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1 | /* Polynomial integer classes. | |
2 | Copyright (C) 2014-2020 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 multiple of B. */ | |
2048 | ||
2049 | template<typename Ca, typename Cb> | |
2050 | inline typename if_nonpoly2<Ca, Cb, bool>::type | |
2051 | multiple_p (Ca a, Cb b) | |
2052 | { | |
2053 | return a % b == 0; | |
2054 | } | |
2055 | ||
2056 | /* Return true if A is a (polynomial) multiple of B. */ | |
2057 | ||
2058 | template<unsigned int N, typename Ca, typename Cb> | |
2059 | inline typename if_nonpoly<Cb, bool>::type | |
2060 | multiple_p (const poly_int_pod<N, Ca> &a, Cb b) | |
2061 | { | |
2062 | for (unsigned int i = 0; i < N; ++i) | |
2063 | if (a.coeffs[i] % b != 0) | |
2064 | return false; | |
2065 | return true; | |
2066 | } | |
2067 | ||
2068 | /* Return true if A is a (constant) multiple of B. */ | |
2069 | ||
2070 | template<unsigned int N, typename Ca, typename Cb> | |
2071 | inline typename if_nonpoly<Ca, bool>::type | |
2072 | multiple_p (Ca a, const poly_int_pod<N, Cb> &b) | |
2073 | { | |
2074 | typedef POLY_INT_TYPE (Ca) int_type; | |
2075 | ||
2076 | /* Do the modulus before the constant check, to catch divide by | |
2077 | potential zeros. */ | |
2078 | return a % b.coeffs[0] == 0 && (a == int_type (0) || b.is_constant ()); | |
2079 | } | |
2080 | ||
2081 | /* Return true if A is a (polynomial) multiple of B. This handles cases | |
2082 | where either B is constant or the multiple is constant. */ | |
2083 | ||
2084 | template<unsigned int N, typename Ca, typename Cb> | |
2085 | inline bool | |
2086 | multiple_p (const poly_int_pod<N, Ca> &a, const poly_int_pod<N, Cb> &b) | |
2087 | { | |
2088 | if (b.is_constant ()) | |
2089 | return multiple_p (a, b.coeffs[0]); | |
2090 | POLY_BINARY_COEFF (Ca, Ca) tmp; | |
2091 | return constant_multiple_p (a, b, &tmp); | |
2092 | } | |
2093 | ||
2094 | /* Return true if A is a (constant) multiple of B, storing the | |
2095 | multiple in *MULTIPLE if so. */ | |
2096 | ||
2097 | template<typename Ca, typename Cb, typename Cm> | |
2098 | inline typename if_nonpoly2<Ca, Cb, bool>::type | |
2099 | multiple_p (Ca a, Cb b, Cm *multiple) | |
2100 | { | |
2101 | if (a % b != 0) | |
2102 | return false; | |
2103 | *multiple = a / b; | |
2104 | return true; | |
2105 | } | |
2106 | ||
2107 | /* Return true if A is a (polynomial) multiple of B, storing the | |
2108 | multiple in *MULTIPLE if so. */ | |
2109 | ||
2110 | template<unsigned int N, typename Ca, typename Cb, typename Cm> | |
2111 | inline typename if_nonpoly<Cb, bool>::type | |
2112 | multiple_p (const poly_int_pod<N, Ca> &a, Cb b, poly_int_pod<N, Cm> *multiple) | |
2113 | { | |
2114 | if (!multiple_p (a, b)) | |
2115 | return false; | |
2116 | for (unsigned int i = 0; i < N; ++i) | |
2117 | multiple->coeffs[i] = a.coeffs[i] / b; | |
2118 | return true; | |
2119 | } | |
2120 | ||
2121 | /* Return true if B is a constant and A is a (constant) multiple of B, | |
2122 | storing the multiple in *MULTIPLE if so. */ | |
