sysdeps/aarch64/fpu/poly_generic.h

   1 /* Generic helpers for evaluating polynomials with various schemes.
   2
   3    Copyright (C) 2023 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
  21 #ifndef VTYPE
  22 # error Cannot use poly_generic without defining VTYPE
  23 #endif
  24 #ifndef VWRAP
  25 # error Cannot use poly_generic without defining VWRAP
  26 #endif
  27 #ifndef FMA
  28 # error Cannot use poly_generic without defining FMA
  29 #endif
  30
  31 static inline VTYPE VWRAP (pairwise_poly_3) (VTYPE x, VTYPE x2,
  32                                              const VTYPE *poly)
  33 {
  34   /* At order 3, Estrin and Pairwise Horner are identical.  */
  35   VTYPE p01 = FMA (poly[1], x, poly[0]);
  36   VTYPE p23 = FMA (poly[3], x, poly[2]);
  37   return FMA (p23, x2, p01);
  38 }
  39
  40 static inline VTYPE VWRAP (estrin_4) (VTYPE x, VTYPE x2, VTYPE x4,
  41                                       const VTYPE *poly)
  42 {
  43   VTYPE p03 = VWRAP (pairwise_poly_3) (x, x2, poly);
  44   return FMA (poly[4], x4, p03);
  45 }
  46 static inline VTYPE VWRAP (estrin_5) (VTYPE x, VTYPE x2, VTYPE x4,
  47                                       const VTYPE *poly)
  48 {
  49   VTYPE p03 = VWRAP (pairwise_poly_3) (x, x2, poly);
  50   VTYPE p45 = FMA (poly[5], x, poly[4]);
  51   return FMA (p45, x4, p03);
  52 }
  53 static inline VTYPE VWRAP (estrin_6) (VTYPE x, VTYPE x2, VTYPE x4,
  54                                       const VTYPE *poly)
  55 {
  56   VTYPE p03 = VWRAP (pairwise_poly_3) (x, x2, poly);
  57   VTYPE p45 = FMA (poly[5], x, poly[4]);
  58   VTYPE p46 = FMA (poly[6], x2, p45);
  59   return FMA (p46, x4, p03);
  60 }
  61 static inline VTYPE VWRAP (estrin_7) (VTYPE x, VTYPE x2, VTYPE x4,
  62                                       const VTYPE *poly)
  63 {
  64   VTYPE p03 = VWRAP (pairwise_poly_3) (x, x2, poly);
  65   VTYPE p47 = VWRAP (pairwise_poly_3) (x, x2, poly + 4);
  66   return FMA (p47, x4, p03);
  67 }
  68 static inline VTYPE VWRAP (estrin_8) (VTYPE x, VTYPE x2, VTYPE x4, VTYPE x8,
  69                                       const VTYPE *poly)
  70 {
  71   return FMA (poly[8], x8, VWRAP (estrin_7) (x, x2, x4, poly));
  72 }
  73 static inline VTYPE VWRAP (estrin_9) (VTYPE x, VTYPE x2, VTYPE x4, VTYPE x8,
  74                                       const VTYPE *poly)
  75 {
  76   VTYPE p89 = FMA (poly[9], x, poly[8]);
  77   return FMA (p89, x8, VWRAP (estrin_7) (x, x2, x4, poly));
  78 }
  79 static inline VTYPE VWRAP (estrin_10) (VTYPE x, VTYPE x2, VTYPE x4, VTYPE x8,
  80                                        const VTYPE *poly)
  81 {
  82   VTYPE p89 = FMA (poly[9], x, poly[8]);
  83   VTYPE p8_10 = FMA (poly[10], x2, p89);
