modules/fdlibm/src/e_log10.cpp

   1
   2 /* @(#)e_log10.c 1.3 95/01/18 */
   3 /*
   4  * ====================================================
   5  * Copyright (C) 1993 by Sun Microsystems, Inc. All rights reserved.
   6  *
   7  * Developed at SunSoft, 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 //#include <sys/cdefs.h>
  15 //__FBSDID("$FreeBSD$");
  16
  17 /*
  18  * Return the base 10 logarithm of x.  See e_log.c and k_log.h for most
  19  * comments.
  20  *
  21  *    log10(x) = (f - 0.5*f*f + k_log1p(f)) / ln10 + k * log10(2)
  22  * in not-quite-routine extra precision.
  23  */
  24
  25 #include <float.h>
  26
  27 #include "math_private.h"
  28 #include "k_log.h"
  29
  30 static const double
  31 two54      =  1.80143985094819840000e+16, /* 0x43500000, 0x00000000 */
  32 ivln10hi   =  4.34294481878168880939e-01, /* 0x3fdbcb7b, 0x15200000 */
  33 ivln10lo   =  2.50829467116452752298e-11, /* 0x3dbb9438, 0xca9aadd5 */
  34 log10_2hi  =  3.01029995663611771306e-01, /* 0x3FD34413, 0x509F6000 */
  35 log10_2lo  =  3.69423907715893078616e-13; /* 0x3D59FEF3, 0x11F12B36 */
  36
  37 static const double zero   =  0.0;
  38 static volatile double vzero = 0.0;
  39
  40 double
  41 __ieee754_log10(double x)
  42 {
  43         double f,hfsq,hi,lo,r,val_hi,val_lo,w,y,y2;
  44         int32_t i,k,hx;
  45         u_int32_t lx;
  46
  47         EXTRACT_WORDS(hx,lx,x);
  48
  49         k=0;
  50         if (hx < 0x00100000) {                  /* x < 2**-1022  */
  51             if (((hx&0x7fffffff)|lx)==0)
  52                 return -two54/vzero;            /* log(+-0)=-inf */
  53             if (hx<0) return (x-x)/zero;        /* log(-#) = NaN */
  54             k -= 54; x *= two54; /* subnormal number, scale up x */
  55             GET_HIGH_WORD(hx,x);
  56         }
  57         if (hx >= 0x7ff00000) return x+x;
  58         if (hx == 0x3ff00000 && lx == 0)
  59             return zero;                        /* log(1) = +0 */
  60         k += (hx>>20)-1023;
  61         hx &= 0x000fffff;
  62         i = (hx+0x95f64)&0x100000;
  63         SET_HIGH_WORD(x,hx|(i^0x3ff00000));     /* normalize x or x/2 */
  64         k += (i>>20);
  65         y = (double)k;
  66         f = x - 1.0;
  67         hfsq = 0.5*f*f;
  68         r = k_log1p(f);
  69
  70         /* See e_log2.c for most details. */
  71         hi = f - hfsq;
  72         SET_LOW_WORD(hi,0);
  73         lo = (f - hi) - hfsq + r;
  74         val_hi = hi*ivln10hi;
  75         y2 = y*log10_2hi;
  76         val_lo = y*log10_2lo + (lo+hi)*ivln10lo + lo*ivln10hi;
  77
  78         /*
  79          * Extra precision in for adding y*log10_2hi is not strictly needed
  80          * since there is no very large cancellation near x = sqrt(2) or
  81          * x = 1/sqrt(2), but we do it anyway since it costs little on CPUs
  82          * with some parallelism and it reduces the error for many args.
  83          */
  84         w = y2 + val_hi;
  85         val_lo += (y2 - w) + val_hi;
  86         val_hi = w;
  87
  88         return val_lo + val_hi;
  89 }