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e535b963 | 1 | /* Polynomial integer classes. |
a945c346 | 2 | Copyright (C) 2014-2024 Free Software Foundation, Inc. |
e535b963 RS |
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 | ||
e535b963 RS |
32 | template<unsigned int N, typename T> class poly_int; |
33 | ||
34 | /* poly_coeff_traiits<T> describes the properties of a poly_int | |
35 | coefficient type T: | |
36 | ||
37 | - poly_coeff_traits<T1>::rank is less than poly_coeff_traits<T2>::rank | |
38 | if T1 can promote to T2. For C-like types the rank is: | |
39 | ||
40 | (2 * number of bytes) + (unsigned ? 1 : 0) | |
41 | ||
42 | wide_ints don't have a normal rank and so use a value of INT_MAX. | |
43 | Any fixed-width integer should be promoted to wide_int if possible | |
44 | and lead to an error otherwise. | |
45 | ||
46 | - poly_coeff_traits<T>::int_type is the type to which an integer | |
47 | literal should be cast before comparing it with T. | |
48 | ||
49 | - poly_coeff_traits<T>::precision is the number of bits that T can hold. | |
50 | ||
51 | - poly_coeff_traits<T>::signedness is: | |
52 | 0 if T is unsigned | |
53 | 1 if T is signed | |
54 | -1 if T has no inherent sign (as for wide_int). | |
55 | ||
56 | - poly_coeff_traits<T>::max_value, if defined, is the maximum value of T. | |
57 | ||
58 | - poly_coeff_traits<T>::result is a type that can hold results of | |
59 | operations on T. This is different from T itself in cases where T | |
eaa41a6d RS |
60 | is the result of an accessor like wi::to_offset. |
61 | ||
62 | - poly_coeff_traits<T>::init_cast<Arg>::type is the type to which | |
63 | an argument of type Arg should be casted before being used to | |
64 | initialize a coefficient of type T. */ | |
e535b963 RS |
65 | template<typename T, wi::precision_type = wi::int_traits<T>::precision_type> |
66 | struct poly_coeff_traits; | |
67 | ||
68 | template<typename T> | |
69 | struct poly_coeff_traits<T, wi::FLEXIBLE_PRECISION> | |
70 | { | |
71 | typedef T result; | |
72 | typedef T int_type; | |
73 | static const int signedness = (T (0) >= T (-1)); | |
74 | static const int precision = sizeof (T) * CHAR_BIT; | |
75 | static const T max_value = (signedness | |
76 | ? ((T (1) << (precision - 2)) | |
77 | + ((T (1) << (precision - 2)) - 1)) | |
78 | : T (-1)); | |
79 | static const int rank = sizeof (T) * 2 + !signedness; | |
eaa41a6d RS |
80 | |
81 | template<typename Arg> | |
82 | struct init_cast { using type = T; }; | |
e535b963 RS |
83 | }; |
84 | ||
85 | template<typename T> | |
86 | struct poly_coeff_traits<T, wi::VAR_PRECISION> | |
87 | { | |
88 | typedef T result; | |
89 | typedef int int_type; | |
90 | static const int signedness = -1; | |
91 | static const int precision = WIDE_INT_MAX_PRECISION; | |
92 | static const int rank = INT_MAX; | |
eaa41a6d RS |
93 | |
94 | template<typename Arg> | |
95 | struct init_cast { using type = const Arg &; }; | |
e535b963 RS |
96 | }; |
97 | ||
0d00385e JJ |
98 | template<typename T> |
99 | struct poly_coeff_traits<T, wi::INL_CONST_PRECISION> | |
100 | { | |
101 | typedef WI_UNARY_RESULT (T) result; | |
102 | typedef int int_type; | |
103 | /* These types are always signed. */ | |
104 | static const int signedness = 1; | |
105 | static const int precision = wi::int_traits<T>::precision; | |
106 | static const int rank = precision * 2 / CHAR_BIT; | |
107 | ||
108 | template<typename Arg> | |
109 | struct init_cast { using type = const Arg &; }; | |
110 | }; | |
111 | ||
e535b963 RS |
112 | template<typename T> |
113 | struct poly_coeff_traits<T, wi::CONST_PRECISION> | |
114 | { | |
115 | typedef WI_UNARY_RESULT (T) result; | |
116 | typedef int int_type; | |
117 | /* These types are always signed. */ | |
118 | static const int signedness = 1; | |
119 | static const int precision = wi::int_traits<T>::precision; | |
120 | static const int rank = precision * 2 / CHAR_BIT; | |
eaa41a6d RS |
121 | |
122 | template<typename Arg> | |
123 | struct init_cast { using type = const Arg &; }; | |
e535b963 RS |
124 | }; |
125 | ||
126 | /* Information about a pair of coefficient types. */ | |
127 | template<typename T1, typename T2> | |
128 | struct poly_coeff_pair_traits | |
129 | { | |
130 | /* True if T1 can represent all the values of T2. | |
131 | ||
132 | Either: | |
133 | ||
134 | - T1 should be a type with the same signedness as T2 and no less | |
135 | precision. This allows things like int16_t -> int16_t and | |
136 | uint32_t -> uint64_t. | |
137 | ||
138 | - T1 should be signed, T2 should be unsigned, and T1 should be | |
139 | wider than T2. This allows things like uint16_t -> int32_t. | |
140 | ||
141 | This rules out cases in which T1 has less precision than T2 or where | |
142 | the conversion would reinterpret the top bit. E.g. int16_t -> uint32_t | |
143 | can be dangerous and should have an explicit cast if deliberate. */ | |
144 | static const bool lossless_p = (poly_coeff_traits<T1>::signedness | |
145 | == poly_coeff_traits<T2>::signedness | |
146 | ? (poly_coeff_traits<T1>::precision | |
147 | >= poly_coeff_traits<T2>::precision) | |
148 | : (poly_coeff_traits<T1>::signedness == 1 | |
149 | && poly_coeff_traits<T2>::signedness == 0 | |
150 | && (poly_coeff_traits<T1>::precision | |
151 | > poly_coeff_traits<T2>::precision))); | |
152 | ||
153 | /* 0 if T1 op T2 should promote to HOST_WIDE_INT, | |
154 | 1 if T1 op T2 should promote to unsigned HOST_WIDE_INT, | |
155 | 2 if T1 op T2 should use wide-int rules. */ | |
156 | #define RANK(X) poly_coeff_traits<X>::rank | |
157 | static const int result_kind | |
158 | = ((RANK (T1) <= RANK (HOST_WIDE_INT) | |
159 | && RANK (T2) <= RANK (HOST_WIDE_INT)) | |
160 | ? 0 | |
161 | : (RANK (T1) <= RANK (unsigned HOST_WIDE_INT) | |
162 | && RANK (T2) <= RANK (unsigned HOST_WIDE_INT)) | |
163 | ? 1 : 2); | |
164 | #undef RANK | |
165 | }; | |
166 | ||
167 | /* SFINAE class that makes T3 available as "type" if T2 can represent all the | |
168 | values in T1. */ | |
169 | template<typename T1, typename T2, typename T3, | |
170 | bool lossless_p = poly_coeff_pair_traits<T1, T2>::lossless_p> | |
171 | struct if_lossless; | |
172 | template<typename T1, typename T2, typename T3> | |
173 | struct if_lossless<T1, T2, T3, true> | |
174 | { | |
175 | typedef T3 type; | |
176 | }; | |
177 | ||
178 | /* poly_int_traits<T> describes an integer type T that might be polynomial | |
179 | or non-polynomial: | |
180 | ||
181 | - poly_int_traits<T>::is_poly is true if T is a poly_int-based type | |
182 | and false otherwise. | |
183 | ||
184 | - poly_int_traits<T>::num_coeffs gives the number of coefficients in T | |
185 | if T is a poly_int and 1 otherwise. | |
186 | ||
187 | - poly_int_traits<T>::coeff_type gives the coefficent type of T if T | |
188 | is a poly_int and T itself otherwise | |
189 | ||
190 | - poly_int_traits<T>::int_type is a shorthand for | |
191 | typename poly_coeff_traits<coeff_type>::int_type. */ | |
192 | template<typename T> | |
193 | struct poly_int_traits | |
194 | { | |
195 | static const bool is_poly = false; | |
196 | static const unsigned int num_coeffs = 1; | |
197 | typedef T coeff_type; | |
198 | typedef typename poly_coeff_traits<T>::int_type int_type; | |
199 | }; | |
200 | template<unsigned int N, typename C> | |
eaa41a6d | 201 | struct poly_int_traits<poly_int<N, C> > |
e535b963 RS |
202 | { |
203 | static const bool is_poly = true; | |
204 | static const unsigned int num_coeffs = N; | |
205 | typedef C coeff_type; | |
206 | typedef typename poly_coeff_traits<C>::int_type int_type; | |
207 | }; | |
e535b963 RS |
208 | |
209 | /* SFINAE class that makes T2 available as "type" if T1 is a non-polynomial | |
210 | type. */ | |
211 | template<typename T1, typename T2 = T1, | |
212 | bool is_poly = poly_int_traits<T1>::is_poly> | |
213 | struct if_nonpoly {}; | |
214 | template<typename T1, typename T2> | |
215 | struct if_nonpoly<T1, T2, false> | |
216 | { | |
217 | typedef T2 type; | |
218 | }; | |
219 | ||
220 | /* SFINAE class that makes T3 available as "type" if both T1 and T2 are | |
221 | non-polynomial types. */ | |
222 | template<typename T1, typename T2, typename T3, | |
223 | bool is_poly1 = poly_int_traits<T1>::is_poly, | |
224 | bool is_poly2 = poly_int_traits<T2>::is_poly> | |
225 | struct if_nonpoly2 {}; | |
226 | template<typename T1, typename T2, typename T3> | |
227 | struct if_nonpoly2<T1, T2, T3, false, false> | |
228 | { | |
229 | typedef T3 type; | |
230 | }; | |
231 | ||
232 | /* SFINAE class that makes T2 available as "type" if T1 is a polynomial | |
233 | type. */ | |
234 | template<typename T1, typename T2 = T1, | |
235 | bool is_poly = poly_int_traits<T1>::is_poly> | |
236 | struct if_poly {}; | |
237 | template<typename T1, typename T2> | |
238 | struct if_poly<T1, T2, true> | |
239 | { | |
240 | typedef T2 type; | |
241 | }; | |
242 | ||
243 | /* poly_result<T1, T2> describes the result of an operation on two | |
244 | types T1 and T2, where at least one of the types is polynomial: | |
245 | ||
246 | - poly_result<T1, T2>::type gives the result type for the operation. | |
247 | The intention is to provide normal C-like rules for integer ranks, | |
248 | except that everything smaller than HOST_WIDE_INT promotes to | |
249 | HOST_WIDE_INT. | |
250 | ||
251 | - poly_result<T1, T2>::cast is the type to which an operand of type | |
252 | T1 should be cast before doing the operation, to ensure that | |
253 | the operation is done at the right precision. Casting to | |
254 | poly_result<T1, T2>::type would also work, but casting to this | |
255 | type is more efficient. */ | |
256 | template<typename T1, typename T2 = T1, | |
257 | int result_kind = poly_coeff_pair_traits<T1, T2>::result_kind> | |
258 | struct poly_result; | |
259 | ||
260 | /* Promote pair to HOST_WIDE_INT. */ | |
261 | template<typename T1, typename T2> | |
262 | struct poly_result<T1, T2, 0> | |
263 | { | |
264 | typedef HOST_WIDE_INT type; | |
265 | /* T1 and T2 are primitive types, so cast values to T before operating | |
266 | on them. */ | |
267 | typedef type cast; | |
268 | }; | |
269 | ||
270 | /* Promote pair to unsigned HOST_WIDE_INT. */ | |
271 | template<typename T1, typename T2> | |
272 | struct poly_result<T1, T2, 1> | |
273 | { | |
274 | typedef unsigned HOST_WIDE_INT type; | |
275 | /* T1 and T2 are primitive types, so cast values to T before operating | |
276 | on them. */ | |
277 | typedef type cast; | |
278 | }; | |
279 | ||
280 | /* Use normal wide-int rules. */ | |
281 | template<typename T1, typename T2> | |
282 | struct poly_result<T1, T2, 2> | |
283 | { | |
284 | typedef WI_BINARY_RESULT (T1, T2) type; | |
285 | /* Don't cast values before operating on them; leave the wi:: routines | |
286 | to handle promotion as necessary. */ | |
287 | typedef const T1 &cast; | |
288 | }; | |
289 | ||
290 | /* The coefficient type for the result of a binary operation on two | |
291 | poly_ints, the first of which has coefficients of type C1 and the | |
292 | second of which has coefficients of type C2. */ | |
293 | #define POLY_POLY_COEFF(C1, C2) typename poly_result<C1, C2>::type | |
294 | ||
295 | /* Enforce that T2 is non-polynomial and provide the cofficient type of | |
296 | the result of a binary operation in which the first operand is a | |
297 | poly_int with coefficients of type C1 and the second operand is | |
298 | a constant of type T2. */ | |
299 | #define POLY_CONST_COEFF(C1, T2) \ | |
300 | POLY_POLY_COEFF (C1, typename if_nonpoly<T2>::type) | |
301 | ||
302 | /* Likewise in reverse. */ | |
303 | #define CONST_POLY_COEFF(T1, C2) \ | |
304 | POLY_POLY_COEFF (typename if_nonpoly<T1>::type, C2) | |
305 | ||
306 | /* The result type for a binary operation on poly_int<N, C1> and | |
307 | poly_int<N, C2>. */ | |
308 | #define POLY_POLY_RESULT(N, C1, C2) poly_int<N, POLY_POLY_COEFF (C1, C2)> | |
309 | ||
310 | /* Enforce that T2 is non-polynomial and provide the result type | |
311 | for a binary operation on poly_int<N, C1> and T2. */ | |
312 | #define POLY_CONST_RESULT(N, C1, T2) poly_int<N, POLY_CONST_COEFF (C1, T2)> | |
313 | ||
314 | /* Enforce that T1 is non-polynomial and provide the result type | |
315 | for a binary operation on T1 and poly_int<N, C2>. */ | |
316 | #define CONST_POLY_RESULT(N, T1, C2) poly_int<N, CONST_POLY_COEFF (T1, C2)> | |
317 | ||
318 | /* Enforce that T1 and T2 are non-polynomial and provide the result type | |
319 | for a binary operation on T1 and T2. */ | |
320 | #define CONST_CONST_RESULT(N, T1, T2) \ | |
321 | POLY_POLY_COEFF (typename if_nonpoly<T1>::type, \ | |
322 | typename if_nonpoly<T2>::type) | |
323 | ||
324 | /* The type to which a coefficient of type C1 should be cast before | |
325 | using it in a binary operation with a coefficient of type C2. */ | |
326 | #define POLY_CAST(C1, C2) typename poly_result<C1, C2>::cast | |
327 | ||
328 | /* Provide the coefficient type for the result of T1 op T2, where T1 | |
329 | and T2 can be polynomial or non-polynomial. */ | |
330 | #define POLY_BINARY_COEFF(T1, T2) \ | |
331 | typename poly_result<typename poly_int_traits<T1>::coeff_type, \ | |
332 | typename poly_int_traits<T2>::coeff_type>::type | |
333 | ||
