Mercurial > sdl-ios-xcode
annotate src/libm/e_log.c @ 2847:7d020441fa81
Don't hardcode RECT for fragment program texture targets.
Now we can generate what a given system needs when compiling the shader.
author | Ryan C. Gordon <icculus@icculus.org> |
---|---|
date | Sun, 07 Dec 2008 07:06:34 +0000 |
parents | a98604b691c8 |
children | dc1eb82ffdaa |
rev | line source |
---|---|
2756
a98604b691c8
Expanded the libm support and put it into a separate directory.
Sam Lantinga <slouken@libsdl.org>
parents:
diff
changeset
|
1 /* @(#)e_log.c 5.1 93/09/24 */ |
a98604b691c8
Expanded the libm support and put it into a separate directory.
Sam Lantinga <slouken@libsdl.org>
parents:
diff
changeset
|
2 /* |
a98604b691c8
Expanded the libm support and put it into a separate directory.
Sam Lantinga <slouken@libsdl.org>
parents:
diff
changeset
|
3 * ==================================================== |
a98604b691c8
Expanded the libm support and put it into a separate directory.
Sam Lantinga <slouken@libsdl.org>
parents:
diff
changeset
|
4 * Copyright (C) 1993 by Sun Microsystems, Inc. All rights reserved. |
a98604b691c8
Expanded the libm support and put it into a separate directory.
Sam Lantinga <slouken@libsdl.org>
parents:
diff
changeset
|
5 * |
a98604b691c8
Expanded the libm support and put it into a separate directory.
Sam Lantinga <slouken@libsdl.org>
parents:
diff
changeset
|
6 * Developed at SunPro, a Sun Microsystems, Inc. business. |
a98604b691c8
Expanded the libm support and put it into a separate directory.
Sam Lantinga <slouken@libsdl.org>
parents:
diff
changeset
|
7 * Permission to use, copy, modify, and distribute this |
a98604b691c8
Expanded the libm support and put it into a separate directory.
Sam Lantinga <slouken@libsdl.org>
parents:
diff
changeset
|
8 * software is freely granted, provided that this notice |
a98604b691c8
Expanded the libm support and put it into a separate directory.
Sam Lantinga <slouken@libsdl.org>
parents:
diff
changeset
|
9 * is preserved. |
a98604b691c8
Expanded the libm support and put it into a separate directory.
Sam Lantinga <slouken@libsdl.org>
parents:
diff
changeset
|
10 * ==================================================== |
a98604b691c8
Expanded the libm support and put it into a separate directory.
Sam Lantinga <slouken@libsdl.org>
parents:
diff
changeset
|
11 */ |
a98604b691c8
Expanded the libm support and put it into a separate directory.
Sam Lantinga <slouken@libsdl.org>
parents:
diff
changeset
|
12 |
a98604b691c8
Expanded the libm support and put it into a separate directory.
Sam Lantinga <slouken@libsdl.org>
parents:
diff
changeset
|
13 #if defined(LIBM_SCCS) && !defined(lint) |
a98604b691c8
Expanded the libm support and put it into a separate directory.
Sam Lantinga <slouken@libsdl.org>
parents:
diff
changeset
|
14 static char rcsid[] = "$NetBSD: e_log.c,v 1.8 1995/05/10 20:45:49 jtc Exp $"; |
a98604b691c8
Expanded the libm support and put it into a separate directory.
Sam Lantinga <slouken@libsdl.org>
parents:
diff
changeset
|
15 #endif |
a98604b691c8
Expanded the libm support and put it into a separate directory.
Sam Lantinga <slouken@libsdl.org>
parents:
diff
changeset
|
16 |
a98604b691c8
Expanded the libm support and put it into a separate directory.
Sam Lantinga <slouken@libsdl.org>
parents:
diff
changeset
|
17 /* __ieee754_log(x) |
a98604b691c8
Expanded the libm support and put it into a separate directory.
Sam Lantinga <slouken@libsdl.org>
parents:
diff
changeset
|
18 * Return the logrithm of x |
a98604b691c8
Expanded the libm support and put it into a separate directory.
Sam Lantinga <slouken@libsdl.org>
parents:
diff
changeset
|
19 * |
a98604b691c8
Expanded the libm support and put it into a separate directory.
