Bug Summary

File:tools/polly/lib/External/isl/isl_equalities.c
Warning:line 722, column 5
Dereference of null pointer (loaded from variable 'T')

Annotated Source Code

1/*
2 * Copyright 2008-2009 Katholieke Universiteit Leuven
3 * Copyright 2010 INRIA Saclay
4 *
5 * Use of this software is governed by the MIT license
6 *
7 * Written by Sven Verdoolaege, K.U.Leuven, Departement
8 * Computerwetenschappen, Celestijnenlaan 200A, B-3001 Leuven, Belgium
9 * and INRIA Saclay - Ile-de-France, Parc Club Orsay Universite,
10 * ZAC des vignes, 4 rue Jacques Monod, 91893 Orsay, France
11 */
12
13#include <isl_mat_private.h>
14#include <isl_vec_private.h>
15#include <isl_seq.h>
16#include "isl_map_private.h"
17#include "isl_equalities.h"
18#include <isl_val_private.h>
19
20/* Given a set of modulo constraints
21 *
22 * c + A y = 0 mod d
23 *
24 * this function computes a particular solution y_0
25 *
26 * The input is given as a matrix B = [ c A ] and a vector d.
27 *
28 * The output is matrix containing the solution y_0 or
29 * a zero-column matrix if the constraints admit no integer solution.
30 *
31 * The given set of constrains is equivalent to
32 *
33 * c + A y = -D x
34 *
35 * with D = diag d and x a fresh set of variables.
36 * Reducing both c and A modulo d does not change the
37 * value of y in the solution and may lead to smaller coefficients.
38 * Let M = [ D A ] and [ H 0 ] = M U, the Hermite normal form of M.
39 * Then
40 * [ x ]
41 * M [ y ] = - c
42 * and so
43 * [ x ]
44 * [ H 0 ] U^{-1} [ y ] = - c
45 * Let
46 * [ A ] [ x ]
47 * [ B ] = U^{-1} [ y ]
48 * then
49 * H A + 0 B = -c
50 *
51 * so B may be chosen arbitrarily, e.g., B = 0, and then
52 *
53 * [ x ] = [ -c ]
54 * U^{-1} [ y ] = [ 0 ]
55 * or
56 * [ x ] [ -c ]
57 * [ y ] = U [ 0 ]
58 * specifically,
59 *
60 * y = U_{2,1} (-c)
61 *
62 * If any of the coordinates of this y are non-integer
63 * then the constraints admit no integer solution and
64 * a zero-column matrix is returned.
65 */
66static struct isl_mat *particular_solution(struct isl_mat *B, struct isl_vec *d)
67{
68 int i, j;
69 struct isl_mat *M = NULL((void*)0);
70 struct isl_mat *C = NULL((void*)0);
71 struct isl_mat *U = NULL((void*)0);
72 struct isl_mat *H = NULL((void*)0);
73 struct isl_mat *cst = NULL((void*)0);
74 struct isl_mat *T = NULL((void*)0);
75
76 M = isl_mat_alloc(B->ctx, B->n_row, B->n_row + B->n_col - 1);
77 C = isl_mat_alloc(B->ctx, 1 + B->n_row, 1);
78 if (!M || !C)
79 goto error;
80 isl_int_set_si(C->row[0][0], 1)isl_sioimath_set_si((C->row[0][0]), 1);
81 for (i = 0; i < B->n_row; ++i) {
82 isl_seq_clr(M->row[i], B->n_row);
83 isl_int_set(M->row[i][i], d->block.data[i])isl_sioimath_set((M->row[i][i]), *(d->block.data[i]));
84 isl_int_neg(C->row[1 + i][0], B->row[i][0])isl_sioimath_neg((C->row[1 + i][0]), *(B->row[i][0]));
85 isl_int_fdiv_r(C->row[1+i][0], C->row[1+i][0], M->row[i][i])isl_sioimath_fdiv_r((C->row[1+i][0]), *(C->row[1+i][0])
, *(M->row[i][i]))
;
86 for (j = 0; j < B->n_col - 1; ++j)
87 isl_int_fdiv_r(M->row[i][B->n_row + j],isl_sioimath_fdiv_r((M->row[i][B->n_row + j]), *(B->
row[i][1 + j]), *(M->row[i][i]))
88 B->row[i][1 + j], M->row[i][i])isl_sioimath_fdiv_r((M->row[i][B->n_row + j]), *(B->
row[i][1 + j]), *(M->row[i][i]))
;
89 }
90 M = isl_mat_left_hermite(M, 0, &U, NULL((void*)0));
91 if (!M || !U)
92 goto error;
93 H = isl_mat_sub_alloc(M, 0, B->n_row, 0, B->n_row);
94 H = isl_mat_lin_to_aff(H);
95 C = isl_mat_inverse_product(H, C);
96 if (!C)
97 goto error;
98 for (i = 0; i < B->n_row; ++i) {
99 if (!isl_int_is_divisible_by(C->row[1+i][0], C->row[0][0])isl_sioimath_is_divisible_by(*(C->row[1+i][0]), *(C->row
[0][0]))
)
100 break;
101 isl_int_divexact(C->row[1+i][0], C->row[1+i][0], C->row[0][0])isl_sioimath_tdiv_q((C->row[1+i][0]), *(C->row[1+i][0])
, *(C->row[0][0]))
;
102 }
103 if (i < B->n_row)
104 cst = isl_mat_alloc(B->ctx, B->n_row, 0);
105 else
106 cst = isl_mat_sub_alloc(C, 1, B->n_row, 0, 1);
107 T = isl_mat_sub_alloc(U, B->n_row, B->n_col - 1, 0, B->n_row);
108 cst = isl_mat_product(T, cst);
109 isl_mat_free(M);
110 isl_mat_free(C);
111 isl_mat_free(U);
112 return cst;
113error:
114 isl_mat_free(M);
115 isl_mat_free(C);
116 isl_mat_free(U);
117 return NULL((void*)0);
118}
119
120/* Compute and return the matrix
121 *
122 * U_1^{-1} diag(d_1, 1, ..., 1)
123 *
124 * with U_1 the unimodular completion of the first (and only) row of B.
