| /* |
| * Copyright 2008-2009 Katholieke Universiteit Leuven |
| * |
| * Use of this software is governed by the GNU LGPLv2.1 license |
| * |
| * Written by Sven Verdoolaege, K.U.Leuven, Departement |
| * Computerwetenschappen, Celestijnenlaan 200A, B-3001 Leuven, Belgium |
| */ |
| |
| #include <isl_ctx_private.h> |
| #include <isl_mat_private.h> |
| #include "isl_map_private.h" |
| #include "isl_tab.h" |
| #include <isl/seq.h> |
| #include <isl_config.h> |
| |
| /* |
| * The implementation of tableaus in this file was inspired by Section 8 |
| * of David Detlefs, Greg Nelson and James B. Saxe, "Simplify: a theorem |
| * prover for program checking". |
| */ |
| |
| struct isl_tab *isl_tab_alloc(struct isl_ctx *ctx, |
| unsigned n_row, unsigned n_var, unsigned M) |
| { |
| int i; |
| struct isl_tab *tab; |
| unsigned off = 2 + M; |
| |
| tab = isl_calloc_type(ctx, struct isl_tab); |
| if (!tab) |
| return NULL; |
| tab->mat = isl_mat_alloc(ctx, n_row, off + n_var); |
| if (!tab->mat) |
| goto error; |
| tab->var = isl_alloc_array(ctx, struct isl_tab_var, n_var); |
| if (!tab->var) |
| goto error; |
| tab->con = isl_alloc_array(ctx, struct isl_tab_var, n_row); |
| if (!tab->con) |
| goto error; |
| tab->col_var = isl_alloc_array(ctx, int, n_var); |
| if (!tab->col_var) |
| goto error; |
| tab->row_var = isl_alloc_array(ctx, int, n_row); |
| if (!tab->row_var) |
| goto error; |
| for (i = 0; i < n_var; ++i) { |
| tab->var[i].index = i; |
| tab->var[i].is_row = 0; |
| tab->var[i].is_nonneg = 0; |
| tab->var[i].is_zero = 0; |
| tab->var[i].is_redundant = 0; |
| tab->var[i].frozen = 0; |
| tab->var[i].negated = 0; |
| tab->col_var[i] = i; |
| } |
| tab->n_row = 0; |
| tab->n_con = 0; |
| tab->n_eq = 0; |
| tab->max_con = n_row; |
| tab->n_col = n_var; |
| tab->n_var = n_var; |
| tab->max_var = n_var; |
| tab->n_param = 0; |
| tab->n_div = 0; |
| tab->n_dead = 0; |
| tab->n_redundant = 0; |
| tab->strict_redundant = 0; |
| tab->need_undo = 0; |
| tab->rational = 0; |
| tab->empty = 0; |
| tab->in_undo = 0; |
| tab->M = M; |
| tab->cone = 0; |
| tab->bottom.type = isl_tab_undo_bottom; |
| tab->bottom.next = NULL; |
| tab->top = &tab->bottom; |
| |
| tab->n_zero = 0; |
| tab->n_unbounded = 0; |
| tab->basis = NULL; |
| |
| return tab; |
| error: |
| isl_tab_free(tab); |
| return NULL; |
| } |
| |
| int isl_tab_extend_cons(struct isl_tab *tab, unsigned n_new) |
| { |
| unsigned off; |
| |
| if (!tab) |
| return -1; |
| |
| off = 2 + tab->M; |
| |
| if (tab->max_con < tab->n_con + n_new) { |
| struct isl_tab_var *con; |
| |
| con = isl_realloc_array(tab->mat->ctx, tab->con, |
| struct isl_tab_var, tab->max_con + n_new); |
| if (!con) |
| return -1; |
| tab->con = con; |
| tab->max_con += n_new; |
| } |
| if (tab->mat->n_row < tab->n_row + n_new) { |
| int *row_var; |
| |
| tab->mat = isl_mat_extend(tab->mat, |
| tab->n_row + n_new, off + tab->n_col); |
| if (!tab->mat) |
| return -1; |
| row_var = isl_realloc_array(tab->mat->ctx, tab->row_var, |
| int, tab->mat->n_row); |
| if (!row_var) |
| return -1; |
| tab->row_var = row_var; |
| if (tab->row_sign) { |
| enum isl_tab_row_sign *s; |
| s = isl_realloc_array(tab->mat->ctx, tab->row_sign, |
| enum isl_tab_row_sign, tab->mat->n_row); |
| if (!s) |
| return -1; |
| tab->row_sign = s; |
| } |
| } |
| return 0; |
| } |
| |
| /* Make room for at least n_new extra variables. |
