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 /// The base 2 logarithm of `x` (f64).
33 #[cfg_attr(all(test, assert_no_panic), no_panic::no_panic)]
log2(mut x: f64) -> f6434 pub fn log2(mut x: f64) -> f64 {
35 let x1p54 = f64::from_bits(0x4350000000000000); // 0x1p54 === 2 ^ 54
36
37 let mut ui: u64 = x.to_bits();
38 let hfsq: f64;
39 let f: f64;
40 let s: f64;
41 let z: f64;
42 let r: f64;
43 let mut w: f64;
44 let t1: f64;
45 let t2: f64;
46 let y: f64;
47 let mut hi: f64;
48 let lo: f64;
49 let mut val_hi: f64;
50 let mut val_lo: f64;
51 let mut hx: u32;
52 let mut k: i32;
53
54 hx = (ui >> 32) as u32;
55 k = 0;
56 if hx < 0x00100000 || (hx >> 31) > 0 {
57 if ui << 1 == 0 {
58 return -1. / (x * x); /* log(+-0)=-inf */
59 }
60 if (hx >> 31) > 0 {
61 return (x - x) / 0.0; /* log(-#) = NaN */
62 }
63 /* subnormal number, scale x up */
64 k -= 54;
65 x *= x1p54;
66 ui = x.to_bits();
67 hx = (ui >> 32) as u32;
68 } else if hx >= 0x7ff00000 {
69 return x;
70 } else if hx == 0x3ff00000 && ui << 32 == 0 {
71 return 0.;
72 }
73
74 /* reduce x into [sqrt(2)/2, sqrt(2)] */
75 hx += 0x3ff00000 - 0x3fe6a09e;
76 k += (hx >> 20) as i32 - 0x3ff;
77 hx = (hx & 0x000fffff) + 0x3fe6a09e;
78 ui = (hx as u64) << 32 | (ui & 0xffffffff);
79 x = f64::from_bits(ui);
80
81 f = x - 1.0;
82 hfsq = 0.5 * f * f;
83 s = f / (2.0 + f);
84 z = s * s;
85 w = z * z;
86 t1 = w * (LG2 + w * (LG4 + w * LG6));
87 t2 = z * (LG1 + w * (LG3 + w * (LG5 + w * LG7)));
88 r = t2 + t1;
89
90 /* hi+lo = f - hfsq + s*(hfsq+R) ~ log(1+f) */
91 hi = f - hfsq;
92 ui = hi.to_bits();
93 ui &= (-1i64 as u64) << 32;
94 hi = f64::from_bits(ui);
95 lo = f - hi - hfsq + s * (hfsq + r);
96
97 val_hi = hi * IVLN2HI;
98 val_lo = (lo + hi) * IVLN2LO + lo * IVLN2HI;
99
100 /* spadd(val_hi, val_lo, y), except for not using double_t: */
101 y = k.into();
102 w = y + val_hi;
103 val_lo += (y - w) + val_hi;
104 val_hi = w;
105
106 val_lo + val_hi
107 }
108