334 | /* The type to which an integer constant should be cast before | |
335 | comparing it with T. */ | |
336 | #define POLY_INT_TYPE(T) typename poly_int_traits<T>::int_type | |
337 | ||
338 | /* RES is a poly_int result that has coefficients of type C and that | |
339 | is being built up a coefficient at a time. Set coefficient number I | |
340 | to VALUE in the most efficient way possible. | |
341 | ||
342 | For primitive C it is better to assign directly, since it avoids | |
343 | any further calls and so is more efficient when the compiler is | |
344 | built at -O0. But for wide-int based C it is better to construct | |
345 | the value in-place. This means that calls out to a wide-int.cc | |
346 | routine can take the address of RES rather than the address of | |
347 | a temporary. | |
348 | ||
4dc7ce6f | 349 | The dummy self-comparison against C * is just a way of checking |
e535b963 RS |
350 | that C gives the right type. */ |
351 | #define POLY_SET_COEFF(C, RES, I, VALUE) \ | |
4dc7ce6f | 352 | ((void) (&(RES).coeffs[0] == (C *) (void *) &(RES).coeffs[0]), \ |
e535b963 RS |
353 | wi::int_traits<C>::precision_type == wi::FLEXIBLE_PRECISION \ |
354 | ? (void) ((RES).coeffs[I] = VALUE) \ | |
355 | : (void) ((RES).coeffs[I].~C (), new (&(RES).coeffs[I]) C (VALUE))) | |
356 | ||
eaa41a6d RS |
357 | /* poly_int_full and poly_int_hungry are used internally within poly_int |
358 | for delegated initializers. poly_int_full indicates that a parameter | |
359 | pack has enough elements to initialize every coefficient. poly_int_hungry | |
360 | indicates that at least one extra zero must be added. */ | |
361 | struct poly_int_full {}; | |
362 | struct poly_int_hungry {}; | |
363 | ||
364 | /* poly_int_fullness<B>::type is poly_int_full when B is true and | |
365 | poly_int_hungry when B is false. */ | |
366 | template<bool> struct poly_int_fullness; | |
367 | template<> struct poly_int_fullness<false> { using type = poly_int_hungry; }; | |
368 | template<> struct poly_int_fullness<true> { using type = poly_int_full; }; | |
369 | ||
370 | /* A class containing polynomial integers. The polynomial has N coefficients | |
371 | of type C, and N - 1 indeterminates. */ | |
e535b963 | 372 | template<unsigned int N, typename C> |
eaa41a6d | 373 | struct poly_int |
e535b963 RS |
374 | { |
375 | public: | |
eaa41a6d RS |
376 | poly_int () = default; |
377 | poly_int (const poly_int &) = default; | |
378 | ||
379 | template<typename Ca> | |
380 | poly_int (const poly_int<N, Ca> &); | |
381 | ||
382 | template<typename ...Cs> | |
383 | constexpr poly_int (const Cs &...); | |
384 | ||
385 | poly_int &operator = (const poly_int &) = default; | |
386 | ||
e535b963 | 387 | template<typename Ca> |
eaa41a6d | 388 | poly_int &operator = (const poly_int<N, Ca> &); |
e535b963 | 389 | template<typename Ca> |
eaa41a6d | 390 | typename if_nonpoly<Ca, poly_int>::type &operator = (const Ca &); |
e535b963 RS |
391 | |
392 | template<typename Ca> | |
eaa41a6d | 393 | poly_int &operator += (const poly_int<N, Ca> &); |
e535b963 | 394 | template<typename Ca> |
eaa41a6d | 395 | typename if_nonpoly<Ca, poly_int>::type &operator += (const Ca &); |
e535b963 RS |
396 | |
397 | template<typename Ca> | |
eaa41a6d | 398 | poly_int &operator -= (const poly_int<N, Ca> &); |
e535b963 | 399 | template<typename Ca> |
eaa41a6d | 400 | typename if_nonpoly<Ca, poly_int>::type &operator -= (const Ca &); |
e535b963 RS |
401 | |
402 | template<typename Ca> | |
eaa41a6d | 403 | typename if_nonpoly<Ca, poly_int>::type &operator *= (const Ca &); |
e535b963 | 404 | |
eaa41a6d | 405 | poly_int &operator <<= (unsigned int); |
e535b963 RS |
406 | |
407 | bool is_constant () const; | |
408 | ||
409 | template<typename T> | |
410 | typename if_lossless<T, C, bool>::type is_constant (T *) const; | |
411 | ||
412 | C to_constant () const; | |
413 | ||
414 | template<typename Ca> | |
eaa41a6d | 415 | static poly_int<N, C> from (const poly_int<N, Ca> &, unsigned int, |
e535b963 RS |
416 | signop); |
417 | template<typename Ca> | |
eaa41a6d | 418 | static poly_int<N, C> from (const poly_int<N, Ca> &, signop); |
e535b963 | 419 | |
eaa41a6d RS |
420 | bool to_shwi (poly_int<N, HOST_WIDE_INT> *) const; |
421 | bool to_uhwi (poly_int<N, unsigned HOST_WIDE_INT> *) const; | |
e535b963 RS |
422 | poly_int<N, HOST_WIDE_INT> force_shwi () const; |
423 | poly_int<N, unsigned HOST_WIDE_INT> force_uhwi () const; | |
424 | ||
425 | #if POLY_INT_CONVERSION | |
426 | operator C () const; | |
427 | #endif | |
428 | ||
429 | C coeffs[N]; | |
eaa41a6d RS |
430 | |
431 | private: | |
432 | template<typename ...Cs> | |
433 | constexpr poly_int (poly_int_full, const Cs &...); | |
434 | ||
435 | template<typename C0, typename ...Cs> | |
436 | constexpr poly_int (poly_int_hungry, const C0 &, const Cs &...); | |
e535b963 RS |
437 | }; |
438 | ||
439 | template<unsigned int N, typename C> | |
440 | template<typename Ca> | |
eaa41a6d RS |
441 | inline |
442 | poly_int<N, C>::poly_int (const poly_int<N, Ca> &a) | |
443 | { | |
444 | for (unsigned int i = 0; i < N; i++) | |
445 | POLY_SET_COEFF (C, *this, i, a.coeffs[i]); | |
446 | } | |
447 | ||
448 | template<unsigned int N, typename C> | |
449 | template<typename ...Cs> | |
450 | inline constexpr | |
451 | poly_int<N, C>::poly_int (const Cs &... cs) | |
452 | : poly_int (typename poly_int_fullness<sizeof... (Cs) >= N>::type (), | |
453 | cs...) {} | |
454 | ||
455 | /* Initialize with c0, cs..., and some trailing zeros. */ | |
456 | template<unsigned int N, typename C> | |
457 | template<typename C0, typename ...Cs> | |
458 | inline constexpr | |
459 | poly_int<N, C>::poly_int (poly_int_hungry, const C0 &c0, const Cs &... cs) | |
460 | : poly_int (c0, cs..., wi::ints_for<C>::zero (c0)) {} | |
461 | ||
462 | /* Initialize with cs... directly, casting where necessary. */ | |
463 | template<unsigned int N, typename C> | |
464 | template<typename ...Cs> | |
465 | inline constexpr | |
466 | poly_int<N, C>::poly_int (poly_int_full, const Cs &... cs) | |
467 | : coeffs { (typename poly_coeff_traits<C>:: | |
468 | template init_cast<Cs>::type (cs))... } {} | |
469 | ||
470 | template<unsigned int N, typename C> | |
471 | template<typename Ca> | |
472 | inline poly_int<N, C>& | |
473 | poly_int<N, C>::operator = (const poly_int<N, Ca> &a) | |
e535b963 RS |
474 | { |
475 | for (unsigned int i = 0; i < N; i++) | |
476 | POLY_SET_COEFF (C, *this, i, a.coeffs[i]); | |
477 | return *this; | |
478 | } | |
479 | ||
480 | template<unsigned int N, typename C> | |
481 | template<typename Ca> | |
eaa41a6d RS |
482 | inline typename if_nonpoly<Ca, poly_int<N, C> >::type & |
483 | poly_int<N, C>::operator = (const Ca &a) | |
e535b963 RS |
484 | { |
485 | POLY_SET_COEFF (C, *this, 0, a); | |
486 | if (N >= 2) | |
487 | for (unsigned int i = 1; i < N; i++) | |
488 | POLY_SET_COEFF (C, *this, i, wi::ints_for<C>::zero (this->coeffs[0])); | |
489 | return *this; | |
490 | } | |
491 | ||
492 | template<unsigned int N, typename C> | |
493 | template<typename Ca> | |
eaa41a6d RS |
494 | inline poly_int<N, C>& |
495 | poly_int<N, C>::operator += (const poly_int<N, Ca> &a) | |
e535b963 RS |
496 | { |
497 | for (unsigned int i = 0; i < N; i++) | |
498 | this->coeffs[i] += a.coeffs[i]; | |
499 | return *this; | |
500 | } | |
501 | ||
502 | template<unsigned int N, typename C> | |
503 | template<typename Ca> | |
eaa41a6d RS |
504 | inline typename if_nonpoly<Ca, poly_int<N, C> >::type & |
505 | poly_int<N, C>::operator += (const Ca &a) | |
e535b963 RS |
506 | { |
507 | this->coeffs[0] += a; | |
508 | return *this; | |
509 | } | |
510 | ||
511 | template<unsigned int N, typename C> | |
512 | template<typename Ca> | |
eaa41a6d RS |
513 | inline poly_int<N, C>& |
514 | poly_int<N, C>::operator -= (const poly_int<N, Ca> &a) | |
e535b963 RS |
515 | { |
516 | for (unsigned int i = 0; i < N; i++) | |
517 | this->coeffs[i] -= a.coeffs[i]; | |
518 | return *this; | |
519 | } | |
520 | ||
521 | template<unsigned int N, typename C> | |
522 | template<typename Ca> | |
eaa41a6d RS |
523 | inline typename if_nonpoly<Ca, poly_int<N, C> >::type & |
524 | poly_int<N, C>::operator -= (const Ca &a) | |
e535b963 RS |
525 | { |
526 | this->coeffs[0] -= a; | |
527 | return *this; | |
528 | } | |
529 | ||
530 | template<unsigned int N, typename C> | |
531 | template<typename Ca> | |
eaa41a6d RS |
532 | inline typename if_nonpoly<Ca, poly_int<N, C> >::type & |
533 | poly_int<N, C>::operator *= (const Ca &a) | |
e535b963 RS |
534 | { |
535 | for (unsigned int i = 0; i < N; i++) | |
536 | this->coeffs[i] *= a; | |
537 | return *this; | |
538 | } | |
539 | ||
540 | template<unsigned int N, typename C> | |
eaa41a6d RS |
541 | inline poly_int<N, C>& |
542 | poly_int<N, C>::operator <<= (unsigned int a) | |
e535b963 RS |
543 | { |
544 | for (unsigned int i = 0; i < N; i++) | |
545 | this->coeffs[i] <<= a; | |
546 | return *this; | |
547 | } | |
548 | ||
549 | /* Return true if the polynomial value is a compile-time constant. */ | |
550 | ||
551 | template<unsigned int N, typename C> | |
552 | inline bool | |
eaa41a6d | 553 | poly_int<N, C>::is_constant () const |
e535b963 RS |
554 | { |
555 | if (N >= 2) | |
556 | for (unsigned int i = 1; i < N; i++) | |
557 | if (this->coeffs[i] != 0) | |
558 | return false; | |
559 | return true; | |
560 | } | |
561 | ||
562 | /* Return true if the polynomial value is a compile-time constant, | |
563 | storing its value in CONST_VALUE if so. */ | |
564 | ||
565 | template<unsigned int N, typename C> | |
566 | template<typename T> | |
567 | inline typename if_lossless<T, C, bool>::type | |
eaa41a6d | 568 | poly_int<N, C>::is_constant (T *const_value) const |
e535b963 RS |
569 | { |
570 | if (is_constant ()) | |
571 | { | |
572 | *const_value = this->coeffs[0]; | |
573 | return true; | |
574 | } | |
575 | return false; | |
576 | } | |
577 | ||
578 | /* Return the value of a polynomial that is already known to be a | |
579 | compile-time constant. | |
580 | ||
581 | NOTE: When using this function, please add a comment above the call | |
582 | explaining why we know the value is constant in that context. */ | |
583 | ||
584 | template<unsigned int N, typename C> | |
585 | inline C | |
eaa41a6d | 586 | poly_int<N, C>::to_constant () const |
e535b963 RS |
587 | { |
588 | gcc_checking_assert (is_constant ()); | |
589 | return this->coeffs[0]; | |
590 | } | |
591 | ||
592 | /* Convert X to a wide_int-based polynomial in which each coefficient | |
593 | has BITSIZE bits. If X's coefficients are smaller than BITSIZE, | |
594 | extend them according to SGN. */ | |
595 | ||
596 | template<unsigned int N, typename C> | |
597 | template<typename Ca> | |
598 | inline poly_int<N, C> | |
eaa41a6d RS |
599 | poly_int<N, C>::from (const poly_int<N, Ca> &a, unsigned int bitsize, |
600 | signop sgn) | |
e535b963 RS |
601 | { |
602 | poly_int<N, C> r; | |
603 | for (unsigned int i = 0; i < N; i++) | |
604 | POLY_SET_COEFF (C, r, i, C::from (a.coeffs[i], bitsize, sgn)); | |
605 | return r; | |
606 | } | |
607 | ||
608 | /* Convert X to a fixed_wide_int-based polynomial, extending according | |
609 | to SGN. */ | |
610 | ||
611 | template<unsigned int N, typename C> | |
612 | template<typename Ca> | |
613 | inline poly_int<N, C> | |
eaa41a6d | 614 | poly_int<N, C>::from (const poly_int<N, Ca> &a, signop sgn) |
e535b963 RS |
615 | { |
616 | poly_int<N, C> r; | |
617 | for (unsigned int i = 0; i < N; i++) | |
618 | POLY_SET_COEFF (C, r, i, C::from (a.coeffs[i], sgn)); | |
619 | return r; | |
620 | } | |
621 | ||
622 | /* Return true if the coefficients of this generic_wide_int-based | |
623 | polynomial can be represented as signed HOST_WIDE_INTs without loss | |
624 | of precision. Store the HOST_WIDE_INT representation in *R if so. */ | |
625 | ||
626 | template<unsigned int N, typename C> | |
627 | inline bool | |
eaa41a6d | 628 | poly_int<N, C>::to_shwi (poly_int<N, HOST_WIDE_INT> *r) const |
e535b963 RS |
629 | { |
630 | for (unsigned int i = 0; i < N; i++) | |
631 | if (!wi::fits_shwi_p (this->coeffs[i])) | |
632 | return false; | |
633 | for (unsigned int i = 0; i < N; i++) | |
634 | r->coeffs[i] = this->coeffs[i].to_shwi (); | |
635 | return true; | |
636 | } | |
637 | ||
638 | /* Return true if the coefficients of this generic_wide_int-based | |
639 | polynomial can be represented as unsigned HOST_WIDE_INTs without | |
640 | loss of precision. Store the unsigned HOST_WIDE_INT representation | |
641 | in *R if so. */ | |
642 | ||
643 | template<unsigned int N, typename C> | |
644 | inline bool | |
eaa41a6d | 645 | poly_int<N, C>::to_uhwi (poly_int<N, unsigned HOST_WIDE_INT> *r) const |
e535b963 RS |
646 | { |
647 | for (unsigned int i = 0; i < N; i++) | |
648 | if (!wi::fits_uhwi_p (this->coeffs[i])) | |
649 | return false; | |
650 | for (unsigned int i = 0; i < N; i++) | |
651 | r->coeffs[i] = this->coeffs[i].to_uhwi (); | |
652 | return true; | |
653 | } | |
654 | ||
655 | /* Force a generic_wide_int-based constant to HOST_WIDE_INT precision, | |
656 | truncating if necessary. */ | |
657 | ||
658 | template<unsigned int N, typename C> | |
659 | inline poly_int<N, HOST_WIDE_INT> | |
eaa41a6d | 660 | poly_int<N, C>::force_shwi () const |
