pxfm/logs/
log10td.rs

1/*
2 * // Copyright (c) Radzivon Bartoshyk 8/2025. All rights reserved.
3 * //
4 * // Redistribution and use in source and binary forms, with or without modification,
5 * // are permitted provided that the following conditions are met:
6 * //
7 * // 1.  Redistributions of source code must retain the above copyright notice, this
8 * // list of conditions and the following disclaimer.
9 * //
10 * // 2.  Redistributions in binary form must reproduce the above copyright notice,
11 * // this list of conditions and the following disclaimer in the documentation
12 * // and/or other materials provided with the distribution.
13 * //
14 * // 3.  Neither the name of the copyright holder nor the names of its
15 * // contributors may be used to endorse or promote products derived from
16 * // this software without specific prior written permission.
17 * //
18 * // THIS SOFTWARE IS PROVIDED BY THE COPYRIGHT HOLDERS AND CONTRIBUTORS "AS IS"
19 * // AND ANY EXPRESS OR IMPLIED WARRANTIES, INCLUDING, BUT NOT LIMITED TO, THE
20 * // IMPLIED WARRANTIES OF MERCHANTABILITY AND FITNESS FOR A PARTICULAR PURPOSE ARE
21 * // DISCLAIMED. IN NO EVENT SHALL THE COPYRIGHT HOLDER OR CONTRIBUTORS BE LIABLE
22 * // FOR ANY DIRECT, INDIRECT, INCIDENTAL, SPECIAL, EXEMPLARY, OR CONSEQUENTIAL
23 * // DAMAGES (INCLUDING, BUT NOT LIMITED TO, PROCUREMENT OF SUBSTITUTE GOODS OR
24 * // SERVICES; LOSS OF USE, DATA, OR PROFITS; OR BUSINESS INTERRUPTION) HOWEVER
25 * // CAUSED AND ON ANY THEORY OF LIABILITY, WHETHER IN CONTRACT, STRICT LIABILITY,
26 * // OR TORT (INCLUDING NEGLIGENCE OR OTHERWISE) ARISING IN ANY WAY OUT OF THE USE
27 * // OF THIS SOFTWARE, EVEN IF ADVISED OF THE POSSIBILITY OF SUCH DAMAGE.
28 */
29use crate::double_double::DoubleDouble;
30use crate::logs::log10td_coeffs::LOG10_NEG_TD;
31use crate::pow_tables::POW_INVERSE;
32use crate::triple_double::TripleDouble;
33
34#[inline(always)]
35fn log10_poly(z: f64) -> TripleDouble {
36    /*
37        Poly generated by Sollya:
38
39        d = [-0.0040283203125,0.0040283203125];
40        f = log10(1+x)/x;
41        pf = fpminimax(f, 10, [|157...|], d, absolute, floating);
42
43        See ./notes/td_log10.sollya
44    */
45    const P: [(u64, u64, u64); 11] = [
46        (0xb8f29c4663277dc0, 0x3c695355baaafad3, 0x3fdbcb7b1526e50e),
47        (0x38ee76408ee1b680, 0xbc595355bab3a517, 0xbfcbcb7b1526e50e),
48        (0x38f58fe4d121c480, 0xbc59c8718361a853, 0x3fc287a7636f435f),
49        (0xb8e80f425616e240, 0xbc49520fd0630f7e, 0xbfbbcb7b1526e50e),
50        (0x38eb058acb9ab2c0, 0x3c443f5b242c637b, 0x3fb63c62775250d8),
51        (0x38c32c088e8da180, 0xbc4a6666386cc60e, 0xbfb287a7636f436c),
52        (0x38bb2e95bc6a3a80, 0x3c45ac4260107e46, 0x3fafc3fa615105f6),
53        (0xb8e14f1e5b926690, 0x3c421ee12f4a23de, 0xbfabcb7b14ed42da),
