| /* |
| * Copyright 2008-2009 Katholieke Universiteit Leuven |
| * Copyright 2010 INRIA Saclay |
| * |
| * 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 |
| * and INRIA Saclay - Ile-de-France, Parc Club Orsay Universite, |
| * ZAC des vignes, 4 rue Jacques Monod, 91893 Orsay, France |
| */ |
| |
| #include <isl_ctx_private.h> |
| #include "isl_map_private.h" |
| #include <isl/seq.h> |
| #include "isl_tab.h" |
| #include "isl_sample.h" |
| #include <isl_mat_private.h> |
| #include <isl_aff_private.h> |
| #include <isl_options_private.h> |
| #include <isl_config.h> |
| |
| /* |
| * The implementation of parametric integer linear programming in this file |
| * was inspired by the paper "Parametric Integer Programming" and the |
| * report "Solving systems of affine (in)equalities" by Paul Feautrier |
| * (and others). |
| * |
| * The strategy used for obtaining a feasible solution is different |
| * from the one used in isl_tab.c. In particular, in isl_tab.c, |
| * upon finding a constraint that is not yet satisfied, we pivot |
| * in a row that increases the constant term of the row holding the |
| * constraint, making sure the sample solution remains feasible |
| * for all the constraints it already satisfied. |
| * Here, we always pivot in the row holding the constraint, |
| * choosing a column that induces the lexicographically smallest |
| * increment to the sample solution. |
| * |
| * By starting out from a sample value that is lexicographically |
| * smaller than any integer point in the problem space, the first |
| * feasible integer sample point we find will also be the lexicographically |
| * smallest. If all variables can be assumed to be non-negative, |
| * then the initial sample value may be chosen equal to zero. |
| * However, we will not make this assumption. Instead, we apply |
| * the "big parameter" trick. Any variable x is then not directly |
| * used in the tableau, but instead it is represented by another |
| * variable x' = M + x, where M is an arbitrarily large (positive) |
| * value. x' is therefore always non-negative, whatever the value of x. |
| * Taking as initial sample value x' = 0 corresponds to x = -M, |
| * which is always smaller than any possible value of x. |
| * |
| * The big parameter trick is used in the main tableau and |
| * also in the context tableau if isl_context_lex is used. |
| * In this case, each tableaus has its own big parameter. |
| * Before doing any real work, we check if all the parameters |
| * happen to be non-negative. If so, we drop the column corresponding |
| * to M from the initial context tableau. |
| * If isl_context_gbr is used, then the big parameter trick is only |
| * used in the main tableau. |
| */ |
| |
| struct isl_context; |
| struct isl_context_op { |
| /* detect nonnegative parameters in context and mark them in tab */ |
| struct isl_tab *(*detect_nonnegative_parameters)( |
| struct isl_context *context, struct isl_tab *tab); |
| /* return temporary reference to basic set representation of context */ |
| struct isl_basic_set *(*peek_basic_set)(struct isl_context *context); |
| /* return temporary reference to tableau representation of context */ |
| struct isl_tab *(*peek_tab)(struct isl_context *context); |
| /* add equality; check is 1 if eq may not be valid; |
| * update is 1 if we may want to call ineq_sign on context later. |
| */ |
| void (*add_eq)(struct isl_context *context, isl_int *eq, |
| int check, int update); |
| /* add inequality; check is 1 if ineq may not be valid; |
| * update is 1 if we may want to call ineq_sign on context later. |
| */ |
| void (*add_ineq)(struct isl_context *context, isl_int *ineq, |
| int check, int update); |
| /* check sign of ineq based on previous information. |
| * strict is 1 if saturation should be treated as a positive sign. |
| */ |
| enum isl_tab_row_sign (*ineq_sign)(struct isl_context *context, |
| isl_int *ineq, int strict); |
| /* check if inequality maintains feasibility */ |
| int (*test_ineq)(struct isl_context *context, isl_int *ineq); |
| /* return index of a div that corresponds to "div" */ |
| int (*get_div)(struct isl_context *context, struct isl_tab *tab, |
| struct isl_vec *div); |
| /* add div "div" to context and return non-negativity */ |
| int (*add_div)(struct isl_context *context, struct isl_vec *div); |
| int (*detect_equalities)(struct isl_context *context, |
| struct isl_tab *tab); |
| /* return row index of "best" split */ |
| int (*best_split)(struct isl_context *context, struct isl_tab *tab); |
| /* check if context has already been determined to be empty */ |
| int (*is_empty)(struct isl_context *context); |
| /* check if context is still usable */ |
| int (*is_ok)(struct isl_context *context); |
| /* save a copy/snapshot of context */ |
| void *(*save)(struct isl_context *context); |
| /* restore saved context */ |
| void (*restore)(struct isl_context *context, void *); |
| /* invalidate context */ |
| void (*invalidate)(struct isl_context *context); |
| /* free context */ |
| void (*free)(struct isl_context *context); |
| }; |
| |
| struct isl_context { |
| struct isl_context_op *op; |
| }; |
| |
| struct isl_context_lex { |
| struct isl_context context; |
| struct isl_tab *tab; |
| }; |
| |
| struct isl_partial_sol { |
| int level; |
| struct isl_basic_set *dom; |
| struct isl_mat *M; |
| |
| struct isl_partial_sol *next; |
| }; |
| |
| struct isl_sol; |
| struct isl_sol_callback { |
| struct isl_tab_callback callback; |
| struct isl_sol *sol; |
| }; |
| |
| /* isl_sol is an interface for constructing a solution to |
| * a parametric integer linear programming problem. |
| * Every time the algorithm reaches a state where a solution |
| * can be read off from the tableau (including cases where the tableau |
| * is empty), the function "add" is called on the isl_sol passed |
| * to find_solutions_main. |
| * |
| * The context tableau is owned by isl_sol and is updated incrementally. |
| * |
| * There are currently two implementations of this interface, |
| * isl_sol_map, which simply collects the solutions in an isl_map |
| * and (optionally) the parts of the context where there is no solution |
| * in an isl_set, and |
| * isl_sol_for, which calls a user-defined function for each part of |
| * the solution. |
| */ |
| struct isl_sol { |
| int error; |
| int rational; |
| int level; |
| int max; |
| int n_out; |
| struct isl_context *context; |
| struct isl_partial_sol *partial; |
| void (*add)(struct isl_sol *sol, |
| struct isl_basic_set *dom, struct isl_mat *M); |
| void (*add_empty)(struct isl_sol *sol, struct isl_basic_set *bset); |
| void (*free)(struct isl_sol *sol); |
| struct isl_sol_callback dec_level; |
| }; |
| |
| static void sol_free(struct isl_sol *sol) |
| { |
| struct isl_partial_sol *partial, *next; |
| if (!sol) |
| return; |
| for (partial = sol->partial; partial; partial = next) { |
| next = partial->next; |
| isl_basic_set_free(partial->dom); |
| isl_mat_free(partial->M); |
| free(partial); |
| } |
| sol->free(sol); |
| } |
| |
| /* Push a partial solution represented by a domain and mapping M |
| * onto the stack of partial solutions. |
| */ |
| static void sol_push_sol(struct isl_sol *sol, |
| struct isl_basic_set *dom, struct isl_mat *M) |
