1 /* Polynomial integer classes. 2 Copyright (C) 2014-2021 Free Software Foundation, Inc. 3 4 This file is part of GCC. 5 6 GCC is free software; you can redistribute it and/or modify it under 7 the terms of the GNU General Public License as published by the Free 8 Software Foundation; either version 3, or (at your option) any later 9 version. 10 11 GCC is distributed in the hope that it will be useful, but WITHOUT ANY 12 WARRANTY; without even the implied warranty of MERCHANTABILITY or 13 FITNESS FOR A PARTICULAR PURPOSE. See the GNU General Public License 14 for more details. 15 16 You should have received a copy of the GNU General Public License 17 along with GCC; see the file COPYING3. If not see 18 <http://www.gnu.org/licenses/>. */ 19 20 /* This file provides a representation of sizes and offsets whose exact 21 values depend on certain runtime properties. The motivating example 22 is the Arm SVE ISA, in which the number of vector elements is only 23 known at runtime. See doc/poly-int.texi for more details. 24 25 Tests for poly-int.h are located in testsuite/gcc.dg/plugin, 26 since they are too expensive (in terms of binary size) to be 27 included as selftests. */ 28 29 #ifndef HAVE_POLY_INT_H 30 #define HAVE_POLY_INT_H 31 32 template<unsigned int N, typename T> struct poly_int_pod; 33 template<unsigned int N, typename T> class poly_int; 34 35 /* poly_coeff_traiits<T> describes the properties of a poly_int 36 coefficient type T: 37 38 - poly_coeff_traits<T1>::rank is less than poly_coeff_traits<T2>::rank 39 if T1 can promote to T2. For C-like types the rank is: 40 41 (2 * number of bytes) + (unsigned ? 1 : 0) 42 43 wide_ints don't have a normal rank and so use a value of INT_MAX. 44 Any fixed-width integer should be promoted to wide_int if possible 45 and lead to an error otherwise. 46 47 - poly_coeff_traits<T>::int_type is the type to which an integer 48 literal should be cast before comparing it with T. 49 50 - poly_coeff_traits<T>::precision is the number of bits that T can hold. 51 52 - poly_coeff_traits<T>::signedness is: 53 0 if T is unsigned 54 1 if T is signed 55 -1 if T has no inherent sign (as for wide_int). 56 57 - poly_coeff_traits<T>::max_value, if defined, is the maximum value of T. 58 59 - poly_coeff_traits<T>::result is a type that can hold results of 60 operations on T. This is different from T itself in cases where T 61 is the result of an accessor like wi::to_offset. */ 62 template<typename T, wi::precision_type = wi::int_traits<T>::precision_type> 63 struct poly_coeff_traits; 64 65 template<typename T> 66 struct poly_coeff_traits<T, wi::FLEXIBLE_PRECISION> 67 { 68 typedef T result; 69 typedef T int_type; 70 static const int signedness = (T (0) >= T (-1)); 71 static const int precision = sizeof (T) * CHAR_BIT; 72 static const T max_value = (signedness 73 ? ((T (1) << (precision - 2)) 74 + ((T (1) << (precision - 2)) - 1)) 75 : T (-1)); 76 static const int rank = sizeof (T) * 2 + !signedness; 77 }; 78 79 template<typename T> 80 struct poly_coeff_traits<T, wi::VAR_PRECISION> 81 { 82 typedef T result; 83 typedef int int_type; 84 static const int signedness = -1; 85 static const int precision = WIDE_INT_MAX_PRECISION; 86 static const int rank = INT_MAX; 87 }; 88 89 template<typename T> 90 struct poly_coeff_traits<T, wi::CONST_PRECISION> 91 { 92 typedef WI_UNARY_RESULT (T) result; 93 typedef int int_type; 94 /* These types are always signed. */ 95 static const int signedness = 1; 96 static const int precision = wi::int_traits<T>::precision; 97 static const int rank = precision * 2 / CHAR_BIT; 98 }; 99 100 /* Information about a pair of coefficient types. */ 101 template<typename T1, typename T2> 102 struct poly_coeff_pair_traits 103 { 104 /* True if T1 can represent all the values of T2. 105 106 Either: 107 108 - T1 should be a type with the same signedness as T2 and no less 109 precision. This allows things like int16_t -> int16_t and 110 uint32_t -> uint64_t. 111 112 - T1 should be signed, T2 should be unsigned, and T1 should be 113 wider than T2. This allows things like uint16_t -> int32_t. 114 115 This rules out cases in which T1 has less precision than T2 or where 116 the conversion would reinterpret the top bit. E.g. int16_t -> uint32_t 117 can be dangerous and should have an explicit cast if deliberate. */ 118 static const bool lossless_p = (poly_coeff_traits<T1>::signedness 119 == poly_coeff_traits<T2>::signedness 120 ? (poly_coeff_traits<T1>::precision 121 >= poly_coeff_traits<T2>::precision) 122 : (poly_coeff_traits<T1>::signedness == 1 123 && poly_coeff_traits<T2>::signedness == 0 124 && (poly_coeff_traits<T1>::precision 125 > poly_coeff_traits<T2>::precision))); 126 127 /* 0 if T1 op T2 should promote to HOST_WIDE_INT, 128 1 if T1 op T2 should promote to unsigned HOST_WIDE_INT, 129 2 if T1 op T2 should use wide-int rules. */ 130 #define RANK(X) poly_coeff_traits<X>::rank 131 static const int result_kind 132 = ((RANK (T1) <= RANK (HOST_WIDE_INT) 133 && RANK (T2) <= RANK (HOST_WIDE_INT)) 134 ? 0 135 : (RANK (T1) <= RANK (unsigned HOST_WIDE_INT) 136 && RANK (T2) <= RANK (unsigned HOST_WIDE_INT)) 137 ? 1 : 2); 138 #undef RANK 139 }; 140 141 /* SFINAE class that makes T3 available as "type" if T2 can represent all the 142 values in T1. */ 143 template<typename T1, typename T2, typename T3, 144 bool lossless_p = poly_coeff_pair_traits<T1, T2>::lossless_p> 145 struct if_lossless; 146 template<typename T1, typename T2, typename T3> 147 struct if_lossless<T1, T2, T3, true> 148 { 149 typedef T3 type; 150 }; 151 152 /* poly_int_traits<T> describes an integer type T that might be polynomial 153 or non-polynomial: 154 155 - poly_int_traits<T>::is_poly is true if T is a poly_int-based type 156 and false otherwise. 157 158 - poly_int_traits<T>::num_coeffs gives the number of coefficients in T 159 if T is a poly_int and 1 otherwise. 160 161 - poly_int_traits<T>::coeff_type gives the coefficent type of T if T 162 is a poly_int and T itself otherwise 163 164 - poly_int_traits<T>::int_type is a shorthand for 165 typename poly_coeff_traits<coeff_type>::int_type. */ 166 template<typename T> 167 struct poly_int_traits 168 { 169 static const bool is_poly = false; 170 static const unsigned int num_coeffs = 1; 171 typedef T coeff_type; 172 typedef typename poly_coeff_traits<T>::int_type int_type; 173 }; 174 template<unsigned int N, typename C> 175 struct poly_int_traits<poly_int_pod<N, C> > 176 { 177 static const bool is_poly = true; 178 static const unsigned int num_coeffs = N; 179 typedef C coeff_type; 180 typedef typename poly_coeff_traits<C>::int_type int_type; 181 }; 182 template<unsigned int N, typename C> 183 struct poly_int_traits<poly_int<N, C> > : poly_int_traits<poly_int_pod<N, C> > 184 { 185 }; 186 187 /* SFINAE class that makes T2 available as "type" if T1 is a non-polynomial 188 type. */ 189 template<typename T1, typename T2 = T1, 190 bool is_poly = poly_int_traits<T1>::is_poly> 191 struct if_nonpoly {}; 192 template<typename T1, typename T2> 193 struct if_nonpoly<T1, T2, false> 194 { 195 typedef T2 type; 196 }; 197 198 /* SFINAE class that makes T3 available as "type" if both T1 and T2 are 199 non-polynomial types. */ 200 template<typename T1, typename T2, typename T3, 201 bool is_poly1 = poly_int_traits<T1>::is_poly, 202 bool is_poly2 = poly_int_traits<T2>::is_poly> 203 struct if_nonpoly2 {}; 204 template<typename T1, typename T2, typename T3> 205 struct if_nonpoly2<T1, T2, T3, false, false> 206 { 207 typedef T3 type; 208 }; 209 210 /* SFINAE class that makes T2 available as "type" if T1 is a polynomial 211 type. */ 212 template<typename T1, typename T2 = T1, 213 bool is_poly = poly_int_traits<T1>::is_poly> 214 struct if_poly {}; 215 template<typename T1, typename T2> 216 struct if_poly<T1, T2, true> 217 { 218 typedef T2 type; 219 }; 220 221 /* poly_result<T1, T2> describes the result of an operation on two 222 types T1 and T2, where at least one of the types is polynomial: 223 224 - poly_result<T1, T2>::type gives the result type for the operation. 225 The intention is to provide normal C-like rules for integer ranks, 226 except that everything smaller than HOST_WIDE_INT promotes to 227 HOST_WIDE_INT. 228 229 - poly_result<T1, T2>::cast is the type to which an operand of type 230 T1 should be cast before doing the operation, to ensure that 231 the operation is done at the right precision. Casting to 232 poly_result<T1, T2>::type would also work, but casting to this 233 type is more efficient. */ 234 template<typename T1, typename T2 = T1, 235 int result_kind = poly_coeff_pair_traits<T1, T2>::result_kind> 236 struct poly_result; 237 238 /* Promote pair to HOST_WIDE_INT. */ 239 template<typename T1, typename T2> 240 struct poly_result<T1, T2, 0> 241 { 242 typedef HOST_WIDE_INT type; 243 /* T1 and T2 are primitive types, so cast values to T before operating 244 on them. */ 245 typedef type cast; 246 }; 247 248 /* Promote pair to unsigned HOST_WIDE_INT. */ 249 template<typename T1, typename T2> 250 struct poly_result<T1, T2, 1> 251 { 252 typedef unsigned HOST_WIDE_INT type; 253 /* T1 and T2 are primitive types, so cast values to T before operating 254 on them. */ 255 typedef type cast; 256 }; 257 258 /* Use normal wide-int rules. */ 259 template<typename T1, typename T2> 260 struct poly_result<T1, T2, 2> 261 { 262 typedef WI_BINARY_RESULT (T1, T2) type; 263 /* Don't cast values before operating on them; leave the wi:: routines 264 to handle promotion as necessary. */ 265 typedef const T1 &cast; 266 }; 267 268 /* The coefficient type for the result of a binary operation on two 269 poly_ints, the first of which has coefficients of type C1 and the 270 second of which has coefficients of type C2. */ 271 #define POLY_POLY_COEFF(C1, C2) typename poly_result<C1, C2>::type 272 273 /* Enforce that T2 is non-polynomial and provide the cofficient type of 274 the result of a binary operation in which the first operand is a 275 poly_int with coefficients of type C1 and the second operand is 276 a constant of type T2. */ 277 #define POLY_CONST_COEFF(C1, T2) \ 278 POLY_POLY_COEFF (C1, typename if_nonpoly<T2>::type) 279 280 /* Likewise in reverse. */ 281 #define CONST_POLY_COEFF(T1, C2) \ 282 POLY_POLY_COEFF (typename if_nonpoly<T1>::type, C2) 283 284 /* The result type for a binary operation on poly_int<N, C1> and 285 poly_int<N, C2>. */ 286 #define POLY_POLY_RESULT(N, C1, C2) poly_int<N, POLY_POLY_COEFF (C1, C2)> 287 288 /* Enforce that T2 is non-polynomial and provide the result type 289 for a binary operation on poly_int<N, C1> and T2. */ 290 #define POLY_CONST_RESULT(N, C1, T2) poly_int<N, POLY_CONST_COEFF (C1, T2)> 291 292 /* Enforce that T1 is non-polynomial and provide the result type 293 for a binary operation on T1 and poly_int<N, C2>. */ 294 #define CONST_POLY_RESULT(N, T1, C2) poly_int<N, CONST_POLY_COEFF (T1, C2)> 295 296 /* Enforce that T1 and T2 are non-polynomial and provide the result type 297 for a binary operation on T1 and T2. */ 298 #define CONST_CONST_RESULT(N, T1, T2) \ 299 POLY_POLY_COEFF (typename if_nonpoly<T1>::type, \ 300 typename if_nonpoly<T2>::type) 301 302 /* The type to which a coefficient of type C1 should be cast before 303 using it in a binary operation with a coefficient of type C2. */ 304 #define POLY_CAST(C1, C2) typename poly_result<C1, C2>::cast 305 306 /* Provide the coefficient type for the result of T1 op T2, where T1 307 and T2 can be polynomial or non-polynomial. */ 308 #define POLY_BINARY_COEFF(T1, T2) \ 309 typename poly_result<typename poly_int_traits<T1>::coeff_type, \ 310 typename poly_int_traits<T2>::coeff_type>::type 311 312 /* The type to which an integer constant should be cast before 313 comparing it with T. */ 314 #define POLY_INT_TYPE(T) typename poly_int_traits<T>::int_type 315 316 /* RES is a poly_int result that has coefficients of type C and that 317 is being built up a coefficient at a time. Set coefficient number I 318 to VALUE in the most efficient way possible. 