e535b963 | 661 | { |
eaa41a6d | 662 | poly_int<N, HOST_WIDE_INT> r; |
e535b963 RS |
663 | for (unsigned int i = 0; i < N; i++) |
664 | r.coeffs[i] = this->coeffs[i].to_shwi (); | |
665 | return r; | |
666 | } | |
667 | ||
668 | /* Force a generic_wide_int-based constant to unsigned HOST_WIDE_INT precision, | |
669 | truncating if necessary. */ | |
670 | ||
671 | template<unsigned int N, typename C> | |
672 | inline poly_int<N, unsigned HOST_WIDE_INT> | |
eaa41a6d | 673 | poly_int<N, C>::force_uhwi () const |
e535b963 | 674 | { |
eaa41a6d | 675 | poly_int<N, unsigned HOST_WIDE_INT> r; |
e535b963 RS |
676 | for (unsigned int i = 0; i < N; i++) |
677 | r.coeffs[i] = this->coeffs[i].to_uhwi (); | |
678 | return r; | |
679 | } | |
680 | ||
681 | #if POLY_INT_CONVERSION | |
682 | /* Provide a conversion operator to constants. */ | |
683 | ||
684 | template<unsigned int N, typename C> | |
685 | inline | |
eaa41a6d | 686 | poly_int<N, C>::operator C () const |
e535b963 RS |
687 | { |
688 | gcc_checking_assert (this->is_constant ()); | |
689 | return this->coeffs[0]; | |
690 | } | |
691 | #endif | |
692 | ||
e535b963 RS |
693 | /* Return true if every coefficient of A is in the inclusive range [B, C]. */ |
694 | ||
695 | template<typename Ca, typename Cb, typename Cc> | |
696 | inline typename if_nonpoly<Ca, bool>::type | |
697 | coeffs_in_range_p (const Ca &a, const Cb &b, const Cc &c) | |
698 | { | |
699 | return a >= b && a <= c; | |
700 | } | |
701 | ||
702 | template<unsigned int N, typename Ca, typename Cb, typename Cc> | |
703 | inline typename if_nonpoly<Ca, bool>::type | |
eaa41a6d | 704 | coeffs_in_range_p (const poly_int<N, Ca> &a, const Cb &b, const Cc &c) |
e535b963 RS |
705 | { |
706 | for (unsigned int i = 0; i < N; i++) | |
707 | if (a.coeffs[i] < b || a.coeffs[i] > c) | |
708 | return false; | |
709 | return true; | |
710 | } | |
711 | ||
712 | namespace wi { | |
713 | /* Poly version of wi::shwi, with the same interface. */ | |
714 | ||
715 | template<unsigned int N> | |
716 | inline poly_int<N, hwi_with_prec> | |
eaa41a6d | 717 | shwi (const poly_int<N, HOST_WIDE_INT> &a, unsigned int precision) |
e535b963 RS |
718 | { |
719 | poly_int<N, hwi_with_prec> r; | |
720 | for (unsigned int i = 0; i < N; i++) | |
721 | POLY_SET_COEFF (hwi_with_prec, r, i, wi::shwi (a.coeffs[i], precision)); | |
722 | return r; | |
723 | } | |
724 | ||
725 | /* Poly version of wi::uhwi, with the same interface. */ | |
726 | ||
727 | template<unsigned int N> | |
728 | inline poly_int<N, hwi_with_prec> | |
eaa41a6d | 729 | uhwi (const poly_int<N, unsigned HOST_WIDE_INT> &a, unsigned int precision) |
e535b963 RS |
730 | { |
731 | poly_int<N, hwi_with_prec> r; | |
732 | for (unsigned int i = 0; i < N; i++) | |
733 | POLY_SET_COEFF (hwi_with_prec, r, i, wi::uhwi (a.coeffs[i], precision)); | |
734 | return r; | |
735 | } | |
736 | ||
737 | /* Poly version of wi::sext, with the same interface. */ | |
738 | ||
739 | template<unsigned int N, typename Ca> | |
740 | inline POLY_POLY_RESULT (N, Ca, Ca) | |
eaa41a6d | 741 | sext (const poly_int<N, Ca> &a, unsigned int precision) |
e535b963 RS |
742 | { |
743 | typedef POLY_POLY_COEFF (Ca, Ca) C; | |
744 | poly_int<N, C> r; | |
745 | for (unsigned int i = 0; i < N; i++) | |
746 | POLY_SET_COEFF (C, r, i, wi::sext (a.coeffs[i], precision)); | |
747 | return r; | |
748 | } | |
749 | ||
750 | /* Poly version of wi::zext, with the same interface. */ | |
751 | ||
752 | template<unsigned int N, typename Ca> | |
753 | inline POLY_POLY_RESULT (N, Ca, Ca) | |
eaa41a6d | 754 | zext (const poly_int<N, Ca> &a, unsigned int precision) |
e535b963 RS |
755 | { |
756 | typedef POLY_POLY_COEFF (Ca, Ca) C; | |
757 | poly_int<N, C> r; | |
758 | for (unsigned int i = 0; i < N; i++) | |
759 | POLY_SET_COEFF (C, r, i, wi::zext (a.coeffs[i], precision)); | |
760 | return r; | |
761 | } | |
762 | } | |
763 | ||
764 | template<unsigned int N, typename Ca, typename Cb> | |
765 | inline POLY_POLY_RESULT (N, Ca, Cb) | |
eaa41a6d | 766 | operator + (const poly_int<N, Ca> &a, const poly_int<N, Cb> &b) |
e535b963 RS |
767 | { |
768 | typedef POLY_CAST (Ca, Cb) NCa; | |
769 | typedef POLY_POLY_COEFF (Ca, Cb) C; | |
770 | poly_int<N, C> r; | |
771 | for (unsigned int i = 0; i < N; i++) | |
772 | POLY_SET_COEFF (C, r, i, NCa (a.coeffs[i]) + b.coeffs[i]); | |
773 | return r; | |
774 | } | |
775 | ||
776 | template<unsigned int N, typename Ca, typename Cb> | |
777 | inline POLY_CONST_RESULT (N, Ca, Cb) | |
eaa41a6d | 778 | operator + (const poly_int<N, Ca> &a, const Cb &b) |
e535b963 RS |
779 | { |
780 | typedef POLY_CAST (Ca, Cb) NCa; | |
781 | typedef POLY_CONST_COEFF (Ca, Cb) C; | |
782 | poly_int<N, C> r; | |
783 | POLY_SET_COEFF (C, r, 0, NCa (a.coeffs[0]) + b); | |
784 | if (N >= 2) | |
785 | for (unsigned int i = 1; i < N; i++) | |
786 | POLY_SET_COEFF (C, r, i, NCa (a.coeffs[i])); | |
787 | return r; | |
788 | } | |
789 | ||
790 | template<unsigned int N, typename Ca, typename Cb> | |
791 | inline CONST_POLY_RESULT (N, Ca, Cb) | |
eaa41a6d | 792 | operator + (const Ca &a, const poly_int<N, Cb> &b) |
e535b963 RS |
793 | { |
794 | typedef POLY_CAST (Cb, Ca) NCb; | |
795 | typedef CONST_POLY_COEFF (Ca, Cb) C; | |
796 | poly_int<N, C> r; | |
797 | POLY_SET_COEFF (C, r, 0, a + NCb (b.coeffs[0])); | |
798 | if (N >= 2) | |
799 | for (unsigned int i = 1; i < N; i++) | |
800 | POLY_SET_COEFF (C, r, i, NCb (b.coeffs[i])); | |
801 | return r; | |
802 | } | |
803 | ||
804 | namespace wi { | |
805 | /* Poly versions of wi::add, with the same interface. */ | |
806 | ||
807 | template<unsigned int N, typename Ca, typename Cb> | |
808 | inline poly_int<N, WI_BINARY_RESULT (Ca, Cb)> | |
eaa41a6d | 809 | add (const poly_int<N, Ca> &a, const poly_int<N, Cb> &b) |
e535b963 RS |
810 | { |
811 | typedef WI_BINARY_RESULT (Ca, Cb) C; | |
812 | poly_int<N, C> r; | |
813 | for (unsigned int i = 0; i < N; i++) | |
814 | POLY_SET_COEFF (C, r, i, wi::add (a.coeffs[i], b.coeffs[i])); | |
815 | return r; | |
816 | } | |
817 | ||
818 | template<unsigned int N, typename Ca, typename Cb> | |
819 | inline poly_int<N, WI_BINARY_RESULT (Ca, Cb)> | |
eaa41a6d | 820 | add (const poly_int<N, Ca> &a, const Cb &b) |
e535b963 RS |
821 | { |
822 | typedef WI_BINARY_RESULT (Ca, Cb) C; | |
823 | poly_int<N, C> r; | |
824 | POLY_SET_COEFF (C, r, 0, wi::add (a.coeffs[0], b)); | |
825 | for (unsigned int i = 1; i < N; i++) | |
826 | POLY_SET_COEFF (C, r, i, wi::add (a.coeffs[i], | |
827 | wi::ints_for<Cb>::zero (b))); | |
828 | return r; | |
829 | } | |
830 | ||
831 | template<unsigned int N, typename Ca, typename Cb> | |
832 | inline poly_int<N, WI_BINARY_RESULT (Ca, Cb)> | |
eaa41a6d | 833 | add (const Ca &a, const poly_int<N, Cb> &b) |
e535b963 RS |
834 | { |
835 | typedef WI_BINARY_RESULT (Ca, Cb) C; | |
836 | poly_int<N, C> r; | |
837 | POLY_SET_COEFF (C, r, 0, wi::add (a, b.coeffs[0])); | |
838 | for (unsigned int i = 1; i < N; i++) | |
839 | POLY_SET_COEFF (C, r, i, wi::add (wi::ints_for<Ca>::zero (a), | |
840 | b.coeffs[i])); | |
841 | return r; | |
842 | } | |
843 | ||
844 | template<unsigned int N, typename Ca, typename Cb> | |
845 | inline poly_int<N, WI_BINARY_RESULT (Ca, Cb)> | |
eaa41a6d | 846 | add (const poly_int<N, Ca> &a, const poly_int<N, Cb> &b, |
4a669ac3 | 847 | signop sgn, wi::overflow_type *overflow) |
e535b963 RS |
848 | { |
849 | typedef WI_BINARY_RESULT (Ca, Cb) C; | |
850 | poly_int<N, C> r; | |
851 | POLY_SET_COEFF (C, r, 0, wi::add (a.coeffs[0], b.coeffs[0], sgn, overflow)); | |
852 | for (unsigned int i = 1; i < N; i++) | |
853 | { | |
4a669ac3 | 854 | wi::overflow_type suboverflow; |
e535b963 RS |
855 | POLY_SET_COEFF (C, r, i, wi::add (a.coeffs[i], b.coeffs[i], sgn, |
856 | &suboverflow)); | |
4a669ac3 | 857 | wi::accumulate_overflow (*overflow, suboverflow); |
e535b963 RS |
858 | } |
859 | return r; | |
860 | } | |
861 | } | |
862 | ||
863 | template<unsigned int N, typename Ca, typename Cb> | |
864 | inline POLY_POLY_RESULT (N, Ca, Cb) | |
eaa41a6d | 865 | operator - (const poly_int<N, Ca> &a, const poly_int<N, Cb> &b) |
e535b963 RS |
866 | { |
867 | typedef POLY_CAST (Ca, Cb) NCa; | |
868 | typedef POLY_POLY_COEFF (Ca, Cb) C; | |
869 | poly_int<N, C> r; | |
870 | for (unsigned int i = 0; i < N; i++) | |
871 | POLY_SET_COEFF (C, r, i, NCa (a.coeffs[i]) - b.coeffs[i]); | |
872 | return r; | |
873 | } | |
874 | ||
875 | template<unsigned int N, typename Ca, typename Cb> | |
876 | inline POLY_CONST_RESULT (N, Ca, Cb) | |
eaa41a6d | 877 | operator - (const poly_int<N, Ca> &a, const Cb &b) |
e535b963 RS |
878 | { |
879 | typedef POLY_CAST (Ca, Cb) NCa; | |
880 | typedef POLY_CONST_COEFF (Ca, Cb) C; | |
881 | poly_int<N, C> r; | |
882 | POLY_SET_COEFF (C, r, 0, NCa (a.coeffs[0]) - b); | |
883 | if (N >= 2) | |
884 | for (unsigned int i = 1; i < N; i++) | |
885 | POLY_SET_COEFF (C, r, i, NCa (a.coeffs[i])); | |
886 | return r; | |
887 | } | |
888 | ||
889 | template<unsigned int N, typename Ca, typename Cb> | |
890 | inline CONST_POLY_RESULT (N, Ca, Cb) | |
eaa41a6d | 891 | operator - (const Ca &a, const poly_int<N, Cb> &b) |
e535b963 RS |
892 | { |
893 | typedef POLY_CAST (Cb, Ca) NCb; | |
894 | typedef CONST_POLY_COEFF (Ca, Cb) C; | |
895 | poly_int<N, C> r; | |
896 | POLY_SET_COEFF (C, r, 0, a - NCb (b.coeffs[0])); | |
897 | if (N >= 2) | |
898 | for (unsigned int i = 1; i < N; i++) | |
899 | POLY_SET_COEFF (C, r, i, -NCb (b.coeffs[i])); | |
900 | return r; | |
901 | } | |
902 | ||
903 | namespace wi { | |
904 | /* Poly versions of wi::sub, with the same interface. */ | |
905 | ||
906 | template<unsigned int N, typename Ca, typename Cb> | |
907 | inline poly_int<N, WI_BINARY_RESULT (Ca, Cb)> | |
eaa41a6d | 908 | sub (const poly_int<N, Ca> &a, const poly_int<N, Cb> &b) |
e535b963 RS |
909 | { |
910 | typedef WI_BINARY_RESULT (Ca, Cb) C; | |
911 | poly_int<N, C> r; | |
912 | for (unsigned int i = 0; i < N; i++) | |
913 | POLY_SET_COEFF (C, r, i, wi::sub (a.coeffs[i], 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)> | |
eaa41a6d | 919 | sub (const poly_int<N, Ca> &a, const Cb &b) |
e535b963 RS |
920 | { |
921 | typedef WI_BINARY_RESULT (Ca, Cb) C; | |
922 | poly_int<N, C> r; | |
923 | POLY_SET_COEFF (C, r, 0, wi::sub (a.coeffs[0], b)); | |
924 | for (unsigned int i = 1; i < N; i++) | |
925 | POLY_SET_COEFF (C, r, i, wi::sub (a.coeffs[i], | |
926 | wi::ints_for<Cb>::zero (b))); | |
927 | return r; | |
928 | } | |
929 | ||
930 | template<unsigned int N, typename Ca, typename Cb> | |
931 | inline poly_int<N, WI_BINARY_RESULT (Ca, Cb)> | |
eaa41a6d | 932 | sub (const Ca &a, const poly_int<N, Cb> &b) |
e535b963 RS |
933 | { |
934 | typedef WI_BINARY_RESULT (Ca, Cb) C; | |
935 | poly_int<N, C> r; | |
936 | POLY_SET_COEFF (C, r, 0, wi::sub (a, b.coeffs[0])); | |
937 | for (unsigned int i = 1; i < N; i++) | |
938 | POLY_SET_COEFF (C, r, i, wi::sub (wi::ints_for<Ca>::zero (a), | |
939 | b.coeffs[i])); | |
940 | return r; | |
941 | } | |
942 | ||
943 | template<unsigned int N, typename Ca, typename Cb> | |
944 | inline poly_int<N, WI_BINARY_RESULT (Ca, Cb)> | |
eaa41a6d | 945 | sub (const poly_int<N, Ca> &a, const poly_int<N, Cb> &b, |
4a669ac3 | 946 | signop sgn, wi::overflow_type *overflow) |
e535b963 RS |
947 | { |
948 | typedef WI_BINARY_RESULT (Ca, Cb) C; | |
949 | poly_int<N, C> r; | |
950 | POLY_SET_COEFF (C, r, 0, wi::sub (a.coeffs[0], b.coeffs[0], sgn, overflow)); | |
951 | for (unsigned int i = 1; i < N; i++) | |
952 | { | |
4a669ac3 | 953 | wi::overflow_type suboverflow; |
e535b963 RS |
954 | POLY_SET_COEFF (C, r, i, wi::sub (a.coeffs[i], b.coeffs[i], sgn, |
955 | &suboverflow)); | |
4a669ac3 | 956 | wi::accumulate_overflow (*overflow, suboverflow); |
e535b963 RS |
957 | } |
958 | return r; | |
959 | } | |
960 | } | |
961 | ||
962 | template<unsigned int N, typename Ca> | |
963 | inline POLY_POLY_RESULT (N, Ca, Ca) | |
eaa41a6d | 964 | operator - (const poly_int<N, Ca> &a) |
e535b963 RS |
965 | { |
966 | typedef POLY_CAST (Ca, Ca) NCa; | |
967 | typedef POLY_POLY_COEFF (Ca, Ca) C; | |
968 | poly_int<N, C> r; | |
969 | for (unsigned int i = 0; i < N; i++) | |
970 | POLY_SET_COEFF (C, r, i, -NCa (a.coeffs[i])); | |
971 | return r; | |
972 | } | |
973 | ||
974 | namespace wi { | |
975 | /* Poly version of wi::neg, with the same interface. */ | |
976 | ||
977 | template<unsigned int N, typename Ca> | |
978 | inline poly_int<N, WI_UNARY_RESULT (Ca)> | |
eaa41a6d | 979 | neg (const poly_int<N, Ca> &a) |
e535b963 RS |
980 | { |
981 | typedef WI_UNARY_RESULT (Ca) C; | |
982 | poly_int<N, C> r; | |
983 | for (unsigned int i = 0; i < N; i++) | |
984 | POLY_SET_COEFF (C, r, i, wi::neg (a.coeffs[i])); | |
985 | return r; | |
986 | } | |
987 | ||
988 | template<unsigned int N, typename Ca> | |
989 | inline poly_int<N, WI_UNARY_RESULT (Ca)> | |
eaa41a6d | 990 | neg (const poly_int<N, Ca> &a, wi::overflow_type *overflow) |
e535b963 RS |
991 | { |
992 | typedef WI_UNARY_RESULT (Ca) C; | |
993 | poly_int<N, C> r; | |
994 | POLY_SET_COEFF (C, r, 0, wi::neg (a.coeffs[0], overflow)); | |
995 | for (unsigned int i = 1; i < N; i++) | |
996 | { | |
4a669ac3 | 997 | wi::overflow_type suboverflow; |
e535b963 | 998 | POLY_SET_COEFF (C, r, i, wi::neg (a.coeffs[i], &suboverflow)); |
