From 993997ca1b77dfdea27ae56f3afacfab26dd4e60 Mon Sep 17 00:00:00 2001 From: Dylan Fleming Date: Mon, 19 May 2025 12:26:50 +0000 Subject: [PATCH] AArch64: Implement AdvSIMD and SVE acospi/f Implement double and single precision variants of the C23 routine acospi for both AdvSIMD and SVE. Reviewed-by: Wilco Dijkstra --- bits/libm-simd-decl-stubs.h | 11 ++ math/bits/mathcalls.h | 1 + sysdeps/aarch64/fpu/Makefile | 1 + sysdeps/aarch64/fpu/Versions | 7 ++ sysdeps/aarch64/fpu/acospi_advsimd.c | 118 ++++++++++++++++++ sysdeps/aarch64/fpu/acospi_sve.c | 112 +++++++++++++++++ sysdeps/aarch64/fpu/acospif_advsimd.c | 106 ++++++++++++++++ sysdeps/aarch64/fpu/acospif_sve.c | 91 ++++++++++++++ sysdeps/aarch64/fpu/advsimd_f32_protos.h | 1 + sysdeps/aarch64/fpu/bits/math-vector.h | 8 ++ .../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 + .../unix/sysv/linux/aarch64/libmvec.abilist | 5 + 15 files changed, 465 insertions(+) create mode 100644 sysdeps/aarch64/fpu/acospi_advsimd.c create mode 100644 sysdeps/aarch64/fpu/acospi_sve.c create mode 100644 sysdeps/aarch64/fpu/acospif_advsimd.c create mode 100644 sysdeps/aarch64/fpu/acospif_sve.c diff --git a/bits/libm-simd-decl-stubs.h b/bits/libm-simd-decl-stubs.h index 529df43c9b..fa9936b3e8 100644 --- a/bits/libm-simd-decl-stubs.h +++ b/bits/libm-simd-decl-stubs.h @@ -373,4 +373,15 @@ #define __DECL_SIMD_tanpif32x #define __DECL_SIMD_tanpif64x #define __DECL_SIMD_tanpif128x + +#define __DECL_SIMD_acospi +#define __DECL_SIMD_acospif +#define __DECL_SIMD_acospil +#define __DECL_SIMD_acospif16 +#define __DECL_SIMD_acospif32 +#define __DECL_SIMD_acospif64 +#define __DECL_SIMD_acospif128 +#define __DECL_SIMD_acospif32x +#define __DECL_SIMD_acospif64x +#define __DECL_SIMD_acospif128x #endif diff --git a/math/bits/mathcalls.h b/math/bits/mathcalls.h index 10f602721f..0836baadd2 100644 --- a/math/bits/mathcalls.h +++ b/math/bits/mathcalls.h @@ -68,6 +68,7 @@ __MATHCALL_VEC (tan,, (_Mdouble_ __x)); #if __GLIBC_USE (IEC_60559_FUNCS_EXT_C23) /* Arc cosine of X, divided by pi. */ __MATHCALL (acospi,, (_Mdouble_ __x)); +__MATHCALL_VEC (acospi,, (_Mdouble_ __x)); /* Arc sine of X, divided by pi. */ __MATHCALL (asinpi,, (_Mdouble_ __x)); /* Arc tangent of X, divided by pi. */ diff --git a/sysdeps/aarch64/fpu/Makefile b/sysdeps/aarch64/fpu/Makefile index aadedf1517..9d858c64da 100644 --- a/sysdeps/aarch64/fpu/Makefile +++ b/sysdeps/aarch64/fpu/Makefile @@ -1,5 +1,6 @@ libmvec-supported-funcs = acos \ acosh \ + acospi \ asin \ asinh \ atan \ diff --git a/sysdeps/aarch64/fpu/Versions b/sysdeps/aarch64/fpu/Versions index 0f9503f9d8..b06c5d2fa3 100644 --- a/sysdeps/aarch64/fpu/Versions +++ b/sysdeps/aarch64/fpu/Versions @@ -157,4 +157,11 @@ libmvec { _ZGVsMxv_tanpi; _ZGVsMxv_tanpif; } + GLIBC_2.42 { + _ZGVnN2v_acospi; + _ZGVnN2v_acospif; + _ZGVnN4v_acospif; + _ZGVsMxv_acospi; + _ZGVsMxv_acospif; + } } diff --git a/sysdeps/aarch64/fpu/acospi_advsimd.c b/sysdeps/aarch64/fpu/acospi_advsimd.c new file mode 100644 index 0000000000..bb6c209e83 --- /dev/null +++ b/sysdeps/aarch64/fpu/acospi_advsimd.c @@ -0,0 +1,118 @@ +/* Double-Precision vector (Advanced SIMD) inverse cospi function + + Copyright (C) 2025 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 + . */ + +#include "v_math.h" + +static const struct data +{ + float64x2_t c0, c2, c4, c6, c8, c10; + uint64x2_t abs_mask; + float64x2_t one, inv_pi; + double c1, c3, c5, c7, c9, c11; +} data = { + /* Coefficients of polynomial P such that asin(x)/pi~ x/pi + x^3 * poly(x^2) + on [ 0x1p-126 0x1p-2 ]. rel error: 0x1.ef9f94b1p-33. Generated using + iterative approach for minimisation of relative error in asinpif Sollya + file. */ + .c0 = V2 (0x1.b2995e7b7b5fbp-5), .c1 = 0x1.8723a1d58d83p-6, + .c2 = V2 (0x1.d1a452eacf2fep-7), .c3 = 0x1.3ce52c4d75582p-7, + .c4 = V2 (0x1.d2b2a0aea27d5p-8), .c5 = 0x1.6a0b9b92cad8bp-8, + .c6 = V2 (0x1.2290c84438caep-8), .c7 = 0x1.efba896580d02p-9, + .c8 = V2 (0x1.44446707af38p-9), .c9 = 0x1.5070b3e7aa03ep-8, + .c10 = V2 (-0x1.c70015d0ebdafp-9), .c11 = 0x1.27029c383fed9p-7, + .abs_mask = V2 (0x7fffffffffffffff), .one = V2 (1.0), + .inv_pi = V2 (0x1.45f306dc9c883p-2), +}; + +/* Double-precision implementation of vector acospi(x). + + For |x| in [0, 0.5], use order-11 polynomial P to approximate asinpi + such that the final approximation of acospi is an odd polynomial: + + acospi(x) ~ 1/2 - (x/pi + x^3 P(x^2)). + + The largest observed error in this region is 1.35 ulp: + _ZGVnN2v_acospi (0x1.fb16ed35a6d64p-2) got 0x1.5722a3dbcafb4p-2 + want 0x1.5722a3dbcafb5p-2. + + For |x| in [0.5, 1.0], use same approximation with a change of variable + + acospi(x) = y/pi + y * z * P(z), with z = (1-x)/2 and y = sqrt(z). + + The largest observed error in this region is 2.55 ulp: + _ZGVnN2v_acospi (0x1.d90d50357410cp-1) got 0x1.ffd43d5dd3a9ep-4 + want 0x1.ffd43d5dd3a9bp-4. */ +float64x2_t VPCS_ATTR NOINLINE V_NAME_D1 (acospi) (float64x2_t x) +{ + const struct data *d = ptr_barrier (&data); + + uint64x2_t ix = vreinterpretq_u64_f64 (x); + uint64x2_t ia = vandq_u64 (ix, d->abs_mask); + + float64x2_t ax = vreinterpretq_f64_u64 (ia); + uint64x2_t a_le_half = vcaltq_f64 (x, v_f64 (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. */ + float64x2_t z2 = vbslq_f64 (a_le_half, vmulq_f64 (x, x), + vfmsq_n_f64 (v_f64 (0.5), ax, 0.5)); + float64x2_t z = vbslq_f64 (a_le_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); + + /* Order-11 Estrin. */ + float64x2_t c13 = vld1q_f64 (&d->c1); + float64x2_t