redistributions in binary form must reproduce the above copyright .\" notice, this list of conditions and the following disclaimer in the .\" documentation and/or other materials provided with the distribution. -.\" 3. All advertising materials mentioning features or use of this software -.\" must display the following acknowledgement: -.\" This product includes software developed by the University of -.\" California, Berkeley and its contributors. -.\" 4. Neither the name of the University nor the names of its contributors +.\" 3. Neither the name of the University nor the names of its contributors .\" may be used to endorse or promote products derived from this software .\" without specific prior written permission. .\" @@ -29,54 +25,41 @@ .\" OUT OF THE USE OF THIS SOFTWARE, EVEN IF ADVISED OF THE POSSIBILITY OF .\" SUCH DAMAGE. .\" -.\" @(#)isinf.3 8.2 (Berkeley) 1/29/94 -.\" $FreeBSD: src/lib/libc/gen/isinf.3,v 1.5.2.3 2003/05/04 22:25:22 murray Exp $ -.\" $DragonFly: src/lib/libc/gen/isinf.3,v 1.2 2003/06/17 04:26:42 dillon Exp $ +.\" from: @(#)rint.3 5.1 (Berkeley) 5/2/91 +.\" $NetBSD: rint.3,v 1.12 2003/08/07 16:44:48 agc Exp $ +.\" $DragonFly: src/lib/libm/man/rint.3,v 1.1 2005/07/26 21:15:20 joerg Exp $ .\" -.Dd January 29, 1994 -.Dt ISINF 3 +.Dd March 10, 1994 +.Dt RINT 3 .Os .Sh NAME -.Nm isinf , -.Nm isnan , -.Nm isnanf -.Nd test for infinity or not-a-number +.Nm rint , +.Nm rintf +.Nd round to integral value in floating-point format .Sh LIBRARY -.Lb libc +.Lb libm .Sh SYNOPSIS .In math.h -.Ft int -.Fn isinf double -.Ft int -.Fn isnan double -.Ft int -.Fn isnanf float +.Ft double +.Fn rint "double x" +.Ft float +.Fn rintf "float x" .Sh DESCRIPTION The -.Fn isinf -function -returns 1 if the number is -.Dq \\*(If , -otherwise 0. -.Pp -The -.Fn isnan -and -.Fn isnanf -functions -return 1 if the double or float (respectively) is -.Dq not-a-number , -otherwise 0. +.Fn rint +function returns the integral value (represented as a double precision number) +nearest to +.Fa x +according to the prevailing rounding mode. .Sh SEE ALSO +.Xr abs 3 , +.Xr ceil 3 , +.Xr fabs 3 , +.Xr floor 3 , +.Xr ieee 3 , .Xr math 3 -.Rs -.%T "IEEE Standard for Binary Floating-Point Arithmetic" -.%Q ANSI -.%R Std 754-1985 -.Re -.Sh BUGS -Neither the -.Tn VAX -nor the Tahoe floating point have distinguished values -for either infinity or not-a-number. -These routines always return 0 on those architectures. +.Sh HISTORY +A +.Fn rint +function appeared in +.At v6 . diff --git a/lib/libc/gen/isinf.3 b/lib/libm/man/round.3 similarity index 50% copy from lib/libc/gen/isinf.3 copy to lib/libm/man/round.3 index cf68a79e5d..a3136e6088 100644 --- a/lib/libc/gen/isinf.3 +++ b/lib/libm/man/round.3 @@ -1,5 +1,5 @@ -.\" Copyright (c) 1991, 1993 -.\" The Regents of the University of California. All rights reserved. +.\" Copyright (c) 2003, Steven G. Kargl +.\" All rights reserved. .\" .\" Redistribution and use in source and binary forms, with or without .\" modification, are permitted provided that the following conditions @@ -9,13 +9,6 @@ .\" 2. Redistributions in binary form must reproduce the above copyright .\" notice, this list of conditions and the following disclaimer in the .\" documentation and/or other materials provided with the distribution. -.\" 3. All advertising materials mentioning features or use of this software -.\" must display the following acknowledgement: -.\" This product includes software developed by the University of -.\" California, Berkeley and its contributors. -.\" 4. Neither the name of the University nor the names of its contributors -.\" may be used to endorse or promote products derived from this software -.\" without specific prior written permission. .\" .\" THIS SOFTWARE IS PROVIDED BY THE REGENTS AND CONTRIBUTORS ``AS IS'' AND .\" ANY EXPRESS OR IMPLIED WARRANTIES, INCLUDING, BUT NOT LIMITED TO, THE @@ -29,54 +22,53 @@ .\" OUT OF THE USE OF THIS SOFTWARE, EVEN IF ADVISED OF THE POSSIBILITY OF .\" SUCH DAMAGE. .\" -.\" @(#)isinf.3 8.2 (Berkeley) 1/29/94 -.\" $FreeBSD: src/lib/libc/gen/isinf.3,v 1.5.2.3 2003/05/04 22:25:22 murray Exp $ -.\" $DragonFly: src/lib/libc/gen/isinf.3,v 1.2 2003/06/17 04:26:42 dillon Exp $ +.\" $FreeBSD: src/lib/msun/man/round.3,v 1.2 2004/06/20 09:27:17 das Exp $ +.\" $NetBSD: round.3,v 1.3 2004/07/15 12:12:39 junyoung Exp $ +.\" $DragonFly: src/lib/libm/man/round.3,v 1.1 2005/07/26 21:15:20 joerg Exp $ .\" -.Dd January 29, 1994 -.Dt ISINF 3 +.Dd July 15, 2004 +.Dt ROUND 3 .Os .Sh NAME -.Nm isinf , -.Nm isnan , -.Nm isnanf -.Nd test for infinity or not-a-number +.Nm round , +.Nm roundf +.Nd round to nearest integral value .Sh LIBRARY -.Lb libc +.Lb libm .Sh SYNOPSIS .In math.h -.Ft int -.Fn isinf double -.Ft int -.Fn isnan double -.Ft int -.Fn isnanf float +.Ft double +.Fn round "double x" +.Ft float +.Fn roundf "float x" .Sh DESCRIPTION The -.Fn isinf -function -returns 1 if the number is -.Dq \\*(If , -otherwise 0. -.Pp -The -.Fn isnan +.Fn round and -.Fn isnanf -functions -return 1 if the double or float (respectively) is -.Dq not-a-number , -otherwise 0. +.Fn roundf +functions return the nearest integral value to +.Fa x ; +if +.Fa x +lies halfway between two integral values, then these +functions return the integral value with the larger +absolute value (i.e., they round away from zero). .Sh SEE ALSO -.Xr math 3 -.Rs -.%T "IEEE Standard for Binary Floating-Point Arithmetic" -.%Q ANSI -.%R Std 754-1985 -.Re -.Sh BUGS -Neither the -.Tn VAX -nor the Tahoe floating point have distinguished values -for either infinity or not-a-number. -These routines always return 0 on those architectures. +.Xr ceil 3 , +.Xr floor 3 , +.Xr ieee 3 , +.Xr math 3 , +.Xr rint 3 +.\" .Xr trunc 3 +.Sh STANDARDS +The +.Fn round +function conforms to +.St -isoC-99 . +.Sh HISTORY +The +.Fn round +and +.Fn roundf +functions appeared in +.Nx 2.0 . diff --git a/lib/libc/gen/isinf.3 b/lib/libm/man/sin.3 similarity index 54% copy from lib/libc/gen/isinf.3 copy to lib/libm/man/sin.3 index cf68a79e5d..d7a4d373ed 100644 --- a/lib/libc/gen/isinf.3 +++ b/lib/libm/man/sin.3 @@ -1,5 +1,5 @@ -.\" Copyright (c) 1991, 1993 -.\" The Regents of the University of California. All rights reserved. +.\" Copyright (c) 1991 The Regents of the University of California. +.\" All rights reserved. .\" .\" Redistribution and use in source and binary forms, with or without .\" modification, are permitted provided that the following conditions @@ -9,11 +9,7 @@ .\" 2. Redistributions in binary form must reproduce the above copyright .\" notice, this list of conditions and the following disclaimer in the .\" documentation and/or other materials provided with the distribution. -.\" 3. All advertising materials mentioning features or use of this software -.\" must display the following acknowledgement: -.\" This product includes software developed by the University of -.\" California, Berkeley and its contributors. -.\" 4. Neither the name of the University nor the names of its contributors +.\" 3. Neither the name of the University nor the names of its contributors .\" may be used to endorse or promote products derived from this software .\" without specific prior written permission. .\" @@ -29,54 +25,50 @@ .\" OUT OF THE USE OF THIS SOFTWARE, EVEN IF ADVISED OF THE POSSIBILITY OF .\" SUCH DAMAGE. .\" -.\" @(#)isinf.3 8.2 (Berkeley) 1/29/94 -.\" $FreeBSD: src/lib/libc/gen/isinf.3,v 1.5.2.3 2003/05/04 22:25:22 murray Exp $ -.\" $DragonFly: src/lib/libc/gen/isinf.3,v 1.2 2003/06/17 04:26:42 dillon Exp $ +.\" from: @(#)sin.3 6.7 (Berkeley) 4/19/91 +.\" $NetBSD: sin.3,v 1.14 2003/08/07 16:44:49 agc Exp $ +.\" $DragonFly: src/lib/libm/man/sin.3,v 1.1 2005/07/26 21:15:20 joerg Exp $ .\" -.Dd January 29, 1994 -.Dt ISINF 3 +.Dd April 19, 1991 +.Dt SIN 3 .Os .Sh NAME -.Nm isinf , -.Nm isnan , -.Nm isnanf -.Nd test for infinity or not-a-number +.Nm sin , +.Nm sinf +.Nd sine function .Sh LIBRARY -.Lb libc +.Lb libm .Sh SYNOPSIS .In math.h -.Ft int -.Fn isinf double -.Ft int -.Fn isnan double -.Ft int -.Fn isnanf float +.Ft double +.Fn sin "double x" +.Ft float +.Fn sinf "float x" .Sh DESCRIPTION The -.Fn isinf -function -returns 1 if the number is -.Dq \\*(If , -otherwise 0. -.Pp +.Fn sin +function computes the sine of +.Fa x +(measured in radians). +A large magnitude argument may yield a result with little +or no significance. +.Sh RETURN VALUES The -.Fn isnan -and -.Fn isnanf -functions -return 1 if the double or float (respectively) is -.Dq not-a-number , -otherwise 0. +.Fn sin +function returns the sine value. .Sh SEE ALSO -.Xr math 3 -.Rs -.%T "IEEE Standard for Binary Floating-Point Arithmetic" -.%Q ANSI -.%R Std 754-1985 -.Re -.Sh BUGS -Neither the -.Tn VAX -nor the Tahoe floating point have distinguished values -for either infinity or not-a-number. -These routines always return 0 on those architectures. +.Xr acos 3 , +.Xr asin 3 , +.Xr atan 3 , +.Xr atan2 3 , +.Xr cos 3 , +.Xr cosh 3 , +.Xr math 3 , +.Xr sinh 3 , +.Xr tan 3 , +.Xr tanh 3 +.Sh STANDARDS +The +.Fn sin +function conforms to +.St -ansiC . diff --git a/lib/libc/gen/isinf.3 b/lib/libm/man/sinh.3 similarity index 54% copy from lib/libc/gen/isinf.3 copy to lib/libm/man/sinh.3 index cf68a79e5d..263dd6039a 100644 --- a/lib/libc/gen/isinf.3 +++ b/lib/libm/man/sinh.3 @@ -1,5 +1,5 @@ -.\" Copyright (c) 1991, 1993 -.\" The Regents of the University of California. All rights reserved. +.\" Copyright (c) 1991 The Regents of the University of California. +.\" All rights reserved. .\" .\" Redistribution and use in source and binary forms, with or without .\" modification, are permitted provided that the following conditions @@ -9,11 +9,7 @@ .\" 2. Redistributions in binary form must reproduce the above copyright .\" notice, this list of conditions and the following disclaimer in the .\" documentation and/or other materials provided with the distribution. -.\" 3. All advertising materials mentioning features or use of this software -.\" must display the following acknowledgement: -.\" This product includes software developed by the University of -.\" California, Berkeley and its contributors. -.\" 4. Neither the name of the University nor the names of its contributors +.\" 3. Neither the name of the University nor the names of its contributors .\" may be used to endorse or promote products derived from this software .\" without specific prior written permission. .\" @@ -29,54 +25,53 @@ .\" OUT OF THE USE OF THIS SOFTWARE, EVEN IF ADVISED OF THE POSSIBILITY OF .\" SUCH DAMAGE. .\" -.\" @(#)isinf.3 8.2 (Berkeley) 1/29/94 -.\" $FreeBSD: src/lib/libc/gen/isinf.3,v 1.5.2.3 2003/05/04 22:25:22 murray Exp $ -.\" $DragonFly: src/lib/libc/gen/isinf.3,v 1.2 2003/06/17 04:26:42 dillon Exp $ +.\" from: @(#)sinh.3 6.6 (Berkeley) 4/19/91 +.\" $NetBSD: sinh.3,v 1.14 2003/08/07 16:44:49 agc Exp $ +.\" $DragonFly: src/lib/libm/man/sinh.3,v 1.1 2005/07/26 21:15:20 joerg Exp $ .\" -.Dd January 29, 1994 -.Dt ISINF 3 +.Dd April 19, 1991 +.Dt SINH 3 .Os .Sh NAME -.Nm isinf , -.Nm isnan , -.Nm isnanf -.Nd test for infinity or not-a-number +.Nm sinh , +.Nm sinhf +.Nd hyperbolic sine function .Sh LIBRARY -.Lb libc +.Lb libm .Sh SYNOPSIS .In math.h -.Ft int -.Fn isinf double -.Ft int -.Fn isnan double -.Ft int -.Fn isnanf float +.Ft double +.Fn sinh "double x" +.Ft float +.Fn sinhf "float x" .Sh DESCRIPTION The -.Fn isinf -function -returns 1 if the number is -.Dq \\*(If , -otherwise 0. -.Pp +.Fn sinh +function computes the hyperbolic sine of +.Fa x . +.Sh RETURN VALUES The -.Fn isnan -and -.Fn isnanf -functions -return 1 if the double or float (respectively) is -.Dq not-a-number , -otherwise 0. +.Fn sinh +function returns the hyperbolic sine value unless +the magnitude of +.Fa x +is too large; in this event, the global variable +.Va errno +is set to +.Er ERANGE . .Sh SEE ALSO -.Xr math 3 -.Rs -.%T "IEEE Standard for Binary Floating-Point Arithmetic" -.%Q ANSI -.%R Std 754-1985 -.Re -.Sh BUGS -Neither the -.Tn VAX -nor the Tahoe floating point have distinguished values -for either infinity or not-a-number. -These routines always return 0 on those architectures. +.Xr acos 3 , +.Xr asin 3 , +.Xr atan 3 , +.Xr atan2 3 , +.Xr cos 3 , +.Xr cosh 3 , +.Xr math 3 , +.Xr sin 3 , +.Xr tan 3 , +.Xr tanh 3 +.Sh STANDARDS +The +.Fn sinh +function conforms to +.St -ansiC . diff --git a/lib/libc/gen/isinf.3 b/lib/libm/man/sqrt.3 similarity index 55% copy from lib/libc/gen/isinf.3 copy to lib/libm/man/sqrt.3 index cf68a79e5d..c520d62429 100644 --- a/lib/libc/gen/isinf.3 +++ b/lib/libm/man/sqrt.3 @@ -1,5 +1,5 @@ -.\" Copyright (c) 1991, 1993 -.\" The Regents of the University of California. All rights reserved. +.\" Copyright (c) 1985, 1991 Regents of the University of California. +.\" All rights reserved. .\" .\" Redistribution and use in source and binary forms, with or without .\" modification, are permitted provided that the following conditions @@ -9,11 +9,7 @@ .\" 2. Redistributions in binary form must reproduce the above copyright .\" notice, this list of conditions and the following disclaimer in the .\" documentation and/or other materials provided with the distribution. -.\" 3. All advertising materials mentioning features or use of this software -.\" must display the following acknowledgement: -.\" This product includes software developed by the University of -.\" California, Berkeley and its contributors. -.\" 4. Neither the name of the University nor the names of its contributors +.\" 3. Neither the name of the University nor the names of its contributors .\" may be used to endorse or promote products derived from this software .\" without specific prior written permission. .\" @@ -29,54 +25,68 @@ .\" OUT OF THE USE OF THIS SOFTWARE, EVEN IF ADVISED OF THE POSSIBILITY OF .\" SUCH DAMAGE. .\" -.\" @(#)isinf.3 8.2 (Berkeley) 1/29/94 -.\" $FreeBSD: src/lib/libc/gen/isinf.3,v 1.5.2.3 2003/05/04 22:25:22 murray Exp $ -.\" $DragonFly: src/lib/libc/gen/isinf.3,v 1.2 2003/06/17 04:26:42 dillon Exp $ +.\" from: @(#)sqrt.3 6.4 (Berkeley) 5/6/91 +.\" $NetBSD: sqrt.3,v 1.13 2003/08/07 16:44:49 agc Exp $ +.\" $DragonFly: src/lib/libm/man/sqrt.3,v 1.1 2005/07/26 21:15:20 joerg Exp $ .\" -.Dd January 29, 1994 -.Dt ISINF 3 +.Dd May 6, 1991 +.Dt SQRT 3 .Os .Sh NAME -.Nm isinf , -.Nm isnan , -.Nm isnanf -.Nd test for infinity or not-a-number +.Nm cbrt , +.Nm cbrtf , +.Nm sqrt , +.Nm sqrtf +.Nd cube root and square root functions .Sh LIBRARY -.Lb libc +.Lb libm .Sh SYNOPSIS .In math.h -.Ft int -.Fn isinf double -.Ft int -.Fn isnan double -.Ft int -.Fn isnanf float +.Ft double +.Fn cbrt "double x" +.Ft float +.Fn cbrtf "float x" +.Ft double +.Fn sqrt "double x" +.Ft float +.Fn sqrtf "float x" .Sh DESCRIPTION The -.Fn isinf -function -returns 1 if the number is -.Dq \\*(If , -otherwise 0. +.Fn cbrt +and +.Fn cbrtf +functions compute +the cube root of +.Ar x . .Pp The -.Fn isnan +.Fn sqrt +and +.Fn sqrtf +functions compute +the non-negative square root of x. +.Sh RETURN VALUES +If x is negative, +.Fn sqrt "x" and -.Fn isnanf -functions -return 1 if the double or float (respectively) is -.Dq not-a-number , -otherwise 0. +.Fn sqrtf "x" +.\" POSIX_MODE +set the global variable +.Va errno +to EDOM. +.\" SYSV_MODE +.\" call +.\" .Xr matherr 3 . .Sh SEE ALSO .Xr math 3 -.Rs -.%T "IEEE Standard for Binary Floating-Point Arithmetic" -.%Q ANSI -.%R Std 754-1985 -.Re -.Sh BUGS -Neither the -.Tn VAX -nor the Tahoe floating point have distinguished values -for either infinity or not-a-number. -These routines always return 0 on those architectures. +.\" .Xr matherr 3 +.Sh STANDARDS +The +.Fn sqrt +function conforms to +.St -ansiC . +.Sh HISTORY +The +.Fn cbrt +function appeared in +.Bx 4.3 . diff --git a/lib/libc/gen/isinf.3 b/lib/libm/man/tan.3 similarity index 54% copy from lib/libc/gen/isinf.3 copy to lib/libm/man/tan.3 index cf68a79e5d..c28df3ec9e 100644 --- a/lib/libc/gen/isinf.3 +++ b/lib/libm/man/tan.3 @@ -1,5 +1,5 @@ -.\" Copyright (c) 1991, 1993 -.\" The Regents of the University of California. All rights reserved. +.\" Copyright (c) 1991 The Regents of the University of California. +.\" All rights reserved. .\" .\" Redistribution and use in source and binary forms, with or without .\" modification, are permitted provided that the following conditions @@ -9,11 +9,7 @@ .\" 2. Redistributions in binary form must reproduce the above copyright .\" notice, this list of conditions and the following disclaimer in the .\" documentation and/or other materials provided with the distribution. -.\" 3. All advertising materials mentioning features or use of this software -.\" must display the following acknowledgement: -.\" This product includes software developed by the University of -.\" California, Berkeley and its contributors. -.\" 4. Neither the name of the University nor the names of its contributors +.\" 3. Neither the name of the University nor the names of its contributors .\" may be used to endorse or promote products derived from this software .\" without specific prior written permission. .\" @@ -29,54 +25,54 @@ .\" OUT OF THE USE OF THIS SOFTWARE, EVEN IF ADVISED OF THE POSSIBILITY OF .\" SUCH DAMAGE. .\" -.\" @(#)isinf.3 8.2 (Berkeley) 1/29/94 -.\" $FreeBSD: src/lib/libc/gen/isinf.3,v 1.5.2.3 2003/05/04 22:25:22 murray Exp $ -.\" $DragonFly: src/lib/libc/gen/isinf.3,v 1.2 2003/06/17 04:26:42 dillon Exp $ +.\" from: @(#)tan.3 5.1 (Berkeley) 5/2/91 +.\" $NetBSD: tan.3,v 1.13 2003/08/07 16:44:49 agc Exp $ +.\" $DragonFly: src/lib/libm/man/tan.3,v 1.1 2005/07/26 21:15:20 joerg Exp $ .\" -.Dd January 29, 1994 -.Dt ISINF 3 +.Dd May 2, 1991 +.Dt TAN 3 .Os .Sh NAME -.Nm isinf , -.Nm isnan , -.Nm isnanf -.Nd test for infinity or not-a-number +.Nm tan , +.Nm tanf +.Nd tangent function .Sh LIBRARY -.Lb libc +.Lb libm .Sh SYNOPSIS .In math.h -.Ft int -.Fn isinf double -.Ft int -.Fn isnan double -.Ft int -.Fn isnanf float +.Ft double +.Fn tan "double x" +.Ft float +.Fn tanf "float x" .Sh DESCRIPTION The -.Fn isinf -function -returns 1 if the number is -.Dq \\*(If , -otherwise 0. -.Pp -The -.Fn isnan +.Fn tan and -.Fn isnanf -functions -return 1 if the double or float (respectively) is -.Dq not-a-number , -otherwise 0. +.Fn tanf +functions compute the tangent of +.Fa x +(measured in radians). +A large magnitude argument may yield a result +with little or no significance. +For a discussion of error due to roundoff, see +.Xr math 3 . +.Sh RETURN VALUES +The +.Fn tan +function returns the tangent value. .Sh SEE ALSO -.Xr math 3 -.Rs -.%T "IEEE Standard for Binary Floating-Point Arithmetic" -.%Q ANSI -.%R Std 754-1985 -.Re -.Sh BUGS -Neither the -.Tn VAX -nor the Tahoe floating point have distinguished values -for either infinity or not-a-number. -These routines always return 0 on those architectures. +.Xr acos 3 , +.Xr asin 3 , +.Xr atan 3 , +.Xr atan2 3 , +.Xr cos 3 , +.Xr cosh 3 , +.Xr math 3 , +.Xr sin 3 , +.Xr sinh 3 , +.Xr tanh 3 +.Sh STANDARDS +The +.Fn tan +function conforms to +.St -ansiC . diff --git a/lib/libc/gen/isinf.3 b/lib/libm/man/tanh.3 similarity index 54% copy from lib/libc/gen/isinf.3 copy to lib/libm/man/tanh.3 index cf68a79e5d..3b53b5ec15 100644 --- a/lib/libc/gen/isinf.3 +++ b/lib/libm/man/tanh.3 @@ -1,5 +1,5 @@ -.\" Copyright (c) 1991, 1993 -.\" The Regents of the University of California. All rights reserved. +.\" Copyright (c) 1991 The Regents of the University of California. +.\" All rights reserved. .\" .\" Redistribution and use in source and binary forms, with or without .\" modification, are permitted provided that the following conditions @@ -9,11 +9,7 @@ .\" 2. Redistributions in binary form must reproduce the above copyright .\" notice, this list of conditions and the following disclaimer in the .\" documentation and/or other materials provided with the distribution. -.\" 3. All advertising materials mentioning features or use of this software -.\" must display the following acknowledgement: -.\" This product includes software developed by the University of -.\" California, Berkeley and its contributors. -.\" 4. Neither the name of the University nor the names of its contributors +.\" 3. Neither the name of the University nor the names of its contributors .\" may be used to endorse or promote products derived from this software .\" without specific prior written permission. .\" @@ -29,54 +25,51 @@ .\" OUT OF THE USE OF THIS SOFTWARE, EVEN IF ADVISED OF THE POSSIBILITY OF .\" SUCH DAMAGE. .\" -.\" @(#)isinf.3 8.2 (Berkeley) 1/29/94 -.\" $FreeBSD: src/lib/libc/gen/isinf.3,v 1.5.2.3 2003/05/04 22:25:22 murray Exp $ -.\" $DragonFly: src/lib/libc/gen/isinf.3,v 1.2 2003/06/17 04:26:42 dillon Exp $ +.\" from: @(#)tanh.3 5.1 (Berkeley) 5/2/91 +.\" $NetBSD: tanh.3,v 1.12 2003/08/07 16:44:49 agc Exp $ +.\" $DragonFly: src/lib/libm/man/tanh.3,v 1.1 2005/07/26 21:15:20 joerg Exp $ .\" -.Dd January 29, 1994 -.Dt ISINF 3 +.Dd May 2, 1991 +.Dt TANH 3 .Os .Sh NAME -.Nm isinf , -.Nm isnan , -.Nm isnanf -.Nd test for infinity or not-a-number +.Nm tanh , +.Nm tanhf +.Nd hyperbolic tangent function .Sh LIBRARY -.Lb libc +.Lb libm .Sh SYNOPSIS .In math.h -.Ft int -.Fn isinf double -.Ft int -.Fn isnan double -.Ft int -.Fn isnanf float +.Ft double +.Fn tanh "double x" +.Ft float +.Fn tanhf "float x" .Sh DESCRIPTION The -.Fn isinf -function -returns 1 if the number is -.Dq \\*(If , -otherwise 0. -.Pp -The -.Fn isnan +.Fn tanh and -.Fn isnanf -functions -return 1 if the double or float (respectively) is -.Dq not-a-number , -otherwise 0. +.Fn tanhf +functions compute the hyperbolic tangent of +.Fa x . +For a discussion of error due to roundoff, see +.Xr math 3 . +.Sh RETURN VALUES +The +.Fn tanh +function returns the hyperbolic tangent value. .Sh SEE ALSO -.Xr math 3 -.Rs -.%T "IEEE Standard for Binary Floating-Point Arithmetic" -.%Q ANSI -.%R Std 754-1985 -.Re -.Sh BUGS -Neither the -.Tn VAX -nor the Tahoe floating point have distinguished values -for either infinity or not-a-number. -These routines always return 0 on those architectures. +.Xr acos 3 , +.Xr asin 3 , +.Xr atan 3 , +.Xr atan2 3 , +.Xr cos 3 , +.Xr cosh 3 , +.Xr math 3 , +.Xr sin 3 , +.Xr sinh 3 , +.Xr tan 3 +.Sh STANDARDS +The +.Fn tanh +function conforms to +.St -ansiC . diff --git a/lib/libm/src/Makefile.inc b/lib/libm/src/Makefile.inc new file mode 100644 index 0000000000..775e7d0c9e --- /dev/null +++ b/lib/libm/src/Makefile.inc @@ -0,0 +1,37 @@ +# $DragonFly: src/lib/libm/src/Makefile.inc,v 1.1 2005/07/26 21:15:20 joerg Exp $ + +.PATH: ${.CURDIR}/src + +# This files are always used. +SRCS+= k_cos.c k_cosf.c k_rem_pio2.c k_rem_pio2f.c k_sin.c k_sinf.c \ + k_tan.c k_tanf.c llrint.c llrintf.c llround.c \ + llroundf.c lrint.c lrintf.c lround.c lroundf.c w_cabs.c w_cabsf.c \ + w_drem.c w_dremf.c w_gamma.c w_gamma_r.c w_gammaf.c w_gammaf_r.c \ + w_lgamma.c w_lgammaf.c + +# This files are only used if the MI Makefile didn't already provide +# them as assembler version. + +MI_FUNCS+= \ + e_acos.c e_acosf.c e_acosh.c e_acoshf.c e_asin.c e_asinf.c \ + e_atan2.c e_atan2f.c e_atanh.c e_atanhf.c e_cosh.c e_coshf.c \ + e_exp.c e_expf.c e_fmod.c e_fmodf.c e_hypot.c e_hypotf.c e_j0.c \ + e_j0f.c e_j1.c e_j1f.c e_jn.c e_jnf.c e_lgamma_r.c e_lgammaf_r.c \ + e_log.c e_log10.c e_log10f.c e_logf.c e_pow.c e_powf.c e_rem_pio2.c \ + e_rem_pio2f.c e_remainder.c e_remainderf.c e_scalb.c e_scalbf.c \ + e_sinh.c e_sinhf.c e_sqrt.c e_sqrtf.c \ + s_asinh.c s_asinhf.c s_atan.c s_atanf.c s_cbrt.c s_cbrtf.c s_ceil.c \ + s_ceilf.c s_copysign.c s_copysignf.c s_cos.c s_cosf.c s_erf.c \ + s_erff.c s_expm1.c s_expm1f.c s_fabsf.c s_finite.c \ + s_finitef.c s_floor.c s_floorf.c s_frexpf.c s_ilogb.c \ + s_ilogbf.c s_ldexpf.c s_log1p.c s_log1pf.c s_logb.c s_logbf.c \ + s_modff.c s_nextafter.c s_nextafterf.c s_rint.c s_rintf.c \ + s_round.c s_roundf.c s_scalbn.c s_scalbnf.c \ + s_signgam.c s_significand.c s_significandf.c s_sin.c s_sinf.c \ + s_tan.c s_tanf.c s_tanh.c s_tanhf.c + +.for f in ${MI_FUNCS} +.if empty(SRCS:M${f:H:R}) +SRCS+= $f +.endif +.endfor diff --git a/lib/libm/src/e_acos.c b/lib/libm/src/e_acos.c new file mode 100644 index 0000000000..685a94e5c4 --- /dev/null +++ b/lib/libm/src/e_acos.c @@ -0,0 +1,102 @@ +/* @(#)e_acos.c 5.1 93/09/24 */ +/* + * ==================================================== + * Copyright (C) 1993 by Sun Microsystems, Inc. All rights reserved. + * + * Developed at SunPro, a Sun Microsystems, Inc. business. + * Permission to use, copy, modify, and distribute this + * software is freely granted, provided that this notice + * is preserved. + * ==================================================== + * + * $NetBSD: e_acos.c,v 1.12 2002/05/26 22:01:47 wiz Exp $ + * $DragonFly: src/lib/libm/src/e_acos.c,v 1.1 2005/07/26 21:15:20 joerg Exp $ + */ + +/* acos(x) + * Method : + * acos(x) = pi/2 - asin(x) + * acos(-x) = pi/2 + asin(x) + * For |x|<=0.5 + * acos(x) = pi/2 - (x + x*x^2*R(x^2)) (see asin.c) + * For x>0.5 + * acos(x) = pi/2 - (pi/2 - 2asin(sqrt((1-x)/2))) + * = 2asin(sqrt((1-x)/2)) + * = 2s + 2s*z*R(z) ...z=(1-x)/2, s=sqrt(z) + * = 2f + (2c + 2s*z*R(z)) + * where f=hi part of s, and c = (z-f*f)/(s+f) is the correction term + * for f so that f+c ~ sqrt(z). + * For x<-0.5 + * acos(x) = pi - 2asin(sqrt((1-|x|)/2)) + * = pi - 0.5*(s+s*z*R(z)), where z=(1-|x|)/2,s=sqrt(z) + * + * Special cases: + * if x is NaN, return x itself; + * if |x|>1, return NaN with invalid signal. + * + * Function needed: sqrt + */ + +#include +#include "math_private.h" + +static const double +one= 1.00000000000000000000e+00, /* 0x3FF00000, 0x00000000 */ +pi = 3.14159265358979311600e+00, /* 0x400921FB, 0x54442D18 */ +pio2_hi = 1.57079632679489655800e+00, /* 0x3FF921FB, 0x54442D18 */ +pio2_lo = 6.12323399573676603587e-17, /* 0x3C91A626, 0x33145C07 */ +pS0 = 1.66666666666666657415e-01, /* 0x3FC55555, 0x55555555 */ +pS1 = -3.25565818622400915405e-01, /* 0xBFD4D612, 0x03EB6F7D */ +pS2 = 2.01212532134862925881e-01, /* 0x3FC9C155, 0x0E884455 */ +pS3 = -4.00555345006794114027e-02, /* 0xBFA48228, 0xB5688F3B */ +pS4 = 7.91534994289814532176e-04, /* 0x3F49EFE0, 0x7501B288 */ +pS5 = 3.47933107596021167570e-05, /* 0x3F023DE1, 0x0DFDF709 */ +qS1 = -2.40339491173441421878e+00, /* 0xC0033A27, 0x1C8A2D4B */ +qS2 = 2.02094576023350569471e+00, /* 0x40002AE5, 0x9C598AC8 */ +qS3 = -6.88283971605453293030e-01, /* 0xBFE6066C, 0x1B8D0159 */ +qS4 = 7.70381505559019352791e-02; /* 0x3FB3B8C5, 0xB12E9282 */ + +double +acos(double x) +{ + double z,p,q,r,w,s,c,df; + int32_t hx,ix; + GET_HIGH_WORD(hx,x); + ix = hx&0x7fffffff; + if(ix>=0x3ff00000) { /* |x| >= 1 */ + u_int32_t lx; + GET_LOW_WORD(lx,x); + if(((ix-0x3ff00000)|lx)==0) { /* |x|==1 */ + if(hx>0) return 0.0; /* acos(1) = 0 */ + else return pi+2.0*pio2_lo; /* acos(-1)= pi */ + } + return (x-x)/(x-x); /* acos(|x|>1) is NaN */ + } + if(ix<0x3fe00000) { /* |x| < 0.5 */ + if(ix<=0x3c600000) return pio2_hi+pio2_lo;/*if|x|<2**-57*/ + z = x*x; + p = z*(pS0+z*(pS1+z*(pS2+z*(pS3+z*(pS4+z*pS5))))); + q = one+z*(qS1+z*(qS2+z*(qS3+z*qS4))); + r = p/q; + return pio2_hi - (x - (pio2_lo-x*r)); + } else if (hx<0) { /* x < -0.5 */ + z = (one+x)*0.5; + p = z*(pS0+z*(pS1+z*(pS2+z*(pS3+z*(pS4+z*pS5))))); + q = one+z*(qS1+z*(qS2+z*(qS3+z*qS4))); + s = sqrt(z); + r = p/q; + w = r*s-pio2_lo; + return pi - 2.0*(s+w); + } else { /* x > 0.5 */ + z = (one-x)*0.5; + s = sqrt(z); + df = s; + SET_LOW_WORD(df,0); + c = (z-df*df)/(s+df); + p = z*(pS0+z*(pS1+z*(pS2+z*(pS3+z*(pS4+z*pS5))))); + q = one+z*(qS1+z*(qS2+z*(qS3+z*qS4))); + r = p/q; + w = r*s+c; + return 2.0*(df+w); + } +} diff --git a/lib/libm/src/e_acosf.c b/lib/libm/src/e_acosf.c new file mode 100644 index 0000000000..627c86d933 --- /dev/null +++ b/lib/libm/src/e_acosf.c @@ -0,0 +1,80 @@ +/* e_acosf.c -- float version of e_acos.c. + * Conversion to float by Ian Lance Taylor, Cygnus Support, ian@cygnus.com. + */ + +/* + * ==================================================== + * Copyright (C) 1993 by Sun Microsystems, Inc. All rights reserved. + * + * Developed at SunPro, a Sun Microsystems, Inc. business. + * Permission to use, copy, modify, and distribute this + * software is freely granted, provided that this notice + * is preserved. + * ==================================================== + * + * $NetBSD: e_acosf.c,v 1.8 2002/05/26 22:01:48 wiz Exp $ + * $DragonFly: src/lib/libm/src/e_acosf.c,v 1.1 2005/07/26 21:15:20 joerg Exp $ + */ + +#include +#include "math_private.h" + +static const float +one = 1.0000000000e+00, /* 0x3F800000 */ +pi = 3.1415925026e+00, /* 0x40490fda */ +pio2_hi = 1.5707962513e+00, /* 0x3fc90fda */ +pio2_lo = 7.5497894159e-08, /* 0x33a22168 */ +pS0 = 1.6666667163e-01, /* 0x3e2aaaab */ +pS1 = -3.2556581497e-01, /* 0xbea6b090 */ +pS2 = 2.0121252537e-01, /* 0x3e4e0aa8 */ +pS3 = -4.0055535734e-02, /* 0xbd241146 */ +pS4 = 7.9153501429e-04, /* 0x3a4f7f04 */ +pS5 = 3.4793309169e-05, /* 0x3811ef08 */ +qS1 = -2.4033949375e+00, /* 0xc019d139 */ +qS2 = 2.0209457874e+00, /* 0x4001572d */ +qS3 = -6.8828397989e-01, /* 0xbf303361 */ +qS4 = 7.7038154006e-02; /* 0x3d9dc62e */ + +float +acosf(float x) +{ + float z,p,q,r,w,s,c,df; + int32_t hx,ix; + GET_FLOAT_WORD(hx,x); + ix = hx&0x7fffffff; + if(ix==0x3f800000) { /* |x|==1 */ + if(hx>0) return 0.0; /* acos(1) = 0 */ + else return pi+(float)2.0*pio2_lo; /* acos(-1)= pi */ + } else if(ix>0x3f800000) { /* |x| >= 1 */ + return (x-x)/(x-x); /* acos(|x|>1) is NaN */ + } + if(ix<0x3f000000) { /* |x| < 0.5 */ + if(ix<=0x23000000) return pio2_hi+pio2_lo;/*if|x|<2**-57*/ + z = x*x; + p = z*(pS0+z*(pS1+z*(pS2+z*(pS3+z*(pS4+z*pS5))))); + q = one+z*(qS1+z*(qS2+z*(qS3+z*qS4))); + r = p/q; + return pio2_hi - (x - (pio2_lo-x*r)); + } else if (hx<0) { /* x < -0.5 */ + z = (one+x)*(float)0.5; + p = z*(pS0+z*(pS1+z*(pS2+z*(pS3+z*(pS4+z*pS5))))); + q = one+z*(qS1+z*(qS2+z*(qS3+z*qS4))); + s = sqrtf(z); + r = p/q; + w = r*s-pio2_lo; + return pi - (float)2.0*(s+w); + } else { /* x > 0.5 */ + int32_t idf; + z = (one-x)*(float)0.5; + s = sqrtf(z); + df = s; + GET_FLOAT_WORD(idf,df); + SET_FLOAT_WORD(df,idf&0xfffff000); + c = (z-df*df)/(s+df); + p = z*(pS0+z*(pS1+z*(pS2+z*(pS3+z*(pS4+z*pS5))))); + q = one+z*(qS1+z*(qS2+z*(qS3+z*qS4))); + r = p/q; + w = r*s+c; + return (float)2.0*(df+w); + } +} diff --git a/lib/libm/src/e_acosh.c b/lib/libm/src/e_acosh.c new file mode 100644 index 0000000000..3ecfcfaa32 --- /dev/null +++ b/lib/libm/src/e_acosh.c @@ -0,0 +1,61 @@ +/* @(#)e_acosh.c 5.1 93/09/24 */ +/* + * ==================================================== + * Copyright (C) 1993 by Sun Microsystems, Inc. All rights reserved. + * + * Developed at SunPro, a Sun Microsystems, Inc. business. + * Permission to use, copy, modify, and distribute this + * software is freely granted, provided that this notice + * is preserved. + * ==================================================== + * + * $NetBSD: e_acosh.c,v 1.12 2002/05/26 22:01:48 wiz Exp $ + * $DragonFly: src/lib/libm/src/e_acosh.c,v 1.1 2005/07/26 21:15:20 joerg Exp $ + */ + + +/* acosh(x) + * Method : + * Based on + * acosh(x) = log [ x + sqrt(x*x-1) ] + * we have + * acosh(x) := log(x)+ln2, if x is large; else + * acosh(x) := log(2x-1/(sqrt(x*x-1)+x)) if x>2; else + * acosh(x) := log1p(t+sqrt(2.0*t+t*t)); where t=x-1. + * + * Special cases: + * acosh(x) is NaN with signal if x<1. + * acosh(NaN) is NaN without signal. + */ + +#include +#include "math_private.h" + +static const double +one = 1.0, +ln2 = 6.93147180559945286227e-01; /* 0x3FE62E42, 0xFEFA39EF */ + +double +acosh(double x) +{ + double t; + int32_t hx; + u_int32_t lx; + EXTRACT_WORDS(hx,lx,x); + if(hx<0x3ff00000) { /* x < 1 */ + return (x-x)/(x-x); + } else if(hx >=0x41b00000) { /* x > 2**28 */ + if(hx >=0x7ff00000) { /* x is inf of NaN */ + return x+x; + } else + return log(x)+ln2; /* acosh(huge)=log(2x) */ + } else if(((hx-0x3ff00000)|lx)==0) { + return 0.0; /* acosh(1) = 0 */ + } else if (hx > 0x40000000) { /* 2**28 > x > 2 */ + t=x*x; + return log(2.0*x-one/(x+sqrt(t-one))); + } else { /* 1 +#include "math_private.h" + +static const float +one = 1.0, +ln2 = 6.9314718246e-01; /* 0x3f317218 */ + +float +acoshf(float x) +{ + float t; + int32_t hx; + GET_FLOAT_WORD(hx,x); + if(hx<0x3f800000) { /* x < 1 */ + return (x-x)/(x-x); + } else if(hx >=0x4d800000) { /* x > 2**28 */ + if(hx >=0x7f800000) { /* x is inf of NaN */ + return x+x; + } else + return logf(x)+ln2; /* acosh(huge)=log(2x) */ + } else if (hx==0x3f800000) { + return 0.0; /* acosh(1) = 0 */ + } else if (hx > 0x40000000) { /* 2**28 > x > 2 */ + t=x*x; + return logf((float)2.0*x-one/(x+sqrtf(t-one))); + } else { /* 10.98 + * asin(x) = pi/2 - 2*(s+s*z*R(z)) + * = pio2_hi - (2*(s+s*z*R(z)) - pio2_lo) + * For x<=0.98, let pio4_hi = pio2_hi/2, then + * f = hi part of s; + * c = sqrt(z) - f = (z-f*f)/(s+f) ...f+c=sqrt(z) + * and + * asin(x) = pi/2 - 2*(s+s*z*R(z)) + * = pio4_hi+(pio4-2s)-(2s*z*R(z)-pio2_lo) + * = pio4_hi+(pio4-2f)-(2s*z*R(z)-(pio2_lo+2c)) + * + * Special cases: + * if x is NaN, return x itself; + * if |x|>1, return NaN with invalid signal. + * + */ + + +#include +#include "math_private.h" + +static const double +one = 1.00000000000000000000e+00, /* 0x3FF00000, 0x00000000 */ +huge = 1.000e+300, +pio2_hi = 1.57079632679489655800e+00, /* 0x3FF921FB, 0x54442D18 */ +pio2_lo = 6.12323399573676603587e-17, /* 0x3C91A626, 0x33145C07 */ +pio4_hi = 7.85398163397448278999e-01, /* 0x3FE921FB, 0x54442D18 */ + /* coefficient for R(x^2) */ +pS0 = 1.66666666666666657415e-01, /* 0x3FC55555, 0x55555555 */ +pS1 = -3.25565818622400915405e-01, /* 0xBFD4D612, 0x03EB6F7D */ +pS2 = 2.01212532134862925881e-01, /* 0x3FC9C155, 0x0E884455 */ +pS3 = -4.00555345006794114027e-02, /* 0xBFA48228, 0xB5688F3B */ +pS4 = 7.91534994289814532176e-04, /* 0x3F49EFE0, 0x7501B288 */ +pS5 = 3.47933107596021167570e-05, /* 0x3F023DE1, 0x0DFDF709 */ +qS1 = -2.40339491173441421878e+00, /* 0xC0033A27, 0x1C8A2D4B */ +qS2 = 2.02094576023350569471e+00, /* 0x40002AE5, 0x9C598AC8 */ +qS3 = -6.88283971605453293030e-01, /* 0xBFE6066C, 0x1B8D0159 */ +qS4 = 7.70381505559019352791e-02; /* 0x3FB3B8C5, 0xB12E9282 */ + +double +asin(double x) +{ + double t,w,p,q,c,r,s; + int32_t hx,ix; + + t = 0; + GET_HIGH_WORD(hx,x); + ix = hx&0x7fffffff; + if(ix>= 0x3ff00000) { /* |x|>= 1 */ + u_int32_t lx; + GET_LOW_WORD(lx,x); + if(((ix-0x3ff00000)|lx)==0) + /* asin(1)=+-pi/2 with inexact */ + return x*pio2_hi+x*pio2_lo; + return (x-x)/(x-x); /* asin(|x|>1) is NaN */ + } else if (ix<0x3fe00000) { /* |x|<0.5 */ + if(ix<0x3e400000) { /* if |x| < 2**-27 */ + if(huge+x>one) return x;/* return x with inexact if x!=0*/ + } else + t = x*x; + p = t*(pS0+t*(pS1+t*(pS2+t*(pS3+t*(pS4+t*pS5))))); + q = one+t*(qS1+t*(qS2+t*(qS3+t*qS4))); + w = p/q; + return x+x*w; + } + /* 1> |x|>= 0.5 */ + w = one-fabs(x); + t = w*0.5; + p = t*(pS0+t*(pS1+t*(pS2+t*(pS3+t*(pS4+t*pS5))))); + q = one+t*(qS1+t*(qS2+t*(qS3+t*qS4))); + s = sqrt(t); + if(ix>=0x3FEF3333) { /* if |x| > 0.975 */ + w = p/q; + t = pio2_hi-(2.0*(s+s*w)-pio2_lo); + } else { + w = s; + SET_LOW_WORD(w,0); + c = (t-w*w)/(s+w); + r = p/q; + p = 2.0*s*r-(pio2_lo-2.0*c); + q = pio4_hi-2.0*w; + t = pio4_hi-(p-q); + } + if(hx>0) return t; else return -t; +} diff --git a/lib/libm/src/e_asinf.c b/lib/libm/src/e_asinf.c new file mode 100644 index 0000000000..a8aa9dffc8 --- /dev/null +++ b/lib/libm/src/e_asinf.c @@ -0,0 +1,85 @@ +/* e_asinf.c -- float version of e_asin.c. + * Conversion to float by Ian Lance Taylor, Cygnus Support, ian@cygnus.com. + */ + +/* + * ==================================================== + * Copyright (C) 1993 by Sun Microsystems, Inc. All rights reserved. + * + * Developed at SunPro, a Sun Microsystems, Inc. business. + * Permission to use, copy, modify, and distribute this + * software is freely granted, provided that this notice + * is preserved. + * ==================================================== + * + * $NetBSD: e_asinf.c,v 1.8 2002/05/26 22:01:48 wiz Exp $ + * $DragonFly: src/lib/libm/src/e_asinf.c,v 1.1 2005/07/26 21:15:20 joerg Exp $ + */ + +#include +#include "math_private.h" + +static const float +one = 1.0000000000e+00, /* 0x3F800000 */ +huge = 1.000e+30, +pio2_hi = 1.5707962513e+00, /* 0x3fc90fda */ +pio2_lo = 7.5497894159e-08, /* 0x33a22168 */ +pio4_hi = 7.8539818525e-01, /* 0x3f490fdb */ + /* coefficient for R(x^2) */ +pS0 = 1.6666667163e-01, /* 0x3e2aaaab */ +pS1 = -3.2556581497e-01, /* 0xbea6b090 */ +pS2 = 2.0121252537e-01, /* 0x3e4e0aa8 */ +pS3 = -4.0055535734e-02, /* 0xbd241146 */ +pS4 = 7.9153501429e-04, /* 0x3a4f7f04 */ +pS5 = 3.4793309169e-05, /* 0x3811ef08 */ +qS1 = -2.4033949375e+00, /* 0xc019d139 */ +qS2 = 2.0209457874e+00, /* 0x4001572d */ +qS3 = -6.8828397989e-01, /* 0xbf303361 */ +qS4 = 7.7038154006e-02; /* 0x3d9dc62e */ + +float +asinf(float x) +{ + float t,w,p,q,c,r,s; + int32_t hx,ix; + + t = 0; + GET_FLOAT_WORD(hx,x); + ix = hx&0x7fffffff; + if(ix==0x3f800000) { + /* asin(1)=+-pi/2 with inexact */ + return x*pio2_hi+x*pio2_lo; + } else if(ix> 0x3f800000) { /* |x|>= 1 */ + return (x-x)/(x-x); /* asin(|x|>1) is NaN */ + } else if (ix<0x3f000000) { /* |x|<0.5 */ + if(ix<0x32000000) { /* if |x| < 2**-27 */ + if(huge+x>one) return x;/* return x with inexact if x!=0*/ + } else + t = x*x; + p = t*(pS0+t*(pS1+t*(pS2+t*(pS3+t*(pS4+t*pS5))))); + q = one+t*(qS1+t*(qS2+t*(qS3+t*qS4))); + w = p/q; + return x+x*w; + } + /* 1> |x|>= 0.5 */ + w = one-fabsf(x); + t = w*(float)0.5; + p = t*(pS0+t*(pS1+t*(pS2+t*(pS3+t*(pS4+t*pS5))))); + q = one+t*(qS1+t*(qS2+t*(qS3+t*qS4))); + s = sqrtf(t); + if(ix>=0x3F79999A) { /* if |x| > 0.975 */ + w = p/q; + t = pio2_hi-((float)2.0*(s+s*w)-pio2_lo); + } else { + int32_t iw; + w = s; + GET_FLOAT_WORD(iw,w); + SET_FLOAT_WORD(w,iw&0xfffff000); + c = (t-w*w)/(s+w); + r = p/q; + p = (float)2.0*s*r-(pio2_lo-(float)2.0*c); + q = pio4_hi-(float)2.0*w; + t = pio4_hi-(p-q); + } + if(hx>0) return t; else return -t; +} diff --git a/lib/libm/src/e_atan2.c b/lib/libm/src/e_atan2.c new file mode 100644 index 0000000000..ff64adfe9d --- /dev/null +++ b/lib/libm/src/e_atan2.c @@ -0,0 +1,121 @@ +/* @(#)e_atan2.c 5.1 93/09/24 */ +/* + * ==================================================== + * Copyright (C) 1993 by Sun Microsystems, Inc. All rights reserved. + * + * Developed at SunPro, a Sun Microsystems, Inc. business. + * Permission to use, copy, modify, and distribute this + * software is freely granted, provided that this notice + * is preserved. + * ==================================================== + * + * $NetBSD: e_atan2.c,v 1.12 2002/05/26 22:01:48 wiz Exp $ + * $DragonFly: src/lib/libm/src/e_atan2.c,v 1.1 2005/07/26 21:15:20 joerg Exp $ + */ + +/* atan2(y,x) + * Method : + * 1. Reduce y to positive by atan2(y,x)=-atan2(-y,x). + * 2. Reduce x to positive by (if x and y are unexceptional): + * ARG (x+iy) = arctan(y/x) ... if x > 0, + * ARG (x+iy) = pi - arctan[y/(-x)] ... if x < 0, + * + * Special cases: + * + * ATAN2((anything), NaN ) is NaN; + * ATAN2(NAN , (anything) ) is NaN; + * ATAN2(+-0, +(anything but NaN)) is +-0 ; + * ATAN2(+-0, -(anything but NaN)) is +-pi ; + * ATAN2(+-(anything but 0 and NaN), 0) is +-pi/2; + * ATAN2(+-(anything but INF and NaN), +INF) is +-0 ; + * ATAN2(+-(anything but INF and NaN), -INF) is +-pi; + * ATAN2(+-INF,+INF ) is +-pi/4 ; + * ATAN2(+-INF,-INF ) is +-3pi/4; + * ATAN2(+-INF, (anything but,0,NaN, and INF)) is +-pi/2; + * + * Constants: + * The hexadecimal values are the intended ones for the following + * constants. The decimal values may be used, provided that the + * compiler will convert from decimal to binary accurately enough + * to produce the hexadecimal values shown. + */ + +#include +#include "math_private.h" + +static const double +tiny = 1.0e-300, +zero = 0.0, +pi_o_4 = 7.8539816339744827900E-01, /* 0x3FE921FB, 0x54442D18 */ +pi_o_2 = 1.5707963267948965580E+00, /* 0x3FF921FB, 0x54442D18 */ +pi = 3.1415926535897931160E+00, /* 0x400921FB, 0x54442D18 */ +pi_lo = 1.2246467991473531772E-16; /* 0x3CA1A626, 0x33145C07 */ + +double +atan2(double y, double x) +{ + double z; + int32_t k,m,hx,hy,ix,iy; + u_int32_t lx,ly; + + EXTRACT_WORDS(hx,lx,x); + ix = hx&0x7fffffff; + EXTRACT_WORDS(hy,ly,y); + iy = hy&0x7fffffff; + if(((ix|((lx|-lx)>>31))>0x7ff00000)|| + ((iy|((ly|-ly)>>31))>0x7ff00000)) /* x or y is NaN */ + return x+y; + if(((hx-0x3ff00000)|lx)==0) return atan(y); /* x=1.0 */ + m = ((hy>>31)&1)|((hx>>30)&2); /* 2*sign(x)+sign(y) */ + + /* when y = 0 */ + if((iy|ly)==0) { + switch(m) { + case 0: + case 1: return y; /* atan(+-0,+anything)=+-0 */ + case 2: return pi+tiny;/* atan(+0,-anything) = pi */ + case 3: return -pi-tiny;/* atan(-0,-anything) =-pi */ + } + } + /* when x = 0 */ + if((ix|lx)==0) return (hy<0)? -pi_o_2-tiny: pi_o_2+tiny; + + /* when x is INF */ + if(ix==0x7ff00000) { + if(iy==0x7ff00000) { + switch(m) { + case 0: return pi_o_4+tiny;/* atan(+INF,+INF) */ + case 1: return -pi_o_4-tiny;/* atan(-INF,+INF) */ + case 2: return 3.0*pi_o_4+tiny;/*atan(+INF,-INF)*/ + case 3: return -3.0*pi_o_4-tiny;/*atan(-INF,-INF)*/ + } + } else { + switch(m) { + case 0: return zero ; /* atan(+...,+INF) */ + case 1: return -zero ; /* atan(-...,+INF) */ + case 2: return pi+tiny ; /* atan(+...,-INF) */ + case 3: return -pi-tiny ; /* atan(-...,-INF) */ + } + } + } + /* when y is INF */ + if(iy==0x7ff00000) return (hy<0)? -pi_o_2-tiny: pi_o_2+tiny; + + /* compute y/x */ + k = (iy-ix)>>20; + if(k > 60) z=pi_o_2+0.5*pi_lo; /* |y/x| > 2**60 */ + else if(hx<0&&k<-60) z=0.0; /* |y|/x < -2**60 */ + else z=atan(fabs(y/x)); /* safe to do y/x */ + switch (m) { + case 0: return z ; /* atan(+,+) */ + case 1: { + u_int32_t zh; + GET_HIGH_WORD(zh,z); + SET_HIGH_WORD(z,zh ^ 0x80000000); + } + return z ; /* atan(-,+) */ + case 2: return pi-(z-pi_lo);/* atan(+,-) */ + default: /* case 3 */ + return (z-pi_lo)-pi;/* atan(-,-) */ + } +} diff --git a/lib/libm/src/e_atan2f.c b/lib/libm/src/e_atan2f.c new file mode 100644 index 0000000000..378d34c0d4 --- /dev/null +++ b/lib/libm/src/e_atan2f.c @@ -0,0 +1,96 @@ +/* e_atan2f.c -- float version of e_atan2.c. + * Conversion to float by Ian Lance Taylor, Cygnus Support, ian@cygnus.com. + */ + +/* + * ==================================================== + * Copyright (C) 1993 by Sun Microsystems, Inc. All rights reserved. + * + * Developed at SunPro, a Sun Microsystems, Inc. business. + * Permission to use, copy, modify, and distribute this + * software is freely granted, provided that this notice + * is preserved. + * ==================================================== + * + * $NetBSD: e_atan2f.c,v 1.7 2002/05/26 22:01:49 wiz Exp $ + * $DragonFly: src/lib/libm/src/e_atan2f.c,v 1.1 2005/07/26 21:15:20 joerg Exp $ + */ + +#include +#include "math_private.h" + +static const float +tiny = 1.0e-30, +zero = 0.0, +pi_o_4 = 7.8539818525e-01, /* 0x3f490fdb */ +pi_o_2 = 1.5707963705e+00, /* 0x3fc90fdb */ +pi = 3.1415925026e+00, /* 0x40490fda */ +pi_lo = 1.5099578832e-07; /* 0x34222168 */ + +float +atan2f(float y, float x) +{ + float z; + int32_t k,m,hx,hy,ix,iy; + + GET_FLOAT_WORD(hx,x); + ix = hx&0x7fffffff; + GET_FLOAT_WORD(hy,y); + iy = hy&0x7fffffff; + if((ix>0x7f800000)|| + (iy>0x7f800000)) /* x or y is NaN */ + return x+y; + if(hx==0x3f800000) return atanf(y); /* x=1.0 */ + m = ((hy>>31)&1)|((hx>>30)&2); /* 2*sign(x)+sign(y) */ + + /* when y = 0 */ + if(iy==0) { + switch(m) { + case 0: + case 1: return y; /* atan(+-0,+anything)=+-0 */ + case 2: return pi+tiny;/* atan(+0,-anything) = pi */ + case 3: return -pi-tiny;/* atan(-0,-anything) =-pi */ + } + } + /* when x = 0 */ + if(ix==0) return (hy<0)? -pi_o_2-tiny: pi_o_2+tiny; + + /* when x is INF */ + if(ix==0x7f800000) { + if(iy==0x7f800000) { + switch(m) { + case 0: return pi_o_4+tiny;/* atan(+INF,+INF) */ + case 1: return -pi_o_4-tiny;/* atan(-INF,+INF) */ + case 2: return (float)3.0*pi_o_4+tiny;/*atan(+INF,-INF)*/ + case 3: return (float)-3.0*pi_o_4-tiny;/*atan(-INF,-INF)*/ + } + } else { + switch(m) { + case 0: return zero ; /* atan(+...,+INF) */ + case 1: return -zero ; /* atan(-...,+INF) */ + case 2: return pi+tiny ; /* atan(+...,-INF) */ + case 3: return -pi-tiny ; /* atan(-...,-INF) */ + } + } + } + /* when y is INF */ + if(iy==0x7f800000) return (hy<0)? -pi_o_2-tiny: pi_o_2+tiny; + + /* compute y/x */ + k = (iy-ix)>>23; + if(k > 60) z=pi_o_2+(float)0.5*pi_lo; /* |y/x| > 2**60 */ + else if(hx<0&&k<-60) z=0.0; /* |y|/x < -2**60 */ + else z=atanf(fabsf(y/x)); /* safe to do y/x */ + switch (m) { + case 0: return z ; /* atan(+,+) */ + case 1: { + u_int32_t zh; + GET_FLOAT_WORD(zh,z); + SET_FLOAT_WORD(z,zh ^ 0x80000000); + } + return z ; /* atan(-,+) */ + case 2: return pi-(z-pi_lo);/* atan(+,-) */ + default: /* case 3 */ + return (z-pi_lo)-pi;/* atan(-,-) */ + } +} diff --git a/lib/libm/src/e_atanh.c b/lib/libm/src/e_atanh.c new file mode 100644 index 0000000000..3b1a8ec05f --- /dev/null +++ b/lib/libm/src/e_atanh.c @@ -0,0 +1,61 @@ +/* @(#)e_atanh.c 5.1 93/09/24 */ +/* + * ==================================================== + * Copyright (C) 1993 by Sun Microsystems, Inc. All rights reserved. + * + * Developed at SunPro, a Sun Microsystems, Inc. business. + * Permission to use, copy, modify, and distribute this + * software is freely granted, provided that this notice + * is preserved. + * ==================================================== + * + * $NetBSD: e_atanh.c,v 1.11 2002/05/26 22:01:49 wiz Exp $ + * $DragonFly: src/lib/libm/src/e_atanh.c,v 1.1 2005/07/26 21:15:20 joerg Exp $ + */ + +/* atanh(x) + * Method : + * 1.Reduced x to positive by atanh(-x) = -atanh(x) + * 2.For x>=0.5 + * 1 2x x + * atanh(x) = --- * log(1 + -------) = 0.5 * log1p(2 * --------) + * 2 1 - x 1 - x + * + * For x<0.5 + * atanh(x) = 0.5*log1p(2x+2x*x/(1-x)) + * + * Special cases: + * atanh(x) is NaN if |x| > 1 with signal; + * atanh(NaN) is that NaN with no signal; + * atanh(+-1) is +-INF with signal. + * + */ + +#include +#include "math_private.h" + +static const double one = 1.0, huge = 1e300; + +static const double zero = 0.0; + +double +atanh(double x) +{ + double t; + int32_t hx,ix; + u_int32_t lx; + EXTRACT_WORDS(hx,lx,x); + ix = hx&0x7fffffff; + if ((ix|((lx|(-lx))>>31))>0x3ff00000) /* |x|>1 */ + return (x-x)/(x-x); + if(ix==0x3ff00000) + return x/zero; + if(ix<0x3e300000&&(huge+x)>zero) return x; /* x<2**-28 */ + SET_HIGH_WORD(x,ix); + if(ix<0x3fe00000) { /* x < 0.5 */ + t = x+x; + t = 0.5*log1p(t+t*x/(one-x)); + } else + t = 0.5*log1p((x+x)/(one-x)); + if(hx>=0) return t; else return -t; +} diff --git a/lib/libm/src/e_atanhf.c b/lib/libm/src/e_atanhf.c new file mode 100644 index 0000000000..31b71fd065 --- /dev/null +++ b/lib/libm/src/e_atanhf.c @@ -0,0 +1,45 @@ +/* e_atanhf.c -- float version of e_atanh.c. + * Conversion to float by Ian Lance Taylor, Cygnus Support, ian@cygnus.com. + */ + +/* + * ==================================================== + * Copyright (C) 1993 by Sun Microsystems, Inc. All rights reserved. + * + * Developed at SunPro, a Sun Microsystems, Inc. business. + * Permission to use, copy, modify, and distribute this + * software is freely granted, provided that this notice + * is preserved. + * ==================================================== + * + * $NetBSD: e_atanhf.c,v 1.7 2002/05/26 22:01:49 wiz Exp $ + * $DragonFly: src/lib/libm/src/e_atanhf.c,v 1.1 2005/07/26 21:15:20 joerg Exp $ + */ + +#include +#include "math_private.h" + +static const float one = 1.0, huge = 1e30; + +static const float zero = 0.0; + +float +atanhf(float x) +{ + float t; + int32_t hx,ix; + GET_FLOAT_WORD(hx,x); + ix = hx&0x7fffffff; + if (ix>0x3f800000) /* |x|>1 */ + return (x-x)/(x-x); + if(ix==0x3f800000) + return x/zero; + if(ix<0x31800000&&(huge+x)>zero) return x; /* x<2**-28 */ + SET_FLOAT_WORD(x,ix); + if(ix<0x3f000000) { /* x < 0.5 */ + t = x+x; + t = (float)0.5*log1pf(t+t*x/(one-x)); + } else + t = (float)0.5*log1pf((x+x)/(one-x)); + if(hx>=0) return t; else return -t; +} diff --git a/lib/libm/src/e_cosh.c b/lib/libm/src/e_cosh.c new file mode 100644 index 0000000000..598c3ada98 --- /dev/null +++ b/lib/libm/src/e_cosh.c @@ -0,0 +1,84 @@ +/* @(#)e_cosh.c 5.1 93/09/24 */ +/* + * ==================================================== + * Copyright (C) 1993 by Sun Microsystems, Inc. All rights reserved. + * + * Developed at SunPro, a Sun Microsystems, Inc. business. + * Permission to use, copy, modify, and distribute this + * software is freely granted, provided that this notice + * is preserved. + * ==================================================== + * + * $NetBSD: e_cosh.c,v 1.11 2002/05/26 22:01:49 wiz Exp $ + * $DragonFly: src/lib/libm/src/e_cosh.c,v 1.1 2005/07/26 21:15:20 joerg Exp $ + */ + +/* cosh(x) + * Method : + * mathematically cosh(x) if defined to be (exp(x)+exp(-x))/2 + * 1. Replace x by |x| (cosh(x) = cosh(-x)). + * 2. + * [ exp(x) - 1 ]^2 + * 0 <= x <= ln2/2 : cosh(x) := 1 + ------------------- + * 2*exp(x) + * + * exp(x) + 1/exp(x) + * ln2/2 <= x <= 22 : cosh(x) := ------------------- + * 2 + * 22 <= x <= lnovft : cosh(x) := exp(x)/2 + * lnovft <= x <= ln2ovft: cosh(x) := exp(x/2)/2 * exp(x/2) + * ln2ovft < x : cosh(x) := huge*huge (overflow) + * + * Special cases: + * cosh(x) is |x| if x is +INF, -INF, or NaN. + * only cosh(0)=1 is exact for finite x. + */ + +#include +#include "math_private.h" + +static const double one = 1.0, half=0.5, huge = 1.0e300; + +double +cosh(double x) +{ + double t,w; + int32_t ix; + u_int32_t lx; + + /* High word of |x|. */ + GET_HIGH_WORD(ix,x); + ix &= 0x7fffffff; + + /* x is INF or NaN */ + if(ix>=0x7ff00000) return x*x; + + /* |x| in [0,0.5*ln2], return 1+expm1(|x|)^2/(2*exp(|x|)) */ + if(ix<0x3fd62e43) { + t = expm1(fabs(x)); + w = one+t; + if (ix<0x3c800000) return w; /* cosh(tiny) = 1 */ + return one+(t*t)/(w+w); + } + + /* |x| in [0.5*ln2,22], return (exp(|x|)+1/exp(|x|)/2; */ + if (ix < 0x40360000) { + t = exp(fabs(x)); + return half*t+half/t; + } + + /* |x| in [22, log(maxdouble)] return half*exp(|x|) */ + if (ix < 0x40862E42) return half*exp(fabs(x)); + + /* |x| in [log(maxdouble), overflowthresold] */ + GET_LOW_WORD(lx,x); + if (ix<0x408633CE || + ((ix==0x408633ce)&&(lx<=(u_int32_t)0x8fb9f87d))) { + w = exp(half*fabs(x)); + t = half*w; + return t*w; + } + + /* |x| > overflowthresold, cosh(x) overflow */ + return huge*huge; +} diff --git a/lib/libm/src/e_coshf.c b/lib/libm/src/e_coshf.c new file mode 100644 index 0000000000..9e47cd507b --- /dev/null +++ b/lib/libm/src/e_coshf.c @@ -0,0 +1,63 @@ +/* e_coshf.c -- float version of e_cosh.c. + * Conversion to float by Ian Lance Taylor, Cygnus Support, ian@cygnus.com. + */ + +/* + * ==================================================== + * Copyright (C) 1993 by Sun Microsystems, Inc. All rights reserved. + * + * Developed at SunPro, a Sun Microsystems, Inc. business. + * Permission to use, copy, modify, and distribute this + * software is freely granted, provided that this notice + * is preserved. + * ==================================================== + * + * $NetBSD: e_coshf.c,v 1.9 2002/05/26 22:01:49 wiz Exp $ + * $DragonFly: src/lib/libm/src/e_coshf.c,v 1.1 2005/07/26 21:15:20 joerg Exp $ + */ + +#include +#include "math_private.h" + +static const float huge = 1.0e30; +static const float one = 1.0, half=0.5; + +float +coshf(float x) +{ + float t,w; + int32_t ix; + + GET_FLOAT_WORD(ix,x); + ix &= 0x7fffffff; + + /* x is INF or NaN */ + if(ix>=0x7f800000) return x*x; + + /* |x| in [0,0.5*ln2], return 1+expm1(|x|)^2/(2*exp(|x|)) */ + if(ix<0x3eb17218) { + t = expm1f(fabsf(x)); + w = one+t; + if (ix<0x24000000) return w; /* cosh(tiny) = 1 */ + return one+(t*t)/(w+w); + } + + /* |x| in [0.5*ln2,22], return (exp(|x|)+1/exp(|x|)/2; */ + if (ix < 0x41b00000) { + t = expf(fabsf(x)); + return half*t+half/t; + } + + /* |x| in [22, log(maxdouble)] return half*exp(|x|) */ + if (ix < 0x42b17180) return half*expf(fabsf(x)); + + /* |x| in [log(maxdouble), overflowthresold] */ + if (ix<=0x42b2d4fc) { + w = expf(half*fabsf(x)); + t = half*w; + return t*w; + } + + /* |x| > overflowthresold, cosh(x) overflow */ + return huge*huge; +} diff --git a/lib/libm/src/e_exp.c b/lib/libm/src/e_exp.c new file mode 100644 index 0000000000..bdbb8f29bc --- /dev/null +++ b/lib/libm/src/e_exp.c @@ -0,0 +1,160 @@ +/* @(#)e_exp.c 5.1 93/09/24 */ +/* + * ==================================================== + * Copyright (C) 1993 by Sun Microsystems, Inc. All rights reserved. + * + * Developed at SunPro, a Sun Microsystems, Inc. business. + * Permission to use, copy, modify, and distribute this + * software is freely granted, provided that this notice + * is preserved. + * ==================================================== + * + * $NetBSD: e_exp.c,v 1.11 2002/05/26 22:01:49 wiz Exp $ + * $DragonFly: src/lib/libm/src/e_exp.c,v 1.1 2005/07/26 21:15:20 joerg Exp $ + */ + +/* exp(x) + * Returns the exponential of x. + * + * Method + * 1. Argument reduction: + * Reduce x to an r so that |r| <= 0.5*ln2 ~ 0.34658. + * Given x, find r and integer k such that + * + * x = k*ln2 + r, |r| <= 0.5*ln2. + * + * Here r will be represented as r = hi-lo for better + * accuracy. + * + * 2. Approximation of exp(r) by a special rational function on + * the interval [0,0.34658]: + * Write + * R(r**2) = r*(exp(r)+1)/(exp(r)-1) = 2 + r*r/6 - r**4/360 + ... + * We use a special Reme algorithm on [0,0.34658] to generate + * a polynomial of degree 5 to approximate R. The maximum error + * of this polynomial approximation is bounded by 2**-59. In + * other words, + * R(z) ~ 2.0 + P1*z + P2*z**2 + P3*z**3 + P4*z**4 + P5*z**5 + * (where z=r*r, and the values of P1 to P5 are listed below) + * and + * | 5 | -59 + * | 2.0+P1*z+...