lib/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  * $NetBSD: e_log10.c,v 1.12 2002/05/26 22:01:51 wiz Exp $
  13  * $DragonFly: src/lib/libm/src/e_log10.c,v 1.1 2005/07/26 21:15:20 joerg Exp $
  14  */
  15
  16 /* log10(x)
  17  * Return the base 10 logarithm of x
  18  *
  19  * Method :
  20  *      Let log10_2hi = leading 40 bits of log10(2) and
  21  *          log10_2lo = log10(2) - log10_2hi,
  22  *          ivln10   = 1/log(10) rounded.
  23  *      Then
  24  *              n = ilogb(x),
  25  *              if(n<0)  n = n+1;
  26  *              x = scalbn(x,-n);
  27  *              log10(x) := n*log10_2hi + (n*log10_2lo + ivln10*log(x))
  28  *
  29  * Note 1:
  30  *      To guarantee log10(10**n)=n, where 10**n is normal, the rounding
  31  *      mode must set to Round-to-Nearest.
  32  * Note 2:
  33  *      [1/log(10)] rounded to 53 bits has error  .198   ulps;
  34  *      log10 is monotonic at all binary break points.
  35  *
  36  * Special cases:
  37  *      log10(x) is NaN with signal if x < 0;
  38  *      log10(+INF) is +INF with no signal; log10(0) is -INF with signal;
  39  *      log10(NaN) is that NaN with no signal;
  40  *      log10(10**N) = N  for N=0,1,...,22.
  41  *
  42  * Constants:
  43  * The hexadecimal values are the intended ones for the following constants.
  44  * The decimal values may be used, provided that the compiler will convert
  45  * from decimal to binary accurately enough to produce the hexadecimal values
  46  * shown.
  47  */
  48
  49 #include <math.h>
  50 #include "math_private.h"
  51
  52 static const double
  53 two54      =  1.80143985094819840000e+16, /* 0x43500000, 0x00000000 */
  54 ivln10     =  4.34294481903251816668e-01, /* 0x3FDBCB7B, 0x1526E50E */
  55 log10_2hi  =  3.01029995663611771306e-01, /* 0x3FD34413, 0x509F6000 */
  56 log10_2lo  =  3.69423907715893078616e-13; /* 0x3D59FEF3, 0x11F12B36 */
  57
  58 static const double zero   =  0.0;
  59
  60 double
  61 log10(double x)
  62 {
  63         double y,z;
  64         int32_t i,k,hx;
  65         u_int32_t lx;
  66
  67         EXTRACT_WORDS(hx,lx,x);
  68
  69         k=0;
  70         if (hx < 0x00100000) {                  /* x < 2**-1022  */
  71             if (((hx&0x7fffffff)|lx)==0)
  72                 return -two54/zero;             /* log(+-0)=-inf */
  73             if (hx<0) return (x-x)/zero;        /* log(-#) = NaN */
  74             k -= 54; x *= two54; /* subnormal number, scale up x */
  75             GET_HIGH_WORD(hx,x);
  76         }
  77         if (hx >= 0x7ff00000) return x+x;
  78         k += (hx>>20)-1023;
  79         i  = ((u_int32_t)k&0x80000000)>>31;
  80         hx = (hx&0x000fffff)|((0x3ff-i)<<20);
  81         y  = (double)(k+i);
  82         SET_HIGH_WORD(x,hx);
  83         z  = y*log10_2lo + ivln10*log(x);
  84         return  z+y*log10_2hi;
  85 }