  84   return FMA (p8_10, x8, VWRAP (estrin_7) (x, x2, x4, poly));
  85 }
  86 static inline VTYPE VWRAP (estrin_11) (VTYPE x, VTYPE x2, VTYPE x4, VTYPE x8,
  87                                        const VTYPE *poly)
  88 {
  89   VTYPE p8_11 = VWRAP (pairwise_poly_3) (x, x2, poly + 8);
  90   return FMA (p8_11, x8, VWRAP (estrin_7) (x, x2, x4, poly));
  91 }
  92 static inline VTYPE VWRAP (estrin_12) (VTYPE x, VTYPE x2, VTYPE x4, VTYPE x8,
  93                                        const VTYPE *poly)
  94 {
  95   return FMA (VWRAP (estrin_4) (x, x2, x4, poly + 8), x8,
  96               VWRAP (estrin_7) (x, x2, x4, poly));
  97 }
  98 static inline VTYPE VWRAP (estrin_13) (VTYPE x, VTYPE x2, VTYPE x4, VTYPE x8,
  99                                        const VTYPE *poly)
 100 {
 101   return FMA (VWRAP (estrin_5) (x, x2, x4, poly + 8), x8,
 102               VWRAP (estrin_7) (x, x2, x4, poly));
 103 }
 104 static inline VTYPE VWRAP (estrin_14) (VTYPE x, VTYPE x2, VTYPE x4, VTYPE x8,
 105                                        const VTYPE *poly)
 106 {
 107   return FMA (VWRAP (estrin_6) (x, x2, x4, poly + 8), x8,
 108               VWRAP (estrin_7) (x, x2, x4, poly));
 109 }
 110 static inline VTYPE VWRAP (estrin_15) (VTYPE x, VTYPE x2, VTYPE x4, VTYPE x8,
 111                                        const VTYPE *poly)
 112 {
 113   return FMA (VWRAP (estrin_7) (x, x2, x4, poly + 8), x8,
 114               VWRAP (estrin_7) (x, x2, x4, poly));
 115 }
 116 static inline VTYPE VWRAP (estrin_16) (VTYPE x, VTYPE x2, VTYPE x4, VTYPE x8,
 117                                        VTYPE x16, const VTYPE *poly)
 118 {
 119   return FMA (poly[16], x16, VWRAP (estrin_15) (x, x2, x4, x8, poly));
 120 }
 121 static inline VTYPE VWRAP (estrin_17) (VTYPE x, VTYPE x2, VTYPE x4, VTYPE x8,
 122                                        VTYPE x16, const VTYPE *poly)
 123 {
 124   VTYPE p16_17 = FMA (poly[17], x, poly[16]);
 125   return FMA (p16_17, x16, VWRAP (estrin_15) (x, x2, x4, x8, poly));
 126 }
 127 static inline VTYPE VWRAP (estrin_18) (VTYPE x, VTYPE x2, VTYPE x4, VTYPE x8,
 128                                        VTYPE x16, const VTYPE *poly)
 129 {
 130   VTYPE p16_17 = FMA (poly[17], x, poly[16]);
 131   VTYPE p16_18 = FMA (poly[18], x2, p16_17);
 132   return FMA (p16_18, x16, VWRAP (estrin_15) (x, x2, x4, x8, poly));
 133 }
 134 static inline VTYPE VWRAP (estrin_19) (VTYPE x, VTYPE x2, VTYPE x4, VTYPE x8,
 135                                        VTYPE x16, const VTYPE *poly)
 136 {
 137   VTYPE p16_19 = VWRAP (pairwise_poly_3) (x, x2, poly + 16);
 138   return FMA (p16_19, x16, VWRAP (estrin_15) (x, x2, x4, x8, poly));
