pxfm/logs/
log10dd.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::log10dd_coeffs::LOG10_NEG_DD;
31use crate::pow_tables::POW_INVERSE;
32
33#[inline(always)]
34fn log10_poly(z: f64) -> DoubleDouble {
35    /*
36      See ./notes/dd_log10.sollya
37    */
38    const P: [(u64, u64); 10] = [
39        (0x3c695355baabd6d2, 0x3fdbcb7b1526e50e),
40        (0xbc595355bababc0c, 0xbfcbcb7b1526e50e),
41        (0xbc59c8c251be5fee, 0x3fc287a7636f435f),
42        (0xbc49515e0a562cbe, 0xbfbbcb7b1526e50e),
43        (0xbc5603802582ebad, 0x3fb63c62775250e2),
44        (0x3c37a0e7de39c80c, 0xbfb287a7636f4371),
45        (0x3c2c4afd722dc9ec, 0x3fafc3fa611f0291),
46        (0xbc4a52f6541b67ee, 0xbfabcb7b14e178e5),
47        (0x3c3ef541147ede8e, 0x3fa8b514ee02cfad),
48        (0xbc28b9ea54e8f3b4, 0xbfa63c9d960501f1),
49    ];
50    let mut t = DoubleDouble::quick_mul_f64_add(
51        DoubleDouble::from_bit_pair(P[9]),
52        z,
53        DoubleDouble::from_bit_pair(P[8]),
54    );
55    t = DoubleDouble::quick_mul_f64_add(t, z, DoubleDouble::from_bit_pair(P[7]));
56    t = DoubleDouble::quick_mul_f64_add(t, z, DoubleDouble::from_bit_pair(P[6]));
57    t = DoubleDouble::quick_mul_f64_add(t, z, DoubleDouble::from_bit_pair(P[5]));
58    t = DoubleDouble::quick_mul_f64_add(t, z, DoubleDouble::from_bit_pair(P[4]));
59    t = DoubleDouble::quick_mul_f64_add(t, z, DoubleDouble::from_bit_pair(P[3]));
60    t = DoubleDouble::quick_mul_f64_add(t, z, DoubleDouble::from_bit_pair(P[2]));
61    t = DoubleDouble::quick_mul_f64_add(t, z, DoubleDouble::from_bit_pair(P[1]));
62    t = DoubleDouble::quick_mul_f64_add(t, z, DoubleDouble::from_bit_pair(P[0]));
63    DoubleDouble::quick_mult_f64(t, z)
64}
65
66#[inline]
67pub(crate) fn log10_dd(x: f64) -> DoubleDouble {
68    let x_u = x.to_bits();
69    let mut m = x_u & 0xfffffffffffff;
70    let mut e: i64 = ((x_u >> 52) & 0x7ff) as i64;
71
72    let t;
73    if e != 0 {
74        t = m | (0x3ffu64 << 52);
75        m = m.wrapping_add(1u64 << 52);
76        e -= 0x3ff;
77    } else {
78        /* x is a subnormal double  */
79        let k = m.leading_zeros() - 11;
80
81        e = -0x3fei64 - k as i64;
82        m = m.wrapping_shl(k);
83        t = m | (0x3ffu64 << 52);
84    }
85
86    /* now |x| = 2^_e*_t = 2^(_e-52)*m with 1 <= _t < 2,
87    and 2^52 <= _m < 2^53 */
88
89    //   log10(x) = log10(t) + E · log10(e)
90    let mut t = f64::from_bits(t);
91
92    // If m > sqrt(2) we divide it by 2 so ensure 1/sqrt(2) < t < sqrt(2)
93    let c: usize = (m >= 0x16a09e667f3bcd) as usize;
94    static CY: [f64; 2] = [1.0, 0.5];
95    static CM: [u64; 2] = [44, 45];
96
97    e = e.wrapping_add(c as i64);
98    let be = e;
99    let i = m >> CM[c];
100    t *= CY[c];
101
102    let r = f64::from_bits(POW_INVERSE[(i - 181) as usize]);
103    let log10_r = DoubleDouble::from_bit_pair(LOG10_NEG_DD[(i - 181) as usize]);
104
105    let z = f64::mul_add(r, t, -1.0);
106
107    const LOG10_2_DD: DoubleDouble =
108        DoubleDouble::from_bit_pair((0xbc49dc1da994fd21, 0x3fd34413509f79ff));
109
110    let v = DoubleDouble::mul_f64_add(LOG10_2_DD, be as f64, log10_r);
111
112    let p = log10_poly(z);
113    DoubleDouble::f64_add(v.hi, DoubleDouble::new(v.lo + p.lo, p.hi))
114}
115
116#[cfg(test)]
117mod tests {
118    use super::*;
119
120    #[test]
121    fn test_log10_dd() {
122        assert_eq!(log10_dd(10.).to_f64(), 1.);
123    }
124}
pxfm/logs/log10dd.rs

pxfm/logs/
log10dd.rs