+P5*z - R(z) | <= 2 + * | | + * The computation of exp(r) thus becomes + * 2*r + * exp(r) = 1 + ------- + * R - r + * r*R1(r) + * = 1 + r + ----------- (for better accuracy) + * 2 - R1(r) + * where + * 2 4 10 + * R1(r) = r - (P1*r + P2*r + ... + P5*r ). + * + * 3. Scale back to obtain exp(x): + * From step 1, we have + * exp(x) = 2^k * exp(r) + * + * Special cases: + * exp(INF) is INF, exp(NaN) is NaN; + * exp(-INF) is 0, and + * for finite argument, only exp(0)=1 is exact. + * + * Accuracy: + * according to an error analysis, the error is always less than + * 1 ulp (unit in the last place). + * + * Misc. info. + * For IEEE double + * if x > 7.09782712893383973096e+02 then exp(x) overflow + * if x < -7.45133219101941108420e+02 then exp(x) underflow + * + * Constants: + * The hexadecimal values are the intended ones for the following + * constants. The decimal values may be used, provided that the + * compiler will convert from decimal to binary accurately enough + * to produce the hexadecimal values shown. + */ + +#include +#include "math_private.h" + +static const double +one = 1.0, +halF[2] = {0.5,-0.5,}, +huge = 1.0e+300, +twom1000= 9.33263618503218878990e-302, /* 2**-1000=0x01700000,0*/ +o_threshold= 7.09782712893383973096e+02, /* 0x40862E42, 0xFEFA39EF */ +u_threshold= -7.45133219101941108420e+02, /* 0xc0874910, 0xD52D3051 */ +ln2HI[2] ={ 6.93147180369123816490e-01, /* 0x3fe62e42, 0xfee00000 */ + -6.93147180369123816490e-01,},/* 0xbfe62e42, 0xfee00000 */ +ln2LO[2] ={ 1.90821492927058770002e-10, /* 0x3dea39ef, 0x35793c76 */ + -1.90821492927058770002e-10,},/* 0xbdea39ef, 0x35793c76 */ +invln2 = 1.44269504088896338700e+00, /* 0x3ff71547, 0x652b82fe */ +P1 = 1.66666666666666019037e-01, /* 0x3FC55555, 0x5555553E */ +P2 = -2.77777777770155933842e-03, /* 0xBF66C16C, 0x16BEBD93 */ +P3 = 6.61375632143793436117e-05, /* 0x3F11566A, 0xAF25DE2C */ +P4 = -1.65339022054652515390e-06, /* 0xBEBBBD41, 0xC5D26BF1 */ +P5 = 4.13813679705723846039e-08; /* 0x3E663769, 0x72BEA4D0 */ + + +double +exp(double x) /* default IEEE double exp */ +{ + double y,hi,lo,c,t; + int32_t k,xsb; + u_int32_t hx; + + hi = lo = 0; + k = 0; + GET_HIGH_WORD(hx,x); + xsb = (hx>>31)&1; /* sign bit of x */ + hx &= 0x7fffffff; /* high word of |x| */ + + /* filter out non-finite argument */ + if(hx >= 0x40862E42) { /* if |x|>=709.78... */ + if(hx>=0x7ff00000) { + u_int32_t lx; + GET_LOW_WORD(lx,x); + if(((hx&0xfffff)|lx)!=0) + return x+x; /* NaN */ + else return (xsb==0)? x:0.0; /* exp(+-inf)={inf,0} */ + } + if(x > o_threshold) return huge*huge; /* overflow */ + if(x < u_threshold) return twom1000*twom1000; /* underflow */ + } + + /* argument reduction */ + if(hx > 0x3fd62e42) { /* if |x| > 0.5 ln2 */ + if(hx < 0x3FF0A2B2) { /* and |x| < 1.5 ln2 */ + hi = x-ln2HI[xsb]; lo=ln2LO[xsb]; k = 1-xsb-xsb; + } else { + k = invln2*x+halF[xsb]; + t = k; + hi = x - t*ln2HI[0]; /* t*ln2HI is exact here */ + lo = t*ln2LO[0]; + } + x = hi - lo; + } + else if(hx < 0x3e300000) { /* when |x|<2**-28 */ + if(huge+x>one) return one+x;/* trigger inexact */ + } + else k = 0; + + /* x is now in primary range */ + t = x*x; + c = x - t*(P1+t*(P2+t*(P3+t*(P4+t*P5)))); + if(k==0) return one-((x*c)/(c-2.0)-x); + else y = one-((lo-(x*c)/(2.0-c))-hi); + if(k >= -1021) { + u_int32_t hy; + GET_HIGH_WORD(hy,y); + SET_HIGH_WORD(y,hy+(k<<20)); /* add k to y's exponent */ + return y; + } else { + u_int32_t hy; + GET_HIGH_WORD(hy,y); + SET_HIGH_WORD(y,hy+((k+1000)<<20)); /* add k to y's exponent */ + return y*twom1000; + } +} diff --git a/lib/libm/src/e_expf.c b/lib/libm/src/e_expf.c new file mode 100644 index 0000000000..30d0ee7496 --- /dev/null +++ b/lib/libm/src/e_expf.c @@ -0,0 +1,97 @@ +/* e_expf.c -- float version of e_exp.c. + * Conversion to float by Ian Lance Taylor, Cygnus Support, ian@cygnus.com. + */ + +/* + * ==================================================== + * Copyright (C) 1993 by Sun Microsystems, Inc. All rights reserved. + * + * Developed at SunPro, a Sun Microsystems, Inc. business. + * Permission to use, copy, modify, and distribute this + * software is freely granted, provided that this notice + * is preserved. + * ==================================================== + * + * $NetBSD: e_expf.c,v 1.9 2002/05/26 22:01:49 wiz Exp $ + * $DragonFly: src/lib/libm/src/e_expf.c,v 1.1 2005/07/26 21:15:20 joerg Exp $ + */ + +#include +#include "math_private.h" + +static const float huge = 1.0e+30; + +static const float +one = 1.0, +halF[2] = {0.5,-0.5,}, +twom100 = 7.8886090522e-31, /* 2**-100=0x0d800000 */ +o_threshold= 8.8721679688e+01, /* 0x42b17180 */ +u_threshold= -1.0397208405e+02, /* 0xc2cff1b5 */ +ln2HI[2] ={ 6.9313812256e-01, /* 0x3f317180 */ + -6.9313812256e-01,}, /* 0xbf317180 */ +ln2LO[2] ={ 9.0580006145e-06, /* 0x3717f7d1 */ + -9.0580006145e-06,}, /* 0xb717f7d1 */ +invln2 = 1.4426950216e+00, /* 0x3fb8aa3b */ +P1 = 1.6666667163e-01, /* 0x3e2aaaab */ +P2 = -2.7777778450e-03, /* 0xbb360b61 */ +P3 = 6.6137559770e-05, /* 0x388ab355 */ +P4 = -1.6533901999e-06, /* 0xb5ddea0e */ +P5 = 4.1381369442e-08; /* 0x3331bb4c */ + +float +expf(float x) /* default IEEE double exp */ +{ + float y,hi,lo,c,t; + int32_t k,xsb; + u_int32_t hx; + + hi = lo = 0; + k = 0; + GET_FLOAT_WORD(hx,x); + xsb = (hx>>31)&1; /* sign bit of x */ + hx &= 0x7fffffff; /* high word of |x| */ + + /* filter out non-finite argument */ + if(hx >= 0x42b17218) { /* if |x|>=88.721... */ + if(hx>0x7f800000) + return x+x; /* NaN */ + if(hx==0x7f800000) + return (xsb==0)? x:0.0; /* exp(+-inf)={inf,0} */ + if(x > o_threshold) return huge*huge; /* overflow */ + if(x < u_threshold) return twom100*twom100; /* underflow */ + } + + /* argument reduction */ + if(hx > 0x3eb17218) { /* if |x| > 0.5 ln2 */ + if(hx < 0x3F851592) { /* and |x| < 1.5 ln2 */ + hi = x-ln2HI[xsb]; lo=ln2LO[xsb]; k = 1-xsb-xsb; + } else { + k = invln2*x+halF[xsb]; + t = k; + hi = x - t*ln2HI[0]; /* t*ln2HI is exact here */ + lo = t*ln2LO[0]; + } + x = hi - lo; + } + else if(hx < 0x31800000) { /* when |x|<2**-28 */ + if(huge+x>one) return one+x;/* trigger inexact */ + } + else k = 0; + + /* x is now in primary range */ + t = x*x; + c = x - t*(P1+t*(P2+t*(P3+t*(P4+t*P5)))); + if(k==0) return one-((x*c)/(c-(float)2.0)-x); + else y = one-((lo-(x*c)/((float)2.0-c))-hi); + if(k >= -125) { + u_int32_t hy; + GET_FLOAT_WORD(hy,y); + SET_FLOAT_WORD(y,hy+(k<<23)); /* add k to y's exponent */ + return y; + } else { + u_int32_t hy; + GET_FLOAT_WORD(hy,y); + SET_FLOAT_WORD(y,hy+((k+100)<<23)); /* add k to y's exponent */ + return y*twom100; + } +} diff --git a/lib/libm/src/e_fmod.c b/lib/libm/src/e_fmod.c new file mode 100644 index 0000000000..ff0edccc18 --- /dev/null +++ b/lib/libm/src/e_fmod.c @@ -0,0 +1,131 @@ +/* @(#)e_fmod.c 5.1 93/09/24 */ +/* + * ==================================================== + * Copyright (C) 1993 by Sun Microsystems, Inc. All rights reserved. + * + * Developed at SunPro, a Sun Microsystems, Inc. business. + * Permission to use, copy, modify, and distribute this + * software is freely granted, provided that this notice + * is preserved. + * ==================================================== + * + * $NetBSD: e_fmod.c,v 1.11 2002/05/26 22:01:49 wiz Exp $ + * $DragonFly: src/lib/libm/src/e_fmod.c,v 1.1 2005/07/26 21:15:20 joerg Exp $ + */ + +/* + * fmod(x,y) + * Return x mod y in exact arithmetic + * Method: shift and subtract + */ + +#include +#include "math_private.h" + +static const double one = 1.0, Zero[] = {0.0, -0.0,}; + +double +fmod(double x, double y) +{ + int32_t n,hx,hy,hz,ix,iy,sx,i; + u_int32_t lx,ly,lz; + + EXTRACT_WORDS(hx,lx,x); + EXTRACT_WORDS(hy,ly,y); + sx = hx&0x80000000; /* sign of x */ + hx ^=sx; /* |x| */ + hy &= 0x7fffffff; /* |y| */ + + /* purge off exception values */ + if((hy|ly)==0||(hx>=0x7ff00000)|| /* y=0,or x not finite */ + ((hy|((ly|-ly)>>31))>0x7ff00000)) /* or y is NaN */ + return (x*y)/(x*y); + if(hx<=hy) { + if((hx>31]; /* |x|=|y| return x*0*/ + } + + /* determine ix = ilogb(x) */ + if(hx<0x00100000) { /* subnormal x */ + if(hx==0) { + for (ix = -1043, i=lx; i>0; i<<=1) ix -=1; + } else { + for (ix = -1022,i=(hx<<11); i>0; i<<=1) ix -=1; + } + } else ix = (hx>>20)-1023; + + /* determine iy = ilogb(y) */ + if(hy<0x00100000) { /* subnormal y */ + if(hy==0) { + for (iy = -1043, i=ly; i>0; i<<=1) iy -=1; + } else { + for (iy = -1022,i=(hy<<11); i>0; i<<=1) iy -=1; + } + } else iy = (hy>>20)-1023; + + /* set up {hx,lx}, {hy,ly} and align y to x */ + if(ix >= -1022) + hx = 0x00100000|(0x000fffff&hx); + else { /* subnormal x, shift x to normal */ + n = -1022-ix; + if(n<=31) { + hx = (hx<>(32-n)); + lx <<= n; + } else { + hx = lx<<(n-32); + lx = 0; + } + } + if(iy >= -1022) + hy = 0x00100000|(0x000fffff&hy); + else { /* subnormal y, shift y to normal */ + n = -1022-iy; + if(n<=31) { + hy = (hy<>(32-n)); + ly <<= n; + } else { + hy = ly<<(n-32); + ly = 0; + } + } + + /* fix point fmod */ + n = ix - iy; + while(n--) { + hz=hx-hy;lz=lx-ly; if(lx>31); lx = lx+lx;} + else { + if((hz|lz)==0) /* return sign(x)*0 */ + return Zero[(u_int32_t)sx>>31]; + hx = hz+hz+(lz>>31); lx = lz+lz; + } + } + hz=hx-hy;lz=lx-ly; if(lx=0) {hx=hz;lx=lz;} + + /* convert back to floating value and restore the sign */ + if((hx|lx)==0) /* return sign(x)*0 */ + return Zero[(u_int32_t)sx>>31]; + while(hx<0x00100000) { /* normalize x */ + hx = hx+hx+(lx>>31); lx = lx+lx; + iy -= 1; + } + if(iy>= -1022) { /* normalize output */ + hx = ((hx-0x00100000)|((iy+1023)<<20)); + INSERT_WORDS(x,hx|sx,lx); + } else { /* subnormal output */ + n = -1022 - iy; + if(n<=20) { + lx = (lx>>n)|((u_int32_t)hx<<(32-n)); + hx >>= n; + } else if (n<=31) { + lx = (hx<<(32-n))|(lx>>n); hx = sx; + } else { + lx = hx>>(n-32); hx = sx; + } + INSERT_WORDS(x,hx|sx,lx); + x *= one; /* create necessary signal */ + } + return x; /* exact output */ +} diff --git a/lib/libm/src/e_fmodf.c b/lib/libm/src/e_fmodf.c new file mode 100644 index 0000000000..21b6c45e2a --- /dev/null +++ b/lib/libm/src/e_fmodf.c @@ -0,0 +1,104 @@ +/* e_fmodf.c -- float version of e_fmod.c. + * Conversion to float by Ian Lance Taylor, Cygnus Support, ian@cygnus.com. + */ + +/* + * ==================================================== + * Copyright (C) 1993 by Sun Microsystems, Inc. All rights reserved. + * + * Developed at SunPro, a Sun Microsystems, Inc. business. + * Permission to use, copy, modify, and distribute this + * software is freely granted, provided that this notice + * is preserved. + * ==================================================== + * + * $NetBSD: e_fmodf.c,v 1.7 2002/05/26 22:01:49 wiz Exp $ + * $DragonFly: src/lib/libm/src/e_fmodf.c,v 1.1 2005/07/26 21:15:20 joerg Exp $ + */ + +/* + * fmodf(x,y) + * Return x mod y in exact arithmetic + * Method: shift and subtract + */ + +#include +#include "math_private.h" + +static const float one = 1.0, Zero[] = {0.0, -0.0,}; + +float +fmodf(float x, float y) +{ + int32_t n,hx,hy,hz,ix,iy,sx,i; + + GET_FLOAT_WORD(hx,x); + GET_FLOAT_WORD(hy,y); + sx = hx&0x80000000; /* sign of x */ + hx ^=sx; /* |x| */ + hy &= 0x7fffffff; /* |y| */ + + /* purge off exception values */ + if(hy==0||(hx>=0x7f800000)|| /* y=0,or x not finite */ + (hy>0x7f800000)) /* or y is NaN */ + return (x*y)/(x*y); + if(hx>31]; /* |x|=|y| return x*0*/ + + /* determine ix = ilogb(x) */ + if(hx<0x00800000) { /* subnormal x */ + for (ix = -126,i=(hx<<8); i>0; i<<=1) ix -=1; + } else ix = (hx>>23)-127; + + /* determine iy = ilogb(y) */ + if(hy<0x00800000) { /* subnormal y */ + for (iy = -126,i=(hy<<8); i>=0; i<<=1) iy -=1; + } else iy = (hy>>23)-127; + + /* set up {hx,lx}, {hy,ly} and align y to x */ + if(ix >= -126) + hx = 0x00800000|(0x007fffff&hx); + else { /* subnormal x, shift x to normal */ + n = -126-ix; + hx = hx<= -126) + hy = 0x00800000|(0x007fffff&hy); + else { /* subnormal y, shift y to normal */ + n = -126-iy; + hy = hy<>31]; + hx = hz+hz; + } + } + hz=hx-hy; + if(hz>=0) {hx=hz;} + + /* convert back to floating value and restore the sign */ + if(hx==0) /* return sign(x)*0 */ + return Zero[(u_int32_t)sx>>31]; + while(hx<0x00800000) { /* normalize x */ + hx = hx+hx; + iy -= 1; + } + if(iy>= -126) { /* normalize output */ + hx = ((hx-0x00800000)|((iy+127)<<23)); + SET_FLOAT_WORD(x,hx|sx); + } else { /* subnormal output */ + n = -126 - iy; + hx >>= n; + SET_FLOAT_WORD(x,hx|sx); + x *= one; /* create necessary signal */ + } + return x; /* exact output */ +} diff --git a/lib/libm/src/e_hypot.c b/lib/libm/src/e_hypot.c new file mode 100644 index 0000000000..20a8774893 --- /dev/null +++ b/lib/libm/src/e_hypot.c @@ -0,0 +1,123 @@ +/* @(#)e_hypot.c 5.1 93/09/24 */ +/* + * ==================================================== + * Copyright (C) 1993 by Sun Microsystems, Inc. All rights reserved. + * + * Developed at SunPro, a Sun Microsystems, Inc. business. + * Permission to use, copy, modify, and distribute this + * software is freely granted, provided that this notice + * is preserved. + * ==================================================== + * + * $NetBSD: e_hypot.c,v 1.12 2002/05/26 22:01:50 wiz Exp $ + * $DragonFly: src/lib/libm/src/e_hypot.c,v 1.1 2005/07/26 21:15:20 joerg Exp $ + */ + +/* hypot(x,y) + * + * Method : + * If (assume round-to-nearest) z=x*x+y*y + * has error less than sqrt(2)/2 ulp, than + * sqrt(z) has error less than 1 ulp (exercise). + * + * So, compute sqrt(x*x+y*y) with some care as + * follows to get the error below 1 ulp: + * + * Assume x>y>0; + * (if possible, set rounding to round-to-nearest) + * 1. if x > 2y use + * x1*x1+(y*y+(x2*(x+x1))) for x*x+y*y + * where x1 = x with lower 32 bits cleared, x2 = x-x1; else + * 2. if x <= 2y use + * t1*y1+((x-y)*(x-y)+(t1*y2+t2*y)) + * where t1 = 2x with lower 32 bits cleared, t2 = 2x-t1, + * y1= y with lower 32 bits chopped, y2 = y-y1. + * + * NOTE: scaling may be necessary if some argument is too + * large or too tiny + * + * Special cases: + * hypot(x,y) is INF if x or y is +INF or -INF; else + * hypot(x,y) is NAN if x or y is NAN. + * + * Accuracy: + * hypot(x,y) returns sqrt(x^2+y^2) with error less + * than 1 ulps (units in the last place) + */ + +#include +#include "math_private.h" + +double +hypot(double x, double y) +{ + double a=x,b=y,t1,t2,y1_,y2,w; + int32_t j,k,ha,hb; + + GET_HIGH_WORD(ha,x); + ha &= 0x7fffffff; + GET_HIGH_WORD(hb,y); + hb &= 0x7fffffff; + if(hb > ha) {a=y;b=x;j=ha; ha=hb;hb=j;} else {a=x;b=y;} + SET_HIGH_WORD(a,ha); /* a <- |a| */ + SET_HIGH_WORD(b,hb); /* b <- |b| */ + if((ha-hb)>0x3c00000) {return a+b;} /* x/y > 2**60 */ + k=0; + if(ha > 0x5f300000) { /* a>2**500 */ + if(ha >= 0x7ff00000) { /* Inf or NaN */ + u_int32_t low; + w = a+b; /* for sNaN */ + GET_LOW_WORD(low,a); + if(((ha&0xfffff)|low)==0) w = a; + GET_LOW_WORD(low,b); + if(((hb^0x7ff00000)|low)==0) w = b; + return w; + } + /* scale a and b by 2**-600 */ + ha -= 0x25800000; hb -= 0x25800000; k += 600; + SET_HIGH_WORD(a,ha); + SET_HIGH_WORD(b,hb); + } + if(hb < 0x20b00000) { /* b < 2**-500 */ + if(hb <= 0x000fffff) { /* subnormal b or 0 */ + u_int32_t low; + GET_LOW_WORD(low,b); + if((hb|low)==0) return a; + t1=0; + SET_HIGH_WORD(t1,0x7fd00000); /* t1=2^1022 */ + b *= t1; + a *= t1; + k -= 1022; + } else { /* scale a and b by 2^600 */ + ha += 0x25800000; /* a *= 2^600 */ + hb += 0x25800000; /* b *= 2^600 */ + k -= 600; + SET_HIGH_WORD(a,ha); + SET_HIGH_WORD(b,hb); + } + } + /* medium size a and b */ + w = a-b; + if (w>b) { + t1 = 0; + SET_HIGH_WORD(t1,ha); + t2 = a-t1; + w = sqrt(t1*t1-(b*(-b)-t2*(a+t1))); + } else { + a = a+a; + y1_ = 0; + SET_HIGH_WORD(y1_,hb); + y2 = b - y1_; + t1 = 0; + SET_HIGH_WORD(t1,ha+0x00100000); + t2 = a - t1; + w = sqrt(t1*y1_-(w*(-w)-(t1*y2+t2*b))); + } + if(k!=0) { + u_int32_t high; + t1 = 1.0; + GET_HIGH_WORD(high,t1); + SET_HIGH_WORD(t1,high+(k<<20)); + return t1*w; + } else return w; +} diff --git a/lib/libm/src/e_hypotf.c b/lib/libm/src/e_hypotf.c new file mode 100644 index 0000000000..9eed0f7bb7 --- /dev/null +++ b/lib/libm/src/e_hypotf.c @@ -0,0 +1,82 @@ +/* e_hypotf.c -- float version of e_hypot.c. + * Conversion to float by Ian Lance Taylor, Cygnus Support, ian@cygnus.com. + */ + +/* + * ==================================================== + * Copyright (C) 1993 by Sun Microsystems, Inc. All rights reserved. + * + * Developed at SunPro, a Sun Microsystems, Inc. business. + * Permission to use, copy, modify, and distribute this + * software is freely granted, provided that this notice + * is preserved. + * ==================================================== + * + * $NetBSD: e_hypotf.c,v 1.8 2002/05/26 22:01:50 wiz Exp $ + * $DragonFly: src/lib/libm/src/e_hypotf.c,v 1.1 2005/07/26 21:15:20 joerg Exp $ + */ + +#include +#include "math_private.h" + +float +hypotf(float x, float y) +{ + float a=x,b=y,t1,t2,y1_,y2,w; + int32_t j,k,ha,hb; + + GET_FLOAT_WORD(ha,x); + ha &= 0x7fffffff; + GET_FLOAT_WORD(hb,y); + hb &= 0x7fffffff; + if(hb > ha) {a=y;b=x;j=ha; ha=hb;hb=j;} else {a=x;b=y;} + SET_FLOAT_WORD(a,ha); /* a <- |a| */ + SET_FLOAT_WORD(b,hb); /* b <- |b| */ + if((ha-hb)>0xf000000) {return a+b;} /* x/y > 2**30 */ + k=0; + if(ha > 0x58800000) { /* a>2**50 */ + if(ha >= 0x7f800000) { /* Inf or NaN */ + w = a+b; /* for sNaN */ + if(ha == 0x7f800000) w = a; + if(hb == 0x7f800000) w = b; + return w; + } + /* scale a and b by 2**-60 */ + ha -= 0x5d800000; hb -= 0x5d800000; k += 60; + SET_FLOAT_WORD(a,ha); + SET_FLOAT_WORD(b,hb); + } + if(hb < 0x26800000) { /* b < 2**-50 */ + if(hb <= 0x007fffff) { /* subnormal b or 0 */ + if(hb==0) return a; + SET_FLOAT_WORD(t1,0x3f000000); /* t1=2^126 */ + b *= t1; + a *= t1; + k -= 126; + } else { /* scale a and b by 2^60 */ + ha += 0x5d800000; /* a *= 2^60 */ + hb += 0x5d800000; /* b *= 2^60 */ + k -= 60; + SET_FLOAT_WORD(a,ha); + SET_FLOAT_WORD(b,hb); + } + } + /* medium size a and b */ + w = a-b; + if (w>b) { + SET_FLOAT_WORD(t1,ha&0xfffff000); + t2 = a-t1; + w = sqrtf(t1*t1-(b*(-b)-t2*(a+t1))); + } else { + a = a+a; + SET_FLOAT_WORD(y1_,hb&0xfffff000); + y2 = b - y1_; + SET_FLOAT_WORD(t1,ha+0x00800000); + t2 = a - t1; + w = sqrtf(t1*y1_-(w*(-w)-(t1*y2+t2*b))); + } + if(k!=0) { + SET_FLOAT_WORD(t1,0x3f800000+(k<<23)); + return t1*w; + } else return w; +} diff --git a/lib/libm/src/e_j0.c b/lib/libm/src/e_j0.c new file mode 100644 index 0000000000..5b14980ead --- /dev/null +++ b/lib/libm/src/e_j0.c @@ -0,0 +1,386 @@ +/* @(#)e_j0.c 5.1 93/09/24 */ +/* + * ==================================================== + * Copyright (C) 1993 by Sun Microsystems, Inc. All rights reserved. + * + * Developed at SunPro, a Sun Microsystems, Inc. business. + * Permission to use, copy, modify, and distribute this + * software is freely granted, provided that this notice + * is preserved. + * ==================================================== + * + * $NetBSD: e_j0.c,v 1.11 2002/05/26 22:01:50 wiz Exp $ + * $DragonFly: src/lib/libm/src/e_j0.c,v 1.1 2005/07/26 21:15:20 joerg Exp $ + */ + +/* j0(x), y0(x) + * Bessel function of the first and second kinds of order zero. + * Method -- j0(x): + * 1. For tiny x, we use j0(x) = 1 - x^2/4 + x^4/64 - ... + * 2. Reduce x to |x| since j0(x)=j0(-x), and + * for x in (0,2) + * j0(x) = 1-z/4+ z^2*R0/S0, where z = x*x; + * (precision: |j0-1+z/4-z^2R0/S0 |<2**-63.67 ) + * for x in (2,inf) + * j0(x) = sqrt(2/(pi*x))*(p0(x)*cos(x0)-q0(x)*sin(x0)) + * where x0 = x-pi/4. It is better to compute sin(x0),cos(x0) + * as follow: + * cos(x0) = cos(x)cos(pi/4)+sin(x)sin(pi/4) + * = 1/sqrt(2) * (cos(x) + sin(x)) + * sin(x0) = sin(x)cos(pi/4)-cos(x)sin(pi/4) + * = 1/sqrt(2) * (sin(x) - cos(x)) + * (To avoid cancellation, use + * sin(x) +- cos(x) = -cos(2x)/(sin(x) -+ cos(x)) + * to compute the worse one.) + * + * 3 Special cases + * j0(nan)= nan + * j0(0) = 1 + * j0(inf) = 0 + * + * Method -- y0(x): + * 1. For x<2. + * Since + * y0(x) = 2/pi*(j0(x)*(ln(x/2)+Euler) + x^2/4 - ...) + * therefore y0(x)-2/pi*j0(x)*ln(x) is an even function. + * We use the following function to approximate y0, + * y0(x) = U(z)/V(z) + (2/pi)*(j0(x)*ln(x)), z= x^2 + * where + * U(z) = u00 + u01*z + ... + u06*z^6 + * V(z) = 1 + v01*z + ... + v04*z^4 + * with absolute approximation error bounded by 2**-72. + * Note: For tiny x, U/V = u0 and j0(x)~1, hence + * y0(tiny) = u0 + (2/pi)*ln(tiny), (choose tiny<2**-27) + * 2. For x>=2. + * y0(x) = sqrt(2/(pi*x))*(p0(x)*cos(x0)+q0(x)*sin(x0)) + * where x0 = x-pi/4. It is better to compute sin(x0),cos(x0) + * by the method mentioned above. + * 3. Special cases: y0(0)=-inf, y0(x<0)=NaN, y0(inf)=0. + */ + +#include +#include "math_private.h" + +static double pzero(double), qzero(double); + +static const double +huge = 1e300, +one = 1.0, +invsqrtpi= 5.64189583547756279280e-01, /* 0x3FE20DD7, 0x50429B6D */ +tpi = 6.36619772367581382433e-01, /* 0x3FE45F30, 0x6DC9C883 */ + /* R0/S0 on [0, 2.00] */ +R02 = 1.56249999999999947958e-02, /* 0x3F8FFFFF, 0xFFFFFFFD */ +R03 = -1.89979294238854721751e-04, /* 0xBF28E6A5, 0xB61AC6E9 */ +R04 = 1.82954049532700665670e-06, /* 0x3EBEB1D1, 0x0C503919 */ +R05 = -4.61832688532103189199e-09, /* 0xBE33D5E7, 0x73D63FCE */ +S01 = 1.56191029464890010492e-02, /* 0x3F8FFCE8, 0x82C8C2A4 */ +S02 = 1.16926784663337450260e-04, /* 0x3F1EA6D2, 0xDD57DBF4 */ +S03 = 5.13546550207318111446e-07, /* 0x3EA13B54, 0xCE84D5A9 */ +S04 = 1.16614003333790000205e-09; /* 0x3E1408BC, 0xF4745D8F */ + +static const double zero = 0.0; + +double +j0(double x) +{ + double z, s,c,ss,cc,r,u,v; + int32_t hx,ix; + + GET_HIGH_WORD(hx,x); + ix = hx&0x7fffffff; + if(ix>=0x7ff00000) return one/(x*x); + x = fabs(x); + if(ix >= 0x40000000) { /* |x| >= 2.0 */ + s = sin(x); + c = cos(x); + ss = s-c; + cc = s+c; + if(ix<0x7fe00000) { /* make sure x+x not overflow */ + z = -cos(x+x); + if ((s*c)0x48000000) z = (invsqrtpi*cc)/sqrt(x); + else { + u = pzero(x); v = qzero(x); + z = invsqrtpi*(u*cc-v*ss)/sqrt(x); + } + return z; + } + if(ix<0x3f200000) { /* |x| < 2**-13 */ + if(huge+x>one) { /* raise inexact if x != 0 */ + if(ix<0x3e400000) return one; /* |x|<2**-27 */ + else return one - 0.25*x*x; + } + } + z = x*x; + r = z*(R02+z*(R03+z*(R04+z*R05))); + s = one+z*(S01+z*(S02+z*(S03+z*S04))); + if(ix < 0x3FF00000) { /* |x| < 1.00 */ + return one + z*(-0.25+(r/s)); + } else { + u = 0.5*x; + return((one+u)*(one-u)+z*(r/s)); + } +} + +static const double +u00 = -7.38042951086872317523e-02, /* 0xBFB2E4D6, 0x99CBD01F */ +u01 = 1.76666452509181115538e-01, /* 0x3FC69D01, 0x9DE9E3FC */ +u02 = -1.38185671945596898896e-02, /* 0xBF8C4CE8, 0xB16CFA97 */ +u03 = 3.47453432093683650238e-04, /* 0x3F36C54D, 0x20B29B6B */ +u04 = -3.81407053724364161125e-06, /* 0xBECFFEA7, 0x73D25CAD */ +u05 = 1.95590137035022920206e-08, /* 0x3E550057, 0x3B4EABD4 */ +u06 = -3.98205194132103398453e-11, /* 0xBDC5E43D, 0x693FB3C8 */ +v01 = 1.27304834834123699328e-02, /* 0x3F8A1270, 0x91C9C71A */ +v02 = 7.60068627350353253702e-05, /* 0x3F13ECBB, 0xF578C6C1 */ +v03 = 2.59150851840457805467e-07, /* 0x3E91642D, 0x7FF202FD */ +v04 = 4.41110311332675467403e-10; /* 0x3DFE5018, 0x3BD6D9EF */ + +double +y0(double x) +{ + double z, s,c,ss,cc,u,v; + int32_t hx,ix,lx; + + EXTRACT_WORDS(hx,lx,x); + ix = 0x7fffffff&hx; + /* Y0(NaN) is NaN, y0(-inf) is Nan, y0(inf) is 0 */ + if(ix>=0x7ff00000) return one/(x+x*x); + if((ix|lx)==0) return -one/zero; + if(hx<0) return zero/zero; + if(ix >= 0x40000000) { /* |x| >= 2.0 */ + /* y0(x) = sqrt(2/(pi*x))*(p0(x)*sin(x0)+q0(x)*cos(x0)) + * where x0 = x-pi/4 + * Better formula: + * cos(x0) = cos(x)cos(pi/4)+sin(x)sin(pi/4) + * = 1/sqrt(2) * (sin(x) + cos(x)) + * sin(x0) = sin(x)cos(3pi/4)-cos(x)sin(3pi/4) + * = 1/sqrt(2) * (sin(x) - cos(x)) + * To avoid cancellation, use + * sin(x) +- cos(x) = -cos(2x)/(sin(x) -+ cos(x)) + * to compute the worse one. + */ + s = sin(x); + c = cos(x); + ss = s-c; + cc = s+c; + /* + * j0(x) = 1/sqrt(pi) * (P(0,x)*cc - Q(0,x)*ss) / sqrt(x) + * y0(x) = 1/sqrt(pi) * (P(0,x)*ss + Q(0,x)*cc) / sqrt(x) + */ + if(ix<0x7fe00000) { /* make sure x+x not overflow */ + z = -cos(x+x); + if ((s*c)0x48000000) z = (invsqrtpi*ss)/sqrt(x); + else { + u = pzero(x); v = qzero(x); + z = invsqrtpi*(u*ss+v*cc)/sqrt(x); + } + return z; + } + if(ix<=0x3e400000) { /* x < 2**-27 */ + return(u00 + tpi*log(x)); + } + z = x*x; + u = u00+z*(u01+z*(u02+z*(u03+z*(u04+z*(u05+z*u06))))); + v = one+z*(v01+z*(v02+z*(v03+z*v04))); + return(u/v + tpi*(j0(x)*log(x))); +} + +/* The asymptotic expansions of pzero is + * 1 - 9/128 s^2 + 11025/98304 s^4 - ..., where s = 1/x. + * For x >= 2, We approximate pzero by + * pzero(x) = 1 + (R/S) + * where R = pR0 + pR1*s^2 + pR2*s^4 + ... + pR5*s^10 + * S = 1 + pS0*s^2 + ... + pS4*s^10 + * and + * | pzero(x)-1-R/S | <= 2 ** ( -60.26) + */ +static const double pR8[6] = { /* for x in [inf, 8]=1/[0,0.125] */ + 0.00000000000000000000e+00, /* 0x00000000, 0x00000000 */ + -7.03124999999900357484e-02, /* 0xBFB1FFFF, 0xFFFFFD32 */ + -8.08167041275349795626e+00, /* 0xC02029D0, 0xB44FA779 */ + -2.57063105679704847262e+02, /* 0xC0701102, 0x7B19E863 */ + -2.48521641009428822144e+03, /* 0xC0A36A6E, 0xCD4DCAFC */ + -5.25304380490729545272e+03, /* 0xC0B4850B, 0x36CC643D */ +}; +static const double pS8[5] = { + 1.16534364619668181717e+02, /* 0x405D2233, 0x07A96751 */ + 3.83374475364121826715e+03, /* 0x40ADF37D, 0x50596938 */ + 4.05978572648472545552e+04, /* 0x40E3D2BB, 0x6EB6B05F */ + 1.16752972564375915681e+05, /* 0x40FC810F, 0x8F9FA9BD */ + 4.76277284146730962675e+04, /* 0x40E74177, 0x4F2C49DC */ +}; + +static const double pR5[6] = { /* for x in [8,4.5454]=1/[0.125,0.22001] */ + -1.14125464691894502584e-11, /* 0xBDA918B1, 0x47E495CC */ + -7.03124940873599280078e-02, /* 0xBFB1FFFF, 0xE69AFBC6 */ + -4.15961064470587782438e+00, /* 0xC010A370, 0xF90C6BBF */ + -6.76747652265167261021e+01, /* 0xC050EB2F, 0x5A7D1783 */ + -3.31231299649172967747e+02, /* 0xC074B3B3, 0x6742CC63 */ + -3.46433388365604912451e+02, /* 0xC075A6EF, 0x28A38BD7 */ +}; +static const double pS5[5] = { + 6.07539382692300335975e+01, /* 0x404E6081, 0x0C98C5DE */ + 1.05125230595704579173e+03, /* 0x40906D02, 0x5C7E2864 */ + 5.97897094333855784498e+03, /* 0x40B75AF8, 0x8FBE1D60 */ + 9.62544514357774460223e+03, /* 0x40C2CCB8, 0xFA76FA38 */ + 2.40605815922939109441e+03, /* 0x40A2CC1D, 0xC70BE864 */ +}; + +static const double pR3[6] = {/* for x in [4.547,2.8571]=1/[0.2199,0.35001] */ + -2.54704601771951915620e-09, /* 0xBE25E103, 0x6FE1AA86 */ + -7.03119616381481654654e-02, /* 0xBFB1FFF6, 0xF7C0E24B */ + -2.40903221549529611423e+00, /* 0xC00345B2, 0xAEA48074 */ + -2.19659774734883086467e+01, /* 0xC035F74A, 0x4CB94E14 */ + -5.80791704701737572236e+01, /* 0xC04D0A22, 0x420A1A45 */ + -3.14479470594888503854e+01, /* 0xC03F72AC, 0xA892D80F */ +}; +static const double pS3[5] = { + 3.58560338055209726349e+01, /* 0x4041ED92, 0x84077DD3 */ + 3.61513983050303863820e+02, /* 0x40769839, 0x464A7C0E */ + 1.19360783792111533330e+03, /* 0x4092A66E, 0x6D1061D6 */ + 1.12799679856907414432e+03, /* 0x40919FFC, 0xB8C39B7E */ + 1.73580930813335754692e+02, /* 0x4065B296, 0xFC379081 */ +}; + +static const double pR2[6] = {/* for x in [2.8570,2]=1/[0.3499,0.5] */ + -8.87534333032526411254e-08, /* 0xBE77D316, 0xE927026D */ + -7.03030995483624743247e-02, /* 0xBFB1FF62, 0x495E1E42 */ + -1.45073846780952986357e+00, /* 0xBFF73639, 0x8A24A843 */ + -7.63569613823527770791e+00, /* 0xC01E8AF3, 0xEDAFA7F3 */ + -1.11931668860356747786e+01, /* 0xC02662E6, 0xC5246303 */ + -3.23364579351335335033e+00, /* 0xC009DE81, 0xAF8FE70F */ +}; +static const double pS2[5] = { + 2.22202997532088808441e+01, /* 0x40363865, 0x908B5959 */ + 1.36206794218215208048e+02, /* 0x4061069E, 0x0EE8878F */ + 2.70470278658083486789e+02, /* 0x4070E786, 0x42EA079B */ + 1.53875394208320329881e+02, /* 0x40633C03, 0x3AB6FAFF */ + 1.46576176948256193810e+01, /* 0x402D50B3, 0x44391809 */ +}; + +static double +pzero(double x) +{ + const double *p,*q; + double z,r,s; + int32_t ix; + + p = q = 0; + GET_HIGH_WORD(ix,x); + ix &= 0x7fffffff; + if(ix>=0x40200000) {p = pR8; q= pS8;} + else if(ix>=0x40122E8B){p = pR5; q= pS5;} + else if(ix>=0x4006DB6D){p = pR3; q= pS3;} + else if(ix>=0x40000000){p = pR2; q= pS2;} + z = one/(x*x); + r = p[0]+z*(p[1]+z*(p[2]+z*(p[3]+z*(p[4]+z*p[5])))); + s = one+z*(q[0]+z*(q[1]+z*(q[2]+z*(q[3]+z*q[4])))); + return one+ r/s; +} + + +/* For x >= 8, the asymptotic expansions of qzero is + * -1/8 s + 75/1024 s^3 - ..., where s = 1/x. + * We approximate pzero by + * qzero(x) = s*(-1.25 + (R/S)) + * where R = qR0 + qR1*s^2 + qR2*s^4 + ... + qR5*s^10 + * S = 1 + qS0*s^2 + ... + qS5*s^12 + * and + * | qzero(x)/s +1.25-R/S | <= 2 ** ( -61.22) + */ +static const double qR8[6] = { /* for x in [inf, 8]=1/[0,0.125] */ + 0.00000000000000000000e+00, /* 0x00000000, 0x00000000 */ + 7.32421874999935051953e-02, /* 0x3FB2BFFF, 0xFFFFFE2C */ + 1.17682064682252693899e+01, /* 0x40278952, 0x5BB334D6 */ + 5.57673380256401856059e+02, /* 0x40816D63, 0x15301825 */ + 8.85919720756468632317e+03, /* 0x40C14D99, 0x3E18F46D */ + 3.70146267776887834771e+04, /* 0x40E212D4, 0x0E901566 */ +}; +static const double qS8[6] = { + 1.63776026895689824414e+02, /* 0x406478D5, 0x365B39BC */ + 8.09834494656449805916e+03, /* 0x40BFA258, 0x4E6B0563 */ + 1.42538291419120476348e+05, /* 0x41016652, 0x54D38C3F */ + 8.03309257119514397345e+05, /* 0x412883DA, 0x83A52B43 */ + 8.40501579819060512818e+05, /* 0x4129A66B, 0x28DE0B3D */ + -3.43899293537866615225e+05, /* 0xC114FD6D, 0x2C9530C5 */ +}; + +static const double qR5[6] = { /* for x in [8,4.5454]=1/[0.125,0.22001] */ + 1.84085963594515531381e-11, /* 0x3DB43D8F, 0x29CC8CD9 */ + 7.32421766612684765896e-02, /* 0x3FB2BFFF, 0xD172B04C */ + 5.83563508962056953777e+00, /* 0x401757B0, 0xB9953DD3 */ + 1.35111577286449829671e+02, /* 0x4060E392, 0x0A8788E9 */ + 1.02724376596164097464e+03, /* 0x40900CF9, 0x9DC8C481 */ + 1.98997785864605384631e+03, /* 0x409F17E9, 0x53C6E3A6 */ +}; +static const double qS5[6] = { + 8.27766102236537761883e+01, /* 0x4054B1B3, 0xFB5E1543 */ + 2.07781416421392987104e+03, /* 0x40A03BA0, 0xDA21C0CE */ + 1.88472887785718085070e+04, /* 0x40D267D2, 0x7B591E6D */ + 5.67511122894947329769e+04, /* 0x40EBB5E3, 0x97E02372 */ + 3.59767538425114471465e+04, /* 0x40E19118, 0x1F7A54A0 */ + -5.35434275601944773371e+03, /* 0xC0B4EA57, 0xBEDBC609 */ +}; + +static const double qR3[6] = {/* for x in [4.547,2.8571]=1/[0.2199,0.35001] */ + 4.37741014089738620906e-09, /* 0x3E32CD03, 0x6ADECB82 */ + 7.32411180042911447163e-02, /* 0x3FB2BFEE, 0x0E8D0842 */ + 3.34423137516170720929e+00, /* 0x400AC0FC, 0x61149CF5 */ + 4.26218440745412650017e+01, /* 0x40454F98, 0x962DAEDD */ + 1.70808091340565596283e+02, /* 0x406559DB, 0xE25EFD1F */ + 1.66733948696651168575e+02, /* 0x4064D77C, 0x81FA21E0 */ +}; +static const double qS3[6] = { + 4.87588729724587182091e+01, /* 0x40486122, 0xBFE343A6 */ + 7.09689221056606015736e+02, /* 0x40862D83, 0x86544EB3 */ + 3.70414822620111362994e+03, /* 0x40ACF04B, 0xE44DFC63 */ + 6.46042516752568917582e+03, /* 0x40B93C6C, 0xD7C76A28 */ + 2.51633368920368957333e+03, /* 0x40A3A8AA, 0xD94FB1C0 */ + -1.49247451836156386662e+02, /* 0xC062A7EB, 0x201CF40F */ +}; + +static const double qR2[6] = {/* for x in [2.8570,2]=1/[0.3499,0.5] */ + 1.50444444886983272379e-07, /* 0x3E84313B, 0x54F76BDB */ + 7.32234265963079278272e-02, /* 0x3FB2BEC5, 0x3E883E34 */ + 1.99819174093815998816e+00, /* 0x3FFFF897, 0xE727779C */ + 1.44956029347885735348e+01, /* 0x402CFDBF, 0xAAF96FE5 */ + 3.16662317504781540833e+01, /* 0x403FAA8E, 0x29FBDC4A */ + 1.62527075710929267416e+01, /* 0x403040B1, 0x71814BB4 */ +}; +static const double qS2[6] = { + 3.03655848355219184498e+01, /* 0x403E5D96, 0xF7C07AED */ + 2.69348118608049844624e+02, /* 0x4070D591, 0xE4D14B40 */ + 8.44783757595320139444e+02, /* 0x408A6645, 0x22B3BF22 */ + 8.82935845112488550512e+02, /* 0x408B977C, 0x9C5CC214 */ + 2.12666388511798828631e+02, /* 0x406A9553, 0x0E001365 */ + -5.31095493882666946917e+00, /* 0xC0153E6A, 0xF8B32931 */ +}; + +static double +qzero(double x) +{ + const double *p,*q; + double s,r,z; + int32_t ix; + + p = q = 0; + GET_HIGH_WORD(ix,x); + ix &= 0x7fffffff; + if(ix>=0x40200000) {p = qR8; q= qS8;} + else if(ix>=0x40122E8B){p = qR5; q= qS5;} + else if(ix>=0x4006DB6D){p = qR3; q= qS3;} + else if(ix>=0x40000000){p = qR2; q= qS2;} + z = one/(x*x); + r = p[0]+z*(p[1]+z*(p[2]+z*(p[3]+z*(p[4]+z*p[5])))); + s = one+z*(q[0]+z*(q[1]+z*(q[2]+z*(q[3]+z*(q[4]+z*q[5]))))); + return (-.125 + r/s)/x; +} diff --git a/lib/libm/src/e_j0f.c b/lib/libm/src/e_j0f.c new file mode 100644 index 0000000000..98aed26f03 --- /dev/null +++ b/lib/libm/src/e_j0f.c @@ -0,0 +1,343 @@ +/* e_j0f.c -- float version of e_j0.c. + * Conversion to float by Ian Lance Taylor, Cygnus Support, ian@cygnus.com. + */ + +/* + * ==================================================== + * Copyright (C) 1993 by Sun Microsystems, Inc. All rights reserved. + * + * Developed at SunPro, a Sun Microsystems, Inc. business. + * Permission to use, copy, modify, and distribute this + * software is freely granted, provided that this notice + * is preserved. + * ==================================================== + * + * $NetBSD: e_j0f.c,v 1.7 2002/05/26 22:01:50 wiz Exp $ + * $DragonFly: src/lib/libm/src/e_j0f.c,v 1.1 2005/07/26 21:15:20 joerg Exp $ + */ + +#include +#include "math_private.h" + +static float pzerof(float), qzerof(float); + +static const float +huge = 1e30, +one = 1.0, +invsqrtpi= 5.6418961287e-01, /* 0x3f106ebb */ +tpi = 6.3661974669e-01, /* 0x3f22f983 */ + /* R0/S0 on [0, 2.00] */ +R02 = 1.5625000000e-02, /* 0x3c800000 */ +R03 = -1.8997929874e-04, /* 0xb947352e */ +R04 = 1.8295404516e-06, /* 0x35f58e88 */ +R05 = -4.6183270541e-09, /* 0xb19eaf3c */ +S01 = 1.5619102865e-02, /* 0x3c7fe744 */ +S02 = 1.1692678527e-04, /* 0x38f53697 */ +S03 = 5.1354652442e-07, /* 0x3509daa6 */ +S04 = 1.1661400734e-09; /* 0x30a045e8 */ + +static const float zero = 0.0; + +float +j0f(float x) +{ + float z, s,c,ss,cc,r,u,v; + int32_t hx,ix; + + GET_FLOAT_WORD(hx,x); + ix = hx&0x7fffffff; + if(ix>=0x7f800000) return one/(x*x); + x = fabsf(x); + if(ix >= 0x40000000) { /* |x| >= 2.0 */ + s = sinf(x); + c = cosf(x); + ss = s-c; + cc = s+c; + if(ix<0x7f000000) { /* make sure x+x not overflow */ + z = -cosf(x+x); + if ((s*c)0x80000000) z = (invsqrtpi*cc)/sqrtf(x); + else { + u = pzerof(x); v = qzerof(x); + z = invsqrtpi*(u*cc-v*ss)/sqrtf(x); + } + return z; + } + if(ix<0x39000000) { /* |x| < 2**-13 */ + if(huge+x>one) { /* raise inexact if x != 0 */ + if(ix<0x32000000) return one; /* |x|<2**-27 */ + else return one - (float)0.25*x*x; + } + } + z = x*x; + r = z*(R02+z*(R03+z*(R04+z*R05))); + s = one+z*(S01+z*(S02+z*(S03+z*S04))); + if(ix < 0x3F800000) { /* |x| < 1.00 */ + return one + z*((float)-0.25+(r/s)); + } else { + u = (float)0.5*x; + return((one+u)*(one-u)+z*(r/s)); + } +} + +static const float +u00 = -7.3804296553e-02, /* 0xbd9726b5 */ +u01 = 1.7666645348e-01, /* 0x3e34e80d */ +u02 = -1.3818567619e-02, /* 0xbc626746 */ +u03 = 3.4745343146e-04, /* 0x39b62a69 */ +u04 = -3.8140706238e-06, /* 0xb67ff53c */ +u05 = 1.9559013964e-08, /* 0x32a802ba */ +u06 = -3.9820518410e-11, /* 0xae2f21eb */ +v01 = 1.2730483897e-02, /* 0x3c509385 */ +v02 = 7.6006865129e-05, /* 0x389f65e0 */ +v03 = 2.5915085189e-07, /* 0x348b216c */ +v04 = 4.4111031494e-10; /* 0x2ff280c2 */ + +float +y0f(float x) +{ + float z, s,c,ss,cc,u,v; + int32_t hx,ix; + + GET_FLOAT_WORD(hx,x); + ix = 0x7fffffff&hx; + /* Y0(NaN) is NaN, y0(-inf) is Nan, y0(inf) is 0 */ + if(ix>=0x7f800000) return one/(x+x*x); + if(ix==0) return -one/zero; + if(hx<0) return zero/zero; + if(ix >= 0x40000000) { /* |x| >= 2.0 */ + /* y0(x) = sqrt(2/(pi*x))*(p0(x)*sin(x0)+q0(x)*cos(x0)) + * where x0 = x-pi/4 + * Better formula: + * cos(x0) = cos(x)cos(pi/4)+sin(x)sin(pi/4) + * = 1/sqrt(2) * (sin(x) + cos(x)) + * sin(x0) = sin(x)cos(3pi/4)-cos(x)sin(3pi/4) + * = 1/sqrt(2) * (sin(x) - cos(x)) + * To avoid cancellation, use + * sin(x) +- cos(x) = -cos(2x)/(sin(x) -+ cos(x)) + * to compute the worse one. + */ + s = sinf(x); + c = cosf(x); + ss = s-c; + cc = s+c; + /* + * j0(x) = 1/sqrt(pi) * (P(0,x)*cc - Q(0,x)*ss) / sqrt(x) + * y0(x) = 1/sqrt(pi) * (P(0,x)*ss + Q(0,x)*cc) / sqrt(x) + */ + if(ix<0x7f000000) { /* make sure x+x not overflow */ + z = -cosf(x+x); + if ((s*c)0x80000000) z = (invsqrtpi*ss)/sqrtf(x); + else { + u = pzerof(x); v = qzerof(x); + z = invsqrtpi*(u*ss+v*cc)/sqrtf(x); + } + return z; + } + if(ix<=0x32000000) { /* x < 2**-27 */ + return(u00 + tpi*logf(x)); + } + z = x*x; + u = u00+z*(u01+z*(u02+z*(u03+z*(u04+z*(u05+z*u06))))); + v = one+z*(v01+z*(v02+z*(v03+z*v04))); + return(u/v + tpi*(j0f(x)*logf(x))); +} + +/* The asymptotic expansions of pzero is + * 1 - 9/128 s^2 + 11025/98304 s^4 - ..., where s = 1/x. + * For x >= 2, We approximate pzero by + * pzero(x) = 1 + (R/S) + * where R = pR0 + pR1*s^2 + pR2*s^4 + ... + pR5*s^10 + * S = 1 + pS0*s^2 + ... + pS4*s^10 + * and + * | pzero(x)-1-R/S | <= 2 ** ( -60.26) + */ +static const float pR8[6] = { /* for x in [inf, 8]=1/[0,0.125] */ + 0.0000000000e+00, /* 0x00000000 */ + -7.0312500000e-02, /* 0xbd900000 */ + -8.0816707611e+00, /* 0xc1014e86 */ + -2.5706311035e+02, /* 0xc3808814 */ + -2.4852163086e+03, /* 0xc51b5376 */ + -5.2530439453e+03, /* 0xc5a4285a */ +}; +static const float pS8[5] = { + 1.1653436279e+02, /* 0x42e91198 */ + 3.8337448730e+03, /* 0x456f9beb */ + 4.0597855469e+04, /* 0x471e95db */ + 1.1675296875e+05, /* 0x47e4087c */ + 4.7627726562e+04, /* 0x473a0bba */ +}; +static const float pR5[6] = { /* for x in [8,4.5454]=1/[0.125,0.22001] */ + -1.1412546255e-11, /* 0xad48c58a */ + -7.0312492549e-02, /* 0xbd8fffff */ + -4.1596107483e+00, /* 0xc0851b88 */ + -6.7674766541e+01, /* 0xc287597b */ + -3.3123129272e+02, /* 0xc3a59d9b */ + -3.4643338013e+02, /* 0xc3ad3779 */ +}; +static const float pS5[5] = { + 6.0753936768e+01, /* 0x42730408 */ + 1.0512523193e+03, /* 0x44836813 */ + 5.9789707031e+03, /* 0x45bad7c4 */ + 9.6254453125e+03, /* 0x461665c8 */ + 2.4060581055e+03, /* 0x451660ee */ +}; + +static const float pR3[6] = {/* for x in [4.547,2.8571]=1/[0.2199,0.35001] */ + -2.5470459075e-09, /* 0xb12f081b */ + -7.0311963558e-02, /* 0xbd8fffb8 */ + -2.4090321064e+00, /* 0xc01a2d95 */ + -2.1965976715e+01, /* 0xc1afba52 */ + -5.8079170227e+01, /* 0xc2685112 */ + -3.1447946548e+01, /* 0xc1fb9565 */ +}; +static const float pS3[5] = { + 3.5856033325e+01, /* 0x420f6c94 */ + 3.6151397705e+02, /* 0x43b4c1ca */ + 1.1936077881e+03, /* 0x44953373 */ + 1.1279968262e+03, /* 0x448cffe6 */ + 1.7358093262e+02, /* 0x432d94b8 */ +}; + +static const float pR2[6] = {/* for x in [2.8570,2]=1/[0.3499,0.5] */ + -8.8753431271e-08, /* 0xb3be98b7 */ + -7.0303097367e-02, /* 0xbd8ffb12 */ + -1.4507384300e+00, /* 0xbfb9b1cc */ + -7.6356959343e+00, /* 0xc0f4579f */ + -1.1193166733e+01, /* 0xc1331736 */ + -3.2336456776e+00, /* 0xc04ef40d */ +}; +static const float pS2[5] = { + 2.2220300674e+01, /* 0x41b1c32d */ + 1.3620678711e+02, /* 0x430834f0 */ + 2.7047027588e+02, /* 0x43873c32 */ + 1.5387539673e+02, /* 0x4319e01a */ + 1.4657617569e+01, /* 0x416a859a */ +}; + +static float +pzerof(float x) +{ + const float *p,*q; + float z,r,s; + int32_t ix; + + p = q = 0; + GET_FLOAT_WORD(ix,x); + ix &= 0x7fffffff; + if(ix>=0x41000000) {p = pR8; q= pS8;} + else if(ix>=0x40f71c58){p = pR5; q= pS5;} + else if(ix>=0x4036db68){p = pR3; q= pS3;} + else if(ix>=0x40000000){p = pR2; q= pS2;} + z = one/(x*x); + r = p[0]+z*(p[1]+z*(p[2]+z*(p[3]+z*(p[4]+z*p[5])))); + s = one+z*(q[0]+z*(q[1]+z*(q[2]+z*(q[3]+z*q[4])))); + return one+ r/s; +} + + +/* For x >= 8, the asymptotic expansions of qzero is + * -1/8 s + 75/1024 s^3 - ..., where s = 1/x. + * We approximate pzero by + * qzero(x) = s*(-1.25 + (R/S)) + * where R = qR0 + qR1*s^2 + qR2*s^4 + ... + qR5*s^10 + * S = 1 + qS0*s^2 + ... + qS5*s^12 + * and + * | qzero(x)/s +1.25-R/S | <= 2 ** ( -61.22) + */ +static const float qR8[6] = { /* for x in [inf, 8]=1/[0,0.125] */ + 0.0000000000e+00, /* 0x00000000 */ + 7.3242187500e-02, /* 0x3d960000 */ + 1.1768206596e+01, /* 0x413c4a93 */ + 5.5767340088e+02, /* 0x440b6b19 */ + 8.8591972656e+03, /* 0x460a6cca */ + 3.7014625000e+04, /* 0x471096a0 */ +}; +static const float qS8[6] = { + 1.6377603149e+02, /* 0x4323c6aa */ + 8.0983447266e+03, /* 0x45fd12c2 */ + 1.4253829688e+05, /* 0x480b3293 */ + 8.0330925000e+05, /* 0x49441ed4 */ + 8.4050156250e+05, /* 0x494d3359 */ + -3.4389928125e+05, /* 0xc8a7eb69 */ +}; + +static const float qR5[6] = { /* for x in [8,4.5454]=1/[0.125,0.22001] */ + 1.8408595828e-11, /* 0x2da1ec79 */ + 7.3242180049e-02, /* 0x3d95ffff */ + 5.8356351852e+00, /* 0x40babd86 */ + 1.3511157227e+02, /* 0x43071c90 */ + 1.0272437744e+03, /* 0x448067cd */ + 1.9899779053e+03, /* 0x44f8bf4b */ +}; +static const float qS5[6] = { + 8.2776611328e+01, /* 0x42a58da0 */ + 2.0778142090e+03, /* 0x4501dd07 */ + 1.8847289062e+04, /* 0x46933e94 */ + 5.6751113281e+04, /* 0x475daf1d */ + 3.5976753906e+04, /* 0x470c88c1 */ + -5.3543427734e+03, /* 0xc5a752be */ +}; + +static const float qR3[6] = {/* for x in [4.547,2.8571]=1/[0.2199,0.35001] */ + 4.3774099900e-09, /* 0x3196681b */ + 7.3241114616e-02, /* 0x3d95ff70 */ + 3.3442313671e+00, /* 0x405607e3 */ + 4.2621845245e+01, /* 0x422a7cc5 */ + 1.7080809021e+02, /* 0x432acedf */ + 1.6673394775e+02, /* 0x4326bbe4 */ +}; +static const float qS3[6] = { + 4.8758872986e+01, /* 0x42430916 */ + 7.0968920898e+02, /* 0x44316c1c */ + 3.7041481934e+03, /* 0x4567825f */ + 6.4604252930e+03, /* 0x45c9e367 */ + 2.5163337402e+03, /* 0x451d4557 */ + -1.4924745178e+02, /* 0xc3153f59 */ +}; + +static const float qR2[6] = {/* for x in [2.8570,2]=1/[0.3499,0.5] */ + 1.5044444979e-07, /* 0x342189db */ + 7.3223426938e-02, /* 0x3d95f62a */ + 1.9981917143e+00, /* 0x3fffc4bf */ + 1.4495602608e+01, /* 0x4167edfd */ + 3.1666231155e+01, /* 0x41fd5471 */ + 1.6252708435e+01, /* 0x4182058c */ +}; +static const float qS2[6] = { + 3.0365585327e+01, /* 0x41f2ecb8 */ + 2.6934811401e+02, /* 0x4386ac8f */ + 8.4478375244e+02, /* 0x44533229 */ + 8.8293585205e+02, /* 0x445cbbe5 */ + 2.1266638184e+02, /* 0x4354aa98 */ + -5.3109550476e+00, /* 0xc0a9f358 */ +}; + +static float +qzerof(float x) +{ + const float *p,*q; + float s,r,z; + int32_t ix; + + p = q = 0; + GET_FLOAT_WORD(ix,x); + ix &= 0x7fffffff; + if(ix>=0x41000000) {p = qR8; q= qS8;} + else if(ix>=0x40f71c58){p = qR5; q= qS5;} + else if(ix>=0x4036db68){p = qR3; q= qS3;} + else if(ix>=0x40000000){p = qR2; q= qS2;} + z = one/(x*x); + r = p[0]+z*(p[1]+z*(p[2]+z*(p[3]+z*(p[4]+z*p[5])))); + s = one+z*(q[0]+z*(q[1]+z*(q[2]+z*(q[3]+z*(q[4]+z*q[5]))))); + return (-(float).125 + r/s)/x; +} diff --git a/lib/libm/src/e_j1.c b/lib/libm/src/e_j1.c new file mode 100644 index 0000000000..da1ac2f33f --- /dev/null +++ b/lib/libm/src/e_j1.c @@ -0,0 +1,381 @@ +/* @(#)e_j1.c 5.1 93/09/24 */ +/* + * ==================================================== + * Copyright (C) 1993 by Sun Microsystems, Inc. All rights reserved. + * + * Developed at SunPro, a Sun Microsystems, Inc. business. + * Permission to use, copy, modify, and distribute this + * software is freely granted, provided that this notice + * is preserved. + * ==================================================== + * + * $NetBSD: e_j1.c,v 1.11 2002/05/26 22:01:50 wiz Exp $ + * $DragonFly: src/lib/libm/src/e_j1.c,v 1.1 2005/07/26 21:15:20 joerg Exp $ + */ + +/* j1(x), y1(x) + * Bessel function of the first and second kinds of order zero. + * Method -- j1(x): + * 1. For tiny x, we use j1(x) = x/2 - x^3/16 + x^5/384 - ... + * 2. Reduce x to |x| since j1(x)=-j1(-x), and + * for x in (0,2) + * j1(x) = x/2 + x*z*R0/S0, where z = x*x; + * (precision: |j1/x - 1/2 - R0/S0 |<2**-61.51 ) + * for x in (2,inf) + * j1(x) = sqrt(2/(pi*x))*(p1(x)*cos(x1)-q1(x)*sin(x1)) + * y1(x) = sqrt(2/(pi*x))*(p1(x)*sin(x1)+q1(x)*cos(x1)) + * where x1 = x-3*pi/4. It is better to compute sin(x1),cos(x1) + * as follow: + * cos(x1) = cos(x)cos(3pi/4)+sin(x)sin(3pi/4) + * = 1/sqrt(2) * (sin(x) - cos(x)) + * sin(x1) = sin(x)cos(3pi/4)-cos(x)sin(3pi/4) + * = -1/sqrt(2) * (sin(x) + cos(x)) + * (To avoid cancellation, use + * sin(x) +- cos(x) = -cos(2x)/(sin(x) -+ cos(x)) + * to compute the worse one.) + * + * 3 Special cases + * j1(nan)= nan + * j1(0) = 0 + * j1(inf) = 0 + * + * Method -- y1(x): + * 1. screen out x<=0 cases: y1(0)=-inf, y1(x<0)=NaN + * 2. For x<2. + * Since + * y1(x) = 2/pi*(j1(x)*(ln(x/2)+Euler)-1/x-x/2+5/64*x^3-...) + * therefore y1(x)-2/pi*j1(x)*ln(x)-1/x is an odd function. + * We use the following function to approximate y1, + * y1(x) = x*U(z)/V(z) + (2/pi)*(j1(x)*ln(x)-1/x), z= x^2 + * where for x in [0,2] (abs err less than 2**-65.89) + * U(z) = U0[0] + U0[1]*z + ... + U0[4]*z^4 + * V(z) = 1 + v0[0]*z + ... + v0[4]*z^5 + * Note: For tiny x, 1/x dominate y1 and hence + * y1(tiny) = -2/pi/tiny, (choose tiny<2**-54) + * 3. For x>=2. + * y1(x) = sqrt(2/(pi*x))*(p1(x)*sin(x1)+q1(x)*cos(x1)) + * where x1 = x-3*pi/4. It is better to compute sin(x1),cos(x1) + * by method mentioned above. + */ + +#include +#include "math_private.h" + +static double pone(double), qone(double); + +static const double +huge = 1e300, +one = 1.0, +invsqrtpi= 5.64189583547756279280e-01, /* 0x3FE20DD7, 0x50429B6D */ +tpi = 6.36619772367581382433e-01, /* 0x3FE45F30, 0x6DC9C883 */ + /* R0/S0 on [0,2] */ +r00 = -6.25000000000000000000e-02, /* 0xBFB00000, 0x00000000 */ +r01 = 1.40705666955189706048e-03, /* 0x3F570D9F, 0x98472C61 */ +r02 = -1.59955631084035597520e-05, /* 0xBEF0C5C6, 0xBA169668 */ +r03 = 4.96727999609584448412e-08, /* 0x3E6AAAFA, 0x46CA0BD9 */ +s01 = 1.91537599538363460805e-02, /* 0x3F939D0B, 0x12637E53 */ +s02 = 1.85946785588630915560e-04, /* 0x3F285F56, 0xB9CDF664 */ +s03 = 1.17718464042623683263e-06, /* 0x3EB3BFF8, 0x333F8498 */ +s04 = 5.04636257076217042715e-09, /* 0x3E35AC88, 0xC97DFF2C */ +s05 = 1.23542274426137913908e-11; /* 0x3DAB2ACF, 0xCFB97ED8 */ + +static const double zero = 0.0; + +double +j1(double x) +{ + double z, s,c,ss,cc,r,u,v,y; + int32_t hx,ix; + + GET_HIGH_WORD(hx,x); + ix = hx&0x7fffffff; + if(ix>=0x7ff00000) return one/x; + y = fabs(x); + if(ix >= 0x40000000) { /* |x| >= 2.0 */ + s = sin(y); + c = cos(y); + ss = -s-c; + cc = s-c; + if(ix<0x7fe00000) { /* make sure y+y not overflow */ + z = cos(y+y); + if ((s*c)>zero) cc = z/ss; + else ss = z/cc; + } + /* + * j1(x) = 1/sqrt(pi) * (P(1,x)*cc - Q(1,x)*ss) / sqrt(x) + * y1(x) = 1/sqrt(pi) * (P(1,x)*ss + Q(1,x)*cc) / sqrt(x) + */ + if(ix>0x48000000) z = (invsqrtpi*cc)/sqrt(y); + else { + u = pone(y); v = qone(y); + z = invsqrtpi*(u*cc-v*ss)/sqrt(y); + } + if(hx<0) return -z; + else return z; + } + if(ix<0x3e400000) { /* |x|<2**-27 */ + if(huge+x>one) return 0.5*x;/* inexact if x!