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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 OFF: [f32; 8] = [0.0, 0.5, 1.0, 0.5, -0.0, -0.5, -1.0, -0.5];
static SGNF: [f32; 2] = [1., -1.];
static SGN: [f64; 2] = [1., -1.];
/// Computes atan(x/y) / PI
///
/// Max found ULP 0.5
#[inline]
pub fn f_atan2pif(y: f32, x: f32) -> f32 {
let tx = x.to_bits();
let ty: u32 = y.to_bits();
let ux: u32 = tx;
let uy: u32 = ty;
let ax: u32 = ux & 0x7fff_ffff;
let ay = uy & 0x7fff_ffff;
if ay >= (0xff << 23) || ax >= (0xff << 23) {
if ay > (0xff << 23) {
return x + y;
} // nan
if ax > (0xff << 23) {
return x + y;
} // nan
let yinf = ay == (0xff << 23);
let xinf = ax == (0xff << 23);
if yinf & xinf {
return if (ux >> 31) != 0 {
0.75 * SGNF[(uy >> 31) as usize]
} else {
0.25 * SGNF[(uy >> 31) as usize]
};
}
if xinf {
return if (ux >> 31) != 0 {
SGNF[(uy >> 31) as usize]
} else {
0.0 * SGNF[(uy >> 31) as usize]
};
}
if yinf {
return 0.5 * SGNF[(uy >> 31) as usize];
}
}
if ay == 0 {
if (ay | ax) == 0 {
let i: u32 = (uy >> 31) * 4 + (ux >> 31) * 2;
return OFF[i as usize];
}
if (ux >> 31) == 0 {
return 0.0 * SGNF[(uy >> 31) as usize];
}
}
if ax == ay {
static S: [f32; 4] = [0.25, 0.75, -0.25, -0.75];
let i = (uy >> 31) * 2 + (ux >> 31);
return S[i as usize];
}
let gt: usize = if ay > ax { 1 } else { 0 };
let i: u32 = (uy >> 31) * 4 + (ux >> 31) * 2 + gt as u32;
let zx = x as f64;
let zy = y as f64;
static M: [f64; 2] = [0., 1.];
let mut z = f_fmla(M[gt], zx, M[1 - gt] * zy) / f_fmla(M[gt], zy, M[1 - gt] * zx);
const CN: [u64; 7] = [
0x3fd45f306dc9c883,
0x3fe988d83a142ada,
0x3fe747bebf492057,
0x3fd2cc5645094ff3,
0x3faa0521c711ab66,
0x3f6881b8058b9a0d,
0x3efb16ff514a0af0,
];
let mut r = f64::from_bits(CN[0]);
let z2 = z * z;
z *= SGN[gt];
// avoid spurious underflow in the polynomial evaluation excluding tiny arguments
if z2 > f64::from_bits(0x3c90000000000000) {
let z4 = z2 * z2;
let z8 = z4 * z4;
let mut cn0 = f_fmla(z2, f64::from_bits(CN[1]), r);
let cn2 = f_fmla(z2, f64::from_bits(CN[3]), f64::from_bits(CN[2]));
let mut cn4 = f_fmla(z2, f64::from_bits(CN[5]), f64::from_bits(CN[4]));
let cn6 = f64::from_bits(CN[6]);
cn0 += z4 * cn2;
cn4 += z4 * cn6;
cn0 += z8 * cn4;
const CD: [u64; 7] = [
0x3ff0000000000000,
0x4006b8b143a3f6da,
0x4008421201d18ed5,
0x3ff8221d086914eb,
0x3fd670657e3a07ba,
0x3fa0f4951fd1e72d,
0x3f4b3874b8798286,
];
let mut cd0 = f_fmla(z2, f64::from_bits(CD[1]), f64::from_bits(CD[0]));
let cd2 = f_fmla(z2, f64::from_bits(CD[3]), f64::from_bits(CD[2]));
let mut cd4 = f_fmla(z2, f64::from_bits(CD[5]), f64::from_bits(CD[4]));
let cd6 = f64::from_bits(CD[6]);
cd0 += z4 * cd2;
cd4 += z4 * cd6;
cd0 += z8 * cd4;
r = cn0 / cd0;
}
f_fmla(z, r, OFF[i as usize] as f64) as f32
}