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
20static void save_alpha(GBR_LP *lp, int first, int n, GBR_type *alpha)
21{
22	int i;
23
24	for (i = 0; i < n; ++i)
25		GBR_lp_get_alpha(lp, first + i, &alpha[i]);
26}
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 */
49struct isl_tab *isl_tab_compute_reduced_basis(struct isl_tab *tab)
50{
51	unsigned dim;
52	struct isl_ctx *ctx;
53	struct isl_mat *B;
54	int i;
55	GBR_LP *lp = NULL;
56	GBR_type F_old, alpha, F_new;
57	int row;
58	isl_int tmp;
59	struct isl_vec *b_tmp;
60	GBR_type *F = NULL;
61	GBR_type *alpha_buffer[2] = { NULL, NULL };
62	GBR_type *alpha_saved;
63	GBR_type F_saved;
64	int use_saved = 0;
65	isl_int mu[2];
66	GBR_type mu_F[2];
67	GBR_type two;
68	GBR_type one;
69	int empty = 0;
70	int fixed = 0;
71	int fixed_saved = 0;
72	int mu_fixed[2];
73	int n_bounded;
74	int gbr_only_first;
75
76	if (!tab)
77		return NULL;
78
79	if (tab->empty)
80		return tab;
81
82	ctx = tab->mat->ctx;
83	gbr_only_first = ctx->opt->gbr_only_first;
84	dim = tab->n_var;
85	B = tab->basis;
86	if (!B)
87		return tab;
88
89	n_bounded = dim - tab->n_unbounded;
90	if (n_bounded <= tab->n_zero + 1)
91		return tab;
92
93	isl_int_init(tmp);
94	isl_int_init(mu[0]);
95	isl_int_init(mu[1]);
96
97	GBR_init(alpha);
98	GBR_init(F_old);
99	GBR_init(F_new);
100	GBR_init(F_saved);
101	GBR_init(mu_F[0]);
102	GBR_init(mu_F[1]);
103	GBR_init(two);
104	GBR_init(one);
105
106	b_tmp = isl_vec_alloc(ctx, dim);
107	if (!b_tmp)
108		goto error;
109
110	F = isl_alloc_array(ctx, GBR_type, n_bounded);
111	alpha_buffer[0] = isl_alloc_array(ctx, GBR_type, n_bounded);
112	alpha_buffer[1] = isl_alloc_array(ctx, GBR_type, n_bounded);
113	alpha_saved = alpha_buffer[0];
114
115	if (!F || !alpha_buffer[0] || !alpha_buffer[1])
116		goto error;
117
118	for (i = 0; i < n_bounded; ++i) {
119		GBR_init(F[i]);
120		GBR_init(alpha_buffer[0][i]);
121		GBR_init(alpha_buffer[1][i]);
122	}
123
124	GBR_set_ui(two, 2);
125	GBR_set_ui(one, 1);
126
127	lp = GBR_lp_init(tab);
128	if (!lp)
129		goto error;
130
131	i = tab->n_zero;
132
133	GBR_lp_set_obj(lp, B->row[1+i]+1, dim);
134	ctx->stats->gbr_solved_lps++;
135	if (GBR_lp_solve(lp) < 0)
136		goto error;
137	GBR_lp_get_obj_val(lp, &F[i]);
138
139	if (GBR_lt(F[i], one)) {
140		if (!GBR_is_zero(F[i])) {
141			empty = GBR_lp_cut(lp, B->row[1+i]+1);
142			if (empty)
143				goto done;
144			GBR_set_ui(F[i], 0);
145		}
146		tab->n_zero++;
147	}
148
149	do {
150		if (i+1 == tab->n_zero) {
151			GBR_lp_set_obj(lp, B->row[1+i+1]+1, dim);
152			ctx->stats->gbr_solved_lps++;
153			if (GBR_lp_solve(lp) < 0)
154				goto error;
155			GBR_lp_get_obj_val(lp, &F_new);
156			fixed = GBR_lp_is_fixed(lp);
157			GBR_set_ui(alpha, 0);
158		} else if (use_saved) {
159			row = GBR_lp_next_row(lp);
160			GBR_set(F_new, F_saved);
161			fixed = fixed_saved;
162			GBR_set(alpha, alpha_saved[i]);
163		} else {
164			row = GBR_lp_add_row(lp, B->row[1+i]+1, dim);
165			GBR_lp_set_obj(lp, B->row[1+i+1]+1, dim);
166			ctx->stats->gbr_solved_lps++;
167			if (GBR_lp_solve(lp) < 0)
168				goto error;
169			GBR_lp_get_obj_val(lp, &F_new);
170			fixed = GBR_lp_is_fixed(lp);
171
172			GBR_lp_get_alpha(lp, row, &alpha);
173
174			if (i > 0)
175				save_alpha(lp, row-i, i, alpha_saved);
176
177			if (GBR_lp_del_row(lp) < 0)
178				goto error;
179		}
180		GBR_set(F[i+1], F_new);
181
182		GBR_floor(mu[0], alpha);
183		GBR_ceil(mu[1], alpha);
184
185		if (isl_int_eq(mu[0], mu[1]))
186			isl_int_set(tmp, mu[0]);
187		else {
188			int j;
189
190			for (j = 0; j <= 1; ++j) {
191				isl_int_set(tmp, mu[j]);
192				isl_seq_combine(b_tmp->el,
193						ctx->one, B->row[1+i+1]+1,
194						tmp, B->row[1+i]+1, dim);
195				GBR_lp_set_obj(lp, b_tmp->el, dim);
196				ctx->stats->gbr_solved_lps++;
197				if (GBR_lp_solve(lp) < 0)
198					goto error;
199				GBR_lp_get_obj_val(lp, &mu_F[j]);