319 320 For primitive C it is better to assign directly, since it avoids 321 any further calls and so is more efficient when the compiler is 322 built at -O0. But for wide-int based C it is better to construct 323 the value in-place. This means that calls out to a wide-int.cc 324 routine can take the address of RES rather than the address of 325 a temporary. 326 327 The dummy comparison against a null C * is just a way of checking 328 that C gives the right type. */ 329 #define POLY_SET_COEFF(C, RES, I, VALUE) \ 330 ((void) (&(RES).coeffs[0] == (C *) 0), \ 331 wi::int_traits<C>::precision_type == wi::FLEXIBLE_PRECISION \ 332 ? (void) ((RES).coeffs[I] = VALUE) \ 333 : (void) ((RES).coeffs[I].~C (), new (&(RES).coeffs[I]) C (VALUE))) 334 335 /* A base POD class for polynomial integers. The polynomial has N 336 coefficients of type C. */ 337 template<unsigned int N, typename C> 338 struct poly_int_pod 339 { 340 public: 341 template<typename Ca> 342 poly_int_pod &operator = (const poly_int_pod<N, Ca> &); 343 template<typename Ca> 344 typename if_nonpoly<Ca, poly_int_pod>::type &operator = (const Ca &); 345 346 template<typename Ca> 347 poly_int_pod &operator += (const poly_int_pod<N, Ca> &); 348 template<typename Ca> 349 typename if_nonpoly<Ca, poly_int_pod>::type &operator += (const Ca &); 350 351 template<typename Ca> 352 poly_int_pod &operator -= (const poly_int_pod<N, Ca> &); 353 template<typename Ca> 354 typename if_nonpoly<Ca, poly_int_pod>::type &operator -= (const Ca &); 355 356 template<typename Ca> 357 typename if_nonpoly<Ca, poly_int_pod>::type &operator *= (const Ca &); 358 359 poly_int_pod &operator <<= (unsigned int); 360 361 bool is_constant () const; 362 363 template<typename T> 364 typename if_lossless<T, C, bool>::type is_constant (T *) const; 365 366 C to_constant () const; 367 368 template<typename Ca> 369 static poly_int<N, C> from (const poly_int_pod<N, Ca> &, unsigned int, 370 signop); 371 template<typename Ca> 372 static poly_int<N, C> from (const poly_int_pod<N, Ca> &, signop); 373 374 bool to_shwi (poly_int_pod<N, HOST_WIDE_INT> *) const; 375 bool to_uhwi (poly_int_pod<N, unsigned HOST_WIDE_INT> *) const; 376 poly_int<N, HOST_WIDE_INT> force_shwi () const; 377 poly_int<N, unsigned HOST_WIDE_INT> force_uhwi () const; 378 379 #if POLY_INT_CONVERSION 380 operator C () const; 381 #endif 382 383 C coeffs[N]; 384 }; 385 386 template<unsigned int N, typename C> 387 template<typename Ca> 388 inline poly_int_pod<N, C>& 389 poly_int_pod<N, C>::operator = (const poly_int_pod<N, Ca> &a) 390 { 391 for (unsigned int i = 0; i < N; i++) 392 POLY_SET_COEFF (C, *this, i, a.coeffs[i]); 393 return *this; 394 } 395 396 template<unsigned int N, typename C> 397 template<typename Ca> 398 inline typename if_nonpoly<Ca, poly_int_pod<N, C> >::type & 399 poly_int_pod<N, C>::operator = (const Ca &a) 400 { 401 POLY_SET_COEFF (C, *this, 0, a); 402 if (N >= 2) 403 for (unsigned int i = 1; i < N; i++) 404 POLY_SET_COEFF (C, *this, i, wi::ints_for<C>::zero (this->coeffs[0])); 405 return *this; 406 } 407 408 template<unsigned int N, typename C> 409 template<typename Ca> 410 inline poly_int_pod<N, C>& 411 poly_int_pod<N, C>::operator += (const poly_int_pod<N, Ca> &a) 412 { 413 for (unsigned int i = 0; i < N; i++) 414 this->coeffs[i] += a.coeffs[i]; 415 return *this; 416 } 417 418 template<unsigned int N, typename C> 419 template<typename Ca> 420 inline typename if_nonpoly<Ca, poly_int_pod<N, C> >::type & 421 poly_int_pod<N, C>::operator += (const Ca &a) 422 { 423 this->coeffs[0] += a; 424 return *this; 425 } 426 427 template<unsigned int N, typename C> 428 template<typename Ca> 429 inline poly_int_pod<N, C>& 430 poly_int_pod<N, C>::operator -= (const poly_int_pod<N, Ca> &a) 431 { 432 for (unsigned int i = 0; i < N; i++) 433 this->coeffs[i] -= a.coeffs[i]; 434 return *this; 435 } 436 437 template<unsigned int N, typename C> 438 template<typename Ca> 439 inline typename if_nonpoly<Ca, poly_int_pod<N, C> >::type & 440 poly_int_pod<N, C>::operator -= (const Ca &a) 441 { 442 this->coeffs[0] -= a; 443 return *this; 444 } 445 446 template<unsigned int N, typename C> 447 template<typename Ca> 448 inline typename if_nonpoly<Ca, poly_int_pod<N, C> >::type & 449 poly_int_pod<N, C>::operator *= (const Ca &a) 450 { 451 for (unsigned int i = 0; i < N; i++) 452 this->coeffs[i] *= a; 453 return *this; 454 } 455 456 template<unsigned int N, typename C> 457 inline poly_int_pod<N, C>& 458 poly_int_pod<N, C>::operator <<= (unsigned int a) 459 { 460 for (unsigned int i = 0; i < N; i++) 461 this->coeffs[i] <<= a; 462 return *this; 463 } 464 465 /* Return true if the polynomial value is a compile-time constant. */ 466 467 template<unsigned int N, typename C> 468 inline bool 469 poly_int_pod<N, C>::is_constant () const 470 { 471 if (N >= 2) 472 for (unsigned int i = 1; i < N; i++) 473 if (this->coeffs[i] != 0) 474 return false; 475 return true; 476 } 477 478 /* Return true if the polynomial value is a compile-time constant, 479 storing its value in CONST_VALUE if so. */ 480 481 template<unsigned int N, typename C> 482 template<typename T> 483 inline typename if_lossless<T, C, bool>::type 484 poly_int_pod<N, C>::is_constant (T *const_value) const 485 { 486 if (is_constant ()) 487 { 488 *const_value = this->coeffs[0]; 489 return true; 490 } 491 return false; 492 } 493 494 /* Return the value of a polynomial that is already known to be a 495 compile-time constant. 496 497 NOTE: When using this function, please add a comment above the call 498 explaining why we know the value is constant in that context. */ 499 500 template<unsigned int N, typename C> 501 inline C 502 poly_int_pod<N, C>::to_constant () const 503 { 504 gcc_checking_assert (is_constant ()); 505 return this->coeffs[0]; 506 } 507 508 /* Convert X to a wide_int-based polynomial in which each coefficient 509 has BITSIZE bits. If X's coefficients are smaller than BITSIZE, 510 extend them according to SGN. */ 511 512 template<unsigned int N, typename C> 513 template<typename Ca> 514 inline poly_int<N, C> 515 poly_int_pod<N, C>::from (const poly_int_pod<N, Ca> &a, 516 unsigned int bitsize, signop sgn) 517 { 518 poly_int<N, C> r; 519 for (unsigned int i = 0; i < N; i++) 520 POLY_SET_COEFF (C, r, i, C::from (a.coeffs[i], bitsize, sgn)); 521 return r; 522 } 523 524 /* Convert X to a fixed_wide_int-based polynomial, extending according 525 to SGN. */ 526 527 template<unsigned int N, typename C> 528 template<typename Ca> 529 inline poly_int<N, C> 530 poly_int_pod<N, C>::from (const poly_int_pod<N, Ca> &a, signop sgn) 531 { 532 poly_int<N, C> r; 533 for (unsigned int i = 0; i < N; i++) 534 POLY_SET_COEFF (C, r, i, C::from (a.coeffs[i], sgn)); 535 return r; 536 } 537 538 /* Return true if the coefficients of this generic_wide_int-based 539 polynomial can be represented as signed HOST_WIDE_INTs without loss 540 of precision. Store the HOST_WIDE_INT representation in *R if so. */ 541 542 template<unsigned int N, typename C> 543 inline bool 544 poly_int_pod<N, C>::to_shwi (poly_int_pod<N, HOST_WIDE_INT> *r) const 545 { 546 for (unsigned int i = 0; i < N; i++) 547 if (!wi::fits_shwi_p (this->coeffs[i])) 548 return false; 549 for (unsigned int i = 0; i < N; i++) 550 r->coeffs[i] = this->coeffs[i].to_shwi (); 551 return true; 552 } 553 554 /* Return true if the coefficients of this generic_wide_int-based 555 polynomial can be represented as unsigned HOST_WIDE_INTs without 556 loss of precision. Store the unsigned HOST_WIDE_INT representation 557 in *R if so. */ 558 559 template<unsigned int N, typename C> 560 inline bool 561 poly_int_pod<N, C>::to_uhwi (poly_int_pod<N, unsigned HOST_WIDE_INT> *r) const 562 { 563 for (unsigned int i = 0; i < N; i++) 564 if (!wi::fits_uhwi_p (this->coeffs[i])) 565 return false; 566 for (unsigned int i = 0; i < N; i++) 567 r->coeffs[i] = this->coeffs[i].to_uhwi (); 568 return true; 569 } 570 571 /* Force a generic_wide_int-based constant to HOST_WIDE_INT precision, 572 truncating if necessary. */ 573 574 template<unsigned int N, typename C> 575 inline poly_int<N, HOST_WIDE_INT> 576 poly_int_pod<N, C>::force_shwi () const 577 { 578 poly_int_pod<N, HOST_WIDE_INT> r; 579 for (unsigned int i = 0; i < N; i++) 580 r.coeffs[i] = this->coeffs[i].to_shwi (); 581 return r; 582 } 583 584 /* Force a generic_wide_int-based constant to unsigned HOST_WIDE_INT precision, 585 truncating if necessary. */ 586 587 template<unsigned int N, typename C> 588 inline poly_int<N, unsigned HOST_WIDE_INT> 589 poly_int_pod<N, C>::force_uhwi () const 590 { 591 poly_int_pod<N, unsigned HOST_WIDE_INT> r; 592 for (unsigned int i = 0; i < N; i++) 593 r.coeffs[i] = this->coeffs[i].to_uhwi (); 594 return r; 595 } 596 597 #if POLY_INT_CONVERSION 598 /* Provide a conversion operator to constants. */ 599 600 template<unsigned int N, typename C> 601 inline 602 poly_int_pod<N, C>::operator C () const 603 { 604 gcc_checking_assert (this->is_constant ()); 605 return this->coeffs[0]; 606 } 607 #endif 608 609 /* The main class for polynomial integers. The class provides 610 constructors that are necessarily missing from the POD base. */ 611 template<unsigned int N, typename C> 612 class poly_int : public poly_int_pod<N, C> 613 { 614 public: 615 poly_int () {} 616 617 template<typename Ca> 618 poly_int (const poly_int<N, Ca> &); 619 template<typename Ca> 620 poly_int (const poly_int_pod<N, Ca> &); 621 template<typename C0> 622 poly_int (const C0 &); 623 template<typename C0, typename C1> 624 poly_int (const C0 &, const C1 &); 625 626 template<typename Ca> 627 poly_int &operator = (const poly_int_pod<N, Ca> &); 628 template<typename Ca> 629 typename if_nonpoly<Ca, poly_int>::type &operator = (const Ca &); 630 631 template<typename Ca> 632 poly_int &operator += (const poly_int_pod<N, Ca> &); 633 template<typename Ca> 634 typename if_nonpoly<Ca, poly_int>::type &operator += (const Ca &); 635 636 template<typename Ca> 637 poly_int &operator -= (const poly_int_pod<N, Ca> &); 638 template<typename Ca> 639 typename if_nonpoly<Ca, poly_int>::type &operator -= (const Ca &); 640 641 template<typename Ca> 642 typename if_nonpoly<Ca, poly_int>::type &operator *= (const Ca &); 643 644 poly_int &operator <<= (unsigned int); 645 }; 646 647 template<unsigned int N, typename C> 648 template<typename Ca> 649 inline 650 