2123 | ||
2124 | template<unsigned int N, typename Ca, typename Cb, typename Cm> | |
2125 | inline typename if_nonpoly<Ca, bool>::type | |
2126 | multiple_p (Ca a, const poly_int_pod<N, Cb> &b, Cm *multiple) | |
2127 | { | |
2128 | typedef POLY_CAST (Ca, Cb) NCa; | |
2129 | ||
2130 | /* Do the modulus before the constant check, to catch divide by | |
2131 | potential zeros. */ | |
2132 | if (a % b.coeffs[0] != 0 || (NCa (a) != 0 && !b.is_constant ())) | |
2133 | return false; | |
2134 | *multiple = a / b.coeffs[0]; | |
2135 | return true; | |
2136 | } | |
2137 | ||
2138 | /* Return true if A is a (polynomial) multiple of B, storing the | |
2139 | multiple in *MULTIPLE if so. This handles cases where either | |
2140 | B is constant or the multiple is constant. */ | |
2141 | ||
2142 | template<unsigned int N, typename Ca, typename Cb, typename Cm> | |
2143 | inline bool | |
2144 | multiple_p (const poly_int_pod<N, Ca> &a, const poly_int_pod<N, Cb> &b, | |
2145 | poly_int_pod<N, Cm> *multiple) | |
2146 | { | |
2147 | if (b.is_constant ()) | |
2148 | return multiple_p (a, b.coeffs[0], multiple); | |
2149 | return constant_multiple_p (a, b, multiple); | |
2150 | } | |
2151 | ||
2152 | /* Return A / B, given that A is known to be a multiple of B. */ | |
2153 | ||
2154 | template<unsigned int N, typename Ca, typename Cb> | |
2155 | inline POLY_CONST_RESULT (N, Ca, Cb) | |
2156 | exact_div (const poly_int_pod<N, Ca> &a, Cb b) | |
2157 | { | |
2158 | typedef POLY_CONST_COEFF (Ca, Cb) C; | |
2159 | poly_int<N, C> r; | |
2160 | for (unsigned int i = 0; i < N; i++) | |
2161 | { | |
2162 | gcc_checking_assert (a.coeffs[i] % b == 0); | |
2163 | POLY_SET_COEFF (C, r, i, a.coeffs[i] / b); | |
2164 | } | |
2165 | return r; | |
2166 | } | |
2167 | ||
2168 | /* Return A / B, given that A is known to be a multiple of B. */ | |
2169 | ||
2170 | template<unsigned int N, typename Ca, typename Cb> | |
2171 | inline POLY_POLY_RESULT (N, Ca, Cb) | |
2172 | exact_div (const poly_int_pod<N, Ca> &a, const poly_int_pod<N, Cb> &b) | |
2173 | { | |
2174 | if (b.is_constant ()) | |
2175 | return exact_div (a, b.coeffs[0]); | |
2176 | ||
2177 | typedef POLY_CAST (Ca, Cb) NCa; | |
2178 | typedef POLY_CAST (Cb, Ca) NCb; | |
2179 | typedef POLY_BINARY_COEFF (Ca, Cb) C; | |
2180 | typedef POLY_INT_TYPE (Cb) int_type; | |
2181 | ||
2182 | gcc_checking_assert (a.coeffs[0] % b.coeffs[0] == 0); | |
2183 | C r = NCa (a.coeffs[0]) / NCb (b.coeffs[0]); | |
2184 | for (unsigned int i = 1; i < N; ++i) | |
2185 | gcc_checking_assert (b.coeffs[i] == int_type (0) | |
2186 | ? a.coeffs[i] == int_type (0) | |
2187 | : (a.coeffs[i] % b.coeffs[i] == 0 | |
2188 | && NCa (a.coeffs[i]) / NCb (b.coeffs[i]) == r)); | |
2189 | ||
2190 | return r; | |
2191 | } | |
2192 | ||
2193 | /* Return true if there is some constant Q and polynomial r such that: | |
2194 | ||
2195 | (1) a = b * Q + r | |
2196 | (2) |b * Q| <= |a| | |
2197 | (3) |r| < |b| | |
2198 | ||
2199 | Store the value Q in *QUOTIENT if so. */ | |
2200 | ||
