forked from OSchip/llvm-project
3672 lines
94 KiB
C
3672 lines
94 KiB
C
/*
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* Copyright 2008-2009 Katholieke Universiteit Leuven
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* Copyright 2013 Ecole Normale Superieure
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* Copyright 2014 INRIA Rocquencourt
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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, K.U.Leuven, Departement
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* Computerwetenschappen, Celestijnenlaan 200A, B-3001 Leuven, Belgium
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* and Ecole Normale Superieure, 45 rue d'Ulm, 75230 Paris, France
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* and Inria Paris - Rocquencourt, Domaine de Voluceau - Rocquencourt,
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* B.P. 105 - 78153 Le Chesnay, France
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*/
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#include <isl_ctx_private.h>
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#include <isl_mat_private.h>
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#include <isl_vec_private.h>
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#include "isl_map_private.h"
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#include "isl_tab.h"
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#include <isl_seq.h>
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#include <isl_config.h>
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/*
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* The implementation of tableaus in this file was inspired by Section 8
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* of David Detlefs, Greg Nelson and James B. Saxe, "Simplify: a theorem
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* prover for program checking".
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*/
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struct isl_tab *isl_tab_alloc(struct isl_ctx *ctx,
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unsigned n_row, unsigned n_var, unsigned M)
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{
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int i;
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struct isl_tab *tab;
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unsigned off = 2 + M;
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tab = isl_calloc_type(ctx, struct isl_tab);
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if (!tab)
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return NULL;
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tab->mat = isl_mat_alloc(ctx, n_row, off + n_var);
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if (!tab->mat)
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goto error;
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tab->var = isl_alloc_array(ctx, struct isl_tab_var, n_var);
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if (n_var && !tab->var)
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goto error;
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tab->con = isl_alloc_array(ctx, struct isl_tab_var, n_row);
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if (n_row && !tab->con)
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goto error;
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tab->col_var = isl_alloc_array(ctx, int, n_var);
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if (n_var && !tab->col_var)
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goto error;
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tab->row_var = isl_alloc_array(ctx, int, n_row);
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if (n_row && !tab->row_var)
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goto error;
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for (i = 0; i < n_var; ++i) {
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tab->var[i].index = i;
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tab->var[i].is_row = 0;
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tab->var[i].is_nonneg = 0;
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tab->var[i].is_zero = 0;
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tab->var[i].is_redundant = 0;
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tab->var[i].frozen = 0;
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tab->var[i].negated = 0;
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tab->col_var[i] = i;
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}
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tab->n_row = 0;
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tab->n_con = 0;
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tab->n_eq = 0;
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tab->max_con = n_row;
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tab->n_col = n_var;
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tab->n_var = n_var;
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tab->max_var = n_var;
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tab->n_param = 0;
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tab->n_div = 0;
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tab->n_dead = 0;
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tab->n_redundant = 0;
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tab->strict_redundant = 0;
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tab->need_undo = 0;
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tab->rational = 0;
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tab->empty = 0;
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tab->in_undo = 0;
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tab->M = M;
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tab->cone = 0;
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tab->bottom.type = isl_tab_undo_bottom;
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tab->bottom.next = NULL;
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tab->top = &tab->bottom;
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tab->n_zero = 0;
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tab->n_unbounded = 0;
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tab->basis = NULL;
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return tab;
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error:
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isl_tab_free(tab);
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return NULL;
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}
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isl_ctx *isl_tab_get_ctx(struct isl_tab *tab)
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{
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return tab ? isl_mat_get_ctx(tab->mat) : NULL;
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}
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int isl_tab_extend_cons(struct isl_tab *tab, unsigned n_new)
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{
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unsigned off;
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if (!tab)
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return -1;
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off = 2 + tab->M;
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if (tab->max_con < tab->n_con + n_new) {
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struct isl_tab_var *con;
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con = isl_realloc_array(tab->mat->ctx, tab->con,
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struct isl_tab_var, tab->max_con + n_new);
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if (!con)
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return -1;
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tab->con = con;
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tab->max_con += n_new;
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}
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if (tab->mat->n_row < tab->n_row + n_new) {
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int *row_var;
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tab->mat = isl_mat_extend(tab->mat,
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tab->n_row + n_new, off + tab->n_col);
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if (!tab->mat)
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return -1;
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row_var = isl_realloc_array(tab->mat->ctx, tab->row_var,
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int, tab->mat->n_row);
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if (!row_var)
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return -1;
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tab->row_var = row_var;
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if (tab->row_sign) {
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enum isl_tab_row_sign *s;
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s = isl_realloc_array(tab->mat->ctx, tab->row_sign,
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enum isl_tab_row_sign, tab->mat->n_row);
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if (!s)
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return -1;
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tab->row_sign = s;
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}
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}
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return 0;
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}
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/* Make room for at least n_new extra variables.
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* Return -1 if anything went wrong.
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*/
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int isl_tab_extend_vars(struct isl_tab *tab, unsigned n_new)
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{
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struct isl_tab_var *var;
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unsigned off = 2 + tab->M;
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if (tab->max_var < tab->n_var + n_new) {
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var = isl_realloc_array(tab->mat->ctx, tab->var,
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struct isl_tab_var, tab->n_var + n_new);
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if (!var)
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return -1;
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tab->var = var;
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tab->max_var = tab->n_var + n_new;
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}
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if (tab->mat->n_col < off + tab->n_col + n_new) {
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int *p;
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tab->mat = isl_mat_extend(tab->mat,
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tab->mat->n_row, off + tab->n_col + n_new);
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if (!tab->mat)
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return -1;
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p = isl_realloc_array(tab->mat->ctx, tab->col_var,
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int, tab->n_col + n_new);
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if (!p)
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return -1;
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tab->col_var = p;
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}
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return 0;
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}
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static void free_undo_record(struct isl_tab_undo *undo)
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{
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switch (undo->type) {
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case isl_tab_undo_saved_basis:
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free(undo->u.col_var);
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break;
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default:;
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}
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free(undo);
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}
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static void free_undo(struct isl_tab *tab)
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{
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struct isl_tab_undo *undo, *next;
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for (undo = tab->top; undo && undo != &tab->bottom; undo = next) {
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next = undo->next;
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free_undo_record(undo);
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}
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tab->top = undo;
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}
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void isl_tab_free(struct isl_tab *tab)
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{
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if (!tab)
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return;
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free_undo(tab);
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isl_mat_free(tab->mat);
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isl_vec_free(tab->dual);
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isl_basic_map_free(tab->bmap);
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free(tab->var);
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free(tab->con);
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free(tab->row_var);
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free(tab->col_var);
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free(tab->row_sign);
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isl_mat_free(tab->samples);
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free(tab->sample_index);
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isl_mat_free(tab->basis);
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free(tab);
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}
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struct isl_tab *isl_tab_dup(struct isl_tab *tab)
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{
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int i;
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struct isl_tab *dup;
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unsigned off;
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if (!tab)
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return NULL;
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off = 2 + tab->M;
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dup = isl_calloc_type(tab->mat->ctx, struct isl_tab);
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if (!dup)
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return NULL;
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dup->mat = isl_mat_dup(tab->mat);
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if (!dup->mat)
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goto error;
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dup->var = isl_alloc_array(tab->mat->ctx, struct isl_tab_var, tab->max_var);
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if (tab->max_var && !dup->var)
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goto error;
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for (i = 0; i < tab->n_var; ++i)
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dup->var[i] = tab->var[i];
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dup->con = isl_alloc_array(tab->mat->ctx, struct isl_tab_var, tab->max_con);
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if (tab->max_con && !dup->con)
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goto error;
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for (i = 0; i < tab->n_con; ++i)
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dup->con[i] = tab->con[i];
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dup->col_var = isl_alloc_array(tab->mat->ctx, int, tab->mat->n_col - off);
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if ((tab->mat->n_col - off) && !dup->col_var)
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goto error;
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for (i = 0; i < tab->n_col; ++i)
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dup->col_var[i] = tab->col_var[i];
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dup->row_var = isl_alloc_array(tab->mat->ctx, int, tab->mat->n_row);
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if (tab->mat->n_row && !dup->row_var)
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goto error;
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for (i = 0; i < tab->n_row; ++i)
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dup->row_var[i] = tab->row_var[i];
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if (tab->row_sign) {
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dup->row_sign = isl_alloc_array(tab->mat->ctx, enum isl_tab_row_sign,
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tab->mat->n_row);
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if (tab->mat->n_row && !dup->row_sign)
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goto error;
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for (i = 0; i < tab->n_row; ++i)
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dup->row_sign[i] = tab->row_sign[i];
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}
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if (tab->samples) {
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dup->samples = isl_mat_dup(tab->samples);
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if (!dup->samples)
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goto error;
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dup->sample_index = isl_alloc_array(tab->mat->ctx, int,
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tab->samples->n_row);
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if (tab->samples->n_row && !dup->sample_index)
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goto error;
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dup->n_sample = tab->n_sample;
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dup->n_outside = tab->n_outside;
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}
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dup->n_row = tab->n_row;
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dup->n_con = tab->n_con;
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dup->n_eq = tab->n_eq;
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dup->max_con = tab->max_con;
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dup->n_col = tab->n_col;
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dup->n_var = tab->n_var;
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dup->max_var = tab->max_var;
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dup->n_param = tab->n_param;
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dup->n_div = tab->n_div;
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dup->n_dead = tab->n_dead;
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dup->n_redundant = tab->n_redundant;
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dup->rational = tab->rational;
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dup->empty = tab->empty;
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dup->strict_redundant = 0;
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dup->need_undo = 0;
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dup->in_undo = 0;
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dup->M = tab->M;
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tab->cone = tab->cone;
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dup->bottom.type = isl_tab_undo_bottom;
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dup->bottom.next = NULL;
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dup->top = &dup->bottom;
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dup->n_zero = tab->n_zero;
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dup->n_unbounded = tab->n_unbounded;
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dup->basis = isl_mat_dup(tab->basis);
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return dup;
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error:
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isl_tab_free(dup);
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return NULL;
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}
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/* Construct the coefficient matrix of the product tableau
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* of two tableaus.
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* mat{1,2} is the coefficient matrix of tableau {1,2}
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* row{1,2} is the number of rows in tableau {1,2}
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* col{1,2} is the number of columns in tableau {1,2}
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* off is the offset to the coefficient column (skipping the
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* denominator, the constant term and the big parameter if any)
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* r{1,2} is the number of redundant rows in tableau {1,2}
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* d{1,2} is the number of dead columns in tableau {1,2}
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*
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* The order of the rows and columns in the result is as explained
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* in isl_tab_product.
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*/
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static struct isl_mat *tab_mat_product(struct isl_mat *mat1,
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struct isl_mat *mat2, unsigned row1, unsigned row2,
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unsigned col1, unsigned col2,
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unsigned off, unsigned r1, unsigned r2, unsigned d1, unsigned d2)
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{
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int i;
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struct isl_mat *prod;
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unsigned n;
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prod = isl_mat_alloc(mat1->ctx, mat1->n_row + mat2->n_row,
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off + col1 + col2);
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if (!prod)
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return NULL;
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n = 0;
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for (i = 0; i < r1; ++i) {
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isl_seq_cpy(prod->row[n + i], mat1->row[i], off + d1);
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isl_seq_clr(prod->row[n + i] + off + d1, d2);
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isl_seq_cpy(prod->row[n + i] + off + d1 + d2,
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mat1->row[i] + off + d1, col1 - d1);
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isl_seq_clr(prod->row[n + i] + off + col1 + d1, col2 - d2);
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}
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n += r1;
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for (i = 0; i < r2; ++i) {
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isl_seq_cpy(prod->row[n + i], mat2->row[i], off);
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isl_seq_clr(prod->row[n + i] + off, d1);
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isl_seq_cpy(prod->row[n + i] + off + d1,
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mat2->row[i] + off, d2);
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isl_seq_clr(prod->row[n + i] + off + d1 + d2, col1 - d1);
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isl_seq_cpy(prod->row[n + i] + off + col1 + d1,
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mat2->row[i] + off + d2, col2 - d2);
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}
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n += r2;
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for (i = 0; i < row1 - r1; ++i) {
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isl_seq_cpy(prod->row[n + i], mat1->row[r1 + i], off + d1);
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isl_seq_clr(prod->row[n + i] + off + d1, d2);
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isl_seq_cpy(prod->row[n + i] + off + d1 + d2,
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mat1->row[r1 + i] + off + d1, col1 - d1);
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isl_seq_clr(prod->row[n + i] + off + col1 + d1, col2 - d2);
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}
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n += row1 - r1;
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for (i = 0; i < row2 - r2; ++i) {
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isl_seq_cpy(prod->row[n + i], mat2->row[r2 + i], off);
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isl_seq_clr(prod->row[n + i] + off, d1);
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isl_seq_cpy(prod->row[n + i] + off + d1,
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mat2->row[r2 + i] + off, d2);
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isl_seq_clr(prod->row[n + i] + off + d1 + d2, col1 - d1);
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isl_seq_cpy(prod->row[n + i] + off + col1 + d1,
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mat2->row[r2 + i] + off + d2, col2 - d2);
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}
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return prod;
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}
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/* Update the row or column index of a variable that corresponds
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* to a variable in the first input tableau.
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*/
|
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static void update_index1(struct isl_tab_var *var,
|
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unsigned r1, unsigned r2, unsigned d1, unsigned d2)
|
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{
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if (var->index == -1)
|
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return;
|
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if (var->is_row && var->index >= r1)
|
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var->index += r2;
|
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if (!var->is_row && var->index >= d1)
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var->index += d2;
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}
|
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|
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/* Update the row or column index of a variable that corresponds
|
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* to a variable in the second input tableau.
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*/
|
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static void update_index2(struct isl_tab_var *var,
|
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unsigned row1, unsigned col1,
|
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unsigned r1, unsigned r2, unsigned d1, unsigned d2)
|
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{
|
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if (var->index == -1)
|
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return;
|
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if (var->is_row) {
|
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if (var->index < r2)
|
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var->index += r1;
|
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else
|
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var->index += row1;
|
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} else {
|
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if (var->index < d2)
|
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var->index += d1;
|
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else
|
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var->index += col1;
|
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}
|
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}
|
|
|
|
/* Create a tableau that represents the Cartesian product of the sets
|
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* represented by tableaus tab1 and tab2.
|
|
* The order of the rows in the product is
|
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* - redundant rows of tab1
|
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* - redundant rows of tab2
|
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* - non-redundant rows of tab1
|
|
* - non-redundant rows of tab2
|
|
* The order of the columns is
|
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* - denominator
|
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* - constant term
|
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* - coefficient of big parameter, if any
|
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* - dead columns of tab1
|
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* - dead columns of tab2
|
|
* - live columns of tab1
|
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* - live columns of tab2
|
|
* The order of the variables and the constraints is a concatenation
|
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* of order in the two input tableaus.
