X-Git-Url: http://review.tizen.org/git/?a=blobdiff_plain;f=isl_tab.c;h=e4cc386679d8760504af441f0741f9241120f479;hb=19596bc4e5cd282b2e75d17077b1aaaeacbfd6f9;hp=3f6d5d131c6005d04679c343b22442e03f2da5a7;hpb=35d050172ce3e402c0d95ac6044a311c16cbeda4;p=platform%2Fupstream%2Fisl.git diff --git a/isl_tab.c b/isl_tab.c index 3f6d5d1..e4cc386 100644 --- a/isl_tab.c +++ b/isl_tab.c @@ -1,5 +1,20 @@ +/* + * Copyright 2008-2009 Katholieke Universiteit Leuven + * Copyright 2013 Ecole Normale Superieure + * + * Use of this software is governed by the MIT license + * + * Written by Sven Verdoolaege, K.U.Leuven, Departement + * Computerwetenschappen, Celestijnenlaan 200A, B-3001 Leuven, Belgium + * and Ecole Normale Superieure, 45 rue d'Ulm, 75230 Paris, France + */ + +#include +#include #include "isl_map_private.h" #include "isl_tab.h" +#include +#include /* * The implementation of tableaus in this file was inspired by Section 8 @@ -8,15 +23,16 @@ */ struct isl_tab *isl_tab_alloc(struct isl_ctx *ctx, - unsigned n_row, unsigned n_var) + 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, 2 + n_var); + 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); @@ -38,6 +54,7 @@ struct isl_tab *isl_tab_alloc(struct isl_ctx *ctx, 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; @@ -46,23 +63,46 @@ struct isl_tab *isl_tab_alloc(struct isl_ctx *ctx, 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; } -static int extend_cons(struct isl_tab *tab, unsigned n_new) +isl_ctx *isl_tab_get_ctx(struct isl_tab *tab) +{ + return tab ? isl_mat_get_ctx(tab->mat) : 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; @@ -77,7 +117,7 @@ static int extend_cons(struct isl_tab *tab, unsigned n_new) int *row_var; tab->mat = isl_mat_extend(tab->mat, - tab->n_row + n_new, tab->n_col); + 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, @@ -85,26 +125,79 @@ static int extend_cons(struct isl_tab *tab, unsigned n_new) 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 (extend_cons(tab, n_new) >= 0) + 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); + free_undo_record(undo); } tab->top = undo; } @@ -116,13 +209,358 @@ void isl_tab_free(struct isl_tab *tab) 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) @@ -131,7 +569,7 @@ static struct isl_tab_var *var_from_index(struct isl_tab *tab, int i) return &tab->con[~i]; } -static struct isl_tab_var *var_from_row(struct isl_tab *tab, int 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]); } @@ -149,13 +587,14 @@ 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][2 + var->index])) + if (!isl_int_is_neg(tab->mat->row[i][off + var->index])) continue; - if (var_from_row(tab, i)->is_nonneg) + if (isl_tab_var_from_row(tab, i)->is_nonneg) return 0; } return 1; @@ -169,18 +608,36 @@ 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][2 + var->index])) + if (!isl_int_is_pos(tab->mat->row[i][off + var->index])) continue; - if (var_from_row(tab, i)->is_nonneg) + 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. @@ -206,23 +663,22 @@ static int pivot_row(struct isl_tab *tab, { 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 (!var_from_row(tab, j)->is_nonneg) + if (!isl_tab_var_from_row(tab, j)->is_nonneg) continue; - if (sgn * isl_int_sgn(tab->mat->row[j][2 + c]) >= 0) + if (sgn * isl_int_sgn(tab->mat->row[j][off + c]) >= 0) continue; if (r < 0) { r = j; continue; } - isl_int_mul(t, tab->mat->row[r][1], tab->mat->row[j][2 + c]); - isl_int_submul(t, tab->mat->row[j][1], tab->mat->row[r][2 + c]); - tsgn = sgn * isl_int_sgn(t); + tsgn = sgn * row_cmp(tab, r, j, c, t); if (tsgn < 0 || (tsgn == 0 && tab->row_var[j] < tab->row_var[r])) r = j; @@ -257,13 +713,13 @@ static void find_pivot(struct isl_tab *tab, *row = *col = -1; isl_assert(tab->mat->ctx, var->is_row, return); - tr = tab->mat->row[var->index]; + 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[2 + j])) + if (isl_int_is_zero(tr[j])) continue; - if (isl_int_sgn(tr[2 + j]) != sgn && + 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]) @@ -272,7 +728,7 @@ static void find_pivot(struct isl_tab *tab, if (c < 0) return; - sgn *= isl_int_sgn(tr[2 + c]); + sgn *= isl_int_sgn(tr[c]); r = pivot_row(tab, skip_var, sgn, c); *row = r < 0 ? var->index : r; *col = c; @@ -282,22 +738,29 @@ static void find_pivot(struct isl_tab *tab, * 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 variables. + * combination of zero or more non-negative constraints. */ -static int is_redundant(struct isl_tab *tab, int row) +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 && !var_from_row(tab, row)->is_nonneg) + 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][2 + i])) + if (isl_int_is_zero(tab->mat->row[row][off + i])) continue; - if (isl_int_is_neg(tab->mat->row[row][2 + i])) + 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; @@ -308,32 +771,164 @@ static int is_redundant(struct isl_tab *tab, int row) 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; - var_from_row(tab, row1)->index = row1; - var_from_row(tab, row2)->index = row2; + 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 void push(struct isl_tab *tab, - enum isl_tab_undo_type type, struct isl_tab_var *var) +static int push_union(struct isl_tab *tab, + enum isl_tab_undo_type type, union isl_tab_undo_val u) WARN_UNUSED; +static int push_union(struct isl_tab *tab, + enum isl_tab_undo_type type, union isl_tab_undo_val u) { struct isl_tab_undo *undo; + if (!tab) + return -1; if (!tab->need_undo) - return; + return 0; undo = isl_alloc_type(tab->mat->ctx, struct isl_tab_undo); - if (!undo) { - free_undo(tab); - tab->top = NULL; - return; - } + if (!undo) + return -1; undo->type = type; - undo->var = var; + 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. @@ -348,36 +943,107 @@ static void push(struct isl_tab *tab, * 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. */ -static int mark_redundant(struct isl_tab *tab, int row) +int isl_tab_mark_redundant(struct isl_tab *tab, int row) { - struct isl_tab_var *var = var_from_row(tab, 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); - if (tab->need_undo || tab->row_var[row] >= 0) { - if (tab->row_var[row] >= 0) { + isl_assert(tab->mat->ctx, row >= tab->n_redundant, return -1); + if (tab->preserve || tab->need_undo || tab->row_var[row] >= 0) { + if (tab->row_var[row] >= 0 && !var->is_nonneg) { var->is_nonneg = 1; - push(tab, isl_tab_undo_nonneg, var); + 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); - push(tab, isl_tab_undo_redundant, var); tab->n_redundant++; - return 0; + 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); - var_from_row(tab, tab->n_row - 1)->index = -1; + isl_tab_var_from_row(tab, tab->n_row - 1)->index = -1; tab->n_row--; return 1; } } -static struct isl_tab *mark_empty(struct isl_tab *tab) +int isl_tab_mark_empty(struct isl_tab *tab) { + if (!tab) + return -1; if (!tab->empty && tab->need_undo) - push(tab, isl_tab_undo_empty, NULL); + if (isl_tab_push(tab, isl_tab_undo_empty) < 0) + return -1; tab->empty = 1; - return tab; + 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 @@ -430,65 +1096,77 @@ static struct isl_tab *mark_empty(struct isl_tab *tab) * 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) * */ -static void pivot(struct isl_tab *tab, int row, int col) +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][2 + col]); + 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][2 + col], mat->row[row][2 + col]); + isl_int_neg(mat->row[row][off + col], mat->row[row][off + col]); } else - for (j = 0; j < 1 + tab->n_col; ++j) { - if (j == 1 + col) + 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->row[row], 2 + tab->n_col); + 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][2 + col])) + 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 < 1 + tab->n_col; ++j) { - if (j == 1 + col) + 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][2 + col], mat->row[row][1 + j]); + mat->row[i][off + col], mat->row[row][1 + j]); } - isl_int_mul(mat->row[i][2 + col], - mat->row[i][2 + col], mat->row[row][2 + col]); - if (!isl_int_is_one(mat->row[row][0])) - isl_seq_normalize(mat->row[i], 2 + tab->n_col); + 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 = var_from_row(tab, row); + 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; + return 0; for (i = tab->n_redundant; i < tab->n_row; ++i) { - if (isl_int_is_zero(mat->row[i][2 + col])) + if (isl_int_is_zero(mat->row[i][off + col])) continue; - if (!var_from_row(tab, i)->frozen && - is_redundant(tab, i)) - if (mark_redundant(tab, i)) + 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) @@ -497,36 +1175,52 @@ static void pivot(struct isl_tab *tab, int row, int col) * If sgn = 0, then the variable is unbounded in both directions, * and we pivot with any row we can find. */ -static void to_row(struct isl_tab *tab, struct isl_tab_var *var, int sign) +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; + return 0; if (sign == 0) { for (r = tab->n_redundant; r < tab->n_row; ++r) - if (!isl_int_is_zero(tab->mat->row[r][2 + var->index])) + if (!isl_int_is_zero(tab->mat->row[r][off+var->index])) break; - isl_assert(tab->mat->ctx, r < tab->n_row, return); + 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); + isl_assert(tab->mat->ctx, r >= 0, return -1); } - pivot(tab, r, var->index); + 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 = 0; i < tab->n_row; ++i) { - if (!var_from_row(tab, i)->is_nonneg) + 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; - assert(!isl_int_is_neg(tab->mat->row[i][1])); + 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()); } } @@ -547,18 +1241,55 @@ static int sign_of_max(struct isl_tab *tab, struct isl_tab_var *var) if (max_is_manifestly_unbounded(tab, var)) return 1; - to_row(tab, var, 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]); - pivot(tab, row, col); + 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 @@ -568,15 +1299,16 @@ static int restore_row(struct isl_tab *tab, struct isl_tab_var *var) { int row, col; - while (isl_int_is_neg(tab->mat->row[var->index][1])) { + while (row_is_neg(tab, var->index)) { find_pivot(tab, var, var, 1, &row, &col); if (row == -1) break; - pivot(tab, row, col); + if (isl_tab_pivot(tab, row, col) < 0) + return -2; if (!var->is_row) /* manifestly unbounded */ return 1; } - return isl_int_sgn(tab->mat->row[var->index][1]); + return row_sgn(tab, var->index); } /* Perform pivots until we are sure that the row variable "var" @@ -594,7 +1326,8 @@ static int at_least_zero(struct isl_tab *tab, struct isl_tab_var *var) break; if (row == var->index) /* manifestly unbounded */ return 1; - pivot(tab, row, col); + if (isl_tab_pivot(tab, row, col) < 0) + return -1; } return !isl_int_is_neg(tab->mat->row[var->index][1]); } @@ -619,7 +1352,7 @@ static int at_least_zero(struct isl_tab *tab, struct isl_tab_var *var) static int sign_of_min(struct isl_tab *tab, struct isl_tab_var *var) { int row, col; - struct isl_tab_var *pivot_var; + struct isl_tab_var *pivot_var = NULL; if (min_is_manifestly_unbounded(tab, var)) return -1; @@ -627,16 +1360,19 @@ static int