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/*
* Single-precision vector atan(x) function.
*
* Copyright (c) 2021-2024, Arm Limited.
* SPDX-License-Identifier: MIT OR Apache-2.0 WITH LLVM-exception
*/
#include "sv_math.h"
#include "test_sig.h"
#include "test_defs.h"
#include "sv_poly_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));
}
TEST_SIG (SV, F, 1, atan, -3.1, 3.1)
TEST_ULP (SV_NAME_F1 (atan), 2.9)
TEST_DISABLE_FENV (SV_NAME_F1 (atan))
TEST_INTERVAL (SV_NAME_F1 (atan), 0.0, 1.0, 40000)
TEST_INTERVAL (SV_NAME_F1 (atan), 1.0, 100.0, 40000)
TEST_INTERVAL (SV_NAME_F1 (atan), 100, inf, 40000)
TEST_INTERVAL (SV_NAME_F1 (atan), -0, -inf, 40000)
CLOSE_SVE_ATTR
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