 139 }
 140
 141 static inline VTYPE VWRAP (horner_3) (VTYPE x, const VTYPE *poly)
 142 {
 143   VTYPE p = FMA (poly[3], x, poly[2]);
 144   p = FMA (x, p, poly[1]);
 145   p = FMA (x, p, poly[0]);
 146   return p;
 147 }
 148 static inline VTYPE VWRAP (horner_4) (VTYPE x, const VTYPE *poly)
 149 {
 150   VTYPE p = FMA (poly[4], x, poly[3]);
 151   p = FMA (x, p, poly[2]);
 152   p = FMA (x, p, poly[1]);
 153   p = FMA (x, p, poly[0]);
 154   return p;
 155 }
 156 static inline VTYPE VWRAP (horner_5) (VTYPE x, const VTYPE *poly)
 157 {
 158   return FMA (x, VWRAP (horner_4) (x, poly + 1), poly[0]);
 159 }
 160 static inline VTYPE VWRAP (horner_6) (VTYPE x, const VTYPE *poly)
 161 {
 162   return FMA (x, VWRAP (horner_5) (x, poly + 1), poly[0]);
 163 }
 164 static inline VTYPE VWRAP (horner_7) (VTYPE x, const VTYPE *poly)
 165 {
 166   return FMA (x, VWRAP (horner_6) (x, poly + 1), poly[0]);
 167 }
 168 static inline VTYPE VWRAP (horner_8) (VTYPE x, const VTYPE *poly)
 169 {
 170   return FMA (x, VWRAP (horner_7) (x, poly + 1), poly[0]);
 171 }
 172 static inline VTYPE VWRAP (horner_9) (VTYPE x, const VTYPE *poly)
 173 {
 174   return FMA (x, VWRAP (horner_8) (x, poly + 1), poly[0]);
 175 }
 176 static inline VTYPE VWRAP (horner_10) (VTYPE x, const VTYPE *poly)
 177 {
 178   return FMA (x, VWRAP (horner_9) (x, poly + 1), poly[0]);
 179 }
 180 static inline VTYPE VWRAP (horner_11) (VTYPE x, const VTYPE *poly)
 181 {
 182   return FMA (x, VWRAP (horner_10) (x, poly + 1), poly[0]);
 183 }
 184 static inline VTYPE VWRAP (horner_12) (VTYPE x, const VTYPE *poly)
 185 {
 186   return FMA (x, VWRAP (horner_11) (x, poly + 1), poly[0]);
 187 }
 188
 189 static inline VTYPE VWRAP (pw_horner_4) (VTYPE x, VTYPE x2, const VTYPE *poly)
 190 {
 191   VTYPE p01 = FMA (poly[1], x, poly[0]);
 192   VTYPE p23 = FMA (poly[3], x, poly[2]);
 193   VTYPE p;
 194   p = FMA (x2, poly[4], p23);
 195   p = FMA (x2, p, p01);
 196   return p;
 197 }
 198 static inline VTYPE VWRAP (pw_horner_5) (VTYPE x, VTYPE x2, const VTYPE *poly)
 199 {
 200   VTYPE p01 = FMA (poly[1], x, poly[0]);
 201   VTYPE p23 = FMA (poly[3], x, poly[2]);
 202   VTYPE p45 = FMA (poly[5], x, poly[4]);
 203   VTYPE p;
 204   p = FMA (x2, p45, p23);
 205   p = FMA (x2, p, p01);
 206   return p;
 207 }
 208 static inline VTYPE VWRAP (pw_horner_6) (VTYPE x, VTYPE x2, const VTYPE *poly)
 209 {
 210   VTYPE p26 = VWRAP (pw_horner_4) (x, x2, poly + 2);
 211   VTYPE p01 = FMA (poly[1], x, poly[0]);
 212   return FMA (x2, p26, p01);
 213 }
 214 static inline VTYPE VWRAP (pw_horner_7) (VTYPE x, VTYPE x2, const VTYPE *poly)
 215 {
 216   VTYPE p27 = VWRAP (pw_horner_5) (x, x2, poly + 2);
 217   VTYPE p01 = FMA (poly[1], x, poly[0]);
