1 /* Software floating-point emulation. 2 Definitions for IEEE Extended Precision. 3 Copyright (C) 1999,2006,2007 Free Software Foundation, Inc. 4 This file is part of the GNU C Library. 5 Contributed by Jakub Jelinek (jj@ultra.linux.cz). 6 7 The GNU C Library is free software; you can redistribute it and/or 8 modify it under the terms of the GNU Lesser General Public 9 License as published by the Free Software Foundation; either 10 version 2.1 of the License, or (at your option) any later version. 11 12 In addition to the permissions in the GNU Lesser General Public 13 License, the Free Software Foundation gives you unlimited 14 permission to link the compiled version of this file into 15 combinations with other programs, and to distribute those 16 combinations without any restriction coming from the use of this 17 file. (The Lesser General Public License restrictions do apply in 18 other respects; for example, they cover modification of the file, 19 and distribution when not linked into a combine executable.) 20 21 The GNU C Library is distributed in the hope that it will be useful, 22 but WITHOUT ANY WARRANTY; without even the implied warranty of 23 MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the GNU 24 Lesser General Public License for more details. 25 26 You should have received a copy of the GNU Lesser General Public 27 License along with the GNU C Library; if not, write to the Free 28 Software Foundation, 51 Franklin Street, Fifth Floor, Boston, 29 MA 02110-1301, USA. */ 30 31 #if _FP_W_TYPE_SIZE < 32 32 #error "Here's a nickel, kid. Go buy yourself a real computer." 33 #endif 34 35 #if _FP_W_TYPE_SIZE < 64 36 #define _FP_FRACTBITS_E (4*_FP_W_TYPE_SIZE) 37 #else 38 #define _FP_FRACTBITS_E (2*_FP_W_TYPE_SIZE) 39 #endif 40 41 #define _FP_FRACBITS_E 64 42 #define _FP_FRACXBITS_E (_FP_FRACTBITS_E - _FP_FRACBITS_E) 43 #define _FP_WFRACBITS_E (_FP_WORKBITS + _FP_FRACBITS_E) 44 #define _FP_WFRACXBITS_E (_FP_FRACTBITS_E - _FP_WFRACBITS_E) 45 #define _FP_EXPBITS_E 15 46 #define _FP_EXPBIAS_E 16383 47 #define _FP_EXPMAX_E 32767 48 49 #define _FP_QNANBIT_E \ 50 ((_FP_W_TYPE)1 << (_FP_FRACBITS_E-2) % _FP_W_TYPE_SIZE) 51 #define _FP_QNANBIT_SH_E \ 52 ((_FP_W_TYPE)1 << (_FP_FRACBITS_E-2+_FP_WORKBITS) % _FP_W_TYPE_SIZE) 53 #define _FP_IMPLBIT_E \ 54 ((_FP_W_TYPE)1 << (_FP_FRACBITS_E-1) % _FP_W_TYPE_SIZE) 55 #define _FP_IMPLBIT_SH_E \ 56 ((_FP_W_TYPE)1 << (_FP_FRACBITS_E-1+_FP_WORKBITS) % _FP_W_TYPE_SIZE) 