| Message ID | 20231103121224.16835-1-Joe.Ramsay@arm.com |
|---|---|
| State | New |
| Headers | show |
| Series | [1/6] aarch64: Add vector implementations of asin routines | expand |
The 11/03/2023 12:12, Joe Ramsay wrote: > --- this is OK to commit. Reviewed-by: Szabolcs Nagy <szabolcs.nagy@arm.com> > Thanks, > Joe > sysdeps/aarch64/fpu/Makefile | 3 +- > sysdeps/aarch64/fpu/Versions | 4 + > sysdeps/aarch64/fpu/asin_advsimd.c | 113 ++++++++++++++++++ > sysdeps/aarch64/fpu/asin_sve.c | 86 +++++++++++++ > sysdeps/aarch64/fpu/asinf_advsimd.c | 104 ++++++++++++++++ > sysdeps/aarch64/fpu/asinf_sve.c | 78 ++++++++++++ > sysdeps/aarch64/fpu/bits/math-vector.h | 4 + > .../fpu/test-double-advsimd-wrappers.c | 1 + > .../aarch64/fpu/test-double-sve-wrappers.c | 1 + > .../aarch64/fpu/test-float-advsimd-wrappers.c | 1 + > sysdeps/aarch64/fpu/test-float-sve-wrappers.c | 1 + > sysdeps/aarch64/libm-test-ulps | 8 ++ > .../unix/sysv/linux/aarch64/libmvec.abilist | 4 + > 13 files changed, 407 insertions(+), 1 deletion(-) > create mode 100644 sysdeps/aarch64/fpu/asin_advsimd.c > create mode 100644 sysdeps/aarch64/fpu/asin_sve.c > create mode 100644 sysdeps/aarch64/fpu/asinf_advsimd.c > create mode 100644 sysdeps/aarch64/fpu/asinf_sve.c > > diff --git a/sysdeps/aarch64/fpu/Makefile b/sysdeps/aarch64/fpu/Makefile > index 1f1ac2a2b8..d7c0bd2ed5 100644 > --- a/sysdeps/aarch64/fpu/Makefile > +++ b/sysdeps/aarch64/fpu/Makefile > @@ -1,4 +1,5 @@ > -libmvec-supported-funcs = cos \ > +libmvec-supported-funcs = asin \ > + cos \ > exp \ > exp10 \ > exp2 \ > diff --git a/sysdeps/aarch64/fpu/Versions b/sysdeps/aarch64/fpu/Versions > index eb5ad50017..0f365a1e2e 100644 > --- a/sysdeps/aarch64/fpu/Versions > +++ b/sysdeps/aarch64/fpu/Versions > @@ -18,6 +18,10 @@ libmvec { > _ZGVsMxv_sinf; > } > GLIBC_2.39 { > + _ZGVnN4v_asinf; > + _ZGVnN2v_asin; > + _ZGVsMxv_asinf; > + _ZGVsMxv_asin; > _ZGVnN4v_exp10f; > _ZGVnN2v_exp10; > _ZGVsMxv_exp10f; > diff --git a/sysdeps/aarch64/fpu/asin_advsimd.c b/sysdeps/aarch64/fpu/asin_advsimd.c > new file mode 100644 > index 0000000000..d2adbc0d87 > --- /dev/null > +++ b/sysdeps/aarch64/fpu/asin_advsimd.c > @@ -0,0 +1,113 @@ > +/* Double-precision AdvSIMD inverse sin > + > + Copyright (C) 2023 Free Software Foundation, Inc. > + This file is part of the GNU C Library. > + > + The GNU C Library is free software; you can redistribute it and/or > + modify it under the terms of the GNU Lesser General Public > + License as published by the Free Software Foundation; either > + version 2.1 of the License, or (at your option) any later version. > + > + The GNU C Library is distributed in the hope that it will be useful, > + but WITHOUT ANY WARRANTY; without even the implied warranty of > + MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the GNU > + Lesser General Public License for more details. > + > + You should have received a copy of the GNU Lesser General Public > + License along with the GNU C Library; if not, see > + <https://www.gnu.org/licenses/>. */ > + > +#include "v_math.h" > +#include "poly_advsimd_f64.h" > + > +static const struct data > +{ > + float64x2_t poly[12]; > + float64x2_t pi_over_2; > + uint64x2_t abs_mask; > +} data = { > + /* Polynomial approximation of (asin(sqrt(x)) - sqrt(x)) / (x * sqrt(x)) > + on [ 0x1p-106, 0x1p-2 ], relative error: 0x1.c3d8e169p-57. */ > + .poly = { V2 (0x1.555555555554ep-3), V2 (0x1.3333333337233p-4), > + V2 (0x1.6db6db67f6d9fp-5), V2 (0x1.f1c71fbd29fbbp-6), > + V2 (0x1.6e8b264d467d6p-6), V2 (0x1.1c5997c357e9dp-6), > + V2 (0x1.c86a22cd9389dp-7), V2 (0x1.856073c22ebbep-7), > + V2 (0x1.fd1151acb6bedp-8), V2 (0x1.087182f799c1dp-6), > + V2 (-0x1.6602748120927p-7), V2 (0x1.cfa0dd1f9478p-6), }, > + .pi_over_2 = V2 (0x1.921fb54442d18p+0), > + .abs_mask = V2 (0x7fffffffffffffff), > +}; > + > +#define AllMask v_u64 (0xffffffffffffffff) > +#define One (0x3ff0000000000000) > +#define Small (0x3e50000000000000) /* 2^-12. */ > + > +#if WANT_SIMD_EXCEPT > +static float64x2_t VPCS_ATTR NOINLINE > +special_case (float64x2_t x, float64x2_t y, uint64x2_t special) > +{ > + return v_call_f64 (asin, x, y, special); > +} > +#endif > + > +/* Double-precision implementation of vector asin(x). > + > + For |x| < Small, approximate asin(x) by x. Small = 2^-12 for correct > + rounding. If WANT_SIMD_EXCEPT = 0, Small = 0 and we proceed with the > + following approximation. > + > + For |x| in [Small, 0.5], use an order 11 polynomial P such that the final > + approximation is an odd polynomial: asin(x) ~ x + x^3 P(x^2). > + > + The largest observed error in this region is 1.01 ulps, > + _ZGVnN2v_asin (0x1.da9735b5a9277p-2) got 0x1.ed78525a927efp-2 > + want 0x1.ed78525a927eep-2. > + > + For |x| in [0.5, 1.0], use same approximation with a change of variable > + > + asin(x) = pi/2 - (y + y * z * P(z)), with z = (1-x)/2 and y = sqrt(z). > + > + The largest observed error in this region is 2.69 ulps, > + _ZGVnN2v_asin (0x1.044ac9819f573p-1) got 0x1.110d7e85fdd5p-1 > + want 0x1.110d7e85fdd53p-1. */ > +float64x2_t VPCS_ATTR V_NAME_D1 (asin) (float64x2_t x) > +{ > + const struct data *d = ptr_barrier (&data); > + > + float64x2_t ax = vabsq_f64 (x); > + > +#if WANT_SIMD_EXCEPT > + /* Special values need to be computed with scalar fallbacks so > + that appropriate exceptions are raised. */ > + uint64x2_t special > + = vcgtq_u64 (vsubq_u64 (vreinterpretq_u64_f64 (ax), v_u64 (Small)), > + v_u64 (One - Small)); > + if (__glibc_unlikely (v_any_u64 (special))) > + return special_case (x, x, AllMask); > +#endif > + > + uint64x2_t a_lt_half = vcltq_f64 (ax, v_f64 (0.5)); > + > + /* Evaluate polynomial Q(x) = y + y * z * P(z) with > + z = x ^ 2 and y = |x| , if |x| < 0.5 > + z = (1 - |x|) / 2 and y = sqrt(z), if |x| >= 0.5. */ > + float64x2_t z2 = vbslq_f64 (a_lt_half, vmulq_f64 (x, x), > + vfmsq_n_f64 (v_f64 (0.5), ax, 0.5)); > + float64x2_t z = vbslq_f64 (a_lt_half, ax, vsqrtq_f64 (z2)); > + > + /* Use a single polynomial approximation P for both intervals. */ > + float64x2_t z4 = vmulq_f64 (z2, z2); > + float64x2_t z8 = vmulq_f64 (z4, z4); > + float64x2_t z16 = vmulq_f64 (z8, z8); > + float64x2_t p = v_estrin_11_f64 (z2, z4, z8, z16, d->poly); > + > + /* Finalize polynomial: z + z * z2 * P(z2). */ > + p = vfmaq_f64 (z, vmulq_f64 (z, z2), p); > + > + /* asin(|x|) = Q(|x|) , for |x| < 0.5 > + = pi/2 - 2 Q(|x|), for |x| >= 0.5. */ > + float64x2_t y = vbslq_f64 (a_lt_half, p, vfmsq_n_f64 (d->pi_over_2, p, 2.0)); > + > + /* Copy sign. */ > + return vbslq_f64 (d->abs_mask, y, x); > +} > diff --git a/sysdeps/aarch64/fpu/asin_sve.c b/sysdeps/aarch64/fpu/asin_sve.c > new file mode 100644 > index 0000000000..fa04d7fca6 > --- /dev/null > +++ b/sysdeps/aarch64/fpu/asin_sve.c > @@ -0,0 +1,86 @@ > +/* Double-precision SVE inverse sin > + > + Copyright (C) 2023 Free Software Foundation, Inc. > + This file is part of the GNU C Library. > + > + The GNU C Library is free software; you can redistribute it and/or > + modify it under the terms of the GNU Lesser General Public > + License as published by the Free Software Foundation; either > + version 2.1 of the License, or (at your option) any later version. > + > + The GNU C Library is distributed in the hope that it will be useful, > + but WITHOUT ANY WARRANTY; without even the implied warranty of > + MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the GNU > + Lesser General Public License for more details. > + > + You should have received a copy of the GNU Lesser General Public > + License along with the GNU C Library; if not, see > + <https://www.gnu.org/licenses/>. */ > + > +#include "sv_math.h" > +#include "poly_sve_f64.h" > + > +static const struct data > +{ > + float64_t poly[12]; > + float64_t pi_over_2f; > +} 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_over_2f = 0x1.921fb54442d18p+0, > +}; > + > +#define P(i) sv_f64 (d->poly[i]) > + > +/* Double-precision SVE implementation of vector asin(x). > + > + For |x| in [0, 0.5], use an order 11 polynomial P such that the final > + approximation is an odd polynomial: asin(x) ~ x + x^3 P(x^2). > + > + The largest observed error in this region is 0.52 ulps, > + _ZGVsMxv_asin(0x1.d95ae04998b6cp-2) got 0x1.ec13757305f27p-2 > + want 0x1.ec13757305f26p-2. > + > + For |x| in [0.5, 1.0], use same approximation with a change of variable > + > + asin(x) = pi/2 - (y + y * z * P(z)), with z = (1-x)/2 and y = sqrt(z). > + > + The largest observed error in this region is 2.69 ulps, > + _ZGVsMxv_asin(0x1.044ac9819f573p-1) got 0x1.110d7e85fdd5p-1 > + want 0x1.110d7e85fdd53p-1. */ > +svfloat64_t SV_NAME_D1 (asin) (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_ge_half = svacge (pg, x, 0.5); > + > + /* Evaluate polynomial Q(x) = y + y * z * P(z) with > + z = x ^ 2 and y = |x| , if |x| < 0.5 > + z = (1 - |x|) / 2 and y = sqrt(z), if |x| >= 0.5. */ > + svfloat64_t z2 = svsel (a_ge_half, svmls_x (pg, sv_f64 (0.5), ax, 0.5), > + svmul_x (pg, x, x)); > + svfloat64_t z = svsqrt_m (ax, a_ge_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); > + > + /* asin(|x|) = Q(|x|) , for |x| < 0.5 > + = pi/2 - 2 Q(|x|), for |x| >= 0.5. */ > + svfloat64_t y = svmad_m (a_ge_half, p, sv_f64 (-2.0), d->pi_over_2f); > + > + /* Copy sign. */ > + return svreinterpret_f64 (svorr_x (pg, svreinterpret_u64 (y), sign)); > +} > diff --git a/sysdeps/aarch64/fpu/asinf_advsimd.c b/sysdeps/aarch64/fpu/asinf_advsimd.c > new file mode 100644 > index 0000000000..3180ae7c8e > --- /dev/null > +++ b/sysdeps/aarch64/fpu/asinf_advsimd.c > @@ -0,0 +1,104 @@ > +/* Single-precision AdvSIMD inverse sin > + > + Copyright (C) 2023 Free Software Foundation, Inc. > + This file is part of the GNU C Library. > + > + The GNU C Library is free software; you can redistribute it and/or > + modify it under the terms of the GNU Lesser General Public > + License as published by the Free Software Foundation; either > + version 2.1 of the License, or (at your option) any later version. > + > + The GNU C Library is distributed in the hope that it will be