| * Return -1 if anything went wrong. |
| */ |
| int isl_tab_extend_vars(struct isl_tab *tab, unsigned n_new) |
| { |
| struct isl_tab_var *var; |
| unsigned off = 2 + tab->M; |
| |
| if (tab->max_var < tab->n_var + n_new) { |
| var = isl_realloc_array(tab->mat->ctx, tab->var, |
| struct isl_tab_var, tab->n_var + n_new); |
| if (!var) |
| return -1; |
| tab->var = var; |
| tab->max_var += n_new; |
| } |
| |
| if (tab->mat->n_col < off + tab->n_col + n_new) { |
| int *p; |
| |
| tab->mat = isl_mat_extend(tab->mat, |
| tab->mat->n_row, off + tab->n_col + n_new); |
| if (!tab->mat) |
| return -1; |
| p = isl_realloc_array(tab->mat->ctx, tab->col_var, |
| int, tab->n_col + n_new); |
| if (!p) |
| return -1; |
| tab->col_var = p; |
| } |
| |
| return 0; |
| } |
| |
| struct isl_tab *isl_tab_extend(struct isl_tab *tab, unsigned n_new) |
| { |
| if (isl_tab_extend_cons(tab, n_new) >= 0) |
| return tab; |
| |
| isl_tab_free(tab); |
| return NULL; |
| } |
| |
| static void free_undo_record(struct isl_tab_undo *undo) |
| { |
| switch (undo->type) { |
| case isl_tab_undo_saved_basis: |
| free(undo->u.col_var); |
| break; |
| default:; |
| } |
| free(undo); |
| } |
| |
| static void free_undo(struct isl_tab *tab) |
| { |
| struct isl_tab_undo *undo, *next; |
| |
| for (undo = tab->top; undo && undo != &tab->bottom; undo = next) { |
| next = undo->next; |
| free_undo_record(undo); |
| } |
| tab->top = undo; |
| } |
| |
| void isl_tab_free(struct isl_tab *tab) |
| { |
| if (!tab) |
| return; |
| free_undo(tab); |
| isl_mat_free(tab->mat); |
| isl_vec_free(tab->dual); |
| isl_basic_map_free(tab->bmap); |
| free(tab->var); |
| free(tab->con); |
| free(tab->row_var); |
| free(tab->col_var); |
| free(tab->row_sign); |
| isl_mat_free(tab->samples); |
| free(tab->sample_index); |
| isl_mat_free(tab->basis); |
| free(tab); |
| } |
| |
| struct isl_tab *isl_tab_dup(struct isl_tab *tab) |
| { |
| int i; |
| struct isl_tab *dup; |
| unsigned off; |
| |
| if (!tab) |
| return NULL; |
| |
| off = 2 + tab->M; |
| dup = isl_calloc_type(tab->mat->ctx, struct isl_tab); |
| if (!dup) |
| return NULL; |
| dup->mat = isl_mat_dup(tab->mat); |
| if (!dup->mat) |
| goto error; |
| dup->var = isl_alloc_array(tab->mat->ctx, struct isl_tab_var, tab->max_var); |
| if (!dup->var) |
| goto error; |
| for (i = 0; i < tab->n_var; ++i) |
| dup->var[i] = tab->var[i]; |
| dup->con = isl_alloc_array(tab->mat->ctx, struct isl_tab_var, tab->max_con); |
| if (!dup->con) |
| goto error; |
| for (i = 0; i < tab->n_con; ++i) |
| dup->con[i] = tab->con[i]; |
| dup->col_var = isl_alloc_array(tab->mat->ctx, int, tab->mat->n_col - off); |
| if (!dup->col_var) |
| goto error; |
| for (i = 0; i < tab->n_col; ++i) |
| dup->col_var[i] = tab->col_var[i]; |
| dup->row_var = isl_alloc_array(tab->mat->ctx, int, tab->mat->n_row); |
| if (!dup->row_var) |
| goto error; |
| for (i = 0; i < tab->n_row; ++i) |
| dup->row_var[i] = tab->row_var[i]; |
| if (tab->row_sign) { |
| dup->row_sign = isl_alloc_array(tab->mat->ctx, enum isl_tab_row_sign, |
| tab->mat->n_row); |
| if (!dup->row_sign) |
| goto error; |
| for (i = 0; i < tab->n_row; ++i) |
| dup->row_sign[i] = tab->row_sign[i]; |
| } |
| if (tab->samples) { |
| dup->samples = isl_mat_dup(tab->samples); |
| if (!dup->samples) |
| goto error; |
| dup->sample_index = isl_alloc_array(tab->mat->ctx, int, |
| tab->samples->n_row); |
| if (!dup->sample_index) |
