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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 <Wilco.Dijkstra@arm.com>
This commit is contained in:
committed by
Wilco Dijkstra
parent
1e84509e00
commit
993997ca1b
@@ -373,4 +373,15 @@
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#define __DECL_SIMD_tanpif32x
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#define __DECL_SIMD_tanpif32x
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#define __DECL_SIMD_tanpif64x
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#define __DECL_SIMD_tanpif64x
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#define __DECL_SIMD_tanpif128x
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#define __DECL_SIMD_tanpif128x
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#define __DECL_SIMD_acospi
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#define __DECL_SIMD_acospif
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#define __DECL_SIMD_acospil
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#define __DECL_SIMD_acospif16
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#define __DECL_SIMD_acospif32
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#define __DECL_SIMD_acospif64
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#define __DECL_SIMD_acospif128
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#define __DECL_SIMD_acospif32x
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#define __DECL_SIMD_acospif64x
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#define __DECL_SIMD_acospif128x
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#endif
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#endif
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@@ -68,6 +68,7 @@ __MATHCALL_VEC (tan,, (_Mdouble_ __x));
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#if __GLIBC_USE (IEC_60559_FUNCS_EXT_C23)
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#if __GLIBC_USE (IEC_60559_FUNCS_EXT_C23)
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/* Arc cosine of X, divided by pi. */
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/* Arc cosine of X, divided by pi. */
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__MATHCALL (acospi,, (_Mdouble_ __x));
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__MATHCALL (acospi,, (_Mdouble_ __x));
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__MATHCALL_VEC (acospi,, (_Mdouble_ __x));
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/* Arc sine of X, divided by pi. */
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/* Arc sine of X, divided by pi. */
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__MATHCALL (asinpi,, (_Mdouble_ __x));
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__MATHCALL (asinpi,, (_Mdouble_ __x));
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/* Arc tangent of X, divided by pi. */
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/* Arc tangent of X, divided by pi. */
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@@ -1,5 +1,6 @@
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libmvec-supported-funcs = acos \
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libmvec-supported-funcs = acos \
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acosh \
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acosh \
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acospi \
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asin \
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asin \
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asinh \
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asinh \
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atan \
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atan \
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@@ -157,4 +157,11 @@ libmvec {
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_ZGVsMxv_tanpi;
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_ZGVsMxv_tanpi;
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_ZGVsMxv_tanpif;
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_ZGVsMxv_tanpif;
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}
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}
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GLIBC_2.42 {
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_ZGVnN2v_acospi;
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_ZGVnN2v_acospif;
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_ZGVnN4v_acospif;
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_ZGVsMxv_acospi;
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_ZGVsMxv_acospif;
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}
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}
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}
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118
sysdeps/aarch64/fpu/acospi_advsimd.c
Normal file
118
sysdeps/aarch64/fpu/acospi_advsimd.c
Normal file
@@ -0,0 +1,118 @@
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/* Double-Precision vector (Advanced SIMD) inverse cospi function
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Copyright (C) 2025 Free Software Foundation, Inc.
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This file is part of the GNU C Library.
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The GNU C Library is free software; you can redistribute it and/or
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modify it under the terms of the GNU Lesser General Public
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License as published by the Free Software Foundation; either
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version 2.1 of the License, or (at your option) any later version.
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The GNU C Library is distributed in the hope that it will be useful,
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but WITHOUT ANY WARRANTY; without even the implied warranty of
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MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the GNU
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Lesser General Public License for more details.
