1
2 /* @(#)e_log10.c 5.1 93/09/24 */
3 /*
4 * ====================================================
5 * Copyright (C) 1993 by Sun Microsystems, Inc. All rights reserved.
6 *
7 * Developed at SunPro, a Sun Microsystems, Inc. business.
8 * Permission to use, copy, modify, and distribute this
9 * software is freely granted, provided that this notice
10 * is preserved.
11 * ====================================================
12 */
13
14 /* log10(x)
15 * Return the base 10 logarithm of x
16 *
17 * Method :
18 * Let log10_2hi = leading 40 bits of log10(2) and
19 * log10_2lo = log10(2) - log10_2hi,
20 * ivln10 = 1/log(10) rounded.
21 * Then
22 * n = ilogb(x),
23 * if(n<0) n = n+1;
24 * x = scalbn(x,-n);
25 * log10(x) := n*log10_2hi + (n*log10_2lo + ivln10*log(x))
26 *
27 * Note 1:
28 * To guarantee log10(10**n)=n, where 10**n is normal, the rounding
29 * mode must set to Round-to-Nearest.
30 * Note 2:
31 * [1/log(10)] rounded to 53 bits has error .198 ulps;
32 * log10 is monotonic at all binary break points.
33 *
34 * Special cases:
35 * log10(x) is NaN with signal if x < 0;
36 * log10(+INF) is +INF with no signal; log10(0) is -INF with signal;
37 * log10(NaN) is that NaN with no signal;
38 * log10(10**N) = N for N=0,1,...,22.
39 *
40 * Constants:
41 * The hexadecimal values are the intended ones for the following constants.
42 * The decimal values may be used, provided that the compiler will convert
43 * from decimal to binary accurately enough to produce the hexadecimal values
44 * shown.
45 */
46
47 #include "fdlibm.h"
48
49 #ifdef _NEED_FLOAT64
50
51 static const __float64
52 two54 = _F_64(1.80143985094819840000e+16), /* 0x43500000, 0x00000000 */
53 ivln10 = _F_64(4.34294481903251816668e-01), /* 0x3FDBCB7B, 0x1526E50E */
54 log10_2hi = _F_64(3.01029995663611771306e-01), /* 0x3FD34413, 0x509F6000 */
55 log10_2lo = _F_64(3.69423907715893078616e-13); /* 0x3D59FEF3, 0x11F12B36 */
56
57 __float64
log1064(__float64 x)58 log1064(__float64 x)
59 {
60 __float64 y, z;
61 __int32_t i, k, hx;
62 __uint32_t lx;
63
64 EXTRACT_WORDS(hx, lx, x);
65
66 k = 0;
67 if (hx < 0x00100000) { /* x < 2**-1022 */
68 if (((hx & 0x7fffffff) | lx) == 0)
69 return __math_divzero(1); /* log(+-0)=-inf */
70 if (hx < 0)
71 return __math_invalid(x); /* log(-#) = NaN */
72 k -= 54;
73 x *= two54; /* subnormal number, scale up x */
74 GET_HIGH_WORD(hx, x);
75 }
76 if (hx >= 0x7ff00000)
77 return x + x;
78 k += (hx >> 20) - 1023;
79 i = ((__uint32_t)k & 0x80000000) >> 31;
80 hx = (hx & 0x000fffff) | ((0x3ff - i) << 20);
81 y = (__float64)(k + i);
82 SET_HIGH_WORD(x, hx);
83 z = y * log10_2lo + ivln10 * log(x);
84 return z + y * log10_2hi;
85 }
86
87 _MATH_ALIAS_d_d(log10)
88
89 #endif /* _NEED_FLOAT64 */
90