125 * The columns of this matrix generate the lattice that satisfies
126 * the single (linear) modulo constraint.
127 */
128static struct isl_mat *parameter_compression_1(
129 struct isl_mat *B, struct isl_vec *d)
130{
131 struct isl_mat *U;
132
133 U = isl_mat_alloc(B->ctx, B->n_col - 1, B->n_col - 1);
134 if (!U)
135 return NULL((void*)0);
136 isl_seq_cpy(U->row[0], B->row[0] + 1, B->n_col - 1);
137 U = isl_mat_unimodular_complete(U, 1);
138 U = isl_mat_right_inverse(U);
139 if (!U)
140 return NULL((void*)0);
141 isl_mat_col_mul(U, 0, d->block.data[0], 0);
142 U = isl_mat_lin_to_aff(U);
143 return U;
144}
145
146/* Compute a common lattice of solutions to the linear modulo
147 * constraints specified by B and d.
148 * See also the documentation of isl_mat_parameter_compression.
149 * We put the matrix
150 *
151 * A = [ L_1^{-T} L_2^{-T} ... L_k^{-T} ]
152 *
153 * on a common denominator. This denominator D is the lcm of modulos d.
154 * Since L_i = U_i^{-1} diag(d_i, 1, ... 1), we have
155 * L_i^{-T} = U_i^T diag(d_i, 1, ... 1)^{-T} = U_i^T diag(1/d_i, 1, ..., 1).
156 * Putting this on the common denominator, we have
157 * D * L_i^{-T} = U_i^T diag(D/d_i, D, ..., D).
158 */
159static struct isl_mat *parameter_compression_multi(
160 struct isl_mat *B, struct isl_vec *d)
161{
162 int i, j, k;
163 isl_int D;
164 struct isl_mat *A = NULL((void*)0), *U = NULL((void*)0);
165 struct isl_mat *T;
166 unsigned size;
167
168 isl_int_init(D)isl_sioimath_init((D));
169
170 isl_vec_lcm(d, &D);
171
172 size = B->n_col - 1;
173 A = isl_mat_alloc(B->ctx, size, B->n_row * size);
174 U = isl_mat_alloc(B->ctx, size, size);
175 if (!U || !A)
176 goto error;
177 for (i = 0; i < B->n_row; ++i) {
178 isl_seq_cpy(U->row[0], B->row[i] + 1, size);
179 U = isl_mat_unimodular_complete(U, 1);
180 if (!U)
181 goto error;
182 isl_int_divexact(D, D, d->block.data[i])isl_sioimath_tdiv_q((D), *(D), *(d->block.data[i]));
183 for (k = 0; k < U->n_col; ++k)
184 isl_int_mul(A->row[k][i*size+0], D, U->row[0][k])isl_sioimath_mul((A->row[k][i*size+0]), *(D), *(U->row[
0][k]))
;
185 isl_int_mul(D, D, d->block.data[i])isl_sioimath_mul((D), *(D), *(d->block.data[i]));
186 for (j = 1; j < U->n_row; ++j)
187 for (k = 0; k < U->n_col; ++k)
188 isl_int_mul(A->row[k][i*size+j],isl_sioimath_mul((A->row[k][i*size+j]), *(D), *(U->row[
j][k]))
189 D, U->row[j][k])isl_sioimath_mul((A->row[k][i*size+j]), *(D), *(U->row[
j][k]))
;
190 }
191 A = isl_mat_left_hermite(A, 0, NULL((void*)0), NULL((void*)0));
192 T = isl_mat_sub_alloc(A, 0, A->n_row, 0, A->n_row);
193 T = isl_mat_lin_to_aff(T);
194 if (!T)
195 goto error;
196 isl_int_set(T->row[0][0], D)isl_sioimath_set((T->row[0][0]), *(D));
197 T = isl_mat_right_inverse(T);
198 if (!T)
199 goto error;
200 isl_assert(T->ctx, isl_int_is_one(T->row[0][0]), goto error)do { if ((isl_sioimath_cmp_si(*(T->row[0][0]), 1) == 0)) break
; do { isl_handle_error(T->ctx, isl_error_unknown, "Assertion \""
"(isl_sioimath_cmp_si(*(T->row[0][0]), 1) == 0)" "\" failed"
, "/tmp/buildd/llvm-toolchain-snapshot-5.0~svn301135/tools/polly/lib/External/isl/isl_equalities.c"
, 200); goto error; } while (0); } while (0)
;
201 T = isl_mat_transpose(T);
202 isl_mat_free(A);
203 isl_mat_free(U);
204
205 isl_int_clear(D)isl_sioimath_clear((D));
206 return T;
207error:
208 isl_mat_free(A);
209 isl_mat_free(U);
210 isl_int_clear(D)isl_sioimath_clear((D));
211 return NULL((void*)0);
212}
213
214/* Given a set of modulo constraints
215 *
216 * c + A y = 0 mod d
217 *
218 * this function returns an affine transformation T,
219 *
220 * y = T y'
221 *
222 * that bijectively maps the integer vectors y' to integer
223 * vectors y that satisfy the modulo constraints.
