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/*
* // Copyright (c) Radzivon Bartoshyk 6/2025. All rights reserved.
* //
* // Redistribution and use in source and binary forms, with or without modification,
* // are permitted provided that the following conditions are met:
* //
* // 1. Redistributions of source code must retain the above copyright notice, this
* // list of conditions and the following disclaimer.
* //
* // 2. Redistributions in binary form must reproduce the above copyright notice,
* // this list of conditions and the following disclaimer in the documentation
* // and/or other materials provided with the distribution.
* //
* // 3. Neither the name of the copyright holder nor the names of its
* // contributors may be used to endorse or promote products derived from
* // this software without specific prior written permission.
* //
* // THIS SOFTWARE IS PROVIDED BY THE COPYRIGHT HOLDERS AND CONTRIBUTORS "AS IS"
* // AND ANY EXPRESS OR IMPLIED WARRANTIES, INCLUDING, BUT NOT LIMITED TO, THE
* // IMPLIED WARRANTIES OF MERCHANTABILITY AND FITNESS FOR A PARTICULAR PURPOSE ARE
* // DISCLAIMED. IN NO EVENT SHALL THE COPYRIGHT HOLDER OR CONTRIBUTORS BE LIABLE
* // FOR ANY DIRECT, INDIRECT, INCIDENTAL, SPECIAL, EXEMPLARY, OR CONSEQUENTIAL
* // DAMAGES (INCLUDING, BUT NOT LIMITED TO, PROCUREMENT OF SUBSTITUTE GOODS OR
* // SERVICES; LOSS OF USE, DATA, OR PROFITS; OR BUSINESS INTERRUPTION) HOWEVER
* // CAUSED AND ON ANY THEORY OF LIABILITY, WHETHER IN CONTRACT, STRICT LIABILITY,
* // OR TORT (INCLUDING NEGLIGENCE OR OTHERWISE) ARISING IN ANY WAY OUT OF THE USE
* // OF THIS SOFTWARE, EVEN IF ADVISED OF THE POSSIBILITY OF SUCH DAMAGE.
*/
use crate::common::f_fmla;
use crate::exp10f::EXP10F_COEFFS;
use crate::logf::f_polyeval3;
/// Computes 10^x - 1
///
/// Max ULP 0.5
#[inline]
pub fn f_exp10m1f(x: f32) -> f32 {
let x_u = x.to_bits();
let x_abs = x_u & 0x7fff_ffffu32;
// When x >= log10(2^128), or x is nan
if x.is_sign_positive() && x_u >= 0x421a_209bu32 {
// x >= log10(2^128) and 10^x - 1 rounds to +inf, or x is +inf or nan
return x + f32::INFINITY;
}
if x_abs <= 0x3b9a_209bu32 {
let dx = x as f64;
let dx_sq = dx * dx;
let c0 = dx * f64::from_bits(EXP10F_COEFFS[0]);
let c1 = f_fmla(
dx,
f64::from_bits(EXP10F_COEFFS[2]),
f64::from_bits(EXP10F_COEFFS[1]),
);
let c2 = f_fmla(
dx,
f64::from_bits(EXP10F_COEFFS[4]),
f64::from_bits(EXP10F_COEFFS[3]),
);
// 10^dx - 1 ~ (1 + COEFFS[0] * dx + ... + COEFFS[4] * dx^5) - 1
// = COEFFS[0] * dx + ... + COEFFS[4] * dx^5
return f_polyeval3(dx_sq, c0, c1, c2) as f32;
}
// When x <= log10(2^-25), or x is nan
if x_u >= 0xc0f0d2f1 {
// exp10m1(-inf) = -1
if x.is_infinite() {
return -1.0;
}
// exp10m1(nan) = nan
if x.is_nan() {
return x;
}
if x_u == 0xc0f0d2f1 {
return f32::from_bits(0xbf7fffff); // -1.0f + 0x1.0p-24f
}
return -1.0;
}
// Exact outputs when x = 1, 2, ..., 10.
// Quick check mask: 0x800f'ffffU = ~(bits of 1.0f | ... | bits of 10.0f)
if x_u & 0x800f_ffffu32 == 0 {
match x_u {
0x3f800000u32 => return 9.0, // x = 1.0f
0x40000000u32 => return 99.0, // x = 2.0f
0x40400000u32 => return 999.0, // x = 3.0f
0x40800000u32 => return 9_999.0, // x = 4.0f
0x40a00000u32 => return 99_999.0, // x = 5.0f
0x40c00000u32 => return 999_999.0, // x = 6.0f
0x40e00000u32 => return 9_999_999.0, // x = 7.0f
0x41000000u32 => return 99_999_999.0, // x = 8.0f
0x41100000u32 => return 999_999_999.0, // x = 9.0f
0x41200000u32 => return 9_999_999_999.0, // x = 10.0f
_ => {}
}
}
// Range reduction: 10^x = 2^(mid + hi) * 10^lo
// rr = (2^(mid + hi), lo)
let rr = crate::exp10f::exp_b_range_reduc(x);
// The low part is approximated by a degree-5 minimax polynomial.
// 10^lo ~ 1 + COEFFS[0] * lo + ... + COEFFS[4] * lo^5
let lo_sq = rr.lo * rr.lo;
let c0 = f_fmla(rr.lo, f64::from_bits(EXP10F_COEFFS[0]), 1.0);
let c1 = f_fmla(
rr.lo,
f64::from_bits(EXP10F_COEFFS[2]),
f64::from_bits(EXP10F_COEFFS[1]),
);
let c2 = f_fmla(
rr.lo,
f64::from_bits(EXP10F_COEFFS[4]),
f64::from_bits(EXP10F_COEFFS[3]),
);
let exp10_lo = f_polyeval3(lo_sq, c0, c1, c2);
// 10^x - 1 = 2^(mid + hi) * 10^lo - 1
// ~ mh * exp10_lo - 1
f_fmla(exp10_lo, rr.hi, -1.0) as f32
}
#[cfg(test)]
mod tests {
use super::*;
#[test]
fn test_exp10m1f() {
assert_eq!(f_exp10m1f(0.0), 0.0);
assert_eq!(f_exp10m1f(1.0), 9.0);
assert_eq!(f_exp10m1f(1.5), 30.622776);
}
}