Sam Lantinga <slouken@libsdl.org>
parents:
diff
changeset
|
20 * Method : |
a98604b691c8
Expanded the libm support and put it into a separate directory.
Sam Lantinga <slouken@libsdl.org>
parents:
diff
changeset
|
21 * 1. Argument Reduction: find k and f such that |
a98604b691c8
Expanded the libm support and put it into a separate directory.
Sam Lantinga <slouken@libsdl.org>
parents:
diff
changeset
|
22 * x = 2^k * (1+f), |
a98604b691c8
Expanded the libm support and put it into a separate directory.
Sam Lantinga <slouken@libsdl.org>
parents:
diff
changeset
|
23 * where sqrt(2)/2 < 1+f < sqrt(2) . |
a98604b691c8
Expanded the libm support and put it into a separate directory.
Sam Lantinga <slouken@libsdl.org>
parents:
diff
changeset
|
24 * |
a98604b691c8
Expanded the libm support and put it into a separate directory.
Sam Lantinga <slouken@libsdl.org>
parents:
diff
changeset
|
25 * 2. Approximation of log(1+f). |
a98604b691c8
Expanded the libm support and put it into a separate directory.
Sam Lantinga <slouken@libsdl.org>
parents:
diff
changeset
|
26 * Let s = f/(2+f) ; based on log(1+f) = log(1+s) - log(1-s) |
a98604b691c8
Expanded the libm support and put it into a separate directory.
Sam Lantinga <slouken@libsdl.org>
parents:
diff
changeset
|
27 * = 2s + 2/3 s**3 + 2/5 s**5 + ....., |
a98604b691c8
Expanded the libm support and put it into a separate directory.
Sam Lantinga <slouken@libsdl.org>
parents:
diff
changeset
|
28 * = 2s + s*R |
a98604b691c8
Expanded the libm support and put it into a separate directory.
Sam Lantinga <slouken@libsdl.org>
parents:
diff
changeset
|
29 * We use a special Reme algorithm on [0,0.1716] to generate |
a98604b691c8
Expanded the libm support and put it into a separate directory.
Sam Lantinga <slouken@libsdl.org>
parents:
diff
changeset
|
30 * a polynomial of degree 14 to approximate R The maximum error |
a98604b691c8
Expanded the libm support and put it into a separate directory.
Sam Lantinga <slouken@libsdl.org>
parents:
diff
changeset
|
31 * of this polynomial approximation is bounded by 2**-58.45. In |
a98604b691c8
Expanded the libm support and put it into a separate directory.
Sam Lantinga <slouken@libsdl.org>
parents:
diff
changeset
|
32 * other words, |
a98604b691c8
Expanded the libm support and put it into a separate directory.
Sam Lantinga <slouken@libsdl.org>
parents:
diff
changeset
|
33 * 2 4 6 8 10 12 14 |
a98604b691c8
Expanded the libm support and put it into a separate directory.
Sam Lantinga <slouken@libsdl.org>
parents:
diff
changeset
|
34 * R(z) ~ Lg1*s +Lg2*s +Lg3*s +Lg4*s +Lg5*s +Lg6*s +Lg7*s |
a98604b691c8
Expanded the libm support and put it into a separate directory.
Sam Lantinga <slouken@libsdl.org>
parents:
diff
changeset
|
35 * (the values of Lg1 to Lg7 are listed in the program) |
a98604b691c8
Expanded the libm support and put it into a separate directory.
Sam Lantinga <slouken@libsdl.org>
parents:
diff
changeset
|
36 * and |
a98604b691c8
Expanded the libm support and put it into a separate directory.
Sam Lantinga <slouken@libsdl.org>
parents:
diff
changeset
|
37 * | 2 14 | -58.45 |
a98604b691c8
Expanded the libm support and put it into a separate directory.
Sam Lantinga <slouken@libsdl.org>
parents:
diff
changeset
|
38 * | Lg1*s +...+Lg7*s - R(z) | <= 2 |
a98604b691c8
Expanded the libm support and put it into a separate directory.
Sam Lantinga <slouken@libsdl.org>
parents:
diff
changeset
|
39 * | | |
a98604b691c8
Expanded the libm support and put it into a separate directory.
