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Diffstat (limited to 'contrib/arm-optimized-routines/math/aarch64/sve/acos.c')
| -rw-r--r-- | contrib/arm-optimized-routines/math/aarch64/sve/acos.c | 93 |
1 files changed, 93 insertions, 0 deletions
diff --git a/contrib/arm-optimized-routines/math/aarch64/sve/acos.c b/contrib/arm-optimized-routines/math/aarch64/sve/acos.c new file mode 100644 index 000000000000..da633392aa3e --- /dev/null +++ b/contrib/arm-optimized-routines/math/aarch64/sve/acos.c @@ -0,0 +1,93 @@ +/* + * Double-precision SVE acos(x) function. + * + * Copyright (c) 2023-2024, Arm Limited. + * SPDX-License-Identifier: MIT OR Apache-2.0 WITH LLVM-exception + */ + +#include "sv_math.h" +#include "sv_poly_f64.h" +#include "test_sig.h" +#include "test_defs.h" + +static const struct data +{ + float64_t poly[12]; + float64_t pi, pi_over_2; +} data = { + /* Polynomial approximation of (asin(sqrt(x)) - sqrt(x)) / (x * sqrt(x)) + on [ 0x1p-106, 0x1p-2 ], relative error: 0x1.c3d8e169p-57. */ + .poly = { 0x1.555555555554ep-3, 0x1.3333333337233p-4, 0x1.6db6db67f6d9fp-5, + 0x1.f1c71fbd29fbbp-6, 0x1.6e8b264d467d6p-6, 0x1.1c5997c357e9dp-6, + 0x1.c86a22cd9389dp-7, 0x1.856073c22ebbep-7, 0x1.fd1151acb6bedp-8, + 0x1.087182f799c1dp-6, -0x1.6602748120927p-7, 0x1.cfa0dd1f9478p-6, }, + .pi = 0x1.921fb54442d18p+1, + .pi_over_2 = 0x1.921fb54442d18p+0, +}; + +/* Double-precision SVE implementation of vector acos(x). + + For |x| in [0, 0.5], use an order 11 polynomial P such that the final + approximation of asin is an odd polynomial: + + acos(x) ~ pi/2 - (x + x^3 P(x^2)). + + The largest observed error in this region is 1.18 ulps, + _ZGVsMxv_acos (0x1.fbc5fe28ee9e3p-2) got 0x1.0d4d0f55667f6p+0 + want 0x1.0d4d0f55667f7p+0. + + For |x| in [0.5, 1.0], use same approximation with a change of variable + + acos(x) = y + y * z * P(z), with z = (1-x)/2 and y = sqrt(z). + + The largest observed error in this region is 1.52 ulps, + _ZGVsMxv_acos (0x1.24024271a500ap-1) got 0x1.ed82df4243f0dp-1 + want 0x1.ed82df4243f0bp-1. */ +svfloat64_t SV_NAME_D1 (acos) (svfloat64_t x, const svbool_t pg) +{ + const struct data *d = ptr_barrier (&data); + + svuint64_t sign = svand_x (pg, svreinterpret_u64 (x), 0x8000000000000000); + svfloat64_t ax = svabs_x (pg, x); + + svbool_t a_gt_half = svacgt (pg, x, 0.5); + + /* Evaluate polynomial Q(x) = z + z * z2 * P(z2) with + z2 = x ^ 2 and z = |x| , if |x| < 0.5 + z2 = (1 - |x|) / 2 and z = sqrt(z2), if |x| >= 0.5. */ + svfloat64_t z2 = svsel (a_gt_half, svmls_x (pg, sv_f64 (0.5), ax, 0.5), + svmul_x (pg, x, x)); + svfloat64_t z = svsqrt_m (ax, a_gt_half, z2); + + /* Use a single polynomial approximation P for both intervals. */ + svfloat64_t z4 = svmul_x (pg, z2, z2); + svfloat64_t z8 = svmul_x (pg, z4, z4); + svfloat64_t z16 = svmul_x (pg, z8, z8); + svfloat64_t p = sv_estrin_11_f64_x (pg, z2, z4, z8, z16, d->poly); + + /* Finalize polynomial: z + z * z2 * P(z2). */ + p = svmla_x (pg, z, svmul_x (pg, z, z2), p); + + /* acos(|x|) = pi/2 - sign(x) * Q(|x|), for |x| < 0.5 + = 2 Q(|x|) , for 0.5 < x < 1.0 + = pi - 2 Q(|x|) , for -1.0 < x < -0.5. */ + svfloat64_t y + = svreinterpret_f64 (svorr_x (pg, svreinterpret_u64 (p), sign)); + + svbool_t is_neg = svcmplt (pg, x, 0.0); + svfloat64_t off = svdup_f64_z (is_neg, d->pi); + svfloat64_t mul = svsel (a_gt_half, sv_f64 (2.0), sv_f64 (-1.0)); + svfloat64_t add = svsel (a_gt_half, off, sv_f64 (d->pi_over_2)); + + return svmla_x (pg, add, mul, y); +} + +TEST_SIG (SV, D, 1, acos, -1.0, 1.0) +TEST_ULP (SV_NAME_D1 (acos), 1.02) +TEST_DISABLE_FENV (SV_NAME_D1 (acos)) +TEST_INTERVAL (SV_NAME_D1 (acos), 0, 0.5, 50000) +TEST_INTERVAL (SV_NAME_D1 (acos), 0.5, 1.0, 50000) +TEST_INTERVAL (SV_NAME_D1 (acos), 1.0, 0x1p11, 50000) +TEST_INTERVAL (SV_NAME_D1 (acos), 0x1p11, inf, 20000) +TEST_INTERVAL (SV_NAME_D1 (acos), -0, -inf, 20000) +CLOSE_SVE_ATTR |