sysdeps/libm-ieee754/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 #if defined(LIBM_SCCS) && !defined(lint)
  14 static char rcsid[] = "$NetBSD: e_log10.c,v 1.9 1995/05/10 20:45:51 jtc Exp $";
  15 #endif
  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 #ifdef __STDC__
  54 static const double
  55 #else
  56 static double
  57 #endif
  58 two54      =  1.80143985094819840000e+16, /* 0x43500000, 0x00000000 */
  59 ivln10     =  4.34294481903251816668e-01, /* 0x3FDBCB7B, 0x1526E50E */
  60 log10_2hi  =  3.01029995663611771306e-01, /* 0x3FD34413, 0x509F6000 */
  61 log10_2lo  =  3.69423907715893078616e-13; /* 0x3D59FEF3, 0x11F12B36 */
  62
  63 #ifdef __STDC__
  64 static const double zero   =  0.0;
  65 #else
  66 static double zero   =  0.0;
  67 #endif
  68
  69 #ifdef __STDC__
  70         double __ieee754_log10(double x)
  71 #else
  72         double __ieee754_log10(x)
  73         double x;
  74 #endif
  75 {
  76         double y,z;
  77         int32_t i,k,hx;
  78         u_int32_t lx;
  79
  80         EXTRACT_WORDS(hx,lx,x);
  81
  82         k=0;
  83         if (hx < 0x00100000) {                  /* x < 2**-1022  */
  84             if (((hx&0x7fffffff)|lx)==0)
  85                 return -two54/(x-x);            /* log(+-0)=-inf */
  86             if (hx<0) return (x-x)/(x-x);       /* log(-#) = NaN */
  87             k -= 54; x *= two54; /* subnormal number, scale up x */
  88             GET_HIGH_WORD(hx,x);
  89         }
  90         if (hx >= 0x7ff00000) return x+x;
  91         k += (hx>>20)-1023;
  92         i  = ((u_int32_t)k&0x80000000)>>31;
  93         hx = (hx&0x000fffff)|((0x3ff-i)<<20);
  94         y  = (double)(k+i);
  95         SET_HIGH_WORD(x,hx);
  96         z  = y*log10_2lo + ivln10*__ieee754_log(x);
  97         return  z+y*log10_2hi;
  98 }