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/*
* // Copyright (c) Radzivon Bartoshyk 4/2025. 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::dekker::Dekker;
use crate::exp::{EXP_REDUCE_T0, EXP_REDUCE_T1, to_denormal};
#[inline]
pub(crate) fn poly_xd_generic<const N: usize>(x: f64, poly: [(u64, u64); N]) -> Dekker {
let zch = poly.last().unwrap();
let mut ch = Dekker::new(f64::from_bits(zch.0), f64::from_bits(zch.1));
for zch in poly.iter().rev().skip(1) {
ch = Dekker::quick_mult_f64(ch, x);
let z0 = Dekker::from_bit_pair(*zch);
ch = Dekker::add(z0, ch);
}
ch
}
#[inline]
pub(crate) fn ldexp(d: f64, i: u64) -> f64 {
let b = d.to_bits();
f64::from_bits(b.wrapping_add(i.wrapping_shl(52)))
}
fn exp2_accurate(x: f64) -> f64 {
let mut ix = x.to_bits();
let sx = 4096.0 * x;
let fx = sx.round_ties_even();
let z = sx - fx;
let k: i64 = fx as i64;
let i1 = k & 0x3f;
let i0 = (k >> 6) & 0x3f;
let ie = k >> 12;
let t0 = Dekker::from_bit_pair(EXP_REDUCE_T0[i0 as usize]);
let t1 = Dekker::from_bit_pair(EXP_REDUCE_T1[i1 as usize]);
let dt = Dekker::mult(t0, t1);
const EXP2_POLY_DD: [(u64, u64); 6] = [
(0x3bbabc9e3b39873e, 0x3f262e42fefa39ef),
(0xbae5e43a53e44950, 0x3e4ebfbdff82c58f),
(0xba0d3a15710d3d83, 0x3d6c6b08d704a0c0),
(0x3914dd5d2a5e025a, 0x3c83b2ab6fba4e77),
(0xb83dc47e47beb9dd, 0x3b95d87fe7a66459),
(0xb744fcd51fcb7640, 0x3aa430912f9fb79d),
];
let mut f = poly_xd_generic(z, EXP2_POLY_DD);
f = Dekker::f64_mult(z, f);
if ix <= 0xc08ff00000000000u64 {
// x >= -1022
// for -0x1.71547652b82fep-54 <= x <= 0x1.71547652b82fdp-53,
// exp2(x) round to x to nearest
if f64::from_bits(0xbc971547652b82fe) <= x && x <= f64::from_bits(0x3ca71547652b82fd) {
return f_fmla(x, 0.5, 1.0);
} else if (k & 0xfff) == 0 {
// 4096*x rounds to 4096*integer
let zf = Dekker::from_exact_add(dt.hi, f.hi);
let zfl = Dekker::from_exact_add(zf.lo, f.lo);
f.hi = zf.hi;
f.lo = zfl.hi;
ix = zfl.hi.to_bits();
if ix & 0x000fffffffffffff == 0 {
// fl is a power of 2
if ((ix >> 52) & 0x7ff) != 0 {
// |fl| is Inf
let v = zfl.lo.to_bits();
let d: i64 = ((((ix as i64) >> 63) ^ ((v as i64) >> 63)) as u64)
.wrapping_shl(1)
.wrapping_add(1) as i64;
ix = ix.wrapping_add(d as u64);
f.lo = f64::from_bits(ix);
}
}
} else {
f = Dekker::mult(f, dt);
f = Dekker::add(dt, f);
}
let hf = Dekker::from_exact_add(f.hi, f.lo);
ldexp(hf.hi, ie as u64)
} else {
ix = 1u64.wrapping_sub(ie as u64).wrapping_shl(52);
f = Dekker::mult(f, dt);
f = Dekker::add(dt, f);
let zve = Dekker::from_exact_add(f64::from_bits(ix), f.hi);
f.hi = zve.hi;
f.lo += zve.lo;
to_denormal(f.to_f64())
}
}
/// Computes exp2
///