224 *
225 * This function is inspired by Section 2.5.3
226 * of B. Meister, "Stating and Manipulating Periodicity in the Polytope
227 * Model. Applications to Program Analysis and Optimization".
228 * However, the implementation only follows the algorithm of that
229 * section for computing a particular solution and not for computing
230 * a general homogeneous solution. The latter is incomplete and
231 * may remove some valid solutions.
232 * Instead, we use an adaptation of the algorithm in Section 7 of
233 * B. Meister, S. Verdoolaege, "Polynomial Approximations in the Polytope
234 * Model: Bringing the Power of Quasi-Polynomials to the Masses".
235 *
236 * The input is given as a matrix B = [ c A ] and a vector d.
237 * Each element of the vector d corresponds to a row in B.
238 * The output is a lower triangular matrix.
239 * If no integer vector y satisfies the given constraints then
240 * a matrix with zero columns is returned.
241 *
242 * We first compute a particular solution y_0 to the given set of
243 * modulo constraints in particular_solution. If no such solution
244 * exists, then we return a zero-columned transformation matrix.
245 * Otherwise, we compute the generic solution to
246 *
247 * A y = 0 mod d
248 *
249 * That is we want to compute G such that
250 *
251 * y = G y''
252 *
253 * with y'' integer, describes the set of solutions.
254 *
255 * We first remove the common factors of each row.
256 * In particular if gcd(A_i,d_i) != 1, then we divide the whole
257 * row i (including d_i) by this common factor. If afterwards gcd(A_i) != 1,
258 * then we divide this row of A by the common factor, unless gcd(A_i) = 0.
259 * In the later case, we simply drop the row (in both A and d).
260 *
261 * If there are no rows left in A, then G is the identity matrix. Otherwise,
262 * for each row i, we now determine the lattice of integer vectors
263 * that satisfies this row. Let U_i be the unimodular extension of the
264 * row A_i. This unimodular extension exists because gcd(A_i) = 1.
265 * The first component of
266 *
267 * y' = U_i y
268 *
269 * needs to be a multiple of d_i. Let y' = diag(d_i, 1, ..., 1) y''.
270 * Then,
271 *
272 * y = U_i^{-1} diag(d_i, 1, ..., 1) y''
273 *
274 * for arbitrary integer vectors y''. That is, y belongs to the lattice
275 * generated by the columns of L_i = U_i^{-1} diag(d_i, 1, ..., 1).
276 * If there is only one row, then G = L_1.
277 *
278 * If there is more than one row left, we need to compute the intersection
279 * of the lattices. That is, we need to compute an L such that
280 *
281 * L = L_i L_i' for all i
282 *
283 * with L_i' some integer matrices. Let A be constructed as follows
284 *
285 * A = [ L_1^{-T} L_2^{-T} ... L_k^{-T} ]
286 *
287 * and computed the Hermite Normal Form of A = [ H 0 ] U
288 * Then,
289 *
290 * L_i^{-T} = H U_{1,i}
291 *
292 * or
293 *
294 * H^{-T} = L_i U_{1,i}^T
295 *
296 * In other words G = L = H^{-T}.
297 * To ensure that G is lower triangular, we compute and use its Hermite
298 * normal form.
299 *
300 * The affine transformation matrix returned is then
301 *
302 * [ 1 0 ]
303 * [ y_0 G ]
304 *
305 * as any y = y_0 + G y' with y' integer is a solution to the original
306 * modulo constraints.
