pxfm/logs/
log2td.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::logs::log2td_coeffs::LOG2_NEG_TD;
30use crate::pow_tables::POW_INVERSE;
31use crate::triple_double::TripleDouble;
32
33#[inline(always)]
34fn log2_poly(z: f64) -> TripleDouble {
35    /*
36      See ./notes/dd_log.sollya
37    */
38    const P: [(u64, u64, u64); 11] = [
39        (0x38cb46674646bfff, 0x3c7777d0ffda0d23, 0x3ff71547652b82fe),
40        (0xb90ea6e2f55cd900, 0xbc6777d0ffe87198, 0xbfe71547652b82fe),
41        (0x391e004d54467330, 0x3c7d27f0556d8546, 0x3fdec709dc3a03fd),
42        (0xb8b2d21aeeb27bff, 0xbc5775b3aa82c433, 0xbfd71547652b82fe),
43        (0xb9164a4a186a0c00, 0x3c7e49c9bdb8b680, 0x3fd2776c50ef9bfe),
44        (0xb8efe23702b5a940, 0x3c6195ba6326b1bf, 0xbfcec709dc3a0414),
45        (0x38d7695a46fb4b00, 0x3c6f82e7add9bb4d, 0x3fca61762a7adf00),
46        (0xb8c00e9d3285e000, 0x3c2caf76a9ee1e78, 0xbfc7154764fba5e4),
47        (0xb8d1ff2b356eee80, 0xbc3f6102bc5ddc49, 0x3fc484b13d3bbed8),
48        (0xb8edd22b4add09c0, 0x3c4c1da4a1a32f3b, 0xbfc2779952952c26),
49        (0x388875bd65660001, 0x3c58e09839d588dd, 0x3fc0c9d962b39a7d),
50    ];
51    let mut t = TripleDouble::from_bit_pair(P[10]);
52    t = TripleDouble::f64_mul_add(z, t, TripleDouble::from_bit_pair(P[9]));
53    t = TripleDouble::f64_mul_add(z, t, TripleDouble::from_bit_pair(P[8]));
54    t = TripleDouble::f64_mul_add(z, t, TripleDouble::from_bit_pair(P[7]));
55    t = TripleDouble::f64_mul_add(z, t, TripleDouble::from_bit_pair(P[6]));
56    t = TripleDouble::f64_mul_add(z, t, TripleDouble::from_bit_pair(P[5]));
57    t = TripleDouble::f64_mul_add(z, t, TripleDouble::from_bit_pair(P[4]));
58    t = TripleDouble::f64_mul_add(z, t, TripleDouble::from_bit_pair(P[3]));
59    t = TripleDouble::f64_mul_add(z, t, TripleDouble::from_bit_pair(P[2]));
60    t = TripleDouble::f64_mul_add(z, t, TripleDouble::from_bit_pair(P[1]));
61    t = TripleDouble::f64_mul_add(z, t, TripleDouble::from_bit_pair(P[0]));
62    TripleDouble::quick_mult_f64(t, z)
63}
64
65#[inline]
66pub(crate) fn log2_td(x: f64) -> TripleDouble {
67    let x_u = x.to_bits();
68    let mut m = x_u & 0xfffffffffffff;
69    let mut e: i64 = ((x_u >> 52) & 0x7ff) as i64;
70
71    let t;
72    if e != 0 {
73        t = m | (0x3ffu64 << 52);
74        m = m.wrapping_add(1u64 << 52);
75        e -= 0x3ff;
76    } else {
77        /* x is a subnormal double  */
78        let k = m.leading_zeros() - 11;
79
80        e = -0x3fei64 - k as i64;
81        m = m.wrapping_shl(k);
82        t = m | (0x3ffu64 << 52);
83    }
84
85    /* now |x| = 2^_e*_t = 2^(_e-52)*m with 1 <= _t < 2,
86    and 2^52 <= _m < 2^53 */
87
88    //   log2(x) = log2(t) + E · log(2)
89    let mut t = f64::from_bits(t);
90
91    // If m > sqrt(2) we divide it by 2 so ensure 1/sqrt(2) < t < sqrt(2)
92    let c: usize = (m >= 0x16a09e667f3bcd) as usize;
93    static CY: [f64; 2] = [1.0, 0.5];
94    static CM: [u64; 2] = [44, 45];
95
96    e = e.wrapping_add(c as i64);
97    let be = e;
98    let i = m >> CM[c];
99    t *= CY[c];
100
101    let r = f64::from_bits(POW_INVERSE[(i - 181) as usize]);
102    let log_r = TripleDouble::from_bit_pair(LOG2_NEG_TD[(i - 181) as usize]);
103
104    let z = f64::mul_add(r, t, -1.0);
105
106    let v = TripleDouble::add_f64(be as f64, log_r);
107    let p = log2_poly(z);
108    TripleDouble::add_f64(v.hi, TripleDouble::new(v.lo + p.lo, v.mid + p.mid, p.hi))
109}
110
111#[cfg(test)]
112mod tests {
113    use crate::logs::log2td::log2_td;
114
115    #[test]
116    fn log2td_test() {
117        assert_eq!(log2_td(0.0040283203125 / 2.).to_f64(), -8.955605880641546);
118    }
119}
pxfm/logs/log2td.rs

pxfm/logs/
log2td.rs