Sam Lantinga <slouken@libsdl.org>
parents:
diff
changeset
|
40 * Note that 2s = f - s*f = f - hfsq + s*hfsq, where hfsq = f*f/2. |
a98604b691c8
Expanded the libm support and put it into a separate directory.
Sam Lantinga <slouken@libsdl.org>
parents:
diff
changeset
|
41 * In order to guarantee error in log below 1ulp, we compute log |
a98604b691c8
Expanded the libm support and put it into a separate directory.
Sam Lantinga <slouken@libsdl.org>
parents:
diff
changeset
|
42 * by |
a98604b691c8
Expanded the libm support and put it into a separate directory.
Sam Lantinga <slouken@libsdl.org>
parents:
diff
changeset
|
43 * log(1+f) = f - s*(f - R) (if f is not too large) |
a98604b691c8
Expanded the libm support and put it into a separate directory.
Sam Lantinga <slouken@libsdl.org>
parents:
diff
changeset
|
44 * log(1+f) = f - (hfsq - s*(hfsq+R)). (better accuracy) |
a98604b691c8
Expanded the libm support and put it into a separate directory.
Sam Lantinga <slouken@libsdl.org>
parents:
diff
changeset
|
45 * |
a98604b691c8
Expanded the libm support and put it into a separate directory.
Sam Lantinga <slouken@libsdl.org>
parents:
diff
changeset
|
46 * 3. Finally, log(x) = k*ln2 + log(1+f). |
a98604b691c8
Expanded the libm support and put it into a separate directory.
Sam Lantinga <slouken@libsdl.org>
parents:
diff
changeset
|
47 * = k*ln2_hi+(f-(hfsq-(s*(hfsq+R)+k*ln2_lo))) |
a98604b691c8
Expanded the libm support and put it into a separate directory.
Sam Lantinga <slouken@libsdl.org>
parents:
diff
changeset
|
48 * Here ln2 is split into two floating point number: |
a98604b691c8
Expanded the libm support and put it into a separate directory.
Sam Lantinga <slouken@libsdl.org>
parents:
diff
changeset
|
49 * ln2_hi + ln2_lo, |
a98604b691c8
Expanded the libm support and put it into a separate directory.
Sam Lantinga <slouken@libsdl.org>
parents:
diff
changeset
|
50 * where n*ln2_hi is always exact for |n| < 2000. |
a98604b691c8
Expanded the libm support and put it into a separate directory.
Sam Lantinga <slouken@libsdl.org>
parents:
diff
changeset
|
51 * |
a98604b691c8
Expanded the libm support and put it into a separate directory.
Sam Lantinga <slouken@libsdl.org>
parents:
diff
changeset
|
52 * Special cases: |
a98604b691c8
Expanded the libm support and put it into a separate directory.
Sam Lantinga <slouken@libsdl.org>
parents:
diff
changeset
|
53 * log(x) is NaN with signal if x < 0 (including -INF) ; |
a98604b691c8
Expanded the libm support and put it into a separate directory.
Sam Lantinga <slouken@libsdl.org>
parents:
diff
changeset
|
54 * log(+INF) is +INF; log(0) is -INF with signal; |
a98604b691c8
Expanded the libm support and put it into a separate directory.
Sam Lantinga <slouken@libsdl.org>
parents:
diff
changeset
|
55 * log(NaN) is that NaN with no signal. |
a98604b691c8
Expanded the libm support and put it into a separate directory.
Sam Lantinga <slouken@libsdl.org>
parents:
diff
changeset
|
56 * |
a98604b691c8
Expanded the libm support and put it into a separate directory.
Sam Lantinga <slouken@libsdl.org>
parents:
diff
changeset
|
57 * Accuracy: |
a98604b691c8
Expanded the libm support and put it into a separate directory.
Sam Lantinga <slouken@libsdl.org>
parents:
diff
changeset
|
58 * according to an error analysis, the error is always less than |
a98604b691c8
Expanded the libm support and put it into a separate directory.
Sam Lantinga <slouken@libsdl.org>
parents:
diff
changeset
|
59 * 1 ulp (unit in the last place). |
a98604b691c8
Expanded the libm support and put it into a separate directory.