| { |
| struct isl_partial_sol *partial; |
| |
| if (sol->error || !dom) |
| goto error; |
| |
| partial = isl_alloc_type(dom->ctx, struct isl_partial_sol); |
| if (!partial) |
| goto error; |
| |
| partial->level = sol->level; |
| partial->dom = dom; |
| partial->M = M; |
| partial->next = sol->partial; |
| |
| sol->partial = partial; |
| |
| return; |
| error: |
| isl_basic_set_free(dom); |
| sol->error = 1; |
| } |
| |
| /* Pop one partial solution from the partial solution stack and |
| * pass it on to sol->add or sol->add_empty. |
| */ |
| static void sol_pop_one(struct isl_sol *sol) |
| { |
| struct isl_partial_sol *partial; |
| |
| partial = sol->partial; |
| sol->partial = partial->next; |
| |
| if (partial->M) |
| sol->add(sol, partial->dom, partial->M); |
| else |
| sol->add_empty(sol, partial->dom); |
| free(partial); |
| } |
| |
| /* Return a fresh copy of the domain represented by the context tableau. |
| */ |
| static struct isl_basic_set *sol_domain(struct isl_sol *sol) |
| { |
| struct isl_basic_set *bset; |
| |
| if (sol->error) |
| return NULL; |
| |
| bset = isl_basic_set_dup(sol->context->op->peek_basic_set(sol->context)); |
| bset = isl_basic_set_update_from_tab(bset, |
| sol->context->op->peek_tab(sol->context)); |
| |
| return bset; |
| } |
| |
| /* Check whether two partial solutions have the same mapping, where n_div |
| * is the number of divs that the two partial solutions have in common. |
| */ |
| static int same_solution(struct isl_partial_sol *s1, struct isl_partial_sol *s2, |
| unsigned n_div) |
| { |
| int i; |
| unsigned dim; |
| |
| if (!s1->M != !s2->M) |
| return 0; |
| if (!s1->M) |
| return 1; |
| |
| dim = isl_basic_set_total_dim(s1->dom) - s1->dom->n_div; |
| |
| for (i = 0; i < s1->M->n_row; ++i) { |
| if (isl_seq_first_non_zero(s1->M->row[i]+1+dim+n_div, |
| s1->M->n_col-1-dim-n_div) != -1) |
| return 0; |
| if (isl_seq_first_non_zero(s2->M->row[i]+1+dim+n_div, |
| s2->M->n_col-1-dim-n_div) != -1) |
| return 0; |
| if (!isl_seq_eq(s1->M->row[i], s2->M->row[i], 1+dim+n_div)) |
| return 0; |
| } |
| return 1; |
| } |
| |
| /* Pop all solutions from the partial solution stack that were pushed onto |
| * the stack at levels that are deeper than the current level. |
| * If the two topmost elements on the stack have the same level |
| * and represent the same solution, then their domains are combined. |
| * This combined domain is the same as the current context domain |
| * as sol_pop is called each time we move back to a higher level. |
| */ |
| static void sol_pop(struct isl_sol *sol) |
| { |
| struct isl_partial_sol *partial; |
| unsigned n_div; |
| |
| if (sol->error) |
| return; |
| |
| if (sol->level == 0) { |
| for (partial = sol->partial; partial; partial = sol->partial) |
| sol_pop_one(sol); |
| return; |
| } |
| |
| partial = sol->partial; |
| if (!partial) |
| return; |
| |
| if (partial->level <= sol->level) |
| return; |
| |
| if (partial->next && partial->next->level == partial->level) { |
| n_div = isl_basic_set_dim( |
| sol->context->op->peek_basic_set(sol->context), |
| isl_dim_div); |
| |
| if (!same_solution(partial, partial->next, n_div)) { |
| sol_pop_one(sol); |
| sol_pop_one(sol); |
| } else { |
| struct isl_basic_set *bset; |
| |
| bset = sol_domain(sol); |
| |
| isl_basic_set_free(partial->next->dom); |
| partial->next->dom = bset; |
| partial->next->level = sol->level; |
| |
| sol->partial = partial->next; |
| isl_basic_set_free(partial->dom); |
| isl_mat_free(partial->M); |
| free(partial); |
| } |
| } else |
| sol_pop_one(sol); |
| } |
| |
| static void sol_dec_level(struct isl_sol *sol) |
| { |
| if (sol->error) |
| return; |
| |
| sol->level--; |
| |
| sol_pop(sol); |
| } |
| |
| static int sol_dec_level_wrap(struct isl_tab_callback *cb) |
| { |
| struct isl_sol_callback *callback = (struct isl_sol_callback *)cb; |
| |
| sol_dec_level(callback->sol); |
| |
| return callback->sol->error ? -1 : 0; |
| } |
| |
| /* Move down to next level and push callback onto context tableau |
| * to decrease the level again when it gets rolled back across |
| * the current state. That is, dec_level will be called with |
| * the context tableau in the same state as it is when inc_level |
| * is called. |
| */ |
| static void sol_inc_level(struct isl_sol *sol) |
| { |
| struct isl_tab *tab; |
| |
| if (sol->error) |
| return; |
| |
| sol->level++; |
| tab = sol->context->op->peek_tab(sol->context); |
| if (isl_tab_push_callback(tab, &sol->dec_level.callback) < 0) |
| sol->error = 1; |
| } |
| |
| static void scale_rows(struct isl_mat *mat, isl_int m, int n_row) |
| { |
| int i; |
| |
| if (isl_int_is_one(m)) |
| return; |
| |
| for (i = 0; i < n_row; ++i) |
| isl_seq_scale(mat->row[i], mat->row[i], m, mat->n_col); |
| } |
| |
| /* Add the solution identified by the tableau and the context tableau. |
| * |
| * The layout of the variables is as follows. |
| * tab->n_var is equal to the total number of variables in the input |
| * map (including divs that were copied from the context) |
| * + the number of extra divs constructed |
| * Of these, the first tab->n_param and the last tab->n_div variables |
| * correspond to the variables in the context, i.e., |
| * tab->n_param + tab->n_div = context_tab->n_var |
| * tab->n_param is equal to the number of parameters and input |
| * dimensions in the input map |
| * tab->n_div is equal to the number of divs in the context |
| * |
| * If there is no solution, then call add_empty with a basic set |
| * that corresponds to the context tableau. (If add_empty is NULL, |
| * then do nothing). |
| * |
| * If there is a solution, then first construct a matrix that maps |
| * all dimensions of the context to the output variables, i.e., |
| * the output dimensions in the input map. |
| * The divs in the input map (if any) that do not correspond to any |
| * div in the context do not appear in the solution. |
| * The algorithm will make sure that they have an integer value, |
| * but these values themselves are of no interest. |
| * We have to be careful not to drop or rearrange any divs in the |
| * context because that would change the meaning of the matrix. |
| * |
| * To extract the value of the output variables, it should be noted |
| * that we always use a big parameter M in the main tableau and so |
| * the variable stored in this tableau is not an output variable x itself, but |
| * x' = M + x (in case of minimization) |
| * or |
| * x' = M - x (in case of maximization) |
| * If x' appears in a column, then its optimal value is zero, |
| * which means that the optimal value of x is an unbounded number |
| * (-M for minimization and M for maximization). |
| * We currently assume that the output dimensions in the original map |
| * are bounded, so this cannot occur. |
| * Similarly, when x' appears in a row, then the coefficient of M in that |
| * row is necessarily 1. |
| * If the row in the tableau represents |
| * d x' = c + d M + e(y) |
| * then, in case of minimization, the corresponding row in the matrix |
| * will be |
| * a c + a e(y) |
| * with a d = m, the (updated) common denominator of the matrix. |
| * In case of maximization, the row will be |
| * -a c - a e(y) |
| */ |
| static void sol_add(struct isl_sol *sol, struct isl_tab *tab) |
