mirror of
https://sourceware.org/git/glibc.git
synced 2024-12-11 22:00:08 +00:00
119 lines
4.2 KiB
C
119 lines
4.2 KiB
C
/* Single-precision vector (SVE) tan function
|
|
|
|
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"
|
|
|
|
static const struct data
|
|
{
|
|
float pio2_1, pio2_2, pio2_3, invpio2;
|
|
float c1, c3, c5;
|
|
float c0, c2, c4, range_val, shift;
|
|
} data = {
|
|
/* Coefficients generated using:
|
|
poly = fpminimax((tan(sqrt(x))-sqrt(x))/x^(3/2),
|
|
deg,
|
|
[|single ...|],
|
|
[a*a;b*b]);
|
|
optimize relative error
|
|
final prec : 23 bits
|
|
deg : 5
|
|
a : 0x1p-126 ^ 2
|
|
b : ((pi) / 0x1p2) ^ 2
|
|
dirty rel error: 0x1.f7c2e4p-25
|
|
dirty abs error: 0x1.f7c2ecp-25. */
|
|
.c0 = 0x1.55555p-2, .c1 = 0x1.11166p-3,
|
|
.c2 = 0x1.b88a78p-5, .c3 = 0x1.7b5756p-6,
|
|
.c4 = 0x1.4ef4cep-8, .c5 = 0x1.0e1e74p-7,
|
|
|
|
.pio2_1 = 0x1.921fb6p+0f, .pio2_2 = -0x1.777a5cp-25f,
|
|
.pio2_3 = -0x1.ee59dap-50f, .invpio2 = 0x1.45f306p-1f,
|
|
.range_val = 0x1p15f, .shift = 0x1.8p+23f
|
|
};
|
|
|
|
static svfloat32_t NOINLINE
|
|
special_case (svfloat32_t x, svfloat32_t y, svbool_t cmp)
|
|
{
|
|
return sv_call_f32 (tanf, x, y, cmp);
|
|
}
|
|
|
|
/* Fast implementation of SVE tanf.
|
|
Maximum error is 3.45 ULP:
|
|
SV_NAME_F1 (tan)(-0x1.e5f0cap+13) got 0x1.ff9856p-1
|
|
want 0x1.ff9850p-1. */
|
|
svfloat32_t SV_NAME_F1 (tan) (svfloat32_t x, const svbool_t pg)
|
|
{
|
|
const struct data *d = ptr_barrier (&data);
|
|
|
|
/* Determine whether input is too large to perform fast regression. */
|
|
svbool_t cmp = svacge (pg, x, d->range_val);
|
|
|
|
svfloat32_t odd_coeffs = svld1rq (svptrue_b32 (), &d->c1);
|
|
svfloat32_t pi_vals = svld1rq (svptrue_b32 (), &d->pio2_1);
|
|
|
|
/* n = rint(x/(pi/2)). */
|
|
svfloat32_t q = svmla_lane (sv_f32 (d->shift), x, pi_vals, 3);
|
|
svfloat32_t n = svsub_x (pg, q, d->shift);
|
|
/* n is already a signed integer, simply convert it. */
|
|
svint32_t in = svcvt_s32_x (pg, n);
|
|
/* Determine if x lives in an interval, where |tan(x)| grows to infinity. */
|
|
svint32_t alt = svand_x (pg, in, 1);
|
|
svbool_t pred_alt = svcmpne (pg, alt, 0);
|
|
|
|
/* r = x - n * (pi/2) (range reduction into 0 .. pi/4). */
|
|
svfloat32_t r;
|
|
r = svmls_lane (x, n, pi_vals, 0);
|
|
r = svmls_lane (r, n, pi_vals, 1);
|
|
r = svmls_lane (r, n, pi_vals, 2);
|
|
|
|
/* If x lives in an interval, where |tan(x)|
|
|
- is finite, then use a polynomial approximation of the form
|
|
tan(r) ~ r + r^3 * P(r^2) = r + r * r^2 * P(r^2).
|
|
- grows to infinity then use symmetries of tangent and the identity
|
|
tan(r) = cotan(pi/2 - r) to express tan(x) as 1/tan(-r). Finally, use
|
|
the same polynomial approximation of tan as above. */
|
|
|
|
/* Perform additional reduction if required. */
|
|
svfloat32_t z = svneg_m (r, pred_alt, r);
|
|
|
|
/* Evaluate polynomial approximation of tangent on [-pi/4, pi/4],
|
|
using Estrin on z^2. */
|
|
svfloat32_t z2 = svmul_x (pg, z, z);
|
|
svfloat32_t p01 = svmla_lane (sv_f32 (d->c0), z2, odd_coeffs, 0);
|
|
svfloat32_t p23 = svmla_lane (sv_f32 (d->c2), z2, odd_coeffs, 1);
|
|
svfloat32_t p45 = svmla_lane (sv_f32 (d->c4), z2, odd_coeffs, 2);
|
|
|
|
svfloat32_t z4 = svmul_x (pg, z2, z2);
|
|
svfloat32_t p = svmla_x (pg, p01, z4, p23);
|
|
|
|
svfloat32_t z8 = svmul_x (pg, z4, z4);
|
|
p = svmla_x (pg, p, z8, p45);
|
|
|
|
svfloat32_t y = svmla_x (pg, z, p, svmul_x (pg, z, z2));
|
|
|
|
/* Transform result back, if necessary. */
|
|
svfloat32_t inv_y = svdivr_x (pg, y, 1.0f);
|
|
|
|
/* No need to pass pg to specialcase here since cmp is a strict subset,
|
|
guaranteed by the cmpge above. */
|
|
if (__glibc_unlikely (svptest_any (pg, cmp)))
|
|
return special_case (x, svsel (pred_alt, inv_y, y), cmp);
|
|
|
|
return svsel (pred_alt, inv_y, y);
|
|
}
|