sign_of_min(struct isl_tab *tab, struct isl_tab_var *var) col = var->index; row = pivot_row(tab, NULL, -1, col); pivot_var = var_from_col(tab, col); - pivot(tab, row, 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) - pivot(tab, row, col); - else - restore_row(tab, var); + 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; } @@ -650,28 +1386,45 @@ static int sign_of_min(struct isl_tab *tab, struct isl_tab_var *var) if (row == -1) return isl_int_sgn(tab->mat->row[var->index][1]); pivot_var = var_from_col(tab, col); - pivot(tab, row, col); + if (isl_tab_pivot(tab, row, col) < 0) + return -2; if (var->is_redundant) return 0; } - if (var->is_nonneg) { + if (pivot_var && var->is_nonneg) { /* pivot back to non-negative value */ - if (!pivot_var->is_redundant && pivot_var->index == row) - pivot(tab, row, col); - else - restore_row(tab, var); + 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 and will be made non-negative again before + * 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. */ -static int min_at_most_neg_one(struct isl_tab *tab, struct isl_tab_var *var) +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; @@ -682,18 +1435,19 @@ static int min_at_most_neg_one(struct isl_tab *tab, struct isl_tab_var *var) col = var->index; row = pivot_row(tab, NULL, -1, col); pivot_var = var_from_col(tab, col); - pivot(tab, row, col); + if (isl_tab_pivot(tab, row, col) < 0) + return -1; if (var->is_redundant) return 0; - if (isl_int_is_neg(tab->mat->row[var->index][1]) && - isl_int_abs_ge(tab->mat->row[var->index][1], - tab->mat->row[var->index][0])) { + if (row_at_most_neg_one(tab, var->index)) { if (var->is_nonneg) { if (!pivot_var->is_redundant && - pivot_var->index == row) - pivot(tab, row, col); - else - restore_row(tab, var); + 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; } @@ -702,22 +1456,26 @@ static int min_at_most_neg_one(struct isl_tab *tab, struct isl_tab_var *var) return 0; do { find_pivot(tab, var, var, -1, &row, &col); - if (row == var->index) + 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); - pivot(tab, row, col); + if (isl_tab_pivot(tab, row, col) < 0) + return -1; if (var->is_redundant) return 0; - } while (!isl_int_is_neg(tab->mat->row[var->index][1]) || - isl_int_abs_lt(tab->mat->row[var->index][1], - tab->mat->row[var->index][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) - pivot(tab, row, col); - restore_row(tab, var); + if (isl_tab_pivot(tab, row, col) < 0) + return -1; + if (restore_row(tab, var) < -1) + return -1; } return 1; } @@ -732,7 +1490,8 @@ static int at_least_one(struct isl_tab *tab, struct isl_tab_var *var) if (max_is_manifestly_unbounded(tab, var)) return 1; - to_row(tab, var, 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); @@ -740,7 +1499,8 @@ static int at_least_one(struct isl_tab *tab, struct isl_tab_var *var) return isl_int_ge(r[1], r[0]); if (row == var->index) /* manifestly unbounded */ return 1; - pivot(tab, row, col); + if (isl_tab_pivot(tab, row, col) < 0) + return -1; } return 1; } @@ -748,12 +1508,13 @@ static int at_least_one(struct isl_tab *tab, struct isl_tab_var *var) 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, 2 + col1, 2 + col2); + tab->mat = isl_mat_swap_cols(tab->mat, off + col1, off + col2); } /* Mark column with index "col" as representing a zero variable. @@ -768,11 +1529,13 @@ static void swap_cols(struct isl_tab *tab, int col1, int col2) * column number may now contain a different column that * hasn't been checked yet. */ -static int kill_col(struct isl_tab *tab, int col) +int isl_tab_kill_col(struct isl_tab *tab, int col) { var_from_col(tab, col)->is_zero = 1; if (tab->need_undo) { - push(tab, isl_tab_undo_zero, var_from_col(tab, col)); + 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++; @@ -786,6 +1549,43 @@ static int kill_col(struct isl_tab *tab, int col) } } +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 @@ -794,32 +1594,46 @@ static int kill_col(struct isl_tab *tab, int col) * then also be written as the negative sum of non-negative variables * and must therefore also be zero. */ -static void close_row(struct isl_tab *tab, struct isl_tab_var *var) +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); + 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) { - if (isl_int_is_zero(mat->row[var->index][2 + 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][2 + j]), return); - if (kill_col(tab, j)) + 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; } - mark_redundant(tab, var->index); + 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". */ -static int allocate_con(struct isl_tab *tab) +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; @@ -828,11 +1642,46 @@ static int allocate_con(struct isl_tab *tab) 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++; - push(tab, isl_tab_undo_allocate, &tab->con[r]); + 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; } @@ -852,15 +1701,19 @@ static int allocate_con(struct isl_tab *tab) * 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. */ -static int add_row(struct isl_tab *tab, isl_int *line) +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 = allocate_con(tab); + r = isl_tab_allocate_con(tab); if (r < 0) return -1; @@ -869,7 +1722,7 @@ static int add_row(struct isl_tab *tab, isl_int *line) 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->n_col); + 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; @@ -883,15 +1736,20 @@ static int add_row(struct isl_tab *tab, isl_int *line) 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->n_col); + 