142 lines
5.0 KiB
Rust
142 lines
5.0 KiB
Rust
/*
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* // Copyright (c) Radzivon Bartoshyk 7/2025. All rights reserved.
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* //
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* // Redistribution and use in source and binary forms, with or without modification,
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* // are permitted provided that the following conditions are met:
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* //
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* // 1. Redistributions of source code must retain the above copyright notice, this
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* // list of conditions and the following disclaimer.
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* //
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* // 2. Redistributions in binary form must reproduce the above copyright notice,
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* // this list of conditions and the following disclaimer in the documentation
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* // and/or other materials provided with the distribution.
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* //
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* // 3. Neither the name of the copyright holder nor the names of its
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* // contributors may be used to endorse or promote products derived from
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* // this software without specific prior written permission.
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* //
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* // THIS SOFTWARE IS PROVIDED BY THE COPYRIGHT HOLDERS AND CONTRIBUTORS "AS IS"
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* // AND ANY EXPRESS OR IMPLIED WARRANTIES, INCLUDING, BUT NOT LIMITED TO, THE
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* // IMPLIED WARRANTIES OF MERCHANTABILITY AND FITNESS FOR A PARTICULAR PURPOSE ARE
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* // DISCLAIMED. IN NO EVENT SHALL THE COPYRIGHT HOLDER OR CONTRIBUTORS BE LIABLE
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* // FOR ANY DIRECT, INDIRECT, INCIDENTAL, SPECIAL, EXEMPLARY, OR CONSEQUENTIAL
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* // DAMAGES (INCLUDING, BUT NOT LIMITED TO, PROCUREMENT OF SUBSTITUTE GOODS OR
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* // SERVICES; LOSS OF USE, DATA, OR PROFITS; OR BUSINESS INTERRUPTION) HOWEVER
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* // CAUSED AND ON ANY THEORY OF LIABILITY, WHETHER IN CONTRACT, STRICT LIABILITY,
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* // OR TORT (INCLUDING NEGLIGENCE OR OTHERWISE) ARISING IN ANY WAY OUT OF THE USE
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* // OF THIS SOFTWARE, EVEN IF ADVISED OF THE POSSIBILITY OF SUCH DAMAGE.
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*/
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use crate::common::f_fmla;
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use crate::exponents::exp10f::EXP10F_COEFFS;
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use crate::polyeval::f_polyeval3;
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#[cold]
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fn exp10m1f_small(x: f32) -> f32 {
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let dx = x as f64;
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let dx_sq = dx * dx;
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let c0 = dx * f64::from_bits(EXP10F_COEFFS[0]);
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let c1 = f_fmla(
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dx,
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f64::from_bits(EXP10F_COEFFS[2]),
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f64::from_bits(EXP10F_COEFFS[1]),
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);
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let c2 = f_fmla(
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dx,
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f64::from_bits(EXP10F_COEFFS[4]),
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f64::from_bits(EXP10F_COEFFS[3]),
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);
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// 10^dx - 1 ~ (1 + COEFFS[0] * dx + ... + COEFFS[4] * dx^5) - 1
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// = COEFFS[0] * dx + ... + COEFFS[4] * dx^5
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f_polyeval3(dx_sq, c0, c1, c2) as f32
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}
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/// Computes 10^x - 1
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///
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/// Max ULP 0.5
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#[inline]
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pub fn f_exp10m1f(x: f32) -> f32 {
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let x_u = x.to_bits();
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let x_abs = x_u & 0x7fff_ffffu32;
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// When x >= log10(2^128), or x is nan
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if x.is_sign_positive() && x_u >= 0x421a_209bu32 {
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// x >= log10(2^128) and 10^x - 1 rounds to +inf, or x is +inf or nan
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return x + f32::INFINITY;
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}
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if x_abs <= 0x3b9a_209bu32 {
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// |x| <= 0.004703594
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return exp10m1f_small(x);
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}
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// When x <= log10(2^-25), or x is nan
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if x_u >= 0xc0f0d2f1 {
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// exp10m1(-inf) = -1
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if x.is_infinite() {
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return -1.0;
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}
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// exp10m1(nan) = nan
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if x.is_nan() {
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return x;
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}
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if x_u == 0xc0f0d2f1 {
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return f32::from_bits(0xbf7fffff); // -1.0f + 0x1.0p-24f
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}
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return -1.0;
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}
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// Exact outputs when x = 1, 2, ..., 10.
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// Quick check mask: 0x800f'ffffU = ~(bits of 1.0f | ... | bits of 10.0f)
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if x_u & 0x800f_ffffu32 == 0 {
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match x_u {
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0x3f800000u32 => return 9.0, // x = 1.0f
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0x40000000u32 => return 99.0, // x = 2.0f
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0x40400000u32 => return 999.0, // x = 3.0f
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0x40800000u32 => return 9_999.0, // x = 4.0f
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0x40a00000u32 => return 99_999.0, // x = 5.0f
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0x40c00000u32 => return 999_999.0, // x = 6.0f
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0x40e00000u32 => return 9_999_999.0, // x = 7.0f
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0x41000000u32 => return 99_999_999.0, // x = 8.0f
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0x41100000u32 => return 999_999_999.0, // x = 9.0f
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0x41200000u32 => return 9_999_999_999.0, // x = 10.0f
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_ => {}
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}
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}
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// Range reduction: 10^x = 2^(mid + hi) * 10^lo
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// rr = (2^(mid + hi), lo)
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let rr = crate::exponents::exp10f::exp_b_range_reduc(x);
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// The low part is approximated by a degree-5 minimax polynomial.
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// 10^lo ~ 1 + COEFFS[0] * lo + ... + COEFFS[4] * lo^5
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let lo_sq = rr.lo * rr.lo;
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let c0 = f_fmla(rr.lo, f64::from_bits(EXP10F_COEFFS[0]), 1.0);
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let c1 = f_fmla(
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rr.lo,
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f64::from_bits(EXP10F_COEFFS[2]),
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f64::from_bits(EXP10F_COEFFS[1]),
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);
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let c2 = f_fmla(
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rr.lo,
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f64::from_bits(EXP10F_COEFFS[4]),
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f64::from_bits(EXP10F_COEFFS[3]),
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);
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let exp10_lo = f_polyeval3(lo_sq, c0, c1, c2);
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// 10^x - 1 = 2^(mid + hi) * 10^lo - 1
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// ~ mh * exp10_lo - 1
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f_fmla(exp10_lo, rr.hi, -1.0) as f32
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}
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#[cfg(test)]
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mod tests {
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use super::*;
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#[test]
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fn test_exp10m1f() {
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assert_eq!(f_exp10m1f(0.0), 0.0);
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assert_eq!(f_exp10m1f(1.0), 9.0);
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assert_eq!(f_exp10m1f(1.5), 30.622776);
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}
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}
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