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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;
static Q: [(u32, u32); 3] = [
(0x7f7fffff, 0x7f7fffff),
(0x7f7fffff, 0x73000000),
(0xbf800000, 0x32800000),
];
static TB: [u64; 16] = [
0x3ff0000000000000,
0x3ff0b5586cf9890f,
0x3ff172b83c7d517b,
0x3ff2387a6e756238,
0x3ff306fe0a31b715,
0x3ff3dea64c123422,
0x3ff4bfdad5362a27,
0x3ff5ab07dd485429,
0x3ff6a09e667f3bcd,
0x3ff7a11473eb0187,
0x3ff8ace5422aa0da,
0x3ff9c49182a3f090,
0x3ffae89f995ad3ad,
0x3ffc199bdd85529c,
0x3ffd5818dcfba487,
0x3ffea4afa2a490da,
];
/// Computes 2^x-1
///
/// Max found ULP 0.5
#[inline]
pub fn f_exp2m1f(x: f32) -> f32 {
let t = x.to_bits();
let z = x as f64;
let ux = t;
let ax = ux & 0x7fff_ffff;
if ux >= 0xc1c80000u32 {
// x <= -25
if ax > (0xffu32 << 23) {
return x + x;
} // nan
// avoid spurious inexact exception for -Inf
if ux == 0xff800000 {
f32::from_bits(Q[2].0)
} else {
let zq = Q[2];
f32::from_bits(zq.0) + f32::from_bits(zq.1)
}
} else if ax >= 0x43000000u32 {
// x >= 128
if ax > (0xffu32 << 23) {
return x + x;
} // nan
// for x=128 and rounding downward or to zero, there is no overflow
let special = if x == 128.0
&& (f32::from_bits(Q[1].0) + f32::from_bits(Q[1].1) == f32::from_bits(Q[1].0))
{
1
} else {
0
};
// avoid spurious inexact exception for +Inf
if ux == 0x7f800000u32 {
x
} else {
f32::from_bits(Q[special].0) + f32::from_bits(Q[special].1)
}
} else if ax < 0x3df95f1fu32 {
// |x| < 8.44e-2/log(2)
let z2: f64 = z * z;
let mut r: f64;
if ax < 0x3d67a4ccu32 {
// |x| < 3.92e-2/log(2)
if ax < 0x3caa2feeu32 {
// |x| < 1.44e-2/log(2)
if ax < 0x3bac1405u32 {
// |x| < 3.64e-3/log(2)
if ax < 0x3a358876u32 {
// |x| < 4.8e-4/log(2)
if ax < 0x37d32ef6u32 {
// |x| < 1.745e-5/log(2)
if ax < 0x331fdd82u32 {
// |x| < 2.58e-8/log(2)
if ax < 0x2538aa3bu32 {
// |x| < 0x1.715476p-53
r = f64::from_bits(0x3fe62e42fefa39ef);
} else {
r = f64::from_bits(0x3fe62e42fefa39f0)
+ z * f64::from_bits(0x3fcebfbdff82c58f);
}
} else {
if ux == 0xb3d85005u32 {
return (f64::from_bits(0xbe72bdf760000000)
- f64::from_bits(0x3b28000000000000))
as f32;
}
if ux == 0x3338428du32 {
return (f64::from_bits(0x3e5fee08a0000000)
+ f64::from_bits(0x3af0000000000000))
as f32;
}
const C: [u64; 3] =
[0x3fe62e42fefa39ef, 0x3fcebfbdff8548fd, 0x3fac6b08d704a06d];
let r0 = f_fmla(z, f64::from_bits(C[2]), f64::from_bits(C[1]));
r = f_fmla(z, r0, f64::from_bits(C[0]));
}
} else {
if ux == 0x388bca4fu32 {
return (f64::from_bits(0x3f08397020000000)
- f64::from_bits(0x3bb8000000000000))
as f32;
}
const C: [u64; 4] = [
0x3fe62e42fefa39ef,
0x3fcebfbdff82c58f,
0x3fac6b08dc82b347,