| goto error; |
| dup->n_sample = tab->n_sample; |
| dup->n_outside = tab->n_outside; |
| } |
| dup->n_row = tab->n_row; |
| dup->n_con = tab->n_con; |
| dup->n_eq = tab->n_eq; |
| dup->max_con = tab->max_con; |
| dup->n_col = tab->n_col; |
| dup->n_var = tab->n_var; |
| dup->max_var = tab->max_var; |
| dup->n_param = tab->n_param; |
| dup->n_div = tab->n_div; |
| dup->n_dead = tab->n_dead; |
| dup->n_redundant = tab->n_redundant; |
| dup->rational = tab->rational; |
| dup->empty = tab->empty; |
| dup->strict_redundant = 0; |
| dup->need_undo = 0; |
| dup->in_undo = 0; |
| dup->M = tab->M; |
| tab->cone = tab->cone; |
| dup->bottom.type = isl_tab_undo_bottom; |
| dup->bottom.next = NULL; |
| dup->top = &dup->bottom; |
| |
| dup->n_zero = tab->n_zero; |
| dup->n_unbounded = tab->n_unbounded; |
| dup->basis = isl_mat_dup(tab->basis); |
| |
| return dup; |
| error: |
| isl_tab_free(dup); |
| return NULL; |
| } |
| |
| /* Construct the coefficient matrix of the product tableau |
| * of two tableaus. |
| * mat{1,2} is the coefficient matrix of tableau {1,2} |
| * row{1,2} is the number of rows in tableau {1,2} |
| * col{1,2} is the number of columns in tableau {1,2} |
| * off is the offset to the coefficient column (skipping the |
| * denominator, the constant term and the big parameter if any) |
| * r{1,2} is the number of redundant rows in tableau {1,2} |
| * d{1,2} is the number of dead columns in tableau {1,2} |
| * |
| * The order of the rows and columns in the result is as explained |
| * in isl_tab_product. |
| */ |
| static struct isl_mat *tab_mat_product(struct isl_mat *mat1, |
| struct isl_mat *mat2, unsigned row1, unsigned row2, |
| unsigned col1, unsigned col2, |
| unsigned off, unsigned r1, unsigned r2, unsigned d1, unsigned d2) |
| { |
| int i; |
| struct isl_mat *prod; |
| unsigned n; |
| |
| prod = isl_mat_alloc(mat1->ctx, mat1->n_row + mat2->n_row, |
| off + col1 + col2); |
| if (!prod) |
| return NULL; |
| |
| n = 0; |
| for (i = 0; i < r1; ++i) { |
| isl_seq_cpy(prod->row[n + i], mat1->row[i], off + d1); |
| isl_seq_clr(prod->row[n + i] + off + d1, d2); |
| isl_seq_cpy(prod->row[n + i] + off + d1 + d2, |
| mat1->row[i] + off + d1, col1 - d1); |
| isl_seq_clr(prod->row[n + i] + off + col1 + d1, col2 - d2); |
| } |
| |
| n += r1; |
| for (i = 0; i < r2; ++i) { |
| isl_seq_cpy(prod->row[n + i], mat2->row[i], off); |
| isl_seq_clr(prod->row[n + i] + off, d1); |
| isl_seq_cpy(prod->row[n + i] + off + d1, |
| mat2->row[i] + off, d2); |
| isl_seq_clr(prod->row[n + i] + off + d1 + d2, col1 - d1); |
| isl_seq_cpy(prod->row[n + i] + off + col1 + d1, |
| mat2->row[i] + off + d2, col2 - d2); |
| } |
| |
| n += r2; |
| for (i = 0; i < row1 - r1; ++i) { |
| isl_seq_cpy(prod->row[n + i], mat1->row[r1 + i], off + d1); |
| isl_seq_clr(prod->row[n + i] + off + d1, d2); |
| isl_seq_cpy(prod->row[n + i] + off + d1 + d2, |
| mat1->row[r1 + i] + off + d1, col1 - d1); |
| isl_seq_clr(prod->row[n + i] + off + col1 + d1, col2 - d2); |
| } |
| |
| n += row1 - r1; |
| for (i = 0; i < row2 - r2; ++i) { |
| isl_seq_cpy(prod->row[n + i], mat2->row[r2 + i], off); |
| isl_seq_clr(prod->row[n + i] + off, d1); |
| isl_seq_cpy(prod->row[n + i] + off + d1, |
| mat2->row[r2 + i] + off, d2); |
| isl_seq_clr(prod->row[n + i] + off + d1 + d2, col1 - d1); |
| isl_seq_cpy(prod->row[n + i] + off + col1 + d1, |
| mat2->row[r2 + i] + off + d2, col2 - d2); |
| } |