=0 necessary */ + } + z = x*x; + r = z*(r00+z*(r01+z*(r02+z*r03))); + s = one+z*(s01+z*(s02+z*(s03+z*(s04+z*s05)))); + r *= x; + return(x*0.5+r/s); +} + +static const double U0[5] = { + -1.96057090646238940668e-01, /* 0xBFC91866, 0x143CBC8A */ + 5.04438716639811282616e-02, /* 0x3FA9D3C7, 0x76292CD1 */ + -1.91256895875763547298e-03, /* 0xBF5F55E5, 0x4844F50F */ + 2.35252600561610495928e-05, /* 0x3EF8AB03, 0x8FA6B88E */ + -9.19099158039878874504e-08, /* 0xBE78AC00, 0x569105B8 */ +}; +static const double V0[5] = { + 1.99167318236649903973e-02, /* 0x3F94650D, 0x3F4DA9F0 */ + 2.02552581025135171496e-04, /* 0x3F2A8C89, 0x6C257764 */ + 1.35608801097516229404e-06, /* 0x3EB6C05A, 0x894E8CA6 */ + 6.22741452364621501295e-09, /* 0x3E3ABF1D, 0x5BA69A86 */ + 1.66559246207992079114e-11, /* 0x3DB25039, 0xDACA772A */ +}; + +double +y1(double x) +{ + double z, s,c,ss,cc,u,v; + int32_t hx,ix,lx; + + EXTRACT_WORDS(hx,lx,x); + ix = 0x7fffffff&hx; + /* if Y1(NaN) is NaN, Y1(-inf) is NaN, Y1(inf) is 0 */ + if(ix>=0x7ff00000) return one/(x+x*x); + if((ix|lx)==0) return -one/zero; + if(hx<0) return zero/zero; + if(ix >= 0x40000000) { /* |x| >= 2.0 */ + s = sin(x); + c = cos(x); + ss = -s-c; + cc = s-c; + if(ix<0x7fe00000) { /* make sure x+x not overflow */ + z = cos(x+x); + if ((s*c)>zero) cc = z/ss; + else ss = z/cc; + } + /* y1(x) = sqrt(2/(pi*x))*(p1(x)*sin(x0)+q1(x)*cos(x0)) + * where x0 = x-3pi/4 + * Better formula: + * cos(x0) = cos(x)cos(3pi/4)+sin(x)sin(3pi/4) + * = 1/sqrt(2) * (sin(x) - cos(x)) + * sin(x0) = sin(x)cos(3pi/4)-cos(x)sin(3pi/4) + * = -1/sqrt(2) * (cos(x) + sin(x)) + * To avoid cancellation, use + * sin(x) +- cos(x) = -cos(2x)/(sin(x) -+ cos(x)) + * to compute the worse one. + */ + if(ix>0x48000000) z = (invsqrtpi*ss)/sqrt(x); + else { + u = pone(x); v = qone(x); + z = invsqrtpi*(u*ss+v*cc)/sqrt(x); + } + return z; + } + if(ix<=0x3c900000) { /* x < 2**-54 */ + return(-tpi/x); + } + z = x*x; + u = U0[0]+z*(U0[1]+z*(U0[2]+z*(U0[3]+z*U0[4]))); + v = one+z*(V0[0]+z*(V0[1]+z*(V0[2]+z*(V0[3]+z*V0[4])))); + return(x*(u/v) + tpi*(j1(x)*log(x)-one/x)); +} + +/* For x >= 8, the asymptotic expansions of pone is + * 1 + 15/128 s^2 - 4725/2^15 s^4 - ..., where s = 1/x. + * We approximate pone by + * pone(x) = 1 + (R/S) + * where R = pr0 + pr1*s^2 + pr2*s^4 + ... + pr5*s^10 + * S = 1 + ps0*s^2 + ... + ps4*s^10 + * and + * | pone(x)-1-R/S | <= 2 ** ( -60.06) + */ + +static const double pr8[6] = { /* for x in [inf, 8]=1/[0,0.125] */ + 0.00000000000000000000e+00, /* 0x00000000, 0x00000000 */ + 1.17187499999988647970e-01, /* 0x3FBDFFFF, 0xFFFFFCCE */ + 1.32394806593073575129e+01, /* 0x402A7A9D, 0x357F7FCE */ + 4.12051854307378562225e+02, /* 0x4079C0D4, 0x652EA590 */ + 3.87474538913960532227e+03, /* 0x40AE457D, 0xA3A532CC */ + 7.91447954031891731574e+03, /* 0x40BEEA7A, 0xC32782DD */ +}; +static const double ps8[5] = { + 1.14207370375678408436e+02, /* 0x405C8D45, 0x8E656CAC */ + 3.65093083420853463394e+03, /* 0x40AC85DC, 0x964D274F */ + 3.69562060269033463555e+04, /* 0x40E20B86, 0x97C5BB7F */ + 9.76027935934950801311e+04, /* 0x40F7D42C, 0xB28F17BB */ + 3.08042720627888811578e+04, /* 0x40DE1511, 0x697A0B2D */ +}; + +static const double pr5[6] = { /* for x in [8,4.5454]=1/[0.125,0.22001] */ + 1.31990519556243522749e-11, /* 0x3DAD0667, 0xDAE1CA7D */ + 1.17187493190614097638e-01, /* 0x3FBDFFFF, 0xE2C10043 */ + 6.80275127868432871736e+00, /* 0x401B3604, 0x6E6315E3 */ + 1.08308182990189109773e+02, /* 0x405B13B9, 0x452602ED */ + 5.17636139533199752805e+02, /* 0x40802D16, 0xD052D649 */ + 5.28715201363337541807e+02, /* 0x408085B8, 0xBB7E0CB7 */ +}; +static const double ps5[5] = { + 5.92805987221131331921e+01, /* 0x404DA3EA, 0xA8AF633D */ + 9.91401418733614377743e+02, /* 0x408EFB36, 0x1B066701 */ + 5.35326695291487976647e+03, /* 0x40B4E944, 0x5706B6FB */ + 7.84469031749551231769e+03, /* 0x40BEA4B0, 0xB8A5BB15 */ + 1.50404688810361062679e+03, /* 0x40978030, 0x036F5E51 */ +}; + +static const double pr3[6] = { + 3.02503916137373618024e-09, /* 0x3E29FC21, 0xA7AD9EDD */ + 1.17186865567253592491e-01, /* 0x3FBDFFF5, 0x5B21D17B */ + 3.93297750033315640650e+00, /* 0x400F76BC, 0xE85EAD8A */ + 3.51194035591636932736e+01, /* 0x40418F48, 0x9DA6D129 */ + 9.10550110750781271918e+01, /* 0x4056C385, 0x4D2C1837 */ + 4.85590685197364919645e+01, /* 0x4048478F, 0x8EA83EE5 */ +}; +static const double ps3[5] = { + 3.47913095001251519989e+01, /* 0x40416549, 0xA134069C */ + 3.36762458747825746741e+02, /* 0x40750C33, 0x07F1A75F */ + 1.04687139975775130551e+03, /* 0x40905B7C, 0x5037D523 */ + 8.90811346398256432622e+02, /* 0x408BD67D, 0xA32E31E9 */ + 1.03787932439639277504e+02, /* 0x4059F26D, 0x7C2EED53 */ +}; + +static const double pr2[6] = {/* for x in [2.8570,2]=1/[0.3499,0.5] */ + 1.07710830106873743082e-07, /* 0x3E7CE9D4, 0xF65544F4 */ + 1.17176219462683348094e-01, /* 0x3FBDFF42, 0xBE760D83 */ + 2.36851496667608785174e+00, /* 0x4002F2B7, 0xF98FAEC0 */ + 1.22426109148261232917e+01, /* 0x40287C37, 0x7F71A964 */ + 1.76939711271687727390e+01, /* 0x4031B1A8, 0x177F8EE2 */ + 5.07352312588818499250e+00, /* 0x40144B49, 0xA574C1FE */ +}; +static const double ps2[5] = { + 2.14364859363821409488e+01, /* 0x40356FBD, 0x8AD5ECDC */ + 1.25290227168402751090e+02, /* 0x405F5293, 0x14F92CD5 */ + 2.32276469057162813669e+02, /* 0x406D08D8, 0xD5A2DBD9 */ + 1.17679373287147100768e+02, /* 0x405D6B7A, 0xDA1884A9 */ + 8.36463893371618283368e+00, /* 0x4020BAB1, 0xF44E5192 */ +}; + +static double +pone(double x) +{ + const double *p,*q; + double z,r,s; + int32_t ix; + + p = q = 0; + GET_HIGH_WORD(ix,x); + ix &= 0x7fffffff; + if(ix>=0x40200000) {p = pr8; q= ps8;} + else if(ix>=0x40122E8B){p = pr5; q= ps5;} + else if(ix>=0x4006DB6D){p = pr3; q= ps3;} + else if(ix>=0x40000000){p = pr2; q= ps2;} + z = one/(x*x); + r = p[0]+z*(p[1]+z*(p[2]+z*(p[3]+z*(p[4]+z*p[5])))); + s = one+z*(q[0]+z*(q[1]+z*(q[2]+z*(q[3]+z*q[4])))); + return one+ r/s; +} + + +/* For x >= 8, the asymptotic expansions of qone is + * 3/8 s - 105/1024 s^3 - ..., where s = 1/x. + * We approximate pone by + * qone(x) = s*(0.375 + (R/S)) + * where R = qr1*s^2 + qr2*s^4 + ... + qr5*s^10 + * S = 1 + qs1*s^2 + ... + qs6*s^12 + * and + * | qone(x)/s -0.375-R/S | <= 2 ** ( -61.13) + */ + +static const double qr8[6] = { /* for x in [inf, 8]=1/[0,0.125] */ + 0.00000000000000000000e+00, /* 0x00000000, 0x00000000 */ + -1.02539062499992714161e-01, /* 0xBFBA3FFF, 0xFFFFFDF3 */ + -1.62717534544589987888e+01, /* 0xC0304591, 0xA26779F7 */ + -7.59601722513950107896e+02, /* 0xC087BCD0, 0x53E4B576 */ + -1.18498066702429587167e+04, /* 0xC0C724E7, 0x40F87415 */ + -4.84385124285750353010e+04, /* 0xC0E7A6D0, 0x65D09C6A */ +}; +static const double qs8[6] = { + 1.61395369700722909556e+02, /* 0x40642CA6, 0xDE5BCDE5 */ + 7.82538599923348465381e+03, /* 0x40BE9162, 0xD0D88419 */ + 1.33875336287249578163e+05, /* 0x4100579A, 0xB0B75E98 */ + 7.19657723683240939863e+05, /* 0x4125F653, 0x72869C19 */ + 6.66601232617776375264e+05, /* 0x412457D2, 0x7719AD5C */ + -2.94490264303834643215e+05, /* 0xC111F969, 0x0EA5AA18 */ +}; + +static const double qr5[6] = { /* for x in [8,4.5454]=1/[0.125,0.22001] */ + -2.08979931141764104297e-11, /* 0xBDB6FA43, 0x1AA1A098 */ + -1.02539050241375426231e-01, /* 0xBFBA3FFF, 0xCB597FEF */ + -8.05644828123936029840e+00, /* 0xC0201CE6, 0xCA03AD4B */ + -1.83669607474888380239e+02, /* 0xC066F56D, 0x6CA7B9B0 */ + -1.37319376065508163265e+03, /* 0xC09574C6, 0x6931734F */ + -2.61244440453215656817e+03, /* 0xC0A468E3, 0x88FDA79D */ +}; +static const double qs5[6] = { + 8.12765501384335777857e+01, /* 0x405451B2, 0xFF5A11B2 */ + 1.99179873460485964642e+03, /* 0x409F1F31, 0xE77BF839 */ + 1.74684851924908907677e+04, /* 0x40D10F1F, 0x0D64CE29 */ + 4.98514270910352279316e+04, /* 0x40E8576D, 0xAABAD197 */ + 2.79480751638918118260e+04, /* 0x40DB4B04, 0xCF7C364B */ + -4.71918354795128470869e+03, /* 0xC0B26F2E, 0xFCFFA004 */ +}; + +static const double qr3[6] = { + -5.07831226461766561369e-09, /* 0xBE35CFA9, 0xD38FC84F */ + -1.02537829820837089745e-01, /* 0xBFBA3FEB, 0x51AEED54 */ + -4.61011581139473403113e+00, /* 0xC01270C2, 0x3302D9FF */ + -5.78472216562783643212e+01, /* 0xC04CEC71, 0xC25D16DA */ + -2.28244540737631695038e+02, /* 0xC06C87D3, 0x4718D55F */ + -2.19210128478909325622e+02, /* 0xC06B66B9, 0x5F5C1BF6 */ +}; +static const double qs3[6] = { + 4.76651550323729509273e+01, /* 0x4047D523, 0xCCD367E4 */ + 6.73865112676699709482e+02, /* 0x40850EEB, 0xC031EE3E */ + 3.38015286679526343505e+03, /* 0x40AA684E, 0x448E7C9A */ + 5.54772909720722782367e+03, /* 0x40B5ABBA, 0xA61D54A6 */ + 1.90311919338810798763e+03, /* 0x409DBC7A, 0x0DD4DF4B */ + -1.35201191444307340817e+02, /* 0xC060E670, 0x290A311F */ +}; + +static const double qr2[6] = {/* for x in [2.8570,2]=1/[0.3499,0.5] */ + -1.78381727510958865572e-07, /* 0xBE87F126, 0x44C626D2 */ + -1.02517042607985553460e-01, /* 0xBFBA3E8E, 0x9148B010 */ + -2.75220568278187460720e+00, /* 0xC0060484, 0x69BB4EDA */ + -1.96636162643703720221e+01, /* 0xC033A9E2, 0xC168907F */ + -4.23253133372830490089e+01, /* 0xC04529A3, 0xDE104AAA */ + -2.13719211703704061733e+01, /* 0xC0355F36, 0x39CF6E52 */ +}; +static const double qs2[6] = { + 2.95333629060523854548e+01, /* 0x403D888A, 0x78AE64FF */ + 2.52981549982190529136e+02, /* 0x406F9F68, 0xDB821CBA */ + 7.57502834868645436472e+02, /* 0x4087AC05, 0xCE49A0F7 */ + 7.39393205320467245656e+02, /* 0x40871B25, 0x48D4C029 */ + 1.55949003336666123687e+02, /* 0x40637E5E, 0x3C3ED8D4 */ + -4.95949898822628210127e+00, /* 0xC013D686, 0xE71BE86B */ +}; + +static double +qone(double x) +{ + const double *p,*q; + double s,r,z; + int32_t ix; + + p = q = 0; + GET_HIGH_WORD(ix,x); + ix &= 0x7fffffff; + if(ix>=0x40200000) {p = qr8; q= qs8;} + else if(ix>=0x40122E8B){p = qr5; q= qs5;} + else if(ix>=0x4006DB6D){p = qr3; q= qs3;} + else if(ix>=0x40000000){p = qr2; q= qs2;} + z = one/(x*x); + r = p[0]+z*(p[1]+z*(p[2]+z*(p[3]+z*(p[4]+z*p[5])))); + s = one+z*(q[0]+z*(q[1]+z*(q[2]+z*(q[3]+z*(q[4]+z*q[5]))))); + return (.375 + r/s)/x; +} diff --git a/lib/libm/src/e_j1f.c b/lib/libm/src/e_j1f.c new file mode 100644 index 0000000000..83495f557c --- /dev/null +++ b/lib/libm/src/e_j1f.c @@ -0,0 +1,339 @@ +/* e_j1f.c -- float version of e_j1.c. + * Conversion to float by Ian Lance Taylor, Cygnus Support, ian@cygnus.com. + */ + +/* + * ==================================================== + * Copyright (C) 1993 by Sun Microsystems, Inc. All rights reserved. + * + * Developed at SunPro, a Sun Microsystems, Inc. business. + * Permission to use, copy, modify, and distribute this + * software is freely granted, provided that this notice + * is preserved. + * ==================================================== + * + * $NetBSD: e_j1f.c,v 1.7 2002/05/26 22:01:50 wiz Exp $ + * $DragonFly: src/lib/libm/src/e_j1f.c,v 1.1 2005/07/26 21:15:20 joerg Exp $ + */ + +#include +#include "math_private.h" + +static float ponef(float), qonef(float); + +static const float +huge = 1e30, +one = 1.0, +invsqrtpi= 5.6418961287e-01, /* 0x3f106ebb */ +tpi = 6.3661974669e-01, /* 0x3f22f983 */ + /* R0/S0 on [0,2] */ +r00 = -6.2500000000e-02, /* 0xbd800000 */ +r01 = 1.4070566976e-03, /* 0x3ab86cfd */ +r02 = -1.5995563444e-05, /* 0xb7862e36 */ +r03 = 4.9672799207e-08, /* 0x335557d2 */ +s01 = 1.9153760746e-02, /* 0x3c9ce859 */ +s02 = 1.8594678841e-04, /* 0x3942fab6 */ +s03 = 1.1771846857e-06, /* 0x359dffc2 */ +s04 = 5.0463624390e-09, /* 0x31ad6446 */ +s05 = 1.2354227016e-11; /* 0x2d59567e */ + +static const float zero = 0.0; + +float +j1f(float x) +{ + float z, s,c,ss,cc,r,u,v,y; + int32_t hx,ix; + + GET_FLOAT_WORD(hx,x); + ix = hx&0x7fffffff; + if(ix>=0x7f800000) return one/x; + y = fabsf(x); + if(ix >= 0x40000000) { /* |x| >= 2.0 */ + s = sinf(y); + c = cosf(y); + ss = -s-c; + cc = s-c; + if(ix<0x7f000000) { /* make sure y+y not overflow */ + z = cosf(y+y); + if ((s*c)>zero) cc = z/ss; + else ss = z/cc; + } + /* + * j1(x) = 1/sqrt(pi) * (P(1,x)*cc - Q(1,x)*ss) / sqrt(x) + * y1(x) = 1/sqrt(pi) * (P(1,x)*ss + Q(1,x)*cc) / sqrt(x) + */ + if(ix>0x80000000) z = (invsqrtpi*cc)/sqrtf(y); + else { + u = ponef(y); v = qonef(y); + z = invsqrtpi*(u*cc-v*ss)/sqrtf(y); + } + if(hx<0) return -z; + else return z; + } + if(ix<0x32000000) { /* |x|<2**-27 */ + if(huge+x>one) return (float)0.5*x;/* inexact if x!=0 necessary */ + } + z = x*x; + r = z*(r00+z*(r01+z*(r02+z*r03))); + s = one+z*(s01+z*(s02+z*(s03+z*(s04+z*s05)))); + r *= x; + return(x*(float)0.5+r/s); +} + +static const float U0[5] = { + -1.9605709612e-01, /* 0xbe48c331 */ + 5.0443872809e-02, /* 0x3d4e9e3c */ + -1.9125689287e-03, /* 0xbafaaf2a */ + 2.3525259166e-05, /* 0x37c5581c */ + -9.1909917899e-08, /* 0xb3c56003 */ +}; +static const float V0[5] = { + 1.9916731864e-02, /* 0x3ca3286a */ + 2.0255257550e-04, /* 0x3954644b */ + 1.3560879779e-06, /* 0x35b602d4 */ + 6.2274145840e-09, /* 0x31d5f8eb */ + 1.6655924903e-11, /* 0x2d9281cf */ +}; + +float +y1f(float x) +{ + float z, s,c,ss,cc,u,v; + int32_t hx,ix; + + GET_FLOAT_WORD(hx,x); + ix = 0x7fffffff&hx; + /* if Y1(NaN) is NaN, Y1(-inf) is NaN, Y1(inf) is 0 */ + if(ix>=0x7f800000) return one/(x+x*x); + if(ix==0) return -one/zero; + if(hx<0) return zero/zero; + if(ix >= 0x40000000) { /* |x| >= 2.0 */ + s = sinf(x); + c = cosf(x); + ss = -s-c; + cc = s-c; + if(ix<0x7f000000) { /* make sure x+x not overflow */ + z = cosf(x+x); + if ((s*c)>zero) cc = z/ss; + else ss = z/cc; + } + /* y1(x) = sqrt(2/(pi*x))*(p1(x)*sin(x0)+q1(x)*cos(x0)) + * where x0 = x-3pi/4 + * Better formula: + * cos(x0) = cos(x)cos(3pi/4)+sin(x)sin(3pi/4) + * = 1/sqrt(2) * (sin(x) - cos(x)) + * sin(x0) = sin(x)cos(3pi/4)-cos(x)sin(3pi/4) + * = -1/sqrt(2) * (cos(x) + sin(x)) + * To avoid cancellation, use + * sin(x) +- cos(x) = -cos(2x)/(sin(x) -+ cos(x)) + * to compute the worse one. + */ + if(ix>0x48000000) z = (invsqrtpi*ss)/sqrtf(x); + else { + u = ponef(x); v = qonef(x); + z = invsqrtpi*(u*ss+v*cc)/sqrtf(x); + } + return z; + } + if(ix<=0x24800000) { /* x < 2**-54 */ + return(-tpi/x); + } + z = x*x; + u = U0[0]+z*(U0[1]+z*(U0[2]+z*(U0[3]+z*U0[4]))); + v = one+z*(V0[0]+z*(V0[1]+z*(V0[2]+z*(V0[3]+z*V0[4])))); + return(x*(u/v) + tpi*(j1f(x)*logf(x)-one/x)); +} + +/* For x >= 8, the asymptotic expansions of pone is + * 1 + 15/128 s^2 - 4725/2^15 s^4 - ..., where s = 1/x. + * We approximate pone by + * pone(x) = 1 + (R/S) + * where R = pr0 + pr1*s^2 + pr2*s^4 + ... + pr5*s^10 + * S = 1 + ps0*s^2 + ... + ps4*s^10 + * and + * | pone(x)-1-R/S | <= 2 ** ( -60.06) + */ + +static const float pr8[6] = { /* for x in [inf, 8]=1/[0,0.125] */ + 0.0000000000e+00, /* 0x00000000 */ + 1.1718750000e-01, /* 0x3df00000 */ + 1.3239480972e+01, /* 0x4153d4ea */ + 4.1205184937e+02, /* 0x43ce06a3 */ + 3.8747453613e+03, /* 0x45722bed */ + 7.9144794922e+03, /* 0x45f753d6 */ +}; +static const float ps8[5] = { + 1.1420736694e+02, /* 0x42e46a2c */ + 3.6509309082e+03, /* 0x45642ee5 */ + 3.6956207031e+04, /* 0x47105c35 */ + 9.7602796875e+04, /* 0x47bea166 */ + 3.0804271484e+04, /* 0x46f0a88b */ +}; + +static const float pr5[6] = { /* for x in [8,4.5454]=1/[0.125,0.22001] */ + 1.3199052094e-11, /* 0x2d68333f */ + 1.1718749255e-01, /* 0x3defffff */ + 6.8027510643e+00, /* 0x40d9b023 */ + 1.0830818176e+02, /* 0x42d89dca */ + 5.1763616943e+02, /* 0x440168b7 */ + 5.2871520996e+02, /* 0x44042dc6 */ +}; +static const float ps5[5] = { + 5.9280597687e+01, /* 0x426d1f55 */ + 9.9140142822e+02, /* 0x4477d9b1 */ + 5.3532670898e+03, /* 0x45a74a23 */ + 7.8446904297e+03, /* 0x45f52586 */ + 1.5040468750e+03, /* 0x44bc0180 */ +}; + +static const float pr3[6] = { + 3.0250391081e-09, /* 0x314fe10d */ + 1.1718686670e-01, /* 0x3defffab */ + 3.9329774380e+00, /* 0x407bb5e7 */ + 3.5119403839e+01, /* 0x420c7a45 */ + 9.1055007935e+01, /* 0x42b61c2a */ + 4.8559066772e+01, /* 0x42423c7c */ +}; +static const float ps3[5] = { + 3.4791309357e+01, /* 0x420b2a4d */ + 3.3676245117e+02, /* 0x43a86198 */ + 1.0468714600e+03, /* 0x4482dbe3 */ + 8.9081134033e+02, /* 0x445eb3ed */ + 1.0378793335e+02, /* 0x42cf936c */ +}; + +static const float pr2[6] = {/* for x in [2.8570,2]=1/[0.3499,0.5] */ + 1.0771083225e-07, /* 0x33e74ea8 */ + 1.1717621982e-01, /* 0x3deffa16 */ + 2.3685150146e+00, /* 0x401795c0 */ + 1.2242610931e+01, /* 0x4143e1bc */ + 1.7693971634e+01, /* 0x418d8d41 */ + 5.0735230446e+00, /* 0x40a25a4d */ +}; +static const float ps2[5] = { + 2.1436485291e+01, /* 0x41ab7dec */ + 1.2529022980e+02, /* 0x42fa9499 */ + 2.3227647400e+02, /* 0x436846c7 */ + 1.1767937469e+02, /* 0x42eb5bd7 */ + 8.3646392822e+00, /* 0x4105d590 */ +}; + +static float +ponef(float x) +{ + const float *p,*q; + float z,r,s; + int32_t ix; + + p = q = 0; + GET_FLOAT_WORD(ix,x); + ix &= 0x7fffffff; + if(ix>=0x41000000) {p = pr8; q= ps8;} + else if(ix>=0x40f71c58){p = pr5; q= ps5;} + else if(ix>=0x4036db68){p = pr3; q= ps3;} + else if(ix>=0x40000000){p = pr2; q= ps2;} + z = one/(x*x); + r = p[0]+z*(p[1]+z*(p[2]+z*(p[3]+z*(p[4]+z*p[5])))); + s = one+z*(q[0]+z*(q[1]+z*(q[2]+z*(q[3]+z*q[4])))); + return one+ r/s; +} + + +/* For x >= 8, the asymptotic expansions of qone is + * 3/8 s - 105/1024 s^3 - ..., where s = 1/x. + * We approximate pone by + * qone(x) = s*(0.375 + (R/S)) + * where R = qr1*s^2 + qr2*s^4 + ... + qr5*s^10 + * S = 1 + qs1*s^2 + ... + qs6*s^12 + * and + * | qone(x)/s -0.375-R/S | <= 2 ** ( -61.13) + */ + +static const float qr8[6] = { /* for x in [inf, 8]=1/[0,0.125] */ + 0.0000000000e+00, /* 0x00000000 */ + -1.0253906250e-01, /* 0xbdd20000 */ + -1.6271753311e+01, /* 0xc1822c8d */ + -7.5960174561e+02, /* 0xc43de683 */ + -1.1849806641e+04, /* 0xc639273a */ + -4.8438511719e+04, /* 0xc73d3683 */ +}; +static const float qs8[6] = { + 1.6139537048e+02, /* 0x43216537 */ + 7.8253862305e+03, /* 0x45f48b17 */ + 1.3387534375e+05, /* 0x4802bcd6 */ + 7.1965775000e+05, /* 0x492fb29c */ + 6.6660125000e+05, /* 0x4922be94 */ + -2.9449025000e+05, /* 0xc88fcb48 */ +}; + +static const float qr5[6] = { /* for x in [8,4.5454]=1/[0.125,0.22001] */ + -2.0897993405e-11, /* 0xadb7d219 */ + -1.0253904760e-01, /* 0xbdd1fffe */ + -8.0564479828e+00, /* 0xc100e736 */ + -1.8366960144e+02, /* 0xc337ab6b */ + -1.3731937256e+03, /* 0xc4aba633 */ + -2.6124443359e+03, /* 0xc523471c */ +}; +static const float qs5[6] = { + 8.1276550293e+01, /* 0x42a28d98 */ + 1.9917987061e+03, /* 0x44f8f98f */ + 1.7468484375e+04, /* 0x468878f8 */ + 4.9851425781e+04, /* 0x4742bb6d */ + 2.7948074219e+04, /* 0x46da5826 */ + -4.7191835938e+03, /* 0xc5937978 */ +}; + +static const float qr3[6] = { + -5.0783124372e-09, /* 0xb1ae7d4f */ + -1.0253783315e-01, /* 0xbdd1ff5b */ + -4.6101160049e+00, /* 0xc0938612 */ + -5.7847221375e+01, /* 0xc267638e */ + -2.2824453735e+02, /* 0xc3643e9a */ + -2.1921012878e+02, /* 0xc35b35cb */ +}; +static const float qs3[6] = { + 4.7665153503e+01, /* 0x423ea91e */ + 6.7386511230e+02, /* 0x4428775e */ + 3.3801528320e+03, /* 0x45534272 */ + 5.5477290039e+03, /* 0x45ad5dd5 */ + 1.9031191406e+03, /* 0x44ede3d0 */ + -1.3520118713e+02, /* 0xc3073381 */ +}; + +static const float qr2[6] = {/* for x in [2.8570,2]=1/[0.3499,0.5] */ + -1.7838172539e-07, /* 0xb43f8932 */ + -1.0251704603e-01, /* 0xbdd1f475 */ + -2.7522056103e+00, /* 0xc0302423 */ + -1.9663616180e+01, /* 0xc19d4f16 */ + -4.2325313568e+01, /* 0xc2294d1f */ + -2.1371921539e+01, /* 0xc1aaf9b2 */ +}; +static const float qs2[6] = { + 2.9533363342e+01, /* 0x41ec4454 */ + 2.5298155212e+02, /* 0x437cfb47 */ + 7.5750280762e+02, /* 0x443d602e */ + 7.3939318848e+02, /* 0x4438d92a */ + 1.5594900513e+02, /* 0x431bf2f2 */ + -4.9594988823e+00, /* 0xc09eb437 */ +}; + +static float +qonef(float x) +{ + const float *p,*q; + float s,r,z; + int32_t ix; + + p = q = 0; + GET_FLOAT_WORD(ix,x); + ix &= 0x7fffffff; + if(ix>=0x40200000) {p = qr8; q= qs8;} + else if(ix>=0x40f71c58){p = qr5; q= qs5;} + else if(ix>=0x4036db68){p = qr3; q= qs3;} + else if(ix>=0x40000000){p = qr2; q= qs2;} + z = one/(x*x); + r = p[0]+z*(p[1]+z*(p[2]+z*(p[3]+z*(p[4]+z*p[5])))); + s = one+z*(q[0]+z*(q[1]+z*(q[2]+z*(q[3]+z*(q[4]+z*q[5]))))); + return ((float).375 + r/s)/x; +} diff --git a/lib/libm/src/e_jn.c b/lib/libm/src/e_jn.c new file mode 100644 index 0000000000..d7188fe4cd --- /dev/null +++ b/lib/libm/src/e_jn.c @@ -0,0 +1,266 @@ +/* @(#)e_jn.c 5.1 93/09/24 */ +/* + * ==================================================== + * Copyright (C) 1993 by Sun Microsystems, Inc. All rights reserved. + * + * Developed at SunPro, a Sun Microsystems, Inc. business. + * Permission to use, copy, modify, and distribute this + * software is freely granted, provided that this notice + * is preserved. + * ==================================================== + * + * $NetBSD: e_jn.c,v 1.12 2002/05/26 22:01:50 wiz Exp $ + * $DragonFly: src/lib/libm/src/e_jn.c,v 1.1 2005/07/26 21:15:20 joerg Exp $ + */ + +/* + * jn(n, x), yn(n, x) + * floating point Bessel's function of the 1st and 2nd kind + * of order n + * + * Special cases: + * y0(0)=y1(0)=yn(n,0) = -inf with division by zero signal; + * y0(-ve)=y1(-ve)=yn(n,-ve) are NaN with invalid signal. + * Note 2. About jn(n,x), yn(n,x) + * For n=0, j0(x) is called, + * for n=1, j1(x) is called, + * for nx, a continued fraction approximation to + * j(n,x)/j(n-1,x) is evaluated and then backward + * recursion is used starting from a supposed value + * for j(n,x). The resulting value of j(0,x) is + * compared with the actual value to correct the + * supposed value of j(n,x). + * + * yn(n,x) is similar in all respects, except + * that forward recursion is used for all + * values of n>1. + * + */ + +#include +#include "math_private.h" + +static const double +invsqrtpi= 5.64189583547756279280e-01, /* 0x3FE20DD7, 0x50429B6D */ +two = 2.00000000000000000000e+00, /* 0x40000000, 0x00000000 */ +one = 1.00000000000000000000e+00; /* 0x3FF00000, 0x00000000 */ + +static const double zero = 0.00000000000000000000e+00; + +double +jn(int n, double x) +{ + int32_t i,hx,ix,lx, sgn; + double a, b, temp, di; + double z, w; + + temp = 0; + /* J(-n,x) = (-1)^n * J(n, x), J(n, -x) = (-1)^n * J(n, x) + * Thus, J(-n,x) = J(n,-x) + */ + EXTRACT_WORDS(hx,lx,x); + ix = 0x7fffffff&hx; + /* if J(n,NaN) is NaN */ + if((ix|((u_int32_t)(lx|-lx))>>31)>0x7ff00000) return x+x; + if(n<0){ + n = -n; + x = -x; + hx ^= 0x80000000; + } + if(n==0) return(j0(x)); + if(n==1) return(j1(x)); + sgn = (n&1)&(hx>>31); /* even n -- 0, odd n -- sign(x) */ + x = fabs(x); + if((ix|lx)==0||ix>=0x7ff00000) /* if x is 0 or inf */ + b = zero; + else if((double)n<=x) { + /* Safe to use J(n+1,x)=2n/x *J(n,x)-J(n-1,x) */ + if(ix>=0x52D00000) { /* x > 2**302 */ + /* (x >> n**2) + * Jn(x) = cos(x-(2n+1)*pi/4)*sqrt(2/x*pi) + * Yn(x) = sin(x-(2n+1)*pi/4)*sqrt(2/x*pi) + * Let s=sin(x), c=cos(x), + * xn=x-(2n+1)*pi/4, sqt2 = sqrt(2),then + * + * n sin(xn)*sqt2 cos(xn)*sqt2 + * ---------------------------------- + * 0 s-c c+s + * 1 -s-c -c+s + * 2 -s+c -c-s + * 3 s+c c-s + */ + switch(n&3) { + case 0: temp = cos(x)+sin(x); break; + case 1: temp = -cos(x)+sin(x); break; + case 2: temp = -cos(x)-sin(x); break; + case 3: temp = cos(x)-sin(x); break; + } + b = invsqrtpi*temp/sqrt(x); + } else { + a = j0(x); + b = j1(x); + for(i=1;i33) /* underflow */ + b = zero; + else { + temp = x*0.5; b = temp; + for (a=one,i=2;i<=n;i++) { + a *= (double)i; /* a = n! */ + b *= temp; /* b = (x/2)^n */ + } + b = b/a; + } + } else { + /* use backward recurrence */ + /* x x^2 x^2 + * J(n,x)/J(n-1,x) = ---- ------ ------ ..... + * 2n - 2(n+1) - 2(n+2) + * + * 1 1 1 + * (for large x) = ---- ------ ------ ..... + * 2n 2(n+1) 2(n+2) + * -- - ------ - ------ - + * x x x + * + * Let w = 2n/x and h=2/x, then the above quotient + * is equal to the continued fraction: + * 1 + * = ----------------------- + * 1 + * w - ----------------- + * 1 + * w+h - --------- + * w+2h - ... + * + * To determine how many terms needed, let + * Q(0) = w, Q(1) = w(w+h) - 1, + * Q(k) = (w+k*h)*Q(k-1) - Q(k-2), + * When Q(k) > 1e4 good for single + * When Q(k) > 1e9 good for double + * When Q(k) > 1e17 good for quadruple + */ + /* determine k */ + double t,v; + double q0,q1,h,tmp; int32_t k,m; + w = (n+n)/(double)x; h = 2.0/(double)x; + q0 = w; z = w+h; q1 = w*z - 1.0; k=1; + while(q1<1.0e9) { + k += 1; z += h; + tmp = z*q1 - q0; + q0 = q1; + q1 = tmp; + } + m = n+n; + for(t=zero, i = 2*(n+k); i>=m; i -= 2) t = one/(i/x-t); + a = t; + b = one; + /* estimate log((2/x)^n*n!) = n*log(2/x)+n*ln(n) + * Hence, if n*(log(2n/x)) > ... + * single 8.8722839355e+01 + * double 7.09782712893383973096e+02 + * long double 1.1356523406294143949491931077970765006170e+04 + * then recurrent value may overflow and the result is + * likely underflow to zero + */ + tmp = n; + v = two/x; + tmp = tmp*log(fabs(v*tmp)); + if(tmp<7.09782712893383973096e+02) { + for(i=n-1,di=(double)(i+i);i>0;i--){ + temp = b; + b *= di; + b = b/x - a; + a = temp; + di -= two; + } + } else { + for(i=n-1,di=(double)(i+i);i>0;i--){ + temp = b; + b *= di; + b = b/x - a; + a = temp; + di -= two; + /* scale b to avoid spurious overflow */ + if(b>1e100) { + a /= b; + t /= b; + b = one; + } + } + } + b = (t*j0(x)/b); + } + } + if(sgn==1) return -b; else return b; +} + +double +yn(int n, double x) +{ + int32_t i,hx,ix,lx; + int32_t sign; + double a, b, temp; + + temp = 0; + EXTRACT_WORDS(hx,lx,x); + ix = 0x7fffffff&hx; + /* if Y(n,NaN) is NaN */ + if((ix|((u_int32_t)(lx|-lx))>>31)>0x7ff00000) return x+x; + if((ix|lx)==0) return -one/zero; + if(hx<0) return zero/zero; + sign = 1; + if(n<0){ + n = -n; + sign = 1 - ((n&1)<<1); + } + if(n==0) return(y0(x)); + if(n==1) return(sign*y1(x)); + if(ix==0x7ff00000) return zero; + if(ix>=0x52D00000) { /* x > 2**302 */ + /* (x >> n**2) + * Jn(x) = cos(x-(2n+1)*pi/4)*sqrt(2/x*pi) + * Yn(x) = sin(x-(2n+1)*pi/4)*sqrt(2/x*pi) + * Let s=sin(x), c=cos(x), + * xn=x-(2n+1)*pi/4, sqt2 = sqrt(2),then + * + * n sin(xn)*sqt2 cos(xn)*sqt2 + * ---------------------------------- + * 0 s-c c+s + * 1 -s-c -c+s + * 2 -s+c -c-s + * 3 s+c c-s + */ + switch(n&3) { + case 0: temp = sin(x)-cos(x); break; + case 1: temp = -sin(x)-cos(x); break; + case 2: temp = -sin(x)+cos(x); break; + case 3: temp = sin(x)+cos(x); break; + } + b = invsqrtpi*temp/sqrt(x); + } else { + u_int32_t high; + a = y0(x); + b = y1(x); + /* quit if b is -inf */ + GET_HIGH_WORD(high,b); + for(i=1;i0) return b; else return -b; +} diff --git a/lib/libm/src/e_jnf.c b/lib/libm/src/e_jnf.c new file mode 100644 index 0000000000..8c434cc100 --- /dev/null +++ b/lib/libm/src/e_jnf.c @@ -0,0 +1,197 @@ +/* e_jnf.c -- float version of e_jn.c. + * Conversion to float by Ian Lance Taylor, Cygnus Support, ian@cygnus.com. + */ + +/* + * ==================================================== + * Copyright (C) 1993 by Sun Microsystems, Inc. All rights reserved. + * + * Developed at SunPro, a Sun Microsystems, Inc. business. + * Permission to use, copy, modify, and distribute this + * software is freely granted, provided that this notice + * is preserved. + * ==================================================== + * + * $NetBSD: e_jnf.c,v 1.9 2002/05/26 22:01:50 wiz Exp $ + * $DragonFly: src/lib/libm/src/e_jnf.c,v 1.1 2005/07/26 21:15:20 joerg Exp $ + */ + +#include +#include "math_private.h" + +static const float +#if 0 +invsqrtpi= 5.6418961287e-01, /* 0x3f106ebb */ +#endif +two = 2.0000000000e+00, /* 0x40000000 */ +one = 1.0000000000e+00; /* 0x3F800000 */ + +static const float zero = 0.0000000000e+00; + +float +jnf(int n, float x) +{ + int32_t i,hx,ix, sgn; + float a, b, temp, di; + float z, w; + + /* J(-n,x) = (-1)^n * J(n, x), J(n, -x) = (-1)^n * J(n, x) + * Thus, J(-n,x) = J(n,-x) + */ + GET_FLOAT_WORD(hx,x); + ix = 0x7fffffff&hx; + /* if J(n,NaN) is NaN */ + if(ix>0x7f800000) return x+x; + if(n<0){ + n = -n; + x = -x; + hx ^= 0x80000000; + } + if(n==0) return(j0f(x)); + if(n==1) return(j1f(x)); + sgn = (n&1)&(hx>>31); /* even n -- 0, odd n -- sign(x) */ + x = fabsf(x); + if(ix==0||ix>=0x7f800000) /* if x is 0 or inf */ + b = zero; + else if((float)n<=x) { + /* Safe to use J(n+1,x)=2n/x *J(n,x)-J(n-1,x) */ + a = j0f(x); + b = j1f(x); + for(i=1;i33) /* underflow */ + b = zero; + else { + temp = x*(float)0.5; b = temp; + for (a=one,i=2;i<=n;i++) { + a *= (float)i; /* a = n! */ + b *= temp; /* b = (x/2)^n */ + } + b = b/a; + } + } else { + /* use backward recurrence */ + /* x x^2 x^2 + * J(n,x)/J(n-1,x) = ---- ------ ------ ..... + * 2n - 2(n+1) - 2(n+2) + * + * 1 1 1 + * (for large x) = ---- ------ ------ ..... + * 2n 2(n+1) 2(n+2) + * -- - ------ - ------ - + * x x x + * + * Let w = 2n/x and h=2/x, then the above quotient + * is equal to the continued fraction: + * 1 + * = ----------------------- + * 1 + * w - ----------------- + * 1 + * w+h - --------- + * w+2h - ... + * + * To determine how many terms needed, let + * Q(0) = w, Q(1) = w(w+h) - 1, + * Q(k) = (w+k*h)*Q(k-1) - Q(k-2), + * When Q(k) > 1e4 good for single + * When Q(k) > 1e9 good for double + * When Q(k) > 1e17 good for quadruple + */ + /* determine k */ + float t,v; + float q0,q1,h,tmp; int32_t k,m; + w = (n+n)/(float)x; h = (float)2.0/(float)x; + q0 = w; z = w+h; q1 = w*z - (float)1.0; k=1; + while(q1<(float)1.0e9) { + k += 1; z += h; + tmp = z*q1 - q0; + q0 = q1; + q1 = tmp; + } + m = n+n; + for(t=zero, i = 2*(n+k); i>=m; i -= 2) t = one/(i/x-t); + a = t; + b = one; + /* estimate log((2/x)^n*n!) = n*log(2/x)+n*ln(n) + * Hence, if n*(log(2n/x)) > ... + * single 8.8722839355e+01 + * double 7.09782712893383973096e+02 + * long double 1.1356523406294143949491931077970765006170e+04 + * then recurrent value may overflow and the result is + * likely underflow to zero + */ + tmp = n; + v = two/x; + tmp = tmp*logf(fabsf(v*tmp)); + if(tmp<(float)8.8721679688e+01) { + for(i=n-1,di=(float)(i+i);i>0;i--){ + temp = b; + b *= di; + b = b/x - a; + a = temp; + di -= two; + } + } else { + for(i=n-1,di=(float)(i+i);i>0;i--){ + temp = b; + b *= di; + b = b/x - a; + a = temp; + di -= two; + /* scale b to avoid spurious overflow */ + if(b>(float)1e10) { + a /= b; + t /= b; + b = one; + } + } + } + b = (t*j0f(x)/b); + } + } + if(sgn==1) return -b; else return b; +} + +float +ynf(int n, float x) +{ + int32_t i,hx,ix,ib; + int32_t sign; + float a, b, temp; + + GET_FLOAT_WORD(hx,x); + ix = 0x7fffffff&hx; + /* if Y(n,NaN) is NaN */ + if(ix>0x7f800000) return x+x; + if(ix==0) return -one/zero; + if(hx<0) return zero/zero; + sign = 1; + if(n<0){ + n = -n; + sign = 1 - ((n&1)<<1); + } + if(n==0) return(y0f(x)); + if(n==1) return(sign*y1f(x)); + if(ix==0x7f800000) return zero; + + a = y0f(x); + b = y1f(x); + /* quit if b is -inf */ + GET_FLOAT_WORD(ib,b); + for(i=1;i0) return b; else return -b; +} diff --git a/lib/libm/src/e_lgamma_r.c b/lib/libm/src/e_lgamma_r.c new file mode 100644 index 0000000000..e0d68fb142 --- /dev/null +++ b/lib/libm/src/e_lgamma_r.c @@ -0,0 +1,296 @@ +/* @(#)er_lgamma.c 5.1 93/09/24 */ +/* + * ==================================================== + * Copyright (C) 1993 by Sun Microsystems, Inc. All rights reserved. + * + * Developed at SunPro, a Sun Microsystems, Inc. business. + * Permission to use, copy, modify, and distribute this + * software is freely granted, provided that this notice + * is preserved. + * ==================================================== + * + * $NetBSD: e_lgamma_r.c,v 1.10 2002/05/26 22:01:51 wiz Exp $ + * $DragonFly: src/lib/libm/src/e_lgamma_r.c,v 1.1 2005/07/26 21:15:20 joerg Exp $ + */ + +/* lgamma_r(x, signgamp) + * Reentrant version of the logarithm of the Gamma function + * with user provide pointer for the sign of Gamma(x). + * + * Method: + * 1. Argument Reduction for 0 < x <= 8 + * Since gamma(1+s)=s*gamma(s), for x in [0,8], we may + * reduce x to a number in [1.5,2.5] by + * lgamma(1+s) = log(s) + lgamma(s) + * for example, + * lgamma(7.3) = log(6.3) + lgamma(6.3) + * = log(6.3*5.3) + lgamma(5.3) + * = log(6.3*5.3*4.3*3.3*2.3) + lgamma(2.3) + * 2. Polynomial approximation of lgamma around its + * minimun ymin=1.461632144968362245 to maintain monotonicity. + * On [ymin-0.23, ymin+0.27] (i.e., [1.23164,1.73163]), use + * Let z = x-ymin; + * lgamma(x) = -1.214862905358496078218 + z^2*poly(z) + * where + * poly(z) is a 14 degree polynomial. + * 2. Rational approximation in the primary interval [2,3] + * We use the following approximation: + * s = x-2.0; + * lgamma(x) = 0.5*s + s*P(s)/Q(s) + * with accuracy + * |P/Q - (lgamma(x)-0.5s)| < 2**-61.71 + * Our algorithms are based on the following observation + * + * zeta(2)-1 2 zeta(3)-1 3 + * lgamma(2+s) = s*(1-Euler) + --------- * s - --------- * s + ... + * 2 3 + * + * where Euler = 0.5771... is the Euler constant, which is very + * close to 0.5. + * + * 3. For x>=8, we have + * lgamma(x)~(x-0.5)log(x)-x+0.5*log(2pi)+1/(12x)-1/(360x**3)+.... + * (better formula: + * lgamma(x)~(x-0.5)*(log(x)-1)-.5*(log(2pi)-1) + ...) + * Let z = 1/x, then we approximation + * f(z) = lgamma(x) - (x-0.5)(log(x)-1) + * by + * 3 5 11 + * w = w0 + w1*z + w2*z + w3*z + ... + w6*z + * where + * |w - f(z)| < 2**-58.74 + * + * 4. For negative x, since (G is gamma function) + * -x*G(-x)*G(x) = pi/sin(pi*x), + * we have + * G(x) = pi/(sin(pi*x)*(-x)*G(-x)) + * since G(-x) is positive, sign(G(x)) = sign(sin(pi*x)) for x<0 + * Hence, for x<0, signgam = sign(sin(pi*x)) and + * lgamma(x) = log(|Gamma(x)|) + * = log(pi/(|x*sin(pi*x)|)) - lgamma(-x); + * Note: one should avoid compute pi*(-x) directly in the + * computation of sin(pi*(-x)). + * + * 5. Special Cases + * lgamma(2+s) ~ s*(1-Euler) for tiny s + * lgamma(1)=lgamma(2)=0 + * lgamma(x) ~ -log(x) for tiny x + * lgamma(0) = lgamma(inf) = inf + * lgamma(-integer) = +-inf + * + */ + +#include +#include "math_private.h" + +static const double +two52= 4.50359962737049600000e+15, /* 0x43300000, 0x00000000 */ +half= 5.00000000000000000000e-01, /* 0x3FE00000, 0x00000000 */ +one = 1.00000000000000000000e+00, /* 0x3FF00000, 0x00000000 */ +pi = 3.14159265358979311600e+00, /* 0x400921FB, 0x54442D18 */ +a0 = 7.72156649015328655494e-02, /* 0x3FB3C467, 0xE37DB0C8 */ +a1 = 3.22467033424113591611e-01, /* 0x3FD4A34C, 0xC4A60FAD */ +a2 = 6.73523010531292681824e-02, /* 0x3FB13E00, 0x1A5562A7 */ +a3 = 2.05808084325167332806e-02, /* 0x3F951322, 0xAC92547B */ +a4 = 7.38555086081402883957e-03, /* 0x3F7E404F, 0xB68FEFE8 */ +a5 = 2.89051383673415629091e-03, /* 0x3F67ADD8, 0xCCB7926B */ +a6 = 1.19270763183362067845e-03, /* 0x3F538A94, 0x116F3F5D */ +a7 = 5.10069792153511336608e-04, /* 0x3F40B6C6, 0x89B99C00 */ +a8 = 2.20862790713908385557e-04, /* 0x3F2CF2EC, 0xED10E54D */ +a9 = 1.08011567247583939954e-04, /* 0x3F1C5088, 0x987DFB07 */ +a10 = 2.52144565451257326939e-05, /* 0x3EFA7074, 0x428CFA52 */ +a11 = 4.48640949618915160150e-05, /* 0x3F07858E, 0x90A45837 */ +tc = 1.46163214496836224576e+00, /* 0x3FF762D8, 0x6356BE3F */ +tf = -1.21486290535849611461e-01, /* 0xBFBF19B9, 0xBCC38A42 */ +/* tt = -(tail of tf) */ +tt = -3.63867699703950536541e-18, /* 0xBC50C7CA, 0xA48A971F */ +t0 = 4.83836122723810047042e-01, /* 0x3FDEF72B, 0xC8EE38A2 */ +t1 = -1.47587722994593911752e-01, /* 0xBFC2E427, 0x8DC6C509 */ +t2 = 6.46249402391333854778e-02, /* 0x3FB08B42, 0x94D5419B */ +t3 = -3.27885410759859649565e-02, /* 0xBFA0C9A8, 0xDF35B713 */ +t4 = 1.79706750811820387126e-02, /* 0x3F9266E7, 0x970AF9EC */ +t5 = -1.03142241298341437450e-02, /* 0xBF851F9F, 0xBA91EC6A */ +t6 = 6.10053870246291332635e-03, /* 0x3F78FCE0, 0xE370E344 */ +t7 = -3.68452016781138256760e-03, /* 0xBF6E2EFF, 0xB3E914D7 */ +t8 = 2.25964780900612472250e-03, /* 0x3F6282D3, 0x2E15C915 */ +t9 = -1.40346469989232843813e-03, /* 0xBF56FE8E, 0xBF2D1AF1 */ +t10 = 8.81081882437654011382e-04, /* 0x3F4CDF0C, 0xEF61A8E9 */ +t11 = -5.38595305356740546715e-04, /* 0xBF41A610, 0x9C73E0EC */ +t12 = 3.15632070903625950361e-04, /* 0x3F34AF6D, 0x6C0EBBF7 */ +t13 = -3.12754168375120860518e-04, /* 0xBF347F24, 0xECC38C38 */ +t14 = 3.35529192635519073543e-04, /* 0x3F35FD3E, 0xE8C2D3F4 */ +u0 = -7.72156649015328655494e-02, /* 0xBFB3C467, 0xE37DB0C8 */ +u1 = 6.32827064025093366517e-01, /* 0x3FE4401E, 0x8B005DFF */ +u2 = 1.45492250137234768737e+00, /* 0x3FF7475C, 0xD119BD6F */ +u3 = 9.77717527963372745603e-01, /* 0x3FEF4976, 0x44EA8450 */ +u4 = 2.28963728064692451092e-01, /* 0x3FCD4EAE, 0xF6010924 */ +u5 = 1.33810918536787660377e-02, /* 0x3F8B678B, 0xBF2BAB09 */ +v1 = 2.45597793713041134822e+00, /* 0x4003A5D7, 0xC2BD619C */ +v2 = 2.12848976379893395361e+00, /* 0x40010725, 0xA42B18F5 */ +v3 = 7.69285150456672783825e-01, /* 0x3FE89DFB, 0xE45050AF */ +v4 = 1.04222645593369134254e-01, /* 0x3FBAAE55, 0xD6537C88 */ +v5 = 3.21709242282423911810e-03, /* 0x3F6A5ABB, 0x57D0CF61 */ +s0 = -7.72156649015328655494e-02, /* 0xBFB3C467, 0xE37DB0C8 */ +s1 = 2.14982415960608852501e-01, /* 0x3FCB848B, 0x36E20878 */ +s2 = 3.25778796408930981787e-01, /* 0x3FD4D98F, 0x4F139F59 */ +s3 = 1.46350472652464452805e-01, /* 0x3FC2BB9C, 0xBEE5F2F7 */ +s4 = 2.66422703033638609560e-02, /* 0x3F9B481C, 0x7E939961 */ +s5 = 1.84028451407337715652e-03, /* 0x3F5E26B6, 0x7368F239 */ +s6 = 3.19475326584100867617e-05, /* 0x3F00BFEC, 0xDD17E945 */ +r1 = 1.39200533467621045958e+00, /* 0x3FF645A7, 0x62C4AB74 */ +r2 = 7.21935547567138069525e-01, /* 0x3FE71A18, 0x93D3DCDC */ +r3 = 1.71933865632803078993e-01, /* 0x3FC601ED, 0xCCFBDF27 */ +r4 = 1.86459191715652901344e-02, /* 0x3F9317EA, 0x742ED475 */ +r5 = 7.77942496381893596434e-04, /* 0x3F497DDA, 0xCA41A95B */ +r6 = 7.32668430744625636189e-06, /* 0x3EDEBAF7, 0xA5B38140 */ +w0 = 4.18938533204672725052e-01, /* 0x3FDACFE3, 0x90C97D69 */ +w1 = 8.33333333333329678849e-02, /* 0x3FB55555, 0x5555553B */ +w2 = -2.77777777728775536470e-03, /* 0xBF66C16C, 0x16B02E5C */ +w3 = 7.93650558643019558500e-04, /* 0x3F4A019F, 0x98CF38B6 */ +w4 = -5.95187557450339963135e-04, /* 0xBF4380CB, 0x8C0FE741 */ +w5 = 8.36339918996282139126e-04, /* 0x3F4B67BA, 0x4CDAD5D1 */ +w6 = -1.63092934096575273989e-03; /* 0xBF5AB89D, 0x0B9E43E4 */ + +static const double zero= 0.00000000000000000000e+00; + +static +double sin_pi(double x) +{ + double y,z; + int n,ix; + + GET_HIGH_WORD(ix,x); + ix &= 0x7fffffff; + + if(ix<0x3fd00000) return __kernel_sin(pi*x,zero,0); + y = -x; /* x is assume negative */ + + /* + * argument reduction, make sure inexact flag not raised if input + * is an integer + */ + z = floor(y); + if(z!