0x3f83b2ab6fbad172,
];
let r0 = f_fmla(z, f64::from_bits(C[3]), f64::from_bits(C[2]));
let r1 = f_fmla(z, f64::from_bits(C[1]), f64::from_bits(C[0]));
r = f_fmla(z2, r0, r1);
}
} else {
const C: [u64; 5] = [
0x3fe62e42fefa39ef,
0x3fcebfbdff82c068,
0x3fac6b08d704a6dc,
0x3f83b2ac262c3eed,
0x3f55d87fe7af779a,
];
let r0 = f_fmla(z, f64::from_bits(C[4]), f64::from_bits(C[3]));
let r1 = f_fmla(z, f64::from_bits(C[1]), f64::from_bits(C[0]));
let w0 = f_fmla(z, r0, f64::from_bits(C[2]));
r = f_fmla(z2, w0, r1);
}
} else {
const C: [u64; 6] = [
0x3fe62e42fefa39f0,
0x3fcebfbdff82c58d,
0x3fac6b08d7011d13,
0x3f83b2ab6fbd267d,
0x3f55d88a81cea49e,
0x3f2430912ea9b963,
];
let r0 = f_fmla(z, f64::from_bits(C[5]), f64::from_bits(C[4]));
let r1 = f_fmla(z, f64::from_bits(C[3]), f64::from_bits(C[2]));
let r2 = f_fmla(z, f64::from_bits(C[1]), f64::from_bits(C[0]));
r = r2 + z2 * f_fmla(z2, r0, r1);
}
} else {
const C: [u64; 7] = [
0x3fe62e42fefa39ef,
0x3fcebfbdff82c639,
0x3fac6b08d7049f1c,
0x3f83b2ab6f5243bd,
0x3f55d87fe80a9e6c,
0x3f2430d0b9257fa8,
0x3eeffcbfc4cf0952,
];
let r0 = f_fmla(z, f64::from_bits(C[6]), f64::from_bits(C[5]));
let r1 = f_fmla(z, f64::from_bits(C[3]), f64::from_bits(C[2]));
let r2 = f_fmla(z, f64::from_bits(C[1]), f64::from_bits(C[0]));
let z0 = f_fmla(z, r0, f64::from_bits(C[4]));
r = f_fmla(z2, f_fmla(z2, z0, r1), r2);
}
} else {
const C: [u64; 8] = [
0x3fe62e42fefa39ef,
0x3fcebfbdff82c591,
0x3fac6b08d704cf6b,
0x3f83b2ab6fba00ce,
0x3f55d87fdfdaadb4,
0x3f24309137333066,
0x3eeffe5e90daf7dd,
0x3eb62c0220eed731,
];
let r0 = f_fmla(z, f64::from_bits(C[7]), f64::from_bits(C[6]));
let r1 = f_fmla(z, f64::from_bits(C[5]), f64::from_bits(C[4]));
let r2 = f_fmla(z, f64::from_bits(C[3]), f64::from_bits(C[2]));
let r3 = f_fmla(z, f64::from_bits(C[1]), f64::from_bits(C[0]));
let w0 = f_fmla(z2, r0, r1);
let w1 = f_fmla(z2, r2, r3);
r = w1 + (z2 * z2) * w0;
}
r *= z;
r as f32
} else {
const C: [u64; 6] = [
0x3fa62e42fefa398b,
0x3f4ebfbdff84555a,
0x3eec6b08d4ad86d3,
0x3e83b2ad1b1716a2,
0x3e15d7472718ce9d,
0x3da4a1d7f457ac56,
];
let a = 16.0 * z;
let ia = a.floor();
let h = a - ia;
let h2 = h * h;
let i: i64 = ia as i64;
let j = i & 0xf;
let mut e = i.wrapping_sub(j);
e >>= 4;
let mut s = f64::from_bits(TB[j as usize]);
let su = ((e as u64).wrapping_add(0x3ffu64)) << 52;
s *= f64::from_bits(su);
let mut c0 = f_fmla(h, f64::from_bits(C[1]), f64::from_bits(C[0]));
let c2 = f_fmla(h, f64::from_bits(C[3]), f64::from_bits(C[2]));
let c4 = f_fmla(h, f64::from_bits(C[5]), f64::from_bits(C[4]));
c0 += h2 * f_fmla(h2, c4, c2);
let w = s * h;
f_fmla(w, c0, s - 1.0) as f32
}
}