compiler/stdc/math/e_log10.c

   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 #ifndef lint
  15 static char rcsid[] = "$FreeBSD: src/lib/msun/src/e_log10.c,v 1.15 2011/10/15 05:23:28 das Exp $";
  16 #endif
  17
  18 /*
  19  * Return the base 10 logarithm of x.  See e_log.c and k_log.h for most
  20  * comments.
  21  *
  22  *    log10(x) = (f - 0.5*f*f + k_log1p(f)) / ln10 + k * log10(2)
  23  * in not-quite-routine extra precision.
  24  */
  25
  26 #include <float.h>
  27 #include "math.h"
  28 #include "math_private.h"
  29 #include "k_log.h"
  30
  31 static const double
  32 two54      =  1.80143985094819840000e+16, /* 0x43500000, 0x00000000 */
  33 ivln10hi   =  4.34294481878168880939e-01, /* 0x3fdbcb7b, 0x15200000 */
  34 ivln10lo   =  2.50829467116452752298e-11, /* 0x3dbb9438, 0xca9aadd5 */
  35 log10_2hi  =  3.01029995663611771306e-01, /* 0x3FD34413, 0x509F6000 */
  36 log10_2lo  =  3.69423907715893078616e-13; /* 0x3D59FEF3, 0x11F12B36 */
  37
  38 static const double zero   =  0.0;
  39 static const volatile double vzero __attribute__ ((__section__(".rodata,\"a\" " SECTIONCOMMENT))) = 0.0;
  40
  41 double
  42 __ieee754_log10(double x)
  43 {
  44         double f,hfsq,hi,lo,r,val_hi,val_lo,w,y,y2;
  45         int32_t i,k,hx;
  46         uint32_t lx;
  47
  48         EXTRACT_WORDS(hx,lx,x);
  49
  50         k=0;
  51         if (hx < 0x00100000) {                  /* x < 2**-1022  */
  52             if (((hx&0x7fffffff)|lx)==0)
  53                 return -two54/vzero;            /* log(+-0)=-inf */
  54             if (hx<0) return (x-x)/zero;        /* log(-#) = NaN */
  55             k -= 54; x *= two54; /* subnormal number, scale up x */
  56             GET_HIGH_WORD(hx,x);
  57         }
  58         if (hx >= 0x7ff00000) return x+x;
  59         if (hx == 0x3ff00000 && lx == 0)
  60             return zero;                        /* log(1) = +0 */
  61         k += (hx>>20)-1023;
  62         hx &= 0x000fffff;
  63         i = (hx+0x95f64)&0x100000;
  64         SET_HIGH_WORD(x,hx|(i^0x3ff00000));     /* normalize x or x/2 */
  65         k += (i>>20);
  66         y = (double)k;
  67         f = x - 1.0;
  68         hfsq = 0.5*f*f;
  69         r = k_log1p(f);
  70
  71         /* See e_log2.c for most details. */
  72         hi = f - hfsq;
  73         SET_LOW_WORD(hi,0);
  74         lo = (f - hi) - hfsq + r;
  75         val_hi = hi*ivln10hi;
  76         y2 = y*log10_2hi;
  77         val_lo = y*log10_2lo + (lo+hi)*ivln10lo + lo*ivln10hi;
  78
  79         /*
  80          * Extra precision in for adding y*log10_2hi is not strictly needed
  81          * since there is no very large cancellation near x = sqrt(2) or
  82          * x = 1/sqrt(2), but we do it anyway since it costs little on CPUs
  83          * with some parallelism and it reduces the error for many args.
  84          */
  85         w = y2 + val_hi;
  86         val_lo += (y2 - w) + val_hi;
  87         val_hi = w;
  88
  89         return val_lo + val_hi;
  90 }
  91
  92 #if     LDBL_MANT_DIG == DBL_MANT_DIG
  93 AROS_MAKE_ASM_SYM(typeof(log10l), log10l, AROS_CSYM_FROM_ASM_NAME(log10l), AROS_CSYM_FROM_ASM_NAME(log10));
  94 AROS_EXPORT_ASM_SYM(AROS_CSYM_FROM_ASM_NAME(log10l));
  95 #endif