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/* Single-precision SVE inverse tan
Copyright (C) 2023 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,
};
#define SignMask (0x80000000)
/* Fast implementation of SVE atanf based on
atan(x) ~ shift + z + z^3 * P(z^2) with reduction to [0,1] using
z=-1/x and shift = pi/2.
Largest observed error is 2.9 ULP, close to +/-1.0:
_ZGVsMxv_atanf (0x1.0468f6p+0) got -0x1.967f06p-1
want -0x1.967fp-1. */
svfloat32_t SV_NAME_F1 (atan) (svfloat32_t x, const svbool_t pg)
{
const struct data *d = ptr_barrier (&data);
/* No need to trigger special case. Small cases, infs and nans
are supported by our approximation technique. */
svuint32_t ix = svreinterpret_u32 (x);
svuint32_t sign = svand_x (pg, ix, SignMask);
/* Argument reduction:
y := arctan(x) for x < 1
y := pi/2 + arctan(-1/x) for x > 1
Hence, use z=-1/a if x>=1, otherwise z=a. */
svbool_t red = svacgt (pg, x, 1.0f);
/* Avoid dependency in abs(x) in division (and comparison). */
svfloat32_t z = svsel (red, svdiv_x (pg, sv_f32 (1.0f), x), x);
/* Use absolute value only when needed (odd powers of z). */
svfloat32_t az = svabs_x (pg, z);
az = svneg_m (az, red, az);
/* Use split 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 y = sv_estrin_7_f32_x (pg, z2, z4, z8, d->poly);
/* y = shift + z + z^3 * P(z^2). */
svfloat32_t z3 = svmul_x (pg, z2, az);
y = svmla_x (pg, az, z3, y);
/* Apply shift as indicated by 'red' predicate. */
y = svadd_m (red, y, sv_f32 (d->pi_over_2));
/* y = atan(x) if x>0, -atan(-x) otherwise. */
return svreinterpret_f32 (sveor_x (pg, svreinterpret_u32 (y), sign));
}
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