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1 /* origin: FreeBSD /usr/src/lib/msun/src/e_log2f.c */ | 1 /* origin: FreeBSD /usr/src/lib/msun/src/e_log2f.c */ |
2 /* | 2 /* |
3 * ==================================================== | 3 * ==================================================== |
4 * Copyright (C) 1993 by Sun Microsystems, Inc. All rights reserved. | 4 * Copyright (C) 1993 by Sun Microsystems, Inc. All rights reserved. |
5 * | 5 * |
6 * Developed at SunPro, a Sun Microsystems, Inc. business. | 6 * Developed at SunPro, a Sun Microsystems, Inc. business. |
7 * Permission to use, copy, modify, and distribute this | 7 * Permission to use, copy, modify, and distribute this |
8 * software is freely granted, provided that this notice | 8 * software is freely granted, provided that this notice |
9 * is preserved. | 9 * is preserved. |
10 * ==================================================== | 10 * ==================================================== |
11 */ | 11 */ |
12 /* | 12 /* |
13 * See comments in log2.c. | 13 * See comments in log2.c. |
14 */ | 14 */ |
15 | 15 |
16 #include <math.h> | 16 #include <math.h> |
17 #include <stdint.h> | 17 #include <stdint.h> |
18 | 18 |
19 static const float | 19 static const float ivln2hi = 1.4428710938e+00, /* 0x3fb8b000 */ |
20 ivln2hi = 1.4428710938e+00, /* 0x3fb8b000 */ | 20 ivln2lo = -1.7605285393e-04, /* 0xb9389ad4 */ |
21 ivln2lo = -1.7605285393e-04, /* 0xb9389ad4 */ | 21 /* |(log(1+s)-log(1-s))/s - Lg(s)| < 2**-34.24 (~[-4.95e-11, 4.97e-11]). */ |
22 /* |(log(1+s)-log(1-s))/s - Lg(s)| < 2**-34.24 (~[-4.95e-11, 4.97e-11]). */ | 22 Lg1 = 0xaaaaaa.0p-24, /* 0.66666662693 */ |
23 Lg1 = 0xaaaaaa.0p-24, /* 0.66666662693 */ | 23 Lg2 = 0xccce13.0p-25, /* 0.40000972152 */ |
24 Lg2 = 0xccce13.0p-25, /* 0.40000972152 */ | 24 Lg3 = 0x91e9ee.0p-25, /* 0.28498786688 */ |
25 Lg3 = 0x91e9ee.0p-25, /* 0.28498786688 */ | 25 Lg4 = 0xf89e26.0p-26; /* 0.24279078841 */ |
26 Lg4 = 0xf89e26.0p-26; /* 0.24279078841 */ | |
27 | 26 |
28 float log2f(float x) | 27 float log2f(float x) { |
29 { | 28 union { |
30 » union {float f; uint32_t i;} u = {x}; | 29 float f; |
31 » float_t hfsq,f,s,z,R,w,t1,t2,hi,lo; | 30 uint32_t i; |
32 » uint32_t ix; | 31 } u = {x}; |
33 » int k; | 32 float_t hfsq, f, s, z, R, w, t1, t2, hi, lo; |
| 33 uint32_t ix; |
| 34 int k; |
34 | 35 |
35 » ix = u.i; | 36 ix = u.i; |
36 » k = 0; | 37 k = 0; |
37 » if (ix < 0x00800000 || ix>>31) { /* x < 2**-126 */ | 38 if (ix < 0x00800000 || ix >> 31) { /* x < 2**-126 */ |
38 » » if (ix<<1 == 0) | 39 if (ix << 1 == 0) |
39 » » » return -1/(x*x); /* log(+-0)=-inf */ | 40 return -1 / (x * x); /* log(+-0)=-inf */ |
40 » » if (ix>>31) | 41 if (ix >> 31) |
41 » » » return (x-x)/0.0f; /* log(-#) = NaN */ | 42 return (x - x) / 0.0f; /* log(-#) = NaN */ |
42 » » /* subnormal number, scale up x */ | 43 /* subnormal number, scale up x */ |
43 » » k -= 25; | 44 k -= 25; |
44 » » x *= 0x1p25f; | 45 x *= 0x1p25f; |
45 » » u.f = x; | 46 u.f = x; |
46 » » ix = u.i; | 47 ix = u.i; |
47 » } else if (ix >= 0x7f800000) { | 48 } else if (ix >= 0x7f800000) { |
48 » » return x; | 49 return x; |
49 » } else if (ix == 0x3f800000) | 50 } else if (ix == 0x3f800000) |
50 » » return 0; | 51 return 0; |
51 | 52 |
52 » /* reduce x into [sqrt(2)/2, sqrt(2)] */ | 53 /* reduce x into [sqrt(2)/2, sqrt(2)] */ |
53 » ix += 0x3f800000 - 0x3f3504f3; | 54 ix += 0x3f800000 - 0x3f3504f3; |
54 » k += (int)(ix>>23) - 0x7f; | 55 k += (int)(ix >> 23) - 0x7f; |
55 » ix = (ix&0x007fffff) + 0x3f3504f3; | 56 ix = (ix & 0x007fffff) + 0x3f3504f3; |
56 » u.i = ix; | 57 u.i = ix; |
57 » x = u.f; | 58 x = u.f; |
58 | 59 |
59 » f = x - 1.0f; | 60 f = x - 1.0f; |
60 » s = f/(2.0f + f); | 61 s = f / (2.0f + f); |
61 » z = s*s; | 62 z = s * s; |
62 » w = z*z; | 63 w = z * z; |
63 » t1= w*(Lg2+w*Lg4); | 64 t1 = w * (Lg2 + w * Lg4); |
64 » t2= z*(Lg1+w*Lg3); | 65 t2 = z * (Lg1 + w * Lg3); |
65 » R = t2 + t1; | 66 R = t2 + t1; |
66 » hfsq = 0.5f*f*f; | 67 hfsq = 0.5f * f * f; |
67 | 68 |
68 » hi = f - hfsq; | 69 hi = f - hfsq; |
69 » u.f = hi; | 70 u.f = hi; |
70 » u.i &= 0xfffff000; | 71 u.i &= 0xfffff000; |
71 » hi = u.f; | 72 hi = u.f; |
72 » lo = f - hi - hfsq + s*(hfsq+R); | 73 lo = f - hi - hfsq + s * (hfsq + R); |
73 » return (lo+hi)*ivln2lo + lo*ivln2hi + hi*ivln2hi + k; | 74 return (lo + hi) * ivln2lo + lo * ivln2hi + hi * ivln2hi + k; |
74 } | 75 } |
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