contrib/openbsd_libm/src/e_log10.c

   1 /* @(#)e_log10.c 5.1 93/09/24 */
   2 /*
   3  * ====================================================
   4  * Copyright (C) 1993 by Sun Microsystems, Inc. All rights reserved.
   5  *
   6  * Developed at SunPro, a Sun Microsystems, Inc. business.
   7  * Permission to use, copy, modify, and distribute this
   8  * software is freely granted, provided that this notice
   9  * is preserved.
  10  * ====================================================
  11  */
  12
  13 /* log10(x)
  14  * Return the base 10 logarithm of x
  15  *
  16  * Method :
  17  *      Let log10_2hi = leading 40 bits of log10(2) and
  18  *          log10_2lo = log10(2) - log10_2hi,
  19  *          ivln10   = 1/log(10) rounded.
  20  *      Then
  21  *              n = ilogb(x),
  22  *              if(n<0)  n = n+1;
  23  *              x = scalbn(x,-n);
  24  *              log10(x) := n*log10_2hi + (n*log10_2lo + ivln10*log(x))
  25  *
  26  * Note 1:
  27  *      To guarantee log10(10**n)=n, where 10**n is normal, the rounding
  28  *      mode must set to Round-to-Nearest.
  29  * Note 2:
  30  *      [1/log(10)] rounded to 53 bits has error  .198   ulps;
  31  *      log10 is monotonic at all binary break points.
  32  *
  33  * Special cases:
  34  *      log10(x) is NaN with signal if x < 0;
  35  *      log10(+INF) is +INF with no signal; log10(0) is -INF with signal;
  36  *      log10(NaN) is that NaN with no signal;
  37  *      log10(10**N) = N  for N=0,1,...,22.
  38  *
  39  * Constants:
  40  * The hexadecimal values are the intended ones for the following constants.
  41  * The decimal values may be used, provided that the compiler will convert
  42  * from decimal to binary accurately enough to produce the hexadecimal values
  43  * shown.
  44  */
  45
  46 #include <float.h>
  47 #include <math.h>
  48
  49 #include "math_private.h"
  50
  51 static const double
  52 two54      =  1.80143985094819840000e+16, /* 0x43500000, 0x00000000 */
  53 ivln10     =  4.34294481903251816668e-01, /* 0x3FDBCB7B, 0x1526E50E */
  54 log10_2hi  =  3.01029995663611771306e-01, /* 0x3FD34413, 0x509F6000 */
  55 log10_2lo  =  3.69423907715893078616e-13; /* 0x3D59FEF3, 0x11F12B36 */
  56
  57 static const double zero   =  0.0;
  58
  59 double
  60 log10(double x)
  61 {
  62         double y,z;
  63         int32_t i,k,hx;
  64         u_int32_t lx;
  65
  66         EXTRACT_WORDS(hx,lx,x);
  67
  68         k=0;
  69         if (hx < 0x00100000) {                  /* x < 2**-1022  */
  70             if (((hx&0x7fffffff)|lx)==0)
  71                 return -two54/zero;             /* log(+-0)=-inf */
  72             if (hx<0) return (x-x)/zero;        /* log(-#) = NaN */
  73             k -= 54; x *= two54; /* subnormal number, scale up x */
  74             GET_HIGH_WORD(hx,x);
  75         }
  76         if (hx >= 0x7ff00000) return x+x;
  77         k += (hx>>20)-1023;
  78         i  = ((u_int32_t)k&0x80000000)>>31;
  79         hx = (hx&0x000fffff)|((0x3ff-i)<<20);
  80         y  = (double)(k+i);
  81         SET_HIGH_WORD(x,hx);
  82         z  = y*log10_2lo + ivln10*log(x);
  83         return  z+y*log10_2hi;
  84 }
  85
  86 #if     LDBL_MANT_DIG == DBL_MANT_DIG
  87 __strong_alias(log10l, log10);
  88 #endif  /* LDBL_MANT_DIG == DBL_MANT_DIG */