| |
| return prod; |
| } |
| |
| /* Update the row or column index of a variable that corresponds |
| * to a variable in the first input tableau. |
| */ |
| static void update_index1(struct isl_tab_var *var, |
| unsigned r1, unsigned r2, unsigned d1, unsigned d2) |
| { |
| if (var->index == -1) |
| return; |
| if (var->is_row && var->index >= r1) |
| var->index += r2; |
| if (!var->is_row && var->index >= d1) |
| var->index += d2; |
| } |
| |
| /* Update the row or column index of a variable that corresponds |
| * to a variable in the second input tableau. |
| */ |
| static void update_index2(struct isl_tab_var *var, |
| unsigned row1, unsigned col1, |
| unsigned r1, unsigned r2, unsigned d1, unsigned d2) |
| { |
| if (var->index == -1) |
| return; |
| if (var->is_row) { |
| if (var->index < r2) |
| var->index += r1; |
| else |
| var->index += row1; |
| } else { |
| if (var->index < d2) |
| var->index += d1; |
| else |
| var->index += col1; |
| } |
| } |
| |
| /* Create a tableau that represents the Cartesian product of the sets |
| * represented by tableaus tab1 and tab2. |
| * The order of the rows in the product is |
| * - redundant rows of tab1 |
| * - redundant rows of tab2 |
| * - non-redundant rows of tab1 |
| * - non-redundant rows of tab2 |
| * The order of the columns is |
| * - denominator |
| * - constant term |
| * - coefficient of big parameter, if any |
| * - dead columns of tab1 |
| * - dead columns of tab2 |
| * - live columns of tab1 |
| * - live columns of tab2 |
| * The order of the variables and the constraints is a concatenation |
| * of order in the two input tableaus. |
| */ |
| 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; |
| |
| if (!tab1 || !tab2) |
| return NULL; |
| |
| isl_assert(tab1->mat->ctx, tab1->M == tab2->M, return NULL); |
| isl_assert(tab1->mat->ctx, tab1->rational == tab2->rational, return NULL); |
| isl_assert(tab1->mat->ctx, tab1->cone == tab2->cone, return NULL); |
| isl_assert(tab1->mat->ctx, !tab1->row_sign, return NULL); |
| 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); |
| |
| 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 (!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 (!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 (!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 (!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->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 (!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; |
| } |
| |
| struct isl_tab *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 tab; |
| error: |
| isl_vec_free(sample); |
| isl_tab_free(tab); |
| return NULL; |
| } |
| |
| 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->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; |
| } |
| } |
| |
| 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; |
| struct isl_mat *mat = tab->mat; |
| struct isl_tab_var *var; |
| unsigned off = 2 + tab->M; |
| |
| if (tab->mat->ctx->abort) { |
| isl_ctx_set_error(tab->mat->ctx, isl_error_abort); |
| 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. |
| * |
| * 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 (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; |
| } |
| |
| /* 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) |
| { |
| int r; |
| int i; |
| unsigned off = 2 + tab->M; |
| |
| isl_assert(tab->mat->ctx, tab->n_col < tab->mat->n_col, return -1); |