| { |
| struct isl_basic_set *bset = NULL; |
| struct isl_mat *mat = NULL; |
| unsigned off; |
| int row; |
| isl_int m; |
| |
| if (sol->error || !tab) |
| goto error; |
| |
| if (tab->empty && !sol->add_empty) |
| return; |
| |
| bset = sol_domain(sol); |
| |
| if (tab->empty) { |
| sol_push_sol(sol, bset, NULL); |
| return; |
| } |
| |
| off = 2 + tab->M; |
| |
| mat = isl_mat_alloc(tab->mat->ctx, 1 + sol->n_out, |
| 1 + tab->n_param + tab->n_div); |
| if (!mat) |
| goto error; |
| |
| isl_int_init(m); |
| |
| isl_seq_clr(mat->row[0] + 1, mat->n_col - 1); |
| isl_int_set_si(mat->row[0][0], 1); |
| for (row = 0; row < sol->n_out; ++row) { |
| int i = tab->n_param + row; |
| int r, j; |
| |
| isl_seq_clr(mat->row[1 + row], mat->n_col); |
| if (!tab->var[i].is_row) { |
| if (tab->M) |
| isl_die(mat->ctx, isl_error_invalid, |
| "unbounded optimum", goto error2); |
| continue; |
| } |
| |
| r = tab->var[i].index; |
| if (tab->M && |
| isl_int_ne(tab->mat->row[r][2], tab->mat->row[r][0])) |
| isl_die(mat->ctx, isl_error_invalid, |
| "unbounded optimum", goto error2); |
| isl_int_gcd(m, mat->row[0][0], tab->mat->row[r][0]); |
| isl_int_divexact(m, tab->mat->row[r][0], m); |
| scale_rows(mat, m, 1 + row); |
| isl_int_divexact(m, mat->row[0][0], tab->mat->row[r][0]); |
| isl_int_mul(mat->row[1 + row][0], m, tab->mat->row[r][1]); |
| for (j = 0; j < tab->n_param; ++j) { |
| int col; |
| if (tab->var[j].is_row) |
| continue; |
| col = tab->var[j].index; |
| isl_int_mul(mat->row[1 + row][1 + j], m, |
| tab->mat->row[r][off + col]); |
| } |
| for (j = 0; j < tab->n_div; ++j) { |
| int col; |
| if (tab->var[tab->n_var - tab->n_div+j].is_row) |
| continue; |
| col = tab->var[tab->n_var - tab->n_div+j].index; |
| isl_int_mul(mat->row[1 + row][1 + tab->n_param + j], m, |
| tab->mat->row[r][off + col]); |
| } |
| if (sol->max) |
| isl_seq_neg(mat->row[1 + row], mat->row[1 + row], |
| mat->n_col); |
| } |
| |
| isl_int_clear(m); |
| |
| sol_push_sol(sol, bset, mat); |
| return; |
| error2: |
| isl_int_clear(m); |
| error: |
| isl_basic_set_free(bset); |
| isl_mat_free(mat); |
| sol->error = 1; |
| } |
| |
| struct isl_sol_map { |
| struct isl_sol sol; |
| struct isl_map *map; |
| struct isl_set *empty; |
| }; |
| |
| static void sol_map_free(struct isl_sol_map *sol_map) |
| { |
| if (!sol_map) |
| return; |
| if (sol_map->sol.context) |
| sol_map->sol.context->op->free(sol_map->sol.context); |
| isl_map_free(sol_map->map); |
| isl_set_free(sol_map->empty); |
| free(sol_map); |
| } |
| |
| static void sol_map_free_wrap(struct isl_sol *sol) |
| { |
| sol_map_free((struct isl_sol_map *)sol); |
| } |
| |
| /* This function is called for parts of the context where there is |
| * no solution, with "bset" corresponding to the context tableau. |
| * Simply add the basic set to the set "empty". |
| */ |
| static void sol_map_add_empty(struct isl_sol_map *sol, |
| struct isl_basic_set *bset) |
| { |
| if (!bset) |
| goto error; |
| isl_assert(bset->ctx, sol->empty, goto error); |
| |
| sol->empty = isl_set_grow(sol->empty, 1); |
| bset = isl_basic_set_simplify(bset); |
| bset = isl_basic_set_finalize(bset); |
| sol->empty = isl_set_add_basic_set(sol->empty, isl_basic_set_copy(bset)); |
| if (!sol->empty) |
| goto error; |
| isl_basic_set_free(bset); |
| return; |
| error: |
| isl_basic_set_free(bset); |
| sol->sol.error = 1; |
| } |
| |
| static void sol_map_add_empty_wrap(struct isl_sol *sol, |
| struct isl_basic_set *bset) |
| { |
| sol_map_add_empty((struct isl_sol_map *)sol, bset); |
| } |
| |
| /* Given a basic map "dom" that represents the context and an affine |
| * matrix "M" that maps the dimensions of the context to the |
| * output variables, construct a basic map with the same parameters |
| * and divs as the context, the dimensions of the context as input |
| * dimensions and a number of output dimensions that is equal to |
| * the number of output dimensions in the input map. |
| * |
| * The constraints and divs of the context are simply copied |
| * from "dom". For each row |
| * x = c + e(y) |
| * an equality |
| * c + e(y) - d x = 0 |
| * is added, with d the common denominator of M. |
| */ |
| static void sol_map_add(struct isl_sol_map *sol, |
| struct isl_basic_set *dom, struct isl_mat *M) |
| { |
| int i; |
| struct isl_basic_map *bmap = NULL; |
| unsigned n_eq; |
| unsigned n_ineq; |
| unsigned nparam; |
| unsigned total; |
| unsigned n_div; |
| unsigned n_out; |
| |
| if (sol->sol.error || !dom || !M) |
| goto error; |
| |
| n_out = sol->sol.n_out; |
| n_eq = dom->n_eq + n_out; |
| n_ineq = dom->n_ineq; |
| n_div = dom->n_div; |
| nparam = isl_basic_set_total_dim(dom) - n_div; |
| total = isl_map_dim(sol->map, isl_dim_all); |
| bmap = isl_basic_map_alloc_space(isl_map_get_space(sol->map), |
| n_div, n_eq, 2 * n_div + n_ineq); |
| if (!bmap) |
| goto error; |
| if (sol->sol.rational) |
| ISL_F_SET(bmap, ISL_BASIC_MAP_RATIONAL); |
| for (i = 0; i < dom->n_div; ++i) { |
| int k = isl_basic_map_alloc_div(bmap); |
| if (k < 0) |
| goto error; |
| isl_seq_cpy(bmap->div[k], dom->div[i], 1 + 1 + nparam); |
| isl_seq_clr(bmap->div[k] + 1 + 1 + nparam, total - nparam); |
| isl_seq_cpy(bmap->div[k] + 1 + 1 + total, |
| dom->div[i] + 1 + 1 + nparam, i); |
| } |
| for (i = 0; i < dom->n_eq; ++i) { |
| int k = isl_basic_map_alloc_equality(bmap); |
| if (k < 0) |
| goto error; |
| isl_seq_cpy(bmap->eq[k], dom->eq[i], 1 + nparam); |
| isl_seq_clr(bmap->eq[k] + 1 + nparam, total - nparam); |
| isl_seq_cpy(bmap->eq[k] + 1 + total, |
| dom->eq[i] + 1 + nparam, n_div); |
| } |
| for (i = 0; i < dom->n_ineq; ++i) { |
| int k = isl_basic_map_alloc_inequality(bmap); |
| if (k < 0) |
| goto error; |
| isl_seq_cpy(bmap->ineq[k], dom->ineq[i], 1 + nparam); |
| isl_seq_clr(bmap->ineq[k] + 1 + nparam, total - nparam); |
| isl_seq_cpy(bmap->ineq[k] + 1 + total, |
| dom->ineq[i] + 1 + nparam, n_div); |
| } |
| for (i = 0; i < M->n_row - 1; ++i) { |
| int k = isl_basic_map_alloc_equality(bmap); |
| if (k < 0) |
| goto error; |
| isl_seq_cpy(bmap->eq[k], M->row[1 + i], 1 + nparam); |
| isl_seq_clr(bmap->eq[k] + 1 + nparam, n_out); |
| isl_int_neg(bmap->eq[k][1 + nparam + i], M->row[0][0]); |
| isl_seq_cpy(bmap->eq[k] + 1 + nparam + n_out, |
| M->row[1 + i] + 1 + nparam, n_div); |
| } |
| bmap = isl_basic_map_simplify(bmap); |
| bmap = isl_basic_map_finalize(bmap); |
| sol->map = isl_map_grow(sol->map, 1); |
| sol->map = isl_map_add_basic_map(sol->map, bmap); |
| isl_basic_set_free(dom); |
| isl_mat_free(M); |
| if (!sol->map) |
| sol->sol.error = 1; |
| return; |
| error: |
| isl_basic_set_free(dom); |
| isl_mat_free(M); |
| isl_basic_map_free(bmap); |
| sol->sol.error = 1; |
| } |
| |
| static void sol_map_add_wrap(struct isl_sol *sol, |
| struct isl_basic_set *dom, struct isl_mat *M) |
| { |
| sol_map_add((struct isl_sol_map *)sol, dom, M); |
| } |
| |
| |
| /* Store the "parametric constant" of row "row" of tableau "tab" in "line", |
| * i.e., the constant term and the coefficients of all variables that |
| * appear in the context tableau. |
| * Note that the coefficient of the big parameter M is NOT copied. |
| * The context tableau may not have a big parameter and even when it |
| * does, it is a different big parameter. |