2201 | template<unsigned int N, typename Ca, typename Cb, typename Cq> | |
2202 | inline typename if_nonpoly2<Cb, Cq, bool>::type | |
2203 | can_div_trunc_p (const poly_int_pod<N, Ca> &a, Cb b, Cq *quotient) | |
2204 | { | |
2205 | typedef POLY_CAST (Ca, Cb) NCa; | |
2206 | typedef POLY_CAST (Cb, Ca) NCb; | |
2207 | ||
2208 | /* Do the division before the constant check, to catch divide by | |
2209 | zero errors. */ | |
2210 | Cq q = NCa (a.coeffs[0]) / NCb (b); | |
2211 | if (!a.is_constant ()) | |
2212 | return false; | |
2213 | *quotient = q; | |
2214 | return true; | |
2215 | } | |
2216 | ||
2217 | template<unsigned int N, typename Ca, typename Cb, typename Cq> | |
2218 | inline typename if_nonpoly<Cq, bool>::type | |
2219 | can_div_trunc_p (const poly_int_pod<N, Ca> &a, | |
2220 | const poly_int_pod<N, Cb> &b, | |
2221 | Cq *quotient) | |
2222 | { | |
2223 | /* We can calculate Q from the case in which the indeterminates | |
2224 | are zero. */ | |
2225 | typedef POLY_CAST (Ca, Cb) NCa; | |
2226 | typedef POLY_CAST (Cb, Ca) NCb; | |
2227 | typedef POLY_INT_TYPE (Ca) ICa; | |
2228 | typedef POLY_INT_TYPE (Cb) ICb; | |
2229 | typedef POLY_BINARY_COEFF (Ca, Cb) C; | |
2230 | C q = NCa (a.coeffs[0]) / NCb (b.coeffs[0]); | |
2231 | ||
2232 | /* Check the other coefficients and record whether the division is exact. | |
2233 | The only difficult case is when it isn't. If we require a and b to | |
2234 | ordered wrt zero, there can be no two coefficients of the same value | |
2235 | that have opposite signs. This means that: | |
2236 | ||
2237 | |a| = |a0| + |a1 * x1| + |a2 * x2| + ... | |
2238 | |b| = |b0| + |b1 * x1| + |b2 * x2| + ... | |
2239 | ||
2240 | The Q we've just calculated guarantees: | |
2241 | ||
2242 | |b0 * Q| <= |a0| | |
2243 | |a0 - b0 * Q| < |b0| | |
2244 | ||
2245 | and so: | |
2246 | ||
2247 | (2) |b * Q| <= |a| | |
2248 | ||
2249 | is satisfied if: | |
2250 | ||
2251 | |bi * xi * Q| <= |ai * xi| | |
2252 | ||
2253 | for each i in [1, N]. This is trivially true when xi is zero. | |
2254 | When it isn't we need: | |
2255 | ||
2256 | (2') |bi * Q| <= |ai| | |
2257 | ||
2258 | r is calculated as: | |
2259 | ||
2260 | r = r0 + r1 * x1 + r2 * x2 + ... | |
2261 | where ri = ai - bi * Q | |
2262 | ||
2263 | Restricting to ordered a and b also guarantees that no two ris | |
2264 | have opposite signs, so we have: | |
2265 | ||
2266 | |r| = |r0| + |r1 * x1| + |r2 * x2| + ... | |
2267 | ||
2268 | We know from the calculation of Q that |r0| < |b0|, so: | |
2269 | ||
2270 | (3) |r| < |b| | |
2271 | ||
2272 | is satisfied if: | |
2273 | ||
2274 | (3') |ai - bi * Q| <= |bi| | |
2275 | ||
2276 | for each i in [1, N]. */ | |
2277 | bool rem_p = NCa (a.coeffs[0]) % NCb (b.coeffs[0]) != 0; | |
2278 | for (unsigned int i = 1; i < N; ++i) | |
2279 | { | |
2280 | if (b.coeffs[i] == ICb (0)) | |
2281 | { | |
2282 | /* For bi == 0 we simply need: (3') |ai| == 0. */ | |
2283 | if (a.coeffs[i] != ICa (0)) | |
2284 | return false; | |
2285 | } | |
2286 | else | |
2287 | { | |
2288 | if (q == 0) | |
2289 | { | |