|
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*/
|
|
struct isl_tab *isl_tab_product(struct isl_tab *tab1, struct isl_tab *tab2)
|
|
{
|
|
int i;
|
|
struct isl_tab *prod;
|
|
unsigned off;
|
|
unsigned r1, r2, d1, d2;
|
|
|
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if (!tab1 || !tab2)
|
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return NULL;
|
|
|
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isl_assert(tab1->mat->ctx, tab1->M == tab2->M, return NULL);
|
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isl_assert(tab1->mat->ctx, tab1->rational == tab2->rational, return NULL);
|
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isl_assert(tab1->mat->ctx, tab1->cone == tab2->cone, return NULL);
|
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isl_assert(tab1->mat->ctx, !tab1->row_sign, return NULL);
|
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isl_assert(tab1->mat->ctx, !tab2->row_sign, return NULL);
|
|
isl_assert(tab1->mat->ctx, tab1->n_param == 0, return NULL);
|
|
isl_assert(tab1->mat->ctx, tab2->n_param == 0, return NULL);
|
|
isl_assert(tab1->mat->ctx, tab1->n_div == 0, return NULL);
|
|
isl_assert(tab1->mat->ctx, tab2->n_div == 0, return NULL);
|
|
|
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off = 2 + tab1->M;
|
|
r1 = tab1->n_redundant;
|
|
r2 = tab2->n_redundant;
|
|
d1 = tab1->n_dead;
|
|
d2 = tab2->n_dead;
|
|
prod = isl_calloc_type(tab1->mat->ctx, struct isl_tab);
|
|
if (!prod)
|
|
return NULL;
|
|
prod->mat = tab_mat_product(tab1->mat, tab2->mat,
|
|
tab1->n_row, tab2->n_row,
|
|
tab1->n_col, tab2->n_col, off, r1, r2, d1, d2);
|
|
if (!prod->mat)
|
|
goto error;
|
|
prod->var = isl_alloc_array(tab1->mat->ctx, struct isl_tab_var,
|
|
tab1->max_var + tab2->max_var);
|
|
if ((tab1->max_var + tab2->max_var) && !prod->var)
|
|
goto error;
|
|
for (i = 0; i < tab1->n_var; ++i) {
|
|
prod->var[i] = tab1->var[i];
|
|
update_index1(&prod->var[i], r1, r2, d1, d2);
|
|
}
|
|
for (i = 0; i < tab2->n_var; ++i) {
|
|
prod->var[tab1->n_var + i] = tab2->var[i];
|
|
update_index2(&prod->var[tab1->n_var + i],
|
|
tab1->n_row, tab1->n_col,
|
|
r1, r2, d1, d2);
|
|
}
|
|
prod->con = isl_alloc_array(tab1->mat->ctx, struct isl_tab_var,
|
|
tab1->max_con + tab2->max_con);
|
|
if ((tab1->max_con + tab2->max_con) && !prod->con)
|
|
goto error;
|
|
for (i = 0; i < tab1->n_con; ++i) {
|
|
prod->con[i] = tab1->con[i];
|
|
update_index1(&prod->con[i], r1, r2, d1, d2);
|
|
}
|
|
for (i = 0; i < tab2->n_con; ++i) {
|
|
prod->con[tab1->n_con + i] = tab2->con[i];
|
|
update_index2(&prod->con[tab1->n_con + i],
|
|
tab1->n_row, tab1->n_col,
|
|
r1, r2, d1, d2);
|
|
}
|
|
prod->col_var = isl_alloc_array(tab1->mat->ctx, int,
|
|
tab1->n_col + tab2->n_col);
|
|
if ((tab1->n_col + tab2->n_col) && !prod->col_var)
|
|
goto error;
|
|
for (i = 0; i < tab1->n_col; ++i) {
|
|
int pos = i < d1 ? i : i + d2;
|
|
prod->col_var[pos] = tab1->col_var[i];
|
|
}
|
|
for (i = 0; i < tab2->n_col; ++i) {
|
|
int pos = i < d2 ? d1 + i : tab1->n_col + i;
|
|
int t = tab2->col_var[i];
|
|
if (t >= 0)
|
|
t += tab1->n_var;
|
|
else
|
|
t -= tab1->n_con;
|
|
prod->col_var[pos] = t;
|
|
}
|
|
prod->row_var = isl_alloc_array(tab1->mat->ctx, int,
|
|
tab1->mat->n_row + tab2->mat->n_row);
|
|
if ((tab1->mat->n_row + tab2->mat->n_row) && !prod->row_var)
|
|
goto error;
|
|
for (i = 0; i < tab1->n_row; ++i) {
|
|
int pos = i < r1 ? i : i + r2;
|
|
prod->row_var[pos] = tab1->row_var[i];
|
|
}
|
|
for (i = 0; i < tab2->n_row; ++i) {
|
|
int pos = i < r2 ? r1 + i : tab1->n_row + i;
|
|
int t = tab2->row_var[i];
|
|
if (t >= 0)
|
|
t += tab1->n_var;
|
|
else
|
|
t -= tab1->n_con;
|
|
prod->row_var[pos] = t;
|
|
}
|
|
prod->samples = NULL;
|
|
prod->sample_index = NULL;
|
|
prod->n_row = tab1->n_row + tab2->n_row;
|
|
prod->n_con = tab1->n_con + tab2->n_con;
|
|
prod->n_eq = 0;
|
|
prod->max_con = tab1->max_con + tab2->max_con;
|
|
prod->n_col = tab1->n_col + tab2->n_col;
|
|
prod->n_var = tab1->n_var + tab2->n_var;
|
|
prod->max_var = tab1->max_var + tab2->max_var;
|
|
prod->n_param = 0;
|
|
prod->n_div = 0;
|
|
prod->n_dead = tab1->n_dead + tab2->n_dead;
|
|
prod->n_redundant = tab1->n_redundant + tab2->n_redundant;
|
|
prod->rational = tab1->rational;
|
|
prod->empty = tab1->empty || tab2->empty;
|
|
prod->strict_redundant = tab1->strict_redundant || tab2->strict_redundant;
|
|
prod->need_undo = 0;
|
|
prod->in_undo = 0;
|
|
prod->M = tab1->M;
|
|
prod->cone = tab1->cone;
|
|
prod->bottom.type = isl_tab_undo_bottom;
|
|
prod->bottom.next = NULL;
|
|
prod->top = &prod->bottom;
|
|
|
|
prod->n_zero = 0;
|
|
prod->n_unbounded = 0;
|
|
prod->basis = NULL;
|
|
|
|
return prod;
|
|
error:
|
|
isl_tab_free(prod);
|
|
return NULL;
|
|
}
|
|
|
|
static struct isl_tab_var *var_from_index(struct isl_tab *tab, int i)
|
|
{
|
|
if (i >= 0)
|
|
return &tab->var[i];
|
|
else
|
|
return &tab->con[~i];
|
|
}
|
|
|
|
struct isl_tab_var *isl_tab_var_from_row(struct isl_tab *tab, int i)
|
|
{
|
|
return var_from_index(tab, tab->row_var[i]);
|
|
}
|
|
|
|
static struct isl_tab_var *var_from_col(struct isl_tab *tab, int i)
|
|
{
|
|
return var_from_index(tab, tab->col_var[i]);
|
|
}
|
|
|
|
/* Check if there are any upper bounds on column variable "var",
|
|
* i.e., non-negative rows where var appears with a negative coefficient.
|
|
* Return 1 if there are no such bounds.
|
|
*/
|
|
static int max_is_manifestly_unbounded(struct isl_tab *tab,
|
|
struct isl_tab_var *var)
|
|
{
|
|
int i;
|
|
unsigned off = 2 + tab->M;
|
|
|
|
if (var->is_row)
|
|
return 0;
|
|
for (i = tab->n_redundant; i < tab->n_row; ++i) {
|
|
if (!isl_int_is_neg(tab->mat->row[i][off + var->index]))
|
|
continue;
|
|
if (isl_tab_var_from_row(tab, i)->is_nonneg)
|
|
return 0;
|
|
}
|
|
return 1;
|
|
}
|
|
|
|
/* Check if there are any lower bounds on column variable "var",
|
|
* i.e., non-negative rows where var appears with a positive coefficient.
|
|
* Return 1 if there are no such bounds.
|
|
*/
|
|
static int min_is_manifestly_unbounded(struct isl_tab *tab,
|
|
struct isl_tab_var *var)
|
|
{
|
|
int i;
|
|
unsigned off = 2 + tab->M;
|
|
|
|
if (var->is_row)
|
|
return 0;
|
|
for (i = tab->n_redundant; i < tab->n_row; ++i) {
|
|
if (!isl_int_is_pos(tab->mat->row[i][off + var->index]))
|
|
continue;
|
|
if (isl_tab_var_from_row(tab, i)->is_nonneg)
|
|
return 0;
|
|
}
|
|
return 1;
|
|
}
|
|
|
|
static int row_cmp(struct isl_tab *tab, int r1, int r2, int c, isl_int *t)
|
|
{
|
|
unsigned off = 2 + tab->M;
|
|
|
|
if (tab->M) {
|
|
int s;
|
|
isl_int_mul(*t, tab->mat->row[r1][2], tab->mat->row[r2][off+c]);
|
|
isl_int_submul(*t, tab->mat->row[r2][2], tab->mat->row[r1][off+c]);
|
|
s = isl_int_sgn(*t);
|
|
if (s)
|
|
return s;
|
|
}
|
|
isl_int_mul(*t, tab->mat->row[r1][1], tab->mat->row[r2][off + c]);
|
|
isl_int_submul(*t, tab->mat->row[r2][1], tab->mat->row[r1][off + c]);
|
|
return isl_int_sgn(*t);
|
|
}
|
|
|
|
/* Given the index of a column "c", return the index of a row
|
|
* that can be used to pivot the column in, with either an increase
|
|
* (sgn > 0) or a decrease (sgn < 0) of the corresponding variable.
|
|
* If "var" is not NULL, then the row returned will be different from
|
|
* the one associated with "var".
|
|
*
|
|
* Each row in the tableau is of the form
|
|
*
|
|
* x_r = a_r0 + \sum_i a_ri x_i
|
|
*
|
|
* Only rows with x_r >= 0 and with the sign of a_ri opposite to "sgn"
|
|
* impose any limit on the increase or decrease in the value of x_c
|
|
* and this bound is equal to a_r0 / |a_rc|. We are therefore looking
|
|
* for the row with the smallest (most stringent) such bound.
|
|
* Note that the common denominator of each row drops out of the fraction.
|
|
* To check if row j has a smaller bound than row r, i.e.,
|
|
* a_j0 / |a_jc| < a_r0 / |a_rc| or a_j0 |a_rc| < a_r0 |a_jc|,
|
|
* we check if -sign(a_jc) (a_j0 a_rc - a_r0 a_jc) < 0,
|
|
* where -sign(a_jc) is equal to "sgn".
|
|
*/
|
|
static int pivot_row(struct isl_tab *tab,
|
|
struct isl_tab_var *var, int sgn, int c)
|
|
{
|
|
int j, r, tsgn;
|
|
isl_int t;
|
|
unsigned off = 2 + tab->M;
|
|
|
|
isl_int_init(t);
|
|
r = -1;
|
|
for (j = tab->n_redundant; j < tab->n_row; ++j) {
|
|
if (var && j == var->index)
|
|
continue;
|
|
if (!isl_tab_var_from_row(tab, j)->is_nonneg)
|
|
continue;
|
|
if (sgn * isl_int_sgn(tab->mat->row[j][off + c]) >= 0)
|
|
continue;
|
|
if (r < 0) {
|
|
r = j;
|
|
continue;
|
|
}
|
|
tsgn = sgn * row_cmp(tab, r, j, c, &t);
|
|
if (tsgn < 0 || (tsgn == 0 &&
|
|
tab->row_var[j] < tab->row_var[r]))
|
|
r = j;
|
|
}
|
|
isl_int_clear(t);
|
|
return r;
|
|
}
|
|
|
|
/* Find a pivot (row and col) that will increase (sgn > 0) or decrease
|
|
* (sgn < 0) the value of row variable var.
|
|
* If not NULL, then skip_var is a row variable that should be ignored
|
|
* while looking for a pivot row. It is usually equal to var.
|
|
*
|
|
* As the given row in the tableau is of the form
|
|
*
|
|
* x_r = a_r0 + \sum_i a_ri x_i
|
|
*
|
|
* we need to find a column such that the sign of a_ri is equal to "sgn"
|
|
* (such that an increase in x_i will have the desired effect) or a
|
|
* column with a variable that may attain negative values.
|
|
* If a_ri is positive, then we need to move x_i in the same direction
|
|
* to obtain the desired effect. Otherwise, x_i has to move in the
|
|
* opposite direction.
|
|
*/
|
|
static void find_pivot(struct isl_tab *tab,
|
|
struct isl_tab_var *var, struct isl_tab_var *skip_var,
|
|
int sgn, int *row, int *col)
|
|
{
|
|
int j, r, c;
|
|
isl_int *tr;
|
|
|
|
*row = *col = -1;
|
|
|
|
isl_assert(tab->mat->ctx, var->is_row, return);
|
|
tr = tab->mat->row[var->index] + 2 + tab->M;
|
|
|
|
c = -1;
|
|
for (j = tab->n_dead; j < tab->n_col; ++j) {
|
|
if (isl_int_is_zero(tr[j]))
|
|
continue;
|
|
if (isl_int_sgn(tr[j]) != sgn &&
|
|
var_from_col(tab, j)->is_nonneg)
|
|
continue;
|
|
if (c < 0 || tab->col_var[j] < tab->col_var[c])
|
|
c = j;
|
|
}
|
|
if (c < 0)
|
|
return;
|
|
|
|
sgn *= isl_int_sgn(tr[c]);
|
|
r = pivot_row(tab, skip_var, sgn, c);
|
|
*row = r < 0 ? var->index : r;
|
|
*col = c;
|
|
}
|
|
|
|
/* Return 1 if row "row" represents an obviously redundant inequality.
|
|
* This means
|
|
* - it represents an inequality or a variable
|
|
* - that is the sum of a non-negative sample value and a positive
|
|
* combination of zero or more non-negative constraints.
|
|
*/
|
|
int isl_tab_row_is_redundant(struct isl_tab *tab, int row)
|
|
{
|
|
int i;
|
|
unsigned off = 2 + tab->M;
|
|
|
|
if (tab->row_var[row] < 0 && !isl_tab_var_from_row(tab, row)->is_nonneg)
|
|
return 0;
|
|
|
|
if (isl_int_is_neg(tab->mat->row[row][1]))
|
|
return 0;
|
|
if (tab->strict_redundant && isl_int_is_zero(tab->mat->row[row][1]))
|
|
return 0;
|
|
if (tab->M && isl_int_is_neg(tab->mat->row[row][2]))
|
|
return 0;
|
|
|
|
for (i = tab->n_dead; i < tab->n_col; ++i) {
|
|
if (isl_int_is_zero(tab->mat->row[row][off + i]))
|
|
continue;
|
|
if (tab->col_var[i] >= 0)
|
|
return 0;
|
|
if (isl_int_is_neg(tab->mat->row[row][off + i]))
|
|
return 0;
|
|
if (!var_from_col(tab, i)->is_nonneg)
|
|
return 0;
|
|
}
|
|
return 1;
|
|
}
|
|
|
|
static void swap_rows(struct isl_tab *tab, int row1, int row2)
|
|
{
|
|
int t;
|
|
enum isl_tab_row_sign s;
|
|
|
|
t = tab->row_var[row1];
|
|
tab->row_var[row1] = tab->row_var[row2];
|
|
tab->row_var[row2] = t;
|
|
isl_tab_var_from_row(tab, row1)->index = row1;
|
|
isl_tab_var_from_row(tab, row2)->index = row2;
|
|
tab->mat = isl_mat_swap_rows(tab->mat, row1, row2);
|
|
|
|
if (!tab->row_sign)
|
|
return;
|
|
s = tab->row_sign[row1];
|
|
tab->row_sign[row1] = tab->row_sign[row2];
|
|
tab->row_sign[row2] = s;
|
|
}
|
|
|
|
static int push_union(struct isl_tab *tab,
|
|
enum isl_tab_undo_type type, union isl_tab_undo_val u) WARN_UNUSED;
|
|
static int push_union(struct isl_tab *tab,
|
|
enum isl_tab_undo_type type, union isl_tab_undo_val u)
|
|
{
|
|
struct isl_tab_undo *undo;
|
|
|
|
if (!tab)
|
|
return -1;
|
|
if (!tab->need_undo)
|
|
return 0;
|
|
|
|
undo = isl_alloc_type(tab->mat->ctx, struct isl_tab_undo);
|
|
if (!undo)
|
|
return -1;
|
|
undo->type = type;
|
|
undo->u = u;
|
|
undo->next = tab->top;
|
|
tab->top = undo;
|
|
|
|
return 0;
|
|
}
|
|
|
|
int isl_tab_push_var(struct isl_tab *tab,
|
|
enum isl_tab_undo_type type, struct isl_tab_var *var)
|
|
{
|
|
union isl_tab_undo_val u;
|
|
if (var->is_row)
|
|
u.var_index = tab->row_var[var->index];
|
|
else
|
|
u.var_index = tab->col_var[var->index];
|
|
return push_union(tab, type, u);
|
|
}
|
|
|
|
int isl_tab_push(struct isl_tab *tab, enum isl_tab_undo_type type)
|
|
{
|
|
union isl_tab_undo_val u = { 0 };
|
|
return push_union(tab, type, u);
|
|
}
|
|
|
|
/* Push a record on the undo stack describing the current basic
|
|
* variables, so that the this state can be restored during rollback.
|
|
*/
|
|
int isl_tab_push_basis(struct isl_tab *tab)
|
|
{
|
|
int i;
|
|
union isl_tab_undo_val u;
|
|
|
|
u.col_var = isl_alloc_array(tab->mat->ctx, int, tab->n_col);
|
|
if (tab->n_col && !u.col_var)
|
|
return -1;
|
|
for (i = 0; i < tab->n_col; ++i)
|
|
u.col_var[i] = tab->col_var[i];
|
|
return push_union(tab, isl_tab_undo_saved_basis, u);
|
|
}
|
|
|
|
int isl_tab_push_callback(struct isl_tab *tab, struct isl_tab_callback *callback)
|
|
{
|
|
union isl_tab_undo_val u;
|
|
u.callback = callback;
|
|
return push_union(tab, isl_tab_undo_callback, u);
|
|
}
|
|
|
|
struct isl_tab *isl_tab_init_samples(struct isl_tab *tab)
|
|
{
|
|
if (!tab)
|
|
return NULL;
|
|
|
|
tab->n_sample = 0;
|
|
tab->n_outside = 0;
|
|
tab->samples = isl_mat_alloc(tab->mat->ctx, 1, 1 + tab->n_var);
|
|
if (!tab->samples)
|
|
goto error;
|
|
tab->sample_index = isl_alloc_array(tab->mat->ctx, int, 1);
|
|
if (!tab->sample_index)
|
|
goto error;
|
|
return tab;
|
|
error:
|
|
isl_tab_free(tab);
|
|
return NULL;
|
|
}
|
|
|
|
int isl_tab_add_sample(struct isl_tab *tab, __isl_take isl_vec *sample)
|
|
{
|
|
if (!tab || !sample)
|
|
goto error;
|
|
|
|
if (tab->n_sample + 1 > tab->samples->n_row) {
|
|
int *t = isl_realloc_array(tab->mat->ctx,
|
|
tab->sample_index, int, tab->n_sample + 1);
|
|
if (!t)
|
|
goto error;
|
|
tab->sample_index = t;
|
|
}
|
|
|
|
tab->samples = isl_mat_extend(tab->samples,
|
|
tab->n_sample + 1, tab->samples->n_col);
|
|
if (!tab->samples)
|
|
goto error;
|
|
|
|
isl_seq_cpy(tab->samples->row[tab->n_sample], sample->el, sample->size);
|
|
isl_vec_free(sample);
|
|
tab->sample_index[tab->n_sample] = tab->n_sample;
|
|
tab->n_sample++;
|
|
|
|
return 0;
|
|
error:
|
|
isl_vec_free(sample);
|
|
return -1;
|
|
}
|
|
|
|
struct isl_tab *isl_tab_drop_sample(struct isl_tab *tab, int s)
|
|
{
|
|
if (s != tab->n_outside) {
|
|
int t = tab->sample_index[tab->n_outside];
|
|
tab->sample_index[tab->n_outside] = tab->sample_index[s];
|
|
tab->sample_index[s] = t;
|
|
isl_mat_swap_rows(tab->samples, tab->n_outside, s);
|
|
}
|
|
tab->n_outside++;
|
|
if (isl_tab_push(tab, isl_tab_undo_drop_sample) < 0) {
|
|
isl_tab_free(tab);
|
|
return NULL;
|
|
}
|
|
|
|
return tab;
|
|
}
|
|
|
|
/* Record the current number of samples so that we can remove newer
|
|
* samples during a rollback.
|
|
*/
|
|
int isl_tab_save_samples(struct isl_tab *tab)
|
|
{
|
|
union isl_tab_undo_val u;
|
|
|
|
if (!tab)
|
|
return -1;
|
|
|
|
u.n = tab->n_sample;
|
|
return push_union(tab, isl_tab_undo_saved_samples, u);
|
|
}
|
|
|
|
/* Mark row with index "row" as being redundant.
|
|
* If we may need to undo the operation or if the row represents
|
|
* a variable of the original problem, the row is kept,
|
|
* but no longer considered when looking for a pivot row.
|
|
* Otherwise, the row is simply removed.
|
|
*
|
|
* The row may be interchanged with some other row. If it
|
|
* is interchanged with a later row, return 1. Otherwise return 0.
