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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
__ieee754_log10(double x)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 }
107