2290 | /* For Q == 0 we simply need: (3') |ai| <= |bi|. */ | |
2291 | if (a.coeffs[i] != ICa (0)) | |
2292 | { | |
2293 | /* Use negative absolute to avoid overflow, i.e. | |
2294 | -|ai| >= -|bi|. */ | |
2295 | C neg_abs_a = (a.coeffs[i] < 0 ? a.coeffs[i] : -a.coeffs[i]); | |
2296 | C neg_abs_b = (b.coeffs[i] < 0 ? b.coeffs[i] : -b.coeffs[i]); | |
2297 | if (neg_abs_a < neg_abs_b) | |
2298 | return false; | |
2299 | rem_p = true; | |
2300 | } | |
2301 | } | |
2302 | else | |
2303 | { | |
2304 | /* Otherwise just check for the case in which ai / bi == Q. */ | |
2305 | if (NCa (a.coeffs[i]) / NCb (b.coeffs[i]) != q) | |
2306 | return false; | |
2307 | if (NCa (a.coeffs[i]) % NCb (b.coeffs[i]) != 0) | |
2308 | rem_p = true; | |
2309 | } | |
2310 | } | |
2311 | } | |
2312 | ||
2313 | /* If the division isn't exact, require both values to be ordered wrt 0, | |
2314 | so that we can guarantee conditions (2) and (3) for all indeterminate | |
2315 | values. */ | |
2316 | if (rem_p && (!ordered_p (a, ICa (0)) || !ordered_p (b, ICb (0)))) | |
2317 | return false; | |
2318 | ||
2319 | *quotient = q; | |
2320 | return true; | |
2321 | } | |
2322 | ||
2323 | /* Likewise, but also store r in *REMAINDER. */ | |
2324 | ||
2325 | template<unsigned int N, typename Ca, typename Cb, typename Cq, typename Cr> | |
2326 | inline typename if_nonpoly<Cq, bool>::type | |
2327 | can_div_trunc_p (const poly_int_pod<N, Ca> &a, | |
2328 | const poly_int_pod<N, Cb> &b, | |
2329 | Cq *quotient, Cr *remainder) | |
2330 | { | |
2331 | if (!can_div_trunc_p (a, b, quotient)) | |
2332 | return false; | |
2333 | *remainder = a - *quotient * b; | |
2334 | return true; | |
2335 | } | |
2336 | ||
2337 | /* Return true if there is some polynomial q and constant R such that: | |
2338 | ||
2339 | (1) a = B * q + R | |
2340 | (2) |B * q| <= |a| | |
2341 | (3) |R| < |B| | |
2342 | ||
2343 | Store the value q in *QUOTIENT if so. */ | |
2344 | ||
2345 | template<unsigned int N, typename Ca, typename Cb, typename Cq> | |
2346 | inline typename if_nonpoly<Cb, bool>::type | |
2347 | can_div_trunc_p (const poly_int_pod<N, Ca> &a, Cb b, | |
2348 | poly_int_pod<N, Cq> *quotient) | |
2349 | { | |
2350 | /* The remainder must be constant. */ | |
2351 | for (unsigned int i = 1; i < N; ++i) | |
2352 | if (a.coeffs[i] % b != 0) | |
2353 | return false; | |
2354 | for (unsigned int i = 0; i < N; ++i) | |
2355 | quotient->coeffs[i] = a.coeffs[i] / b; | |
2356 | return true; | |
2357 | } | |
2358 | ||
2359 | /* Likewise, but also store R in *REMAINDER. */ | |
2360 | ||
2361 | template<unsigned int N, typename Ca, typename Cb, typename Cq, typename Cr> | |
2362 | inline typename if_nonpoly<Cb, bool>::type | |
2363 | can_div_trunc_p (const poly_int_pod<N, Ca> &a, Cb b, | |
2364 | poly_int_pod<N, Cq> *quotient, Cr *remainder) | |
2365 | { | |
2366 | if (!can_div_trunc_p (a, b, quotient)) | |
2367 | return false; | |
2368 | *remainder = a.coeffs[0] % b; | |
2369 | return true; | |
2370 | } | |
2371 | ||
2372 | /* Return true if we can compute A / B at compile time, rounding towards zero. | |