poly_int<N, C>::poly_int (const poly_int<N, Ca> &a) 651 { 652 for (unsigned int i = 0; i < N; i++) 653 POLY_SET_COEFF (C, *this, i, a.coeffs[i]); 654 } 655 656 template<unsigned int N, typename C> 657 template<typename Ca> 658 inline 659 poly_int<N, C>::poly_int (const poly_int_pod<N, Ca> &a) 660 { 661 for (unsigned int i = 0; i < N; i++) 662 POLY_SET_COEFF (C, *this, i, a.coeffs[i]); 663 } 664 665 template<unsigned int N, typename C> 666 template<typename C0> 667 inline 668 poly_int<N, C>::poly_int (const C0 &c0) 669 { 670 POLY_SET_COEFF (C, *this, 0, c0); 671 for (unsigned int i = 1; i < N; i++) 672 POLY_SET_COEFF (C, *this, i, wi::ints_for<C>::zero (this->coeffs[0])); 673 } 674 675 template<unsigned int N, typename C> 676 template<typename C0, typename C1> 677 inline 678 poly_int<N, C>::poly_int (const C0 &c0, const C1 &c1) 679 { 680 STATIC_ASSERT (N >= 2); 681 POLY_SET_COEFF (C, *this, 0, c0); 682 POLY_SET_COEFF (C, *this, 1, c1); 683 for (unsigned int i = 2; i < N; i++) 684 POLY_SET_COEFF (C, *this, i, wi::ints_for<C>::zero (this->coeffs[0])); 685 } 686 687 template<unsigned int N, typename C> 688 template<typename Ca> 689 inline poly_int<N, C>& 690 poly_int<N, C>::operator = (const poly_int_pod<N, Ca> &a) 691 { 692 for (unsigned int i = 0; i < N; i++) 693 this->coeffs[i] = a.coeffs[i]; 694 return *this; 695 } 696 697 template<unsigned int N, typename C> 698 template<typename Ca> 699 inline typename if_nonpoly<Ca, poly_int<N, C> >::type & 700 poly_int<N, C>::operator = (const Ca &a) 701 { 702 this->coeffs[0] = a; 703 if (N >= 2) 704 for (unsigned int i = 1; i < N; i++) 705 this->coeffs[i] = wi::ints_for<C>::zero (this->coeffs[0]); 706 return *this; 707 } 708 709 template<unsigned int N, typename C> 710 template<typename Ca> 711 inline poly_int<N, C>& 712 poly_int<N, C>::operator += (const poly_int_pod<N, Ca> &a) 713 { 714 for (unsigned int i = 0; i < N; i++) 715 this->coeffs[i] += a.coeffs[i]; 716 return *this; 717 } 718 719 template<unsigned int N, typename C> 720 template<typename Ca> 721 inline typename if_nonpoly<Ca, poly_int<N, C> >::type & 722 poly_int<N, C>::operator += (const Ca &a) 723 { 724 this->coeffs[0] += a; 725 return *this; 726 } 727 728 template<unsigned int N, typename C> 729 template<typename Ca> 730 inline poly_int<N, C>& 731 poly_int<N, C>::operator -= (const poly_int_pod<N, Ca> &a) 732 { 733 for (unsigned int i = 0; i < N; i++) 734 this->coeffs[i] -= a.coeffs[i]; 735 return *this; 736 } 737 738 template<unsigned int N, typename C> 739 template<typename Ca> 740 inline typename if_nonpoly<Ca, poly_int<N, C> >::type & 741 poly_int<N, C>::operator -= (const Ca &a) 742 { 743 this->coeffs[0] -= a; 744 return *this; 745 } 746 747 template<unsigned int N, typename C> 748 template<typename Ca> 749 inline typename if_nonpoly<Ca, poly_int<N, C> >::type & 750 poly_int<N, C>::operator *= (const Ca &a) 751 { 752 for (unsigned int i = 0; i < N; i++) 753 this->coeffs[i] *= a; 754 return *this; 755 } 756 757 template<unsigned int N, typename C> 758 inline poly_int<N, C>& 759 poly_int<N, C>::operator <<= (unsigned int a) 760 { 761 for (unsigned int i = 0; i < N; i++) 762 this->coeffs[i] <<= a; 763 return *this; 764 } 765 766 /* Return true if every coefficient of A is in the inclusive range [B, C]. */ 767 768 template<typename Ca, typename Cb, typename Cc> 769 inline typename if_nonpoly<Ca, bool>::type 770 coeffs_in_range_p (const Ca &a, const Cb &b, const Cc &c) 771 { 772 return a >= b && a <= c; 773 } 774 775 template<unsigned int N, typename Ca, typename Cb, typename Cc> 776 inline typename if_nonpoly<Ca, bool>::type 777 coeffs_in_range_p (const poly_int_pod<N, Ca> &a, const Cb &b, const Cc &c) 778 { 779 for (unsigned int i = 0; i < N; i++) 780 if (a.coeffs[i] < b || a.coeffs[i] > c) 781 return false; 782 return true; 783 } 784 785 namespace wi { 786 /* Poly version of wi::shwi, with the same interface. */ 787 788 template<unsigned int N> 789 inline poly_int<N, hwi_with_prec> 790 shwi (const poly_int_pod<N, HOST_WIDE_INT> &a, unsigned int precision) 791 { 792 poly_int<N, hwi_with_prec> r; 793 for (unsigned int i = 0; i < N; i++) 794 POLY_SET_COEFF (hwi_with_prec, r, i, wi::shwi (a.coeffs[i], precision)); 795 return r; 796 } 797 798 /* Poly version of wi::uhwi, with the same interface. */ 799 800 template<unsigned int N> 801 inline poly_int<N, hwi_with_prec> 802 uhwi (const poly_int_pod<N, unsigned HOST_WIDE_INT> &a, unsigned int precision) 803 { 804 poly_int<N, hwi_with_prec> r; 805 for (unsigned int i = 0; i < N; i++) 806 POLY_SET_COEFF (hwi_with_prec, r, i, wi::uhwi (a.coeffs[i], precision)); 807 return r; 808 } 809 810 /* Poly version of wi::sext, with the same interface. */ 811 812 template<unsigned int N, typename Ca> 813 inline POLY_POLY_RESULT (N, Ca, Ca) 814 sext (const poly_int_pod<N, Ca> &a, unsigned int precision) 815 { 816 typedef POLY_POLY_COEFF (Ca, Ca) C; 817 poly_int<N, C> r; 818 for (unsigned int i = 0; i < N; i++) 819 POLY_SET_COEFF (C, r, i, wi::sext (a.coeffs[i], precision)); 820 return r; 821 } 822 823 /* Poly version of wi::zext, with the same interface. */ 824 825 template<unsigned int N, typename Ca> 826 inline POLY_POLY_RESULT (N, Ca, Ca) 827 zext (const poly_int_pod<N, Ca> &a, unsigned int precision) 828 { 829 typedef POLY_POLY_COEFF (Ca, Ca) C; 830 poly_int<N, C> r; 831 for (unsigned int i = 0; i < N; i++) 832 POLY_SET_COEFF (C, r, i, wi::zext (a.coeffs[i], precision)); 833 return r; 834 } 835 } 836 837 template<unsigned int N, typename Ca, typename Cb> 838 inline POLY_POLY_RESULT (N, Ca, Cb) 839 operator + (const poly_int_pod<N, Ca> &a, const poly_int_pod<N, Cb> &b) 840 { 841 typedef POLY_CAST (Ca, Cb) NCa; 842 typedef POLY_POLY_COEFF (Ca, Cb) C; 843 poly_int<N, C> r; 844 for (unsigned int i = 0; i < N; i++) 845 POLY_SET_COEFF (C, r, i, NCa (a.coeffs[i]) + b.coeffs[i]); 846 return r; 847 } 848 849 template<unsigned int N, typename Ca, typename Cb> 850 inline POLY_CONST_RESULT (N, Ca, Cb) 851 operator + (const poly_int_pod<N, Ca> &a, const Cb &b) 852 { 853 typedef POLY_CAST (Ca, Cb) NCa; 854 typedef POLY_CONST_COEFF (Ca, Cb) C; 855 poly_int<N, C> r; 856 POLY_SET_COEFF (C, r, 0, NCa (a.coeffs[0]) + b); 857 if (N >= 2) 858 for (unsigned int i = 1; i < N; i++) 859 POLY_SET_COEFF (C, r, i, NCa (a.coeffs[i])); 860 return r; 861 } 862 863 template<unsigned int N, typename Ca, typename Cb> 864 inline CONST_POLY_RESULT (N, Ca, Cb) 865 operator + (const Ca &a, const poly_int_pod<N, Cb> &b) 866 { 867 typedef POLY_CAST (Cb, Ca) NCb; 868 typedef CONST_POLY_COEFF (Ca, Cb) C; 869 poly_int<N, C> r; 870 POLY_SET_COEFF (C, r, 0, a + NCb (b.coeffs[0])); 871 if (N >= 2) 872 for (unsigned int i = 1; i < N; i++) 873 POLY_SET_COEFF (C, r, i, NCb (b.coeffs[i])); 874 return r; 875 } 876 877 namespace wi { 878 /* Poly versions of wi::add, with the same interface. */ 879 880 template<unsigned int N, typename Ca, typename Cb> 881 inline poly_int<N, WI_BINARY_RESULT (Ca, Cb)> 882 add (const poly_int_pod<N, Ca> &a, const poly_int_pod<N, Cb> &b) 883 { 884 typedef WI_BINARY_RESULT (Ca, Cb) C; 885 poly_int<N, C> r; 886 for (unsigned int i = 0; i < N; i++) 887 POLY_SET_COEFF (C, r, i, wi::add (a.coeffs[i], b.coeffs[i])); 888 return r; 889 } 890 891 template<unsigned int N, typename Ca, typename Cb> 892 inline poly_int<N, WI_BINARY_RESULT (Ca, Cb)> 893 add (const poly_int_pod<N, Ca> &a, const Cb &b) 894 { 895 typedef WI_BINARY_RESULT (Ca, Cb) C; 896 poly_int<N, C> r; 897 POLY_SET_COEFF (C, r, 0, wi::add (a.coeffs[0], b)); 898 for (unsigned int i = 1; i < N; i++) 899 POLY_SET_COEFF (C, r, i, wi::add (a.coeffs[i], 900 wi::ints_for<Cb>::zero (b))); 901 return r; 902 } 903 904 template<unsigned int N, typename Ca, typename Cb> 905 inline poly_int<N, WI_BINARY_RESULT (Ca, Cb)> 906 add (const Ca &a, const poly_int_pod<N, Cb> &b) 907 { 908 typedef WI_BINARY_RESULT (Ca, Cb) C; 909 poly_int<N, C> r; 910 POLY_SET_COEFF (C, r, 0, wi::add (a, b.coeffs[0])); 911 for (unsigned int i = 1; i < N; i++) 912 POLY_SET_COEFF (C, r, i, wi::add (wi::ints_for<Ca>::zero (a), 913 b.coeffs[i])); 914 return r; 915 } 916 917 template<unsigned int N, typename Ca, typename Cb> 918 inline poly_int<N, WI_BINARY_RESULT (Ca, Cb)> 919 add (const poly_int_pod<N, Ca> &a, const poly_int_pod<N, Cb> &b, 920 signop sgn, wi::overflow_type *overflow) 921 { 922 typedef WI_BINARY_RESULT (Ca, Cb) C; 923 poly_int<N, C> r; 924 POLY_SET_COEFF (C, r, 0, wi::add (a.coeffs[0], b.coeffs[0], sgn, overflow)); 925 for (unsigned int i = 1; i < N; i++) 926 { 927 wi::overflow_type suboverflow; 928 POLY_SET_COEFF (C, r, i, wi::add (a.coeffs[i], b.coeffs[i], sgn, 929 &suboverflow)); 930 wi::accumulate_overflow (*overflow, suboverflow); 931 } 932 return r; 933 } 934 } 935 936 template<unsigned int N, typename Ca, typename Cb> 937 inline POLY_POLY_RESULT (N, Ca, Cb) 938 operator - (const poly_int_pod<N, Ca> &a, const poly_int_pod<N, Cb> &b) 939 { 940 typedef POLY_CAST (Ca, Cb) NCa; 941 typedef POLY_POLY_COEFF (Ca, Cb) C; 942 poly_int<N, C> r; 943 for (unsigned int i = 0; i < N; i++) 944 POLY_SET_COEFF (C, r, i, NCa (a.coeffs[i]) - b.coeffs[i]); 945 return r; 946 } 947 948 template<unsigned int N, typename Ca, typename Cb> 949 inline POLY_CONST_RESULT (N, Ca, Cb) 950 operator - (const poly_int_pod<N, Ca> &a, const Cb &b) 951 { 952 typedef POLY_CAST (Ca, Cb) NCa; 953 typedef POLY_CONST_COEFF (Ca, Cb) C; 954 poly_int<N, C> r; 955 POLY_SET_COEFF (C, r, 0, NCa (a.coeffs[0]) - b); 956 if (N >= 2) 957 for (unsigned int i = 1; i < N; i++) 958 POLY_SET_COEFF (C, r, i, NCa (a.coeffs[i])); 959 return r; 960 } 961 962 template<unsigned int N, typename Ca, typename Cb> 963 inline CONST_POLY_RESULT (N, Ca, Cb) 964 operator - (const Ca &a, const poly_int_pod<N, Cb> &b) 965 { 966 typedef POLY_CAST (Cb, Ca) NCb; 967 typedef CONST_POLY_COEFF (Ca, Cb) C; 968 poly_int<N, C> r; 969 POLY_SET_COEFF (C, r, 0, a - NCb (b.coeffs[0])); 970 if (N >= 2) 971 for (unsigned int i = 1; i < N; i++) 972 POLY_SET_COEFF (C, r, i, -NCb (b.coeffs[i])); 973 return r; 974 } 975 976 namespace wi { 977 /* Poly versions of wi::sub, with the same interface. */ 978 979 template<unsigned int N, typename Ca, typename Cb> 980 inline poly_int<N, WI_BINARY_RESULT (Ca, Cb)> 981 sub (const poly_int_pod<N, Ca> &a, const poly_int_pod<N, Cb> &b) 982 { 983 typedef WI_BINARY_RESULT (Ca, Cb) C; 984 poly_int<N, C> r; 985 for (unsigned int i = 0; i < N; i++) 986 POLY_SET_COEFF (C, r, i, wi::sub (a.coeffs[i], b.coeffs[i])); 987 return r; 988 } 989 990 template<unsigned int N, typename Ca, typename Cb> 991 inline poly_int<N, WI_BINARY_RESULT (Ca, Cb)> 992 sub (const poly_int_pod<N, Ca> &a, const Cb &b) 993 { 994 typedef WI_BINARY_RESULT (Ca, Cb) C; 995 poly_int<N, C> r; 996 POLY_SET_COEFF (C, r, 0, wi::sub (a.coeffs[0], b)); 997 for (unsigned int i = 1; i < N; i++) 998 POLY_SET_COEFF (C, r, i, wi::sub (a.coeffs[i], 999 wi::ints_for<Cb>::zero (b))); 1000 return r; 1001 } 1002 1003 template<unsigned int N, typename Ca, typename Cb> 1004 inline poly_int<N, WI_BINARY_RESULT (Ca, Cb)> 1005 sub (const Ca &a, const poly_int_pod<N, Cb> &b) 1006 { 1007 typedef WI_BINARY_RESULT (Ca, Cb) C; 1008 poly_int<N, C> r; 1009 POLY_SET_COEFF (C, r, 0, wi::sub (a, b.coeffs[0])); 1010 for (unsigned int i = 1; i < N; i++) 1011 POLY_SET_COEFF (C, r, i, wi::sub (wi::ints_for<Ca>::zero (a), 1012 b.coeffs[i])); 1013 return r; 1014 } 1015 1016 template<unsigned int N, typename Ca, typename Cb> 1017 inline poly_int<N, WI_BINARY_RESULT (Ca, Cb)> 1018 sub (const poly_int_pod<N, Ca> &a, const poly_int_pod<N, Cb> &b, 1019 signop sgn, wi::overflow_type *overflow) 1020 { 1021 typedef WI_BINARY_RESULT (Ca, Cb) C; 1022 poly_int<N, C> r; 1023 POLY_SET_COEFF (C, r, 0, wi::sub (a.coeffs[0], b.coeffs[0], sgn, overflow)); 1024 for (unsigned int i = 1; i < N; i++) 1025 { 1026 wi::overflow_type suboverflow; 1027 POLY_SET_COEFF (C, r, i, wi::sub (a.coeffs[i], b.coeffs[i], sgn, 1028 &suboverflow)); 1029 wi::accumulate_overflow (*overflow, suboverflow); 1030 } 1031 return r; 1032 } 1033 } 1034 1035 template<unsigned int N, typename Ca> 1036 inline POLY_POLY_RESULT (N, Ca, Ca) 1037 operator - (const poly_int_pod<N, Ca> &a) 1038 { 1039 typedef POLY_CAST (Ca, Ca) NCa; 1040 typedef POLY_POLY_COEFF (Ca, Ca) C; 1041 poly_int<N, C> r; 1042 for (unsigned int i = 0; i < N; i++) 1043 POLY_SET_COEFF (C, r, i, -NCa (a.coeffs[i])); 1044 return r; 1045 } 1046 1047 namespace wi { 1048 /* Poly version of wi::neg, with the same interface. */ 1049 1050 template<unsigned int N, typename Ca> 1051 inline poly_int<N, WI_UNARY_RESULT (Ca)> 1052 neg (const poly_int_pod<N, Ca> &a) 1053 { 1054 typedef WI_UNARY_RESULT (Ca) C; 1055 poly_int<N, C> r; 1056 for (unsigned int i = 0; i < N; i++) 1057 POLY_SET_COEFF (C, r, i, wi::neg (a.coeffs[i])); 1058 return r; 1059 } 1060 1061 template<unsigned int N, typename Ca> 1062 inline poly_int<N, WI_UNARY_RESULT (Ca)> 1063 neg (const poly_int_pod<N, Ca> &a, wi::overflow_type *overflow) 1064 { 1065 typedef WI_UNARY_RESULT (Ca) C; 1066 poly_int<N, C> r; 1067 POLY_SET_COEFF (C, r, 0, wi::neg (a.coeffs[0], overflow)); 1068 for (unsigned int i = 1; i < N; i++) 1069 { 1070 wi::overflow_type suboverflow; 1071 POLY_SET_COEFF (C, r, i, wi::neg (a.coeffs[i], &suboverflow)); 1072 wi::accumulate_overflow (*overflow, suboverflow); 1073 } 1074 return r; 1075 } 1076 } 1077 1078 template<unsigned int N, typename Ca> 1079 inline POLY_POLY_RESULT (N, Ca, Ca) 1080 operator ~ (const poly_int_pod<N, Ca> &a) 1081 { 1082 if (N >= 2) 1083 return -1 - a; 1084 return ~a.coeffs[0]; 1085 } 1086 1087 template<unsigned int N, typename Ca, typename Cb> 1088 inline POLY_CONST_RESULT (N, Ca, Cb) 1089 operator * (const poly_int_pod<N, Ca> &a, const Cb &b) 1090 { 1091 typedef POLY_CAST (Ca, Cb) NCa; 1092 typedef POLY_CONST_COEFF (Ca, Cb) C; 1093 poly_int<N, C> r; 1094 for (unsigned int i = 0; i < N; i++) 1095 POLY_SET_COEFF (C, r, i, NCa (a.coeffs[i]) * b); 1096 return r; 1097 } 1098 1099 template<unsigned int N, typename Ca, typename Cb> 1100 inline CONST_POLY_RESULT (N, Ca, Cb) 1101 operator * (const Ca &a, const poly_int_pod<N, Cb> &b) 1102 { 1103 typedef POLY_CAST (Ca, Cb) NCa; 1104 typedef CONST_POLY_COEFF (Ca, Cb) C; 1105 poly_int<N, C> r; 1106 for (unsigned int i = 0; i < N; i++) 1107 POLY_SET_COEFF (C, r, i, NCa (a) * b.coeffs[i]); 1108 return r; 1109 } 1110 1111 namespace wi { 1112 /* Poly versions of wi::mul, with the same interface. */ 1113 1114 template<unsigned int N, typename Ca, typename Cb> 1115 inline poly_int<N, WI_BINARY_RESULT (Ca, Cb)> 1116 mul (const poly_int_pod<N, Ca> &a, const Cb &b) 1117 { 1118 typedef WI_BINARY_RESULT (Ca, Cb) C; 1119 poly_int<N, C> r; 1120 for (unsigned int i = 0; i < N; i++) 1121 POLY_SET_COEFF (C, r, i, wi::mul (a.coeffs[i], b)); 1122 return r; 1123 } 1124 1125 template<unsigned int N, typename Ca, typename Cb> 1126 inline poly_int<N, WI_BINARY_RESULT (Ca, Cb)> 1127 mul (const Ca &a, const poly_int_pod<N, Cb> &b) 1128 { 1129 typedef WI_BINARY_RESULT (Ca, Cb) C; 1130 poly_int<N, C> r; 1131 for (unsigned int i = 0; i < N; i++) 1132 POLY_SET_COEFF (C, r, i, wi::mul (a, b.coeffs[i])); 1133 return r; 1134 } 1135 1136 template<unsigned int N, typename Ca, typename Cb> 1137 inline poly_int<N, WI_BINARY_RESULT (Ca, Cb)> 1138 mul (const poly_int_pod<N, Ca> &a, const Cb &b, 1139 signop sgn, wi::overflow_type *overflow) 1140 { 1141 typedef WI_BINARY_RESULT (Ca, Cb) C; 1142 poly_int<N, C> r; 1143 POLY_SET_COEFF (C, r, 0, wi::mul (a.coeffs[0], b, sgn, overflow)); 1144 for (unsigned int i = 1; i < N; i++) 1145 { 1146 wi::overflow_type suboverflow; 1147 POLY_SET_COEFF (C, r, i, wi::mul (a.coeffs[i], b, sgn, &suboverflow)); 1148 wi::accumulate_overflow (*overflow, suboverflow); 1149 } 1150 return r; 1151 } 1152 } 1153 1154 template<unsigned int N, typename Ca, typename Cb> 1155 inline POLY_POLY_RESULT (N, Ca, Ca) 1156 operator << (const poly_int_pod<N, Ca> &a, const Cb &b) 1157 { 1158 typedef POLY_CAST (Ca, Ca) NCa; 1159 typedef POLY_POLY_COEFF (Ca, Ca) C; 1160 poly_int<N, C> r; 1161 for (unsigned int i = 0; i < N; i++) 1162 POLY_SET_COEFF (C, r, i, NCa (a.coeffs[i]) << b); 1163 return r; 1164 } 1165 1166 namespace wi { 1167 /* Poly version of wi::lshift, with the same interface. */ 1168 1169 template<unsigned int N, typename Ca, typename Cb> 1170 inline poly_int<N, WI_BINARY_RESULT (Ca, Ca)> 1171 lshift (const poly_int_pod<N, Ca> &a, const Cb &b) 1172 { 1173 typedef WI_BINARY_RESULT (Ca, Ca) C; 1174 poly_int<N, C> r; 1175 for (unsigned int i = 0; i < N; i++) 1176 POLY_SET_COEFF (C, r, i, wi::lshift (a.coeffs[i], b)); 1177 return r; 1178 } 1179 } 1180 1181 /* Return true if a0 + a1 * x might equal b0 + b1 * x for some nonnegative 1182 integer x. */ 1183 1184 template<typename Ca, typename Cb> 1185 inline bool 1186 maybe_eq_2 (const Ca &a0, const Ca &a1, const Cb &b0, const Cb &b1) 1187 { 1188 if (a1 != b1) 1189 /* a0 + a1 * x == b0 + b1 * x 1190 ==> (a1 - b1) * x == b0 - a0 1191 ==> x == (b0 - a0) / (a1 - b1) 1192 1193 We need to test whether that's a valid value of x. 1194 (b0 - a0) and (a1 - b1) must not have opposite signs 1195 and the result must be integral. */ 1196 return (a1 < b1 1197 ? b0 <= a0 && (a0 - b0) % (b1 - a1) == 0 1198 : b0 >= a0 && (b0 - a0) % (a1 - b1) == 0); 1199 return a0 == b0; 1200 } 1201 1202 /* Return true if a0 + a1 * x might equal b for some nonnegative 1203 integer x. */ 1204 1205 template<typename Ca, typename Cb> 1206 inline bool 1207 maybe_eq_2 (const Ca &a0, const Ca &a1, const Cb &b) 1208 { 1209 if (a1 != 0) 1210 /* a0 + a1 * x == b 1211 ==> x == (b - a0) / a1 1212 1213 We need to test whether that's a valid value of x. 1214 (b - a0) and a1 must not have opposite signs and the 1215 result must be integral. */ 1216 return (a1 < 0 1217 ? b <= a0 && (a0 - b) % a1 == 0 1218 : b >= a0 && (b - a0) % a1 == 0); 1219 return a0 == b; 1220 } 1221 1222 /* Return true if A might equal B for some indeterminate values. */ 1223 1224 template<unsigned int N, typename Ca, typename Cb> 1225 inline bool 1226 maybe_eq (const poly_int_pod<N, Ca> &a, const poly_int_pod<N, Cb> &b) 1227 { 1228 STATIC_ASSERT (N <= 2); 1229 if (N == 2) 1230 return maybe_eq_2 (a.coeffs[0], a.coeffs[1], b.coeffs[0], b.coeffs[1]); 1231 return a.coeffs[0] == b.coeffs[0]; 1232 } 1233 1234 template<unsigned int N, typename Ca, typename Cb> 1235 inline typename if_nonpoly<Cb, bool>::type 1236 maybe_eq (const poly_int_pod<N, Ca> &a, const Cb &b) 1237 { 1238 STATIC_ASSERT (N <= 2); 1239 if (N == 2) 1240 return maybe_eq_2 (a.coeffs[0], a.coeffs[1], b); 1241 return a.coeffs[0] == b; 1242 } 1243 1244 template<unsigned int N, typename Ca, typename Cb> 1245 inline typename if_nonpoly<Ca, bool>::type 1246 maybe_eq (const Ca &a, const poly_int_pod<N, Cb> &b) 1247 { 1248 STATIC_ASSERT (N <= 2); 1249 if (N == 2) 1250 return maybe_eq_2 (b.coeffs[0], b.coeffs[1], a); 1251 return a == b.coeffs[0]; 1252 } 1253 1254 template<typename Ca, typename Cb> 1255 inline typename if_nonpoly2<Ca, Cb, bool>::type 1256 maybe_eq (const Ca &a, const Cb &b) 1257 { 1258 return a == b; 1259 } 1260 1261 /* Return true if A might not equal B for some indeterminate values. */ 1262 1263 template<unsigned int N, typename Ca, typename Cb> 1264 inline bool 1265 maybe_ne (const poly_int_pod<N, Ca> &a, const poly_int_pod<N, Cb> &b) 1266 { 1267 if (N >= 2) 1268 for (unsigned int i = 1; i < N; i++) 1269 if (a.coeffs[i] != b.coeffs[i]) 1270 return true; 1271 return a.coeffs[0] != b.coeffs[0]; 1272 } 1273 1274 template<unsigned int N, typename Ca, typename Cb> 1275 inline typename if_nonpoly<Cb, bool>::type 1276 maybe_ne (const poly_int_pod<N, Ca> &a, const Cb &b) 1277 { 1278 if (N >= 2) 1279 for (unsigned int i = 1; i < N; i++) 1280 if (a.coeffs[i] != 0) 1281 return true; 1282 return a.coeffs[0] != b; 1283 } 1284 1285 template<unsigned int N, typename Ca, typename Cb> 1286 inline typename if_nonpoly<Ca, bool>::type 1287 maybe_ne (const Ca &a, const poly_int_pod<N, Cb> &b) 1288 { 1289 if (N >= 2) 1290 for (unsigned int i = 1; i < N; i++) 1291 if (b.coeffs[i] != 0) 1292 return true; 1293 return a != b.coeffs[0]; 1294 } 1295 1296 template<typename Ca, typename Cb> 1297 inline typename if_nonpoly2<Ca, Cb, bool>::type 1298 maybe_ne (const Ca &a, const Cb &b) 1299 { 1300 return a != b; 1301 } 1302 1303 /* Return true if A is known to be equal to B. */ 1304 #define known_eq(A, B) (!maybe_ne (A, B)) 1305 1306 /* Return true if A is known to be unequal to B. */ 1307 #define known_ne(A, B) (!maybe_eq (A, B)) 1308 1309 /* Return true if A might be less than or equal to B for some 1310 indeterminate values. */ 1311 1312 template<unsigned int N, typename Ca, typename Cb> 1313 inline bool 1314 maybe_le (const poly_int_pod<N, Ca> &a, const poly_int_pod<N, Cb> &b) 1315 { 1316 if (N >= 2) 1317 for (unsigned int i = 1; i < N; i++) 1318 if (a.coeffs[i] < b.coeffs[i]) 1319 return true; 1320 return a.coeffs[0] <= b.coeffs[0]; 1321 } 1322 1323 template<unsigned int N, typename Ca, typename Cb> 1324 inline typename if_nonpoly<Cb, bool>::type 1325 maybe_le (const poly_int_pod<N, Ca> &a, const Cb &b) 1326 { 1327 if (N >= 2) 1328 for (unsigned int i = 1; i < N; i++) 1329 if (a.coeffs[i] < 0) 1330 return true; 1331 return a.coeffs[0] <= b; 1332 } 1333 1334 template<unsigned int N, typename Ca, typename Cb> 1335 inline typename if_nonpoly<Ca, bool>::type 1336 maybe_le (const Ca &a, const poly_int_pod<N, Cb> &b) 1337 { 1338 if (N >= 2) 1339 for (unsigned int i = 1; i < N; i++) 1340 if (b.coeffs[i] > 0) 1341 return true; 1342 return a <= b.coeffs[0]; 1343 } 1344 1345 template<typename Ca, typename Cb> 1346 inline typename if_nonpoly2<Ca, Cb, bool>::type 1347 maybe_le (const Ca &a, const Cb &b) 1348 { 1349 return a <= b; 1350 } 1351 1352 /* Return true if A might be less than B for some indeterminate values. */ 1353 1354 template<unsigned int N, typename Ca, typename Cb> 1355 inline bool 1356 maybe_lt (const poly_int_pod<N, Ca> &a, const poly_int_pod<N, Cb> &b) 1357 { 1358 if (N >= 2) 1359 for (unsigned int i = 1; i < N; i++) 1360 if (a.coeffs[i] < b.coeffs[i]) 1361 return true; 1362 return a.coeffs[0] < b.coeffs[0]; 1363 } 1364 1365 template<unsigned int N, typename Ca, typename Cb> 1366 inline typename if_nonpoly<Cb, bool>::type 1367 maybe_lt (const poly_int_pod<N, Ca> &a, const Cb &b) 1368 { 1369 if (N >= 2) 1370 for (unsigned int i = 1; i < N; i++) 1371 if (a.coeffs[i] < 0) 