57 #define _FP_OVERFLOW_E \ 58 ((_FP_W_TYPE)1 << (_FP_WFRACBITS_E % _FP_W_TYPE_SIZE)) 59 60 typedef float XFtype __attribute__((mode(XF))); 61 62 #if _FP_W_TYPE_SIZE < 64 63 64 union _FP_UNION_E 65 { 66 XFtype flt; 67 struct 68 { 69 #if __BYTE_ORDER == __BIG_ENDIAN 70 unsigned long pad1 : _FP_W_TYPE_SIZE; 71 unsigned long pad2 : (_FP_W_TYPE_SIZE - 1 - _FP_EXPBITS_E); 72 unsigned long sign : 1; 73 unsigned long exp : _FP_EXPBITS_E; 74 unsigned long frac1 : _FP_W_TYPE_SIZE; 75 unsigned long frac0 : _FP_W_TYPE_SIZE; 76 #else 77 unsigned long frac0 : _FP_W_TYPE_SIZE; 78 unsigned long frac1 : _FP_W_TYPE_SIZE; 79 unsigned exp : _FP_EXPBITS_E; 80 unsigned sign : 1; 81 #endif /* not bigendian */ 82 } bits __attribute__((packed)); 83 }; 84 85 86 #define FP_DECL_E(X) _FP_DECL(4,X) 87 88 #define FP_UNPACK_RAW_E(X, val) \ 89 do { \ 90 union _FP_UNION_E _flo; _flo.flt = (val); \ 91 \ 92 X##_f[2] = 0; X##_f[3] = 0; \ 93 X##_f[0] = _flo.bits.frac0; \ 94 X##_f[1] = _flo.bits.frac1; \ 95 X##_e = _flo.bits.exp; \ 96 X##_s = _flo.bits.sign; \ 97 } while (0) 98 99 #define FP_UNPACK_RAW_EP(X, val) \ 100 do { \ 101 union _FP_UNION_E *_flo = \ 102 (union _FP_UNION_E *)(val); \ 103 \ 104 X##_f[2] = 0; X##_f[3] = 0; \ 105 X##_f[0] = _flo->bits.frac0; \ 106 X##_f[1] = _flo->bits.frac1; \ 107 X##_e = _flo->bits.exp; \ 108 X##_s = _flo->bits.sign; \ 109 } while (0) 110 111 #define FP_PACK_RAW_E(val, X) \ 112 do { \ 113 union _FP_UNION_E _flo; \ 114 \ 115 if (X##_e) X##_f[1] |= _FP_IMPLBIT_E; \ 116 else X##_f[1] &= ~(_FP_IMPLBIT_E); \ 117 _flo.bits.frac0 = X##_f[0]; \ 118 _flo.bits.frac1 = X##_f[1]; \ 119 _flo.bits.exp = X##_e; \ 120 _flo.bits.sign = X##_s; \ 121 \ 122 (val) = _flo.flt; \ 123 } while (0) 124 125 #define FP_PACK_RAW_EP(val, X) \ 126 do { \ 127 if (!FP_INHIBIT_RESULTS) \ 128 { \ 129 union _FP_UNION_E *_flo = \ 130 (union _FP_UNION_E *)(val); \ 131 \ 132 if (X##_e) X##_f[1] |= _FP_IMPLBIT_E; \ 133 else X##_f[1] &= ~(_FP_IMPLBIT_E); \ 134 _flo->bits.frac0 = X##_f[0]; \ 135 _flo->bits.frac1 = X##_f[1]; \ 136 _flo->bits.exp = X##_e; \ 137 _flo->bits.sign = X##_s; \ 138 } \ 139 } while (0) 140 141 #define FP_UNPACK_E(X,val) \ 142 do { \ 143 FP_UNPACK_RAW_E(X,val); \ 144 _FP_UNPACK_CANONICAL(E,4,X); \ 145 } while (0) 146 147 #define FP_UNPACK_EP(X,val) \ 148 do { \ 149 FP_UNPACK_RAW_EP(X,val); \ 150 _FP_UNPACK_CANONICAL(E,4,X); \ 151 } while (0) 152 153 #define FP_UNPACK_SEMIRAW_E(X,val) \ 