| */ |
| static void get_row_parameter_line(struct isl_tab *tab, int row, isl_int *line) |
| { |
| int i; |
| unsigned off = 2 + tab->M; |
| |
| isl_int_set(line[0], tab->mat->row[row][1]); |
| for (i = 0; i < tab->n_param; ++i) { |
| if (tab->var[i].is_row) |
| isl_int_set_si(line[1 + i], 0); |
| else { |
| int col = tab->var[i].index; |
| isl_int_set(line[1 + i], tab->mat->row[row][off + col]); |
| } |
| } |
| for (i = 0; i < tab->n_div; ++i) { |
| if (tab->var[tab->n_var - tab->n_div + i].is_row) |
| isl_int_set_si(line[1 + tab->n_param + i], 0); |
| else { |
| int col = tab->var[tab->n_var - tab->n_div + i].index; |
| isl_int_set(line[1 + tab->n_param + i], |
| tab->mat->row[row][off + col]); |
| } |
| } |
| } |
| |
| /* Check if rows "row1" and "row2" have identical "parametric constants", |
| * as explained above. |
| * In this case, we also insist that the coefficients of the big parameter |
| * be the same as the values of the constants will only be the same |
| * if these coefficients are also the same. |
| */ |
| static int identical_parameter_line(struct isl_tab *tab, int row1, int row2) |
| { |
| int i; |
| unsigned off = 2 + tab->M; |
| |
| if (isl_int_ne(tab->mat->row[row1][1], tab->mat->row[row2][1])) |
| return 0; |
| |
| if (tab->M && isl_int_ne(tab->mat->row[row1][2], |
| tab->mat->row[row2][2])) |
| return 0; |
| |
| for (i = 0; i < tab->n_param + tab->n_div; ++i) { |
| int pos = i < tab->n_param ? i : |
| tab->n_var - tab->n_div + i - tab->n_param; |
| int col; |
| |
| if (tab->var[pos].is_row) |
| continue; |
| col = tab->var[pos].index; |
| if (isl_int_ne(tab->mat->row[row1][off + col], |
| tab->mat->row[row2][off + col])) |
| return 0; |
| } |
| return 1; |
| } |
| |
| /* Return an inequality that expresses that the "parametric constant" |
| * should be non-negative. |
| * This function is only called when the coefficient of the big parameter |
| * is equal to zero. |
| */ |
| static struct isl_vec *get_row_parameter_ineq(struct isl_tab *tab, int row) |
| { |
| struct isl_vec *ineq; |
| |
| ineq = isl_vec_alloc(tab->mat->ctx, 1 + tab->n_param + tab->n_div); |
| if (!ineq) |
| return NULL; |
| |
| get_row_parameter_line(tab, row, ineq->el); |
| if (ineq) |
| ineq = isl_vec_normalize(ineq); |
| |
| return ineq; |
| } |
| |
| /* Return a integer division for use in a parametric cut based on the given row. |
| * In particular, let the parametric constant of the row be |
| * |
| * \sum_i a_i y_i |
| * |
| * where y_0 = 1, but none of the y_i corresponds to the big parameter M. |
| * The div returned is equal to |
| * |
| * floor(\sum_i {-a_i} y_i) = floor((\sum_i (-a_i mod d) y_i)/d) |
| */ |
| static struct isl_vec *get_row_parameter_div(struct isl_tab *tab, int row) |
| { |
| struct isl_vec *div; |
| |
| div = isl_vec_alloc(tab->mat->ctx, 1 + 1 + tab->n_param + tab->n_div); |
| if (!div) |
| return NULL; |
| |
| isl_int_set(div->el[0], tab->mat->row[row][0]); |
| get_row_parameter_line(tab, row, div->el + 1); |
| div = isl_vec_normalize(div); |
| isl_seq_neg(div->el + 1, div->el + 1, div->size - 1); |
| isl_seq_fdiv_r(div->el + 1, div->el + 1, div->el[0], div->size - 1); |
| |
| return div; |
| } |
| |
| /* Return a integer division for use in transferring an integrality constraint |
| * to the context. |
| * In particular, let the parametric constant of the row be |
| * |
| * \sum_i a_i y_i |
| * |
| * where y_0 = 1, but none of the y_i corresponds to the big parameter M. |
| * The the returned div is equal to |
| * |
| * floor(\sum_i {a_i} y_i) = floor((\sum_i (a_i mod d) y_i)/d) |
| */ |
| static struct isl_vec *get_row_split_div(struct isl_tab *tab, int row) |
| { |
| struct isl_vec *div; |
| |
| div = isl_vec_alloc(tab->mat->ctx, 1 + 1 + tab->n_param + tab->n_div); |
| if (!div) |
| return NULL; |
| |
| isl_int_set(div->el[0], tab->mat->row[row][0]); |
| get_row_parameter_line(tab, row, div->el + 1); |
| div = isl_vec_normalize(div); |
| isl_seq_fdiv_r(div->el + 1, div->el + 1, div->el[0], div->size - 1); |
| |
| return div; |
| } |
| |
| /* 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_set *bset, unsigned div) |
| { |
| unsigned total; |
| unsigned div_pos; |
| struct isl_vec *ineq; |
| |
| if (!bset) |
| return NULL; |
| |
| total = isl_basic_set_total_dim(bset); |
| div_pos = 1 + total - bset->n_div + div; |
| |
| ineq = isl_vec_alloc(bset->ctx, 1 + total); |
| if (!ineq) |
| return NULL; |
| |
| isl_seq_cpy(ineq->el, bset->div[div] + 1, 1 + total); |
| isl_int_neg(ineq->el[div_pos], bset->div[div][0]); |
| return ineq; |
| } |
| |
| /* Given a row in the tableau and a div that was created |
| * using get_row_split_div and that has been constrained to equality, i.e., |
| * |
| * d = floor(\sum_i {a_i} y_i) = \sum_i {a_i} y_i |
| * |
| * replace the expression "\sum_i {a_i} y_i" in the row by d, |
| * i.e., we subtract "\sum_i {a_i} y_i" and add 1 d. |
| * The coefficients of the non-parameters in the tableau have been |
| * verified to be integral. We can therefore simply replace coefficient b |
| * by floor(b). For the coefficients of the parameters we have |
| * floor(a_i) = a_i - {a_i}, while for the other coefficients, we have |
| * floor(b) = b. |
| */ |
| static struct isl_tab *set_row_cst_to_div(struct isl_tab *tab, int row, int div) |
| { |
| isl_seq_fdiv_q(tab->mat->row[row] + 1, tab->mat->row[row] + 1, |
| tab->mat->row[row][0], 1 + tab->M + tab->n_col); |
| |
| isl_int_set_si(tab->mat->row[row][0], 1); |
| |
| if (tab->var[tab->n_var - tab->n_div + div].is_row) { |
| int drow = tab->var[tab->n_var - tab->n_div + div].index; |
| |
| isl_assert(tab->mat->ctx, |
| isl_int_is_one(tab->mat->row[drow][0]), goto error); |
| isl_seq_combine(tab->mat->row[row] + 1, |
| tab->mat->ctx->one, tab->mat->row[row] + 1, |
| tab->mat->ctx->one, tab->mat->row[drow] + 1, |
| 1 + tab->M + tab->n_col); |
| } else { |
| int dcol = tab->var[tab->n_var - tab->n_div + div].index; |
| |
| isl_int_add_ui(tab->mat->row[row][2 + tab->M + dcol], |
| tab->mat->row[row][2 + tab->M + dcol], 1); |
| } |
| |
| return tab; |
| error: |
| isl_tab_free(tab); |
| return NULL; |
| } |
| |
| /* Check if the (parametric) constant of the given row is obviously |
| * negative, meaning that we don't need to consult the context tableau. |
| * If there is a big parameter and its coefficient is non-zero, |
| * then this coefficient determines the outcome. |
| * Otherwise, we check whether the constant is negative and |
| * all non-zero coefficients of parameters are negative and |
| * belong to non-negative parameters. |
| */ |
| static int is_obviously_neg(struct isl_tab *tab, int row) |
| { |
| int i; |
| int col; |
| unsigned off = 2 + tab->M; |
| |
| 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; |
| } |
| |
| if (isl_int_is_nonneg(tab->mat->row[row][1])) |
| return 0; |
| for (i = 0; i < tab->n_param; ++i) { |
| /* Eliminated parameter */ |
| if (tab->var[i].is_row) |
| continue; |
| col = tab->var[i].index; |
| if (isl_int_is_zero(tab->mat->row[row][off + col])) |
| continue; |
| if (!tab->var[i].is_nonneg) |
| return 0; |
| if (isl_int_is_pos(tab->mat->row[row][off + col])) |
| return 0; |
| } |
| for (i = 0; i < tab->n_div; ++i) { |
| if (tab->var[tab->n_var - tab->n_div + i].is_row) |
