pxfm/logs/
log1pf.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
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::common::f_fmla;
30use crate::logs::{LOG_R_DD, LOG_RANGE_REDUCTION};
31use crate::polyeval::{f_estrin_polyeval8, f_polyeval6};
32
33#[inline]
34pub(crate) fn core_logf(x: f64) -> f64 {
35    let x_u = x.to_bits();
36
37    const E_BIAS: u64 = (1u64 << (11 - 1u64)) - 1u64;
38
39    let mut x_e: i32 = -(E_BIAS as i32);
40
41    // log2(x) = log2(2^x_e * x_m)
42    //         = x_e + log2(x_m)
43    // Range reduction for log2(x_m):
44    // For each x_m, we would like to find r such that:
45    //   -2^-8 <= r * x_m - 1 < 2^-7
46    let shifted = (x_u >> 45) as i32;
47    let index = shifted & 0x7F;
48    let r = f64::from_bits(LOG_RANGE_REDUCTION[index as usize]);
49
50    // Add unbiased exponent. Add an extra 1 if the 8 leading fractional bits are
51    // all 1's.
52    x_e = x_e.wrapping_add(x_u.wrapping_add(1u64 << 45).wrapping_shr(52) as i32);
53    let e_x = x_e as f64;
54
55    const LOG_2_HI: f64 = f64::from_bits(0x3fe62e42fefa3800);
56    const LOG_2_LO: f64 = f64::from_bits(0x3d2ef35793c76730);
57
58    let log_r_dd = LOG_R_DD[index as usize];
59
60    // hi is exact
61    let hi = f_fmla(e_x, LOG_2_HI, f64::from_bits(log_r_dd.1));
62    let lo = f_fmla(e_x, LOG_2_LO, f64::from_bits(log_r_dd.0));
63
64    // Set m = 1.mantissa.
65    let x_m = (x_u & 0x000F_FFFF_FFFF_FFFFu64) | 0x3FF0_0000_0000_0000u64;
66    let m = f64::from_bits(x_m);
67
68    let u;
69    #[cfg(any(
70        all(
71            any(target_arch = "x86", target_arch = "x86_64"),
72            target_feature = "fma"
73        ),
74        target_arch = "aarch64"
75    ))]
76    {
77        u = f_fmla(r, m, -1.0); // exact
78    }
79    #[cfg(not(any(
80        all(
81            any(target_arch = "x86", target_arch = "x86_64"),
82            target_feature = "fma"
83        ),
84        target_arch = "aarch64"
85    )))]
86    {
87        use crate::logs::LOG_CD;
88        let c_m = x_m & 0x3FFF_E000_0000_0000u64;
89        let c = f64::from_bits(c_m);
90        u = f_fmla(r, m - c, f64::from_bits(LOG_CD[index as usize])); // exact
91    }
92
93    let r1 = hi;
94    // Polynomial for log(1+x)/x generated in Sollya:
95    // d = [-2^-8, 2^-7];
96    // f_log = log(1 + x)/x;
97    // Q = fpminimax(f_log, 5, [|D...|], d);
98    // See ./notes/log1pf_core.sollya
99    let p = f_polyeval6(
100        u,
101        f64::from_bits(0x3fefffffffffffff),
102        f64::from_bits(0xbfdffffffffff3e6),
103        f64::from_bits(0x3fd5555555626b74),
104        f64::from_bits(0xbfd0000026aeecc8),
105        f64::from_bits(0x3fc9999114d16c06),
106        f64::from_bits(0xbfc51e433a85278a),
107    );
108    f_fmla(p, u, r1) + lo
109}
110
111/// Computes log(x+1)
112///
113/// Max ULP 0.5
114#[inline]
115pub fn f_log1pf(x: f32) -> f32 {
116    let ux = x.to_bits().wrapping_shl(1);
117    if ux >= 0xffu32 << 24 || ux == 0 {
118        // |x| == 0, |x| == inf, x == NaN
119        if ux == 0 {
120            return x;
121        }
122        if x.is_infinite() {
123            return if x.is_sign_positive() {