154 do { \ 155 FP_UNPACK_RAW_E(X,val); \ 156 _FP_UNPACK_SEMIRAW(E,4,X); \ 157 } while (0) 158 159 #define FP_UNPACK_SEMIRAW_EP(X,val) \ 160 do { \ 161 FP_UNPACK_RAW_EP(X,val); \ 162 _FP_UNPACK_SEMIRAW(E,4,X); \ 163 } while (0) 164 165 #define FP_PACK_E(val,X) \ 166 do { \ 167 _FP_PACK_CANONICAL(E,4,X); \ 168 FP_PACK_RAW_E(val,X); \ 169 } while (0) 170 171 #define FP_PACK_EP(val,X) \ 172 do { \ 173 _FP_PACK_CANONICAL(E,4,X); \ 174 FP_PACK_RAW_EP(val,X); \ 175 } while (0) 176 177 #define FP_PACK_SEMIRAW_E(val,X) \ 178 do { \ 179 _FP_PACK_SEMIRAW(E,4,X); \ 180 FP_PACK_RAW_E(val,X); \ 181 } while (0) 182 183 #define FP_PACK_SEMIRAW_EP(val,X) \ 184 do { \ 185 _FP_PACK_SEMIRAW(E,4,X); \ 186 FP_PACK_RAW_EP(val,X); \ 187 } while (0) 188 189 #define FP_ISSIGNAN_E(X) _FP_ISSIGNAN(E,4,X) 190 #define FP_NEG_E(R,X) _FP_NEG(E,4,R,X) 191 #define FP_ADD_E(R,X,Y) _FP_ADD(E,4,R,X,Y) 192 #define FP_SUB_E(R,X,Y) _FP_SUB(E,4,R,X,Y) 193 #define FP_MUL_E(R,X,Y) _FP_MUL(E,4,R,X,Y) 194 #define FP_DIV_E(R,X,Y) _FP_DIV(E,4,R,X,Y) 195 #define FP_SQRT_E(R,X) _FP_SQRT(E,4,R,X) 196 197 /* 198 * Square root algorithms: 199 * We have just one right now, maybe Newton approximation 200 * should be added for those machines where division is fast. 201 * This has special _E version because standard _4 square 202 * root would not work (it has to start normally with the 203 * second word and not the first), but as we have to do it 204 * anyway, we optimize it by doing most of the calculations 205 * in two UWtype registers instead of four. 206 */ 207 208 #define _FP_SQRT_MEAT_E(R, S, T, X, q) \ 209 do { \ 210 q = (_FP_W_TYPE)1 << (_FP_W_TYPE_SIZE - 1); \ 211 _FP_FRAC_SRL_4(X, (_FP_WORKBITS)); \ 212 while (q) \ 213 { \ 214 T##_f[1] = S##_f[1] + q; \ 215 if (T##_f[1] <= X##_f[1]) \ 216 { \ 217 S##_f[1] = T##_f[1] + q; \ 218 X##_f[1] -= T##_f[1]; \ 219 R##_f[1] += q; \ 220 } \ 221 _FP_FRAC_SLL_2(X, 1); \ 222 q >>= 1; \ 223 } \ 224 q = (_FP_W_TYPE)1 << (_FP_W_TYPE_SIZE - 1); \ 225 while (q) \ 226 { \ 227 T##_f[0] = S##_f[0] + q; \ 228 T##_f[1] = S##_f[1]; \ 229 if (T##_f[1] < X##_f[1] || \ 230 (T##_f[1] == X##_f[1] && \ 231 T##_f[0] <= X##_f[0])) \ 232 { \ 233 S##_f[0] = T##_f[0] + q; \ 234 S##_f[1] += (T##_f[0] > S##_f[0]); \ 235 _FP_FRAC_DEC_2(X, T); \ 236 R##_f[0] += q; \ 237 } \ 238 _FP_FRAC_SLL_2(X, 1); \ 239 q >>= 1; \ 240 } \ 241 _FP_FRAC_SLL_4(R, (_FP_WORKBITS)); \ 242 if (X##_f[0] | X##_f[1]) \ 243 { \ 244 if (S##_f[1] < X##_f[1] || \ 245 (S##_f[1] == X##_f[1] && \ 246 S##_f[0] < X##_f[0])) \ 247 R##_f[0] |= _FP_WORK_ROUND; \ 248 R##_f[0] |= _FP_WORK_STICKY; \ 249 } \ 250 } while (0) 251 252 #define FP_CMP_E(r,X,Y,un) _FP_CMP(E,4,r,X,Y,un) 253 #define FP_CMP_EQ_E(r,X,Y) _FP_CMP_EQ(E,4,r,X,Y) 254 #define FP_CMP_UNORD_E(r,X,Y) _FP_CMP_UNORD(E,4,r,X,Y) 255 256 #define FP_TO_INT_E(r,X,rsz,rsg) _FP_TO_INT(E,4,r,X,rsz,rsg) 257 #define FP_FROM_INT_E(X,r,rs,rt) _FP_FROM_INT(E,4,X,r,rs,rt) 258 259 #define _FP_FRAC_HIGH_E(X) (X##_f[2]) 260 #define _FP_FRAC_HIGH_RAW_E(X) (X##_f[1]) 261 262 #else /* not _FP_W_TYPE_SIZE < 64 */ 263 union _FP_UNION_E 264 { 265 XFtype flt; 266 struct { 267 #if __BYTE_ORDER == __BIG_ENDIAN 268 _FP_W_TYPE pad : (_FP_W_TYPE_SIZE - 1 - _FP_EXPBITS_E); 269 unsigned sign : 1; 270 unsigned exp : _FP_EXPBITS_E; 271 _FP_W_TYPE frac : _FP_W_TYPE_SIZE; 272 #else 273 _FP_W_TYPE frac : _FP_W_TYPE_SIZE; 274 unsigned exp : _FP_EXPBITS_E; 275 unsigned sign : 1; 276 #endif 277 } bits; 278 }; 279 280 #define FP_DECL_E(X) _FP_DECL(2,X) 281 282 #define FP_UNPACK_RAW_E(X, val) \ 283 do { \ 284 union _FP_UNION_E _flo; _flo.flt = (val); \ 285 \ 286 X##_f0 = _flo.bits.frac; \ 287 X##_f1 = 0; \ 288 X##_e = _flo.bits.exp; \ 289 X##_s = _flo.bits.sign; \ 290 } while (0) 291 292 #define FP_UNPACK_RAW_EP(X, val) \ 293 do { \ 294 union _FP_UNION_E *_flo = \ 295 (union _FP_UNION_E *)(val); \ 296 \ 297 X##_f0 = _flo->bits.frac; \ 298 X##_f1 = 0; \ 299 X##_e = _flo->bits.exp; \ 300 X##_s = _flo->bits.sign; \ 301 } while (0) 302 303 #define FP_PACK_RAW_E(val, X) \ 304 do { \ 305 union _FP_UNION_E _flo; \ 306 \ 307 if (X##_e) X##_f0 |= _FP_IMPLBIT_E; \ 308 else X##_f0 &= ~(_FP_IMPLBIT_E); \ 309 _flo.bits.frac = X##_f0; \ 310 _flo.bits.exp = X##_e; \ 311 _flo.bits.sign = X##_s; \ 312 \ 313 (val) = _flo.flt; \ 314 } while (0) 315 316 #define FP_PACK_RAW_EP(fs, val, X) \ 317 do { \ 318 if (!FP_INHIBIT_RESULTS) \ 319 { \ 320 union _FP_UNION_E *_flo = \ 321 (union _FP_UNION_E *)(val); \ 322 \ 323 if (X##_e) X##_f0 |= _FP_IMPLBIT_E; \ 324 else X##_f0 &= ~(_FP_IMPLBIT_E); \ 325 _flo->bits.frac = X##_f0; \ 326 _flo->bits.exp = X##_e; \ 327 _flo->bits.sign = X##_s; \ 328 } \ 329 } while (0) 330 331 332 #define FP_UNPACK_E(X,val) \ 333 do { \ 334 FP_UNPACK_RAW_E(X,val); \ 335 _FP_UNPACK_CANONICAL(E,2,X); \ 336 } while (0) 337 338 #define FP_UNPACK_EP(X,val) \ 339 do { \ 340 FP_UNPACK_RAW_EP(X,val); \ 341 _FP_UNPACK_CANONICAL(E,2,X); \ 