1372 return true; 1373 return a.coeffs[0] < b; 1374 } 1375 1376 template<unsigned int N, typename Ca, typename Cb> 1377 inline typename if_nonpoly<Ca, bool>::type 1378 maybe_lt (const Ca &a, const poly_int_pod<N, Cb> &b) 1379 { 1380 if (N >= 2) 1381 for (unsigned int i = 1; i < N; i++) 1382 if (b.coeffs[i] > 0) 1383 return true; 1384 return a < b.coeffs[0]; 1385 } 1386 1387 template<typename Ca, typename Cb> 1388 inline typename if_nonpoly2<Ca, Cb, bool>::type 1389 maybe_lt (const Ca &a, const Cb &b) 1390 { 1391 return a < b; 1392 } 1393 1394 /* Return true if A may be greater than or equal to B. */ 1395 #define maybe_ge(A, B) maybe_le (B, A) 1396 1397 /* Return true if A may be greater than B. */ 1398 #define maybe_gt(A, B) maybe_lt (B, A) 1399 1400 /* Return true if A is known to be less than or equal to B. */ 1401 #define known_le(A, B) (!maybe_gt (A, B)) 1402 1403 /* Return true if A is known to be less than B. */ 1404 #define known_lt(A, B) (!maybe_ge (A, B)) 1405 1406 /* Return true if A is known to be greater than B. */ 1407 #define known_gt(A, B) (!maybe_le (A, B)) 1408 1409 /* Return true if A is known to be greater than or equal to B. */ 1410 #define known_ge(A, B) (!maybe_lt (A, B)) 1411 1412 /* Return true if A and B are ordered by the partial ordering known_le. */ 1413 1414 template<typename T1, typename T2> 1415 inline bool 1416 ordered_p (const T1 &a, const T2 &b) 1417 { 1418 return ((poly_int_traits<T1>::num_coeffs == 1 1419 && poly_int_traits<T2>::num_coeffs == 1) 1420 || known_le (a, b) 1421 || known_le (b, a)); 1422 } 1423 1424 /* Assert that A and B are known to be ordered and return the minimum 1425 of the two. 1426 1427 NOTE: When using this function, please add a comment above the call 1428 explaining why we know the values are ordered in that context. */ 1429 1430 template<unsigned int N, typename Ca, typename Cb> 1431 inline POLY_POLY_RESULT (N, Ca, Cb) 1432 ordered_min (const poly_int_pod<N, Ca> &a, const poly_int_pod<N, Cb> &b) 1433 { 1434 if (known_le (a, b)) 1435 return a; 1436 else 1437 { 1438 if (N > 1) 1439 gcc_checking_assert (known_le (b, a)); 1440 return b; 1441 } 1442 } 1443 1444 template<unsigned int N, typename Ca, typename Cb> 1445 inline CONST_POLY_RESULT (N, Ca, Cb) 1446 ordered_min (const Ca &a, const poly_int_pod<N, Cb> &b) 1447 { 1448 if (known_le (a, b)) 1449 return a; 1450 else 1451 { 1452 if (N > 1) 1453 gcc_checking_assert (known_le (b, a)); 1454 return b; 1455 } 1456 } 1457 1458 template<unsigned int N, typename Ca, typename Cb> 1459 inline POLY_CONST_RESULT (N, Ca, Cb) 1460 ordered_min (const poly_int_pod<N, Ca> &a, const Cb &b) 1461 { 1462 if (known_le (a, b)) 1463 return a; 1464 else 1465 { 1466 if (N > 1) 1467 gcc_checking_assert (known_le (b, a)); 1468 return b; 1469 } 1470 } 1471 1472 /* Assert that A and B are known to be ordered and return the maximum 1473 of the two. 1474 1475 NOTE: When using this function, please add a comment above the call 1476 explaining why we know the values are ordered in that context. */ 1477 1478 template<unsigned int N, typename Ca, typename Cb> 1479 inline POLY_POLY_RESULT (N, Ca, Cb) 1480 ordered_max (const poly_int_pod<N, Ca> &a, const poly_int_pod<N, Cb> &b) 1481 { 1482 if (known_le (a, b)) 1483 return b; 1484 else 1485 { 1486 if (N > 1) 1487 gcc_checking_assert (known_le (b, a)); 1488 return a; 1489 } 1490 } 1491 1492 template<unsigned int N, typename Ca, typename Cb> 1493 inline CONST_POLY_RESULT (N, Ca, Cb) 1494 ordered_max (const Ca &a, const poly_int_pod<N, Cb> &b) 1495 { 1496 if (known_le (a, b)) 1497 return b; 1498 else 1499 { 1500 if (N > 1) 1501 gcc_checking_assert (known_le (b, a)); 1502 return a; 1503 } 1504 } 1505 1506 template<unsigned int N, typename Ca, typename Cb> 1507 inline POLY_CONST_RESULT (N, Ca, Cb) 1508 ordered_max (const poly_int_pod<N, Ca> &a, const Cb &b) 1509 { 1510 if (known_le (a, b)) 1511 return b; 1512 else 1513 { 1514 if (N > 1) 1515 gcc_checking_assert (known_le (b, a)); 1516 return a; 1517 } 1518 } 1519 1520 /* Return a constant lower bound on the value of A, which is known 1521 to be nonnegative. */ 1522 1523 template<unsigned int N, typename Ca> 1524 inline Ca 1525 constant_lower_bound (const poly_int_pod<N, Ca> &a) 1526 { 1527 gcc_checking_assert (known_ge (a, POLY_INT_TYPE (Ca) (0))); 1528 return a.coeffs[0]; 1529 } 1530 1531 /* Return the constant lower bound of A, given that it is no less than B. */ 1532 1533 template<unsigned int N, typename Ca, typename Cb> 1534 inline POLY_CONST_COEFF (Ca, Cb) 1535 constant_lower_bound_with_limit (const poly_int_pod<N, Ca> &a, const Cb &b) 1536 { 1537 if (known_ge (a, b)) 1538 return a.coeffs[0]; 1539 return b; 1540 } 1541 1542 /* Return the constant upper bound of A, given that it is no greater 1543 than B. */ 1544 1545 template<unsigned int N, typename Ca, typename Cb> 1546 inline POLY_CONST_COEFF (Ca, Cb) 1547 constant_upper_bound_with_limit (const poly_int_pod<N, Ca> &a, const Cb &b) 1548 { 1549 if (known_le (a, b)) 1550 return a.coeffs[0]; 1551 return b; 1552 } 1553 1554 /* Return a value that is known to be no greater than A and B. This 1555 will be the greatest lower bound for some indeterminate values but 1556 not necessarily for all. */ 1557 1558 template<unsigned int N, typename Ca, typename Cb> 1559 inline POLY_CONST_RESULT (N, Ca, Cb) 1560 lower_bound (const poly_int_pod<N, Ca> &a, const Cb &b) 1561 { 1562 typedef POLY_CAST (Ca, Cb) NCa; 1563 typedef POLY_CAST (Cb, Ca) NCb; 1564 typedef POLY_INT_TYPE (Cb) ICb; 1565 typedef POLY_CONST_COEFF (Ca, Cb) C; 1566 1567 poly_int<N, C> r; 1568 POLY_SET_COEFF (C, r, 0, MIN (NCa (a.coeffs[0]), NCb (b))); 1569 if (N >= 2) 1570 for (unsigned int i = 1; i < N; i++) 1571 POLY_SET_COEFF (C, r, i, MIN (NCa (a.coeffs[i]), ICb (0))); 1572 return r; 1573 } 1574 1575 template<unsigned int N, typename Ca, typename Cb> 1576 inline CONST_POLY_RESULT (N, Ca, Cb) 1577 lower_bound (const Ca &a, const poly_int_pod<N, Cb> &b) 1578 { 1579 return lower_bound (b, a); 1580 } 1581 1582 template<unsigned int N, typename Ca, typename Cb> 1583 inline POLY_POLY_RESULT (N, Ca, Cb) 1584 lower_bound (const poly_int_pod<N, Ca> &a, const poly_int_pod<N, Cb> &b) 1585 { 1586 typedef POLY_CAST (Ca, Cb) NCa; 1587 typedef POLY_CAST (Cb, Ca) NCb; 1588 typedef POLY_POLY_COEFF (Ca, Cb) C; 1589 1590 poly_int<N, C> r; 1591 for (unsigned int i = 0; i < N; i++) 1592 POLY_SET_COEFF (C, r, i, MIN (NCa (a.coeffs[i]), NCb (b.coeffs[i]))); 1593 return r; 1594 } 1595 1596 template<typename Ca, typename Cb> 1597 inline CONST_CONST_RESULT (N, Ca, Cb) 1598 lower_bound (const Ca &a, const Cb &b) 1599 { 1600 return a < b ? a : b; 1601 } 1602 1603 /* Return a value that is known to be no less than A and B. This will 1604 be the least upper bound for some indeterminate values but not 1605 necessarily for all. */ 1606 1607 template<unsigned int N, typename Ca, typename Cb> 1608 inline POLY_CONST_RESULT (N, Ca, Cb) 1609 upper_bound (const poly_int_pod<N, Ca> &a, const Cb &b) 1610 { 1611 typedef POLY_CAST (Ca, Cb) NCa; 1612 typedef POLY_CAST (Cb, Ca) NCb; 1613 typedef POLY_INT_TYPE (Cb) ICb; 1614 typedef POLY_CONST_COEFF (Ca, Cb) C; 1615 1616 poly_int<N, C> r; 1617 POLY_SET_COEFF (C, r, 0, MAX (NCa (a.coeffs[0]), NCb (b))); 1618 if (N >= 2) 1619 for (unsigned int i = 1; i < N; i++) 1620 POLY_SET_COEFF (C, r, i, MAX (NCa (a.coeffs[i]), ICb (0))); 1621 return r; 1622 } 1623 1624 template<unsigned int N, typename Ca, typename Cb> 1625 inline CONST_POLY_RESULT (N, Ca, Cb) 1626 upper_bound (const Ca &a, const poly_int_pod<N, Cb> &b) 1627 { 1628 return upper_bound (b, a); 1629 } 1630 1631 template<unsigned int N, typename Ca, typename Cb> 1632 inline POLY_POLY_RESULT (N, Ca, Cb) 1633 upper_bound (const poly_int_pod<N, Ca> &a, const poly_int_pod<N, Cb> &b) 1634 { 1635 typedef POLY_CAST (Ca, Cb) NCa; 1636 typedef POLY_CAST (Cb, Ca) NCb; 1637 typedef POLY_POLY_COEFF (Ca, Cb) C; 1638 1639 poly_int<N, C> r; 1640 for (unsigned int i = 0; i < N; i++) 1641 POLY_SET_COEFF (C, r, i, MAX (NCa (a.coeffs[i]), NCb (b.coeffs[i]))); 1642 return r; 1643 } 1644 1645 /* Return the greatest common divisor of all nonzero coefficients, or zero 1646 if all coefficients are zero. */ 1647 1648 template<unsigned int N, typename Ca> 1649 inline POLY_BINARY_COEFF (Ca, Ca) 1650 coeff_gcd (const poly_int_pod<N, Ca> &a) 1651 { 1652 /* Find the first nonzero coefficient, stopping at 0 whatever happens. */ 1653 unsigned int i; 1654 for (i = N - 1; i > 0; --i) 1655 if (a.coeffs[i] != 0) 1656 break; 1657 typedef POLY_BINARY_COEFF (Ca, Ca) C; 1658 C r = a.coeffs[i]; 1659 for (unsigned int j = 0; j < i; ++j) 1660 if (a.coeffs[j] != 0) 1661 r = gcd (r, C (a.coeffs[j])); 1662 return r; 1663 } 1664 1665 /* Return a value that is a multiple of both A and B. This will be the 1666 least common multiple for some indeterminate values but necessarily 1667 for all. */ 1668 1669 template<unsigned int N, typename Ca, typename Cb> 1670 POLY_CONST_RESULT (N, Ca, Cb) 1671 common_multiple (const poly_int_pod<N, Ca> &a, Cb b) 1672 { 1673 POLY_BINARY_COEFF (Ca, Ca) xgcd = coeff_gcd (a); 1674 return a * (least_common_multiple (xgcd, b) / xgcd); 1675 } 1676 1677 template<unsigned int N, typename Ca, typename Cb> 1678 inline CONST_POLY_RESULT (N, Ca, Cb) 1679 common_multiple (const Ca &a, const poly_int_pod<N, Cb> &b) 1680 { 1681 return common_multiple (b, a); 1682 } 1683 1684 /* Return a value that is a multiple of both A and B, asserting that 1685 such a value exists. The result will be the least common multiple 1686 for some indeterminate values but necessarily for all. 1687 1688 NOTE: When using this function, please add a comment above the call 1689 explaining why we know the values have a common multiple (which might 1690 for example be because we know A / B is rational). */ 1691 1692 template<unsigned int N, typename Ca, typename Cb> 1693 POLY_POLY_RESULT (N, Ca, Cb) 1694 force_common_multiple (const poly_int_pod<N, Ca> &a, 1695 const poly_int_pod<N, Cb> &b) 1696 { 1697 if (b.is_constant ()) 1698 return common_multiple (a, b.coeffs[0]); 1699 if (a.is_constant ()) 1700 return common_multiple (a.coeffs[0], b); 1701 1702 typedef POLY_CAST (Ca, Cb) NCa; 1703 typedef POLY_CAST (Cb, Ca) NCb; 1704 typedef POLY_BINARY_COEFF (Ca, Cb) C; 1705 typedef POLY_INT_TYPE (Ca) ICa; 1706 1707 for (unsigned int i = 1; i < N; ++i) 1708 if (a.coeffs[i] != ICa (0)) 1709 { 1710 C lcm = least_common_multiple (NCa (a.coeffs[i]), NCb (b.coeffs[i])); 1711 C amul = lcm / a.coeffs[i]; 1712 C bmul = lcm / b.coeffs[i]; 1713 for (unsigned int j = 0; j < N; ++j) 1714 gcc_checking_assert (a.coeffs[j] * amul == b.coeffs[j] * bmul); 1715 return a * amul; 1716 } 1717 gcc_unreachable (); 1718 } 1719 1720 /* Compare A and B for sorting purposes, returning -1 if A should come 1721 before B, 0 if A and B are identical, and 1 if A should come after B. 1722 This is a lexicographical compare of the coefficients in reverse order. 