=y) { /* inexact anyway */ + y *= 0.5; + y = 2.0*(y - floor(y)); /* y = |x| mod 2.0 */ + n = (int) (y*4.0); + } else { + if(ix>=0x43400000) { + y = zero; n = 0; /* y must be even */ + } else { + if(ix<0x43300000) z = y+two52; /* exact */ + GET_LOW_WORD(n,z); + n &= 1; + y = n; + n<<= 2; + } + } + switch (n) { + case 0: y = __kernel_sin(pi*y,zero,0); break; + case 1: + case 2: y = __kernel_cos(pi*(0.5-y),zero); break; + case 3: + case 4: y = __kernel_sin(pi*(one-y),zero,0); break; + case 5: + case 6: y = -__kernel_cos(pi*(y-1.5),zero); break; + default: y = __kernel_sin(pi*(y-2.0),zero,0); break; + } + return -y; +} + + +double +lgamma_r(double x, int *signgamp) +{ + double t,y,z,nadj,p,p1,p2,p3,q,r,w; + int i,hx,lx,ix; + + nadj = 0; + EXTRACT_WORDS(hx,lx,x); + + /* purge off +-inf, NaN, +-0, and negative arguments */ + *signgamp = 1; + ix = hx&0x7fffffff; + if(ix>=0x7ff00000) return x*x; + if((ix|lx)==0) return one/zero; + if(ix<0x3b900000) { /* |x|<2**-70, return -log(|x|) */ + if(hx<0) { + *signgamp = -1; + return -log(-x); + } else return -log(x); + } + if(hx<0) { + if(ix>=0x43300000) /* |x|>=2**52, must be -integer */ + return one/zero; + t = sin_pi(x); + if(t==zero) return one/zero; /* -integer */ + nadj = log(pi/fabs(t*x)); + if(t=0x3FE76944) {y = one-x; i= 0;} + else if(ix>=0x3FCDA661) {y= x-(tc-one); i=1;} + else {y = x; i=2;} + } else { + r = zero; + if(ix>=0x3FFBB4C3) {y=2.0-x;i=0;} /* [1.7316,2] */ + else if(ix>=0x3FF3B4C4) {y=x-tc;i=1;} /* [1.23,1.73] */ + else {y=x-one;i=2;} + } + switch(i) { + case 0: + z = y*y; + p1 = a0+z*(a2+z*(a4+z*(a6+z*(a8+z*a10)))); + p2 = z*(a1+z*(a3+z*(a5+z*(a7+z*(a9+z*a11))))); + p = y*p1+p2; + r += (p-0.5*y); break; + case 1: + z = y*y; + w = z*y; + p1 = t0+w*(t3+w*(t6+w*(t9 +w*t12))); /* parallel comp */ + p2 = t1+w*(t4+w*(t7+w*(t10+w*t13))); + p3 = t2+w*(t5+w*(t8+w*(t11+w*t14))); + p = z*p1-(tt-w*(p2+y*p3)); + r += (tf + p); break; + case 2: + p1 = y*(u0+y*(u1+y*(u2+y*(u3+y*(u4+y*u5))))); + p2 = one+y*(v1+y*(v2+y*(v3+y*(v4+y*v5)))); + r += (-0.5*y + p1/p2); + } + } + else if(ix<0x40200000) { /* x < 8.0 */ + i = (int)x; + t = zero; + y = x-(double)i; + p = y*(s0+y*(s1+y*(s2+y*(s3+y*(s4+y*(s5+y*s6)))))); + q = one+y*(r1+y*(r2+y*(r3+y*(r4+y*(r5+y*r6))))); + r = half*y+p/q; + z = one; /* lgamma(1+s) = log(s) + lgamma(s) */ + switch(i) { + case 7: z *= (y+6.0); /* FALLTHRU */ + case 6: z *= (y+5.0); /* FALLTHRU */ + case 5: z *= (y+4.0); /* FALLTHRU */ + case 4: z *= (y+3.0); /* FALLTHRU */ + case 3: z *= (y+2.0); /* FALLTHRU */ + r += log(z); break; + } + /* 8.0 <= x < 2**58 */ + } else if (ix < 0x43900000) { + t = log(x); + z = one/x; + y = z*z; + w = w0+z*(w1+y*(w2+y*(w3+y*(w4+y*(w5+y*w6))))); + r = (x-half)*(t-one)+w; + } else + /* 2**58 <= x <= inf */ + r = x*(log(x)-one); + if(hx<0) r = nadj - r; + return r; +} diff --git a/lib/libm/src/e_lgammaf_r.c b/lib/libm/src/e_lgammaf_r.c new file mode 100644 index 0000000000..dbe06c50d4 --- /dev/null +++ b/lib/libm/src/e_lgammaf_r.c @@ -0,0 +1,232 @@ +/* e_lgammaf_r.c -- float version of e_lgamma_r.c. + * Conversion to float by Ian Lance Taylor, Cygnus Support, ian@cygnus.com. + */ + +/* + * ==================================================== + * Copyright (C) 1993 by Sun Microsystems, Inc. All rights reserved. + * + * Developed at SunPro, a Sun Microsystems, Inc. business. + * Permission to use, copy, modify, and distribute this + * software is freely granted, provided that this notice + * is preserved. + * ==================================================== + * + * $NetBSD: e_lgammaf_r.c,v 1.6 2002/05/26 22:01:51 wiz Exp $ + * $DragonFly: src/lib/libm/src/e_lgammaf_r.c,v 1.1 2005/07/26 21:15:20 joerg Exp $ + */ + +#include +#include "math_private.h" + +static const float +two23= 8.3886080000e+06, /* 0x4b000000 */ +half= 5.0000000000e-01, /* 0x3f000000 */ +one = 1.0000000000e+00, /* 0x3f800000 */ +pi = 3.1415927410e+00, /* 0x40490fdb */ +a0 = 7.7215664089e-02, /* 0x3d9e233f */ +a1 = 3.2246702909e-01, /* 0x3ea51a66 */ +a2 = 6.7352302372e-02, /* 0x3d89f001 */ +a3 = 2.0580807701e-02, /* 0x3ca89915 */ +a4 = 7.3855509982e-03, /* 0x3bf2027e */ +a5 = 2.8905137442e-03, /* 0x3b3d6ec6 */ +a6 = 1.1927076848e-03, /* 0x3a9c54a1 */ +a7 = 5.1006977446e-04, /* 0x3a05b634 */ +a8 = 2.2086278477e-04, /* 0x39679767 */ +a9 = 1.0801156895e-04, /* 0x38e28445 */ +a10 = 2.5214456400e-05, /* 0x37d383a2 */ +a11 = 4.4864096708e-05, /* 0x383c2c75 */ +tc = 1.4616321325e+00, /* 0x3fbb16c3 */ +tf = -1.2148628384e-01, /* 0xbdf8cdcd */ +/* tt = -(tail of tf) */ +tt = 6.6971006518e-09, /* 0x31e61c52 */ +t0 = 4.8383611441e-01, /* 0x3ef7b95e */ +t1 = -1.4758771658e-01, /* 0xbe17213c */ +t2 = 6.4624942839e-02, /* 0x3d845a15 */ +t3 = -3.2788541168e-02, /* 0xbd064d47 */ +t4 = 1.7970675603e-02, /* 0x3c93373d */ +t5 = -1.0314224288e-02, /* 0xbc28fcfe */ +t6 = 6.1005386524e-03, /* 0x3bc7e707 */ +t7 = -3.6845202558e-03, /* 0xbb7177fe */ +t8 = 2.2596477065e-03, /* 0x3b141699 */ +t9 = -1.4034647029e-03, /* 0xbab7f476 */ +t10 = 8.8108185446e-04, /* 0x3a66f867 */ +t11 = -5.3859531181e-04, /* 0xba0d3085 */ +t12 = 3.1563205994e-04, /* 0x39a57b6b */ +t13 = -3.1275415677e-04, /* 0xb9a3f927 */ +t14 = 3.3552918467e-04, /* 0x39afe9f7 */ +u0 = -7.7215664089e-02, /* 0xbd9e233f */ +u1 = 6.3282704353e-01, /* 0x3f2200f4 */ +u2 = 1.4549225569e+00, /* 0x3fba3ae7 */ +u3 = 9.7771751881e-01, /* 0x3f7a4bb2 */ +u4 = 2.2896373272e-01, /* 0x3e6a7578 */ +u5 = 1.3381091878e-02, /* 0x3c5b3c5e */ +v1 = 2.4559779167e+00, /* 0x401d2ebe */ +v2 = 2.1284897327e+00, /* 0x4008392d */ +v3 = 7.6928514242e-01, /* 0x3f44efdf */ +v4 = 1.0422264785e-01, /* 0x3dd572af */ +v5 = 3.2170924824e-03, /* 0x3b52d5db */ +s0 = -7.7215664089e-02, /* 0xbd9e233f */ +s1 = 2.1498242021e-01, /* 0x3e5c245a */ +s2 = 3.2577878237e-01, /* 0x3ea6cc7a */ +s3 = 1.4635047317e-01, /* 0x3e15dce6 */ +s4 = 2.6642270386e-02, /* 0x3cda40e4 */ +s5 = 1.8402845599e-03, /* 0x3af135b4 */ +s6 = 3.1947532989e-05, /* 0x3805ff67 */ +r1 = 1.3920053244e+00, /* 0x3fb22d3b */ +r2 = 7.2193557024e-01, /* 0x3f38d0c5 */ +r3 = 1.7193385959e-01, /* 0x3e300f6e */ +r4 = 1.8645919859e-02, /* 0x3c98bf54 */ +r5 = 7.7794247773e-04, /* 0x3a4beed6 */ +r6 = 7.3266842264e-06, /* 0x36f5d7bd */ +w0 = 4.1893854737e-01, /* 0x3ed67f1d */ +w1 = 8.3333335817e-02, /* 0x3daaaaab */ +w2 = -2.7777778450e-03, /* 0xbb360b61 */ +w3 = 7.9365057172e-04, /* 0x3a500cfd */ +w4 = -5.9518753551e-04, /* 0xba1c065c */ +w5 = 8.3633989561e-04, /* 0x3a5b3dd2 */ +w6 = -1.6309292987e-03; /* 0xbad5c4e8 */ + +static const float zero= 0.0000000000e+00; + +static float +sin_pif(float x) +{ + float y,z; + int n,ix; + + GET_FLOAT_WORD(ix,x); + ix &= 0x7fffffff; + + if(ix<0x3e800000) return __kernel_sinf(pi*x,zero,0); + y = -x; /* x is assume negative */ + + /* + * argument reduction, make sure inexact flag not raised if input + * is an integer + */ + z = floorf(y); + if(z!=y) { /* inexact anyway */ + y *= (float)0.5; + y = (float)2.0*(y - floorf(y)); /* y = |x| mod 2.0 */ + n = (int) (y*(float)4.0); + } else { + if(ix>=0x4b800000) { + y = zero; n = 0; /* y must be even */ + } else { + if(ix<0x4b000000) z = y+two23; /* exact */ + GET_FLOAT_WORD(n,z); + n &= 1; + y = n; + n<<= 2; + } + } + switch (n) { + case 0: y = __kernel_sinf(pi*y,zero,0); break; + case 1: + case 2: y = __kernel_cosf(pi*((float)0.5-y),zero); break; + case 3: + case 4: y = __kernel_sinf(pi*(one-y),zero,0); break; + case 5: + case 6: y = -__kernel_cosf(pi*(y-(float)1.5),zero); break; + default: y = __kernel_sinf(pi*(y-(float)2.0),zero,0); break; + } + return -y; +} + + +float +lgammaf_r(float x, int *signgamp) +{ + float t,y,z,nadj,p,p1,p2,p3,q,r,w; + int i,hx,ix; + + nadj = 0; + GET_FLOAT_WORD(hx,x); + + /* purge off +-inf, NaN, +-0, and negative arguments */ + *signgamp = 1; + ix = hx&0x7fffffff; + if(ix>=0x7f800000) return x*x; + if(ix==0) return one/zero; + if(ix<0x1c800000) { /* |x|<2**-70, return -log(|x|) */ + if(hx<0) { + *signgamp = -1; + return -logf(-x); + } else return -logf(x); + } + if(hx<0) { + if(ix>=0x4b000000) /* |x|>=2**23, must be -integer */ + return one/zero; + t = sin_pif(x); + if(t==zero) return one/zero; /* -integer */ + nadj = logf(pi/fabsf(t*x)); + if(t=0x3f3b4a20) {y = one-x; i= 0;} + else if(ix>=0x3e6d3308) {y= x-(tc-one); i=1;} + else {y = x; i=2;} + } else { + r = zero; + if(ix>=0x3fdda618) {y=(float)2.0-x;i=0;} /* [1.7316,2] */ + else if(ix>=0x3F9da620) {y=x-tc;i=1;} /* [1.23,1.73] */ + else {y=x-one;i=2;} + } + switch(i) { + case 0: + z = y*y; + p1 = a0+z*(a2+z*(a4+z*(a6+z*(a8+z*a10)))); + p2 = z*(a1+z*(a3+z*(a5+z*(a7+z*(a9+z*a11))))); + p = y*p1+p2; + r += (p-(float)0.5*y); break; + case 1: + z = y*y; + w = z*y; + p1 = t0+w*(t3+w*(t6+w*(t9 +w*t12))); /* parallel comp */ + p2 = t1+w*(t4+w*(t7+w*(t10+w*t13))); + p3 = t2+w*(t5+w*(t8+w*(t11+w*t14))); + p = z*p1-(tt-w*(p2+y*p3)); + r += (tf + p); break; + case 2: + p1 = y*(u0+y*(u1+y*(u2+y*(u3+y*(u4+y*u5))))); + p2 = one+y*(v1+y*(v2+y*(v3+y*(v4+y*v5)))); + r += (-(float)0.5*y + p1/p2); + } + } + else if(ix<0x41000000) { /* x < 8.0 */ + i = (int)x; + t = zero; + y = x-(float)i; + p = y*(s0+y*(s1+y*(s2+y*(s3+y*(s4+y*(s5+y*s6)))))); + q = one+y*(r1+y*(r2+y*(r3+y*(r4+y*(r5+y*r6))))); + r = half*y+p/q; + z = one; /* lgamma(1+s) = log(s) + lgamma(s) */ + switch(i) { + case 7: z *= (y+(float)6.0); /* FALLTHRU */ + case 6: z *= (y+(float)5.0); /* FALLTHRU */ + case 5: z *= (y+(float)4.0); /* FALLTHRU */ + case 4: z *= (y+(float)3.0); /* FALLTHRU */ + case 3: z *= (y+(float)2.0); /* FALLTHRU */ + r += logf(z); break; + } + /* 8.0 <= x < 2**58 */ + } else if (ix < 0x5c800000) { + t = logf(x); + z = one/x; + y = z*z; + w = w0+z*(w1+y*(w2+y*(w3+y*(w4+y*(w5+y*w6))))); + r = (x-half)*(t-one)+w; + } else + /* 2**58 <= x <= inf */ + r = x*(logf(x)-one); + if(hx<0) r = nadj - r; + return r; +} diff --git a/lib/libm/src/e_log.c b/lib/libm/src/e_log.c new file mode 100644 index 0000000000..2c304e079f --- /dev/null +++ b/lib/libm/src/e_log.c @@ -0,0 +1,134 @@ +/* @(#)e_log.c 5.1 93/09/24 */ +/* + * ==================================================== + * Copyright (C) 1993 by Sun Microsystems, Inc. All rights reserved. + * + * Developed at SunPro, a Sun Microsystems, Inc. business. + * Permission to use, copy, modify, and distribute this + * software is freely granted, provided that this notice + * is preserved. + * ==================================================== + * + * $NetBSD: e_log.c,v 1.12 2002/05/26 22:01:51 wiz Exp $ + * $DragonFly: src/lib/libm/src/e_log.c,v 1.1 2005/07/26 21:15:20 joerg Exp $ + */ + +/* log(x) + * Return the logrithm of x + * + * Method : + * 1. Argument Reduction: find k and f such that + * x = 2^k * (1+f), + * where sqrt(2)/2 < 1+f < sqrt(2) . + * + * 2. Approximation of log(1+f). + * Let s = f/(2+f) ; based on log(1+f) = log(1+s) - log(1-s) + * = 2s + 2/3 s**3 + 2/5 s**5 + ....., + * = 2s + s*R + * We use a special Reme algorithm on [0,0.1716] to generate + * a polynomial of degree 14 to approximate R The maximum error + * of this polynomial approximation is bounded by 2**-58.45. In + * other words, + * 2 4 6 8 10 12 14 + * R(z) ~ Lg1*s +Lg2*s +Lg3*s +Lg4*s +Lg5*s +Lg6*s +Lg7*s + * (the values of Lg1 to Lg7 are listed in the program) + * and + * | 2 14 | -58.45 + * | Lg1*s +...+Lg7*s - R(z) | <= 2 + * | | + * Note that 2s = f - s*f = f - hfsq + s*hfsq, where hfsq = f*f/2. + * In order to guarantee error in log below 1ulp, we compute log + * by + * log(1+f) = f - s*(f - R) (if f is not too large) + * log(1+f) = f - (hfsq - s*(hfsq+R)). (better accuracy) + * + * 3. Finally, log(x) = k*ln2 + log(1+f). + * = k*ln2_hi+(f-(hfsq-(s*(hfsq+R)+k*ln2_lo))) + * Here ln2 is split into two floating point number: + * ln2_hi + ln2_lo, + * where n*ln2_hi is always exact for |n| < 2000. + * + * Special cases: + * log(x) is NaN with signal if x < 0 (including -INF) ; + * log(+INF) is +INF; log(0) is -INF with signal; + * log(NaN) is that NaN with no signal. + * + * Accuracy: + * according to an error analysis, the error is always less than + * 1 ulp (unit in the last place). + * + * Constants: + * The hexadecimal values are the intended ones for the following + * constants. The decimal values may be used, provided that the + * compiler will convert from decimal to binary accurately enough + * to produce the hexadecimal values shown. + */ + +#include +#include "math_private.h" + +static const double +ln2_hi = 6.93147180369123816490e-01, /* 3fe62e42 fee00000 */ +ln2_lo = 1.90821492927058770002e-10, /* 3dea39ef 35793c76 */ +two54 = 1.80143985094819840000e+16, /* 43500000 00000000 */ +Lg1 = 6.666666666666735130e-01, /* 3FE55555 55555593 */ +Lg2 = 3.999999999940941908e-01, /* 3FD99999 9997FA04 */ +Lg3 = 2.857142874366239149e-01, /* 3FD24924 94229359 */ +Lg4 = 2.222219843214978396e-01, /* 3FCC71C5 1D8E78AF */ +Lg5 = 1.818357216161805012e-01, /* 3FC74664 96CB03DE */ +Lg6 = 1.531383769920937332e-01, /* 3FC39A09 D078C69F */ +Lg7 = 1.479819860511658591e-01; /* 3FC2F112 DF3E5244 */ + +static const double zero = 0.0; + +double +log(double x) +{ + double hfsq,f,s,z,R,w,t1,t2,dk; + int32_t k,hx,i,j; + u_int32_t lx; + + EXTRACT_WORDS(hx,lx,x); + + k=0; + if (hx < 0x00100000) { /* x < 2**-1022 */ + if (((hx&0x7fffffff)|lx)==0) + return -two54/zero; /* log(+-0)=-inf */ + if (hx<0) return (x-x)/zero; /* log(-#) = NaN */ + k -= 54; x *= two54; /* subnormal number, scale up x */ + GET_HIGH_WORD(hx,x); + } + if (hx >= 0x7ff00000) return x+x; + k += (hx>>20)-1023; + hx &= 0x000fffff; + i = (hx+0x95f64)&0x100000; + SET_HIGH_WORD(x,hx|(i^0x3ff00000)); /* normalize x or x/2 */ + k += (i>>20); + f = x-1.0; + if((0x000fffff&(2+hx))<3) { /* |f| < 2**-20 */ + if(f==zero) { if(k==0) return zero; else {dk=(double)k; + return dk*ln2_hi+dk*ln2_lo;} + } + R = f*f*(0.5-0.33333333333333333*f); + if(k==0) return f-R; else {dk=(double)k; + return dk*ln2_hi-((R-dk*ln2_lo)-f);} + } + s = f/(2.0+f); + dk = (double)k; + z = s*s; + i = hx-0x6147a; + w = z*z; + j = 0x6b851-hx; + t1= w*(Lg2+w*(Lg4+w*Lg6)); + t2= z*(Lg1+w*(Lg3+w*(Lg5+w*Lg7))); + i |= j; + R = t2+t1; + if(i>0) { + hfsq=0.5*f*f; + if(k==0) return f-(hfsq-s*(hfsq+R)); else + return dk*ln2_hi-((hfsq-(s*(hfsq+R)+dk*ln2_lo))-f); + } else { + if(k==0) return f-s*(f-R); else + return dk*ln2_hi-((s*(f-R)-dk*ln2_lo)-f); + } +} diff --git a/lib/libm/src/e_log10.c b/lib/libm/src/e_log10.c new file mode 100644 index 0000000000..610b39258e --- /dev/null +++ b/lib/libm/src/e_log10.c @@ -0,0 +1,85 @@ +/* @(#)e_log10.c 5.1 93/09/24 */ +/* + * ==================================================== + * Copyright (C) 1993 by Sun Microsystems, Inc. All rights reserved. + * + * Developed at SunPro, a Sun Microsystems, Inc. business. + * Permission to use, copy, modify, and distribute this + * software is freely granted, provided that this notice + * is preserved. + * ==================================================== + * + * $NetBSD: e_log10.c,v 1.12 2002/05/26 22:01:51 wiz Exp $ + * $DragonFly: src/lib/libm/src/e_log10.c,v 1.1 2005/07/26 21:15:20 joerg Exp $ + */ + +/* log10(x) + * Return the base 10 logarithm of x + * + * Method : + * Let log10_2hi = leading 40 bits of log10(2) and + * log10_2lo = log10(2) - log10_2hi, + * ivln10 = 1/log(10) rounded. + * Then + * n = ilogb(x), + * if(n<0) n = n+1; + * x = scalbn(x,-n); + * log10(x) := n*log10_2hi + (n*log10_2lo + ivln10*log(x)) + * + * Note 1: + * To guarantee log10(10**n)=n, where 10**n is normal, the rounding + * mode must set to Round-to-Nearest. + * Note 2: + * [1/log(10)] rounded to 53 bits has error .198 ulps; + * log10 is monotonic at all binary break points. + * + * Special cases: + * log10(x) is NaN with signal if x < 0; + * log10(+INF) is +INF with no signal; log10(0) is -INF with signal; + * log10(NaN) is that NaN with no signal; + * log10(10**N) = N for N=0,1,...,22. + * + * Constants: + * The hexadecimal values are the intended ones for the following constants. + * The decimal values may be used, provided that the compiler will convert + * from decimal to binary accurately enough to produce the hexadecimal values + * shown. + */ + +#include +#include "math_private.h" + +static const double +two54 = 1.80143985094819840000e+16, /* 0x43500000, 0x00000000 */ +ivln10 = 4.34294481903251816668e-01, /* 0x3FDBCB7B, 0x1526E50E */ +log10_2hi = 3.01029995663611771306e-01, /* 0x3FD34413, 0x509F6000 */ +log10_2lo = 3.69423907715893078616e-13; /* 0x3D59FEF3, 0x11F12B36 */ + +static const double zero = 0.0; + +double +log10(double x) +{ + double y,z; + int32_t i,k,hx; + u_int32_t lx; + + EXTRACT_WORDS(hx,lx,x); + + k=0; + if (hx < 0x00100000) { /* x < 2**-1022 */ + if (((hx&0x7fffffff)|lx)==0) + return -two54/zero; /* log(+-0)=-inf */ + if (hx<0) return (x-x)/zero; /* log(-#) = NaN */ + k -= 54; x *= two54; /* subnormal number, scale up x */ + GET_HIGH_WORD(hx,x); + } + if (hx >= 0x7ff00000) return x+x; + k += (hx>>20)-1023; + i = ((u_int32_t)k&0x80000000)>>31; + hx = (hx&0x000fffff)|((0x3ff-i)<<20); + y = (double)(k+i); + SET_HIGH_WORD(x,hx); + z = y*log10_2lo + ivln10*log(x); + return z+y*log10_2hi; +} diff --git a/lib/libm/src/e_log10f.c b/lib/libm/src/e_log10f.c new file mode 100644 index 0000000000..b5689d76be --- /dev/null +++ b/lib/libm/src/e_log10f.c @@ -0,0 +1,54 @@ +/* e_log10f.c -- float version of e_log10.c. + * Conversion to float by Ian Lance Taylor, Cygnus Support, ian@cygnus.com. + */ + +/* + * ==================================================== + * Copyright (C) 1993 by Sun Microsystems, Inc. All rights reserved. + * + * Developed at SunPro, a Sun Microsystems, Inc. business. + * Permission to use, copy, modify, and distribute this + * software is freely granted, provided that this notice + * is preserved. + * ==================================================== + * + * $NetBSD: e_log10f.c,v 1.8 2002/05/26 22:01:51 wiz Exp $ + * $DragonFly: src/lib/libm/src/e_log10f.c,v 1.1 2005/07/26 21:15:20 joerg Exp $ + */ + +#include +#include "math_private.h" + +static const float +two25 = 3.3554432000e+07, /* 0x4c000000 */ +ivln10 = 4.3429449201e-01, /* 0x3ede5bd9 */ +log10_2hi = 3.0102920532e-01, /* 0x3e9a2080 */ +log10_2lo = 7.9034151668e-07; /* 0x355427db */ + +static const float zero = 0.0; + +float +log10f(float x) +{ + float y,z; + int32_t i,k,hx; + + GET_FLOAT_WORD(hx,x); + + k=0; + if (hx < 0x00800000) { /* x < 2**-126 */ + if ((hx&0x7fffffff)==0) + return -two25/zero; /* log(+-0)=-inf */ + if (hx<0) return (x-x)/zero; /* log(-#) = NaN */ + k -= 25; x *= two25; /* subnormal number, scale up x */ + GET_FLOAT_WORD(hx,x); + } + if (hx >= 0x7f800000) return x+x; + k += (hx>>23)-127; + i = ((u_int32_t)k&0x80000000)>>31; + hx = (hx&0x007fffff)|((0x7f-i)<<23); + y = (float)(k+i); + SET_FLOAT_WORD(x,hx); + z = y*log10_2lo + ivln10*logf(x); + return z+y*log10_2hi; +} diff --git a/lib/libm/src/e_logf.c b/lib/libm/src/e_logf.c new file mode 100644 index 0000000000..38282d1d54 --- /dev/null +++ b/lib/libm/src/e_logf.c @@ -0,0 +1,85 @@ +/* e_logf.c -- float version of e_log.c. + * Conversion to float by Ian Lance Taylor, Cygnus Support, ian@cygnus.com. + */ + +/* + * ==================================================== + * Copyright (C) 1993 by Sun Microsystems, Inc. All rights reserved. + * + * Developed at SunPro, a Sun Microsystems, Inc. business. + * Permission to use, copy, modify, and distribute this + * software is freely granted, provided that this notice + * is preserved. + * ==================================================== + * + * $NetBSD: e_logf.c,v 1.8 2002/05/26 22:01:51 wiz Exp $ + * $DragonFly: src/lib/libm/src/e_logf.c,v 1.1 2005/07/26 21:15:20 joerg Exp $ + */ + +#include +#include "math_private.h" + +static const float +ln2_hi = 6.9313812256e-01, /* 0x3f317180 */ +ln2_lo = 9.0580006145e-06, /* 0x3717f7d1 */ +two25 = 3.355443200e+07, /* 0x4c000000 */ +Lg1 = 6.6666668653e-01, /* 3F2AAAAB */ +Lg2 = 4.0000000596e-01, /* 3ECCCCCD */ +Lg3 = 2.8571429849e-01, /* 3E924925 */ +Lg4 = 2.2222198546e-01, /* 3E638E29 */ +Lg5 = 1.8183572590e-01, /* 3E3A3325 */ +Lg6 = 1.5313838422e-01, /* 3E1CD04F */ +Lg7 = 1.4798198640e-01; /* 3E178897 */ + +static const float zero = 0.0; + +float +logf(float x) +{ + float hfsq,f,s,z,R,w,t1,t2,dk; + int32_t k,ix,i,j; + + GET_FLOAT_WORD(ix,x); + + k=0; + if (ix < 0x00800000) { /* x < 2**-126 */ + if ((ix&0x7fffffff)==0) + return -two25/zero; /* log(+-0)=-inf */ + if (ix<0) return (x-x)/zero; /* log(-#) = NaN */ + k -= 25; x *= two25; /* subnormal number, scale up x */ + GET_FLOAT_WORD(ix,x); + } + if (ix >= 0x7f800000) return x+x; + k += (ix>>23)-127; + ix &= 0x007fffff; + i = (ix+(0x95f64<<3))&0x800000; + SET_FLOAT_WORD(x,ix|(i^0x3f800000)); /* normalize x or x/2 */ + k += (i>>23); + f = x-(float)1.0; + if((0x007fffff&(15+ix))<16) { /* |f| < 2**-20 */ + if(f==zero) { if(k==0) return zero; else {dk=(float)k; + return dk*ln2_hi+dk*ln2_lo;} + } + R = f*f*((float)0.5-(float)0.33333333333333333*f); + if(k==0) return f-R; else {dk=(float)k; + return dk*ln2_hi-((R-dk*ln2_lo)-f);} + } + s = f/((float)2.0+f); + dk = (float)k; + z = s*s; + i = ix-(0x6147a<<3); + w = z*z; + j = (0x6b851<<3)-ix; + t1= w*(Lg2+w*(Lg4+w*Lg6)); + t2= z*(Lg1+w*(Lg3+w*(Lg5+w*Lg7))); + i |= j; + R = t2+t1; + if(i>0) { + hfsq=(float)0.5*f*f; + if(k==0) return f-(hfsq-s*(hfsq+R)); else + return dk*ln2_hi-((hfsq-(s*(hfsq+R)+dk*ln2_lo))-f); + } else { + if(k==0) return f-s*(f-R); else + return dk*ln2_hi-((s*(f-R)-dk*ln2_lo)-f); + } +} diff --git a/lib/libm/src/e_pow.c b/lib/libm/src/e_pow.c new file mode 100644 index 0000000000..c4d18ce549 --- /dev/null +++ b/lib/libm/src/e_pow.c @@ -0,0 +1,300 @@ +/* @(#)e_pow.c 5.1 93/09/24 */ +/* + * ==================================================== + * Copyright (C) 1993 by Sun Microsystems, Inc. All rights reserved. + * + * Developed at SunPro, a Sun Microsystems, Inc. business. + * Permission to use, copy, modify, and distribute this + * software is freely granted, provided that this notice + * is preserved. + * ==================================================== + * + * $NetBSD: e_pow.c,v 1.13 2004/06/30 18:43:15 drochner Exp $ + * $DragonFly: src/lib/libm/src/e_pow.c,v 1.1 2005/07/26 21:15:20 joerg Exp $ + */ + +/* pow(x,y) return x**y + * + * n + * Method: Let x = 2 * (1+f) + * 1. Compute and return log2(x) in two pieces: + * log2(x) = w1 + w2, + * where w1 has 53-24 = 29 bit trailing zeros. + * 2. Perform y*log2(x) = n+y' by simulating multi-precision + * arithmetic, where |y'|<=0.5. + * 3. Return x**y = 2**n*exp(y'*log2) + * + * Special cases: + * 1. (anything) ** 0 is 1 + * 2. (anything) ** 1 is itself + * 3. (anything) ** NAN is NAN + * 4. NAN ** (anything except 0) is NAN + * 5. +-(|x| > 1) ** +INF is +INF + * 6. +-(|x| > 1) ** -INF is +0 + * 7. +-(|x| < 1) ** +INF is +0 + * 8. +-(|x| < 1) ** -INF is +INF + * 9. +-1 ** +-INF is NAN + * 10. +0 ** (+anything except 0, NAN) is +0 + * 11. -0 ** (+anything except 0, NAN, odd integer) is +0 + * 12. +0 ** (-anything except 0, NAN) is +INF + * 13. -0 ** (-anything except 0, NAN, odd integer) is +INF + * 14. -0 ** (odd integer) = -( +0 ** (odd integer) ) + * 15. +INF ** (+anything except 0,NAN) is +INF + * 16. +INF ** (-anything except 0,NAN) is +0 + * 17. -INF ** (anything) = -0 ** (-anything) + * 18. (-anything) ** (integer) is (-1)**(integer)*(+anything**integer) + * 19. (-anything except 0 and inf) ** (non-integer) is NAN + * + * Accuracy: + * pow(x,y) returns x**y nearly rounded. In particular + * pow(integer,integer) + * always returns the correct integer provided it is + * representable. + * + * Constants : + * The hexadecimal values are the intended ones for the following + * constants. The decimal values may be used, provided that the + * compiler will convert from decimal to binary accurately enough + * to produce the hexadecimal values shown. + */ + +#include +#include "math_private.h" + +static const double +bp[] = {1.0, 1.5,}, +dp_h[] = { 0.0, 5.84962487220764160156e-01,}, /* 0x3FE2B803, 0x40000000 */ +dp_l[] = { 0.0, 1.35003920212974897128e-08,}, /* 0x3E4CFDEB, 0x43CFD006 */ +zero = 0.0, +one = 1.0, +two = 2.0, +two53 = 9007199254740992.0, /* 0x43400000, 0x00000000 */ +huge = 1.0e300, +tiny = 1.0e-300, + /* poly coefs for (3/2)*(log(x)-2s-2/3*s**3 */ +L1 = 5.99999999999994648725e-01, /* 0x3FE33333, 0x33333303 */ +L2 = 4.28571428578550184252e-01, /* 0x3FDB6DB6, 0xDB6FABFF */ +L3 = 3.33333329818377432918e-01, /* 0x3FD55555, 0x518F264D */ +L4 = 2.72728123808534006489e-01, /* 0x3FD17460, 0xA91D4101 */ +L5 = 2.30660745775561754067e-01, /* 0x3FCD864A, 0x93C9DB65 */ +L6 = 2.06975017800338417784e-01, /* 0x3FCA7E28, 0x4A454EEF */ +P1 = 1.66666666666666019037e-01, /* 0x3FC55555, 0x5555553E */ +P2 = -2.77777777770155933842e-03, /* 0xBF66C16C, 0x16BEBD93 */ +P3 = 6.61375632143793436117e-05, /* 0x3F11566A, 0xAF25DE2C */ +P4 = -1.65339022054652515390e-06, /* 0xBEBBBD41, 0xC5D26BF1 */ +P5 = 4.13813679705723846039e-08, /* 0x3E663769, 0x72BEA4D0 */ +lg2 = 6.93147180559945286227e-01, /* 0x3FE62E42, 0xFEFA39EF */ +lg2_h = 6.93147182464599609375e-01, /* 0x3FE62E43, 0x00000000 */ +lg2_l = -1.90465429995776804525e-09, /* 0xBE205C61, 0x0CA86C39 */ +ovt = 8.0085662595372944372e-0017, /* -(1024-log2(ovfl+.5ulp)) */ +cp = 9.61796693925975554329e-01, /* 0x3FEEC709, 0xDC3A03FD =2/(3ln2) */ +cp_h = 9.61796700954437255859e-01, /* 0x3FEEC709, 0xE0000000 =(float)cp */ +cp_l = -7.02846165095275826516e-09, /* 0xBE3E2FE0, 0x145B01F5 =tail of cp_h*/ +ivln2 = 1.44269504088896338700e+00, /* 0x3FF71547, 0x652B82FE =1/ln2 */ +ivln2_h = 1.44269502162933349609e+00, /* 0x3FF71547, 0x60000000 =24b 1/ln2*/ +ivln2_l = 1.92596299112661746887e-08; /* 0x3E54AE0B, 0xF85DDF44 =1/ln2 tail*/ + +double +pow(double x, double y) +{ + double z,ax,z_h,z_l,p_h,p_l; + double y1_,t1,t2,r,s,t,u,v,w; + int32_t i,j,k,yisint,n; + int32_t hx,hy,ix,iy; + u_int32_t lx,ly; + + EXTRACT_WORDS(hx,lx,x); + EXTRACT_WORDS(hy,ly,y); + ix = hx&0x7fffffff; iy = hy&0x7fffffff; + + /* y==zero: x**0 = 1 */ + if((iy|ly)==0) return one; + + /* +-NaN return x+y */ + if(ix > 0x7ff00000 || ((ix==0x7ff00000)&&(lx!=0)) || + iy > 0x7ff00000 || ((iy==0x7ff00000)&&(ly!=0))) + return x+y; + + /* determine if y is an odd int when x < 0 + * yisint = 0 ... y is not an integer + * yisint = 1 ... y is an odd int + * yisint = 2 ... y is an even int + */ + yisint = 0; + if(hx<0) { + if(iy>=0x43400000) yisint = 2; /* even integer y */ + else if(iy>=0x3ff00000) { + k = (iy>>20)-0x3ff; /* exponent */ + if(k>20) { + j = ly>>(52-k); + if((j<<(52-k))==ly) yisint = 2-(j&1); + } else if(ly==0) { + j = iy>>(20-k); + if((j<<(20-k))==iy) yisint = 2-(j&1); + } + } + } + + /* special value of y */ + if(ly==0) { + if (iy==0x7ff00000) { /* y is +-inf */ + if(((ix-0x3ff00000)|lx)==0) + return y - y; /* inf**+-1 is NaN */ + else if (ix >= 0x3ff00000)/* (|x|>1)**+-inf = inf,0 */ + return (hy>=0)? y: zero; + else /* (|x|<1)**-,+inf = inf,0 */ + return (hy<0)?-y: zero; + } + if(iy==0x3ff00000) { /* y is +-1 */ + if(hy<0) return one/x; else return x; + } + if(hy==0x40000000) return x*x; /* y is 2 */ + if(hy==0x3fe00000) { /* y is 0.5 */ + if(hx>=0) /* x >= +0 */ + return sqrt(x); + } + } + + ax = fabs(x); + /* special value of x */ + if(lx==0) { + if(ix==0x7ff00000||ix==0||ix==0x3ff00000){ + z = ax; /*x is +-0,+-inf,+-1*/ + if(hy<0) z = one/z; /* z = (1/|x|) */ + if(hx<0) { + if(((ix-0x3ff00000)|yisint)==0) { + z = (z-z)/(z-z); /* (-1)**non-int is NaN */ + } else if(yisint==1) + z = -z; /* (x<0)**odd = -(|x|**odd) */ + } + return z; + } + } + + n = (hx>>31)+1; + + /* (x<0)**(non-int) is NaN */ + if((n|yisint)==0) return (x-x)/(x-x); + + s = one; /* s (sign of result -ve**odd) = -1 else = 1 */ + if((n|(yisint-1))==0) s = -one;/* (-ve)**(odd int) */ + + /* |y| is huge */ + if(iy>0x41e00000) { /* if |y| > 2**31 */ + if(iy>0x43f00000){ /* if |y| > 2**64, must o/uflow */ + if(ix<=0x3fefffff) return (hy<0)? huge*huge:tiny*tiny; + if(ix>=0x3ff00000) return (hy>0)? huge*huge:tiny*tiny; + } + /* over/underflow if x is not close to one */ + if(ix<0x3fefffff) return (hy<0)? s*huge*huge:s*tiny*tiny; + if(ix>0x3ff00000) return (hy>0)? s*huge*huge:s*tiny*tiny; + /* now |1-x| is tiny <= 2**-20, suffice to compute + log(x) by x-x^2/2+x^3/3-x^4/4 */ + t = ax-one; /* t has 20 trailing zeros */ + w = (t*t)*(0.5-t*(0.3333333333333333333333-t*0.25)); + u = ivln2_h*t; /* ivln2_h has 21 sig. bits */ + v = t*ivln2_l-w*ivln2; + t1 = u+v; + SET_LOW_WORD(t1,0); + t2 = v-(t1-u); + } else { + double ss,s2,s_h,s_l,t_h,t_l; + n = 0; + /* take care subnormal number */ + if(ix<0x00100000) + {ax *= two53; n -= 53; GET_HIGH_WORD(ix,ax); } + n += ((ix)>>20)-0x3ff; + j = ix&0x000fffff; + /* determine interval */ + ix = j|0x3ff00000; /* normalize ix */ + if(j<=0x3988E) k=0; /* |x|>1)|0x20000000)+0x00080000+(k<<18)); + t_l = ax - (t_h-bp[k]); + s_l = v*((u-s_h*t_h)-s_h*t_l); + /* compute log(ax) */ + s2 = ss*ss; + r = s2*s2*(L1+s2*(L2+s2*(L3+s2*(L4+s2*(L5+s2*L6))))); + r += s_l*(s_h+ss); + s2 = s_h*s_h; + t_h = 3.0+s2+r; + SET_LOW_WORD(t_h,0); + t_l = r-((t_h-3.0)-s2); + /* u+v = ss*(1+...) */ + u = s_h*t_h; + v = s_l*t_h+t_l*ss; + /* 2/(3log2)*(ss+...) */ + p_h = u+v; + SET_LOW_WORD(p_h,0); + p_l = v-(p_h-u); + z_h = cp_h*p_h; /* cp_h+cp_l = 2/(3*log2) */ + z_l = cp_l*p_h+p_l*cp+dp_l[k]; + /* log2(ax) = (ss+..)*2/(3*log2) = n + dp_h + z_h + z_l */ + t = (double)n; + t1 = (((z_h+z_l)+dp_h[k])+t); + SET_LOW_WORD(t1,0); + t2 = z_l-(((t1-t)-dp_h[k])-z_h); + } + + /* split up y into y1_+y2 and compute (y1_+y2)*(t1+t2) */ + y1_ = y; + SET_LOW_WORD(y1_,0); + p_l = (y-y1_)*t1+y*t2; + p_h = y1_*t1; + z = p_l+p_h; + EXTRACT_WORDS(j,i,z); + if (j>=0x40900000) { /* z >= 1024 */ + if(((j-0x40900000)|i)!=0) /* if z > 1024 */ + return s*huge*huge; /* overflow */ + else { + if(p_l+ovt>z-p_h) return s*huge*huge; /* overflow */ + } + } else if((j&0x7fffffff)>=0x4090cc00 ) { /* z <= -1075 */ + if(((j-0xc090cc00)|i)!=0) /* z < -1075 */ + return s*tiny*tiny; /* underflow */ + else { + if(p_l<=z-p_h) return s*tiny*tiny; /* underflow */ + } + } + /* + * compute 2**(p_h+p_l) + */ + i = j&0x7fffffff; + k = (i>>20)-0x3ff; + n = 0; + if(i>0x3fe00000) { /* if |z| > 0.5, set n = [z+0.5] */ + n = j+(0x00100000>>(k+1)); + k = ((n&0x7fffffff)>>20)-0x3ff; /* new k for n */ + t = zero; + SET_HIGH_WORD(t,n&~(0x000fffff>>k)); + n = ((n&0x000fffff)|0x00100000)>>(20-k); + if(j<0) n = -n; + p_h -= t; + } + t = p_l+p_h; + SET_LOW_WORD(t,0); + u = t*lg2_h; + v = (p_l-(t-p_h))*lg2+t*lg2_l; + z = u+v; + w = v-(z-u); + t = z*z; + t1 = z - t*(P1+t*(P2+t*(P3+t*(P4+t*P5)))); + r = (z*t1)/(t1-two)-(w+z*w); + z = one-(r-z); + GET_HIGH_WORD(j,z); + j += (n<<20); + if((j>>20)<=0) z = scalbn(z,n); /* subnormal output */ + else SET_HIGH_WORD(z,j); + return s*z; +} diff --git a/lib/libm/src/e_powf.c b/lib/libm/src/e_powf.c new file mode 100644 index 0000000000..be54cc5a30 --- /dev/null +++ b/lib/libm/src/e_powf.c @@ -0,0 +1,244 @@ +/* e_powf.c -- float version of e_pow.c. + * Conversion to float by Ian Lance Taylor, Cygnus Support, ian@cygnus.com. + */ + +/* + * ==================================================== + * Copyright (C) 1993 by Sun Microsystems, Inc. All rights reserved. + * + * Developed at SunPro, a Sun Microsystems, Inc. business. + * Permission to use, copy, modify, and distribute this + * software is freely granted, provided that this notice + * is preserved. + * ==================================================== + * + * $NetBSD: e_powf.c,v 1.11 2004/06/30 18:45:25 drochner Exp $ + * $DragonFly: src/lib/libm/src/e_powf.c,v 1.1 2005/07/26 21:15:20 joerg Exp $ + */ + +#include +#include "math_private.h" + +static const float huge = 1.0e+30, tiny = 1.0e-30; + +static const float +bp[] = {1.0, 1.5,}, +dp_h[] = { 0.0, 5.84960938e-01,}, /* 0x3f15c000 */ +dp_l[] = { 0.0, 1.56322085e-06,}, /* 0x35d1cfdc */ +zero = 0.0, +one = 1.0, +two = 2.0, +two24 = 16777216.0, /* 0x4b800000 */ + /* poly coefs for (3/2)*(log(x)-2s-2/3*s**3 */ +L1 = 6.0000002384e-01, /* 0x3f19999a */ +L2 = 4.2857143283e-01, /* 0x3edb6db7 */ +L3 = 3.3333334327e-01, /* 0x3eaaaaab */ +L4 = 2.7272811532e-01, /* 0x3e8ba305 */ +L5 = 2.3066075146e-01, /* 0x3e6c3255 */ +L6 = 2.0697501302e-01, /* 0x3e53f142 */ +P1 = 1.6666667163e-01, /* 0x3e2aaaab */ +P2 = -2.7777778450e-03, /* 0xbb360b61 */ +P3 = 6.6137559770e-05, /* 0x388ab355 */ +P4 = -1.6533901999e-06, /* 0xb5ddea0e */ +P5 = 4.1381369442e-08, /* 0x3331bb4c */ +lg2 = 6.9314718246e-01, /* 0x3f317218 */ +lg2_h = 6.93145752e-01, /* 0x3f317200 */ +lg2_l = 1.42860654e-06, /* 0x35bfbe8c */ +ovt = 4.2995665694e-08, /* -(128-log2(ovfl+.5ulp)) */ +cp = 9.6179670095e-01, /* 0x3f76384f =2/(3ln2) */ +cp_h = 9.6179199219e-01, /* 0x3f763800 =head of cp */ +cp_l = 4.7017383622e-06, /* 0x369dc3a0 =tail of cp_h */ +ivln2 = 1.4426950216e+00, /* 0x3fb8aa3b =1/ln2 */ +ivln2_h = 1.4426879883e+00, /* 0x3fb8aa00 =16b 1/ln2*/ +ivln2_l = 7.0526075433e-06; /* 0x36eca570 =1/ln2 tail*/ + +float +powf(float x, float y) +{ + float z,ax,z_h,z_l,p_h,p_l; + float y1_,t1,t2,r,s,t,u,v,w; + int32_t i,j,k,yisint,n; + int32_t hx,hy,ix,iy,is; + + GET_FLOAT_WORD(hx,x); + GET_FLOAT_WORD(hy,y); + ix = hx&0x7fffffff; iy = hy&0x7fffffff; + + /* y==zero: x**0 = 1 */ + if(iy==0) return one; + + /* +-NaN return x+y */ + if(ix > 0x7f800000 || + iy > 0x7f800000) + return x+y; + + /* determine if y is an odd int when x < 0 + * yisint = 0 ... y is not an integer + * yisint = 1 ... y is an odd int + * yisint = 2 ... y is an even int + */ + yisint = 0; + if(hx<0) { + if(iy>=0x4b800000) yisint = 2; /* even integer y */ + else if(iy>=0x3f800000) { + k = (iy>>23)-0x7f; /* exponent */ + j = iy>>(23-k); + if((j<<(23-k))==iy) yisint = 2-(j&1); + } + } + + /* special value of y */ + if (iy==0x7f800000) { /* y is +-inf */ + if (ix==0x3f800000) + return y - y; /* inf**+-1 is NaN */ + else if (ix > 0x3f800000)/* (|x|>1)**+-inf = inf,0 */ + return (hy>=0)? y: zero; + else /* (|x|<1)**-,+inf = inf,0 */ + return (hy<0)?-y: zero; + } + if(iy==0x3f800000) { /* y is +-1 */ + if(hy<0) return one/x; else return x; + } + if(hy==0x40000000) return x*x; /* y is 2 */ + if(hy==0x3f000000) { /* y is 0.5 */ + if(hx>=0) /* x >= +0 */ + return sqrtf(x); + } + + ax = fabsf(x); + /* special value of x */ + if(ix==0x7f800000||ix==0||ix==0x3f800000){ + z = ax; /*x is +-0,+-inf,+-1*/ + if(hy<0) z = one/z; /* z = (1/|x|) */ + if(hx<0) { + if(((ix-0x3f800000)|yisint)==0) { + z = (z-z)/(z-z); /* (-1)**non-int is NaN */ + } else if(yisint==1) + z = -z; /* (x<0)**odd = -(|x|**odd) */ + } + return z; + } + + /* (x<0)**(non-int) is NaN */ + if(((((u_int32_t)hx>>31)-1)|yisint)==0) return (x-x)/(x-x); + + /* |y| is huge */ + if(iy>0x4d000000) { /* if |y| > 2**27 */ + /* over/underflow if x is not close to one */ + if(ix<0x3f7ffff8) return (hy<0)? huge*huge:tiny*tiny; + if(ix>0x3f800007) return (hy>0)? huge*huge:tiny*tiny; + /* now |1-x| is tiny <= 2**-20, suffice to compute + log(x) by x-x^2/2+x^3/3-x^4/4 */ + t = ax-one; /* t has 20 trailing zeros */ + w = (t*t)*((float)0.5-t*((float)0.333333333333-t*(float)0.25)); + u = ivln2_h*t; /* ivln2_h has 16 sig. bits */ + v = t*ivln2_l-w*ivln2; + t1 = u+v; + GET_FLOAT_WORD(is,t1); + SET_FLOAT_WORD(t1,is&0xfffff000); + t2 = v-(t1-u); + } else { + float s2,s_h,s_l,t_h,t_l; + n = 0; + /* take care subnormal number */ + if(ix<0x00800000) + {ax *= two24; n -= 24; GET_FLOAT_WORD(ix,ax); } + n += ((ix)>>23)-0x7f; + j = ix&0x007fffff; + /* determine interval */ + ix = j|0x3f800000; /* normalize ix */ + if(j<=0x1cc471) k=0; /* |x|>1)|0x20000000)+0x0040000+(k<<21)); + t_l = ax - (t_h-bp[k]); + s_l = v*((u-s_h*t_h)-s_h*t_l); + /* compute log(ax) */ + s2 = s*s; + r = s2*s2*(L1+s2*(L2+s2*(L3+s2*(L4+s2*(L5+s2*L6))))); + r += s_l*(s_h+s); + s2 = s_h*s_h; + t_h = (float)3.0+s2+r; + GET_FLOAT_WORD(is,t_h); + SET_FLOAT_WORD(t_h,is&0xfffff000); + t_l = r-((t_h-(float)3.0)-s2); + /* u+v = s*(1+...) */ + u = s_h*t_h; + v = s_l*t_h+t_l*s; + /* 2/(3log2)*(s+...) */ + p_h = u+v; + GET_FLOAT_WORD(is,p_h); + SET_FLOAT_WORD(p_h,is&0xfffff000); + p_l = v-(p_h-u); + z_h = cp_h*p_h; /* cp_h+cp_l = 2/(3*log2) */ + z_l = cp_l*p_h+p_l*cp+dp_l[k]; + /* log2(ax) = (s+..)*2/(3*log2) = n + dp_h + z_h + z_l */ + t = (float)n; + t1 = (((z_h+z_l)+dp_h[k])+t); + GET_FLOAT_WORD(is,t1); + SET_FLOAT_WORD(t1,is&0xfffff000); + t2 = z_l-(((t1-t)-dp_h[k])-z_h); + } + + s = one; /* s (sign of result -ve**odd) = -1 else = 1 */ + if(((((u_int32_t)hx>>31)-1)|(yisint-1))==0) + s = -one; /* (-ve)**(odd int) */ + + /* split up y into y1_+y2 and compute (y1_+y2)*(t1+t2) */ + GET_FLOAT_WORD(is,y); + SET_FLOAT_WORD(y1_,is&0xfffff000); + p_l = (y-y1_)*t1+y*t2; + p_h = y1_*t1; + z = p_l+p_h; + GET_FLOAT_WORD(j,z); + if (j>0x43000000) /* if z > 128 */ + return s*huge*huge; /* overflow */ + else if (j==0x43000000) { /* if z == 128 */ + if(p_l+ovt>z-p_h) return s*huge*huge; /* overflow */ + } + else if ((j&0x7fffffff)>0x43160000) /* z <= -150 */ + return s*tiny*tiny; /* underflow */ + else if (j==0xc3160000){ /* z == -150 */ + if(p_l<=z-p_h) return s*tiny*tiny; /* underflow */ + } + /* + * compute 2**(p_h+p_l) + */ + i = j&0x7fffffff; + k = (i>>23)-0x7f; + n = 0; + if(i>0x3f000000) { /* if |z| > 0.5, set n = [z+0.5] */ + n = j+(0x00800000>>(k+1)); + k = ((n&0x7fffffff)>>23)-0x7f; /* new k for n */ + SET_FLOAT_WORD(t,n&~(0x007fffff>>k)); + n = ((n&0x007fffff)|0x00800000)>>(23-k); + if(j<0) n = -n; + p_h -= t; + } + t = p_l+p_h; + GET_FLOAT_WORD(is,t); + SET_FLOAT_WORD(t,is&0xfffff000); + u = t*lg2_h; + v = (p_l-(t-p_h))*lg2+t*lg2_l; + z = u+v; + w = v-(z-u); + t = z*z; + t1 = z - t*(P1+t*(P2+t*(P3+t*(P4+t*P5)))); + r = (z*t1)/(t1-two)-(w+z*w); + z = one-(r-z); + GET_FLOAT_WORD(j,z); + j += (n<<23); + if((j>>23)<=0) z = scalbnf(z,n); /* subnormal output */ + else SET_FLOAT_WORD(z,j); + return s*z; +} diff --git a/lib/libm/src/e_rem_pio2.c b/lib/libm/src/e_rem_pio2.c new file mode 100644 index 0000000000..369b7d5db3 --- /dev/null +++ b/lib/libm/src/e_rem_pio2.c @@ -0,0 +1,167 @@ +/* @(#)e_rem_pio2.c 5.1 93/09/24 */ +/* + * ==================================================== + * Copyright (C) 1993 by Sun Microsystems, Inc. All rights reserved. + * + * Developed at SunPro, a Sun Microsystems, Inc. business. + * Permission to use, copy, modify, and distribute this + * software is freely granted, provided that this notice + * is preserved. + * ==================================================== + * + * $NetBSD: e_rem_pio2.c,v 1.11 2002/05/26 22:01:52 wiz Exp $ + * $DragonFly: src/lib/libm/src/e_rem_pio2.c,v 1.1 2005/07/26 21:15:20 joerg Exp $ + */ + +/* __libm_rem_pio2(x,y) + * + * return the remainder of x rem pi/2 in y[0]+y[1] + * use __kernel_rem_pio2() + */ + +#include +#include "math_private.h" + +/* + * Table of constants for 2/pi, 396 Hex digits (476 decimal) of 2/pi + */ +static const int32_t two_over_pi[] = { +0xA2F983, 0x6E4E44, 0x1529FC, 0x2757D1, 0xF534DD, 0xC0DB62, +0x95993C, 0x439041, 0xFE5163, 0xABDEBB, 0xC561B7, 0x246E3A, +0x424DD2, 0xE00649, 0x2EEA09, 0xD1921C, 0xFE1DEB, 0x1CB129, +0xA73EE8, 0x8235F5, 0x2EBB44, 0x84E99C, 0x7026B4, 0x5F7E41, +0x3991D6, 0x398353, 0x39F49C, 0x845F8B, 0xBDF928, 0x3B1FF8, +0x97FFDE, 0x05980F, 0xEF2F11, 0x8B5A0A, 0x6D1F6D, 0x367ECF, +0x27CB09, 0xB74F46, 0x3F669E, 0x5FEA2D, 0x7527BA, 0xC7EBE5, +0xF17B3D, 0x0739F7, 0x8A5292, 0xEA6BFB, 0x5FB11F, 0x8D5D08, +0x560330, 0x46FC7B, 0x6BABF0, 0xCFBC20, 0x9AF436, 0x1DA9E3, +0x91615E, 0xE61B08, 0x659985, 0x5F14A0, 0x68408D, 0xFFD880, +0x4D7327, 0x310606, 0x1556CA, 0x73A8C9, 0x60E27B, 0xC08C6B, +}; + +static const int32_t npio2_hw[] = { +0x3FF921FB, 0x400921FB, 0x4012D97C, 0x401921FB, 0x401F6A7A, 0x4022D97C, +0x4025FDBB, 0x402921FB, 0x402C463A, 0x402F6A7A, 0x4031475C, 0x4032D97C, +0x40346B9C, 0x4035FDBB, 0x40378FDB, 0x403921FB, 0x403AB41B, 0x403C463A, +0x403DD85A, 0x403F6A7A, 0x40407E4C, 0x4041475C, 0x4042106C, 0x4042D97C, +0x4043A28C, 0x40446B9C, 0x404534AC, 0x4045FDBB, 0x4046C6CB, 0x40478FDB, +0x404858EB, 0x404921FB, +}; + +/* + * invpio2: 53 bits of 2/pi + * pio2_1: first 33 bit of pi/2 + * pio2_1t: pi/2 - pio2_1 + * pio2_2: second 33 bit of pi/2 + * pio2_2t: pi/2 - (pio2_1+pio2_2) + * pio2_3: third 33 bit of pi/2 + * pio2_3t: pi/2 - (pio2_1+pio2_2+pio2_3) + */ + +static const double +zero = 0.00000000000000000000e+00, /* 0x00000000, 0x00000000 */ +half = 5.00000000000000000000e-01, /* 0x3FE00000, 0x00000000 */ +two24 = 1.67772160000000000000e+07, /* 0x41700000, 0x00000000 */ +invpio2 = 6.36619772367581382433e-01, /* 0x3FE45F30, 0x6DC9C883 */ +pio2_1 = 1.57079632673412561417e+00, /* 0x3FF921FB, 0x54400000 */ +pio2_1t = 6.07710050650619224932e-11, /* 0x3DD0B461, 0x1A626331 */ +pio2_2 = 6.07710050630396597660e-11, /* 0x3DD0B461, 0x1A600000 */ +pio2_2t = 2.02226624879595063154e-21, /* 0x3BA3198A, 0x2E037073 */ +pio2_3 = 2.02226624871116645580e-21, /* 0x3BA3198A, 0x2E000000 */ +pio2_3t = 8.47842766036889956997e-32; /* 0x397B839A, 0x252049C1 */ + +int32_t +__libm_rem_pio2(double x, double *y) +{ + double z,w,t,r,fn; + double tx[3]; + int32_t e0,i,j,nx,n,ix,hx; + u_int32_t low; + + z = 0; + GET_HIGH_WORD(hx,x); /* high word of x */ + ix = hx&0x7fffffff; + if(ix<=0x3fe921fb) /* |x| ~<= pi/4 , no need for reduction */ + {y[0] = x; y[1] = 0; return 0;} + if(ix<0x4002d97c) { /* |x| < 3pi/4, special case with n=+-1 */ + if(hx>0) { + z = x - pio2_1; + if(ix!=0x3ff921fb) { /* 33+53 bit pi is good enough */ + y[0] = z - pio2_1t; + y[1] = (z-y[0])-pio2_1t; + } else { /* near pi/2, use 33+33+53 bit pi */ + z -= pio2_2; + y[0] = z - pio2_2t; + y[1] = (z-y[0])-pio2_2t; + } + return 1; + } else { /* negative x */ + z = x + pio2_1; + if(ix!=0x3ff921fb) { /* 33+53 bit pi is good enough */ + y[0] = z + pio2_1t; + y[1] = (z-y[0])+pio2_1t; + } else { /* near pi/2, use 33+33+53 bit pi */ + z += pio2_2; + y[0] = z + pio2_2t; + y[1] = (z-y[0])+pio2_2t; + } + return -1; + } + } + if(ix<=0x413921fb) { /* |x| ~<= 2^19*(pi/2), medium size */ + t = fabs(x); + n = (int32_t) (t*invpio2+half); + fn = (double)n; + r = t-fn*pio2_1; + w = fn*pio2_1t; /* 1st round good to 85 bit */ + if(n<32&&ix!=npio2_hw[n-1]) { + y[0] = r-w; /* quick check no cancellation */ + } else { + u_int32_t high; + j = ix>>20; + y[0] = r-w; + GET_HIGH_WORD(high,y[0]); + i = j-((high>>20)&0x7ff); + if(i>16) { /* 2nd iteration needed, good to 118 */ + t = r; + w = fn*pio2_2; + r = t-w; + w = fn*pio2_2t-((t-r)-w); + y[0] = r-w; + GET_HIGH_WORD(high,y[0]); + i = j-((high>>20)&0x7ff); + if(i>49) { /* 3rd iteration need, 151 bits acc */ + t = r; /* will cover all possible cases */ + w = fn*pio2_3; + r = t-w; + w = fn*pio2_3t-((t-r)-w); + y[0] = r-w; + } + } + } + y[1] = (r-y[0])-w; + if(hx<0) {y[0] = -y[0]; y[1] = -y[1]; return -n;} + else return n; + } + /* + * all other (large) arguments + */ + if(ix>=0x7ff00000) { /* x is inf or NaN */ + y[0]=y[1]=x-x; return 0; + } + /* set z = scalbn(|x|,ilogb(x)-23) */ + GET_LOW_WORD(low,x); + SET_LOW_WORD(z,low); + e0 = (ix>>20)-1046; /* e0 = ilogb(z)-23; */ + SET_HIGH_WORD(z, ix - ((int32_t)(e0<<20))); + for(i=0;i<2;i++) { + tx[i] = (double)((int32_t)(z)); + z = (z-tx[i])*two24; + } + tx[2] = z; + nx = 3; + while(tx[nx-1]==zero) nx--; /* skip zero term */ + n = __kernel_rem_pio2(tx,y,e0,nx,2,two_over_pi); + if(hx<0) {y[0] = -y[0]; y[1] = -y[1]; return -n;} + return n; +} diff --git a/lib/libm/src/e_rem_pio2f.c b/lib/libm/src/e_rem_pio2f.c new file mode 100644 index 0000000000..494572db7d --- /dev/null +++ b/lib/libm/src/e_rem_pio2f.c @@ -0,0 +1,179 @@ +/* e_rem_pio2f.c -- float version of e_rem_pio2.c + * Conversion to float by Ian Lance Taylor, Cygnus Support, ian@cygnus.com. + */ + +/* + * ==================================================== + * Copyright (C) 1993 by Sun Microsystems, Inc. All rights reserved. + * + * Developed at SunPro, a Sun Microsystems, Inc. business. + * Permission to use, copy, modify, and distribute this + * software is freely granted, provided that this notice + * is preserved. + * ==================================================== + * + * $NetBSD: e_rem_pio2f.c,v 1.8 2002/05/26 22:01:52 wiz Exp $ + * $DragonFly: src/lib/libm/src/e_rem_pio2f.c,v 1.1 2005/07/26 21:15:20 joerg Exp $ + */ + +/* __libm_rem_pio2f(x,y) + * + * return the remainder of x rem pi/2 in y[0]+y[1] + * use __kernel_rem_pio2f() + */ + +#include +#include "math_private.h" + +/* + * Table of constants for 2/pi, 396 Hex digits (476 decimal) of 2/pi + */ +static const int32_t two_over_pi[] = { +0xA2, 0xF9, 0x83, 0x6E, 0x4E, 0x44, 0x15, 0x29, 0xFC, +0x27, 0x57, 0xD1, 0xF5, 0x34, 0xDD, 0xC0, 0xDB, 0x62, +0x95, 0x99, 0x3C, 0x43, 0x90, 0x41, 0xFE, 0x51, 0x63, +0xAB, 0xDE, 0xBB, 0xC5, 0x61, 0xB7, 0x24, 0x6E, 0x3A, +0x42, 0x4D, 0xD2, 0xE0, 0x06, 0x49, 0x2E, 0xEA, 0x09, +0xD1, 0x92, 0x1C, 0xFE, 0x1D, 0xEB, 0x1C, 0xB1, 0x29, +0xA7, 0x3E, 0xE8, 0x82, 0x35, 0xF5, 0x2E, 0xBB, 0x44, +0x84, 0xE9, 0x9C, 0x70, 0x26, 0xB4, 0x5F, 0x7E, 0x41, +0x39, 0x91, 0xD6, 0x39, 0x83, 0x53, 0x39, 0xF4, 0x9C, +0x84, 0x5F, 0x8B, 0xBD, 0xF9, 0x28, 0x3B, 0x1F, 0xF8, +0x97, 0xFF, 0xDE, 0x05, 0x98, 0x0F, 0xEF, 0x2F, 0x11, +0x8B, 0x5A, 0x0A, 0x6D, 0x1F, 0x6D, 0x36, 0x7E, 0xCF, +0x27, 0xCB, 0x09, 0xB7, 0x4F, 0x46, 0x3F, 0x66, 0x9E, +0x5F, 0xEA, 0x2D, 0x75, 0x27, 0xBA, 0xC7, 0xEB, 0xE5, +0xF1, 0x7B, 0x3D, 0x07, 0x39, 0xF7, 0x8A, 0x52, 0x92, +0xEA, 0x6B, 0xFB, 0x5F, 0xB1, 0x1F, 0x8D, 0x5D, 0x08, +0x56, 0x03, 0x30, 0x46, 0xFC, 0x7B, 0x6B, 0xAB, 0xF0, +0xCF, 0xBC, 0x20, 0x9A, 0xF4, 0x36, 0x1D, 0xA9, 0xE3, +0x91, 0x61, 0x5E, 0xE6, 0x1B, 0x08, 0x65, 0x99, 0x85, +0x5F, 0x14, 0xA0, 0x68, 0x40, 0x8D, 0xFF, 0xD8, 0x80, +0x4D, 0x73, 0x27, 0x31, 0x06, 0x06, 0x15, 0x56, 0xCA, +0x73, 0xA8, 0xC9, 0x60, 0xE2, 0x7B, 0xC0, 0x8C, 0x6B, +}; + +/* This array is like the one in e_rem_pio2.c, but the numbers are + single precision and the last 8 bits are forced to 0. */ +static const int32_t npio2_hw[] = { +0x3fc90f00, 0x40490f00, 0x4096cb00, 0x40c90f00, 0x40fb5300, 0x4116cb00, +0x412fed00, 0x41490f00, 0x41623100, 0x417b5300, 0x418a3a00, 0x4196cb00, +0x41a35c00, 0x41afed00, 0x41bc7e00, 0x41c90f00, 0x41d5a000, 0x41e23100, +0x41eec200, 0x41fb5300, 0x4203f200, 0x420a3a00, 0x42108300, 0x4216cb00, +0x421d1400, 0x42235c00, 0x4229a500, 0x422fed00, 0x42363600, 0x423c7e00, +0x4242c700, 0x42490f00 +}; + +/* + * invpio2: 24 bits of 2/pi + * pio2_1: first 17 bit of pi/2 + * pio2_1t: pi/2 - pio2_1 + * pio2_2: second 17 bit of pi/2 + * pio2_2t: pi/2 - (pio2_1+pio2_2) + * pio2_3: third 17 bit of pi/2 + * pio2_3t: pi/2 - (pio2_1+pio2_2+pio2_3) + */ + +static const float +zero = 0.0000000000e+00, /* 0x00000000 */ +half = 5.0000000000e-01, /* 0x3f000000 */ +two8 = 2.5600000000e+02, /* 0x43800000 */ +invpio2 = 6.3661980629e-01, /* 0x3f22f984 */ +pio2_1 = 1.5707855225e+00, /* 0x3fc90f80 */ +pio2_1t = 1.0804334124e-05, /* 0x37354443 */ +pio2_2 = 1.0804273188e-05, /* 0x37354400 */ +pio2_2t = 6.0770999344e-11, /* 0x2e85a308 */ +pio2_3 = 6.0770943833e-11, /* 0x2e85a300 */ +pio2_3t = 6.1232342629e-17; /* 0x248d3132 */ + +int32_t +__libm_rem_pio2f(float x, float *y) +{ + float z,w,t,r,fn; + float tx[3]; + int32_t e0,i,j,nx,n,ix,hx; + + GET_FLOAT_WORD(hx,x); + ix = hx&0x7fffffff; + if(ix<=0x3f490fd8) /* |x| ~<= pi/4 , no need for reduction */ + {y[0] = x; y[1] = 0; return 0;} + if(ix<0x4016cbe4) { /* |x| < 3pi/4, special case with n=+-1 */ + if(hx>0) { + z = x - pio2_1; + if((ix&0xfffffff0)!=0x3fc90fd0) { /* 24+24 bit pi OK */ + y[0] = z - pio2_1t; + y[1] = (z-y[0])-pio2_1t; + } else { /* near pi/2, use 24+24+24 bit pi */ + z -= pio2_2; + y[0] = z - pio2_2t; + y[1] = (z-y[0])-pio2_2t; + } + return 1; + } else { /* negative x */ + z = x + pio2_1; + if((ix&0xfffffff0)!=0x3fc90fd0) { /* 24+24 bit pi OK */ + y[0] = z + pio2_1t; + y[1] = (z-y[0])+pio2_1t; + } else { /* near pi/2, use 24+24+24 bit pi */ + z += pio2_2; + y[0] = z + pio2_2t; + y[1] = (z-y[0])+pio2_2t; + } + return -1; + } + } + if(ix<=0x43490f80) { /* |x| ~<= 2^7*(pi/2), medium size */ + t = fabsf(x); + n = (int32_t) (t*invpio2+half); + fn = (float)n; + r = t-fn*pio2_1; + w = fn*pio2_1t; /* 1st round good to 40 bit */ + if(n<32&&(ix&0xffffff00)!