2373 | Store the result in QUOTIENT if so. | |
2374 | ||
2375 | This handles cases in which either B is constant or the result is | |
2376 | constant. */ | |
2377 | ||
2378 | template<unsigned int N, typename Ca, typename Cb, typename Cq> | |
2379 | inline bool | |
2380 | can_div_trunc_p (const poly_int_pod<N, Ca> &a, | |
2381 | const poly_int_pod<N, Cb> &b, | |
2382 | poly_int_pod<N, Cq> *quotient) | |
2383 | { | |
2384 | if (b.is_constant ()) | |
2385 | return can_div_trunc_p (a, b.coeffs[0], quotient); | |
2386 | if (!can_div_trunc_p (a, b, "ient->coeffs[0])) | |
2387 | return false; | |
2388 | for (unsigned int i = 1; i < N; ++i) | |
2389 | quotient->coeffs[i] = 0; | |
2390 | return true; | |
2391 | } | |
2392 | ||
2393 | /* Return true if there is some constant Q and polynomial r such that: | |
2394 | ||
2395 | (1) a = b * Q + r | |
2396 | (2) |a| <= |b * Q| | |
2397 | (3) |r| < |b| | |
2398 | ||
2399 | Store the value Q in *QUOTIENT if so. */ | |
2400 | ||
2401 | template<unsigned int N, typename Ca, typename Cb, typename Cq> | |
2402 | inline typename if_nonpoly<Cq, bool>::type | |
2403 | can_div_away_from_zero_p (const poly_int_pod<N, Ca> &a, | |
2404 | const poly_int_pod<N, Cb> &b, | |
2405 | Cq *quotient) | |
2406 | { | |
2407 | if (!can_div_trunc_p (a, b, quotient)) | |
2408 | return false; | |
2409 | if (maybe_ne (*quotient * b, a)) | |
2410 | *quotient += (*quotient < 0 ? -1 : 1); | |
2411 | return true; | |
2412 | } | |
2413 | ||
2414 | /* Use print_dec to print VALUE to FILE, where SGN is the sign | |
2415 | of the values. */ | |
2416 | ||
2417 | template<unsigned int N, typename C> | |
2418 | void | |
2419 | print_dec (const poly_int_pod<N, C> &value, FILE *file, signop sgn) | |
2420 | { | |
2421 | if (value.is_constant ()) | |
2422 | print_dec (value.coeffs[0], file, sgn); | |
2423 | else | |
2424 | { | |
2425 | fprintf (file, "["); | |
2426 | for (unsigned int i = 0; i < N; ++i) | |
2427 | { | |
2428 | print_dec (value.coeffs[i], file, sgn); | |
2429 | fputc (i == N - 1 ? ']' : ',', file); | |
2430 | } | |
2431 | } | |
2432 | } | |
2433 | ||
2434 | /* Likewise without the signop argument, for coefficients that have an | |
2435 | inherent signedness. */ | |
2436 | ||
2437 | template<unsigned int N, typename C> | |
2438 | void | |
2439 | print_dec (const poly_int_pod<N, C> &value, FILE *file) | |
2440 | { | |
2441 | STATIC_ASSERT (poly_coeff_traits<C>::signedness >= 0); | |
2442 | print_dec (value, file, | |
2443 | poly_coeff_traits<C>::signedness ? SIGNED : UNSIGNED); | |
2444 | } | |
2445 | ||
2446 | /* Use print_hex to print VALUE to FILE. */ | |
2447 | ||
2448 | template<unsigned int N, typename C> | |
2449 | void | |
2450 | print_hex (const poly_int_pod<N, C> &value, FILE *file) | |
2451 | { | |
2452 | if (value.is_constant ()) | |
2453 | print_hex (value.coeffs[0], file); | |
2454 | else | |
2455 | { | |
2456 | fprintf (file, "["); | |
2457 | for (unsigned int i = 0; i < N; ++i) | |
2458 | { | |
2459 | print_hex (value.coeffs[i], file); | |
