sysdeps/ieee754/dbl-64/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 /* __ieee754_log10(x)
  14  * Return the base 10 logarithm of x
  15  *
  16  * Method :
  17  *      Let log10_2hi = leading 40 bits of log10(2) and
  18  *          log10_2lo = log10(2) - log10_2hi,
  19  *          ivln10   = 1/log(10) rounded.
  20  *      Then
  21  *              n = ilogb(x),
  22  *              if(n<0)  n = n+1;
  23  *              x = scalbn(x,-n);
  24  *              log10(x) := n*log10_2hi + (n*log10_2lo + ivln10*log(x))
  25  *
  26  * Note 1:
  27  *      To guarantee log10(10**n)=n, where 10**n is normal, the rounding
  28  *      mode must set to Round-to-Nearest.
  29  * Note 2:
  30  *      [1/log(10)] rounded to 53 bits has error  .198   ulps;
  31  *      log10 is monotonic at all binary break points.
  32  *
  33  * Special cases:
  34  *      log10(x) is NaN with signal if x < 0;
  35  *      log10(+INF) is +INF with no signal; log10(0) is -INF with signal;
  36  *      log10(NaN) is that NaN with no signal;
  37  *      log10(10**N) = N  for N=0,1,...,22.
  38  *
  39  * Constants:
  40  * The hexadecimal values are the intended ones for the following constants.
  41  * The decimal values may be used, provided that the compiler will convert
  42  * from decimal to binary accurately enough to produce the hexadecimal values
  43  * shown.
  44  */
  45
  46 #include <math.h>
  47 #include <math_private.h>
  48
  49 static const double two54 = 1.80143985094819840000e+16;         /* 0x43500000, 0x00000000 */
  50 static const double ivln10 = 4.34294481903251816668e-01;        /* 0x3FDBCB7B, 0x1526E50E */
  51 static const double log10_2hi = 3.01029995663611771306e-01;     /* 0x3FD34413, 0x509F6000 */
  52 static const double log10_2lo = 3.69423907715893078616e-13;     /* 0x3D59FEF3, 0x11F12B36 */
  53
  54 double
  55 __ieee754_log10 (double x)
  56 {
  57   double y, z;
  58   int32_t i, k, hx;
  59   u_int32_t lx;
  60
  61   EXTRACT_WORDS (hx, lx, x);
  62
  63   k = 0;
  64   if (hx < 0x00100000)
  65     {                           /* x < 2**-1022  */
  66       if (__builtin_expect (((hx & 0x7fffffff) | lx) == 0, 0))
  67         return -two54 / (x - x);        /* log(+-0)=-inf */
  68       if (__builtin_expect (hx < 0, 0))
  69         return (x - x) / (x - x);       /* log(-#) = NaN */
  70       k -= 54;
  71       x *= two54;               /* subnormal number, scale up x */
  72       GET_HIGH_WORD (hx, x);
  73     }
  74   if (__builtin_expect (hx >= 0x7ff00000, 0))
  75     return x + x;
  76   k += (hx >> 20) - 1023;
  77   i = ((u_int32_t) k & 0x80000000) >> 31;
  78   hx = (hx & 0x000fffff) | ((0x3ff - i) << 20);
  79   y = (double) (k + i);
  80   SET_HIGH_WORD (x, hx);
  81   z = y * log10_2lo + ivln10 * __ieee754_log (x);
  82   return z + y * log10_2hi;
  83 }
  84
  85 strong_alias (__ieee754_log10, __log10_finite)