|
|
* If the rows are checked in order in the calling function,
|
|
* then a return value of 1 means that the row with the given
|
|
* row number may now contain a different row that hasn't been checked yet.
|
|
*/
|
|
int isl_tab_mark_redundant(struct isl_tab *tab, int row)
|
|
{
|
|
struct isl_tab_var *var = isl_tab_var_from_row(tab, row);
|
|
var->is_redundant = 1;
|
|
isl_assert(tab->mat->ctx, row >= tab->n_redundant, return -1);
|
|
if (tab->preserve || tab->need_undo || tab->row_var[row] >= 0) {
|
|
if (tab->row_var[row] >= 0 && !var->is_nonneg) {
|
|
var->is_nonneg = 1;
|
|
if (isl_tab_push_var(tab, isl_tab_undo_nonneg, var) < 0)
|
|
return -1;
|
|
}
|
|
if (row != tab->n_redundant)
|
|
swap_rows(tab, row, tab->n_redundant);
|
|
tab->n_redundant++;
|
|
return isl_tab_push_var(tab, isl_tab_undo_redundant, var);
|
|
} else {
|
|
if (row != tab->n_row - 1)
|
|
swap_rows(tab, row, tab->n_row - 1);
|
|
isl_tab_var_from_row(tab, tab->n_row - 1)->index = -1;
|
|
tab->n_row--;
|
|
return 1;
|
|
}
|
|
}
|
|
|
|
/* Mark "tab" as a rational tableau.
|
|
* If it wasn't marked as a rational tableau already and if we may
|
|
* need to undo changes, then arrange for the marking to be undone
|
|
* during the undo.
|
|
*/
|
|
int isl_tab_mark_rational(struct isl_tab *tab)
|
|
{
|
|
if (!tab)
|
|
return -1;
|
|
if (!tab->rational && tab->need_undo)
|
|
if (isl_tab_push(tab, isl_tab_undo_rational) < 0)
|
|
return -1;
|
|
tab->rational = 1;
|
|
return 0;
|
|
}
|
|
|
|
int isl_tab_mark_empty(struct isl_tab *tab)
|
|
{
|
|
if (!tab)
|
|
return -1;
|
|
if (!tab->empty && tab->need_undo)
|
|
if (isl_tab_push(tab, isl_tab_undo_empty) < 0)
|
|
return -1;
|
|
tab->empty = 1;
|
|
return 0;
|
|
}
|
|
|
|
int isl_tab_freeze_constraint(struct isl_tab *tab, int con)
|
|
{
|
|
struct isl_tab_var *var;
|
|
|
|
if (!tab)
|
|
return -1;
|
|
|
|
var = &tab->con[con];
|
|
if (var->frozen)
|
|
return 0;
|
|
if (var->index < 0)
|
|
return 0;
|
|
var->frozen = 1;
|
|
|
|
if (tab->need_undo)
|
|
return isl_tab_push_var(tab, isl_tab_undo_freeze, var);
|
|
|
|
return 0;
|
|
}
|
|
|
|
/* Update the rows signs after a pivot of "row" and "col", with "row_sgn"
|
|
* the original sign of the pivot element.
|
|
* We only keep track of row signs during PILP solving and in this case
|
|
* we only pivot a row with negative sign (meaning the value is always
|
|
* non-positive) using a positive pivot element.
|
|
*
|
|
* For each row j, the new value of the parametric constant is equal to
|
|
*
|
|
* a_j0 - a_jc a_r0/a_rc
|
|
*
|
|
* where a_j0 is the original parametric constant, a_rc is the pivot element,
|
|
* a_r0 is the parametric constant of the pivot row and a_jc is the
|
|
* pivot column entry of the row j.
|
|
* Since a_r0 is non-positive and a_rc is positive, the sign of row j
|
|
* remains the same if a_jc has the same sign as the row j or if
|
|
* a_jc is zero. In all other cases, we reset the sign to "unknown".
|
|
*/
|
|
static void update_row_sign(struct isl_tab *tab, int row, int col, int row_sgn)
|
|
{
|
|
int i;
|
|
struct isl_mat *mat = tab->mat;
|
|
unsigned off = 2 + tab->M;
|
|
|
|
if (!tab->row_sign)
|
|
return;
|
|
|
|
if (tab->row_sign[row] == 0)
|
|
return;
|
|
isl_assert(mat->ctx, row_sgn > 0, return);
|
|
isl_assert(mat->ctx, tab->row_sign[row] == isl_tab_row_neg, return);
|
|
tab->row_sign[row] = isl_tab_row_pos;
|
|
for (i = 0; i < tab->n_row; ++i) {
|
|
int s;
|
|
if (i == row)
|
|
continue;
|
|
s = isl_int_sgn(mat->row[i][off + col]);
|
|
if (!s)
|
|
continue;
|
|
if (!tab->row_sign[i])
|
|
continue;
|
|
if (s < 0 && tab->row_sign[i] == isl_tab_row_neg)
|
|
continue;
|
|
if (s > 0 && tab->row_sign[i] == isl_tab_row_pos)
|
|
continue;
|
|
tab->row_sign[i] = isl_tab_row_unknown;
|
|
}
|
|
}
|
|
|
|
/* Given a row number "row" and a column number "col", pivot the tableau
|
|
* such that the associated variables are interchanged.
|
|
* The given row in the tableau expresses
|
|
*
|
|
* x_r = a_r0 + \sum_i a_ri x_i
|
|
*
|
|
* or
|
|
*
|
|
* x_c = 1/a_rc x_r - a_r0/a_rc + sum_{i \ne r} -a_ri/a_rc
|
|
*
|
|
* Substituting this equality into the other rows
|
|
*
|
|
* x_j = a_j0 + \sum_i a_ji x_i
|
|
*
|
|
* with a_jc \ne 0, we obtain
|
|
*
|
|
* x_j = a_jc/a_rc x_r + a_j0 - a_jc a_r0/a_rc + sum a_ji - a_jc a_ri/a_rc
|
|
*
|
|
* The tableau
|
|
*
|
|
* n_rc/d_r n_ri/d_r
|
|
* n_jc/d_j n_ji/d_j
|
|
*
|
|
* where i is any other column and j is any other row,
|
|
* is therefore transformed into
|
|
*
|
|
* s(n_rc)d_r/|n_rc| -s(n_rc)n_ri/|n_rc|
|
|
* s(n_rc)d_r n_jc/(|n_rc| d_j) (n_ji |n_rc| - s(n_rc)n_jc n_ri)/(|n_rc| d_j)
|
|
*
|
|
* The transformation is performed along the following steps
|
|
*
|
|
* d_r/n_rc n_ri/n_rc
|
|
* n_jc/d_j n_ji/d_j
|
|
*
|
|
* s(n_rc)d_r/|n_rc| -s(n_rc)n_ri/|n_rc|
|
|
* n_jc/d_j n_ji/d_j
|
|
*
|
|
* s(n_rc)d_r/|n_rc| -s(n_rc)n_ri/|n_rc|
|
|
* n_jc/(|n_rc| d_j) n_ji/(|n_rc| d_j)
|
|
*
|
|
* s(n_rc)d_r/|n_rc| -s(n_rc)n_ri/|n_rc|
|
|
* n_jc/(|n_rc| d_j) (n_ji |n_rc|)/(|n_rc| d_j)
|
|
*
|
|
* s(n_rc)d_r/|n_rc| -s(n_rc)n_ri/|n_rc|
|
|
* n_jc/(|n_rc| d_j) (n_ji |n_rc| - s(n_rc)n_jc n_ri)/(|n_rc| d_j)
|
|
*
|
|
* s(n_rc)d_r/|n_rc| -s(n_rc)n_ri/|n_rc|
|
|
* s(n_rc)d_r n_jc/(|n_rc| d_j) (n_ji |n_rc| - s(n_rc)n_jc n_ri)/(|n_rc| d_j)
|
|
*
|
|
*/
|
|
int isl_tab_pivot(struct isl_tab *tab, int row, int col)
|
|
{
|
|
int i, j;
|
|
int sgn;
|
|
int t;
|
|
isl_ctx *ctx;
|
|
struct isl_mat *mat = tab->mat;
|
|
struct isl_tab_var *var;
|
|
unsigned off = 2 + tab->M;
|
|
|
|
ctx = isl_tab_get_ctx(tab);
|
|
if (isl_ctx_next_operation(ctx) < 0)
|
|
return -1;
|
|
|
|
isl_int_swap(mat->row[row][0], mat->row[row][off + col]);
|
|
sgn = isl_int_sgn(mat->row[row][0]);
|
|
if (sgn < 0) {
|
|
isl_int_neg(mat->row[row][0], mat->row[row][0]);
|
|
isl_int_neg(mat->row[row][off + col], mat->row[row][off + col]);
|
|
} else
|
|
for (j = 0; j < off - 1 + tab->n_col; ++j) {
|
|
if (j == off - 1 + col)
|
|
continue;
|
|
isl_int_neg(mat->row[row][1 + j], mat->row[row][1 + j]);
|
|
}
|
|
if (!isl_int_is_one(mat->row[row][0]))
|
|
isl_seq_normalize(mat->ctx, mat->row[row], off + tab->n_col);
|
|
for (i = 0; i < tab->n_row; ++i) {
|
|
if (i == row)
|
|
continue;
|
|
if (isl_int_is_zero(mat->row[i][off + col]))
|
|
continue;
|
|
isl_int_mul(mat->row[i][0], mat->row[i][0], mat->row[row][0]);
|
|
for (j = 0; j < off - 1 + tab->n_col; ++j) {
|
|
if (j == off - 1 + col)
|
|
continue;
|
|
isl_int_mul(mat->row[i][1 + j],
|
|
mat->row[i][1 + j], mat->row[row][0]);
|
|
isl_int_addmul(mat->row[i][1 + j],
|
|
mat->row[i][off + col], mat->row[row][1 + j]);
|
|
}
|
|
isl_int_mul(mat->row[i][off + col],
|
|
mat->row[i][off + col], mat->row[row][off + col]);
|
|
if (!isl_int_is_one(mat->row[i][0]))
|
|
isl_seq_normalize(mat->ctx, mat->row[i], off + tab->n_col);
|
|
}
|
|
t = tab->row_var[row];
|
|
tab->row_var[row] = tab->col_var[col];
|
|
tab->col_var[col] = t;
|
|
var = isl_tab_var_from_row(tab, row);
|
|
var->is_row = 1;
|
|
var->index = row;
|
|
var = var_from_col(tab, col);
|
|
var->is_row = 0;
|
|
var->index = col;
|
|
update_row_sign(tab, row, col, sgn);
|
|
if (tab->in_undo)
|
|
return 0;
|
|
for (i = tab->n_redundant; i < tab->n_row; ++i) {
|
|
if (isl_int_is_zero(mat->row[i][off + col]))
|
|
continue;
|
|
if (!isl_tab_var_from_row(tab, i)->frozen &&
|
|
isl_tab_row_is_redundant(tab, i)) {
|
|
int redo = isl_tab_mark_redundant(tab, i);
|
|
if (redo < 0)
|
|
return -1;
|
|
if (redo)
|
|
--i;
|
|
}
|
|
}
|
|
return 0;
|
|
}
|
|
|
|
/* If "var" represents a column variable, then pivot is up (sgn > 0)
|
|
* or down (sgn < 0) to a row. The variable is assumed not to be
|
|
* unbounded in the specified direction.
|
|
* If sgn = 0, then the variable is unbounded in both directions,
|
|
* and we pivot with any row we can find.
|
|
*/
|
|
static int to_row(struct isl_tab *tab, struct isl_tab_var *var, int sign) WARN_UNUSED;
|
|
static int to_row(struct isl_tab *tab, struct isl_tab_var *var, int sign)
|
|
{
|
|
int r;
|
|
unsigned off = 2 + tab->M;
|
|
|
|
if (var->is_row)
|
|
return 0;
|
|
|
|
if (sign == 0) {
|
|
for (r = tab->n_redundant; r < tab->n_row; ++r)
|
|
if (!isl_int_is_zero(tab->mat->row[r][off+var->index]))
|
|
break;
|
|
isl_assert(tab->mat->ctx, r < tab->n_row, return -1);
|
|
} else {
|
|
r = pivot_row(tab, NULL, sign, var->index);
|
|
isl_assert(tab->mat->ctx, r >= 0, return -1);
|
|
}
|
|
|
|
return isl_tab_pivot(tab, r, var->index);
|
|
}
|
|
|
|
/* Check whether all variables that are marked as non-negative
|
|
* also have a non-negative sample value. This function is not
|
|
* called from the current code but is useful during debugging.
|
|
*/
|
|
static void check_table(struct isl_tab *tab) __attribute__ ((unused));
|
|
static void check_table(struct isl_tab *tab)
|
|
{
|
|
int i;
|
|
|
|
if (tab->empty)
|
|
return;
|
|
for (i = tab->n_redundant; i < tab->n_row; ++i) {
|
|
struct isl_tab_var *var;
|
|
var = isl_tab_var_from_row(tab, i);
|
|
if (!var->is_nonneg)
|
|
continue;
|
|
if (tab->M) {
|
|
isl_assert(tab->mat->ctx,
|
|
!isl_int_is_neg(tab->mat->row[i][2]), abort());
|
|
if (isl_int_is_pos(tab->mat->row[i][2]))
|
|
continue;
|
|
}
|
|
isl_assert(tab->mat->ctx, !isl_int_is_neg(tab->mat->row[i][1]),
|
|
abort());
|
|
}
|
|
}
|
|
|
|
/* Return the sign of the maximal value of "var".
|
|
* If the sign is not negative, then on return from this function,
|
|
* the sample value will also be non-negative.
|
|
*
|
|
* If "var" is manifestly unbounded wrt positive values, we are done.
|
|
* Otherwise, we pivot the variable up to a row if needed
|
|
* Then we continue pivoting down until either
|
|
* - no more down pivots can be performed
|
|
* - the sample value is positive
|
|
* - the variable is pivoted into a manifestly unbounded column
|
|
*/
|
|
static int sign_of_max(struct isl_tab *tab, struct isl_tab_var *var)
|
|
{
|
|
int row, col;
|
|
|
|
if (max_is_manifestly_unbounded(tab, var))
|
|
return 1;
|
|
if (to_row(tab, var, 1) < 0)
|
|
return -2;
|
|
while (!isl_int_is_pos(tab->mat->row[var->index][1])) {
|
|
find_pivot(tab, var, var, 1, &row, &col);
|
|
if (row == -1)
|
|
return isl_int_sgn(tab->mat->row[var->index][1]);
|
|
if (isl_tab_pivot(tab, row, col) < 0)
|
|
return -2;
|
|
if (!var->is_row) /* manifestly unbounded */
|
|
return 1;
|
|
}
|
|
return 1;
|
|
}
|
|
|
|
int isl_tab_sign_of_max(struct isl_tab *tab, int con)
|
|
{
|
|
struct isl_tab_var *var;
|
|
|
|
if (!tab)
|
|
return -2;
|
|
|
|
var = &tab->con[con];
|
|
isl_assert(tab->mat->ctx, !var->is_redundant, return -2);
|
|
isl_assert(tab->mat->ctx, !var->is_zero, return -2);
|
|
|
|
return sign_of_max(tab, var);
|
|
}
|
|
|
|
static int row_is_neg(struct isl_tab *tab, int row)
|
|
{
|
|
if (!tab->M)
|
|
return isl_int_is_neg(tab->mat->row[row][1]);
|
|
if (isl_int_is_pos(tab->mat->row[row][2]))
|
|
return 0;
|
|
if (isl_int_is_neg(tab->mat->row[row][2]))
|
|
return 1;
|
|
return isl_int_is_neg(tab->mat->row[row][1]);
|
|
}
|
|
|
|
static int row_sgn(struct isl_tab *tab, int row)
|
|
{
|
|
if (!tab->M)
|
|
return isl_int_sgn(tab->mat->row[row][1]);
|
|
if (!isl_int_is_zero(tab->mat->row[row][2]))
|
|
return isl_int_sgn(tab->mat->row[row][2]);
|
|
else
|
|
return isl_int_sgn(tab->mat->row[row][1]);
|
|
}
|
|
|
|
/* Perform pivots until the row variable "var" has a non-negative
|
|
* sample value or until no more upward pivots can be performed.
|
|
* Return the sign of the sample value after the pivots have been
|
|
* performed.
|
|
*/
|
|
static int restore_row(struct isl_tab *tab, struct isl_tab_var *var)
|
|
{
|
|
int row, col;
|
|
|
|
while (row_is_neg(tab, var->index)) {
|
|
find_pivot(tab, var, var, 1, &row, &col);
|
|
if (row == -1)
|
|
break;
|
|
if (isl_tab_pivot(tab, row, col) < 0)
|
|
return -2;
|
|
if (!var->is_row) /* manifestly unbounded */
|
|
return 1;
|
|
}
|
|
return row_sgn(tab, var->index);
|
|
}
|
|
|
|
/* Perform pivots until we are sure that the row variable "var"
|
|
* can attain non-negative values. After return from this
|
|
* function, "var" is still a row variable, but its sample
|
|
* value may not be non-negative, even if the function returns 1.
|
|
*/
|
|
static int at_least_zero(struct isl_tab *tab, struct isl_tab_var *var)
|
|
{
|
|
int row, col;
|
|
|
|
while (isl_int_is_neg(tab->mat->row[var->index][1])) {
|
|
find_pivot(tab, var, var, 1, &row, &col);
|
|
if (row == -1)
|
|
break;
|
|
if (row == var->index) /* manifestly unbounded */
|
|
return 1;
|
|
if (isl_tab_pivot(tab, row, col) < 0)
|
|
return -1;
|
|
}
|
|
return !isl_int_is_neg(tab->mat->row[var->index][1]);
|
|
}
|
|
|
|
/* Return a negative value if "var" can attain negative values.
|
|
* Return a non-negative value otherwise.
|
|
*
|
|
* If "var" is manifestly unbounded wrt negative values, we are done.
|
|
* Otherwise, if var is in a column, we can pivot it down to a row.
|
|
* Then we continue pivoting down until either
|
|
* - the pivot would result in a manifestly unbounded column
|
|
* => we don't perform the pivot, but simply return -1
|
|
* - no more down pivots can be performed
|
|
* - the sample value is negative
|
|
* If the sample value becomes negative and the variable is supposed
|
|
* to be nonnegative, then we undo the last pivot.