307 */
308struct isl_mat *isl_mat_parameter_compression(
309 struct isl_mat *B, struct isl_vec *d)
310{
311 int i;
312 struct isl_mat *cst = NULL((void*)0);
313 struct isl_mat *T = NULL((void*)0);
314 isl_int D;
315
316 if (!B || !d)
317 goto error;
318 isl_assert(B->ctx, B->n_row == d->size, goto error)do { if (B->n_row == d->size) break; do { isl_handle_error
(B->ctx, isl_error_unknown, "Assertion \"" "B->n_row == d->size"
"\" failed", "/tmp/buildd/llvm-toolchain-snapshot-5.0~svn301135/tools/polly/lib/External/isl/isl_equalities.c"
, 318); goto error; } while (0); } while (0)
;
319 cst = particular_solution(B, d);
320 if (!cst)
321 goto error;
322 if (cst->n_col == 0) {
323 T = isl_mat_alloc(B->ctx, B->n_col, 0);
324 isl_mat_free(cst);
325 isl_mat_free(B);
326 isl_vec_free(d);
327 return T;
328 }
329 isl_int_init(D)isl_sioimath_init((D));
330 /* Replace a*g*row = 0 mod g*m by row = 0 mod m */
331 for (i = 0; i < B->n_row; ++i) {
332 isl_seq_gcd(B->row[i] + 1, B->n_col - 1, &D);
333 if (isl_int_is_one(D)(isl_sioimath_cmp_si(*(D), 1) == 0))
334 continue;
335 if (isl_int_is_zero(D)(isl_sioimath_sgn(*(D)) == 0)) {
336 B = isl_mat_drop_rows(B, i, 1);
337 d = isl_vec_cow(d);
338 if (!B || !d)
339 goto error2;
340 isl_seq_cpy(d->block.data+i, d->block.data+i+1,
341 d->size - (i+1));
342 d->size--;
343 i--;
344 continue;
345 }
346 B = isl_mat_cow(B);
347 if (!B)
348 goto error2;
349 isl_seq_scale_down(B->row[i] + 1, B->row[i] + 1, D, B->n_col-1);
350 isl_int_gcd(D, D, d->block.data[i])isl_sioimath_gcd((D), *(D), *(d->block.data[i]));
351 d = isl_vec_cow(d);
352 if (!d)
353 goto error2;
354 isl_int_divexact(d->block.data[i], d->block.data[i], D)isl_sioimath_tdiv_q((d->block.data[i]), *(d->block.data
[i]), *(D))
;
355 }
356 isl_int_clear(D)isl_sioimath_clear((D));
357 if (B->n_row == 0)
358 T = isl_mat_identity(B->ctx, B->n_col);
359 else if (B->n_row == 1)
360 T = parameter_compression_1(B, d);
361 else
362 T = parameter_compression_multi(B, d);
363 T = isl_mat_left_hermite(T, 0, NULL((void*)0), NULL((void*)0));
364 if (!T)
365 goto error;
366 isl_mat_sub_copy(T->ctx, T->row + 1, cst->row, cst->n_row, 0, 0, 1);
367 isl_mat_free(cst);
368 isl_mat_free(B);
369 isl_vec_free(d);
370 return T;
371error2:
372 isl_int_clear(D)isl_sioimath_clear((D));
373error:
374 isl_mat_free(cst);
375 isl_mat_free(B);
376 isl_vec_free(d);
377 return NULL((void*)0);
378}
379
380/* Given a set of equalities
381 *
382 * B(y) + A x = 0 (*)
383 *
384 * compute and return an affine transformation T,
385 *
386 * y = T y'
387 *
388 * that bijectively maps the integer vectors y' to integer
389 * vectors y that satisfy the modulo constraints for some value of x.
390 *
391 * Let [H 0] be the Hermite Normal Form of A, i.e.,
392 *
393 * A = [H 0] Q
394 *
395 * Then y is a solution of (*) iff
396 *
397 * H^-1 B(y) (= - [I 0] Q x)
398 *
399 * is an integer vector. Let d be the common denominator of H^-1.
400 * We impose
401 *
402 * d H^-1 B(y) = 0 mod d
403 *
404 * and compute the solution using isl_mat_parameter_compression.
405 */
406__isl_give isl_mat *isl_mat_parameter_compression_ext(__isl_take isl_mat *B,
407 __isl_take isl_mat *A)
408{
409 isl_ctx *ctx;
410 isl_vec *d;
411 int n_row, n_col;
412
413 if (!A)
414 return isl_mat_free(B);
415
416 ctx = isl_mat_get_ctx(A);
417 n_row = A->n_row;
418 n_col = A->n_col;
419 A = isl_mat_left_hermite(A, 0, NULL((void*)0), NULL((void*)0));
420 A = isl_mat_drop_cols(A, n_row, n_col - n_row);
421 A = isl_mat_lin_to_aff(A);
422 A = isl_mat_right_inverse(A);
423 d = isl_vec_alloc(ctx, n_row);
424 if (A)
425 d = isl_vec_set(d, A->row[0][0]);
426 A = isl_mat_drop_rows(A, 0, 1);
427 A = isl_mat_drop_cols(A, 0, 1);
428 B = isl_mat_product(A, B);
429
430 return isl_mat_parameter_compression(B, d);
431}
432
433/* Return a compression matrix that indicates that there are no solutions
434 * to the original constraints. In particular, return a zero-column
435 * matrix with 1 + dim rows. If "T2" is not NULL, then assign *T2
436 * the inverse of this matrix. *T2 may already have been assigned
437 * matrix, so free it first.
438 * "free1", "free2" and "free3" are temporary matrices that are
439 * not useful when an empty compression is returned. They are
440 * simply freed.
441 */
442static __isl_give isl_mat *empty_compression(isl_ctx *ctx, unsigned dim,
443 __isl_give isl_mat **T2, __isl_take isl_mat *free1,
444 __isl_take isl_mat *free2, __isl_take isl_mat *free3)
445{
446 isl_mat_free(free1);
447 isl_mat_free(free2);
448 isl_mat_free(free3);
449 if (T2) {
450 isl_mat_free(*T2);
451 *T2 = isl_mat_alloc(ctx, 0, 1 + dim);
452 }
453 return isl_mat_alloc(ctx, 1 + dim, 0);
454}
455
456/* Given a matrix that maps a (possibly) parametric domain to
457 * a parametric domain, add in rows that map the "nparam" parameters onto
458 * themselves.
