Coverage Report

Created: 2017-11-21 03:47

/Users/buildslave/jenkins/workspace/clang-stage2-coverage-R/llvm/tools/polly/lib/External/isl/basis_reduction_templ.c
Line
Count
Source (jump to first uncovered line)
1
/*
2
 * Copyright 2006-2007 Universiteit Leiden
3
 * Copyright 2008-2009 Katholieke Universiteit Leuven
4
 *
5
 * Use of this software is governed by the MIT license
6
 *
7
 * Written by Sven Verdoolaege, Leiden Institute of Advanced Computer Science,
8
 * Universiteit Leiden, Niels Bohrweg 1, 2333 CA Leiden, The Netherlands
9
 * and K.U.Leuven, Departement Computerwetenschappen, Celestijnenlaan 200A,
10
 * B-3001 Leuven, Belgium
11
 */
12
13
#include <stdlib.h>
14
#include <isl_ctx_private.h>
15
#include <isl_map_private.h>
16
#include <isl_vec_private.h>
17
#include <isl_options_private.h>
18
#include "isl_basis_reduction.h"
19
20
static void save_alpha(GBR_LP *lp, int first, int n, GBR_type *alpha)
21
21.6k
{
22
21.6k
  int i;
23
21.6k
24
83.2k
  for (i = 0; i < n; 
++i61.5k
)
25
61.5k
    GBR_lp_get_alpha(lp, first + i, &alpha[i]);
26
21.6k
}
27
28
/* Compute a reduced basis for the set represented by the tableau "tab".
29
 * tab->basis, which must be initialized by the calling function to an affine
30
 * unimodular basis, is updated to reflect the reduced basis.
31
 * The first tab->n_zero rows of the basis (ignoring the constant row)
32
 * are assumed to correspond to equalities and are left untouched.
33
 * tab->n_zero is updated to reflect any additional equalities that
34
 * have been detected in the first rows of the new basis.
35
 * The final tab->n_unbounded rows of the basis are assumed to correspond
36
 * to unbounded directions and are also left untouched.
37
 * In particular this means that the remaining rows are assumed to
38
 * correspond to bounded directions.
39
 *
40
 * This function implements the algorithm described in
41
 * "An Implementation of the Generalized Basis Reduction Algorithm
42
 *  for Integer Programming" of Cook el al. to compute a reduced basis.
43
 * We use \epsilon = 1/4.
44
 *
45
 * If ctx->opt->gbr_only_first is set, the user is only interested
46
 * in the first direction.  In this case we stop the basis reduction when
47
 * the width in the first direction becomes smaller than 2.
48
 */
49
struct isl_tab *isl_tab_compute_reduced_basis(struct isl_tab *tab)
50
2.92k
{
51
2.92k
  unsigned dim;
52
2.92k
  struct isl_ctx *ctx;
53
2.92k
  struct isl_mat *B;
54
2.92k
  int i;
55
2.92k
  GBR_LP *lp = NULL;
56
2.92k
  GBR_type F_old, alpha, F_new;
57
2.92k
  int row;
58
2.92k
  isl_int tmp;
59
2.92k
  struct isl_vec *b_tmp;
60
2.92k
  GBR_type *F = NULL;
61
2.92k
  GBR_type *alpha_buffer[2] = { NULL, NULL };
62
2.92k
  GBR_type *alpha_saved;
63
2.92k
  GBR_type F_saved;
64
2.92k
  int use_saved = 0;
65
2.92k
  isl_int mu[2];
66
2.92k
  GBR_type mu_F[2];
67
2.92k
  GBR_type two;
68
2.92k
  GBR_type one;
69
2.92k
  int empty = 0;
70
2.92k
  int fixed = 0;
71
2.92k
  int fixed_saved = 0;
72
2.92k
  int mu_fixed[2];
73
2.92k
  int n_bounded;
74
2.92k
  int gbr_only_first;
75
2.92k
76
2.92k
  if (!tab)
77
0
    return NULL;
78
2.92k
79
2.92k
  if (tab->empty)
80
0
    return tab;
81
2.92k
82
2.92k
  ctx = tab->mat->ctx;
83
2.92k
  gbr_only_first = ctx->opt->gbr_only_first;
84
2.92k
  dim = tab->n_var;
85
2.92k
  B = tab->basis;
86
2.92k
  if (!B)
87
0
    return tab;
88
2.92k
89
2.92k
  n_bounded = dim - tab->n_unbounded;
90
2.92k
  if (n_bounded <= tab->n_zero + 1)
91
0
    return tab;
92
2.92k
93
2.92k
  isl_int_init(tmp);
94
2.92k
  isl_int_init(mu[0]);
95
2.92k
  isl_int_init(mu[1]);
96
2.92k
97
2.92k
  GBR_init(alpha);
98
2.92k
  GBR_init(F_old);
99
2.92k
  GBR_init(F_new);
100
2.92k
  GBR_init(F_saved);
101
2.92k
  GBR_init(mu_F[0]);
102
2.92k
  GBR_init(mu_F[1]);
103
2.92k
  GBR_init(two);
104
2.92k
  GBR_init(one);
105
2.92k
106
2.92k
  b_tmp = isl_vec_alloc(ctx, dim);
107
2.92k
  if (!b_tmp)
108
0
    goto error;
109
2.92k
110
2.92k
  F = isl_alloc_array(ctx, GBR_type, n_bounded);
111
2.92k
  alpha_buffer[0] = isl_alloc_array(ctx, GBR_type, n_bounded);
112
2.92k
  alpha_buffer[1] = isl_alloc_array(ctx, GBR_type, n_bounded);
113
2.92k
  alpha_saved = alpha_buffer[0];
114
2.92k
115
2.92k
  if (!F || !alpha_buffer[0] || !alpha_buffer[1])
116
0
    goto error;
117
2.92k
118
18.4k
  
