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
  13 #include <sys/cdefs.h>
  14 #if defined(LIBM_SCCS) && !defined(lint)
  15 __RCSID("$NetBSD: e_log10.c,v 1.12 2002/05/26 22:01:51 wiz Exp $");
  16 #endif
  17
  18 /* __ieee754_log10(x)
  19  * Return the base 10 logarithm of x
  20  *
  21  * Method :
  22  *      Let log10_2hi = leading 40 bits of log10(2) and
  23  *          log10_2lo = log10(2) - log10_2hi,
  24  *          ivln10   = 1/log(10) rounded.
  25  *      Then
  26  *              n = ilogb(x),
  27  *              if(n<0)  n = n+1;
  28  *              x = scalbn(x,-n);
  29  *              log10(x) := n*log10_2hi + (n*log10_2lo + ivln10*log(x))
  30  *
  31  * Note 1:
  32  *      To guarantee log10(10**n)=n, where 10**n is normal, the rounding
  33  *      mode must set to Round-to-Nearest.
  34  * Note 2:
  35  *      [1/log(10)] rounded to 53 bits has error  .198   ulps;
  36  *      log10 is monotonic at all binary break points.
  37  *
  38  * Special cases:
  39  *      log10(x) is NaN with signal if x < 0;
  40  *      log10(+INF) is +INF with no signal; log10(0) is -INF with signal;
  41  *      log10(NaN) is that NaN with no signal;
  42  *      log10(10**N) = N  for N=0,1,...,22.
  43  *
  44  * Constants:
  45  * The hexadecimal values are the intended ones for the following constants.
  46  * The decimal values may be used, provided that the compiler will convert
  47  * from decimal to binary accurately enough to produce the hexadecimal values
  48  * shown.
  49  */
  50
  51 #include "math.h"
  52 #include "math_private.h"
  53
  54 static const double
  55 two54      =  1.80143985094819840000e+16, /* 0x43500000, 0x00000000 */
  56 ivln10     =  4.34294481903251816668e-01, /* 0x3FDBCB7B, 0x1526E50E */
  57 log10_2hi  =  3.01029995663611771306e-01, /* 0x3FD34413, 0x509F6000 */
  58 log10_2lo  =  3.69423907715893078616e-13; /* 0x3D59FEF3, 0x11F12B36 */
  59
  60 static const double zero   =  0.0;
  61
  62 double
  63 __ieee754_log10(double x)
  64 {
  65         double y,z;
  66         int32_t i,k,hx;
  67         u_int32_t lx;
  68
  69         EXTRACT_WORDS(hx,lx,x);
  70
  71         k=0;
  72         if (hx < 0x00100000) {                  /* x < 2**-1022  */
  73             if (((hx&0x7fffffff)|lx)==0)
  74                 return -two54/zero;             /* log(+-0)=-inf */
  75             if (hx<0) return (x-x)/zero;        /* log(-#) = NaN */
  76             k -= 54; x *= two54; /* subnormal number, scale up x */
  77             GET_HIGH_WORD(hx,x);
  78         }
  79         if (hx >= 0x7ff00000) return x+x;
  80         k += (hx>>20)-1023;
  81         i  = ((u_int32_t)k&0x80000000)>>31;
  82         hx = (hx&0x000fffff)|((0x3ff-i)<<20);
  83         y  = (double)(k+i);
  84         SET_HIGH_WORD(x,hx);
  85         z  = y*log10_2lo + ivln10*__ieee754_log(x);
  86         return  z+y*log10_2hi;
  87 }