libm/e_log10.c

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