Sam Lantinga <slouken@libsdl.org>
parents:
diff
changeset
|
60 * |
a98604b691c8
Expanded the libm support and put it into a separate directory.
Sam Lantinga <slouken@libsdl.org>
parents:
diff
changeset
|
61 * Constants: |
a98604b691c8
Expanded the libm support and put it into a separate directory.
Sam Lantinga <slouken@libsdl.org>
parents:
diff
changeset
|
62 * The hexadecimal values are the intended ones for the following |
a98604b691c8
Expanded the libm support and put it into a separate directory.
Sam Lantinga <slouken@libsdl.org>
parents:
diff
changeset
|
63 * constants. The decimal values may be used, provided that the |
a98604b691c8
Expanded the libm support and put it into a separate directory.
Sam Lantinga <slouken@libsdl.org>
parents:
diff
changeset
|
64 * compiler will convert from decimal to binary accurately enough |
a98604b691c8
Expanded the libm support and put it into a separate directory.
Sam Lantinga <slouken@libsdl.org>
parents:
diff
changeset
|
65 * to produce the hexadecimal values shown. |
a98604b691c8
Expanded the libm support and put it into a separate directory.
Sam Lantinga <slouken@libsdl.org>
parents:
diff
changeset
|
66 */ |
a98604b691c8
Expanded the libm support and put it into a separate directory.
Sam Lantinga <slouken@libsdl.org>
parents:
diff
changeset
|
67 |
a98604b691c8
Expanded the libm support and put it into a separate directory.
Sam Lantinga <slouken@libsdl.org>
parents:
diff
changeset
|
68 #include "math.h" |
a98604b691c8
Expanded the libm support and put it into a separate directory.
Sam Lantinga <slouken@libsdl.org>
parents:
diff
changeset
|
69 #include "math_private.h" |
a98604b691c8
Expanded the libm support and put it into a separate directory.
Sam Lantinga <slouken@libsdl.org>
parents:
diff
changeset
|
70 |
a98604b691c8
Expanded the libm support and put it into a separate directory.
Sam Lantinga <slouken@libsdl.org>
parents:
diff
changeset
|
71 #ifdef __STDC__ |
a98604b691c8
Expanded the libm support and put it into a separate directory.
Sam Lantinga <slouken@libsdl.org>
parents:
diff
changeset
|
72 static const double |
a98604b691c8
Expanded the libm support and put it into a separate directory.
Sam Lantinga <slouken@libsdl.org>
parents:
diff
changeset
|
73 #else |
a98604b691c8
Expanded the libm support and put it into a separate directory.
Sam Lantinga <slouken@libsdl.org>
parents:
diff
changeset
|
74 static double |
a98604b691c8
Expanded the libm support and put it into a separate directory.
Sam Lantinga <slouken@libsdl.org>
parents:
diff
changeset
|
75 #endif |
a98604b691c8
Expanded the libm support and put it into a separate directory.
Sam Lantinga <slouken@libsdl.org>
parents:
diff
changeset
|
76 ln2_hi = 6.93147180369123816490e-01, /* 3fe62e42 fee00000 */ |
a98604b691c8
Expanded the libm support and put it into a separate directory.
Sam Lantinga <slouken@libsdl.org>
parents:
diff
changeset
|
77 ln2_lo = 1.90821492927058770002e-10, /* 3dea39ef 35793c76 */ |
a98604b691c8
Expanded the libm support and put it into a separate directory.
Sam Lantinga <slouken@libsdl.org>
parents:
diff
changeset
|
78 two54 = 1.80143985094819840000e+16, /* 43500000 00000000 */ |
a98604b691c8
Expanded the libm support and put it into a separate directory.
Sam Lantinga <slouken@libsdl.org>
parents:
diff
changeset
|
79 Lg1 = 6.666666666666735130e-01, /* 3FE55555 55555593 */ |
a98604b691c8
Expanded the libm support and put it into a separate directory.
Sam Lantinga <slouken@libsdl.org>
parents:
diff
changeset
|
80 Lg2 = 3.999999999940941908e-01, /* 3FD99999 9997FA04 */ |
a98604b691c8
Expanded the libm support and put it into a separate directory.