459 */
460static __isl_give isl_mat *insert_parameter_rows(__isl_take isl_mat *mat,
461 unsigned nparam)
462{
463 int i;
464
465 if (nparam == 0)
466 return mat;
467 if (!mat)
468 return NULL((void*)0);
469
470 mat = isl_mat_insert_rows(mat, 1, nparam);
471 if (!mat)
472 return NULL((void*)0);
473
474 for (i = 0; i < nparam; ++i) {
475 isl_seq_clr(mat->row[1 + i], mat->n_col);
476 isl_int_set(mat->row[1 + i][1 + i], mat->row[0][0])isl_sioimath_set((mat->row[1 + i][1 + i]), *(mat->row[0
][0]))
;
477 }
478
479 return mat;
480}
481
482/* Given a set of equalities
483 *
484 * -C(y) + M x = 0
485 *
486 * this function computes a unimodular transformation from a lower-dimensional
487 * space to the original space that bijectively maps the integer points x'
488 * in the lower-dimensional space to the integer points x in the original
489 * space that satisfy the equalities.
490 *
491 * The input is given as a matrix B = [ -C M ] and the output is a
492 * matrix that maps [1 x'] to [1 x].
493 * The number of equality constraints in B is assumed to be smaller than
494 * or equal to the number of variables x.
495 * "first" is the position of the first x variable.
496 * The preceding variables are considered to be y-variables.
497 * If T2 is not NULL, then *T2 is set to a matrix mapping [1 x] to [1 x'].
498 *
499 * First compute the (left) Hermite normal form of M,
500 *
501 * M [U1 U2] = M U = H = [H1 0]
502 * or
503 * M = H Q = [H1 0] [Q1]
504 * [Q2]
505 *
506 * with U, Q unimodular, Q = U^{-1} (and H lower triangular).
507 * Define the transformed variables as
508 *
509 * x = [U1 U2] [ x1' ] = [U1 U2] [Q1] x
510 * [ x2' ] [Q2]
511 *
512 * The equalities then become
513 *
514 * -C(y) + H1 x1' = 0 or x1' = H1^{-1} C(y) = C'(y)
515 *
516 * If the denominator of the constant term does not divide the
517 * the common denominator of the coefficients of y, then every
518 * integer point is mapped to a non-integer point and then the original set
519 * has no integer solutions (since the x' are a unimodular transformation
520 * of the x). In this case, a zero-column matrix is returned.
521 * Otherwise, the transformation is given by
522 *
523 * x = U1 H1^{-1} C(y) + U2 x2'
524 *
525 * The inverse transformation is simply
526 *
527 * x2' = Q2 x
528 */
529__isl_give isl_mat *isl_mat_final_variable_compression(__isl_take isl_mat *B,
530 int first, __isl_give isl_mat **T2)
531{
532 int i, n;
533 isl_ctx *ctx;
534 isl_mat *H = NULL((void*)0), *C, *H1, *U = NULL((void*)0), *U1, *U2;
535 unsigned dim;
536
537 if (T2)
538 *T2 = NULL((void*)0);
539 if (!B)
540 goto error;
541
542 ctx = isl_mat_get_ctx(B);
543 dim = B->n_col - 1;
544 n = dim - first;
545 if (n < B->n_row)
546 isl_die(ctx, isl_error_invalid, "too many equality constraints",do { isl_handle_error(ctx, isl_error_invalid, "too many equality constraints"
, "/tmp/buildd/llvm-toolchain-snapshot-5.0~svn301135/tools/polly/lib/External/isl/isl_equalities.c"
, 547); goto error; } while (0)
547 goto error)do { isl_handle_error(ctx, isl_error_invalid, "too many equality constraints"
, "/tmp/buildd/llvm-toolchain-snapshot-5.0~svn301135/tools/polly/lib/External/isl/isl_equalities.c"
, 547); goto error; } while (0)
;
548 H = isl_mat_sub_alloc(B, 0, B->n_row, 1 + first, n);
549 H = isl_mat_left_hermite(H, 0, &U, T2);
550 if (!H || !U || (T2 && !*T2))
551 goto error;
552 if (T2) {
553 *T2 = isl_mat_drop_rows(*T2, 0, B->n_row);
554 *T2 = isl_mat_diagonal(isl_mat_identity(ctx, 1 + first), *T2);
555 if (!*T2)
556 goto error;
557 }
558 C = isl_mat_alloc(ctx, 1 + B->n_row, 1 + first);
559 if (!C)
560 goto error;
561 isl_int_set_si(C->row[0][0], 1)isl_sioimath_set_si((C->row[0][0]), 1);
562 isl_seq_clr(C->row[0] + 1, first);
563 isl_mat_sub_neg(ctx, C->row + 1, B->row, B->n_row, 0, 0, 1 + first);
564 H1 = isl_mat_sub_alloc(H, 0, H->n_row, 0, H->n_row);
565 H1 = isl_mat_lin_to_aff(H1);
566 C = isl_mat_inverse_product(H1, C);
567 if (!C)
568 goto error;
569 isl_mat_free(H);
570 if (!isl_int_is_one(C->row[0][0])(isl_sioimath_cmp_si(*(C->row[0][0]), 1) == 0)) {
571 isl_int g;
572
573 isl_int_init(g)isl_sioimath_init((g));
574 for (i = 0; i < B->n_row; ++i) {
575 isl_seq_gcd(C->row[1 + i] + 1, first, &g);
576 isl_int_gcd(g, g, C->row[0][0])isl_sioimath_gcd((g), *(g), *(C->row[0][0]));
577 if (!isl_int_is_divisible_by(C->row[1 + i][0], g)isl_sioimath_is_divisible_by(*(C->row[1 + i][0]), *(g)))
578 break;
579 }
580 isl_int_clear(g)isl_sioimath_clear((g));
581
582 if (i < B->n_row)
583 return empty_compression(ctx, dim, T2, B, C, U);
584 C = isl_mat_normalize(C);
585 }
586 U1 = isl_mat_sub_alloc(U, 0, U->n_row, 0, B->n_row);
587 U1 = isl_mat_lin_to_aff(U1);
588 U2 = isl_mat_sub_alloc(U, 0, U->n_row, B->n_row, U->n_row - B->n_row);
589 U2 = isl_mat_lin_to_aff(U2);
590 isl_mat_free(U);
591 C = isl_mat_product(U1, C);
592 C = isl_mat_aff_direct_sum(C, U2);
593 C = insert_parameter_rows(C, first);
594
595 isl_mat_free(B);
596
597 return C;
598error:
599 isl_mat_free(B);
600 isl_mat_free(H);
601 isl_mat_free(U);
602 if (T2) {
603 isl_mat_free(*T2);
604 *T2 = NULL((void*)0);
605 }
606 return NULL((void*)0);
607}
608
609/* Given a set of equalities
610 *
611 * M x - c = 0
612 *
613 * this function computes a unimodular transformation from a lower-dimensional
614 * space to the original space that bijectively maps the integer points x'
615 * in the lower-dimensional space to the integer points x in the original
616 * space that satisfy the equalities.