124                f32::INFINITY
125            } else {
126                f32::NAN
127            };
128        }
129        return x + f32::NAN;
130    }
131
132    let xd = x as f64;
133    let ax = x.to_bits() & 0x7fff_ffffu32;
134
135    // Use log1p(x) = log(1 + x) for |x| > 2^-6;
136    if ax > 0x3c80_0000u32 {
137        if x == -1. {
138            return f32::NEG_INFINITY;
139        }
140        let x1p = xd + 1.;
141        if x1p <= 0. {
142            if x1p == 0. {
143                return f32::NEG_INFINITY;
144            }
145            return f32::NAN;
146        }
147        return core_logf(x1p) as f32;
148    }
149
150    // log(1+x) is expected to be used near zero
151    // Polynomial generated by Sollya:
152    // d = [-2^-6; 2^-6];
153    // f_log1pf = log(1+x)/x;
154    // Q = fpminimax(f_log1pf, 7, [|0, D...|], d);
155    // See ./notes/log1pf.sollya
156
157    let p = f_estrin_polyeval8(
158        xd,
159        f64::from_bits(0x3ff0000000000000),
160        f64::from_bits(0xbfe0000000000000),
161        f64::from_bits(0x3fd5555555556aad),
162        f64::from_bits(0xbfd000000000181a),
163        f64::from_bits(0x3fc999998998124e),
164        f64::from_bits(0xbfc55555452e2a2b),
165        f64::from_bits(0x3fc24adb8cde4aa7),
166        f64::from_bits(0xbfc0019db915ef6f),
167    ) * xd;
168    p as f32
169}
170
171#[inline]
172pub(crate) fn core_log1pf(x: f32) -> f64 {
173    let xd = x as f64;
174    let ax = x.to_bits() & 0x7fff_ffffu32;
175
176    // Use log1p(x) = log(1 + x) for |x| > 2^-6;
177    if ax > 0x3c80_0000u32 {
178        let x1p = xd + 1.;
179        return core_logf(x1p);
180    }
181
182    // log(1+x) is expected to be used near zero
183    // Polynomial generated by Sollya:
184    // d = [-2^-6; 2^-6];
185    // f_log1pf = log(1+x)/x;
186    // Q = fpminimax(f_log1pf, 7, [|0, D...|], d);
187    // See ./notes/log1pf.sollya
188
189    f_estrin_polyeval8(
190        xd,
191        f64::from_bits(0x3ff0000000000000),
192        f64::from_bits(0xbfe0000000000000),
193        f64::from_bits(0x3fd5555555556aad),
194        f64::from_bits(0xbfd000000000181a),
195        f64::from_bits(0x3fc999998998124e),
196        f64::from_bits(0xbfc55555452e2a2b),
197        f64::from_bits(0x3fc24adb8cde4aa7),
198        f64::from_bits(0xbfc0019db915ef6f),
199    ) * xd
200}
201
202#[cfg(test)]
203mod tests {
204    use super::*;
205
206    #[test]
207    fn log1pf_works() {
208        assert!(f_log1pf(f32::from_bits(0xffefb9a7)).is_nan());
209        assert!(f_log1pf(f32::NAN).is_nan());
210        assert_eq!(f_log1pf(f32::from_bits(0x41078feb)), 2.2484074);
211        assert_eq!(f_log1pf(-0.0000014305108), -0.0000014305118);
212        assert_eq!(f_log1pf(0.0), 0.0);
213        assert_eq!(f_log1pf(2.0), 1.0986123);
214        assert_eq!(f_log1pf(-0.7), -1.2039728);
215        assert_eq!(f_log1pf(-0.0000000000043243), -4.3243e-12);
216        assert_eq!(f_log1pf(f32::INFINITY), f32::INFINITY);
217        assert!(f_log1pf(-2.0).is_nan());
218        assert!(f_log1pf(f32::NAN).is_nan());
219    }
220}
pxfm/logs/log1pf.rs

pxfm/logs/
log1pf.rs
