forked from OSchip/llvm-project
358 lines
8.3 KiB
C
358 lines
8.3 KiB
C
/*
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* Copyright 2006-2007 Universiteit Leiden
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* Copyright 2008-2009 Katholieke Universiteit Leuven
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*
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* Use of this software is governed by the MIT license
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*
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* Written by Sven Verdoolaege, Leiden Institute of Advanced Computer Science,
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* Universiteit Leiden, Niels Bohrweg 1, 2333 CA Leiden, The Netherlands
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* and K.U.Leuven, Departement Computerwetenschappen, Celestijnenlaan 200A,
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* B-3001 Leuven, Belgium
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*/
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#include <stdlib.h>
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#include <isl_ctx_private.h>
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#include <isl_map_private.h>
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#include <isl_vec_private.h>
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#include <isl_options_private.h>
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#include "isl_basis_reduction.h"
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static void save_alpha(GBR_LP *lp, int first, int n, GBR_type *alpha)
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{
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int i;
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for (i = 0; i < n; ++i)
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GBR_lp_get_alpha(lp, first + i, &alpha[i]);
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}
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/* Compute a reduced basis for the set represented by the tableau "tab".
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* tab->basis, which must be initialized by the calling function to an affine
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* unimodular basis, is updated to reflect the reduced basis.
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* The first tab->n_zero rows of the basis (ignoring the constant row)
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* are assumed to correspond to equalities and are left untouched.
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* tab->n_zero is updated to reflect any additional equalities that
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* have been detected in the first rows of the new basis.
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* The final tab->n_unbounded rows of the basis are assumed to correspond
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* to unbounded directions and are also left untouched.
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* In particular this means that the remaining rows are assumed to
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* correspond to bounded directions.
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*
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* This function implements the algorithm described in
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* "An Implementation of the Generalized Basis Reduction Algorithm
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* for Integer Programming" of Cook el al. to compute a reduced basis.
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* We use \epsilon = 1/4.
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*
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* If ctx->opt->gbr_only_first is set, the user is only interested
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* in the first direction. In this case we stop the basis reduction when
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* the width in the first direction becomes smaller than 2.
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*/
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struct isl_tab *isl_tab_compute_reduced_basis(struct isl_tab *tab)
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{
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unsigned dim;
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struct isl_ctx *ctx;
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struct isl_mat *B;
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int i;
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GBR_LP *lp = NULL;
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GBR_type F_old, alpha, F_new;
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int row;
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isl_int tmp;
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struct isl_vec *b_tmp;
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GBR_type *F = NULL;
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GBR_type *alpha_buffer[2] = { NULL, NULL };
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GBR_type *alpha_saved;
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GBR_type F_saved;
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int use_saved = 0;
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isl_int mu[2];
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GBR_type mu_F[2];
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GBR_type two;
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GBR_type one;
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int empty = 0;
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int fixed = 0;
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int fixed_saved = 0;
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int mu_fixed[2];
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int n_bounded;
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int gbr_only_first;
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if (!tab)
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return NULL;
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if (tab->empty)
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return tab;
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ctx = tab->mat->ctx;
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gbr_only_first = ctx->opt->gbr_only_first;
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dim = tab->n_var;
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B = tab->basis;
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if (!B)
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return tab;
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n_bounded = dim - tab->n_unbounded;
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if (n_bounded <= tab->n_zero + 1)
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return tab;
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isl_int_init(tmp);
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isl_int_init(mu[0]);
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isl_int_init(mu[1]);
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GBR_init(alpha);
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GBR_init(F_old);
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GBR_init(F_new);
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GBR_init(F_saved);
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GBR_init(mu_F[0]);
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GBR_init(mu_F[1]);
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GBR_init(two);
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GBR_init(one);
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b_tmp = isl_vec_alloc(ctx, dim);
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if (!b_tmp)
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goto error;
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F = isl_alloc_array(ctx, GBR_type, n_bounded);
