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/*
* Single-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_f32.h"
#include "pl_sig.h"
#include "pl_test.h"
static const struct data
{
float32x4_t poly[6];
float32x4_t range_val;
} data = {
/* Taylor series coefficents for sin(pi * x). */
.poly = { V4 (0x1.921fb6p1f), V4 (-0x1.4abbcep2f), V4 (0x1.466bc6p1f),
V4 (-0x1.32d2ccp-1f), V4 (0x1.50783p-4f), V4 (-0x1.e30750p-8f) },
.range_val = V4 (0x1p31f),
};
static float32x4_t VPCS_ATTR NOINLINE
special_case (float32x4_t x, float32x4_t y, uint32x4_t odd, uint32x4_t cmp)
{
y = vreinterpretq_f32_u32 (veorq_u32 (vreinterpretq_u32_f32 (y), odd));
return v_call_f32 (cospif, x, y, cmp);
}
/* Approximation for vector single-precision cospi(x)
Maximum Error: 3.17 ULP:
_ZGVnN4v_cospif(0x1.d341a8p-5) got 0x1.f7cd56p-1
want 0x1.f7cd5p-1. */
float32x4_t VPCS_ATTR V_NAME_F1 (cospi) (float32x4_t x)
{
const struct data *d = ptr_barrier (&data);
#if WANT_SIMD_EXCEPT
float32x4_t r = vabsq_f32 (x);
uint32x4_t cmp = vcaleq_f32 (v_f32 (0x1p32f), x);
/* When WANT_SIMD_EXCEPT = 1, special lanes should be zero'd
to avoid them overflowing and throwing exceptions. */
r = v_zerofy_f32 (r, cmp);
uint32x4_t odd = vshlq_n_u32 (vcvtnq_u32_f32 (r), 31);
#else
float32x4_t r = x;
uint32x4_t cmp = vcageq_f32 (r, d->range_val);
uint32x4_t odd
= vshlq_n_u32 (vreinterpretq_u32_s32 (vcvtaq_s32_f32 (r)), 31);
#endif
/* r = x - rint(x). */
r = vsubq_f32 (r, vrndaq_f32 (r));
/* cospi(x) = sinpi(0.5 - abs(x)) for values -1/2 .. 1/2. */
r = vsubq_f32 (v_f32 (0.5f), vabsq_f32 (r));
/* Pairwise Horner approximation for y = sin(r * pi). */
float32x4_t r2 = vmulq_f32 (r, r);
float32x4_t r4 = vmulq_f32 (r2, r2);
float32x4_t y = vmulq_f32 (v_pw_horner_5_f32 (r2, r4, d->poly), r);
/* Fallback to scalar. */
if (unlikely (v_any_u32 (cmp)))
return special_case (x, y, odd, cmp);
/* Reintroduce the sign bit for inputs which round to odd. */
return vreinterpretq_f32_u32 (veorq_u32 (vreinterpretq_u32_f32 (y), odd));
}
PL_SIG (V, F, 1, cospi, -0.9, 0.9)
PL_TEST_ULP (V_NAME_F1 (cospi), 2.67)
PL_TEST_EXPECT_FENV (V_NAME_F1 (cospi), WANT_SIMD_EXCEPT)
PL_TEST_SYM_INTERVAL (V_NAME_F1 (cospi), 0, 0x1p-31, 5000)
PL_TEST_SYM_INTERVAL (V_NAME_F1 (cospi), 0x1p-31, 0.5, 10000)
PL_TEST_SYM_INTERVAL (V_NAME_F1 (cospi), 0.5, 0x1p32f, 10000)
PL_TEST_SYM_INTERVAL (V_NAME_F1 (cospi), 0x1p32f, inf, 10000)
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