200				mu_fixed[j] = GBR_lp_is_fixed(lp);
201				if (i > 0)
202					save_alpha(lp, row-i, i, alpha_buffer[j]);
203			}
204
205			if (GBR_lt(mu_F[0], mu_F[1]))
206				j = 0;
207			else
208				j = 1;
209
210			isl_int_set(tmp, mu[j]);
211			GBR_set(F_new, mu_F[j]);
212			fixed = mu_fixed[j];
213			alpha_saved = alpha_buffer[j];
214		}
215		isl_seq_combine(B->row[1+i+1]+1, ctx->one, B->row[1+i+1]+1,
216				tmp, B->row[1+i]+1, dim);
217
218		if (i+1 == tab->n_zero && fixed) {
219			if (!GBR_is_zero(F[i+1])) {
220				empty = GBR_lp_cut(lp, B->row[1+i+1]+1);
221				if (empty)
222					goto done;
223				GBR_set_ui(F[i+1], 0);
224			}
225			tab->n_zero++;
226		}
227
228		GBR_set(F_old, F[i]);
229
230		use_saved = 0;
231		/* mu_F[0] = 4 * F_new; mu_F[1] = 3 * F_old */
232		GBR_set_ui(mu_F[0], 4);
233		GBR_mul(mu_F[0], mu_F[0], F_new);
234		GBR_set_ui(mu_F[1], 3);
235		GBR_mul(mu_F[1], mu_F[1], F_old);
236		if (GBR_lt(mu_F[0], mu_F[1])) {
237			B = isl_mat_swap_rows(B, 1 + i, 1 + i + 1);
238			if (i > tab->n_zero) {
239				use_saved = 1;
240				GBR_set(F_saved, F_new);
241				fixed_saved = fixed;
242				if (GBR_lp_del_row(lp) < 0)
243					goto error;
244				--i;
245			} else {
246				GBR_set(F[tab->n_zero], F_new);
247				if (gbr_only_first && GBR_lt(F[tab->n_zero], two))
248					break;
249
250				if (fixed) {
251					if (!GBR_is_zero(F[tab->n_zero])) {
252						empty = GBR_lp_cut(lp, B->row[1+tab->n_zero]+1);
253						if (empty)
254							goto done;
255						GBR_set_ui(F[tab->n_zero], 0);
256					}
257					tab->n_zero++;
258				}
259			}
260		} else {
261			GBR_lp_add_row(lp, B->row[1+i]+1, dim);
262			++i;
263		}
264	} while (i < n_bounded - 1);
265
266	if (0) {
267done:
268		if (empty < 0) {
269error:
270			isl_mat_free(B);
271			B = NULL;
272		}
273	}
274
275	GBR_lp_delete(lp);
276
277	if (alpha_buffer[1])
278		for (i = 0; i < n_bounded; ++i) {
279			GBR_clear(F[i]);
280			GBR_clear(alpha_buffer[0][i]);
281			GBR_clear(alpha_buffer[1][i]);
282		}
283	free(F);
284	free(alpha_buffer[0]);
285	free(alpha_buffer[1]);
286
287	isl_vec_free(b_tmp);
288
289	GBR_clear(alpha);
290	GBR_clear(F_old);
291	GBR_clear(F_new);
292	GBR_clear(F_saved);
293	GBR_clear(mu_F[0]);
294	GBR_clear(mu_F[1]);
295	GBR_clear(two);
296	GBR_clear(one);
297
298	isl_int_clear(tmp);
299	isl_int_clear(mu[0]);
300	isl_int_clear(mu[1]);
301
302	tab->basis = B;
303
304	return tab;
305}
306
307/* Compute an affine form of a reduced basis of the given basic
308 * non-parametric set, which is assumed to be bounded and not
309 * include any integer divisions.
310 * The first column and the first row correspond to the constant term.
311 *
312 * If the input contains any equalities, we first create an initial
313 * basis with the equalities first.  Otherwise, we start off with
314 * the identity matrix.
315 */
316__isl_give isl_mat *isl_basic_set_reduced_basis(__isl_keep isl_basic_set *bset)
317{
318	struct isl_mat *basis;
319	struct isl_tab *tab;
320
321	if (isl_basic_set_check_no_locals(bset) < 0 ||
322	    isl_basic_set_check_no_params(bset) < 0)
323		return NULL;
324
325	tab = isl_tab_from_basic_set(bset, 0);
326	if (!tab)
327		return NULL;
328
329	if (bset->n_eq == 0)
330		tab->basis = isl_mat_identity(bset->ctx, 1 + tab->n_var);
331	else {
332		isl_mat *eq;
333		isl_size nvar = isl_basic_set_dim(bset, isl_dim_all);
334		if (nvar < 0)
335			goto error;
336		eq = isl_mat_sub_alloc6(bset->ctx, bset->eq, 0, bset->n_eq,
337					1, nvar);
338		eq = isl_mat_left_hermite(eq, 0, NULL, &tab->basis);
339		tab->basis = isl_mat_lin_to_aff(tab->basis);
340		tab->n_zero = bset->n_eq;
341		isl_mat_free(eq);
342	}
343	tab = isl_tab_compute_reduced_basis(tab);
344	if (!tab)
345		return NULL;
346
347	basis = isl_mat_copy(tab->basis);
348
349	isl_tab_free(tab);
350
351	return basis;
352error:
353	isl_tab_free(tab);
354	return NULL;
355}
356