617 *
618 * The input is given as a matrix B = [ -c M ] and the output is a
619 * matrix that maps [1 x'] to [1 x].
620 * The number of equality constraints in B is assumed to be smaller than
621 * or equal to the number of variables x.
622 * If T2 is not NULL, then *T2 is set to a matrix mapping [1 x] to [1 x'].
623 */
624__isl_give isl_mat *isl_mat_variable_compression(__isl_take isl_mat *B,
625 __isl_give isl_mat **T2)
626{
627 return isl_mat_final_variable_compression(B, 0, T2);
628}
629
630/* Return "bset" and set *T and *T2 to the identity transformation
631 * on "bset" (provided T and T2 are not NULL).
632 */
633static __isl_give isl_basic_setisl_basic_map *return_with_identity(
634 __isl_take isl_basic_setisl_basic_map *bset, __isl_give isl_mat **T,
635 __isl_give isl_mat **T2)
636{
637 unsigned dim;
638 isl_mat *id;
639
640 if (!bset)
641 return NULL((void*)0);
642 if (!T && !T2)
643 return bset;
644
645 dim = isl_basic_set_dim(bset, isl_dim_set);
646 id = isl_mat_identity(isl_basic_map_get_ctx(bset), 1 + dim);
647 if (T)
648 *T = isl_mat_copy(id);
649 if (T2)
650 *T2 = isl_mat_copy(id);
651 isl_mat_free(id);
652
653 return bset;
654}
655
656/* Use the n equalities of bset to unimodularly transform the
657 * variables x such that n transformed variables x1' have a constant value
658 * and rewrite the constraints of bset in terms of the remaining
659 * transformed variables x2'. The matrix pointed to by T maps
660 * the new variables x2' back to the original variables x, while T2
661 * maps the original variables to the new variables.
662 */
663static struct isl_basic_setisl_basic_map *compress_variables(
664 struct isl_basic_setisl_basic_map *bset, struct isl_mat **T, struct isl_mat **T2)
665{
666 struct isl_mat *B, *TC;
667 unsigned dim;
668
669 if (T)
670 *T = NULL((void*)0);
671 if (T2)
672 *T2 = NULL((void*)0);
673 if (!bset)
674 goto error;
675 isl_assert(bset->ctx, isl_basic_set_n_param(bset) == 0, goto error)do { if (isl_basic_set_n_param(bset) == 0) break; do { isl_handle_error
(bset->ctx, isl_error_unknown, "Assertion \"" "isl_basic_set_n_param(bset) == 0"
"\" failed", "/tmp/buildd/llvm-toolchain-snapshot-5.0~svn301135/tools/polly/lib/External/isl/isl_equalities.c"
, 675); goto error; } while (0); } while (0)
;
676 isl_assert(bset->ctx, bset->n_div == 0, goto error)do { if (bset->n_div == 0) break; do { isl_handle_error(bset
->ctx, isl_error_unknown, "Assertion \"" "bset->n_div == 0"
"\" failed", "/tmp/buildd/llvm-toolchain-snapshot-5.0~svn301135/tools/polly/lib/External/isl/isl_equalities.c"
, 676); goto error; } while (0); } while (0)
;
677 dim = isl_basic_set_n_dim(bset);
678 isl_assert(bset->ctx, bset->n_eq <= dim, goto error)do { if (bset->n_eq <= dim) break; do { isl_handle_error
(bset->ctx, isl_error_unknown, "Assertion \"" "bset->n_eq <= dim"
"\" failed", "/tmp/buildd/llvm-toolchain-snapshot-5.0~svn301135/tools/polly/lib/External/isl/isl_equalities.c"
, 678); goto error; } while (0); } while (0)
;
679 if (bset->n_eq == 0)
680 return return_with_identity(bset, T, T2);
681
682 B = isl_mat_sub_alloc6(bset->ctx, bset->eq, 0, bset->n_eq, 0, 1 + dim);
683 TC = isl_mat_variable_compression(B, T2);
684 if (!TC)
685 goto error;
686 if (TC->n_col == 0) {
687 isl_mat_free(TC);
688 if (T2) {
689 isl_mat_free(*T2);
690 *T2 = NULL((void*)0);
691 }
692 bset = isl_basic_set_set_to_empty(bset);
693 return return_with_identity(bset, T, T2);
694 }
695
696 bset = isl_basic_set_preimage(bset, T ? isl_mat_copy(TC) : TC);
697 if (T)
698 *T = TC;
699 return bset;
700error:
701 isl_basic_set_free(bset);
702 return NULL((void*)0);
703}
704
705struct isl_basic_setisl_basic_map *isl_basic_set_remove_equalities(
706 struct isl_basic_setisl_basic_map *bset, struct isl_mat **T, struct isl_mat **T2)
707{
708 if (T)
1
Assuming 'T' is null
2
Taking false branch
709 *T = NULL((void*)0);
710 if (T2)
3
Assuming 'T2' is null
4
Taking false branch
711 *T2 = NULL((void*)0);
712 if (!bset)
5
Assuming 'bset' is non-null
6
Taking false branch
