1
2
3
4
5
6
7
8
9
10
11
12
13
14
15
16
17
18
19
20
21
22
23
24
25
26
27
28
29
30
31
32
33
34
35
36
37
38
39
40
41
42
43
44
45
46
47
48
49
50
51
52
53
54
55
56
57
58
59
60
61
62
63
64
65
66
67
68
69
70
71
72
73
74
75
76
77
78
79
80
81
82
83
84
85
86
87
88
89
90
91
92
93
94
95
96
97
98
99
100
101
102
103
104
105
106
107
108
109
110
111
112
113
114
115
116
117
|
/* origin: FreeBSD /usr/src/lib/msun/src/e_log10.c */
/*
* ====================================================
* Copyright (C) 1993 by Sun Microsystems, Inc. All rights reserved.
*
* Developed at SunSoft, a Sun Microsystems, Inc. business.
* Permission to use, copy, modify, and distribute this
* software is freely granted, provided that this notice
* is preserved.
* ====================================================
*/
/*
* Return the base 10 logarithm of x. See log.c for most comments.
*
* Reduce x to 2^k (1+f) and calculate r = log(1+f) - f + f*f/2
* as in log.c, then combine and scale in extra precision:
* log10(x) = (f - f*f/2 + r)/log(10) + k*log10(2)
*/
use core::f64;
const IVLN10HI: f64 = 4.34294481878168880939e-01; /* 0x3fdbcb7b, 0x15200000 */
const IVLN10LO: f64 = 2.50829467116452752298e-11; /* 0x3dbb9438, 0xca9aadd5 */
const LOG10_2HI: f64 = 3.01029995663611771306e-01; /* 0x3FD34413, 0x509F6000 */
const LOG10_2LO: f64 = 3.69423907715893078616e-13; /* 0x3D59FEF3, 0x11F12B36 */
const LG1: f64 = 6.666666666666735130e-01; /* 3FE55555 55555593 */
const LG2: f64 = 3.999999999940941908e-01; /* 3FD99999 9997FA04 */
const LG3: f64 = 2.857142874366239149e-01; /* 3FD24924 94229359 */
const LG4: f64 = 2.222219843214978396e-01; /* 3FCC71C5 1D8E78AF */
const LG5: f64 = 1.818357216161805012e-01; /* 3FC74664 96CB03DE */
const LG6: f64 = 1.531383769920937332e-01; /* 3FC39A09 D078C69F */
const LG7: f64 = 1.479819860511658591e-01; /* 3FC2F112 DF3E5244 */
#[cfg_attr(all(test, assert_no_panic), no_panic::no_panic)]
pub fn log10(mut x: f64) -> f64 {
let x1p54 = f64::from_bits(0x4350000000000000); // 0x1p54 === 2 ^ 54
let mut ui: u64 = x.to_bits();
let hfsq: f64;
let f: f64;
let s: f64;
let z: f64;
let r: f64;
let mut w: f64;
let t1: f64;
let t2: f64;
let dk: f64;
let y: f64;
let mut hi: f64;
let lo: f64;
let mut val_hi: f64;
let mut val_lo: f64;
let mut hx: u32;
let mut k: i32;
hx = (ui >> 32) as u32;
k = 0;
if hx < 0x00100000 || (hx >> 31) > 0 {
if ui << 1 == 0 {
return -1. / (x * x); /* log(+-0)=-inf */
}
if (hx >> 31) > 0 {
return (x - x) / 0.0; /* log(-#) = NaN */
}
/* subnormal number, scale x up */
k -= 54;
x *= x1p54;
ui = x.to_bits();
hx = (ui >> 32) as u32;
} else if hx >= 0x7ff00000 {
return x;
} else if hx == 0x3ff00000 && ui << 32 == 0 {
return 0.;
}
/* reduce x into [sqrt(2)/2, sqrt(2)] */
hx += 0x3ff00000 - 0x3fe6a09e;
k += (hx >> 20) as i32 - 0x3ff;
hx = (hx & 0x000fffff) + 0x3fe6a09e;
ui = (hx as u64) << 32 | (ui & 0xffffffff);
x = f64::from_bits(ui);
f = x - 1.0;
hfsq = 0.5 * f * f;
s = f / (2.0 + f);
z = s * s;
w = z * z;
t1 = w * (LG2 + w * (LG4 + w * LG6));
t2 = z * (LG1 + w * (LG3 + w * (LG5 + w * LG7)));
r = t2 + t1;
/* See log2.c for details. */
/* hi+lo = f - hfsq + s*(hfsq+R) ~ log(1+f) */
hi = f - hfsq;
ui = hi.to_bits();
ui &= (-1i64 as u64) << 32;
hi = f64::from_bits(ui);
lo = f - hi - hfsq + s * (hfsq + r);
/* val_hi+val_lo ~ log10(1+f) + k*log10(2) */
val_hi = hi * IVLN10HI;
dk = k as f64;
y = dk * LOG10_2HI;
val_lo = dk * LOG10_2LO + (lo + hi) * IVLN10LO + lo * IVLN10HI;
/*
* Extra precision in for adding y is not strictly needed
* since there is no very large cancellation near x = sqrt(2) or
* x = 1/sqrt(2), but we do it anyway since it costs little on CPUs
* with some parallelism and it reduces the error for many args.
*/
w = y + val_hi;
val_lo += (y - w) + val_hi;
val_hi = w;
val_lo + val_hi
}
|