2460 | fputc (i == N - 1 ? ']' : ',', file); | |
2461 | } | |
2462 | } | |
2463 | } | |
2464 | ||
2465 | /* Helper for calculating the distance between two points P1 and P2, | |
2466 | in cases where known_le (P1, P2). T1 and T2 are the types of the | |
2467 | two positions, in either order. The coefficients of P2 - P1 have | |
2468 | type unsigned HOST_WIDE_INT if the coefficients of both T1 and T2 | |
2469 | have C++ primitive type, otherwise P2 - P1 has its usual | |
2470 | wide-int-based type. | |
2471 | ||
2472 | The actual subtraction should look something like this: | |
2473 | ||
2474 | typedef poly_span_traits<T1, T2> span_traits; | |
2475 | span_traits::cast (P2) - span_traits::cast (P1) | |
2476 | ||
2477 | Applying the cast before the subtraction avoids undefined overflow | |
2478 | for signed T1 and T2. | |
2479 | ||
2480 | The implementation of the cast tries to avoid unnecessary arithmetic | |
2481 | or copying. */ | |
2482 | template<typename T1, typename T2, | |
2483 | typename Res = POLY_BINARY_COEFF (POLY_BINARY_COEFF (T1, T2), | |
2484 | unsigned HOST_WIDE_INT)> | |
2485 | struct poly_span_traits | |
2486 | { | |
2487 | template<typename T> | |
2488 | static const T &cast (const T &x) { return x; } | |
2489 | }; | |
2490 | ||
2491 | template<typename T1, typename T2> | |
2492 | struct poly_span_traits<T1, T2, unsigned HOST_WIDE_INT> | |
2493 | { | |
2494 | template<typename T> | |
2495 | static typename if_nonpoly<T, unsigned HOST_WIDE_INT>::type | |
2496 | cast (const T &x) { return x; } | |
2497 | ||
2498 | template<unsigned int N, typename T> | |
2499 | static poly_int<N, unsigned HOST_WIDE_INT> | |
2500 | cast (const poly_int_pod<N, T> &x) { return x; } | |
2501 | }; | |
2502 | ||
2503 | /* Return true if SIZE represents a known size, assuming that all-ones | |
2504 | indicates an unknown size. */ | |
2505 | ||
2506 | template<typename T> | |
2507 | inline bool | |
2508 | known_size_p (const T &a) | |
2509 | { | |
2510 | return maybe_ne (a, POLY_INT_TYPE (T) (-1)); | |
2511 | } | |
2512 | ||
2513 | /* Return true if range [POS, POS + SIZE) might include VAL. | |
2514 | SIZE can be the special value -1, in which case the range is | |
2515 | open-ended. */ | |
2516 | ||
2517 | template<typename T1, typename T2, typename T3> | |
2518 | inline bool | |
2519 | maybe_in_range_p (const T1 &val, const T2 &pos, const T3 &size) | |
2520 | { | |
2521 | typedef poly_span_traits<T1, T2> start_span; | |
2522 | typedef poly_span_traits<T3, T3> size_span; | |
2523 | if (known_lt (val, pos)) | |
2524 | return false; | |
2525 | if (!known_size_p (size)) | |
2526 | return true; | |
2527 | if ((poly_int_traits<T1>::num_coeffs > 1 | |
2528 | || poly_int_traits<T2>::num_coeffs > 1) | |
2529 | && maybe_lt (val, pos)) | |
2530 | /* In this case we don't know whether VAL >= POS is true at compile | |
2531 | time, so we can't prove that VAL >= POS + SIZE. */ | |
2532 | return true; | |
2533 | return maybe_lt (start_span::cast (val) - start_span::cast (pos), | |
