sysdeps/aarch64/fpu/erf_sve.c

   1 /* Double-precision vector (SVE) erf function
   2
   3    Copyright (C) 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 "sv_math.h"
  21
  22 static const struct data
  23 {
  24   double third;
  25   double tenth, two_over_five, two_over_fifteen;
  26   double two_over_nine, two_over_fortyfive;
  27   double max, shift;
  28 } data = {
  29   .third = 0x1.5555555555556p-2, /* used to compute 2/3 and 1/6 too.  */
  30   .two_over_fifteen = 0x1.1111111111111p-3,
  31   .tenth = -0x1.999999999999ap-4,
  32   .two_over_five = -0x1.999999999999ap-2,
  33   .two_over_nine = -0x1.c71c71c71c71cp-3,
  34   .two_over_fortyfive = 0x1.6c16c16c16c17p-5,
  35   .max = 5.9921875, /* 6 - 1/128.  */
  36   .shift = 0x1p45,
  37 };
  38
  39 #define SignMask (0x8000000000000000)
  40
  41 /* Double-precision implementation of vector erf(x).
  42    Approximation based on series expansion near x rounded to
  43    nearest multiple of 1/128.
  44    Let d = x - r, and scale = 2 / sqrt(pi) * exp(-r^2). For x near r,
  45    erf(x) ~ erf(r) + scale * d * [
  46        + 1
  47        - r d
  48        + 1/3 (2 r^2 - 1) d^2
  49        - 1/6 (r (2 r^2 - 3)) d^3
  50        + 1/30 (4 r^4 - 12 r^2 + 3) d^4
  51        - 1/90 (4 r^4 - 20 r^2 + 15) d^5
  52      ]
  53
  54    Maximum measure error: 2.29 ULP
  55    _ZGVsMxv_erf(-0x1.00003c924e5d1p-8) got -0x1.20dd59132ebadp-8
  56                                       want -0x1.20dd59132ebafp-8.  */
  57 svfloat64_t SV_NAME_D1 (erf) (svfloat64_t x, const svbool_t pg)
  58 {
  59   const struct data *dat = ptr_barrier (&data);
  60
  61   /* |x| >= 6.0 - 1/128. Opposite conditions except none of them catch NaNs so
  62      they can be used in lookup and BSLs to yield the expected results.  */
  63   svbool_t a_ge_max = svacge (pg, x, dat->max);
  64   svbool_t a_lt_max = svaclt (pg, x, dat->max);
  65
  66   /* Set r to multiple of 1/128 nearest to |x|.  */
  67   svfloat64_t a = svabs_x (pg, x);
  68   svfloat64_t shift = sv_f64 (dat->shift);
  69   svfloat64_t z = svadd_x (pg, a, shift);
  70   svuint64_t i
  71       = svsub_x (pg, svreinterpret_u64 (z), svreinterpret_u64 (shift));
  72
  73   /* Lookup without shortcut for small values but with predicate to avoid
  74      segfault for large values and NaNs.  */
  75   svfloat64_t r = svsub_x (pg, z, shift);
  76   svfloat64_t erfr = svld1_gather_index (a_lt_max, __sv_erf_data.erf, i);
  77   svfloat64_t scale = svld1_gather_index (a_lt_max, __sv_erf_data.scale, i);
  78
  79   /* erf(x) ~ erf(r) + scale * d * poly (r, d).  */
  80   svfloat64_t d = svsub_x (pg, a, r);
  81   svfloat64_t d2 = svmul_x (pg, d, d);
  82   svfloat64_t r2 = svmul_x (pg, r, r);
  83
  84   /* poly (d, r) = 1 + p1(r) * d + p2(r) * d^2 + ... + p5(r) * d^5.  */
  85   svfloat64_t p1 = r;
  86   svfloat64_t third = sv_f64 (dat->third);
  87   svfloat64_t twothird = svmul_x (pg, third, 2.0);
  88   svfloat64_t sixth = svmul_x (pg, third, 0.5);
  89   svfloat64_t p2 = svmls_x (pg, third, r2, twothird);
  90   svfloat64_t p3 = svmad_x (pg, r2, third, -0.5);
  91   p3 = svmul_x (pg, r, p3);
  92   svfloat64_t p4
  93       = svmla_x (pg, sv_f64 (dat->two_over_five), r2, dat->two_over_fifteen);
  94   p4 = svmls_x (pg, sv_f64 (dat->tenth), r2, p4);
  95   svfloat64_t p5
  96       = svmla_x (pg, sv_f64 (dat->two_over_nine), r2, dat->two_over_fortyfive);
  97   p5 = svmla_x (pg, sixth, r2, p5);
  98   p5 = svmul_x (pg, r, p5);
  99
 100   svfloat64_t p34 = svmla_x (pg, p3, d, p4);
 101   svfloat64_t p12 = svmla_x (pg, p1, d, p2);
 102   svfloat64_t y = svmla_x (pg, p34, d2, p5);
 103   y = svmla_x (pg, p12, d2, y);
 104
 105   y = svmla_x (pg, erfr, scale, svmls_x (pg, d, d2, y));
 106
 107   /* Solves the |x| = inf and NaN cases.  */
 108   y = svsel (a_ge_max, sv_f64 (1.0), y);
 109
 110   /* Copy sign.  */
 111   svuint64_t ix = svreinterpret_u64 (x);
 112   svuint64_t iy = svreinterpret_u64 (y);
 113   svuint64_t sign = svand_x (pg, ix, SignMask);
 114   return svreinterpret_f64 (svorr_x (pg, sign, iy));
 115 }