2023-11-03 12:12:21 +00:00
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/* Single-precision SVE inverse tan
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2024-01-01 18:12:26 +00:00
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Copyright (C) 2023-2024 Free Software Foundation, Inc.
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2023-11-03 12:12:21 +00:00
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This file is part of the GNU C Library.
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The GNU C Library is free software; you can redistribute it and/or
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modify it under the terms of the GNU Lesser General Public
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License as published by the Free Software Foundation; either
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version 2.1 of the License, or (at your option) any later version.
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The GNU C Library is distributed in the hope that it will be useful,
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but WITHOUT ANY WARRANTY; without even the implied warranty of
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MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the GNU
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Lesser General Public License for more details.
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You should have received a copy of the GNU Lesser General Public
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License along with the GNU C Library; if not, see
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<https://www.gnu.org/licenses/>. */
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#include "sv_math.h"
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#include "poly_sve_f32.h"
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static const struct data
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{
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float32_t poly[8];
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float32_t pi_over_2;
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} data = {
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/* Coefficients of polynomial P such that atan(x)~x+x*P(x^2) on
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[2**-128, 1.0]. */
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.poly = { -0x1.55555p-2f, 0x1.99935ep-3f, -0x1.24051ep-3f, 0x1.bd7368p-4f,
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-0x1.491f0ep-4f, 0x1.93a2c0p-5f, -0x1.4c3c60p-6f, 0x1.01fd88p-8f },
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.pi_over_2 = 0x1.921fb6p+0f,
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};
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#define SignMask (0x80000000)
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/* Fast implementation of SVE atanf based on
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atan(x) ~ shift + z + z^3 * P(z^2) with reduction to [0,1] using
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z=-1/x and shift = pi/2.
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Largest observed error is 2.9 ULP, close to +/-1.0:
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_ZGVsMxv_atanf (0x1.0468f6p+0) got -0x1.967f06p-1
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want -0x1.967fp-1. */
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svfloat32_t SV_NAME_F1 (atan) (svfloat32_t x, const svbool_t pg)
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{
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const struct data *d = ptr_barrier (&data);
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/* No need to trigger special case. Small cases, infs and nans
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are supported by our approximation technique. */
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svuint32_t ix = svreinterpret_u32 (x);
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svuint32_t sign = svand_x (pg, ix, SignMask);
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/* Argument reduction:
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y := arctan(x) for x < 1
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y := pi/2 + arctan(-1/x) for x > 1
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Hence, use z=-1/a if x>=1, otherwise z=a. */
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svbool_t red = svacgt (pg, x, 1.0f);
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/* Avoid dependency in abs(x) in division (and comparison). */
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svfloat32_t z = svsel (red, svdiv_x (pg, sv_f32 (1.0f), x), x);
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/* Use absolute value only when needed (odd powers of z). */
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svfloat32_t az = svabs_x (pg, z);
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az = svneg_m (az, red, az);
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/* Use split Estrin scheme for P(z^2) with deg(P)=7. */
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svfloat32_t z2 = svmul_x (pg, z, z);
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svfloat32_t z4 = svmul_x (pg, z2, z2);
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svfloat32_t z8 = svmul_x (pg, z4, z4);
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svfloat32_t y = sv_estrin_7_f32_x (pg, z2, z4, z8, d->poly);
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/* y = shift + z + z^3 * P(z^2). */
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svfloat32_t z3 = svmul_x (pg, z2, az);
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y = svmla_x (pg, az, z3, y);
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/* Apply shift as indicated by 'red' predicate. */
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y = svadd_m (red, y, sv_f32 (d->pi_over_2));
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/* y = atan(x) if x>0, -atan(-x) otherwise. */
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return svreinterpret_f32 (sveor_x (pg, svreinterpret_u32 (y), sign));
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}
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