1#include "SDL_internal.h"
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#if defined(_MSC_VER) /* Handle Microsoft VC++ compiler specifics. */
14/* C4723: potential divide by zero. */
15#pragma warning ( disable : 4723 )
16#endif
17
18/* __ieee754_log10(x)
19 * Return the base 10 logarithm of x
20 *
21 * Method :
22 * Let log10_2hi = leading 40 bits of log10(2) and
23 * log10_2lo = log10(2) - log10_2hi,
24 * ivln10 = 1/log(10) rounded.
25 * Then
26 * n = ilogb(x),
27 * if(n<0) n = n+1;
28 * x = scalbn(x,-n);
29 * log10(x) := n*log10_2hi + (n*log10_2lo + ivln10*log(x))
30 *
31 * Note 1:
32 * To guarantee log10(10**n)=n, where 10**n is normal, the rounding
33 * mode must set to Round-to-Nearest.
34 * Note 2:
35 * [1/log(10)] rounded to 53 bits has error .198 ulps;
36 * log10 is monotonic at all binary break points.
37 *
38 * Special cases:
39 * log10(x) is NaN with signal if x < 0;
40 * log10(+INF) is +INF with no signal; log10(0) is -INF with signal;
41 * log10(NaN) is that NaN with no signal;
42 * log10(10**N) = N for N=0,1,...,22.
43 *
44 * Constants:
45 * The hexadecimal values are the intended ones for the following constants.
46 * The decimal values may be used, provided that the compiler will convert
47 * from decimal to binary accurately enough to produce the hexadecimal values
48 * shown.
49 */
50
51#include "math_libm.h"
52#include "math_private.h"
53
54static const double
55two54 = 1.80143985094819840000e+16, /* 0x43500000, 0x00000000 */
56ivln10 = 4.34294481903251816668e-01, /* 0x3FDBCB7B, 0x1526E50E */
57log10_2hi = 3.01029995663611771306e-01, /* 0x3FD34413, 0x509F6000 */
58log10_2lo = 3.69423907715893078616e-13; /* 0x3D59FEF3, 0x11F12B36 */
59
60static const double zero = 0.0;
61
62double attribute_hidden __ieee754_log10(double x)
63{
64 double y,z;
65 int32_t i,k,hx;
66 u_int32_t lx;
67
68 EXTRACT_WORDS(hx,lx,x);
69
70 k=0;
71 if (hx < 0x00100000) { /* x < 2**-1022 */
72 if (((hx&0x7fffffff)|lx)==0)
73 return -two54/zero; /* log(+-0)=-inf */
74 if (hx<0) return (x-x)/zero; /* log(-#) = NaN */
75 k -= 54; x *= two54; /* subnormal number, scale up x */
76 GET_HIGH_WORD(hx,x);
77 }
78 if (hx >= 0x7ff00000) return x+x;
79 k += (hx>>20)-1023;
80 i = ((u_int32_t)k&0x80000000)>>31;
81 hx = (hx&0x000fffff)|((0x3ff-i)<<20);
82 y = (double)(k+i);
83 SET_HIGH_WORD(x,hx);
84 z = y*log10_2lo + ivln10*__ieee754_log(x);
85 return z+y*log10_2hi;
86}
87
88/*
89 * wrapper log10(X)
90 */
91#ifndef _IEEE_LIBM
92double log10(double x)
93{
94 double z = __ieee754_log10(x);
95 if (_LIB_VERSION == _IEEE_ || isnan(x))
96 return z;
97 if (x <= 0.0) {
98 if(x == 0.0)
99 return __kernel_standard(x, x, 18); /* log10(0) */
100 return __kernel_standard(x, x, 19); /* log10(x<0) */
101 }
102 return z;
103}
104#else
105strong_alias(__ieee754_log10, log10)
106#endif
107libm_hidden_def(log10)
108