=npio2_hw[n-1]) { + y[0] = r-w; /* quick check no cancellation */ + } else { + u_int32_t high; + j = ix>>23; + y[0] = r-w; + GET_FLOAT_WORD(high,y[0]); + i = j-((high>>23)&0xff); + if(i>8) { /* 2nd iteration needed, good to 57 */ + t = r; + w = fn*pio2_2; + r = t-w; + w = fn*pio2_2t-((t-r)-w); + y[0] = r-w; + GET_FLOAT_WORD(high,y[0]); + i = j-((high>>23)&0xff); + if(i>25) { /* 3rd iteration need, 74 bits acc */ + t = r; /* will cover all possible cases */ + w = fn*pio2_3; + r = t-w; + w = fn*pio2_3t-((t-r)-w); + y[0] = r-w; + } + } + } + y[1] = (r-y[0])-w; + if(hx<0) {y[0] = -y[0]; y[1] = -y[1]; return -n;} + else return n; + } + /* + * all other (large) arguments + */ + if(ix>=0x7f800000) { /* x is inf or NaN */ + y[0]=y[1]=x-x; return 0; + } + /* set z = scalbn(|x|,ilogb(x)-7) */ + e0 = (ix>>23)-134; /* e0 = ilogb(z)-7; */ + SET_FLOAT_WORD(z, ix - ((int32_t)(e0<<23))); + for(i=0;i<2;i++) { + tx[i] = (float)((int32_t)(z)); + z = (z-tx[i])*two8; + } + tx[2] = z; + nx = 3; + while(tx[nx-1]==zero) nx--; /* skip zero term */ + n = __kernel_rem_pio2f(tx,y,e0,nx,2,two_over_pi); + if(hx<0) {y[0] = -y[0]; y[1] = -y[1]; return -n;} + return n; +} diff --git a/lib/libm/src/e_remainder.c b/lib/libm/src/e_remainder.c new file mode 100644 index 0000000000..9d01ed01ad --- /dev/null +++ b/lib/libm/src/e_remainder.c @@ -0,0 +1,71 @@ +/* @(#)e_remainder.c 5.1 93/09/24 */ +/* + * ==================================================== + * Copyright (C) 1993 by Sun Microsystems, Inc. All rights reserved. + * + * Developed at SunPro, a Sun Microsystems, Inc. business. + * Permission to use, copy, modify, and distribute this + * software is freely granted, provided that this notice + * is preserved. + * ==================================================== + * + * $NetBSD: e_remainder.c,v 1.11 2002/05/26 22:01:52 wiz Exp $ + * $DragonFly: src/lib/libm/src/e_remainder.c,v 1.1 2005/07/26 21:15:20 joerg Exp $ + */ + +/* remainder(x,p) + * Return : + * returns x REM p = x - [x/p]*p as if in infinite + * precise arithmetic, where [x/p] is the (infinite bit) + * integer nearest x/p (in half way case choose the even one). + * Method : + * Based on fmod() return x-[x/p]chopped*p exactlp. + */ + +#include +#include "math_private.h" + +static const double zero = 0.0; + + +double +remainder(double x, double p) +{ + int32_t hx,hp; + u_int32_t sx,lx,lp; + double p_half; + + EXTRACT_WORDS(hx,lx,x); + EXTRACT_WORDS(hp,lp,p); + sx = hx&0x80000000; + hp &= 0x7fffffff; + hx &= 0x7fffffff; + + /* purge off exception values */ + if((hp|lp)==0) return (x*p)/(x*p); /* p = 0 */ + if((hx>=0x7ff00000)|| /* x not finite */ + ((hp>=0x7ff00000)&& /* p is NaN */ + (((hp-0x7ff00000)|lp)!=0))) + return (x*p)/(x*p); + + + if (hp<=0x7fdfffff) x = fmod(x,p+p); /* now x < 2p */ + if (((hx-hp)|(lx-lp))==0) return zero*x; + x = fabs(x); + p = fabs(p); + if (hp<0x00200000) { + if(x+x>p) { + x-=p; + if(x+x>=p) x -= p; + } + } else { + p_half = 0.5*p; + if(x>p_half) { + x-=p; + if(x>=p_half) x -= p; + } + } + GET_HIGH_WORD(hx,x); + SET_HIGH_WORD(x,hx^sx); + return x; +} diff --git a/lib/libm/src/e_remainderf.c b/lib/libm/src/e_remainderf.c new file mode 100644 index 0000000000..d609965eca --- /dev/null +++ b/lib/libm/src/e_remainderf.c @@ -0,0 +1,64 @@ +/* e_remainderf.c -- float version of e_remainder.c. + * Conversion to float by Ian Lance Taylor, Cygnus Support, ian@cygnus.com. + */ + +/* + * ==================================================== + * Copyright (C) 1993 by Sun Microsystems, Inc. All rights reserved. + * + * Developed at SunPro, a Sun Microsystems, Inc. business. + * Permission to use, copy, modify, and distribute this + * software is freely granted, provided that this notice + * is preserved. + * ==================================================== + * + * $NetBSD: e_remainderf.c,v 1.7 2002/05/26 22:01:52 wiz Exp $ + * $DragonFly: src/lib/libm/src/e_remainderf.c,v 1.1 2005/07/26 21:15:20 joerg Exp $ + */ + +#include +#include "math_private.h" + +static const float zero = 0.0; + + +float +remainderf(float x, float p) +{ + int32_t hx,hp; + u_int32_t sx; + float p_half; + + GET_FLOAT_WORD(hx,x); + GET_FLOAT_WORD(hp,p); + sx = hx&0x80000000; + hp &= 0x7fffffff; + hx &= 0x7fffffff; + + /* purge off exception values */ + if(hp==0) return (x*p)/(x*p); /* p = 0 */ + if((hx>=0x7f800000)|| /* x not finite */ + ((hp>0x7f800000))) /* p is NaN */ + return (x*p)/(x*p); + + + if (hp<=0x7effffff) x = fmodf(x,p+p); /* now x < 2p */ + if ((hx-hp)==0) return zero*x; + x = fabsf(x); + p = fabsf(p); + if (hp<0x01000000) { + if(x+x>p) { + x-=p; + if(x+x>=p) x -= p; + } + } else { + p_half = (float)0.5*p; + if(x>p_half) { + x-=p; + if(x>=p_half) x -= p; + } + } + GET_FLOAT_WORD(hx,x); + SET_FLOAT_WORD(x,hx^sx); + return x; +} diff --git a/lib/libm/src/e_scalb.c b/lib/libm/src/e_scalb.c new file mode 100644 index 0000000000..2ee62b04e7 --- /dev/null +++ b/lib/libm/src/e_scalb.c @@ -0,0 +1,46 @@ +/* @(#)e_scalb.c 5.1 93/09/24 */ +/* + * ==================================================== + * Copyright (C) 1993 by Sun Microsystems, Inc. All rights reserved. + * + * Developed at SunPro, a Sun Microsystems, Inc. business. + * Permission to use, copy, modify, and distribute this + * software is freely granted, provided that this notice + * is preserved. + * ==================================================== + * + * $NetBSD: e_scalb.c,v 1.9 2002/05/26 22:01:52 wiz Exp $ + * $DragonFly: src/lib/libm/src/e_scalb.c,v 1.1 2005/07/26 21:15:20 joerg Exp $ + */ + +/* + * scalb(x, fn) is provide for + * passing various standard test suite. One + * should use scalbn() instead. + */ + +#include +#include "math_private.h" + +#ifdef _SCALB_INT +double +scalb(double x, int fn) +#else +double +scalb(double x, double fn) +#endif +{ +#ifdef _SCALB_INT + return scalbn(x,fn); +#else + if (isnan(x)||isnan(fn)) return x*fn; + if (!finite(fn)) { + if(fn>0.0) return x*fn; + else return x/(-fn); + } + if (rint(fn)!=fn) return (fn-fn)/(fn-fn); + if ( fn > 65000.0) return scalbn(x, 65000); + if (-fn > 65000.0) return scalbn(x,-65000); + return scalbn(x,(int)fn); +#endif +} diff --git a/lib/libm/src/e_scalbf.c b/lib/libm/src/e_scalbf.c new file mode 100644 index 0000000000..61994e17b0 --- /dev/null +++ b/lib/libm/src/e_scalbf.c @@ -0,0 +1,43 @@ +/* e_scalbf.c -- float version of e_scalb.c. + * Conversion to float by Ian Lance Taylor, Cygnus Support, ian@cygnus.com. + */ + +/* + * ==================================================== + * Copyright (C) 1993 by Sun Microsystems, Inc. All rights reserved. + * + * Developed at SunPro, a Sun Microsystems, Inc. business. + * Permission to use, copy, modify, and distribute this + * software is freely granted, provided that this notice + * is preserved. + * ==================================================== + * + * $NetBSD: e_scalbf.c,v 1.6 2002/05/26 22:01:52 wiz Exp $ + * $DragonFly: src/lib/libm/src/e_scalbf.c,v 1.1 2005/07/26 21:15:20 joerg Exp $ + */ + +#include +#include "math_private.h" + +#ifdef _SCALB_INT +float +scalbf(float x, int fn) +#else +float +scalbf(float x, float fn) +#endif +{ +#ifdef _SCALB_INT + return scalbnf(x,fn); +#else + if (isnanf(x)||isnanf(fn)) return x*fn; + if (!finitef(fn)) { + if(fn>(float)0.0) return x*fn; + else return x/(-fn); + } + if (rintf(fn)!=fn) return (fn-fn)/(fn-fn); + if ( fn > (float)65000.0) return scalbnf(x, 65000); + if (-fn > (float)65000.0) return scalbnf(x,-65000); + return scalbnf(x,(int)fn); +#endif +} diff --git a/lib/libm/src/e_sinh.c b/lib/libm/src/e_sinh.c new file mode 100644 index 0000000000..4d54278b5c --- /dev/null +++ b/lib/libm/src/e_sinh.c @@ -0,0 +1,77 @@ +/* @(#)e_sinh.c 5.1 93/09/24 */ +/* + * ==================================================== + * Copyright (C) 1993 by Sun Microsystems, Inc. All rights reserved. + * + * Developed at SunPro, a Sun Microsystems, Inc. business. + * Permission to use, copy, modify, and distribute this + * software is freely granted, provided that this notice + * is preserved. + * ==================================================== + * + * $NetBSD: e_sinh.c,v 1.11 2002/05/26 22:01:52 wiz Exp $ + * $DragonFly: src/lib/libm/src/e_sinh.c,v 1.1 2005/07/26 21:15:20 joerg Exp $ + */ + +/* sinh(x) + * Method : + * mathematically sinh(x) if defined to be (exp(x)-exp(-x))/2 + * 1. Replace x by |x| (sinh(-x) = -sinh(x)). + * 2. + * E + E/(E+1) + * 0 <= x <= 22 : sinh(x) := --------------, E=expm1(x) + * 2 + * + * 22 <= x <= lnovft : sinh(x) := exp(x)/2 + * lnovft <= x <= ln2ovft: sinh(x) := exp(x/2)/2 * exp(x/2) + * ln2ovft < x : sinh(x) := x*shuge (overflow) + * + * Special cases: + * sinh(x) is |x| if x is +INF, -INF, or NaN. + * only sinh(0)=0 is exact for finite x. + */ + +#include +#include "math_private.h" + +static const double one = 1.0, shuge = 1.0e307; + +double +sinh(double x) +{ + double t,w,h; + int32_t ix,jx; + u_int32_t lx; + + /* High word of |x|. */ + GET_HIGH_WORD(jx,x); + ix = jx&0x7fffffff; + + /* x is INF or NaN */ + if(ix>=0x7ff00000) return x+x; + + h = 0.5; + if (jx<0) h = -h; + /* |x| in [0,22], return sign(x)*0.5*(E+E/(E+1))) */ + if (ix < 0x40360000) { /* |x|<22 */ + if (ix<0x3e300000) /* |x|<2**-28 */ + if(shuge+x>one) return x;/* sinh(tiny) = tiny with inexact */ + t = expm1(fabs(x)); + if(ix<0x3ff00000) return h*(2.0*t-t*t/(t+one)); + return h*(t+t/(t+one)); + } + + /* |x| in [22, log(maxdouble)] return 0.5*exp(|x|) */ + if (ix < 0x40862E42) return h*exp(fabs(x)); + + /* |x| in [log(maxdouble), overflowthresold] */ + GET_LOW_WORD(lx,x); + if (ix<0x408633CE || ((ix==0x408633ce)&&(lx<=(u_int32_t)0x8fb9f87d))) { + w = exp(0.5*fabs(x)); + t = h*w; + return t*w; + } + + /* |x| > overflowthresold, sinh(x) overflow */ + return x*shuge; +} diff --git a/lib/libm/src/e_sinhf.c b/lib/libm/src/e_sinhf.c new file mode 100644 index 0000000000..cf33533fa4 --- /dev/null +++ b/lib/libm/src/e_sinhf.c @@ -0,0 +1,59 @@ +/* e_sinhf.c -- float version of e_sinh.c. + * Conversion to float by Ian Lance Taylor, Cygnus Support, ian@cygnus.com. + */ + +/* + * ==================================================== + * Copyright (C) 1993 by Sun Microsystems, Inc. All rights reserved. + * + * Developed at SunPro, a Sun Microsystems, Inc. business. + * Permission to use, copy, modify, and distribute this + * software is freely granted, provided that this notice + * is preserved. + * ==================================================== + * + * $NetBSD: e_sinhf.c,v 1.7 2002/05/26 22:01:52 wiz Exp $ + * $DragonFly: src/lib/libm/src/e_sinhf.c,v 1.1 2005/07/26 21:15:20 joerg Exp $ + */ + +#include +#include "math_private.h" + +static const float one = 1.0, shuge = 1.0e37; + +float +sinhf(float x) +{ + float t,w,h; + int32_t ix,jx; + + GET_FLOAT_WORD(jx,x); + ix = jx&0x7fffffff; + + /* x is INF or NaN */ + if(ix>=0x7f800000) return x+x; + + h = 0.5; + if (jx<0) h = -h; + /* |x| in [0,22], return sign(x)*0.5*(E+E/(E+1))) */ + if (ix < 0x41b00000) { /* |x|<22 */ + if (ix<0x31800000) /* |x|<2**-28 */ + if(shuge+x>one) return x;/* sinh(tiny) = tiny with inexact */ + t = expm1f(fabsf(x)); + if(ix<0x3f800000) return h*((float)2.0*t-t*t/(t+one)); + return h*(t+t/(t+one)); + } + + /* |x| in [22, log(maxdouble)] return 0.5*exp(|x|) */ + if (ix < 0x42b17180) return h*expf(fabsf(x)); + + /* |x| in [log(maxdouble), overflowthresold] */ + if (ix<=0x42b2d4fc) { + w = expf((float)0.5*fabsf(x)); + t = h*w; + return t*w; + } + + /* |x| > overflowthresold, sinh(x) overflow */ + return x*shuge; +} diff --git a/lib/libm/src/e_sqrt.c b/lib/libm/src/e_sqrt.c new file mode 100644 index 0000000000..fd79eec5e2 --- /dev/null +++ b/lib/libm/src/e_sqrt.c @@ -0,0 +1,444 @@ +/* @(#)e_sqrt.c 5.1 93/09/24 */ +/* + * ==================================================== + * Copyright (C) 1993 by Sun Microsystems, Inc. All rights reserved. + * + * Developed at SunPro, a Sun Microsystems, Inc. business. + * Permission to use, copy, modify, and distribute this + * software is freely granted, provided that this notice + * is preserved. + * ==================================================== + * + * $NetBSD: e_sqrt.c,v 1.12 2002/05/26 22:01:52 wiz Exp $ + * $DragonFly: src/lib/libm/src/e_sqrt.c,v 1.1 2005/07/26 21:15:20 joerg Exp $ + */ + +/* sqrt(x) + * Return correctly rounded sqrt. + * ------------------------------------------ + * | Use the hardware sqrt if you have one | + * ------------------------------------------ + * Method: + * Bit by bit method using integer arithmetic. (Slow, but portable) + * 1. Normalization + * Scale x to y in [1,4) with even powers of 2: + * find an integer k such that 1 <= (y=x*2^(2k)) < 4, then + * sqrt(x) = 2^k * sqrt(y) + * 2. Bit by bit computation + * Let q = sqrt(y) truncated to i bit after binary point (q = 1), + * i 0 + * i+1 2 + * s = 2*q , and y = 2 * ( y - q ). (1) + * i i i i + * + * To compute q from q , one checks whether + * i+1 i + * + * -(i+1) 2 + * (q + 2 ) <= y. (2) + * i + * -(i+1) + * If (2) is false, then q = q ; otherwise q = q + 2 . + * i+1 i i+1 i + * + * With some algebric manipulation, it is not difficult to see + * that (2) is equivalent to + * -(i+1) + * s + 2 <= y (3) + * i i + * + * The advantage of (3) is that s and y can be computed by + * i i + * the following recurrence formula: + * if (3) is false + * + * s = s , y = y ; (4) + * i+1 i i+1 i + * + * otherwise, + * -i -(i+1) + * s = s + 2 , y = y - s - 2 (5) + * i+1 i i+1 i i + * + * One may easily use induction to prove (4) and (5). + * Note. Since the left hand side of (3) contain only i+2 bits, + * it does not necessary to do a full (53-bit) comparison + * in (3). + * 3. Final rounding + * After generating the 53 bits result, we compute one more bit. + * Together with the remainder, we can decide whether the + * result is exact, bigger than 1/2ulp, or less than 1/2ulp + * (it will never equal to 1/2ulp). + * The rounding mode can be detected by checking whether + * huge + tiny is equal to huge, and whether huge - tiny is + * equal to huge for some floating point number "huge" and "tiny". + * + * Special cases: + * sqrt(+-0) = +-0 ... exact + * sqrt(inf) = inf + * sqrt(-ve) = NaN ... with invalid signal + * sqrt(NaN) = NaN ... with invalid signal for signaling NaN + * + * Other methods : see the appended file at the end of the program below. + *--------------- + */ + +#include +#include "math_private.h" + +static const double one = 1.0, tiny=1.0e-300; + +double +sqrt(double x) +{ + double z; + int32_t sign = (int)0x80000000; + int32_t ix0,s0,q,m,t,i; + u_int32_t r,t1,s1,ix1,q1; + + EXTRACT_WORDS(ix0,ix1,x); + + /* take care of Inf and NaN */ + if((ix0&0x7ff00000)==0x7ff00000) { + return x*x+x; /* sqrt(NaN)=NaN, sqrt(+inf)=+inf + sqrt(-inf)=sNaN */ + } + /* take care of zero */ + if(ix0<=0) { + if(((ix0&(~sign))|ix1)==0) return x;/* sqrt(+-0) = +-0 */ + else if(ix0<0) + return (x-x)/(x-x); /* sqrt(-ve) = sNaN */ + } + /* normalize x */ + m = (ix0>>20); + if(m==0) { /* subnormal x */ + while(ix0==0) { + m -= 21; + ix0 |= (ix1>>11); ix1 <<= 21; + } + for(i=0;(ix0&0x00100000)==0;i++) ix0<<=1; + m -= i-1; + ix0 |= (ix1>>(32-i)); + ix1 <<= i; + } + m -= 1023; /* unbias exponent */ + ix0 = (ix0&0x000fffff)|0x00100000; + if(m&1){ /* odd m, double x to make it even */ + ix0 += ix0 + ((ix1&sign)>>31); + ix1 += ix1; + } + m >>= 1; /* m = [m/2] */ + + /* generate sqrt(x) bit by bit */ + ix0 += ix0 + ((ix1&sign)>>31); + ix1 += ix1; + q = q1 = s0 = s1 = 0; /* [q,q1] = sqrt(x) */ + r = 0x00200000; /* r = moving bit from right to left */ + + while(r!=0) { + t = s0+r; + if(t<=ix0) { + s0 = t+r; + ix0 -= t; + q += r; + } + ix0 += ix0 + ((ix1&sign)>>31); + ix1 += ix1; + r>>=1; + } + + r = sign; + while(r!=0) { + t1 = s1+r; + t = s0; + if((t>31); + ix1 += ix1; + r>>=1; + } + + /* use floating add to find out rounding direction */ + if((ix0|ix1)!=0) { + z = one-tiny; /* trigger inexact flag */ + if (z>=one) { + z = one+tiny; + if (q1==(u_int32_t)0xffffffff) { q1=0; q += 1;} + else if (z>one) { + if (q1==(u_int32_t)0xfffffffe) q+=1; + q1+=2; + } else + q1 += (q1&1); + } + } + ix0 = (q>>1)+0x3fe00000; + ix1 = q1>>1; + if ((q&1)==1) ix1 |= sign; + ix0 += (m <<20); + INSERT_WORDS(z,ix0,ix1); + return z; +} + +/* +Other methods (use floating-point arithmetic) +------------- +(This is a copy of a drafted paper by Prof W. Kahan +and K.C. Ng, written in May, 1986) + + Two algorithms are given here to implement sqrt(x) + (IEEE double precision arithmetic) in software. + Both supply sqrt(x) correctly rounded. The first algorithm (in + Section A) uses newton iterations and involves four divisions. + The second one uses reciproot iterations to avoid division, but + requires more multiplications. Both algorithms need the ability + to chop results of arithmetic operations instead of round them, + and the INEXACT flag to indicate when an arithmetic operation + is executed exactly with no roundoff error, all part of the + standard (IEEE 754-1985). The ability to perform shift, add, + subtract and logical AND operations upon 32-bit words is needed + too, though not part of the standard. + +A. sqrt(x) by Newton Iteration + + (1) Initial approximation + + Let x0 and x1 be the leading and the trailing 32-bit words of + a floating point number x (in IEEE double format) respectively + + 1 11 52 ...widths + ------------------------------------------------------ + x: |s| e | f | + ------------------------------------------------------ + msb lsb msb lsb ...order + + + ------------------------ ------------------------ + x0: |s| e | f1 | x1: | f2 | + ------------------------ ------------------------ + + By performing shifts and subtracts on x0 and x1 (both regarded + as integers), we obtain an 8-bit approximation of sqrt(x) as + follows. + + k := (x0>>1) + 0x1ff80000; + y0 := k - T1[31&(k>>15)]. ... y ~ sqrt(x) to 8 bits + Here k is a 32-bit integer and T1[] is an integer array containing + correction terms. Now magically the floating value of y (y's + leading 32-bit word is y0, the value of its trailing word is 0) + approximates sqrt(x) to almost 8-bit. + + Value of T1: + static int T1[32]= { + 0, 1024, 3062, 5746, 9193, 13348, 18162, 23592, + 29598, 36145, 43202, 50740, 58733, 67158, 75992, 85215, + 83599, 71378, 60428, 50647, 41945, 34246, 27478, 21581, + 16499, 12183, 8588, 5674, 3403, 1742, 661, 130,}; + + (2) Iterative refinement + + Apply Heron's rule three times to y, we have y approximates + sqrt(x) to within 1 ulp (Unit in the Last Place): + + y := (y+x/y)/2 ... almost 17 sig. bits + y := (y+x/y)/2 ... almost 35 sig. bits + y := y-(y-x/y)/2 ... within 1 ulp + + + Remark 1. + Another way to improve y to within 1 ulp is: + + y := (y+x/y) ... almost 17 sig. bits to 2*sqrt(x) + y := y - 0x00100006 ... almost 18 sig. bits to sqrt(x) + + 2 + (x-y )*y + y := y + 2* ---------- ...within 1 ulp + 2 + 3y + x + + + This formula has one division fewer than the one above; however, + it requires more multiplications and additions. Also x must be + scaled in advance to avoid spurious overflow in evaluating the + expression 3y*y+x. Hence it is not recommended uless division + is slow. If division is very slow, then one should use the + reciproot algorithm given in section B. + + (3) Final adjustment + + By twiddling y's last bit it is possible to force y to be + correctly rounded according to the prevailing rounding mode + as follows. Let r and i be copies of the rounding mode and + inexact flag before entering the square root program. Also we + use the expression y+-ulp for the next representable floating + numbers (up and down) of y. Note that y+-ulp = either fixed + point y+-1, or multiply y by nextafter(1,+-inf) in chopped + mode. + + I := FALSE; ... reset INEXACT flag I + R := RZ; ... set rounding mode to round-toward-zero + z := x/y; ... chopped quotient, possibly inexact + If(not I) then { ... if the quotient is exact + if(z=y) { + I := i; ... restore inexact flag + R := r; ... restore rounded mode + return sqrt(x):=y. + } else { + z := z - ulp; ... special rounding + } + } + i := TRUE; ... sqrt(x) is inexact + If (r=RN) then z=z+ulp ... rounded-to-nearest + If (r=RP) then { ... round-toward-+inf + y = y+ulp; z=z+ulp; + } + y := y+z; ... chopped sum + y0:=y0-0x00100000; ... y := y/2 is correctly rounded. + I := i; ... restore inexact flag + R := r; ... restore rounded mode + return sqrt(x):=y. + + (4) Special cases + + Square root of +inf, +-0, or NaN is itself; + Square root of a negative number is NaN with invalid signal. + + +B. sqrt(x) by Reciproot Iteration + + (1) Initial approximation + + Let x0 and x1 be the leading and the trailing 32-bit words of + a floating point number x (in IEEE double format) respectively + (see section A). By performing shifs and subtracts on x0 and y0, + we obtain a 7.8-bit approximation of 1/sqrt(x) as follows. + + k := 0x5fe80000 - (x0>>1); + y0:= k - T2[63&(k>>14)]. ... y ~ 1/sqrt(x) to 7.8 bits + + Here k is a 32-bit integer and T2[] is an integer array + containing correction terms. Now magically the floating + value of y (y's leading 32-bit word is y0, the value of + its trailing word y1 is set to zero) approximates 1/sqrt(x) + to almost 7.8-bit. + + Value of T2: + static int T2[64]= { + 0x1500, 0x2ef8, 0x4d67, 0x6b02, 0x87be, 0xa395, 0xbe7a, 0xd866, + 0xf14a, 0x1091b,0x11fcd,0x13552,0x14999,0x15c98,0x16e34,0x17e5f, + 0x18d03,0x19a01,0x1a545,0x1ae8a,0x1b5c4,0x1bb01,0x1bfde,0x1c28d, + 0x1c2de,0x1c0db,0x1ba73,0x1b11c,0x1a4b5,0x1953d,0x18266,0x16be0, + 0x1683e,0x179d8,0x18a4d,0x19992,0x1a789,0x1b445,0x1bf61,0x1c989, + 0x1d16d,0x1d77b,0x1dddf,0x1e2ad,0x1e5bf,0x1e6e8,0x1e654,0x1e3cd, + 0x1df2a,0x1d635,0x1cb16,0x1be2c,0x1ae4e,0x19bde,0x1868e,0x16e2e, + 0x1527f,0x1334a,0x11051,0xe951, 0xbe01, 0x8e0d, 0x5924, 0x1edd,}; + + (2) Iterative refinement + + Apply Reciproot iteration three times to y and multiply the + result by x to get an approximation z that matches sqrt(x) + to about 1 ulp. To be exact, we will have + -1ulp < sqrt(x)-z<1.0625ulp. + + ... set rounding mode to Round-to-nearest + y := y*(1.5-0.5*x*y*y) ... almost 15 sig. bits to 1/sqrt(x) + y := y*((1.5-2^-30)+0.5*x*y*y)... about 29 sig. bits to 1/sqrt(x) + ... special arrangement for better accuracy + z := x*y ... 29 bits to sqrt(x), with z*y<1 + z := z + 0.5*z*(1-z*y) ... about 1 ulp to sqrt(x) + + Remark 2. The constant 1.5-2^-30 is chosen to bias the error so that + (a) the term z*y in the final iteration is always less than 1; + (b) the error in the final result is biased upward so that + -1 ulp < sqrt(x) - z < 1.0625 ulp + instead of |sqrt(x)-z|<1.03125ulp. + + (3) Final adjustment + + By twiddling y's last bit it is possible to force y to be + correctly rounded according to the prevailing rounding mode + as follows. Let r and i be copies of the rounding mode and + inexact flag before entering the square root program. Also we + use the expression y+-ulp for the next representable floating + numbers (up and down) of y. Note that y+-ulp = either fixed + point y+-1, or multiply y by nextafter(1,+-inf) in chopped + mode. + + R := RZ; ... set rounding mode to round-toward-zero + switch(r) { + case RN: ... round-to-nearest + if(x<= z*(z-ulp)...chopped) z = z - ulp; else + if(x<= z*(z+ulp)...chopped) z = z; else z = z+ulp; + break; + case RZ:case RM: ... round-to-zero or round-to--inf + R:=RP; ... reset rounding mod to round-to-+inf + if(x=(z+ulp)*(z+ulp) ...rounded up) z = z+ulp; + break; + case RP: ... round-to-+inf + if(x>(z+ulp)*(z+ulp)...chopped) z = z+2*ulp; else + if(x>z*z ...chopped) z = z+ulp; + break; + } + + Remark 3. The above comparisons can be done in fixed point. For + example, to compare x and w=z*z chopped, it suffices to compare + x1 and w1 (the trailing parts of x and w), regarding them as + two's complement integers. + + ...Is z an exact square root? + To determine whether z is an exact square root of x, let z1 be the + trailing part of z, and also let x0 and x1 be the leading and + trailing parts of x. + + If ((z1&0x03ffffff)!=0) ... not exact if trailing 26 bits of z!=0 + I := 1; ... Raise Inexact flag: z is not exact + else { + j := 1 - [(x0>>20)&1] ... j = logb(x) mod 2 + k := z1 >> 26; ... get z's 25-th and 26-th + fraction bits + I := i or (k&j) or ((k&(j+j+1))!=(x1&3)); + } + R:= r ... restore rounded mode + return sqrt(x):=z. + + If multiplication is cheaper than the foregoing red tape, the + Inexact flag can be evaluated by + + I := i; + I := (z*z!=x) or I. + + Note that z*z can overwrite I; this value must be sensed if it is + True. + + Remark 4. If z*z = x exactly, then bit 25 to bit 0 of z1 must be + zero. + + -------------------- + z1: | f2 | + -------------------- + bit 31 bit 0 + + Further more, bit 27 and 26 of z1, bit 0 and 1 of x1, and the odd + or even of logb(x) have the following relations: + + ------------------------------------------------- + bit 27,26 of z1 bit 1,0 of x1 logb(x) + ------------------------------------------------- + 00 00 odd and even + 01 01 even + 10 10 odd + 10 00 even + 11 01 even + ------------------------------------------------- + + (4) Special cases (see (4) of Section A). + + */ + diff --git a/lib/libm/src/e_sqrtf.c b/lib/libm/src/e_sqrtf.c new file mode 100644 index 0000000000..eaad9f3fc0 --- /dev/null +++ b/lib/libm/src/e_sqrtf.c @@ -0,0 +1,88 @@ +/* e_sqrtf.c -- float version of e_sqrt.c. + * Conversion to float by Ian Lance Taylor, Cygnus Support, ian@cygnus.com. + */ + +/* + * ==================================================== + * Copyright (C) 1993 by Sun Microsystems, Inc. All rights reserved. + * + * Developed at SunPro, a Sun Microsystems, Inc. business. + * Permission to use, copy, modify, and distribute this + * software is freely granted, provided that this notice + * is preserved. + * ==================================================== + * + * $NetBSD: e_sqrtf.c,v 1.7 2002/05/26 22:01:53 wiz Exp $ + * $DragonFly: src/lib/libm/src/e_sqrtf.c,v 1.1 2005/07/26 21:15:20 joerg Exp $ + */ + +#include +#include "math_private.h" + +static const float one = 1.0, tiny=1.0e-30; + +float +sqrtf(float x) +{ + float z; + int32_t sign = (int)0x80000000; + int32_t ix,s,q,m,t,i; + u_int32_t r; + + GET_FLOAT_WORD(ix,x); + + /* take care of Inf and NaN */ + if((ix&0x7f800000)==0x7f800000) { + return x*x+x; /* sqrt(NaN)=NaN, sqrt(+inf)=+inf + sqrt(-inf)=sNaN */ + } + /* take care of zero */ + if(ix<=0) { + if((ix&(~sign))==0) return x;/* sqrt(+-0) = +-0 */ + else if(ix<0) + return (x-x)/(x-x); /* sqrt(-ve) = sNaN */ + } + /* normalize x */ + m = (ix>>23); + if(m==0) { /* subnormal x */ + for(i=0;(ix&0x00800000)==0;i++) ix<<=1; + m -= i-1; + } + m -= 127; /* unbias exponent */ + ix = (ix&0x007fffff)|0x00800000; + if(m&1) /* odd m, double x to make it even */ + ix += ix; + m >>= 1; /* m = [m/2] */ + + /* generate sqrt(x) bit by bit */ + ix += ix; + q = s = 0; /* q = sqrt(x) */ + r = 0x01000000; /* r = moving bit from right to left */ + + while(r!=0) { + t = s+r; + if(t<=ix) { + s = t+r; + ix -= t; + q += r; + } + ix += ix; + r>>=1; + } + + /* use floating add to find out rounding direction */ + if(ix!=0) { + z = one-tiny; /* trigger inexact flag */ + if (z>=one) { + z = one+tiny; + if (z>one) + q += 2; + else + q += (q&1); + } + } + ix = (q>>1)+0x3f000000; + ix += (m <<23); + SET_FLOAT_WORD(z,ix); + return z; +} diff --git a/lib/libm/src/k_cos.c b/lib/libm/src/k_cos.c new file mode 100644 index 0000000000..5657f3e0da --- /dev/null +++ b/lib/libm/src/k_cos.c @@ -0,0 +1,87 @@ +/* @(#)k_cos.c 5.1 93/09/24 */ +/* + * ==================================================== + * Copyright (C) 1993 by Sun Microsystems, Inc. All rights reserved. + * + * Developed at SunPro, a Sun Microsystems, Inc. business. + * Permission to use, copy, modify, and distribute this + * software is freely granted, provided that this notice + * is preserved. + * ==================================================== + * + * $NetBSD: k_cos.c,v 1.11 2002/05/26 22:01:53 wiz Exp $ + * $DragonFly: src/lib/libm/src/k_cos.c,v 1.1 2005/07/26 21:15:20 joerg Exp $ + */ + +/* + * __kernel_cos( x, y ) + * kernel cos function on [-pi/4, pi/4], pi/4 ~ 0.785398164 + * Input x is assumed to be bounded by ~pi/4 in magnitude. + * Input y is the tail of x. + * + * Algorithm + * 1. Since cos(-x) = cos(x), we need only to consider positive x. + * 2. if x < 2^-27 (hx<0x3e400000 0), return 1 with inexact if x!=0. + * 3. cos(x) is approximated by a polynomial of degree 14 on + * [0,pi/4] + * 4 14 + * cos(x) ~ 1 - x*x/2 + C1*x + ... + C6*x + * where the remez error is + * + * | 2 4 6 8 10 12 14 | -58 + * |cos(x)-(1-.5*x +C1*x +C2*x +C3*x +C4*x +C5*x +C6*x )| <= 2 + * | | + * + * 4 6 8 10 12 14 + * 4. let r = C1*x +C2*x +C3*x +C4*x +C5*x +C6*x , then + * cos(x) = 1 - x*x/2 + r + * since cos(x+y) ~ cos(x) - sin(x)*y + * ~ cos(x) - x*y, + * a correction term is necessary in cos(x) and hence + * cos(x+y) = 1 - (x*x/2 - (r - x*y)) + * For better accuracy when x > 0.3, let qx = |x|/4 with + * the last 32 bits mask off, and if x > 0.78125, let qx = 0.28125. + * Then + * cos(x+y) = (1-qx) - ((x*x/2-qx) - (r-x*y)). + * Note that 1-qx and (x*x/2-qx) is EXACT here, and the + * magnitude of the latter is at least a quarter of x*x/2, + * thus, reducing the rounding error in the subtraction. + */ + +#include +#include "math_private.h" + +static const double +one = 1.00000000000000000000e+00, /* 0x3FF00000, 0x00000000 */ +C1 = 4.16666666666666019037e-02, /* 0x3FA55555, 0x5555554C */ +C2 = -1.38888888888741095749e-03, /* 0xBF56C16C, 0x16C15177 */ +C3 = 2.48015872894767294178e-05, /* 0x3EFA01A0, 0x19CB1590 */ +C4 = -2.75573143513906633035e-07, /* 0xBE927E4F, 0x809C52AD */ +C5 = 2.08757232129817482790e-09, /* 0x3E21EE9E, 0xBDB4B1C4 */ +C6 = -1.13596475577881948265e-11; /* 0xBDA8FAE9, 0xBE8838D4 */ + +double +__kernel_cos(double x, double y) +{ + double a,hz,z,r,qx; + int32_t ix; + GET_HIGH_WORD(ix,x); + ix &= 0x7fffffff; /* ix = |x|'s high word*/ + if(ix<0x3e400000) { /* if x < 2**27 */ + if(((int)x)==0) return one; /* generate inexact */ + } + z = x*x; + r = z*(C1+z*(C2+z*(C3+z*(C4+z*(C5+z*C6))))); + if(ix < 0x3FD33333) /* if |x| < 0.3 */ + return one - (0.5*z - (z*r - x*y)); + else { + if(ix > 0x3fe90000) { /* x > 0.78125 */ + qx = 0.28125; + } else { + INSERT_WORDS(qx,ix-0x00200000,0); /* x/4 */ + } + hz = 0.5*z-qx; + a = one-qx; + return a - (hz - (z*r-x*y)); + } +} diff --git a/lib/libm/src/k_cosf.c b/lib/libm/src/k_cosf.c new file mode 100644 index 0000000000..3de14271dc --- /dev/null +++ b/lib/libm/src/k_cosf.c @@ -0,0 +1,55 @@ +/* k_cosf.c -- float version of k_cos.c + * Conversion to float by Ian Lance Taylor, Cygnus Support, ian@cygnus.com. + */ + +/* + * ==================================================== + * Copyright (C) 1993 by Sun Microsystems, Inc. All rights reserved. + * + * Developed at SunPro, a Sun Microsystems, Inc. business. + * Permission to use, copy, modify, and distribute this + * software is freely granted, provided that this notice + * is preserved. + * ==================================================== + * + * $NetBSD: k_cosf.c,v 1.7 2002/05/26 22:01:53 wiz Exp $ + * $DragonFly: src/lib/libm/src/k_cosf.c,v 1.1 2005/07/26 21:15:20 joerg Exp $ + */ + +#include +#include "math_private.h" + +static const float +one = 1.0000000000e+00, /* 0x3f800000 */ +C1 = 4.1666667908e-02, /* 0x3d2aaaab */ +C2 = -1.3888889225e-03, /* 0xbab60b61 */ +C3 = 2.4801587642e-05, /* 0x37d00d01 */ +C4 = -2.7557314297e-07, /* 0xb493f27c */ +C5 = 2.0875723372e-09, /* 0x310f74f6 */ +C6 = -1.1359647598e-11; /* 0xad47d74e */ + +float +__kernel_cosf(float x, float y) +{ + float a,hz,z,r,qx; + int32_t ix; + GET_FLOAT_WORD(ix,x); + ix &= 0x7fffffff; /* ix = |x|'s high word*/ + if(ix<0x32000000) { /* if x < 2**27 */ + if(((int)x)==0) return one; /* generate inexact */ + } + z = x*x; + r = z*(C1+z*(C2+z*(C3+z*(C4+z*(C5+z*C6))))); + if(ix < 0x3e99999a) /* if |x| < 0.3 */ + return one - ((float)0.5*z - (z*r - x*y)); + else { + if(ix > 0x3f480000) { /* x > 0.78125 */ + qx = (float)0.28125; + } else { + SET_FLOAT_WORD(qx,ix-0x01000000); /* x/4 */ + } + hz = (float)0.5*z-qx; + a = one-qx; + return a - (hz - (z*r-x*y)); + } +} diff --git a/lib/libm/src/k_rem_pio2.c b/lib/libm/src/k_rem_pio2.c new file mode 100644 index 0000000000..c731d2bb83 --- /dev/null +++ b/lib/libm/src/k_rem_pio2.c @@ -0,0 +1,303 @@ +/* @(#)k_rem_pio2.c 5.1 93/09/24 */ +/* + * ==================================================== + * Copyright (C) 1993 by Sun Microsystems, Inc. All rights reserved. + * + * Developed at SunPro, a Sun Microsystems, Inc. business. + * Permission to use, copy, modify, and distribute this + * software is freely granted, provided that this notice + * is preserved. + * ==================================================== + * + * $NetBSD: k_rem_pio2.c,v 1.11 2003/01/04 23:43:03 wiz Exp $ + * $DragonFly: src/lib/libm/src/k_rem_pio2.c,v 1.1 2005/07/26 21:15:20 joerg Exp $ + */ + +/* + * __kernel_rem_pio2(x,y,e0,nx,prec,ipio2) + * double x[],y[]; int e0,nx,prec; int ipio2[]; + * + * __kernel_rem_pio2 return the last three digits of N with + * y = x - N*pi/2 + * so that |y| < pi/2. + * + * The method is to compute the integer (mod 8) and fraction parts of + * (2/pi)*x without doing the full multiplication. In general we + * skip the part of the product that are known to be a huge integer ( + * more accurately, = 0 mod 8 ). Thus the number of operations are + * independent of the exponent of the input. + * + * (2/pi) is represented by an array of 24-bit integers in ipio2[]. + * + * Input parameters: + * x[] The input value (must be positive) is broken into nx + * pieces of 24-bit integers in double precision format. + * x[i] will be the i-th 24 bit of x. The scaled exponent + * of x[0] is given in input parameter e0 (i.e., x[0]*2^e0 + * match x's up to 24 bits. + * + * Example of breaking a double positive z into x[0]+x[1]+x[2]: + * e0 = ilogb(z)-23 + * z = scalbn(z,-e0) + * for i = 0,1,2 + * x[i] = floor(z) + * z = (z-x[i])*2**24 + * + * + * y[] output result in an array of double precision numbers. + * The dimension of y[] is: + * 24-bit precision 1 + * 53-bit precision 2 + * 64-bit precision 2 + * 113-bit precision 3 + * The actual value is the sum of them. Thus for 113-bit + * precison, one may have to do something like: + * + * long double t,w,r_head, r_tail; + * t = (long double)y[2] + (long double)y[1]; + * w = (long double)y[0]; + * r_head = t+w; + * r_tail = w - (r_head - t); + * + * e0 The exponent of x[0] + * + * nx dimension of x[] + * + * prec an integer indicating the precision: + * 0 24 bits (single) + * 1 53 bits (double) + * 2 64 bits (extended) + * 3 113 bits (quad) + * + * ipio2[] + * integer array, contains the (24*i)-th to (24*i+23)-th + * bit of 2/pi after binary point. The corresponding + * floating value is + * + * ipio2[i] * 2^(-24(i+1)). + * + * External function: + * double scalbn(), floor(); + * + * + * Here is the description of some local variables: + * + * jk jk+1 is the initial number of terms of ipio2[] needed + * in the computation. The recommended value is 2,3,4, + * 6 for single, double, extended,and quad. + * + * jz local integer variable indicating the number of + * terms of ipio2[] used. + * + * jx nx - 1 + * + * jv index for pointing to the suitable ipio2[] for the + * computation. In general, we want + * ( 2^e0*x[0] * ipio2[jv-1]*2^(-24jv) )/8 + * is an integer. Thus + * e0-3-24*jv >= 0 or (e0-3)/24 >= jv + * Hence jv = max(0,(e0-3)/24). + * + * jp jp+1 is the number of terms in PIo2[] needed, jp = jk. + * + * q[] double array with integral value, representing the + * 24-bits chunk of the product of x and 2/pi. + * + * q0 the corresponding exponent of q[0]. Note that the + * exponent for q[i] would be q0-24*i. + * + * PIo2[] double precision array, obtained by cutting pi/2 + * into 24 bits chunks. + * + * f[] ipio2[] in floating point + * + * iq[] integer array by breaking up q[] in 24-bits chunk. + * + * fq[] final product of x*(2/pi) in fq[0],..,fq[jk] + * + * ih integer. If >0 it indicates q[] is >= 0.5, hence + * it also indicates the *sign* of the result. + * + */ + + +/* + * Constants: + * The hexadecimal values are the intended ones for the following + * constants. The decimal values may be used, provided that the + * compiler will convert from decimal to binary accurately enough + * to produce the hexadecimal values shown. + */ + +#include +#include "math_private.h" + +static const int init_jk[] = {2,3,4,6}; /* initial value for jk */ + +static const double PIo2[] = { + 1.57079625129699707031e+00, /* 0x3FF921FB, 0x40000000 */ + 7.54978941586159635335e-08, /* 0x3E74442D, 0x00000000 */ + 5.39030252995776476554e-15, /* 0x3CF84698, 0x80000000 */ + 3.28200341580791294123e-22, /* 0x3B78CC51, 0x60000000 */ + 1.27065575308067607349e-29, /* 0x39F01B83, 0x80000000 */ + 1.22933308981111328932e-36, /* 0x387A2520, 0x40000000 */ + 2.73370053816464559624e-44, /* 0x36E38222, 0x80000000 */ + 2.16741683877804819444e-51, /* 0x3569F31D, 0x00000000 */ +}; + +static const double +zero = 0.0, +one = 1.0, +two24 = 1.67772160000000000000e+07, /* 0x41700000, 0x00000000 */ +twon24 = 5.96046447753906250000e-08; /* 0x3E700000, 0x00000000 */ + +int +__kernel_rem_pio2(double *x, double *y, int e0, int nx, int prec, const int32_t *ipio2) +{ + int32_t jz,jx,jv,jp,jk,carry,n,iq[20],i,j,k,m,q0,ih; + double z,fw,f[20],fq[20],q[20]; + + /* initialize jk*/ + jk = init_jk[prec]; + jp = jk; + + /* determine jx,jv,q0, note that 3>q0 */ + jx = nx-1; + jv = (e0-3)/24; if(jv<0) jv=0; + q0 = e0-24*(jv+1); + + /* set up f[0] to f[jx+jk] where f[jx+jk] = ipio2[jv+jk] */ + j = jv-jx; m = jx+jk; + for(i=0;i<=m;i++,j++) f[i] = (j<0)? zero : (double) ipio2[j]; + + /* compute q[0],q[1],...q[jk] */ + for (i=0;i<=jk;i++) { + for(j=0,fw=0.0;j<=jx;j++) fw += x[j]*f[jx+i-j]; q[i] = fw; + } + + jz = jk; +recompute: + /* distill q[] into iq[] reversingly */ + for(i=0,j=jz,z=q[jz];j>0;i++,j--) { + fw = (double)((int32_t)(twon24* z)); + iq[i] = (int32_t)(z-two24*fw); + z = q[j-1]+fw; + } + + /* compute n */ + z = scalbn(z,q0); /* actual value of z */ + z -= 8.0*floor(z*0.125); /* trim off integer >= 8 */ + n = (int32_t) z; + z -= (double)n; + ih = 0; + if(q0>0) { /* need iq[jz-1] to determine n */ + i = (iq[jz-1]>>(24-q0)); n += i; + iq[jz-1] -= i<<(24-q0); + ih = iq[jz-1]>>(23-q0); + } + else if(q0==0) ih = iq[jz-1]>>23; + else if(z>=0.5) ih=2; + + if(ih>0) { /* q > 0.5 */ + n += 1; carry = 0; + for(i=0;i0) { /* rare case: chance is 1 in 12 */ + switch(q0) { + case 1: + iq[jz-1] &= 0x7fffff; break; + case 2: + iq[jz-1] &= 0x3fffff; break; + } + } + if(ih==2) { + z = one - z; + if(carry!=0) z -= scalbn(one,q0); + } + } + + /* check if recomputation is needed */ + if(z==zero) { + j = 0; + for (i=jz-1;i>=jk;i--) j |= iq[i]; + if(j==0) { /* need recomputation */ + for(k=1;iq[jk-k]==0;k++); /* k = no. of terms needed */ + + for(i=jz+1;i<=jz+k;i++) { /* add q[jz+1] to q[jz+k] */ + f[jx+i] = (double) ipio2[jv+i]; + for(j=0,fw=0.0;j<=jx;j++) fw += x[j]*f[jx+i-j]; + q[i] = fw; + } + jz += k; + goto recompute; + } + } + + /* chop off zero terms */ + if(z==0.0) { + jz -= 1; q0 -= 24; + while(iq[jz]==0) { jz--; q0-=24;} + } else { /* break z into 24-bit if necessary */ + z = scalbn(z,-q0); + if(z>=two24) { + fw = (double)((int32_t)(twon24*z)); + iq[jz] = (int32_t)(z-two24*fw); + jz += 1; q0 += 24; + iq[jz] = (int32_t) fw; + } else iq[jz] = (int32_t) z ; + } + + /* convert integer "bit" chunk to floating-point value */ + fw = scalbn(one,q0); + for(i=jz;i>=0;i--) { + q[i] = fw*(double)iq[i]; fw*=twon24; + } + + /* compute PIo2[0,...,jp]*q[jz,...,0] */ + for(i=jz;i>=0;i--) { + for(fw=0.0,k=0;k<=jp&&k<=jz-i;k++) fw += PIo2[k]*q[i+k]; + fq[jz-i] = fw; + } + + /* compress fq[] into y[] */ + switch(prec) { + case 0: + fw = 0.0; + for (i=jz;i>=0;i--) fw += fq[i]; + y[0] = (ih==0)? fw: -fw; + break; + case 1: + case 2: + fw = 0.0; + for (i=jz;i>=0;i--) fw += fq[i]; + y[0] = (ih==0)? fw: -fw; + fw = fq[0]-fw; + for (i=1;i<=jz;i++) fw += fq[i]; + y[1] = (ih==0)? fw: -fw; + break; + case 3: /* painful */ + for (i=jz;i>0;i--) { + fw = fq[i-1]+fq[i]; + fq[i] += fq[i-1]-fw; + fq[i-1] = fw; + } + for (i=jz;i>1;i--) { + fw = fq[i-1]+fq[i]; + fq[i] += fq[i-1]-fw; + fq[i-1] = fw; + } + for (fw=0.0,i=jz;i>=2;i--) fw += fq[i]; + if(ih==0) { + y[0] = fq[0]; y[1] = fq[1]; y[2] = fw; + } else { + y[0] = -fq[0]; y[1] = -fq[1]; y[2] = -fw; + } + } + return n&7; +} diff --git a/lib/libm/src/k_rem_pio2f.c b/lib/libm/src/k_rem_pio2f.c new file mode 100644 index 0000000000..c65f33c21d --- /dev/null +++ b/lib/libm/src/k_rem_pio2f.c @@ -0,0 +1,196 @@ +/* k_rem_pio2f.c -- float version of k_rem_pio2.c + * Conversion to float by Ian Lance Taylor, Cygnus Support, ian@cygnus.com. + */ + +/* + * ==================================================== + * Copyright (C) 1993 by Sun Microsystems, Inc. All rights reserved. + * + * Developed at SunPro, a Sun Microsystems, Inc. business. + * Permission to use, copy, modify, and distribute this + * software is freely granted, provided that this notice + * is preserved. + * ==================================================== + * + * $NetBSD: k_rem_pio2f.c,v 1.7 2002/05/26 22:01:53 wiz Exp $ + * $DragonFly: src/lib/libm/src/k_rem_pio2f.c,v 1.1 2005/07/26 21:15:20 joerg Exp $ + */ + +#include +#include "math_private.h" + +/* In the float version, the input parameter x contains 8 bit + integers, not 24 bit integers. 113 bit precision is not supported. */ + +static const int init_jk[] = {4,7,9}; /* initial value for jk */ + +static const float PIo2[] = { + 1.5703125000e+00, /* 0x3fc90000 */ + 4.5776367188e-04, /* 0x39f00000 */ + 2.5987625122e-05, /* 0x37da0000 */ + 7.5437128544e-08, /* 0x33a20000 */ + 6.0026650317e-11, /* 0x2e840000 */ + 7.3896444519e-13, /* 0x2b500000 */ + 5.3845816694e-15, /* 0x27c20000 */ + 5.6378512969e-18, /* 0x22d00000 */ + 8.3009228831e-20, /* 0x1fc40000 */ + 3.2756352257e-22, /* 0x1bc60000 */ + 6.3331015649e-25, /* 0x17440000 */ +}; + +static const float +zero = 0.0, +one = 1.0, +two8 = 2.5600000000e+02, /* 0x43800000 */ +twon8 = 3.9062500000e-03; /* 0x3b800000 */ + +int +__kernel_rem_pio2f(float *x, float *y, int e0, int nx, int prec, const int32_t *ipio2) +{ + int32_t jz,jx,jv,jp,jk,carry,n,iq[20],i,j,k,m,q0,ih; + float z,fw,f[20],fq[20],q[20]; + + /* initialize jk*/ + jk = init_jk[prec]; + jp = jk; + + /* determine jx,jv,q0, note that 3>q0 */ + jx = nx-1; + jv = (e0-3)/8; if(jv<0) jv=0; + q0 = e0-8*(jv+1); + + /* set up f[0] to f[jx+jk] where f[jx+jk] = ipio2[jv+jk] */ + j = jv-jx; m = jx+jk; + for(i=0;i<=m;i++,j++) f[i] = (j<0)? zero : (float) ipio2[j]; + + /* compute q[0],q[1],...q[jk] */ + for (i=0;i<=jk;i++) { + for(j=0,fw=0.0;j<=jx;j++) fw += x[j]*f[jx+i-j]; q[i] = fw; + } + + jz = jk; +recompute: + /* distill q[] into iq[] reversingly */ + for(i=0,j=jz,z=q[jz];j>0;i++,j--) { + fw = (float)((int32_t)(twon8* z)); + iq[i] = (int32_t)(z-two8*fw); + z = q[j-1]+fw; + } + + /* compute n */ + z = scalbnf(z,q0); /* actual value of z */ + z -= (float)8.0*floorf(z*(float)0.125); /* trim off integer >= 8 */ + n = (int32_t) z; + z -= (float)n; + ih = 0; + if(q0>0) { /* need iq[jz-1] to determine n */ + i = (iq[jz-1]>>(8-q0)); n += i; + iq[jz-1] -= i<<(8-q0); + ih = iq[jz-1]>>(7-q0); + } + else if(q0==0) ih = iq[jz-1]>>8; + else if(z>=(float)0.5) ih=2; + + if(ih>0) { /* q > 0.5 */ + n += 1; carry = 0; + for(i=0;i0) { /* rare case: chance is 1 in 12 */ + switch(q0) { + case 1: + iq[jz-1] &= 0x7f; break; + case 2: + iq[jz-1] &= 0x3f; break; + } + } + if(ih==2) { + z = one - z; + if(carry!=0) z -= scalbnf(one,q0); + } + } + + /* check if recomputation is needed */ + if(z==zero) { + j = 0; + for (i=jz-1;i>=jk;i--) j |= iq[i]; + if(j==0) { /* need recomputation */ + for(k=1;iq[jk-k]==0;k++); /* k = no. of terms needed */ + + for(i=jz+1;i<=jz+k;i++) { /* add q[jz+1] to q[jz+k] */ + f[jx+i] = (float) ipio2[jv+i]; + for(j=0,fw=0.0;j<=jx;j++) fw += x[j]*f[jx+i-j]; + q[i] = fw; + } + jz += k; + goto recompute; + } + } + + /* chop off zero terms */ + if(z==(float)0.0) { + jz -= 1; q0 -= 8; + while(iq[jz]==0) { jz--; q0-=8;} + } else { /* break z into 8-bit if necessary */ + z = scalbnf(z,-q0); + if(z>=two8) { + fw = (float)((int32_t)(twon8*z)); + iq[jz] = (int32_t)(z-two8*fw); + jz += 1; q0 += 8; + iq[jz] = (int32_t) fw; + } else iq[jz] = (int32_t) z ; + } + + /* convert integer "bit" chunk to floating-point value */ + fw = scalbnf(one,q0); + for(i=jz;i>=0;i--) { + q[i] = fw*(float)iq[i]; fw*=twon8; + } + + /* compute PIo2[0,...,jp]*q[jz,...,0] */ + for(i=jz;i>=0;i--) { + for(fw=0.0,k=0;k<=jp&&k<=jz-i;k++) fw += PIo2[k]*q[i+k]; + fq[jz-i] = fw; + } + + /* compress fq[] into y[] */ + switch(prec) { + case 0: + fw = 0.0; + for (i=jz;i>=0;i--) fw += fq[i]; + y[0] = (ih==0)? fw: -fw; + break; + case 1: + case 2: + fw = 0.0; + for (i=jz;i>=0;i--) fw += fq[i]; + y[0] = (ih==0)? fw: -fw; + fw = fq[0]-fw; + for (i=1;i<=jz;i++) fw += fq[i]; + y[1] = (ih==0)? fw: -fw; + break; + case 3: /* painful */ + for (i=jz;i>0;i--) { + fw = fq[i-1]+fq[i]; + fq[i] += fq[i-1]-fw; + fq[i-1] = fw; + } + for (i=jz;i>1;i--) { + fw = fq[i-1]+fq[i]; + fq[i] += fq[i-1]-fw; + fq[i-1] = fw; + } + for (fw=0.0,i=jz;i>=2;i--) fw += fq[i]; + if(ih==0) { + y[0] = fq[0]; y[1] = fq[1]; y[2] = fw; + } else { + y[0] = -fq[0]; y[1] = -fq[1]; y[2] = -fw; + } + } + return n&7; +} diff --git a/lib/libm/src/k_sin.c b/lib/libm/src/k_sin.c new file mode 100644 index 0000000000..5cc78c2bdb --- /dev/null +++ b/lib/libm/src/k_sin.c @@ -0,0 +1,70 @@ +/* @(#)k_sin.c 5.1 93/09/24 */ +/* + * ==================================================== + * Copyright (C) 1993 by Sun Microsystems, Inc. All rights reserved. + * + * Developed at SunPro, a Sun Microsystems, Inc. business. + * Permission to use, copy, modify, and distribute this + * software is freely granted, provided that this notice + * is preserved. + * ==================================================== + * + * $NetBSD: k_sin.c,v 1.11 2002/05/26 22:01:53 wiz Exp $ + * $DragonFly: src/lib/libm/src/k_sin.c,v 1.1 2005/07/26 21:15:20 joerg Exp $ + */ + +/* __kernel_sin( x, y, iy) + * kernel sin function on [-pi/4, pi/4], pi/4 ~ 0.7854 + * Input x is assumed to be bounded by ~pi/4 in magnitude. + * Input y is the tail of x. + * Input iy indicates whether y is 0. (if iy=0, y assume to be 0). + * + * Algorithm + * 1. Since sin(-x) = -sin(x), we need only to consider positive x. + * 2. if x < 2^-27 (hx<0x3e400000 0), return x with inexact if x!