1 /* mpfr_set_ld -- convert a machine long double to
2 a multiple precision floating-point number
4 Copyright 2002, 2003, 2004, 2005, 2006, 2007, 2008, 2009, 2010, 2011 Free Software Foundation, Inc.
5 Contributed by the Arenaire and Caramel projects, INRIA.
7 This file is part of the GNU MPFR Library.
9 The GNU MPFR Library is free software; you can redistribute it and/or modify
10 it under the terms of the GNU Lesser General Public License as published by
11 the Free Software Foundation; either version 3 of the License, or (at your
12 option) any later version.
14 The GNU MPFR Library is distributed in the hope that it will be useful, but
15 WITHOUT ANY WARRANTY; without even the implied warranty of MERCHANTABILITY
16 or FITNESS FOR A PARTICULAR PURPOSE. See the GNU Lesser General Public
17 License for more details.
19 You should have received a copy of the GNU Lesser General Public License
20 along with the GNU MPFR Library; see the file COPYING.LESSER. If not, see
21 http://www.gnu.org/licenses/ or write to the Free Software Foundation, Inc.,
22 51 Franklin St, Fifth Floor, Boston, MA 02110-1301, USA. */
26 #define MPFR_NEED_LONGLONG_H
27 #include "mpfr-impl.h"
29 /* Various i386 systems have been seen with <float.h> LDBL constants equal
30 to the DBL ones, whereas they ought to be bigger, reflecting the 10-byte
31 IEEE extended format on that processor. gcc 3.2.1 on FreeBSD and Solaris
32 has been seen with the problem, and gcc 2.95.4 on FreeBSD 4.7. */
34 #if HAVE_LDOUBLE_IEEE_EXT_LITTLE
39 { '\377','\377','\377','\377',
40 '\377','\377','\377','\377',
43 #define MPFR_LDBL_MAX (ldbl_max_struct.d)
45 #define MPFR_LDBL_MAX LDBL_MAX
48 #ifndef HAVE_LDOUBLE_IEEE_EXT_LITTLE
52 mpfr_set_ld (mpfr_ptr r, long double d, mpfr_rnd_t rnd_mode)
55 int inexact, shift_exp;
57 MPFR_SAVE_EXPO_DECL (expo);
60 LONGDOUBLE_NAN_ACTION (d, goto nan);
63 if (d > MPFR_LDBL_MAX)
68 else if (d < -MPFR_LDBL_MAX)
75 return mpfr_set_d (r, (double) d, rnd_mode);
77 mpfr_init2 (t, MPFR_LDBL_MANT_DIG);
78 mpfr_init2 (u, IEEE_DBL_MANT_DIG);
80 MPFR_SAVE_EXPO_MARK (expo);
84 MPFR_SET_ZERO (t); /* The sign doesn't matter. */
85 shift_exp = 0; /* invariant: remainder to deal with is d*2^shift_exp */
86 while (x != (long double) 0.0)
88 /* Check overflow of double */
89 if (x > (long double) DBL_MAX || (-x) > (long double) DBL_MAX)
91 long double div9, div10, div11, div12, div13;
93 #define TWO_64 18446744073709551616.0 /* 2^64 */
94 #define TWO_128 (TWO_64 * TWO_64)
95 #define TWO_256 (TWO_128 * TWO_128)
96 div9 = (long double) (double) (TWO_256 * TWO_256); /* 2^(2^9) */
98 div11 = div10 * div10; /* 2^(2^11) */
99 div12 = div11 * div11; /* 2^(2^12) */
100 div13 = div12 * div12; /* 2^(2^13) */
101 if (ABS (x) >= div13)
103 x /= div13; /* exact */
105 mpfr_div_2si (t, t, 8192, MPFR_RNDZ);
107 if (ABS (x) >= div12)
109 x /= div12; /* exact */
111 mpfr_div_2si (t, t, 4096, MPFR_RNDZ);
113 if (ABS (x) >= div11)
115 x /= div11; /* exact */
117 mpfr_div_2si (t, t, 2048, MPFR_RNDZ);
119 if (ABS (x) >= div10)
121 x /= div10; /* exact */
123 mpfr_div_2si (t, t, 1024, MPFR_RNDZ);
125 /* warning: we may have DBL_MAX=2^1024*(1-2^(-53)) < x < 2^1024,
126 therefore we have one extra exponent reduction step */
129 x /= div9; /* exact */
131 mpfr_div_2si (t, t, 512, MPFR_RNDZ);
133 } /* Check overflow of double */
134 else /* no overflow on double */
136 long double div9, div10, div11;
138 div9 = (long double) (double) 7.4583407312002067432909653e-155;
139 /* div9 = 2^(-2^9) */
