sysdeps/aarch64/fpu/atan2f_advsimd.c

   1 /* Single-precision AdvSIMD atan2
   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[8];
  26   float32x4_t pi_over_2;
  27 } data = {
  28   /* Coefficients of polynomial P such that atan(x)~x+x*P(x^2) on
  29      [2**-128, 1.0].
  30      Generated using fpminimax between FLT_MIN and 1.  */
  31   .poly = { V4 (-0x1.55555p-2f), V4 (0x1.99935ep-3f), V4 (-0x1.24051ep-3f),
  32             V4 (0x1.bd7368p-4f), V4 (-0x1.491f0ep-4f), V4 (0x1.93a2c0p-5f),
  33             V4 (-0x1.4c3c60p-6f), V4 (0x1.01fd88p-8f) },
  34   .pi_over_2 = V4 (0x1.921fb6p+0f),
  35 };
  36
  37 #define SignMask v_u32 (0x80000000)
  38
  39 /* Special cases i.e. 0, infinity and nan (fall back to scalar calls).  */
  40 static float32x4_t VPCS_ATTR NOINLINE
  41 special_case (float32x4_t y, float32x4_t x, float32x4_t ret, uint32x4_t cmp)
  42 {
  43   return v_call2_f32 (atan2f, y, x, ret, cmp);
  44 }
  45
  46 /* Returns 1 if input is the bit representation of 0, infinity or nan.  */
  47 static inline uint32x4_t
  48 zeroinfnan (uint32x4_t i)
  49 {
  50   /* 2 * i - 1 >= 2 * 0x7f800000lu - 1.  */
  51   return vcgeq_u32 (vsubq_u32 (vmulq_n_u32 (i, 2), v_u32 (1)),
  52                     v_u32 (2 * 0x7f800000lu - 1));
  53 }
  54
  55 /* Fast implementation of vector atan2f. Maximum observed error is
  56    2.95 ULP in [0x1.9300d6p+6 0x1.93c0c6p+6] x [0x1.8c2dbp+6 0x1.8cea6p+6]:
  57    _ZGVnN4vv_atan2f (0x1.93836cp+6, 0x1.8cae1p+6) got 0x1.967f06p-1
  58                                                  want 0x1.967f00p-1.  */
  59 float32x4_t VPCS_ATTR NOINLINE V_NAME_F2 (atan2) (float32x4_t y, float32x4_t x)
  60 {
  61   const struct data *data_ptr = ptr_barrier (&data);
  62
  63   uint32x4_t ix = vreinterpretq_u32_f32 (x);
  64   uint32x4_t iy = vreinterpretq_u32_f32 (y);
  65
  66   uint32x4_t special_cases = vorrq_u32 (zeroinfnan (ix), zeroinfnan (iy));
  67
  68   uint32x4_t sign_x = vandq_u32 (ix, SignMask);
  69   uint32x4_t sign_y = vandq_u32 (iy, SignMask);
  70   uint32x4_t sign_xy = veorq_u32 (sign_x, sign_y);
  71
  72   float32x4_t ax = vabsq_f32 (x);
  73   float32x4_t ay = vabsq_f32 (y);
  74
  75   uint32x4_t pred_xlt0 = vcltzq_f32 (x);
  76   uint32x4_t pred_aygtax = vcgtq_f32 (ay, ax);
  77
  78   /* Set up z for call to atanf.  */
  79   float32x4_t n = vbslq_f32 (pred_aygtax, vnegq_f32 (ax), ay);
  80   float32x4_t d = vbslq_f32 (pred_aygtax, ay, ax);
  81   float32x4_t z = vdivq_f32 (n, d);
  82
  83   /* Work out the correct shift.  */
  84   float32x4_t shift = vreinterpretq_f32_u32 (
  85       vandq_u32 (pred_xlt0, vreinterpretq_u32_f32 (v_f32 (-2.0f))));
  86   shift = vbslq_f32 (pred_aygtax, vaddq_f32 (shift, v_f32 (1.0f)), shift);
  87   shift = vmulq_f32 (shift, data_ptr->pi_over_2);
  88
  89   /* Calculate the polynomial approximation.
  90      Use 2-level Estrin scheme for P(z^2) with deg(P)=7. However,
  91      a standard implementation using z8 creates spurious underflow
  92      in the very last fma (when z^8 is small enough).
  93      Therefore, we split the last fma into a mul and an fma.
  94      Horner and single-level Estrin have higher errors that exceed
  95      threshold.  */
  96   float32x4_t z2 = vmulq_f32 (z, z);
  97   float32x4_t z4 = vmulq_f32 (z2, z2);
  98
  99   float32x4_t ret = vfmaq_f32 (
 100       v_pairwise_poly_3_f32 (z2, z4, data_ptr->poly), z4,
 101       vmulq_f32 (z4, v_pairwise_poly_3_f32 (z2, z4, data_ptr->poly + 4)));
 102
 103   /* y = shift + z * P(z^2).  */
 104   ret = vaddq_f32 (vfmaq_f32 (z, ret, vmulq_f32 (z2, z)), shift);
 105
 106   /* Account for the sign of y.  */
 107   ret = vreinterpretq_f32_u32 (
 108       veorq_u32 (vreinterpretq_u32_f32 (ret), sign_xy));
 109
 110   if (__glibc_unlikely (v_any_u32 (special_cases)))
 111     {
 112       return special_case (y, x, ret, special_cases);
 113     }
 114
 115   return ret;
 116 }
 117 libmvec_hidden_def (V_NAME_F2 (atan2))
 118 HALF_WIDTH_ALIAS_F2(atan2)