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 | |
54 | static const double |
55 | two54 = 1.80143985094819840000e+16, /* 0x43500000, 0x00000000 */ |
56 | ivln10 = 4.34294481903251816668e-01, /* 0x3FDBCB7B, 0x1526E50E */ |
57 | log10_2hi = 3.01029995663611771306e-01, /* 0x3FD34413, 0x509F6000 */ |
58 | log10_2lo = 3.69423907715893078616e-13; /* 0x3D59FEF3, 0x11F12B36 */ |
59 | |
60 | static const double zero = 0.0; |
61 | |
62 | double 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 |
92 | double 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 |
105 | strong_alias(__ieee754_log10, log10) |
106 | #endif |
107 | libm_hidden_def(log10) |
108 | |