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You should have received a copy of the GNU Lesser General Public
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License along with the GNU C Library; if not, see
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<https://www.gnu.org/licenses/>. */
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#include "v_math.h"
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static const struct data
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{
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float64x2_t c0, c2, c4, c6, c8, c10;
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uint64x2_t abs_mask;
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float64x2_t one, inv_pi;
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double c1, c3, c5, c7, c9, c11;
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} data = {
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/* Coefficients of polynomial P such that asin(x)/pi~ x/pi + x^3 * poly(x^2)
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on [ 0x1p-126 0x1p-2 ]. rel error: 0x1.ef9f94b1p-33. Generated using
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iterative approach for minimisation of relative error in asinpif Sollya
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file. */
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.c0 = V2 (0x1.b2995e7b7b5fbp-5), .c1 = 0x1.8723a1d58d83p-6,
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.c2 = V2 (0x1.d1a452eacf2fep-7), .c3 = 0x1.3ce52c4d75582p-7,
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.c4 = V2 (0x1.d2b2a0aea27d5p-8), .c5 = 0x1.6a0b9b92cad8bp-8,
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.c6 = V2 (0x1.2290c84438caep-8), .c7 = 0x1.efba896580d02p-9,
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.c8 = V2 (0x1.44446707af38p-9), .c9 = 0x1.5070b3e7aa03ep-8,
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.c10 = V2 (-0x1.c70015d0ebdafp-9), .c11 = 0x1.27029c383fed9p-7,
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.abs_mask = V2 (0x7fffffffffffffff), .one = V2 (1.0),
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.inv_pi = V2 (0x1.45f306dc9c883p-2),
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};
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/* Double-precision implementation of vector acospi(x).
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For |x| in [0, 0.5], use order-11 polynomial P to approximate asinpi
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such that the final approximation of acospi is an odd polynomial:
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acospi(x) ~ 1/2 - (x/pi + x^3 P(x^2)).
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The largest observed error in this region is 1.35 ulp:
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_ZGVnN2v_acospi (0x1.fb16ed35a6d64p-2) got 0x1.5722a3dbcafb4p-2
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want 0x1.5722a3dbcafb5p-2.
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For |x| in [0.5, 1.0], use same approximation with a change of variable
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acospi(x) = y/pi + y * z * P(z), with z = (1-x)/2 and y = sqrt(z).
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The largest observed error in this region is 2.55 ulp:
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_ZGVnN2v_acospi (0x1.d90d50357410cp-1) got 0x1.ffd43d5dd3a9ep-4
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want 0x1.ffd43d5dd3a9bp-4. */
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float64x2_t VPCS_ATTR NOINLINE V_NAME_D1 (acospi) (float64x2_t x)
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{
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const struct data *d = ptr_barrier (&data);
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uint64x2_t ix = vreinterpretq_u64_f64 (x);
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uint64x2_t ia = vandq_u64 (ix, d->abs_mask);
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float64x2_t ax = vreinterpretq_f64_u64 (ia);
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uint64x2_t a_le_half = vcaltq_f64 (x, v_f64 (0.5));
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/* Evaluate polynomial Q(x) = z + z * z2 * P(z2) with
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z2 = x ^ 2 and z = |x| , if |x| < 0.5
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z2 = (1 - |x|) / 2 and z = sqrt(z2), if |x| >= 0.5. */
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float64x2_t z2 = vbslq_f64 (a_le_half, vmulq_f64 (x, x),
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vfmsq_n_f64 (v_f64 (0.5), ax, 0.5));
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float64x2_t z = vbslq_f64 (a_le_half, ax, vsqrtq_f64 (z2));
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/* Use a single polynomial approximation P for both intervals. */
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float64x2_t z4 = vmulq_f64 (z2, z2);
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float64x2_t z8 = vmulq_f64 (z4, z4);
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/* Order-11 Estrin. */
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float64x2_t c13 = vld1q_f64 (&d->c1);
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float64x2_t c57 = vld1q_f64 (&d->c5);
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float64x2_t c911 = vld1q_f64 (&d->c9);
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float64x2_t p01 = vfmaq_laneq_f64 (d->c0, z2, c13, 0);
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float64x2_t p23 = vfmaq_laneq_f64 (d->c2, z2, c13, 1);
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float64x2_t p03 = vfmaq_f64 (p01, z4, p23);
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float64x2_t p45 = vfmaq_laneq_f64 (d->c4, z2, c57, 0);
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float64x2_t p67 = vfmaq_laneq_f64 (d->c6, z2, c57, 1);
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float64x2_t p47 = vfmaq_f64 (p45, z4, p67);
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float64x2_t p89 = vfmaq_laneq_f64 (d->c8, z2, c911, 0);
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float64x2_t p1011 = vfmaq_laneq_f64 (d->c10, z2, c911, 1);
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float64x2_t p811 = vfmaq_f64 (p89, z4, p1011);
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float64x2_t p411 = vfmaq_f64 (p47, z8, p811);
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float64x2_t p = vfmaq_f64 (p03, z8, p411);
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/* Finalize polynomial: z + z * z2 * P(z2). */
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p = vfmaq_f64 (d->inv_pi, z2, p);
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p = vmulq_f64 (p, z);
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/* acospi(|x|)
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= 1/2 - sign(x) * Q(|x|), for |x| < 0.5
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= 2 Q(|x|) , for 0.5 < x < 1.0
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= 1 - 2 Q(|x|) , for -1.0 < x < -0.5. */
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float64x2_t y = vbslq_f64 (d->abs_mask, p, x);
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uint64x2_t is_neg = vcltzq_f64 (x);
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float64x2_t off = vreinterpretq_f64_u64 (
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vandq_u64 (is_neg, vreinterpretq_u64_f64 (d->one)));
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float64x2_t mul = vbslq_f64 (a_le_half, d->one, v_f64 (-2.0));
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float64x2_t add = vbslq_f64 (a_le_half, v_f64 (0.5), off);
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return vfmsq_f64 (add, mul, y);
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}
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112
sysdeps/aarch64/fpu/acospi_sve.c
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112
sysdeps/aarch64/fpu/acospi_sve.c
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@@ -0,0 +1,112 @@
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/* Double-Precision vector (SVE) inverse cospi function
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Copyright (C) 2025 Free Software Foundation, Inc.