1 + tab->M + tab->n_col); } else - isl_int_addmul(row[2 + tab->var[i].index], + 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(row, 2 + tab->n_col); + 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; } @@ -905,62 +1763,99 @@ static int drop_row(struct isl_tab *tab, int row) 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. */ -struct isl_tab *isl_tab_add_ineq(struct isl_tab *tab, isl_int *ineq) +int isl_tab_add_ineq(struct isl_tab *tab, isl_int *ineq) { int r; int sgn; + isl_int cst; if (!tab) - return NULL; - r = add_row(tab, ineq); + 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) - goto error; + return -1; tab->con[r].is_nonneg = 1; - push(tab, isl_tab_undo_nonneg, &tab->con[r]); - if (is_redundant(tab, tab->con[r].index)) { - mark_redundant(tab, tab->con[r].index); - return tab; + 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 mark_empty(tab); - if (tab->con[r].is_row && is_redundant(tab, tab->con[r].index)) - mark_redundant(tab, tab->con[r].index); - return tab; -error: - isl_tab_free(tab); - return NULL; + 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; + 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); - pivot(tab, row, col); + if (isl_tab_pivot(tab, row, col) < 0) + return -1; if (!var->is_row) - return; + return 0; } for (i = tab->n_dead; i < tab->n_col; ++i) - if (!isl_int_is_zero(tab->mat->row[var->index][2 + 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); - pivot(tab, var->index, i); + if (isl_tab_pivot(tab, var->index, i) < 0) + return -1; return 0; } @@ -977,17 +1872,19 @@ static struct isl_tab *add_eq(struct isl_tab *tab, isl_int *eq) if (!tab) return NULL; - r = add_row(tab, eq); + 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->n_dead, + 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; - pivot(tab, r, i); - kill_col(tab, i); + 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; @@ -996,38 +1893,328 @@ error: 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. */ -struct isl_tab *isl_tab_add_valid_eq(struct isl_tab *tab, isl_int *eq) +int isl_tab_add_valid_eq(struct isl_tab *tab, isl_int *eq) { struct isl_tab_var *var; - int i; int r; if (!tab) - return NULL; - r = add_row(tab, eq); + return -1; + r = isl_tab_add_row(tab, eq); if (r < 0) - goto error; + return -1; var = &tab->con[r]; r = var->index; - if (isl_int_is_neg(tab->mat->row[r][1])) + 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) - goto error; + return -1; var->is_nonneg = 0; - kill_col(tab, var->index); + if (isl_tab_kill_col(tab, var->index) < 0) + return -1; - return tab; + 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_tab_free(tab); - return NULL; + isl_vec_free(ineq); + return -1; } -struct isl_tab *isl_tab_from_basic_map(struct isl_basic_map *bmap) +/* Check whether the div described by "div" is obviously non-negative. + * If we are using a big parameter, then we will encode the div + * as div' = M + div, which is always non-negative. + * Otherwise, we check whether div is a non-negative affine combination + * of non-negative variables. + */ +static int div_is_nonneg(struct isl_tab *tab, __isl_keep isl_vec *div) +{ + int i; + + if (tab->M) + return 1; + + if (isl_int_is_neg(div->el[1])) + return 0; + + for (i = 0; i < tab->n_var; ++i) { + if (isl_int_is_neg(div->el[2 + i])) + return 0; + if (isl_int_is_zero(div->el[2 + i])) + continue; + if (!tab->var[i].is_nonneg) + return 0; + } + + return 1; +} + +/* Add an extra div, prescribed by "div" to the tableau and + * the associated bmap (which is assumed to be non-NULL). + * + * If add_ineq is not NULL, then this function is used instead + * of isl_tab_add_ineq to add the div constraints. + * This complication is needed because the code in isl_tab_pip + * wants to perform some extra processing when an inequality + * is added to the tableau. + */ +int isl_tab_add_div(struct isl_tab *tab, __isl_keep isl_vec *div, + int (*add_ineq)(void *user, isl_int *), void *user) +{ + int r; + int k; + int nonneg; + + if (!tab || !div) + return -1; + + isl_assert(tab->mat->ctx, tab->bmap, return -1); + + nonneg = div_is_nonneg(tab, div); + + if (isl_tab_extend_cons(tab, 3) < 0) + return -1; + if (isl_tab_extend_vars(tab, 1) < 0) + return -1; + r = isl_tab_allocate_var(tab); + if (r < 0) + return -1; + + if (nonneg) + tab->var[r].is_nonneg = 1; + + tab->bmap = isl_basic_map_extend_space(tab->bmap, + isl_basic_map_get_space(tab->bmap), 1, 0, 2); + k = isl_basic_map_alloc_div(tab->bmap); + if (k < 0) + return -1; + isl_seq_cpy(tab->bmap->div[k], div->el, div->size); + if (isl_tab_push(tab, isl_tab_undo_bmap_div) < 0) + return -1; + + if (add_div_constraints(tab, k, add_ineq, user) < 0) + return -1; + + return r; +} + +/* If "track" is set, then we want to keep track of all constraints in tab + * in its bmap field. This field is initialized from a copy of "bmap", + * so we need to make sure that all constraints in "bmap" also appear + * in the constructed tab. + */ +__isl_give struct isl_tab *isl_tab_from_basic_map( + __isl_keep isl_basic_map *bmap, int track) { int i; struct isl_tab *tab; @@ -1036,63 +2223,85 @@ struct isl_tab *isl_tab_from_basic_map(struct isl_basic_map *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)); + isl_basic_map_total_dim(bmap), 0); if (!tab) return NULL; + tab->preserve = track; tab->rational = ISL_F_ISSET(bmap, ISL_BASIC_MAP_RATIONAL); - if (ISL_F_ISSET(bmap, ISL_BASIC_MAP_EMPTY)) - return mark_empty(tab); + if (ISL_F_ISSET(bmap, ISL_BASIC_MAP_EMPTY)) { + if (isl_tab_mark_empty(tab) < 