|
|
* However, if the last pivot has made the pivoting variable
|
|
* obviously redundant, then it may have moved to another row.
|
|
* In that case we look for upward pivots until we reach a non-negative
|
|
* value again.
|
|
*/
|
|
static int sign_of_min(struct isl_tab *tab, struct isl_tab_var *var)
|
|
{
|
|
int row, col;
|
|
struct isl_tab_var *pivot_var = NULL;
|
|
|
|
if (min_is_manifestly_unbounded(tab, var))
|
|
return -1;
|
|
if (!var->is_row) {
|
|
col = var->index;
|
|
row = pivot_row(tab, NULL, -1, col);
|
|
pivot_var = var_from_col(tab, col);
|
|
if (isl_tab_pivot(tab, row, col) < 0)
|
|
return -2;
|
|
if (var->is_redundant)
|
|
return 0;
|
|
if (isl_int_is_neg(tab->mat->row[var->index][1])) {
|
|
if (var->is_nonneg) {
|
|
if (!pivot_var->is_redundant &&
|
|
pivot_var->index == row) {
|
|
if (isl_tab_pivot(tab, row, col) < 0)
|
|
return -2;
|
|
} else
|
|
if (restore_row(tab, var) < -1)
|
|
return -2;
|
|
}
|
|
return -1;
|
|
}
|
|
}
|
|
if (var->is_redundant)
|
|
return 0;
|
|
while (!isl_int_is_neg(tab->mat->row[var->index][1])) {
|
|
find_pivot(tab, var, var, -1, &row, &col);
|
|
if (row == var->index)
|
|
return -1;
|
|
if (row == -1)
|
|
return isl_int_sgn(tab->mat->row[var->index][1]);
|
|
pivot_var = var_from_col(tab, col);
|
|
if (isl_tab_pivot(tab, row, col) < 0)
|
|
return -2;
|
|
if (var->is_redundant)
|
|
return 0;
|
|
}
|
|
if (pivot_var && var->is_nonneg) {
|
|
/* pivot back to non-negative value */
|
|
if (!pivot_var->is_redundant && pivot_var->index == row) {
|
|
if (isl_tab_pivot(tab, row, col) < 0)
|
|
return -2;
|
|
} else
|
|
if (restore_row(tab, var) < -1)
|
|
return -2;
|
|
}
|
|
return -1;
|
|
}
|
|
|
|
static int row_at_most_neg_one(struct isl_tab *tab, int row)
|
|
{
|
|
if (tab->M) {
|
|
if (isl_int_is_pos(tab->mat->row[row][2]))
|
|
return 0;
|
|
if (isl_int_is_neg(tab->mat->row[row][2]))
|
|
return 1;
|
|
}
|
|
return isl_int_is_neg(tab->mat->row[row][1]) &&
|
|
isl_int_abs_ge(tab->mat->row[row][1],
|
|
tab->mat->row[row][0]);
|
|
}
|
|
|
|
/* Return 1 if "var" can attain values <= -1.
|
|
* Return 0 otherwise.
|
|
*
|
|
* If the variable "var" is supposed to be non-negative (is_nonneg is set),
|
|
* then the sample value of "var" is assumed to be non-negative when the
|
|
* the function is called. If 1 is returned then the constraint
|
|
* is not redundant and the sample value is made non-negative again before
|
|
* the function returns.
|
|
*/
|
|
int isl_tab_min_at_most_neg_one(struct isl_tab *tab, struct isl_tab_var *var)
|
|
{
|
|
int row, col;
|
|
struct isl_tab_var *pivot_var;
|
|
|
|
if (min_is_manifestly_unbounded(tab, var))
|
|
return 1;
|
|
if (!var->is_row) {
|
|
col = var->index;
|
|
row = pivot_row(tab, NULL, -1, col);
|
|
pivot_var = var_from_col(tab, col);
|
|
if (isl_tab_pivot(tab, row, col) < 0)
|
|
return -1;
|
|
if (var->is_redundant)
|
|
return 0;
|
|
if (row_at_most_neg_one(tab, var->index)) {
|
|
if (var->is_nonneg) {
|
|
if (!pivot_var->is_redundant &&
|
|
pivot_var->index == row) {
|
|
if (isl_tab_pivot(tab, row, col) < 0)
|
|
return -1;
|
|
} else
|
|
if (restore_row(tab, var) < -1)
|
|
return -1;
|
|
}
|
|
return 1;
|
|
}
|
|
}
|
|
if (var->is_redundant)
|
|
return 0;
|
|
do {
|
|
find_pivot(tab, var, var, -1, &row, &col);
|
|
if (row == var->index) {
|
|
if (var->is_nonneg && restore_row(tab, var) < -1)
|
|
return -1;
|
|
return 1;
|
|
}
|
|
if (row == -1)
|
|
return 0;
|
|
pivot_var = var_from_col(tab, col);
|
|
if (isl_tab_pivot(tab, row, col) < 0)
|
|
return -1;
|
|
if (var->is_redundant)
|
|
return 0;
|
|
} while (!row_at_most_neg_one(tab, var->index));
|
|
if (var->is_nonneg) {
|
|
/* pivot back to non-negative value */
|
|
if (!pivot_var->is_redundant && pivot_var->index == row)
|
|
if (isl_tab_pivot(tab, row, col) < 0)
|
|
return -1;
|
|
if (restore_row(tab, var) < -1)
|
|
return -1;
|
|
}
|
|
return 1;
|
|
}
|
|
|
|
/* Return 1 if "var" can attain values >= 1.
|
|
* Return 0 otherwise.
|
|
*/
|
|
static int at_least_one(struct isl_tab *tab, struct isl_tab_var *var)
|
|
{
|
|
int row, col;
|
|
isl_int *r;
|
|
|
|
if (max_is_manifestly_unbounded(tab, var))
|
|
return 1;
|
|
if (to_row(tab, var, 1) < 0)
|
|
return -1;
|
|
r = tab->mat->row[var->index];
|
|
while (isl_int_lt(r[1], r[0])) {
|
|
find_pivot(tab, var, var, 1, &row, &col);
|
|
if (row == -1)
|
|
return isl_int_ge(r[1], r[0]);
|
|
if (row == var->index) /* manifestly unbounded */
|
|
return 1;
|
|
if (isl_tab_pivot(tab, row, col) < 0)
|
|
return -1;
|
|
}
|
|
return 1;
|
|
}
|
|
|
|
static void swap_cols(struct isl_tab *tab, int col1, int col2)
|
|
{
|
|
int t;
|
|
unsigned off = 2 + tab->M;
|
|
t = tab->col_var[col1];
|
|
tab->col_var[col1] = tab->col_var[col2];
|
|
tab->col_var[col2] = t;
|
|
var_from_col(tab, col1)->index = col1;
|
|
var_from_col(tab, col2)->index = col2;
|
|
tab->mat = isl_mat_swap_cols(tab->mat, off + col1, off + col2);
|
|
}
|
|
|
|
/* Mark column with index "col" as representing a zero variable.
|
|
* If we may need to undo the operation the column is kept,
|
|
* but no longer considered.
|
|
* Otherwise, the column is simply removed.
|
|
*
|
|
* The column may be interchanged with some other column. If it
|
|
* is interchanged with a later column, return 1. Otherwise return 0.
|
|
* If the columns are checked in order in the calling function,
|
|
* then a return value of 1 means that the column with the given
|
|
* column number may now contain a different column that
|
|
* hasn't been checked yet.
|
|
*/
|
|
int isl_tab_kill_col(struct isl_tab *tab, int col)
|
|
{
|
|
var_from_col(tab, col)->is_zero = 1;
|
|
if (tab->need_undo) {
|
|
if (isl_tab_push_var(tab, isl_tab_undo_zero,
|
|
var_from_col(tab, col)) < 0)
|
|
return -1;
|
|
if (col != tab->n_dead)
|
|
swap_cols(tab, col, tab->n_dead);
|
|
tab->n_dead++;
|
|
return 0;
|
|
} else {
|
|
if (col != tab->n_col - 1)
|
|
swap_cols(tab, col, tab->n_col - 1);
|
|
var_from_col(tab, tab->n_col - 1)->index = -1;
|
|
tab->n_col--;
|
|
return 1;
|
|
}
|
|
}
|
|
|
|
static int row_is_manifestly_non_integral(struct isl_tab *tab, int row)
|
|
{
|
|
unsigned off = 2 + tab->M;
|
|
|
|
if (tab->M && !isl_int_eq(tab->mat->row[row][2],
|
|
tab->mat->row[row][0]))
|
|
return 0;
|
|
if (isl_seq_first_non_zero(tab->mat->row[row] + off + tab->n_dead,
|
|
tab->n_col - tab->n_dead) != -1)
|
|
return 0;
|
|
|
|
return !isl_int_is_divisible_by(tab->mat->row[row][1],
|
|
tab->mat->row[row][0]);
|
|
}
|
|
|
|
/* For integer tableaus, check if any of the coordinates are stuck
|
|
* at a non-integral value.
|
|
*/
|
|
static int tab_is_manifestly_empty(struct isl_tab *tab)
|
|
{
|
|
int i;
|
|
|
|
if (tab->empty)
|
|
return 1;
|
|
if (tab->rational)
|
|
return 0;
|
|
|
|
for (i = 0; i < tab->n_var; ++i) {
|
|
if (!tab->var[i].is_row)
|
|
continue;
|
|
if (row_is_manifestly_non_integral(tab, tab->var[i].index))
|
|
return 1;
|
|
}
|
|
|
|
return 0;
|
|
}
|
|
|
|
/* Row variable "var" is non-negative and cannot attain any values
|
|
* larger than zero. This means that the coefficients of the unrestricted
|
|
* column variables are zero and that the coefficients of the non-negative
|
|
* column variables are zero or negative.
|
|
* Each of the non-negative variables with a negative coefficient can
|
|
* then also be written as the negative sum of non-negative variables
|
|
* and must therefore also be zero.
|
|
*/
|
|
static int close_row(struct isl_tab *tab, struct isl_tab_var *var) WARN_UNUSED;
|
|
static int close_row(struct isl_tab *tab, struct isl_tab_var *var)
|
|
{
|
|
int j;
|
|
struct isl_mat *mat = tab->mat;
|
|
unsigned off = 2 + tab->M;
|
|
|
|
isl_assert(tab->mat->ctx, var->is_nonneg, return -1);
|
|
var->is_zero = 1;
|
|
if (tab->need_undo)
|
|
if (isl_tab_push_var(tab, isl_tab_undo_zero, var) < 0)
|
|
return -1;
|
|
for (j = tab->n_dead; j < tab->n_col; ++j) {
|
|
int recheck;
|
|
if (isl_int_is_zero(mat->row[var->index][off + j]))
|
|
continue;
|
|
isl_assert(tab->mat->ctx,
|
|
isl_int_is_neg(mat->row[var->index][off + j]), return -1);
|
|
recheck = isl_tab_kill_col(tab, j);
|
|
if (recheck < 0)
|
|
return -1;
|
|
if (recheck)
|
|
--j;
|
|
}
|
|
if (isl_tab_mark_redundant(tab, var->index) < 0)
|
|
return -1;
|
|
if (tab_is_manifestly_empty(tab) && isl_tab_mark_empty(tab) < 0)
|
|
return -1;
|
|
return 0;
|
|
}
|
|
|
|
/* Add a constraint to the tableau and allocate a row for it.
|
|
* Return the index into the constraint array "con".
|
|
*/
|
|
int isl_tab_allocate_con(struct isl_tab *tab)
|
|
{
|
|
int r;
|
|
|
|
isl_assert(tab->mat->ctx, tab->n_row < tab->mat->n_row, return -1);
|
|
isl_assert(tab->mat->ctx, tab->n_con < tab->max_con, return -1);
|
|
|
|
r = tab->n_con;
|
|
tab->con[r].index = tab->n_row;
|
|
tab->con[r].is_row = 1;
|
|
tab->con[r].is_nonneg = 0;
|
|
tab->con[r].is_zero = 0;
|
|
tab->con[r].is_redundant = 0;
|
|
tab->con[r].frozen = 0;
|
|
tab->con[r].negated = 0;
|
|
tab->row_var[tab->n_row] = ~r;
|
|
|
|
tab->n_row++;
|
|
tab->n_con++;
|
|
if (isl_tab_push_var(tab, isl_tab_undo_allocate, &tab->con[r]) < 0)
|
|
return -1;
|
|
|
|
return r;
|
|
}
|
|
|
|
/* Move the entries in tab->var up one position, starting at "first",
|
|
* creating room for an extra entry at position "first".
|
|
* Since some of the entries of tab->row_var and tab->col_var contain
|
|
* indices into this array, they have to be updated accordingly.
|
|
*/
|
|
static int var_insert_entry(struct isl_tab *tab, int first)
|
|
{
|
|
int i;
|
|
|
|
if (tab->n_var >= tab->max_var)
|
|
isl_die(isl_tab_get_ctx(tab), isl_error_internal,
|
|
"not enough room for new variable", return -1);
|
|
if (first > tab->n_var)
|
|
isl_die(isl_tab_get_ctx(tab), isl_error_internal,
|
|
"invalid initial position", return -1);
|
|
|
|
for (i = tab->n_var - 1; i >= first; --i) {
|
|
tab->var[i + 1] = tab->var[i];
|
|
if (tab->var[i + 1].is_row)
|
|
tab->row_var[tab->var[i + 1].index]++;
|
|
else
|
|
tab->col_var[tab->var[i + 1].index]++;
|
|
}
|
|
|
|
tab->n_var++;
|
|
|
|
return 0;
|
|
}
|
|
|
|
/* Drop the entry at position "first" in tab->var, moving all
|
|
* subsequent entries down.
|
|
* Since some of the entries of tab->row_var and tab->col_var contain
|
|
* indices into this array, they have to be updated accordingly.
|
|
*/
|
|
static int var_drop_entry(struct isl_tab *tab, int first)
|
|
{
|
|
int i;
|
|
|
|
if (first >= tab->n_var)
|
|
isl_die(isl_tab_get_ctx(tab), isl_error_internal,
|
|
"invalid initial position", return -1);
|
|
|
|
tab->n_var--;
|
|
|
|
for (i = first; i < tab->n_var; ++i) {
|
|
tab->var[i] = tab->var[i + 1];
|
|
if (tab->var[i + 1].is_row)
|
|
tab->row_var[tab->var[i].index]--;
|
|
else
|
|
tab->col_var[tab->var[i].index]--;
|
|
}
|
|
|
|
return 0;
|
|
}
|
|
|
|
/* Add a variable to the tableau at position "r" and allocate a column for it.
|
|
* Return the index into the variable array "var", i.e., "r",
|
|
* or -1 on error.
|
|
*/
|
|
int isl_tab_insert_var(struct isl_tab *tab, int r)
|
|
{
|
|
int i;
|
|
unsigned off = 2 + tab->M;
|
|
|
|
isl_assert(tab->mat->ctx, tab->n_col < tab->mat->n_col, return -1);
|
|
|
|
if (var_insert_entry(tab, r) < 0)
|
|
return -1;
|
|
|
|
tab->var[r].index = tab->n_col;
|
|
tab->var[r].is_row = 0;
|
|
tab->var[r].is_nonneg = 0;
|
|
tab->var[r].is_zero = 0;
|
|
tab->var[r].is_redundant = 0;
|
|
tab->var[r].frozen = 0;
|
|
tab->var[r].negated = 0;
|
|
tab->col_var[tab->n_col] = r;
|
|
|
|
for (i = 0; i < tab->n_row; ++i)
|
|
isl_int_set_si(tab->mat->row[i][off + tab->n_col], 0);
|
|
|
|
tab->n_col++;
|
|
if (isl_tab_push_var(tab, isl_tab_undo_allocate, &tab->var[r]) < 0)
|
|
return -1;
|
|
|
|
return r;
|
|
}
|
|
|
|
/* Add a variable to the tableau and allocate a column for it.
|
|
* Return the index into the variable array "var".
|
|
*/
|
|
int isl_tab_allocate_var(struct isl_tab *tab)
|
|
{
|
|
if (!tab)
|
|
return -1;
|
|
|
|
return isl_tab_insert_var(tab, tab->n_var);
|
|
}
|
|
|
|
/* Add a row to the tableau. The row is given as an affine combination
|
|
* of the original variables and needs to be expressed in terms of the
|
|
* column variables.
|
|
*
|
|
* We add each term in turn.
|
|
* If r = n/d_r is the current sum and we need to add k x, then
|
|
* if x is a column variable, we increase the numerator of
|
|
* this column by k d_r
|
|
* if x = f/d_x is a row variable, then the new representation of r is
|
|
*
|
|
* n k f d_x/g n + d_r/g k f m/d_r n + m/d_g k f
|
|
* --- + --- = ------------------- = -------------------
|
|
* d_r d_r d_r d_x/g m
|
|
*
|
|
* with g the gcd of d_r and d_x and m the lcm of d_r and d_x.
|
|
*
|
|
* If tab->M is set, then, internally, each variable x is represented
|
|
* as x' - M. We then also need no subtract k d_r from the coefficient of M.