Sam Lantinga <slouken@libsdl.org>
parents:
diff
changeset
|
81 Lg3 = 2.857142874366239149e-01, /* 3FD24924 94229359 */ |
a98604b691c8
Expanded the libm support and put it into a separate directory.
Sam Lantinga <slouken@libsdl.org>
parents:
diff
changeset
|
82 Lg4 = 2.222219843214978396e-01, /* 3FCC71C5 1D8E78AF */ |
a98604b691c8
Expanded the libm support and put it into a separate directory.
Sam Lantinga <slouken@libsdl.org>
parents:
diff
changeset
|
83 Lg5 = 1.818357216161805012e-01, /* 3FC74664 96CB03DE */ |
a98604b691c8
Expanded the libm support and put it into a separate directory.
Sam Lantinga <slouken@libsdl.org>
parents:
diff
changeset
|
84 Lg6 = 1.531383769920937332e-01, /* 3FC39A09 D078C69F */ |
a98604b691c8
Expanded the libm support and put it into a separate directory.
Sam Lantinga <slouken@libsdl.org>
parents:
diff
changeset
|
85 Lg7 = 1.479819860511658591e-01; /* 3FC2F112 DF3E5244 */ |
a98604b691c8
Expanded the libm support and put it into a separate directory.
Sam Lantinga <slouken@libsdl.org>
parents:
diff
changeset
|
86 |
a98604b691c8
Expanded the libm support and put it into a separate directory.
Sam Lantinga <slouken@libsdl.org>
parents:
diff
changeset
|
87 #ifdef __STDC__ |
a98604b691c8
Expanded the libm support and put it into a separate directory.
Sam Lantinga <slouken@libsdl.org>
parents:
diff
changeset
|
88 static const double zero = 0.0; |
a98604b691c8
Expanded the libm support and put it into a separate directory.
Sam Lantinga <slouken@libsdl.org>
parents:
diff
changeset
|
89 #else |
a98604b691c8
Expanded the libm support and put it into a separate directory.
Sam Lantinga <slouken@libsdl.org>
parents:
diff
changeset
|
90 static double zero = 0.0; |
a98604b691c8
Expanded the libm support and put it into a separate directory.
Sam Lantinga <slouken@libsdl.org>
parents:
diff
changeset
|
91 #endif |
a98604b691c8
Expanded the libm support and put it into a separate directory.
Sam Lantinga <slouken@libsdl.org>
parents:
diff
changeset
|
92 |
a98604b691c8
Expanded the libm support and put it into a separate directory.
Sam Lantinga <slouken@libsdl.org>
parents:
diff
changeset
|
93 #ifdef __STDC__ |
a98604b691c8
Expanded the libm support and put it into a separate directory.
Sam Lantinga <slouken@libsdl.org>
parents:
diff
changeset
|
94 double attribute_hidden |
a98604b691c8
Expanded the libm support and put it into a separate directory.
Sam Lantinga <slouken@libsdl.org>
parents:
diff
changeset
|
95 __ieee754_log(double x) |
a98604b691c8
Expanded the libm support and put it into a separate directory.
Sam Lantinga <slouken@libsdl.org>
parents:
diff
changeset
|
96 #else |
a98604b691c8
Expanded the libm support and put it into a separate directory.
Sam Lantinga <slouken@libsdl.org>
parents:
diff
changeset
|
97 double attribute_hidden |
a98604b691c8
Expanded the libm support and put it into a separate directory.
Sam Lantinga <slouken@libsdl.org>
parents:
diff
changeset
|
98 __ieee754_log(x) |
a98604b691c8
Expanded the libm support and put it into a separate directory.
Sam Lantinga <slouken@libsdl.org>
parents:
diff
changeset
|
99 double x; |
a98604b691c8
Expanded the libm support and put it into a separate directory.
Sam Lantinga <slouken@libsdl.org>
parents:
diff
changeset
|
100 #endif |
a98604b691c8
Expanded the libm support and put it into a separate directory.
Sam Lantinga <slouken@libsdl.org>
parents:
diff
changeset
|
101 { |
a98604b691c8
Expanded the libm support and put it into a separate directory.