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This file is part of the GNU C Library.
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The GNU C Library is free software; you can redistribute it and/or
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modify it under the terms of the GNU Lesser General Public
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License as published by the Free Software Foundation; either
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version 2.1 of the License, or (at your option) any later version.
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The GNU C Library is distributed in the hope that it will be useful,
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but WITHOUT ANY WARRANTY; without even the implied warranty of
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MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the GNU
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Lesser General Public License for more details.
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You should have received a copy of the GNU Lesser General Public
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License along with the GNU C Library; if not, see
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<https://www.gnu.org/licenses/>. */
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#include "sv_math.h"
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static const struct data
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{
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float64_t c1, c3, c5, c7, c9, c11;
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float64_t c0, c2, c4, c6, c8, c10;
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float64_t inv_pi, half;
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} data = {
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/* Coefficients of polynomial P such that asin(x)/pi~ x/pi + x^3 * poly(x^2)
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on [ 0x1p-126 0x1p-2 ]. rel error: 0x1.ef9f94b1p-33. Generated using
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iterative approach for minimisation of relative error in asinpif Sollya
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file. */
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.c0 = 0x1.b2995e7b7b5fbp-5, .c1 = 0x1.8723a1d58d83p-6,
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.c2 = 0x1.d1a452eacf2fep-7, .c3 = 0x1.3ce52c4d75582p-7,
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.c4 = 0x1.d2b2a0aea27d5p-8, .c5 = 0x1.6a0b9b92cad8bp-8,
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.c6 = 0x1.2290c84438caep-8, .c7 = 0x1.efba896580d02p-9,
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.c8 = 0x1.44446707af38p-9, .c9 = 0x1.5070b3e7aa03ep-8,
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.c10 = -0x1.c70015d0ebdafp-9, .c11 = 0x1.27029c383fed9p-7,
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.inv_pi = 0x1.45f306dc9c883p-2, .half = 0.5,
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};
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/* Double-precision SVE implementation of vector acospi(x).
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For |x| in [0, 0.5], use order 11 polynomial P to approximate asinpi
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such that the final approximation of acospi is:
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acospi(x) ~ 1/2 - (x/pi + x^3 P(x^2)).
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The largest observed error in this region is 1.35 ulp:
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_ZGVsMxv_acospi (0x1.fb014996aea18p-2) got 0x1.572a91755bbf6p-2
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want 0x1.572a91755bbf7p-2.
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For |x| in [0.5, 1.0], use same approximation with a change of variable
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acospi(x) = y/pi + y * z * P(z), with z = (1-x)/2 and y = sqrt(z).
