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 #if defined(_MSC_VER) /* Handle Microsoft VC++ compiler specifics. */
13 /* C4723: potential divide by zero. */
14 #pragma warning ( disable : 4723 )
15 #endif
16
17 /* __ieee754_log10(x)
18 * Return the base 10 logarithm of x
19 *
20 * Method :
21 * Let log10_2hi = leading 40 bits of log10(2) and
22 * log10_2lo = log10(2) - log10_2hi,
23 * ivln10 = 1/log(10) rounded.
24 * Then
25 * n = ilogb(x),
26 * if(n<0) n = n+1;
27 * x = scalbn(x,-n);
28 * log10(x) := n*log10_2hi + (n*log10_2lo + ivln10*log(x))
29 *
30 * Note 1:
31 * To guarantee log10(10**n)=n, where 10**n is normal, the rounding
32 * mode must set to Round-to-Nearest.
33 * Note 2:
34 * [1/log(10)] rounded to 53 bits has error .198 ulps;
35 * log10 is monotonic at all binary break points.
36 *
37 * Special cases:
38 * log10(x) is NaN with signal if x < 0;
39 * log10(+INF) is +INF with no signal; log10(0) is -INF with signal;
40 * log10(NaN) is that NaN with no signal;
41 * log10(10**N) = N for N=0,1,...,22.
42 *
43 * Constants:
44 * The hexadecimal values are the intended ones for the following constants.
45 * The decimal values may be used, provided that the compiler will convert
46 * from decimal to binary accurately enough to produce the hexadecimal values
47 * shown.
48 */
49
50 #include "math_libm.h"
51 #include "math_private.h"
52
53 static const double
54 two54 = 1.80143985094819840000e+16, /* 0x43500000, 0x00000000 */
55 ivln10 = 4.34294481903251816668e-01, /* 0x3FDBCB7B, 0x1526E50E */
56 log10_2hi = 3.01029995663611771306e-01, /* 0x3FD34413, 0x509F6000 */
57 log10_2lo = 3.69423907715893078616e-13; /* 0x3D59FEF3, 0x11F12B36 */
58
59 static const double zero = 0.0;
60
__ieee754_log10(double x)61 double attribute_hidden __ieee754_log10(double x)
62 {
63 double y,z;
64 int32_t i,k,hx;
65 u_int32_t lx;
66
67 EXTRACT_WORDS(hx,lx,x);
68
69 k=0;
70 if (hx < 0x00100000) { /* x < 2**-1022 */
71 if (((hx&0x7fffffff)|lx)==0)
72 return -two54/zero; /* log(+-0)=-inf */
73 if (hx<0) return (x-x)/zero; /* log(-#) = NaN */
74 k -= 54; x *= two54; /* subnormal number, scale up x */
75 GET_HIGH_WORD(hx,x);
76 }
77 if (hx >= 0x7ff00000) return x+x;
78 k += (hx>>20)-1023;
79 i = ((u_int32_t)k&0x80000000)>>31;
80 hx = (hx&0x000fffff)|((0x3ff-i)<<20);
81 y = (double)(k+i);
82 SET_HIGH_WORD(x,hx);
83 z = y*log10_2lo + ivln10*__ieee754_log(x);
84 return z+y*log10_2hi;
85 }
86
87 /*
88 * wrapper log10(X)
89 */
90 #ifndef _IEEE_LIBM
log10(double x)91 double log10(double x)
92 {
93 double z = __ieee754_log10(x);
94 if (_LIB_VERSION == _IEEE_ || isnan(x))
95 return z;
96 if (x <= 0.0) {
97 if(x == 0.0)
98 return __kernel_standard(x, x, 18); /* log10(0) */
99 return __kernel_standard(x, x, 19); /* log10(x<0) */
100 }
101 return z;
102 }
103 #else
104 strong_alias(__ieee754_log10, log10)
105 #endif
106 libm_hidden_def(log10)
107