=0. + * 3. sin(x) is approximated by a polynomial of degree 13 on + * [0,pi/4] + * 3 13 + * sin(x) ~ x + S1*x + ... + S6*x + * where + * + * |sin(x) 2 4 6 8 10 12 | -58 + * |----- - (1+S1*x +S2*x +S3*x +S4*x +S5*x +S6*x )| <= 2 + * | x | + * + * 4. sin(x+y) = sin(x) + sin'(x')*y + * ~ sin(x) + (1-x*x/2)*y + * For better accuracy, let + * 3 2 2 2 2 + * r = x *(S2+x *(S3+x *(S4+x *(S5+x *S6)))) + * then 3 2 + * sin(x) = x + (S1*x + (x *(r-y/2)+y)) + */ + +#include +#include "math_private.h" + +static const double +half = 5.00000000000000000000e-01, /* 0x3FE00000, 0x00000000 */ +S1 = -1.66666666666666324348e-01, /* 0xBFC55555, 0x55555549 */ +S2 = 8.33333333332248946124e-03, /* 0x3F811111, 0x1110F8A6 */ +S3 = -1.98412698298579493134e-04, /* 0xBF2A01A0, 0x19C161D5 */ +S4 = 2.75573137070700676789e-06, /* 0x3EC71DE3, 0x57B1FE7D */ +S5 = -2.50507602534068634195e-08, /* 0xBE5AE5E6, 0x8A2B9CEB */ +S6 = 1.58969099521155010221e-10; /* 0x3DE5D93A, 0x5ACFD57C */ + +double +__kernel_sin(double x, double y, int iy) +{ + double z,r,v; + int32_t ix; + GET_HIGH_WORD(ix,x); + ix &= 0x7fffffff; /* high word of x */ + if(ix<0x3e400000) /* |x| < 2**-27 */ + {if((int)x==0) return x;} /* generate inexact */ + z = x*x; + v = z*x; + r = S2+z*(S3+z*(S4+z*(S5+z*S6))); + if(iy==0) return x+v*(S1+z*r); + else return x-((z*(half*y-v*r)-y)-v*S1); +} diff --git a/lib/libm/src/k_sinf.c b/lib/libm/src/k_sinf.c new file mode 100644 index 0000000000..671adca356 --- /dev/null +++ b/lib/libm/src/k_sinf.c @@ -0,0 +1,45 @@ +/* k_sinf.c -- float version of k_sin.c + * Conversion to float by Ian Lance Taylor, Cygnus Support, ian@cygnus.com. + */ + +/* + * ==================================================== + * Copyright (C) 1993 by Sun Microsystems, Inc. All rights reserved. + * + * Developed at SunPro, a Sun Microsystems, Inc. business. + * Permission to use, copy, modify, and distribute this + * software is freely granted, provided that this notice + * is preserved. + * ==================================================== + * + * $NetBSD: k_sinf.c,v 1.7 2002/05/26 22:01:53 wiz Exp $ + * $DragonFly: src/lib/libm/src/k_sinf.c,v 1.1 2005/07/26 21:15:20 joerg Exp $ + */ + +#include +#include "math_private.h" + +static const float +half = 5.0000000000e-01,/* 0x3f000000 */ +S1 = -1.6666667163e-01, /* 0xbe2aaaab */ +S2 = 8.3333337680e-03, /* 0x3c088889 */ +S3 = -1.9841270114e-04, /* 0xb9500d01 */ +S4 = 2.7557314297e-06, /* 0x3638ef1b */ +S5 = -2.5050759689e-08, /* 0xb2d72f34 */ +S6 = 1.5896910177e-10; /* 0x2f2ec9d3 */ + +float +__kernel_sinf(float x, float y, int iy) +{ + float z,r,v; + int32_t ix; + GET_FLOAT_WORD(ix,x); + ix &= 0x7fffffff; /* high word of x */ + if(ix<0x32000000) /* |x| < 2**-27 */ + {if((int)x==0) return x;} /* generate inexact */ + z = x*x; + v = z*x; + r = S2+z*(S3+z*(S4+z*(S5+z*S6))); + if(iy==0) return x+v*(S1+z*r); + else return x-((z*(half*y-v*r)-y)-v*S1); +} diff --git a/lib/libm/src/k_tan.c b/lib/libm/src/k_tan.c new file mode 100644 index 0000000000..715509587a --- /dev/null +++ b/lib/libm/src/k_tan.c @@ -0,0 +1,154 @@ +/* @(#)k_tan.c 5.1 93/09/24 */ +/* + * ==================================================== + * Copyright (C) 1993 by Sun Microsystems, Inc. All rights reserved. + * + * Developed at SunPro, a Sun Microsystems, Inc. business. + * Permission to use, copy, modify, and distribute this + * software is freely granted, provided that this notice + * is preserved. + * ==================================================== + * + * $NetBSD: k_tan.c,v 1.12 2004/07/22 18:24:09 drochner Exp $ + * $DragonFly: src/lib/libm/src/k_tan.c,v 1.1 2005/07/26 21:15:20 joerg Exp $ + */ + +/* __kernel_tan( x, y, k ) + * kernel tan function on [-pi/4, pi/4], pi/4 ~ 0.7854 + * Input x is assumed to be bounded by ~pi/4 in magnitude. + * Input y is the tail of x. + * Input k indicates whether tan (if k=1) or + * -1/tan (if k= -1) is returned. + * + * Algorithm + * 1. Since tan(-x) = -tan(x), we need only to consider positive x. + * 2. if x < 2^-28 (hx<0x3e300000 0), return x with inexact if x!=0. + * 3. tan(x) is approximated by a odd polynomial of degree 27 on + * [0,0.67434] + * 3 27 + * tan(x) ~ x + T1*x + ... + T13*x + * where + * + * |tan(x) 2 4 26 | -59.2 + * |----- - (1+T1*x +T2*x +.... +T13*x )| <= 2 + * | x | + * + * Note: tan(x+y) = tan(x) + tan'(x)*y + * ~ tan(x) + (1+x*x)*y + * Therefore, for better accuracy in computing tan(x+y), let + * 3 2 2 2 2 + * r = x *(T2+x *(T3+x *(...+x *(T12+x *T13)))) + * then + * 3 2 + * tan(x+y) = x + (T1*x + (x *(r+y)+y)) + * + * 4. For x in [0.67434,pi/4], let y = pi/4 - x, then + * tan(x) = tan(pi/4-y) = (1-tan(y))/(1+tan(y)) + * = 1 - 2*(tan(y) - (tan(y)^2)/(1+tan(y))) + */ + +#include +#include "math_private.h" + +static const double xxx[] = { + 3.33333333333334091986e-01, /* 3FD55555, 55555563 */ + 1.33333333333201242699e-01, /* 3FC11111, 1110FE7A */ + 5.39682539762260521377e-02, /* 3FABA1BA, 1BB341FE */ + 2.18694882948595424599e-02, /* 3F9664F4, 8406D637 */ + 8.86323982359930005737e-03, /* 3F8226E3, E96E8493 */ + 3.59207910759131235356e-03, /* 3F6D6D22, C9560328 */ + 1.45620945432529025516e-03, /* 3F57DBC8, FEE08315 */ + 5.88041240820264096874e-04, /* 3F4344D8, F2F26501 */ + 2.46463134818469906812e-04, /* 3F3026F7, 1A8D1068 */ + 7.81794442939557092300e-05, /* 3F147E88, A03792A6 */ + 7.14072491382608190305e-05, /* 3F12B80F, 32F0A7E9 */ + -1.85586374855275456654e-05, /* BEF375CB, DB605373 */ + 2.59073051863633712884e-05, /* 3EFB2A70, 74BF7AD4 */ +/* one */ 1.00000000000000000000e+00, /* 3FF00000, 00000000 */ +/* pio4 */ 7.85398163397448278999e-01, /* 3FE921FB, 54442D18 */ +/* pio4lo */ 3.06161699786838301793e-17 /* 3C81A626, 33145C07 */ +}; +#define one xxx[13] +#define pio4 xxx[14] +#define pio4lo xxx[15] +#define T xxx + +double +__kernel_tan(double x, double y, int iy) +{ + double z, r, v, w, s; + int32_t ix, hx; + + GET_HIGH_WORD(hx, x); /* high word of x */ + ix = hx & 0x7fffffff; /* high word of |x| */ + if (ix < 0x3e300000) { /* x < 2**-28 */ + if ((int) x == 0) { /* generate inexact */ + u_int32_t low; + GET_LOW_WORD(low, x); + if(((ix | low) | (iy + 1)) == 0) + return one / fabs(x); + else { + if (iy == 1) + return x; + else { /* compute -1 / (x+y) carefully */ + double a, t; + + z = w = x + y; + SET_LOW_WORD(z, 0); + v = y - (z - x); + t = a = -one / w; + SET_LOW_WORD(t, 0); + s = one + t * z; + return t + a * (s + t * v); + } + } + } + } + if (ix >= 0x3FE59428) { /* |x| >= 0.6744 */ + if (hx < 0) { + x = -x; + y = -y; + } + z = pio4 - x; + w = pio4lo - y; + x = z + w; + y = 0.0; + } + z = x * x; + w = z * z; + /* + * Break x^5*(T[1]+x^2*T[2]+...) into + * x^5(T[1]+x^4*T[3]+...+x^20*T[11]) + + * x^5(x^2*(T[2]+x^4*T[4]+...+x^22*[T12])) + */ + r = T[1] + w * (T[3] + w * (T[5] + w * (T[7] + w * (T[9] + + w * T[11])))); + v = z * (T[2] + w * (T[4] + w * (T[6] + w * (T[8] + w * (T[10] + + w * T[12]))))); + s = z * x; + r = y + z * (s * (r + v) + y); + r += T[0] * s; + w = x + r; + if (ix >= 0x3FE59428) { + v = (double) iy; + return (double) (1 - ((hx >> 30) & 2)) * + (v - 2.0 * (x - (w * w / (w + v) - r))); + } + if (iy == 1) + return w; + else { + /* + * if allow error up to 2 ulp, simply return + * -1.0 / (x+r) here + */ + /* compute -1.0 / (x+r) accurately */ + double a, t; + z = w; + SET_LOW_WORD(z, 0); + v = r - (z - x); /* z+v = r+x */ + t = a = -1.0 / w; /* a = -1.0/w */ + SET_LOW_WORD(t, 0); + s = 1.0 + t * z; + return t + a * (s + t * v); + } +} diff --git a/lib/libm/src/k_tanf.c b/lib/libm/src/k_tanf.c new file mode 100644 index 0000000000..d58336da04 --- /dev/null +++ b/lib/libm/src/k_tanf.c @@ -0,0 +1,92 @@ +/* k_tanf.c -- float version of k_tan.c + * Conversion to float by Ian Lance Taylor, Cygnus Support, ian@cygnus.com. + */ + +/* + * ==================================================== + * Copyright (C) 1993 by Sun Microsystems, Inc. All rights reserved. + * + * Developed at SunPro, a Sun Microsystems, Inc. business. + * Permission to use, copy, modify, and distribute this + * software is freely granted, provided that this notice + * is preserved. + * ==================================================== + * + * $NetBSD: k_tanf.c,v 1.7 2002/05/26 22:01:54 wiz Exp $ + * $DragonFly: src/lib/libm/src/k_tanf.c,v 1.1 2005/07/26 21:15:20 joerg Exp $ + */ + +#include +#include "math_private.h" +static const float +one = 1.0000000000e+00, /* 0x3f800000 */ +pio4 = 7.8539812565e-01, /* 0x3f490fda */ +pio4lo= 3.7748947079e-08, /* 0x33222168 */ +T[] = { + 3.3333334327e-01, /* 0x3eaaaaab */ + 1.3333334029e-01, /* 0x3e088889 */ + 5.3968254477e-02, /* 0x3d5d0dd1 */ + 2.1869488060e-02, /* 0x3cb327a4 */ + 8.8632395491e-03, /* 0x3c11371f */ + 3.5920790397e-03, /* 0x3b6b6916 */ + 1.4562094584e-03, /* 0x3abede48 */ + 5.8804126456e-04, /* 0x3a1a26c8 */ + 2.4646313977e-04, /* 0x398137b9 */ + 7.8179444245e-05, /* 0x38a3f445 */ + 7.1407252108e-05, /* 0x3895c07a */ + -1.8558637748e-05, /* 0xb79bae5f */ + 2.5907305826e-05, /* 0x37d95384 */ +}; + +float +__kernel_tanf(float x, float y, int iy) +{ + float z,r,v,w,s; + int32_t ix,hx; + GET_FLOAT_WORD(hx,x); + ix = hx&0x7fffffff; /* high word of |x| */ + if(ix<0x31800000) /* x < 2**-28 */ + {if((int)x==0) { /* generate inexact */ + if((ix|(iy+1))==0) return one/fabsf(x); + else return (iy==1)? x: -one/x; + } + } + if(ix>=0x3f2ca140) { /* |x|>=0.6744 */ + if(hx<0) {x = -x; y = -y;} + z = pio4-x; + w = pio4lo-y; + x = z+w; y = 0.0; + } + z = x*x; + w = z*z; + /* Break x^5*(T[1]+x^2*T[2]+...) into + * x^5(T[1]+x^4*T[3]+...+x^20*T[11]) + + * x^5(x^2*(T[2]+x^4*T[4]+...+x^22*[T12])) + */ + r = T[1]+w*(T[3]+w*(T[5]+w*(T[7]+w*(T[9]+w*T[11])))); + v = z*(T[2]+w*(T[4]+w*(T[6]+w*(T[8]+w*(T[10]+w*T[12]))))); + s = z*x; + r = y + z*(s*(r+v)+y); + r += T[0]*s; + w = x+r; + if(ix>=0x3f2ca140) { + v = (float)iy; + return (float)(1-((hx>>30)&2))*(v-(float)2.0*(x-(w*w/(w+v)-r))); + } + if(iy==1) return w; + else { /* if allow error up to 2 ulp, + simply return -1.0/(x+r) here */ + /* compute -1.0/(x+r) accurately */ + float a,t; + int32_t i; + z = w; + GET_FLOAT_WORD(i,z); + SET_FLOAT_WORD(z,i&0xfffff000); + v = r-(z - x); /* z+v = r+x */ + t = a = -(float)1.0/w; /* a = -1.0/w */ + GET_FLOAT_WORD(i,t); + SET_FLOAT_WORD(t,i&0xfffff000); + s = (float)1.0+t*z; + return t+a*(s+t*v); + } +} diff --git a/lib/libm/src/llrint.c b/lib/libm/src/llrint.c new file mode 100644 index 0000000000..426f20370e --- /dev/null +++ b/lib/libm/src/llrint.c @@ -0,0 +1,14 @@ +/* + * Written by Matthias Drochner . + * Public domain. + * + * $NetBSD: llrint.c,v 1.2 2004/10/13 15:18:32 drochner Exp $ + * $DragonFly: src/lib/libm/src/llrint.c,v 1.1 2005/07/26 21:15:20 joerg Exp $ + */ + +#define LRINTNAME llrint +#define RESTYPE long long int +#define RESTYPE_MIN LLONG_MIN +#define RESTYPE_MAX LLONG_MAX + +#include "lrint.c" diff --git a/lib/libm/src/llrintf.c b/lib/libm/src/llrintf.c new file mode 100644 index 0000000000..6ecb638c18 --- /dev/null +++ b/lib/libm/src/llrintf.c @@ -0,0 +1,14 @@ +/* + * Written by Matthias Drochner . + * Public domain. + * + * $NetBSD: llrintf.c,v 1.2 2004/10/13 15:18:32 drochner Exp $ + * $DragonFly: src/lib/libm/src/llrintf.c,v 1.1 2005/07/26 21:15:20 joerg Exp $ + */ + +#define LRINTNAME llrintf +#define RESTYPE long long int +#define RESTYPE_MIN LLONG_MIN +#define RESTYPE_MAX LLONG_MAX + +#include "lrintf.c" diff --git a/lib/libm/src/llround.c b/lib/libm/src/llround.c new file mode 100644 index 0000000000..119d688c16 --- /dev/null +++ b/lib/libm/src/llround.c @@ -0,0 +1,14 @@ +/* + * Written by Matthias Drochner . + * Public domain. + * + * $NetBSD: llround.c,v 1.2 2004/10/13 15:18:32 drochner Exp $ + * $DragonFly: src/lib/libm/src/llround.c,v 1.1 2005/07/26 21:15:20 joerg Exp $ + */ + +#define LROUNDNAME llround +#define RESTYPE long long int +#define RESTYPE_MIN LLONG_MIN +#define RESTYPE_MAX LLONG_MAX + +#include "lround.c" diff --git a/lib/libm/src/llroundf.c b/lib/libm/src/llroundf.c new file mode 100644 index 0000000000..ed70bfb552 --- /dev/null +++ b/lib/libm/src/llroundf.c @@ -0,0 +1,14 @@ +/* + * Written by Matthias Drochner . + * Public domain. + * + * $NetBSD: llroundf.c,v 1.2 2004/10/13 15:18:32 drochner Exp $ + * $DragonFly: src/lib/libm/src/llroundf.c,v 1.1 2005/07/26 21:15:20 joerg Exp $ + */ + +#define LROUNDNAME llroundf +#define RESTYPE long long int +#define RESTYPE_MIN LLONG_MIN +#define RESTYPE_MAX LLONG_MAX + +#include "lroundf.c" diff --git a/lib/libm/src/lrint.c b/lib/libm/src/lrint.c new file mode 100644 index 0000000000..4869f211cb --- /dev/null +++ b/lib/libm/src/lrint.c @@ -0,0 +1,93 @@ +/*- + * Copyright (c) 2004 + * Matthias Drochner. All rights reserved. + * + * Redistribution and use in source and binary forms, with or without + * modification, are permitted provided that the following conditions + * are met: + * 1. Redistributions of source code must retain the above copyright + * notice, this list of conditions and the following disclaimer. + * 2. Redistributions in binary form must reproduce the above copyright + * notice, this list of conditions and the following disclaimer in the + * documentation and/or other materials provided with the distribution. + * + * THIS SOFTWARE IS PROVIDED BY THE AUTHOR AND CONTRIBUTORS ``AS IS'' AND + * ANY EXPRESS OR IMPLIED WARRANTIES, INCLUDING, BUT NOT LIMITED TO, THE + * IMPLIED WARRANTIES OF MERCHANTABILITY AND FITNESS FOR A PARTICULAR PURPOSE + * ARE DISCLAIMED. IN NO EVENT SHALL THE AUTHOR OR CONTRIBUTORS BE LIABLE + * FOR ANY DIRECT, INDIRECT, INCIDENTAL, SPECIAL, EXEMPLARY, OR CONSEQUENTIAL + * DAMAGES (INCLUDING, BUT NOT LIMITED TO, PROCUREMENT OF SUBSTITUTE GOODS + * OR SERVICES; LOSS OF USE, DATA, OR PROFITS; OR BUSINESS INTERRUPTION) + * HOWEVER CAUSED AND ON ANY THEORY OF LIABILITY, WHETHER IN CONTRACT, STRICT + * LIABILITY, OR TORT (INCLUDING NEGLIGENCE OR OTHERWISE) ARISING IN ANY WAY + * OUT OF THE USE OF THIS SOFTWARE, EVEN IF ADVISED OF THE POSSIBILITY OF + * SUCH DAMAGE. + * + * $NetBSD: lrint.c,v 1.3 2004/10/13 15:18:32 drochner Exp $ + * $DragonFly: src/lib/libm/src/lrint.c,v 1.1 2005/07/26 21:15:20 joerg Exp $ + */ + +#include +#include +#include +#include "math_private.h" + +#ifndef LRINTNAME +#define LRINTNAME lrint +#define RESTYPE long int +#define RESTYPE_MIN LONG_MIN +#define RESTYPE_MAX LONG_MAX +#endif + +#define RESTYPE_BITS (sizeof(RESTYPE) * 8) + +static const double +TWO52[2]={ + 4.50359962737049600000e+15, /* 0x43300000, 0x00000000 */ + -4.50359962737049600000e+15, /* 0xC3300000, 0x00000000 */ +}; + +RESTYPE +LRINTNAME(double x) +{ + u_int32_t i0, i1; + int e, s, shift; + RESTYPE res; + + GET_HIGH_WORD(i0, x); + e = i0 >> 20; + s = e >> DBL_EXPBITS; + e = (e & 0x7ff) - DBL_EXP_BIAS; + + /* 1.0 x 2^-1 is the smallest number which can be rounded to 1 */ + if (e < -1) + return (0); + /* 1.0 x 2^31 (or 2^63) is already too large */ + if (e >= (int)RESTYPE_BITS - 1) + return (s ? RESTYPE_MIN : RESTYPE_MAX); /* ??? unspecified */ + + /* >= 2^52 is already an exact integer */ + if (e < DBL_FRACBITS) { + /* round, using current direction */ + x += TWO52[s]; + x -= TWO52[s]; + } + + EXTRACT_WORDS(i0, i1, x); + e = ((i0 >> 20) & 0x7ff) - DBL_EXP_BIAS; + i0 &= 0xfffff; + i0 |= (1 << 20); + + shift = e - DBL_FRACBITS; + if (shift >=0) + res = (shift < 32 ? (RESTYPE)i1 << shift : 0); + else + res = (shift > -32 ? i1 >> -shift : 0); + shift += 32; + if (shift >=0) + res |= (shift < 32 ? (RESTYPE)i0 << shift : 0); + else + res |= (shift > -32 ? i0 >> -shift : 0); + + return (s ? -res : res); +} diff --git a/lib/libm/src/lrintf.c b/lib/libm/src/lrintf.c new file mode 100644 index 0000000000..e65b880d76 --- /dev/null +++ b/lib/libm/src/lrintf.c @@ -0,0 +1,88 @@ +/*- + * Copyright (c) 2004 + * Matthias Drochner. All rights reserved. + * + * Redistribution and use in source and binary forms, with or without + * modification, are permitted provided that the following conditions + * are met: + * 1. Redistributions of source code must retain the above copyright + * notice, this list of conditions and the following disclaimer. + * 2. Redistributions in binary form must reproduce the above copyright + * notice, this list of conditions and the following disclaimer in the + * documentation and/or other materials provided with the distribution. + * + * THIS SOFTWARE IS PROVIDED BY THE AUTHOR AND CONTRIBUTORS ``AS IS'' AND + * ANY EXPRESS OR IMPLIED WARRANTIES, INCLUDING, BUT NOT LIMITED TO, THE + * IMPLIED WARRANTIES OF MERCHANTABILITY AND FITNESS FOR A PARTICULAR PURPOSE + * ARE DISCLAIMED. IN NO EVENT SHALL THE AUTHOR OR CONTRIBUTORS BE LIABLE + * FOR ANY DIRECT, INDIRECT, INCIDENTAL, SPECIAL, EXEMPLARY, OR CONSEQUENTIAL + * DAMAGES (INCLUDING, BUT NOT LIMITED TO, PROCUREMENT OF SUBSTITUTE GOODS + * OR SERVICES; LOSS OF USE, DATA, OR PROFITS; OR BUSINESS INTERRUPTION) + * HOWEVER CAUSED AND ON ANY THEORY OF LIABILITY, WHETHER IN CONTRACT, STRICT + * LIABILITY, OR TORT (INCLUDING NEGLIGENCE OR OTHERWISE) ARISING IN ANY WAY + * OUT OF THE USE OF THIS SOFTWARE, EVEN IF ADVISED OF THE POSSIBILITY OF + * SUCH DAMAGE. + * + * $NetBSD: lrintf.c,v 1.3 2004/10/13 15:18:32 drochner Exp $ + * $DragonFly: src/lib/libm/src/lrintf.c,v 1.1 2005/07/26 21:15:20 joerg Exp $ + */ + +#include +#include +#include +#include "math_private.h" + +#ifndef LRINTNAME +#define LRINTNAME lrintf +#define RESTYPE long int +#define RESTYPE_MIN LONG_MIN +#define RESTYPE_MAX LONG_MAX +#endif + +#define RESTYPE_BITS (sizeof(RESTYPE) * 8) + +static const float +TWO23[2]={ + 8.3886080000e+06, /* 0x4b000000 */ + -8.3886080000e+06, /* 0xcb000000 */ +}; + +RESTYPE +LRINTNAME(float x) +{ + u_int32_t i0; + int e, s, shift; + RESTYPE res; + + GET_FLOAT_WORD(i0, x); + e = i0 >> SNG_FRACBITS; + s = e >> SNG_EXPBITS; + e = (e & 0xff) - SNG_EXP_BIAS; + + /* 1.0 x 2^-1 is the smallest number which can be rounded to 1 */ + if (e < -1) + return (0); + /* 1.0 x 2^31 (or 2^63) is already too large */ + if (e >= (int)RESTYPE_BITS - 1) + return (s ? RESTYPE_MIN : RESTYPE_MAX); /* ??? unspecified */ + + /* >= 2^23 is already an exact integer */ + if (e < SNG_FRACBITS) { + /* round, using current direction */ + x += TWO23[s]; + x -= TWO23[s]; + } + + GET_FLOAT_WORD(i0, x); + e = ((i0 >> SNG_FRACBITS) & 0xff) - SNG_EXP_BIAS; + i0 &= 0x7fffff; + i0 |= (1 << SNG_FRACBITS); + + shift = e - SNG_FRACBITS; + if (shift >=0) + res = (shift < 32 ? (RESTYPE)i0 << shift : 0); + else + res = (shift > -32 ? i0 >> -shift : 0); + + return (s ? -res : res); +} diff --git a/lib/libm/src/lround.c b/lib/libm/src/lround.c new file mode 100644 index 0000000000..c0b8885969 --- /dev/null +++ b/lib/libm/src/lround.c @@ -0,0 +1,86 @@ +/*- + * Copyright (c) 2004 + * Matthias Drochner. All rights reserved. + * + * Redistribution and use in source and binary forms, with or without + * modification, are permitted provided that the following conditions + * are met: + * 1. Redistributions of source code must retain the above copyright + * notice, this list of conditions and the following disclaimer. + * 2. Redistributions in binary form must reproduce the above copyright + * notice, this list of conditions and the following disclaimer in the + * documentation and/or other materials provided with the distribution. + * + * THIS SOFTWARE IS PROVIDED BY THE AUTHOR AND CONTRIBUTORS ``AS IS'' AND + * ANY EXPRESS OR IMPLIED WARRANTIES, INCLUDING, BUT NOT LIMITED TO, THE + * IMPLIED WARRANTIES OF MERCHANTABILITY AND FITNESS FOR A PARTICULAR PURPOSE + * ARE DISCLAIMED. IN NO EVENT SHALL THE AUTHOR OR CONTRIBUTORS BE LIABLE + * FOR ANY DIRECT, INDIRECT, INCIDENTAL, SPECIAL, EXEMPLARY, OR CONSEQUENTIAL + * DAMAGES (INCLUDING, BUT NOT LIMITED TO, PROCUREMENT OF SUBSTITUTE GOODS + * OR SERVICES; LOSS OF USE, DATA, OR PROFITS; OR BUSINESS INTERRUPTION) + * HOWEVER CAUSED AND ON ANY THEORY OF LIABILITY, WHETHER IN CONTRACT, STRICT + * LIABILITY, OR TORT (INCLUDING NEGLIGENCE OR OTHERWISE) ARISING IN ANY WAY + * OUT OF THE USE OF THIS SOFTWARE, EVEN IF ADVISED OF THE POSSIBILITY OF + * SUCH DAMAGE. + * + * $NetBSD: lround.c,v 1.2 2004/10/13 15:18:32 drochner Exp $ + * $DragonFly: src/lib/libm/src/lround.c,v 1.1 2005/07/26 21:15:20 joerg Exp $ + */ + +#include +#include +#include +#include "math_private.h" + +#ifndef LROUNDNAME +#define LROUNDNAME lround +#define RESTYPE long int +#define RESTYPE_MIN LONG_MIN +#define RESTYPE_MAX LONG_MAX +#endif + +#define RESTYPE_BITS (sizeof(RESTYPE) * 8) + +RESTYPE +LROUNDNAME(double x) +{ + u_int32_t i0, i1; + int e, s, shift; + RESTYPE res; + + GET_HIGH_WORD(i0, x); + e = i0 >> 20; + s = e >> DBL_EXPBITS; + e = (e & 0x7ff) - DBL_EXP_BIAS; + + /* 1.0 x 2^-1 is the smallest number which can be rounded to 1 */ + if (e < -1) + return (0); + /* 1.0 x 2^31 (or 2^63) is already too large */ + if (e >= (int)RESTYPE_BITS - 1) + return (s ? RESTYPE_MIN : RESTYPE_MAX); /* ??? unspecified */ + + /* >= 2^52 is already an exact integer */ + if (e < DBL_FRACBITS) { + /* add 0.5, extraction below will truncate */ + x += (s ? -0.5 : 0.5); + } + + EXTRACT_WORDS(i0, i1, x); + e = ((i0 >> 20) & 0x7ff) - DBL_EXP_BIAS; + i0 &= 0xfffff; + i0 |= (1 << 20); + + shift = e - DBL_FRACBITS; + if (shift >=0) + res = (shift < 32 ? (RESTYPE)i1 << shift : 0); + else + res = (shift > -32 ? i1 >> -shift : 0); + shift += 32; + if (shift >=0) + res |= (shift < 32 ? (RESTYPE)i0 << shift : 0); + else + res |= (shift > -32 ? i0 >> -shift : 0); + + return (s ? -res : res); +} diff --git a/lib/libm/src/lroundf.c b/lib/libm/src/lroundf.c new file mode 100644 index 0000000000..455de176b0 --- /dev/null +++ b/lib/libm/src/lroundf.c @@ -0,0 +1,81 @@ +/*- + * Copyright (c) 2004 + * Matthias Drochner. All rights reserved. + * + * Redistribution and use in source and binary forms, with or without + * modification, are permitted provided that the following conditions + * are met: + * 1. Redistributions of source code must retain the above copyright + * notice, this list of conditions and the following disclaimer. + * 2. Redistributions in binary form must reproduce the above copyright + * notice, this list of conditions and the following disclaimer in the + * documentation and/or other materials provided with the distribution. + * + * THIS SOFTWARE IS PROVIDED BY THE AUTHOR AND CONTRIBUTORS ``AS IS'' AND + * ANY EXPRESS OR IMPLIED WARRANTIES, INCLUDING, BUT NOT LIMITED TO, THE + * IMPLIED WARRANTIES OF MERCHANTABILITY AND FITNESS FOR A PARTICULAR PURPOSE + * ARE DISCLAIMED. IN NO EVENT SHALL THE AUTHOR OR CONTRIBUTORS BE LIABLE + * FOR ANY DIRECT, INDIRECT, INCIDENTAL, SPECIAL, EXEMPLARY, OR CONSEQUENTIAL + * DAMAGES (INCLUDING, BUT NOT LIMITED TO, PROCUREMENT OF SUBSTITUTE GOODS + * OR SERVICES; LOSS OF USE, DATA, OR PROFITS; OR BUSINESS INTERRUPTION) + * HOWEVER CAUSED AND ON ANY THEORY OF LIABILITY, WHETHER IN CONTRACT, STRICT + * LIABILITY, OR TORT (INCLUDING NEGLIGENCE OR OTHERWISE) ARISING IN ANY WAY + * OUT OF THE USE OF THIS SOFTWARE, EVEN IF ADVISED OF THE POSSIBILITY OF + * SUCH DAMAGE. + * + * $NetBSD: lroundf.c,v 1.2 2004/10/13 15:18:32 drochner Exp $ + * $DragonFly: src/lib/libm/src/lroundf.c,v 1.1 2005/07/26 21:15:20 joerg Exp $ + */ + +#include +#include +#include +#include "math_private.h" + +#ifndef LROUNDNAME +#define LROUNDNAME lroundf +#define RESTYPE long int +#define RESTYPE_MIN LONG_MIN +#define RESTYPE_MAX LONG_MAX +#endif + +#define RESTYPE_BITS (sizeof(RESTYPE) * 8) + +RESTYPE +LROUNDNAME(float x) +{ + u_int32_t i0; + int e, s, shift; + RESTYPE res; + + GET_FLOAT_WORD(i0, x); + e = i0 >> SNG_FRACBITS; + s = e >> SNG_EXPBITS; + e = (e & 0xff) - SNG_EXP_BIAS; + + /* 1.0 x 2^-1 is the smallest number which can be rounded to 1 */ + if (e < -1) + return (0); + /* 1.0 x 2^31 (or 2^63) is already too large */ + if (e >= (int)RESTYPE_BITS - 1) + return (s ? RESTYPE_MIN : RESTYPE_MAX); /* ??? unspecified */ + + /* >= 2^23 is already an exact integer */ + if (e < SNG_FRACBITS) { + /* add 0.5, extraction below will truncate */ + x += (s ? -0.5 : 0.5); + } + + GET_FLOAT_WORD(i0, x); + e = ((i0 >> SNG_FRACBITS) & 0xff) - SNG_EXP_BIAS; + i0 &= 0x7fffff; + i0 |= (1 << SNG_FRACBITS); + + shift = e - SNG_FRACBITS; + if (shift >=0) + res = (shift < 32 ? (RESTYPE)i0 << shift : 0); + else + res = (shift > -32 ? i0 >> -shift : 0); + + return (s ? -res : res); +} diff --git a/lib/libm/src/math_private.h b/lib/libm/src/math_private.h new file mode 100644 index 0000000000..675a9c5b6b --- /dev/null +++ b/lib/libm/src/math_private.h @@ -0,0 +1,181 @@ +/* + * ==================================================== + * Copyright (C) 1993 by Sun Microsystems, Inc. All rights reserved. + * + * Developed at SunPro, a Sun Microsystems, Inc. business. + * Permission to use, copy, modify, and distribute this + * software is freely granted, provided that this notice + * is preserved. + * ==================================================== + */ + +/* + * from: @(#)fdlibm.h 5.1 93/09/24 + * $NetBSD: math_private.h,v 1.11 2001/02/21 18:09:26 bjh21 Exp $ + * $DragonFly: src/lib/libm/src/math_private.h,v 1.1 2005/07/26 21:15:20 joerg Exp $ + */ + +#ifndef _MATH_PRIVATE_H_ +#define _MATH_PRIVATE_H_ + +#include + +/* The original fdlibm code used statements like: + n0 = ((*(int*)&one)>>29)^1; * index of high word * + ix0 = *(n0+(int*)&x); * high word of x * + ix1 = *((1-n0)+(int*)&x); * low word of x * + to dig two 32 bit words out of the 64 bit IEEE floating point + value. That is non-ANSI, and, moreover, the gcc instruction + scheduler gets it wrong. We instead use the following macros. + Unlike the original code, we determine the endianness at compile + time, not at run time; I don't see much benefit to selecting + endianness at run time. */ + +/* A union which permits us to convert between a double and two 32 bit + ints. */ + +/* + * The ARM ports are little endian except for the FPA word order which is + * big endian. + */ + +#if (BYTE_ORDER == BIG_ENDIAN) || (defined(__arm__) && !defined(__VFP_FP__)) + +typedef union +{ + double value; + struct + { + u_int32_t msw; + u_int32_t lsw; + } parts; +} ieee_double_shape_type; + +#endif + +#if (BYTE_ORDER == LITTLE_ENDIAN) && \ + !(defined(__arm__) && !defined(__VFP_FP__)) + +typedef union +{ + double value; + struct + { + u_int32_t lsw; + u_int32_t msw; + } parts; +} ieee_double_shape_type; + +#endif + +/* Get two 32 bit ints from a double. */ + +#define EXTRACT_WORDS(ix0,ix1,d) \ +do { \ + ieee_double_shape_type ew_u; \ + ew_u.value = (d); \ + (ix0) = ew_u.parts.msw; \ + (ix1) = ew_u.parts.lsw; \ +} while (0) + +/* Get the more significant 32 bit int from a double. */ + +#define GET_HIGH_WORD(i,d) \ +do { \ + ieee_double_shape_type gh_u; \ + gh_u.value = (d); \ + (i) = gh_u.parts.msw; \ +} while (0) + +/* Get the less significant 32 bit int from a double. */ + +#define GET_LOW_WORD(i,d) \ +do { \ + ieee_double_shape_type gl_u; \ + gl_u.value = (d); \ + (i) = gl_u.parts.lsw; \ +} while (0) + +/* Set a double from two 32 bit ints. */ + +#define INSERT_WORDS(d,ix0,ix1) \ +do { \ + ieee_double_shape_type iw_u; \ + iw_u.parts.msw = (ix0); \ + iw_u.parts.lsw = (ix1); \ + (d) = iw_u.value; \ +} while (0) + +/* Set the more significant 32 bits of a double from an int. */ + +#define SET_HIGH_WORD(d,v) \ +do { \ + ieee_double_shape_type sh_u; \ + sh_u.value = (d); \ + sh_u.parts.msw = (v); \ + (d) = sh_u.value; \ +} while (0) + +/* Set the less significant 32 bits of a double from an int. */ + +#define SET_LOW_WORD(d,v) \ +do { \ + ieee_double_shape_type sl_u; \ + sl_u.value = (d); \ + sl_u.parts.lsw = (v); \ + (d) = sl_u.value; \ +} while (0) + +/* A union which permits us to convert between a float and a 32 bit + int. */ + +typedef union +{ + float value; + u_int32_t word; +} ieee_float_shape_type; + +/* Get a 32 bit int from a float. */ + +#define GET_FLOAT_WORD(i,d) \ +do { \ + ieee_float_shape_type gf_u; \ + gf_u.value = (d); \ + (i) = gf_u.word; \ +} while (0) + +/* Set a float from a 32 bit int. */ + +#define SET_FLOAT_WORD(d,i) \ +do { \ + ieee_float_shape_type sf_u; \ + sf_u.word = (i); \ + (d) = sf_u.value; \ +} while (0) + +__BEGIN_DECLS +#pragma GCC visibility push(hidden) + +/* ieee style elementary functions */ +int __libm_rem_pio2(double, double*); + +/* fdlibm kernel function */ +double __kernel_sin(double, double, int); +double __kernel_cos(double, double); +double __kernel_tan(double, double, int); +int __kernel_rem_pio2(double*, double*, int, int, int, const int*); + + +/* ieee style elementary float functions */ +int __libm_rem_pio2f(float,float*); + +/* float versions of fdlibm kernel functions */ +float __kernel_sinf(float, float, int); +float __kernel_cosf(float, float); +float __kernel_tanf(float, float, int); +int __kernel_rem_pio2f(float*, float*, int, int, int, const int*); + +#pragma GCC visibility pop +__END_DECLS + +#endif /* _MATH_PRIVATE_H_ */ diff --git a/lib/libm/src/s_asinh.c b/lib/libm/src/s_asinh.c new file mode 100644 index 0000000000..02f3ad1c02 --- /dev/null +++ b/lib/libm/src/s_asinh.c @@ -0,0 +1,56 @@ +/* @(#)s_asinh.c 5.1 93/09/24 */ +/* + * ==================================================== + * Copyright (C) 1993 by Sun Microsystems, Inc. All rights reserved. + * + * Developed at SunPro, a Sun Microsystems, Inc. business. + * Permission to use, copy, modify, and distribute this + * software is freely granted, provided that this notice + * is preserved. + * ==================================================== + * + * $NetBSD: s_asinh.c,v 1.12 2002/05/26 22:01:54 wiz Exp $ + * $DragonFly: src/lib/libm/src/s_asinh.c,v 1.1 2005/07/26 21:15:20 joerg Exp $ + */ + +/* asinh(x) + * Method : + * Based on + * asinh(x) = sign(x) * log [ |x| + sqrt(x*x+1) ] + * we have + * asinh(x) := x if 1+x*x=1, + * := sign(x)*(log(x)+ln2)) for large |x|, else + * := sign(x)*log(2|x|+1/(|x|+sqrt(x*x+1))) if|x|>2, else + * := sign(x)*log1p(|x| + x^2/(1 + sqrt(1+x^2))) + */ + +#include +#include "math_private.h" + +static const double +one = 1.00000000000000000000e+00, /* 0x3FF00000, 0x00000000 */ +ln2 = 6.93147180559945286227e-01, /* 0x3FE62E42, 0xFEFA39EF */ +huge= 1.00000000000000000000e+300; + +double +asinh(double x) +{ + double t,w; + int32_t hx,ix; + GET_HIGH_WORD(hx,x); + ix = hx&0x7fffffff; + if(ix>=0x7ff00000) return x+x; /* x is inf or NaN */ + if(ix< 0x3e300000) { /* |x|<2**-28 */ + if(huge+x>one) return x; /* return x inexact except 0 */ + } + if(ix>0x41b00000) { /* |x| > 2**28 */ + w = log(fabs(x))+ln2; + } else if (ix>0x40000000) { /* 2**28 > |x| > 2.0 */ + t = fabs(x); + w = log(2.0*t+one/(sqrt(x*x+one)+t)); + } else { /* 2.0 > |x| > 2**-28 */ + t = x*x; + w =log1p(fabs(x)+t/(one+sqrt(one+t))); + } + if(hx>0) return w; else return -w; +} diff --git a/lib/libm/src/s_asinhf.c b/lib/libm/src/s_asinhf.c new file mode 100644 index 0000000000..5908cd816f --- /dev/null +++ b/lib/libm/src/s_asinhf.c @@ -0,0 +1,48 @@ +/* s_asinhf.c -- float version of s_asinh.c. + * Conversion to float by Ian Lance Taylor, Cygnus Support, ian@cygnus.com. + */ + +/* + * ==================================================== + * Copyright (C) 1993 by Sun Microsystems, Inc. All rights reserved. + * + * Developed at SunPro, a Sun Microsystems, Inc. business. + * Permission to use, copy, modify, and distribute this + * software is freely granted, provided that this notice + * is preserved. + * ==================================================== + * + * $NetBSD: s_asinhf.c,v 1.8 2002/05/26 22:01:54 wiz Exp $ + * $DragonFly: src/lib/libm/src/s_asinhf.c,v 1.1 2005/07/26 21:15:20 joerg Exp $ + */ + +#include +#include "math_private.h" + +static const float +one = 1.0000000000e+00, /* 0x3F800000 */ +ln2 = 6.9314718246e-01, /* 0x3f317218 */ +huge= 1.0000000000e+30; + +float +asinhf(float x) +{ + float t,w; + int32_t hx,ix; + GET_FLOAT_WORD(hx,x); + ix = hx&0x7fffffff; + if(ix>=0x7f800000) return x+x; /* x is inf or NaN */ + if(ix< 0x31800000) { /* |x|<2**-28 */ + if(huge+x>one) return x; /* return x inexact except 0 */ + } + if(ix>0x4d800000) { /* |x| > 2**28 */ + w = logf(fabsf(x))+ln2; + } else if (ix>0x40000000) { /* 2**28 > |x| > 2.0 */ + t = fabsf(x); + w = logf((float)2.0*t+one/(sqrtf(x*x+one)+t)); + } else { /* 2.0 > |x| > 2**-28 */ + t = x*x; + w =log1pf(fabsf(x)+t/(one+sqrtf(one+t))); + } + if(hx>0) return w; else return -w; +} diff --git a/lib/libm/src/s_atan.c b/lib/libm/src/s_atan.c new file mode 100644 index 0000000000..cceeeb09e9 --- /dev/null +++ b/lib/libm/src/s_atan.c @@ -0,0 +1,118 @@ +/* @(#)s_atan.c 5.1 93/09/24 */ +/* + * ==================================================== + * Copyright (C) 1993 by Sun Microsystems, Inc. All rights reserved. + * + * Developed at SunPro, a Sun Microsystems, Inc. business. + * Permission to use, copy, modify, and distribute this + * software is freely granted, provided that this notice + * is preserved. + * ==================================================== + * + * $NetBSD: s_atan.c,v 1.11 2002/05/26 22:01:54 wiz Exp $ + * $DragonFly: src/lib/libm/src/s_atan.c,v 1.1 2005/07/26 21:15:20 joerg Exp $ + */ + +/* atan(x) + * Method + * 1. Reduce x to positive by atan(x) = -atan(-x). + * 2. According to the integer k=4t+0.25 chopped, t=x, the argument + * is further reduced to one of the following intervals and the + * arctangent of t is evaluated by the corresponding formula: + * + * [0,7/16] atan(x) = t-t^3*(a1+t^2*(a2+...(a10+t^2*a11)...) + * [7/16,11/16] atan(x) = atan(1/2) + atan( (t-0.5)/(1+t/2) ) + * [11/16.19/16] atan(x) = atan( 1 ) + atan( (t-1)/(1+t) ) + * [19/16,39/16] atan(x) = atan(3/2) + atan( (t-1.5)/(1+1.5t) ) + * [39/16,INF] atan(x) = atan(INF) + atan( -1/t ) + * + * Constants: + * The hexadecimal values are the intended ones for the following + * constants. The decimal values may be used, provided that the + * compiler will convert from decimal to binary accurately enough + * to produce the hexadecimal values shown. + */ + +#include +#include "math_private.h" + +static const double atanhi[] = { + 4.63647609000806093515e-01, /* atan(0.5)hi 0x3FDDAC67, 0x0561BB4F */ + 7.85398163397448278999e-01, /* atan(1.0)hi 0x3FE921FB, 0x54442D18 */ + 9.82793723247329054082e-01, /* atan(1.5)hi 0x3FEF730B, 0xD281F69B */ + 1.57079632679489655800e+00, /* atan(inf)hi 0x3FF921FB, 0x54442D18 */ +}; + +static const double atanlo[] = { + 2.26987774529616870924e-17, /* atan(0.5)lo 0x3C7A2B7F, 0x222F65E2 */ + 3.06161699786838301793e-17, /* atan(1.0)lo 0x3C81A626, 0x33145C07 */ + 1.39033110312309984516e-17, /* atan(1.5)lo 0x3C700788, 0x7AF0CBBD */ + 6.12323399573676603587e-17, /* atan(inf)lo 0x3C91A626, 0x33145C07 */ +}; + +static const double aT[] = { + 3.33333333333329318027e-01, /* 0x3FD55555, 0x5555550D */ + -1.99999999998764832476e-01, /* 0xBFC99999, 0x9998EBC4 */ + 1.42857142725034663711e-01, /* 0x3FC24924, 0x920083FF */ + -1.11111104054623557880e-01, /* 0xBFBC71C6, 0xFE231671 */ + 9.09088713343650656196e-02, /* 0x3FB745CD, 0xC54C206E */ + -7.69187620504482999495e-02, /* 0xBFB3B0F2, 0xAF749A6D */ + 6.66107313738753120669e-02, /* 0x3FB10D66, 0xA0D03D51 */ + -5.83357013379057348645e-02, /* 0xBFADDE2D, 0x52DEFD9A */ + 4.97687799461593236017e-02, /* 0x3FA97B4B, 0x24760DEB */ + -3.65315727442169155270e-02, /* 0xBFA2B444, 0x2C6A6C2F */ + 1.62858201153657823623e-02, /* 0x3F90AD3A, 0xE322DA11 */ +}; + + static const double +one = 1.0, +huge = 1.0e300; + +double +atan(double x) +{ + double w,s1,s2,z; + int32_t ix,hx,id; + + GET_HIGH_WORD(hx,x); + ix = hx&0x7fffffff; + if(ix>=0x44100000) { /* if |x| >= 2^66 */ + u_int32_t low; + GET_LOW_WORD(low,x); + if(ix>0x7ff00000|| + (ix==0x7ff00000&&(low!=0))) + return x+x; /* NaN */ + if(hx>0) return atanhi[3]+atanlo[3]; + else return -atanhi[3]-atanlo[3]; + } if (ix < 0x3fdc0000) { /* |x| < 0.4375 */ + if (ix < 0x3e200000) { /* |x| < 2^-29 */ + if(huge+x>one) return x; /* raise inexact */ + } + id = -1; + } else { + x = fabs(x); + if (ix < 0x3ff30000) { /* |x| < 1.1875 */ + if (ix < 0x3fe60000) { /* 7/16 <=|x|<11/16 */ + id = 0; x = (2.0*x-one)/(2.0+x); + } else { /* 11/16<=|x|< 19/16 */ + id = 1; x = (x-one)/(x+one); + } + } else { + if (ix < 0x40038000) { /* |x| < 2.4375 */ + id = 2; x = (x-1.5)/(one+1.5*x); + } else { /* 2.4375 <= |x| < 2^66 */ + id = 3; x = -1.0/x; + } + }} + /* end of argument reduction */ + z = x*x; + w = z*z; + /* break sum from i=0 to 10 aT[i]z**(i+1) into odd and even poly */ + s1 = z*(aT[0]+w*(aT[2]+w*(aT[4]+w*(aT[6]+w*(aT[8]+w*aT[10]))))); + s2 = w*(aT[1]+w*(aT[3]+w*(aT[5]+w*(aT[7]+w*aT[9])))); + if (id<0) return x - x*(s1+s2); + else { + z = atanhi[id] - ((x*(s1+s2) - atanlo[id]) - x); + return (hx<0)? -z:z; + } +} diff --git a/lib/libm/src/s_atanf.c b/lib/libm/src/s_atanf.c new file mode 100644 index 0000000000..573d5cdb3c --- /dev/null +++ b/lib/libm/src/s_atanf.c @@ -0,0 +1,98 @@ +/* s_atanf.c -- float version of s_atan.c. + * Conversion to float by Ian Lance Taylor, Cygnus Support, ian@cygnus.com. + */ + +/* + * ==================================================== + * Copyright (C) 1993 by Sun Microsystems, Inc. All rights reserved. + * + * Developed at SunPro, a Sun Microsystems, Inc. business. + * Permission to use, copy, modify, and distribute this + * software is freely granted, provided that this notice + * is preserved. + * ==================================================== + * + * $NetBSD: s_atanf.c,v 1.7 2002/05/26 22:01:54 wiz Exp $ + * $DragonFly: src/lib/libm/src/s_atanf.c,v 1.1 2005/07/26 21:15:20 joerg Exp $ + */ + +#include +#include "math_private.h" + +static const float atanhi[] = { + 4.6364760399e-01, /* atan(0.5)hi 0x3eed6338 */ + 7.8539812565e-01, /* atan(1.0)hi 0x3f490fda */ + 9.8279368877e-01, /* atan(1.5)hi 0x3f7b985e */ + 1.5707962513e+00, /* atan(inf)hi 0x3fc90fda */ +}; + +static const float atanlo[] = { + 5.0121582440e-09, /* atan(0.5)lo 0x31ac3769 */ + 3.7748947079e-08, /* atan(1.0)lo 0x33222168 */ + 3.4473217170e-08, /* atan(1.5)lo 0x33140fb4 */ + 7.5497894159e-08, /* atan(inf)lo 0x33a22168 */ +}; + +static const float aT[] = { + 3.3333334327e-01, /* 0x3eaaaaaa */ + -2.0000000298e-01, /* 0xbe4ccccd */ + 1.4285714924e-01, /* 0x3e124925 */ + -1.1111110449e-01, /* 0xbde38e38 */ + 9.0908870101e-02, /* 0x3dba2e6e */ + -7.6918758452e-02, /* 0xbd9d8795 */ + 6.6610731184e-02, /* 0x3d886b35 */ + -5.8335702866e-02, /* 0xbd6ef16b */ + 4.9768779427e-02, /* 0x3d4bda59 */ + -3.6531571299e-02, /* 0xbd15a221 */ + 1.6285819933e-02, /* 0x3c8569d7 */ +}; + +static const float +one = 1.0, +huge = 1.0e30; + +float +atanf(float x) +{ + float w,s1,s2,z; + int32_t ix,hx,id; + + GET_FLOAT_WORD(hx,x); + ix = hx&0x7fffffff; + if(ix>=0x50800000) { /* if |x| >= 2^34 */ + if(ix>0x7f800000) + return x+x; /* NaN */ + if(hx>0) return atanhi[3]+atanlo[3]; + else return -atanhi[3]-atanlo[3]; + } if (ix < 0x3ee00000) { /* |x| < 0.4375 */ + if (ix < 0x31000000) { /* |x| < 2^-29 */ + if(huge+x>one) return x; /* raise inexact */ + } + id = -1; + } else { + x = fabsf(x); + if (ix < 0x3f980000) { /* |x| < 1.1875 */ + if (ix < 0x3f300000) { /* 7/16 <=|x|<11/16 */ + id = 0; x = ((float)2.0*x-one)/((float)2.0+x); + } else { /* 11/16<=|x|< 19/16 */ + id = 1; x = (x-one)/(x+one); + } + } else { + if (ix < 0x401c0000) { /* |x| < 2.4375 */ + id = 2; x = (x-(float)1.5)/(one+(float)1.5*x); + } else { /* 2.4375 <= |x| < 2^66 */ + id = 3; x = -(float)1.0/x; + } + }} + /* end of argument reduction */ + z = x*x; + w = z*z; + /* break sum from i=0 to 10 aT[i]z**(i+1) into odd and even poly */ + s1 = z*(aT[0]+w*(aT[2]+w*(aT[4]+w*(aT[6]+w*(aT[8]+w*aT[10]))))); + s2 = w*(aT[1]+w*(aT[3]+w*(aT[5]+w*(aT[7]+w*aT[9])))); + if (id<0) return x - x*(s1+s2); + else { + z = atanhi[id] - ((x*(s1+s2) - atanlo[id]) - x); + return (hx<0)? -z:z; + } +} diff --git a/lib/libm/src/s_cbrt.c b/lib/libm/src/s_cbrt.c new file mode 100644 index 0000000000..afe8fb8dd8 --- /dev/null +++ b/lib/libm/src/s_cbrt.c @@ -0,0 +1,80 @@ +/* @(#)s_cbrt.c 5.1 93/09/24 */ +/* + * ==================================================== + * Copyright (C) 1993 by Sun Microsystems, Inc. All rights reserved. + * + * Developed at SunPro, a Sun Microsystems, Inc. business. + * Permission to use, copy, modify, and distribute this + * software is freely granted, provided that this notice + * is preserved. + * ==================================================== + * + * $NetBSD: s_cbrt.c,v 1.11 2002/05/26 22:01:54 wiz Exp $ + * $DragonFly: src/lib/libm/src/s_cbrt.c,v 1.1 2005/07/26 21:15:20 joerg Exp $ + */ + +#include +#include "math_private.h" + +/* cbrt(x) + * Return cube root of x + */ +static const u_int32_t + B1 = 715094163, /* B1 = (682-0.03306235651)*2**20 */ + B2 = 696219795; /* B2 = (664-0.03306235651)*2**20 */ + +static const double +C = 5.42857142857142815906e-01, /* 19/35 = 0x3FE15F15, 0xF15F15F1 */ +D = -7.05306122448979611050e-01, /* -864/1225 = 0xBFE691DE, 0x2532C834 */ +E = 1.41428571428571436819e+00, /* 99/70 = 0x3FF6A0EA, 0x0EA0EA0F */ +F = 1.60714285714285720630e+00, /* 45/28 = 0x3FF9B6DB, 0x6DB6DB6E */ +G = 3.57142857142857150787e-01; /* 5/14 = 0x3FD6DB6D, 0xB6DB6DB7 */ + +double +cbrt(double x) +{ + int32_t hx; + double r,s,t=0.0,w; + u_int32_t sign; + u_int32_t high,low; + + GET_HIGH_WORD(hx,x); + sign=hx&0x80000000; /* sign= sign(x) */ + hx ^=sign; + if(hx>=0x7ff00000) return(x+x); /* cbrt(NaN,INF) is itself */ + GET_LOW_WORD(low,x); + if((hx|low)==0) + return(x); /* cbrt(0) is itself */ + + SET_HIGH_WORD(x,hx); /* x <- |x| */ + /* rough cbrt to 5 bits */ + if(hx<0x00100000) /* subnormal number */ + {SET_HIGH_WORD(t,0x43500000); /* set t= 2**54 */ + t*=x; GET_HIGH_WORD(high,t); SET_HIGH_WORD(t,high/3+B2); + } + else + SET_HIGH_WORD(t,hx/3+B1); + + + /* new cbrt to 23 bits, may be implemented in single precision */ + r=t*t/x; + s=C+r*t; + t*=G+F/(s+E+D/s); + + /* chopped to 20 bits and make it larger than cbrt(x) */ + GET_HIGH_WORD(high,t); + INSERT_WORDS(t,high+0x00000001,0); + + + /* one step newton iteration to 53 bits with error less than 0.667 ulps */ + s=t*t; /* t*t is exact */ + r=x/s; + w=t+t; + r=(r-t)/(w+r); /* r-s is exact */ + t=t+t*r; + + /* retore the sign bit */ + GET_HIGH_WORD(high,t); + SET_HIGH_WORD(t,high|sign); + return(t); +} diff --git a/lib/libm/src/s_cbrtf.c b/lib/libm/src/s_cbrtf.c new file mode 100644 index 0000000000..e2d43a6227 --- /dev/null +++ b/lib/libm/src/s_cbrtf.c @@ -0,0 +1,70 @@ +/* s_cbrtf.c -- float version of s_cbrt.c. + * Conversion to float by Ian Lance Taylor, Cygnus Support, ian@cygnus.com. + */ + +/* + * ==================================================== + * Copyright (C) 1993 by Sun Microsystems, Inc. All rights reserved. + * + * Developed at SunPro, a Sun Microsystems, Inc. business. + * Permission to use, copy, modify, and distribute this + * software is freely granted, provided that this notice + * is preserved. + * ==================================================== + * + * $NetBSD: s_cbrtf.c,v 1.7 2002/05/26 22:01:54 wiz Exp $ + * $DragonFly: src/lib/libm/src/s_cbrtf.c,v 1.1 2005/07/26 21:15:20 joerg Exp $ + */ + +#include +#include "math_private.h" + +/* cbrtf(x) + * Return cube root of x + */ +static const unsigned + B1 = 709958130, /* B1 = (84+2/3-0.03306235651)*2**23 */ + B2 = 642849266; /* B2 = (76+2/3-0.03306235651)*2**23 */ + +static const float +C = 5.4285717010e-01, /* 19/35 = 0x3f0af8b0 */ +D = -7.0530611277e-01, /* -864/1225 = 0xbf348ef1 */ +E = 1.4142856598e+00, /* 99/70 = 0x3fb50750 */ +F = 1.6071428061e+00, /* 45/28 = 0x3fcdb6db */ +G = 3.5714286566e-01; /* 5/14 = 0x3eb6db6e */ + +float +cbrtf(float x) +{ + float r,s,t; + int32_t hx; + u_int32_t sign; + u_int32_t high; + + GET_FLOAT_WORD(hx,x); + sign=hx&0x80000000; /* sign= sign(x) */ + hx ^=sign; + if(hx>=0x7f800000) return(x+x); /* cbrt(NaN,INF) is itself */ + if(hx==0) + return(x); /* cbrt(0) is itself */ + + SET_FLOAT_WORD(x,hx); /* x <- |x| */ + /* rough cbrt to 5 bits */ + if(hx<0x00800000) /* subnormal number */ + {SET_FLOAT_WORD(t,0x4b800000); /* set t= 2**24 */ + t*=x; GET_FLOAT_WORD(high,t); SET_FLOAT_WORD(t,high/3+B2); + } + else + SET_FLOAT_WORD(t,hx/3+B1); + + + /* new cbrt to 23 bits */ + r=t*t/x; + s=C+r*t; + t*=G+F/(s+E+D/s); + + /* retore the sign bit */ + GET_FLOAT_WORD(high,t); + SET_FLOAT_WORD(t,high|sign); + return(t); +} diff --git a/lib/libm/src/s_ceil.c b/lib/libm/src/s_ceil.c new file mode 100644 index 0000000000..0453476218 --- /dev/null +++ b/lib/libm/src/s_ceil.c @@ -0,0 +1,71 @@ +/* @(#)s_ceil.c 5.1 93/09/24 */ +/* + * ==================================================== + * Copyright (C) 1993 by Sun Microsystems, Inc. All rights reserved. + * + * Developed at SunPro, a Sun Microsystems, Inc. business. + * Permission to use, copy, modify, and distribute this + * software is freely granted, provided that this notice + * is preserved. + * ==================================================== + * + * $NetBSD: s_ceil.c,v 1.11 2002/05/26 22:01:54 wiz Exp $ + * $DragonFly: src/lib/libm/src/s_ceil.c,v 1.1 2005/07/26 21:15:20 joerg Exp $ + */ + +/* + * ceil(x) + * Return x rounded toward -inf to integral value + * Method: + * Bit twiddling. + * Exception: + * Inexact flag raised if x not equal to ceil(x). + */ + +#include +#include "math_private.h" + +static const double huge = 1.0e300; + +double +ceil(double x) +{ + int32_t i0,i1,j0; + u_int32_t i,j; + EXTRACT_WORDS(i0,i1,x); + j0 = ((i0>>20)&0x7ff)-0x3ff; + if(j0<20) { + if(j0<0) { /* raise inexact if x != 0 */ + if(huge+x>0.0) {/* return 0*sign(x) if |x|<1 */ + if(i0<0) {i0=0x80000000;i1=0;} + else if((i0|i1)!=0) { i0=0x3ff00000;i1=0;} + } + } else { + i = (0x000fffff)>>j0; + if(((i0&i)|i1)==0) return x; /* x is integral */ + if(huge+x>0.0) { /* raise inexact flag */ + if(i0>0) i0 += (0x00100000)>>j0; + i0 &= (~i); i1=0; + } + } + } else if (j0>51) { + if(j0==0x400) return x+x; /* inf or NaN */ + else return x; /* x is integral */ + } else { + i = ((u_int32_t)(0xffffffff))>>(j0-20); + if((i1&i)==0) return x; /* x is integral */ + if(huge+x>0.0) { /* raise inexact flag */ + if(i0>0) { + if(j0==20) i0+=1; + else { + j = i1 + (1<<(52-j0)); + if(j +#include "math_private.h" + +static const float huge = 1.0e30; + +float +ceilf(float x) +{ + int32_t i0,j0; + u_int32_t i; + + GET_FLOAT_WORD(i0,x); + j0 = ((i0>>23)&0xff)-0x7f; + if(j0<23) { + if(j0<0) { /* raise inexact if x != 0 */ + if(huge+x>(float)0.0) {/* return 0*sign(x) if |x|<1 */ + if(i0<0) {i0=0x80000000;} + else if(i0!