|
|
*/
|
|
int isl_tab_add_row(struct isl_tab *tab, isl_int *line)
|
|
{
|
|
int i;
|
|
int r;
|
|
isl_int *row;
|
|
isl_int a, b;
|
|
unsigned off = 2 + tab->M;
|
|
|
|
r = isl_tab_allocate_con(tab);
|
|
if (r < 0)
|
|
return -1;
|
|
|
|
isl_int_init(a);
|
|
isl_int_init(b);
|
|
row = tab->mat->row[tab->con[r].index];
|
|
isl_int_set_si(row[0], 1);
|
|
isl_int_set(row[1], line[0]);
|
|
isl_seq_clr(row + 2, tab->M + tab->n_col);
|
|
for (i = 0; i < tab->n_var; ++i) {
|
|
if (tab->var[i].is_zero)
|
|
continue;
|
|
if (tab->var[i].is_row) {
|
|
isl_int_lcm(a,
|
|
row[0], tab->mat->row[tab->var[i].index][0]);
|
|
isl_int_swap(a, row[0]);
|
|
isl_int_divexact(a, row[0], a);
|
|
isl_int_divexact(b,
|
|
row[0], tab->mat->row[tab->var[i].index][0]);
|
|
isl_int_mul(b, b, line[1 + i]);
|
|
isl_seq_combine(row + 1, a, row + 1,
|
|
b, tab->mat->row[tab->var[i].index] + 1,
|
|
1 + tab->M + tab->n_col);
|
|
} else
|
|
isl_int_addmul(row[off + tab->var[i].index],
|
|
line[1 + i], row[0]);
|
|
if (tab->M && i >= tab->n_param && i < tab->n_var - tab->n_div)
|
|
isl_int_submul(row[2], line[1 + i], row[0]);
|
|
}
|
|
isl_seq_normalize(tab->mat->ctx, row, off + tab->n_col);
|
|
isl_int_clear(a);
|
|
isl_int_clear(b);
|
|
|
|
if (tab->row_sign)
|
|
tab->row_sign[tab->con[r].index] = isl_tab_row_unknown;
|
|
|
|
return r;
|
|
}
|
|
|
|
static int drop_row(struct isl_tab *tab, int row)
|
|
{
|
|
isl_assert(tab->mat->ctx, ~tab->row_var[row] == tab->n_con - 1, return -1);
|
|
if (row != tab->n_row - 1)
|
|
swap_rows(tab, row, tab->n_row - 1);
|
|
tab->n_row--;
|
|
tab->n_con--;
|
|
return 0;
|
|
}
|
|
|
|
/* Drop the variable in column "col" along with the column.
|
|
* The column is removed first because it may need to be moved
|
|
* into the last position and this process requires
|
|
* the contents of the col_var array in a state
|
|
* before the removal of the variable.
|
|
*/
|
|
static int drop_col(struct isl_tab *tab, int col)
|
|
{
|
|
int var;
|
|
|
|
var = tab->col_var[col];
|
|
if (col != tab->n_col - 1)
|
|
swap_cols(tab, col, tab->n_col - 1);
|
|
tab->n_col--;
|
|
if (var_drop_entry(tab, var) < 0)
|
|
return -1;
|
|
return 0;
|
|
}
|
|
|
|
/* Add inequality "ineq" and check if it conflicts with the
|
|
* previously added constraints or if it is obviously redundant.
|
|
*/
|
|
int isl_tab_add_ineq(struct isl_tab *tab, isl_int *ineq)
|
|
{
|
|
int r;
|
|
int sgn;
|
|
isl_int cst;
|
|
|
|
if (!tab)
|
|
return -1;
|
|
if (tab->bmap) {
|
|
struct isl_basic_map *bmap = tab->bmap;
|
|
|
|
isl_assert(tab->mat->ctx, tab->n_eq == bmap->n_eq, return -1);
|
|
isl_assert(tab->mat->ctx,
|
|
tab->n_con == bmap->n_eq + bmap->n_ineq, return -1);
|
|
tab->bmap = isl_basic_map_add_ineq(tab->bmap, ineq);
|
|
if (isl_tab_push(tab, isl_tab_undo_bmap_ineq) < 0)
|
|
return -1;
|
|
if (!tab->bmap)
|
|
return -1;
|
|
}
|
|
if (tab->cone) {
|
|
isl_int_init(cst);
|
|
isl_int_set_si(cst, 0);
|
|
isl_int_swap(ineq[0], cst);
|
|
}
|
|
r = isl_tab_add_row(tab, ineq);
|
|
if (tab->cone) {
|
|
isl_int_swap(ineq[0], cst);
|
|
isl_int_clear(cst);
|
|
}
|
|
if (r < 0)
|
|
return -1;
|
|
tab->con[r].is_nonneg = 1;
|
|
if (isl_tab_push_var(tab, isl_tab_undo_nonneg, &tab->con[r]) < 0)
|
|
return -1;
|
|
if (isl_tab_row_is_redundant(tab, tab->con[r].index)) {
|
|
if (isl_tab_mark_redundant(tab, tab->con[r].index) < 0)
|
|
return -1;
|
|
return 0;
|
|
}
|
|
|
|
sgn = restore_row(tab, &tab->con[r]);
|
|
if (sgn < -1)
|
|
return -1;
|
|
if (sgn < 0)
|
|
return isl_tab_mark_empty(tab);
|
|
if (tab->con[r].is_row && isl_tab_row_is_redundant(tab, tab->con[r].index))
|
|
if (isl_tab_mark_redundant(tab, tab->con[r].index) < 0)
|
|
return -1;
|
|
return 0;
|
|
}
|
|
|
|
/* Pivot a non-negative variable down until it reaches the value zero
|
|
* and then pivot the variable into a column position.
|
|
*/
|
|
static int to_col(struct isl_tab *tab, struct isl_tab_var *var) WARN_UNUSED;
|
|
static int to_col(struct isl_tab *tab, struct isl_tab_var *var)
|
|
{
|
|
int i;
|
|
int row, col;
|
|
unsigned off = 2 + tab->M;
|
|
|
|
if (!var->is_row)
|
|
return 0;
|
|
|
|
while (isl_int_is_pos(tab->mat->row[var->index][1])) {
|
|
find_pivot(tab, var, NULL, -1, &row, &col);
|
|
isl_assert(tab->mat->ctx, row != -1, return -1);
|
|
if (isl_tab_pivot(tab, row, col) < 0)
|
|
return -1;
|
|
if (!var->is_row)
|
|
return 0;
|
|
}
|
|
|
|
for (i = tab->n_dead; i < tab->n_col; ++i)
|
|
if (!isl_int_is_zero(tab->mat->row[var->index][off + i]))
|
|
break;
|
|
|
|
isl_assert(tab->mat->ctx, i < tab->n_col, return -1);
|
|
if (isl_tab_pivot(tab, var->index, i) < 0)
|
|
return -1;
|
|
|
|
return 0;
|
|
}
|
|
|
|
/* We assume Gaussian elimination has been performed on the equalities.
|
|
* The equalities can therefore never conflict.
|
|
* Adding the equalities is currently only really useful for a later call
|
|
* to isl_tab_ineq_type.
|
|
*/
|
|
static struct isl_tab *add_eq(struct isl_tab *tab, isl_int *eq)
|
|
{
|
|
int i;
|
|
int r;
|
|
|
|
if (!tab)
|
|
return NULL;
|
|
r = isl_tab_add_row(tab, eq);
|
|
if (r < 0)
|
|
goto error;
|
|
|
|
r = tab->con[r].index;
|
|
i = isl_seq_first_non_zero(tab->mat->row[r] + 2 + tab->M + tab->n_dead,
|
|
tab->n_col - tab->n_dead);
|
|
isl_assert(tab->mat->ctx, i >= 0, goto error);
|
|
i += tab->n_dead;
|
|
if (isl_tab_pivot(tab, r, i) < 0)
|
|
goto error;
|
|
if (isl_tab_kill_col(tab, i) < 0)
|
|
goto error;
|
|
tab->n_eq++;
|
|
|
|
return tab;
|
|
error:
|
|
isl_tab_free(tab);
|
|
return NULL;
|
|
}
|
|
|
|
static int row_is_manifestly_zero(struct isl_tab *tab, int row)
|
|
{
|
|
unsigned off = 2 + tab->M;
|
|
|
|
if (!isl_int_is_zero(tab->mat->row[row][1]))
|
|
return 0;
|
|
if (tab->M && !isl_int_is_zero(tab->mat->row[row][2]))
|
|
return 0;
|
|
return isl_seq_first_non_zero(tab->mat->row[row] + off + tab->n_dead,
|
|
tab->n_col - tab->n_dead) == -1;
|
|
}
|
|
|
|
/* Add an equality that is known to be valid for the given tableau.
|
|
*/
|
|
int isl_tab_add_valid_eq(struct isl_tab *tab, isl_int *eq)
|
|
{
|
|
struct isl_tab_var *var;
|
|
int r;
|
|
|
|
if (!tab)
|
|
return -1;
|
|
r = isl_tab_add_row(tab, eq);
|
|
if (r < 0)
|
|
return -1;
|
|
|
|
var = &tab->con[r];
|
|
r = var->index;
|
|
if (row_is_manifestly_zero(tab, r)) {
|
|
var->is_zero = 1;
|
|
if (isl_tab_mark_redundant(tab, r) < 0)
|
|
return -1;
|
|
return 0;
|
|
}
|
|
|
|
if (isl_int_is_neg(tab->mat->row[r][1])) {
|
|
isl_seq_neg(tab->mat->row[r] + 1, tab->mat->row[r] + 1,
|
|
1 + tab->n_col);
|
|
var->negated = 1;
|
|
}
|
|
var->is_nonneg = 1;
|
|
if (to_col(tab, var) < 0)
|
|
return -1;
|
|
var->is_nonneg = 0;
|
|
if (isl_tab_kill_col(tab, var->index) < 0)
|
|
return -1;
|
|
|
|
return 0;
|
|
}
|
|
|
|
static int add_zero_row(struct isl_tab *tab)
|
|
{
|
|
int r;
|
|
isl_int *row;
|
|
|
|
r = isl_tab_allocate_con(tab);
|
|
if (r < 0)
|
|
return -1;
|
|
|
|
row = tab->mat->row[tab->con[r].index];
|
|
isl_seq_clr(row + 1, 1 + tab->M + tab->n_col);
|
|
isl_int_set_si(row[0], 1);
|
|
|
|
return r;
|
|
}
|
|
|
|
/* Add equality "eq" and check if it conflicts with the
|
|
* previously added constraints or if it is obviously redundant.
|
|
*/
|
|
int isl_tab_add_eq(struct isl_tab *tab, isl_int *eq)
|
|
{
|
|
struct isl_tab_undo *snap = NULL;
|
|
struct isl_tab_var *var;
|
|
int r;
|
|
int row;
|
|
int sgn;
|
|
isl_int cst;
|
|
|
|
if (!tab)
|
|
return -1;
|
|
isl_assert(tab->mat->ctx, !tab->M, return -1);
|
|
|
|
if (tab->need_undo)
|
|
snap = isl_tab_snap(tab);
|
|
|
|
if (tab->cone) {
|
|
isl_int_init(cst);
|
|
isl_int_set_si(cst, 0);
|
|
isl_int_swap(eq[0], cst);
|
|
}
|
|
r = isl_tab_add_row(tab, eq);
|
|
if (tab->cone) {
|
|
isl_int_swap(eq[0], cst);
|
|
isl_int_clear(cst);
|
|
}
|
|
if (r < 0)
|
|
return -1;
|
|
|
|
var = &tab->con[r];
|
|
row = var->index;
|
|
if (row_is_manifestly_zero(tab, row)) {
|
|
if (snap)
|
|
return isl_tab_rollback(tab, snap);
|
|
return drop_row(tab, row);
|
|
}
|
|
|
|
if (tab->bmap) {
|
|
tab->bmap = isl_basic_map_add_ineq(tab->bmap, eq);
|
|
if (isl_tab_push(tab, isl_tab_undo_bmap_ineq) < 0)
|
|
return -1;
|
|
isl_seq_neg(eq, eq, 1 + tab->n_var);
|
|
tab->bmap = isl_basic_map_add_ineq(tab->bmap, eq);
|
|
isl_seq_neg(eq, eq, 1 + tab->n_var);
|
|
if (isl_tab_push(tab, isl_tab_undo_bmap_ineq) < 0)
|
|
return -1;
|
|
if (!tab->bmap)
|
|
return -1;
|
|
if (add_zero_row(tab) < 0)
|
|
return -1;
|
|
}
|
|
|
|
sgn = isl_int_sgn(tab->mat->row[row][1]);
|
|
|
|
if (sgn > 0) {
|
|
isl_seq_neg(tab->mat->row[row] + 1, tab->mat->row[row] + 1,
|
|
1 + tab->n_col);
|
|
var->negated = 1;
|
|
sgn = -1;
|
|
}
|
|
|
|
if (sgn < 0) {
|
|
sgn = sign_of_max(tab, var);
|
|
if (sgn < -1)
|
|
return -1;
|
|
if (sgn < 0) {
|
|
if (isl_tab_mark_empty(tab) < 0)
|
|
return -1;
|
|
return 0;
|
|
}
|
|
}
|
|
|
|
var->is_nonneg = 1;
|
|
if (to_col(tab, var) < 0)
|
|
return -1;
|
|
var->is_nonneg = 0;
|
|
if (isl_tab_kill_col(tab, var->index) < 0)
|
|
return -1;
|
|
|
|
return 0;
|
|
}
|
|
|
|
/* Construct and return an inequality that expresses an upper bound
|
|
* on the given div.
|
|
* In particular, if the div is given by
|
|
*
|
|
* d = floor(e/m)
|
|
*
|
|
* then the inequality expresses
|
|
*
|
|
* m d <= e
|
|
*/
|
|
static struct isl_vec *ineq_for_div(struct isl_basic_map *bmap, unsigned div)
|
|
{
|
|
unsigned total;
|
|
unsigned div_pos;
|
|
struct isl_vec *ineq;
|
|
|
|
if (!bmap)
|
|
return NULL;
|
|
|
|
total = isl_basic_map_total_dim(bmap);
|
|
div_pos = 1 + total - bmap->n_div + div;
|
|
|
|
ineq = isl_vec_alloc(bmap->ctx, 1 + total);
|
|
if (!ineq)
|
|
return NULL;
|
|
|
|
isl_seq_cpy(ineq->el, bmap->div[div] + 1, 1 + total);
|
|
isl_int_neg(ineq->el[div_pos], bmap->div[div][0]);
|
|
return ineq;
|
|
}
|
|
|
|
/* For a div d = floor(f/m), add the constraints
|
|
*
|
|
* f - m d >= 0
|
|
* -(f-(m-1)) + m d >= 0
|
|
*
|
|
* Note that the second constraint is the negation of
|
|
*
|
|
* f - m d >= m
|
|
*
|
|
* If add_ineq is not NULL, then this function is used
|
|
* instead of isl_tab_add_ineq to effectively add the inequalities.
|
|
*/
|
|
static int add_div_constraints(struct isl_tab *tab, unsigned div,
|
|
int (*add_ineq)(void *user, isl_int *), void *user)
|
|
{
|
|
unsigned total;
|
|
unsigned div_pos;
|
|
struct isl_vec *ineq;
|
|
|
|
total = isl_basic_map_total_dim(tab->bmap);
|
|
div_pos = 1 + total - tab->bmap->n_div + div;
|
|
|
|
ineq = ineq_for_div(tab->bmap, div);
|
|
if (!ineq)
|
|
goto error;
|
|
|
|
if (add_ineq) {
|
|
if (add_ineq(user, ineq->el) < 0)
|
|
goto error;
|
|
} else {
|
|
if (isl_tab_add_ineq(tab, ineq->el) < 0)
|
|
goto error;
|
|
}
|
|
|
|
isl_seq_neg(ineq->el, tab->bmap->div[div] + 1, 1 + total);
|
|
isl_int_set(ineq->el[div_pos], tab->bmap->div[div][0]);
|
|
isl_int_add(ineq->el[0], ineq->el[0], ineq->el[div_pos]);
|
|
isl_int_sub_ui(ineq->el[0], ineq->el[0], 1);
|
|
|
|
if (add_ineq) {
|
|
if (add_ineq(user, ineq->el) < 0)
|
|
goto error;
|
|
} else {
|
|
if (isl_tab_add_ineq(tab, ineq->el) < 0)
|
|
goto error;
|
|
}
|
|
|
|
isl_vec_free(ineq);
|
|
|
|
return 0;
|
|
error:
|
|
isl_vec_free(ineq);
|
|
return -1;
|
|
}
|
|
|
|
/* Check whether the div described by "div" is obviously non-negative.
|
|
* If we are using a big parameter, then we will encode the div
|
|
* as div' = M + div, which is always non-negative.
|
|
* Otherwise, we check whether div is a non-negative affine combination
|
|
* of non-negative variables.
|
|
*/
|
|
static int div_is_nonneg(struct isl_tab *tab, __isl_keep isl_vec *div)
|
|
{
|
|
int i;
|
|
|
|
if (tab->M)
|
|
return 1;
|
|
|
|
if (isl_int_is_neg(div->el[1]))
|
|
return 0;
|
|
|
|
for (i = 0; i < tab->n_var; ++i) {
|
|
if (isl_int_is_neg(div->el[2 + i]))
|
|
return 0;
|
|
if (isl_int_is_zero(div->el[2 + i]))
|
|
continue;
|
|
if (!tab->var[i].is_nonneg)
|
|
return 0;
|
|
}
|
|
|
|
return 1;
|
|
}
|
|
|
|
/* Add an extra div, prescribed by "div" to the tableau and
|
|
* the associated bmap (which is assumed to be non-NULL).
|
|
*
|
|
* If add_ineq is not NULL, then this function is used instead
|
|
* of isl_tab_add_ineq to add the div constraints.
|
|
* This complication is needed because the code in isl_tab_pip
|
|
* wants to perform some extra processing when an inequality
|
|
* is added to the tableau.
|
|
*/
|
|
int isl_tab_add_div(struct isl_tab *tab, __isl_keep isl_vec *div,
|
|
int (*add_ineq)(void *user, isl_int *), void *user)
|
|
{
|
|
int r;
|
|
int k;
|
|
int nonneg;
|
|
|
|
if (!tab || !div)
|
|
return -1;
|
|
|
|
isl_assert(tab->mat->ctx, tab->bmap, return -1);
|
|
|
|
nonneg = div_is_nonneg(tab, div);
|
|
|
|
if (isl_tab_extend_cons(tab, 3) < 0)
|
|
return -1;
|
|
if (isl_tab_extend_vars(tab, 1) < 0)
|
|
return -1;
|
|
r = isl_tab_allocate_var(tab);
|
|
if (r < 0)
|
|
return -1;
|
|
|
|
if (nonneg)
|
|
tab->var[r].is_nonneg = 1;
|
|
|
|
tab->bmap = isl_basic_map_extend_space(tab->bmap,
|
|
isl_basic_map_get_space(tab->bmap), 1, 0, 2);
|
|
k = isl_basic_map_alloc_div(tab->bmap);
|
|
if (k < 0)
|
|
return -1;
|
|
isl_seq_cpy(tab->bmap->div[k], div->el, div->size);
|
|
if (isl_tab_push(tab, isl_tab_undo_bmap_div) < 0)
|
|
return -1;
|
|
|
|
if (add_div_constraints(tab, k, add_ineq, user) < 0)
|
|
return -1;
|
|
|
|
return r;
|
|
}
|
|
|
|
/* If "track" is set, then we want to keep track of all constraints in tab
|
|
* in its bmap field. This field is initialized from a copy of "bmap",
|
|
* so we need to make sure that all constraints in "bmap" also appear
|
|
* in the constructed tab.
