sysdeps/aarch64/fpu/log_advsimd.c

   1 /* Double-precision vector (Advanced SIMD) log 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 "v_math.h"
  21
  22 static const struct data
  23 {
  24   uint64x2_t min_norm;
  25   uint32x4_t special_bound;
  26   float64x2_t poly[5];
  27   float64x2_t ln2;
  28   uint64x2_t sign_exp_mask;
  29 } data = {
  30   /* Worst-case error: 1.17 + 0.5 ulp.
  31      Rel error: 0x1.6272e588p-56 in [ -0x1.fc1p-9 0x1.009p-8 ].  */
  32   .poly = { V2 (-0x1.ffffffffffff7p-2), V2 (0x1.55555555170d4p-2),
  33             V2 (-0x1.0000000399c27p-2), V2 (0x1.999b2e90e94cap-3),
  34             V2 (-0x1.554e550bd501ep-3) },
  35   .ln2 = V2 (0x1.62e42fefa39efp-1),
  36   .min_norm = V2 (0x0010000000000000),
  37   .special_bound = V4 (0x7fe00000), /* asuint64(inf) - min_norm.  */
  38   .sign_exp_mask = V2 (0xfff0000000000000)
  39 };
  40
  41 #define A(i) d->poly[i]
  42 #define N (1 << V_LOG_TABLE_BITS)
  43 #define IndexMask (N - 1)
  44 #define Off v_u64 (0x3fe6900900000000)
  45
  46 struct entry
  47 {
  48   float64x2_t invc;
  49   float64x2_t logc;
  50 };
  51
  52 static inline struct entry
  53 lookup (uint64x2_t i)
  54 {
  55   /* Since N is a power of 2, n % N = n & (N - 1).  */
  56   struct entry e;
  57   uint64_t i0 = (i[0] >> (52 - V_LOG_TABLE_BITS)) & IndexMask;
  58   uint64_t i1 = (i[1] >> (52 - V_LOG_TABLE_BITS)) & IndexMask;
  59   float64x2_t e0 = vld1q_f64 (&__v_log_data.table[i0].invc);
  60   float64x2_t e1 = vld1q_f64 (&__v_log_data.table[i1].invc);
  61   e.invc = vuzp1q_f64 (e0, e1);
  62   e.logc = vuzp2q_f64 (e0, e1);
  63   return e;
  64 }
  65
  66 static float64x2_t VPCS_ATTR NOINLINE
  67 special_case (float64x2_t x, float64x2_t y, float64x2_t hi, float64x2_t r2,
  68               uint32x2_t cmp)
  69 {
  70   return v_call_f64 (log, x, vfmaq_f64 (hi, y, r2), vmovl_u32 (cmp));
  71 }
  72
  73 float64x2_t VPCS_ATTR V_NAME_D1 (log) (float64x2_t x)
  74 {
  75   const struct data *d = ptr_barrier (&data);
  76   float64x2_t z, r, r2, p, y, kd, hi;
  77   uint64x2_t ix, iz, tmp;
  78   uint32x2_t cmp;
  79   int64x2_t k;
  80   struct entry e;
  81
  82   ix = vreinterpretq_u64_f64 (x);
  83   cmp = vcge_u32 (vsubhn_u64 (ix, d->min_norm),
  84                   vget_low_u32 (d->special_bound));
  85
  86   /* x = 2^k z; where z is in range [Off,2*Off) and exact.
  87      The range is split into N subintervals.
  88      The ith subinterval contains z and c is near its center.  */
  89   tmp = vsubq_u64 (ix, Off);
  90   k = vshrq_n_s64 (vreinterpretq_s64_u64 (tmp), 52); /* arithmetic shift.  */
  91   iz = vsubq_u64 (ix, vandq_u64 (tmp, d->sign_exp_mask));
  92   z = vreinterpretq_f64_u64 (iz);
  93   e = lookup (tmp);
  94
  95   /* log(x) = log1p(z/c-1) + log(c) + k*Ln2.  */
  96   r = vfmaq_f64 (v_f64 (-1.0), z, e.invc);
  97   kd = vcvtq_f64_s64 (k);
  98
  99   /* hi = r + log(c) + k*Ln2.  */
 100   hi = vfmaq_f64 (vaddq_f64 (e.logc, r), kd, d->ln2);
 101   /* y = r2*(A0 + r*A1 + r2*(A2 + r*A3 + r2*A4)) + hi.  */
 102   r2 = vmulq_f64 (r, r);
 103   y = vfmaq_f64 (A (2), A (3), r);
 104   p = vfmaq_f64 (A (0), A (1), r);
 105   y = vfmaq_f64 (y, A (4), r2);
 106   y = vfmaq_f64 (p, y, r2);
 107
 108   if (__glibc_unlikely (v_any_u32h (cmp)))
 109     return special_case (x, y, hi, r2, cmp);
 110   return vfmaq_f64 (hi, y, r2);
 111 }