1 /*
2 * ====================================================
3 * Copyright (C) 1993 by Sun Microsystems, Inc. All rights reserved.
4 *
5 * Developed at SunPro, a Sun Microsystems, Inc. business.
6 * Permission to use, copy, modify, and distribute this
7 * software is freely granted, provided that this notice
8 * is preserved.
9 * ====================================================
10 */
11
12 /* __ieee754_log10(x)
13 * Return the base 10 logarithm of x
14 *
15 * Method :
16 * Let log10_2hi = leading 40 bits of log10(2) and
17 * log10_2lo = log10(2) - log10_2hi,
18 * ivln10 = 1/log(10) rounded.
19 * Then
20 * n = ilogb(x),
21 * if(n<0) n = n+1;
22 * x = scalbn(x,-n);
23 * log10(x) := n*log10_2hi + (n*log10_2lo + ivln10*log(x))
24 *
25 * Note 1:
26 * To guarantee log10(10**n)=n, where 10**n is normal, the rounding
27 * mode must set to Round-to-Nearest.
28 * Note 2:
29 * [1/log(10)] rounded to 53 bits has error .198 ulps;
30 * log10 is monotonic at all binary break points.
31 *
32 * Special cases:
33 * log10(x) is NaN with signal if x < 0;
34 * log10(+INF) is +INF with no signal; log10(0) is -INF with signal;
35 * log10(NaN) is that NaN with no signal;
36 * log10(10**N) = N for N=0,1,...,22.
37 *
38 * Constants:
39 * The hexadecimal values are the intended ones for the following constants.
40 * The decimal values may be used, provided that the compiler will convert
41 * from decimal to binary accurately enough to produce the hexadecimal values
42 * shown.
43 */
44
45 #include "math.h"
46 #include "math_private.h"
47
48 static const double
49 two54 = 1.80143985094819840000e+16, /* 0x43500000, 0x00000000 */
50 ivln10 = 4.34294481903251816668e-01, /* 0x3FDBCB7B, 0x1526E50E */
51 log10_2hi = 3.01029995663611771306e-01, /* 0x3FD34413, 0x509F6000 */
52 log10_2lo = 3.69423907715893078616e-13; /* 0x3D59FEF3, 0x11F12B36 */
53
54 static const double zero = 0.0;
55
__ieee754_log10(double x)56 double __ieee754_log10(double x)
57 {
58 double y,z;
59 int32_t i,k,hx;
60 u_int32_t lx;
61
62 EXTRACT_WORDS(hx,lx,x);
63
64 k=0;
65 if (hx < 0x00100000) { /* x < 2**-1022 */
66 if (((hx&0x7fffffff)|lx)==0)
67 return -two54/zero; /* log(+-0)=-inf */
68 if (hx<0) return (x-x)/zero; /* log(-#) = NaN */
69 k -= 54; x *= two54; /* subnormal number, scale up x */
70 GET_HIGH_WORD(hx,x);
71 }
72 if (hx >= 0x7ff00000) return x+x;
73 k += (hx>>20)-1023;
74 i = ((u_int32_t)k&0x80000000)>>31;
75 hx = (hx&0x000fffff)|((0x3ff-i)<<20);
76 y = (double)(k+i);
77 SET_HIGH_WORD(x,hx);
78 z = y*log10_2lo + ivln10*__ieee754_log(x);
79 return z+y*log10_2hi;
80 }
81
82 /*
83 * wrapper log10(X)
84 */
85 #ifndef _IEEE_LIBM
log10(double x)86 double log10(double x)
87 {
88 double z = __ieee754_log10(x);
89 if (_LIB_VERSION == _IEEE_ || isnan(x))
90 return z;
91 if (x <= 0.0) {
92 if(x == 0.0)
93 return __kernel_standard(x, x, 18); /* log10(0) */
94 return __kernel_standard(x, x, 19); /* log10(x<0) */
95 }
96 return z;
97 }
98 #else
99 strong_alias(__ieee754_log10, log10)
100 #endif
101 libm_hidden_def(log10)
102