0) + goto error; + goto done; + } for (i = 0; i < bmap->n_eq; ++i) { tab = add_eq(tab, bmap->eq[i]); if (!tab) return tab; } for (i = 0; i < bmap->n_ineq; ++i) { - tab = isl_tab_add_ineq(tab, bmap->ineq[i]); - if (!tab || tab->empty) - return tab; + if (isl_tab_add_ineq(tab, bmap->ineq[i]) < 0) + goto error; + if (tab->empty) + goto done; } +done: + if (track && isl_tab_track_bmap(tab, isl_basic_map_copy(bmap)) < 0) + goto error; return tab; +error: + isl_tab_free(tab); + return NULL; } -struct isl_tab *isl_tab_from_basic_set(struct isl_basic_set *bset) +__isl_give struct isl_tab *isl_tab_from_basic_set( + __isl_keep isl_basic_set *bset, int track) { - return isl_tab_from_basic_map((struct isl_basic_map *)bset); + return isl_tab_from_basic_map(bset, track); } -/* Construct a tableau corresponding to the recession cone of "bmap". +/* Construct a tableau corresponding to the recession cone of "bset". */ -struct isl_tab *isl_tab_from_recession_cone(struct isl_basic_map *bmap) +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 (!bmap) + if (!bset) return NULL; - tab = isl_tab_alloc(bmap->ctx, bmap->n_eq + bmap->n_ineq, - isl_basic_map_total_dim(bmap)); + 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(bmap, ISL_BASIC_MAP_RATIONAL); + tab->rational = ISL_F_ISSET(bset, ISL_BASIC_SET_RATIONAL); + tab->cone = 1; isl_int_init(cst); - for (i = 0; i < bmap->n_eq; ++i) { - isl_int_swap(bmap->eq[i][0], cst); - tab = add_eq(tab, bmap->eq[i]); - isl_int_swap(bmap->eq[i][0], 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 < bmap->n_ineq; ++i) { + for (i = 0; i < bset->n_ineq; ++i) { int r; - isl_int_swap(bmap->ineq[i][0], cst); - r = add_row(tab, bmap->ineq[i]); - isl_int_swap(bmap->ineq[i][0], cst); + 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; - push(tab, isl_tab_undo_nonneg, &tab->con[r]); + if (isl_tab_push_var(tab, isl_tab_undo_nonneg, &tab->con[r]) < 0) + goto error; } done: isl_int_clear(cst); @@ -1120,12 +2329,17 @@ int isl_tab_cone_is_bounded(struct isl_tab *tab) for (;;) { for (i = tab->n_redundant; i < tab->n_row; ++i) { struct isl_tab_var *var; - var = var_from_row(tab, i); + int sgn; + var = isl_tab_var_from_row(tab, i); if (!var->is_nonneg) continue; - if (sign_of_max(tab, var) != 0) + sgn = sign_of_max(tab, var); + if (sgn < -1) + return -1; + if (sgn != 0) return 0; - close_row(tab, var); + if (close_row(tab, var) < 0) + return -1; break; } if (tab->n_dead == tab->n_col) @@ -1206,7 +2420,7 @@ struct isl_vec *isl_tab_get_sample_value(struct isl_tab *tab) 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]); } - isl_seq_normalize(vec->block.data, vec->size); + vec = isl_vec_normalize(vec); isl_int_clear(m); return vec; @@ -1241,6 +2455,8 @@ struct isl_basic_map *isl_basic_map_update_from_tab(struct isl_basic_map *bmap, 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); @@ -1263,15 +2479,20 @@ struct isl_basic_set *isl_basic_set_update_from_tab(struct isl_basic_set *bset, * the resulting tableau is empty. * Otherwise, we know the value will be zero and we close the row. */ -static struct isl_tab *cut_to_hyperplane(struct isl_tab *tab, - struct isl_tab_var *var) +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 (extend_cons(tab, 1) < 0) - goto error; + if (isl_tab_extend_cons(tab, 1) < 0) + return -1; r = tab->n_con; tab->con[r].index = tab->n_row; @@ -1280,6 +2501,7 @@ static struct isl_tab *cut_to_hyperplane(struct isl_tab *tab, 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]; @@ -1290,25 +2512,30 @@ static struct isl_tab *cut_to_hyperplane(struct isl_tab *tab, } else { isl_int_set_si(row[0], 1); isl_seq_clr(row + 1, 1 + tab->n_col); - isl_int_set_si(row[2 + var->index], -1); + isl_int_set_si(row[off + var->index], -1); } tab->n_row++; tab->n_con++; - push(tab, isl_tab_undo_allocate, &tab->con[r]); + 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 < 0) - return mark_empty(tab); + 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; - push(tab, isl_tab_undo_nonneg, &tab->con[r]); + if (isl_tab_push_var(tab, isl_tab_undo_nonneg, &tab->con[r]) < 0) + return -1; /* sgn == 0 */ - close_row(tab, &tab->con[r]); + if (close_row(tab, &tab->con[r]) < 0) + return -1; - return tab; -error: - isl_tab_free(tab); - return NULL; + return 0; } /* Given a tableau "tab" and an inequality constraint "con" of the tableau, @@ -1319,53 +2546,101 @@ error: * 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 && (var->index < 0 || var->index < tab->n_redundant)) + isl_die(tab->mat->ctx, isl_error_invalid, + "cannot relax redundant constraint", goto error); + if (!var->is_row && (var->index < 0 || var->index < tab->n_dead)) + isl_die(tab->mat->ctx, isl_error_invalid, + "cannot relax dead constraint", goto error); + if (!var->is_row && !max_is_manifestly_unbounded(tab, var)) - to_row(tab, var, 1); + 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) + 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]); - else { + 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][2 + var->index])) + 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][2 + var->index]); + tab->mat->row[i][off + var->index]); } } - push(tab, isl_tab_undo_relax, var); + if (isl_tab_push_var(tab, isl_tab_undo_relax, var) < 0) + goto error; return tab; +error: + isl_tab_free(tab); + return NULL; +} + +/* Remove the sign constraint from constraint "con". + * + * If the constraint variable was originally marked non-negative, + * then we make sure we mark it non-negative again during rollback. + */ +int isl_tab_unrestrict(struct