1723 1724 A consequence of this is that all constant sizes come before all 1725 non-constant ones, regardless of magnitude (since a size is never 1726 negative). This is what most callers want. For example, when laying 1727 data out on the stack, it's better to keep all the constant-sized 1728 data together so that it can be accessed as a constant offset from a 1729 single base. */ 1730 1731 template<unsigned int N, typename Ca, typename Cb> 1732 inline int 1733 compare_sizes_for_sort (const poly_int_pod<N, Ca> &a, 1734 const poly_int_pod<N, Cb> &b) 1735 { 1736 for (unsigned int i = N; i-- > 0; ) 1737 if (a.coeffs[i] != b.coeffs[i]) 1738 return a.coeffs[i] < b.coeffs[i] ? -1 : 1; 1739 return 0; 1740 } 1741 1742 /* Return true if we can calculate VALUE & (ALIGN - 1) at compile time. */ 1743 1744 template<unsigned int N, typename Ca, typename Cb> 1745 inline bool 1746 can_align_p (const poly_int_pod<N, Ca> &value, Cb align) 1747 { 1748 for (unsigned int i = 1; i < N; i++) 1749 if ((value.coeffs[i] & (align - 1)) != 0) 1750 return false; 1751 return true; 1752 } 1753 1754 /* Return true if we can align VALUE up to the smallest multiple of 1755 ALIGN that is >= VALUE. Store the aligned value in *ALIGNED if so. */ 1756 1757 template<unsigned int N, typename Ca, typename Cb> 1758 inline bool 1759 can_align_up (const poly_int_pod<N, Ca> &value, Cb align, 1760 poly_int_pod<N, Ca> *aligned) 1761 { 1762 if (!can_align_p (value, align)) 1763 return false; 1764 *aligned = value + (-value.coeffs[0] & (align - 1)); 1765 return true; 1766 } 1767 1768 /* Return true if we can align VALUE down to the largest multiple of 1769 ALIGN that is <= VALUE. Store the aligned value in *ALIGNED if so. */ 1770 1771 template<unsigned int N, typename Ca, typename Cb> 1772 inline bool 1773 can_align_down (const poly_int_pod<N, Ca> &value, Cb align, 1774 poly_int_pod<N, Ca> *aligned) 1775 { 1776 if (!can_align_p (value, align)) 1777 return false; 1778 *aligned = value - (value.coeffs[0] & (align - 1)); 1779 return true; 1780 } 1781 1782 /* Return true if we can align A and B up to the smallest multiples of 1783 ALIGN that are >= A and B respectively, and if doing so gives the 1784 same value. */ 1785 1786 template<unsigned int N, typename Ca, typename Cb, typename Cc> 1787 inline bool 1788 known_equal_after_align_up (const poly_int_pod<N, Ca> &a, 1789 const poly_int_pod<N, Cb> &b, 1790 Cc align) 1791 { 1792 poly_int<N, Ca> aligned_a; 1793 poly_int<N, Cb> aligned_b; 1794 return (can_align_up (a, align, &aligned_a) 1795 && can_align_up (b, align, &aligned_b) 1796 && known_eq (aligned_a, aligned_b)); 1797 } 1798 1799 /* Return true if we can align A and B down to the largest multiples of 1800 ALIGN that are <= A and B respectively, and if doing so gives the 1801 same value. */ 1802 1803 template<unsigned int N, typename Ca, typename Cb, typename Cc> 1804 inline bool 1805 known_equal_after_align_down (const poly_int_pod<N, Ca> &a, 1806 const poly_int_pod<N, Cb> &b, 1807 Cc align) 1808 { 1809 poly_int<N, Ca> aligned_a; 1810 poly_int<N, Cb> aligned_b; 1811 return (can_align_down (a, align, &aligned_a) 1812 && can_align_down (b, align, &aligned_b) 1813 && known_eq (aligned_a, aligned_b)); 1814 } 1815 1816 /* Assert that we can align VALUE to ALIGN at compile time and return 1817 the smallest multiple of ALIGN that is >= VALUE. 1818 1819 NOTE: When using this function, please add a comment above the call 1820 explaining why we know the non-constant coefficients must already 1821 be a multiple of ALIGN. */ 1822 1823 template<unsigned int N, typename Ca, typename Cb> 1824 inline poly_int<N, Ca> 1825 force_align_up (const poly_int_pod<N, Ca> &value, Cb align) 1826 { 1827 gcc_checking_assert (can_align_p (value, align)); 1828 return value + (-value.coeffs[0] & (align - 1)); 1829 } 1830 1831 /* Assert that we can align VALUE to ALIGN at compile time and return 1832 the largest multiple of ALIGN that is <= VALUE. 1833 1834 NOTE: When using this function, please add a comment above the call 1835 explaining why we know the non-constant coefficients must already 1836 be a multiple of ALIGN. */ 1837 1838 template<unsigned int N, typename Ca, typename Cb> 1839 inline poly_int<N, Ca> 1840 force_align_down (const poly_int_pod<N, Ca> &value, Cb align) 1841 { 1842 gcc_checking_assert (can_align_p (value, align)); 1843 return value - (value.coeffs[0] & (align - 1)); 1844 } 1845 1846 /* Return a value <= VALUE that is a multiple of ALIGN. It will be the 1847 greatest such value for some indeterminate values but not necessarily 1848 for all. */ 1849 1850 template<unsigned int N, typename Ca, typename Cb> 1851 inline poly_int<N, Ca> 1852 aligned_lower_bound (const poly_int_pod<N, Ca> &value, Cb align) 1853 { 1854 poly_int<N, Ca> r; 1855 for (unsigned int i = 0; i < N; i++) 1856 /* This form copes correctly with more type combinations than 1857 value.coeffs[i] & -align would. */ 1858 POLY_SET_COEFF (Ca, r, i, (value.coeffs[i] 1859 - (value.coeffs[i] & (align - 1)))); 1860 return r; 1861 } 1862 1863 /* Return a value >= VALUE that is a multiple of ALIGN. It will be the 1864 least such value for some indeterminate values but not necessarily 1865 for all. */ 1866 1867 template<unsigned int N, typename Ca, typename Cb> 1868 inline poly_int<N, Ca> 1869 aligned_upper_bound (const poly_int_pod<N, Ca> &value, Cb align) 1870 { 1871 poly_int<N, Ca> r; 1872 for (unsigned int i = 0; i < N; i++) 1873 POLY_SET_COEFF (Ca, r, i, (value.coeffs[i] 1874 + (-value.coeffs[i] & (align - 1)))); 1875 return r; 1876 } 1877 1878 /* Assert that we can align VALUE to ALIGN at compile time. Align VALUE 1879 down to the largest multiple of ALIGN that is <= VALUE, then divide by 1880 ALIGN. 1881 1882 NOTE: When using this function, please add a comment above the call 1883 explaining why we know the non-constant coefficients must already 1884 be a multiple of ALIGN. */ 1885 1886 template<unsigned int N, typename Ca, typename Cb> 1887 inline poly_int<N, Ca> 1888 force_align_down_and_div (const poly_int_pod<N, Ca> &value, Cb align) 1889 { 1890 gcc_checking_assert (can_align_p (value, align)); 1891 1892 poly_int<N, Ca> r; 1893 POLY_SET_COEFF (Ca, r, 0, ((value.coeffs[0] 1894 - (value.coeffs[0] & (align - 1))) 1895 / align)); 1896 if (N >= 2) 1897 for (unsigned int i = 1; i < N; i++) 1898 POLY_SET_COEFF (Ca, r, i, value.coeffs[i] / align); 1899 return r; 1900 } 1901 1902 /* Assert that we can align VALUE to ALIGN at compile time. Align VALUE 1903 up to the smallest multiple of ALIGN that is >= VALUE, then divide by 1904 ALIGN. 1905 1906 NOTE: When using this function, please add a comment above the call 1907 explaining why we know the non-constant coefficients must already 1908 be a multiple of ALIGN. */ 1909 1910 template<unsigned int N, typename Ca, typename Cb> 1911 inline poly_int<N, Ca> 1912 force_align_up_and_div (const poly_int_pod<N, Ca> &value, Cb align) 1913 { 1914 gcc_checking_assert (can_align_p (value, align)); 1915 1916 poly_int<N, Ca> r; 1917 POLY_SET_COEFF (Ca, r, 0, ((value.coeffs[0] 1918 + (-value.coeffs[0] & (align - 1))) 1919 / align)); 1920 if (N >= 2) 1921 for (unsigned int i = 1; i < N; i++) 1922 POLY_SET_COEFF (Ca, r, i, value.coeffs[i] / align); 1923 return r; 1924 } 1925 1926 /* Return true if we know at compile time the difference between VALUE 1927 and the equal or preceding multiple of ALIGN. Store the value in 1928 *MISALIGN if so. */ 1929 1930 template<unsigned int N, typename Ca, typename Cb, typename Cm> 1931 inline bool 1932 known_misalignment (const poly_int_pod<N, Ca> &value, Cb align, Cm *misalign) 1933 { 1934 gcc_checking_assert (align != 0); 1935 if (!can_align_p (value, align)) 1936 return false; 1937 *misalign = value.coeffs[0] & (align - 1); 1938 return true; 1939 } 1940 1941 /* Return X & (Y - 1), asserting that this value is known. Please add 1942 an a comment above callers to this function to explain why the condition 1943 is known to hold. */ 1944 1945 template<unsigned int N, typename Ca, typename Cb> 1946 inline POLY_BINARY_COEFF (Ca, Ca) 1947 force_get_misalignment (const poly_int_pod<N, Ca> &a, Cb align) 1948 { 1949 gcc_checking_assert (can_align_p (a, align)); 1950 return a.coeffs[0] & (align - 1); 1951 } 1952 1953 /* Return the maximum alignment that A is known to have. Return 0 1954 if A is known to be zero. */ 1955 1956 template<unsigned int N, typename Ca> 1957 inline POLY_BINARY_COEFF (Ca, Ca) 1958 known_alignment (const poly_int_pod<N, Ca> &a) 1959 { 1960 typedef POLY_BINARY_COEFF (Ca, Ca) C; 1961 C r = a.coeffs[0]; 1962 for (unsigned int i = 1; i < N; ++i) 1963 r |= a.coeffs[i]; 1964 return r & -r; 1965 } 1966 1967 /* Return true if we can compute A | B at compile time, storing the 1968 result in RES if so. */ 1969 1970 template<unsigned int N, typename Ca, typename Cb, typename Cr> 1971 inline typename if_nonpoly<Cb, bool>::type 1972 can_ior_p (const poly_int_pod<N, Ca> &a, Cb b, Cr *result) 1973 { 1974 /* Coefficients 1 and above must be a multiple of something greater 1975 than B. */ 1976 typedef POLY_INT_TYPE (Ca) int_type; 1977 if (N >= 2) 1978 for (unsigned int i = 1; i < N; i++) 1979 if ((-(a.coeffs[i] & -a.coeffs[i]) & b) != int_type (0)) 1980 return false; 1981 *result = a; 1982 result->coeffs[0] |= b; 1983 return true; 1984 } 1985 1986 /* Return true if A is a constant multiple of B, storing the 1987 multiple in *MULTIPLE if so. */ 1988 1989 template<unsigned int N, typename Ca, typename Cb, typename Cm> 1990 inline typename if_nonpoly<Cb, bool>::type 1991 constant_multiple_p (const poly_int_pod<N, Ca> &a, Cb b, Cm *multiple) 1992 { 1993 typedef POLY_CAST (Ca, Cb) NCa; 1994 typedef POLY_CAST (Cb, Ca) NCb; 1995 1996 /* Do the modulus before the constant check, to catch divide by 1997 zero errors. */ 1998 if (NCa (a.coeffs[0]) % NCb (b) != 0 || !a.is_constant ()) 1999 return false; 2000 *multiple = NCa (a.coeffs[0]) / NCb (b); 2001 return true; 2002 } 2003 2004 template<unsigned int N, typename Ca, typename Cb, typename Cm> 2005 inline typename if_nonpoly<Ca, bool>::type 2006 constant_multiple_p (Ca a, const poly_int_pod<N, Cb> &b, Cm *multiple) 2007 { 2008 typedef POLY_CAST (Ca, Cb) NCa; 2009 typedef POLY_CAST (Cb, Ca) NCb; 2010 typedef POLY_INT_TYPE (Ca) int_type; 2011 2012 /* Do the modulus before the constant check, to catch divide by 2013 zero errors. */ 2014 if (NCa (a) % NCb (b.coeffs[0]) != 0 2015 || (a != int_type (0) && !b.is_constant ())) 2016 return false; 2017 *multiple = NCa (a) / NCb (b.coeffs[0]); 2018 return true; 2019 } 2020 2021 template<unsigned int N, typename Ca, typename Cb, typename Cm> 2022 inline bool 2023 constant_multiple_p (const poly_int_pod<N, Ca> &a, 2024 const poly_int_pod<N, Cb> &b, Cm *multiple) 2025 { 2026 typedef POLY_CAST (Ca, Cb) NCa; 2027 typedef POLY_CAST (Cb, Ca) NCb; 2028 typedef POLY_INT_TYPE (Ca) ICa; 2029 typedef POLY_INT_TYPE (Cb) ICb; 2030 typedef POLY_BINARY_COEFF (Ca, Cb) C; 2031 2032 if (NCa (a.coeffs[0]) % NCb (b.coeffs[0]) != 0) 2033 return false; 2034 2035 C r = NCa (a.coeffs[0]) / NCb (b.coeffs[0]); 2036 for (unsigned int i = 1; i < N; ++i) 2037 if (b.coeffs[i] == ICb (0) 2038 ? a.coeffs[i] != ICa (0) 2039 : (NCa (a.coeffs[i]) % NCb (b.coeffs[i]) != 0 2040 || NCa (a.coeffs[i]) / NCb (b.coeffs[i]) != r)) 2041 return false; 2042 2043 *multiple = r; 2044 return true; 2045 } 2046 2047 /* Return true if A is a constant