2534 | size_span::cast (size)); | |
2535 | } | |
2536 | ||
2537 | /* Return true if range [POS, POS + SIZE) is known to include VAL. | |
2538 | SIZE can be the special value -1, in which case the range is | |
2539 | open-ended. */ | |
2540 | ||
2541 | template<typename T1, typename T2, typename T3> | |
2542 | inline bool | |
2543 | known_in_range_p (const T1 &val, const T2 &pos, const T3 &size) | |
2544 | { | |
2545 | typedef poly_span_traits<T1, T2> start_span; | |
2546 | typedef poly_span_traits<T3, T3> size_span; | |
2547 | return (known_size_p (size) | |
2548 | && known_ge (val, pos) | |
2549 | && known_lt (start_span::cast (val) - start_span::cast (pos), | |
2550 | size_span::cast (size))); | |
2551 | } | |
2552 | ||
2553 | /* Return true if the two ranges [POS1, POS1 + SIZE1) and [POS2, POS2 + SIZE2) | |
2554 | might overlap. SIZE1 and/or SIZE2 can be the special value -1, in which | |
2555 | case the range is open-ended. */ | |
2556 | ||
2557 | template<typename T1, typename T2, typename T3, typename T4> | |
2558 | inline bool | |
2559 | ranges_maybe_overlap_p (const T1 &pos1, const T2 &size1, | |
2560 | const T3 &pos2, const T4 &size2) | |
2561 | { | |
2562 | if (maybe_in_range_p (pos2, pos1, size1)) | |
2563 | return maybe_ne (size2, POLY_INT_TYPE (T4) (0)); | |
2564 | if (maybe_in_range_p (pos1, pos2, size2)) | |
2565 | return maybe_ne (size1, POLY_INT_TYPE (T2) (0)); | |
2566 | return false; | |
2567 | } | |
2568 | ||
2569 | /* Return true if the two ranges [POS1, POS1 + SIZE1) and [POS2, POS2 + SIZE2) | |
2570 | are known to overlap. SIZE1 and/or SIZE2 can be the special value -1, | |
2571 | in which case the range is open-ended. */ | |
2572 | ||
2573 | template<typename T1, typename T2, typename T3, typename T4> | |
2574 | inline bool | |
2575 | ranges_known_overlap_p (const T1 &pos1, const T2 &size1, | |
2576 | const T3 &pos2, const T4 &size2) | |
2577 | { | |
2578 | typedef poly_span_traits<T1, T3> start_span; | |
2579 | typedef poly_span_traits<T2, T2> size1_span; | |
2580 | typedef poly_span_traits<T4, T4> size2_span; | |
2581 | /* known_gt (POS1 + SIZE1, POS2) [infinite precision] | |
2582 | --> known_gt (SIZE1, POS2 - POS1) [infinite precision] | |
2583 | --> known_gt (SIZE1, POS2 - lower_bound (POS1, POS2)) [infinite precision] | |
2584 | ^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^ always nonnegative | |
2585 | --> known_gt (SIZE1, span1::cast (POS2 - lower_bound (POS1, POS2))). | |
2586 | ||
2587 | Using the saturating subtraction enforces that SIZE1 must be | |
2588 | nonzero, since known_gt (0, x) is false for all nonnegative x. | |
2589 | If POS2.coeff[I] < POS1.coeff[I] for some I > 0, increasing | |
2590 | indeterminate number I makes the unsaturated condition easier to | |
2591 | satisfy, so using a saturated coefficient of zero tests the case in | |
2592 | which the indeterminate is zero (the minimum value). */ | |
2593 | return (known_size_p (size1) | |
2594 | && known_size_p (size2) | |
2595 | && known_lt (start_span::cast (pos2) | |
