toolchain/gcc/newlib/libm/math/e_log10.c

   1
   2 /* @(#)e_log10.c 5.1 93/09/24 */
   3 /*
   4  * ====================================================
   5  * Copyright (C) 1993 by Sun Microsystems, Inc. All rights reserved.
   6  *
   7  * Developed at SunPro, a Sun Microsystems, Inc. business.
   8  * Permission to use, copy, modify, and distribute this
   9  * software is freely granted, provided that this notice
  10  * is preserved.
  11  * ====================================================
  12  */
  13
  14 /* __ieee754_log10(x)
  15  * Return the base 10 logarithm of x
  16  *
  17  * Method :
  18  *      Let log10_2hi = leading 40 bits of log10(2) and
  19  *          log10_2lo = log10(2) - log10_2hi,
  20  *          ivln10   = 1/log(10) rounded.
  21  *      Then
  22  *              n = ilogb(x),
  23  *              if(n<0)  n = n+1;
  24  *              x = scalbn(x,-n);
  25  *              log10(x) := n*log10_2hi + (n*log10_2lo + ivln10*log(x))
  26  *
  27  * Note 1:
  28  *      To guarantee log10(10**n)=n, where 10**n is normal, the rounding
  29  *      mode must set to Round-to-Nearest.
  30  * Note 2:
  31  *      [1/log(10)] rounded to 53 bits has error  .198   ulps;
  32  *      log10 is monotonic at all binary break points.
  33  *
  34  * Special cases:
  35  *      log10(x) is NaN with signal if x < 0;
  36  *      log10(+INF) is +INF with no signal; log10(0) is -INF with signal;
  37  *      log10(NaN) is that NaN with no signal;
  38  *      log10(10**N) = N  for N=0,1,...,22.
  39  *
  40  * Constants:
  41  * The hexadecimal values are the intended ones for the following constants.
  42  * The decimal values may be used, provided that the compiler will convert
  43  * from decimal to binary accurately enough to produce the hexadecimal values
  44  * shown.
  45  */
  46
  47 #include "fdlibm.h"
  48
  49 #ifndef _DOUBLE_IS_32BITS
  50
  51 #ifdef __STDC__
  52 static const double
  53 #else
  54 static double
  55 #endif
  56 two54      =  1.80143985094819840000e+16, /* 0x43500000, 0x00000000 */
  57 ivln10     =  4.34294481903251816668e-01, /* 0x3FDBCB7B, 0x1526E50E */
  58 log10_2hi  =  3.01029995663611771306e-01, /* 0x3FD34413, 0x509F6000 */
  59 log10_2lo  =  3.69423907715893078616e-13; /* 0x3D59FEF3, 0x11F12B36 */
  60
  61 #ifdef __STDC__
  62 static const double zero   =  0.0;
  63 #else
  64 static double zero   =  0.0;
  65 #endif
  66
  67 #ifdef __STDC__
  68         double __ieee754_log10(double x)
  69 #else
  70         double __ieee754_log10(x)
  71         double x;
  72 #endif
  73 {
  74         double y,z;
  75         __int32_t i,k,hx;
  76         __uint32_t lx;
  77
  78         EXTRACT_WORDS(hx,lx,x);
  79
  80         k=0;
  81         if (hx < 0x00100000) {                  /* x < 2**-1022  */
  82             if (((hx&0x7fffffff)|lx)==0)
  83                 return -two54/zero;             /* log(+-0)=-inf */
  84             if (hx<0) return (x-x)/zero;        /* log(-#) = NaN */
  85             k -= 54; x *= two54; /* subnormal number, scale up x */
  86             GET_HIGH_WORD(hx,x);
  87         }
  88         if (hx >= 0x7ff00000) return x+x;
  89         k += (hx>>20)-1023;
  90         i  = ((__uint32_t)k&0x80000000)>>31;
  91         hx = (hx&0x000fffff)|((0x3ff-i)<<20);
  92         y  = (double)(k+i);
  93         SET_HIGH_WORD(x,hx);
  94         z  = y*log10_2lo + ivln10*__ieee754_log(x);
  95         return  z+y*log10_2hi;
  96 }
  97
  98 #endif /* defined(_DOUBLE_IS_32BITS) */