4a669ac3 | 999 | wi::accumulate_overflow (*overflow, suboverflow); |
e535b963 RS |
1000 | } |
1001 | return r; | |
1002 | } | |
1003 | } | |
1004 | ||
1005 | template<unsigned int N, typename Ca> | |
1006 | inline POLY_POLY_RESULT (N, Ca, Ca) | |
eaa41a6d | 1007 | operator ~ (const poly_int<N, Ca> &a) |
e535b963 RS |
1008 | { |
1009 | if (N >= 2) | |
1010 | return -1 - a; | |
1011 | return ~a.coeffs[0]; | |
1012 | } | |
1013 | ||
1014 | template<unsigned int N, typename Ca, typename Cb> | |
1015 | inline POLY_CONST_RESULT (N, Ca, Cb) | |
eaa41a6d | 1016 | operator * (const poly_int<N, Ca> &a, const Cb &b) |
e535b963 RS |
1017 | { |
1018 | typedef POLY_CAST (Ca, Cb) NCa; | |
1019 | typedef POLY_CONST_COEFF (Ca, Cb) C; | |
1020 | poly_int<N, C> r; | |
1021 | for (unsigned int i = 0; i < N; i++) | |
1022 | POLY_SET_COEFF (C, r, i, NCa (a.coeffs[i]) * b); | |
1023 | return r; | |
1024 | } | |
1025 | ||
1026 | template<unsigned int N, typename Ca, typename Cb> | |
1027 | inline CONST_POLY_RESULT (N, Ca, Cb) | |
eaa41a6d | 1028 | operator * (const Ca &a, const poly_int<N, Cb> &b) |
e535b963 RS |
1029 | { |
1030 | typedef POLY_CAST (Ca, Cb) NCa; | |
1031 | typedef CONST_POLY_COEFF (Ca, Cb) C; | |
1032 | poly_int<N, C> r; | |
1033 | for (unsigned int i = 0; i < N; i++) | |
1034 | POLY_SET_COEFF (C, r, i, NCa (a) * b.coeffs[i]); | |
1035 | return r; | |
1036 | } | |
1037 | ||
1038 | namespace wi { | |
1039 | /* Poly versions of wi::mul, with the same interface. */ | |
1040 | ||
1041 | template<unsigned int N, typename Ca, typename Cb> | |
1042 | inline poly_int<N, WI_BINARY_RESULT (Ca, Cb)> | |
eaa41a6d | 1043 | mul (const poly_int<N, Ca> &a, const Cb &b) |
e535b963 RS |
1044 | { |
1045 | typedef WI_BINARY_RESULT (Ca, Cb) C; | |
1046 | poly_int<N, C> r; | |
1047 | for (unsigned int i = 0; i < N; i++) | |
1048 | POLY_SET_COEFF (C, r, i, wi::mul (a.coeffs[i], b)); | |
1049 | return r; | |
1050 | } | |
1051 | ||
1052 | template<unsigned int N, typename Ca, typename Cb> | |
1053 | inline poly_int<N, WI_BINARY_RESULT (Ca, Cb)> | |
eaa41a6d | 1054 | mul (const Ca &a, const poly_int<N, Cb> &b) |
e535b963 RS |
1055 | { |
1056 | typedef WI_BINARY_RESULT (Ca, Cb) C; | |
1057 | poly_int<N, C> r; | |
1058 | for (unsigned int i = 0; i < N; i++) | |
1059 | POLY_SET_COEFF (C, r, i, wi::mul (a, b.coeffs[i])); | |
1060 | return r; | |
1061 | } | |
1062 | ||
1063 | template<unsigned int N, typename Ca, typename Cb> | |
1064 | inline poly_int<N, WI_BINARY_RESULT (Ca, Cb)> | |
eaa41a6d | 1065 | mul (const poly_int<N, Ca> &a, const Cb &b, |
4a669ac3 | 1066 | signop sgn, wi::overflow_type *overflow) |
e535b963 RS |
1067 | { |
1068 | typedef WI_BINARY_RESULT (Ca, Cb) C; | |
1069 | poly_int<N, C> r; | |
1070 | POLY_SET_COEFF (C, r, 0, wi::mul (a.coeffs[0], b, sgn, overflow)); | |
1071 | for (unsigned int i = 1; i < N; i++) | |
1072 | { | |
4a669ac3 | 1073 | wi::overflow_type suboverflow; |
e535b963 | 1074 | POLY_SET_COEFF (C, r, i, wi::mul (a.coeffs[i], b, sgn, &suboverflow)); |
4a669ac3 | 1075 | wi::accumulate_overflow (*overflow, suboverflow); |
e535b963 RS |
1076 | } |
1077 | return r; | |
1078 | } | |
1079 | } | |
1080 | ||
1081 | template<unsigned int N, typename Ca, typename Cb> | |
1082 | inline POLY_POLY_RESULT (N, Ca, Ca) | |
eaa41a6d | 1083 | operator << (const poly_int<N, Ca> &a, const Cb &b) |
e535b963 RS |
1084 | { |
1085 | typedef POLY_CAST (Ca, Ca) NCa; | |
1086 | typedef POLY_POLY_COEFF (Ca, Ca) C; | |
1087 | poly_int<N, C> r; | |
1088 | for (unsigned int i = 0; i < N; i++) | |
1089 | POLY_SET_COEFF (C, r, i, NCa (a.coeffs[i]) << b); | |
1090 | return r; | |
1091 | } | |
1092 | ||
1093 | namespace wi { | |
1094 | /* Poly version of wi::lshift, with the same interface. */ | |
1095 | ||
1096 | template<unsigned int N, typename Ca, typename Cb> | |
1097 | inline poly_int<N, WI_BINARY_RESULT (Ca, Ca)> | |
eaa41a6d | 1098 | lshift (const poly_int<N, Ca> &a, const Cb &b) |
e535b963 RS |
1099 | { |
1100 | typedef WI_BINARY_RESULT (Ca, Ca) C; | |
1101 | poly_int<N, C> r; | |
1102 | for (unsigned int i = 0; i < N; i++) | |
1103 | POLY_SET_COEFF (C, r, i, wi::lshift (a.coeffs[i], b)); | |
1104 | return r; | |
1105 | } | |
1106 | } | |
1107 | ||
faabc751 RB |
1108 | /* Poly version of sext_hwi, with the same interface. */ |
1109 | ||
1110 | template<unsigned int N, typename C> | |
1111 | inline poly_int<N, HOST_WIDE_INT> | |
1112 | sext_hwi (const poly_int<N, C> &a, unsigned int precision) | |
1113 | { | |
eaa41a6d | 1114 | poly_int<N, HOST_WIDE_INT> r; |
faabc751 RB |
1115 | for (unsigned int i = 0; i < N; i++) |
1116 | r.coeffs[i] = sext_hwi (a.coeffs[i], precision); | |
1117 | return r; | |
1118 | } | |
1119 | ||
1120 | ||
e535b963 RS |
1121 | /* Return true if a0 + a1 * x might equal b0 + b1 * x for some nonnegative |
1122 | integer x. */ | |
1123 | ||
1124 | template<typename Ca, typename Cb> | |
1125 | inline bool | |
1126 | maybe_eq_2 (const Ca &a0, const Ca &a1, const Cb &b0, const Cb &b1) | |
1127 | { | |
1128 | if (a1 != b1) | |
1129 | /* a0 + a1 * x == b0 + b1 * x | |
1130 | ==> (a1 - b1) * x == b0 - a0 | |
1131 | ==> x == (b0 - a0) / (a1 - b1) | |
1132 | ||
1133 | We need to test whether that's a valid value of x. | |
1134 | (b0 - a0) and (a1 - b1) must not have opposite signs | |
1135 | and the result must be integral. */ | |
1136 | return (a1 < b1 | |
1137 | ? b0 <= a0 && (a0 - b0) % (b1 - a1) == 0 | |
1138 | : b0 >= a0 && (b0 - a0) % (a1 - b1) == 0); | |
1139 | return a0 == b0; | |
1140 | } | |
1141 | ||
1142 | /* Return true if a0 + a1 * x might equal b for some nonnegative | |
1143 | integer x. */ | |
1144 | ||
1145 | template<typename Ca, typename Cb> | |
1146 | inline bool | |
1147 | maybe_eq_2 (const Ca &a0, const Ca &a1, const Cb &b) | |
1148 | { | |
1149 | if (a1 != 0) | |
1150 | /* a0 + a1 * x == b | |
1151 | ==> x == (b - a0) / a1 | |
1152 | ||
1153 | We need to test whether that's a valid value of x. | |
1154 | (b - a0) and a1 must not have opposite signs and the | |
1155 | result must be integral. */ | |
1156 | return (a1 < 0 | |
1157 | ? b <= a0 && (a0 - b) % a1 == 0 | |
1158 | : b >= a0 && (b - a0) % a1 == 0); | |
1159 | return a0 == b; | |
1160 | } | |
1161 | ||
1162 | /* Return true if A might equal B for some indeterminate values. */ | |
1163 | ||
1164 | template<unsigned int N, typename Ca, typename Cb> | |
1165 | inline bool | |
eaa41a6d | 1166 | maybe_eq (const poly_int<N, Ca> &a, const poly_int<N, Cb> &b) |
e535b963 RS |
1167 | { |
1168 | STATIC_ASSERT (N <= 2); | |
1169 | if (N == 2) | |
1170 | return maybe_eq_2 (a.coeffs[0], a.coeffs[1], b.coeffs[0], b.coeffs[1]); | |
1171 | return a.coeffs[0] == b.coeffs[0]; | |
1172 | } | |
1173 | ||
1174 | template<unsigned int N, typename Ca, typename Cb> | |
1175 | inline typename if_nonpoly<Cb, bool>::type | |
eaa41a6d | 1176 | maybe_eq (const poly_int<N, Ca> &a, const Cb &b) |
e535b963 RS |
1177 | { |
1178 | STATIC_ASSERT (N <= 2); | |
1179 | if (N == 2) | |
1180 | return maybe_eq_2 (a.coeffs[0], a.coeffs[1], b); | |
1181 | return a.coeffs[0] == b; | |
1182 | } | |
1183 | ||
1184 | template<unsigned int N, typename Ca, typename Cb> | |
1185 | inline typename if_nonpoly<Ca, bool>::type | |
eaa41a6d | 1186 | maybe_eq (const Ca &a, const poly_int<N, Cb> &b) |
e535b963 RS |
1187 | { |
1188 | STATIC_ASSERT (N <= 2); | |
1189 | if (N == 2) | |
1190 | return maybe_eq_2 (b.coeffs[0], b.coeffs[1], a); | |
1191 | return a == b.coeffs[0]; | |
1192 | } | |
1193 | ||
1194 | template<typename Ca, typename Cb> | |
1195 | inline typename if_nonpoly2<Ca, Cb, bool>::type | |
1196 | maybe_eq (const Ca &a, const Cb &b) | |
1197 | { | |
1198 | return a == b; | |
1199 | } | |
1200 | ||
1201 | /* Return true if A might not equal B for some indeterminate values. */ | |
1202 | ||
1203 | template<unsigned int N, typename Ca, typename Cb> | |
1204 | inline bool | |
eaa41a6d | 1205 | maybe_ne (const poly_int<N, Ca> &a, const poly_int<N, Cb> &b) |
e535b963 RS |
1206 | { |
1207 | if (N >= 2) | |
1208 | for (unsigned int i = 1; i < N; i++) | |
1209 | if (a.coeffs[i] != b.coeffs[i]) | |
1210 | return true; | |
1211 | return a.coeffs[0] != b.coeffs[0]; | |
1212 | } | |
1213 | ||
1214 | template<unsigned int N, typename Ca, typename Cb> | |
1215 | inline typename if_nonpoly<Cb, bool>::type | |
eaa41a6d | 1216 | maybe_ne (const poly_int<N, Ca> &a, const Cb &b) |
e535b963 RS |
1217 | { |
1218 | if (N >= 2) | |
1219 | for (unsigned int i = 1; i < N; i++) | |
1220 | if (a.coeffs[i] != 0) | |
1221 | return true; | |
1222 | return a.coeffs[0] != b; | |
1223 | } | |
1224 | ||
1225 | template<unsigned int N, typename Ca, typename Cb> | |
1226 | inline typename if_nonpoly<Ca, bool>::type | |
eaa41a6d | 1227 | maybe_ne (const Ca &a, const poly_int<N, Cb> &b) |
e535b963 RS |
1228 | { |
1229 | if (N >= 2) | |
1230 | for (unsigned int i = 1; i < N; i++) | |
01512446 | 1231 | if (b.coeffs[i] != 0) |
e535b963 RS |
1232 | return true; |
1233 | return a != b.coeffs[0]; | |
1234 | } | |
1235 | ||
1236 | template<typename Ca, typename Cb> | |
1237 | inline typename if_nonpoly2<Ca, Cb, bool>::type | |
1238 | maybe_ne (const Ca &a, const Cb &b) | |
1239 | { | |
1240 | return a != b; | |
1241 | } | |
1242 | ||
1243 | /* Return true if A is known to be equal to B. */ | |
1244 | #define known_eq(A, B) (!maybe_ne (A, B)) | |
1245 | ||
1246 | /* Return true if A is known to be unequal to B. */ | |
1247 | #define known_ne(A, B) (!maybe_eq (A, B)) | |
1248 | ||
1249 | /* Return true if A might be less than or equal to B for some | |
1250 | indeterminate values. */ | |
1251 | ||
1252 | template<unsigned int N, typename Ca, typename Cb> | |
1253 | inline bool | |
eaa41a6d | 1254 | maybe_le (const poly_int<N, Ca> &a, const poly_int<N, Cb> &b) |
e535b963 RS |
1255 | { |
1256 | if (N >= 2) | |
1257 | for (unsigned int i = 1; i < N; i++) | |
1258 | if (a.coeffs[i] < b.coeffs[i]) | |
1259 | return true; | |
1260 | return a.coeffs[0] <= b.coeffs[0]; | |
1261 | } | |
1262 | ||
1263 | template<unsigned int N, typename Ca, typename Cb> | |
1264 | inline typename if_nonpoly<Cb, bool>::type | |
eaa41a6d | 1265 | maybe_le (const poly_int<N, Ca> &a, const Cb &b) |
e535b963 RS |
1266 | { |
1267 | if (N >= 2) | |
1268 | for (unsigned int i = 1; i < N; i++) | |
1269 | if (a.coeffs[i] < 0) | |
1270 | return true; | |
1271 | return a.coeffs[0] <= b; | |
1272 | } | |
1273 | ||
1274 | template<unsigned int N, typename Ca, typename Cb> | |
1275 | inline typename if_nonpoly<Ca, bool>::type | |
eaa41a6d | 1276 | maybe_le (const Ca &a, const poly_int<N, Cb> &b) |
e535b963 RS |
1277 | { |
1278 | if (N >= 2) | |
1279 | for (unsigned int i = 1; i < N; i++) | |
01512446 | 1280 | if (b.coeffs[i] > 0) |
e535b963 RS |
1281 | return true; |
1282 | return a <= b.coeffs[0]; | |
1283 | } | |
1284 | ||
1285 | template<typename Ca, typename Cb> | |
1286 | inline typename if_nonpoly2<Ca, Cb, bool>::type | |
1287 | maybe_le (const Ca &a, const Cb &b) | |
1288 | { | |
1289 | return a <= b; | |
1290 | } | |
1291 | ||
1292 | /* Return true if A might be less than B for some indeterminate values. */ | |
1293 | ||
1294 | template<unsigned int N, typename Ca, typename Cb> | |
1295 | inline bool | |
eaa41a6d | 1296 | maybe_lt (const poly_int<N, Ca> &a, const poly_int<N, Cb> &b) |
e535b963 RS |
1297 | { |
1298 | if (N >= 2) | |
1299 | for (unsigned int i = 1; i < N; i++) | |
1300 | if (a.coeffs[i] < b.coeffs[i]) | |
1301 | return true; | |
1302 | return a.coeffs[0] < b.coeffs[0]; | |
1303 | } | |
1304 | ||
1305 | template<unsigned int N, typename Ca, typename Cb> | |
1306 | inline typename if_nonpoly<Cb, bool>::type | |
eaa41a6d | 1307 | maybe_lt (const poly_int<N, Ca> &a, const Cb &b) |
e535b963 RS |
1308 | { |
1309 | if (N >= 2) | |
1310 | for (unsigned int i = 1; i < N; i++) | |
1311 | if (a.coeffs[i] < 0) | |
1312 | return true; | |
1313 | return a.coeffs[0] < b; | |
1314 | } | |
1315 | ||
1316 | template<unsigned int N, typename Ca, typename Cb> | |
1317 | inline typename if_nonpoly<Ca, bool>::type | |
eaa41a6d | 1318 | maybe_lt (const Ca &a, const poly_int<N, Cb> &b) |
e535b963 RS |
1319 | { |
1320 | if (N >= 2) | |
1321 | for (unsigned int i = 1; i < N; i++) | |
01512446 | 1322 | if (b.coeffs[i] > 0) |
e535b963 RS |
1323 | return true; |
1324 | return a < b.coeffs[0]; | |
1325 | } | |
1326 | ||
1327 | template<typename Ca, typename Cb> | |
1328 | inline typename if_nonpoly2<Ca, Cb, bool>::type | |
1329 | maybe_lt (const Ca &a, const Cb &b) | |
1330 | { | |
1331 | return a < b; | |
1332 | } | |
1333 | ||
1334 | /* Return true if A may be greater than or equal to B. */ | |
1335 | #define maybe_ge(A, B) maybe_le (B, A) | |
1336 | ||
1337 | /* Return true if A may be greater than B. */ | |
1338 | #define maybe_gt(A, B) maybe_lt (B, A) | |
1339 | ||
1340 | /* Return true if A is known to be less than or equal to B. */ | |
1341 | #define known_le(A, B) (!maybe_gt (A, B)) | |
1342 | ||
1343 | /* Return true if A is known to be less than B. */ | |
1344 | #define known_lt(A, B) (!maybe_ge (A, B)) | |
1345 | ||
1346 | /* Return true if A is known to be greater than B. */ | |
1347 | #define known_gt(A, B) (!maybe_le (A, B)) | |
1348 | ||
