lib/msun/src/e_log10.c

   1
   2 /* @(#)e_log10.c 1.3 95/01/18 */
   3 /*
   4  * ====================================================
   5  * Copyright (C) 1993 by Sun Microsystems, Inc. All rights reserved.
   6  *
   7  * Developed at SunSoft, a Sun Microsystems, Inc. business.
   8  * Permission to use, copy, modify, and distribute this
   9  * software is freely granted, provided that this notice
  10  * is preserved.
  11  * ====================================================
  12  */
  13
  14 #include <sys/cdefs.h>
  15 __FBSDID("$FreeBSD$");
  16
  17 /* __ieee754_log10(x)
  18  * Return the base 10 logarithm of x
  19  *
  20  * Method :
  21  *      Let log10_2hi = leading 40 bits of log10(2) and
  22  *          log10_2lo = log10(2) - log10_2hi,
  23  *          ivln10   = 1/log(10) rounded.
  24  *      Then
  25  *              n = ilogb(x),
  26  *              if(n<0)  n = n+1;
  27  *              x = scalbn(x,-n);
  28  *              log10(x) := n*log10_2hi + (n*log10_2lo + ivln10*log(x))
  29  *
  30  * Note 1:
  31  *      To guarantee log10(10**n)=n, where 10**n is normal, the rounding
  32  *      mode must set to Round-to-Nearest.
  33  * Note 2:
  34  *      [1/log(10)] rounded to 53 bits has error  .198   ulps;
  35  *      log10 is monotonic at all binary break points.
  36  *
  37  * Special cases:
  38  *      log10(x) is NaN with signal if x < 0;
  39  *      log10(+INF) is +INF with no signal; log10(0) is -INF with signal;
  40  *      log10(NaN) is that NaN with no signal;
  41  *      log10(10**N) = N  for N=0,1,...,22.
  42  *
  43  * Constants:
  44  * The hexadecimal values are the intended ones for the following constants.
  45  * The decimal values may be used, provided that the compiler will convert
  46  * from decimal to binary accurately enough to produce the hexadecimal values
  47  * shown.
  48  */
  49
  50 #include "math.h"
  51 #include "math_private.h"
  52
  53 static const double
  54 two54      =  1.80143985094819840000e+16, /* 0x43500000, 0x00000000 */
  55 ivln10     =  4.34294481903251816668e-01, /* 0x3FDBCB7B, 0x1526E50E */
  56 log10_2hi  =  3.01029995663611771306e-01, /* 0x3FD34413, 0x509F6000 */
  57 log10_2lo  =  3.69423907715893078616e-13; /* 0x3D59FEF3, 0x11F12B36 */
  58
  59 static const double zero   =  0.0;
  60
  61 double
  62 __ieee754_log10(double x)
  63 {
  64         double y,z;
  65         int32_t i,k,hx;
  66         u_int32_t lx;
  67
  68         EXTRACT_WORDS(hx,lx,x);
  69
  70         k=0;
  71         if (hx < 0x00100000) {                  /* x < 2**-1022  */
  72             if (((hx&0x7fffffff)|lx)==0)
  73                 return -two54/zero;             /* log(+-0)=-inf */
  74             if (hx<0) return (x-x)/zero;        /* log(-#) = NaN */
  75             k -= 54; x *= two54; /* subnormal number, scale up x */
  76             GET_HIGH_WORD(hx,x);
  77         }
  78         if (hx >= 0x7ff00000) return x+x;
  79         k += (hx>>20)-1023;
  80         i  = ((u_int32_t)k&0x80000000)>>31;
  81         hx = (hx&0x000fffff)|((0x3ff-i)<<20);
  82         y  = (double)(k+i);
  83         SET_HIGH_WORD(x,hx);
  84         z  = y*log10_2lo + ivln10*__ieee754_log(x);
  85         return  z+y*log10_2hi;
  86 }