/// Max found ULP 0.5015
#[inline]
pub fn f_exp2(x: f64) -> f64 {
let mut ix = x.to_bits();
let ax = ix.wrapping_shl(1);
if ax == 0 {
return 1.0;
}
if ax >= 0x8120000000000000u64 {
// |x| >= 1024
if ax > 0xffe0000000000000u64 {
return x + x; // nan
}
if ax == 0xffe0000000000000u64 {
return if (ix >> 63) != 0 { 0.0 } else { x };
}
// +/-inf
if (ix >> 63) != 0 {
// x <= -1024
if ix >= 0xc090cc0000000000u64 {
// x <= -1075
const Z: f64 = f64::from_bits(0x0010000000000000);
return Z * Z;
}
} else {
// x >= 1024
return f64::from_bits(0x7fe0000000000000) * x;
}
}
// for |x| <= 0x1.71547652b82fep-54, 2^x rounds to 1 to nearest
// this avoids a spurious underflow in z*z below
if ax <= 0x792e2a8eca5705fcu64 {
return 1.0 + f64::copysign(f64::from_bits(0x3c90000000000000), x);
}
let m = ix.wrapping_shl(12);
let ex = (ax >> 53).wrapping_sub(0x3ff);
let frac = ex >> 63 | m << (ex & 63);
let sx = 4096.0 * x;
let fx = sx.round_ties_even();
let z = sx - fx;
let z2 = z * z;
let k = fx as i64;
let i1 = k & 0x3f;
let i0 = (k >> 6) & 0x3f;
let ie = k >> 12;
let t00 = EXP_REDUCE_T0[i0 as usize];
let t01 = EXP_REDUCE_T1[i1 as usize];
let t0 = Dekker::new(f64::from_bits(t00.0), f64::from_bits(t00.1));
let t1 = Dekker::new(f64::from_bits(t01.0), f64::from_bits(t01.1));
let ti0 = Dekker::quick_mult(t0, t1);
const C: [u64; 4] = [
0x3f262e42fefa39ef,
0x3e4ebfbdff82c58f,
0x3d6c6b08d73b3e01,
0x3c83b2ab6fdda001,
];
let tz = ti0.hi * z;
let mut fh = ti0.hi;
let p0 = f_fmla(z, f64::from_bits(C[1]), f64::from_bits(C[0]));
let p1 = f_fmla(z, f64::from_bits(C[3]), f64::from_bits(C[2]));
let p2 = f_fmla(z2, p1, p0);
let mut fl = f_fmla(tz, p2, ti0.lo);
const EPS: f64 = f64::from_bits(0x3c0833beace2b6fe);
if ix <= 0xc08ff00000000000u64 {
// x >= -1022
if frac != 0 {
let ub = fh + (fl + EPS);
fh += fl - EPS;
if ub != fh {
return exp2_accurate(x);
}
}
fh = ldexp(fh, ie as u64);
} else {
// subnormal case
ix = 1u64.wrapping_sub(ie as u64).wrapping_shl(52);
let rs = Dekker::from_exact_add(f64::from_bits(ix), fh);
fl += rs.lo;
fh = rs.hi;
if frac != 0 {
let ub = fh + (fl + EPS);
fh += fl - EPS;
if ub != fh {
return exp2_accurate(x);
}
}
// when 2^x is exact, no underflow should be raised
fh = to_denormal(fh);
}
fh
}
#[cfg(test)]
mod tests {
use super::*;
#[test]
fn test_exp2d() {
println!("{}", (-144.0000000002624f64).exp2());
println!("{}", f_exp2(-144.0000000002624));
// assert_eq!(f_exp2(2.0), 4.0);
// assert_eq!(f_exp2(3.0), 8.0);
// assert_eq!(f_exp2(4.0), 16.0);
// assert!((f_exp2(0.35f64) - 0.35f64.exp2()).abs() < 1e-8);
// assert!((f_exp2(-0.6f64) - (-0.6f64).exp2()).abs() < 1e-8);
}
}