=0) { i0=0x3f800000;} + } + } else { + i = (0x007fffff)>>j0; + if((i0&i)==0) return x; /* x is integral */ + if(huge+x>(float)0.0) { /* raise inexact flag */ + if(i0>0) i0 += (0x00800000)>>j0; + i0 &= (~i); + } + } + } else { + if(j0==0x80) return x+x; /* inf or NaN */ + else return x; /* x is integral */ + } + SET_FLOAT_WORD(x,i0); + return x; +} diff --git a/lib/libm/src/s_copysign.c b/lib/libm/src/s_copysign.c new file mode 100644 index 0000000000..475c221051 --- /dev/null +++ b/lib/libm/src/s_copysign.c @@ -0,0 +1,33 @@ +/* @(#)s_copysign.c 5.1 93/09/24 */ +/* + * ==================================================== + * Copyright (C) 1993 by Sun Microsystems, Inc. All rights reserved. + * + * Developed at SunPro, a Sun Microsystems, Inc. business. + * Permission to use, copy, modify, and distribute this + * software is freely granted, provided that this notice + * is preserved. + * ==================================================== + * + * $NetBSD: s_copysign.c,v 1.11 2002/05/26 22:01:54 wiz Exp $ + * $DragonFly: src/lib/libm/src/s_copysign.c,v 1.1 2005/07/26 21:15:20 joerg Exp $ + */ + +/* + * copysign(double x, double y) + * copysign(x,y) returns a value with the magnitude of x and + * with the sign bit of y. + */ + +#include +#include "math_private.h" + +double +copysign(double x, double y) +{ + u_int32_t hx,hy; + GET_HIGH_WORD(hx,x); + GET_HIGH_WORD(hy,y); + SET_HIGH_WORD(x,(hx&0x7fffffff)|(hy&0x80000000)); + return x; +} diff --git a/lib/libm/src/s_copysignf.c b/lib/libm/src/s_copysignf.c new file mode 100644 index 0000000000..0880dbe66d --- /dev/null +++ b/lib/libm/src/s_copysignf.c @@ -0,0 +1,36 @@ +/* s_copysignf.c -- float version of s_copysign.c. + * Conversion to float by Ian Lance Taylor, Cygnus Support, ian@cygnus.com. + */ + +/* + * ==================================================== + * Copyright (C) 1993 by Sun Microsystems, Inc. All rights reserved. + * + * Developed at SunPro, a Sun Microsystems, Inc. business. + * Permission to use, copy, modify, and distribute this + * software is freely granted, provided that this notice + * is preserved. + * ==================================================== + * + * $NetBSD: s_copysignf.c,v 1.7 2002/05/26 22:01:54 wiz Exp $ + * $DragonFly: src/lib/libm/src/s_copysignf.c,v 1.1 2005/07/26 21:15:20 joerg Exp $ + */ + +/* + * copysignf(float x, float y) + * copysignf(x,y) returns a value with the magnitude of x and + * with the sign bit of y. + */ + +#include +#include "math_private.h" + +float +copysignf(float x, float y) +{ + u_int32_t ix,iy; + GET_FLOAT_WORD(ix,x); + GET_FLOAT_WORD(iy,y); + SET_FLOAT_WORD(x,(ix&0x7fffffff)|(iy&0x80000000)); + return x; +} diff --git a/lib/libm/src/s_cos.c b/lib/libm/src/s_cos.c new file mode 100644 index 0000000000..629a66e8fd --- /dev/null +++ b/lib/libm/src/s_cos.c @@ -0,0 +1,77 @@ +/* @(#)s_cos.c 5.1 93/09/24 */ +/* + * ==================================================== + * Copyright (C) 1993 by Sun Microsystems, Inc. All rights reserved. + * + * Developed at SunPro, a Sun Microsystems, Inc. business. + * Permission to use, copy, modify, and distribute this + * software is freely granted, provided that this notice + * is preserved. + * ==================================================== + * + * $NetBSD: s_cos.c,v 1.10 2002/05/26 22:01:54 wiz Exp $ + * $DragonFly: src/lib/libm/src/s_cos.c,v 1.1 2005/07/26 21:15:20 joerg Exp $ + */ + +/* cos(x) + * Return cosine function of x. + * + * kernel function: + * __kernel_sin ... sine function on [-pi/4,pi/4] + * __kernel_cos ... cosine function on [-pi/4,pi/4] + * __libm_rem_pio2 ... argument reduction routine + * + * Method. + * Let S,C and T denote the sin, cos and tan respectively on + * [-PI/4, +PI/4]. Reduce the argument x to y1+y2 = x-k*pi/2 + * in [-pi/4 , +pi/4], and let n = k mod 4. + * We have + * + * n sin(x) cos(x) tan(x) + * ---------------------------------------------------------- + * 0 S C T + * 1 C -S -1/T + * 2 -S -C T + * 3 -C S -1/T + * ---------------------------------------------------------- + * + * Special cases: + * Let trig be any of sin, cos, or tan. + * trig(+-INF) is NaN, with signals; + * trig(NaN) is that NaN; + * + * Accuracy: + * TRIG(x) returns trig(x) nearly rounded + */ + +#include +#include "math_private.h" + +double +cos(double x) +{ + double y[2],z=0.0; + int32_t n, ix; + + /* High word of x. */ + GET_HIGH_WORD(ix,x); + + /* |x| ~< pi/4 */ + ix &= 0x7fffffff; + if(ix <= 0x3fe921fb) return __kernel_cos(x,z); + + /* cos(Inf or NaN) is NaN */ + else if (ix>=0x7ff00000) return x-x; + + /* argument reduction needed */ + else { + n = __libm_rem_pio2(x,y); + switch(n&3) { + case 0: return __kernel_cos(y[0],y[1]); + case 1: return -__kernel_sin(y[0],y[1],1); + case 2: return -__kernel_cos(y[0],y[1]); + default: + return __kernel_sin(y[0],y[1],1); + } + } +} diff --git a/lib/libm/src/s_cosf.c b/lib/libm/src/s_cosf.c new file mode 100644 index 0000000000..3c463c0677 --- /dev/null +++ b/lib/libm/src/s_cosf.c @@ -0,0 +1,48 @@ +/* s_cosf.c -- float version of s_cos.c. + * Conversion to float by Ian Lance Taylor, Cygnus Support, ian@cygnus.com. + */ + +/* + * ==================================================== + * Copyright (C) 1993 by Sun Microsystems, Inc. All rights reserved. + * + * Developed at SunPro, a Sun Microsystems, Inc. business. + * Permission to use, copy, modify, and distribute this + * software is freely granted, provided that this notice + * is preserved. + * ==================================================== + * + * $NetBSD: s_cosf.c,v 1.8 2002/05/26 22:01:55 wiz Exp $ + * $DragonFly: src/lib/libm/src/s_cosf.c,v 1.1 2005/07/26 21:15:20 joerg Exp $ + */ + +#include +#include "math_private.h" + +float +cosf(float x) +{ + float y[2],z=0.0; + int32_t n,ix; + + GET_FLOAT_WORD(ix,x); + + /* |x| ~< pi/4 */ + ix &= 0x7fffffff; + if(ix <= 0x3f490fd8) return __kernel_cosf(x,z); + + /* cos(Inf or NaN) is NaN */ + else if (ix>=0x7f800000) return x-x; + + /* argument reduction needed */ + else { + n = __libm_rem_pio2f(x,y); + switch(n&3) { + case 0: return __kernel_cosf(y[0],y[1]); + case 1: return -__kernel_sinf(y[0],y[1],1); + case 2: return -__kernel_cosf(y[0],y[1]); + default: + return __kernel_sinf(y[0],y[1],1); + } + } +} diff --git a/lib/libm/src/s_erf.c b/lib/libm/src/s_erf.c new file mode 100644 index 0000000000..3064a00ab6 --- /dev/null +++ b/lib/libm/src/s_erf.c @@ -0,0 +1,301 @@ +/* @(#)s_erf.c 5.1 93/09/24 */ +/* + * ==================================================== + * Copyright (C) 1993 by Sun Microsystems, Inc. All rights reserved. + * + * Developed at SunPro, a Sun Microsystems, Inc. business. + * Permission to use, copy, modify, and distribute this + * software is freely granted, provided that this notice + * is preserved. + * ==================================================== + * + * $NetBSD: s_erf.c,v 1.11 2002/05/26 22:01:55 wiz Exp $ + * $DragonFly: src/lib/libm/src/s_erf.c,v 1.1 2005/07/26 21:15:20 joerg Exp $ + */ + +/* double erf(double x) + * double erfc(double x) + * x + * 2 |\ + * erf(x) = --------- | exp(-t*t)dt + * sqrt(pi) \| + * 0 + * + * erfc(x) = 1-erf(x) + * Note that + * erf(-x) = -erf(x) + * erfc(-x) = 2 - erfc(x) + * + * Method: + * 1. For |x| in [0, 0.84375] + * erf(x) = x + x*R(x^2) + * erfc(x) = 1 - erf(x) if x in [-.84375,0.25] + * = 0.5 + ((0.5-x)-x*R) if x in [0.25,0.84375] + * where R = P/Q where P is an odd poly of degree 8 and + * Q is an odd poly of degree 10. + * -57.90 + * | R - (erf(x)-x)/x | <= 2 + * + * + * Remark. The formula is derived by noting + * erf(x) = (2/sqrt(pi))*(x - x^3/3 + x^5/10 - x^7/42 + ....) + * and that + * 2/sqrt(pi) = 1.128379167095512573896158903121545171688 + * is close to one. The interval is chosen because the fix + * point of erf(x) is near 0.6174 (i.e., erf(x)=x when x is + * near 0.6174), and by some experiment, 0.84375 is chosen to + * guarantee the error is less than one ulp for erf. + * + * 2. For |x| in [0.84375,1.25], let s = |x| - 1, and + * c = 0.84506291151 rounded to single (24 bits) + * erf(x) = sign(x) * (c + P1(s)/Q1(s)) + * erfc(x) = (1-c) - P1(s)/Q1(s) if x > 0 + * 1+(c+P1(s)/Q1(s)) if x < 0 + * |P1/Q1 - (erf(|x|)-c)| <= 2**-59.06 + * Remark: here we use the taylor series expansion at x=1. + * erf(1+s) = erf(1) + s*Poly(s) + * = 0.845.. + P1(s)/Q1(s) + * That is, we use rational approximation to approximate + * erf(1+s) - (c = (single)0.84506291151) + * Note that |P1/Q1|< 0.078 for x in [0.84375,1.25] + * where + * P1(s) = degree 6 poly in s + * Q1(s) = degree 6 poly in s + * + * 3. For x in [1.25,1/0.35(~2.857143)], + * erfc(x) = (1/x)*exp(-x*x-0.5625+R1/S1) + * erf(x) = 1 - erfc(x) + * where + * R1(z) = degree 7 poly in z, (z=1/x^2) + * S1(z) = degree 8 poly in z + * + * 4. For x in [1/0.35,28] + * erfc(x) = (1/x)*exp(-x*x-0.5625+R2/S2) if x > 0 + * = 2.0 - (1/x)*exp(-x*x-0.5625+R2/S2) if -6 x >= 28 + * erf(x) = sign(x) *(1 - tiny) (raise inexact) + * erfc(x) = tiny*tiny (raise underflow) if x > 0 + * = 2 - tiny if x<0 + * + * 7. Special case: + * erf(0) = 0, erf(inf) = 1, erf(-inf) = -1, + * erfc(0) = 1, erfc(inf) = 0, erfc(-inf) = 2, + * erfc/erf(NaN) is NaN + */ + + +#include +#include "math_private.h" + +static const double +tiny = 1e-300, +half= 5.00000000000000000000e-01, /* 0x3FE00000, 0x00000000 */ +one = 1.00000000000000000000e+00, /* 0x3FF00000, 0x00000000 */ +two = 2.00000000000000000000e+00, /* 0x40000000, 0x00000000 */ + /* c = (float)0.84506291151 */ +erx = 8.45062911510467529297e-01, /* 0x3FEB0AC1, 0x60000000 */ +/* + * Coefficients for approximation to erf on [0,0.84375] + */ +efx = 1.28379167095512586316e-01, /* 0x3FC06EBA, 0x8214DB69 */ +efx8= 1.02703333676410069053e+00, /* 0x3FF06EBA, 0x8214DB69 */ +pp0 = 1.28379167095512558561e-01, /* 0x3FC06EBA, 0x8214DB68 */ +pp1 = -3.25042107247001499370e-01, /* 0xBFD4CD7D, 0x691CB913 */ +pp2 = -2.84817495755985104766e-02, /* 0xBF9D2A51, 0xDBD7194F */ +pp3 = -5.77027029648944159157e-03, /* 0xBF77A291, 0x236668E4 */ +pp4 = -2.37630166566501626084e-05, /* 0xBEF8EAD6, 0x120016AC */ +qq1 = 3.97917223959155352819e-01, /* 0x3FD97779, 0xCDDADC09 */ +qq2 = 6.50222499887672944485e-02, /* 0x3FB0A54C, 0x5536CEBA */ +qq3 = 5.08130628187576562776e-03, /* 0x3F74D022, 0xC4D36B0F */ +qq4 = 1.32494738004321644526e-04, /* 0x3F215DC9, 0x221C1A10 */ +qq5 = -3.96022827877536812320e-06, /* 0xBED09C43, 0x42A26120 */ +/* + * Coefficients for approximation to erf in [0.84375,1.25] + */ +pa0 = -2.36211856075265944077e-03, /* 0xBF6359B8, 0xBEF77538 */ +pa1 = 4.14856118683748331666e-01, /* 0x3FDA8D00, 0xAD92B34D */ +pa2 = -3.72207876035701323847e-01, /* 0xBFD7D240, 0xFBB8C3F1 */ +pa3 = 3.18346619901161753674e-01, /* 0x3FD45FCA, 0x805120E4 */ +pa4 = -1.10894694282396677476e-01, /* 0xBFBC6398, 0x3D3E28EC */ +pa5 = 3.54783043256182359371e-02, /* 0x3FA22A36, 0x599795EB */ +pa6 = -2.16637559486879084300e-03, /* 0xBF61BF38, 0x0A96073F */ +qa1 = 1.06420880400844228286e-01, /* 0x3FBB3E66, 0x18EEE323 */ +qa2 = 5.40397917702171048937e-01, /* 0x3FE14AF0, 0x92EB6F33 */ +qa3 = 7.18286544141962662868e-02, /* 0x3FB2635C, 0xD99FE9A7 */ +qa4 = 1.26171219808761642112e-01, /* 0x3FC02660, 0xE763351F */ +qa5 = 1.36370839120290507362e-02, /* 0x3F8BEDC2, 0x6B51DD1C */ +qa6 = 1.19844998467991074170e-02, /* 0x3F888B54, 0x5735151D */ +/* + * Coefficients for approximation to erfc in [1.25,1/0.35] + */ +ra0 = -9.86494403484714822705e-03, /* 0xBF843412, 0x600D6435 */ +ra1 = -6.93858572707181764372e-01, /* 0xBFE63416, 0xE4BA7360 */ +ra2 = -1.05586262253232909814e+01, /* 0xC0251E04, 0x41B0E726 */ +ra3 = -6.23753324503260060396e+01, /* 0xC04F300A, 0xE4CBA38D */ +ra4 = -1.62396669462573470355e+02, /* 0xC0644CB1, 0x84282266 */ +ra5 = -1.84605092906711035994e+02, /* 0xC067135C, 0xEBCCABB2 */ +ra6 = -8.12874355063065934246e+01, /* 0xC0545265, 0x57E4D2F2 */ +ra7 = -9.81432934416914548592e+00, /* 0xC023A0EF, 0xC69AC25C */ +sa1 = 1.96512716674392571292e+01, /* 0x4033A6B9, 0xBD707687 */ +sa2 = 1.37657754143519042600e+02, /* 0x4061350C, 0x526AE721 */ +sa3 = 4.34565877475229228821e+02, /* 0x407B290D, 0xD58A1A71 */ +sa4 = 6.45387271733267880336e+02, /* 0x40842B19, 0x21EC2868 */ +sa5 = 4.29008140027567833386e+02, /* 0x407AD021, 0x57700314 */ +sa6 = 1.08635005541779435134e+02, /* 0x405B28A3, 0xEE48AE2C */ +sa7 = 6.57024977031928170135e+00, /* 0x401A47EF, 0x8E484A93 */ +sa8 = -6.04244152148580987438e-02, /* 0xBFAEEFF2, 0xEE749A62 */ +/* + * Coefficients for approximation to erfc in [1/.35,28] + */ +rb0 = -9.86494292470009928597e-03, /* 0xBF843412, 0x39E86F4A */ +rb1 = -7.99283237680523006574e-01, /* 0xBFE993BA, 0x70C285DE */ +rb2 = -1.77579549177547519889e+01, /* 0xC031C209, 0x555F995A */ +rb3 = -1.60636384855821916062e+02, /* 0xC064145D, 0x43C5ED98 */ +rb4 = -6.37566443368389627722e+02, /* 0xC083EC88, 0x1375F228 */ +rb5 = -1.02509513161107724954e+03, /* 0xC0900461, 0x6A2E5992 */ +rb6 = -4.83519191608651397019e+02, /* 0xC07E384E, 0x9BDC383F */ +sb1 = 3.03380607434824582924e+01, /* 0x403E568B, 0x261D5190 */ +sb2 = 3.25792512996573918826e+02, /* 0x40745CAE, 0x221B9F0A */ +sb3 = 1.53672958608443695994e+03, /* 0x409802EB, 0x189D5118 */ +sb4 = 3.19985821950859553908e+03, /* 0x40A8FFB7, 0x688C246A */ +sb5 = 2.55305040643316442583e+03, /* 0x40A3F219, 0xCEDF3BE6 */ +sb6 = 4.74528541206955367215e+02, /* 0x407DA874, 0xE79FE763 */ +sb7 = -2.24409524465858183362e+01; /* 0xC03670E2, 0x42712D62 */ + +double +erf(double x) +{ + int32_t hx,ix,i; + double R,S,P,Q,s,y,z,r; + GET_HIGH_WORD(hx,x); + ix = hx&0x7fffffff; + if(ix>=0x7ff00000) { /* erf(nan)=nan */ + i = ((u_int32_t)hx>>31)<<1; + return (double)(1-i)+one/x; /* erf(+-inf)=+-1 */ + } + + if(ix < 0x3feb0000) { /* |x|<0.84375 */ + if(ix < 0x3e300000) { /* |x|<2**-28 */ + if (ix < 0x00800000) + return 0.125*(8.0*x+efx8*x); /*avoid underflow */ + return x + efx*x; + } + z = x*x; + r = pp0+z*(pp1+z*(pp2+z*(pp3+z*pp4))); + s = one+z*(qq1+z*(qq2+z*(qq3+z*(qq4+z*qq5)))); + y = r/s; + return x + x*y; + } + if(ix < 0x3ff40000) { /* 0.84375 <= |x| < 1.25 */ + s = fabs(x)-one; + P = pa0+s*(pa1+s*(pa2+s*(pa3+s*(pa4+s*(pa5+s*pa6))))); + Q = one+s*(qa1+s*(qa2+s*(qa3+s*(qa4+s*(qa5+s*qa6))))); + if(hx>=0) return erx + P/Q; else return -erx - P/Q; + } + if (ix >= 0x40180000) { /* inf>|x|>=6 */ + if(hx>=0) return one-tiny; else return tiny-one; + } + x = fabs(x); + s = one/(x*x); + if(ix< 0x4006DB6E) { /* |x| < 1/0.35 */ + R=ra0+s*(ra1+s*(ra2+s*(ra3+s*(ra4+s*( + ra5+s*(ra6+s*ra7)))))); + S=one+s*(sa1+s*(sa2+s*(sa3+s*(sa4+s*( + sa5+s*(sa6+s*(sa7+s*sa8))))))); + } else { /* |x| >= 1/0.35 */ + R=rb0+s*(rb1+s*(rb2+s*(rb3+s*(rb4+s*( + rb5+s*rb6))))); + S=one+s*(sb1+s*(sb2+s*(sb3+s*(sb4+s*( + sb5+s*(sb6+s*sb7)))))); + } + z = x; + SET_LOW_WORD(z,0); + r = exp(-z*z-0.5625)*exp((z-x)*(z+x)+R/S); + if(hx>=0) return one-r/x; else return r/x-one; +} + +double +erfc(double x) +{ + int32_t hx,ix; + double R,S,P,Q,s,y,z,r; + GET_HIGH_WORD(hx,x); + ix = hx&0x7fffffff; + if(ix>=0x7ff00000) { /* erfc(nan)=nan */ + /* erfc(+-inf)=0,2 */ + return (double)(((u_int32_t)hx>>31)<<1)+one/x; + } + + if(ix < 0x3feb0000) { /* |x|<0.84375 */ + if(ix < 0x3c700000) /* |x|<2**-56 */ + return one-x; + z = x*x; + r = pp0+z*(pp1+z*(pp2+z*(pp3+z*pp4))); + s = one+z*(qq1+z*(qq2+z*(qq3+z*(qq4+z*qq5)))); + y = r/s; + if(hx < 0x3fd00000) { /* x<1/4 */ + return one-(x+x*y); + } else { + r = x*y; + r += (x-half); + return half - r ; + } + } + if(ix < 0x3ff40000) { /* 0.84375 <= |x| < 1.25 */ + s = fabs(x)-one; + P = pa0+s*(pa1+s*(pa2+s*(pa3+s*(pa4+s*(pa5+s*pa6))))); + Q = one+s*(qa1+s*(qa2+s*(qa3+s*(qa4+s*(qa5+s*qa6))))); + if(hx>=0) { + z = one-erx; return z - P/Q; + } else { + z = erx+P/Q; return one+z; + } + } + if (ix < 0x403c0000) { /* |x|<28 */ + x = fabs(x); + s = one/(x*x); + if(ix< 0x4006DB6D) { /* |x| < 1/.35 ~ 2.857143*/ + R=ra0+s*(ra1+s*(ra2+s*(ra3+s*(ra4+s*( + ra5+s*(ra6+s*ra7)))))); + S=one+s*(sa1+s*(sa2+s*(sa3+s*(sa4+s*( + sa5+s*(sa6+s*(sa7+s*sa8))))))); + } else { /* |x| >= 1/.35 ~ 2.857143 */ + if(hx<0&&ix>=0x40180000) return two-tiny;/* x < -6 */ + R=rb0+s*(rb1+s*(rb2+s*(rb3+s*(rb4+s*( + rb5+s*rb6))))); + S=one+s*(sb1+s*(sb2+s*(sb3+s*(sb4+s*( + sb5+s*(sb6+s*sb7)))))); + } + z = x; + SET_LOW_WORD(z,0); + r = exp(-z*z-0.5625)* + exp((z-x)*(z+x)+R/S); + if(hx>0) return r/x; else return two-r/x; + } else { + if(hx>0) return tiny*tiny; else return two-tiny; + } +} diff --git a/lib/libm/src/s_erff.c b/lib/libm/src/s_erff.c new file mode 100644 index 0000000000..273a068972 --- /dev/null +++ b/lib/libm/src/s_erff.c @@ -0,0 +1,210 @@ +/* s_erff.c -- float version of s_erf.c. + * Conversion to float by Ian Lance Taylor, Cygnus Support, ian@cygnus.com. + */ + +/* + * ==================================================== + * Copyright (C) 1993 by Sun Microsystems, Inc. All rights reserved. + * + * Developed at SunPro, a Sun Microsystems, Inc. business. + * Permission to use, copy, modify, and distribute this + * software is freely granted, provided that this notice + * is preserved. + * ==================================================== + * + * $NetBSD: s_erff.c,v 1.7 2002/05/26 22:01:55 wiz Exp $ + * $DragonFly: src/lib/libm/src/s_erff.c,v 1.1 2005/07/26 21:15:20 joerg Exp $ + */ + +#include +#include "math_private.h" + +static const float +tiny = 1e-30, +half= 5.0000000000e-01, /* 0x3F000000 */ +one = 1.0000000000e+00, /* 0x3F800000 */ +two = 2.0000000000e+00, /* 0x40000000 */ + /* c = (subfloat)0.84506291151 */ +erx = 8.4506291151e-01, /* 0x3f58560b */ +/* + * Coefficients for approximation to erf on [0,0.84375] + */ +efx = 1.2837916613e-01, /* 0x3e0375d4 */ +efx8= 1.0270333290e+00, /* 0x3f8375d4 */ +pp0 = 1.2837916613e-01, /* 0x3e0375d4 */ +pp1 = -3.2504209876e-01, /* 0xbea66beb */ +pp2 = -2.8481749818e-02, /* 0xbce9528f */ +pp3 = -5.7702702470e-03, /* 0xbbbd1489 */ +pp4 = -2.3763017452e-05, /* 0xb7c756b1 */ +qq1 = 3.9791721106e-01, /* 0x3ecbbbce */ +qq2 = 6.5022252500e-02, /* 0x3d852a63 */ +qq3 = 5.0813062117e-03, /* 0x3ba68116 */ +qq4 = 1.3249473704e-04, /* 0x390aee49 */ +qq5 = -3.9602282413e-06, /* 0xb684e21a */ +/* + * Coefficients for approximation to erf in [0.84375,1.25] + */ +pa0 = -2.3621185683e-03, /* 0xbb1acdc6 */ +pa1 = 4.1485610604e-01, /* 0x3ed46805 */ +pa2 = -3.7220788002e-01, /* 0xbebe9208 */ +pa3 = 3.1834661961e-01, /* 0x3ea2fe54 */ +pa4 = -1.1089469492e-01, /* 0xbde31cc2 */ +pa5 = 3.5478305072e-02, /* 0x3d1151b3 */ +pa6 = -2.1663755178e-03, /* 0xbb0df9c0 */ +qa1 = 1.0642088205e-01, /* 0x3dd9f331 */ +qa2 = 5.4039794207e-01, /* 0x3f0a5785 */ +qa3 = 7.1828655899e-02, /* 0x3d931ae7 */ +qa4 = 1.2617121637e-01, /* 0x3e013307 */ +qa5 = 1.3637083583e-02, /* 0x3c5f6e13 */ +qa6 = 1.1984500103e-02, /* 0x3c445aa3 */ +/* + * Coefficients for approximation to erfc in [1.25,1/0.35] + */ +ra0 = -9.8649440333e-03, /* 0xbc21a093 */ +ra1 = -6.9385856390e-01, /* 0xbf31a0b7 */ +ra2 = -1.0558626175e+01, /* 0xc128f022 */ +ra3 = -6.2375331879e+01, /* 0xc2798057 */ +ra4 = -1.6239666748e+02, /* 0xc322658c */ +ra5 = -1.8460508728e+02, /* 0xc3389ae7 */ +ra6 = -8.1287437439e+01, /* 0xc2a2932b */ +ra7 = -9.8143291473e+00, /* 0xc11d077e */ +sa1 = 1.9651271820e+01, /* 0x419d35ce */ +sa2 = 1.3765776062e+02, /* 0x4309a863 */ +sa3 = 4.3456588745e+02, /* 0x43d9486f */ +sa4 = 6.4538726807e+02, /* 0x442158c9 */ +sa5 = 4.2900814819e+02, /* 0x43d6810b */ +sa6 = 1.0863500214e+02, /* 0x42d9451f */ +sa7 = 6.5702495575e+00, /* 0x40d23f7c */ +sa8 = -6.0424413532e-02, /* 0xbd777f97 */ +/* + * Coefficients for approximation to erfc in [1/.35,28] + */ +rb0 = -9.8649431020e-03, /* 0xbc21a092 */ +rb1 = -7.9928326607e-01, /* 0xbf4c9dd4 */ +rb2 = -1.7757955551e+01, /* 0xc18e104b */ +rb3 = -1.6063638306e+02, /* 0xc320a2ea */ +rb4 = -6.3756646729e+02, /* 0xc41f6441 */ +rb5 = -1.0250950928e+03, /* 0xc480230b */ +rb6 = -4.8351919556e+02, /* 0xc3f1c275 */ +sb1 = 3.0338060379e+01, /* 0x41f2b459 */ +sb2 = 3.2579251099e+02, /* 0x43a2e571 */ +sb3 = 1.5367296143e+03, /* 0x44c01759 */ +sb4 = 3.1998581543e+03, /* 0x4547fdbb */ +sb5 = 2.5530502930e+03, /* 0x451f90ce */ +sb6 = 4.7452853394e+02, /* 0x43ed43a7 */ +sb7 = -2.2440952301e+01; /* 0xc1b38712 */ + +float +erff(float x) +{ + int32_t hx,ix,i; + float R,S,P,Q,s,y,z,r; + GET_FLOAT_WORD(hx,x); + ix = hx&0x7fffffff; + if(ix>=0x7f800000) { /* erf(nan)=nan */ + i = ((u_int32_t)hx>>31)<<1; + return (float)(1-i)+one/x; /* erf(+-inf)=+-1 */ + } + + if(ix < 0x3f580000) { /* |x|<0.84375 */ + if(ix < 0x31800000) { /* |x|<2**-28 */ + if (ix < 0x04000000) + /*avoid underflow */ + return (float)0.125*((float)8.0*x+efx8*x); + return x + efx*x; + } + z = x*x; + r = pp0+z*(pp1+z*(pp2+z*(pp3+z*pp4))); + s = one+z*(qq1+z*(qq2+z*(qq3+z*(qq4+z*qq5)))); + y = r/s; + return x + x*y; + } + if(ix < 0x3fa00000) { /* 0.84375 <= |x| < 1.25 */ + s = fabsf(x)-one; + P = pa0+s*(pa1+s*(pa2+s*(pa3+s*(pa4+s*(pa5+s*pa6))))); + Q = one+s*(qa1+s*(qa2+s*(qa3+s*(qa4+s*(qa5+s*qa6))))); + if(hx>=0) return erx + P/Q; else return -erx - P/Q; + } + if (ix >= 0x40c00000) { /* inf>|x|>=6 */ + if(hx>=0) return one-tiny; else return tiny-one; + } + x = fabsf(x); + s = one/(x*x); + if(ix< 0x4036DB6E) { /* |x| < 1/0.35 */ + R=ra0+s*(ra1+s*(ra2+s*(ra3+s*(ra4+s*( + ra5+s*(ra6+s*ra7)))))); + S=one+s*(sa1+s*(sa2+s*(sa3+s*(sa4+s*( + sa5+s*(sa6+s*(sa7+s*sa8))))))); + } else { /* |x| >= 1/0.35 */ + R=rb0+s*(rb1+s*(rb2+s*(rb3+s*(rb4+s*( + rb5+s*rb6))))); + S=one+s*(sb1+s*(sb2+s*(sb3+s*(sb4+s*( + sb5+s*(sb6+s*sb7)))))); + } + GET_FLOAT_WORD(ix,x); + SET_FLOAT_WORD(z,ix&0xfffff000); + r = expf(-z*z-(float)0.5625)*expf((z-x)*(z+x)+R/S); + if(hx>=0) return one-r/x; else return r/x-one; +} + +float +erfcf(float x) +{ + int32_t hx,ix; + float R,S,P,Q,s,y,z,r; + GET_FLOAT_WORD(hx,x); + ix = hx&0x7fffffff; + if(ix>=0x7f800000) { /* erfc(nan)=nan */ + /* erfc(+-inf)=0,2 */ + return (float)(((u_int32_t)hx>>31)<<1)+one/x; + } + + if(ix < 0x3f580000) { /* |x|<0.84375 */ + if(ix < 0x23800000) /* |x|<2**-56 */ + return one-x; + z = x*x; + r = pp0+z*(pp1+z*(pp2+z*(pp3+z*pp4))); + s = one+z*(qq1+z*(qq2+z*(qq3+z*(qq4+z*qq5)))); + y = r/s; + if(hx < 0x3e800000) { /* x<1/4 */ + return one-(x+x*y); + } else { + r = x*y; + r += (x-half); + return half - r ; + } + } + if(ix < 0x3fa00000) { /* 0.84375 <= |x| < 1.25 */ + s = fabsf(x)-one; + P = pa0+s*(pa1+s*(pa2+s*(pa3+s*(pa4+s*(pa5+s*pa6))))); + Q = one+s*(qa1+s*(qa2+s*(qa3+s*(qa4+s*(qa5+s*qa6))))); + if(hx>=0) { + z = one-erx; return z - P/Q; + } else { + z = erx+P/Q; return one+z; + } + } + if (ix < 0x41e00000) { /* |x|<28 */ + x = fabsf(x); + s = one/(x*x); + if(ix< 0x4036DB6D) { /* |x| < 1/.35 ~ 2.857143*/ + R=ra0+s*(ra1+s*(ra2+s*(ra3+s*(ra4+s*( + ra5+s*(ra6+s*ra7)))))); + S=one+s*(sa1+s*(sa2+s*(sa3+s*(sa4+s*( + sa5+s*(sa6+s*(sa7+s*sa8))))))); + } else { /* |x| >= 1/.35 ~ 2.857143 */ + if(hx<0&&ix>=0x40c00000) return two-tiny;/* x < -6 */ + R=rb0+s*(rb1+s*(rb2+s*(rb3+s*(rb4+s*( + rb5+s*rb6))))); + S=one+s*(sb1+s*(sb2+s*(sb3+s*(sb4+s*( + sb5+s*(sb6+s*sb7)))))); + } + GET_FLOAT_WORD(ix,x); + SET_FLOAT_WORD(z,ix&0xfffff000); + r = expf(-z*z-(float)0.5625)* + expf((z-x)*(z+x)+R/S); + if(hx>0) return r/x; else return two-r/x; + } else { + if(hx>0) return tiny*tiny; else return two-tiny; + } +} diff --git a/lib/libm/src/s_expm1.c b/lib/libm/src/s_expm1.c new file mode 100644 index 0000000000..28327fb701 --- /dev/null +++ b/lib/libm/src/s_expm1.c @@ -0,0 +1,221 @@ +/* @(#)s_expm1.c 5.1 93/09/24 */ +/* + * ==================================================== + * Copyright (C) 1993 by Sun Microsystems, Inc. All rights reserved. + * + * Developed at SunPro, a Sun Microsystems, Inc. business. + * Permission to use, copy, modify, and distribute this + * software is freely granted, provided that this notice + * is preserved. + * ==================================================== + * + * $NetBSD: s_expm1.c,v 1.12 2002/05/26 22:01:55 wiz Exp $ + * $DragonFly: src/lib/libm/src/s_expm1.c,v 1.1 2005/07/26 21:15:20 joerg Exp $ + */ + +/* expm1(x) + * Returns exp(x)-1, the exponential of x minus 1. + * + * Method + * 1. Argument reduction: + * Given x, find r and integer k such that + * + * x = k*ln2 + r, |r| <= 0.5*ln2 ~ 0.34658 + * + * Here a correction term c will be computed to compensate + * the error in r when rounded to a floating-point number. + * + * 2. Approximating expm1(r) by a special rational function on + * the interval [0,0.34658]: + * Since + * r*(exp(r)+1)/(exp(r)-1) = 2+ r^2/6 - r^4/360 + ... + * we define R1(r*r) by + * r*(exp(r)+1)/(exp(r)-1) = 2+ r^2/6 * R1(r*r) + * That is, + * R1(r**2) = 6/r *((exp(r)+1)/(exp(r)-1) - 2/r) + * = 6/r * ( 1 + 2.0*(1/(exp(r)-1) - 1/r)) + * = 1 - r^2/60 + r^4/2520 - r^6/100800 + ... + * We use a special Reme algorithm on [0,0.347] to generate + * a polynomial of degree 5 in r*r to approximate R1. The + * maximum error of this polynomial approximation is bounded + * by 2**-61. In other words, + * R1(z) ~ 1.0 + Q1*z + Q2*z**2 + Q3*z**3 + Q4*z**4 + Q5*z**5 + * where Q1 = -1.6666666666666567384E-2, + * Q2 = 3.9682539681370365873E-4, + * Q3 = -9.9206344733435987357E-6, + * Q4 = 2.5051361420808517002E-7, + * Q5 = -6.2843505682382617102E-9; + * (where z=r*r, and the values of Q1 to Q5 are listed below) + * with error bounded by + * | 5 | -61 + * | 1.0+Q1*z+...+Q5*z - R1(z) | <= 2 + * | | + * + * expm1(r) = exp(r)-1 is then computed by the following + * specific way which minimize the accumulation rounding error: + * 2 3 + * r r [ 3 - (R1 + R1*r/2) ] + * expm1(r) = r + --- + --- * [--------------------] + * 2 2 [ 6 - r*(3 - R1*r/2) ] + * + * To compensate the error in the argument reduction, we use + * expm1(r+c) = expm1(r) + c + expm1(r)*c + * ~ expm1(r) + c + r*c + * Thus c+r*c will be added in as the correction terms for + * expm1(r+c). Now rearrange the term to avoid optimization + * screw up: + * ( 2 2 ) + * ({ ( r [ R1 - (3 - R1*r/2) ] ) } r ) + * expm1(r+c)~r - ({r*(--- * [--------------------]-c)-c} - --- ) + * ({ ( 2 [ 6 - r*(3 - R1*r/2) ] ) } 2 ) + * ( ) + * + * = r - E + * 3. Scale back to obtain expm1(x): + * From step 1, we have + * expm1(x) = either 2^k*[expm1(r)+1] - 1 + * = or 2^k*[expm1(r) + (1-2^-k)] + * 4. Implementation notes: + * (A). To save one multiplication, we scale the coefficient Qi + * to Qi*2^i, and replace z by (x^2)/2. + * (B). To achieve maximum accuracy, we compute expm1(x) by + * (i) if x < -56*ln2, return -1.0, (raise inexact if x!=inf) + * (ii) if k=0, return r-E + * (iii) if k=-1, return 0.5*(r-E)-0.5 + * (iv) if k=1 if r < -0.25, return 2*((r+0.5)- E) + * else return 1.0+2.0*(r-E); + * (v) if (k<-2||k>56) return 2^k(1-(E-r)) - 1 (or exp(x)-1) + * (vi) if k <= 20, return 2^k((1-2^-k)-(E-r)), else + * (vii) return 2^k(1-((E+2^-k)-r)) + * + * Special cases: + * expm1(INF) is INF, expm1(NaN) is NaN; + * expm1(-INF) is -1, and + * for finite argument, only expm1(0)=0 is exact. + * + * Accuracy: + * according to an error analysis, the error is always less than + * 1 ulp (unit in the last place). + * + * Misc. info. + * For IEEE double + * if x > 7.09782712893383973096e+02 then expm1(x) overflow + * + * Constants: + * The hexadecimal values are the intended ones for the following + * constants. The decimal values may be used, provided that the + * compiler will convert from decimal to binary accurately enough + * to produce the hexadecimal values shown. + */ + +#include +#include "math_private.h" + +static const double +one = 1.0, +huge = 1.0e+300, +tiny = 1.0e-300, +o_threshold = 7.09782712893383973096e+02,/* 0x40862E42, 0xFEFA39EF */ +ln2_hi = 6.93147180369123816490e-01,/* 0x3fe62e42, 0xfee00000 */ +ln2_lo = 1.90821492927058770002e-10,/* 0x3dea39ef, 0x35793c76 */ +invln2 = 1.44269504088896338700e+00,/* 0x3ff71547, 0x652b82fe */ + /* scaled coefficients related to expm1 */ +Q1 = -3.33333333333331316428e-02, /* BFA11111 111110F4 */ +Q2 = 1.58730158725481460165e-03, /* 3F5A01A0 19FE5585 */ +Q3 = -7.93650757867487942473e-05, /* BF14CE19 9EAADBB7 */ +Q4 = 4.00821782732936239552e-06, /* 3ED0CFCA 86E65239 */ +Q5 = -2.01099218183624371326e-07; /* BE8AFDB7 6E09C32D */ + +double +expm1(double x) +{ + double y,hi,lo,c,t,e,hxs,hfx,r1; + int32_t k,xsb; + u_int32_t hx; + + c = 0; + GET_HIGH_WORD(hx,x); + xsb = hx&0x80000000; /* sign bit of x */ + if(xsb==0) y=x; else y= -x; /* y = |x| */ + hx &= 0x7fffffff; /* high word of |x| */ + + /* filter out huge and non-finite argument */ + if(hx >= 0x4043687A) { /* if |x|>=56*ln2 */ + if(hx >= 0x40862E42) { /* if |x|>=709.78... */ + if(hx>=0x7ff00000) { + u_int32_t low; + GET_LOW_WORD(low,x); + if(((hx&0xfffff)|low)!=0) + return x+x; /* NaN */ + else return (xsb==0)? x:-1.0;/* exp(+-inf)={inf,-1} */ + } + if(x > o_threshold) return huge*huge; /* overflow */ + } + if(xsb!=0) { /* x < -56*ln2, return -1.0 with inexact */ + if(x+tiny<0.0) /* raise inexact */ + return tiny-one; /* return -1 */ + } + } + + /* argument reduction */ + if(hx > 0x3fd62e42) { /* if |x| > 0.5 ln2 */ + if(hx < 0x3FF0A2B2) { /* and |x| < 1.5 ln2 */ + if(xsb==0) + {hi = x - ln2_hi; lo = ln2_lo; k = 1;} + else + {hi = x + ln2_hi; lo = -ln2_lo; k = -1;} + } else { + k = invln2*x+((xsb==0)?0.5:-0.5); + t = k; + hi = x - t*ln2_hi; /* t*ln2_hi is exact here */ + lo = t*ln2_lo; + } + x = hi - lo; + c = (hi-x)-lo; + } + else if(hx < 0x3c900000) { /* when |x|<2**-54, return x */ + t = huge+x; /* return x with inexact flags when x!=0 */ + return x - (t-(huge+x)); + } + else k = 0; + + /* x is now in primary range */ + hfx = 0.5*x; + hxs = x*hfx; + r1 = one+hxs*(Q1+hxs*(Q2+hxs*(Q3+hxs*(Q4+hxs*Q5)))); + t = 3.0-r1*hfx; + e = hxs*((r1-t)/(6.0 - x*t)); + if(k==0) return x - (x*e-hxs); /* c is 0 */ + else { + e = (x*(e-c)-c); + e -= hxs; + if(k== -1) return 0.5*(x-e)-0.5; + if(k==1) { + if(x < -0.25) return -2.0*(e-(x+0.5)); + else return one+2.0*(x-e); + } + if (k <= -2 || k>56) { /* suffice to return exp(x)-1 */ + u_int32_t high; + y = one-(e-x); + GET_HIGH_WORD(high,y); + SET_HIGH_WORD(y,high+(k<<20)); /* add k to y's exponent */ + return y-one; + } + t = one; + if(k<20) { + u_int32_t high; + SET_HIGH_WORD(t,0x3ff00000 - (0x200000>>k)); /* t=1-2^-k */ + y = t-(e-x); + GET_HIGH_WORD(high,y); + SET_HIGH_WORD(y,high+(k<<20)); /* add k to y's exponent */ + } else { + u_int32_t high; + SET_HIGH_WORD(t,((0x3ff-k)<<20)); /* 2^-k */ + y = x-(e+t); + y += one; + GET_HIGH_WORD(high,y); + SET_HIGH_WORD(y,high+(k<<20)); /* add k to y's exponent */ + } + } + return y; +} diff --git a/lib/libm/src/s_expm1f.c b/lib/libm/src/s_expm1f.c new file mode 100644 index 0000000000..ba9862535c --- /dev/null +++ b/lib/libm/src/s_expm1f.c @@ -0,0 +1,126 @@ +/* s_expm1f.c -- float version of s_expm1.c. + * Conversion to float by Ian Lance Taylor, Cygnus Support, ian@cygnus.com. + */ + +/* + * ==================================================== + * Copyright (C) 1993 by Sun Microsystems, Inc. All rights reserved. + * + * Developed at SunPro, a Sun Microsystems, Inc. business. + * Permission to use, copy, modify, and distribute this + * software is freely granted, provided that this notice + * is preserved. + * ==================================================== + * + * $NetBSD: s_expm1f.c,v 1.10 2002/05/26 22:01:55 wiz Exp $ + * $DragonFly: src/lib/libm/src/s_expm1f.c,v 1.1 2005/07/26 21:15:20 joerg Exp $ + */ + +#include +#include "math_private.h" + +static const float huge = 1.0e+30, tiny = 1.0e-30; + +static const float +one = 1.0, +o_threshold = 8.8721679688e+01,/* 0x42b17180 */ +ln2_hi = 6.9313812256e-01,/* 0x3f317180 */ +ln2_lo = 9.0580006145e-06,/* 0x3717f7d1 */ +invln2 = 1.4426950216e+00,/* 0x3fb8aa3b */ + /* scaled coefficients related to expm1 */ +Q1 = -3.3333335072e-02, /* 0xbd088889 */ +Q2 = 1.5873016091e-03, /* 0x3ad00d01 */ +Q3 = -7.9365076090e-05, /* 0xb8a670cd */ +Q4 = 4.0082177293e-06, /* 0x36867e54 */ +Q5 = -2.0109921195e-07; /* 0xb457edbb */ + +float +expm1f(float x) +{ + float y,hi,lo,c,t,e,hxs,hfx,r1; + int32_t k,xsb; + u_int32_t hx; + + c = 0; + GET_FLOAT_WORD(hx,x); + xsb = hx&0x80000000; /* sign bit of x */ + if(xsb==0) y=x; else y= -x; /* y = |x| */ + hx &= 0x7fffffff; /* high word of |x| */ + + /* filter out huge and non-finite argument */ + if(hx >= 0x4195b844) { /* if |x|>=27*ln2 */ + if(hx >= 0x42b17218) { /* if |x|>=88.721... */ + if(hx>0x7f800000) + return x+x; /* NaN */ + if(hx==0x7f800000) + return (xsb==0)? x:-1.0;/* exp(+-inf)={inf,-1} */ + if(x > o_threshold) return huge*huge; /* overflow */ + } + if(xsb!=0) { /* x < -27*ln2, return -1.0 with inexact */ + if(x+tiny<(float)0.0) /* raise inexact */ + return tiny-one; /* return -1 */ + } + } + + /* argument reduction */ + if(hx > 0x3eb17218) { /* if |x| > 0.5 ln2 */ + if(hx < 0x3F851592) { /* and |x| < 1.5 ln2 */ + if(xsb==0) + {hi = x - ln2_hi; lo = ln2_lo; k = 1;} + else + {hi = x + ln2_hi; lo = -ln2_lo; k = -1;} + } else { + k = invln2*x+((xsb==0)?(float)0.5:(float)-0.5); + t = k; + hi = x - t*ln2_hi; /* t*ln2_hi is exact here */ + lo = t*ln2_lo; + } + x = hi - lo; + c = (hi-x)-lo; + } + else if(hx < 0x33000000) { /* when |x|<2**-25, return x */ + t = huge+x; /* return x with inexact flags when x!=0 */ + return x - (t-(huge+x)); + } + else k = 0; + + /* x is now in primary range */ + hfx = (float)0.5*x; + hxs = x*hfx; + r1 = one+hxs*(Q1+hxs*(Q2+hxs*(Q3+hxs*(Q4+hxs*Q5)))); + t = (float)3.0-r1*hfx; + e = hxs*((r1-t)/((float)6.0 - x*t)); + if(k==0) return x - (x*e-hxs); /* c is 0 */ + else { + e = (x*(e-c)-c); + e -= hxs; + if(k== -1) return (float)0.5*(x-e)-(float)0.5; + if(k==1) { + if(x < (float)-0.25) return -(float)2.0*(e-(x+(float)0.5)); + else return one+(float)2.0*(x-e); + } + if (k <= -2 || k>56) { /* suffice to return exp(x)-1 */ + int32_t i; + y = one-(e-x); + GET_FLOAT_WORD(i,y); + SET_FLOAT_WORD(y,i+(k<<23)); /* add k to y's exponent */ + return y-one; + } + t = one; + if(k<23) { + int32_t i; + SET_FLOAT_WORD(t,0x3f800000 - (0x1000000>>k)); /* t=1-2^-k */ + y = t-(e-x); + GET_FLOAT_WORD(i,y); + SET_FLOAT_WORD(y,i+(k<<23)); /* add k to y's exponent */ + } else { + int32_t i; + SET_FLOAT_WORD(t,((0x7f-k)<<23)); /* 2^-k */ + y = x-(e+t); + y += one; + GET_FLOAT_WORD(i,y); + SET_FLOAT_WORD(y,i+(k<<23)); /* add k to y's exponent */ + } + } + return y; +} diff --git a/lib/libm/src/s_fabsf.c b/lib/libm/src/s_fabsf.c new file mode 100644 index 0000000000..8d81c3d536 --- /dev/null +++ b/lib/libm/src/s_fabsf.c @@ -0,0 +1,33 @@ +/* s_fabsf.c -- float version of s_fabs.c. + * Conversion to float by Ian Lance Taylor, Cygnus Support, ian@cygnus.com. + */ + +/* + * ==================================================== + * Copyright (C) 1993 by Sun Microsystems, Inc. All rights reserved. + * + * Developed at SunPro, a Sun Microsystems, Inc. business. + * Permission to use, copy, modify, and distribute this + * software is freely granted, provided that this notice + * is preserved. + * ==================================================== + * + * $NetBSD: s_fabsf.c,v 1.7 2002/05/26 22:01:55 wiz Exp $ + * $DragonFly: src/lib/libm/src/s_fabsf.c,v 1.1 2005/07/26 21:15:20 joerg Exp $ + */ + +/* + * fabsf(x) returns the absolute value of x. + */ + +#include +#include "math_private.h" + +float +fabsf(float x) +{ + u_int32_t ix; + GET_FLOAT_WORD(ix,x); + SET_FLOAT_WORD(x,ix&0x7fffffff); + return x; +} diff --git a/lib/libm/src/s_finite.c b/lib/libm/src/s_finite.c new file mode 100644 index 0000000000..1c05415d62 --- /dev/null +++ b/lib/libm/src/s_finite.c @@ -0,0 +1,30 @@ +/* @(#)s_finite.c 5.1 93/09/24 */ +/* + * ==================================================== + * Copyright (C) 1993 by Sun Microsystems, Inc. All rights reserved. + * + * Developed at SunPro, a Sun Microsystems, Inc. business. + * Permission to use, copy, modify, and distribute this + * software is freely granted, provided that this notice + * is preserved. + * ==================================================== + * + * $NetBSD: s_finite.c,v 1.11 2002/05/26 22:01:55 wiz Exp $ + * $DragonFly: src/lib/libm/src/s_finite.c,v 1.1 2005/07/26 21:15:20 joerg Exp $ + */ + +/* + * finite(x) returns 1 is x is finite, else 0; + * no branching! + */ + +#include +#include "math_private.h" + +int +finite(double x) +{ + int32_t hx; + GET_HIGH_WORD(hx,x); + return (int)((u_int32_t)((hx&0x7fffffff)-0x7ff00000)>>31); +} diff --git a/lib/libm/src/s_finitef.c b/lib/libm/src/s_finitef.c new file mode 100644 index 0000000000..fd788dd7e8 --- /dev/null +++ b/lib/libm/src/s_finitef.c @@ -0,0 +1,33 @@ +/* s_finitef.c -- float version of s_finite.c. + * Conversion to float by Ian Lance Taylor, Cygnus Support, ian@cygnus.com. + */ + +/* + * ==================================================== + * Copyright (C) 1993 by Sun Microsystems, Inc. All rights reserved. + * + * Developed at SunPro, a Sun Microsystems, Inc. business. + * Permission to use, copy, modify, and distribute this + * software is freely granted, provided that this notice + * is preserved. + * ==================================================== + * + * $NetBSD: s_finitef.c,v 1.7 2002/05/26 22:01:55 wiz Exp $ + * $DragonFly: src/lib/libm/src/s_finitef.c,v 1.1 2005/07/26 21:15:20 joerg Exp $ + */ + +/* + * finitef(x) returns 1 is x is finite, else 0; + * no branching! + */ + +#include +#include "math_private.h" + +int +finitef(float x) +{ + int32_t ix; + GET_FLOAT_WORD(ix,x); + return (int)((u_int32_t)((ix&0x7fffffff)-0x7f800000)>>31); +} diff --git a/lib/libm/src/s_floor.c b/lib/libm/src/s_floor.c new file mode 100644 index 0000000000..1bf0966902 --- /dev/null +++ b/lib/libm/src/s_floor.c @@ -0,0 +1,72 @@ +/* @(#)s_floor.c 5.1 93/09/24 */ +/* + * ==================================================== + * Copyright (C) 1993 by Sun Microsystems, Inc. All rights reserved. + * + * Developed at SunPro, a Sun Microsystems, Inc. business. + * Permission to use, copy, modify, and distribute this + * software is freely granted, provided that this notice + * is preserved. + * ==================================================== + * + * $NetBSD: s_floor.c,v 1.11 2002/05/26 22:01:56 wiz Exp $ + * $DragonFly: src/lib/libm/src/s_floor.c,v 1.1 2005/07/26 21:15:20 joerg Exp $ + */ + +/* + * floor(x) + * Return x rounded toward -inf to integral value + * Method: + * Bit twiddling. + * Exception: + * Inexact flag raised if x not equal to floor(x). + */ + +#include +#include "math_private.h" + +static const double huge = 1.0e300; + +double +floor(double x) +{ + int32_t i0,i1,j0; + u_int32_t i,j; + EXTRACT_WORDS(i0,i1,x); + j0 = ((i0>>20)&0x7ff)-0x3ff; + if(j0<20) { + if(j0<0) { /* raise inexact if x != 0 */ + if(huge+x>0.0) {/* return 0*sign(x) if |x|<1 */ + if(i0>=0) {i0=i1=0;} + else if(((i0&0x7fffffff)|i1)!=0) + { i0=0xbff00000;i1=0;} + } + } else { + i = (0x000fffff)>>j0; + if(((i0&i)|i1)==0) return x; /* x is integral */ + if(huge+x>0.0) { /* raise inexact flag */ + if(i0<0) i0 += (0x00100000)>>j0; + i0 &= (~i); i1=0; + } + } + } else if (j0>51) { + if(j0==0x400) return x+x; /* inf or NaN */ + else return x; /* x is integral */ + } else { + i = ((u_int32_t)(0xffffffff))>>(j0-20); + if((i1&i)==0) return x; /* x is integral */ + if(huge+x>0.0) { /* raise inexact flag */ + if(i0<0) { + if(j0==20) i0+=1; + else { + j = i1+(1<<(52-j0)); + if(j +#include "math_private.h" + +static const float huge = 1.0e30; + +float +floorf(float x) +{ + int32_t i0,j0; + u_int32_t i; + GET_FLOAT_WORD(i0,x); + j0 = ((i0>>23)&0xff)-0x7f; + if(j0<23) { + if(j0<0) { /* raise inexact if x != 0 */ + if(huge+x>(float)0.0) {/* return 0*sign(x) if |x|<1 */ + if(i0>=0) {i0=0;} + else if((i0&0x7fffffff)!=0) + { i0=0xbf800000;} + } + } else { + i = (0x007fffff)>>j0; + if((i0&i)==0) return x; /* x is integral */ + if(huge+x>(float)0.0) { /* raise inexact flag */ + if(i0<0) i0 += (0x00800000)>>j0; + i0 &= (~i); + } + } + } else { + if(j0==0x80) return x+x; /* inf or NaN */ + else return x; /* x is integral */ + } + SET_FLOAT_WORD(x,i0); + return x; +} diff --git a/lib/libm/src/s_frexpf.c b/lib/libm/src/s_frexpf.c new file mode 100644 index 0000000000..c7df686ff6 --- /dev/null +++ b/lib/libm/src/s_frexpf.c @@ -0,0 +1,43 @@ +/* s_frexpf.c -- float version of s_frexp.c. + * Conversion to float by Ian Lance Taylor, Cygnus Support, ian@cygnus.com. + */ + +/* + * ==================================================== + * Copyright (C) 1993 by Sun Microsystems, Inc. All rights reserved. + * + * Developed at SunPro, a Sun Microsystems, Inc. business. + * Permission to use, copy, modify, and distribute this + * software is freely granted, provided that this notice + * is preserved. + * ==================================================== + * + * $NetBSD: s_frexpf.c,v 1.9 2002/12/05 16:03:42 scw Exp $ + * $DragonFly: src/lib/libm/src/s_frexpf.c,v 1.1 2005/07/26 21:15:20 joerg Exp $ + */ + +#include +#include "math_private.h" + +static const float +two25 = 3.3554432000e+07; /* 0x4c000000 */ + +float +frexpf(float x, int *eptr) +{ + int32_t hx,ix; + GET_FLOAT_WORD(hx,x); + ix = 0x7fffffff&hx; + *eptr = 0; + if(ix>=0x7f800000||(ix==0)) return x; /* 0,inf,nan */ + if (ix<0x00800000) { /* subnormal */ + x *= two25; + GET_FLOAT_WORD(hx,x); + ix = hx&0x7fffffff; + *eptr = -25; + } + *eptr += (ix>>23)-126; + hx = (hx&0x807fffff)|0x3f000000; + *(int*)(void*)&x = hx; + return x; +} diff --git a/lib/libm/src/s_ilogb.c b/lib/libm/src/s_ilogb.c new file mode 100644 index 0000000000..235f01d9f0 --- /dev/null +++ b/lib/libm/src/s_ilogb.c @@ -0,0 +1,46 @@ +/* @(#)s_ilogb.c 5.1 93/09/24 */ +/* + * ==================================================== + * Copyright (C) 1993 by Sun Microsystems, Inc. All rights reserved. + * + * Developed at SunPro, a Sun Microsystems, Inc. business. + * Permission to use, copy, modify, and distribute this + * software is freely granted, provided that this notice + * is preserved. + * ==================================================== + * + * $NetBSD: s_ilogb.c,v 1.12 2002/05/26 22:01:56 wiz Exp $ + * $DragonFly: src/lib/libm/src/s_ilogb.c,v 1.1 2005/07/26 21:15:20 joerg Exp $ + */ + +/* ilogb(double x) + * return the binary exponent of non-zero x + * ilogb(0) = 0x80000001 + * ilogb(inf/NaN) = 0x7fffffff (no signal is raised) + */ + +#include +#include "math_private.h" + +int +ilogb(double x) +{ + int32_t hx,lx,ix; + + GET_HIGH_WORD(hx,x); + hx &= 0x7fffffff; + if(hx<0x00100000) { + GET_LOW_WORD(lx,x); + if((hx|lx)==0) + return 0x80000001; /* ilogb(0) = 0x80000001 */ + else /* subnormal x */ + if(hx==0) { + for (ix = -1043; lx>0; lx<<=1) ix -=1; + } else { + for (ix = -1022,hx<<=11; hx>0; hx<<=1) ix -=1; + } + return ix; + } + else if (hx<0x7ff00000) return (hx>>20)-1023; + else return 0x7fffffff; +} diff --git a/lib/libm/src/s_ilogbf.c b/lib/libm/src/s_ilogbf.c new file mode 100644 index 0000000000..85b24537f5 --- /dev/null +++ b/lib/libm/src/s_ilogbf.c @@ -0,0 +1,38 @@ +/* s_ilogbf.c -- float version of s_ilogb.c. + * Conversion to float by Ian Lance Taylor, Cygnus Support, ian@cygnus.com. + */ + +/* + * ==================================================== + * Copyright (C) 1993 by Sun Microsystems, Inc. All rights reserved. + * + * Developed at SunPro, a Sun Microsystems, Inc. business. + * Permission to use, copy, modify, and distribute this + * software is freely granted, provided that this notice + * is preserved. + * ==================================================== + * + * $NetBSD: s_ilogbf.c,v 1.7 2002/05/26 22:01:56 wiz Exp $ + * $DragonFly: src/lib/libm/src/s_ilogbf.c,v 1.1 2005/07/26 21:15:20 joerg Exp $ + */ + +#include +#include "math_private.h" + +int +ilogbf(float x) +{ + int32_t hx,ix; + + GET_FLOAT_WORD(hx,x); + hx &= 0x7fffffff; + if(hx<0x00800000) { + if(hx==0) + return 0x80000001; /* ilogb(0) = 0x80000001 */ + else /* subnormal x */ + for (ix = -126,hx<<=8; hx>0; hx<<=1) ix -=1; + return ix; + } + else if (hx<0x7f800000) return (hx>>23)-127; + else return 0x7fffffff; +} diff --git a/lib/libm/src/s_ldexpf.c b/lib/libm/src/s_ldexpf.c new file mode 100644 index 0000000000..f6a69a46d6 --- /dev/null +++ b/lib/libm/src/s_ldexpf.c @@ -0,0 +1,30 @@ +/* s_ldexpf.c -- float version of s_ldexp.c. + * Conversion to float by Ian Lance Taylor, Cygnus Support, ian@cygnus.com. + */ + +/* + * ==================================================== + * Copyright (C) 1993 by Sun Microsystems, Inc. All rights reserved. + * + * Developed at SunPro, a Sun Microsystems, Inc. business. + * Permission to use, copy, modify, and distribute this + * software is freely granted, provided that this notice + * is preserved. + * ==================================================== + * + * $NetBSD: s_ldexpf.c,v 1.6 2002/05/26 22:01:57 wiz Exp $ + * $DragonFly: src/lib/libm/src/s_ldexpf.c,v 1.1 2005/07/26 21:15:20 joerg Exp $ + */ + +#include +#include "math_private.h" +#include + +float +ldexpf(float value, int expo) +{ + if(!finitef(value)||value==(float)0.0) return value; + value = scalbnf(value,expo); + if(!finitef(value)||value==(float)0.0) errno = ERANGE; + return value; +} diff --git a/lib/libm/src/s_log1p.c b/lib/libm/src/s_log1p.c new file mode 100644 index 0000000000..835c830298 --- /dev/null +++ b/lib/libm/src/s_log1p.c @@ -0,0 +1,163 @@ +/* @(#)s_log1p.c 5.1 93/09/24 */ +/* + * ==================================================== + * Copyright (C) 1993 by Sun Microsystems, Inc. All rights reserved. + * + * Developed at SunPro, a Sun Microsystems, Inc. business. + * Permission to use, copy, modify, and distribute this + * software is freely granted, provided that this notice + * is preserved. + * ==================================================== + * + * $NetBSD: s_log1p.c,v 1.12 2002/05/26 22:01:57 wiz Exp $ + * $DragonFly: src/lib/libm/src/s_log1p.c,v 1.1 2005/07/26 21:15:20 joerg Exp $ + */ + +/* double log1p(double x) + * + * Method : + * 1. Argument Reduction: find k and f such that + * 1+x = 2^k * (1+f), + * where sqrt(2)/2 < 1+f < sqrt(2) . + * + * Note. If k=0, then f=x is exact. However, if k!=0, then f + * may not be representable exactly. In that case, a correction + * term is need. Let u=1+x rounded. Let c = (1+x)-u, then + * log(1+x) - log(u) ~ c/u. Thus, we proceed to compute log(u), + * and add back the correction term c/u. + * (Note: when x > 2**53, one can simply return log(x)) + * + * 2. Approximation of log1p(f). + * Let s = f/(2+f) ; based on log(1+f) = log(1+s) - log(1-s) + * = 2s + 2/3 s**3 + 2/5 s**5 + ....., + * = 2s + s*R + * We use a special Reme algorithm on [0,0.1716] to generate + * a polynomial of degree 14 to approximate R The maximum error + * of this polynomial approximation is bounded by 2**-58.45. In + * other words, + * 2 4 6 8 10 12 14 + * R(z) ~ Lp1*s +Lp2*s +Lp3*s +Lp4*s +Lp5*s +Lp6*s +Lp7*s + * (the values of Lp1 to Lp7 are listed in the program) + * and + * | 2 14 | -58.45 + * | Lp1*s +...