Coverage Report

Created: 2017-10-03 07:32

/Users/buildslave/jenkins/sharedspace/clang-stage2-coverage-R@2/llvm/tools/polly/lib/External/isl/isl_equalities.c
Line
Count
Source (jump to first uncovered line)
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
 */
66
static struct isl_mat *particular_solution(struct isl_mat *B, struct isl_vec *d)
67
14.8k
{
68
14.8k
  int i, j;
69
14.8k
  struct isl_mat *M = NULL;
70
14.8k
  struct isl_mat *C = NULL;
71
14.8k
  struct isl_mat *U = NULL;
72
14.8k
  struct isl_mat *H = NULL;
73
14.8k
  struct isl_mat *cst = NULL;
74
14.8k
  struct isl_mat *T = NULL;
75
14.8k
76
14.8k
  M = isl_mat_alloc(B->ctx, B->n_row, B->n_row + B->n_col - 1);
77
14.8k
  C = isl_mat_alloc(B->ctx, 1 + B->n_row, 1);
78
14.8k
  if (
!M || 14.8k
!C14.8k
)
79
0
    goto error;
80
14.8k
  
isl_int_set_si14.8k
(C->row[0][0], 1);
81
33.3k
  for (i = 0; 
i < B->n_row33.3k
;
++i18.5k
) {
82
18.5k
    isl_seq_clr(M->row[i], B->n_row);
83
18.5k
    isl_int_set(M->row[i][i], d->block.data[i]);
84
18.5k
    isl_int_neg(C->row[1 + i][0], B->row[i][0]);
85
18.5k
    isl_int_fdiv_r(C->row[1+i][0], C->row[1+i][0], M->row[i][i]);
86
85.2k
    for (j = 0; 
j < B->n_col - 185.2k
;
++j66.6k
)
87
66.6k
      isl_int_fdiv_r(M->row[i][B->n_row + j],
88
18.5k
          B->row[i][1 + j], M->row[i][i]);
89
18.5k
  }
90
14.8k
  M = isl_mat_left_hermite(M, 0, &U, NULL);
91
14.8k
  if (
!M || 14.8k
!U14.8k
)
92
0
    goto error;
93
14.8k
  H = isl_mat_sub_alloc(M, 0, B->n_row, 0, B->n_row);
94
14.8k
  H = isl_mat_lin_to_aff(H);
95
14.8k
  C = isl_mat_inverse_product(H, C);
96
14.8k
  if (!C)
97
0
    goto error;
98
31.9k
  
for (i = 0; 14.8k
i < B->n_row31.9k
;
++i17.1k
) {
99
18.5k
    if (
!18.5k
isl_int_is_divisible_by18.5k
(C->row[1+i][0], C->row[0][0]))
100
1.40k
      break;
101
17.1k
    
