StdLib/LibC/Math/e_log10.c

   1 /** @file
   2   Compute the base 10 logrithm of x.
   3
   4   Copyright (c) 2010 - 2011, Intel Corporation. All rights reserved.<BR>
   5   This program and the accompanying materials are licensed and made available under
   6   the terms and conditions of the BSD License that accompanies this distribution.
   7   The full text of the license may be found at
   8   http://opensource.org/licenses/bsd-license.
   9
  10   THE PROGRAM IS DISTRIBUTED UNDER THE BSD LICENSE ON AN "AS IS" BASIS,
  11   WITHOUT WARRANTIES OR REPRESENTATIONS OF ANY KIND, EITHER EXPRESS OR IMPLIED.
  12
  13  * ====================================================
  14  * Copyright (C) 1993 by Sun Microsystems, Inc. All rights reserved.
  15  *
  16  * Developed at SunPro, a Sun Microsystems, Inc. business.
  17  * Permission to use, copy, modify, and distribute this
  18  * software is freely granted, provided that this notice
  19  * is preserved.
  20  * ====================================================
  21
  22   e_log10.c 5.1 93/09/24
  23   NetBSD: e_log10.c,v 1.12 2002/05/26 22:01:51 wiz Exp
  24 **/
  25 #include  <LibConfig.h>
  26 #include  <sys/EfiCdefs.h>
  27
  28 /* __ieee754_log10(x)
  29  * Return the base 10 logarithm of x
  30  *
  31  * Method :
  32  *  Let log10_2hi = leading 40 bits of log10(2) and
  33  *      log10_2lo = log10(2) - log10_2hi,
  34  *      ivln10   = 1/log(10) rounded.
  35  *  Then
  36  *    n = ilogb(x),
  37  *    if(n<0)  n = n+1;
  38  *    x = scalbn(x,-n);
  39  *    log10(x) := n*log10_2hi + (n*log10_2lo + ivln10*log(x))
  40  *
  41  * Note 1:
  42  *  To guarantee log10(10**n)=n, where 10**n is normal, the rounding
  43  *  mode must set to Round-to-Nearest.
  44  * Note 2:
  45  *  [1/log(10)] rounded to 53 bits has error  .198   ulps;
  46  *  log10 is monotonic at all binary break points.
  47  *
  48  * Special cases:
  49  *  log10(x) is NaN with signal if x < 0;
  50  *  log10(+INF) is +INF with no signal; log10(0) is -INF with signal;
  51  *  log10(NaN) is that NaN with no signal;
  52  *  log10(10**N) = N  for N=0,1,...,22.
  53  *
  54  * Constants:
  55  * The hexadecimal values are the intended ones for the following constants.
  56  * The decimal values may be used, provided that the compiler will convert
  57  * from decimal to binary accurately enough to produce the hexadecimal values
  58  * shown.
  59  */
  60
  61 #include "math.h"
  62 #include "math_private.h"
  63 #include  <errno.h>
  64
  65 #if defined(_MSC_VER)           /* Handle Microsoft VC++ compiler specifics. */
  66   // potential divide by 0 -- near line 80, (x-x)/zero is on purpose
  67   #pragma warning ( disable : 4723 )
  68 #endif
  69
  70 static const double
  71 two54      =  1.80143985094819840000e+16, /* 0x43500000, 0x00000000 */
  72 ivln10     =  4.34294481903251816668e-01, /* 0x3FDBCB7B, 0x1526E50E */
  73 log10_2hi  =  3.01029995663611771306e-01, /* 0x3FD34413, 0x509F6000 */
  74 log10_2lo  =  3.69423907715893078616e-13; /* 0x3D59FEF3, 0x11F12B36 */
  75
  76 static const double zero   =  0.0;
  77
  78 double
  79 __ieee754_log10(double x)
  80 {
  81   double y,z;
  82   int32_t i,k,hx;
  83   u_int32_t lx;
  84
  85   EXTRACT_WORDS(hx,lx,x);
  86
  87   k=0;
  88   if (hx < 0x00100000) {            /* x < 2**-1022  */
  89     if (((hx&0x7fffffff)|lx)==0)
  90       return -two54/zero;           /* log(+-0)=-inf */
  91     if (hx<0) {
  92       errno = EDOM;
  93       return (x-x)/zero;            /* log(-#) = NaN */
  94     }
  95     k -= 54; x *= two54;            /* subnormal number, scale up x */
  96     GET_HIGH_WORD(hx,x);
  97   }
  98   if (hx >= 0x7ff00000) return x+x;
  99   k += (hx>>20)-1023;
 100   i  = ((u_int32_t)k&0x80000000)>>31;
 101   hx = (hx&0x000fffff)|((0x3ff-i)<<20);
 102   y  = (double)(k+i);
 103   SET_HIGH_WORD(x,hx);
 104   z  = y*log10_2lo + ivln10*__ieee754_log(x);
 105   return  z+y*log10_2hi;
 106 }