isl_tab *tab, int con) +{ + struct isl_tab_var *var; + + if (!tab) + return -1; + + var = &tab->con[con]; + if (!var->is_nonneg) + return 0; + + var->is_nonneg = 0; + if (isl_tab_push_var(tab, isl_tab_undo_unrestrict, var) < 0) + return -1; + + return 0; } -struct isl_tab *isl_tab_select_facet(struct isl_tab *tab, int con) +int isl_tab_select_facet(struct isl_tab *tab, int con) { if (!tab) - return NULL; + 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])) && - isl_seq_first_non_zero(tab->mat->row[row] + 2 + tab->n_dead, - tab->n_col - tab->n_dead) != -1; + 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. @@ -1384,21 +2659,21 @@ static int may_be_equality(struct isl_tab *tab, int row) * tableau is integer), then we restrict the value to being zero * by adding an opposite non-negative variable. */ -struct isl_tab *isl_tab_detect_equalities(struct isl_tab *tab) +int isl_tab_detect_implicit_equalities(struct isl_tab *tab) { int i; unsigned n_marked; if (!tab) - return NULL; + return -1; if (tab->empty) - return tab; + return 0; if (tab->n_dead == tab->n_col) - return tab; + return 0; n_marked = 0; for (i = tab->n_redundant; i < tab->n_row; ++i) { - struct isl_tab_var *var = var_from_row(tab, 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) @@ -1412,8 +2687,9 @@ struct isl_tab *isl_tab_detect_equalities(struct isl_tab *tab) } while (n_marked) { struct isl_tab_var *var; + int sgn; for (i = tab->n_redundant; i < tab->n_row; ++i) { - var = var_from_row(tab, i); + var = isl_tab_var_from_row(tab, i); if (var->marked) break; } @@ -1428,14 +2704,19 @@ struct isl_tab *isl_tab_detect_equalities(struct isl_tab *tab) } var->marked = 0; n_marked--; - if (sign_of_max(tab, var) == 0) - close_row(tab, var); - else if (!tab->rational && !at_least_one(tab, var)) { - tab = cut_to_hyperplane(tab, var); - return isl_tab_detect_equalities(tab); + 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 = var_from_row(tab, i); + var = isl_tab_var_from_row(tab, i); if (!var->marked) continue; if (may_be_equality(tab, i)) @@ -1445,7 +2726,124 @@ struct isl_tab *isl_tab_detect_equalities(struct isl_tab *tab) } } - return tab; + return 0; +} + +/* Update the element of row_var or col_var that corresponds to + * constraint tab->con[i] to a move from position "old" to position "i". + */ +static int update_con_after_move(struct isl_tab *tab, int i, int old) +{ + int *p; + int index; + + index = tab->con[i].index; + if (index == -1) + return 0; + p = tab->con[i].is_row ? tab->row_var : tab->col_var; + if (p[index] != ~old) + isl_die(tab->mat->ctx, isl_error_internal, + "broken internal state", return -1); + p[index] = ~i; + + return 0; +} + +/* Rotate the "n" constraints starting at "first" to the right, + * putting the last constraint in the position of the first constraint. + */ +static int rotate_constraints(struct isl_tab *tab, int first, int n) +{ + int i, last; + struct isl_tab_var var; + + if (n <= 1) + return 0; + + last = first + n - 1; + var = tab->con[last]; + for (i = last; i > first; --i) { + tab->con[i] = tab->con[i - 1]; + if (update_con_after_move(tab, i, i - 1) < 0) + return -1; + } + tab->con[first] = var; + if (update_con_after_move(tab, first, last) < 0) + return -1; + + return 0; +} + +/* Make the equalities that are implicit in "bmap" but that have been + * detected in the corresponding "tab" explicit in "bmap" and update + * "tab" to reflect the new order of the constraints. + * + * In particular, if inequality i is an implicit equality then + * isl_basic_map_inequality_to_equality will move the inequality + * in front of the other equality and it will move the last inequality + * in the position of inequality i. + * In the tableau, the inequalities of "bmap" are stored after the equalities + * and so the original order + * + * E E E E E A A A I B B B B L + * + * is changed into + * + * I E E E E E A A A L B B B B + * + * where I is the implicit equality, the E are equalities, + * the A inequalities before I, the B inequalities after I and + * L the last inequality. + * We therefore need to rotate to the right two sets of constraints, + * those up to and including I and those after I. + * + * If "tab" contains any constraints that are not in "bmap" then they + * appear after those in "bmap" and they should be left untouched. + * + * Note that this function leaves "bmap" in a temporary state + * as it does not call isl_basic_map_gauss. Calling this function + * is the responsibility of the caller. + */ +__isl_give isl_basic_map *isl_tab_make_equalities_explicit(struct isl_tab *tab, + __isl_take isl_basic_map *bmap) +{ + int i; + + if (!tab || !bmap) + return isl_basic_map_free(bmap); + if (tab->empty) + return bmap; + + for (i = bmap->n_ineq - 1; i >= 0; --i) { + if (!isl_tab_is_equality(tab, bmap->n_eq + i)) + continue; + isl_basic_map_inequality_to_equality(bmap, i); + if (rotate_constraints(tab, 0, tab->n_eq + i + 1) < 0) + return isl_basic_map_free(bmap); + if (rotate_constraints(tab, tab->n_eq + i + 1, + bmap->n_ineq - i) < 0) + return isl_basic_map_free(bmap); + tab->n_eq++; + } + + return bmap; +} + +static int con_is_redundant(struct isl_tab *tab, struct isl_tab_var *var) +{ + if (!tab) + return -1; + if (tab->rational) { + int sgn = sign_of_min(tab, var); + if (sgn < -1) + return -1; + return sgn >= 0; + } else { + int irred = isl_tab_min_at_most_neg_one(tab, var); + if (irred < 0) + return -1; + return !irred; + } } /* Check for (near) redundant constraints. @@ -1461,21 +2859,21 @@ struct isl_tab *isl_tab_detect_equalities(struct