Sam Lantinga <slouken@libsdl.org>
parents:
diff
changeset
|
102 double hfsq, f, s, z, R, w, t1, t2, dk; |
a98604b691c8
Expanded the libm support and put it into a separate directory.
Sam Lantinga <slouken@libsdl.org>
parents:
diff
changeset
|
103 int32_t k, hx, i, j; |
a98604b691c8
Expanded the libm support and put it into a separate directory.
Sam Lantinga <slouken@libsdl.org>
parents:
diff
changeset
|
104 u_int32_t lx; |
a98604b691c8
Expanded the libm support and put it into a separate directory.
Sam Lantinga <slouken@libsdl.org>
parents:
diff
changeset
|
105 |
a98604b691c8
Expanded the libm support and put it into a separate directory.
Sam Lantinga <slouken@libsdl.org>
parents:
diff
changeset
|
106 EXTRACT_WORDS(hx, lx, x); |
a98604b691c8
Expanded the libm support and put it into a separate directory.
Sam Lantinga <slouken@libsdl.org>
parents:
diff
changeset
|
107 |
a98604b691c8
Expanded the libm support and put it into a separate directory.
Sam Lantinga <slouken@libsdl.org>
parents:
diff
changeset
|
108 k = 0; |
a98604b691c8
Expanded the libm support and put it into a separate directory.
Sam Lantinga <slouken@libsdl.org>
parents:
diff
changeset
|
109 if (hx < 0x00100000) { /* x < 2**-1022 */ |
a98604b691c8
Expanded the libm support and put it into a separate directory.
Sam Lantinga <slouken@libsdl.org>
parents:
diff
changeset
|
110 if (((hx & 0x7fffffff) | lx) == 0) |
a98604b691c8
Expanded the libm support and put it into a separate directory.
Sam Lantinga <slouken@libsdl.org>
parents:
diff
changeset
|
111 return -two54 / zero; /* log(+-0)=-inf */ |
a98604b691c8
Expanded the libm support and put it into a separate directory.
Sam Lantinga <slouken@libsdl.org>
parents:
diff
changeset
|
112 if (hx < 0) |
a98604b691c8
Expanded the libm support and put it into a separate directory.
Sam Lantinga <slouken@libsdl.org>
parents:
diff
changeset
|
113 return (x - x) / zero; /* log(-#) = NaN */ |
a98604b691c8
Expanded the libm support and put it into a separate directory.
Sam Lantinga <slouken@libsdl.org>
parents:
diff
changeset
|
114 k -= 54; |
a98604b691c8
Expanded the libm support and put it into a separate directory.
Sam Lantinga <slouken@libsdl.org>
parents:
diff
changeset
|
115 x *= two54; /* subnormal number, scale up x */ |
a98604b691c8
Expanded the libm support and put it into a separate directory.
Sam Lantinga <slouken@libsdl.org>
parents:
diff
changeset
|
116 GET_HIGH_WORD(hx, x); |
a98604b691c8
Expanded the libm support and put it into a separate directory.
Sam Lantinga <slouken@libsdl.org>
parents:
diff
changeset
|
117 } |
a98604b691c8
Expanded the libm support and put it into a separate directory.
Sam Lantinga <slouken@libsdl.org>
parents:
diff
changeset
|
118 if (hx >= 0x7ff00000) |
a98604b691c8
Expanded the libm support and put it into a separate directory.
Sam Lantinga <slouken@libsdl.org>
parents:
diff
changeset
|
119 return x + x; |
a98604b691c8
Expanded the libm support and put it into a separate directory.
Sam Lantinga <slouken@libsdl.org>
parents:
diff
changeset
|
120 k += (hx >> 20) - 1023; |
a98604b691c8
Expanded the libm support and put it into a separate directory.
Sam Lantinga <slouken@libsdl.org>
parents:
diff
changeset
|
121 hx &= 0x000fffff; |
a98604b691c8
Expanded the libm support and put it into a separate directory.
Sam Lantinga <slouken@libsdl.org>
parents:
diff
changeset
|
122 i = (hx + 0x95f64) & 0x100000; |
a98604b691c8
Expanded the libm support and put it into a separate directory.