c57 = vld1q_f64 (&d->c5); + float64x2_t c911 = vld1q_f64 (&d->c9); + + float64x2_t p01 = vfmaq_laneq_f64 (d->c0, z2, c13, 0); + float64x2_t p23 = vfmaq_laneq_f64 (d->c2, z2, c13, 1); + float64x2_t p03 = vfmaq_f64 (p01, z4, p23); + + float64x2_t p45 = vfmaq_laneq_f64 (d->c4, z2, c57, 0); + float64x2_t p67 = vfmaq_laneq_f64 (d->c6, z2, c57, 1); + float64x2_t p47 = vfmaq_f64 (p45, z4, p67); + + float64x2_t p89 = vfmaq_laneq_f64 (d->c8, z2, c911, 0); + float64x2_t p1011 = vfmaq_laneq_f64 (d->c10, z2, c911, 1); + float64x2_t p811 = vfmaq_f64 (p89, z4, p1011); + + float64x2_t p411 = vfmaq_f64 (p47, z8, p811); + float64x2_t p = vfmaq_f64 (p03, z8, p411); + + /* Finalize polynomial: z + z * z2 * P(z2). */ + p = vfmaq_f64 (d->inv_pi, z2, p); + p = vmulq_f64 (p, z); + + /* acospi(|x|) + = 1/2 - sign(x) * Q(|x|), for |x| < 0.5 + = 2 Q(|x|) , for 0.5 < x < 1.0 + = 1 - 2 Q(|x|) , for -1.0 < x < -0.5. */ + float64x2_t y = vbslq_f64 (d->abs_mask, p, x); + uint64x2_t is_neg = vcltzq_f64 (x); + float64x2_t off = vreinterpretq_f64_u64 ( + vandq_u64 (is_neg, vreinterpretq_u64_f64 (d->one))); + float64x2_t mul = vbslq_f64 (a_le_half, d->one, v_f64 (-2.0)); + float64x2_t add = vbslq_f64 (a_le_half, v_f64 (0.5), off); + + return vfmsq_f64 (add, mul, y); +} diff --git a/sysdeps/aarch64/fpu/acospi_sve.c b/sysdeps/aarch64/fpu/acospi_sve.c new file mode 100644 index 0000000000..e41eaadf5d --- /dev/null +++ b/sysdeps/aarch64/fpu/acospi_sve.c @@ -0,0 +1,112 @@ +/* Double-Precision vector (SVE) inverse cospi function + + Copyright (C) 2025 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 + . */ + +#include "sv_math.h" + +static const struct data +{ + float64_t c1, c3, c5, c7, c9, c11; + float64_t c0, c2, c4, c6, c8, c10; + float64_t inv_pi, half; +} data = { + /* Coefficients of polynomial P such that asin(x)/pi~ x/pi + x^3 * poly(x^2) + on [ 0x1p-126 0x1p-2 ]. rel error: 0x1.ef9f94b1p-33. Generated using + iterative approach for minimisation of relative error in asinpif Sollya + file. */ + .c0 = 0x1.b2995e7b7b5fbp-5, .c1 = 0x1.8723a1d58d83p-6, + .c2 = 0x1.d1a452eacf2fep-7, .c3 = 0x1.3ce52c4d75582p-7, + .c4 = 0x1.d2b2a0aea27d5p-8, .c5 = 0x1.6a0b9b92cad8bp-8, + .c6 = 0x1.2290c84438caep-8, .c7 = 0x1.efba896580d02p-9, + .c8 = 0x1.44446707af38p-9, .c9 = 0x1.5070b3e7aa03ep-8, + .c10 = -0x1.c70015d0ebdafp-9, .c11 = 0x1.27029c383fed9p-7, + .inv_pi = 0x1.45f306dc9c883p-2, .half = 0.5, +}; + +/* Double-precision SVE implementation of vector acospi(x). + + For |x| in [0, 0.5], use order 11 polynomial P to approximate asinpi + such that the final approximation of acospi is: + + acospi(x) ~ 1/2 - (x/pi + x^3 P(x^2)). + + The largest observed error in this region is 1.35 ulp: + _ZGVsMxv_acospi (0x1.fb014996aea18p-2) got 