1/* @(#)e_log10.c 5.1 93/09/24 */
2/*
3 * ====================================================
4 * Copyright (C) 1993 by Sun Microsystems, Inc. All rights reserved.
5 *
6 * Developed at SunPro, a Sun Microsystems, Inc. business.
7 * Permission to use, copy, modify, and distribute this
8 * software is freely granted, provided that this notice
9 * is preserved.
10 * ====================================================
11 */
12
13/* __ieee754_log10(x)
14 * Return the base 10 logarithm of x
15 *
16 * Method :
17 * Let log10_2hi = leading 40 bits of log10(2) and
18 * log10_2lo = log10(2) - log10_2hi,
19 * ivln10 = 1/log(10) rounded.
20 * Then
21 * n = ilogb(x),
22 * if(n<0) n = n+1;
23 * x = scalbn(x,-n);
24 * log10(x) := n*log10_2hi + (n*log10_2lo + ivln10*log(x))
25 *
26 * Note 1:
27 * To guarantee log10(10**n)=n, where 10**n is normal, the rounding
28 * mode must set to Round-to-Nearest.
29 * Note 2:
30 * [1/log(10)] rounded to 53 bits has error .198 ulps;
31 * log10 is monotonic at all binary break points.
32 *
33 * Special cases:
34 * log10(x) is NaN with signal if x < 0;
35 * log10(+INF) is +INF with no signal; log10(0) is -INF with signal;
36 * log10(NaN) is that NaN with no signal;
37 * log10(10**N) = N for N=0,1,...,22.
38 *
39 * Constants:
40 * The hexadecimal values are the intended ones for the following constants.
41 * The decimal values may be used, provided that the compiler will convert
42 * from decimal to binary accurately enough to produce the hexadecimal values
43 * shown.
44 */
45
46#include <math.h>
47#include <math_private.h>
48#include <stdint.h>
49
50static const double two54 = 1.80143985094819840000e+16; /* 0x4350000000000000 */
51static const double ivln10 = 4.34294481903251816668e-01; /* 0x3FDBCB7B1526E50E */
52static const double log10_2hi = 3.01029995663611771306e-01; /* 0x3FD34413509F6000 */
53static const double log10_2lo = 3.69423907715893078616e-13; /* 0x3D59FEF311F12B36 */
54
55double
56__ieee754_log10 (double x)
57{
58 double y, z;
59 int64_t i, hx;
60 int32_t k;
61
62 EXTRACT_WORDS64 (hx, x);
63
64 k = 0;
65 if (hx < INT64_C(0x0010000000000000))
66 { /* x < 2**-1022 */
67 if (__glibc_unlikely ((hx & UINT64_C(0x7fffffffffffffff)) == 0))
68 return -two54 / (x - x); /* log(+-0)=-inf */
69 if (__glibc_unlikely (hx < 0))
70 return (x - x) / (x - x); /* log(-#) = NaN */
71 k -= 54;
72 x *= two54; /* subnormal number, scale up x */
73 EXTRACT_WORDS64 (hx, x);
74 }
75 /* scale up resulted in a NaN number */
76 if (__glibc_unlikely (hx >= UINT64_C(0x7ff0000000000000)))
77 return x + x;
78 k += (hx >> 52) - 1023;
79 i = ((uint64_t) k & UINT64_C(0x8000000000000000)) >> 63;
80 hx = (hx & UINT64_C(0x000fffffffffffff)) | ((0x3ff - i) << 52);
81 y = (double) (k + i);
82 INSERT_WORDS64 (x, hx);
83 z = y * log10_2lo + ivln10 * __ieee754_log (x);
84 return z + y * log10_2hi;
85}
86
87strong_alias (__ieee754_log10, __log10_finite)
88