Sam Lantinga <slouken@libsdl.org>
parents:
diff
changeset
|
123 SET_HIGH_WORD(x, hx | (i ^ 0x3ff00000)); /* normalize x or x/2 */ |
a98604b691c8
Expanded the libm support and put it into a separate directory.
Sam Lantinga <slouken@libsdl.org>
parents:
diff
changeset
|
124 k += (i >> 20); |
a98604b691c8
Expanded the libm support and put it into a separate directory.
Sam Lantinga <slouken@libsdl.org>
parents:
diff
changeset
|
125 f = x - 1.0; |
a98604b691c8
Expanded the libm support and put it into a separate directory.
Sam Lantinga <slouken@libsdl.org>
parents:
diff
changeset
|
126 if ((0x000fffff & (2 + hx)) < 3) { /* |f| < 2**-20 */ |
a98604b691c8
Expanded the libm support and put it into a separate directory.
Sam Lantinga <slouken@libsdl.org>
parents:
diff
changeset
|
127 if (f == zero) { |
a98604b691c8
Expanded the libm support and put it into a separate directory.
Sam Lantinga <slouken@libsdl.org>
parents:
diff
changeset
|
128 if (k == 0) |
a98604b691c8
Expanded the libm support and put it into a separate directory.
Sam Lantinga <slouken@libsdl.org>
parents:
diff
changeset
|
129 return zero; |
a98604b691c8
Expanded the libm support and put it into a separate directory.
Sam Lantinga <slouken@libsdl.org>
parents:
diff
changeset
|
130 else { |
a98604b691c8
Expanded the libm support and put it into a separate directory.
Sam Lantinga <slouken@libsdl.org>
parents:
diff
changeset
|
131 dk = (double) k; |
a98604b691c8
Expanded the libm support and put it into a separate directory.
Sam Lantinga <slouken@libsdl.org>
parents:
diff
changeset
|
132 return dk * ln2_hi + dk * ln2_lo; |
a98604b691c8
Expanded the libm support and put it into a separate directory.
Sam Lantinga <slouken@libsdl.org>
parents:
diff
changeset
|
133 } |
a98604b691c8
Expanded the libm support and put it into a separate directory.
Sam Lantinga <slouken@libsdl.org>
parents:
diff
changeset
|
134 } |
a98604b691c8
Expanded the libm support and put it into a separate directory.
Sam Lantinga <slouken@libsdl.org>
parents:
diff
changeset
|
135 R = f * f * (0.5 - 0.33333333333333333 * f); |
a98604b691c8
Expanded the libm support and put it into a separate directory.
Sam Lantinga <slouken@libsdl.org>
parents:
diff
changeset
|
136 if (k == 0) |
a98604b691c8
Expanded the libm support and put it into a separate directory.
Sam Lantinga <slouken@libsdl.org>
parents:
diff
changeset
|
137 return f - R; |
a98604b691c8
Expanded the libm support and put it into a separate directory.
Sam Lantinga <slouken@libsdl.org>
parents:
diff
changeset
|
138 else { |
a98604b691c8
Expanded the libm support and put it into a separate directory.
Sam Lantinga <slouken@libsdl.org>
parents:
diff
changeset
|
139 dk = (double) k; |
a98604b691c8
Expanded the libm support and put it into a separate directory.
Sam Lantinga <slouken@libsdl.org>
parents:
diff
changeset
|
140 return dk * ln2_hi - ((R - dk * ln2_lo) - f); |
a98604b691c8
Expanded the libm support and put it into a separate directory.
Sam Lantinga <slouken@libsdl.org>
parents:
diff
changeset
|
141 } |
a98604b691c8
Expanded the libm support and put it into a separate directory.
Sam Lantinga <slouken@libsdl.org>
parents:
diff
changeset
|
142 } |
a98604b691c8
Expanded the libm support and put it into a separate directory.
Sam Lantinga <slouken@libsdl.org>
parents:
diff
changeset
|
143 s = f / (2.0 + f); |
a98604b691c8
Expanded the libm support and put it into a separate directory.
Sam Lantinga <slouken@libsdl.org>
parents:
diff
changeset
|
144 dk = (double) k; |
a98604b691c8
Expanded the libm support and put it into a separate directory.