isl_int_divexact17.1k
(C->row[1+i][0], C->row[1+i][0], C->row[0][0]);
102
17.1k
  }
103
14.8k
  if (i < B->n_row)
104
1.40k
    cst = isl_mat_alloc(B->ctx, B->n_row, 0);
105
14.8k
  else
106
13.4k
    cst = isl_mat_sub_alloc(C, 1, B->n_row, 0, 1);
107
14.8k
  T = isl_mat_sub_alloc(U, B->n_row, B->n_col - 1, 0, B->n_row);
108
14.8k
  cst = isl_mat_product(T, cst);
109
14.8k
  isl_mat_free(M);
110
14.8k
  isl_mat_free(C);
111
14.8k
  isl_mat_free(U);
112
14.8k
  return cst;
113
0
error:
114
0
  isl_mat_free(M);
115
0
  isl_mat_free(C);
116
0
  isl_mat_free(U);
117
0
  return NULL;
118
14.8k
}
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
 */
128
static struct isl_mat *parameter_compression_1(
129
      struct isl_mat *B, struct isl_vec *d)
130
10.8k
{
131
10.8k
  struct isl_mat *U;
132
10.8k
133
10.8k
  U = isl_mat_alloc(B->ctx, B->n_col - 1, B->n_col - 1);
134
10.8k
  if (!U)
135
0
    return NULL;
136
10.8k
  isl_seq_cpy(U->row[0], B->row[0] + 1, B->n_col - 1);
137
10.8k
  U = isl_mat_unimodular_complete(U, 1);
138
10.8k
  U = isl_mat_right_inverse(U);
139
10.8k
  if (!U)
140
0
    return NULL;
141
10.8k
  isl_mat_col_mul(U, 0, d->block.data[0], 0);
142
10.8k
  U = isl_mat_lin_to_aff(U);
143
10.8k
  return U;
144
10.8k
}
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
 */
159
static struct isl_mat *parameter_compression_multi(
160
      struct isl_mat *B, struct isl_vec *d)
161
2.46k
{
162
2.46k
  int i, j, k;
163
2.46k
  isl_int D;
164
2.46k
  struct isl_mat *A = NULL, *U = NULL;
165
2.46k
  struct isl_mat *T;
166
2.46k
  unsigned size;
167
2.46k
168
2.46k
  isl_int_init(D);
169
2.46k
170
2.46k
  isl_vec_lcm(d, &D);
171
2.46k
172
2.46k
  size = B->n_col - 1;
173
2.46k
  A = isl_mat_alloc(B->ctx, size, B->n_row * size);
174
2.46k
  U = isl_mat_alloc(B->ctx, size, size);
175
2.46k
  if (
!U || 2.46k
!A2.46k
)
176
0
    goto error;
177
7.69k
  
for (i = 0; 2.46k
i < B->n_row7.69k
;
++i5.23k
) {
178
5.23k
    isl_seq_cpy(U->row[0], B->row[i] + 1, size);
179
5.23k
    U = isl_mat_unimodular_complete(U, 1);
180
5.23k
    if (!U)
181
0
      goto error;
182
5.23k
    
isl_int_divexact5.23k
(D, D, d->block.data[i]);
183
29.2k
    for (k = 0; 
k < U->n_col29.2k
;
++k24.0k
)
184
24.0k
      isl_int_mul(A->row[k][i*size+0], D, U->row[0][k]);
185
5.23k
    isl_int_mul(D, D, d->block.data[i]);
186
24.0k
    for (j = 1; 
j < U->n_row24.0k
;
++j18.7k
)
187
140k
      
for (k = 0; 18.7k
k < U->n_col140k
;
++k121k
)
188
121k
        isl_int_mul(A->row[k][i*size+j],
189
5.23k
            D, U->row[j][k]);
190
5.23k
  }
191
2.46k
  A = isl_mat_left_hermite(A, 0, NULL, NULL);
192
2.46k
  T = isl_mat_sub_alloc(A, 0, A->n_row, 0, A->n_row);
193
2.46k
  T = isl_mat_lin_to_aff(T);
194
2.46k
  if (!T)
195
0
    goto error;
196
2.46k
  
isl_int_set2.46k
(T->row[0][0], D);
197
2.46k
  T = isl_mat_right_inverse(T);
198
2.46k
  if (!T)
199
0
    goto error;
200
2.46k
  
isl_assert2.46k
(T->ctx, isl_int_is_one(T->row[0][0]), goto error);
201
2.46k
  T = isl_mat_transpose(T);
202
2.46k
  isl_mat_free(A);
203
2.46k
  isl_mat_free(U);
204
2.46k
205
2.46k
  isl_int_clear(D);
206
2.46k
  return T;
207
0
error:
208
0
  isl_mat_free(A);
209
0
  isl_mat_free(U);
210
0
  isl_int_clear(D);
211
0
  return NULL;
212
2.46k
}
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
 */
308
__isl_give isl_mat *isl_mat_parameter_compression(__isl_take isl_mat *B,
309
  __isl_take isl_vec *d)
310
14.8k
{
311
14.8k
  int i;
312
14.8k
  struct isl_mat *cst = NULL;
313
14.8k
  struct isl_mat *T = NULL;
314
14.8k
  isl_int D;
315
14.8k
316
14.8k
  if (
!B || 14.8k
!d14.8k
)
317
0
    goto error;
318
14.8k
  
