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/* Single-precision vector (SVE) sin function.
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"
static const struct data
{
float poly[4];
/* Pi-related values to be loaded as one quad-word and used with
svmla_lane_f32. */
float negpi1, negpi2, negpi3, invpi;
float shift;
} data = {
.poly = {
/* Non-zero coefficients from the degree 9 Taylor series expansion of
sin. */
-0x1.555548p-3f, 0x1.110df4p-7f, -0x1.9f42eap-13f, 0x1.5b2e76p-19f
},
.negpi1 = -0x1.921fb6p+1f,
.negpi2 = 0x1.777a5cp-24f,
.negpi3 = 0x1.ee59dap-49f,
.invpi = 0x1.45f306p-2f,
.shift = 0x1.8p+23f
};
#define RangeVal 0x49800000 /* asuint32 (0x1p20f). */
#define C(i) sv_f32 (d->poly[i])
static svfloat32_t NOINLINE
special_case (svfloat32_t x, svfloat32_t y, svbool_t cmp)
{
return sv_call_f32 (sinf, x, y, cmp);
}
/* A fast SVE implementation of sinf.
Maximum error: 1.89 ULPs.
This maximum error is achieved at multiple values in [-2^18, 2^18]
but one example is:
SV_NAME_F1 (sin)(0x1.9247a4p+0) got 0x1.fffff6p-1 want 0x1.fffffap-1. */
svfloat32_t SV_NAME_F1 (sin) (svfloat32_t x, const svbool_t pg)
{
const struct data *d = ptr_barrier (&data);
svfloat32_t ax = svabs_f32_x (pg, x);
svuint32_t sign = sveor_u32_x (pg, svreinterpret_u32_f32 (x),
svreinterpret_u32_f32 (ax));
svbool_t cmp = svcmpge_n_u32 (pg, svreinterpret_u32_f32 (ax), RangeVal);
/* pi_vals are a quad-word of helper values - the first 3 elements contain
-pi in extended precision, the last contains 1 / pi. */
svfloat32_t pi_vals = svld1rq_f32 (svptrue_b32 (), &d->negpi1);
/* n = rint(|x|/pi). */
svfloat32_t n = svmla_lane_f32 (sv_f32 (d->shift), ax, pi_vals, 3);
svuint32_t odd = svlsl_n_u32_x (pg, svreinterpret_u32_f32 (n), 31);
n = svsub_n_f32_x (pg, n, d->shift);
/* r = |x| - n*pi (range reduction into -pi/2 .. pi/2). */
svfloat32_t r;
r = svmla_lane_f32 (ax, n, pi_vals, 0);
r = svmla_lane_f32 (r, n, pi_vals, 1);
r = svmla_lane_f32 (r, n, pi_vals, 2);
/* sin(r) approx using a degree 9 polynomial from the Taylor series
expansion. Note that only the odd terms of this are non-zero. */
svfloat32_t r2 = svmul_f32_x (pg, r, r);
svfloat32_t y;
y = svmla_f32_x (pg, C (2), r2, C (3));
y = svmla_f32_x (pg, C (1), r2, y);
y = svmla_f32_x (pg, C (0), r2, y);
y = svmla_f32_x (pg, r, r, svmul_f32_x (pg, y, r2));
/* sign = y^sign^odd. */
y = svreinterpret_f32_u32 (sveor_u32_x (pg, svreinterpret_u32_f32 (y),
sveor_u32_x (pg, sign, odd)));
if (__glibc_unlikely (svptest_any (pg, cmp)))
return special_case (x, y, cmp);
return y;
}
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