multiple of B. */ 2048 2049 template<unsigned int N, typename Ca, typename Cb> 2050 inline typename if_nonpoly<Cb, bool>::type 2051 constant_multiple_p (const poly_int_pod<N, Ca> &a, Cb b) 2052 { 2053 typedef POLY_CAST (Ca, Cb) NCa; 2054 typedef POLY_CAST (Cb, Ca) NCb; 2055 2056 /* Do the modulus before the constant check, to catch divide by 2057 zero errors. */ 2058 if (NCa (a.coeffs[0]) % NCb (b) != 0 || !a.is_constant ()) 2059 return false; 2060 return true; 2061 } 2062 2063 template<unsigned int N, typename Ca, typename Cb> 2064 inline typename if_nonpoly<Ca, bool>::type 2065 constant_multiple_p (Ca a, const poly_int_pod<N, Cb> &b) 2066 { 2067 typedef POLY_CAST (Ca, Cb) NCa; 2068 typedef POLY_CAST (Cb, Ca) NCb; 2069 typedef POLY_INT_TYPE (Ca) int_type; 2070 2071 /* Do the modulus before the constant check, to catch divide by 2072 zero errors. */ 2073 if (NCa (a) % NCb (b.coeffs[0]) != 0 2074 || (a != int_type (0) && !b.is_constant ())) 2075 return false; 2076 return true; 2077 } 2078 2079 template<unsigned int N, typename Ca, typename Cb> 2080 inline bool 2081 constant_multiple_p (const poly_int_pod<N, Ca> &a, 2082 const poly_int_pod<N, Cb> &b) 2083 { 2084 typedef POLY_CAST (Ca, Cb) NCa; 2085 typedef POLY_CAST (Cb, Ca) NCb; 2086 typedef POLY_INT_TYPE (Ca) ICa; 2087 typedef POLY_INT_TYPE (Cb) ICb; 2088 typedef POLY_BINARY_COEFF (Ca, Cb) C; 2089 2090 if (NCa (a.coeffs[0]) % NCb (b.coeffs[0]) != 0) 2091 return false; 2092 2093 C r = NCa (a.coeffs[0]) / NCb (b.coeffs[0]); 2094 for (unsigned int i = 1; i < N; ++i) 2095 if (b.coeffs[i] == ICb (0) 2096 ? a.coeffs[i] != ICa (0) 2097 : (NCa (a.coeffs[i]) % NCb (b.coeffs[i]) != 0 2098 || NCa (a.coeffs[i]) / NCb (b.coeffs[i]) != r)) 2099 return false; 2100 return true; 2101 } 2102 2103 2104 /* Return true if A is a multiple of B. */ 2105 2106 template<typename Ca, typename Cb> 2107 inline typename if_nonpoly2<Ca, Cb, bool>::type 2108 multiple_p (Ca a, Cb b) 2109 { 2110 return a % b == 0; 2111 } 2112 2113 /* Return true if A is a (polynomial) multiple of B. */ 2114 2115 template<unsigned int N, typename Ca, typename Cb> 2116 inline typename if_nonpoly<Cb, bool>::type 2117 multiple_p (const poly_int_pod<N, Ca> &a, Cb b) 2118 { 2119 for (unsigned int i = 0; i < N; ++i) 2120 if (a.coeffs[i] % b != 0) 2121 return false; 2122 return true; 2123 } 2124 2125 /* Return true if A is a (constant) multiple of B. */ 2126 2127 template<unsigned int N, typename Ca, typename Cb> 2128 inline typename if_nonpoly<Ca, bool>::type 2129 multiple_p (Ca a, const poly_int_pod<N, Cb> &b) 2130 { 2131 typedef POLY_INT_TYPE (Ca) int_type; 2132 2133 /* Do the modulus before the constant check, to catch divide by 2134 potential zeros. */ 2135 return a % b.coeffs[0] == 0 && (a == int_type (0) || b.is_constant ()); 2136 } 2137 2138 /* Return true if A is a (polynomial) multiple of B. This handles cases 2139 where either B is constant or the multiple is constant. */ 2140 2141 template<unsigned int N, typename Ca, typename Cb> 2142 inline bool 2143 multiple_p (const poly_int_pod<N, Ca> &a, const poly_int_pod<N, Cb> &b) 2144 { 2145 if (b.is_constant ()) 2146 return multiple_p (a, b.coeffs[0]); 2147 POLY_BINARY_COEFF (Ca, Ca) tmp; 2148 return constant_multiple_p (a, b, &tmp); 2149 } 2150 2151 /* Return true if A is a (constant) multiple of B, storing the 2152 multiple in *MULTIPLE if so. */ 2153 2154 template<typename Ca, typename Cb, typename Cm> 2155 inline typename if_nonpoly2<Ca, Cb, bool>::type 2156 multiple_p (Ca a, Cb b, Cm *multiple) 2157 { 2158 if (a % b != 0) 2159 return false; 2160 *multiple = a / b; 2161 return true; 2162 } 2163 2164 /* Return true if A is a (polynomial) multiple of B, storing the 2165 multiple in *MULTIPLE if so. */ 2166 2167 template<unsigned int N, typename Ca, typename Cb, typename Cm> 2168 inline typename if_nonpoly<Cb, bool>::type 2169 multiple_p (const poly_int_pod<N, Ca> &a, Cb b, poly_int_pod<N, Cm> *multiple) 2170 { 2171 if (!multiple_p (a, b)) 2172 return false; 2173 for (unsigned int i = 0; i < N; ++i) 2174 multiple->coeffs[i] = a.coeffs[i] / b; 2175 return true; 2176 } 2177 2178 /* Return true if B is a constant and A is a (constant) multiple of B, 2179 storing the multiple in *MULTIPLE if so. */ 2180 2181 template<unsigned int N, typename Ca, typename Cb, typename Cm> 2182 inline typename if_nonpoly<Ca, bool>::type 2183 multiple_p (Ca a, const poly_int_pod<N, Cb> &b, Cm *multiple) 2184 { 2185 typedef POLY_CAST (Ca, Cb) NCa; 2186 2187 /* Do the modulus before the constant check, to catch divide by 2188 potential zeros. */ 2189 if (a % b.coeffs[0] != 0 || (NCa (a) != 0 && !b.is_constant ())) 2190 return false; 2191 *multiple = a / b.coeffs[0]; 2192 return true; 2193 } 2194 2195 /* Return true if A is a (polynomial) multiple of B, storing the 2196 multiple in *MULTIPLE if so. This handles cases where either 2197 B is constant or the multiple is constant. */ 2198 2199 template<unsigned int N, typename Ca, typename Cb, typename Cm> 2200 inline bool 2201 multiple_p (const poly_int_pod<N, Ca> &a, const poly_int_pod<N, Cb> &b, 2202 poly_int_pod<N, Cm> *multiple) 2203 { 2204 if (b.is_constant ()) 2205 return multiple_p (a, b.coeffs[0], multiple); 2206 return constant_multiple_p (a, b, multiple); 2207 } 2208 2209 /* Return A / B, given that A is known to be a multiple of B. */ 2210 2211 template<unsigned int N, typename Ca, typename Cb> 2212 inline POLY_CONST_RESULT (N, Ca, Cb) 2213 exact_div (const poly_int_pod<N, Ca> &a, Cb b) 2214 { 2215 typedef POLY_CONST_COEFF (Ca, Cb) C; 2216 poly_int<N, C> r; 2217 for (unsigned int i = 0; i < N; i++) 2218 { 2219 gcc_checking_assert (a.coeffs[i] % b == 0); 2220 POLY_SET_COEFF (C, r, i, a.coeffs[i] / b); 2221 } 2222 return r; 2223 } 2224 2225 /* Return A / B, given that A is known to be a multiple of B. */ 2226 2227 template<unsigned int N, typename Ca, typename Cb> 2228 inline POLY_POLY_RESULT (N, Ca, Cb) 2229 exact_div (const poly_int_pod<N, Ca> &a, const poly_int_pod<N, Cb> &b) 2230 { 2231 if (b.is_constant ()) 2232 return exact_div (a, b.coeffs[0]); 2233 2234 typedef POLY_CAST (Ca, Cb) NCa; 2235 typedef POLY_CAST (Cb, Ca) NCb; 2236 typedef POLY_BINARY_COEFF (Ca, Cb) C; 2237 typedef POLY_INT_TYPE (Cb) int_type; 2238 2239 gcc_checking_assert (a.coeffs[0] % b.coeffs[0] == 0); 2240 C r = NCa (a.coeffs[0]) / NCb (b.coeffs[0]); 2241 for (unsigned int i = 1; i < N; ++i) 2242 gcc_checking_assert (b.coeffs[i] == int_type (0) 2243 ? a.coeffs[i] == int_type (0) 2244 : (a.coeffs[i] % b.coeffs[i] == 0 2245 && NCa (a.coeffs[i]) / NCb (b.coeffs[i]) == r)); 2246 2247 return r; 2248 } 2249 2250 /* Return true if there is some constant Q and polynomial r such that: 2251 2252 (1) a = b * Q + r 2253 (2) |b * Q| <= |a| 2254 (3) |r| < |b| 2255 2256 Store the value Q in *QUOTIENT if so. */ 2257 2258 template<unsigned int N, typename Ca, typename Cb, typename Cq> 2259 inline typename if_nonpoly2<Cb, Cq, bool>::type 2260 can_div_trunc_p (const poly_int_pod<N, Ca> &a, Cb b, Cq *quotient) 2261 { 2262 typedef POLY_CAST (Ca, Cb) NCa; 2263 typedef POLY_CAST (Cb, Ca) NCb; 2264 2265 /* Do the division before the constant check, to catch divide by 2266 zero errors. */ 2267 Cq q = NCa (a.coeffs[0]) / NCb (b); 2268 if (!a.is_constant ()) 2269 return false; 2270 *quotient = q; 2271 return true; 2272 } 2273 2274 template<unsigned int N, typename Ca, typename Cb, typename Cq> 2275 inline typename if_nonpoly<Cq, bool>::type 2276 can_div_trunc_p (const poly_int_pod<N, Ca> &a, 2277 const poly_int_pod<N, Cb> &b, 2278 Cq *quotient) 2279 { 2280 /* We can calculate Q from the case in which the indeterminates 2281 are zero. */ 2282 typedef POLY_CAST (Ca, Cb) NCa; 2283 typedef POLY_CAST (Cb, Ca) NCb; 2284 typedef POLY_INT_TYPE (Ca) ICa; 2285 typedef POLY_INT_TYPE (Cb) ICb; 2286 typedef POLY_BINARY_COEFF (Ca, Cb) C; 2287 C q = NCa (a.coeffs[0]) / NCb (b.coeffs[0]); 2288 2289 /* Check the other coefficients and record whether the division is exact. 2290 The only difficult case is when it isn't. If we require a and b to 2291 ordered wrt zero, there can be no two coefficients of the same value 2292 that have opposite signs. This means that: 2293 2294 |a| = |a0| + |a1 * x1| + |a2 * x2| + ... 2295 |b| = |b0| + |b1 * x1| + |b2 * x2| + ... 2296 2297 The Q we've just calculated guarantees: 2298 2299 |b0 * Q| <= |a0| 2300 |a0 - b0 * Q| < |b0| 2301 2302 and so: 2303 2304 (2) |b * Q| <= |a| 2305 2306 is satisfied if: 2307 2308 |bi * xi * Q| <= |ai * xi| 2309 2310 for each i in [1, N]. This is trivially true when xi is zero. 2311 When it isn't we need: 2312 2313 (2') |bi * Q| <= |ai| 2314 2315 r is calculated as: 2316 2317 r = r0 + r1 * x1 + r2 * x2 + ... 2318 where ri = ai - bi * Q 2319 2320 Restricting to ordered a and b also guarantees that no two ris 2321 have opposite signs, so we have: 2322 2323 |r| = |r0| + |r1 * x1| + |r2 * x2| + ... 2324 2325 We know from the calculation of Q that |r0| < |b0|, so: 2326 2327 (3) |r| < |b| 2328 2329 is satisfied if: 2330 2331 (3') |ai - bi * Q| <= |bi| 2332 2333 for each i in [1, N]. */ 2334 bool rem_p = NCa (a.coeffs[0]) % NCb (b.coeffs[0]) != 0; 2335 for (unsigned int i = 1; i < N; ++i) 2336 { 2337 if (b.coeffs[i] == ICb (0)) 2338 { 2339 /* For bi == 0 we simply need: (3') |ai| == 0. */ 2340 if (a.coeffs[i] != ICa (0)) 2341 return false; 2342 } 2343 else 2344 { 2345 if (q == 0) 2346 { 2347 /* For Q == 0 we simply need: (3') |ai| <= |bi|. */ 2348 if (a.coeffs[i] != ICa (0)) 2349 { 2350 /* Use negative absolute to avoid overflow, i.e. 2351 -|ai| >= -|bi|. */ 2352 C neg_abs_a = (a.coeffs[i] < 0 ? a.coeffs[i] : -a.coeffs[i]); 2353 C neg_abs_b = (b.coeffs[i] < 0 ? b.coeffs[i] : -b.coeffs[i]); 2354 if (neg_abs_a < neg_abs_b) 2355 return false; 2356 rem_p = true; 2357 } 2358 } 2359 else 2360 { 2361 /* Otherwise just check for the case in which ai / bi == Q. */ 2362 if (NCa (a.coeffs[i]) / NCb (b.coeffs[i]) != q) 2363 return false; 2364 if (NCa (a.coeffs[i]) % NCb (b.coeffs[i]) != 0) 2365 rem_p = true; 2366 } 2367 } 2368 } 2369 2370 /* If the division isn't exact, require both values to be ordered wrt 0, 2371 so that we can guarantee conditions (2) and (3) for all indeterminate 2372 values. */ 2373 if (rem_p && (!ordered_p (a, ICa (0)) || !ordered_p (b, ICb (0)))) 2374 return false; 2375 2376 *quotient = q; 2377 return true; 2378 } 2379 2380 /* Likewise, but also store r in *REMAINDER. */ 2381 2382 template<unsigned int N, typename Ca, typename Cb, typename Cq, typename Cr> 2383 inline typename if_nonpoly<Cq, bool>::type 2384 can_div_trunc_p (const poly_int_pod<N, Ca> &a, 2385 const poly_int_pod<N, Cb> &b, 2386 Cq *quotient, Cr *remainder) 2387 { 2388 if (!can_div_trunc_p (a, b, quotient)) 2389 return false; 2390 *remainder = a - *quotient * b; 2391 return true; 2392 } 2393 2394 /* Return true if there is some polynomial q and constant R such that: 2395 2396 (1) a = B * q + R 2397 (2) |B * q| <= |a| 2398 (3) |R| < |B| 2399 2400 Store the value q in *QUOTIENT if so. */ 2401 2402 template<unsigned int N, typename Ca, typename Cb, typename Cq> 2403 inline typename if_nonpoly<Cb, bool>::type 2404 can_div_trunc_p (const poly_int_pod<N, Ca> &a, Cb b, 2405 