| continue; |
| col = tab->var[tab->n_var - tab->n_div + i].index; |
| if (isl_int_is_zero(tab->mat->row[row][off + col])) |
| continue; |
| if (!tab->var[tab->n_var - tab->n_div + i].is_nonneg) |
| return 0; |
| if (isl_int_is_pos(tab->mat->row[row][off + col])) |
| return 0; |
| } |
| return 1; |
| } |
| |
| /* Check if the (parametric) constant of the given row is obviously |
| * non-negative, meaning that we don't need to consult the context tableau. |
| * If there is a big parameter and its coefficient is non-zero, |
| * then this coefficient determines the outcome. |
| * Otherwise, we check whether the constant is non-negative and |
| * all non-zero coefficients of parameters are positive and |
| * belong to non-negative parameters. |
| */ |
| static int is_obviously_nonneg(struct isl_tab *tab, int row) |
| { |
| int i; |
| int col; |
| unsigned off = 2 + tab->M; |
| |
| if (tab->M) { |
| if (isl_int_is_pos(tab->mat->row[row][2])) |
| return 1; |
| if (isl_int_is_neg(tab->mat->row[row][2])) |
| return 0; |
| } |
| |
| if (isl_int_is_neg(tab->mat->row[row][1])) |
| return 0; |
| for (i = 0; i < tab->n_param; ++i) { |
| /* Eliminated parameter */ |
| if (tab->var[i].is_row) |
| continue; |
| col = tab->var[i].index; |
| if (isl_int_is_zero(tab->mat->row[row][off + col])) |
| continue; |
| if (!tab->var[i].is_nonneg) |
| return 0; |
| if (isl_int_is_neg(tab->mat->row[row][off + col])) |
| return 0; |
| } |
| for (i = 0; i < tab->n_div; ++i) { |
| if (tab->var[tab->n_var - tab->n_div + i].is_row) |
| continue; |
| col = tab->var[tab->n_var - tab->n_div + i].index; |
| if (isl_int_is_zero(tab->mat->row[row][off + col])) |
| continue; |
| if (!tab->var[tab->n_var - tab->n_div + i].is_nonneg) |
| return 0; |
| if (isl_int_is_neg(tab->mat->row[row][off + col])) |
| return 0; |
| } |
| return 1; |
| } |
| |
| /* Given a row r and two columns, return the column that would |
| * lead to the lexicographically smallest increment in the sample |
| * solution when leaving the basis in favor of the row. |
| * Pivoting with column c will increment the sample value by a non-negative |
| * constant times a_{V,c}/a_{r,c}, with a_{V,c} the elements of column c |
| * corresponding to the non-parametric variables. |
| * If variable v appears in a column c_v, the a_{v,c} = 1 iff c = c_v, |
| * with all other entries in this virtual row equal to zero. |
| * If variable v appears in a row, then a_{v,c} is the element in column c |
| * of that row. |
| * |
| * Let v be the first variable with a_{v,c1}/a_{r,c1} != a_{v,c2}/a_{r,c2}. |
| * Then if a_{v,c1}/a_{r,c1} < a_{v,c2}/a_{r,c2}, i.e., |
| * a_{v,c2} a_{r,c1} - a_{v,c1} a_{r,c2} > 0, c1 results in the minimal |
| * increment. Otherwise, it's c2. |
| */ |
| static int lexmin_col_pair(struct isl_tab *tab, |
| int row, int col1, int col2, isl_int tmp) |
| { |
| int i; |
| isl_int *tr; |
| |
| tr = tab->mat->row[row] + 2 + tab->M; |
| |
| for (i = tab->n_param; i < tab->n_var - tab->n_div; ++i) { |
| int s1, s2; |
| isl_int *r; |
| |
| if (!tab->var[i].is_row) { |
| if (tab->var[i].index == col1) |
| return col2; |
| if (tab->var[i].index == col2) |
| return col1; |
| continue; |
| } |
| |
| if (tab->var[i].index == row) |
| continue; |
| |
| r = tab->mat->row[tab->var[i].index] + 2 + tab->M; |
| s1 = isl_int_sgn(r[col1]); |
| s2 = isl_int_sgn(r[col2]); |
| if (s1 == 0 && s2 == 0) |
| continue; |
| if (s1 < s2) |
| return col1; |
| if (s2 < s1) |
| return col2; |
| |
| isl_int_mul(tmp, r[col2], tr[col1]); |
| isl_int_submul(tmp, r[col1], tr[col2]); |
| if (isl_int_is_pos(tmp)) |
| return col1; |
| if (isl_int_is_neg(tmp)) |
| return col2; |
| } |
| return -1; |
| } |
| |
| /* Given a row in the tableau, find and return the column that would |
| * result in the lexicographically smallest, but positive, increment |
| * in the sample point. |
| * If there is no such column, then return tab->n_col. |
| * If anything goes wrong, return -1. |
| */ |
| static int lexmin_pivot_col(struct isl_tab *tab, int row) |
| { |
| int j; |
| int col = tab->n_col; |
| isl_int *tr; |
| isl_int tmp; |
| |
| tr = tab->mat->row[row] + 2 + tab->M; |
| |
| isl_int_init(tmp); |
| |
| for (j = tab->n_dead; j < tab->n_col; ++j) { |
| if (tab->col_var[j] >= 0 && |
| (tab->col_var[j] < tab->n_param || |
| tab->col_var[j] >= tab->n_var - tab->n_div)) |
| continue; |
| |
| if (!isl_int_is_pos(tr[j])) |
| continue; |
| |
| if (col == tab->n_col) |
| col = j; |
| else |
| col = lexmin_col_pair(tab, row, col, j, tmp); |
| isl_assert(tab->mat->ctx, col >= 0, goto error); |
| } |
| |
| isl_int_clear(tmp); |
| return col; |
| error: |
| isl_int_clear(tmp); |
| return -1; |
| } |
| |
| /* Return the first known violated constraint, i.e., a non-negative |
| * constraint that currently has an either obviously negative value |
| * or a previously determined to be negative value. |
| * |
| * If any constraint has a negative coefficient for the big parameter, |
| * if any, then we return one of these first. |
| */ |
| static int first_neg(struct isl_tab *tab) |
| { |
| int row; |
| |
| if (tab->M) |
| for (row = tab->n_redundant; row < tab->n_row; ++row) { |
| if (!isl_tab_var_from_row(tab, row)->is_nonneg) |
| continue; |
| if (!isl_int_is_neg(tab->mat->row[row][2])) |
| continue; |
| if (tab->row_sign) |
| tab->row_sign[row] = isl_tab_row_neg; |
| return row; |
| } |
| for (row = tab->n_redundant; row < tab->n_row; ++row) { |
| if (!isl_tab_var_from_row(tab, row)->is_nonneg) |
| continue; |
| if (tab->row_sign) { |
| if (tab->row_sign[row] == 0 && |
| is_obviously_neg(tab, row)) |
| tab->row_sign[row] = isl_tab_row_neg; |
| if (tab->row_sign[row] != isl_tab_row_neg) |
| continue; |
| } else if (!is_obviously_neg(tab, row)) |
| continue; |
| return row; |
| } |
| return -1; |
| } |
| |
| /* Check whether the invariant that all columns are lexico-positive |
| * is satisfied. This function is not called from the current code |
| * but is useful during debugging. |
| */ |
| static void check_lexpos(struct isl_tab *tab) __attribute__ ((unused)); |
| static void check_lexpos(struct isl_tab *tab) |
| { |
| unsigned off = 2 + tab->M; |
| int col; |
| int var; |
| int row; |
| |
| for (col = tab->n_dead; col < tab->n_col; ++col) { |
| if (tab->col_var[col] >= 0 && |
| (tab->col_var[col] < tab->n_param || |
| tab->col_var[col] >= tab->n_var - tab->n_div)) |
| continue; |
| for (var = tab->n_param; var < tab->n_var - tab->n_div; ++var) { |
| if (!tab->var[var].is_row) { |
| if (tab->var[var].index == col) |
| break; |
| else |
| continue; |
| } |
| row = tab->var[var].index; |
| if (isl_int_is_zero(tab->mat->row[row][off + col])) |
| continue; |
| if (isl_int_is_pos(tab->mat->row[row][off + col])) |
| break; |
| fprintf(stderr, "lexneg column %d (row %d)\n", |
| col, row); |
| } |
| if (var >= tab->n_var - tab->n_div) |
| fprintf(stderr, "zero column %d\n", col); |
| } |
| } |
| |
| /* Report to the caller that the given constraint is part of an encountered |
| * conflict. |
| */ |
| static int report_conflicting_constraint(struct isl_tab *tab, int con) |
| { |
| return tab->conflict(con, tab->conflict_user); |
| } |
| |
| /* Given a conflicting row in the tableau, report all constraints |
| * involved in the row to the caller. That is, the row itself |
