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1 | /* origin: FreeBSD /usr/src/lib/msun/src/e_log10.c */ |
2 | /* | |
3 | * ==================================================== | |
4 | * Copyright (C) 1993 by Sun Microsystems, Inc. All rights reserved. | |
5 | * | |
6 | * Developed at SunSoft, 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 | * Return the base 10 logarithm of x. See log.c for most comments. | |
14 | * | |
15 | * Reduce x to 2^k (1+f) and calculate r = log(1+f) - f + f*f/2 | |
16 | * as in log.c, then combine and scale in extra precision: | |
17 | * log10(x) = (f - f*f/2 + r)/log(10) + k*log10(2) | |
18 | */ | |
19 | ||
20 | use core::f64; | |
21 | ||
22 | const IVLN10HI: f64 = 4.34294481878168880939e-01; /* 0x3fdbcb7b, 0x15200000 */ | |
23 | const IVLN10LO: f64 = 2.50829467116452752298e-11; /* 0x3dbb9438, 0xca9aadd5 */ | |
24 | const LOG10_2HI: f64 = 3.01029995663611771306e-01; /* 0x3FD34413, 0x509F6000 */ | |
25 | const LOG10_2LO: f64 = 3.69423907715893078616e-13; /* 0x3D59FEF3, 0x11F12B36 */ | |
26 | const LG1: f64 = 6.666666666666735130e-01; /* 3FE55555 55555593 */ | |
27 | const LG2: f64 = 3.999999999940941908e-01; /* 3FD99999 9997FA04 */ | |
28 | const LG3: f64 = 2.857142874366239149e-01; /* 3FD24924 94229359 */ | |
29 | const LG4: f64 = 2.222219843214978396e-01; /* 3FCC71C5 1D8E78AF */ | |
30 | const LG5: f64 = 1.818357216161805012e-01; /* 3FC74664 96CB03DE */ | |
31 | const LG6: f64 = 1.531383769920937332e-01; /* 3FC39A09 D078C69F */ | |
32 | const LG7: f64 = 1.479819860511658591e-01; /* 3FC2F112 DF3E5244 */ | |
33 | ||
48663c56 | 34 | #[cfg_attr(all(test, assert_no_panic), no_panic::no_panic)] |
8faf50e0 XL |
35 | pub fn log10(mut x: f64) -> f64 { |
36 | let x1p54 = f64::from_bits(0x4350000000000000); // 0x1p54 === 2 ^ 54 | |
37 | ||
38 | let mut ui: u64 = x.to_bits(); | |
39 | let hfsq: f64; | |
40 | let f: f64; | |
41 | let s: f64; | |
42 | let z: f64; | |
43 | let r: f64; | |
44 | let mut w: f64; | |
45 | let t1: f64; | |
46 | let t2: f64; | |
47 | let dk: f64; | |
48 | let y: f64; | |
49 | let mut hi: f64; | |
50 | let lo: f64; | |
51 | let mut val_hi: f64; | |
52 | let mut val_lo: f64; | |
53 | let mut hx: u32; | |
54 | let mut k: i32; | |
55 | ||
56 | hx = (ui >> 32) as u32; | |
57 | k = 0; | |
58 | if hx < 0x00100000 || (hx >> 31) > 0 { | |
59 | if ui << 1 == 0 { | |
60 | return -1. / (x * x); /* log(+-0)=-inf */ | |
61 | } | |
62 | if (hx >> 31) > 0 { | |
63 | return (x - x) / 0.0; /* log(-#) = NaN */ | |
64 | } | |
65 | /* subnormal number, scale x up */ | |
66 | k -= 54; | |
67 | x *= x1p54; | |
68 | ui = x.to_bits(); | |
69 | hx = (ui >> 32) as u32; | |
70 | } else if hx >= 0x7ff00000 { | |
71 | return x; | |
72 | } else if hx == 0x3ff00000 && ui << 32 == 0 { | |
73 | return 0.; | |
74 | } | |
75 | ||
76 | /* reduce x into [sqrt(2)/2, sqrt(2)] */ | |
77 | hx += 0x3ff00000 - 0x3fe6a09e; | |
78 | k += (hx >> 20) as i32 - 0x3ff; | |
79 | hx = (hx & 0x000fffff) + 0x3fe6a09e; | |
80 | ui = (hx as u64) << 32 | (ui & 0xffffffff); | |
81 | x = f64::from_bits(ui); | |
82 | ||
83 | f = x - 1.0; | |
84 | hfsq = 0.5 * f * f; | |
85 | s = f / (2.0 + f); | |
86 | z = s * s; | |
87 | w = z * z; | |
88 | t1 = w * (LG2 + w * (LG4 + w * LG6)); | |
89 | t2 = z * (LG1 + w * (LG3 + w * (LG5 + w * LG7))); | |
90 | r = t2 + t1; | |
91 | ||
92 | /* See log2.c for details. */ | |
93 | /* hi+lo = f - hfsq + s*(hfsq+R) ~ log(1+f) */ | |
94 | hi = f - hfsq; | |
95 | ui = hi.to_bits(); | |
96 | ui &= (-1i64 as u64) << 32; | |
97 | hi = f64::from_bits(ui); | |
98 | lo = f - hi - hfsq + s * (hfsq + r); | |
99 | ||
100 | /* val_hi+val_lo ~ log10(1+f) + k*log10(2) */ | |
101 | val_hi = hi * IVLN10HI; | |
102 | dk = k as f64; | |
103 | y = dk * LOG10_2HI; | |
104 | val_lo = dk * LOG10_2LO + (lo + hi) * IVLN10LO + lo * IVLN10HI; | |
105 | ||
106 | /* | |
107 | * Extra precision in for adding y is not strictly needed | |
108 | * since there is no very large cancellation near x = sqrt(2) or | |
109 | * x = 1/sqrt(2), but we do it anyway since it costs little on CPUs | |
110 | * with some parallelism and it reduces the error for many args. | |
111 | */ | |
112 | w = y + val_hi; | |
113 | val_lo += (y - w) + val_hi; | |
114 | val_hi = w; | |
115 | ||
48663c56 | 116 | val_lo + val_hi |
8faf50e0 | 117 | } |