|
|
*/
|
|
__isl_give struct isl_tab *isl_tab_from_basic_map(
|
|
__isl_keep isl_basic_map *bmap, int track)
|
|
{
|
|
int i;
|
|
struct isl_tab *tab;
|
|
|
|
if (!bmap)
|
|
return NULL;
|
|
tab = isl_tab_alloc(bmap->ctx,
|
|
isl_basic_map_total_dim(bmap) + bmap->n_ineq + 1,
|
|
isl_basic_map_total_dim(bmap), 0);
|
|
if (!tab)
|
|
return NULL;
|
|
tab->preserve = track;
|
|
tab->rational = ISL_F_ISSET(bmap, ISL_BASIC_MAP_RATIONAL);
|
|
if (ISL_F_ISSET(bmap, ISL_BASIC_MAP_EMPTY)) {
|
|
if (isl_tab_mark_empty(tab) < 0)
|
|
goto error;
|
|
goto done;
|
|
}
|
|
for (i = 0; i < bmap->n_eq; ++i) {
|
|
tab = add_eq(tab, bmap->eq[i]);
|
|
if (!tab)
|
|
return tab;
|
|
}
|
|
for (i = 0; i < bmap->n_ineq; ++i) {
|
|
if (isl_tab_add_ineq(tab, bmap->ineq[i]) < 0)
|
|
goto error;
|
|
if (tab->empty)
|
|
goto done;
|
|
}
|
|
done:
|
|
if (track && isl_tab_track_bmap(tab, isl_basic_map_copy(bmap)) < 0)
|
|
goto error;
|
|
return tab;
|
|
error:
|
|
isl_tab_free(tab);
|
|
return NULL;
|
|
}
|
|
|
|
__isl_give struct isl_tab *isl_tab_from_basic_set(
|
|
__isl_keep isl_basic_set *bset, int track)
|
|
{
|
|
return isl_tab_from_basic_map(bset, track);
|
|
}
|
|
|
|
/* Construct a tableau corresponding to the recession cone of "bset".
|
|
*/
|
|
struct isl_tab *isl_tab_from_recession_cone(__isl_keep isl_basic_set *bset,
|
|
int parametric)
|
|
{
|
|
isl_int cst;
|
|
int i;
|
|
struct isl_tab *tab;
|
|
unsigned offset = 0;
|
|
|
|
if (!bset)
|
|
return NULL;
|
|
if (parametric)
|
|
offset = isl_basic_set_dim(bset, isl_dim_param);
|
|
tab = isl_tab_alloc(bset->ctx, bset->n_eq + bset->n_ineq,
|
|
isl_basic_set_total_dim(bset) - offset, 0);
|
|
if (!tab)
|
|
return NULL;
|
|
tab->rational = ISL_F_ISSET(bset, ISL_BASIC_SET_RATIONAL);
|
|
tab->cone = 1;
|
|
|
|
isl_int_init(cst);
|
|
isl_int_set_si(cst, 0);
|
|
for (i = 0; i < bset->n_eq; ++i) {
|
|
isl_int_swap(bset->eq[i][offset], cst);
|
|
if (offset > 0) {
|
|
if (isl_tab_add_eq(tab, bset->eq[i] + offset) < 0)
|
|
goto error;
|
|
} else
|
|
tab = add_eq(tab, bset->eq[i]);
|
|
isl_int_swap(bset->eq[i][offset], cst);
|
|
if (!tab)
|
|
goto done;
|
|
}
|
|
for (i = 0; i < bset->n_ineq; ++i) {
|
|
int r;
|
|
isl_int_swap(bset->ineq[i][offset], cst);
|
|
r = isl_tab_add_row(tab, bset->ineq[i] + offset);
|
|
isl_int_swap(bset->ineq[i][offset], cst);
|
|
if (r < 0)
|
|
goto error;
|
|
tab->con[r].is_nonneg = 1;
|
|
if (isl_tab_push_var(tab, isl_tab_undo_nonneg, &tab->con[r]) < 0)
|
|
goto error;
|
|
}
|
|
done:
|
|
isl_int_clear(cst);
|
|
return tab;
|
|
error:
|
|
isl_int_clear(cst);
|
|
isl_tab_free(tab);
|
|
return NULL;
|
|
}
|
|
|
|
/* Assuming "tab" is the tableau of a cone, check if the cone is
|
|
* bounded, i.e., if it is empty or only contains the origin.
|
|
*/
|
|
int isl_tab_cone_is_bounded(struct isl_tab *tab)
|
|
{
|
|
int i;
|
|
|
|
if (!tab)
|
|
return -1;
|
|
if (tab->empty)
|
|
return 1;
|
|
if (tab->n_dead == tab->n_col)
|
|
return 1;
|
|
|
|
for (;;) {
|
|
for (i = tab->n_redundant; i < tab->n_row; ++i) {
|
|
struct isl_tab_var *var;
|
|
int sgn;
|
|
var = isl_tab_var_from_row(tab, i);
|
|
if (!var->is_nonneg)
|
|
continue;
|
|
sgn = sign_of_max(tab, var);
|
|
if (sgn < -1)
|
|
return -1;
|
|
if (sgn != 0)
|
|
return 0;
|
|
if (close_row(tab, var) < 0)
|
|
return -1;
|
|
break;
|
|
}
|
|
if (tab->n_dead == tab->n_col)
|
|
return 1;
|
|
if (i == tab->n_row)
|
|
return 0;
|
|
}
|
|
}
|
|
|
|
int isl_tab_sample_is_integer(struct isl_tab *tab)
|
|
{
|
|
int i;
|
|
|
|
if (!tab)
|
|
return -1;
|
|
|
|
for (i = 0; i < tab->n_var; ++i) {
|
|
int row;
|
|
if (!tab->var[i].is_row)
|
|
continue;
|
|
row = tab->var[i].index;
|
|
if (!isl_int_is_divisible_by(tab->mat->row[row][1],
|
|
tab->mat->row[row][0]))
|
|
return 0;
|
|
}
|
|
return 1;
|
|
}
|
|
|
|
static struct isl_vec *extract_integer_sample(struct isl_tab *tab)
|
|
{
|
|
int i;
|
|
struct isl_vec *vec;
|
|
|
|
vec = isl_vec_alloc(tab->mat->ctx, 1 + tab->n_var);
|
|
if (!vec)
|
|
return NULL;
|
|
|
|
isl_int_set_si(vec->block.data[0], 1);
|
|
for (i = 0; i < tab->n_var; ++i) {
|
|
if (!tab->var[i].is_row)
|
|
isl_int_set_si(vec->block.data[1 + i], 0);
|
|
else {
|
|
int row = tab->var[i].index;
|
|
isl_int_divexact(vec->block.data[1 + i],
|
|
tab->mat->row[row][1], tab->mat->row[row][0]);
|
|
}
|
|
}
|
|
|
|
return vec;
|
|
}
|
|
|
|
struct isl_vec *isl_tab_get_sample_value(struct isl_tab *tab)
|
|
{
|
|
int i;
|
|
struct isl_vec *vec;
|
|
isl_int m;
|
|
|
|
if (!tab)
|
|
return NULL;
|
|
|
|
vec = isl_vec_alloc(tab->mat->ctx, 1 + tab->n_var);
|
|
if (!vec)
|
|
return NULL;
|
|
|
|
isl_int_init(m);
|
|
|
|
isl_int_set_si(vec->block.data[0], 1);
|
|
for (i = 0; i < tab->n_var; ++i) {
|
|
int row;
|
|
if (!tab->var[i].is_row) {
|
|
isl_int_set_si(vec->block.data[1 + i], 0);
|
|
continue;
|
|
}
|
|
row = tab->var[i].index;
|
|
isl_int_gcd(m, vec->block.data[0], tab->mat->row[row][0]);
|
|
isl_int_divexact(m, tab->mat->row[row][0], m);
|
|
isl_seq_scale(vec->block.data, vec->block.data, m, 1 + i);
|
|
isl_int_divexact(m, vec->block.data[0], tab->mat->row[row][0]);
|
|
isl_int_mul(vec->block.data[1 + i], m, tab->mat->row[row][1]);
|
|
}
|
|
vec = isl_vec_normalize(vec);
|
|
|
|
isl_int_clear(m);
|
|
return vec;
|
|
}
|
|
|
|
/* Update "bmap" based on the results of the tableau "tab".
|
|
* In particular, implicit equalities are made explicit, redundant constraints
|
|
* are removed and if the sample value happens to be integer, it is stored
|
|
* in "bmap" (unless "bmap" already had an integer sample).
|
|
*
|
|
* The tableau is assumed to have been created from "bmap" using
|
|
* isl_tab_from_basic_map.
|
|
*/
|
|
struct isl_basic_map *isl_basic_map_update_from_tab(struct isl_basic_map *bmap,
|
|
struct isl_tab *tab)
|
|
{
|
|
int i;
|
|
unsigned n_eq;
|
|
|
|
if (!bmap)
|
|
return NULL;
|
|
if (!tab)
|
|
return bmap;
|
|
|
|
n_eq = tab->n_eq;
|
|
if (tab->empty)
|
|
bmap = isl_basic_map_set_to_empty(bmap);
|
|
else
|
|
for (i = bmap->n_ineq - 1; i >= 0; --i) {
|
|
if (isl_tab_is_equality(tab, n_eq + i))
|
|
isl_basic_map_inequality_to_equality(bmap, i);
|
|
else if (isl_tab_is_redundant(tab, n_eq + i))
|
|
isl_basic_map_drop_inequality(bmap, i);
|
|
}
|
|
if (bmap->n_eq != n_eq)
|
|
isl_basic_map_gauss(bmap, NULL);
|
|
if (!tab->rational &&
|
|
!bmap->sample && isl_tab_sample_is_integer(tab))
|
|
bmap->sample = extract_integer_sample(tab);
|
|
return bmap;
|
|
}
|
|
|
|
struct isl_basic_set *isl_basic_set_update_from_tab(struct isl_basic_set *bset,
|
|
struct isl_tab *tab)
|
|
{
|
|
return (struct isl_basic_set *)isl_basic_map_update_from_tab(
|
|
(struct isl_basic_map *)bset, tab);
|
|
}
|
|
|
|
/* Given a non-negative variable "var", add a new non-negative variable
|
|
* that is the opposite of "var", ensuring that var can only attain the
|
|
* value zero.
|
|
* If var = n/d is a row variable, then the new variable = -n/d.
|
|
* If var is a column variables, then the new variable = -var.
|
|
* If the new variable cannot attain non-negative values, then
|
|
* the resulting tableau is empty.
|
|
* Otherwise, we know the value will be zero and we close the row.
|
|
*/
|
|
static int cut_to_hyperplane(struct isl_tab *tab, struct isl_tab_var *var)
|
|
{
|
|
unsigned r;
|
|
isl_int *row;
|
|
int sgn;
|
|
unsigned off = 2 + tab->M;
|
|
|
|
if (var->is_zero)
|
|
return 0;
|
|
isl_assert(tab->mat->ctx, !var->is_redundant, return -1);
|
|
isl_assert(tab->mat->ctx, var->is_nonneg, return -1);
|
|
|
|
if (isl_tab_extend_cons(tab, 1) < 0)
|
|
return -1;
|
|
|
|
r = tab->n_con;
|
|
tab->con[r].index = tab->n_row;
|
|
tab->con[r].is_row = 1;
|
|
tab->con[r].is_nonneg = 0;
|
|
tab->con[r].is_zero = 0;
|
|
tab->con[r].is_redundant = 0;
|
|
tab->con[r].frozen = 0;
|
|
tab->con[r].negated = 0;
|
|
tab->row_var[tab->n_row] = ~r;
|
|
row = tab->mat->row[tab->n_row];
|
|
|
|
if (var->is_row) {
|
|
isl_int_set(row[0], tab->mat->row[var->index][0]);
|
|
isl_seq_neg(row + 1,
|
|
tab->mat->row[var->index] + 1, 1 + tab->n_col);
|
|
} else {
|
|
isl_int_set_si(row[0], 1);
|
|
isl_seq_clr(row + 1, 1 + tab->n_col);
|
|
isl_int_set_si(row[off + var->index], -1);
|
|
}
|
|
|
|
tab->n_row++;
|
|
tab->n_con++;
|
|
if (isl_tab_push_var(tab, isl_tab_undo_allocate, &tab->con[r]) < 0)
|
|
return -1;
|
|
|
|
sgn = sign_of_max(tab, &tab->con[r]);
|
|
if (sgn < -1)
|
|
return -1;
|
|
if (sgn < 0) {
|
|
if (isl_tab_mark_empty(tab) < 0)
|
|
return -1;
|
|
return 0;
|
|
}
|
|
tab->con[r].is_nonneg = 1;
|
|
if (isl_tab_push_var(tab, isl_tab_undo_nonneg, &tab->con[r]) < 0)
|
|
return -1;
|
|
/* sgn == 0 */
|
|
if (close_row(tab, &tab->con[r]) < 0)
|
|
return -1;
|
|
|
|
return 0;
|
|
}
|
|
|
|
/* Given a tableau "tab" and an inequality constraint "con" of the tableau,
|
|
* relax the inequality by one. That is, the inequality r >= 0 is replaced
|
|
* by r' = r + 1 >= 0.
|
|
* If r is a row variable, we simply increase the constant term by one
|
|
* (taking into account the denominator).
|
|
* If r is a column variable, then we need to modify each row that
|
|
* refers to r = r' - 1 by substituting this equality, effectively
|
|
* subtracting the coefficient of the column from the constant.
|
|
* We should only do this if the minimum is manifestly unbounded,
|
|
* however. Otherwise, we may end up with negative sample values
|
|
* for non-negative variables.
|
|
* So, if r is a column variable with a minimum that is not
|
|
* manifestly unbounded, then we need to move it to a row.
|
|
* However, the sample value of this row may be negative,
|
|
* even after the relaxation, so we need to restore it.
|
|
* We therefore prefer to pivot a column up to a row, if possible.
|
|
*/
|
|
int isl_tab_relax(struct isl_tab *tab, int con)
|
|
{
|
|
struct isl_tab_var *var;
|
|
|
|
if (!tab)
|
|
return -1;
|
|
|
|
var = &tab->con[con];
|
|
|
|
if (var->is_row && (var->index < 0 || var->index < tab->n_redundant))
|
|
isl_die(tab->mat->ctx, isl_error_invalid,
|
|
"cannot relax redundant constraint", return -1);
|
|
if (!var->is_row && (var->index < 0 || var->index < tab->n_dead))
|
|
isl_die(tab->mat->ctx, isl_error_invalid,
|
|
"cannot relax dead constraint", return -1);
|
|
|
|
if (!var->is_row && !max_is_manifestly_unbounded(tab, var))
|
|
if (to_row(tab, var, 1) < 0)
|
|
return -1;
|
|
if (!var->is_row && !min_is_manifestly_unbounded(tab, var))
|
|
if (to_row(tab, var, -1) < 0)
|
|
return -1;
|
|
|
|
if (var->is_row) {
|
|
isl_int_add(tab->mat->row[var->index][1],
|
|
tab->mat->row[var->index][1], tab->mat->row[var->index][0]);
|
|
if (restore_row(tab, var) < 0)
|
|
return -1;
|
|
} else {
|
|
int i;
|
|
unsigned off = 2 + tab->M;
|
|
|
|
for (i = 0; i < tab->n_row; ++i) {
|
|
if (isl_int_is_zero(tab->mat->row[i][off + var->index]))
|
|
continue;
|
|
isl_int_sub(tab->mat->row[i][1], tab->mat->row[i][1],
|
|
tab->mat->row[i][off + var->index]);
|
|
}
|
|
|
|
}
|
|
|
|
if (isl_tab_push_var(tab, isl_tab_undo_relax, var) < 0)
|
|
return -1;
|
|
|
|
return 0;
|
|
}
|
|
|
|
/* Replace the variable v at position "pos" in the tableau "tab"
|
|
* by v' = v + shift.
|
|
*
|
|
* If the variable is in a column, then we first check if we can
|
|
* simply plug in v = v' - shift. The effect on a row with
|
|
* coefficient f/d for variable v is that the constant term c/d
|
|
* is replaced by (c - f * shift)/d. If shift is positive and
|
|
* f is negative for each row that needs to remain non-negative,
|
|
* then this is clearly safe. In other words, if the minimum of v
|
|
* is manifestly unbounded, then we can keep v in a column position.
|
|
* Otherwise, we can pivot it down to a row.
|
|
* Similarly, if shift is negative, we need to check if the maximum
|
|
* of is manifestly unbounded.
|
|
*
|
|
* If the variable is in a row (from the start or after pivoting),
|
|
* then the constant term c/d is replaced by (c + d * shift)/d.
|
|
*/
|
|
int isl_tab_shift_var(struct isl_tab *tab, int pos, isl_int shift)
|
|
{
|
|
struct isl_tab_var *var;
|
|
|
|
if (!tab)
|
|
return -1;
|
|
if (isl_int_is_zero(shift))
|
|
return 0;
|
|
|
|
var = &tab->var[pos];
|
|
if (!var->is_row) {
|
|
if (isl_int_is_neg(shift)) {
|
|
if (!max_is_manifestly_unbounded(tab, var))
|
|
if (to_row(tab, var, 1) < 0)
|
|
return -1;
|
|
} else {
|
|
if (!min_is_manifestly_unbounded(tab, var))
|
|
if (to_row(tab, var, -1) < 0)
|
|
return -1;
|
|
}
|
|
}
|
|
|
|
if (var->is_row) {
|
|
isl_int_addmul(tab->mat->row[var->index][1],
|
|
shift, tab->mat->row[var->index][0]);
|
|
} else {
|
|
int i;
|
|
unsigned off = 2 + tab->M;
|
|
|
|
for (i = 0; i < tab->n_row; ++i) {
|
|
if (isl_int_is_zero(tab->mat->row[i][off + var->index]))
|
|
continue;
|
|
isl_int_submul(tab->mat->row[i][1],
|
|
shift, tab->mat->row[i][off + var->index]);
|
|
}
|
|
|
|
}
|
|
|
|
return 0;
|
|
}
|
|
|
|
/* Remove the sign constraint from constraint "con".