isl_tab *tab) * If not, we mark the row as being redundant (assuming it hasn't * been detected as being obviously redundant in the mean time). */ -struct isl_tab *isl_tab_detect_redundant(struct isl_tab *tab) +int isl_tab_detect_redundant(struct isl_tab *tab) { int i; unsigned n_marked; if (!tab) - return NULL; + return -1; if (tab->empty) - return tab; + return 0; if (tab->n_redundant == tab->n_row) - return tab; + return 0; n_marked = 0; for (i = tab->n_redundant; i < tab->n_row; ++i) { - struct isl_tab_var *var = var_from_row(tab, 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++; @@ -1489,8 +2887,9 @@ struct isl_tab *isl_tab_detect_redundant(struct isl_tab *tab) } while (n_marked) { struct isl_tab_var *var; + int red; for (i = tab->n_redundant; i < tab->n_row; ++i) { - var = var_from_row(tab, i); + var = isl_tab_var_from_row(tab, i); if (var->marked) break; } @@ -1505,10 +2904,12 @@ struct isl_tab *isl_tab_detect_redundant(struct isl_tab *tab) } var->marked = 0; n_marked--; - if ((tab->rational ? (sign_of_min(tab, var) >= 0) - : !min_at_most_neg_one(tab, var)) && - !var->is_redundant) - mark_redundant(tab, var->index); + 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) @@ -1520,12 +2921,13 @@ struct isl_tab *isl_tab_detect_redundant(struct isl_tab *tab) } } - return tab; + return 0; } int isl_tab_is_equality(struct isl_tab *tab, int con) { int row; + unsigned off; if (!tab) return -1; @@ -1538,17 +2940,19 @@ int isl_tab_is_equality(struct isl_tab *tab, int con) row = tab->con[con].index; + off = 2 + tab->M; return isl_int_is_zero(tab->mat->row[row][1]) && - isl_seq_first_non_zero(tab->mat->row[row] + 2 + tab->n_dead, + (!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 minimial value of the affine expression "f" with denominator +/* 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, - * minmimal value returned in *opt). + * 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, @@ -1559,16 +2963,17 @@ enum isl_lp_result isl_tab_min(struct isl_tab *tab, 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 = add_row(tab, f); + r = isl_tab_add_row(tab, f); if (r < 0) return isl_lp_error; var = &tab->con[r]; - isl_int_mul(tab->mat->row[var->index][0], - tab->mat->row[var->index][0], denom); for (;;) { int row, col; find_pivot(tab, var, var, -1, &row, &col); @@ -1578,10 +2983,11 @@ enum isl_lp_result isl_tab_min(struct isl_tab *tab, } if (row == -1) break; - pivot(tab, row, col); + if (isl_tab_pivot(tab, row, col) < 0) + return isl_lp_error; } - if (isl_tab_rollback(tab, snap) < 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; @@ -1591,16 +2997,21 @@ enum isl_lp_result isl_tab_min(struct isl_tab *tab, 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) { - if (tab->con[i].is_row) + int pos; + if (tab->con[i].is_row) { isl_int_set_si(tab->dual->el[1 + i], 0); - else { - int pos = 2 + tab->con[i].index; + 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 (res == isl_lp_ok) { + 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]); @@ -1608,14 +3019,13 @@ enum isl_lp_result isl_tab_min(struct isl_tab *tab, 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) { - int row; - unsigned n_col; - if (!tab) return -1; if (tab->con[con].is_zero) @@ -1638,59 +3048,224 @@ struct isl_tab_undo *isl_tab_snap(struct isl_tab *tab) /* Undo the operation performed by isl_tab_relax. */ -static void unrelax(struct isl_tab *tab, struct isl_tab_var *var) +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)) - to_row(tab, var, 1); + if (to_row(tab, var, 1) < 0) + return -1; - if (var->is_row) + 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]); - else { + 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][2 + var->index])) + 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][2 + var->index]); + tab->mat->row[i][off + var->index]); } } + + return 0; +} + +/* Undo the operation performed by isl_tab_unrestrict. + * + * In particular, mark the variable as being non-negative and make + * sure the sample value respects this constraint. + */ +static int ununrestrict(struct isl_tab *tab, struct isl_tab_var *var) +{ + var->is_nonneg = 1; + + if (var->is_row && restore_row(tab, var) < -1) + return -1; + + return 0; } -static void perform_undo(struct isl_tab *tab, struct isl_tab_undo *undo) +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) { - switch(undo->type) { - case isl_tab_undo_empty: - tab->empty = 0; - break; + struct isl_tab_var *var = var_from_index(tab, undo->u.var_index); + switch (undo->type) { case isl_tab_undo_nonneg: - undo->var->is_nonneg = 0; + var->is_nonneg = 0; break; case isl_tab_undo_redundant: - undo->var->is_redundant = 0; + 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: - undo->var->is_zero = 0; - tab->n_dead--; + var->is_zero = 0; + if (!var->is_row) + tab->n_dead--; break; case isl_tab_undo_allocate: - if (!undo->var->is_row) { - if (!max_is_manifestly_unbounded(tab, undo->var)) - to_row(tab, undo->var, 1); - else if (!min_is_manifestly_unbounded(tab, undo->var)) - to_row(tab, undo->var, -1); - else - to_row(tab, undo->var, 0); + 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); + case isl_tab_undo_unrestrict: + return ununrestrict(tab, var); + default: + isl_die(tab->mat->ctx, isl_error_internal, + "perform_undo_var called on invalid undo record", + return -1); + } + + return 0; +} + +/* Restore the tableau to the state where the basic variables + * are those in "col_var". + * We first construct a list of variables that are currently in + * the basis, but shouldn't. Then we iterate over all variables + * that should be in the basis and for each one that is currently + * not in the basis, we exchange it with one of the elements of the + * list constructed before. + * We can always find an appropriate variable to pivot with because + * the current basis is mapped to the old basis by a non-singular + * matrix and so we can never end up with a zero row. + */ +static int restore_basis(struct isl_tab *tab, int *col_var) +{ + int i, j; + int n_extra = 0; + int *extra = NULL; /* current columns that contain bad stuff */ + unsigned off = 2 + tab->M; + + extra = isl_alloc_array(tab->mat->ctx, int, tab->n_col); + if (!