140 div10 = div9 * div9; /* 2^(-2^10) */
141 div11 = div10 * div10; /* 2^(-2^11) if extended precision */
142 /* since -DBL_MAX <= x <= DBL_MAX, the cast to double should not
144 if (ABS(x) < div10 &&
145 div11 != (long double) 0.0 &&
146 div11 / div10 == div10) /* possible underflow */
148 long double div12, div13;
149 /* After the divisions, any bit of x must be >= div10,
150 hence the possible division by div9. */
151 div12 = div11 * div11; /* 2^(-2^12) */
152 div13 = div12 * div12; /* 2^(-2^13) */
153 if (ABS (x) <= div13)
155 x /= div13; /* exact */
157 mpfr_mul_2si (t, t, 8192, MPFR_RNDZ);
159 if (ABS (x) <= div12)
161 x /= div12; /* exact */
163 mpfr_mul_2si (t, t, 4096, MPFR_RNDZ);
165 if (ABS (x) <= div11)
167 x /= div11; /* exact */
169 mpfr_mul_2si (t, t, 2048, MPFR_RNDZ);
171 if (ABS (x) <= div10)
173 x /= div10; /* exact */
175 mpfr_mul_2si (t, t, 1024, MPFR_RNDZ);
179 x /= div9; /* exact */
181 mpfr_mul_2si (t, t, 512, MPFR_RNDZ);
184 else /* no underflow */
186 inexact = mpfr_set_d (u, (double) x, MPFR_RNDZ);
187 MPFR_ASSERTD (inexact == 0);
188 if (mpfr_add (t, t, u, MPFR_RNDZ) != 0)
190 if (!mpfr_number_p (t))
192 /* Inexact. This cannot happen unless the C implementation
193 "lies" on the precision or when long doubles are
194 implemented with FP expansions like under Mac OS X. */
195 if (MPFR_PREC (t) != MPFR_PREC (r) + 1)
197 /* We assume that MPFR_PREC (r) < MPFR_PREC_MAX.
198 The precision MPFR_PREC (r) + 1 allows us to
199 deduce the rounding bit and the sticky bit. */
200 mpfr_set_prec (t, MPFR_PREC (r) + 1);
208 /* Since mpfr_add was inexact, the sticky bit is 1. */
210 rb_mask = MPFR_LIMB_ONE <<
212 (MPFR_PREC (r) & (GMP_NUMB_BITS - 1)));
213 if (rnd_mode == MPFR_RNDN)
214 rnd_mode = (*tp & rb_mask) ^ MPFR_IS_NEG (t) ?
215 MPFR_RNDU : MPFR_RNDD;
220 x -= (long double) mpfr_get_d1 (u); /* exact */
224 inexact = mpfr_mul_2si (r, t, shift_exp, rnd_mode);
228 MPFR_SAVE_EXPO_FREE (expo);
229 return mpfr_check_range (r, inexact, rnd_mode);
236 #else /* IEEE Extended Little Endian Code */
239 mpfr_set_ld (mpfr_ptr r, long double d, mpfr_rnd_t rnd_mode)
241 int inexact, i, k, cnt;
243 mp_limb_t tmpmant[MPFR_LIMBS_PER_LONG_DOUBLE];
244 mpfr_long_double_t x;
247 MPFR_SAVE_EXPO_DECL (expo);
250 if (MPFR_UNLIKELY (d != d))
256 else if (MPFR_UNLIKELY (d > MPFR_LDBL_MAX))
262 else if (MPFR_UNLIKELY (d < -MPFR_LDBL_MAX))
269 else if (MPFR_UNLIKELY (d == 0.0))
280 /* now d is neither 0, nor NaN nor Inf */
281 MPFR_SAVE_EXPO_MARK (expo);
283 MPFR_MANT (tmp) = tmpmant;
284 MPFR_PREC (tmp) = 64;
288 signd = MPFR_SIGN_POS;
291 signd = MPFR_SIGN_NEG;
295 /* Extract mantissa */
296 #if GMP_NUMB_BITS >= 64
297 tmpmant[0] = ((mp_limb_t) x.s.manh << 32) | ((mp_limb_t) x.s.manl);
299 tmpmant[0] = (mp_limb_t) x.s.manl;
300 tmpmant[1] = (mp_limb_t) x.s.manh;
303 /* Normalize mantissa */
304 i = MPFR_LIMBS_PER_LONG_DOUBLE;
305 MPN_NORMALIZE_NOT_ZERO (tmpmant, i);
306 k = MPFR_LIMBS_PER_LONG_DOUBLE - i;
307 count_leading_zeros (cnt, tmpmant[i - 1]);
308 if (MPFR_LIKELY (cnt != 0))
309 mpn_lshift (tmpmant + k, tmpmant, i, cnt);
311 MPN_COPY (tmpmant + k, tmpmant, i);
312 if (MPFR_UNLIKELY (k != 0))
313 MPN_ZERO (tmpmant, k);
316 exp = (mpfr_exp_t) ((x.s.exph << 8) + x.s.expl); /* 15-bit unsigned int */
317 if (MPFR_UNLIKELY (exp == 0))
322 MPFR_SET_EXP (tmp, exp - cnt - k * GMP_NUMB_BITS);
325 inexact = mpfr_set4 (r, tmp, rnd_mode, signd);
327 MPFR_SAVE_EXPO_FREE (expo);
328 return mpfr_check_range (r, inexact, rnd_mode);