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The largest observed error in this region is 2.55 ulp:
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_ZGVsMxv_acospi(0x1.d90d50357410cp-1) got 0x1.ffd43d5dd3a9ep-4
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want 0x1.ffd43d5dd3a9bp-4. */
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svfloat64_t SV_NAME_D1 (acospi) (svfloat64_t x, const svbool_t pg)
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{
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const struct data *d = ptr_barrier (&data);
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svbool_t ptrue = svptrue_b64 ();
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svuint64_t sign = svand_x (pg, svreinterpret_u64 (x), 0x8000000000000000);
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svfloat64_t ax = svabs_x (pg, x);
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svbool_t a_gt_half = svacgt (pg, x, 0.5f);
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/* Evaluate polynomial Q(x) = z + z * z2 * P(z2) with
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z2 = x ^ 2 and z = |x| , if |x| < 0.5
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z2 = (1 - |x|) / 2 and z = sqrt(z2), if |x| >= 0.5. */
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svfloat64_t z2 = svsel (a_gt_half, svmls_x (pg, sv_f64 (0.5), ax, 0.5),
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svmul_x (ptrue, x, x));
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svfloat64_t z = svsqrt_m (ax, a_gt_half, z2);
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/* Order-11 Estrin. */
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svfloat64_t z4 = svmul_x (ptrue, z2, z2);
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svfloat64_t z8 = svmul_x (ptrue, z4, z4);
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svfloat64_t c13 = svld1rq (ptrue, &d->c1);
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svfloat64_t c57 = svld1rq (ptrue, &d->c5);
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svfloat64_t c911 = svld1rq (ptrue, &d->c9);
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svfloat64_t p01 = svmla_lane (sv_f64 (d->c0), z2, c13, 0);
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svfloat64_t p23 = svmla_lane (sv_f64 (d->c2), z2, c13, 1);
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svfloat64_t p03 = svmla_x (pg, p01, z4, p23);
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svfloat64_t p45 = svmla_lane (sv_f64 (d->c4), z2, c57, 0);
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svfloat64_t p67 = svmla_lane (sv_f64 (d->c6), z2, c57, 1);
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svfloat64_t p47 = svmla_x (pg, p45, z4, p67);
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svfloat64_t p89 = svmla_lane (sv_f64 (d->c8), z2, c911, 0);
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svfloat64_t p1011 = svmla_lane (sv_f64 (d->c10), z2, c911, 1);
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svfloat64_t p811 = svmla_x (pg, p89, z4, p1011);
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svfloat64_t p411 = svmla_x (pg, p47, z8, p811);
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svfloat64_t p = svmla_x (pg, p03, z8, p411);
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p = svmla_x (pg, sv_f64 (d->inv_pi), z2, p);
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p = svmul_x (ptrue, p, z);
