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1 /* origin: FreeBSD /usr/src/lib/msun/src/e_log10f.c */ | 1 /* origin: FreeBSD /usr/src/lib/msun/src/e_log10f.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 log10.c. | 13 * See comments in log10.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 ivln10hi = 4.3432617188e-01, /* 0x3ede6000 */ |
20 ivln10hi = 4.3432617188e-01, /* 0x3ede6000 */ | 20 ivln10lo = -3.1689971365e-05, /* 0xb804ead9 */ |
21 ivln10lo = -3.1689971365e-05, /* 0xb804ead9 */ | 21 log10_2hi = 3.0102920532e-01, /* 0x3e9a2080 */ |
22 log10_2hi = 3.0102920532e-01, /* 0x3e9a2080 */ | 22 log10_2lo = 7.9034151668e-07, /* 0x355427db */ |
23 log10_2lo = 7.9034151668e-07, /* 0x355427db */ | 23 /* |(log(1+s)-log(1-s))/s - Lg(s)| < 2**-34.24 (~[-4.95e-11, 4.97e-11]). */ |
24 /* |(log(1+s)-log(1-s))/s - Lg(s)| < 2**-34.24 (~[-4.95e-11, 4.97e-11]). */ | 24 Lg1 = 0xaaaaaa.0p-24, /* 0.66666662693 */ |
25 Lg1 = 0xaaaaaa.0p-24, /* 0.66666662693 */ | 25 Lg2 = 0xccce13.0p-25, /* 0.40000972152 */ |
26 Lg2 = 0xccce13.0p-25, /* 0.40000972152 */ | 26 Lg3 = 0x91e9ee.0p-25, /* 0.28498786688 */ |
27 Lg3 = 0x91e9ee.0p-25, /* 0.28498786688 */ | 27 Lg4 = 0xf89e26.0p-26; /* 0.24279078841 */ |
28 Lg4 = 0xf89e26.0p-26; /* 0.24279078841 */ | |
29 | 28 |
30 float log10f(float x) | 29 float log10f(float x) { |
31 { | 30 union { |
32 » union {float f; uint32_t i;} u = {x}; | 31 float f; |
33 » float_t hfsq,f,s,z,R,w,t1,t2,dk,hi,lo; | 32 uint32_t i; |
34 » uint32_t ix; | 33 } u = {x}; |
35 » int k; | 34 float_t hfsq, f, s, z, R, w, t1, t2, dk, hi, lo; |
| 35 uint32_t ix; |
| 36 int k; |
36 | 37 |
37 » ix = u.i; | 38 ix = u.i; |
38 » k = 0; | 39 k = 0; |
39 » if (ix < 0x00800000 || ix>>31) { /* x < 2**-126 */ | 40 if (ix < 0x00800000 || ix >> 31) { /* x < 2**-126 */ |
40 » » if (ix<<1 == 0) | 41 if (ix << 1 == 0) |
41 » » » return -1/(x*x); /* log(+-0)=-inf */ | 42 return -1 / (x * x); /* log(+-0)=-inf */ |
42 » » if (ix>>31) | 43 if (ix >> 31) |
43 » » » return (x-x)/0.0f; /* log(-#) = NaN */ | 44 return (x - x) / 0.0f; /* log(-#) = NaN */ |
44 » » /* subnormal number, scale up x */ | 45 /* subnormal number, scale up x */ |
45 » » k -= 25; | 46 k -= 25; |
46 » » x *= 0x1p25f; | 47 x *= 0x1p25f; |
47 » » u.f = x; | 48 u.f = x; |
48 » » ix = u.i; | 49 ix = u.i; |
49 » } else if (ix >= 0x7f800000) { | 50 } else if (ix >= 0x7f800000) { |
50 » » return x; | 51 return x; |
51 » } else if (ix == 0x3f800000) | 52 } else if (ix == 0x3f800000) |
52 » » return 0; | 53 return 0; |
53 | 54 |
54 » /* reduce x into [sqrt(2)/2, sqrt(2)] */ | 55 /* reduce x into [sqrt(2)/2, sqrt(2)] */ |
55 » ix += 0x3f800000 - 0x3f3504f3; | 56 ix += 0x3f800000 - 0x3f3504f3; |
56 » k += (int)(ix>>23) - 0x7f; | 57 k += (int)(ix >> 23) - 0x7f; |
57 » ix = (ix&0x007fffff) + 0x3f3504f3; | 58 ix = (ix & 0x007fffff) + 0x3f3504f3; |
58 » u.i = ix; | 59 u.i = ix; |
59 » x = u.f; | 60 x = u.f; |
60 | 61 |
61 » f = x - 1.0f; | 62 f = x - 1.0f; |
62 » s = f/(2.0f + f); | 63 s = f / (2.0f + f); |
63 » z = s*s; | 64 z = s * s; |
64 » w = z*z; | 65 w = z * z; |
65 » t1= w*(Lg2+w*Lg4); | 66 t1 = w * (Lg2 + w * Lg4); |
66 » t2= z*(Lg1+w*Lg3); | 67 t2 = z * (Lg1 + w * Lg3); |
67 » R = t2 + t1; | 68 R = t2 + t1; |
68 » hfsq = 0.5f*f*f; | 69 hfsq = 0.5f * f * f; |
69 | 70 |
70 » hi = f - hfsq; | 71 hi = f - hfsq; |
71 » u.f = hi; | 72 u.f = hi; |
72 » u.i &= 0xfffff000; | 73 u.i &= 0xfffff000; |
73 » hi = u.f; | 74 hi = u.f; |
74 » lo = f - hi - hfsq + s*(hfsq+R); | 75 lo = f - hi - hfsq + s * (hfsq + R); |
75 » dk = k; | 76 dk = k; |
76 » return dk*log10_2lo + (lo+hi)*ivln10lo + lo*ivln10hi + hi*ivln10hi + dk*
log10_2hi; | 77 return dk * log10_2lo + (lo + hi) * ivln10lo + lo * ivln10hi + hi * ivln10hi + |
| 78 dk * log10_2hi; |
77 } | 79 } |
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