54        (0x38d4b4d370b610e0, 0x3c47e2c6f24d3d30, 0x3fa8b4df2ef1a288),
55        (0x38bd632a8b3a6500, 0xbc1a922cdefb3bb1, 0xbfa63c98a8c44069),
56        (0xb8c077b6551291c0, 0x3c4337142dd97816, 0x3fa4372045637cca),
57    ];
58    let mut t = TripleDouble::f64_mul_add(
59        z,
60        TripleDouble::from_bit_pair(P[9]),
61        TripleDouble::from_bit_pair(P[8]),
62    );
63    t = TripleDouble::f64_mul_add(z, t, TripleDouble::from_bit_pair(P[7]));
64    t = TripleDouble::f64_mul_add(z, t, TripleDouble::from_bit_pair(P[6]));
65    t = TripleDouble::f64_mul_add(z, t, TripleDouble::from_bit_pair(P[5]));
66    t = TripleDouble::f64_mul_add(z, t, TripleDouble::from_bit_pair(P[4]));
67    t = TripleDouble::f64_mul_add(z, t, TripleDouble::from_bit_pair(P[3]));
68    t = TripleDouble::f64_mul_add(z, t, TripleDouble::from_bit_pair(P[2]));
69    t = TripleDouble::f64_mul_add(z, t, TripleDouble::from_bit_pair(P[1]));
70    t = TripleDouble::f64_mul_add(z, t, TripleDouble::from_bit_pair(P[0]));
71    TripleDouble::quick_mult_f64(t, z)
72}
73
74#[inline]
75pub(crate) fn log10_td(x: f64) -> TripleDouble {
76    let x_u = x.to_bits();
77    let mut m = x_u & 0xfffffffffffff;
78    let mut e: i64 = ((x_u >> 52) & 0x7ff) as i64;
79
80    let t;
81    if e != 0 {
82        t = m | (0x3ffu64 << 52);
83        m = m.wrapping_add(1u64 << 52);
84        e -= 0x3ff;
85    } else {
86        /* x is a subnormal double  */
87        let k = m.leading_zeros() - 11;
88
89        e = -0x3fei64 - k as i64;
90        m = m.wrapping_shl(k);
91        t = m | (0x3ffu64 << 52);
92    }
93
94    /* now |x| = 2^_e*_t = 2^(_e-52)*m with 1 <= _t < 2,
95    and 2^52 <= _m < 2^53 */
96
97    //   log10(x) = log10(t) + E · log10(e)
98    let mut t = f64::from_bits(t);
99
100    // If m > sqrt(2) we divide it by 2 so ensure 1/sqrt(2) < t < sqrt(2)
101    let c: usize = (m >= 0x16a09e667f3bcd) as usize;
102    static CY: [f64; 2] = [1.0, 0.5];
103    static CM: [u64; 2] = [44, 45];
104
105    e = e.wrapping_add(c as i64);
106    let be = e;
107    let i = m >> CM[c];
108    t *= CY[c];
109
110    let r = f64::from_bits(POW_INVERSE[(i - 181) as usize]);
111    let log10_r = TripleDouble::from_bit_pair(LOG10_NEG_TD[(i - 181) as usize]);
112
113    let z = f64::mul_add(r, t, -1.0);
114
115    const LOG10_2_DD: DoubleDouble =
116        DoubleDouble::from_bit_pair((0xbc49dc1da994fd21, 0x3fd34413509f79ff));
117
118    let v = TripleDouble::f64_mul_dd_add(be as f64, LOG10_2_DD, log10_r);
119
120    let p = log10_poly(z);
121    TripleDouble::add_f64(v.hi, TripleDouble::new(v.lo + p.lo, v.mid + p.mid, p.hi))
122}
123
124#[cfg(test)]
125mod tests {
126    use super::*;
127
128    #[test]
129    fn test_log10_dd() {
130        assert_eq!(log10_td(10.).to_f64(), 1.);
131    }
132}
pxfm/logs/log10td.rs

pxfm/logs/
log10td.rs