| * (if represents a constraint) and all constraint columns with |
| * non-zero (and therefore negative) coefficient. |
| */ |
| static int report_conflict(struct isl_tab *tab, int row) |
| { |
| int j; |
| isl_int *tr; |
| |
| if (!tab->conflict) |
| return 0; |
| |
| if (tab->row_var[row] < 0 && |
| report_conflicting_constraint(tab, ~tab->row_var[row]) < 0) |
| return -1; |
| |
| tr = tab->mat->row[row] + 2 + tab->M; |
| |
| for (j = tab->n_dead; j < tab->n_col; ++j) { |
| if (tab->col_var[j] >= 0 && |
| (tab->col_var[j] < tab->n_param || |
| tab->col_var[j] >= tab->n_var - tab->n_div)) |
| continue; |
| |
| if (!isl_int_is_neg(tr[j])) |
| continue; |
| |
| if (tab->col_var[j] < 0 && |
| report_conflicting_constraint(tab, ~tab->col_var[j]) < 0) |
| return -1; |
| } |
| |
| return 0; |
| } |
| |
| /* Resolve all known or obviously violated constraints through pivoting. |
| * In particular, as long as we can find any violated constraint, we |
| * look for a pivoting column that would result in the lexicographically |
| * smallest increment in the sample point. If there is no such column |
| * then the tableau is infeasible. |
| */ |
| static int restore_lexmin(struct isl_tab *tab) WARN_UNUSED; |
| static int restore_lexmin(struct isl_tab *tab) |
| { |
| int row, col; |
| |
| if (!tab) |
| return -1; |
| if (tab->empty) |
| return 0; |
| while ((row = first_neg(tab)) != -1) { |
| col = lexmin_pivot_col(tab, row); |
| if (col >= tab->n_col) { |
| if (report_conflict(tab, row) < 0) |
| return -1; |
| if (isl_tab_mark_empty(tab) < 0) |
| return -1; |
| return 0; |
| } |
| if (col < 0) |
| return -1; |
| if (isl_tab_pivot(tab, row, col) < 0) |
| return -1; |
| } |
| return 0; |
| } |
| |
| /* Given a row that represents an equality, look for an appropriate |
| * pivoting column. |
| * In particular, if there are any non-zero coefficients among |
| * the non-parameter variables, then we take the last of these |
| * variables. Eliminating this variable in terms of the other |
| * variables and/or parameters does not influence the property |
| * that all column in the initial tableau are lexicographically |
| * positive. The row corresponding to the eliminated variable |
| * will only have non-zero entries below the diagonal of the |
| * initial tableau. That is, we transform |
| * |
| * I I |
| * 1 into a |
| * I I |
| * |
| * If there is no such non-parameter variable, then we are dealing with |
| * pure parameter equality and we pick any parameter with coefficient 1 or -1 |
| * for elimination. This will ensure that the eliminated parameter |
| * always has an integer value whenever all the other parameters are integral. |
| * If there is no such parameter then we return -1. |
| */ |
| static int last_var_col_or_int_par_col(struct isl_tab *tab, int row) |
| { |
| unsigned off = 2 + tab->M; |
| int i; |
| |
| for (i = tab->n_var - tab->n_div - 1; i >= 0 && i >= tab->n_param; --i) { |
| int col; |
| if (tab->var[i].is_row) |
| continue; |
| col = tab->var[i].index; |
| if (col <= tab->n_dead) |
| continue; |
| if (!isl_int_is_zero(tab->mat->row[row][off + col])) |
| return col; |
| } |
| for (i = tab->n_dead; i < tab->n_col; ++i) { |
| if (isl_int_is_one(tab->mat->row[row][off + i])) |
| return i; |
| if (isl_int_is_negone(tab->mat->row[row][off + i])) |
| return i; |
| } |
| return -1; |
| } |
| |
| /* Add an equality that is known to be valid to the tableau. |
| * We first check if we can eliminate a variable or a parameter. |
| * If not, we add the equality as two inequalities. |
| * In this case, the equality was a pure parameter equality and there |
| * is no need to resolve any constraint violations. |
| */ |
| static struct isl_tab *add_lexmin_valid_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 = last_var_col_or_int_par_col(tab, r); |
| if (i < 0) { |
| tab->con[r].is_nonneg = 1; |
| if (isl_tab_push_var(tab, isl_tab_undo_nonneg, &tab->con[r]) < 0) |
| goto error; |
| isl_seq_neg(eq, eq, 1 + tab->n_var); |
| r = isl_tab_add_row(tab, eq); |
| 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; |
| } else { |
| 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; |
| } |
| |
| /* Check if the given row is a pure constant. |
| */ |
| static int is_constant(struct isl_tab *tab, int row) |
| { |
| unsigned off = 2 + tab->M; |
| |
| 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 may or may not be valid to the tableau. |
| * If the resulting row is a pure constant, then it must be zero. |
| * Otherwise, the resulting tableau is empty. |
| * |
| * If the row is not a pure constant, then we add two inequalities, |
| * each time checking that they can be satisfied. |
| * In the end we try to use one of the two constraints to eliminate |
| * a column. |
| */ |
| static int add_lexmin_eq(struct isl_tab *tab, isl_int *eq) WARN_UNUSED; |
| static int add_lexmin_eq(struct isl_tab *tab, isl_int *eq) |
| { |
| int r1, r2; |
| int row; |
| struct isl_tab_undo *snap; |
| |
| if (!tab) |
| return -1; |
| snap = isl_tab_snap(tab); |
| r1 = isl_tab_add_row(tab, eq); |
| if (r1 < 0) |
| return -1; |
| tab->con[r1].is_nonneg = 1; |
| if (isl_tab_push_var(tab, isl_tab_undo_nonneg, &tab->con[r1]) < 0) |
| return -1; |
| |
| row = tab->con[r1].index; |
| if (is_constant(tab, row)) { |
| if (!isl_int_is_zero(tab->mat->row[row][1]) || |
| (tab->M && !isl_int_is_zero(tab->mat->row[row][2]))) { |
| if (isl_tab_mark_empty(tab) < 0) |
| return -1; |
| return 0; |
| } |
| if (isl_tab_rollback(tab, snap) < 0) |
| return -1; |
| return 0; |
| } |
| |
| if (restore_lexmin(tab) < 0) |
| return -1; |
| if (tab->empty) |
| return 0; |
| |
| isl_seq_neg(eq, eq, 1 + tab->n_var); |
| |
| r2 = isl_tab_add_row(tab, eq); |
| if (r2 < 0) |
| return -1; |
| tab->con[r2].is_nonneg = 1; |
| if (isl_tab_push_var(tab, isl_tab_undo_nonneg, &tab->con[r2]) < 0) |
| return -1; |
| |
| if (restore_lexmin(tab) < 0) |
| return -1; |
| if (tab->empty) |
| return 0; |
| |
| if (!tab->con[r1].is_row) { |
| if (isl_tab_kill_col(tab, tab->con[r1].index) < 0) |
| return -1; |
| } else if (!tab->con[r2].is_row) { |
| if (isl_tab_kill_col(tab, tab->con[r2].index) < 0) |
| return -1; |
| } |
| |
| 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; |
| } |
| |
| return 0; |
| } |
| |
| /* Add an inequality to the tableau, resolving violations using |
| * restore_lexmin. |
| */ |
| static struct isl_tab *add_lexmin_ineq(struct isl_tab *tab, isl_int *ineq) |
| { |
| int r; |
| |
| if (!tab) |
| return NULL; |
| if (tab->bmap) { |
| tab->bmap = isl_basic_map_add_ineq(tab->bmap, ineq); |
| if (isl_tab_push(tab, isl_tab_undo_bmap_ineq) < 0) |
| goto error; |
| if (!tab->bmap) |
| goto error; |
| } |
| r = isl_tab_add_row(tab, ineq); |
| 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; |
| if (isl_tab_row_is_redundant(tab, tab->con[r].index)) { |
| if (isl_tab_mark_redundant(tab, tab->con[r].index) < 0) |
| goto error; |
| return tab; |
| } |
| |
| if (restore_lexmin(tab) < 0) |
| goto error; |
| if (!tab->empty && 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) |
| goto error; |
| return tab; |
| error: |
| isl_tab_free(tab); |
| return NULL; |
| } |
| |
| /* Check if the coefficients of the parameters are all integral. |
| */ |