|
|
*
|
|
* If the constraint variable was originally marked non-negative,
|
|
* then we make sure we mark it non-negative again during rollback.
|
|
*/
|
|
int isl_tab_unrestrict(struct isl_tab *tab, int con)
|
|
{
|
|
struct isl_tab_var *var;
|
|
|
|
if (!tab)
|
|
return -1;
|
|
|
|
var = &tab->con[con];
|
|
if (!var->is_nonneg)
|
|
return 0;
|
|
|
|
var->is_nonneg = 0;
|
|
if (isl_tab_push_var(tab, isl_tab_undo_unrestrict, var) < 0)
|
|
return -1;
|
|
|
|
return 0;
|
|
}
|
|
|
|
int isl_tab_select_facet(struct isl_tab *tab, int con)
|
|
{
|
|
if (!tab)
|
|
return -1;
|
|
|
|
return cut_to_hyperplane(tab, &tab->con[con]);
|
|
}
|
|
|
|
static int may_be_equality(struct isl_tab *tab, int row)
|
|
{
|
|
return tab->rational ? isl_int_is_zero(tab->mat->row[row][1])
|
|
: isl_int_lt(tab->mat->row[row][1],
|
|
tab->mat->row[row][0]);
|
|
}
|
|
|
|
/* Check for (near) equalities among the constraints.
|
|
* A constraint is an equality if it is non-negative and if
|
|
* its maximal value is either
|
|
* - zero (in case of rational tableaus), or
|
|
* - strictly less than 1 (in case of integer tableaus)
|
|
*
|
|
* We first mark all non-redundant and non-dead variables that
|
|
* are not frozen and not obviously not an equality.
|
|
* Then we iterate over all marked variables if they can attain
|
|
* any values larger than zero or at least one.
|
|
* If the maximal value is zero, we mark any column variables
|
|
* that appear in the row as being zero and mark the row as being redundant.
|
|
* Otherwise, if the maximal value is strictly less than one (and the
|
|
* tableau is integer), then we restrict the value to being zero
|
|
* by adding an opposite non-negative variable.
|
|
*/
|
|
int isl_tab_detect_implicit_equalities(struct isl_tab *tab)
|
|
{
|
|
int i;
|
|
unsigned n_marked;
|
|
|
|
if (!tab)
|
|
return -1;
|
|
if (tab->empty)
|
|
return 0;
|
|
if (tab->n_dead == tab->n_col)
|
|
return 0;
|
|
|
|
n_marked = 0;
|
|
for (i = tab->n_redundant; i < tab->n_row; ++i) {
|
|
struct isl_tab_var *var = isl_tab_var_from_row(tab, i);
|
|
var->marked = !var->frozen && var->is_nonneg &&
|
|
may_be_equality(tab, i);
|
|
if (var->marked)
|
|
n_marked++;
|
|
}
|
|
for (i = tab->n_dead; i < tab->n_col; ++i) {
|
|
struct isl_tab_var *var = var_from_col(tab, i);
|
|
var->marked = !var->frozen && var->is_nonneg;
|
|
if (var->marked)
|
|
n_marked++;
|
|
}
|
|
while (n_marked) {
|
|
struct isl_tab_var *var;
|
|
int sgn;
|
|
for (i = tab->n_redundant; i < tab->n_row; ++i) {
|
|
var = isl_tab_var_from_row(tab, i);
|
|
if (var->marked)
|
|
break;
|
|
}
|
|
if (i == tab->n_row) {
|
|
for (i = tab->n_dead; i < tab->n_col; ++i) {
|
|
var = var_from_col(tab, i);
|
|
if (var->marked)
|
|
break;
|
|
}
|
|
if (i == tab->n_col)
|
|
break;
|
|
}
|
|
var->marked = 0;
|
|
n_marked--;
|
|
sgn = sign_of_max(tab, var);
|
|
if (sgn < 0)
|
|
return -1;
|
|
if (sgn == 0) {
|
|
if (close_row(tab, var) < 0)
|
|
return -1;
|
|
} else if (!tab->rational && !at_least_one(tab, var)) {
|
|
if (cut_to_hyperplane(tab, var) < 0)
|
|
return -1;
|
|
return isl_tab_detect_implicit_equalities(tab);
|
|
}
|
|
for (i = tab->n_redundant; i < tab->n_row; ++i) {
|
|
var = isl_tab_var_from_row(tab, i);
|
|
if (!var->marked)
|
|
continue;
|
|
if (may_be_equality(tab, i))
|
|
continue;
|
|
var->marked = 0;
|
|
n_marked--;
|
|
}
|
|
}
|
|
|
|
return 0;
|
|
}
|
|
|
|
/* Update the element of row_var or col_var that corresponds to
|
|
* constraint tab->con[i] to a move from position "old" to position "i".
|
|
*/
|
|
static int update_con_after_move(struct isl_tab *tab, int i, int old)
|
|
{
|
|
int *p;
|
|
int index;
|
|
|
|
index = tab->con[i].index;
|
|
if (index == -1)
|
|
return 0;
|
|
p = tab->con[i].is_row ? tab->row_var : tab->col_var;
|
|
if (p[index] != ~old)
|
|
isl_die(tab->mat->ctx, isl_error_internal,
|
|
"broken internal state", return -1);
|
|
p[index] = ~i;
|
|
|
|
return 0;
|
|
}
|
|
|
|
/* Rotate the "n" constraints starting at "first" to the right,
|
|
* putting the last constraint in the position of the first constraint.
|
|
*/
|
|
static int rotate_constraints(struct isl_tab *tab, int first, int n)
|
|
{
|
|
int i, last;
|
|
struct isl_tab_var var;
|
|
|
|
if (n <= 1)
|
|
return 0;
|
|
|
|
last = first + n - 1;
|
|
var = tab->con[last];
|
|
for (i = last; i > first; --i) {
|
|
tab->con[i] = tab->con[i - 1];
|
|
if (update_con_after_move(tab, i, i - 1) < 0)
|
|
return -1;
|
|
}
|
|
tab->con[first] = var;
|
|
if (update_con_after_move(tab, first, last) < 0)
|
|
return -1;
|
|
|
|
return 0;
|
|
}
|
|
|
|
/* Make the equalities that are implicit in "bmap" but that have been
|
|
* detected in the corresponding "tab" explicit in "bmap" and update
|
|
* "tab" to reflect the new order of the constraints.
|
|
*
|
|
* In particular, if inequality i is an implicit equality then
|
|
* isl_basic_map_inequality_to_equality will move the inequality
|
|
* in front of the other equality and it will move the last inequality
|
|
* in the position of inequality i.
|
|
* In the tableau, the inequalities of "bmap" are stored after the equalities
|
|
* and so the original order
|
|
*
|
|
* E E E E E A A A I B B B B L
|
|
*
|
|
* is changed into
|
|
*
|
|
* I E E E E E A A A L B B B B
|
|
*
|
|
* where I is the implicit equality, the E are equalities,
|
|
* the A inequalities before I, the B inequalities after I and
|
|
* L the last inequality.
|
|
* We therefore need to rotate to the right two sets of constraints,
|
|
* those up to and including I and those after I.
|
|
*
|
|
* If "tab" contains any constraints that are not in "bmap" then they
|
|
* appear after those in "bmap" and they should be left untouched.
|
|
*
|
|
* Note that this function leaves "bmap" in a temporary state
|
|
* as it does not call isl_basic_map_gauss. Calling this function
|
|
* is the responsibility of the caller.
|
|
*/
|
|
__isl_give isl_basic_map *isl_tab_make_equalities_explicit(struct isl_tab *tab,
|
|
__isl_take isl_basic_map *bmap)
|
|
{
|
|
int i;
|
|
|
|
if (!tab || !bmap)
|
|
return isl_basic_map_free(bmap);
|
|
if (tab->empty)
|
|
return bmap;
|
|
|
|
for (i = bmap->n_ineq - 1; i >= 0; --i) {
|
|
if (!isl_tab_is_equality(tab, bmap->n_eq + i))
|
|
continue;
|
|
isl_basic_map_inequality_to_equality(bmap, i);
|
|
if (rotate_constraints(tab, 0, tab->n_eq + i + 1) < 0)
|
|
return isl_basic_map_free(bmap);
|
|
if (rotate_constraints(tab, tab->n_eq + i + 1,
|
|
bmap->n_ineq - i) < 0)
|
|
return isl_basic_map_free(bmap);
|
|
tab->n_eq++;
|
|
}
|
|
|
|
return bmap;
|
|
}
|
|
|
|
static int con_is_redundant(struct isl_tab *tab, struct isl_tab_var *var)
|
|
{
|
|
if (!tab)
|
|
return -1;
|
|
if (tab->rational) {
|
|
int sgn = sign_of_min(tab, var);
|
|
if (sgn < -1)
|
|
return -1;
|
|
return sgn >= 0;
|
|
} else {
|
|
int irred = isl_tab_min_at_most_neg_one(tab, var);
|
|
if (irred < 0)
|
|
return -1;
|
|
return !irred;
|
|
}
|
|
}
|
|
|
|
/* Check for (near) redundant constraints.
|
|
* A constraint is redundant if it is non-negative and if
|
|
* its minimal value (temporarily ignoring the non-negativity) is either
|
|
* - zero (in case of rational tableaus), or
|
|
* - strictly larger than -1 (in case of integer tableaus)
|
|
*
|
|
* We first mark all non-redundant and non-dead variables that
|
|
* are not frozen and not obviously negatively unbounded.
|
|
* Then we iterate over all marked variables if they can attain
|
|
* any values smaller than zero or at most negative one.
|
|
* If not, we mark the row as being redundant (assuming it hasn't
|
|
* been detected as being obviously redundant in the mean time).
|
|
*/
|
|
int isl_tab_detect_redundant(struct isl_tab *tab)
|
|
{
|
|
int i;
|
|
unsigned n_marked;
|
|
|
|
if (!tab)
|
|
return -1;
|
|
if (tab->empty)
|
|
return 0;
|
|
if (tab->n_redundant == tab->n_row)
|
|
return 0;
|
|
|
|
n_marked = 0;
|
|
for (i = tab->n_redundant; i < tab->n_row; ++i) {
|
|
struct isl_tab_var *var = isl_tab_var_from_row(tab, i);
|
|
var->marked = !var->frozen && var->is_nonneg;
|
|
if (var->marked)
|
|
n_marked++;
|
|
}
|
|
for (i = tab->n_dead; i < tab->n_col; ++i) {
|
|
struct isl_tab_var *var = var_from_col(tab, i);
|
|
var->marked = !var->frozen && var->is_nonneg &&
|
|
!min_is_manifestly_unbounded(tab, var);
|
|
if (var->marked)
|
|
n_marked++;
|
|
}
|
|
while (n_marked) {
|
|
struct isl_tab_var *var;
|
|
int red;
|
|
for (i = tab->n_redundant; i < tab->n_row; ++i) {
|
|
var = isl_tab_var_from_row(tab, i);
|
|
if (var->marked)
|
|
break;
|
|
}
|
|
if (i == tab->n_row) {
|
|
for (i = tab->n_dead; i < tab->n_col; ++i) {
|
|
var = var_from_col(tab, i);
|
|
if (var->marked)
|
|
break;
|
|
}
|
|
if (i == tab->n_col)
|
|
break;
|
|
}
|
|
var->marked = 0;
|
|
n_marked--;
|
|
red = con_is_redundant(tab, var);
|
|
if (red < 0)
|
|
return -1;
|
|
if (red && !var->is_redundant)
|
|
if (isl_tab_mark_redundant(tab, var->index) < 0)
|
|
return -1;
|
|
for (i = tab->n_dead; i < tab->n_col; ++i) {
|
|
var = var_from_col(tab, i);
|
|
if (!var->marked)
|
|
continue;
|
|
if (!min_is_manifestly_unbounded(tab, var))
|
|
continue;
|
|
var->marked = 0;
|
|
n_marked--;
|
|
}
|
|
}
|
|
|
|
return 0;
|
|
}
|
|
|
|
int isl_tab_is_equality(struct isl_tab *tab, int con)
|
|
{
|
|
int row;
|
|
unsigned off;
|
|
|
|
if (!tab)
|
|
return -1;
|
|
if (tab->con[con].is_zero)
|
|
return 1;
|
|
if (tab->con[con].is_redundant)
|
|
return 0;
|
|
if (!tab->con[con].is_row)
|
|
return tab->con[con].index < tab->n_dead;
|
|
|
|
row = tab->con[con].index;
|
|
|
|
off = 2 + tab->M;
|
|
return isl_int_is_zero(tab->mat->row[row][1]) &&
|
|
(!tab->M || isl_int_is_zero(tab->mat->row[row][2])) &&
|
|
isl_seq_first_non_zero(tab->mat->row[row] + off + tab->n_dead,
|
|
tab->n_col - tab->n_dead) == -1;
|
|
}
|
|
|
|
/* Return the minimal value of the affine expression "f" with denominator
|
|
* "denom" in *opt, *opt_denom, assuming the tableau is not empty and
|
|
* the expression cannot attain arbitrarily small values.
|
|
* If opt_denom is NULL, then *opt is rounded up to the nearest integer.
|
|
* The return value reflects the nature of the result (empty, unbounded,
|
|
* minimal value returned in *opt).
|
|
*/
|
|
enum isl_lp_result isl_tab_min(struct isl_tab *tab,
|
|
isl_int *f, isl_int denom, isl_int *opt, isl_int *opt_denom,
|
|
unsigned flags)
|
|
{
|
|
int r;
|
|
enum isl_lp_result res = isl_lp_ok;
|
|
struct isl_tab_var *var;
|
|
struct isl_tab_undo *snap;
|
|
|
|
if (!tab)
|
|
return isl_lp_error;
|
|
|
|
if (tab->empty)
|
|
return isl_lp_empty;
|
|
|
|
snap = isl_tab_snap(tab);
|
|
r = isl_tab_add_row(tab, f);
|
|
if (r < 0)
|
|
return isl_lp_error;
|
|
var = &tab->con[r];
|
|
for (;;) {
|
|
int row, col;
|
|
find_pivot(tab, var, var, -1, &row, &col);
|
|
if (row == var->index) {
|
|
res = isl_lp_unbounded;
|
|
break;
|
|
}
|
|
if (row == -1)
|
|
break;
|
|
if (isl_tab_pivot(tab, row, col) < 0)
|
|
return isl_lp_error;
|
|
}
|
|
isl_int_mul(tab->mat->row[var->index][0],
|
|
tab->mat->row[var->index][0], denom);
|
|
if (ISL_FL_ISSET(flags, ISL_TAB_SAVE_DUAL)) {
|
|
int i;
|
|
|
|
isl_vec_free(tab->dual);
|
|
tab->dual = isl_vec_alloc(tab->mat->ctx, 1 + tab->n_con);
|
|
if (!tab->dual)
|
|
return isl_lp_error;
|
|
isl_int_set(tab->dual->el[0], tab->mat->row[var->index][0]);
|
|
for (i = 0; i < tab->n_con; ++i) {
|
|
int pos;
|
|
if (tab->con[i].is_row) {
|
|
isl_int_set_si(tab->dual->el[1 + i], 0);
|
|
continue;
|
|
}
|
|
pos = 2 + tab->M + tab->con[i].index;
|
|
if (tab->con[i].negated)
|
|
isl_int_neg(tab->dual->el[1 + i],
|
|
tab->mat->row[var->index][pos]);
|
|
else
|
|
isl_int_set(tab->dual->el[1 + i],
|
|
tab->mat->row[var->index][pos]);
|
|
}
|
|
}
|
|
if (opt && res == isl_lp_ok) {
|
|
if (opt_denom) {
|
|
isl_int_set(*opt, tab->mat->row[var->index][1]);
|
|
isl_int_set(*opt_denom, tab->mat->row[var->index][0]);
|
|
} else
|
|
isl_int_cdiv_q(*opt, tab->mat->row[var->index][1],
|
|
tab->mat->row[var->index][0]);
|
|
}
|
|
if (isl_tab_rollback(tab, snap) < 0)
|
|
return isl_lp_error;
|
|
return res;
|
|
}
|
|
|
|
/* Is the constraint at position "con" marked as being redundant?
|
|
* If it is marked as representing an equality, then it is not
|
|
* considered to be redundant.
|
|
* Note that isl_tab_mark_redundant marks both the isl_tab_var as
|
|
* redundant and moves the corresponding row into the first
|
|
* tab->n_redundant positions (or removes the row, assigning it index -1),
|
|
* so the final test is actually redundant itself.
|
|
*/
|
|
int isl_tab_is_redundant(struct isl_tab *tab, int con)
|
|
{
|
|
if (!tab)
|
|
return -1;
|
|
if (con < 0 || con >= tab->n_con)
|
|
isl_die(isl_tab_get_ctx(tab), isl_error_invalid,
|
|
"position out of bounds", return -1);
|
|
if (tab->con[con].is_zero)
|
|
return 0;
|
|
if (tab->con[con].is_redundant)
|
|
return 1;
|
|
return tab->con[con].is_row && tab->con[con].index < tab->n_redundant;
|
|
}
|
|
|
|
/* Take a snapshot of the tableau that can be restored by s call to
|
|
* isl_tab_rollback.
|
|
*/
|
|
struct isl_tab_undo *isl_tab_snap(struct isl_tab *tab)
|
|
{
|
|
if (!tab)
|
|
return NULL;
|
|
tab->need_undo = 1;
|
|
return tab->top;
|
|
}
|
|
|
|
/* Undo the operation performed by isl_tab_relax.
|
|
*/
|
|
static int unrelax(struct isl_tab *tab, struct isl_tab_var *var) WARN_UNUSED;
|
|
static int unrelax(struct isl_tab *tab, struct isl_tab_var *var)
|
|
{
|
|
unsigned off = 2 + tab->M;
|
|
|
|
if (!var->is_row && !max_is_manifestly_unbounded(tab, var))
|
|
if (to_row(tab, var, 1) < 0)
|
|
return -1;
|
|
|
|
if (var->is_row) {
|
|
isl_int_sub(tab->mat->row[var->index][1],
|
|
tab->mat->row[var->index][1], tab->mat->row[var->index][0]);
|
|
if (var->is_nonneg) {
|
|
int sgn = restore_row(tab, var);
|
|
isl_assert(tab->mat->ctx, sgn >= 0, return -1);
|
|
}
|
|
} else {
|
|
int i;
|
|
|
|
for (i = 0; i < tab->n_row; ++i) {
|
|
if (isl_int_is_zero(tab->mat->row[i][off + var->index]))
|
|
continue;
|
|
isl_int_add(tab->mat->row[i][1], tab->mat->row[i][1],
|
|
tab->mat->row[i][off + var->index]);
|
|
}
|
|
|
|
}
|
|
|
|
return 0;
|
|
}
|
|
|
|
/* Undo the operation performed by isl_tab_unrestrict.