useful, > + but WITHOUT ANY WARRANTY; without even the implied warranty of > + MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the GNU > + Lesser General Public License for more details. > + > + You should have received a copy of the GNU Lesser General Public > + License along with the GNU C Library; if not, see > + <https://www.gnu.org/licenses/>. */ > + > +#include "v_math.h" > +#include "poly_advsimd_f32.h" > + > +static const struct data > +{ > + float32x4_t poly[5]; > + float32x4_t pi_over_2f; > +} 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 = { V4 (0x1.55555ep-3), V4 (0x1.33261ap-4), V4 (0x1.70d7dcp-5), > + V4 (0x1.b059dp-6), V4 (0x1.3af7d8p-5) }, > + .pi_over_2f = V4 (0x1.921fb6p+0f), > +}; > + > +#define AbsMask 0x7fffffff > +#define Half 0x3f000000 > +#define One 0x3f800000 > +#define Small 0x39800000 /* 2^-12. */ > + > +#if WANT_SIMD_EXCEPT > +static float32x4_t VPCS_ATTR NOINLINE > +special_case (float32x4_t x, float32x4_t y, uint32x4_t special) > +{ > + return v_call_f32 (asinf, x, y, special); > +} > +#endif > + > +/* Single-precision implementation of vector asin(x). > + > + For |x| < Small, approximate asin(x) by x. Small = 2^-12 for correct > + rounding. If WANT_SIMD_EXCEPT = 0, Small = 0 and we proceed with the > + following approximation. > + > + For |x| in [Small, 0.5], use order 4 polynomial P such that the final > + approximation is an odd polynomial: asin(x) ~ x + x^3 P(x^2). > + > + The largest observed error in this region is 0.83 ulps, > + _ZGVnN4v_asinf (0x1.ea00f4p-2) got 0x1.fef15ep-2 want 0x1.fef15cp-2. > + > + For |x| in [0.5, 1.0], use same approximation with a change of variable > + > + asin(x) = pi/2 - (y + y * z * P(z)), with z = (1-x)/2 and y = sqrt(z). > + > + The largest observed error in this region is 2.41 ulps, > + _ZGVnN4v_asinf (0x1.00203ep-1) got 0x1.0c3a64p-1 want 0x1.0c3a6p-1. */ > +float32x4_t VPCS_ATTR V_NAME_F1 (asin) (float32x4_t x) > +{ > + const struct data *d = ptr_barrier (&data); > + > + uint32x4_t ix = vreinterpretq_u32_f32 (x); > + uint32x4_t ia = vandq_u32 (ix, v_u32 (AbsMask)); > + > +#if WANT_SIMD_EXCEPT > + /* Special values need to be computed with scalar fallbacks so > + that appropriate fp exceptions are raised. */ > + uint32x4_t special > + = vcgtq_u32 (vsubq_u32 (ia, v_u32 (Small)), v_u32 (One - Small)); > + if (__glibc_unlikely (v_any_u32 (special))) > + return special_case (x, x, v_u32 (0xffffffff)); > +#endif > + > + float32x4_t ax = vreinterpretq_f32_u32 (ia); > + uint32x4_t a_lt_half = vcltq_u32 (ia, v_u32 (Half)); > + > + /* Evaluate polynomial Q(x) = y + y * z * P(z) with > + z = x ^ 2 and y = |x| , if |x| < 0.5 > + z = (1 - |x|) / 2 and y = sqrt(z), if |x| >= 0.5. */ > + float32x4_t z2 = vbslq_f32 (a_lt_half, vmulq_f32 (x, x), > + vfmsq_n_f32 (v_f32 (0.5), ax, 0.5)); > + float32x4_t z = vbslq_f32 (a_lt_half, ax, vsqrtq_f32 (z2)); > + > + /* Use a single polynomial approximation P for both intervals. */ > + float32x4_t p = v_horner_4_f32 (z2, d->poly); > + /* Finalize polynomial: z + z * z2 * P(z2). */ > + p = vfmaq_f32 (z, vmulq_f32 (z, z2), p); > + > + /* asin(|x|) = Q(|x|) , for |x| < 0.5 > + = pi/2 - 2 Q(|x|), for |x| >= 0.5. */ > + float32x4_t y > + = vbslq_f32 (a_lt_half, p, vfmsq_n_f32 (d->pi_over_2f, p, 2.0)); > + > + /* Copy sign. */ > + return vbslq_f32 (v_u32 (AbsMask), y, x); > +} > diff --git a/sysdeps/aarch64/fpu/asinf_sve.c b/sysdeps/aarch64/fpu/asinf_sve.c > new file mode 100644 > index 0000000000..5abe710b5a > --- /dev/null > +++ b/sysdeps/aarch64/fpu/asinf_sve.c > @@ -0,0 +1,78 @@ > +/* Single-precision SVE inverse sin > + > + Copyright (C) 2023 Free Software Foundation, Inc. > + This file is part of the GNU C Library. > + > + The GNU C Library is free software; you can redistribute it and/or > + modify it under the terms of the GNU Lesser General Public > + License as published by the Free Software Foundation; either > + version 2.1 of the License, or (at your option) any later version. > + > + The GNU C Library is distributed in the hope that it will be useful, > + but WITHOUT ANY WARRANTY; without even the implied warranty of > + MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the GNU > + Lesser General Public License for more details. > + > + You should have received a copy of the GNU Lesser General Public > + License along with the GNU C Library; if not, see > + <https://www.gnu.org/licenses/>. */ > + > +#include "sv_math.h" > +#include "poly_sve_f32.h" > + > +static const struct data > +{ > + float32_t poly[5]; > + float32_t pi_over_2f; > +} 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_over_2f = 0x1.921fb6p+0f, > +}; > + > +/* Single-precision SVE implementation of vector asin(x). > + > + For |x| in [0, 0.5], use order 4 polynomial P such that the final > + approximation is an odd polynomial: asin(x) ~ x + x^3 P(x^2). > + > + The largest observed error in this region is 0.83 ulps, > + _ZGVsMxv_asinf (0x1.ea00f4p-2) got 0x1.fef15ep-2 > + want 0x1.fef15cp-2. > + > + For |x| in [0.5, 1.0], use same approximation with a change of variable > + > + asin(x) = pi/2 - (y + y * z * P(z)), with z = (1-x)/2 and y = sqrt(z). > + > + The largest observed error in this region is 2.41 ulps, > + _ZGVsMxv_asinf (-0x1.00203ep-1) got -0x1.0c3a64p-1 > + want -0x1.0c3a6p-1. */ > +svfloat32_t SV_NAME_F1 (asin) (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_ge_half = svacge (pg, x, 0.5); > + > + /* Evaluate polynomial Q(x) = y + y * z * P(z) with > + z = x ^ 2 and y = |x| , if |x| < 0.5 > + z = (1 - |x|) / 2 and y = sqrt(z), if |x| >= 0.5. */ > + svfloat32_t z2 = svsel (a_ge_half, svmls_x (pg, sv_f32 (0.5), ax, 0.5), > + svmul_x (pg, x, x)); > + svfloat32_t z = svsqrt_m (ax, a_ge_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); > + > + /* asin(|x|) = Q(|x|) , for |x| < 0.5 > + = pi/2 - 2 Q(|x|), for |x| >= 0.5. */ > + svfloat32_t y = svmad_m (a_ge_half, p, sv_f32 (-2.0), d->pi_over_2f); > + > + /* Copy sign. */ > + return svreinterpret_f32 (svorr_x (pg, svreinterpret_u32 (y), sign)); > +} > diff --git a/sysdeps/aarch64/fpu/bits/math-vector.h b/sysdeps/aarch64/fpu/bits/math-vector.h > index 06587ffa91..03778faf96 100644 > --- a/sysdeps/aarch64/fpu/bits/math-vector.h > +++ b/sysdeps/aarch64/fpu/bits/math-vector.h > @@ -49,6 +49,7 @@ typedef __SVBool_t __sv_bool_t; > > # define __vpcs __attribute__ ((__aarch64_vector_pcs__)) > > +__vpcs __f32x4_t _ZGVnN4v_asinf (__f32x4_t); > __vpcs __f32x4_t _ZGVnN4v_cosf (__f32x4_t); > __vpcs __f32x4_t _ZGVnN4v_expf (__f32x4_t); > __vpcs __f32x4_t _ZGVnN4v_exp10f (__f32x4_t); > @@ -59,6 +60,7 @@ __vpcs __f32x4_t _ZGVnN4v_log2f (__f32x4_t); > __vpcs __f32x4_t _ZGVnN4v_sinf (__f32x4_t); > __vpcs __f32x4_t _ZGVnN4v_tanf (__f32x4_t); > > +__vpcs __f64x2_t _ZGVnN2v_asin (__f64x2_t); > __vpcs __f64x2_t _ZGVnN2v_cos (__f64x2_t); > __vpcs __f64x2_t _ZGVnN2v_exp (__f64x2_t); > __vpcs __f64x2_t _ZGVnN2v_exp10 (__f64x2_t); > @@ -74,6 +76,7 @@ __vpcs __f64x2_t _ZGVnN2v_tan (__f64x2_t); > > #ifdef __SVE_VEC_MATH_SUPPORTED > > +__sv_f32_t _ZGVsMxv_asinf (__sv_f32_t, __sv_bool_t); > __sv_f32_t _ZGVsMxv_cosf (__sv_f32_t, __sv_bool_t); > __sv_f32_t _ZGVsMxv_expf (__sv_f32_t, __sv_bool_t); > __sv_f32_t _ZGVsMxv_exp10f (__sv_f32_t, __sv_bool_t); > @@ -84,6 +87,7 @@ __sv_f32_t _ZGVsMxv_log2f (__sv_f32_t, __sv_bool_t); > __sv_f32_t _ZGVsMxv_sinf (__sv_f32_t, __sv_bool_t); > __sv_f32_t _ZGVsMxv_tanf (__sv_f32_t, __sv_bool_t); > > +__sv_f64_t _ZGVsMxv_asin (__sv_f64_t, __sv_bool_t); > __sv_f64_t _ZGVsMxv_cos (__sv_f64_t, __sv_bool_t); > __sv_f64_t _ZGVsMxv_exp (__sv_f64_t, __sv_bool_t); > __sv_f64_t _ZGVsMxv_exp10 (__sv_f64_t, __sv_bool_t); > diff --git a/sysdeps/aarch64/fpu/test-double-advsimd-wrappers.c b/sysdeps/aarch64/fpu/test-double-advsimd-wrappers.c > index 26d5ecf66f..b5ccd6b1cc 100644 > --- a/sysdeps/aarch64/fpu/test-double-advsimd-wrappers.c > +++ b/sysdeps/aarch64/fpu/test-double-advsimd-wrappers.c > @@ -23,6 +23,7 @@ > > #define VEC_TYPE float64x2_t > > +VPCS_VECTOR_WRAPPER (asin_advsimd, _ZGVnN2v_asin) > VPCS_VECTOR_WRAPPER (cos_advsimd, _ZGVnN2v_cos) > VPCS_VECTOR_WRAPPER (exp_advsimd, _ZGVnN2v_exp) > VPCS_VECTOR_WRAPPER (exp10_advsimd, _ZGVnN2v_exp10) > diff --git a/sysdeps/aarch64/fpu/test-double-sve-wrappers.c b/sysdeps/aarch64/fpu/test-double-sve-wrappers.c > index 86efd60779..fc3b20f421 100644 > --- a/sysdeps/aarch64/fpu/test-double-sve-wrappers.c > +++ b/sysdeps/aarch64/fpu/test-double-sve-wrappers.c > @@ -32,6 +32,7 @@ > return svlastb_f64 (svptrue_b64 (), mr); \ > } > > +SVE_VECTOR_WRAPPER (asin_sve, _ZGVsMxv_asin) > SVE_VECTOR_WRAPPER (cos_sve, _ZGVsMxv_cos) > SVE_VECTOR_WRAPPER (exp_sve, _ZGVsMxv_exp) > SVE_VECTOR_WRAPPER (exp10_sve, _ZGVsMxv_exp10) > diff --git a/sysdeps/aarch64/fpu/test-float-advsimd-wrappers.c b/sysdeps/aarch64/fpu/test-float-advsimd-wrappers.c > index 8f7ebea1ac..0a36aa91f5 100644 > --- a/sysdeps/aarch64/fpu/test-float-advsimd-wrappers.c > +++ b/sysdeps/aarch64/fpu/test-float-advsimd-wrappers.c > @@ -23,6 +23,7 @@ > > #define VEC_TYPE float32x4_t > > +VPCS_VECTOR_WRAPPER (asinf_advsimd, _ZGVnN4v_asinf) > VPCS_VECTOR_WRAPPER (cosf_advsimd, _ZGVnN4v_cosf) > VPCS_VECTOR_WRAPPER (expf_advsimd, _ZGVnN4v_expf) > VPCS_VECTOR_WRAPPER (exp10f_advsimd, _ZGVnN4v_exp10f) > diff --git a/sysdeps/aarch64/fpu/test-float-sve-wrappers.c b/sysdeps/aarch64/fpu/test-float-sve-wrappers.c > index 885e58ac39..f7e4882c7a 100644 > --- a/sysdeps/aarch64/fpu/test-float-sve-wrappers.c > +++ b/sysdeps/aarch64/fpu/test-float-sve-wrappers.c > @@ -32,6 +32,7 @@ > return svlastb_f32 (svptrue_b32 (), mr); \ > } > > +SVE_VECTOR_WRAPPER (asinf_sve, _ZGVsMxv_asinf) > SVE_VECTOR_WRAPPER (cosf_sve, _ZGVsMxv_cosf) > SVE_VECTOR_WRAPPER (expf_sve, _ZGVsMxv_expf) > SVE_VECTOR_WRAPPER (exp10f_sve, _ZGVsMxv_exp10f) > diff --git a/sysdeps/aarch64/libm-test-ulps b/sysdeps/aarch64/libm-test-ulps > index d117209c06..1edc0fc343 100644 > --- a/sysdeps/aarch64/libm-test-ulps > +++ b/sysdeps/aarch64/libm-test-ulps > @@ -46,11 +46,19 @@ double: 1 > float: 1 > ldouble: 1 > > +Function: "asin_advsimd": > +double: 2 > +float: 2 > + > Function: "asin_downward": > double: 1 > float: 1 > ldouble: 2 > > +Function: "asin_sve": > +double: 2 > +float: 2 > + > Function: "asin_towardzero": > double: 1 > float: 1 > diff --git a/sysdeps/unix/sysv/linux/aarch64/libmvec.abilist b/sysdeps/unix/sysv/linux/aarch64/libmvec.abilist > index cad774521a..6431c3fe65 100644 > --- a/sysdeps/unix/sysv/linux/aarch64/libmvec.abilist > +++ b/sysdeps/unix/sysv/linux/aarch64/libmvec.abilist > @@ -14,16 +14,20 @@ GLIBC_2.38 _ZGVsMxv_log F > GLIBC_2.38 _ZGVsMxv_logf F > GLIBC_2.38 _ZGVsMxv_sin F > GLIBC_2.38 _ZGVsMxv_sinf F > +GLIBC_2.39 _ZGVnN2v_asin F > GLIBC_2.39 _ZGVnN2v_exp10 F > GLIBC_2.39 _ZGVnN2v_exp2 F > GLIBC_2.39 _ZGVnN2v_log10 F > GLIBC_2.39 _ZGVnN2v_log2 F > GLIBC_2.39 _ZGVnN2v_tan F > +GLIBC_2.39 _ZGVnN4v_asinf F > GLIBC_2.39 _ZGVnN4v_exp10f F > GLIBC_2.39 _ZGVnN4v_exp2f F > GLIBC_2.39 _ZGVnN4v_log10f F > GLIBC_2.39 _ZGVnN4v_log2f F > GLIBC_2.39 _ZGVnN4v_tanf F > +GLIBC_2.39 _ZGVsMxv_asin F > +GLIBC_2.39 _ZGVsMxv_asinf F > GLIBC_2.39 _ZGVsMxv_exp10 F > GLIBC_2.39 _ZGVsMxv_exp10f F > GLIBC_2.39 _ZGVsMxv_exp2 F > -- > 2.27.0 >
diff --git a/sysdeps/aarch64/fpu/Makefile b/sysdeps/aarch64/fpu/Makefile index 1f1ac2a2b8..d7c0bd2ed5 100644 --- a/sysdeps/aarch64/fpu/Makefile +++ b/sysdeps/aarch64/fpu/Makefile @@ -1,4 +1,5 @@ -libmvec-supported-funcs = cos \ +libmvec-supported-funcs = asin \ + cos \ exp \ exp10 \ exp2 \ diff --git a/sysdeps/aarch64/fpu/Versions b/sysdeps/aarch64/fpu/Versions index eb5ad50017..0f365a1e2e 100644 --- a/sysdeps/aarch64/fpu/Versions +++ b/sysdeps/aarch64/fpu/Versions @@ -18,6 +18,10 @@ libmvec { _ZGVsMxv_sinf; } GLIBC_2.39 { + _ZGVnN4v_asinf; + _ZGVnN2v_asin; + _ZGVsMxv_asinf; + _ZGVsMxv_asin; _ZGVnN4v_exp10f; _ZGVnN2v_exp10; _ZGVsMxv_exp10f; diff --git a/sysdeps/aarch64/fpu/asin_advsimd.c b/sysdeps/aarch64/fpu/asin_advsimd.c new file mode 100644 index 0000000000..d2adbc0d87 --- /dev/null +++ b/sysdeps/aarch64/fpu/asin_advsimd.c @@ -0,0 +1,113 @@ +/* Double-precision AdvSIMD inverse sin + + Copyright (C) 2023 Free Software Foundation, Inc. + This file is part of the GNU C Library. + + The GNU C Library is free software; you can redistribute it and/or + modify it under the terms of the GNU Lesser General Public + License as published by the Free Software Foundation; either + version 2.1 of the License, or (at your option) any later version. + + The GNU C Library is distributed in the hope that it will be useful, + but WITHOUT ANY WARRANTY; without even the implied warranty of + MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the GNU + Lesser General Public License for more details. + + You should have received a copy of the GNU Lesser General Public + License along with the GNU C Library; if not, see + <https://www.gnu.org/licenses/>. */ + +#include "v_math.h" +#include "poly_advsimd_f64.h" + +static const struct data +{ + float64x2_t poly[12]; + float64x2_t pi_over_2; + uint64x2_t abs_mask; +} data = { + /* Polynomial approximation of (asin(sqrt(x)) - sqrt(x)) / (x * sqrt(x)) + on [ 0x1p-106, 0x1p-2 ], relative error: 0x1.c3d8e169p-57. */ + .poly = { V2 (0x1.555555555554ep-3), V2 (0x1.3333333337233p-4), + V2 (0x1.6db6db67f6d9fp-5), V2 (0x1.f1c71fbd29fbbp-6), + V2 (0x1.6e8b264d467d6p-6), V2 (0x1.1c5997c357e9dp-6), + V2 (0x1.c86a22cd9389dp-7), V2 (0x1.856073c22ebbep-7), + V2 (0x1.fd1151acb6bedp-8), V2 (0x1.087182f799c1dp-6), + V2 (-0x1.6602748120927p-7), V2 (0x1.cfa0dd1f9478p-6), }, + .pi_over_2 = V2 (0x1.921fb54442d18p+0), + .abs_mask = V2 (0x7fffffffffffffff), +}; + +#define AllMask v_u64 (0xffffffffffffffff) +#define One (0x3ff0000000000000) +#define Small (0x3e50000000000000) /* 2^-12. */ + +#if WANT_SIMD_EXCEPT +static float64x2_t VPCS_ATTR NOINLINE +special_case (float64x2_t x, float64x2_t y, uint64x2_t special) +{ + return v_call_f64 (asin, x, y, special); +} +#endif + +/* Double-precision implementation of vector asin(x). + + For |x| < Small, approximate asin(x) by x. Small = 2^-12 for correct + rounding. If WANT_SIMD_EXCEPT = 0, Small = 0 and we proceed with the + following approximation. + + For |x| in [Small, 0.5], use an order 11 polynomial P such that the final + approximation is an odd polynomial: asin(x) ~ x + x^3 P(x^2). + + The largest observed error in this region is 1.01 ulps, + _ZGVnN2v_asin (0x1.da9735b5a9277p-2) got 0x1.ed78525a927efp-2 + want 0x1.ed78525a927eep-2. + + For |x| in [0.5, 1.0], use same approximation with a change of variable + + asin(x) = pi/2 - (y + y * z * P(z)), with z = (1-x)/2 and y = sqrt(z). + + The largest observed error in this region is 2.69 ulps, + _ZGVnN2v_asin (0x1.044ac9819f573p-1) got 0x1.110d7e85fdd5p-1 + want 0x1.110d7e85fdd53p-1. */ +float64x2_t VPCS_ATTR V_NAME_D1 (asin) (float64x2_t x) +{ + const struct data *d = ptr_barrier (&data); + + float64x2_t ax = vabsq_f64 (x); + +#if WANT_SIMD_EXCEPT + /* Special values need to be computed with scalar fallbacks so + that appropriate exceptions are raised. */ + uint64x2_t