2596 | - start_span::cast (lower_bound (pos1, pos2)), | |
2597 | size1_span::cast (size1)) | |
2598 | && known_lt (start_span::cast (pos1) | |
2599 | - start_span::cast (lower_bound (pos1, pos2)), | |
2600 | size2_span::cast (size2))); | |
2601 | } | |
2602 | ||
2603 | /* Return true if range [POS1, POS1 + SIZE1) is known to be a subrange of | |
2604 | [POS2, POS2 + SIZE2). SIZE1 and/or SIZE2 can be the special value -1, | |
2605 | in which case the range is open-ended. */ | |
2606 | ||
2607 | template<typename T1, typename T2, typename T3, typename T4> | |
2608 | inline bool | |
2609 | known_subrange_p (const T1 &pos1, const T2 &size1, | |
2610 | const T3 &pos2, const T4 &size2) | |
2611 | { | |
2612 | typedef typename poly_int_traits<T2>::coeff_type C2; | |
2613 | typedef poly_span_traits<T1, T3> start_span; | |
2614 | typedef poly_span_traits<T2, T4> size_span; | |
2615 | return (known_gt (size1, POLY_INT_TYPE (T2) (0)) | |
2616 | && (poly_coeff_traits<C2>::signedness > 0 | |
2617 | || known_size_p (size1)) | |
2618 | && known_size_p (size2) | |
2619 | && known_ge (pos1, pos2) | |
2620 | && known_le (size1, size2) | |
2621 | && known_le (start_span::cast (pos1) - start_span::cast (pos2), | |
2622 | size_span::cast (size2) - size_span::cast (size1))); | |
2623 | } | |
2624 | ||
2625 | /* Return true if the endpoint of the range [POS, POS + SIZE) can be | |
2626 | stored in a T, or if SIZE is the special value -1, which makes the | |
2627 | range open-ended. */ | |
2628 | ||
2629 | template<typename T> | |
2630 | inline typename if_nonpoly<T, bool>::type | |
2631 | endpoint_representable_p (const T &pos, const T &size) | |
2632 | { | |
2633 | return (!known_size_p (size) | |
2634 | || pos <= poly_coeff_traits<T>::max_value - size); | |
2635 | } | |
2636 | ||
2637 | template<unsigned int N, typename C> | |
2638 | inline bool | |
2639 | endpoint_representable_p (const poly_int_pod<N, C> &pos, | |
2640 | const poly_int_pod<N, C> &size) | |
2641 | { | |
2642 | if (known_size_p (size)) | |
2643 | for (unsigned int i = 0; i < N; ++i) | |
2644 | if (pos.coeffs[i] > poly_coeff_traits<C>::max_value - size.coeffs[i]) | |
2645 | return false; | |
2646 | return true; | |
2647 | } | |
2648 | ||
2649 | template<unsigned int N, typename C> | |
2650 | void | |
2651 | gt_ggc_mx (poly_int_pod<N, C> *) | |
2652 | { | |
2653 | } | |
2654 | ||
2655 | template<unsigned int N, typename C> | |
2656 | void | |
2657 | gt_pch_nx (poly_int_pod<N, C> *) | |
2658 | { | |
2659 | } | |
2660 | ||
2661 | template<unsigned int N, typename C> | |
2662 | void | |
2663 | gt_pch_nx (poly_int_pod<N, C> *, void (*) (void *, void *), void *) | |
2664 | { | |
2665 | } | |
2666 | ||
2667 | #undef POLY_SET_COEFF | |
2668 | #undef POLY_INT_TYPE | |
2669 | #undef POLY_BINARY_COEFF | |
2670 | #undef CONST_CONST_RESULT | |
2671 | #undef POLY_CONST_RESULT | |
2672 | #undef CONST_POLY_RESULT | |
2673 | #undef POLY_POLY_RESULT | |
2674 | #undef POLY_CONST_COEFF | |
2675 | #undef CONST_POLY_COEFF | |
2676 | #undef POLY_POLY_COEFF | |
2677 | ||
2678 | #endif |