isl_assert14.8k
(B->ctx, B->n_row == d->size, goto error);
319
14.8k
  cst = particular_solution(B, d);
320
14.8k
  if (!cst)
321
0
    goto error;
322
14.8k
  
if (14.8k
cst->n_col == 014.8k
) {
323
1.40k
    T = isl_mat_alloc(B->ctx, B->n_col, 0);
324
1.40k
    isl_mat_free(cst);
325
1.40k
    isl_mat_free(B);
326
1.40k
    isl_vec_free(d);
327
1.40k
    return T;
328
1.40k
  }
329
13.4k
  
isl_int_init13.4k
(D);
330
13.4k
  /* Replace a*g*row = 0 mod g*m by row = 0 mod m */
331
29.7k
  for (i = 0; 
i < B->n_row29.7k
;
++i16.2k
) {
332
16.2k
    isl_seq_gcd(B->row[i] + 1, B->n_col - 1, &D);
333
16.2k
    if (isl_int_is_one(D))
334
15.4k
      continue;
335
848
    
if (848
isl_int_is_zero848
(D)) {
336
228
      B = isl_mat_drop_rows(B, i, 1);
337
228
      d = isl_vec_cow(d);
338
228
      if (
!B || 228
!d228
)
339
0
        goto error2;
340
228
      isl_seq_cpy(d->block.data+i, d->block.data+i+1,
341
228
              d->size - (i+1));
342
228
      d->size--;
343
228
      i--;
344
228
      continue;
345
228
    }
346
620
    B = isl_mat_cow(B);
347
620
    if (!B)
348
0
      goto error2;
349
620
    isl_seq_scale_down(B->row[i] + 1, B->row[i] + 1, D, B->n_col-1);
350
620
    isl_int_gcd(D, D, d->block.data[i]);
351
620
    d = isl_vec_cow(d);
352
620
    if (!d)
353
0
      goto error2;
354
620
    
isl_int_divexact620
(d->block.data[i], d->block.data[i], D);
355
620
  }
356
13.4k
  
isl_int_clear13.4k
(D);
357
13.4k
  if (B->n_row == 0)
358
163
    T = isl_mat_identity(B->ctx, B->n_col);
359
13.2k
  else 
if (13.2k
B->n_row == 113.2k
)
360
10.8k
    T = parameter_compression_1(B, d);
361
13.2k
  else
362
2.46k
    T = parameter_compression_multi(B, d);
363
13.4k
  T = isl_mat_left_hermite(T, 0, NULL, NULL);
364
13.4k
  if (!T)
365
0
    goto error;
366
13.4k
  isl_mat_sub_copy(T->ctx, T->row + 1, cst->row, cst->n_row, 0, 0, 1);
367
13.4k
  isl_mat_free(cst);
368
13.4k
  isl_mat_free(B);
369
13.4k
  isl_vec_free(d);
370
13.4k
  return T;
371
0
error2:
372
0
  isl_int_clear(D);
373
0
error:
374
0
  isl_mat_free(cst);
375
0
  isl_mat_free(B);
376
0
  isl_vec_free(d);
377
0
  return NULL;
378
14.8k
}
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
10
{
409
10
  isl_ctx *ctx;
410
10
  isl_vec *d;
411
10
  int n_row, n_col;
412
10
413
10
  if (!A)
414
0
    return isl_mat_free(B);
415
10
416
10
  ctx = isl_mat_get_ctx(A);
417
10
  n_row = A->n_row;
418
10
  n_col = A->n_col;
419
10
  A = isl_mat_left_hermite(A, 0, NULL, NULL);
420
10
  A = isl_mat_drop_cols(A, n_row, n_col - n_row);
421
10
  A = isl_mat_lin_to_aff(A);
422
10
  A = isl_mat_right_inverse(A);
423
10
  d = isl_vec_alloc(ctx, n_row);
424
10
  if (A)
425
10
    d = isl_vec_set(d, A->row[0][0]);
426
10
  A = isl_mat_drop_rows(A, 0, 1);
427
10
  A = isl_mat_drop_cols(A, 0, 1);
428
10
  B = isl_mat_product(A, B);
429
10
430
10
  return isl_mat_parameter_compression(B, d);
431
10
}
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
 */
442
static __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
23
{
446
23
  isl_mat_free(free1);
447
23
  isl_mat_free(free2);
448
23
  isl_mat_free(free3);
449
23
  if (
T223
) {
450
13
    isl_mat_free(*T2);
451
13
    *T2 = isl_mat_alloc(ctx, 0, 1 + dim);
452
13
  }
453
23
  return isl_mat_alloc(ctx, 1 + dim, 0);
454
23
}
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
 */
460
static __isl_give isl_mat *insert_parameter_rows(__isl_take isl_mat *mat,
461
  unsigned nparam)
462
140k
{
463
140k
  int i;
464
140k
465
140k
  if (nparam == 0)
466
140k
    return mat;
467
1
  