for (i = 0; 2.92k
i < n_bounded;
++i15.5k
) {
119
15.5k
    GBR_init(F[i]);
120
15.5k
    GBR_init(alpha_buffer[0][i]);
121
15.5k
    GBR_init(alpha_buffer[1][i]);
122
15.5k
  }
123
2.92k
124
2.92k
  GBR_set_ui(two, 2);
125
2.92k
  GBR_set_ui(one, 1);
126
2.92k
127
2.92k
  lp = GBR_lp_init(tab);
128
2.92k
  if (!lp)
129
0
    goto error;
130
2.92k
131
2.92k
  i = tab->n_zero;
132
2.92k
133
2.92k
  GBR_lp_set_obj(lp, B->row[1+i]+1, dim);
134
2.92k
  ctx->stats->gbr_solved_lps++;
135
2.92k
  if (GBR_lp_solve(lp) < 0)
136
0
    goto error;
137
2.92k
  GBR_lp_get_obj_val(lp, &F[i]);
138
2.92k
139
2.92k
  if (GBR_lt(F[i], one)) {
140
0
    if (!GBR_is_zero(F[i])) {
141
0
      empty = GBR_lp_cut(lp, B->row[1+i]+1);
142
0
      if (empty)
143
0
        goto done;
144
0
      GBR_set_ui(F[i], 0);
145
0
    }
146
0
    tab->n_zero++;
147
0
  }
148
2.92k
149
30.2k
  
do 2.92k
{
150
30.2k
    if (i+1 == tab->n_zero) {
151
0
      GBR_lp_set_obj(lp, B->row[1+i+1]+1, dim);
152
0
      ctx->stats->gbr_solved_lps++;
153
0
      if (GBR_lp_solve(lp) < 0)
154
0
        goto error;
155
0
      GBR_lp_get_obj_val(lp, &F_new);
156
0
      fixed = GBR_lp_is_fixed(lp);
157
0
      GBR_set_ui(alpha, 0);
158
0
    } else
159
30.2k
    if (use_saved) {
160
10.1k
      row = GBR_lp_next_row(lp);
161
10.1k
      GBR_set(F_new, F_saved);
162
10.1k
      fixed = fixed_saved;
163
10.1k
      GBR_set(alpha, alpha_saved[i]);
164
20.0k
    } else {
165
20.0k
      row = GBR_lp_add_row(lp, B->row[1+i]+1, dim);
166
20.0k
      GBR_lp_set_obj(lp, B->row[1+i+1]+1, dim);
167
20.0k
      ctx->stats->gbr_solved_lps++;
168
20.0k
      if (GBR_lp_solve(lp) < 0)
169
0
        goto error;
170
20.0k
      GBR_lp_get_obj_val(lp, &F_new);
171
20.0k
      fixed = GBR_lp_is_fixed(lp);
172
20.0k
173
20.0k
      GBR_lp_get_alpha(lp, row, &alpha);
174
20.0k
175
20.0k
      if (i > 0)
176
15.0k
        save_alpha(lp, row-i, i, alpha_saved);
177
20.0k
178
20.0k
      if (GBR_lp_del_row(lp) < 0)
179
0
        goto error;
180
30.2k
    }
181
30.2k
    GBR_set(F[i+1], F_new);
182
30.2k
183
30.2k
    GBR_floor(mu[0], alpha);
184
30.2k
    GBR_ceil(mu[1], alpha);
185
30.2k
186
30.2k
    if (isl_int_eq(mu[0], mu[1]))
187
30.2k
      
