libm/math/
log2f.rs

1/* origin: FreeBSD /usr/src/lib/msun/src/e_log2f.c */
2/*
3 * ====================================================
4 * Copyright (C) 1993 by Sun Microsystems, Inc. All rights reserved.
5 *
6 * Developed at SunPro, 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 * See comments in log2.c.
14 */
15
16const IVLN2HI: f32 = 1.4428710938e+00; /* 0x3fb8b000 */
17const IVLN2LO: f32 = -1.7605285393e-04; /* 0xb9389ad4 */
18/* |(log(1+s)-log(1-s))/s - Lg(s)| < 2**-34.24 (~[-4.95e-11, 4.97e-11]). */
19const LG1: f32 = 0.66666662693; /* 0xaaaaaa.0p-24 */
20const LG2: f32 = 0.40000972152; /* 0xccce13.0p-25 */
21const LG3: f32 = 0.28498786688; /* 0x91e9ee.0p-25 */
22const LG4: f32 = 0.24279078841; /* 0xf89e26.0p-26 */
23
24/// The base 2 logarithm of `x` (f32).
25#[cfg_attr(assert_no_panic, no_panic::no_panic)]
26pub fn log2f(mut x: f32) -> f32 {
27    let x1p25f = f32::from_bits(0x4c000000); // 0x1p25f === 2 ^ 25
28
29    let mut ui: u32 = x.to_bits();
30    let hfsq: f32;
31    let f: f32;
32    let s: f32;
33    let z: f32;
34    let r: f32;
35    let w: f32;
36    let t1: f32;
37    let t2: f32;
38    let mut hi: f32;
39    let lo: f32;
40    let mut ix: u32;
41    let mut k: i32;
42
43    ix = ui;
44    k = 0;
45    if ix < 0x00800000 || (ix >> 31) > 0 {
46        /* x < 2**-126  */
47        if ix << 1 == 0 {
48            return -1. / (x * x); /* log(+-0)=-inf */
49        }
50        if (ix >> 31) > 0 {
51            return (x - x) / 0.0; /* log(-#) = NaN */
52        }
53        /* subnormal number, scale up x */
54        k -= 25;
55        x *= x1p25f;
56        ui = x.to_bits();
57        ix = ui;
58    } else if ix >= 0x7f800000 {
59        return x;
60    } else if ix == 0x3f800000 {
61        return 0.;
62    }
63
64    /* reduce x into [sqrt(2)/2, sqrt(2)] */
65    ix += 0x3f800000 - 0x3f3504f3;
66    k += (ix >> 23) as i32 - 0x7f;
67    ix = (ix & 0x007fffff) + 0x3f3504f3;
68    ui = ix;
69    x = f32::from_bits(ui);
70
71    f = x - 1.0;
72    s = f / (2.0 + f);
73    z = s * s;
74    w = z * z;
75    t1 = w * (LG2 + w * LG4);
76    t2 = z * (LG1 + w * LG3);
77    r = t2 + t1;
78    hfsq = 0.5 * f * f;
79
80    hi = f - hfsq;
81    ui = hi.to_bits();
82    ui &= 0xfffff000;
83    hi = f32::from_bits(ui);
84    lo = f - hi - hfsq + s * (hfsq + r);
85    (lo + hi) * IVLN2LO + lo * IVLN2HI + hi * IVLN2HI + k as f32
86}
libm/math/log2f.rs

libm/math/
log2f.rs
