libm/math/
log10.rs

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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
20use core::f64;
21
22const IVLN10HI: f64 = 4.34294481878168880939e-01; /* 0x3fdbcb7b, 0x15200000 */
23const IVLN10LO: f64 = 2.50829467116452752298e-11; /* 0x3dbb9438, 0xca9aadd5 */
24const LOG10_2HI: f64 = 3.01029995663611771306e-01; /* 0x3FD34413, 0x509F6000 */
25const LOG10_2LO: f64 = 3.69423907715893078616e-13; /* 0x3D59FEF3, 0x11F12B36 */
26const LG1: f64 = 6.666666666666735130e-01; /* 3FE55555 55555593 */
27const LG2: f64 = 3.999999999940941908e-01; /* 3FD99999 9997FA04 */
28const LG3: f64 = 2.857142874366239149e-01; /* 3FD24924 94229359 */
29const LG4: f64 = 2.222219843214978396e-01; /* 3FCC71C5 1D8E78AF */
30const LG5: f64 = 1.818357216161805012e-01; /* 3FC74664 96CB03DE */
31const LG6: f64 = 1.531383769920937332e-01; /* 3FC39A09 D078C69F */
32const LG7: f64 = 1.479819860511658591e-01; /* 3FC2F112 DF3E5244 */
33
34/// The base 10 logarithm of `x` (f64).
35#[cfg_attr(all(test, assert_no_panic), no_panic::no_panic)]
36pub fn log10(mut x: f64) -> f64 {
37    let x1p54 = f64::from_bits(0x4350000000000000); // 0x1p54 === 2 ^ 54
38
39    let mut ui: u64 = x.to_bits();
40    let hfsq: f64;
41    let f: f64;
42    let s: f64;
43    let z: f64;
44    let r: f64;
45    let mut w: f64;
46    let t1: f64;
47    let t2: f64;
48    let dk: f64;
49    let y: f64;
50    let mut hi: f64;
51    let lo: f64;
52    let mut val_hi: f64;
53    let mut val_lo: f64;
54    let mut hx: u32;
55    let mut k: i32;
56
57    hx = (ui >> 32) as u32;
58    k = 0;
59    if hx < 0x00100000 || (hx >> 31) > 0 {
60        if ui << 1 == 0 {
61            return -1. / (x * x); /* log(+-0)=-inf */
62        }
63        if (hx >> 31) > 0 {
64            return (x - x) / 0.0; /* log(-#) = NaN */
65        }
66        /* subnormal number, scale x up */
67        k -= 54;
68        x *= x1p54;
69        ui = x.to_bits();
70        hx = (ui >> 32) as u32;
71    } else if hx >= 0x7ff00000 {
72        return x;
73    } else if hx == 0x3ff00000 && ui << 32 == 0 {
74        return 0.;
75    }
76
77    /* reduce x into [sqrt(2)/2, sqrt(2)] */
78    hx += 0x3ff00000 - 0x3fe6a09e;
79    k += (hx >> 20) as i32 - 0x3ff;
80    hx = (hx & 0x000fffff) + 0x3fe6a09e;
81    ui = (hx as u64) << 32 | (ui & 0xffffffff);
82    x = f64::from_bits(ui);
83
84    f = x - 1.0;
85    hfsq = 0.5 * f * f;
86    s = f / (2.0 + f);
87    z = s * s;
88    w = z * z;
89    t1 = w * (LG2 + w * (LG4 + w * LG6));
90    t2 = z * (LG1 + w * (LG3 + w * (LG5 + w * LG7)));
91    r = t2 + t1;
92
93    /* See log2.c for details. */
94    /* hi+lo = f - hfsq + s*(hfsq+R) ~ log(1+f) */
95    hi = f - hfsq;
96    ui = hi.to_bits();
97    ui &= (-1i64 as u64) << 32;
98    hi = f64::from_bits(ui);
99    lo = f - hi - hfsq + s * (hfsq + r);
100
101    /* val_hi+val_lo ~ log10(1+f) + k*log10(2) */
102    val_hi = hi * IVLN10HI;
103    dk = k as f64;
104    y = dk * LOG10_2HI;
105    val_lo = dk * LOG10_2LO + (lo + hi) * IVLN10LO + lo * IVLN10HI;
106
107    /*
108     * Extra precision in for adding y is not strictly needed
109     * since there is no very large cancellation near x = sqrt(2) or
110     * x = 1/sqrt(2), but we do it anyway since it costs little on CPUs
111     * with some parallelism and it reduces the error for many args.
112     */
113    w = y + val_hi;
114    val_lo += (y - w) + val_hi;
115    val_hi = w;
116
117    val_lo + val_hi
118}
libm/math/log10.rs

libm/math/
log10.rs
