1 /* Copyright JS Foundation and other contributors, http://js.foundation
2 *
3 * Licensed under the Apache License, Version 2.0 (the "License");
4 * you may not use this file except in compliance with the License.
5 * You may obtain a copy of the License at
6 *
7 * http://www.apache.org/licenses/LICENSE-2.0
8 *
9 * Unless required by applicable law or agreed to in writing, software
10 * distributed under the License is distributed on an "AS IS" BASIS
11 * WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied.
12 * See the License for the specific language governing permissions and
13 * limitations under the License.
14 *
15 * This file is based on work under the following copyright and permission
16 * notice:
17 *
18 * Copyright (C) 1993 by Sun Microsystems, Inc. All rights reserved.
19 *
20 * Developed at SunSoft, a Sun Microsystems, Inc. business.
21 * Permission to use, copy, modify, and distribute this
22 * software is freely granted, provided that this notice
23 * is preserved.
24 *
25 * @(#)e_log10.c 1.3 95/01/18
26 */
27
28 #include "jerry-libm-internal.h"
29
30 /* log10(x)
31 * Return the base 10 logarithm of x
32 *
33 * Method :
34 * Let log10_2hi = leading 40 bits of log10(2) and
35 * log10_2lo = log10(2) - log10_2hi,
36 * ivln10 = 1/log(10) rounded.
37 * Then
38 * n = ilogb(x),
39 * if(n<0) n = n+1;
40 * x = scalbn(x,-n);
41 * log10(x) := n*log10_2hi + (n*log10_2lo + ivln10*log(x))
42 *
43 * Note 1:
44 * To guarantee log10(10**n)=n, where 10**n is normal, the rounding
45 * mode must set to Round-to-Nearest.
46 * Note 2:
47 * [1/log(10)] rounded to 53 bits has error .198 ulps;
48 * log10 is monotonic at all binary break points.
49 *
50 * Special cases:
51 * log10(x) is NaN with signal if x < 0;
52 * log10(+INF) is +INF with no signal; log10(0) is -INF with signal;
53 * log10(NaN) is that NaN with no signal;
54 * log10(10**N) = N for N=0,1,...,22.
55 *
56 * Constants:
57 * The hexadecimal values are the intended ones for the following constants.
58 * The decimal values may be used, provided that the compiler will convert
59 * from decimal to binary accurately enough to produce the hexadecimal values
60 * shown.
61 */
62
63 #define zero 0.0
64 #define two54 1.80143985094819840000e+16 /* 0x43500000, 0x00000000 */
65 #define ivln10 4.34294481903251816668e-01 /* 0x3FDBCB7B, 0x1526E50E */
66 #define log10_2hi 3.01029995663611771306e-01 /* 0x3FD34413, 0x509F6000 */
67 #define log10_2lo 3.69423907715893078616e-13 /* 0x3D59FEF3, 0x11F12B36 */
68
69 double
log10(double x)70 log10 (double x)
71 {
72 double y, z;
73 int i, k, hx;
74 unsigned lx;
75 double_accessor temp;
76
77 hx = __HI (x); /* high word of x */
78 lx = __LO (x); /* low word of x */
79
80 k = 0;
81 if (hx < 0x00100000)
82 {
83 /* x < 2**-1022 */
84 if (((hx & 0x7fffffff) | lx) == 0)
85 {
86 /* log(+-0)=-inf */
87 return -two54 / zero;
88 }
89 if (hx < 0)
90 {
91 /* log(-#) = NaN */
92 return (x - x) / zero;
93 }
94 k -= 54;
95 x *= two54; /* subnormal number, scale up x */
96 hx = __HI (x); /* high word of x */
97 }
98 if (hx >= 0x7ff00000)
99 {
100 return x + x;
101 }
102 k += (hx >> 20) - 1023;
103 i = ((unsigned) k & 0x80000000) >> 31;
104 hx = (hx & 0x000fffff) | ((0x3ff - i) << 20);
105 y = (double) (k + i);
106 temp.dbl = x;
107 temp.as_int.hi = hx;
108 z = y * log10_2lo + ivln10 * log (temp.dbl);
109 return z + y * log10_2hi;
110 } /* log10 */
111
112 #undef zero
113 #undef two54
114 #undef ivln10
115 #undef log10_2hi
116 #undef log10_2lo
117