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/* Single-precision SVE atan2
Copyright (C) 2023-2024 Free Software Foundation, Inc.
This file is part of the GNU C Library.
The GNU C Library is free software; you can redistribute it and/or
modify it under the terms of the GNU Lesser General Public
License as published by the Free Software Foundation; either
version 2.1 of the License, or (at your option) any later version.
The GNU C Library is distributed in the hope that it will be useful,
but WITHOUT ANY WARRANTY; without even the implied warranty of
MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the GNU
Lesser General Public License for more details.
You should have received a copy of the GNU Lesser General Public
License along with the GNU C Library; if not, see
<https://www.gnu.org/licenses/>. */
#include "sv_math.h"
#include "poly_sve_f32.h"
static const struct data
{
float32_t poly[8];
float32_t pi_over_2;
} data = {
/* Coefficients of polynomial P such that atan(x)~x+x*P(x^2) on
[2**-128, 1.0]. */
.poly = { -0x1.55555p-2f, 0x1.99935ep-3f, -0x1.24051ep-3f, 0x1.bd7368p-4f,
-0x1.491f0ep-4f, 0x1.93a2c0p-5f, -0x1.4c3c60p-6f, 0x1.01fd88p-8f },
.pi_over_2 = 0x1.921fb6p+0f,
};
/* Special cases i.e. 0, infinity, nan (fall back to scalar calls). */
static svfloat32_t NOINLINE
special_case (svfloat32_t y, svfloat32_t x, svfloat32_t ret,
const svbool_t cmp)
{
return sv_call2_f32 (atan2f, y, x, ret, cmp);
}
/* Returns a predicate indicating true if the input is the bit representation
of 0, infinity or nan. */
static inline svbool_t
zeroinfnan (svuint32_t i, const svbool_t pg)
{
return svcmpge (pg, svsub_x (pg, svlsl_x (pg, i, 1), 1),
sv_u32 (2 * 0x7f800000lu - 1));
}
/* Fast implementation of SVE atan2f based on atan(x) ~ shift + z + z^3 *
P(z^2) with reduction to [0,1] using z=1/x and shift = pi/2. Maximum
observed error is 2.95 ULP:
_ZGVsMxvv_atan2f (0x1.93836cp+6, 0x1.8cae1p+6) got 0x1.967f06p-1
want 0x1.967f00p-1. */
svfloat32_t SV_NAME_F2 (atan2) (svfloat32_t y, svfloat32_t x, const svbool_t pg)
{
const struct data *data_ptr = ptr_barrier (&data);
svuint32_t ix = svreinterpret_u32 (x);
svuint32_t iy = svreinterpret_u32 (y);
svbool_t cmp_x = zeroinfnan (ix, pg);
svbool_t cmp_y = zeroinfnan (iy, pg);
svbool_t cmp_xy = svorr_z (pg, cmp_x, cmp_y);
svfloat32_t ax = svabs_x (pg, x);
svfloat32_t ay = svabs_x (pg, y);
svuint32_t iax = svreinterpret_u32 (ax);
svuint32_t iay = svreinterpret_u32 (ay);
svuint32_t sign_x = sveor_x (pg, ix, iax);
svuint32_t sign_y = sveor_x (pg, iy, iay);
svuint32_t sign_xy = sveor_x (pg, sign_x, sign_y);
svbool_t pred_aygtax = svcmpgt (pg, ay, ax);
/* Set up z for call to atan. */
svfloat32_t n = svsel (pred_aygtax, svneg_x (pg, ax), ay);
svfloat32_t d = svsel (pred_aygtax, ay, ax);
svfloat32_t z = svdiv_x (pg, n, d);
/* Work out the correct shift. */
svfloat32_t shift = svreinterpret_f32 (svlsr_x (pg, sign_x, 1));
shift = svsel (pred_aygtax, sv_f32 (1.0), shift);
shift = svreinterpret_f32 (svorr_x (pg, sign_x, svreinterpret_u32 (shift)));
shift = svmul_x (pg, shift, sv_f32 (data_ptr->pi_over_2));
/* Use pure Estrin scheme for P(z^2) with deg(P)=7. */
svfloat32_t z2 = svmul_x (pg, z, z);
svfloat32_t z4 = svmul_x (pg, z2, z2);
svfloat32_t z8 = svmul_x (pg, z4, z4);
svfloat32_t ret = sv_estrin_7_f32_x (pg, z2, z4, z8, data_ptr->poly);
/* ret = shift + z + z^3 * P(z^2). */
svfloat32_t z3 = svmul_x (pg, z2, z);
ret = svmla_x (pg, z, z3, ret);
ret = svadd_m (pg, ret, shift);
/* Account for the sign of x and y. */
if (__glibc_unlikely (svptest_any (pg, cmp_xy)))
return special_case (
y, x,
svreinterpret_f32 (sveor_x (pg, svreinterpret_u32 (ret), sign_xy)),
cmp_xy);
return svreinterpret_f32 (sveor_x (pg, svreinterpret_u32 (ret), sign_xy));
}
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