| static int integer_parameter(struct isl_tab *tab, int row) |
| { |
| int i; |
| int col; |
| unsigned off = 2 + tab->M; |
| |
| for (i = 0; i < tab->n_param; ++i) { |
| /* Eliminated parameter */ |
| if (tab->var[i].is_row) |
| continue; |
| col = tab->var[i].index; |
| if (!isl_int_is_divisible_by(tab->mat->row[row][off + col], |
| tab->mat->row[row][0])) |
| return 0; |
| } |
| for (i = 0; i < tab->n_div; ++i) { |
| if (tab->var[tab->n_var - tab->n_div + i].is_row) |
| continue; |
| col = tab->var[tab->n_var - tab->n_div + i].index; |
| if (!isl_int_is_divisible_by(tab->mat->row[row][off + col], |
| tab->mat->row[row][0])) |
| return 0; |
| } |
| return 1; |
| } |
| |
| /* Check if the coefficients of the non-parameter variables are all integral. |
| */ |
| static int integer_variable(struct isl_tab *tab, int row) |
| { |
| int i; |
| unsigned off = 2 + tab->M; |
| |
| for (i = tab->n_dead; i < tab->n_col; ++i) { |
| if (tab->col_var[i] >= 0 && |
| (tab->col_var[i] < tab->n_param || |
| tab->col_var[i] >= tab->n_var - tab->n_div)) |
| continue; |
| if (!isl_int_is_divisible_by(tab->mat->row[row][off + i], |
| tab->mat->row[row][0])) |
| return 0; |
| } |
| return 1; |
| } |
| |
| /* Check if the constant term is integral. |
| */ |
| static int integer_constant(struct isl_tab *tab, int row) |
| { |
| return isl_int_is_divisible_by(tab->mat->row[row][1], |
| tab->mat->row[row][0]); |
| } |
| |
| #define I_CST 1 << 0 |
| #define I_PAR 1 << 1 |
| #define I_VAR 1 << 2 |
| |
| /* Check for next (non-parameter) variable after "var" (first if var == -1) |
| * that is non-integer and therefore requires a cut and return |
| * the index of the variable. |
| * For parametric tableaus, there are three parts in a row, |
| * the constant, the coefficients of the parameters and the rest. |
| * For each part, we check whether the coefficients in that part |
| * are all integral and if so, set the corresponding flag in *f. |
| * If the constant and the parameter part are integral, then the |
| * current sample value is integral and no cut is required |
| * (irrespective of whether the variable part is integral). |
| */ |
| static int next_non_integer_var(struct isl_tab *tab, int var, int *f) |
| { |
| var = var < 0 ? tab->n_param : var + 1; |
| |
| for (; var < tab->n_var - tab->n_div; ++var) { |
| int flags = 0; |
| int row; |
| if (!tab->var[var].is_row) |
| continue; |
| row = tab->var[var].index; |
| if (integer_constant(tab, row)) |
| ISL_FL_SET(flags, I_CST); |
| if (integer_parameter(tab, row)) |
| ISL_FL_SET(flags, I_PAR); |
| if (ISL_FL_ISSET(flags, I_CST) && ISL_FL_ISSET(flags, I_PAR)) |
| continue; |
| if (integer_variable(tab, row)) |
| ISL_FL_SET(flags, I_VAR); |
| *f = flags; |
| return var; |
| } |
| return -1; |
| } |
| |
| /* Check for first (non-parameter) variable that is non-integer and |
| * therefore requires a cut and return the corresponding row. |
| * For parametric tableaus, there are three parts in a row, |
| * the constant, the coefficients of the parameters and the rest. |
| * For each part, we check whether the coefficients in that part |
| * are all integral and if so, set the corresponding flag in *f. |
| * If the constant and the parameter part are integral, then the |
| * current sample value is integral and no cut is required |
| * (irrespective of whether the variable part is integral). |
| */ |
| static int first_non_integer_row(struct isl_tab *tab, int *f) |
| { |
| int var = next_non_integer_var(tab, -1, f); |
| |
| return var < 0 ? -1 : tab->var[var].index; |
| } |
| |
| /* Add a (non-parametric) cut to cut away the non-integral sample |
| * value of the given row. |
| * |
| * If the row is given by |
| * |
| * m r = f + \sum_i a_i y_i |
| * |
| * then the cut is |
| * |
| * c = - {-f/m} + \sum_i {a_i/m} y_i >= 0 |
| * |
| * The big parameter, if any, is ignored, since it is assumed to be big |
| * enough to be divisible by any integer. |
| * If the tableau is actually a parametric tableau, then this function |
| * is only called when all coefficients of the parameters are integral. |
| * The cut therefore has zero coefficients for the parameters. |
| * |
| * The current value is known to be negative, so row_sign, if it |
| * exists, is set accordingly. |
| * |
| * Return the row of the cut or -1. |
| */ |
| static int add_cut(struct isl_tab *tab, int row) |
| { |
| int i; |
| int r; |
| isl_int *r_row; |
| unsigned off = 2 + tab->M; |
| |
| if (isl_tab_extend_cons(tab, 1) < 0) |
| return -1; |
| r = isl_tab_allocate_con(tab); |
| if (r < 0) |
| return -1; |
| |
| r_row = tab->mat->row[tab->con[r].index]; |
| isl_int_set(r_row[0], tab->mat->row[row][0]); |
| isl_int_neg(r_row[1], tab->mat->row[row][1]); |
| isl_int_fdiv_r(r_row[1], r_row[1], tab->mat->row[row][0]); |
| isl_int_neg(r_row[1], r_row[1]); |
| if (tab->M) |
| isl_int_set_si(r_row[2], 0); |
| for (i = 0; i < tab->n_col; ++i) |
| isl_int_fdiv_r(r_row[off + i], |
| tab->mat->row[row][off + i], tab->mat->row[row][0]); |
| |
| tab->con[r].is_nonneg = 1; |
| if (isl_tab_push_var(tab, isl_tab_undo_nonneg, &tab->con[r]) < 0) |
| return -1; |
| if (tab->row_sign) |
| tab->row_sign[tab->con[r].index] = isl_tab_row_neg; |
| |
| return tab->con[r].index; |
| } |
| |
| /* Given a non-parametric tableau, add cuts until an integer |
| * sample point is obtained or until the tableau is determined |
| * to be integer infeasible. |
| * As long as there is any non-integer value in the sample point, |
| * we add appropriate cuts, if possible, for each of these |
| * non-integer values and then resolve the violated |
| * cut constraints using restore_lexmin. |
| * If one of the corresponding rows is equal to an integral |
| * combination of variables/constraints plus a non-integral constant, |
| * then there is no way to obtain an integer point and we return |
| * a tableau that is marked empty. |
| */ |
| static struct isl_tab *cut_to_integer_lexmin(struct isl_tab *tab) |
| { |
| int var; |
| int row; |
| int flags; |
| |
| if (!tab) |
| return NULL; |
| if (tab->empty) |
| return tab; |
| |
| while ((var = next_non_integer_var(tab, -1, &flags)) != -1) { |
| do { |
| if (ISL_FL_ISSET(flags, I_VAR)) { |
| if (isl_tab_mark_empty(tab) < 0) |
| goto error; |
| return tab; |
| } |
| row = tab->var[var].index; |
| row = add_cut(tab, row); |
| if (row < 0) |
| goto error; |
| } while ((var = next_non_integer_var(tab, var, &flags)) != -1); |
| if (restore_lexmin(tab) < 0) |
| goto error; |
| if (tab->empty) |
| break; |
| } |
| return tab; |
| error: |
| isl_tab_free(tab); |
| return NULL; |
| } |
| |
| /* Check whether all the currently active samples also satisfy the inequality |
| * "ineq" (treated as an equality if eq is set). |
| * Remove those samples that do not. |
| */ |
| static struct isl_tab *check_samples(struct isl_tab *tab, isl_int *ineq, int eq) |
| { |
| int i; |
| isl_int v; |
| |
| if (!tab) |
| return NULL; |
| |
| isl_assert(tab->mat->ctx, tab->bmap, goto error); |
| isl_assert(tab->mat->ctx, tab->samples, goto error); |
| isl_assert(tab->mat->ctx, tab->samples->n_col == 1 + tab->n_var, goto error); |
| |
| isl_int_init(v); |
| for (i = tab->n_outside; i < tab->n_sample; ++i) { |
| int sgn; |
| isl_seq_inner_product(ineq, tab->samples->row[i], |