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alpha_buffer[0] = isl_alloc_array(ctx, GBR_type, n_bounded);
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alpha_buffer[1] = isl_alloc_array(ctx, GBR_type, n_bounded);
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alpha_saved = alpha_buffer[0];
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if (!F || !alpha_buffer[0] || !alpha_buffer[1])
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goto error;
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for (i = 0; i < n_bounded; ++i) {
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GBR_init(F[i]);
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GBR_init(alpha_buffer[0][i]);
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GBR_init(alpha_buffer[1][i]);
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}
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GBR_set_ui(two, 2);
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GBR_set_ui(one, 1);
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lp = GBR_lp_init(tab);
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if (!lp)
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goto error;
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i = tab->n_zero;
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GBR_lp_set_obj(lp, B->row[1+i]+1, dim);
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ctx->stats->gbr_solved_lps++;
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if (GBR_lp_solve(lp) < 0)
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goto error;
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GBR_lp_get_obj_val(lp, &F[i]);
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if (GBR_lt(F[i], one)) {
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if (!GBR_is_zero(F[i])) {
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empty = GBR_lp_cut(lp, B->row[1+i]+1);
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if (empty)
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goto done;
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GBR_set_ui(F[i], 0);
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}
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tab->n_zero++;
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}
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do {
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if (i+1 == tab->n_zero) {
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GBR_lp_set_obj(lp, B->row[1+i+1]+1, dim);
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ctx->stats->gbr_solved_lps++;
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if (GBR_lp_solve(lp) < 0)
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goto error;
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GBR_lp_get_obj_val(lp, &F_new);
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fixed = GBR_lp_is_fixed(lp);
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GBR_set_ui(alpha, 0);
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} else
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if (use_saved) {
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row = GBR_lp_next_row(lp);
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GBR_set(F_new, F_saved);
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fixed = fixed_saved;
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GBR_set(alpha, alpha_saved[i]);
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} else {
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row = GBR_lp_add_row(lp, B->row[1+i]+1, dim);
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GBR_lp_set_obj(lp, B->row[1+i+1]+1, dim);
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ctx->stats->gbr_solved_lps++;
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if (GBR_lp_solve(lp) < 0)
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goto error;
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GBR_lp_get_obj_val(lp, &F_new);
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fixed = GBR_lp_is_fixed(lp);
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GBR_lp_get_alpha(lp, row, &alpha);
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if (i > 0)
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save_alpha(lp, row-i, i, alpha_saved);
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if (GBR_lp_del_row(lp) < 0)
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goto error;
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}
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GBR_set(F[i+1], F_new);
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GBR_floor(mu[0], alpha);
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GBR_ceil(mu[1], alpha);
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if (isl_int_eq(mu[0], mu[1]))
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isl_int_set(tmp, mu[0]);
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else {
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int j;
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for (j = 0; j <= 1; ++j) {
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isl_int_set(tmp, mu[j]);
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isl_seq_combine(b_tmp->el,
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ctx->one, B->row[1+i+1]+1,
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tmp, B->row[1+i]+1, dim);
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GBR_lp_set_obj(lp, b_tmp->el, dim);
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ctx->stats->gbr_solved_lps++;
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if (GBR_lp_solve(lp) < 0)
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goto error;
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GBR_lp_get_obj_val(lp, &mu_F[j]);
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mu_fixed[j] = GBR_lp_is_fixed(lp);
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if (i > 0)
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save_alpha(lp, row-i, i, alpha_buffer[j]);
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}
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if (GBR_lt(mu_F[0], mu_F[1]))
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j = 0;
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else
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j = 1;
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isl_int_set(tmp, mu[j]);
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GBR_set(F_new, mu_F[j]);
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fixed = mu_fixed[j];
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alpha_saved = alpha_buffer[j];
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}
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isl_seq_combine(B->row[1+i+1]+1, ctx->one, B->row[1+i+1]+1,
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tmp, B->row[1+i]+1, dim);
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if (i+1 == tab->n_zero && fixed) {
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if (!GBR_is_zero(F[i+1])) {
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empty = GBR_lp_cut(lp, B->row[1+i+1]+1);
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if (empty)
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goto done;
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GBR_set_ui(F[i+1], 0);
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}
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tab->n_zero++;
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}
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GBR_set(F_old, F[i]);
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use_saved = 0;
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/* mu_F[0] = 4 * F_new; mu_F[1] = 3 * F_old */
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GBR_set_ui(mu_F[0], 4);
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GBR_mul(mu_F[0], mu_F[0], F_new);
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GBR_set_ui(mu_F[1], 3);
