pxfm/exponents/
exp10f.rs

1/*
2 * // Copyright (c) Radzivon Bartoshyk 6/2025. 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
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27 * // OF THIS SOFTWARE, EVEN IF ADVISED OF THE POSSIBILITY OF SUCH DAMAGE.
28 */
29use crate::common::{f_fmla, f_fmlaf};
30use crate::polyeval::f_polyeval7;
31use crate::round::RoundFinite;
32
33pub(crate) struct ExpBReduc {
34    pub(crate) hi: f64,
35    pub(crate) lo: f64,
36}
37
38const MID_BITS: u32 = 5;
39const MID_MASK: usize = (1 << MID_BITS) - 1;
40const LOG2_B: f64 = f64::from_bits(0x400a934f0979a371) * (1 << MID_BITS) as f64;
41const M_LOGB_2_HI: f64 = f64::from_bits(0xbfd34413509f8000) / (1 << MID_BITS) as f64;
42const M_LOGB_2_LO: f64 = f64::from_bits(0x3d380433b83b532a) / (1 << MID_BITS) as f64;
43const EXP_2_MID: [u64; 32] = [
44    0x3ff0000000000000,
45    0x3ff059b0d3158574,
46    0x3ff0b5586cf9890f,
47    0x3ff11301d0125b51,
48    0x3ff172b83c7d517b,
49    0x3ff1d4873168b9aa,
50    0x3ff2387a6e756238,
51    0x3ff29e9df51fdee1,
52    0x3ff306fe0a31b715,
53    0x3ff371a7373aa9cb,
54    0x3ff3dea64c123422,
55    0x3ff44e086061892d,
56    0x3ff4bfdad5362a27,
57    0x3ff5342b569d4f82,
58    0x3ff5ab07dd485429,
59    0x3ff6247eb03a5585,
60    0x3ff6a09e667f3bcd,
61    0x3ff71f75e8ec5f74,
62    0x3ff7a11473eb0187,
63    0x3ff82589994cce13,
64    0x3ff8ace5422aa0db,
65    0x3ff93737b0cdc5e5,
66    0x3ff9c49182a3f090,
67    0x3ffa5503b23e255d,
68    0x3ffae89f995ad3ad,
69    0x3ffb7f76f2fb5e47,
70    0x3ffc199bdd85529c,
71    0x3ffcb720dcef9069,
72    0x3ffd5818dcfba487,
73    0x3ffdfc97337b9b5f,
74    0x3ffea4afa2a490da,
75    0x3fff50765b6e4540,
76];
77
78// Approximating 10^dx with degree-5 minimax polynomial generated by Sollya:
79// > Q = fpminimax((10^x - 1)/x, 4, [|D...|], [-log10(2)/2^6, log10(2)/2^6]);
80// Then:
81//   10^dx ~ P(dx) = 1 + COEFFS[0] * dx + ... + COEFFS[4] * dx^5.
82pub(crate) const EXP10F_COEFFS: [u64; 5] = [
83    0x40026bb1bbb55515,
84    0x40053524c73bd3ea,
85    0x4000470591dff149,
86    0x3ff2bd7c0a9fbc4d,
87    0x3fe1429e74a98f43,
88];
89
90/// Range reduction function equivalent to exp_b_range_reduc
91#[inline]
92pub(crate) fn exp_b_range_reduc(x: f32) -> ExpBReduc {
93    let xd = x as f64;
94
95    // kd = round(log2(b) * x)
96    let kd = (LOG2_B * xd).round_finite();
97    let k = unsafe { kd.to_int_unchecked::<i32>() }; // it's already not indeterminate.