342 } while (0) 343 344 #define FP_UNPACK_SEMIRAW_E(X,val) \ 345 do { \ 346 FP_UNPACK_RAW_E(X,val); \ 347 _FP_UNPACK_SEMIRAW(E,2,X); \ 348 } while (0) 349 350 #define FP_UNPACK_SEMIRAW_EP(X,val) \ 351 do { \ 352 FP_UNPACK_RAW_EP(X,val); \ 353 _FP_UNPACK_SEMIRAW(E,2,X); \ 354 } while (0) 355 356 #define FP_PACK_E(val,X) \ 357 do { \ 358 _FP_PACK_CANONICAL(E,2,X); \ 359 FP_PACK_RAW_E(val,X); \ 360 } while (0) 361 362 #define FP_PACK_EP(val,X) \ 363 do { \ 364 _FP_PACK_CANONICAL(E,2,X); \ 365 FP_PACK_RAW_EP(val,X); \ 366 } while (0) 367 368 #define FP_PACK_SEMIRAW_E(val,X) \ 369 do { \ 370 _FP_PACK_SEMIRAW(E,2,X); \ 371 FP_PACK_RAW_E(val,X); \ 372 } while (0) 373 374 #define FP_PACK_SEMIRAW_EP(val,X) \ 375 do { \ 376 _FP_PACK_SEMIRAW(E,2,X); \ 377 FP_PACK_RAW_EP(val,X); \ 378 } while (0) 379 380 #define FP_ISSIGNAN_E(X) _FP_ISSIGNAN(E,2,X) 381 #define FP_NEG_E(R,X) _FP_NEG(E,2,R,X) 382 #define FP_ADD_E(R,X,Y) _FP_ADD(E,2,R,X,Y) 383 #define FP_SUB_E(R,X,Y) _FP_SUB(E,2,R,X,Y) 384 #define FP_MUL_E(R,X,Y) _FP_MUL(E,2,R,X,Y) 385 #define FP_DIV_E(R,X,Y) _FP_DIV(E,2,R,X,Y) 386 #define FP_SQRT_E(R,X) _FP_SQRT(E,2,R,X) 387 388 /* 389 * Square root algorithms: 390 * We have just one right now, maybe Newton approximation 391 * should be added for those machines where division is fast. 392 * We optimize it by doing most of the calculations 393 * in one UWtype registers instead of two, although we don't 394 * have to. 395 */ 396 #define _FP_SQRT_MEAT_E(R, S, T, X, q) \ 397 do { \ 398 q = (_FP_W_TYPE)1 << (_FP_W_TYPE_SIZE - 1); \ 399 _FP_FRAC_SRL_2(X, (_FP_WORKBITS)); \ 400 while (q) \ 401 { \ 402 T##_f0 = S##_f0 + q; \ 403 if (T##_f0 <= X##_f0) \ 404 { \ 405 S##_f0 = T##_f0 + q; \ 406 X##_f0 -= T##_f0; \ 407 R##_f0 += q; \ 408 } \ 409 _FP_FRAC_SLL_1(X, 1); \ 410 q >>= 1; \ 411 } \ 412 _FP_FRAC_SLL_2(R, (_FP_WORKBITS)); \ 413 if (X##_f0) \ 414 { \ 415 if (S##_f0 < X##_f0) \ 416 R##_f0 |= _FP_WORK_ROUND; \ 417 R##_f0 |= _FP_WORK_STICKY; \ 418 } \ 419 } while (0) 420 421 #define FP_CMP_E(r,X,Y,un) _FP_CMP(E,2,r,X,Y,un) 422 #define FP_CMP_EQ_E(r,X,Y) _FP_CMP_EQ(E,2,r,X,Y) 423 #define FP_CMP_UNORD_E(r,X,Y) _FP_CMP_UNORD(E,2,r,X,Y) 424 425 #define FP_TO_INT_E(r,X,rsz,rsg) _FP_TO_INT(E,2,r,X,rsz,rsg) 426 #define FP_FROM_INT_E(X,r,rs,rt) _FP_FROM_INT(E,2,X,r,rs,rt) 427 428 #define _FP_FRAC_HIGH_E(X) (X##_f1) 429 #define _FP_FRAC_HIGH_RAW_E(X) (X##_f0) 430 431 #endif /* not _FP_W_TYPE_SIZE < 64 */ 432