poly_int_pod<N, Cq> *quotient) 2406 { 2407 /* The remainder must be constant. */ 2408 for (unsigned int i = 1; i < N; ++i) 2409 if (a.coeffs[i] % b != 0) 2410 return false; 2411 for (unsigned int i = 0; i < N; ++i) 2412 quotient->coeffs[i] = a.coeffs[i] / b; 2413 return true; 2414 } 2415 2416 /* Likewise, but also store R in *REMAINDER. */ 2417 2418 template<unsigned int N, typename Ca, typename Cb, typename Cq, typename Cr> 2419 inline typename if_nonpoly<Cb, bool>::type 2420 can_div_trunc_p (const poly_int_pod<N, Ca> &a, Cb b, 2421 poly_int_pod<N, Cq> *quotient, Cr *remainder) 2422 { 2423 if (!can_div_trunc_p (a, b, quotient)) 2424 return false; 2425 *remainder = a.coeffs[0] % b; 2426 return true; 2427 } 2428 2429 /* Return true if we can compute A / B at compile time, rounding towards zero. 2430 Store the result in QUOTIENT if so. 2431 2432 This handles cases in which either B is constant or the result is 2433 constant. */ 2434 2435 template<unsigned int N, typename Ca, typename Cb, typename Cq> 2436 inline bool 2437 can_div_trunc_p (const poly_int_pod<N, Ca> &a, 2438 const poly_int_pod<N, Cb> &b, 2439 poly_int_pod<N, Cq> *quotient) 2440 { 2441 if (b.is_constant ()) 2442 return can_div_trunc_p (a, b.coeffs[0], quotient); 2443 if (!can_div_trunc_p (a, b, "ient->coeffs[0])) 2444 return false; 2445 for (unsigned int i = 1; i < N; ++i) 2446 quotient->coeffs[i] = 0; 2447 return true; 2448 } 2449 2450 /* Return true if there is some constant Q and polynomial r such that: 2451 2452 (1) a = b * Q + r 2453 (2) |a| <= |b * Q| 2454 (3) |r| < |b| 2455 2456 Store the value Q in *QUOTIENT if so. */ 2457 2458 template<unsigned int N, typename Ca, typename Cb, typename Cq> 2459 inline typename if_nonpoly<Cq, bool>::type 2460 can_div_away_from_zero_p (const poly_int_pod<N, Ca> &a, 2461 const poly_int_pod<N, Cb> &b, 2462 Cq *quotient) 2463 { 2464 if (!can_div_trunc_p (a, b, quotient)) 2465 return false; 2466 if (maybe_ne (*quotient * b, a)) 2467 *quotient += (*quotient < 0 ? -1 : 1); 2468 return true; 2469 } 2470 2471 /* Use print_dec to print VALUE to FILE, where SGN is the sign 2472 of the values. */ 2473 2474 template<unsigned int N, typename C> 2475 void 2476 print_dec (const poly_int_pod<N, C> &value, FILE *file, signop sgn) 2477 { 2478 if (value.is_constant ()) 2479 print_dec (value.coeffs[0], file, sgn); 2480 else 2481 { 2482 fprintf (file, "["); 2483 for (unsigned int i = 0; i < N; ++i) 2484 { 2485 print_dec (value.coeffs[i], file, sgn); 2486 fputc (i == N - 1 ? ']' : ',', file); 2487 } 2488 } 2489 } 2490 2491 /* Likewise without the signop argument, for coefficients that have an 2492 inherent signedness. */ 2493 2494 template<unsigned int N, typename C> 2495 void 2496 print_dec (const poly_int_pod<N, C> &value, FILE *file) 2497 { 2498 STATIC_ASSERT (poly_coeff_traits<C>::signedness >= 0); 2499 print_dec (value, file, 2500 poly_coeff_traits<C>::signedness ? SIGNED : UNSIGNED); 2501 } 2502 2503 /* Use print_hex to print VALUE to FILE. */ 2504 2505 template<unsigned int N, typename C> 2506 void 2507 print_hex (const poly_int_pod<N, C> &value, FILE *file) 2508 { 2509 if (value.is_constant ()) 2510 print_hex (value.coeffs[0], file); 2511 else 2512 { 2513 fprintf (file, "["); 2514 for (unsigned int i = 0; i < N; ++i) 2515 { 2516 print_hex (value.coeffs[i], file); 2517 fputc (i == N - 1 ? ']' : ',', file); 2518 } 2519 } 2520 } 2521 2522 /* Helper for calculating the distance between two points P1 and P2, 2523 in cases where known_le (P1, P2). T1 and T2 are the types of the 2524 two positions, in either order. The coefficients of P2 - P1 have 2525 type unsigned HOST_WIDE_INT if the coefficients of both T1 and T2 2526 have C++ primitive type, otherwise P2 - P1 has its usual 2527 wide-int-based type. 2528 2529 The actual subtraction should look something like this: 2530 2531 typedef poly_span_traits<T1, T2> span_traits; 2532 span_traits::cast (P2) - span_traits::cast (P1) 2533 2534 Applying the cast before the subtraction avoids undefined overflow 2535 for signed T1 and T2. 2536 2537 The implementation of the cast tries to avoid unnecessary arithmetic 2538 or copying. */ 2539 template<typename T1, typename T2, 2540 typename Res = POLY_BINARY_COEFF (POLY_BINARY_COEFF (T1, T2), 2541 unsigned HOST_WIDE_INT)> 2542 struct poly_span_traits 2543 { 2544 template<typename T> 2545 static const T &cast (const T &x) { return x; } 2546 }; 2547 2548 template<typename T1, typename T2> 2549 struct poly_span_traits<T1, T2, unsigned HOST_WIDE_INT> 2550 { 2551 template<typename T> 2552 static typename if_nonpoly<T, unsigned HOST_WIDE_INT>::type 2553 cast (const T &x) { return x; } 2554 2555 template<unsigned int N, typename T> 2556 static poly_int<N, unsigned HOST_WIDE_INT> 2557 cast (const poly_int_pod<N, T> &x) { return x; } 2558 }; 2559 2560 /* Return true if SIZE represents a known size, assuming that all-ones 2561 indicates an unknown size. */ 2562 2563 template<typename T> 2564 inline bool 2565 known_size_p (const T &a) 2566 { 2567 return maybe_ne (a, POLY_INT_TYPE (T) (-1)); 2568 } 2569 2570 /* Return true if range [POS, POS + SIZE) might include VAL. 2571 SIZE can be the special value -1, in which case the range is 2572 open-ended. */ 2573 2574 template<typename T1, typename T2, typename T3> 2575 inline bool 2576 maybe_in_range_p (const T1 &val, const T2 &pos, const T3 &size) 2577 { 2578 typedef poly_span_traits<T1, T2> start_span; 2579 typedef poly_span_traits<T3, T3> size_span; 2580 if (known_lt (val, pos)) 2581 return false; 2582 if (!known_size_p (size)) 2583 return true; 2584 if ((poly_int_traits<T1>::num_coeffs > 1 2585 || poly_int_traits<T2>::num_coeffs > 1) 2586 && maybe_lt (val, pos)) 2587 /* In this case we don't know whether VAL >= POS is true at compile 2588 time, so we can't prove that VAL >= POS + SIZE. */ 2589 return true; 2590 return maybe_lt (start_span::cast (val) - start_span::cast (pos), 2591 size_span::cast (size)); 2592 } 2593 2594 /* Return true if range [POS, POS + SIZE) is known to include VAL. 2595 SIZE can be the special value -1, in which case the range is 2596 open-ended. */ 2597 2598 template<typename T1, typename T2, typename T3> 2599 inline bool 2600 known_in_range_p (const T1 &val, const T2 &pos, const T3 &size) 2601 { 2602 typedef poly_span_traits<T1, T2> start_span; 2603 typedef poly_span_traits<T3, T3> size_span; 2604 return (known_size_p (size) 2605 && known_ge (val, pos) 2606 && known_lt (start_span::cast (val) - start_span::cast (pos), 2607 size_span::cast (size))); 2608 } 2609 2610 /* Return true if the two ranges [POS1, POS1 + SIZE1) and [POS2, POS2 + SIZE2) 2611 might overlap. SIZE1 and/or SIZE2 can be the special value -1, in which 2612 case the range is open-ended. */ 2613 2614 template<typename T1, typename T2, typename T3, typename T4> 2615 inline bool 2616 ranges_maybe_overlap_p (const T1 &pos1, const T2 &size1, 2617 const T3 &pos2, const T4 &size2) 2618 { 2619 if (maybe_in_range_p (pos2, pos1, size1)) 2620 return maybe_ne (size2, POLY_INT_TYPE (T4) (0)); 2621 if (maybe_in_range_p (pos1, pos2, size2)) 2622 return maybe_ne (size1, POLY_INT_TYPE (T2) (0)); 2623 return false; 2624 } 2625 2626 /* Return true if the two ranges [POS1, POS1 + SIZE1) and [POS2, POS2 + SIZE2) 2627 are known to overlap. SIZE1 and/or SIZE2 can be the special value -1, 2628 in which case the range is open-ended. */ 2629 2630 template<typename T1, typename T2, typename T3, typename T4> 2631 inline bool 2632 ranges_known_overlap_p (const T1 &pos1, const T2 &size1, 2633 const T3 &pos2, const T4 &size2) 2634 { 2635 typedef poly_span_traits<T1, T3> start_span; 2636 typedef poly_span_traits<T2, T2> size1_span; 2637 typedef poly_span_traits<T4, T4> size2_span; 2638 /* known_gt (POS1 + SIZE1, POS2) [infinite precision] 2639 --> known_gt (SIZE1, POS2 - POS1) [infinite precision] 2640 --> known_gt (SIZE1, POS2 - lower_bound (POS1, POS2)) [infinite precision] 2641 ^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^ always nonnegative 2642 --> known_gt (SIZE1, span1::cast (POS2 - lower_bound (POS1, POS2))). 2643 2644 Using the saturating subtraction enforces that SIZE1 must be 2645 nonzero, since known_gt (0, x) is false for all nonnegative x. 2646 If POS2.coeff[I] < POS1.coeff[I] for some I > 0, increasing 2647 indeterminate number I makes the unsaturated condition easier to 2648 satisfy, so using a saturated coefficient of zero tests the case in 2649 which the indeterminate is zero (the minimum value). */ 2650 return (known_size_p (size1) 2651 && known_size_p (size2) 2652 && known_lt (start_span::cast (pos2) 2653 - start_span::cast (lower_bound (pos1, pos2)), 2654 size1_span::cast (size1)) 2655 && known_lt (start_span::cast (pos1) 2656 - start_span::cast (lower_bound (pos1, pos2)), 2657 size2_span::cast (size2))); 2658 } 2659 2660 /* Return true if range [POS1, POS1 + SIZE1) is known to be a subrange of 2661 [POS2, POS2 + SIZE2). SIZE1 and/or SIZE2 can be the special value -1, 2662 in which case the range is open-ended. */ 2663 2664 template<typename T1, typename T2, typename T3, typename T4> 2665 inline bool 2666 known_subrange_p (const T1 &pos1, const T2 &size1, 2667 const T3 &pos2, const T4 &size2) 2668 { 2669 typedef typename poly_int_traits<T2>::coeff_type C2; 2670 typedef poly_span_traits<T1, T3> start_span; 2671 typedef poly_span_traits<T2, T4> size_span; 2672 return (known_gt (size1, POLY_INT_TYPE (T2) (0)) 2673 && (poly_coeff_traits<C2>::signedness > 0 2674 || known_size_p (size1)) 2675 && known_size_p (size2) 2676 && known_ge (pos1, pos2) 2677 && known_le (size1, size2) 2678 && known_le (start_span::cast (pos1) - start_span::cast (pos2), 2679 size_span::cast (size2) - size_span::cast (size1))); 2680 } 2681 2682 /* Return true if the endpoint of the range [POS, POS + SIZE) can be 2683 stored in a T, or if SIZE is the special value -1, which makes the 2684 range open-ended. */ 2685 2686 template<typename T> 2687 inline typename if_nonpoly<T, bool>::type 2688 endpoint_representable_p (const T &pos, const T &size) 2689 { 2690 return (!known_size_p (size) 2691 || pos <= poly_coeff_traits<T>::max_value - size); 2692 } 2693 2694 template<unsigned int N, typename C> 2695 inline bool 2696 endpoint_representable_p (const poly_int_pod<N, C> &pos, 2697 const poly_int_pod<N, C> &size) 2698 { 2699 if (known_size_p (size)) 2700 for (unsigned int i = 0; i < N; ++i) 2701 if (pos.coeffs[i] > poly_coeff_traits<C>::max_value - size.coeffs[i]) 2702 return false; 2703 return true; 2704 } 2705 2706 template<unsigned int N, typename C> 2707 void 2708 gt_ggc_mx (poly_int_pod<N, C> *) 2709 { 2710 } 2711 2712 template<unsigned int N, typename C> 2713 void 2714 gt_pch_nx (poly_int_pod<N, C> *) 2715 { 2716 } 2717 2718 template<unsigned int N, typename C> 2719 void 2720 gt_pch_nx (poly_int_pod<N, C> *, void (*) (void *, void *), void *) 2721 { 2722 } 2723 2724 #undef POLY_SET_COEFF 2725 #undef POLY_INT_TYPE 2726 #undef POLY_BINARY_COEFF 2727 #undef CONST_CONST_RESULT 2728 #undef POLY_CONST_RESULT 2729 #undef CONST_POLY_RESULT 2730 #undef POLY_POLY_RESULT 2731 #undef POLY_CONST_COEFF 2732 #undef CONST_POLY_COEFF 2733 #undef POLY_POLY_COEFF 2734 2735 #endif 2736