sysdeps/aarch64/fpu/expf_sve.c

   1 /* Single-precision vector (SVE) exp function.
   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 "sv_math.h"
  21
  22 static const struct data
  23 {
  24   float poly[5];
  25   float inv_ln2, ln2_hi, ln2_lo, shift, thres;
  26 } data = {
  27   /* Coefficients copied from the polynomial in AdvSIMD variant, reversed for
  28      compatibility with polynomial helpers.  */
  29   .poly = { 0x1.ffffecp-1f, 0x1.fffdb6p-2f, 0x1.555e66p-3f, 0x1.573e2ep-5f,
  30             0x1.0e4020p-7f },
  31   .inv_ln2 = 0x1.715476p+0f,
  32   .ln2_hi = 0x1.62e4p-1f,
  33   .ln2_lo = 0x1.7f7d1cp-20f,
  34   /* 1.5*2^17 + 127.  */
  35   .shift = 0x1.903f8p17f,
  36   /* Roughly 87.3. For x < -Thres, the result is subnormal and not handled
  37      correctly by FEXPA.  */
  38   .thres = 0x1.5d5e2ap+6f,
  39 };
  40
  41 #define C(i) sv_f32 (d->poly[i])
  42 #define ExponentBias 0x3f800000
  43
  44 static svfloat32_t NOINLINE
  45 special_case (svfloat32_t x, svfloat32_t y, svbool_t special)
  46 {
  47   return sv_call_f32 (expf, x, y, special);
  48 }
  49
  50 /* Optimised single-precision SVE exp function.
  51    Worst-case error is 1.04 ulp:
  52    SV_NAME_F1 (exp)(0x1.a8eda4p+1) got 0x1.ba74bcp+4
  53                                   want 0x1.ba74bap+4.  */
  54 svfloat32_t SV_NAME_F1 (exp) (svfloat32_t x, const svbool_t pg)
  55 {
  56   const struct data *d = ptr_barrier (&data);
  57
  58   /* exp(x) = 2^n (1 + poly(r)), with 1 + poly(r) in [1/sqrt(2),sqrt(2)]
  59      x = ln2*n + r, with r in [-ln2/2, ln2/2].  */
  60
  61   /* Load some constants in quad-word chunks to minimise memory access (last
  62      lane is wasted).  */
  63   svfloat32_t invln2_and_ln2 = svld1rq (svptrue_b32 (), &d->inv_ln2);
  64
  65   /* n = round(x/(ln2/N)).  */
  66   svfloat32_t z = svmla_lane (sv_f32 (d->shift), x, invln2_and_ln2, 0);
  67   svfloat32_t n = svsub_x (pg, z, d->shift);
  68
  69   /* r = x - n*ln2/N.  */
  70   svfloat32_t r = svmls_lane (x, n, invln2_and_ln2, 1);
  71   r = svmls_lane (r, n, invln2_and_ln2, 2);
  72
  73   /* scale = 2^(n/N).  */
  74   svbool_t is_special_case = svacgt (pg, x, d->thres);
  75   svfloat32_t scale = svexpa (svreinterpret_u32 (z));
  76
  77   /* y = exp(r) - 1 ~= r + C0 r^2 + C1 r^3 + C2 r^4 + C3 r^5 + C4 r^6.  */
  78   svfloat32_t p12 = svmla_x (pg, C (1), C (2), r);
  79   svfloat32_t p34 = svmla_x (pg, C (3), C (4), r);
  80   svfloat32_t r2 = svmul_x (pg, r, r);
  81   svfloat32_t p14 = svmla_x (pg, p12, p34, r2);
  82   svfloat32_t p0 = svmul_x (pg, r, C (0));
  83   svfloat32_t poly = svmla_x (pg, p0, r2, p14);
  84
  85   if (__glibc_unlikely (svptest_any (pg, is_special_case)))
  86     return special_case (x, svmla_x (pg, scale, scale, poly), is_special_case);
  87
  88   return svmla_x (pg, scale, scale, poly);
  89 }