111819Sjulian/* 211819Sjulian * Single-precision SVE asin(x) function. 311819Sjulian * 411819Sjulian * Copyright (c) 2023, Arm Limited. 511819Sjulian * SPDX-License-Identifier: MIT OR Apache-2.0 WITH LLVM-exception 611819Sjulian */ 711819Sjulian 811819Sjulian#include "sv_math.h" 911819Sjulian#include "poly_sve_f32.h" 1011819Sjulian#include "pl_sig.h" 1111819Sjulian#include "pl_test.h" 1211819Sjulian 1311819Sjulianstatic const struct data 1411819Sjulian{ 1511819Sjulian float32_t poly[5]; 1611819Sjulian float32_t pi_over_2f; 1711819Sjulian} data = { 1811819Sjulian /* Polynomial approximation of (asin(sqrt(x)) - sqrt(x)) / (x * sqrt(x)) on 1911819Sjulian [ 0x1p-24 0x1p-2 ] order = 4 rel error: 0x1.00a23bbp-29 . */ 2011819Sjulian .poly = { 0x1.55555ep-3, 0x1.33261ap-4, 0x1.70d7dcp-5, 0x1.b059dp-6, 2111819Sjulian 0x1.3af7d8p-5, }, 2211819Sjulian .pi_over_2f = 0x1.921fb6p+0f, 2311819Sjulian}; 2411819Sjulian 2511819Sjulian/* Single-precision SVE implementation of vector asin(x). 2611819Sjulian 2711819Sjulian For |x| in [0, 0.5], use order 4 polynomial P such that the final 2811819Sjulian approximation is an odd polynomial: asin(x) ~ x + x^3 P(x^2). 2911819Sjulian 3011819Sjulian The largest observed error in this region is 0.83 ulps, 3111819Sjulian _ZGVsMxv_asinf (0x1.ea00f4p-2) got 0x1.fef15ep-2 3211819Sjulian want 0x1.fef15cp-2. 3311819Sjulian 3411819Sjulian For |x| in [0.5, 1.0], use same approximation with a change of variable 3511819Sjulian 3611819Sjulian asin(x) = pi/2 - (y + y * z * P(z)), with z = (1-x)/2 and y = sqrt(z). 3711819Sjulian 3811819Sjulian The largest observed error in this region is 2.41 ulps, 3911819Sjulian _ZGVsMxv_asinf (-0x1.00203ep-1) got -0x1.0c3a64p-1 4011819Sjulian want -0x1.0c3a6p-1. */ 4111819Sjuliansvfloat32_t SV_NAME_F1 (asin) (svfloat32_t x, const svbool_t pg) 4211819Sjulian{ 4311819Sjulian const struct data *d = ptr_barrier (&data); 4411819Sjulian 4511819Sjulian svuint32_t sign = svand_x (pg, svreinterpret_u32 (x), 0x80000000); 4611819Sjulian 4711819Sjulian svfloat32_t ax = svabs_x (pg, x); 4811819Sjulian svbool_t a_ge_half = svacge (pg, x, 0.5); 4911819Sjulian 5011819Sjulian /* Evaluate polynomial Q(x) = y + y * z * P(z) with 5111819Sjulian z = x ^ 2 and y = |x| , if |x| < 0.5 5211819Sjulian z = (1 - |x|) / 2 and y = sqrt(z), if |x| >= 0.5. */ 5311819Sjulian svfloat32_t z2 = svsel (a_ge_half, svmls_x (pg, sv_f32 (0.5), ax, 0.5), 5411819Sjulian svmul_x (pg, x, x)); 5511819Sjulian svfloat32_t z = svsqrt_m (ax, a_ge_half, z2); 5611819Sjulian 5711819Sjulian /* Use a single polynomial approximation P for both intervals. */ 5811819Sjulian svfloat32_t p = sv_horner_4_f32_x (pg, z2, d->poly); 5911819Sjulian /* Finalize polynomial: z + z * z2 * P(z2). */ 6011819Sjulian p = svmla_x (pg, z, svmul_x (pg, z, z2), p); 6111819Sjulian 6211819Sjulian /* asin(|x|) = Q(|x|) , for |x| < 0.5 6311819Sjulian = pi/2 - 2 Q(|x|), for |x| >= 0.5. */ 6411819Sjulian svfloat32_t y = svmad_m (a_ge_half, p, sv_f32 (-2.0), d->pi_over_2f); 6511819Sjulian 6611819Sjulian /* Copy sign. */ 6711819Sjulian return svreinterpret_f32 (svorr_x (pg, svreinterpret_u32 (y), sign)); 6811819Sjulian} 6911819Sjulian 7011819SjulianPL_SIG (SV, F, 1, asin, -1.0, 1.0) 7111819SjulianPL_TEST_ULP (SV_NAME_F1 (asin), 1.91) 7211819SjulianPL_TEST_INTERVAL (SV_NAME_F1 (asin), 0, 0.5, 50000) 7311819SjulianPL_TEST_INTERVAL (SV_NAME_F1 (asin), 0.5, 1.0, 50000) 7411819SjulianPL_TEST_INTERVAL (SV_NAME_F1 (asin), 1.0, 0x1p11, 50000) 7511819SjulianPL_TEST_INTERVAL (SV_NAME_F1 (asin), 0x1p11, inf, 20000) 7611819SjulianPL_TEST_INTERVAL (SV_NAME_F1 (asin), -0, -inf, 20000)