1 /* origin: FreeBSD /usr/src/lib/msun/src/e_log2.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 2 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 * log2(x) = (f - f*f/2 + r)/log(2) + k
18 */
19
20 use core::f64;
21
22 const IVLN2HI: f64 = 1.44269504072144627571e+00; /* 0x3ff71547, 0x65200000 */
23 const IVLN2LO: f64 = 1.67517131648865118353e-10; /* 0x3de705fc, 0x2eefa200 */
24 const LG1: f64 = 6.666666666666735130e-01; /* 3FE55555 55555593 */
25 const LG2: f64 = 3.999999999940941908e-01; /* 3FD99999 9997FA04 */
26 const LG3: f64 = 2.857142874366239149e-01; /* 3FD24924 94229359 */
27 const LG4: f64 = 2.222219843214978396e-01; /* 3FCC71C5 1D8E78AF */
28 const LG5: f64 = 1.818357216161805012e-01; /* 3FC74664 96CB03DE */
29 const LG6: f64 = 1.531383769920937332e-01; /* 3FC39A09 D078C69F */
30 const LG7: f64 = 1.479819860511658591e-01; /* 3FC2F112 DF3E5244 */
31
32 #[cfg_attr(all(test, assert_no_panic), no_panic::no_panic)]
log2(mut x: f64) -> f6433 pub fn log2(mut x: f64) -> f64 {
34 let x1p54 = f64::from_bits(0x4350000000000000); // 0x1p54 === 2 ^ 54
35
36 let mut ui: u64 = x.to_bits();
37 let hfsq: f64;
38 let f: f64;
39 let s: f64;
40 let z: f64;
41 let r: f64;
42 let mut w: f64;
43 let t1: f64;
44 let t2: f64;
45 let y: f64;
46 let mut hi: f64;
47 let lo: f64;
48 let mut val_hi: f64;
49 let mut val_lo: f64;
50 let mut hx: u32;
51 let mut k: i32;
52
53 hx = (ui >> 32) as u32;
54 k = 0;
55 if hx < 0x00100000 || (hx >> 31) > 0 {
56 if ui << 1 == 0 {
57 return -1. / (x * x); /* log(+-0)=-inf */
58 }
59 if (hx >> 31) > 0 {
60 return (x - x) / 0.0; /* log(-#) = NaN */
61 }
62 /* subnormal number, scale x up */
63 k -= 54;
64 x *= x1p54;
65 ui = x.to_bits();
66 hx = (ui >> 32) as u32;
67 } else if hx >= 0x7ff00000 {
68 return x;
69 } else if hx == 0x3ff00000 && ui << 32 == 0 {
70 return 0.;
71 }
72
73 /* reduce x into [sqrt(2)/2, sqrt(2)] */
74 hx += 0x3ff00000 - 0x3fe6a09e;
75 k += (hx >> 20) as i32 - 0x3ff;
76 hx = (hx & 0x000fffff) + 0x3fe6a09e;
77 ui = (hx as u64) << 32 | (ui & 0xffffffff);
78 x = f64::from_bits(ui);
79
80 f = x - 1.0;
81 hfsq = 0.5 * f * f;
82 s = f / (2.0 + f);
83 z = s * s;
84 w = z * z;
85 t1 = w * (LG2 + w * (LG4 + w * LG6));
86 t2 = z * (LG1 + w * (LG3 + w * (LG5 + w * LG7)));
87 r = t2 + t1;
88
89 /* hi+lo = f - hfsq + s*(hfsq+R) ~ log(1+f) */
90 hi = f - hfsq;
91 ui = hi.to_bits();
92 ui &= (-1i64 as u64) << 32;
93 hi = f64::from_bits(ui);
94 lo = f - hi - hfsq + s * (hfsq + r);
95
96 val_hi = hi * IVLN2HI;
97 val_lo = (lo + hi) * IVLN2LO + lo * IVLN2HI;
98
99 /* spadd(val_hi, val_lo, y), except for not using double_t: */
100 y = k.into();
101 w = y + val_hi;
102 val_lo += (y - w) + val_hi;
103 val_hi = w;
104
105 val_lo + val_hi
106 }
107