sysdeps/aarch64/fpu/log10_sve.c

   1 /* Double-precision vector (SVE) log10 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 #include "poly_sve_f64.h"
  22
  23 #define Min 0x0010000000000000
  24 #define Max 0x7ff0000000000000
  25 #define Thres 0x7fe0000000000000 /* Max - Min.  */
  26 #define Off 0x3fe6900900000000
  27 #define N (1 << V_LOG10_TABLE_BITS)
  28
  29 static svfloat64_t NOINLINE
  30 special_case (svfloat64_t x, svfloat64_t y, svbool_t special)
  31 {
  32   return sv_call_f64 (log10, x, y, special);
  33 }
  34
  35 /* SVE log10 algorithm.
  36    Maximum measured error is 2.46 ulps.
  37    SV_NAME_D1 (log10)(0x1.131956cd4b627p+0) got 0x1.fffbdf6eaa669p-6
  38                                            want 0x1.fffbdf6eaa667p-6.  */
  39 svfloat64_t SV_NAME_D1 (log10) (svfloat64_t x, const svbool_t pg)
  40 {
  41   svuint64_t ix = svreinterpret_u64 (x);
  42   svbool_t special = svcmpge (pg, svsub_x (pg, ix, Min), Thres);
  43
  44   /* x = 2^k z; where z is in range [Off,2*Off) and exact.
  45      The range is split into N subintervals.
  46      The ith subinterval contains z and c is near its center.  */
  47   svuint64_t tmp = svsub_x (pg, ix, Off);
  48   svuint64_t i = svlsr_x (pg, tmp, 51 - V_LOG10_TABLE_BITS);
  49   i = svand_x (pg, i, (N - 1) << 1);
  50   svfloat64_t k = svcvt_f64_x (pg, svasr_x (pg, svreinterpret_s64 (tmp), 52));
  51   svfloat64_t z = svreinterpret_f64 (
  52       svsub_x (pg, ix, svand_x (pg, tmp, 0xfffULL << 52)));
  53
  54   /* log(x) = k*log(2) + log(c) + log(z/c).  */
  55   svfloat64_t invc = svld1_gather_index (pg, &__v_log10_data.table[0].invc, i);
  56   svfloat64_t logc
  57       = svld1_gather_index (pg, &__v_log10_data.table[0].log10c, i);
  58
  59   /* We approximate log(z/c) with a polynomial P(x) ~= log(x + 1):
  60      r = z/c - 1 (we look up precomputed 1/c)
  61      log(z/c) ~= P(r).  */
  62   svfloat64_t r = svmad_x (pg, invc, z, -1.0);
  63
  64   /* hi = log(c) + k*log(2).  */
  65   svfloat64_t w = svmla_x (pg, logc, r, __v_log10_data.invln10);
  66   svfloat64_t hi = svmla_x (pg, w, k, __v_log10_data.log10_2);
  67
  68   /* y = r2*(A0 + r*A1 + r2*(A2 + r*A3 + r2*A4)) + hi.  */
  69   svfloat64_t r2 = svmul_x (pg, r, r);
  70   svfloat64_t y = sv_pw_horner_4_f64_x (pg, r, r2, __v_log10_data.poly);
  71
  72   if (__glibc_unlikely (svptest_any (pg, special)))
  73     return special_case (x, svmla_x (svnot_z (pg, special), hi, r2, y),
  74                          special);
  75   return svmla_x (pg, hi, r2, y);
  76 }