0x1.572a91755bbf6p-2 + want 0x1.572a91755bbf7p-2. + + For |x| in [0.5, 1.0], use same approximation with a change of variable + + acospi(x) = y/pi + y * z * P(z), with z = (1-x)/2 and y = sqrt(z). + + The largest observed error in this region is 2.55 ulp: + _ZGVsMxv_acospi(0x1.d90d50357410cp-1) got 0x1.ffd43d5dd3a9ep-4 + want 0x1.ffd43d5dd3a9bp-4. */ +svfloat64_t SV_NAME_D1 (acospi) (svfloat64_t x, const svbool_t pg) +{ + const struct data *d = ptr_barrier (&data); + svbool_t ptrue = svptrue_b64 (); + + 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, 0.5f); + + /* 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 (ptrue, x, x)); + svfloat64_t z = svsqrt_m (ax, a_gt_half, z2); + + /* Order-11 Estrin. */ + svfloat64_t z4 = svmul_x (ptrue, z2, z2); + svfloat64_t z8 = svmul_x (ptrue, z4, z4); + + svfloat64_t c13 = svld1rq (ptrue, &d->c1); + svfloat64_t c57 = svld1rq (ptrue, &d->c5); + svfloat64_t c911 = svld1rq (ptrue, &d->c9); + + svfloat64_t p01 = svmla_lane (sv_f64 (d->c0), z2, c13, 0); + svfloat64_t p23 = svmla_lane (sv_f64 (d->c2), z2, c13, 1); + svfloat64_t p03 = svmla_x (pg, p01, z4, p23); + + svfloat64_t p45 = svmla_lane (sv_f64 (d->c4), z2, c57, 0); + svfloat64_t p67 = svmla_lane (sv_f64 (d->c6), z2, c57, 1); + svfloat64_t p47 = svmla_x (pg, p45, z4, p67); + + svfloat64_t p89 = svmla_lane (sv_f64 (d->c8), z2, c911, 0); + svfloat64_t p1011 = svmla_lane (sv_f64 (d->c10), z2, c911, 1); + svfloat64_t p811 = svmla_x (pg, p89, z4, p1011); + + svfloat64_t p411 = svmla_x (pg, p47, z8, p811); + svfloat64_t p = svmla_x (pg, p03, z8, p411); + + p = svmla_x (pg, sv_f64 (d->inv_pi), z2, p); + p = svmul_x (ptrue, p, z); + + /* acospi(|x|) = 1/2 - sign(x) * Q(|x|), for |x| < 0.5 + = 2 Q(|x|) , for 0.5 < x < 1.0 + = 1 - 2 Q(|x|) , for -1.0 < x < -0.5. */ + svfloat64_t mul = svreinterpret_f64 ( + svlsl_m (a_gt_half, svreinterpret_u64 (sv_f64 (1.0)), 10)); + mul = svreinterpret_f64 (sveor_x (ptrue, svreinterpret_u64 (mul), sign)); + svfloat64_t add = svreinterpret_f64 ( + svorr_x (ptrue, sign, svreinterpret_u64 (sv_f64 (d->half)))); + add = svsub_m (a_gt_half, sv_f64 (d->half), add); + + return svmsb_x (pg, p, mul, add); +} diff --git a/sysdeps/aarch64/fpu/acospif_advsimd.c b/sysdeps/aarch64/fpu/acospif_advsimd.c new file mode 100644 index 0000000000..8486b62c57 --- /dev/null +++ b/sysdeps/aarch64/fpu/acospif_advsimd.c @@ -0,0 +1,106 @@ +/* Single-Precision vector (Advanced SIMD) inverse cospi function + + Copyright (C) 2025 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 + . */ + +#include "v_math.h" + +static const struct data +{ + float32x4_t c0, c2, c4, inv_pi; + float c1, c3, c5, null; +} data = { + /* Coefficients of polynomial P such that asin(x)/pi~ x/pi + x^3 * poly(x^2) + on [ 0x1p-126 0x1p-2 ]. rel error: 0x1.ef9f94b1p-33. Generated using + iterative approach for minimisation of relative error in asinpif Sollya + file. */ + .c0 = V4 (0x1.b2995ep-5f), .c1 = 0x1.8724ep-6f, + .c2 = V4 (0x1.d1301ep-7f), .c3 = 0x1.446d3cp-7f, + .c4 = V4 (0x1.654848p-8f), .c5 = 0x1.5fdaa8p-7f, + .inv_pi = V4 (0x1.45f306p-2f), +}; + +#define AbsMask 0x7fffffff + +/* Single-precision implementation of vector acospi(x). + + For |x| in [0, 0.5], use order 5 polynomial P to approximate asinpi + such that the final approximation of acospi is an odd polynomial: + + acospi(x) ~ 1/2 - (x/pi + x^3 P(x^2)). + + The largest observed error in this region is 1.23 ulps, + _ZGVnN4v_acospif (0x1.fee13ep-2) got 0x1.55beb4p-2 want 0x1.55beb2p-2. + + For |x| in [0.5, 1.0], use same approximation with a change of variable + + acospi(x) = y/pi + y * z * P(z), with z = (1-x)/2 and y = sqrt(z). + + The largest observed error in this region is 2.53 ulps, + _ZGVnN4v_acospif (0x1.6ad644p-1) got 0x1.fe8f96p-3 + want 0x1.fe8f9cp-3. */ +float32x4_t VPCS_ATTR NOINLINE V_NAME_F1 (acospi) (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)); + + float32x4_t ax = vreinterpretq_f32_u32 (ia); + uint32x4_t a_le_half = vcaltq_f32 (x, v_f32 (0.5f)); + + /* 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. */ + + float32x4_t z2 = vbslq_f32 (a_le_half, vmulq_f32 (x, x), + vfmsq_n_f32 (v_f32 (0.5f), ax, 0.5f)); + float32x4_t z = vbslq_f32 (a_le_half, ax, vsqrtq_f32 (z2)); + + /* Use a single polynomial approximation P for both intervals. */ + + /* Order-5 Estrin evaluation scheme. */ + float32x4_t z4 = vmulq_f32 (z2, z2); + float32x4_t z8 = vmulq_f32 (z4, z4); + float32x4_t c135 = vld1q_f32 (&d->c1); + float32x4_t p01 = vfmaq_laneq_f32 (d->c0, z2, c135, 0); + float32x4_t p23 = vfmaq_laneq_f32 (d->c2, z2, c135, 1); + float32x4_t p03 = vfmaq_f32 (p01, z4, p23); + float32x4_t p45 = vfmaq_laneq_f32 (d->c4, z2, c135, 2); + float32x4_t p = vfmaq_f32 (p03, z8, p45); + /* Add 1/pi as final coeff. */ + p = vfmaq_f32 (d->inv_pi, z2, p); + + /* Finalize polynomial: z * P(z^2). */ + p = vmulq_f32 (z, p); + + /* acospi(|x|) + = 1/2 - sign(x) * Q(|x|), for |x| < 0.5 + = 2 Q(|x|) , for 0.5 < x < 1.0 + = 1 - 2 Q(|x|) , for -1.0 < x < -0.5. */ + + float32x4_t y = vbslq_f32 (v_u32 (AbsMask), p, x); + uint32x4_t is_neg = vcltzq_f32 (x); + float32x4_t off = vreinterpretq_f32_u32 ( + vandq_u32 (vreinterpretq_u32_f32 (v_f32 (1.0f)), is_neg)); + float32x4_t mul = vbslq_f32 (a_le_half, v_f32 (1.0f), v_f32 (-2.0f)); + float32x4_t add = vbslq_f32 (a_le_half, v_f32 (0.5f), off); + + return vfmsq_f32 (add, mul, y); +} +libmvec_hidden_def (V_NAME_F1 (acospi)) +HALF_WIDTH_ALIAS_F1 (acospi) diff --git a/sysdeps/aarch64/fpu/acospif_sve.c