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/*
* Double-precision vector cospi function.
*
* Copyright (c) 2023, Arm Limited.
* SPDX-License-Identifier: MIT OR Apache-2.0 WITH LLVM-exception
*/
#include "mathlib.h"
#include "v_math.h"
#include "poly_advsimd_f64.h"
#include "pl_sig.h"
#include "pl_test.h"
static const struct data
{
float64x2_t poly[10];
float64x2_t range_val;
} data = {
/* Polynomial coefficients generated using Remez algorithm,
see sinpi.sollya for details. */
.poly = { V2 (0x1.921fb54442d184p1), V2 (-0x1.4abbce625be53p2),
V2 (0x1.466bc6775ab16p1), V2 (-0x1.32d2cce62dc33p-1),
V2 (0x1.507834891188ep-4), V2 (-0x1.e30750a28c88ep-8),
V2 (0x1.e8f48308acda4p-12), V2 (-0x1.6fc0032b3c29fp-16),
V2 (0x1.af86ae521260bp-21), V2 (-0x1.012a9870eeb7dp-25) },
.range_val = V2 (0x1p63),
};
static float64x2_t VPCS_ATTR NOINLINE
special_case (float64x2_t x, float64x2_t y, uint64x2_t odd, uint64x2_t cmp)
{
/* Fall back to scalar code. */
y = vreinterpretq_f64_u64 (veorq_u64 (vreinterpretq_u64_f64 (y), odd));
return v_call_f64 (cospi, x, y, cmp);
}
/* Approximation for vector double-precision cospi(x).
Maximum Error 3.06 ULP:
_ZGVnN2v_cospi(0x1.7dd4c0b03cc66p-5) got 0x1.fa854babfb6bep-1
want 0x1.fa854babfb6c1p-1. */
float64x2_t VPCS_ATTR V_NAME_D1 (cospi) (float64x2_t x)
{
const struct data *d = ptr_barrier (&data);
#if WANT_SIMD_EXCEPT
float64x2_t r = vabsq_f64 (x);
uint64x2_t cmp = vcaleq_f64 (v_f64 (0x1p64), x);
/* When WANT_SIMD_EXCEPT = 1, special lanes should be zero'd
to avoid them overflowing and throwing exceptions. */
r = v_zerofy_f64 (r, cmp);
uint64x2_t odd = vshlq_n_u64 (vcvtnq_u64_f64 (r), 63);
#else
float64x2_t r = x;
uint64x2_t cmp = vcageq_f64 (r, d->range_val);
uint64x2_t odd
= vshlq_n_u64 (vreinterpretq_u64_s64 (vcvtaq_s64_f64 (r)), 63);
#endif
r = vsubq_f64 (r, vrndaq_f64 (r));
/* cospi(x) = sinpi(0.5 - abs(x)) for values -1/2 .. 1/2. */
r = vsubq_f64 (v_f64 (0.5), vabsq_f64 (r));
/* y = sin(r). */
float64x2_t r2 = vmulq_f64 (r, r);
float64x2_t r4 = vmulq_f64 (r2, r2);
float64x2_t y = vmulq_f64 (v_pw_horner_9_f64 (r2, r4, d->poly), r);
/* Fallback to scalar. */
if (unlikely (v_any_u64 (cmp)))
return special_case (x, y, odd, cmp);
/* Reintroduce the sign bit for inputs which round to odd. */
return vreinterpretq_f64_u64 (veorq_u64 (vreinterpretq_u64_f64 (y), odd));
}
PL_SIG (V, D, 1, cospi, -0.9, 0.9)
PL_TEST_ULP (V_NAME_D1 (cospi), 2.56)
PL_TEST_EXPECT_FENV (V_NAME_D1 (cospi), WANT_SIMD_EXCEPT)
PL_TEST_SYM_INTERVAL (V_NAME_D1 (cospi), 0, 0x1p-63, 5000)
PL_TEST_SYM_INTERVAL (V_NAME_D1 (cospi), 0x1p-63, 0.5, 10000)
PL_TEST_SYM_INTERVAL (V_NAME_D1 (cospi), 0.5, 0x1p51, 10000)
PL_TEST_SYM_INTERVAL (V_NAME_D1 (cospi), 0x1p51, inf, 10000)
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