gonzui

    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: /* LINTLIBRARY */
   14: 
   15: /* log10(x)
   16:  * Return the base 10 logarithm of x
   17:  * 
   18:  * Method :
   19:  *      Let log10_2hi = leading 40 bits of log10(2) and
   20:  *          log10_2lo = log10(2) - log10_2hi,
   21:  *          ivln10   = 1/log(10) rounded.
   22:  *      Then
   23:  *              n = ilogb(x), 
   24:  *              if(n<0)  n = n+1;
   25:  *              x = scalbn(x,-n);
   26:  *              log10(x) := n*log10_2hi + (n*log10_2lo + ivln10*log(x))
   27:  *
   28:  * Note 1:
   29:  *      To guarantee log10(10**n)=n, where 10**n is normal, the rounding 
   30:  *      mode must set to Round-to-Nearest.
   31:  * Note 2:
   32:  *      [1/log(10)] rounded to 53 bits has error  .198   ulps;
   33:  *      log10 is monotonic at all binary break points.
   34:  *
   35:  * Special cases:
   36:  *      log10(x) is NaN with signal if x < 0; 
   37:  *      log10(+INF) is +INF with no signal; log10(0) is -INF with signal;
   38:  *      log10(NaN) is that NaN with no signal;
   39:  *      log10(10**N) = N  for N=0,1,...,22.
   40:  *
   41:  * Constants:
   42:  * The hexadecimal values are the intended ones for the following constants.
   43:  * The decimal values may be used, provided that the compiler will convert
   44:  * from decimal to binary accurately enough to produce the hexadecimal values
   45:  * shown.
   46:  */
   47: 
   48: #include <sys/cdefs.h>
   49: #include <float.h>
   50: #include <math.h>
   51: 
   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: 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*log(x);
   86:         return  z+y*log10_2hi;
   87: }
   88: 
   89: #if     LDBL_MANT_DIG == 53
   90: #ifdef  lint
   91: /* PROTOLIB1 */
   92: long double log10l(long double);
   93: #else   /* lint */
   94: __weak_alias(log10l, log10);
   95: #endif  /* lint */
   96: #endif  /* LDBL_MANT_DIG == 53 */