713 return NULL((void*)0);
714 isl_assert(bset->ctx, isl_basic_set_n_param(bset) == 0, goto error)do { if (isl_basic_set_n_param(bset) == 0) break; do { isl_handle_error
(bset->ctx, isl_error_unknown, "Assertion \"" "isl_basic_set_n_param(bset) == 0"
"\" failed", "/tmp/buildd/llvm-toolchain-snapshot-5.0~svn301135/tools/polly/lib/External/isl/isl_equalities.c"
, 714); goto error; } while (0); } while (0)
;
715 bset = isl_basic_set_gauss(bset, NULL((void*)0));
716 if (ISL_F_ISSET(bset, ISL_BASIC_SET_EMPTY)(!!(((bset)->flags) & ((1 << 1)))))
717 return return_with_identity(bset, T, T2);
718 bset = compress_variables(bset, T, T2);
719 return bset;
720error:
721 isl_basic_set_free(bset);
722 *T = NULL((void*)0);
7
Dereference of null pointer (loaded from variable 'T')
723 return NULL((void*)0);
724}
725
726/* Check if dimension dim belongs to a residue class
727 * i_dim \equiv r mod m
728 * with m != 1 and if so return m in *modulo and r in *residue.
729 * As a special case, when i_dim has a fixed value v, then
730 * *modulo is set to 0 and *residue to v.
731 *
732 * If i_dim does not belong to such a residue class, then *modulo
733 * is set to 1 and *residue is set to 0.
734 */
735isl_stat isl_basic_set_dim_residue_class(__isl_keep isl_basic_setisl_basic_map *bset,
736 int pos, isl_int *modulo, isl_int *residue)
737{
738 isl_bool fixed;
739 struct isl_ctx *ctx;
740 struct isl_mat *H = NULL((void*)0), *U = NULL((void*)0), *C, *H1, *U1;
741 unsigned total;
742 unsigned nparam;
743
744 if (!bset || !modulo || !residue)
745 return isl_stat_error;
746
747 fixed = isl_basic_set_plain_dim_is_fixed(bset, pos, residue);
748 if (fixed < 0)
749 return isl_stat_error;
750 if (fixed) {
751 isl_int_set_si(*modulo, 0)isl_sioimath_set_si((*modulo), 0);
752 return isl_stat_ok;
753 }
754
755 ctx = isl_basic_set_get_ctx(bset);
756 total = isl_basic_set_total_dim(bset);
757 nparam = isl_basic_set_n_param(bset);
758 H = isl_mat_sub_alloc6(ctx, bset->eq, 0, bset->n_eq, 1, total);
759 H = isl_mat_left_hermite(H, 0, &U, NULL((void*)0));
760 if (!H)
761 return isl_stat_error;
762
763 isl_seq_gcd(U->row[nparam + pos]+bset->n_eq,
764 total-bset->n_eq, modulo);
765 if (isl_int_is_zero(*modulo)(isl_sioimath_sgn(*(*modulo)) == 0))
766 isl_int_set_si(*modulo, 1)isl_sioimath_set_si((*modulo), 1);
767 if (isl_int_is_one(*modulo)(isl_sioimath_cmp_si(*(*modulo), 1) == 0)) {
768 isl_int_set_si(*residue, 0)isl_sioimath_set_si((*residue), 0);
769 isl_mat_free(H);
770 isl_mat_free(U);
771 return isl_stat_ok;
772 }
773
774 C = isl_mat_alloc(ctx, 1 + bset->n_eq, 1);
775 if (!C)
776 goto error;
777 isl_int_set_si(C->row[0][0], 1)isl_sioimath_set_si((C->row[0][0]), 1);
778 isl_mat_sub_neg(ctx, C->row + 1, bset->eq, bset->n_eq, 0, 0, 1);
779 H1 = isl_mat_sub_alloc(H, 0, H->n_row, 0, H->n_row);
780 H1 = isl_mat_lin_to_aff(H1);
781 C = isl_mat_inverse_product(H1, C);
782 isl_mat_free(H);
783 U1 = isl_mat_sub_alloc(U, nparam+pos, 1, 0, bset->n_eq);
784 U1 = isl_mat_lin_to_aff(U1);
785 isl_mat_free(U);
786 C = isl_mat_product(U1, C);
787 if (!C)
788 return isl_stat_error;
789 if (!isl_int_is_divisible_by(C->row[1][0], C->row[0][0])isl_sioimath_is_divisible_by(*(C->row[1][0]), *(C->row[
0][0]))
) {
790 bset = isl_basic_set_copy(bset);
791 bset = isl_basic_set_set_to_empty(bset);
792 isl_basic_set_free(bset);
793 isl_int_set_si(*modulo, 1)isl_sioimath_set_si((*modulo), 1);
794 isl_int_set_si(*residue, 0)isl_sioimath_set_si((*residue), 0);
795 return isl_stat_ok;
796 }
797 isl_int_divexact(*residue, C->row[1][0], C->row[0][0])isl_sioimath_tdiv_q((*residue), *(C->row[1][0]), *(C->row
[0][0]))
;
798 isl_int_fdiv_r(*residue, *residue, *modulo)isl_sioimath_fdiv_r((*residue), *(*residue), *(*modulo));
799 isl_mat_free(C);
800 return isl_stat_ok;
801error:
802 isl_mat_free(H);
803 isl_mat_free(U);
804 return isl_stat_error;
805}
806
807/* Check if dimension dim belongs to a residue class
808 * i_dim \equiv r mod m
809 * with m != 1 and if so return m in *modulo and r in *residue.