special + = vcgtq_u64 (vsubq_u64 (vreinterpretq_u64_f64 (ax), v_u64 (Small)), + v_u64 (One - Small)); + if (__glibc_unlikely (v_any_u64 (special))) + return special_case (x, x, AllMask); +#endif + + uint64x2_t a_lt_half = vcltq_f64 (ax, v_f64 (0.5)); + + /* Evaluate polynomial Q(x) = y + y * z * P(z) with + z = x ^ 2 and y = |x| , if |x| < 0.5 + z = (1 - |x|) / 2 and y = sqrt(z), if |x| >= 0.5. */ + float64x2_t z2 = vbslq_f64 (a_lt_half, vmulq_f64 (x, x), + vfmsq_n_f64 (v_f64 (0.5), ax, 0.5)); + float64x2_t z = vbslq_f64 (a_lt_half, ax, vsqrtq_f64 (z2)); + + /* Use a single polynomial approximation P for both intervals. */ + float64x2_t z4 = vmulq_f64 (z2, z2); + float64x2_t z8 = vmulq_f64 (z4, z4); + float64x2_t z16 = vmulq_f64 (z8, z8); + float64x2_t p = v_estrin_11_f64 (z2, z4, z8, z16, d->poly); + + /* Finalize polynomial: z + z * z2 * P(z2). */ + p = vfmaq_f64 (z, vmulq_f64 (z, z2), p); + + /* asin(|x|) = Q(|x|) , for |x| < 0.5 + = pi/2 - 2 Q(|x|), for |x| >= 0.5. */ + float64x2_t y = vbslq_f64 (a_lt_half, p, vfmsq_n_f64 (d->pi_over_2, p, 2.0)); + + /* Copy sign. */ + return vbslq_f64 (d->abs_mask, y, x); +} diff --git a/sysdeps/aarch64/fpu/asin_sve.c b/sysdeps/aarch64/fpu/asin_sve.c new file mode 100644 index 0000000000..fa04d7fca6 --- /dev/null +++ b/sysdeps/aarch64/fpu/asin_sve.c @@ -0,0 +1,86 @@ +/* Double-precision SVE inverse sin + + Copyright (C) 2023 Free Software Foundation, Inc. + This file is part of the GNU C Library. + + The GNU C Library is free software; you can redistribute it and/or + modify it under the terms of the GNU Lesser General Public + License as published by the Free Software Foundation; either + version 2.1 of the License, or (at your option) any later version. + + The GNU C Library is distributed in the hope that it will be useful, + but WITHOUT ANY WARRANTY; without even the implied warranty of + MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the GNU + Lesser General Public License for more details. + + You should have received a copy of the GNU Lesser General Public + License along with the GNU C Library; if not, see + <https://www.gnu.org/licenses/>. */ + +#include "sv_math.h" +#include "poly_sve_f64.h" + +static const struct data +{ + float64_t poly[12]; + float64_t pi_over_2f; +} 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_over_2f = 0x1.921fb54442d18p+0, +}; + +#define P(i) sv_f64 (d->poly[i]) + +/* Double-precision SVE implementation of vector asin(x). + + For |x| in [0, 0.5], use an order 11 polynomial P such that the final + approximation is an odd polynomial: asin(x) ~ x + x^3 P(x^2). + + The largest observed error in this region is 0.52 ulps, + _ZGVsMxv_asin(0x1.d95ae04998b6cp-2) got 0x1.ec13757305f27p-2 + want 0x1.ec13757305f26p-2. + + For |x| in [0.5, 1.0], use same approximation with a change of variable + + asin(x) = pi/2 - (y + y * z * P(z)), with z = (1-x)/2 and y = sqrt(z). + + The largest observed error in this region is 2.69 ulps, + _ZGVsMxv_asin(0x1.044ac9819f573p-1) got 0x1.110d7e85fdd5p-1 + want 0x1.110d7e85fdd53p-1. */ +svfloat64_t SV_NAME_D1 (asin) (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_ge_half = svacge (pg, x, 0.5); + + /* Evaluate polynomial Q(x) = y + y * z * P(z) with + z = x ^ 2 and y = |x| , if |x| < 0.5 + z = (1 - |x|) / 2 and y = sqrt(z), if |x| >= 0.5. */ + svfloat64_t z2 = svsel (a_ge_half, svmls_x (pg, sv_f64 (0.5), ax, 0.5), + svmul_x (pg, x, x)); + svfloat64_t z = svsqrt_m (ax, a_ge_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); + + /* asin(|x|) = Q(|x|) , for |x| < 0.5 + = pi/2 - 2 Q(|x|), for |x| >= 0.5. */ + svfloat64_t y = svmad_m (a_ge_half, p, sv_f64 (-2.0), d->pi_over_2f); + + /* Copy sign. */ + return svreinterpret_f64 (svorr_x (pg, svreinterpret_u64 (y), sign)); +} diff --git a/sysdeps/aarch64/fpu/asinf_advsimd.c b/sysdeps/aarch64/fpu/asinf_advsimd.c new file mode 100644 index 0000000000..3180ae7c8e --- /dev/null +++ b/sysdeps/aarch64/fpu/asinf_advsimd.c @@ -0,0 +1,104 @@ +/* Single-precision AdvSIMD inverse sin + + Copyright (C) 2023 Free Software Foundation, Inc. + This file is part of the GNU C Library. + + The GNU C Library is free software; you can redistribute it and/or + modify it under the terms of the GNU Lesser General Public + License as published by the Free Software Foundation; either + version 2.1 of the License, or (at your option) any later version. + + The GNU C Library is distributed in the hope that it will be useful, + but WITHOUT ANY WARRANTY; without even the implied warranty of + MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the GNU + Lesser General Public License for more details. + + You should have received a copy of the GNU Lesser General Public + License along with the GNU C Library; if not, see + <https://www.gnu.org/licenses/>. */ + +#include "v_math.h" +#include "poly_advsimd_f32.h" + +static const struct data +{ + float32x4_t poly[5]; + float32x4_t pi_over_2f; +} 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 = { V4 (0x1.55555ep-3), V4 (0x1.33261ap-4), V4 (0x1.70d7dcp-5), + V4 (0x1.b059dp-6), V4 (0x1.3af7d8p-5) }, + .pi_over_2f = V4 (0x1.921fb6p+0f), +}; + +#define AbsMask 0x7fffffff +#define Half 0x3f000000 +#define One 0x3f800000 +#define Small 0x39800000 /* 2^-12. */ + +#if WANT_SIMD_EXCEPT +static float32x4_t VPCS_ATTR NOINLINE +special_case (float32x4_t x, float32x4_t y, uint32x4_t special) +{ + return v_call_f32 (asinf, x, y, special); +} +#endif + +/* Single-precision implementation of vector asin(x). + + For |x| < Small, approximate asin(x) by x. Small = 2^-12 for correct + rounding. If WANT_SIMD_EXCEPT = 0, Small = 0 and we proceed with the + following approximation. + + For |x| in [Small, 0.5], use order 4 polynomial P such that the final + approximation is an odd polynomial: asin(x) ~ x + x^3 P(x^2). + + The largest observed error in this region is 0.83 ulps, + _ZGVnN4v_asinf (0x1.ea00f4p-2) got 0x1.fef15ep-2 want 0x1.fef15cp-2. + + For |x| in [0.5, 1.0], use same approximation with a change of variable + + asin(x) = pi/2 - (y + y * z * P(z)), with z = (1-x)/2 and y = sqrt(z). + + The largest observed error in this region is 2.41 ulps, + _ZGVnN4v_asinf (0x1.00203ep-1) got 0x1.0c3a64p-1 want 0x1.0c3a6p-1. */ +float32x4_t VPCS_ATTR V_NAME_F1 (asin) (float32x4_t x) +{ + const struct data *d = ptr_barrier (&data); + + uint32x4_t ix = vreinterpretq_u32_f32 (x); + uint32x4_t ia = vandq_u32 (ix, v_u32 (AbsMask)); + +#if WANT_SIMD_EXCEPT + /* Special values need to be computed with scalar fallbacks so + that appropriate fp exceptions are raised. */ + uint32x4_t special + = vcgtq_u32 (vsubq_u32 (ia, v_u32 (Small)), v_u32 (One - Small)); + if (__glibc_unlikely (v_any_u32 (special))) + return special_case (x, x, v_u32 (0xffffffff)); +#endif + + float32x4_t ax = vreinterpretq_f32_u32 (ia); + uint32x4_t a_lt_half = vcltq_u32 (ia, v_u32 (Half)); + + /* Evaluate polynomial Q(x) = y + y * z * P(z) with + z = x ^ 2 and y = |x| , if |x| < 0.5 + z = (1 - |x|) / 2 and y = sqrt(z), if |x| >= 0.5. */ + float32x4_t z2 = vbslq_f32 (a_lt_half, vmulq_f32 (x, x), + vfmsq_n_f32 (v_f32 (0.5), ax, 0.5)); + float32x4_t z = vbslq_f32 (a_lt_half, ax, vsqrtq_f32 (z2)); + + /* Use a single polynomial approximation P for both intervals. */ + float32x4_t p = v_horner_4_f32 (z2, d->poly); + /* Finalize polynomial: z + z * z2 * P(z2). */ + p = vfmaq_f32 (z, vmulq_f32 (z, z2), p); + + /* asin(|x|) = Q(|x|) , for |x| < 0.5 + = pi/2 - 2 Q(|x|), for |x| >= 0.5. */ + float32x4_t y + = vbslq_f32 (a_lt_half, p, vfmsq_n_f32 (d->pi_over_2f, p, 2.0)); + + /* Copy sign. */ + return vbslq_f32 (v_u32 (AbsMask), y, x); +} diff --git a/sysdeps/aarch64/fpu/asinf_sve.c b/sysdeps/aarch64/fpu/asinf_sve.c new file mode 100644 index 0000000000..5abe710b5a --- /dev/null +++ b/sysdeps/aarch64/fpu/asinf_sve.c @@ -0,0 +1,78 @@ +/* Single-precision SVE inverse sin + + Copyright (C) 2023 Free Software Foundation, Inc. + This file is part of the GNU C Library. + + The GNU C Library is free software; you can redistribute it and/or + modify it under the terms of the GNU Lesser General Public + License as published by the Free Software Foundation; either + version 2.1 of the License, or (at your option) any later version. + + The GNU C Library is distributed in the hope that it will be useful, + but WITHOUT ANY WARRANTY; without even the implied warranty of + MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the GNU + Lesser General Public License for more details. + + You should have received a copy of the GNU Lesser General Public + License along with the GNU C Library; if not, see + <https://www.gnu.org/licenses/>. */ + +#include "sv_math.h" +#include "poly_sve_f32.h" + +static const struct data +{ + float32_t poly[5]; + float32_t pi_over_2f; +} 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_over_2f = 0x1.921fb6p+0f, +}; + +/* Single-precision SVE implementation of vector asin(x). + + For |x| in [0, 0.5], use order 4 polynomial P such that the final + approximation is an odd polynomial: asin(x) ~ x + x^3 P(x^2). + + The largest observed error in this region is 0.83 ulps, + _ZGVsMxv_asinf (0x1.ea00f4p-2) got 0x1.fef15ep-2 + want 0x1.fef15cp-2. + + For |x| in [0.5, 1.0], use same approximation with a change of variable + + asin(x) = pi/2 - (y + y * z * P(z)), with z = (1-x)/2 and y = sqrt(z). + + The largest observed error in this region is 2.41 ulps, + _ZGVsMxv_asinf (-0x1.00203ep-1) got -0x1.0c3a64p-1 + want -0x1.0c3a6p-1. */ +svfloat32_t SV_NAME_F1 (asin) (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_ge_half = svacge (pg, x, 0.5); + + /* Evaluate polynomial Q(x) = y + y * z * P(z) with + z = x ^ 2 and y = |x| , if |x| < 0.5 + z = (1 - |x|) / 2 and y = sqrt(z), if |x| >= 0.5. */ + svfloat32_t z2 = svsel (a_ge_half, svmls_x (pg, sv_f32 (0.5), ax, 0.5), + svmul_x (pg, x, x)); + svfloat32_t z = svsqrt_m (ax, a_ge_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); + + /* asin(|x|) = Q(|x|) , for |x| < 0.5 + = pi/2 - 2 Q(|x|), for |x| >= 0.5. */ + svfloat32_t