1349 | /* Return true if A is known to be greater than or equal to B. */ | |
1350 | #define known_ge(A, B) (!maybe_lt (A, B)) | |
1351 | ||
1352 | /* Return true if A and B are ordered by the partial ordering known_le. */ | |
1353 | ||
1354 | template<typename T1, typename T2> | |
1355 | inline bool | |
1356 | ordered_p (const T1 &a, const T2 &b) | |
1357 | { | |
1358 | return ((poly_int_traits<T1>::num_coeffs == 1 | |
1359 | && poly_int_traits<T2>::num_coeffs == 1) | |
1360 | || known_le (a, b) | |
1361 | || known_le (b, a)); | |
1362 | } | |
1363 | ||
1364 | /* Assert that A and B are known to be ordered and return the minimum | |
1365 | of the two. | |
1366 | ||
1367 | NOTE: When using this function, please add a comment above the call | |
1368 | explaining why we know the values are ordered in that context. */ | |
1369 | ||
1370 | template<unsigned int N, typename Ca, typename Cb> | |
1371 | inline POLY_POLY_RESULT (N, Ca, Cb) | |
eaa41a6d | 1372 | ordered_min (const poly_int<N, Ca> &a, const poly_int<N, Cb> &b) |
e535b963 RS |
1373 | { |
1374 | if (known_le (a, b)) | |
1375 | return a; | |
1376 | else | |
1377 | { | |
1378 | if (N > 1) | |
1379 | gcc_checking_assert (known_le (b, a)); | |
1380 | return b; | |
1381 | } | |
1382 | } | |
1383 | ||
1384 | template<unsigned int N, typename Ca, typename Cb> | |
1385 | inline CONST_POLY_RESULT (N, Ca, Cb) | |
eaa41a6d | 1386 | ordered_min (const Ca &a, const poly_int<N, Cb> &b) |
e535b963 RS |
1387 | { |
1388 | if (known_le (a, b)) | |
1389 | return a; | |
1390 | else | |
1391 | { | |
1392 | if (N > 1) | |
1393 | gcc_checking_assert (known_le (b, a)); | |
1394 | return b; | |
1395 | } | |
1396 | } | |
1397 | ||
1398 | template<unsigned int N, typename Ca, typename Cb> | |
1399 | inline POLY_CONST_RESULT (N, Ca, Cb) | |
eaa41a6d | 1400 | ordered_min (const poly_int<N, Ca> &a, const Cb &b) |
e535b963 RS |
1401 | { |
1402 | if (known_le (a, b)) | |
1403 | return a; | |
1404 | else | |
1405 | { | |
1406 | if (N > 1) | |
1407 | gcc_checking_assert (known_le (b, a)); | |
1408 | return b; | |
1409 | } | |
1410 | } | |
1411 | ||
1412 | /* Assert that A and B are known to be ordered and return the maximum | |
1413 | of the two. | |
1414 | ||
1415 | NOTE: When using this function, please add a comment above the call | |
1416 | explaining why we know the values are ordered in that context. */ | |
1417 | ||
1418 | template<unsigned int N, typename Ca, typename Cb> | |
1419 | inline POLY_POLY_RESULT (N, Ca, Cb) | |
eaa41a6d | 1420 | ordered_max (const poly_int<N, Ca> &a, const poly_int<N, Cb> &b) |
e535b963 RS |
1421 | { |
1422 | if (known_le (a, b)) | |
1423 | return b; | |
1424 | else | |
1425 | { | |
1426 | if (N > 1) | |
1427 | gcc_checking_assert (known_le (b, a)); | |
1428 | return a; | |
1429 | } | |
1430 | } | |
1431 | ||
1432 | template<unsigned int N, typename Ca, typename Cb> | |
1433 | inline CONST_POLY_RESULT (N, Ca, Cb) | |
eaa41a6d | 1434 | ordered_max (const Ca &a, const poly_int<N, Cb> &b) |
e535b963 RS |
1435 | { |
1436 | if (known_le (a, b)) | |
1437 | return b; | |
1438 | else | |
1439 | { | |
1440 | if (N > 1) | |
1441 | gcc_checking_assert (known_le (b, a)); | |
1442 | return a; | |
1443 | } | |
1444 | } | |
1445 | ||
1446 | template<unsigned int N, typename Ca, typename Cb> | |
1447 | inline POLY_CONST_RESULT (N, Ca, Cb) | |
eaa41a6d | 1448 | ordered_max (const poly_int<N, Ca> &a, const Cb &b) |
e535b963 RS |
1449 | { |
1450 | if (known_le (a, b)) | |
1451 | return b; | |
1452 | else | |
1453 | { | |
1454 | if (N > 1) | |
1455 | gcc_checking_assert (known_le (b, a)); | |
1456 | return a; | |
1457 | } | |
1458 | } | |
1459 | ||
1460 | /* Return a constant lower bound on the value of A, which is known | |
1461 | to be nonnegative. */ | |
1462 | ||
1463 | template<unsigned int N, typename Ca> | |
1464 | inline Ca | |
eaa41a6d | 1465 | constant_lower_bound (const poly_int<N, Ca> &a) |
e535b963 RS |
1466 | { |
1467 | gcc_checking_assert (known_ge (a, POLY_INT_TYPE (Ca) (0))); | |
1468 | return a.coeffs[0]; | |
1469 | } | |
1470 | ||
96eb7d7a RS |
1471 | /* Return the constant lower bound of A, given that it is no less than B. */ |
1472 | ||
1473 | template<unsigned int N, typename Ca, typename Cb> | |
1474 | inline POLY_CONST_COEFF (Ca, Cb) | |
eaa41a6d | 1475 | constant_lower_bound_with_limit (const poly_int<N, Ca> &a, const Cb &b) |
96eb7d7a RS |
1476 | { |
1477 | if (known_ge (a, b)) | |
1478 | return a.coeffs[0]; | |
1479 | return b; | |
1480 | } | |
1481 | ||
1482 | /* Return the constant upper bound of A, given that it is no greater | |
1483 | than B. */ | |
1484 | ||
1485 | template<unsigned int N, typename Ca, typename Cb> | |
1486 | inline POLY_CONST_COEFF (Ca, Cb) | |
eaa41a6d | 1487 | constant_upper_bound_with_limit (const poly_int<N, Ca> &a, const Cb &b) |
96eb7d7a RS |
1488 | { |
1489 | if (known_le (a, b)) | |
1490 | return a.coeffs[0]; | |
1491 | return b; | |
1492 | } | |
1493 | ||
e535b963 RS |
1494 | /* Return a value that is known to be no greater than A and B. This |
1495 | will be the greatest lower bound for some indeterminate values but | |
1496 | not necessarily for all. */ | |
1497 | ||
1498 | template<unsigned int N, typename Ca, typename Cb> | |
1499 | inline POLY_CONST_RESULT (N, Ca, Cb) | |
eaa41a6d | 1500 | lower_bound (const poly_int<N, Ca> &a, const Cb &b) |
e535b963 RS |
1501 | { |
1502 | typedef POLY_CAST (Ca, Cb) NCa; | |
1503 | typedef POLY_CAST (Cb, Ca) NCb; | |
1504 | typedef POLY_INT_TYPE (Cb) ICb; | |
1505 | typedef POLY_CONST_COEFF (Ca, Cb) C; | |
1506 | ||
1507 | poly_int<N, C> r; | |
1508 | POLY_SET_COEFF (C, r, 0, MIN (NCa (a.coeffs[0]), NCb (b))); | |
1509 | if (N >= 2) | |
1510 | for (unsigned int i = 1; i < N; i++) | |
1511 | POLY_SET_COEFF (C, r, i, MIN (NCa (a.coeffs[i]), ICb (0))); | |
1512 | return r; | |
1513 | } | |
1514 | ||
1515 | template<unsigned int N, typename Ca, typename Cb> | |
1516 | inline CONST_POLY_RESULT (N, Ca, Cb) | |
eaa41a6d | 1517 | lower_bound (const Ca &a, const poly_int<N, Cb> &b) |
e535b963 RS |
1518 | { |
1519 | return lower_bound (b, a); | |
1520 | } | |
1521 | ||
1522 | template<unsigned int N, typename Ca, typename Cb> | |
1523 | inline POLY_POLY_RESULT (N, Ca, Cb) | |
eaa41a6d | 1524 | lower_bound (const poly_int<N, Ca> &a, const poly_int<N, Cb> &b) |
e535b963 RS |
1525 | { |
1526 | typedef POLY_CAST (Ca, Cb) NCa; | |
1527 | typedef POLY_CAST (Cb, Ca) NCb; | |
1528 | typedef POLY_POLY_COEFF (Ca, Cb) C; | |
1529 | ||
1530 | poly_int<N, C> r; | |
1531 | for (unsigned int i = 0; i < N; i++) | |
1532 | POLY_SET_COEFF (C, r, i, MIN (NCa (a.coeffs[i]), NCb (b.coeffs[i]))); | |
1533 | return r; | |
1534 | } | |
1535 | ||
1536 | template<typename Ca, typename Cb> | |
1537 | inline CONST_CONST_RESULT (N, Ca, Cb) | |
1538 | lower_bound (const Ca &a, const Cb &b) | |
1539 | { | |
1540 | return a < b ? a : b; | |
1541 | } | |
1542 | ||
1543 | /* Return a value that is known to be no less than A and B. This will | |
1544 | be the least upper bound for some indeterminate values but not | |
1545 | necessarily for all. */ | |
1546 | ||
1547 | template<unsigned int N, typename Ca, typename Cb> | |
1548 | inline POLY_CONST_RESULT (N, Ca, Cb) | |
eaa41a6d | 1549 | upper_bound (const poly_int<N, Ca> &a, const Cb &b) |
e535b963 RS |
1550 | { |
1551 | typedef POLY_CAST (Ca, Cb) NCa; | |
1552 | typedef POLY_CAST (Cb, Ca) NCb; | |
1553 | typedef POLY_INT_TYPE (Cb) ICb; | |
1554 | typedef POLY_CONST_COEFF (Ca, Cb) C; | |
1555 | ||
1556 | poly_int<N, C> r; | |
1557 | POLY_SET_COEFF (C, r, 0, MAX (NCa (a.coeffs[0]), NCb (b))); | |
1558 | if (N >= 2) | |
1559 | for (unsigned int i = 1; i < N; i++) | |
1560 | POLY_SET_COEFF (C, r, i, MAX (NCa (a.coeffs[i]), ICb (0))); | |
1561 | return r; | |
1562 | } | |
1563 | ||
1564 | template<unsigned int N, typename Ca, typename Cb> | |
1565 | inline CONST_POLY_RESULT (N, Ca, Cb) | |
eaa41a6d | 1566 | upper_bound (const Ca &a, const poly_int<N, Cb> &b) |
e535b963 RS |
1567 | { |
1568 | return upper_bound (b, a); | |
1569 | } | |
1570 | ||
1571 | template<unsigned int N, typename Ca, typename Cb> | |
1572 | inline POLY_POLY_RESULT (N, Ca, Cb) | |
eaa41a6d | 1573 | upper_bound (const poly_int<N, Ca> &a, const poly_int<N, Cb> &b) |
e535b963 RS |
1574 | { |
1575 | typedef POLY_CAST (Ca, Cb) NCa; | |
1576 | typedef POLY_CAST (Cb, Ca) NCb; | |
1577 | typedef POLY_POLY_COEFF (Ca, Cb) C; | |
1578 | ||
1579 | poly_int<N, C> r; | |
1580 | for (unsigned int i = 0; i < N; i++) | |
1581 | POLY_SET_COEFF (C, r, i, MAX (NCa (a.coeffs[i]), NCb (b.coeffs[i]))); | |
1582 | return r; | |
1583 | } | |
1584 | ||
1585 | /* Return the greatest common divisor of all nonzero coefficients, or zero | |
1586 | if all coefficients are zero. */ | |
1587 | ||
1588 | template<unsigned int N, typename Ca> | |
1589 | inline POLY_BINARY_COEFF (Ca, Ca) | |
eaa41a6d | 1590 | coeff_gcd (const poly_int<N, Ca> &a) |
e535b963 RS |
1591 | { |
1592 | /* Find the first nonzero coefficient, stopping at 0 whatever happens. */ | |
1593 | unsigned int i; | |
1594 | for (i = N - 1; i > 0; --i) | |
1595 | if (a.coeffs[i] != 0) | |
1596 | break; | |
1597 | typedef POLY_BINARY_COEFF (Ca, Ca) C; | |
1598 | C r = a.coeffs[i]; | |
1599 | for (unsigned int j = 0; j < i; ++j) | |
1600 | if (a.coeffs[j] != 0) | |
1601 | r = gcd (r, C (a.coeffs[j])); | |
1602 | return r; | |
1603 | } | |
1604 | ||
1605 | /* Return a value that is a multiple of both A and B. This will be the | |
1606 | least common multiple for some indeterminate values but necessarily | |
1607 | for all. */ | |
1608 | ||
1609 | template<unsigned int N, typename Ca, typename Cb> | |
1610 | POLY_CONST_RESULT (N, Ca, Cb) | |
eaa41a6d | 1611 | common_multiple (const poly_int<N, Ca> &a, Cb b) |
e535b963 RS |
1612 | { |
1613 | POLY_BINARY_COEFF (Ca, Ca) xgcd = coeff_gcd (a); | |
1614 | return a * (least_common_multiple (xgcd, b) / xgcd); | |
1615 | } | |
1616 | ||
1617 | template<unsigned int N, typename Ca, typename Cb> | |
1618 | inline CONST_POLY_RESULT (N, Ca, Cb) | |
eaa41a6d | 1619 | common_multiple (const Ca &a, const poly_int<N, Cb> &b) |
e535b963 RS |
1620 | { |
1621 | return common_multiple (b, a); | |
1622 | } | |
1623 | ||
1624 | /* Return a value that is a multiple of both A and B, asserting that | |
1625 | such a value exists. The result will be the least common multiple | |
1626 | for some indeterminate values but necessarily for all. | |
1627 | ||
1628 | NOTE: When using this function, please add a comment above the call | |
1629 | explaining why we know the values have a common multiple (which might | |
1630 | for example be because we know A / B is rational). */ | |
1631 | ||
1632 | template<unsigned int N, typename Ca, typename Cb> | |
1633 | POLY_POLY_RESULT (N, Ca, Cb) | |
eaa41a6d | 1634 | force_common_multiple (const poly_int<N, Ca> &a, const poly_int<N, Cb> &b) |
e535b963 RS |
1635 | { |
1636 | if (b.is_constant ()) | |
1637 | return common_multiple (a, b.coeffs[0]); | |
1638 | if (a.is_constant ()) | |
1639 | return common_multiple (a.coeffs[0], b); | |
1640 | ||
1641 | typedef POLY_CAST (Ca, Cb) NCa; | |
1642 | typedef POLY_CAST (Cb, Ca) NCb; | |
1643 | typedef POLY_BINARY_COEFF (Ca, Cb) C; | |
1644 | typedef POLY_INT_TYPE (Ca) ICa; | |
1645 | ||
1646 | for (unsigned int i = 1; i < N; ++i) | |
1647 | if (a.coeffs[i] != ICa (0)) | |
1648 | { | |
1649 | C lcm = least_common_multiple (NCa (a.coeffs[i]), NCb (b.coeffs[i])); | |
1650 | C amul = lcm / a.coeffs[i]; | |
1651 | C bmul = lcm / b.coeffs[i]; | |
1652 | for (unsigned int j = 0; j < N; ++j) | |
1653 | gcc_checking_assert (a.coeffs[j] * amul == b.coeffs[j] * bmul); | |
1654 | return a * amul; | |
1655 | } | |
1656 | gcc_unreachable (); | |
1657 | } | |
1658 | ||
1659 | /* Compare A and B for sorting purposes, returning -1 if A should come | |
1660 | before B, 0 if A and B are identical, and 1 if A should come after B. | |
1661 | This is a lexicographical compare of the coefficients in reverse order. | |
1662 | ||
1663 | A consequence of this is that all constant sizes come before all | |
1664 | non-constant ones, regardless of magnitude (since a size is never | |
1665 | negative). This is what most callers want. For example, when laying | |
1666 | data out on the stack, it's better to keep all the constant-sized | |
1667 | data together so that it can be accessed as a constant offset from a | |
1668 | single base. */ | |
1669 | ||
1670 | template<unsigned int N, typename Ca, typename Cb> | |
1671 | inline int | |
eaa41a6d | 1672 | compare_sizes_for_sort (const poly_int<N, Ca> &a, const poly_int<N, Cb> &b) |
e535b963 RS |
1673 | { |
1674 | for (unsigned int i = N; i-- > 0; ) | |
1675 | if (a.coeffs[i] != b.coeffs[i]) | |
1676 | return a.coeffs[i] < b.coeffs[i] ? -1 : 1; | |
1677 | return 0; | |
1678 | } | |
1679 | ||
1680 | /* Return true if we can calculate VALUE & (ALIGN - 1) at compile time. */ | |
1681 | ||
1682 | template<unsigned int N, typename Ca, typename Cb> | |
1683 | inline bool | |
eaa41a6d | 1684 | can_align_p (const poly_int<N, Ca> &value, Cb align) |
e535b963 RS |
1685 | { |
1686 | for (unsigned int i = 1; i < N; i++) | |
1687 | if ((value.coeffs[i] & (align - 1)) != 0) | |
1688 | return false; | |
1689 | return true; | |
1690 | } | |