 218   return FMA (x2, p27, p01);
 219 }
 220 static inline VTYPE VWRAP (pw_horner_8) (VTYPE x, VTYPE x2, const VTYPE *poly)
 221 {
 222   VTYPE p28 = VWRAP (pw_horner_6) (x, x2, poly + 2);
 223   VTYPE p01 = FMA (poly[1], x, poly[0]);
 224   return FMA (x2, p28, p01);
 225 }
 226 static inline VTYPE VWRAP (pw_horner_9) (VTYPE x, VTYPE x2, const VTYPE *poly)
 227 {
 228   VTYPE p29 = VWRAP (pw_horner_7) (x, x2, poly + 2);
 229   VTYPE p01 = FMA (poly[1], x, poly[0]);
 230   return FMA (x2, p29, p01);
 231 }
 232 static inline VTYPE VWRAP (pw_horner_10) (VTYPE x, VTYPE x2, const VTYPE *poly)
 233 {
 234   VTYPE p2_10 = VWRAP (pw_horner_8) (x, x2, poly + 2);
 235   VTYPE p01 = FMA (poly[1], x, poly[0]);
 236   return FMA (x2, p2_10, p01);
 237 }
 238 static inline VTYPE VWRAP (pw_horner_11) (VTYPE x, VTYPE x2, const VTYPE *poly)
 239 {
 240   VTYPE p2_11 = VWRAP (pw_horner_9) (x, x2, poly + 2);
 241   VTYPE p01 = FMA (poly[1], x, poly[0]);
 242   return FMA (x2, p2_11, p01);
 243 }
 244 static inline VTYPE VWRAP (pw_horner_12) (VTYPE x, VTYPE x2, const VTYPE *poly)
 245 {
 246   VTYPE p2_12 = VWRAP (pw_horner_10) (x, x2, poly + 2);
 247   VTYPE p01 = FMA (poly[1], x, poly[0]);
 248   return FMA (x2, p2_12, p01);
 249 }
 250 static inline VTYPE VWRAP (pw_horner_13) (VTYPE x, VTYPE x2, const VTYPE *poly)
 251 {
 252   VTYPE p2_13 = VWRAP (pw_horner_11) (x, x2, poly + 2);
 253   VTYPE p01 = FMA (poly[1], x, poly[0]);
 254   return FMA (x2, p2_13, p01);
 255 }
 256 static inline VTYPE VWRAP (pw_horner_14) (VTYPE x, VTYPE x2, const VTYPE *poly)
 257 {
 258   VTYPE p2_14 = VWRAP (pw_horner_12) (x, x2, poly + 2);
 259   VTYPE p01 = FMA (poly[1], x, poly[0]);
 260   return FMA (x2, p2_14, p01);
 261 }
 262 static inline VTYPE VWRAP (pw_horner_15) (VTYPE x, VTYPE x2, const VTYPE *poly)
 263 {
 264   VTYPE p2_15 = VWRAP (pw_horner_13) (x, x2, poly + 2);
 265   VTYPE p01 = FMA (poly[1], x, poly[0]);
 266   return FMA (x2, p2_15, p01);
 267 }
 268 static inline VTYPE VWRAP (pw_horner_16) (VTYPE x, VTYPE x2, const VTYPE *poly)
 269 {
 270   VTYPE p2_16 = VWRAP (pw_horner_14) (x, x2, poly + 2);
 271   VTYPE p01 = FMA (poly[1], x, poly[0]);
 272   return FMA (x2, p2_16, p01);
 273 }
 274 static inline VTYPE VWRAP (pw_horner_17) (VTYPE x, VTYPE x2, const VTYPE *poly)
 275 {
 276   VTYPE p2_17 = VWRAP (pw_horner_15) (x, x2, poly + 2);
 277   VTYPE p01 = FMA (poly[1], x, poly[0]);
 278   return FMA (x2, p2_17, p01);
 279 }
 280 static inline VTYPE VWRAP (pw_horner_18) (VTYPE x, VTYPE x2, const VTYPE *poly)
 281 {
 282   VTYPE p2_18 = VWRAP (pw_horner_16) (x, x2, poly + 2);
 283   VTYPE p01 = FMA (poly[1], x, poly[0]);
 284   return FMA (x2, p2_18, p01);
 285 }