isl_int_set24.2k
(tmp, mu[0]);
188
30.2k
    else {
189
6.00k
      int j;
190
6.00k
191
18.0k
      for (j = 0; j <= 1; 
++j12.0k
) {
192
12.0k
        isl_int_set(tmp, mu[j]);
193
12.0k
        isl_seq_combine(b_tmp->el,
194
12.0k
            ctx->one, B->row[1+i+1]+1,
195
12.0k
            tmp, B->row[1+i]+1, dim);
196
12.0k
        GBR_lp_set_obj(lp, b_tmp->el, dim);
197
12.0k
        ctx->stats->gbr_solved_lps++;
198
12.0k
        if (GBR_lp_solve(lp) < 0)
199
0
          goto error;
200
12.0k
        GBR_lp_get_obj_val(lp, &mu_F[j]);
201
12.0k
        mu_fixed[j] = GBR_lp_is_fixed(lp);
202
12.0k
        if (i > 0)
203
6.63k
          save_alpha(lp, row-i, i, alpha_buffer[j]);
204
12.0k
      }
205
6.00k
206
6.00k
      if (GBR_lt(mu_F[0], mu_F[1]))
207
6.00k
        
j = 03.10k
;
208
2.90k
      else
209
2.90k
        j = 1;
210
6.00k
211
6.00k
      isl_int_set(tmp, mu[j]);
212
6.00k
      GBR_set(F_new, mu_F[j]);
213
6.00k
      fixed = mu_fixed[j];
214
6.00k
      alpha_saved = alpha_buffer[j];
215
6.00k
    }
216
30.2k
    isl_seq_combine(B->row[1+i+1]+1, ctx->one, B->row[1+i+1]+1,
217
30.2k
        tmp, B->row[1+i]+1, dim);
218
30.2k
219
30.2k
    if (i+1 == tab->n_zero && 
fixed0
) {
220
0
      if (!GBR_is_zero(F[i+1])) {
221
0
        empty = GBR_lp_cut(lp, B->row[1+i+1]+1);
222
0
        if (empty)
223
0
          goto done;
224
0
        GBR_set_ui(F[i+1], 0);
225
0
      }
226
0
      tab->n_zero++;
227
0
    }
228
30.2k
229
30.2k
    GBR_set(F_old, F[i]);
230
30.2k
231
30.2k
    use_saved = 0;
232
30.2k
    /* mu_F[0] = 4 * F_new; mu_F[1] = 3 * F_old */
233
30.2k
    GBR_set_ui(mu_F[0], 4);
234
30.2k
    GBR_mul(mu_F[0], mu_F[0], F_new);
235
30.2k
    GBR_set_ui(mu_F[1], 3);
236
30.2k
    GBR_mul(mu_F[1], mu_F[1], F_old);
237
30.2k
    if (GBR_lt(mu_F[0], mu_F[1])) {
238
15.6k
      B = isl_mat_swap_rows(B, 1 + i, 1 + i + 1);
239
15.6k
      if (i > tab->n_zero) {
240
10.1k
        use_saved = 1;
241
10.1k
        GBR_set(F_saved, F_new);
242
10.1k
        fixed_saved = fixed;
243
10.1k
        if (GBR_lp_del_row(lp) < 0)
244
0
          goto error;
245
10.1k
        --i;
246
10.1k
      } else {
247
5.50k
        GBR_set(F[tab->n_zero], F_new);
248
5.50k
        if (gbr_only_first && GBR_lt(F[tab->n_zero], two))
249
5.50k
          