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/* acospi(|x|) = 1/2 - sign(x) * Q(|x|), for |x| < 0.5
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= 2 Q(|x|) , for 0.5 < x < 1.0
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= 1 - 2 Q(|x|) , for -1.0 < x < -0.5. */
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svfloat64_t mul = svreinterpret_f64 (
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svlsl_m (a_gt_half, svreinterpret_u64 (sv_f64 (1.0)), 10));
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mul = svreinterpret_f64 (sveor_x (ptrue, svreinterpret_u64 (mul), sign));
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svfloat64_t add = svreinterpret_f64 (
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|
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);
|
||||||
|
}
|
106
sysdeps/aarch64/fpu/acospif_advsimd.c
Normal file
106
sysdeps/aarch64/fpu/acospif_advsimd.c
Normal file
@@ -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
|
||||||
|
<https://www.gnu.org/licenses/>. */
|
||||||
|
|
||||||
|
#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)
|
91
sysdeps/aarch64/fpu/acospif_sve.c
Normal file
91
sysdeps/aarch64/fpu/acospif_sve.c
Normal file
@@ -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
|
||||||
|
<https://www.gnu.org/licenses/>. */
|
||||||
|
|
||||||
|
#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);
|
||||||
|
}
|
@@ -19,6 +19,7 @@
|
|||||||
|
|
||||||
libmvec_hidden_proto (V_NAME_F1(acos));
|
libmvec_hidden_proto (V_NAME_F1(acos));
|
||||||
libmvec_hidden_proto (V_NAME_F1(acosh));
|
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(asin));
|
||||||
libmvec_hidden_proto (V_NAME_F1(asinh));
|
libmvec_hidden_proto (V_NAME_F1(asinh));
|
||||||
libmvec_hidden_proto (V_NAME_F1(atan));
|
libmvec_hidden_proto (V_NAME_F1(atan));
|
||||||
|
@@ -37,6 +37,10 @@
|
|||||||
# define __DECL_SIMD_acosh __DECL_SIMD_aarch64
|
# define __DECL_SIMD_acosh __DECL_SIMD_aarch64
|
||||||
# undef __DECL_SIMD_acoshf
|
# undef __DECL_SIMD_acoshf
|
||||||
# define __DECL_SIMD_acoshf __DECL_SIMD_aarch64
|
# 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
|
# undef __DECL_SIMD_asin
|
||||||
# define __DECL_SIMD_asin __DECL_SIMD_aarch64
|
# define __DECL_SIMD_asin __DECL_SIMD_aarch64
|
||||||
# undef __DECL_SIMD_asinf
|
# 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 _ZGVnN4vv_atan2f (__f32x4_t, __f32x4_t);
|
||||||
__vpcs __f32x4_t _ZGVnN4v_acosf (__f32x4_t);
|
__vpcs __f32x4_t _ZGVnN4v_acosf (__f32x4_t);
|
||||||
__vpcs __f32x4_t _ZGVnN4v_acoshf (__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_asinf (__f32x4_t);
|
||||||
__vpcs __f32x4_t _ZGVnN4v_asinhf (__f32x4_t);
|
__vpcs __f32x4_t _ZGVnN4v_asinhf (__f32x4_t);
|
||||||
__vpcs __f32x4_t _ZGVnN4v_atanf (__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 _ZGVnN2vv_atan2 (__f64x2_t, __f64x2_t);
|
||||||
__vpcs __f64x2_t _ZGVnN2v_acos (__f64x2_t);
|
__vpcs __f64x2_t _ZGVnN2v_acos (__f64x2_t);
|
||||||
__vpcs __f64x2_t _ZGVnN2v_acosh (__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_asin (__f64x2_t);
|
||||||
__vpcs __f64x2_t _ZGVnN2v_asinh (__f64x2_t);
|
__vpcs __f64x2_t _ZGVnN2v_asinh (__f64x2_t);
|
||||||
__vpcs __f64x2_t _ZGVnN2v_atan (__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 _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_acosf (__sv_f32_t, __sv_bool_t);
|
||||||
__sv_f32_t _ZGVsMxv_acoshf (__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_asinf (__sv_f32_t, __sv_bool_t);
|