if (1
!mat1
)
468
0
    return NULL;
469
1
470
1
  mat = isl_mat_insert_rows(mat, 1, nparam);
471
1
  if (!mat)
472
0
    return NULL;
473
1
474
2
  
for (i = 0; 1
i < nparam2
;
++i1
) {
475
1
    isl_seq_clr(mat->row[1 + i], mat->n_col);
476
1
    isl_int_set(mat->row[1 + i][1 + i], mat->row[0][0]);
477
1
  }
478
140k
479
140k
  return mat;
480
140k
}
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
140k
{
532
140k
  int i, n;
533
140k
  isl_ctx *ctx;
534
140k
  isl_mat *H = NULL, *C, *H1, *U = NULL, *U1, *U2;
535
140k
  unsigned dim;
536
140k
537
140k
  if (T2)
538
38.8k
    *T2 = NULL;
539
140k
  if (!B)
540
0
    goto error;
541
140k
542
140k
  ctx = isl_mat_get_ctx(B);
543
140k
  dim = B->n_col - 1;
544
140k
  n = dim - first;
545
140k
  if (n < B->n_row)
546
0
    isl_die(ctx, isl_error_invalid, "too many equality constraints",
547
140k
      goto error);
548
140k
  H = isl_mat_sub_alloc(B, 0, B->n_row, 1 + first, n);
549
140k
  H = isl_mat_left_hermite(H, 0, &U, T2);
550
140k
  if (
!H || 140k
!U140k
||
(T2 && 140k
!*T238.8k
))
551
0
    goto error;
552
140k
  
if (140k
T2140k
) {
553
38.8k
    *T2 = isl_mat_drop_rows(*T2, 0, B->n_row);
554
38.8k
    *T2 = isl_mat_diagonal(isl_mat_identity(ctx, 1 + first), *T2);
555
38.8k
    if (!*T2)
556
0
      goto error;
557
140k
  }
558
140k
  C = isl_mat_alloc(ctx, 1 + B->n_row, 1 + first);
559
140k
  if (!C)
560
0
    goto error;
561
140k
  