Sam Lantinga <slouken@libsdl.org>
parents:
diff
changeset
|
145 z = s * s; |
a98604b691c8
Expanded the libm support and put it into a separate directory.
Sam Lantinga <slouken@libsdl.org>
parents:
diff
changeset
|
146 i = hx - 0x6147a; |
a98604b691c8
Expanded the libm support and put it into a separate directory.
Sam Lantinga <slouken@libsdl.org>
parents:
diff
changeset
|
147 w = z * z; |
a98604b691c8
Expanded the libm support and put it into a separate directory.
Sam Lantinga <slouken@libsdl.org>
parents:
diff
changeset
|
148 j = 0x6b851 - hx; |
a98604b691c8
Expanded the libm support and put it into a separate directory.
Sam Lantinga <slouken@libsdl.org>
parents:
diff
changeset
|
149 t1 = w * (Lg2 + w * (Lg4 + w * Lg6)); |
a98604b691c8
Expanded the libm support and put it into a separate directory.
Sam Lantinga <slouken@libsdl.org>
parents:
diff
changeset
|
150 t2 = z * (Lg1 + w * (Lg3 + w * (Lg5 + w * Lg7))); |
a98604b691c8
Expanded the libm support and put it into a separate directory.
Sam Lantinga <slouken@libsdl.org>
parents:
diff
changeset
|
151 i |= j; |
a98604b691c8
Expanded the libm support and put it into a separate directory.
Sam Lantinga <slouken@libsdl.org>
parents:
diff
changeset
|
152 R = t2 + t1; |
a98604b691c8
Expanded the libm support and put it into a separate directory.
Sam Lantinga <slouken@libsdl.org>
parents:
diff
changeset
|
153 if (i > 0) { |
a98604b691c8
Expanded the libm support and put it into a separate directory.
Sam Lantinga <slouken@libsdl.org>
parents:
diff
changeset
|
154 hfsq = 0.5 * f * f; |
a98604b691c8
Expanded the libm support and put it into a separate directory.
Sam Lantinga <slouken@libsdl.org>
parents:
diff
changeset
|
155 if (k == 0) |
a98604b691c8
Expanded the libm support and put it into a separate directory.
Sam Lantinga <slouken@libsdl.org>
parents:
diff
changeset
|
156 return f - (hfsq - s * (hfsq + R)); |
a98604b691c8
Expanded the libm support and put it into a separate directory.
Sam Lantinga <slouken@libsdl.org>
parents:
diff
changeset
|
157 else |
a98604b691c8
Expanded the libm support and put it into a separate directory.
Sam Lantinga <slouken@libsdl.org>
parents:
diff
changeset
|
158 return dk * ln2_hi - ((hfsq - (s * (hfsq + R) + dk * ln2_lo)) - |
a98604b691c8
Expanded the libm support and put it into a separate directory.
Sam Lantinga <slouken@libsdl.org>
parents:
diff
changeset
|
159 f); |
a98604b691c8
Expanded the libm support and put it into a separate directory.
Sam Lantinga <slouken@libsdl.org>
parents:
diff
changeset
|
160 } else { |
a98604b691c8
Expanded the libm support and put it into a separate directory.
Sam Lantinga <slouken@libsdl.org>
parents:
diff
changeset
|
161 if (k == 0) |
a98604b691c8
Expanded the libm support and put it into a separate directory.
Sam Lantinga <slouken@libsdl.org>
parents:
diff
changeset
|
162 return f - s * (f - R); |
a98604b691c8
Expanded the libm support and put it into a separate directory.
Sam Lantinga <slouken@libsdl.org>
parents:
diff
changeset
|
163 else |
a98604b691c8
Expanded the libm support and put it into a separate directory.
Sam Lantinga <slouken@libsdl.org>
parents:
diff
changeset
|
164 return dk * ln2_hi - ((s * (f - R) - dk * ln2_lo) - f); |
a98604b691c8
Expanded the libm support and put it into a separate directory.
Sam Lantinga <slouken@libsdl.org>
parents:
diff
changeset
|
165 } |
a98604b691c8
Expanded the libm support and put it into a separate directory.
Sam Lantinga <slouken@libsdl.org>
parents:
diff
changeset
|
166 } |