y = svmad_m (a_ge_half, p, sv_f32 (-2.0), d->pi_over_2f); + + /* Copy sign. */ + return svreinterpret_f32 (svorr_x (pg, svreinterpret_u32 (y), sign)); +} diff --git a/sysdeps/aarch64/fpu/bits/math-vector.h b/sysdeps/aarch64/fpu/bits/math-vector.h index 06587ffa91..03778faf96 100644 --- a/sysdeps/aarch64/fpu/bits/math-vector.h +++ b/sysdeps/aarch64/fpu/bits/math-vector.h @@ -49,6 +49,7 @@ typedef __SVBool_t __sv_bool_t; # define __vpcs __attribute__ ((__aarch64_vector_pcs__)) +__vpcs __f32x4_t _ZGVnN4v_asinf (__f32x4_t); __vpcs __f32x4_t _ZGVnN4v_cosf (__f32x4_t); __vpcs __f32x4_t _ZGVnN4v_expf (__f32x4_t); __vpcs __f32x4_t _ZGVnN4v_exp10f (__f32x4_t); @@ -59,6 +60,7 @@ __vpcs __f32x4_t _ZGVnN4v_log2f (__f32x4_t); __vpcs __f32x4_t _ZGVnN4v_sinf (__f32x4_t); __vpcs __f32x4_t _ZGVnN4v_tanf (__f32x4_t); +__vpcs __f64x2_t _ZGVnN2v_asin (__f64x2_t); __vpcs __f64x2_t _ZGVnN2v_cos (__f64x2_t); __vpcs __f64x2_t _ZGVnN2v_exp (__f64x2_t); __vpcs __f64x2_t _ZGVnN2v_exp10 (__f64x2_t); @@ -74,6 +76,7 @@ __vpcs __f64x2_t _ZGVnN2v_tan (__f64x2_t); #ifdef __SVE_VEC_MATH_SUPPORTED +__sv_f32_t _ZGVsMxv_asinf (__sv_f32_t, __sv_bool_t); __sv_f32_t _ZGVsMxv_cosf (__sv_f32_t, __sv_bool_t); __sv_f32_t _ZGVsMxv_expf (__sv_f32_t, __sv_bool_t); __sv_f32_t _ZGVsMxv_exp10f (__sv_f32_t, __sv_bool_t); @@ -84,6 +87,7 @@ __sv_f32_t _ZGVsMxv_log2f (__sv_f32_t, __sv_bool_t); __sv_f32_t _ZGVsMxv_sinf (__sv_f32_t, __sv_bool_t); __sv_f32_t _ZGVsMxv_tanf (__sv_f32_t, __sv_bool_t); +__sv_f64_t _ZGVsMxv_asin (__sv_f64_t, __sv_bool_t); __sv_f64_t _ZGVsMxv_cos (__sv_f64_t, __sv_bool_t); __sv_f64_t _ZGVsMxv_exp (__sv_f64_t, __sv_bool_t); __sv_f64_t _ZGVsMxv_exp10 (__sv_f64_t, __sv_bool_t); diff --git a/sysdeps/aarch64/fpu/test-double-advsimd-wrappers.c b/sysdeps/aarch64/fpu/test-double-advsimd-wrappers.c index 26d5ecf66f..b5ccd6b1cc 100644 --- a/sysdeps/aarch64/fpu/test-double-advsimd-wrappers.c +++ b/sysdeps/aarch64/fpu/test-double-advsimd-wrappers.c @@ -23,6 +23,7 @@ #define VEC_TYPE float64x2_t +VPCS_VECTOR_WRAPPER (asin_advsimd, _ZGVnN2v_asin) VPCS_VECTOR_WRAPPER (cos_advsimd, _ZGVnN2v_cos) VPCS_VECTOR_WRAPPER (exp_advsimd, _ZGVnN2v_exp) VPCS_VECTOR_WRAPPER (exp10_advsimd, _ZGVnN2v_exp10) diff --git a/sysdeps/aarch64/fpu/test-double-sve-wrappers.c b/sysdeps/aarch64/fpu/test-double-sve-wrappers.c index 86efd60779..fc3b20f421 100644 --- a/sysdeps/aarch64/fpu/test-double-sve-wrappers.c +++ b/sysdeps/aarch64/fpu/test-double-sve-wrappers.c @@ -32,6 +32,7 @@ return svlastb_f64 (svptrue_b64 (), mr); \ } +SVE_VECTOR_WRAPPER (asin_sve, _ZGVsMxv_asin) SVE_VECTOR_WRAPPER (cos_sve, _ZGVsMxv_cos) SVE_VECTOR_WRAPPER (exp_sve, _ZGVsMxv_exp) SVE_VECTOR_WRAPPER (exp10_sve, _ZGVsMxv_exp10) diff --git a/sysdeps/aarch64/fpu/test-float-advsimd-wrappers.c b/sysdeps/aarch64/fpu/test-float-advsimd-wrappers.c index 8f7ebea1ac..0a36aa91f5 100644 --- a/sysdeps/aarch64/fpu/test-float-advsimd-wrappers.c +++ b/sysdeps/aarch64/fpu/test-float-advsimd-wrappers.c @@ -23,6 +23,7 @@ #define VEC_TYPE float32x4_t +VPCS_VECTOR_WRAPPER (asinf_advsimd, _ZGVnN4v_asinf) VPCS_VECTOR_WRAPPER (cosf_advsimd, _ZGVnN4v_cosf) VPCS_VECTOR_WRAPPER (expf_advsimd, _ZGVnN4v_expf) VPCS_VECTOR_WRAPPER (exp10f_advsimd, _ZGVnN4v_exp10f) diff --git a/sysdeps/aarch64/fpu/test-float-sve-wrappers.c b/sysdeps/aarch64/fpu/test-float-sve-wrappers.c index 885e58ac39..f7e4882c7a 100644 --- a/sysdeps/aarch64/fpu/test-float-sve-wrappers.c +++ b/sysdeps/aarch64/fpu/test-float-sve-wrappers.c @@ -32,6 +32,7 @@ return svlastb_f32 (svptrue_b32 (), mr); \ } +SVE_VECTOR_WRAPPER (asinf_sve, _ZGVsMxv_asinf) SVE_VECTOR_WRAPPER (cosf_sve, _ZGVsMxv_cosf) SVE_VECTOR_WRAPPER (expf_sve, _ZGVsMxv_expf) SVE_VECTOR_WRAPPER (exp10f_sve, _ZGVsMxv_exp10f) diff --git a/sysdeps/aarch64/libm-test-ulps b/sysdeps/aarch64/libm-test-ulps index d117209c06..1edc0fc343 100644 --- a/sysdeps/aarch64/libm-test-ulps +++ b/sysdeps/aarch64/libm-test-ulps @@ -46,11 +46,19 @@ double: 1 float: 1 ldouble: 1 +Function: "asin_advsimd": +double: 2 +float: 2 + Function: "asin_downward": double: 1 float: 1 ldouble: 2 +Function: "asin_sve": +double: 2 +float: 2 + Function: "asin_towardzero": double: 1 float: 1 diff --git a/sysdeps/unix/sysv/linux/aarch64/libmvec.abilist b/sysdeps/unix/sysv/linux/aarch64/libmvec.abilist index cad774521a..6431c3fe65 100644 --- a/sysdeps/unix/sysv/linux/aarch64/libmvec.abilist +++ b/sysdeps/unix/sysv/linux/aarch64/libmvec.abilist @@ -14,16 +14,20 @@ GLIBC_2.38 _ZGVsMxv_log F GLIBC_2.38 _ZGVsMxv_logf F GLIBC_2.38 _ZGVsMxv_sin F GLIBC_2.38 _ZGVsMxv_sinf F +GLIBC_2.39 _ZGVnN2v_asin F GLIBC_2.39 _ZGVnN2v_exp10 F GLIBC_2.39 _ZGVnN2v_exp2 F GLIBC_2.39 _ZGVnN2v_log10 F GLIBC_2.39 _ZGVnN2v_log2 F GLIBC_2.39 _ZGVnN2v_tan F +GLIBC_2.39 _ZGVnN4v_asinf F GLIBC_2.39 _ZGVnN4v_exp10f F GLIBC_2.39 _ZGVnN4v_exp2f F GLIBC_2.39 _ZGVnN4v_log10f F GLIBC_2.39 _ZGVnN4v_log2f F GLIBC_2.39 _ZGVnN4v_tanf F +GLIBC_2.39 _ZGVsMxv_asin F +GLIBC_2.39 _ZGVsMxv_asinf F GLIBC_2.39 _ZGVsMxv_exp10 F GLIBC_2.39 _ZGVsMxv_exp10f F GLIBC_2.39 _ZGVsMxv_exp2 F