1691 | ||
1692 | /* Return true if we can align VALUE up to the smallest multiple of | |
1693 | ALIGN that is >= VALUE. Store the aligned value in *ALIGNED if so. */ | |
1694 | ||
1695 | template<unsigned int N, typename Ca, typename Cb> | |
1696 | inline bool | |
eaa41a6d RS |
1697 | can_align_up (const poly_int<N, Ca> &value, Cb align, |
1698 | poly_int<N, Ca> *aligned) | |
e535b963 RS |
1699 | { |
1700 | if (!can_align_p (value, align)) | |
1701 | return false; | |
1702 | *aligned = value + (-value.coeffs[0] & (align - 1)); | |
1703 | return true; | |
1704 | } | |
1705 | ||
1706 | /* Return true if we can align VALUE down to the largest multiple of | |
1707 | ALIGN that is <= VALUE. Store the aligned value in *ALIGNED if so. */ | |
1708 | ||
1709 | template<unsigned int N, typename Ca, typename Cb> | |
1710 | inline bool | |
eaa41a6d RS |
1711 | can_align_down (const poly_int<N, Ca> &value, Cb align, |
1712 | poly_int<N, Ca> *aligned) | |
e535b963 RS |
1713 | { |
1714 | if (!can_align_p (value, align)) | |
1715 | return false; | |
1716 | *aligned = value - (value.coeffs[0] & (align - 1)); | |
1717 | return true; | |
1718 | } | |
1719 | ||
1720 | /* Return true if we can align A and B up to the smallest multiples of | |
1721 | ALIGN that are >= A and B respectively, and if doing so gives the | |
1722 | same value. */ | |
1723 | ||
1724 | template<unsigned int N, typename Ca, typename Cb, typename Cc> | |
1725 | inline bool | |
eaa41a6d RS |
1726 | known_equal_after_align_up (const poly_int<N, Ca> &a, |
1727 | const poly_int<N, Cb> &b, | |
e535b963 RS |
1728 | Cc align) |
1729 | { | |
1730 | poly_int<N, Ca> aligned_a; | |
1731 | poly_int<N, Cb> aligned_b; | |
1732 | return (can_align_up (a, align, &aligned_a) | |
1733 | && can_align_up (b, align, &aligned_b) | |
1734 | && known_eq (aligned_a, aligned_b)); | |
1735 | } | |
1736 | ||
1737 | /* Return true if we can align A and B down to the largest multiples of | |
1738 | ALIGN that are <= A and B respectively, and if doing so gives the | |
1739 | same value. */ | |
1740 | ||
1741 | template<unsigned int N, typename Ca, typename Cb, typename Cc> | |
1742 | inline bool | |
eaa41a6d RS |
1743 | known_equal_after_align_down (const poly_int<N, Ca> &a, |
1744 | const poly_int<N, Cb> &b, | |
e535b963 RS |
1745 | Cc align) |
1746 | { | |
1747 | poly_int<N, Ca> aligned_a; | |
1748 | poly_int<N, Cb> aligned_b; | |
1749 | return (can_align_down (a, align, &aligned_a) | |
1750 | && can_align_down (b, align, &aligned_b) | |
1751 | && known_eq (aligned_a, aligned_b)); | |
1752 | } | |
1753 | ||
1754 | /* Assert that we can align VALUE to ALIGN at compile time and return | |
1755 | the smallest multiple of ALIGN that is >= VALUE. | |
1756 | ||
1757 | NOTE: When using this function, please add a comment above the call | |
1758 | explaining why we know the non-constant coefficients must already | |
1759 | be a multiple of ALIGN. */ | |
1760 | ||
1761 | template<unsigned int N, typename Ca, typename Cb> | |
1762 | inline poly_int<N, Ca> | |
eaa41a6d | 1763 | force_align_up (const poly_int<N, Ca> &value, Cb align) |
e535b963 RS |
1764 | { |
1765 | gcc_checking_assert (can_align_p (value, align)); | |
1766 | return value + (-value.coeffs[0] & (align - 1)); | |
1767 | } | |
1768 | ||
1769 | /* Assert that we can align VALUE to ALIGN at compile time and return | |
1770 | the largest multiple of ALIGN that is <= VALUE. | |
1771 | ||
1772 | NOTE: When using this function, please add a comment above the call | |
1773 | explaining why we know the non-constant coefficients must already | |
1774 | be a multiple of ALIGN. */ | |
1775 | ||
1776 | template<unsigned int N, typename Ca, typename Cb> | |
1777 | inline poly_int<N, Ca> | |
eaa41a6d | 1778 | force_align_down (const poly_int<N, Ca> &value, Cb align) |
e535b963 RS |
1779 | { |
1780 | gcc_checking_assert (can_align_p (value, align)); | |
1781 | return value - (value.coeffs[0] & (align - 1)); | |
1782 | } | |
1783 | ||
1784 | /* Return a value <= VALUE that is a multiple of ALIGN. It will be the | |
1785 | greatest such value for some indeterminate values but not necessarily | |
1786 | for all. */ | |
1787 | ||
1788 | template<unsigned int N, typename Ca, typename Cb> | |
1789 | inline poly_int<N, Ca> | |
eaa41a6d | 1790 | aligned_lower_bound (const poly_int<N, Ca> &value, Cb align) |
e535b963 RS |
1791 | { |
1792 | poly_int<N, Ca> r; | |
1793 | for (unsigned int i = 0; i < N; i++) | |
1794 | /* This form copes correctly with more type combinations than | |
1795 | value.coeffs[i] & -align would. */ | |
1796 | POLY_SET_COEFF (Ca, r, i, (value.coeffs[i] | |
1797 | - (value.coeffs[i] & (align - 1)))); | |
1798 | return r; | |
1799 | } | |
1800 | ||
1801 | /* Return a value >= VALUE that is a multiple of ALIGN. It will be the | |
1802 | least such value for some indeterminate values but not necessarily | |
1803 | for all. */ | |
1804 | ||
1805 | template<unsigned int N, typename Ca, typename Cb> | |
1806 | inline poly_int<N, Ca> | |
eaa41a6d | 1807 | aligned_upper_bound (const poly_int<N, Ca> &value, Cb align) |
e535b963 RS |
1808 | { |
1809 | poly_int<N, Ca> r; | |
1810 | for (unsigned int i = 0; i < N; i++) | |
1811 | POLY_SET_COEFF (Ca, r, i, (value.coeffs[i] | |
1812 | + (-value.coeffs[i] & (align - 1)))); | |
1813 | return r; | |
1814 | } | |
1815 | ||
1816 | /* Assert that we can align VALUE to ALIGN at compile time. Align VALUE | |
1817 | down to the largest multiple of ALIGN that is <= VALUE, then divide by | |
1818 | ALIGN. | |
1819 | ||
1820 | NOTE: When using this function, please add a comment above the call | |
1821 | explaining why we know the non-constant coefficients must already | |
1822 | be a multiple of ALIGN. */ | |
1823 | ||
1824 | template<unsigned int N, typename Ca, typename Cb> | |
1825 | inline poly_int<N, Ca> | |
eaa41a6d | 1826 | force_align_down_and_div (const poly_int<N, Ca> &value, Cb align) |
e535b963 RS |
1827 | { |
1828 | gcc_checking_assert (can_align_p (value, align)); | |
1829 | ||
1830 | poly_int<N, Ca> r; | |
1831 | POLY_SET_COEFF (Ca, r, 0, ((value.coeffs[0] | |
1832 | - (value.coeffs[0] & (align - 1))) | |
1833 | / align)); | |
1834 | if (N >= 2) | |
1835 | for (unsigned int i = 1; i < N; i++) | |
1836 | POLY_SET_COEFF (Ca, r, i, value.coeffs[i] / align); | |
1837 | return r; | |
1838 | } | |
1839 | ||
1840 | /* Assert that we can align VALUE to ALIGN at compile time. Align VALUE | |
1841 | up to the smallest multiple of ALIGN that is >= VALUE, then divide by | |
1842 | ALIGN. | |
1843 | ||
1844 | NOTE: When using this function, please add a comment above the call | |
1845 | explaining why we know the non-constant coefficients must already | |
1846 | be a multiple of ALIGN. */ | |
1847 | ||
1848 | template<unsigned int N, typename Ca, typename Cb> | |
1849 | inline poly_int<N, Ca> | |
eaa41a6d | 1850 | force_align_up_and_div (const poly_int<N, Ca> &value, Cb align) |
e535b963 RS |
1851 | { |
1852 | gcc_checking_assert (can_align_p (value, align)); | |
1853 | ||
1854 | poly_int<N, Ca> r; | |
1855 | POLY_SET_COEFF (Ca, r, 0, ((value.coeffs[0] | |
1856 | + (-value.coeffs[0] & (align - 1))) | |
1857 | / align)); | |
1858 | if (N >= 2) | |
1859 | for (unsigned int i = 1; i < N; i++) | |
1860 | POLY_SET_COEFF (Ca, r, i, value.coeffs[i] / align); | |
1861 | return r; | |
1862 | } | |
1863 | ||
1864 | /* Return true if we know at compile time the difference between VALUE | |
1865 | and the equal or preceding multiple of ALIGN. Store the value in | |
1866 | *MISALIGN if so. */ | |
1867 | ||
1868 | template<unsigned int N, typename Ca, typename Cb, typename Cm> | |
1869 | inline bool | |
eaa41a6d | 1870 | known_misalignment (const poly_int<N, Ca> &value, Cb align, Cm *misalign) |
e535b963 RS |
1871 | { |
1872 | gcc_checking_assert (align != 0); | |
1873 | if (!can_align_p (value, align)) | |
1874 | return false; | |
1875 | *misalign = value.coeffs[0] & (align - 1); | |
1876 | return true; | |
1877 | } | |
1878 | ||
1879 | /* Return X & (Y - 1), asserting that this value is known. Please add | |
1880 | an a comment above callers to this function to explain why the condition | |
1881 | is known to hold. */ | |
1882 | ||
1883 | template<unsigned int N, typename Ca, typename Cb> | |
1884 | inline POLY_BINARY_COEFF (Ca, Ca) | |
eaa41a6d | 1885 | force_get_misalignment (const poly_int<N, Ca> &a, Cb align) |
e535b963 RS |
1886 | { |
1887 | gcc_checking_assert (can_align_p (a, align)); | |
1888 | return a.coeffs[0] & (align - 1); | |
1889 | } | |
1890 | ||
1891 | /* Return the maximum alignment that A is known to have. Return 0 | |
1892 | if A is known to be zero. */ | |
1893 | ||
1894 | template<unsigned int N, typename Ca> | |
1895 | inline POLY_BINARY_COEFF (Ca, Ca) | |
eaa41a6d | 1896 | known_alignment (const poly_int<N, Ca> &a) |
e535b963 RS |
1897 | { |
1898 | typedef POLY_BINARY_COEFF (Ca, Ca) C; | |
1899 | C r = a.coeffs[0]; | |
1900 | for (unsigned int i = 1; i < N; ++i) | |
1901 | r |= a.coeffs[i]; | |
1902 | return r & -r; | |
1903 | } | |
1904 | ||
1905 | /* Return true if we can compute A | B at compile time, storing the | |
1906 | result in RES if so. */ | |
1907 | ||
1908 | template<unsigned int N, typename Ca, typename Cb, typename Cr> | |
1909 | inline typename if_nonpoly<Cb, bool>::type | |
eaa41a6d | 1910 | can_ior_p (const poly_int<N, Ca> &a, Cb b, Cr *result) |
e535b963 RS |
1911 | { |
1912 | /* Coefficients 1 and above must be a multiple of something greater | |
1913 | than B. */ | |
1914 | typedef POLY_INT_TYPE (Ca) int_type; | |
1915 | if (N >= 2) | |
1916 | for (unsigned int i = 1; i < N; i++) | |
1917 | if ((-(a.coeffs[i] & -a.coeffs[i]) & b) != int_type (0)) | |
1918 | return false; | |
1919 | *result = a; | |
1920 | result->coeffs[0] |= b; | |
1921 | return true; | |
1922 | } | |
1923 | ||
1924 | /* Return true if A is a constant multiple of B, storing the | |
1925 | multiple in *MULTIPLE if so. */ | |
1926 | ||
1927 | template<unsigned int N, typename Ca, typename Cb, typename Cm> | |
1928 | inline typename if_nonpoly<Cb, bool>::type | |
eaa41a6d | 1929 | constant_multiple_p (const poly_int<N, Ca> &a, Cb b, Cm *multiple) |
e535b963 RS |
1930 | { |
1931 | typedef POLY_CAST (Ca, Cb) NCa; | |
1932 | typedef POLY_CAST (Cb, Ca) NCb; | |
1933 | ||
1934 | /* Do the modulus before the constant check, to catch divide by | |
1935 | zero errors. */ | |
1936 | if (NCa (a.coeffs[0]) % NCb (b) != 0 || !a.is_constant ()) | |
1937 | return false; | |
1938 | *multiple = NCa (a.coeffs[0]) / NCb (b); | |
1939 | return true; | |
1940 | } | |
1941 | ||
1942 | template<unsigned int N, typename Ca, typename Cb, typename Cm> | |
1943 | inline typename if_nonpoly<Ca, bool>::type | |
eaa41a6d | 1944 | constant_multiple_p (Ca a, const poly_int<N, Cb> &b, Cm *multiple) |
e535b963 RS |
1945 | { |
1946 | typedef POLY_CAST (Ca, Cb) NCa; | |
1947 | typedef POLY_CAST (Cb, Ca) NCb; | |
1948 | typedef POLY_INT_TYPE (Ca) int_type; | |
1949 | ||
1950 | /* Do the modulus before the constant check, to catch divide by | |
1951 | zero errors. */ | |
1952 | if (NCa (a) % NCb (b.coeffs[0]) != 0 | |
1953 | || (a != int_type (0) && !b.is_constant ())) | |
1954 | return false; | |
1955 | *multiple = NCa (a) / NCb (b.coeffs[0]); | |
1956 | return true; | |
1957 | } | |
1958 | ||
1959 | template<unsigned int N, typename Ca, typename Cb, typename Cm> | |
1960 | inline bool | |
eaa41a6d RS |
1961 | constant_multiple_p (const poly_int<N, Ca> &a, |
1962 | const poly_int<N, Cb> &b, Cm *multiple) | |
e535b963 RS |
1963 | { |
1964 | typedef POLY_CAST (Ca, Cb) NCa; | |
1965 | typedef POLY_CAST (Cb, Ca) NCb; | |
1966 | typedef POLY_INT_TYPE (Ca) ICa; | |
1967 | typedef POLY_INT_TYPE (Cb) ICb; | |
1968 | typedef POLY_BINARY_COEFF (Ca, Cb) C; | |
1969 | ||
1970 | if (NCa (a.coeffs[0]) % NCb (b.coeffs[0]) != 0) | |
1971 | return false; | |
1972 | ||
1973 | C r = NCa (a.coeffs[0]) / NCb (b.coeffs[0]); | |
1974 | for (unsigned int i = 1; i < N; ++i) | |
1975 | if (b.coeffs[i] == ICb (0) | |
1976 | ? a.coeffs[i] != ICa (0) | |
1977 | : (NCa (a.coeffs[i]) % NCb (b.coeffs[i]) != 0 | |
1978 | || NCa (a.coeffs[i]) / NCb (b.coeffs[i]) != r)) | |
1979 | return false; | |
1980 | ||
1981 | *multiple = r; | |
1982 | return true; | |
1983 | } | |
1984 | ||
abe93733 YY |
1985 | /* Return true if A is a constant multiple of B. */ |
1986 | ||
1987 | template<unsigned int N, typename Ca, typename Cb> | |
1988 | inline typename if_nonpoly<Cb, bool>::type | |
eaa41a6d | 1989 | constant_multiple_p (const poly_int<N, Ca> &a, Cb b) |
abe93733 YY |
1990 | { |
1991 | typedef POLY_CAST (Ca, Cb) NCa; | |
1992 | typedef POLY_CAST (Cb, Ca) NCb; | |
1993 | ||
1994 | /* Do the modulus before the constant check, to catch divide by | |
1995 | zero errors. */ | |
1996 | if (NCa (a.coeffs[0]) % NCb (b) != 0 || !a.is_constant ()) | |
1997 | return false; | |
1998 | return true; | |
1999 | } | |
2000 | ||
2001 | template<unsigned int N, typename Ca, typename Cb> | |
2002 | inline typename if_nonpoly<Ca, bool>::type | |
eaa41a6d | 2003 | constant_multiple_p (Ca a, const poly_int<N, Cb> &b) |
abe93733 YY |
2004 | { |
2005 | typedef POLY_CAST (Ca, Cb) NCa; | |
2006 | typedef POLY_CAST (Cb, Ca) NCb; | |
