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 | |
34 | #[cfg_attr (all(test, assert_no_panic), no_panic::no_panic)] |
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 | |
116 | val_lo + val_hi |
117 | } |
118 | |