sysdeps/aarch64/fpu/exp2_sve.c

   1 /* Double-precision vector (SVE) exp2 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 N (1 << V_EXP_TABLE_BITS)
  24
  25 #define BigBound 1022
  26 #define UOFlowBound 1280
  27
  28 static const struct data
  29 {
  30   double poly[4];
  31   double shift, big_bound, uoflow_bound;
  32 } data = {
  33   /* Coefficients are computed using Remez algorithm with
  34      minimisation of the absolute error.  */
  35   .poly = { 0x1.62e42fefa3686p-1, 0x1.ebfbdff82c241p-3, 0x1.c6b09b16de99ap-5,
  36             0x1.3b2abf5571ad8p-7 },
  37   .shift = 0x1.8p52 / N,
  38   .uoflow_bound = UOFlowBound,
  39   .big_bound = BigBound,
  40 };
  41
  42 #define SpecialOffset 0x6000000000000000 /* 0x1p513.  */
  43 /* SpecialBias1 + SpecialBias1 = asuint(1.0).  */
  44 #define SpecialBias1 0x7000000000000000 /* 0x1p769.  */
  45 #define SpecialBias2 0x3010000000000000 /* 0x1p-254.  */
  46
  47 /* Update of both special and non-special cases, if any special case is
  48    detected.  */
  49 static inline svfloat64_t
  50 special_case (svbool_t pg, svfloat64_t s, svfloat64_t y, svfloat64_t n,
  51               const struct data *d)
  52 {
  53   /* s=2^n may overflow, break it up into s=s1*s2,
  54      such that exp = s + s*y can be computed as s1*(s2+s2*y)
  55      and s1*s1 overflows only if n>0.  */
  56
  57   /* If n<=0 then set b to 0x6, 0 otherwise.  */
  58   svbool_t p_sign = svcmple (pg, n, 0.0); /* n <= 0.  */
  59   svuint64_t b = svdup_u64_z (p_sign, SpecialOffset);
  60
  61   /* Set s1 to generate overflow depending on sign of exponent n.  */
  62   svfloat64_t s1 = svreinterpret_f64 (svsubr_x (pg, b, SpecialBias1));
  63   /* Offset s to avoid overflow in final result if n is below threshold.  */
  64   svfloat64_t s2 = svreinterpret_f64 (
  65       svadd_x (pg, svsub_x (pg, svreinterpret_u64 (s), SpecialBias2), b));
  66
  67   /* |n| > 1280 => 2^(n) overflows.  */
  68   svbool_t p_cmp = svacgt (pg, n, d->uoflow_bound);
  69
  70   svfloat64_t r1 = svmul_x (pg, s1, s1);
  71   svfloat64_t r2 = svmla_x (pg, s2, s2, y);
  72   svfloat64_t r0 = svmul_x (pg, r2, s1);
  73
  74   return svsel (p_cmp, r1, r0);
  75 }
  76
  77 /* Fast vector implementation of exp2.
  78    Maximum measured error is 1.65 ulp.
  79    _ZGVsMxv_exp2(-0x1.4c264ab5b559bp-6) got 0x1.f8db0d4df721fp-1
  80                                        want 0x1.f8db0d4df721dp-1.  */
  81 svfloat64_t SV_NAME_D1 (exp2) (svfloat64_t x, svbool_t pg)
  82 {
  83   const struct data *d = ptr_barrier (&data);
  84   svbool_t no_big_scale = svacle (pg, x, d->big_bound);
  85   svbool_t special = svnot_z (pg, no_big_scale);
  86
  87   /* Reduce x to k/N + r, where k is integer and r in [-1/2N, 1/2N].  */
  88   svfloat64_t shift = sv_f64 (d->shift);
  89   svfloat64_t kd = svadd_x (pg, x, shift);
  90   svuint64_t ki = svreinterpret_u64 (kd);
  91   /* kd = k/N.  */
  92   kd = svsub_x (pg, kd, shift);
  93   svfloat64_t r = svsub_x (pg, x, kd);
  94
  95   /* scale ~= 2^(k/N).  */
  96   svuint64_t idx = svand_x (pg, ki, N - 1);
  97   svuint64_t sbits = svld1_gather_index (pg, __v_exp_data, idx);
  98   /* This is only a valid scale when -1023*N < k < 1024*N.  */
  99   svuint64_t top = svlsl_x (pg, ki, 52 - V_EXP_TABLE_BITS);
 100   svfloat64_t scale = svreinterpret_f64 (svadd_x (pg, sbits, top));
 101
 102   /* Approximate exp2(r) using polynomial.  */
 103   svfloat64_t r2 = svmul_x (pg, r, r);
 104   svfloat64_t p = sv_pairwise_poly_3_f64_x (pg, r, r2, d->poly);
 105   svfloat64_t y = svmul_x (pg, r, p);
 106
 107   /* Assemble exp2(x) = exp2(r) * scale.  */
 108   if (__glibc_unlikely (svptest_any (pg, special)))
 109     return special_case (pg, scale, y, kd, d);
 110   return svmla_x (pg, scale, scale, y);
 111 }