sysdeps/aarch64/fpu/asinf_advsimd.c

   1 /* Single-precision AdvSIMD inverse sin
   2
   3    Copyright (C) 2023-2024 Free Software Foundation, Inc.
   4    This file is part of the GNU C Library.
   5
   6    The GNU C Library is free software; you can redistribute it and/or
   7    modify it under the terms of the GNU Lesser General Public
   8    License as published by the Free Software Foundation; either
   9    version 2.1 of the License, or (at your option) any later version.
  10
  11    The GNU C Library is distributed in the hope that it will be useful,
  12    but WITHOUT ANY WARRANTY; without even the implied warranty of
  13    MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE.  See the GNU
  14    Lesser General Public License for more details.
  15
  16    You should have received a copy of the GNU Lesser General Public
  17    License along with the GNU C Library; if not, see
  18    <https://www.gnu.org/licenses/>.  */
  19
  20 #include "v_math.h"
  21 #include "poly_advsimd_f32.h"
  22
  23 static const struct data
  24 {
  25   float32x4_t poly[5];
  26   float32x4_t pi_over_2f;
  27 } data = {
  28   /* Polynomial approximation of  (asin(sqrt(x)) - sqrt(x)) / (x * sqrt(x))  on
  29      [ 0x1p-24 0x1p-2 ] order = 4 rel error: 0x1.00a23bbp-29 .  */
  30   .poly = { V4 (0x1.55555ep-3), V4 (0x1.33261ap-4), V4 (0x1.70d7dcp-5),
  31             V4 (0x1.b059dp-6), V4 (0x1.3af7d8p-5) },
  32   .pi_over_2f = V4 (0x1.921fb6p+0f),
  33 };
  34
  35 #define AbsMask 0x7fffffff
  36 #define Half 0x3f000000
  37 #define One 0x3f800000
  38 #define Small 0x39800000 /* 2^-12.  */
  39
  40 #if WANT_SIMD_EXCEPT
  41 static float32x4_t VPCS_ATTR NOINLINE
  42 special_case (float32x4_t x, float32x4_t y, uint32x4_t special)
  43 {
  44   return v_call_f32 (asinf, x, y, special);
  45 }
  46 #endif
  47
  48 /* Single-precision implementation of vector asin(x).
  49
  50    For |x| < Small, approximate asin(x) by x. Small = 2^-12 for correct
  51    rounding. If WANT_SIMD_EXCEPT = 0, Small = 0 and we proceed with the
  52    following approximation.
  53
  54    For |x| in [Small, 0.5], use order 4 polynomial P such that the final
  55    approximation is an odd polynomial: asin(x) ~ x + x^3 P(x^2).
  56
  57     The largest observed error in this region is 0.83 ulps,
  58       _ZGVnN4v_asinf (0x1.ea00f4p-2) got 0x1.fef15ep-2 want 0x1.fef15cp-2.
  59
  60     For |x| in [0.5, 1.0], use same approximation with a change of variable
  61
  62     asin(x) = pi/2 - (y + y * z * P(z)), with  z = (1-x)/2 and y = sqrt(z).
  63
  64    The largest observed error in this region is 2.41 ulps,
  65      _ZGVnN4v_asinf (0x1.00203ep-1) got 0x1.0c3a64p-1 want 0x1.0c3a6p-1.  */
  66 float32x4_t VPCS_ATTR NOINLINE V_NAME_F1 (asin) (float32x4_t x)
  67 {
  68   const struct data *d = ptr_barrier (&data);
  69
  70   uint32x4_t ix = vreinterpretq_u32_f32 (x);
  71   uint32x4_t ia = vandq_u32 (ix, v_u32 (AbsMask));
  72
  73 #if WANT_SIMD_EXCEPT
  74   /* Special values need to be computed with scalar fallbacks so
  75      that appropriate fp exceptions are raised.  */
  76   uint32x4_t special
  77       = vcgtq_u32 (vsubq_u32 (ia, v_u32 (Small)), v_u32 (One - Small));
  78   if (__glibc_unlikely (v_any_u32 (special)))
  79     return special_case (x, x, v_u32 (0xffffffff));
  80 #endif
  81
  82   float32x4_t ax = vreinterpretq_f32_u32 (ia);
  83   uint32x4_t a_lt_half = vcltq_u32 (ia, v_u32 (Half));
  84
  85   /* Evaluate polynomial Q(x) = y + y * z * P(z) with
  86      z = x ^ 2 and y = |x|            , if |x| < 0.5
  87      z = (1 - |x|) / 2 and y = sqrt(z), if |x| >= 0.5.  */
  88   float32x4_t z2 = vbslq_f32 (a_lt_half, vmulq_f32 (x, x),
  89                               vfmsq_n_f32 (v_f32 (0.5), ax, 0.5));
  90   float32x4_t z = vbslq_f32 (a_lt_half, ax, vsqrtq_f32 (z2));
  91
  92   /* Use a single polynomial approximation P for both intervals.  */
  93   float32x4_t p = v_horner_4_f32 (z2, d->poly);
  94   /* Finalize polynomial: z + z * z2 * P(z2).  */
  95   p = vfmaq_f32 (z, vmulq_f32 (z, z2), p);
  96
  97   /* asin(|x|) = Q(|x|)         , for |x| < 0.5
  98                = pi/2 - 2 Q(|x|), for |x| >= 0.5.  */
  99   float32x4_t y
 100       = vbslq_f32 (a_lt_half, p, vfmsq_n_f32 (d->pi_over_2f, p, 2.0));
 101
 102   /* Copy sign.  */
 103   return vbslq_f32 (v_u32 (AbsMask), y, x);
 104 }
 105 libmvec_hidden_def (V_NAME_F1 (asin))
 106 HALF_WIDTH_ALIAS_F1 (asin)