||||||
__sv_f32_t _ZGVsMxv_asinhf (__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);
|
__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 _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_acos (__sv_f64_t, __sv_bool_t);
|
||||||
__sv_f64_t _ZGVsMxv_acosh (__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_asin (__sv_f64_t, __sv_bool_t);
|
||||||
__sv_f64_t _ZGVsMxv_asinh (__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);
|
__sv_f64_t _ZGVsMxv_atan (__sv_f64_t, __sv_bool_t);
|
||||||
|
@@ -25,6 +25,7 @@
|
|||||||
|
|
||||||
VPCS_VECTOR_WRAPPER (acos_advsimd, _ZGVnN2v_acos)
|
VPCS_VECTOR_WRAPPER (acos_advsimd, _ZGVnN2v_acos)
|
||||||
VPCS_VECTOR_WRAPPER (acosh_advsimd, _ZGVnN2v_acosh)
|
VPCS_VECTOR_WRAPPER (acosh_advsimd, _ZGVnN2v_acosh)
|
||||||
|
VPCS_VECTOR_WRAPPER (acospi_advsimd, _ZGVnN2v_acospi)
|
||||||
VPCS_VECTOR_WRAPPER (asin_advsimd, _ZGVnN2v_asin)
|
VPCS_VECTOR_WRAPPER (asin_advsimd, _ZGVnN2v_asin)
|
||||||
VPCS_VECTOR_WRAPPER (asinh_advsimd, _ZGVnN2v_asinh)
|
VPCS_VECTOR_WRAPPER (asinh_advsimd, _ZGVnN2v_asinh)
|
||||||
VPCS_VECTOR_WRAPPER (atan_advsimd, _ZGVnN2v_atan)
|
VPCS_VECTOR_WRAPPER (atan_advsimd, _ZGVnN2v_atan)
|
||||||
|
@@ -44,6 +44,7 @@
|
|||||||
|
|
||||||
SVE_VECTOR_WRAPPER (acos_sve, _ZGVsMxv_acos)
|
SVE_VECTOR_WRAPPER (acos_sve, _ZGVsMxv_acos)
|
||||||
SVE_VECTOR_WRAPPER (acosh_sve, _ZGVsMxv_acosh)
|
SVE_VECTOR_WRAPPER (acosh_sve, _ZGVsMxv_acosh)
|
||||||
|
SVE_VECTOR_WRAPPER (acospi_sve, _ZGVsMxv_acospi)
|
||||||
SVE_VECTOR_WRAPPER (asin_sve, _ZGVsMxv_asin)
|
SVE_VECTOR_WRAPPER (asin_sve, _ZGVsMxv_asin)
|
||||||
SVE_VECTOR_WRAPPER (asinh_sve, _ZGVsMxv_asinh)
|
SVE_VECTOR_WRAPPER (asinh_sve, _ZGVsMxv_asinh)
|
||||||
SVE_VECTOR_WRAPPER (atan_sve, _ZGVsMxv_atan)
|
SVE_VECTOR_WRAPPER (atan_sve, _ZGVsMxv_atan)
|
||||||
|
@@ -25,6 +25,7 @@
|
|||||||
|
|
||||||
VPCS_VECTOR_WRAPPER (acosf_advsimd, _ZGVnN4v_acosf)
|
VPCS_VECTOR_WRAPPER (acosf_advsimd, _ZGVnN4v_acosf)
|
||||||
VPCS_VECTOR_WRAPPER (acoshf_advsimd, _ZGVnN4v_acoshf)
|
VPCS_VECTOR_WRAPPER (acoshf_advsimd, _ZGVnN4v_acoshf)
|
||||||
|
VPCS_VECTOR_WRAPPER (acospif_advsimd, _ZGVnN4v_acospif)
|
||||||
VPCS_VECTOR_WRAPPER (asinf_advsimd, _ZGVnN4v_asinf)
|
VPCS_VECTOR_WRAPPER (asinf_advsimd, _ZGVnN4v_asinf)
|
||||||
VPCS_VECTOR_WRAPPER (asinhf_advsimd, _ZGVnN4v_asinhf)
|
VPCS_VECTOR_WRAPPER (asinhf_advsimd, _ZGVnN4v_asinhf)
|
||||||
VPCS_VECTOR_WRAPPER (atanf_advsimd, _ZGVnN4v_atanf)
|
VPCS_VECTOR_WRAPPER (atanf_advsimd, _ZGVnN4v_atanf)
|
||||||
|
@@ -44,6 +44,7 @@
|
|||||||
|
|
||||||
SVE_VECTOR_WRAPPER (acosf_sve, _ZGVsMxv_acosf)
|
SVE_VECTOR_WRAPPER (acosf_sve, _ZGVsMxv_acosf)
|
||||||
SVE_VECTOR_WRAPPER (acoshf_sve, _ZGVsMxv_acoshf)
|
SVE_VECTOR_WRAPPER (acoshf_sve, _ZGVsMxv_acoshf)
|
||||||
|
SVE_VECTOR_WRAPPER (acospif_sve, _ZGVsMxv_acospif)
|
||||||
SVE_VECTOR_WRAPPER (asinf_sve, _ZGVsMxv_asinf)
|
SVE_VECTOR_WRAPPER (asinf_sve, _ZGVsMxv_asinf)
|
||||||
SVE_VECTOR_WRAPPER (asinhf_sve, _ZGVsMxv_asinhf)
|
SVE_VECTOR_WRAPPER (asinhf_sve, _ZGVsMxv_asinhf)
|
||||||
SVE_VECTOR_WRAPPER (atanf_sve, _ZGVsMxv_atanf)
|
SVE_VECTOR_WRAPPER (atanf_sve, _ZGVsMxv_atanf)
|
||||||
|
@@ -148,3 +148,8 @@ GLIBC_2.41 _ZGVsMxv_sinpi F
|
|||||||
GLIBC_2.41 _ZGVsMxv_sinpif F
|
GLIBC_2.41 _ZGVsMxv_sinpif F
|
||||||
GLIBC_2.41 _ZGVsMxv_tanpi F
|
GLIBC_2.41 _ZGVsMxv_tanpi F
|
||||||
GLIBC_2.41 _ZGVsMxv_tanpif 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
|
||||||
|
Reference in New Issue
Block a user