810 * As a special case, when i_dim has a fixed value v, then
811 * *modulo is set to 0 and *residue to v.
812 *
813 * If i_dim does not belong to such a residue class, then *modulo
814 * is set to 1 and *residue is set to 0.
815 */
816isl_stat isl_set_dim_residue_class(__isl_keep isl_setisl_map *set,
817 int pos, isl_int *modulo, isl_int *residue)
818{
819 isl_int m;
820 isl_int r;
821 int i;
822
823 if (!set || !modulo || !residue)
824 return isl_stat_error;
825
826 if (set->n == 0) {
827 isl_int_set_si(*modulo, 0)isl_sioimath_set_si((*modulo), 0);
828 isl_int_set_si(*residue, 0)isl_sioimath_set_si((*residue), 0);
829 return isl_stat_ok;
830 }
831
832 if (isl_basic_set_dim_residue_class(set->p[0], pos, modulo, residue)<0)
833 return isl_stat_error;
834
835 if (set->n == 1)
836 return isl_stat_ok;
837
838 if (isl_int_is_one(*modulo)(isl_sioimath_cmp_si(*(*modulo), 1) == 0))
839 return isl_stat_ok;
840
841 isl_int_init(m)isl_sioimath_init((m));
842 isl_int_init(r)isl_sioimath_init((r));
843
844 for (i = 1; i < set->n; ++i) {
845 if (isl_basic_set_dim_residue_class(set->p[i], pos, &m, &r) < 0)
846 goto error;
847 isl_int_gcd(*modulo, *modulo, m)isl_sioimath_gcd((*modulo), *(*modulo), *(m));
848 isl_int_sub(m, *residue, r)isl_sioimath_sub((m), *(*residue), *(r));
849 isl_int_gcd(*modulo, *modulo, m)isl_sioimath_gcd((*modulo), *(*modulo), *(m));
850 if (!isl_int_is_zero(*modulo)(isl_sioimath_sgn(*(*modulo)) == 0))
851 isl_int_fdiv_r(*residue, *residue, *modulo)isl_sioimath_fdiv_r((*residue), *(*residue), *(*modulo));
852 if (isl_int_is_one(*modulo)(isl_sioimath_cmp_si(*(*modulo), 1) == 0))
853 break;
854 }
855
856 isl_int_clear(m)isl_sioimath_clear((m));
857 isl_int_clear(r)isl_sioimath_clear((r));
858
859 return isl_stat_ok;
860error:
861 isl_int_clear(m)isl_sioimath_clear((m));
862 isl_int_clear(r)isl_sioimath_clear((r));
863 return isl_stat_error;
864}
865
866/* Check if dimension "dim" belongs to a residue class
867 * i_dim \equiv r mod m
868 * with m != 1 and if so return m in *modulo and r in *residue.
869 * As a special case, when i_dim has a fixed value v, then
870 * *modulo is set to 0 and *residue to v.
871 *
872 * If i_dim does not belong to such a residue class, then *modulo
873 * is set to 1 and *residue is set to 0.
874 */
875isl_stat isl_set_dim_residue_class_val(__isl_keep isl_setisl_map *set,
876 int pos, __isl_give isl_val **modulo, __isl_give isl_val **residue)
877{
878 *modulo = NULL((void*)0);
879 *residue = NULL((void*)0);
880 if (!set)
881 return isl_stat_error;
882 *modulo = isl_val_alloc(isl_set_get_ctx(set));
883 *residue = isl_val_alloc(isl_set_get_ctx(set));
884 if (!*modulo || !*residue)
885 goto error;
886 if (isl_set_dim_residue_class(set, pos,
887 &(*modulo)->n, &(*residue)->n) < 0)
888 goto error;
889 isl_int_set_si((*modulo)->d, 1)isl_sioimath_set_si(((*modulo)->d), 1);
890 isl_int_set_si((*residue)->d, 1)isl_sioimath_set_si(((*residue)->d), 1);
891 return isl_stat_ok;
892error:
893 isl_val_free(*modulo);
894 isl_val_free(*residue);
895 return isl_stat_error;
896}