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); } - drop_row(tab, undo->var->index); + 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: - unrelax(tab, undo->var); + case isl_tab_undo_unrestrict: + return perform_undo_var(tab, undo); + case isl_tab_undo_bmap_eq: + return isl_basic_map_free_equality(tab->bmap, 1); + case isl_tab_undo_bmap_ineq: + return isl_basic_map_free_inequality(tab->bmap, 1); + case isl_tab_undo_bmap_div: + if (isl_basic_map_free_div(tab->bmap, 1) < 0) + return -1; + if (tab->samples) + tab->samples->n_col--; break; + case isl_tab_undo_saved_basis: + if (restore_basis(tab, undo->u.col_var) < 0) + return -1; + break; + case isl_tab_undo_drop_sample: + tab->n_outside--; + break; + case isl_tab_undo_saved_samples: + drop_samples_since(tab, undo->u.n); + break; + case isl_tab_undo_callback: + return undo->u.callback->run(undo->u.callback); + default: + isl_assert(tab->mat->ctx, 0, return -1); } + return 0; } /* Return the tableau to the state it was in when the snapshot "snap" @@ -1708,8 +3283,13 @@ int isl_tab_rollback(struct isl_tab *tab, struct isl_tab_undo *snap) next = undo->next; if (undo == snap) break; - perform_undo(tab, undo); - free(undo); + 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; @@ -1724,32 +3304,36 @@ int isl_tab_rollback(struct isl_tab *tab, struct isl_tab_undo *snap) * 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 = -1 -r', with r' an inequality - * of the tableau, then the inequality is adjacent (but opposite) - * to the inequality r'. + * 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; - if (!isl_int_is_negone(tab->mat->row[row][1])) - return isl_ineq_separate; - pos = isl_seq_first_non_zero(tab->mat->row[row] + 2 + tab->n_dead, + pos = isl_seq_first_non_zero(tab->mat->row[row] + off + tab->n_dead, tab->n_col - tab->n_dead); - if (pos == -1) - return isl_ineq_adj_eq; + 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_is_negone(tab->mat->row[row][2 + tab->n_dead + pos])) + 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] + 2 + tab->n_dead + pos + 1, + 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; @@ -1773,41 +3357,87 @@ enum isl_ineq_type isl_tab_ineq_type(struct isl_tab *tab, isl_int *ineq) if (!tab) return isl_ineq_error; - if (extend_cons(tab, 1) < 0) + if (isl_tab_extend_cons(tab, 1) < 0) return isl_ineq_error; snap = isl_tab_snap(tab); - con = add_row(tab, ineq); + con = isl_tab_add_row(tab, ineq); if (con < 0) goto error; row = tab->con[con].index; - if (is_redundant(tab, row)) + 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]))) { - if (at_least_zero(tab, &tab->con[con])) + 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 if (tab->rational ? (sign_of_min(tab, &tab->con[con]) < 0) - : min_at_most_neg_one(tab, &tab->con[con])) - type = isl_ineq_cut; - else - type = isl_ineq_redundant; + } 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: - isl_tab_rollback(tab, snap); return isl_ineq_error; } -void isl_tab_dump(struct isl_tab *tab, FILE *out, int indent) +int isl_tab_track_bmap(struct isl_tab *tab, __isl_take isl_basic_map *bmap) +{ + bmap = isl_basic_map_cow(bmap); + if (!tab || !bmap) + goto error; + + if (tab->empty) { + bmap = isl_basic_map_set_to_empty(bmap); + if (!bmap) + goto error; + tab->bmap = bmap; + return 0; + } + + isl_assert(tab->mat->ctx, tab->n_eq == bmap->n_eq, goto error); + isl_assert(tab->mat->ctx, + tab->n_con == bmap->n_eq + bmap->n_ineq, goto error); + + tab->bmap = bmap; + + return 0; +error: + isl_basic_map_free(bmap); + return -1; +} + +int isl_tab_track_bset(struct isl_tab *tab, __isl_take isl_basic_set *bset) +{ + return isl_tab_track_bmap(tab, (isl_basic_map *)bset); +} + +__isl_keep isl_basic_set *isl_tab_peek_bset(struct isl_tab *tab) +{ + if (!tab) + return NULL; + + return (isl_basic_set *)tab->bmap; +} + +static void isl_tab_print_internal(__isl_keep struct isl_tab *tab, + FILE *out, int indent) { unsigned r, c; int i; @@ -1826,7 +3456,9 @@ void isl_tab_dump(struct isl_tab *tab, FILE *out, int indent) fprintf(out, "%*s[", indent, ""); for (i = 0; i < tab->n_var; ++i) { if (i) - fprintf(out, ", "); + 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]" : @@ -1845,10 +3477,21 @@ void isl_tab_dump(struct isl_tab *tab, FILE *out, int indent) fprintf(out, "]\n"); fprintf(out, "%*s[", indent, ""); for (i = 0; i < tab->n_row; ++i) { + const char *sign = ""; if (i) fprintf(out, ", "); - fprintf(out, "r%d: %d%s", i, tab->row_var[i], - var_from_row(tab, i)->is_nonneg ? " [>=0]" : ""); + 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, ""); @@ -1862,8 +3505,15 @@ void isl_tab_dump(struct isl_tab *tab, FILE *out, int indent) r = tab->mat->n_row; tab->mat->n_row = tab->n_row; c = tab->mat->n_col; - tab->mat->n_col = 2 + tab->n_col; - isl_mat_dump(tab->mat, out, indent); + 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); }