+Lp7*s - R(z) | <= 2 + * | | + * Note that 2s = f - s*f = f - hfsq + s*hfsq, where hfsq = f*f/2. + * In order to guarantee error in log below 1ulp, we compute log + * by + * log1p(f) = f - (hfsq - s*(hfsq+R)). + * + * 3. Finally, log1p(x) = k*ln2 + log1p(f). + * = k*ln2_hi+(f-(hfsq-(s*(hfsq+R)+k*ln2_lo))) + * Here ln2 is split into two floating point number: + * ln2_hi + ln2_lo, + * where n*ln2_hi is always exact for |n| < 2000. + * + * Special cases: + * log1p(x) is NaN with signal if x < -1 (including -INF) ; + * log1p(+INF) is +INF; log1p(-1) is -INF with signal; + * log1p(NaN) is that NaN with no signal. + * + * Accuracy: + * according to an error analysis, the error is always less than + * 1 ulp (unit in the last place). + * + * Constants: + * The hexadecimal values are the intended ones for the following + * constants. The decimal values may be used, provided that the + * compiler will convert from decimal to binary accurately enough + * to produce the hexadecimal values shown. + * + * Note: Assuming log() return accurate answer, the following + * algorithm can be used to compute log1p(x) to within a few ULP: + * + * u = 1+x; + * if(u==1.0) return x ; else + * return log(u)*(x/(u-1.0)); + * + * See HP-15C Advanced Functions Handbook, p.193. + */ + +#include +#include "math_private.h" + +static const double +ln2_hi = 6.93147180369123816490e-01, /* 3fe62e42 fee00000 */ +ln2_lo = 1.90821492927058770002e-10, /* 3dea39ef 35793c76 */ +two54 = 1.80143985094819840000e+16, /* 43500000 00000000 */ +Lp1 = 6.666666666666735130e-01, /* 3FE55555 55555593 */ +Lp2 = 3.999999999940941908e-01, /* 3FD99999 9997FA04 */ +Lp3 = 2.857142874366239149e-01, /* 3FD24924 94229359 */ +Lp4 = 2.222219843214978396e-01, /* 3FCC71C5 1D8E78AF */ +Lp5 = 1.818357216161805012e-01, /* 3FC74664 96CB03DE */ +Lp6 = 1.531383769920937332e-01, /* 3FC39A09 D078C69F */ +Lp7 = 1.479819860511658591e-01; /* 3FC2F112 DF3E5244 */ + +static const double zero = 0.0; + +double +log1p(double x) +{ + double hfsq,f,c,s,z,R,u; + int32_t k,hx,hu,ax; + + f = c = 0; + hu = 0; + GET_HIGH_WORD(hx,x); + ax = hx&0x7fffffff; + + k = 1; + if (hx < 0x3FDA827A) { /* x < 0.41422 */ + if(ax>=0x3ff00000) { /* x <= -1.0 */ + if(x==-1.0) return -two54/zero; /* log1p(-1)=+inf */ + else return (x-x)/(x-x); /* log1p(x<-1)=NaN */ + } + if(ax<0x3e200000) { /* |x| < 2**-29 */ + if(two54+x>zero /* raise inexact */ + &&ax<0x3c900000) /* |x| < 2**-54 */ + return x; + else + return x - x*x*0.5; + } + if(hx>0||hx<=((int32_t)0xbfd2bec3)) { + k=0;f=x;hu=1;} /* -0.2929= 0x7ff00000) return x+x; + if(k!=0) { + if(hx<0x43400000) { + u = 1.0+x; + GET_HIGH_WORD(hu,u); + k = (hu>>20)-1023; + c = (k>0)? 1.0-(u-x):x-(u-1.0);/* correction term */ + c /= u; + } else { + u = x; + GET_HIGH_WORD(hu,u); + k = (hu>>20)-1023; + c = 0; + } + hu &= 0x000fffff; + if(hu<0x6a09e) { + SET_HIGH_WORD(u,hu|0x3ff00000); /* normalize u */ + } else { + k += 1; + SET_HIGH_WORD(u,hu|0x3fe00000); /* normalize u/2 */ + hu = (0x00100000-hu)>>2; + } + f = u-1.0; + } + hfsq=0.5*f*f; + if(hu==0) { /* |f| < 2**-20 */ + if(f==zero) { if(k==0) return zero; + else {c += k*ln2_lo; return k*ln2_hi+c;} + } + R = hfsq*(1.0-0.66666666666666666*f); + if(k==0) return f-R; else + return k*ln2_hi-((R-(k*ln2_lo+c))-f); + } + s = f/(2.0+f); + z = s*s; + R = z*(Lp1+z*(Lp2+z*(Lp3+z*(Lp4+z*(Lp5+z*(Lp6+z*Lp7)))))); + if(k==0) return f-(hfsq-s*(hfsq+R)); else + return k*ln2_hi-((hfsq-(s*(hfsq+R)+(k*ln2_lo+c)))-f); +} diff --git a/lib/libm/src/s_log1pf.c b/lib/libm/src/s_log1pf.c new file mode 100644 index 0000000000..091eb686a9 --- /dev/null +++ b/lib/libm/src/s_log1pf.c @@ -0,0 +1,102 @@ +/* s_log1pf.c -- float version of s_log1p.c. + * Conversion to float by Ian Lance Taylor, Cygnus Support, ian@cygnus.com. + */ + +/* + * ==================================================== + * Copyright (C) 1993 by Sun Microsystems, Inc. All rights reserved. + * + * Developed at SunPro, a Sun Microsystems, Inc. business. + * Permission to use, copy, modify, and distribute this + * software is freely granted, provided that this notice + * is preserved. + * ==================================================== + * + * $NetBSD: s_log1pf.c,v 1.8 2002/05/26 22:01:57 wiz Exp $ + * $DragonFly: src/lib/libm/src/s_log1pf.c,v 1.1 2005/07/26 21:15:20 joerg Exp $ + */ + +#include +#include "math_private.h" + +static const float +ln2_hi = 6.9313812256e-01, /* 0x3f317180 */ +ln2_lo = 9.0580006145e-06, /* 0x3717f7d1 */ +two25 = 3.355443200e+07, /* 0x4c000000 */ +Lp1 = 6.6666668653e-01, /* 3F2AAAAB */ +Lp2 = 4.0000000596e-01, /* 3ECCCCCD */ +Lp3 = 2.8571429849e-01, /* 3E924925 */ +Lp4 = 2.2222198546e-01, /* 3E638E29 */ +Lp5 = 1.8183572590e-01, /* 3E3A3325 */ +Lp6 = 1.5313838422e-01, /* 3E1CD04F */ +Lp7 = 1.4798198640e-01; /* 3E178897 */ + +static const float zero = 0.0; + +float +log1pf(float x) +{ + float hfsq,f,c,s,z,R,u; + int32_t k,hx,hu,ax; + + f = c = 0; + hu = 0; + GET_FLOAT_WORD(hx,x); + ax = hx&0x7fffffff; + + k = 1; + if (hx < 0x3ed413d7) { /* x < 0.41422 */ + if(ax>=0x3f800000) { /* x <= -1.0 */ + if(x==(float)-1.0) return -two25/zero; /* log1p(-1)=+inf */ + else return (x-x)/(x-x); /* log1p(x<-1)=NaN */ + } + if(ax<0x31000000) { /* |x| < 2**-29 */ + if(two25+x>zero /* raise inexact */ + &&ax<0x24800000) /* |x| < 2**-54 */ + return x; + else + return x - x*x*(float)0.5; + } + if(hx>0||hx<=((int32_t)0xbe95f61f)) { + k=0;f=x;hu=1;} /* -0.2929= 0x7f800000) return x+x; + if(k!=0) { + if(hx<0x5a000000) { + u = (float)1.0+x; + GET_FLOAT_WORD(hu,u); + k = (hu>>23)-127; + /* correction term */ + c = (k>0)? (float)1.0-(u-x):x-(u-(float)1.0); + c /= u; + } else { + u = x; + GET_FLOAT_WORD(hu,u); + k = (hu>>23)-127; + c = 0; + } + hu &= 0x007fffff; + if(hu<0x3504f7) { + SET_FLOAT_WORD(u,hu|0x3f800000);/* normalize u */ + } else { + k += 1; + SET_FLOAT_WORD(u,hu|0x3f000000); /* normalize u/2 */ + hu = (0x00800000-hu)>>2; + } + f = u-(float)1.0; + } + hfsq=(float)0.5*f*f; + if(hu==0) { /* |f| < 2**-20 */ + if(f==zero) { if(k==0) return zero; + else {c += k*ln2_lo; return k*ln2_hi+c;} + } + R = hfsq*((float)1.0-(float)0.66666666666666666*f); + if(k==0) return f-R; else + return k*ln2_hi-((R-(k*ln2_lo+c))-f); + } + s = f/((float)2.0+f); + z = s*s; + R = z*(Lp1+z*(Lp2+z*(Lp3+z*(Lp4+z*(Lp5+z*(Lp6+z*Lp7)))))); + if(k==0) return f-(hfsq-s*(hfsq+R)); else + return k*ln2_hi-((hfsq-(s*(hfsq+R)+(k*ln2_lo+c)))-f); +} diff --git a/lib/libm/src/s_logb.c b/lib/libm/src/s_logb.c new file mode 100644 index 0000000000..2707b66c50 --- /dev/null +++ b/lib/libm/src/s_logb.c @@ -0,0 +1,37 @@ +/* @(#)s_logb.c 5.1 93/09/24 */ +/* + * ==================================================== + * Copyright (C) 1993 by Sun Microsystems, Inc. All rights reserved. + * + * Developed at SunPro, a Sun Microsystems, Inc. business. + * Permission to use, copy, modify, and distribute this + * software is freely granted, provided that this notice + * is preserved. + * ==================================================== + * + * $NetBSD: s_logb.c,v 1.11 2002/05/26 22:01:57 wiz Exp $ + * $DragonFly: src/lib/libm/src/s_logb.c,v 1.1 2005/07/26 21:15:20 joerg Exp $ + */ + +/* + * double logb(x) + * IEEE 754 logb. Included to pass IEEE test suite. Not recommend. + * Use ilogb instead. + */ + +#include +#include "math_private.h" + +double +logb(double x) +{ + int32_t lx,ix; + EXTRACT_WORDS(ix,lx,x); + ix &= 0x7fffffff; /* high |x| */ + if((ix|lx)==0) return -1.0/fabs(x); + if(ix>=0x7ff00000) return x*x; + if((ix>>=20)==0) /* IEEE 754 logb */ + return -1022.0; + else + return (double) (ix-1023); +} diff --git a/lib/libm/src/s_logbf.c b/lib/libm/src/s_logbf.c new file mode 100644 index 0000000000..73e43be95f --- /dev/null +++ b/lib/libm/src/s_logbf.c @@ -0,0 +1,34 @@ +/* s_logbf.c -- float version of s_logb.c. + * Conversion to float by Ian Lance Taylor, Cygnus Support, ian@cygnus.com. + */ + +/* + * ==================================================== + * Copyright (C) 1993 by Sun Microsystems, Inc. All rights reserved. + * + * Developed at SunPro, a Sun Microsystems, Inc. business. + * Permission to use, copy, modify, and distribute this + * software is freely granted, provided that this notice + * is preserved. + * ==================================================== + * + * $NetBSD: s_logbf.c,v 1.7 2002/05/26 22:01:57 wiz Exp $ + * $DragonFly: src/lib/libm/src/s_logbf.c,v 1.1 2005/07/26 21:15:20 joerg Exp $ + */ + +#include +#include "math_private.h" + +float +logbf(float x) +{ + int32_t ix; + GET_FLOAT_WORD(ix,x); + ix &= 0x7fffffff; /* high |x| */ + if(ix==0) return (float)-1.0/fabsf(x); + if(ix>=0x7f800000) return x*x; + if((ix>>=23)==0) /* IEEE 754 logb */ + return -126.0; + else + return (float) (ix-127); +} diff --git a/lib/libm/src/s_modff.c b/lib/libm/src/s_modff.c new file mode 100644 index 0000000000..6e073378d1 --- /dev/null +++ b/lib/libm/src/s_modff.c @@ -0,0 +1,55 @@ +/* s_modff.c -- float version of s_modf.c. + * Conversion to float by Ian Lance Taylor, Cygnus Support, ian@cygnus.com. + */ + +/* + * ==================================================== + * Copyright (C) 1993 by Sun Microsystems, Inc. All rights reserved. + * + * Developed at SunPro, a Sun Microsystems, Inc. business. + * Permission to use, copy, modify, and distribute this + * software is freely granted, provided that this notice + * is preserved. + * ==================================================== + * + * $NetBSD: s_modff.c,v 1.7 2002/05/26 22:01:57 wiz Exp $ + * $DragonFly: src/lib/libm/src/s_modff.c,v 1.1 2005/07/26 21:15:20 joerg Exp $ + */ + +#include +#include "math_private.h" + +static const float one = 1.0; + +float +modff(float x, float *iptr) +{ + int32_t i0,j0_; + u_int32_t i; + GET_FLOAT_WORD(i0,x); + j0_ = ((i0>>23)&0xff)-0x7f; /* exponent of x */ + if(j0_<23) { /* integer part in x */ + if(j0_<0) { /* |x|<1 */ + SET_FLOAT_WORD(*iptr,i0&0x80000000); /* *iptr = +-0 */ + return x; + } else { + i = (0x007fffff)>>j0_; + if((i0&i)==0) { /* x is integral */ + u_int32_t ix; + *iptr = x; + GET_FLOAT_WORD(ix,x); + SET_FLOAT_WORD(x,ix&0x80000000); /* return +-0 */ + return x; + } else { + SET_FLOAT_WORD(*iptr,i0&(~i)); + return x - *iptr; + } + } + } else { /* no fraction part */ + u_int32_t ix; + *iptr = x*one; + GET_FLOAT_WORD(ix,x); + SET_FLOAT_WORD(x,ix&0x80000000); /* return +-0 */ + return x; + } +} diff --git a/lib/libm/src/s_nextafter.c b/lib/libm/src/s_nextafter.c new file mode 100644 index 0000000000..fcc94ccc3f --- /dev/null +++ b/lib/libm/src/s_nextafter.c @@ -0,0 +1,74 @@ +/* @(#)s_nextafter.c 5.1 93/09/24 */ +/* + * ==================================================== + * Copyright (C) 1993 by Sun Microsystems, Inc. All rights reserved. + * + * Developed at SunPro, a Sun Microsystems, Inc. business. + * Permission to use, copy, modify, and distribute this + * software is freely granted, provided that this notice + * is preserved. + * ==================================================== + * + * $NetBSD: s_nextafter.c,v 1.11 2002/05/26 22:01:57 wiz Exp $ + * $DragonFly: src/lib/libm/src/s_nextafter.c,v 1.1 2005/07/26 21:15:20 joerg Exp $ + */ + +/* IEEE functions + * nextafter(x,y) + * return the next machine floating-point number of x in the + * direction toward y. + * Special cases: + */ + +#include +#include "math_private.h" + +double +nextafter(double x, double y) +{ + int32_t hx,hy,ix,iy; + u_int32_t lx,ly; + + EXTRACT_WORDS(hx,lx,x); + EXTRACT_WORDS(hy,ly,y); + ix = hx&0x7fffffff; /* |x| */ + iy = hy&0x7fffffff; /* |y| */ + + if(((ix>=0x7ff00000)&&((ix-0x7ff00000)|lx)!=0) || /* x is nan */ + ((iy>=0x7ff00000)&&((iy-0x7ff00000)|ly)!=0)) /* y is nan */ + return x+y; + if(x==y) return x; /* x=y, return x */ + if((ix|lx)==0) { /* x == 0 */ + INSERT_WORDS(x,hy&0x80000000,1); /* return +-minsubnormal */ + y = x*x; + if(y==x) return y; else return x; /* raise underflow flag */ + } + if(hx>=0) { /* x > 0 */ + if(hx>hy||((hx==hy)&&(lx>ly))) { /* x > y, x -= ulp */ + if(lx==0) hx -= 1; + lx -= 1; + } else { /* x < y, x += ulp */ + lx += 1; + if(lx==0) hx += 1; + } + } else { /* x < 0 */ + if(hy>=0||hx>hy||((hx==hy)&&(lx>ly))){/* x < y, x -= ulp */ + if(lx==0) hx -= 1; + lx -= 1; + } else { /* x > y, x += ulp */ + lx += 1; + if(lx==0) hx += 1; + } + } + hy = hx&0x7ff00000; + if(hy>=0x7ff00000) return x+x; /* overflow */ + if(hy<0x00100000) { /* underflow */ + y = x*x; + if(y!=x) { /* raise underflow flag */ + INSERT_WORDS(y,hx,lx); + return y; + } + } + INSERT_WORDS(x,hx,lx); + return x; +} diff --git a/lib/libm/src/s_nextafterf.c b/lib/libm/src/s_nextafterf.c new file mode 100644 index 0000000000..ca0e8fa79e --- /dev/null +++ b/lib/libm/src/s_nextafterf.c @@ -0,0 +1,65 @@ +/* s_nextafterf.c -- float version of s_nextafter.c. + * Conversion to float by Ian Lance Taylor, Cygnus Support, ian@cygnus.com. + */ + +/* + * ==================================================== + * Copyright (C) 1993 by Sun Microsystems, Inc. All rights reserved. + * + * Developed at SunPro, a Sun Microsystems, Inc. business. + * Permission to use, copy, modify, and distribute this + * software is freely granted, provided that this notice + * is preserved. + * ==================================================== + * + * $NetBSD: s_nextafterf.c,v 1.7 2002/05/26 22:01:58 wiz Exp $ + * $DragonFly: src/lib/libm/src/s_nextafterf.c,v 1.1 2005/07/26 21:15:20 joerg Exp $ + */ + +#include +#include "math_private.h" + +float +nextafterf(float x, float y) +{ + int32_t hx,hy,ix,iy; + + GET_FLOAT_WORD(hx,x); + GET_FLOAT_WORD(hy,y); + ix = hx&0x7fffffff; /* |x| */ + iy = hy&0x7fffffff; /* |y| */ + + if((ix>0x7f800000) || /* x is nan */ + (iy>0x7f800000)) /* y is nan */ + return x+y; + if(x==y) return x; /* x=y, return x */ + if(ix==0) { /* x == 0 */ + SET_FLOAT_WORD(x,(hy&0x80000000)|1);/* return +-minsubnormal */ + y = x*x; + if(y==x) return y; else return x; /* raise underflow flag */ + } + if(hx>=0) { /* x > 0 */ + if(hx>hy) { /* x > y, x -= ulp */ + hx -= 1; + } else { /* x < y, x += ulp */ + hx += 1; + } + } else { /* x < 0 */ + if(hy>=0||hx>hy){ /* x < y, x -= ulp */ + hx -= 1; + } else { /* x > y, x += ulp */ + hx += 1; + } + } + hy = hx&0x7f800000; + if(hy>=0x7f800000) return x+x; /* overflow */ + if(hy<0x00800000) { /* underflow */ + y = x*x; + if(y!=x) { /* raise underflow flag */ + SET_FLOAT_WORD(y,hx); + return y; + } + } + SET_FLOAT_WORD(x,hx); + return x; +} diff --git a/lib/libm/src/s_rint.c b/lib/libm/src/s_rint.c new file mode 100644 index 0000000000..8d88f25d87 --- /dev/null +++ b/lib/libm/src/s_rint.c @@ -0,0 +1,77 @@ +/* @(#)s_rint.c 5.1 93/09/24 */ +/* + * ==================================================== + * Copyright (C) 1993 by Sun Microsystems, Inc. All rights reserved. + * + * Developed at SunPro, a Sun Microsystems, Inc. business. + * Permission to use, copy, modify, and distribute this + * software is freely granted, provided that this notice + * is preserved. + * ==================================================== + * + * $NetBSD: s_rint.c,v 1.11 2002/05/26 22:01:58 wiz Exp $ + * $DragonFly: src/lib/libm/src/s_rint.c,v 1.1 2005/07/26 21:15:20 joerg Exp $ + */ + +/* + * rint(x) + * Return x rounded to integral value according to the prevailing + * rounding mode. + * Method: + * Using floating addition. + * Exception: + * Inexact flag raised if x not equal to rint(x). + */ + +#include +#include "math_private.h" + +static const double +TWO52[2]={ + 4.50359962737049600000e+15, /* 0x43300000, 0x00000000 */ + -4.50359962737049600000e+15, /* 0xC3300000, 0x00000000 */ +}; + +double +rint(double x) +{ + int32_t i0,j0,sx; + u_int32_t i,i1; + double w,t; + EXTRACT_WORDS(i0,i1,x); + sx = (i0>>31)&1; + j0 = ((i0>>20)&0x7ff)-0x3ff; + if(j0<20) { + if(j0<0) { + if(((i0&0x7fffffff)|i1)==0) return x; + i1 |= (i0&0x0fffff); + i0 &= 0xfffe0000; + i0 |= ((i1|-i1)>>12)&0x80000; + SET_HIGH_WORD(x,i0); + w = TWO52[sx]+x; + t = w-TWO52[sx]; + GET_HIGH_WORD(i0,t); + SET_HIGH_WORD(t,(i0&0x7fffffff)|(sx<<31)); + return t; + } else { + i = (0x000fffff)>>j0; + if(((i0&i)|i1)==0) return x; /* x is integral */ + i>>=1; + if(((i0&i)|i1)!=0) { + if(j0==19) i1 = 0x40000000; else + i0 = (i0&(~i))|((0x20000)>>j0); + } + } + } else if (j0>51) { + if(j0==0x400) return x+x; /* inf or NaN */ + else return x; /* x is integral */ + } else { + i = ((u_int32_t)(0xffffffff))>>(j0-20); + if((i1&i)==0) return x; /* x is integral */ + i>>=1; + if((i1&i)!=0) i1 = (i1&(~i))|((0x40000000)>>(j0-20)); + } + INSERT_WORDS(x,i0,i1); + w = TWO52[sx]+x; + return w-TWO52[sx]; +} diff --git a/lib/libm/src/s_rintf.c b/lib/libm/src/s_rintf.c new file mode 100644 index 0000000000..9ec603b0ab --- /dev/null +++ b/lib/libm/src/s_rintf.c @@ -0,0 +1,62 @@ +/* s_rintf.c -- float version of s_rint.c. + * Conversion to float by Ian Lance Taylor, Cygnus Support, ian@cygnus.com. + */ + +/* + * ==================================================== + * Copyright (C) 1993 by Sun Microsystems, Inc. All rights reserved. + * + * Developed at SunPro, a Sun Microsystems, Inc. business. + * Permission to use, copy, modify, and distribute this + * software is freely granted, provided that this notice + * is preserved. + * ==================================================== + * + * $NetBSD: s_rintf.c,v 1.7 2002/05/26 22:01:58 wiz Exp $ + * $DragonFly: src/lib/libm/src/s_rintf.c,v 1.1 2005/07/26 21:15:20 joerg Exp $ + */ + +#include +#include "math_private.h" + +static const float +TWO23[2]={ + 8.3886080000e+06, /* 0x4b000000 */ + -8.3886080000e+06, /* 0xcb000000 */ +}; + +float +rintf(float x) +{ + int32_t i0,j0,sx; + u_int32_t i,i1; + float w,t; + GET_FLOAT_WORD(i0,x); + sx = (i0>>31)&1; + j0 = ((i0>>23)&0xff)-0x7f; + if(j0<23) { + if(j0<0) { + if((i0&0x7fffffff)==0) return x; + i1 = (i0&0x07fffff); + i0 &= 0xfff00000; + i0 |= ((i1|-i1)>>9)&0x400000; + SET_FLOAT_WORD(x,i0); + w = TWO23[sx]+x; + t = w-TWO23[sx]; + GET_FLOAT_WORD(i0,t); + SET_FLOAT_WORD(t,(i0&0x7fffffff)|(sx<<31)); + return t; + } else { + i = (0x007fffff)>>j0; + if((i0&i)==0) return x; /* x is integral */ + i>>=1; + if((i0&i)!=0) i0 = (i0&(~i))|((0x100000)>>j0); + } + } else { + if(j0==0x80) return x+x; /* inf or NaN */ + else return x; /* x is integral */ + } + SET_FLOAT_WORD(x,i0); + w = TWO23[sx]+x; + return w-TWO23[sx]; +} diff --git a/lib/libm/src/s_round.c b/lib/libm/src/s_round.c new file mode 100644 index 0000000000..bd9d158565 --- /dev/null +++ b/lib/libm/src/s_round.c @@ -0,0 +1,54 @@ +/*- + * Copyright (c) 2003, Steven G. Kargl + * All rights reserved. + * + * Redistribution and use in source and binary forms, with or without + * modification, are permitted provided that the following conditions + * are met: + * 1. Redistributions of source code must retain the above copyright + * notice unmodified, this list of conditions, and the following + * disclaimer. + * 2. Redistributions in binary form must reproduce the above copyright + * notice, this list of conditions and the following disclaimer in the + * documentation and/or other materials provided with the distribution. + * + * THIS SOFTWARE IS PROVIDED BY THE AUTHOR ``AS IS'' AND ANY EXPRESS OR + * IMPLIED WARRANTIES, INCLUDING, BUT NOT LIMITED TO, THE IMPLIED WARRANTIES + * OF MERCHANTABILITY AND FITNESS FOR A PARTICULAR PURPOSE ARE DISCLAIMED. + * IN NO EVENT SHALL THE AUTHOR BE LIABLE FOR ANY DIRECT, INDIRECT, + * INCIDENTAL, SPECIAL, EXEMPLARY, OR CONSEQUENTIAL DAMAGES (INCLUDING, BUT + * NOT LIMITED TO, PROCUREMENT OF SUBSTITUTE GOODS OR SERVICES; LOSS OF USE, + * DATA, OR PROFITS; OR BUSINESS INTERRUPTION) HOWEVER CAUSED AND ON ANY + * THEORY OF LIABILITY, WHETHER IN CONTRACT, STRICT LIABILITY, OR TORT + * (INCLUDING NEGLIGENCE OR OTHERWISE) ARISING IN ANY WAY OUT OF THE USE OF + * THIS SOFTWARE, EVEN IF ADVISED OF THE POSSIBILITY OF SUCH DAMAGE. + * + * $FreeBSD: src/lib/msun/src/s_round.c,v 1.1 2004/06/07 08:05:36 das Exp $ + * $NetBSD: s_round.c,v 1.1 2004/07/10 13:49:10 junyoung Exp $ + * $DragonFly: src/lib/libm/src/s_round.c,v 1.1 2005/07/26 21:15:20 joerg Exp $ + */ + +#include + +double +round(double x) +{ + double t; + int i; + + i = fpclassify(x); + if (i == FP_INFINITE || i == FP_NAN) + return (x); + + if (x >= 0.0) { + t = ceil(x); + if (t - x > 0.5) + t -= 1.0; + return (t); + } else { + t = ceil(-x); + if (t + x > 0.5) + t -= 1.0; + return (-t); + } +} diff --git a/lib/libm/src/s_roundf.c b/lib/libm/src/s_roundf.c new file mode 100644 index 0000000000..734bf83a30 --- /dev/null +++ b/lib/libm/src/s_roundf.c @@ -0,0 +1,54 @@ +/*- + * Copyright (c) 2003, Steven G. Kargl + * All rights reserved. + * + * Redistribution and use in source and binary forms, with or without + * modification, are permitted provided that the following conditions + * are met: + * 1. Redistributions of source code must retain the above copyright + * notice unmodified, this list of conditions, and the following + * disclaimer. + * 2. Redistributions in binary form must reproduce the above copyright + * notice, this list of conditions and the following disclaimer in the + * documentation and/or other materials provided with the distribution. + * + * THIS SOFTWARE IS PROVIDED BY THE AUTHOR ``AS IS'' AND ANY EXPRESS OR + * IMPLIED WARRANTIES, INCLUDING, BUT NOT LIMITED TO, THE IMPLIED WARRANTIES + * OF MERCHANTABILITY AND FITNESS FOR A PARTICULAR PURPOSE ARE DISCLAIMED. + * IN NO EVENT SHALL THE AUTHOR BE LIABLE FOR ANY DIRECT, INDIRECT, + * INCIDENTAL, SPECIAL, EXEMPLARY, OR CONSEQUENTIAL DAMAGES (INCLUDING, BUT + * NOT LIMITED TO, PROCUREMENT OF SUBSTITUTE GOODS OR SERVICES; LOSS OF USE, + * DATA, OR PROFITS; OR BUSINESS INTERRUPTION) HOWEVER CAUSED AND ON ANY + * THEORY OF LIABILITY, WHETHER IN CONTRACT, STRICT LIABILITY, OR TORT + * (INCLUDING NEGLIGENCE OR OTHERWISE) ARISING IN ANY WAY OUT OF THE USE OF + * THIS SOFTWARE, EVEN IF ADVISED OF THE POSSIBILITY OF SUCH DAMAGE. + * + * $FreeBSD: src/lib/msun/src/s_roundf.c,v 1.1 2004/06/07 08:05:36 das Exp $ + * $NetBSD: s_roundf.c,v 1.1 2004/07/10 13:49:10 junyoung Exp $ + * $DragonFly: src/lib/libm/src/s_roundf.c,v 1.1 2005/07/26 21:15:20 joerg Exp $ + */ + +#include + +float +roundf(float x) +{ + float t; + int i; + + i = fpclassify(x); + if (i == FP_INFINITE || i == FP_NAN) + return (x); + + if (x >= 0.0) { + t = ceilf(x); + if (t - x > 0.5) + t -= 1.0; + return (t); + } else { + t = ceilf(-x); + if (t + x > 0.5) + t -= 1.0; + return (-t); + } +} diff --git a/lib/libm/src/s_scalbn.c b/lib/libm/src/s_scalbn.c new file mode 100644 index 0000000000..bc110374c2 --- /dev/null +++ b/lib/libm/src/s_scalbn.c @@ -0,0 +1,58 @@ +/* @(#)s_scalbn.c 5.1 93/09/24 */ +/* + * ==================================================== + * Copyright (C) 1993 by Sun Microsystems, Inc. All rights reserved. + * + * Developed at SunPro, a Sun Microsystems, Inc. business. + * Permission to use, copy, modify, and distribute this + * software is freely granted, provided that this notice + * is preserved. + * ==================================================== + * + * $NetBSD: s_scalbn.c,v 1.12 2002/05/26 22:01:58 wiz Exp $ + * $DragonFly: src/lib/libm/src/s_scalbn.c,v 1.1 2005/07/26 21:15:20 joerg Exp $ + */ + +/* + * scalbn (double x, int n) + * scalbn(x,n) returns x* 2**n computed by exponent + * manipulation rather than by actually performing an + * exponentiation or a multiplication. + */ + +#include +#include "math_private.h" + +static const double +two54 = 1.80143985094819840000e+16, /* 0x43500000, 0x00000000 */ +twom54 = 5.55111512312578270212e-17, /* 0x3C900000, 0x00000000 */ +huge = 1.0e+300, +tiny = 1.0e-300; + +double +scalbn(double x, int n) +{ + int32_t k,hx,lx; + EXTRACT_WORDS(hx,lx,x); + k = (hx&0x7ff00000)>>20; /* extract exponent */ + if (k==0) { /* 0 or subnormal x */ + if ((lx|(hx&0x7fffffff))==0) return x; /* +-0 */ + x *= two54; + GET_HIGH_WORD(hx,x); + k = ((hx&0x7ff00000)>>20) - 54; + if (n< -50000) return tiny*x; /*underflow*/ + } + if (k==0x7ff) return x+x; /* NaN or Inf */ + k = k+n; + if (k > 0x7fe) return huge*copysign(huge,x); /* overflow */ + if (k > 0) /* normal result */ + {SET_HIGH_WORD(x,(hx&0x800fffff)|(k<<20)); return x;} + if (k <= -54) { + if (n > 50000) /* in case integer overflow in n+k */ + return huge*copysign(huge,x); /*overflow*/ + else return tiny*copysign(tiny,x); /*underflow*/ + } + k += 54; /* subnormal result */ + SET_HIGH_WORD(x,(hx&0x800fffff)|(k<<20)); + return x*twom54; +} diff --git a/lib/libm/src/s_scalbnf.c b/lib/libm/src/s_scalbnf.c new file mode 100644 index 0000000000..8aefff74d4 --- /dev/null +++ b/lib/libm/src/s_scalbnf.c @@ -0,0 +1,54 @@ +/* s_scalbnf.c -- float version of s_scalbn.c. + * Conversion to float by Ian Lance Taylor, Cygnus Support, ian@cygnus.com. + */ + +/* + * ==================================================== + * Copyright (C) 1993 by Sun Microsystems, Inc. All rights reserved. + * + * Developed at SunPro, a Sun Microsystems, Inc. business. + * Permission to use, copy, modify, and distribute this + * software is freely granted, provided that this notice + * is preserved. + * ==================================================== + * + * $NetBSD: s_scalbnf.c,v 1.8 2002/05/26 22:01:58 wiz Exp $ + * $DragonFly: src/lib/libm/src/s_scalbnf.c,v 1.1 2005/07/26 21:15:20 joerg Exp $ + */ + +#include +#include "math_private.h" + +static const float +two25 = 3.355443200e+07, /* 0x4c000000 */ +twom25 = 2.9802322388e-08, /* 0x33000000 */ +huge = 1.0e+30, +tiny = 1.0e-30; + +float +scalbnf(float x, int n) +{ + int32_t k,ix; + GET_FLOAT_WORD(ix,x); + k = (ix&0x7f800000)>>23; /* extract exponent */ + if (k==0) { /* 0 or subnormal x */ + if ((ix&0x7fffffff)==0) return x; /* +-0 */ + x *= two25; + GET_FLOAT_WORD(ix,x); + k = ((ix&0x7f800000)>>23) - 25; + if (n< -50000) return tiny*x; /*underflow*/ + } + if (k==0xff) return x+x; /* NaN or Inf */ + k = k+n; + if (k > 0xfe) return huge*copysignf(huge,x); /* overflow */ + if (k > 0) /* normal result */ + {SET_FLOAT_WORD(x,(ix&0x807fffff)|(k<<23)); return x;} + if (k <= -25) { + if (n > 50000) /* in case integer overflow in n+k */ + return huge*copysignf(huge,x); /*overflow*/ + else return tiny*copysignf(tiny,x); /*underflow*/ + } + k += 25; /* subnormal result */ + SET_FLOAT_WORD(x,(ix&0x807fffff)|(k<<23)); + return x*twom25; +} diff --git a/lib/libm/src/s_signgam.c b/lib/libm/src/s_signgam.c new file mode 100644 index 0000000000..4d6345119b --- /dev/null +++ b/lib/libm/src/s_signgam.c @@ -0,0 +1,7 @@ +/* $NetBSD: s_signgam.c,v 1.4 1998/01/09 03:15:46 perry Exp $ */ +/* $DragonFly: src/lib/libm/src/s_signgam.c,v 1.1 2005/07/26 21:15:20 joerg Exp $ */ + +#include +#include "math_private.h" + +int signgam = 0; diff --git a/lib/libm/src/s_significand.c b/lib/libm/src/s_significand.c new file mode 100644 index 0000000000..85f3d7a07d --- /dev/null +++ b/lib/libm/src/s_significand.c @@ -0,0 +1,29 @@ +/* @(#)s_signif.c 5.1 93/09/24 */ +/* + * ==================================================== + * Copyright (C) 1993 by Sun Microsystems, Inc. All rights reserved. + * + * Developed at SunPro, a Sun Microsystems, Inc. business. + * Permission to use, copy, modify, and distribute this + * software is freely granted, provided that this notice + * is preserved. + * ==================================================== + * + * $NetBSD: s_significand.c,v 1.9 2002/05/26 22:01:58 wiz Exp $ + * $DragonFly: src/lib/libm/src/s_significand.c,v 1.1 2005/07/26 21:15:20 joerg Exp $ + */ + +/* + * significand(x) computes just + * scalb(x, (double) -ilogb(x)), + * for exercising the fraction-part(F) IEEE 754-1985 test vector. + */ + +#include +#include "math_private.h" + +double +significand(double x) +{ + return scalb(x,(double) -ilogb(x)); +} diff --git a/lib/libm/src/s_significandf.c b/lib/libm/src/s_significandf.c new file mode 100644 index 0000000000..cb90887a3f --- /dev/null +++ b/lib/libm/src/s_significandf.c @@ -0,0 +1,26 @@ +/* s_significandf.c -- float version of s_significand.c. + * Conversion to float by Ian Lance Taylor, Cygnus Support, ian@cygnus.com. + */ + +/* + * ==================================================== + * Copyright (C) 1993 by Sun Microsystems, Inc. All rights reserved. + * + * Developed at SunPro, a Sun Microsystems, Inc. business. + * Permission to use, copy, modify, and distribute this + * software is freely granted, provided that this notice + * is preserved. + * ==================================================== + * + * $NetBSD: s_significandf.c,v 1.6 2002/05/26 22:01:58 wiz Exp $ + * $DragonFly: src/lib/libm/src/s_significandf.c,v 1.1 2005/07/26 21:15:20 joerg Exp $ + */ + +#include +#include "math_private.h" + +float +significandf(float x) +{ + return scalbf(x,(float) -ilogbf(x)); +} diff --git a/lib/libm/src/s_sin.c b/lib/libm/src/s_sin.c new file mode 100644 index 0000000000..a045b877f4 --- /dev/null +++ b/lib/libm/src/s_sin.c @@ -0,0 +1,77 @@ +/* @(#)s_sin.c 5.1 93/09/24 */ +/* + * ==================================================== + * Copyright (C) 1993 by Sun Microsystems, Inc. All rights reserved. + * + * Developed at SunPro, a Sun Microsystems, Inc. business. + * Permission to use, copy, modify, and distribute this + * software is freely granted, provided that this notice + * is preserved. + * ==================================================== + * + * $NetBSD: s_sin.c,v 1.10 2002/05/26 22:01:58 wiz Exp $ + * $DragonFly: src/lib/libm/src/s_sin.c,v 1.1 2005/07/26 21:15:20 joerg Exp $ + */ + +/* sin(x) + * Return sine function of x. + * + * kernel function: + * __kernel_sin ... sine function on [-pi/4,pi/4] + * __kernel_cos ... cose function on [-pi/4,pi/4] + * __libm_rem_pio2 ... argument reduction routine + * + * Method. + * Let S,C and T denote the sin, cos and tan respectively on + * [-PI/4, +PI/4]. Reduce the argument x to y1+y2 = x-k*pi/2 + * in [-pi/4 , +pi/4], and let n = k mod 4. + * We have + * + * n sin(x) cos(x) tan(x) + * ---------------------------------------------------------- + * 0 S C T + * 1 C -S -1/T + * 2 -S -C T + * 3 -C S -1/T + * ---------------------------------------------------------- + * + * Special cases: + * Let trig be any of sin, cos, or tan. + * trig(+-INF) is NaN, with signals; + * trig(NaN) is that NaN; + * + * Accuracy: + * TRIG(x) returns trig(x) nearly rounded + */ + +#include +#include "math_private.h" + +double +sin(double x) +{ + double y[2],z=0.0; + int32_t n, ix; + + /* High word of x. */ + GET_HIGH_WORD(ix,x); + + /* |x| ~< pi/4 */ + ix &= 0x7fffffff; + if(ix <= 0x3fe921fb) return __kernel_sin(x,z,0); + + /* sin(Inf or NaN) is NaN */ + else if (ix>=0x7ff00000) return x-x; + + /* argument reduction needed */ + else { + n = __libm_rem_pio2(x,y); + switch(n&3) { + case 0: return __kernel_sin(y[0],y[1],1); + case 1: return __kernel_cos(y[0],y[1]); + case 2: return -__kernel_sin(y[0],y[1],1); + default: + return -__kernel_cos(y[0],y[1]); + } + } +} diff --git a/lib/libm/src/s_sinf.c b/lib/libm/src/s_sinf.c new file mode 100644 index 0000000000..7bea34f6cc --- /dev/null +++ b/lib/libm/src/s_sinf.c @@ -0,0 +1,48 @@ +/* s_sinf.c -- float version of s_sin.c. + * Conversion to float by Ian Lance Taylor, Cygnus Support, ian@cygnus.com. + */ + +/* + * ==================================================== + * Copyright (C) 1993 by Sun Microsystems, Inc. All rights reserved. + * + * Developed at SunPro, a Sun Microsystems, Inc. business. + * Permission to use, copy, modify, and distribute this + * software is freely granted, provided that this notice + * is preserved. + * ==================================================== + * + * $NetBSD: s_sinf.c,v 1.7 2002/05/26 22:01:58 wiz Exp $ + * $DragonFly: src/lib/libm/src/s_sinf.c,v 1.1 2005/07/26 21:15:20 joerg Exp $ + */ + +#include +#include "math_private.h" + +float +sinf(float x) +{ + float y[2],z=0.0; + int32_t n, ix; + + GET_FLOAT_WORD(ix,x); + + /* |x| ~< pi/4 */ + ix &= 0x7fffffff; + if(ix <= 0x3f490fd8) return __kernel_sinf(x,z,0); + + /* sin(Inf or NaN) is NaN */ + else if (ix>=0x7f800000) return x-x; + + /* argument reduction needed */ + else { + n = __libm_rem_pio2f(x,y); + switch(n&3) { + case 0: return __kernel_sinf(y[0],y[1],1); + case 1: return __kernel_cosf(y[0],y[1]); + case 2: return -__kernel_sinf(y[0],y[1],1); + default: + return -__kernel_cosf(y[0],y[1]); + } + } +} diff --git a/lib/libm/src/s_tan.c b/lib/libm/src/s_tan.c new file mode 100644 index 0000000000..d39bcb707f --- /dev/null +++ b/lib/libm/src/s_tan.c @@ -0,0 +1,71 @@ +/* @(#)s_tan.c 5.1 93/09/24 */ +/* + * ==================================================== + * Copyright (C) 1993 by Sun Microsystems, Inc. All rights reserved. + * + * Developed at SunPro, a Sun Microsystems, Inc. business. + * Permission to use, copy, modify, and distribute this + * software is freely granted, provided that this notice + * is preserved. + * ==================================================== + * + * $NetBSD: s_tan.c,v 1.10 2002/05/26 22:01:58 wiz Exp $ + * $DragonFly: src/lib/libm/src/s_tan.c,v 1.1 2005/07/26 21:15:20 joerg Exp $ + */ + +/* tan(x) + * Return tangent function of x. + * + * kernel function: + * __kernel_tan ... tangent function on [-pi/4,pi/4] + * __libm_rem_pio2 ... argument reduction routine + * + * Method. + * Let S,C and T denote the sin, cos and tan respectively on + * [-PI/4, +PI/4]. Reduce the argument x to y1+y2 = x-k*pi/2 + * in [-pi/4 , +pi/4], and let n = k mod 4. + * We have + * + * n sin(x) cos(x) tan(x) + * ---------------------------------------------------------- + * 0 S C T + * 1 C -S -1/T + * 2 -S -C T + * 3 -C S -1/T + * ---------------------------------------------------------- + * + * Special cases: + * Let trig be any of sin, cos, or tan. + * trig(+-INF) is NaN, with signals; + * trig(NaN) is that NaN; + * + * Accuracy: + * TRIG(x) returns trig(x) nearly rounded + */ + +#include +#include "math_private.h" + +double +tan(double x) +{ + double y[2],z=0.0; + int32_t n, ix; + + /* High word of x. */ + GET_HIGH_WORD(ix,x); + + /* |x| ~< pi/4 */ + ix &= 0x7fffffff; + if(ix <= 0x3fe921fb) return __kernel_tan(x,z,1); + + /* tan(Inf or NaN) is NaN */ + else if (ix>=0x7ff00000) return x-x; /* NaN */ + + /* argument reduction needed */ + else { + n = __libm_rem_pio2(x,y); + return __kernel_tan(y[0],y[1],1-((n&1)<<1)); /* 1 -- n even + -1 -- n odd */ + } +} diff --git a/lib/libm/src/s_tanf.c b/lib/libm/src/s_tanf.c new file mode 100644 index 0000000000..00265ff48f --- /dev/null +++ b/lib/libm/src/s_tanf.c @@ -0,0 +1,43 @@ +/* s_tanf.c -- float version of s_tan.c. + * Conversion to float by Ian Lance Taylor, Cygnus Support, ian@cygnus.com. + */ + +/* + * ==================================================== + * Copyright (C) 1993 by Sun Microsystems, Inc. All rights reserved. + * + * Developed at SunPro, a Sun Microsystems, Inc. business. + * Permission to use, copy, modify, and distribute this + * software is freely granted, provided that this notice + * is preserved. + * ==================================================== + * + * $NetBSD: s_tanf.c,v 1.7 2002/05/26 22:01:58 wiz Exp $ + * $DragonFly: src/lib/libm/src/s_tanf.c,v 1.1 2005/07/26 21:15:20 joerg Exp $ + */ + +#include +#include "math_private.h" + +float +tanf(float x) +{ + float y[2],z=0.0; + int32_t n, ix; + + GET_FLOAT_WORD(ix,x); + + /* |x| ~< pi/4 */ + ix &= 0x7fffffff; + if(ix <= 0x3f490fda) return __kernel_tanf(x,z,1); + + /* tan(Inf or NaN) is NaN */ + else if (ix>=0x7f800000) return x-x; /* NaN */ + + /* argument reduction needed */ + else { + n = __libm_rem_pio2f(x,y); + return __kernel_tanf(y[0],y[1],1-((n&1)<<1)); /* 1 -- n even + -1 -- n odd */ + } +} diff --git a/lib/libm/src/s_tanh.c b/lib/libm/src/s_tanh.c new file mode 100644 index 0000000000..88eb29491e --- /dev/null +++ b/lib/libm/src/s_tanh.c @@ -0,0 +1,77 @@ +/* @(#)s_tanh.c 5.1 93/09/24 */ +/* + * ==================================================== + * Copyright (C) 1993 by Sun Microsystems, Inc. All rights reserved. + * + * Developed at SunPro, a Sun Microsystems, Inc. business. + * Permission to use, copy, modify, and distribute this + * software is freely granted, provided that this notice + * is preserved. + * ==================================================== + * + * $NetBSD: s_tanh.c,v 1.10 2002/05/26 22:01:59 wiz Exp $ + * $DragonFly: src/lib/libm/src/s_tanh.c,v 1.1 2005/07/26 21:15:20 joerg Exp $ + */ + +/* Tanh(x) + * Return the Hyperbolic Tangent of x + * + * Method : + * x -x + * e - e + * 0. tanh(x) is defined to be ----------- + * x -x + * e + e + * 1. reduce x to non-negative by tanh(-x) = -tanh(x). + * 2. 0 <= x <= 2**-55 : tanh(x) := x*(one+x) + * -t + * 2**-55 < x <= 1 : tanh(x) := -----; t = expm1(-2x) + * t + 2 + * 2 + * 1 <= x <= 22.0 : tanh(x) := 1- ----- ; t=expm1(2x) + * t + 2 + * 22.0 < x <= INF : tanh(x) := 1. + * + * Special cases: + * tanh(NaN) is NaN; + * only tanh(0)=0 is exact for finite argument. + */ + +#include +#include "math_private.h" + +static const double one=1.0, two=2.0, tiny = 1.0e-300; + +double +tanh(double x) +{ + double t,z; + int32_t jx,ix; + + /* High word of |x|. */ + GET_HIGH_WORD(jx,x); + ix = jx&0x7fffffff; + + /* x is INF or NaN */ + if(ix>=0x7ff00000) { + if (jx>=0) return one/x+one; /* tanh(+-inf)=+-1 */ + else return one/x-one; /* tanh(NaN) = NaN */ + } + + /* |x| < 22 */ + if (ix < 0x40360000) { /* |x|<22 */ + if (ix<0x3c800000) /* |x|<2**-55 */ + return x*(one+x); /* tanh(small) = small */ + if (ix>=0x3ff00000) { /* |x|>=1 */ + t = expm1(two*fabs(x)); + z = one - two/(t+two); + } else { + t = expm1(-two*fabs(x)); + z= -t/(t+two); + } + /* |x| > 22, return +-1 */ + } else { + z = one - tiny; /* raised inexact flag */ + } + return (jx>=0)? z: -z; +} diff --git a/lib/libm/src/s_tanhf.c b/lib/libm/src/s_tanhf.c new file mode 100644 index 0000000000..9673e7df7e --- /dev/null +++ b/lib/libm/src/s_tanhf.c @@ -0,0 +1,55 @@ +/* s_tanhf.c -- float version of s_tanh.c. + * Conversion to float by Ian Lance Taylor, Cygnus Support, ian@cygnus.com. + */ + +/* + * ==================================================== + * Copyright (C) 1993 by Sun Microsystems, Inc. All rights reserved. + * + * Developed at SunPro, a Sun Microsystems, Inc. business. + * Permission to use, copy, modify, and distribute this + * software is freely granted, provided that this notice + * is preserved. + * ==================================================== + * + * $NetBSD: s_tanhf.c,v 1.7 2002/05/26 22:01:59 wiz Exp $ + * $DragonFly: src/lib/libm/src/s_tanhf.c,v 1.1 2005/07/26 21:15:20 joerg Exp $ + */ + +#include +#include "math_private.h" + +static const float one=1.0, two=2.0, tiny = 1.0e-30; + +float +tanhf(float x) +{ + float t,z; + int32_t jx,ix; + + GET_FLOAT_WORD(jx,x); + ix = jx&0x7fffffff; + + /* x is INF or NaN */ + if(ix>=0x7f800000) { + if (jx>=0) return one/x+one; /* tanh(+-inf)=+-1 */ + else return one/x-one; /* tanh(NaN) = NaN */ + } + + /* |x| < 22 */ + if (ix < 0x41b00000) { /* |x|<22 */ + if (ix<0x24000000) /* |x|<2**-55 */ + return x*(one+x); /* tanh(small) = small */ + if (ix>=0x3f800000) { /* |x|>=1 */ + t = expm1f(two*fabsf(x)); + z = one - two/(t+two); + } else { + t = expm1f(-two*fabsf(x)); + z= -t/(t+two); + } + /* |x| > 22, return +-1 */ + } else { + z = one - tiny; /* raised inexact flag */ + } + return (jx>=0)? z: -z; +} diff --git a/lib/libm/src/w_cabs.c b/lib/libm/src/w_cabs.c new file mode 100644 index 0000000000..7e9318e575 --- /dev/null +++ b/lib/libm/src/w_cabs.c @@ -0,0 +1,18 @@ +/* + * cabs() wrapper for hypot(). + * + * Written by J.T. Conklin, + * Placed into the Public Domain, 1994. + * + * $NetBSD: w_cabs.c,v 1.4 2001/01/06 00:15:00 christos Exp $ + * $DragonFly: src/lib/libm/src/w_cabs.c,v 1.1 2005/07/26 21:15:20 joerg Exp $ + */ + +#include +#include + +double +cabs(double complex z) +{ + return hypot(creal(z), cimag(z)); +} diff --git a/lib/libm/src/w_cabsf.c b/lib/libm/src/w_cabsf.c new file mode 100644 index 0000000000..8021b6e586 --- /dev/null +++ b/lib/libm/src/w_cabsf.c @@ -0,0 +1,18 @@ +/* + * cabsf() wrapper for hypotf(). + * + * Written by J.T. Conklin, + * Placed into the Public Domain, 1994. + * + * $NetBSD: w_cabsf.c,v 1.4 2001/01/06 00:15:00 christos Exp $ + * $DragonFly: src/lib/libm/src/w_cabsf.c,v 1.1 2005/07/26 21:15:20 joerg Exp $ + */ + +#include +#include + +float +cabsf(float complex z) +{ + return hypot(crealf(z), cimagf(z)); +} diff --git a/lib/libm/src/w_drem.c b/lib/libm/src/w_drem.c new file mode 100644 index 0000000000..6dcaee1f20 --- /dev/null +++ b/lib/libm/src/w_drem.c @@ -0,0 +1,17 @@ +/* + * drem() wrapper for remainder(). + * + * Written by J.T. Conklin, + * Placed into the Public Domain, 1994. + * + * $NetBSD: w_drem.c,v 1.4 2004/06/25 15:57:38 drochner Exp $ + * $DragonFly: src/lib/libm/src/w_drem.c,v 1.1 2005/07/26 21:15:20 joerg Exp $ + */ + +#include + +double +drem(double x, double y) +{ + return remainder(x, y); +} diff --git a/lib/libm/src/w_dremf.c b/lib/libm/src/w_dremf.c new file mode 100644 index 0000000000..7cb50fdd48 --- /dev/null +++ b/lib/libm/src/w_dremf.c @@ -0,0 +1,18 @@ +/* + * dremf() wrapper for remainderf(). + * + * Written by J.T. Conklin, + * Placed into the Public Domain, 1994. + * + * $NetBSD: w_dremf.c,v 1.4 2004/06/25 15:57:38 drochner Exp $ + * $DragonFly: src/lib/libm/src/w_dremf.c,v 1.1 2005/07/26 21:15:20 joerg Exp $ + */ + +#include +#include "math_private.h" + +float +dremf(float x, float y) +{ + return remainderf(x, y); +} diff --git a/lib/libm/src/w_gamma.c b/lib/libm/src/w_gamma.c new file mode 100644 index 0000000000..e9ab9bd99a --- /dev/null +++ b/lib/libm/src/w_gamma.c @@ -0,0 +1,29 @@ +/* @(#)w_gamma.c 5.1 93/09/24 */ +/* + * ==================================================== + * Copyright (C) 1993 by Sun Microsystems, Inc. All rights reserved. + * + * Developed at SunPro, a Sun Microsystems, Inc. business. + * Permission to use, copy, modify, and distribute this + * software is freely granted, provided that this notice + * is preserved. + * ==================================================== + * + * $NetBSD: w_gamma.c,v 1.11 2002/05/26 22:02:00 wiz Exp $ + * $DragonFly: src/lib/libm/src/w_gamma.c,v 1.1 2005/07/26 21:15:20 joerg Exp $ + */ + +/* double gamma(double x) + * Return the logarithm of the Gamma function of x. + * + * Method: call gamma_r + */ + +#include +#include "math_private.h" + +double +gamma(double x) +{ + return lgamma_r(x,&signgam); +} diff --git a/lib/libm/src/w_gamma_r.c b/lib/libm/src/w_gamma_r.c new file mode 100644 index 0000000000..e294e1181c --- /dev/null +++ b/lib/libm/src/w_gamma_r.c @@ -0,0 +1,27 @@ +/* @(#)wr_gamma.c 5.1 93/09/24 */ +/* + * ==================================================== + * Copyright (C) 1993 by Sun Microsystems, Inc. All rights reserved. + * + * Developed at SunPro, a Sun Microsystems, Inc. business. + * Permission to use, copy, modify, and distribute this + * software is freely granted, provided that this notice + * is preserved. + * ==================================================== + * + * $NetBSD: w_gamma_r.c,v 1.11 2002/05/26 22:02:00 wiz Exp $ + * $DragonFly: src/lib/libm/src/w_gamma_r.c,v 1.1 2005/07/26 21:15:20 joerg Exp $ + */ + +/* + * wrapper double gamma_r(double x, int *signgamp) + */ + +#include +#include "math_private.h" + +double +gamma_r(double x, int *signgamp) /* wrapper lgamma_r */ +{ + return lgamma_r(x,signgamp); +} diff --git a/lib/libm/src/w_gammaf.c b/lib/libm/src/w_gammaf.c new file mode 100644 index 0000000000..9502d8691d --- /dev/null +++ b/lib/libm/src/w_gammaf.c @@ -0,0 +1,26 @@ +/* w_gammaf.c -- float version of w_gamma.c. + * Conversion to float by Ian Lance Taylor, Cygnus Support, ian@cygnus.com. + */ + +/* + * ==================================================== + * Copyright (C) 1993 by Sun Microsystems, Inc. All rights reserved. + * + * Developed at SunPro, a Sun Microsystems, Inc. business. + * Permission to use, copy, modify, and distribute this + * software is freely granted, provided that this notice + * is preserved. + * ==================================================== + * + * $NetBSD: w_gammaf.c,v 1.8 2002/05/26 22:02:01 wiz Exp $ + * $DragonFly: src/lib/libm/src/w_gammaf.c,v 1.1 2005/07/26 21:15:20 joerg Exp $ + */ + +#include +#include "math_private.h" + +float +gammaf(float x) +{ + return lgammaf_r(x,&signgam); +} diff --git a/lib/libm/src/w_gammaf_r.c b/lib/libm/src/w_gammaf_r.c new file mode 100644 index 0000000000..2a70a8153b --- /dev/null +++ b/lib/libm/src/w_gammaf_r.c @@ -0,0 +1,30 @@ +/* w_gammaf_r.c -- float version of w_gamma_r.c. + * Conversion to float by Ian Lance Taylor, Cygnus Support, ian@cygnus.com. + */ + +/* + * ==================================================== + * Copyright (C) 1993 by Sun Microsystems, Inc. All rights reserved. + * + * Developed at SunPro, a Sun Microsystems, Inc. business. + * Permission to use, copy, modify, and distribute this + * software is freely granted, provided that this notice + * is preserved. + * ==================================================== + * + * $NetBSD: w_gammaf_r.c,v 1.8 2002/05/26 22:02:01 wiz Exp $ + * $DragonFly: src/lib/libm/src/w_gammaf_r.c,v 1.1 2005/07/26 21:15:20 joerg Exp $ + */ + +/* + * wrapper float gammaf_r(float x, int *signgamp) + */ + +#include +#include "math_private.h" + +float +gammaf_r(float x, int *signgamp) /* wrapper lgammaf_r */ +{ + return lgammaf_r(x,signgamp); +} diff --git a/lib/libm/src/w_lgamma.c b/lib/libm/src/w_lgamma.c new file mode 100644 index 0000000000..df79712ab8 --- /dev/null +++ b/lib/libm/src/w_lgamma.c @@ -0,0 +1,28 @@ +/* @(#)w_lgamma.c 5.1 93/09/24 */ +/* + * ==================================================== + * Copyright (C) 1993 by Sun Microsystems, Inc. All rights reserved. + * + * Developed at SunPro, a Sun Microsystems, Inc. business. + * Permission to use, copy, modify, and distribute this + * software is freely granted, provided that this notice + * is preserved. + * ==================================================== + * + * $NetBSD: w_lgamma.c,v 1.10 2002/05/26 22:02:02 wiz Exp $ + * $DragonFly: src/lib/libm/src/w_lgamma.c,v 1.1 2005/07/26 21:15:20 joerg Exp $ + */ + +/* + * double lgamma(double x) + * Return the logarithm of the Gamma function of x. + */ + +#include +#include "math_private.h" + +double +lgamma(double x) +{ + return lgamma_r(x,&signgam); +} diff --git a/lib/libm/src/w_lgammaf.c b/lib/libm/src/w_lgammaf.c new file mode 100644 index 0000000000..13b3041dbd --- /dev/null +++ b/lib/libm/src/w_lgammaf.c @@ -0,0 +1,26 @@ +/* w_lgammaf.c -- float version of w_lgamma.c. + * Conversion to float by Ian Lance Taylor, Cygnus Support, ian@cygnus.com. + */ + +/* + * ==================================================== + * Copyright (C) 1993 by Sun Microsystems, Inc. All rights reserved. + * + * Developed at SunPro, a Sun Microsystems, Inc. business. + * Permission to use, copy, modify, and distribute this + * software is freely granted, provided that this notice + * is preserved. + * ==================================================== + * + * $NetBSD: w_lgammaf.c,v 1.7 2002/05/26 22:02:02 wiz Exp $ + * $DragonFly: src/lib/libm/src/w_lgammaf.c,v 1.1 2005/07/26 21:15:20 joerg Exp $ + */ + +#include +#include "math_private.h" + +float +lgammaf(float x) +{ + return lgammaf_r(x,&signgam); +} diff --git a/sys/cpu/i386/include/math.h b/sys/cpu/i386/include/math.h new file mode 100644 index 0000000000..cd4fc98997 --- /dev/null +++ b/sys/cpu/i386/include/math.h @@ -0,0 +1,5 @@ +/* $NetBSD: math.h,v 1.2 2003/10/28 00:55:28 kleink Exp $ */ +/* $DragonFly: src/sys/cpu/i386/include/math.h,v 1.1 2005/07/26 21:15:20 joerg Exp $ */ + +#define __HAVE_LONG_DOUBLE +#define __HAVE_NANF diff --git a/sys/i386/include/math.h b/sys/i386/include/math.h new file mode 100644 index 0000000000..d55a4355ad --- /dev/null +++ b/sys/i386/include/math.h @@ -0,0 +1,5 @@ +/* $NetBSD: math.h,v 1.2 2003/10/28 00:55:28 kleink Exp $ */ +/* $DragonFly: src/sys/i386/include/Attic/math.h,v 1.1 2005/07/26 21:15:20 joerg Exp $ */ + +#define __HAVE_LONG_DOUBLE +#define __HAVE_NANF -- 2.41.0