2007 | typedef POLY_INT_TYPE (Ca) int_type; | |
2008 | ||
2009 | /* Do the modulus before the constant check, to catch divide by | |
2010 | zero errors. */ | |
2011 | if (NCa (a) % NCb (b.coeffs[0]) != 0 | |
2012 | || (a != int_type (0) && !b.is_constant ())) | |
2013 | return false; | |
2014 | return true; | |
2015 | } | |
2016 | ||
2017 | template<unsigned int N, typename Ca, typename Cb> | |
2018 | inline bool | |
eaa41a6d | 2019 | constant_multiple_p (const poly_int<N, Ca> &a, const poly_int<N, Cb> &b) |
abe93733 YY |
2020 | { |
2021 | typedef POLY_CAST (Ca, Cb) NCa; | |
2022 | typedef POLY_CAST (Cb, Ca) NCb; | |
2023 | typedef POLY_INT_TYPE (Ca) ICa; | |
2024 | typedef POLY_INT_TYPE (Cb) ICb; | |
2025 | typedef POLY_BINARY_COEFF (Ca, Cb) C; | |
2026 | ||
2027 | if (NCa (a.coeffs[0]) % NCb (b.coeffs[0]) != 0) | |
2028 | return false; | |
2029 | ||
2030 | C r = NCa (a.coeffs[0]) / NCb (b.coeffs[0]); | |
2031 | for (unsigned int i = 1; i < N; ++i) | |
2032 | if (b.coeffs[i] == ICb (0) | |
2033 | ? a.coeffs[i] != ICa (0) | |
2034 | : (NCa (a.coeffs[i]) % NCb (b.coeffs[i]) != 0 | |
2035 | || NCa (a.coeffs[i]) / NCb (b.coeffs[i]) != r)) | |
2036 | return false; | |
2037 | return true; | |
2038 | } | |
2039 | ||
2040 | ||
e535b963 RS |
2041 | /* Return true if A is a multiple of B. */ |
2042 | ||
2043 | template<typename Ca, typename Cb> | |
2044 | inline typename if_nonpoly2<Ca, Cb, bool>::type | |
2045 | multiple_p (Ca a, Cb b) | |
2046 | { | |
27d229f7 | 2047 | return a % b == 0; |
e535b963 RS |
2048 | } |
2049 | ||
2050 | /* Return true if A is a (polynomial) multiple of B. */ | |
2051 | ||
2052 | template<unsigned int N, typename Ca, typename Cb> | |
2053 | inline typename if_nonpoly<Cb, bool>::type | |
eaa41a6d | 2054 | multiple_p (const poly_int<N, Ca> &a, Cb b) |
e535b963 RS |
2055 | { |
2056 | for (unsigned int i = 0; i < N; ++i) | |
2057 | if (a.coeffs[i] % b != 0) | |
2058 | return false; | |
2059 | return true; | |
2060 | } | |
2061 | ||
2062 | /* Return true if A is a (constant) multiple of B. */ | |
2063 | ||
2064 | template<unsigned int N, typename Ca, typename Cb> | |
2065 | inline typename if_nonpoly<Ca, bool>::type | |
eaa41a6d | 2066 | multiple_p (Ca a, const poly_int<N, Cb> &b) |
e535b963 RS |
2067 | { |
2068 | typedef POLY_INT_TYPE (Ca) int_type; | |
2069 | ||
2070 | /* Do the modulus before the constant check, to catch divide by | |
2071 | potential zeros. */ | |
2072 | return a % b.coeffs[0] == 0 && (a == int_type (0) || b.is_constant ()); | |
2073 | } | |
2074 | ||
2075 | /* Return true if A is a (polynomial) multiple of B. This handles cases | |
2076 | where either B is constant or the multiple is constant. */ | |
2077 | ||
2078 | template<unsigned int N, typename Ca, typename Cb> | |
2079 | inline bool | |
eaa41a6d | 2080 | multiple_p (const poly_int<N, Ca> &a, const poly_int<N, Cb> &b) |
e535b963 RS |
2081 | { |
2082 | if (b.is_constant ()) | |
2083 | return multiple_p (a, b.coeffs[0]); | |
2084 | POLY_BINARY_COEFF (Ca, Ca) tmp; | |
2085 | return constant_multiple_p (a, b, &tmp); | |
2086 | } | |
2087 | ||
2088 | /* Return true if A is a (constant) multiple of B, storing the | |
2089 | multiple in *MULTIPLE if so. */ | |
2090 | ||
2091 | template<typename Ca, typename Cb, typename Cm> | |
2092 | inline typename if_nonpoly2<Ca, Cb, bool>::type | |
2093 | multiple_p (Ca a, Cb b, Cm *multiple) | |
2094 | { | |
2095 | if (a % b != 0) | |
2096 | return false; | |
2097 | *multiple = a / b; | |
2098 | return true; | |
2099 | } | |
2100 | ||
2101 | /* Return true if A is a (polynomial) multiple of B, storing the | |
2102 | multiple in *MULTIPLE if so. */ | |
2103 | ||
2104 | template<unsigned int N, typename Ca, typename Cb, typename Cm> | |
2105 | inline typename if_nonpoly<Cb, bool>::type | |
eaa41a6d | 2106 | multiple_p (const poly_int<N, Ca> &a, Cb b, poly_int<N, Cm> *multiple) |
e535b963 RS |
2107 | { |
2108 | if (!multiple_p (a, b)) | |
2109 | return false; | |
2110 | for (unsigned int i = 0; i < N; ++i) | |
2111 | multiple->coeffs[i] = a.coeffs[i] / b; | |
2112 | return true; | |
2113 | } | |
2114 | ||
2115 | /* Return true if B is a constant and A is a (constant) multiple of B, | |
2116 | storing the multiple in *MULTIPLE if so. */ | |
2117 | ||
2118 | template<unsigned int N, typename Ca, typename Cb, typename Cm> | |
2119 | inline typename if_nonpoly<Ca, bool>::type | |
eaa41a6d | 2120 | multiple_p (Ca a, const poly_int<N, Cb> &b, Cm *multiple) |
e535b963 RS |
2121 | { |
2122 | typedef POLY_CAST (Ca, Cb) NCa; | |
2123 | ||
2124 | /* Do the modulus before the constant check, to catch divide by | |
2125 | potential zeros. */ | |
2126 | if (a % b.coeffs[0] != 0 || (NCa (a) != 0 && !b.is_constant ())) | |
2127 | return false; | |
2128 | *multiple = a / b.coeffs[0]; | |
2129 | return true; | |
2130 | } | |
2131 | ||
2132 | /* Return true if A is a (polynomial) multiple of B, storing the | |
2133 | multiple in *MULTIPLE if so. This handles cases where either | |
2134 | B is constant or the multiple is constant. */ | |
2135 | ||
2136 | template<unsigned int N, typename Ca, typename Cb, typename Cm> | |
2137 | inline bool | |
eaa41a6d RS |
2138 | multiple_p (const poly_int<N, Ca> &a, const poly_int<N, Cb> &b, |
2139 | poly_int<N, Cm> *multiple) | |
e535b963 RS |
2140 | { |
2141 | if (b.is_constant ()) | |
2142 | return multiple_p (a, b.coeffs[0], multiple); | |
2143 | return constant_multiple_p (a, b, multiple); | |
2144 | } | |
2145 | ||
2146 | /* Return A / B, given that A is known to be a multiple of B. */ | |
2147 | ||
2148 | template<unsigned int N, typename Ca, typename Cb> | |
2149 | inline POLY_CONST_RESULT (N, Ca, Cb) | |
eaa41a6d | 2150 | exact_div (const poly_int<N, Ca> &a, Cb b) |
e535b963 RS |
2151 | { |
2152 | typedef POLY_CONST_COEFF (Ca, Cb) C; | |
2153 | poly_int<N, C> r; | |
2154 | for (unsigned int i = 0; i < N; i++) | |
2155 | { | |
2156 | gcc_checking_assert (a.coeffs[i] % b == 0); | |
2157 | POLY_SET_COEFF (C, r, i, a.coeffs[i] / b); | |
2158 | } | |
2159 | return r; | |
2160 | } | |
2161 | ||
2162 | /* Return A / B, given that A is known to be a multiple of B. */ | |
2163 | ||
2164 | template<unsigned int N, typename Ca, typename Cb> | |
2165 | inline POLY_POLY_RESULT (N, Ca, Cb) | |
eaa41a6d | 2166 | exact_div (const poly_int<N, Ca> &a, const poly_int<N, Cb> &b) |
e535b963 RS |
2167 | { |
2168 | if (b.is_constant ()) | |
2169 | return exact_div (a, b.coeffs[0]); | |
2170 | ||
2171 | typedef POLY_CAST (Ca, Cb) NCa; | |
2172 | typedef POLY_CAST (Cb, Ca) NCb; | |
2173 | typedef POLY_BINARY_COEFF (Ca, Cb) C; | |
2174 | typedef POLY_INT_TYPE (Cb) int_type; | |
2175 | ||
2176 | gcc_checking_assert (a.coeffs[0] % b.coeffs[0] == 0); | |
2177 | C r = NCa (a.coeffs[0]) / NCb (b.coeffs[0]); | |
2178 | for (unsigned int i = 1; i < N; ++i) | |
2179 | gcc_checking_assert (b.coeffs[i] == int_type (0) | |
2180 | ? a.coeffs[i] == int_type (0) | |
2181 | : (a.coeffs[i] % b.coeffs[i] == 0 | |
2182 | && NCa (a.coeffs[i]) / NCb (b.coeffs[i]) == r)); | |
2183 | ||
2184 | return r; | |
2185 | } | |
2186 | ||
2187 | /* Return true if there is some constant Q and polynomial r such that: | |
2188 | ||
2189 | (1) a = b * Q + r | |
2190 | (2) |b * Q| <= |a| | |
2191 | (3) |r| < |b| | |
2192 | ||
2193 | Store the value Q in *QUOTIENT if so. */ | |
2194 | ||
2195 | template<unsigned int N, typename Ca, typename Cb, typename Cq> | |
2196 | inline typename if_nonpoly2<Cb, Cq, bool>::type | |
eaa41a6d | 2197 | can_div_trunc_p (const poly_int<N, Ca> &a, Cb b, Cq *quotient) |
e535b963 RS |
2198 | { |
2199 | typedef POLY_CAST (Ca, Cb) NCa; | |
2200 | typedef POLY_CAST (Cb, Ca) NCb; | |
2201 | ||
2202 | /* Do the division before the constant check, to catch divide by | |
2203 | zero errors. */ | |
2204 | Cq q = NCa (a.coeffs[0]) / NCb (b); | |
2205 | if (!a.is_constant ()) | |
2206 | return false; | |
2207 | *quotient = q; | |
2208 | return true; | |
2209 | } | |
2210 | ||
2211 | template<unsigned int N, typename Ca, typename Cb, typename Cq> | |
2212 | inline typename if_nonpoly<Cq, bool>::type | |
eaa41a6d | 2213 | can_div_trunc_p (const poly_int<N, Ca> &a, const poly_int<N, Cb> &b, |
e535b963 RS |
2214 | Cq *quotient) |
2215 | { | |
2216 | /* We can calculate Q from the case in which the indeterminates | |
2217 | are zero. */ | |
2218 | typedef POLY_CAST (Ca, Cb) NCa; | |
2219 | typedef POLY_CAST (Cb, Ca) NCb; | |
2220 | typedef POLY_INT_TYPE (Ca) ICa; | |
2221 | typedef POLY_INT_TYPE (Cb) ICb; | |
2222 | typedef POLY_BINARY_COEFF (Ca, Cb) C; | |
2223 | C q = NCa (a.coeffs[0]) / NCb (b.coeffs[0]); | |
2224 | ||
2225 | /* Check the other coefficients and record whether the division is exact. | |
2226 | The only difficult case is when it isn't. If we require a and b to | |
2227 | ordered wrt zero, there can be no two coefficients of the same value | |
2228 | that have opposite signs. This means that: | |
2229 | ||
2230 | |a| = |a0| + |a1 * x1| + |a2 * x2| + ... | |
2231 | |b| = |b0| + |b1 * x1| + |b2 * x2| + ... | |
2232 | ||
2233 | The Q we've just calculated guarantees: | |
2234 | ||
2235 | |b0 * Q| <= |a0| | |
2236 | |a0 - b0 * Q| < |b0| | |
2237 | ||
2238 | and so: | |
2239 | ||
2240 | (2) |b * Q| <= |a| | |
2241 | ||
2242 | is satisfied if: | |
2243 | ||
2244 | |bi * xi * Q| <= |ai * xi| | |
2245 | ||
2246 | for each i in [1, N]. This is trivially true when xi is zero. | |
2247 | When it isn't we need: | |
2248 | ||
2249 | (2') |bi * Q| <= |ai| | |
2250 | ||
2251 | r is calculated as: | |
2252 | ||
2253 | r = r0 + r1 * x1 + r2 * x2 + ... | |
2254 | where ri = ai - bi * Q | |
2255 | ||
2256 | Restricting to ordered a and b also guarantees that no two ris | |
2257 | have opposite signs, so we have: | |
2258 | ||
2259 | |r| = |r0| + |r1 * x1| + |r2 * x2| + ... | |
2260 | ||
2261 | We know from the calculation of Q that |r0| < |b0|, so: | |
2262 | ||
2263 | (3) |r| < |b| | |
2264 | ||
2265 | is satisfied if: | |
2266 | ||
2267 | (3') |ai - bi * Q| <= |bi| | |
2268 | ||
2269 | for each i in [1, N]. */ | |
2270 | bool rem_p = NCa (a.coeffs[0]) % NCb (b.coeffs[0]) != 0; | |
2271 | for (unsigned int i = 1; i < N; ++i) | |
2272 | { | |
2273 | if (b.coeffs[i] == ICb (0)) | |
2274 | { | |
2275 | /* For bi == 0 we simply need: (3') |ai| == 0. */ | |
2276 | if (a.coeffs[i] != ICa (0)) | |
2277 | return false; | |
2278 | } | |
2279 | else | |
2280 | { | |
95247186 RS |
2281 | /* The only unconditional arithmetic that we can do on ai, |
2282 | bi and Q is ai / bi and ai % bi. (ai == minimum int and | |
2283 | bi == -1 would be UB in the caller.) Anything else runs | |
2284 | the risk of overflow. */ | |
2285 | auto qi = NCa (a.coeffs[i]) / NCb (b.coeffs[i]); | |
2286 | auto ri = NCa (a.coeffs[i]) % NCb (b.coeffs[i]); | |
2287 | /* (2') and (3') are satisfied when ai /[trunc] bi == q. | |
2288 | So is the stricter condition |ai - bi * Q| < |bi|. */ | |
2289 | if (qi == q) | |
2290 | rem_p |= (ri != 0); | |
2291 | /* The only other case is when: | |
2292 | ||
2293 | |bi * Q| + |bi| = |ai| (for (2')) | |
2294 | and |ai - bi * Q| = |bi| (for (3')) | |
2295 | ||
2296 | The first is equivalent to |bi|(|Q| + 1) == |ai|. | |
2297 | The second requires ai == bi * (Q + 1) or ai == bi * (Q - 1). */ | |
2298 | else if (ri != 0) | |
2299 | return false; | |
2300 | else if (q <= 0 && qi < q && qi + 1 == q) | |
2301 | ; | |
2302 | else if (q >= 0 && qi > q && qi - 1 == q) | |
2303 | ; | |
e535b963 | 2304 | else |
95247186 | 2305 | return false; |
e535b963 RS |
2306 | } |
2307 | } | |
2308 | ||
2309 | /* If the division isn't exact, require both values to be ordered wrt 0, | |
2310 | so that we can guarantee conditions (2) and (3) for all indeterminate | |
2311 | values. */ | |
2312 | if (rem_p && (!ordered_p (a, ICa (0)) || !ordered_p (b, ICb (0)))) | |
2313 | return false; | |
2314 | ||
2315 | *quotient = q; | |
2316 | return true; | |
2317 | } | |
2318 | ||
2319 | /* Likewise, but also store r in *REMAINDER. */ | |
2320 | ||
2321 | template<unsigned int N, typename Ca, typename Cb, typename Cq, typename Cr> | |
2322 | inline typename if_nonpoly<Cq, bool>::type | |
eaa41a6d | 2323 | can_div_trunc_p (const poly_int<N, Ca> &a, const poly_int<N, Cb> &b, |
e535b963 RS |
2324 | Cq *quotient, Cr *remainder) |
2325 | { | |
2326 | if (!can_div_trunc_p (a, b, quotient)) | |
2327 | return false; | |
2328 | *remainder = a - *quotient * b; | |
2329 | return true; | |
2330 | } | |
2331 | ||
2332 | /* Return true if there is some polynomial q and constant R such that: | |
2333 | ||
2334 | (1) a = B * q + R | |
2335 | (2) |B * q| <= |a| | |
2336 | (3) |R| < |B| | |
2337 | ||
2338 | Store the value q in *QUOTIENT if so. */ | |
2339 | ||
2340 | template<unsigned int N, typename Ca, typename Cb, typename Cq> | |
2341 | inline typename if_nonpoly<Cb, bool>::type | |
eaa41a6d RS |
2342 | can_div_trunc_p (const poly_int<N, Ca> &a, Cb b, |
2343 | poly_int<N, Cq> *quotient) | |
e535b963 RS |
2344 | { |
2345 | /* The remainder must be constant. */ | |
2346 | for (unsigned int i = 1; i < N; ++i) | |
2347 | if (a.coeffs[i] % b != 0) | |
2348 | return false; | |
2349 | for (unsigned int i = 0; i < N; ++i) | |
2350 | quotient->coeffs[i] = a.coeffs[i] / b; | |
2351 | return true; | |