break1.91k
;
250
3.58k
251
3.58k
        if (fixed) {
252
0
          if (!GBR_is_zero(F[tab->n_zero])) {
253
0
            empty = GBR_lp_cut(lp, B->row[1+tab->n_zero]+1);
254
0
            if (empty)
255
0
              goto done;
256
0
            GBR_set_ui(F[tab->n_zero], 0);
257
0
          }
258
0
          tab->n_zero++;
259
0
        }
260
5.50k
      }
261
15.6k
    } else {
262
14.5k
      GBR_lp_add_row(lp, B->row[1+i]+1, dim);
263
14.5k
      ++i;
264
14.5k
    }
265
30.2k
  } while (
i < n_bounded - 128.3k
);
266
2.92k
267
2.92k
  if (0) {
268
0
done:
269
0
    if (empty < 0) {
270
0
error:
271
0
      isl_mat_free(B);
272
0
      B = NULL;
273
0
    }
274
0
  }
275
2.92k
276
2.92k
  GBR_lp_delete(lp);
277
2.92k
278
2.92k
  if (alpha_buffer[1])
279
18.4k
    
for (i = 0; 2.92k
i < n_bounded;
++i15.5k
) {
280
15.5k
      GBR_clear(F[i]);
281
15.5k
      GBR_clear(alpha_buffer[0][i]);
282
15.5k
      GBR_clear(alpha_buffer[1][i]);
283
2.92k
    }
284
2.92k
  free(F);
285
2.92k
  free(alpha_buffer[0]);
286
2.92k
  free(alpha_buffer[1]);
287
2.92k
288
2.92k
  isl_vec_free(b_tmp);
289
2.92k
290
2.92k
  GBR_clear(alpha);
291
2.92k
  GBR_clear(F_old);
292
2.92k
  GBR_clear(F_new);
293
2.92k
  GBR_clear(F_saved);
294
2.92k
  GBR_clear(mu_F[0]);
295
2.92k
  GBR_clear(mu_F[1]);
296
2.92k
  GBR_clear(two);
297
2.92k
  GBR_clear(one);
298
2.92k
299
2.92k
  isl_int_clear(tmp);
300
2.92k
  isl_int_clear(mu[0]);
301
2.92k
  isl_int_clear(mu[1]);
302
2.92k
303
2.92k
  tab->basis = B;
304
2.92k
305
2.92k
  return tab;
306
2.92k
}
307
308
/* Compute an affine form of a reduced basis of the given basic
309
 * non-parametric set, which is assumed to be bounded and not
310
 * include any integer divisions.
311
 * The first column and the first row correspond to the constant term.
312
 *
313
 * If the input contains any equalities, we first create an initial
314
 * basis with the equalities first.  Otherwise, we start off with
315
 * the identity matrix.
316
 */
317
__isl_give isl_mat *isl_basic_set_reduced_basis(__isl_keep isl_basic_set *bset)
318
0
{
319
0
  struct isl_mat *basis;
320
0
  struct isl_tab *tab;
321
0
322
0
  if (!bset)
323
0
    return NULL;
324
0
325
0
  if (isl_basic_set_dim(bset, isl_dim_div) != 0)
326
0
    isl_die(bset->ctx, isl_error_invalid,
327
0
      "no integer division allowed", return NULL);
328
0
  if (isl_basic_set_dim(bset, isl_dim_param) != 0)
329
0
    isl_die(bset->ctx, isl_error_invalid,
330
0
      "no parameters allowed", return NULL);
331
0
332
0
  tab = isl_tab_from_basic_set(bset, 0);
333
0
  if (!tab)
334
0
    return NULL;
335
0
336
0
  if (bset->n_eq == 0)
337
0
    tab->basis = isl_mat_identity(bset->ctx, 1 + tab->n_var);
338
0
  else {
339
0
    isl_mat *eq;
340
0
    unsigned nvar = isl_basic_set_total_dim(bset);
341
0
    eq = isl_mat_sub_alloc6(bset->ctx, bset->eq, 0, bset->n_eq,
342
0
          1, nvar);
343
0
    eq = isl_mat_left_hermite(eq, 0, NULL, &tab->basis);
344
0
    tab->basis = isl_mat_lin_to_aff(tab->basis);
345
0
    tab->n_zero = bset->n_eq;
346
0
    isl_mat_free(eq);
347
0
  }
348
0
  tab = isl_tab_compute_reduced_basis(tab);
349
0
  if (!tab)
350
0
    return NULL;
351
0
352
0
  basis = isl_mat_copy(tab->basis);
353
0
354
0
  isl_tab_free(tab);
355
0
356
0
  return basis;
357
0
}