isl_int_set_si140k
(C->row[0][0], 1);
562
140k
  isl_seq_clr(C->row[0] + 1, first);
563
140k
  isl_mat_sub_neg(ctx, C->row + 1, B->row, B->n_row, 0, 0, 1 + first);
564
140k
  H1 = isl_mat_sub_alloc(H, 0, H->n_row, 0, H->n_row);
565
140k
  H1 = isl_mat_lin_to_aff(H1);
566
140k
  C = isl_mat_inverse_product(H1, C);
567
140k
  if (!C)
568
0
    goto error;
569
140k
  isl_mat_free(H);
570
140k
  if (
!140k
isl_int_is_one140k
(C->row[0][0])) {
571
794
    isl_int g;
572
794
573
794
    isl_int_init(g);
574
4.00k
    for (i = 0; 
i < B->n_row4.00k
;
++i3.21k
) {
575
3.23k
      isl_seq_gcd(C->row[1 + i] + 1, first, &g);
576
3.23k
      isl_int_gcd(g, g, C->row[0][0]);
577
3.23k
      if (
!3.23k
isl_int_is_divisible_by3.23k
(C->row[1 + i][0], g))
578
23
        break;
579
3.23k
    }
580
794
    isl_int_clear(g);
581
794
582
794
    if (i < B->n_row)
583
23
      return empty_compression(ctx, dim, T2, B, C, U);
584
771
    C = isl_mat_normalize(C);
585
771
  }
586
140k
  U1 = isl_mat_sub_alloc(U, 0, U->n_row, 0, B->n_row);
587
140k
  U1 = isl_mat_lin_to_aff(U1);
588
140k
  U2 = isl_mat_sub_alloc(U, 0, U->n_row, B->n_row, U->n_row - B->n_row);
589
140k
  U2 = isl_mat_lin_to_aff(U2);
590
140k
  isl_mat_free(U);
591
140k
  C = isl_mat_product(U1, C);
592
140k
  C = isl_mat_aff_direct_sum(C, U2);
593
140k
  C = insert_parameter_rows(C, first);
594
140k
595
140k
  isl_mat_free(B);
596
140k
597
140k
  return C;
598
0
error:
599
0
  isl_mat_free(B);
600
0
  isl_mat_free(H);
601
0
  isl_mat_free(U);
602
0
  if (
T20
) {
603
0
    isl_mat_free(*T2);
604
0
    *T2 = NULL;
605
0
  }
606
0
  return NULL;
607
140k
}
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
140k
{
627
140k
  return isl_mat_final_variable_compression(B, 0, T2);
628
140k
}
629
630
/* Return "bset" and set *T and *T2 to the identity transformation
631
 * on "bset" (provided T and T2 are not NULL).
632
 */
633
static __isl_give isl_basic_set *return_with_identity(
634
  __isl_take isl_basic_set *bset, __isl_give isl_mat **T,
635
  __isl_give isl_mat **T2)
636
10
{
637
10
  unsigned dim;
638
10
  isl_mat *id;
639
10
640
10
  if (!bset)
641
0
    return NULL;
642
10
  
if (10
!T && 10
!T20
)
643
0
    return bset;
644
10
645
10
  dim = isl_basic_set_dim(bset, isl_dim_set);
646
10
  id = isl_mat_identity(isl_basic_map_get_ctx(bset), 1 + dim);
647
10
  if (T)
648
10
    *T = isl_mat_copy(id);
649
10
  if (T2)
650
0
    *T2 = isl_mat_copy(id);
651
10
  isl_mat_free(id);
652
10
653
10
  return bset;
654
10
}
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
 */
663
static struct isl_basic_set *compress_variables(
664
  struct isl_basic_set *bset, struct isl_mat **T, struct isl_mat **T2)
665
120k
{
666
120k
  struct isl_mat *B, *TC;
667
120k
  unsigned dim;
668
120k
669
120k
  if (T)
670
120k
    *T = NULL;
671
120k
  if (T2)
672
29.5k
    *T2 = NULL;
673
120k
  if (!bset)
674
0
    goto error;
675
120k
  
isl_assert120k
(bset->ctx, isl_basic_set_n_param(bset) == 0, goto error);
676
120k
  
isl_assert120k
(bset->ctx, bset->n_div == 0, goto error);
677
120k
  dim = isl_basic_set_n_dim(bset);
678
120k
  isl_assert(bset->ctx, bset->n_eq <= dim, goto error);
679
120k
  
if (120k
bset->n_eq == 0120k
)
680
0
    return return_with_identity(bset, T, T2);
681
120k
682
120k
  B = isl_mat_sub_alloc6(bset->ctx, bset->eq, 0, bset->n_eq, 0, 1 + dim);
683
120k
  TC = isl_mat_variable_compression(B, T2);
684
120k
  if (!TC)
685
0
    goto error;
686
120k
  
if (120k
TC->n_col == 0120k
) {
687
10
    isl_mat_free(TC);
688
10
    if (
T210
) {
689
0
      isl_mat_free(*T2);
690
0
      *T2 = NULL;
691
0
    }
692
10
    bset = isl_basic_set_set_to_empty(bset);
693
10
    return return_with_identity(bset, T, T2);
694
10
  }
695
120k
696
120k
  