b/sysdeps/aarch64/fpu/acospif_sve.c new file mode 100644 index 0000000000..ea4fc4a275 --- /dev/null +++ b/sysdeps/aarch64/fpu/acospif_sve.c @@ -0,0 +1,91 @@ +/* Single-Precision vector (SVE) inverse cospi function + + Copyright (C) 2025 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 + . */ + +#include "sv_math.h" + +static const struct data +{ + float32_t c0, c1, c2, c3, c4, inv_pi, half; +} data = { + /* Coefficients of polynomial P such that asin(x)/pi~ x/pi + x^3 * poly(x^2) + on [ 0x1p-126 0x1p-2 ]. rel error: 0x1.ef9f94b1p-33. Generated using + iterative approach for minimisation of relative error. */ + .c0 = 0x1.b29968p-5f, .c1 = 0x1.871424p-6f, .c2 = 0x1.d56e44p-7f, + .c3 = 0x1.149bb8p-7f, .c4 = 0x1.8e07fep-7f, .inv_pi = 0x1.45f306p-2f, + .half = 0.5f, +}; + +/* Single-precision SVE implementation of vector acospi(x). + + For |x| in [0, 0.5], use order 5 polynomial P to approximate asinpi + such that the final approximation of acospi is: + + acospi(x) ~ 1/2 - (x/pi + x^3 P(x^2)). + + The largest observed error in this region is 1.3 ulps, + _ZGVsMxv_acospif(0x1.ffa9d2p-2) got 0x1.557504p-2 + want 0x1.557502p-2. + + For |x| in [0.5, 1.0], use same approximation with a change of variable + + acospi(x) = y/pi + y * z * P(z), with z = (1-x)/2 and y = sqrt(z). + + The largest observed error in this region is 2.61 ulps, + _ZGVsMxv_acospif (0x1.6b232ep-1) got 0x1.fe04bap-3 + want 0x1.fe04cp-3. */ +svfloat32_t SV_NAME_F1 (acospi) (svfloat32_t x, const svbool_t pg) +{ + const struct data *d = ptr_barrier (&data); + + svbool_t ptrue = svptrue_b32 (); + + 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, 0.5f); + + /* 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 (0.5f), ax, 0.5f), + svmul_x (ptrue, x, x)); + svfloat32_t z = svsqrt_m (ax, a_gt_half, z2); + + /* Use a single polynomial approximation P for both intervals. */ + svfloat32_t p = svmla_x (pg, sv_f32 (d->c3), z2, d->c4); + p = svmad_x (pg, z2, p, d->c2); + p = svmad_x (pg, z2, p, d->c1); + p = svmad_x (pg, z2, p, d->c0); + /* Add 1/pi as final coeff. */ + p = svmla_x (pg, sv_f32 (d->inv_pi), z2, p); + /* Finalize polynomial: z * P(z^2). */ + p = svmul_x (ptrue, z, p); + + /* acospi(|x|) + = 1/2 - sign(x) * Q(|x|), for |x| < 0.5 + = 2 Q(|x|) , for 0.5 < x < 1.0 + = 1 - 2 Q(|x|) , for -1.0 < x < -0.5. */ + svfloat32_t y + = svreinterpret_f32 (svorr_x (ptrue, svreinterpret_u32 (p), sign)); + svfloat32_t mul = svsel (a_gt_half, sv_f32 (2.0f), sv_f32 (-1.0f)); + svfloat32_t add = svreinterpret_f32 ( + svorr_x (ptrue, sign, svreinterpret_u32 (sv_f32 (d->half)))); + add = svsub_m (a_gt_half, sv_f32 (d->half), add); + + return svmad_x (pg, y, mul, add); +} diff --git a/sysdeps/aarch64/fpu/advsimd_f32_protos.h