| isl_assert(tab->mat->ctx, tab->n_var < tab->max_var, return -1); |
| |
| r = tab->n_var; |
| 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_var++; |
| tab->n_col++; |
| if (isl_tab_push_var(tab, isl_tab_undo_allocate, &tab->var[r]) < 0) |
| return -1; |
| |
| return r; |
| } |
| |
| /* 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; |
| } |
| |
| static int drop_col(struct isl_tab *tab, int col) |
| { |
| isl_assert(tab->mat->ctx, tab->col_var[col] == tab->n_var - 1, return -1); |
| if (col != tab->n_col - 1) |
| swap_cols(tab, col, tab->n_col - 1); |
| tab->n_col--; |
| tab->n_var--; |
| 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_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_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) { |
| if (isl_tab_rollback(tab, snap) < 0) |
| return -1; |
| } else |
| drop_row(tab, row); |
| return 0; |
| } |
| |
| 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_dim(tab->bmap, |
| isl_basic_map_get_dim(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; |
| } |
| |
| struct isl_tab *isl_tab_from_basic_map(struct isl_basic_map *bmap) |
| { |
| 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->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; |
| return tab; |
| } |
| 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) |
| return tab; |
| } |
| return tab; |
| error: |
| isl_tab_free(tab); |
| return NULL; |
| } |
| |
| struct isl_tab *isl_tab_from_basic_set(struct isl_basic_set *bset) |
| { |
| return isl_tab_from_basic_map((struct isl_basic_map *)bset); |
| } |
| |
| /* 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); |
| 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. |
| */ |
| struct isl_tab *isl_tab_relax(struct isl_tab *tab, int con) |
| { |
| struct isl_tab_var *var; |
| unsigned off = 2 + tab->M; |
| |
| if (!tab) |
| return NULL; |
| |
| var = &tab->con[con]; |
| |
| if (!var->is_row && !max_is_manifestly_unbounded(tab, var)) |
| if (to_row(tab, var, 1) < 0) |
| goto error; |
| if (!var->is_row && !min_is_manifestly_unbounded(tab, var)) |
| if (to_row(tab, var, -1) < 0) |
| goto error; |
| |
| 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) |
| goto error; |
| } 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_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) |
| goto error; |
| |
| return tab; |
| error: |
| isl_tab_free(tab); |
| return NULL; |
| } |
| |
| 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; |
| } |
| |
| 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; |
| } |
| |
| int isl_tab_is_redundant(struct isl_tab *tab, int con) |
| { |
| if (!tab) |
| 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; |
| } |
| |
| 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); |
| drop_col(tab, var->index); |
| break; |
| } |
| 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; |
| } |
| drop_row(tab, var->index); |
| break; |
| case isl_tab_undo_relax: |
| return unrelax(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 (!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_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: |
| 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) |
| { |
| if (!tab || !bmap) |
| goto error; |
| |
| 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 = 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); |
| } |