libm/math/
log10.rs

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

libm/math/
log10.rs