bset = isl_basic_set_preimage(bset, T ? 120k
isl_mat_copy(TC)120k
:
TC0
);
697
120k
  if (T)
698
120k
    *T = TC;
699
120k
  return bset;
700
0
error:
701
0
  isl_basic_set_free(bset);
702
0
  return NULL;
703
120k
}
704
705
struct isl_basic_set *isl_basic_set_remove_equalities(
706
  struct isl_basic_set *bset, struct isl_mat **T, struct isl_mat **T2)
707
120k
{
708
120k
  if (T)
709
120k
    *T = NULL;
710
120k
  if (T2)
711
29.5k
    *T2 = NULL;
712
120k
  if (!bset)
713
0
    return NULL;
714
120k
  
isl_assert120k
(bset->ctx, isl_basic_set_n_param(bset) == 0, goto error);
715
120k
  bset = isl_basic_set_gauss(bset, NULL);
716
120k
  if (ISL_F_ISSET(bset, ISL_BASIC_SET_EMPTY))
717
0
    return return_with_identity(bset, T, T2);
718
120k
  bset = compress_variables(bset, T, T2);
719
120k
  return bset;
720
0
error:
721
0
  isl_basic_set_free(bset);
722
0
  *T = NULL;
723
0
  return NULL;
724
120k
}
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
 */
735
isl_stat isl_basic_set_dim_residue_class(__isl_keep isl_basic_set *bset,
736
  int pos, isl_int *modulo, isl_int *residue)
737
74
{
738
74
  isl_bool fixed;
739
74
  struct isl_ctx *ctx;
740
74
  struct isl_mat *H = NULL, *U = NULL, *C, *H1, *U1;
741
74
  unsigned total;
742
74
  unsigned nparam;
743
74
744
74
  if (
!bset || 74
!modulo74
||
!residue74
)
745
0
    return isl_stat_error;
746
74
747
74
  fixed = isl_basic_set_plain_dim_is_fixed(bset, pos, residue);
748
74
  if (fixed < 0)
749
0
    return isl_stat_error;
750
74
  
if (74
fixed74
) {
751
0
    isl_int_set_si(*modulo, 0);
752
0
    return isl_stat_ok;
753
0
  }
754
74
755
74
  ctx = isl_basic_set_get_ctx(bset);
756
74
  total = isl_basic_set_total_dim(bset);
757
74
  nparam = isl_basic_set_n_param(bset);
758
74
  H = isl_mat_sub_alloc6(ctx, bset->eq, 0, bset->n_eq, 1, total);
759
74
  H = isl_mat_left_hermite(H, 0, &U, NULL);
760
74
  if (!H)
761
0
    return isl_stat_error;
762
74
763
74
  isl_seq_gcd(U->row[nparam + pos]+bset->n_eq,
764
74
      total-bset->n_eq, modulo);
765
74
  if (isl_int_is_zero(*modulo))
766
0
    isl_int_set_si(*modulo, 1);
767
74
  if (
isl_int_is_one74
(*modulo)) {
768
59
    isl_int_set_si(*residue, 0);
769
59
    isl_mat_free(H);
770
59
    isl_mat_free(U);
771
59
    return isl_stat_ok;
772
59
  }
773
15
774
15
  C = isl_mat_alloc(ctx, 1 + bset->n_eq, 1);
775
15
  if (!C)
776
0
    goto error;
777
15
  
isl_int_set_si15
(C->row[0][0], 1);
778
15
  isl_mat_sub_neg(ctx, C->row + 1, bset->eq, bset->n_eq, 0, 0, 1);
779
15
  H1 = isl_mat_sub_alloc(H, 0, H->n_row, 0, H->n_row);
780
15
  H1 = isl_mat_lin_to_aff(H1);
781
15
  C = isl_mat_inverse_product(H1, C);
782
15
  isl_mat_free(H);
783
15
  U1 = isl_mat_sub_alloc(U, nparam+pos, 1, 0, bset->n_eq);
784
15
  U1 = isl_mat_lin_to_aff(U1);
785
15
  isl_mat_free(U);
786
15
  C = isl_mat_product(U1, C);
787
15
  if (!C)
788
0
    return isl_stat_error;
789
15
  
