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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, min_normal_f64};
use crate::dekker::Dekker;
use crate::sin::{
LargeArgumentReduction, SIN_K_PI_OVER_128, get_sin_k_rational, range_reduction_small,
sincos_eval,
};
use crate::sincos_dyadic::{range_reduction_small_f128, sincos_eval_dyadic};
/// Sine and cosine for double precision
///
/// ULP 0.5005
#[inline]
pub fn f_sincos(x: f64) -> (f64, f64) {
let x_e = (x.to_bits() >> 52) & 0x7ff;
const E_BIAS: u64 = (1u64 << (11 - 1u64)) - 1u64;
let y: Dekker;
let k;
let mut argument_reduction = LargeArgumentReduction::default();
// |x| < 2^32 (with FMA) or |x| < 2^23 (w/o FMA)
if x_e < E_BIAS + 16 {
// |x| < 2^-26
if x_e < E_BIAS - 7 {
if x_e < E_BIAS - 27 {
// Signed zeros.
if x == 0.0 {
return (x, 1.0);
}
// For |x| < 2^-26, |sin(x) - x| < ulp(x)/2.
let s_sin = f_fmla(x, f64::from_bits(0xbc90000000000000), x);
let s_cos = 1.0 - min_normal_f64();
return (s_sin, s_cos);
}
k = 0;
y = Dekker::new(0.0, x);
} else {
// // Small range reduction.
(y, k) = range_reduction_small(x);
}
} else {
// Inf or NaN
if x_e > 2 * E_BIAS {
// sin(+-Inf) = NaN
return (x + f64::NAN, x + f64::NAN);
}
// Large range reduction.
(k, y) = argument_reduction.reduce_new(x);
}
let r_sincos = sincos_eval(y);
let (sin_y, cos_y) = (r_sincos.v_sin, r_sincos.v_cos);
// Fast look up version, but needs 256-entry table.
// cos(k * pi/128) = sin(k * pi/128 + pi/2) = sin((k + 64) * pi/128).
let sk = SIN_K_PI_OVER_128[(k & 255) as usize];
let ck = SIN_K_PI_OVER_128[((k.wrapping_add(64)) & 255) as usize];
let sin_k = Dekker::new(f64::from_bits(sk.0), f64::from_bits(sk.1));
let cos_k = Dekker::new(f64::from_bits(ck.0), f64::from_bits(ck.1));
let msin_k = Dekker::new(-sin_k.lo, -sin_k.hi);
// After range reduction, k = round(x * 128 / pi) and y = x - k * (pi / 128).
// So k is an integer and -pi / 256 <= y <= pi / 256.
// Then sin(x) = sin((k * pi/128 + y)
// = sin(y) * cos(k*pi/128) + cos(y) * sin(k*pi/128)
let sin_k_cos_y = Dekker::quick_mult(cos_y, sin_k);
let cos_k_sin_y = Dekker::quick_mult(sin_y, cos_k);
// cos(x) = cos((k * pi/128 + y)
// = cos(y) * cos(k*pi/128) - sin(y) * sin(k*pi/128)
let cos_k_cos_y = Dekker::quick_mult(cos_y, cos_k);
let msin_k_sin_y = Dekker::quick_mult(sin_y, msin_k);
let mut sin_dd = Dekker::from_full_exact_add(sin_k_cos_y.hi, cos_k_sin_y.hi);
let mut cos_dd = Dekker::from_full_exact_add(cos_k_cos_y.hi, msin_k_sin_y.hi);
sin_dd.lo += sin_k_cos_y.lo + cos_k_sin_y.lo;
cos_dd.lo += msin_k_sin_y.lo + cos_k_cos_y.lo;
let sin_lp = sin_dd.lo + r_sincos.err;
let sin_lm = sin_dd.lo - r_sincos.err;
let cos_lp = cos_dd.lo + r_sincos.err;
let cos_lm = cos_dd.lo - r_sincos.err;
let sin_upper = sin_dd.hi + sin_lp;
let sin_lower = sin_dd.hi + sin_lm;
let cos_upper = cos_dd.hi + cos_lp;
let cos_lower = cos_dd.hi + cos_lm;
// Ziv's rounding test.
if sin_upper == sin_lower && cos_upper == cos_lower {
return (sin_upper, cos_upper);
}
let u_f128 = if x_e < E_BIAS + 16 {
range_reduction_small_f128(x)
} else {
argument_reduction.accurate()
};
let r_sincos = sincos_eval_dyadic(&u_f128);
// cos(k * pi/128) = sin(k * pi/128 + pi/2) = sin((k + 64) * pi/128).
let sin_k_f128 = get_sin_k_rational(k);
let cos_k_f128 = get_sin_k_rational(k.wrapping_add(64));
let msin_k_f128 = get_sin_k_rational(k.wrapping_add(128));
let sin_x = if sin_upper == sin_lower {
sin_upper
} else {
// sin(x) = sin((k * pi/128 + u)
// = sin(u) * cos(k*pi/128) + cos(u) * sin(k*pi/128)
((sin_k_f128 * r_sincos.v_cos) + (cos_k_f128 * r_sincos.v_sin)).fast_as_f64()
};
let cos_x = if cos_upper == cos_lower {
cos_upper
} else {
// cos(x) = cos((k * pi/128 + u)
// = cos(u) * cos(k*pi/128) - sin(u) * sin(k*pi/128)
((cos_k_f128 * r_sincos.v_cos) + (msin_k_f128 * r_sincos.v_sin)).fast_as_f64()
};
(sin_x, cos_x)
}
#[cfg(test)]
mod tests {
use super::*;
#[test]
fn sincos_test() {
let zx_0 = f_sincos(0.0);
assert_eq!(zx_0.0, 0.0);
assert_eq!(zx_0.1, 1.0);
let zx_1 = f_sincos(1.0);
assert_eq!(zx_1.0, 0.8414709848078965);
assert_eq!(zx_1.1, 0.5403023058681398);
let zx_0_p5 = f_sincos(-0.5);
assert_eq!(zx_0_p5.0, -0.479425538604203);
assert_eq!(zx_0_p5.1, 0.8775825618903728);
}
}