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
20 use core::f64;
21
22 const IVLN10HI: f64 = 4.34294481878168880939e-01; /* 0x3fdbcb7b, 0x15200000 */
23 const IVLN10LO: f64 = 2.50829467116452752298e-11; /* 0x3dbb9438, 0xca9aadd5 */
24 const LOG10_2HI: f64 = 3.01029995663611771306e-01; /* 0x3FD34413, 0x509F6000 */
25 const LOG10_2LO: f64 = 3.69423907715893078616e-13; /* 0x3D59FEF3, 0x11F12B36 */
26 const LG1: f64 = 6.666666666666735130e-01; /* 3FE55555 55555593 */
27 const LG2: f64 = 3.999999999940941908e-01; /* 3FD99999 9997FA04 */
28 const LG3: f64 = 2.857142874366239149e-01; /* 3FD24924 94229359 */
29 const LG4: f64 = 2.222219843214978396e-01; /* 3FCC71C5 1D8E78AF */
30 const LG5: f64 = 1.818357216161805012e-01; /* 3FC74664 96CB03DE */
31 const LG6: f64 = 1.531383769920937332e-01; /* 3FC39A09 D078C69F */
32 const 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)]
log10(mut x: f64) -> f6436 pub 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 }
119