b/sysdeps/aarch64/fpu/advsimd_f32_protos.h index 38681a43ee..f260fa2a5c 100644 --- a/sysdeps/aarch64/fpu/advsimd_f32_protos.h +++ b/sysdeps/aarch64/fpu/advsimd_f32_protos.h @@ -19,6 +19,7 @@ libmvec_hidden_proto (V_NAME_F1(acos)); libmvec_hidden_proto (V_NAME_F1(acosh)); +libmvec_hidden_proto (V_NAME_F1(acospi)); libmvec_hidden_proto (V_NAME_F1(asin)); libmvec_hidden_proto (V_NAME_F1(asinh)); libmvec_hidden_proto (V_NAME_F1(atan)); diff --git a/sysdeps/aarch64/fpu/bits/math-vector.h b/sysdeps/aarch64/fpu/bits/math-vector.h index 5152c0d26d..e828300062 100644 --- a/sysdeps/aarch64/fpu/bits/math-vector.h +++ b/sysdeps/aarch64/fpu/bits/math-vector.h @@ -37,6 +37,10 @@ # define __DECL_SIMD_acosh __DECL_SIMD_aarch64 # undef __DECL_SIMD_acoshf # define __DECL_SIMD_acoshf __DECL_SIMD_aarch64 +# undef __DECL_SIMD_acospi +# define __DECL_SIMD_acospi __DECL_SIMD_aarch64 +# undef __DECL_SIMD_acospif +# define __DECL_SIMD_acospif __DECL_SIMD_aarch64 # undef __DECL_SIMD_asin # define __DECL_SIMD_asin __DECL_SIMD_aarch64 # undef __DECL_SIMD_asinf @@ -178,6 +182,7 @@ typedef __SVBool_t __sv_bool_t; __vpcs __f32x4_t _ZGVnN4vv_atan2f (__f32x4_t, __f32x4_t); __vpcs __f32x4_t _ZGVnN4v_acosf (__f32x4_t); __vpcs __f32x4_t _ZGVnN4v_acoshf (__f32x4_t); +__vpcs __f32x4_t _ZGVnN4v_acospif (__f32x4_t); __vpcs __f32x4_t _ZGVnN4v_asinf (__f32x4_t); __vpcs __f32x4_t _ZGVnN4v_asinhf (__f32x4_t); __vpcs __f32x4_t _ZGVnN4v_atanf (__f32x4_t); @@ -209,6 +214,7 @@ __vpcs __f32x4_t _ZGVnN4v_tanpif (__f32x4_t); __vpcs __f64x2_t _ZGVnN2vv_atan2 (__f64x2_t, __f64x2_t); __vpcs __f64x2_t _ZGVnN2v_acos (__f64x2_t); __vpcs __f64x2_t _ZGVnN2v_acosh (__f64x2_t); +__vpcs __f64x2_t _ZGVnN2v_acospi (__f64x2_t); __vpcs __f64x2_t _ZGVnN2v_asin (__f64x2_t); __vpcs __f64x2_t _ZGVnN2v_asinh (__f64x2_t); __vpcs __f64x2_t _ZGVnN2v_atan (__f64x2_t); @@ -245,6 +251,7 @@ __vpcs __f64x2_t _ZGVnN2v_tanpi (__f64x2_t); __sv_f32_t _ZGVsMxvv_atan2f (__sv_f32_t, __sv_f32_t, __sv_bool_t); __sv_f32_t _ZGVsMxv_acosf (__sv_f32_t, __sv_bool_t); __sv_f32_t _ZGVsMxv_acoshf (__sv_f32_t, __sv_bool_t); +__sv_f32_t _ZGVsMxv_acospif (__sv_f32_t, __sv_bool_t); __sv_f32_t _ZGVsMxv_asinf (__sv_f32_t, __sv_bool_t); __sv_f32_t _ZGVsMxv_asinhf (__sv_f32_t, __sv_bool_t); __sv_f32_t _ZGVsMxv_atanf (__sv_f32_t, __sv_bool_t); @@ -276,6 +283,7 @@ __sv_f32_t _ZGVsMxv_tanpif (__sv_f32_t, __sv_bool_t); __sv_f64_t _ZGVsMxvv_atan2 (__sv_f64_t, __sv_f64_t, __sv_bool_t); __sv_f64_t _ZGVsMxv_acos (__sv_f64_t, __sv_bool_t); __sv_f64_t _ZGVsMxv_acosh (__sv_f64_t, __sv_bool_t); +__sv_f64_t _ZGVsMxv_acospi (__sv_f64_t, __sv_bool_t); __sv_f64_t _ZGVsMxv_asin (__sv_f64_t, __sv_bool_t); __sv_f64_t _ZGVsMxv_asinh (__sv_f64_t, __sv_bool_t); __sv_f64_t _ZGVsMxv_atan (__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 