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2aa62f2b 1/** @file\r
2 Compute the base 10 logrithm of x.\r
3\r
4 Copyright (c) 2010 - 2011, Intel Corporation. All rights reserved.<BR>\r
5 This program and the accompanying materials are licensed and made available under\r
6 the terms and conditions of the BSD License that accompanies this distribution.\r
7 The full text of the license may be found at\r
8 http://opensource.org/licenses/bsd-license.\r
9\r
10 THE PROGRAM IS DISTRIBUTED UNDER THE BSD LICENSE ON AN "AS IS" BASIS,\r
11 WITHOUT WARRANTIES OR REPRESENTATIONS OF ANY KIND, EITHER EXPRESS OR IMPLIED.\r
12\r
13 * ====================================================\r
14 * Copyright (C) 1993 by Sun Microsystems, Inc. All rights reserved.\r
15 *\r
16 * Developed at SunPro, a Sun Microsystems, Inc. business.\r
17 * Permission to use, copy, modify, and distribute this\r
18 * software is freely granted, provided that this notice\r
19 * is preserved.\r
20 * ====================================================\r
21\r
22 e_log10.c 5.1 93/09/24\r
23 NetBSD: e_log10.c,v 1.12 2002/05/26 22:01:51 wiz Exp\r
24**/\r
25#include <LibConfig.h>\r
26#include <sys/EfiCdefs.h>\r
27\r
28/* __ieee754_log10(x)\r
29 * Return the base 10 logarithm of x\r
30 *\r
31 * Method :\r
32 * Let log10_2hi = leading 40 bits of log10(2) and\r
33 * log10_2lo = log10(2) - log10_2hi,\r
34 * ivln10 = 1/log(10) rounded.\r
35 * Then\r
36 * n = ilogb(x),\r
37 * if(n<0) n = n+1;\r
38 * x = scalbn(x,-n);\r
39 * log10(x) := n*log10_2hi + (n*log10_2lo + ivln10*log(x))\r
40 *\r
41 * Note 1:\r
42 * To guarantee log10(10**n)=n, where 10**n is normal, the rounding\r
43 * mode must set to Round-to-Nearest.\r
44 * Note 2:\r
45 * [1/log(10)] rounded to 53 bits has error .198 ulps;\r
46 * log10 is monotonic at all binary break points.\r
47 *\r
48 * Special cases:\r
49 * log10(x) is NaN with signal if x < 0;\r
50 * log10(+INF) is +INF with no signal; log10(0) is -INF with signal;\r
51 * log10(NaN) is that NaN with no signal;\r
52 * log10(10**N) = N for N=0,1,...,22.\r
53 *\r
54 * Constants:\r
55 * The hexadecimal values are the intended ones for the following constants.\r
56 * The decimal values may be used, provided that the compiler will convert\r
57 * from decimal to binary accurately enough to produce the hexadecimal values\r
58 * shown.\r
59 */\r
60\r
61#include "math.h"\r
62#include "math_private.h"\r
63#include <errno.h>\r
64\r
65#if defined(_MSC_VER) /* Handle Microsoft VC++ compiler specifics. */\r
66 // potential divide by 0 -- near line 80, (x-x)/zero is on purpose\r
67 #pragma warning ( disable : 4723 )\r
68#endif\r
69\r
70static const double\r
71two54 = 1.80143985094819840000e+16, /* 0x43500000, 0x00000000 */\r
72ivln10 = 4.34294481903251816668e-01, /* 0x3FDBCB7B, 0x1526E50E */\r
73log10_2hi = 3.01029995663611771306e-01, /* 0x3FD34413, 0x509F6000 */\r
74log10_2lo = 3.69423907715893078616e-13; /* 0x3D59FEF3, 0x11F12B36 */\r
75\r
76static const double zero = 0.0;\r
77\r
78double\r
79__ieee754_log10(double x)\r
80{\r
81 double y,z;\r
82 int32_t i,k,hx;\r
83 u_int32_t lx;\r
84\r
85 EXTRACT_WORDS(hx,lx,x);\r
86\r
87 k=0;\r
88 if (hx < 0x00100000) { /* x < 2**-1022 */\r
89 if (((hx&0x7fffffff)|lx)==0)\r
90 return -two54/zero; /* log(+-0)=-inf */\r
91 if (hx<0) {\r
92 errno = EDOM;\r
93 return (x-x)/zero; /* log(-#) = NaN */\r
94 }\r
95 k -= 54; x *= two54; /* subnormal number, scale up x */\r
96 GET_HIGH_WORD(hx,x);\r
97 }\r
98 if (hx >= 0x7ff00000) return x+x;\r
99 k += (hx>>20)-1023;\r
100 i = ((u_int32_t)k&0x80000000)>>31;\r
101 hx = (hx&0x000fffff)|((0x3ff-i)<<20);\r
102 y = (double)(k+i);\r
103 SET_HIGH_WORD(x,hx);\r
104 z = y*log10_2lo + ivln10*__ieee754_log(x);\r
105 return z+y*log10_2hi;\r
106}\r