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/*
* Core approximation for double-precision vector sincos
*
* Copyright (c) 2023, Arm Limited.
* SPDX-License-Identifier: MIT OR Apache-2.0 WITH LLVM-exception
*/
#include "sv_math.h"
#include "poly_sve_f64.h"
static const struct sv_sincos_data
{
double sin_poly[7], cos_poly[6], pio2[3];
double inv_pio2, shift, range_val;
} sv_sincos_data = {
.inv_pio2 = 0x1.45f306dc9c882p-1,
.pio2 = { 0x1.921fb50000000p+0, 0x1.110b460000000p-26,
0x1.1a62633145c07p-54 },
.shift = 0x1.8p52,
.sin_poly = { /* Computed using Remez in [-pi/2, pi/2]. */
-0x1.555555555547bp-3, 0x1.1111111108a4dp-7,
-0x1.a01a019936f27p-13, 0x1.71de37a97d93ep-19,
-0x1.ae633919987c6p-26, 0x1.60e277ae07cecp-33,
-0x1.9e9540300a1p-41 },
.cos_poly = { /* Computed using Remez in [-pi/4, pi/4]. */
0x1.555555555554cp-5, -0x1.6c16c16c1521fp-10,
0x1.a01a019cbf62ap-16, -0x1.27e4f812b681ep-22,
0x1.1ee9f152a57cdp-29, -0x1.8fb131098404bp-37 },
.range_val = 0x1p23, };
static inline svbool_t
check_ge_rangeval (svbool_t pg, svfloat64_t x, const struct sv_sincos_data *d)
{
svbool_t in_bounds = svaclt (pg, x, d->range_val);
return svnot_z (pg, in_bounds);
}
/* Double-precision vector function allowing calculation of both sin and cos in
one function call, using shared argument reduction and separate polynomials.
Largest observed error is for sin, 3.22 ULP:
v_sincos_sin (0x1.d70eef40f39b1p+12) got -0x1.ffe9537d5dbb7p-3
want -0x1.ffe9537d5dbb4p-3. */
static inline svfloat64x2_t
sv_sincos_inline (svbool_t pg, svfloat64_t x, const struct sv_sincos_data *d)
{
/* q = nearest integer to 2 * x / pi. */
svfloat64_t q = svsub_x (pg, svmla_x (pg, sv_f64 (d->shift), x, d->inv_pio2),
d->shift);
svint64_t n = svcvt_s64_x (pg, q);
/* Reduce x such that r is in [ -pi/4, pi/4 ]. */
svfloat64_t r = x;
r = svmls_x (pg, r, q, d->pio2[0]);
r = svmls_x (pg, r, q, d->pio2[1]);
r = svmls_x (pg, r, q, d->pio2[2]);
svfloat64_t r2 = svmul_x (pg, r, r), r3 = svmul_x (pg, r2, r),
r4 = svmul_x (pg, r2, r2);
/* Approximate sin(r) ~= r + r^3 * poly_sin(r^2). */
svfloat64_t s = sv_pw_horner_6_f64_x (pg, r2, r4, d->sin_poly);
s = svmla_x (pg, r, r3, s);
/* Approximate cos(r) ~= 1 - (r^2)/2 + r^4 * poly_cos(r^2). */
svfloat64_t c = sv_pw_horner_5_f64_x (pg, r2, r4, d->cos_poly);
c = svmad_x (pg, c, r2, -0.5);
c = svmad_x (pg, c, r2, 1);
svuint64_t un = svreinterpret_u64 (n);
/* If odd quadrant, swap cos and sin. */
svbool_t swap = svcmpeq (pg, svlsl_x (pg, un, 63), 0);
svfloat64_t ss = svsel (swap, s, c);
svfloat64_t cc = svsel (swap, c, s);
/* Fix signs according to quadrant.
ss = asdouble(asuint64(ss) ^ ((n & 2) << 62))
cc = asdouble(asuint64(cc) & (((n + 1) & 2) << 62)). */
svuint64_t sin_sign = svlsl_x (pg, svand_x (pg, un, 2), 62);
svuint64_t cos_sign = svlsl_x (
pg, svand_x (pg, svreinterpret_u64 (svadd_x (pg, n, 1)), 2), 62);
ss = svreinterpret_f64 (sveor_x (pg, svreinterpret_u64 (ss), sin_sign));
cc = svreinterpret_f64 (sveor_x (pg, svreinterpret_u64 (cc), cos_sign));
return svcreate2 (ss, cc);
}
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