07133ebc56..6a96e129e6 100644 --- a/sysdeps/aarch64/fpu/test-double-advsimd-wrappers.c +++ b/sysdeps/aarch64/fpu/test-double-advsimd-wrappers.c @@ -25,6 +25,7 @@ VPCS_VECTOR_WRAPPER (acos_advsimd, _ZGVnN2v_acos) VPCS_VECTOR_WRAPPER (acosh_advsimd, _ZGVnN2v_acosh) +VPCS_VECTOR_WRAPPER (acospi_advsimd, _ZGVnN2v_acospi) VPCS_VECTOR_WRAPPER (asin_advsimd, _ZGVnN2v_asin) VPCS_VECTOR_WRAPPER (asinh_advsimd, _ZGVnN2v_asinh) VPCS_VECTOR_WRAPPER (atan_advsimd, _ZGVnN2v_atan) diff --git a/sysdeps/aarch64/fpu/test-double-sve-wrappers.c b/sysdeps/aarch64/fpu/test-double-sve-wrappers.c index 02953cbd5e..101a8dd23a 100644 --- a/sysdeps/aarch64/fpu/test-double-sve-wrappers.c +++ b/sysdeps/aarch64/fpu/test-double-sve-wrappers.c @@ -44,6 +44,7 @@ SVE_VECTOR_WRAPPER (acos_sve, _ZGVsMxv_acos) SVE_VECTOR_WRAPPER (acosh_sve, _ZGVsMxv_acosh) +SVE_VECTOR_WRAPPER (acospi_sve, _ZGVsMxv_acospi) SVE_VECTOR_WRAPPER (asin_sve, _ZGVsMxv_asin) SVE_VECTOR_WRAPPER (asinh_sve, _ZGVsMxv_asinh) SVE_VECTOR_WRAPPER (atan_sve, _ZGVsMxv_atan) diff --git a/sysdeps/aarch64/fpu/test-float-advsimd-wrappers.c b/sysdeps/aarch64/fpu/test-float-advsimd-wrappers.c index 118bbb0dcf..4fa3bd36cb 100644 --- a/sysdeps/aarch64/fpu/test-float-advsimd-wrappers.c +++ b/sysdeps/aarch64/fpu/test-float-advsimd-wrappers.c @@ -25,6 +25,7 @@ VPCS_VECTOR_WRAPPER (acosf_advsimd, _ZGVnN4v_acosf) VPCS_VECTOR_WRAPPER (acoshf_advsimd, _ZGVnN4v_acoshf) +VPCS_VECTOR_WRAPPER (acospif_advsimd, _ZGVnN4v_acospif) VPCS_VECTOR_WRAPPER (asinf_advsimd, _ZGVnN4v_asinf) VPCS_VECTOR_WRAPPER (asinhf_advsimd, _ZGVnN4v_asinhf) VPCS_VECTOR_WRAPPER (atanf_advsimd, _ZGVnN4v_atanf) diff --git a/sysdeps/aarch64/fpu/test-float-sve-wrappers.c b/sysdeps/aarch64/fpu/test-float-sve-wrappers.c index f5e7c8cdb7..0690c7185c 100644 --- a/sysdeps/aarch64/fpu/test-float-sve-wrappers.c +++ b/sysdeps/aarch64/fpu/test-float-sve-wrappers.c @@ -44,6 +44,7 @@ SVE_VECTOR_WRAPPER (acosf_sve, _ZGVsMxv_acosf) SVE_VECTOR_WRAPPER (acoshf_sve, _ZGVsMxv_acoshf) +SVE_VECTOR_WRAPPER (acospif_sve, _ZGVsMxv_acospif) SVE_VECTOR_WRAPPER (asinf_sve, _ZGVsMxv_asinf) SVE_VECTOR_WRAPPER (asinhf_sve, _ZGVsMxv_asinhf) SVE_VECTOR_WRAPPER (atanf_sve, _ZGVsMxv_atanf) diff --git a/sysdeps/unix/sysv/linux/aarch64/libmvec.abilist b/sysdeps/unix/sysv/linux/aarch64/libmvec.abilist index a56ce7f4e2..47d48d3506 100644 --- a/sysdeps/unix/sysv/linux/aarch64/libmvec.abilist +++ b/sysdeps/unix/sysv/linux/aarch64/libmvec.abilist @@ -148,3 +148,8 @@ GLIBC_2.41 _ZGVsMxv_sinpi F GLIBC_2.41 _ZGVsMxv_sinpif F GLIBC_2.41 _ZGVsMxv_tanpi F GLIBC_2.41 _ZGVsMxv_tanpif F +GLIBC_2.42 _ZGVnN2v_acospi F +GLIBC_2.42 _ZGVnN2v_acospif F +GLIBC_2.42 _ZGVnN4v_acospif F +GLIBC_2.42 _ZGVsMxv_acospi F +GLIBC_2.42 _ZGVsMxv_acospif F