2352 | } | |
2353 | ||
2354 | /* Likewise, but also store R in *REMAINDER. */ | |
2355 | ||
2356 | template<unsigned int N, typename Ca, typename Cb, typename Cq, typename Cr> | |
2357 | inline typename if_nonpoly<Cb, bool>::type | |
eaa41a6d RS |
2358 | can_div_trunc_p (const poly_int<N, Ca> &a, Cb b, |
2359 | poly_int<N, Cq> *quotient, Cr *remainder) | |
e535b963 RS |
2360 | { |
2361 | if (!can_div_trunc_p (a, b, quotient)) | |
2362 | return false; | |
2363 | *remainder = a.coeffs[0] % b; | |
2364 | return true; | |
2365 | } | |
2366 | ||
5284e559 RS |
2367 | /* Return true if we can compute A / B at compile time, rounding towards zero. |
2368 | Store the result in QUOTIENT if so. | |
2369 | ||
2370 | This handles cases in which either B is constant or the result is | |
2371 | constant. */ | |
2372 | ||
2373 | template<unsigned int N, typename Ca, typename Cb, typename Cq> | |
2374 | inline bool | |
eaa41a6d RS |
2375 | can_div_trunc_p (const poly_int<N, Ca> &a, const poly_int<N, Cb> &b, |
2376 | poly_int<N, Cq> *quotient) | |
5284e559 RS |
2377 | { |
2378 | if (b.is_constant ()) | |
2379 | return can_div_trunc_p (a, b.coeffs[0], quotient); | |
2380 | if (!can_div_trunc_p (a, b, "ient->coeffs[0])) | |
2381 | return false; | |
2382 | for (unsigned int i = 1; i < N; ++i) | |
2383 | quotient->coeffs[i] = 0; | |
2384 | return true; | |
2385 | } | |
2386 | ||
e535b963 RS |
2387 | /* Return true if there is some constant Q and polynomial r such that: |
2388 | ||
2389 | (1) a = b * Q + r | |
2390 | (2) |a| <= |b * Q| | |
2391 | (3) |r| < |b| | |
2392 | ||
2393 | Store the value Q in *QUOTIENT if so. */ | |
2394 | ||
2395 | template<unsigned int N, typename Ca, typename Cb, typename Cq> | |
2396 | inline typename if_nonpoly<Cq, bool>::type | |
eaa41a6d | 2397 | can_div_away_from_zero_p (const poly_int<N, Ca> &a, const poly_int<N, Cb> &b, |
e535b963 RS |
2398 | Cq *quotient) |
2399 | { | |
2400 | if (!can_div_trunc_p (a, b, quotient)) | |
2401 | return false; | |
2402 | if (maybe_ne (*quotient * b, a)) | |
2403 | *quotient += (*quotient < 0 ? -1 : 1); | |
2404 | return true; | |
2405 | } | |
2406 | ||
2407 | /* Use print_dec to print VALUE to FILE, where SGN is the sign | |
2408 | of the values. */ | |
2409 | ||
2410 | template<unsigned int N, typename C> | |
2411 | void | |
eaa41a6d | 2412 | print_dec (const poly_int<N, C> &value, FILE *file, signop sgn) |
e535b963 RS |
2413 | { |
2414 | if (value.is_constant ()) | |
2415 | print_dec (value.coeffs[0], file, sgn); | |
2416 | else | |
2417 | { | |
2418 | fprintf (file, "["); | |
2419 | for (unsigned int i = 0; i < N; ++i) | |
2420 | { | |
2421 | print_dec (value.coeffs[i], file, sgn); | |
2422 | fputc (i == N - 1 ? ']' : ',', file); | |
2423 | } | |
2424 | } | |
2425 | } | |
2426 | ||
2427 | /* Likewise without the signop argument, for coefficients that have an | |
2428 | inherent signedness. */ | |
2429 | ||
2430 | template<unsigned int N, typename C> | |
2431 | void | |
eaa41a6d | 2432 | print_dec (const poly_int<N, C> &value, FILE *file) |
e535b963 RS |
2433 | { |
2434 | STATIC_ASSERT (poly_coeff_traits<C>::signedness >= 0); | |
2435 | print_dec (value, file, | |
2436 | poly_coeff_traits<C>::signedness ? SIGNED : UNSIGNED); | |
2437 | } | |
2438 | ||
370c2ebe RS |
2439 | /* Use print_hex to print VALUE to FILE. */ |
2440 | ||
2441 | template<unsigned int N, typename C> | |
2442 | void | |
eaa41a6d | 2443 | print_hex (const poly_int<N, C> &value, FILE *file) |
370c2ebe RS |
2444 | { |
2445 | if (value.is_constant ()) | |
2446 | print_hex (value.coeffs[0], file); | |
2447 | else | |
2448 | { | |
2449 | fprintf (file, "["); | |
2450 | for (unsigned int i = 0; i < N; ++i) | |
2451 | { | |
2452 | print_hex (value.coeffs[i], file); | |
2453 | fputc (i == N - 1 ? ']' : ',', file); | |
2454 | } | |
2455 | } | |
2456 | } | |
2457 | ||
535808fd RS |
2458 | /* Helper for calculating the distance between two points P1 and P2, |
2459 | in cases where known_le (P1, P2). T1 and T2 are the types of the | |
2460 | two positions, in either order. The coefficients of P2 - P1 have | |
2461 | type unsigned HOST_WIDE_INT if the coefficients of both T1 and T2 | |
2462 | have C++ primitive type, otherwise P2 - P1 has its usual | |
2463 | wide-int-based type. | |
2464 | ||
2465 | The actual subtraction should look something like this: | |
2466 | ||
2467 | typedef poly_span_traits<T1, T2> span_traits; | |
2468 | span_traits::cast (P2) - span_traits::cast (P1) | |
2469 | ||
2470 | Applying the cast before the subtraction avoids undefined overflow | |
2471 | for signed T1 and T2. | |
2472 | ||
2473 | The implementation of the cast tries to avoid unnecessary arithmetic | |
2474 | or copying. */ | |
2475 | template<typename T1, typename T2, | |
2476 | typename Res = POLY_BINARY_COEFF (POLY_BINARY_COEFF (T1, T2), | |
2477 | unsigned HOST_WIDE_INT)> | |
e535b963 RS |
2478 | struct poly_span_traits |
2479 | { | |
e535b963 RS |
2480 | template<typename T> |
2481 | static const T &cast (const T &x) { return x; } | |
2482 | }; | |
2483 | ||
535808fd RS |
2484 | template<typename T1, typename T2> |
2485 | struct poly_span_traits<T1, T2, unsigned HOST_WIDE_INT> | |
e535b963 RS |
2486 | { |
2487 | template<typename T> | |
2488 | static typename if_nonpoly<T, unsigned HOST_WIDE_INT>::type | |
2489 | cast (const T &x) { return x; } | |
2490 | ||
2491 | template<unsigned int N, typename T> | |
2492 | static poly_int<N, unsigned HOST_WIDE_INT> | |
eaa41a6d | 2493 | cast (const poly_int<N, T> &x) { return x; } |
e535b963 RS |
2494 | }; |
2495 | ||
2496 | /* Return true if SIZE represents a known size, assuming that all-ones | |
2497 | indicates an unknown size. */ | |
2498 | ||
2499 | template<typename T> | |
2500 | inline bool | |
2501 | known_size_p (const T &a) | |
2502 | { | |
2503 | return maybe_ne (a, POLY_INT_TYPE (T) (-1)); | |
2504 | } | |
2505 | ||
2506 | /* Return true if range [POS, POS + SIZE) might include VAL. | |
2507 | SIZE can be the special value -1, in which case the range is | |
2508 | open-ended. */ | |
2509 | ||
2510 | template<typename T1, typename T2, typename T3> | |
2511 | inline bool | |
2512 | maybe_in_range_p (const T1 &val, const T2 &pos, const T3 &size) | |
2513 | { | |
535808fd RS |
2514 | typedef poly_span_traits<T1, T2> start_span; |
2515 | typedef poly_span_traits<T3, T3> size_span; | |
e535b963 RS |
2516 | if (known_lt (val, pos)) |
2517 | return false; | |
2518 | if (!known_size_p (size)) | |
2519 | return true; | |
2520 | if ((poly_int_traits<T1>::num_coeffs > 1 | |
2521 | || poly_int_traits<T2>::num_coeffs > 1) | |
2522 | && maybe_lt (val, pos)) | |
2523 | /* In this case we don't know whether VAL >= POS is true at compile | |
2524 | time, so we can't prove that VAL >= POS + SIZE. */ | |
2525 | return true; | |
535808fd RS |
2526 | return maybe_lt (start_span::cast (val) - start_span::cast (pos), |
2527 | size_span::cast (size)); | |
e535b963 RS |
2528 | } |
2529 | ||
2530 | /* Return true if range [POS, POS + SIZE) is known to include VAL. | |
2531 | SIZE can be the special value -1, in which case the range is | |
2532 | open-ended. */ | |
2533 | ||
2534 | template<typename T1, typename T2, typename T3> | |
2535 | inline bool | |
2536 | known_in_range_p (const T1 &val, const T2 &pos, const T3 &size) | |
2537 | { | |
535808fd RS |
2538 | typedef poly_span_traits<T1, T2> start_span; |
2539 | typedef poly_span_traits<T3, T3> size_span; | |
e535b963 RS |
2540 | return (known_size_p (size) |
2541 | && known_ge (val, pos) | |
535808fd RS |
2542 | && known_lt (start_span::cast (val) - start_span::cast (pos), |
2543 | size_span::cast (size))); | |
e535b963 RS |
2544 | } |
2545 | ||
2546 | /* Return true if the two ranges [POS1, POS1 + SIZE1) and [POS2, POS2 + SIZE2) | |
2547 | might overlap. SIZE1 and/or SIZE2 can be the special value -1, in which | |
2548 | case the range is open-ended. */ | |
2549 | ||
2550 | template<typename T1, typename T2, typename T3, typename T4> | |
2551 | inline bool | |
2552 | ranges_maybe_overlap_p (const T1 &pos1, const T2 &size1, | |
2553 | const T3 &pos2, const T4 &size2) | |
2554 | { | |
2555 | if (maybe_in_range_p (pos2, pos1, size1)) | |
2556 | return maybe_ne (size2, POLY_INT_TYPE (T4) (0)); | |
2557 | if (maybe_in_range_p (pos1, pos2, size2)) | |
2558 | return maybe_ne (size1, POLY_INT_TYPE (T2) (0)); | |
2559 | return false; | |
2560 | } | |
2561 | ||
2562 | /* Return true if the two ranges [POS1, POS1 + SIZE1) and [POS2, POS2 + SIZE2) | |
2563 | are known to overlap. SIZE1 and/or SIZE2 can be the special value -1, | |
2564 | in which case the range is open-ended. */ | |
2565 | ||
2566 | template<typename T1, typename T2, typename T3, typename T4> | |
2567 | inline bool | |
2568 | ranges_known_overlap_p (const T1 &pos1, const T2 &size1, | |
2569 | const T3 &pos2, const T4 &size2) | |
2570 | { | |
535808fd RS |
2571 | typedef poly_span_traits<T1, T3> start_span; |
2572 | typedef poly_span_traits<T2, T2> size1_span; | |
2573 | typedef poly_span_traits<T4, T4> size2_span; | |
e535b963 RS |
2574 | /* known_gt (POS1 + SIZE1, POS2) [infinite precision] |
2575 | --> known_gt (SIZE1, POS2 - POS1) [infinite precision] | |
2576 | --> known_gt (SIZE1, POS2 - lower_bound (POS1, POS2)) [infinite precision] | |
2577 | ^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^ always nonnegative | |
2578 | --> known_gt (SIZE1, span1::cast (POS2 - lower_bound (POS1, POS2))). | |
2579 | ||
2580 | Using the saturating subtraction enforces that SIZE1 must be | |
2581 | nonzero, since known_gt (0, x) is false for all nonnegative x. | |
2582 | If POS2.coeff[I] < POS1.coeff[I] for some I > 0, increasing | |
2583 | indeterminate number I makes the unsaturated condition easier to | |
2584 | satisfy, so using a saturated coefficient of zero tests the case in | |
2585 | which the indeterminate is zero (the minimum value). */ | |
2586 | return (known_size_p (size1) | |
2587 | && known_size_p (size2) | |
535808fd RS |
2588 | && known_lt (start_span::cast (pos2) |
2589 | - start_span::cast (lower_bound (pos1, pos2)), | |
2590 | size1_span::cast (size1)) | |
2591 | && known_lt (start_span::cast (pos1) | |
2592 | - start_span::cast (lower_bound (pos1, pos2)), | |
2593 | size2_span::cast (size2))); | |
e535b963 RS |
2594 | } |
2595 | ||
2596 | /* Return true if range [POS1, POS1 + SIZE1) is known to be a subrange of | |
2597 | [POS2, POS2 + SIZE2). SIZE1 and/or SIZE2 can be the special value -1, | |
2598 | in which case the range is open-ended. */ | |
2599 | ||
2600 | template<typename T1, typename T2, typename T3, typename T4> | |
2601 | inline bool | |
2602 | known_subrange_p (const T1 &pos1, const T2 &size1, | |
2603 | const T3 &pos2, const T4 &size2) | |
2604 | { | |
2605 | typedef typename poly_int_traits<T2>::coeff_type C2; | |
535808fd RS |
2606 | typedef poly_span_traits<T1, T3> start_span; |
2607 | typedef poly_span_traits<T2, T4> size_span; | |
e535b963 RS |
2608 | return (known_gt (size1, POLY_INT_TYPE (T2) (0)) |
2609 | && (poly_coeff_traits<C2>::signedness > 0 | |
2610 | || known_size_p (size1)) | |
2611 | && known_size_p (size2) | |
2612 | && known_ge (pos1, pos2) | |
2613 | && known_le (size1, size2) | |
535808fd RS |
2614 | && known_le (start_span::cast (pos1) - start_span::cast (pos2), |
2615 | size_span::cast (size2) - size_span::cast (size1))); | |
e535b963 RS |
2616 | } |
2617 | ||
2618 | /* Return true if the endpoint of the range [POS, POS + SIZE) can be | |
2619 | stored in a T, or if SIZE is the special value -1, which makes the | |
2620 | range open-ended. */ | |
2621 | ||
2622 | template<typename T> | |
2623 | inline typename if_nonpoly<T, bool>::type | |
2624 | endpoint_representable_p (const T &pos, const T &size) | |
2625 | { | |
2626 | return (!known_size_p (size) | |
2627 | || pos <= poly_coeff_traits<T>::max_value - size); | |
2628 | } | |
2629 | ||
2630 | template<unsigned int N, typename C> | |
2631 | inline bool | |
eaa41a6d RS |
2632 | endpoint_representable_p (const poly_int<N, C> &pos, |
2633 | const poly_int<N, C> &size) | |
e535b963 RS |
2634 | { |
2635 | if (known_size_p (size)) | |
2636 | for (unsigned int i = 0; i < N; ++i) | |
2637 | if (pos.coeffs[i] > poly_coeff_traits<C>::max_value - size.coeffs[i]) | |
2638 | return false; | |
2639 | return true; | |
2640 | } | |
2641 | ||
2642 | template<unsigned int N, typename C> | |
2643 | void | |
eaa41a6d | 2644 | gt_ggc_mx (poly_int<N, C> *) |
e535b963 RS |
2645 | { |
2646 | } | |
2647 | ||
2648 | template<unsigned int N, typename C> | |
2649 | void | |
eaa41a6d | 2650 | gt_pch_nx (poly_int<N, C> *) |
e535b963 RS |
2651 | { |
2652 | } | |
2653 | ||
2654 | template<unsigned int N, typename C> | |
2655 | void | |
eaa41a6d | 2656 | gt_pch_nx (poly_int<N, C> *, gt_pointer_operator, void *) |
e535b963 RS |
2657 | { |
2658 | } | |
2659 | ||
2660 | #undef POLY_SET_COEFF | |
2661 | #undef POLY_INT_TYPE | |
2662 | #undef POLY_BINARY_COEFF | |
2663 | #undef CONST_CONST_RESULT | |
2664 | #undef POLY_CONST_RESULT | |
2665 | #undef CONST_POLY_RESULT | |
2666 | #undef POLY_POLY_RESULT | |
2667 | #undef POLY_CONST_COEFF | |
2668 | #undef CONST_POLY_COEFF | |
2669 | #undef POLY_POLY_COEFF | |
2670 | ||
2671 | #endif |