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116 lines
4.1 KiB
C
116 lines
4.1 KiB
C
/* Single-precision AdvSIMD inverse cos
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Copyright (C) 2023-2024 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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#include "poly_advsimd_f32.h"
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static const struct data
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{
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float32x4_t poly[5];
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float32x4_t pi_over_2f, pif;
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} data = {
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/* Polynomial approximation of (asin(sqrt(x)) - sqrt(x)) / (x * sqrt(x)) on
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[ 0x1p-24 0x1p-2 ] order = 4 rel error: 0x1.00a23bbp-29 . */
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.poly = { V4 (0x1.55555ep-3), V4 (0x1.33261ap-4), V4 (0x1.70d7dcp-5),
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V4 (0x1.b059dp-6), V4 (0x1.3af7d8p-5) },
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.pi_over_2f = V4 (0x1.921fb6p+0f),
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.pif = V4 (0x1.921fb6p+1f),
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};
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#define AbsMask 0x7fffffff
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#define Half 0x3f000000
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#define One 0x3f800000
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#define Small 0x32800000 /* 2^-26. */
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#if WANT_SIMD_EXCEPT
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static float32x4_t VPCS_ATTR NOINLINE
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special_case (float32x4_t x, float32x4_t y, uint32x4_t special)
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{
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return v_call_f32 (acosf, x, y, special);
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}
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#endif
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/* Single-precision implementation of vector acos(x).
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For |x| < Small, approximate acos(x) by pi/2 - x. Small = 2^-26 for correct
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rounding.
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If WANT_SIMD_EXCEPT = 0, Small = 0 and we proceed with the following
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approximation.
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For |x| in [Small, 0.5], use order 4 polynomial P such that the final
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approximation of asin is an odd polynomial:
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acos(x) ~ pi/2 - (x + x^3 P(x^2)).
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The largest observed error in this region is 1.26 ulps,
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_ZGVnN4v_acosf (0x1.843bfcp-2) got 0x1.2e934cp+0 want 0x1.2e934ap+0.
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For |x| in [0.5, 1.0], use same approximation with a change of variable
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acos(x) = y + 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 1.32 ulps,
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_ZGVnN4v_acosf (0x1.15ba56p-1) got 0x1.feb33p-1
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want 0x1.feb32ep-1. */
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float32x4_t VPCS_ATTR NOINLINE V_NAME_F1 (acos) (float32x4_t x)
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{
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const struct data *d = ptr_barrier (&data);
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uint32x4_t ix = vreinterpretq_u32_f32 (x);
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uint32x4_t ia = vandq_u32 (ix, v_u32 (AbsMask));
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#if WANT_SIMD_EXCEPT
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/* A single comparison for One, Small and QNaN. */
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uint32x4_t special
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= vcgtq_u32 (vsubq_u32 (ia, v_u32 (Small)), v_u32 (One - Small));
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if (__glibc_unlikely (v_any_u32 (special)))
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return special_case (x, x, v_u32 (0xffffffff));
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#endif
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float32x4_t ax = vreinterpretq_f32_u32 (ia);
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uint32x4_t a_le_half = vcleq_u32 (ia, v_u32 (Half));
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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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float32x4_t z2 = vbslq_f32 (a_le_half, vmulq_f32 (x, x),
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vfmsq_n_f32 (v_f32 (0.5), ax, 0.5));
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float32x4_t z = vbslq_f32 (a_le_half, ax, vsqrtq_f32 (z2));
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/* Use a single polynomial approximation P for both intervals. */
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float32x4_t p = v_horner_4_f32 (z2, d->poly);
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/* Finalize polynomial: z + z * z2 * P(z2). */
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p = vfmaq_f32 (z, vmulq_f32 (z, z2), p);
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/* acos(|x|) = pi/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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= pi - 2 Q(|x|) , for -1.0 < x < -0.5. */
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float32x4_t y = vbslq_f32 (v_u32 (AbsMask), p, x);
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uint32x4_t is_neg = vcltzq_f32 (x);
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float32x4_t off = vreinterpretq_f32_u32 (
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vandq_u32 (vreinterpretq_u32_f32 (d->pif), is_neg));
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float32x4_t mul = vbslq_f32 (a_le_half, v_f32 (-1.0), v_f32 (2.0));
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float32x4_t add = vbslq_f32 (a_le_half, d->pi_over_2f, off);
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return vfmaq_f32 (add, mul, y);
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}
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libmvec_hidden_def (V_NAME_F1(acos))
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HALF_WIDTH_ALIAS_F1 (acos)
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