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GBR_mul(mu_F[1], mu_F[1], F_old);
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if (GBR_lt(mu_F[0], mu_F[1])) {
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B = isl_mat_swap_rows(B, 1 + i, 1 + i + 1);
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if (i > tab->n_zero) {
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use_saved = 1;
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GBR_set(F_saved, F_new);
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fixed_saved = fixed;
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if (GBR_lp_del_row(lp) < 0)
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goto error;
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--i;
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} else {
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GBR_set(F[tab->n_zero], F_new);
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if (gbr_only_first && GBR_lt(F[tab->n_zero], two))
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break;
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if (fixed) {
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if (!GBR_is_zero(F[tab->n_zero])) {
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empty = GBR_lp_cut(lp, B->row[1+tab->n_zero]+1);
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if (empty)
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goto done;
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GBR_set_ui(F[tab->n_zero], 0);
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}
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tab->n_zero++;
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}
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}
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} else {
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GBR_lp_add_row(lp, B->row[1+i]+1, dim);
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++i;
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}
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} while (i < n_bounded - 1);
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if (0) {
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done:
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if (empty < 0) {
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error:
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isl_mat_free(B);
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B = NULL;
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}
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}
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GBR_lp_delete(lp);
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if (alpha_buffer[1])
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for (i = 0; i < n_bounded; ++i) {
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GBR_clear(F[i]);
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GBR_clear(alpha_buffer[0][i]);
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GBR_clear(alpha_buffer[1][i]);
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}
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free(F);
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free(alpha_buffer[0]);
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free(alpha_buffer[1]);
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isl_vec_free(b_tmp);
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GBR_clear(alpha);
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GBR_clear(F_old);
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GBR_clear(F_new);
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GBR_clear(F_saved);
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GBR_clear(mu_F[0]);
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GBR_clear(mu_F[1]);
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GBR_clear(two);
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GBR_clear(one);
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isl_int_clear(tmp);
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isl_int_clear(mu[0]);
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isl_int_clear(mu[1]);
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tab->basis = B;
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return tab;
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}
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/* Compute an affine form of a reduced basis of the given basic
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* non-parametric set, which is assumed to be bounded and not
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* include any integer divisions.
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* The first column and the first row correspond to the constant term.
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*
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* If the input contains any equalities, we first create an initial
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* basis with the equalities first. Otherwise, we start off with
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* the identity matrix.
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*/
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struct isl_mat *isl_basic_set_reduced_basis(struct isl_basic_set *bset)
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{
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struct isl_mat *basis;
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struct isl_tab *tab;
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if (!bset)
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return NULL;
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if (isl_basic_set_dim(bset, isl_dim_div) != 0)
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isl_die(bset->ctx, isl_error_invalid,
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"no integer division allowed", return NULL);
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if (isl_basic_set_dim(bset, isl_dim_param) != 0)
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isl_die(bset->ctx, isl_error_invalid,
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"no parameters allowed", return NULL);
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tab = isl_tab_from_basic_set(bset, 0);
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if (!tab)
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return NULL;
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if (bset->n_eq == 0)
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tab->basis = isl_mat_identity(bset->ctx, 1 + tab->n_var);
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else {
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isl_mat *eq;
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unsigned nvar = isl_basic_set_total_dim(bset);
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eq = isl_mat_sub_alloc6(bset->ctx, bset->eq, 0, bset->n_eq,
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1, nvar);
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eq = isl_mat_left_hermite(eq, 0, NULL, &tab->basis);
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tab->basis = isl_mat_lin_to_aff(tab->basis);
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tab->n_zero = bset->n_eq;
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isl_mat_free(eq);
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}
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tab = isl_tab_compute_reduced_basis(tab);
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if (!tab)
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return NULL;
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basis = isl_mat_copy(tab->basis);
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isl_tab_free(tab);
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return basis;
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}
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