98
99    // hi = floor(kd / 2^MID_BITS)
100    let exp_hi = (k.wrapping_shr(MID_BITS) as u64).wrapping_shl(52); // 52 = fraction bits in f64
101
102    // mh = 2^hi * 2^mid
103    let mid_index = (k as usize) & MID_MASK;
104    let mh_bits = EXP_2_MID[mid_index].wrapping_add(exp_hi);
105    let mh = f64::from_bits(mh_bits);
106
107    // dx = x - (hi + mid) * log(2)
108    let z0 = f_fmla(kd, M_LOGB_2_HI, xd);
109    let dx = f_fmla(kd, M_LOGB_2_LO, z0);
110
111    ExpBReduc { lo: dx, hi: mh }
112}
113
114/// Computes exp10
115///
116/// Max found ULP 0.49999508
117#[inline]
118pub fn f_exp10f(x: f32) -> f32 {
119    let x_u = x.to_bits();
120    let x_abs = x_u & 0x7fffffff;
121
122    // When |x| >= log10(2^128), or x is nan
123    if x_abs >= 0x421a209bu32 {
124        // When x < log10(2^-150) or nan
125        if x_u > 0xc2349e35u32 {
126            // exp(-Inf) = 0
127            if x.is_infinite() {
128                return 0.0;
129            }
130            // exp(nan) = nan
131            if x.is_nan() {
132                return x;
133            }
134            return 0.0;
135        }
136        // x >= log10(2^128) or nan
137        if x > 0. && (x_u >= 0x421a209bu32) {
138            // x is +inf or nan
139            return x + f32::INFINITY;
140        }
141    }
142
143    if x_abs <= 0x3d000000u32 {
144        // |x| < 1/32
145        if x_abs <= 0x3b9a209bu32 {
146            if x_u == 0xb25e5bd9u32 {
147                // x = -1.2943e-08
148                return 1.;
149            }
150            // |x| < 2^-25
151            // 10^x ~ 1 + log(10) * x
152            if x_abs <= 0x32800000u32 {
153                return f_fmlaf(x, f32::from_bits(0x40135da2), 1.0);
154            }
155        }
156
157        let xd = x as f64;
158
159        // Special polynomial for small x.
160        // Generated by Sollya:
161        // d = [-1/32, 1/32];
162        // f_exp10f = (10^y - 1)/y;
163        // Q = fpminimax(f_exp10f, 6, [|D...|], d, relative, floating);
164
165        // See ./notes/exp10f_small.sollya
166        let p = f_polyeval7(
167            xd,
168            f64::from_bits(0x40026bb1bbb55516),
169            f64::from_bits(0x40053524c73cfbf6),
170            f64::from_bits(0x4000470591de0b07),
171            f64::from_bits(0x3ff2bd760599f3a5),
172            f64::from_bits(0x3fe142a001511a6f),
173            f64::from_bits(0x3fca7feffa781d53),
174            f64::from_bits(0x3fb16e53492c0f0e),
175        );
176        return f_fmla(p, xd, 1.) as f32;
177    }
178
179    // Range reduction: 10^x = 2^(mid + hi) * 10^lo
180    //   rr = (2^(mid + hi), lo)
181    let rr = exp_b_range_reduc(x);
182
183    // The low part is approximated by a degree-5 minimax polynomial.
184    // 10^lo ~ 1 + COEFFS[0] * lo + ... + COEFFS[4] * lo^5
185    let lo2 = rr.lo * rr.lo;
186    // c0 = 1 + COEFFS[0] * lo
187    let c0 = f_fmla(rr.lo, f64::from_bits(EXP10F_COEFFS[0]), 1.0);
188    // c1 = COEFFS[1] + COEFFS[2] * lo
189    let c1 = f_fmla(
190        rr.lo,
191        f64::from_bits(EXP10F_COEFFS[2]),
192        f64::from_bits(EXP10F_COEFFS[1]),
193    );
194    // c2 = COEFFS[3] + COEFFS[4] * lo
195    let c2 = f_fmla(
196        rr.lo,
197        f64::from_bits(EXP10F_COEFFS[4]),
198        f64::from_bits(EXP10F_COEFFS[3]),
199    );
200    // p = c1 + c2 * lo^2
201    //   = COEFFS[1] + COEFFS[2] * lo + COEFFS[3] * lo^2 + COEFFS[4] * lo^3
202    let p = f_fmla(lo2, c2, c1);
203    // 10^lo ~ c0 + p * lo^2
204    // 10^x = 2^(mid + hi) * 10^lo
205    //      ~ mh * (c0 + p * lo^2)
206    //      = (mh * c0) + p * (mh * lo^2)
207    f_fmla(p, lo2 * rr.hi, c0 * rr.hi) as f32
208}
209
210#[cfg(test)]
211mod tests {
212    use super::*;
213
214    #[test]
215    fn test_exp10f() {
216        assert_eq!(f_exp10f(-1. / 64.), 0.9646616);
217        assert_eq!(f_exp10f(1. / 64.), 1.0366329);
218        assert_eq!(f_exp10f(1.), 10.0);
219        assert_eq!(f_exp10f(2.), 100.0);
220        assert_eq!(f_exp10f(3.), 1000.0);
221        assert_eq!(f_exp10f(f32::INFINITY), f32::INFINITY);
222        assert_eq!(f_exp10f(f32::NEG_INFINITY), 0.);
223        assert!(f_exp10f(f32::NAN).is_nan());
224    }
225}
pxfm/exponents/exp10f.rs

pxfm/exponents/
exp10f.rs