if (15
!15
isl_int_is_divisible_by15
(C->row[1][0], C->row[0][0])) {
790
0
    bset = isl_basic_set_copy(bset);
791
0
    bset = isl_basic_set_set_to_empty(bset);
792
0
    isl_basic_set_free(bset);
793
0
    isl_int_set_si(*modulo, 1);
794
0
    isl_int_set_si(*residue, 0);
795
0
    return isl_stat_ok;
796
0
  }
797
15
  
isl_int_divexact15
(*residue, C->row[1][0], C->row[0][0]);
798
15
  isl_int_fdiv_r(*residue, *residue, *modulo);
799
15
  isl_mat_free(C);
800
15
  return isl_stat_ok;
801
0
error:
802
0
  isl_mat_free(H);
803
0
  isl_mat_free(U);
804
0
  return isl_stat_error;
805
74
}
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
 */
816
isl_stat isl_set_dim_residue_class(__isl_keep isl_set *set,
817
  int pos, isl_int *modulo, isl_int *residue)
818
73
{
819
73
  isl_int m;
820
73
  isl_int r;
821
73
  int i;
822
73
823
73
  if (
!set || 73
!modulo73
||
!residue73
)
824
0
    return isl_stat_error;
825
73
826
73
  
if (73
set->n == 073
) {
827
0
    isl_int_set_si(*modulo, 0);
828
0
    isl_int_set_si(*residue, 0);
829
0
    return isl_stat_ok;
830
0
  }
831
73
832
73
  
if (73
isl_basic_set_dim_residue_class(set->p[0], pos, modulo, residue)<073
)
833
0
    return isl_stat_error;
834
73
835
73
  
if (73
set->n == 173
)
836
64
    return isl_stat_ok;
837
9
838
9
  
if (9
isl_int_is_one9
(*modulo))
839
8
    return isl_stat_ok;
840
1
841
1
  
isl_int_init1
(m);
842
1
  isl_int_init(r);
843
1
844
2
  for (i = 1; 
i < set->n2
;
++i1
) {
845
1
    if (isl_basic_set_dim_residue_class(set->p[i], pos, &m, &r) < 0)
846
0
      goto error;
847
1
    
isl_int_gcd1
(*modulo, *modulo, m);
848
1
    isl_int_sub(m, *residue, r);
849
1
    isl_int_gcd(*modulo, *modulo, m);
850
1
    if (
!1
isl_int_is_zero1
(*modulo))
851
1
      isl_int_fdiv_r(*residue, *residue, *modulo);
852
1
    if (isl_int_is_one(*modulo))
853
0
      break;
854
1
  }
855
1
856
1
  
isl_int_clear1
(m);
857
1
  isl_int_clear(r);
858
1
859
1
  return isl_stat_ok;
860
0
error:
861
0
  isl_int_clear(m);
862
0
  isl_int_clear(r);
863
0
  return isl_stat_error;
864
73
}
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
 */
875
isl_stat isl_set_dim_residue_class_val(__isl_keep isl_set *set,
876
  int pos, __isl_give isl_val **modulo, __isl_give isl_val **residue)
877
72
{
878
72
  *modulo = NULL;
879
72
  *residue = NULL;
880
72
  if (!set)
881
0
    return isl_stat_error;
882
72
  *modulo = isl_val_alloc(isl_set_get_ctx(set));
883
72
  *residue = isl_val_alloc(isl_set_get_ctx(set));
884
72
  if (
!*modulo || 72
!*residue72
)
885
0
    goto error;
886
72
  
if (72
isl_set_dim_residue_class(set, pos,
887
72
          &(*modulo)->n, &(*residue)->n) < 0)
888
0
    goto error;
889
72
  
isl_int_set_si72
((*modulo)->d, 1);
890
72
  isl_int_set_si((*residue)->d, 1);
891
72
  return isl_stat_ok;
892
0
error:
893
0
  isl_val_free(*modulo);
894
0
  isl_val_free(*residue);
895
0
  return isl_stat_error;
896
72
}