|
|
*
|
|
* In particular, mark the variable as being non-negative and make
|
|
* sure the sample value respects this constraint.
|
|
*/
|
|
static int ununrestrict(struct isl_tab *tab, struct isl_tab_var *var)
|
|
{
|
|
var->is_nonneg = 1;
|
|
|
|
if (var->is_row && restore_row(tab, var) < -1)
|
|
return -1;
|
|
|
|
return 0;
|
|
}
|
|
|
|
static int perform_undo_var(struct isl_tab *tab, struct isl_tab_undo *undo) WARN_UNUSED;
|
|
static int perform_undo_var(struct isl_tab *tab, struct isl_tab_undo *undo)
|
|
{
|
|
struct isl_tab_var *var = var_from_index(tab, undo->u.var_index);
|
|
switch (undo->type) {
|
|
case isl_tab_undo_nonneg:
|
|
var->is_nonneg = 0;
|
|
break;
|
|
case isl_tab_undo_redundant:
|
|
var->is_redundant = 0;
|
|
tab->n_redundant--;
|
|
restore_row(tab, isl_tab_var_from_row(tab, tab->n_redundant));
|
|
break;
|
|
case isl_tab_undo_freeze:
|
|
var->frozen = 0;
|
|
break;
|
|
case isl_tab_undo_zero:
|
|
var->is_zero = 0;
|
|
if (!var->is_row)
|
|
tab->n_dead--;
|
|
break;
|
|
case isl_tab_undo_allocate:
|
|
if (undo->u.var_index >= 0) {
|
|
isl_assert(tab->mat->ctx, !var->is_row, return -1);
|
|
return drop_col(tab, var->index);
|
|
}
|
|
if (!var->is_row) {
|
|
if (!max_is_manifestly_unbounded(tab, var)) {
|
|
if (to_row(tab, var, 1) < 0)
|
|
return -1;
|
|
} else if (!min_is_manifestly_unbounded(tab, var)) {
|
|
if (to_row(tab, var, -1) < 0)
|
|
return -1;
|
|
} else
|
|
if (to_row(tab, var, 0) < 0)
|
|
return -1;
|
|
}
|
|
return drop_row(tab, var->index);
|
|
case isl_tab_undo_relax:
|
|
return unrelax(tab, var);
|
|
case isl_tab_undo_unrestrict:
|
|
return ununrestrict(tab, var);
|
|
default:
|
|
isl_die(tab->mat->ctx, isl_error_internal,
|
|
"perform_undo_var called on invalid undo record",
|
|
return -1);
|
|
}
|
|
|
|
return 0;
|
|
}
|
|
|
|
/* Restore the tableau to the state where the basic variables
|
|
* are those in "col_var".
|
|
* We first construct a list of variables that are currently in
|
|
* the basis, but shouldn't. Then we iterate over all variables
|
|
* that should be in the basis and for each one that is currently
|
|
* not in the basis, we exchange it with one of the elements of the
|
|
* list constructed before.
|
|
* We can always find an appropriate variable to pivot with because
|
|
* the current basis is mapped to the old basis by a non-singular
|
|
* matrix and so we can never end up with a zero row.
|
|
*/
|
|
static int restore_basis(struct isl_tab *tab, int *col_var)
|
|
{
|
|
int i, j;
|
|
int n_extra = 0;
|
|
int *extra = NULL; /* current columns that contain bad stuff */
|
|
unsigned off = 2 + tab->M;
|
|
|
|
extra = isl_alloc_array(tab->mat->ctx, int, tab->n_col);
|
|
if (tab->n_col && !extra)
|
|
goto error;
|
|
for (i = 0; i < tab->n_col; ++i) {
|
|
for (j = 0; j < tab->n_col; ++j)
|
|
if (tab->col_var[i] == col_var[j])
|
|
break;
|
|
if (j < tab->n_col)
|
|
continue;
|
|
extra[n_extra++] = i;
|
|
}
|
|
for (i = 0; i < tab->n_col && n_extra > 0; ++i) {
|
|
struct isl_tab_var *var;
|
|
int row;
|
|
|
|
for (j = 0; j < tab->n_col; ++j)
|
|
if (col_var[i] == tab->col_var[j])
|
|
break;
|
|
if (j < tab->n_col)
|
|
continue;
|
|
var = var_from_index(tab, col_var[i]);
|
|
row = var->index;
|
|
for (j = 0; j < n_extra; ++j)
|
|
if (!isl_int_is_zero(tab->mat->row[row][off+extra[j]]))
|
|
break;
|
|
isl_assert(tab->mat->ctx, j < n_extra, goto error);
|
|
if (isl_tab_pivot(tab, row, extra[j]) < 0)
|
|
goto error;
|
|
extra[j] = extra[--n_extra];
|
|
}
|
|
|
|
free(extra);
|
|
return 0;
|
|
error:
|
|
free(extra);
|
|
return -1;
|
|
}
|
|
|
|
/* Remove all samples with index n or greater, i.e., those samples
|
|
* that were added since we saved this number of samples in
|
|
* isl_tab_save_samples.
|
|
*/
|
|
static void drop_samples_since(struct isl_tab *tab, int n)
|
|
{
|
|
int i;
|
|
|
|
for (i = tab->n_sample - 1; i >= 0 && tab->n_sample > n; --i) {
|
|
if (tab->sample_index[i] < n)
|
|
continue;
|
|
|
|
if (i != tab->n_sample - 1) {
|
|
int t = tab->sample_index[tab->n_sample-1];
|
|
tab->sample_index[tab->n_sample-1] = tab->sample_index[i];
|
|
tab->sample_index[i] = t;
|
|
isl_mat_swap_rows(tab->samples, tab->n_sample-1, i);
|
|
}
|
|
tab->n_sample--;
|
|
}
|
|
}
|
|
|
|
static int perform_undo(struct isl_tab *tab, struct isl_tab_undo *undo) WARN_UNUSED;
|
|
static int perform_undo(struct isl_tab *tab, struct isl_tab_undo *undo)
|
|
{
|
|
switch (undo->type) {
|
|
case isl_tab_undo_rational:
|
|
tab->rational = 0;
|
|
break;
|
|
case isl_tab_undo_empty:
|
|
tab->empty = 0;
|
|
break;
|
|
case isl_tab_undo_nonneg:
|
|
case isl_tab_undo_redundant:
|
|
case isl_tab_undo_freeze:
|
|
case isl_tab_undo_zero:
|
|
case isl_tab_undo_allocate:
|
|
case isl_tab_undo_relax:
|
|
case isl_tab_undo_unrestrict:
|
|
return perform_undo_var(tab, undo);
|
|
case isl_tab_undo_bmap_eq:
|
|
return isl_basic_map_free_equality(tab->bmap, 1);
|
|
case isl_tab_undo_bmap_ineq:
|
|
return isl_basic_map_free_inequality(tab->bmap, 1);
|
|
case isl_tab_undo_bmap_div:
|
|
if (isl_basic_map_free_div(tab->bmap, 1) < 0)
|
|
return -1;
|
|
if (tab->samples)
|
|
tab->samples->n_col--;
|
|
break;
|
|
case isl_tab_undo_saved_basis:
|
|
if (restore_basis(tab, undo->u.col_var) < 0)
|
|
return -1;
|
|
break;
|
|
case isl_tab_undo_drop_sample:
|
|
tab->n_outside--;
|
|
break;
|
|
case isl_tab_undo_saved_samples:
|
|
drop_samples_since(tab, undo->u.n);
|
|
break;
|
|
case isl_tab_undo_callback:
|
|
return undo->u.callback->run(undo->u.callback);
|
|
default:
|
|
isl_assert(tab->mat->ctx, 0, return -1);
|
|
}
|
|
return 0;
|
|
}
|
|
|
|
/* Return the tableau to the state it was in when the snapshot "snap"
|
|
* was taken.
|
|
*/
|
|
int isl_tab_rollback(struct isl_tab *tab, struct isl_tab_undo *snap)
|
|
{
|
|
struct isl_tab_undo *undo, *next;
|
|
|
|
if (!tab)
|
|
return -1;
|
|
|
|
tab->in_undo = 1;
|
|
for (undo = tab->top; undo && undo != &tab->bottom; undo = next) {
|
|
next = undo->next;
|
|
if (undo == snap)
|
|
break;
|
|
if (perform_undo(tab, undo) < 0) {
|
|
tab->top = undo;
|
|
free_undo(tab);
|
|
tab->in_undo = 0;
|
|
return -1;
|
|
}
|
|
free_undo_record(undo);
|
|
}
|
|
tab->in_undo = 0;
|
|
tab->top = undo;
|
|
if (!undo)
|
|
return -1;
|
|
return 0;
|
|
}
|
|
|
|
/* The given row "row" represents an inequality violated by all
|
|
* points in the tableau. Check for some special cases of such
|
|
* separating constraints.
|
|
* In particular, if the row has been reduced to the constant -1,
|
|
* then we know the inequality is adjacent (but opposite) to
|
|
* an equality in the tableau.
|
|
* If the row has been reduced to r = c*(-1 -r'), with r' an inequality
|
|
* of the tableau and c a positive constant, then the inequality
|
|
* is adjacent (but opposite) to the inequality r'.
|
|
*/
|
|
static enum isl_ineq_type separation_type(struct isl_tab *tab, unsigned row)
|
|
{
|
|
int pos;
|
|
unsigned off = 2 + tab->M;
|
|
|
|
if (tab->rational)
|
|
return isl_ineq_separate;
|
|
|
|
if (!isl_int_is_one(tab->mat->row[row][0]))
|
|
return isl_ineq_separate;
|
|
|
|
pos = isl_seq_first_non_zero(tab->mat->row[row] + off + tab->n_dead,
|
|
tab->n_col - tab->n_dead);
|
|
if (pos == -1) {
|
|
if (isl_int_is_negone(tab->mat->row[row][1]))
|
|
return isl_ineq_adj_eq;
|
|
else
|
|
return isl_ineq_separate;
|
|
}
|
|
|
|
if (!isl_int_eq(tab->mat->row[row][1],
|
|
tab->mat->row[row][off + tab->n_dead + pos]))
|
|
return isl_ineq_separate;
|
|
|
|
pos = isl_seq_first_non_zero(
|
|
tab->mat->row[row] + off + tab->n_dead + pos + 1,
|
|
tab->n_col - tab->n_dead - pos - 1);
|
|
|
|
return pos == -1 ? isl_ineq_adj_ineq : isl_ineq_separate;
|
|
}
|
|
|
|
/* Check the effect of inequality "ineq" on the tableau "tab".
|
|
* The result may be
|
|
* isl_ineq_redundant: satisfied by all points in the tableau
|
|
* isl_ineq_separate: satisfied by no point in the tableau
|
|
* isl_ineq_cut: satisfied by some by not all points
|
|
* isl_ineq_adj_eq: adjacent to an equality
|
|
* isl_ineq_adj_ineq: adjacent to an inequality.
|
|
*/
|
|
enum isl_ineq_type isl_tab_ineq_type(struct isl_tab *tab, isl_int *ineq)
|
|
{
|
|
enum isl_ineq_type type = isl_ineq_error;
|
|
struct isl_tab_undo *snap = NULL;
|
|
int con;
|
|
int row;
|
|
|
|
if (!tab)
|
|
return isl_ineq_error;
|
|
|
|
if (isl_tab_extend_cons(tab, 1) < 0)
|
|
return isl_ineq_error;
|
|
|
|
snap = isl_tab_snap(tab);
|
|
|
|
con = isl_tab_add_row(tab, ineq);
|
|
if (con < 0)
|
|
goto error;
|
|
|
|
row = tab->con[con].index;
|
|
if (isl_tab_row_is_redundant(tab, row))
|
|
type = isl_ineq_redundant;
|
|
else if (isl_int_is_neg(tab->mat->row[row][1]) &&
|
|
(tab->rational ||
|
|
isl_int_abs_ge(tab->mat->row[row][1],
|
|
tab->mat->row[row][0]))) {
|
|
int nonneg = at_least_zero(tab, &tab->con[con]);
|
|
if (nonneg < 0)
|
|
goto error;
|
|
if (nonneg)
|
|
type = isl_ineq_cut;
|
|
else
|
|
type = separation_type(tab, row);
|
|
} else {
|
|
int red = con_is_redundant(tab, &tab->con[con]);
|
|
if (red < 0)
|
|
goto error;
|
|
if (!red)
|
|
type = isl_ineq_cut;
|
|
else
|
|
type = isl_ineq_redundant;
|
|
}
|
|
|
|
if (isl_tab_rollback(tab, snap))
|
|
return isl_ineq_error;
|
|
return type;
|
|
error:
|
|
return isl_ineq_error;
|
|
}
|
|
|
|
int isl_tab_track_bmap(struct isl_tab *tab, __isl_take isl_basic_map *bmap)
|
|
{
|
|
bmap = isl_basic_map_cow(bmap);
|
|
if (!tab || !bmap)
|
|
goto error;
|
|
|
|
if (tab->empty) {
|
|
bmap = isl_basic_map_set_to_empty(bmap);
|
|
if (!bmap)
|
|
goto error;
|
|
tab->bmap = bmap;
|
|
return 0;
|
|
}
|
|
|
|
isl_assert(tab->mat->ctx, tab->n_eq == bmap->n_eq, goto error);
|
|
isl_assert(tab->mat->ctx,
|
|
tab->n_con == bmap->n_eq + bmap->n_ineq, goto error);
|
|
|
|
tab->bmap = bmap;
|
|
|
|
return 0;
|
|
error:
|
|
isl_basic_map_free(bmap);
|
|
return -1;
|
|
}
|
|
|
|
int isl_tab_track_bset(struct isl_tab *tab, __isl_take isl_basic_set *bset)
|
|
{
|
|
return isl_tab_track_bmap(tab, (isl_basic_map *)bset);
|
|
}
|
|
|
|
__isl_keep isl_basic_set *isl_tab_peek_bset(struct isl_tab *tab)
|
|
{
|
|
if (!tab)
|
|
return NULL;
|
|
|
|
return (isl_basic_set *)tab->bmap;
|
|
}
|
|
|
|
static void isl_tab_print_internal(__isl_keep struct isl_tab *tab,
|
|
FILE *out, int indent)
|
|
{
|
|
unsigned r, c;
|
|
int i;
|
|
|
|
if (!tab) {
|
|
fprintf(out, "%*snull tab\n", indent, "");
|
|
return;
|
|
}
|
|
fprintf(out, "%*sn_redundant: %d, n_dead: %d", indent, "",
|
|
tab->n_redundant, tab->n_dead);
|
|
if (tab->rational)
|
|
fprintf(out, ", rational");
|
|
if (tab->empty)
|
|
fprintf(out, ", empty");
|
|
fprintf(out, "\n");
|
|
fprintf(out, "%*s[", indent, "");
|
|
for (i = 0; i < tab->n_var; ++i) {
|
|
if (i)
|
|
fprintf(out, (i == tab->n_param ||
|
|
i == tab->n_var - tab->n_div) ? "; "
|
|
: ", ");
|
|
fprintf(out, "%c%d%s", tab->var[i].is_row ? 'r' : 'c',
|
|
tab->var[i].index,
|
|
tab->var[i].is_zero ? " [=0]" :
|
|
tab->var[i].is_redundant ? " [R]" : "");
|
|
}
|
|
fprintf(out, "]\n");
|
|
fprintf(out, "%*s[", indent, "");
|
|
for (i = 0; i < tab->n_con; ++i) {
|
|
if (i)
|
|
fprintf(out, ", ");
|
|
fprintf(out, "%c%d%s", tab->con[i].is_row ? 'r' : 'c',
|
|
tab->con[i].index,
|
|
tab->con[i].is_zero ? " [=0]" :
|
|
tab->con[i].is_redundant ? " [R]" : "");
|
|
}
|
|
fprintf(out, "]\n");
|
|
fprintf(out, "%*s[", indent, "");
|
|
for (i = 0; i < tab->n_row; ++i) {
|
|
const char *sign = "";
|
|
if (i)
|
|
fprintf(out, ", ");
|
|
if (tab->row_sign) {
|
|
if (tab->row_sign[i] == isl_tab_row_unknown)
|
|
sign = "?";
|
|
else if (tab->row_sign[i] == isl_tab_row_neg)
|
|
sign = "-";
|
|
else if (tab->row_sign[i] == isl_tab_row_pos)
|
|
sign = "+";
|
|
else
|
|
sign = "+-";
|
|
}
|
|
fprintf(out, "r%d: %d%s%s", i, tab->row_var[i],
|
|
isl_tab_var_from_row(tab, i)->is_nonneg ? " [>=0]" : "", sign);
|
|
}
|
|
fprintf(out, "]\n");
|
|
fprintf(out, "%*s[", indent, "");
|
|
for (i = 0; i < tab->n_col; ++i) {
|
|
if (i)
|
|
fprintf(out, ", ");
|
|
fprintf(out, "c%d: %d%s", i, tab->col_var[i],
|
|
var_from_col(tab, i)->is_nonneg ? " [>=0]" : "");
|
|
}
|
|
fprintf(out, "]\n");
|
|
r = tab->mat->n_row;
|
|
tab->mat->n_row = tab->n_row;
|
|
c = tab->mat->n_col;
|
|
tab->mat->n_col = 2 + tab->M + tab->n_col;
|
|
isl_mat_print_internal(tab->mat, out, indent);
|
|
tab->mat->n_row = r;
|
|
tab->mat->n_col = c;
|
|
if (tab->bmap)
|
|
isl_basic_map_print_internal(tab->bmap, out, indent);
|
|
}
|
|
|
|
void isl_tab_dump(__isl_keep struct isl_tab *tab)
|
|
{
|
|
isl_tab_print_internal(tab, stderr, 0);
|
|
}
|