diff options
Diffstat (limited to 'pl/math/sv_acosf_1u4.c')
| -rw-r--r-- | pl/math/sv_acosf_1u4.c | 84 |
1 files changed, 84 insertions, 0 deletions
diff --git a/pl/math/sv_acosf_1u4.c b/pl/math/sv_acosf_1u4.c new file mode 100644 index 000000000000..7ac59ceedfbd --- /dev/null +++ b/pl/math/sv_acosf_1u4.c @@ -0,0 +1,84 @@ +/* + * Single-precision SVE acos(x) function. + * + * Copyright (c) 2023, Arm Limited. + * SPDX-License-Identifier: MIT OR Apache-2.0 WITH LLVM-exception + */ + +#include "sv_math.h" +#include "poly_sve_f32.h" +#include "pl_sig.h" +#include "pl_test.h" + +static const struct data +{ + float32_t poly[5]; + float32_t pi, pi_over_2; +} data = { + /* Polynomial approximation of (asin(sqrt(x)) - sqrt(x)) / (x * sqrt(x)) on + [ 0x1p-24 0x1p-2 ] order = 4 rel error: 0x1.00a23bbp-29 . */ + .poly = { 0x1.55555ep-3, 0x1.33261ap-4, 0x1.70d7dcp-5, 0x1.b059dp-6, + 0x1.3af7d8p-5, }, + .pi = 0x1.921fb6p+1f, + .pi_over_2 = 0x1.921fb6p+0f, +}; + +/* Single-precision SVE implementation of vector acos(x). + + For |x| in [0, 0.5], use order 4 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 1.16 ulps, + _ZGVsMxv_acosf(0x1.ffbeccp-2) got 0x1.0c27f8p+0 + want 0x1.0c27f6p+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 1.32 ulps, + _ZGVsMxv_acosf (0x1.15ba56p-1) got 0x1.feb33p-1 + want 0x1.feb32ep-1. */ +svfloat32_t SV_NAME_F1 (acos) (svfloat32_t x, const svbool_t pg) +{ + const struct data *d = ptr_barrier (&data); + + svuint32_t sign = svand_x (pg, svreinterpret_u32 (x), 0x80000000); + svfloat32_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. */ + svfloat32_t z2 = svsel (a_gt_half, svmls_x (pg, sv_f32 (0.5), ax, 0.5), + svmul_x (pg, x, x)); + svfloat32_t z = svsqrt_m (ax, a_gt_half, z2); + + /* Use a single polynomial approximation P for both intervals. */ + svfloat32_t p = sv_horner_4_f32_x (pg, z2, 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. */ + svfloat32_t y + = svreinterpret_f32 (svorr_x (pg, svreinterpret_u32 (p), sign)); + + svbool_t is_neg = svcmplt (pg, x, 0.0); + svfloat32_t off = svdup_f32_z (is_neg, d->pi); + svfloat32_t mul = svsel (a_gt_half, sv_f32 (2.0), sv_f32 (-1.0)); + svfloat32_t add = svsel (a_gt_half, off, sv_f32 (d->pi_over_2)); + + return svmla_x (pg, add, mul, y); +} + +PL_SIG (SV, F, 1, acos, -1.0, 1.0) +PL_TEST_ULP (SV_NAME_F1 (acos), 0.82) +PL_TEST_INTERVAL (SV_NAME_F1 (acos), 0, 0.5, 50000) +PL_TEST_INTERVAL (SV_NAME_F1 (acos), 0.5, 1.0, 50000) +PL_TEST_INTERVAL (SV_NAME_F1 (acos), 1.0, 0x1p11, 50000) +PL_TEST_INTERVAL (SV_NAME_F1 (acos), 0x1p11, inf, 20000) +PL_TEST_INTERVAL (SV_NAME_F1 (acos), -0, -inf, 20000) |