| 1 + tab->n_var, &v); |
| sgn = isl_int_sgn(v); |
| if (eq ? (sgn == 0) : (sgn >= 0)) |
| continue; |
| tab = isl_tab_drop_sample(tab, i); |
| if (!tab) |
| break; |
| } |
| isl_int_clear(v); |
| |
| return tab; |
| error: |
| isl_tab_free(tab); |
| return NULL; |
| } |
| |
| /* Check whether the sample value of the tableau is finite, |
| * i.e., either the tableau does not use a big parameter, or |
| * all values of the variables are equal to the big parameter plus |
| * some constant. This constant is the actual sample value. |
| */ |
| static int sample_is_finite(struct isl_tab *tab) |
| { |
| int i; |
| |
| if (!tab->M) |
| return 1; |
| |
| for (i = 0; i < tab->n_var; ++i) { |
| int row; |
| if (!tab->var[i].is_row) |
| return 0; |
| row = tab->var[i].index; |
| if (isl_int_ne(tab->mat->row[row][0], tab->mat->row[row][2])) |
| return 0; |
| } |
| return 1; |
| } |
| |
| /* Check if the context tableau of sol has any integer points. |
| * Leave tab in empty state if no integer point can be found. |
| * If an integer point can be found and if moreover it is finite, |
| * then it is added to the list of sample values. |
| * |
| * This function is only called when none of the currently active sample |
| * values satisfies the most recently added constraint. |
| */ |
| static struct isl_tab *check_integer_feasible(struct isl_tab *tab) |
| { |
| struct isl_tab_undo *snap; |
| |
| if (!tab) |
| return NULL; |
| |
| snap = isl_tab_snap(tab); |
| if (isl_tab_push_basis(tab) < 0) |
| goto error; |
| |
| tab = cut_to_integer_lexmin(tab); |
| if (!tab) |
| goto error; |
| |
| if (!tab->empty && sample_is_finite(tab)) { |
| struct isl_vec *sample; |
| |
| sample = isl_tab_get_sample_value(tab); |
| |
| tab = isl_tab_add_sample(tab, sample); |
| } |
| |
| if (!tab->empty && isl_tab_rollback(tab, snap) < 0) |
| goto error; |
| |
| return tab; |
| error: |
| isl_tab_free(tab); |
| return NULL; |
| } |
| |
| /* Check if any of the currently active sample values satisfies |
| * the inequality "ineq" (an equality if eq is set). |
| */ |
| static int tab_has_valid_sample(struct isl_tab *tab, isl_int *ineq, int eq) |
| { |
| int i; |
| isl_int v; |
| |
| if (!tab) |
| return -1; |
| |
| isl_assert(tab->mat->ctx, tab->bmap, return -1); |
| isl_assert(tab->mat->ctx, tab->samples, return -1); |
| isl_assert(tab->mat->ctx, tab->samples->n_col == 1 + tab->n_var, return -1); |
| |
| isl_int_init(v); |
| for (i = tab->n_outside; i < tab->n_sample; ++i) { |
| int sgn; |
| isl_seq_inner_product(ineq, tab->samples->row[i], |
| 1 + tab->n_var, &v); |
| sgn = isl_int_sgn(v); |
| if (eq ? (sgn == 0) : (sgn >= 0)) |
| break; |
| } |
| isl_int_clear(v); |
| |
| return i < tab->n_sample; |
| } |
| |
| /* Add a div specified by "div" to the tableau "tab" and return |
| * 1 if the div is obviously non-negative. |
| */ |
| static int context_tab_add_div(struct isl_tab *tab, struct isl_vec *div, |
| int (*add_ineq)(void *user, isl_int *), void *user) |
| { |
| int i; |
| int r; |
| struct isl_mat *samples; |
| int nonneg; |
| |
| r = isl_tab_add_div(tab, div, add_ineq, user); |
| if (r < 0) |
| return -1; |
| nonneg = tab->var[r].is_nonneg; |
| tab->var[r].frozen = 1; |
| |
| samples = isl_mat_extend(tab->samples, |
| tab->n_sample, 1 + tab->n_var); |
| tab->samples = samples; |
| if (!samples) |
| return -1; |
| for (i = tab->n_outside; i < samples->n_row; ++i) { |
| isl_seq_inner_product(div->el + 1, samples->row[i], |
| div->size - 1, &samples->row[i][samples->n_col - 1]); |
| isl_int_fdiv_q(samples->row[i][samples->n_col - 1], |
| samples->row[i][samples->n_col - 1], div->el[0]); |
| } |
| |
| return nonneg; |
| } |
| |
| /* Add a div specified by "div" to both the main tableau and |
| * the context tableau. In case of the main tableau, we only |
| * need to add an extra div. In the context tableau, we also |
| * need to express the meaning of the div. |
| * Return the index of the div or -1 if anything went wrong. |
| */ |
| static int add_div(struct isl_tab *tab, struct isl_context *context, |
| struct isl_vec *div) |
| { |
| int r; |
| int nonneg; |
| |
| if ((nonneg = context->op->add_div(context, div)) < 0) |
| goto error; |
| |
| if (!context->op->is_ok(context)) |
| goto error; |
| |
| if (isl_tab_extend_vars(tab, 1) < 0) |
| goto error; |
| r = isl_tab_allocate_var(tab); |
| if (r < 0) |
| goto error; |
| if (nonneg) |
| tab->var[r].is_nonneg = 1; |
| tab->var[r].frozen = 1; |
| tab->n_div++; |
| |
| return tab->n_div - 1; |
| error: |
| context->op->invalidate(context); |
| return -1; |
| } |
| |
| static int find_div(struct isl_tab *tab, isl_int *div, isl_int denom) |
| { |
| int i; |
| unsigned total = isl_basic_map_total_dim(tab->bmap); |
| |
| for (i = 0; i < tab->bmap->n_div; ++i) { |
| if (isl_int_ne(tab->bmap->div[i][0], denom)) |
| continue; |
| if (!isl_seq_eq(tab->bmap->div[i] + 1, div, 1 + total)) |
| continue; |
| return i; |
| } |
| return -1; |
| } |
| |
| /* Return the index of a div that corresponds to "div". |
| * We first check if we already have such a div and if not, we create one. |
| */ |
| static int get_div(struct isl_tab *tab, struct isl_context *context, |
| struct isl_vec *div) |
| { |
| int d; |
| struct isl_tab *context_tab = context->op->peek_tab(context); |
| |
| if (!context_tab) |
| return -1; |
| |
| d = find_div(context_tab, div->el + 1, div->el[0]); |
| if (d != -1) |
| return d; |
| |
| return add_div(tab, context, div); |
| } |
| |
| /* Add a parametric cut to cut away the non-integral sample value |
| * of the give row. |
| * Let a_i be the coefficients of the constant term and the parameters |
| * and let b_i be the coefficients of the variables or constraints |
| * in basis of the tableau. |
| * Let q be the div q = floor(\sum_i {-a_i} y_i). |
| * |
| * The cut is expressed as |
| * |
| * c = \sum_i -{-a_i} y_i + \sum_i {b_i} x_i + q >= 0 |
| * |
| * If q did not already exist in the context tableau, then it is added first. |
| * If q is in a column of the main tableau then the "+ q" can be accomplished |
| * by setting the corresponding entry to the denominator of the constraint. |
| * If q happens to be in a row of the main tableau, then the corresponding |
| * row needs to be added instead (taking care of the denominators). |
| * Note that this is very unlikely, but perhaps not entirely impossible. |
| * |
| * The current value of the cut is known to be negative (or at least |
| * non-positive), so row_sign is set accordingly. |
| * |
| * Return the row of the cut or -1. |
| */ |
| static int add_parametric_cut(struct isl_tab *tab, int row, |
| struct isl_context *context) |
| { |
| struct isl_vec *div; |
| int d; |
| int i; |
| int r; |
| isl_int *r_row; |
| int col; |
| int n; |
| unsigned off = 2 + tab->M; |
| |
| if (!context) |
| return -1; |
| |
| div = get_row_parameter_div(tab, row); |
| if (!div) |
| return -1; |
| |
| n = tab->n_div; |
| d = context->op->get_div(context, tab, div); |
| if (d < 0) |
| return -1; |
| |
| if (isl_tab_extend_cons(tab, 1) < 0) |
| return -1; |
| r = isl_tab_allocate_con(tab); |
| if (r < 0) |
| return -1; |
| |
| r_row = tab->mat->row[tab->con[r].index]; |
| isl_int_set(r_row[0], tab->mat->row[row][0]); |
| isl_int_neg(r_row[1], tab->mat->row[row][1]); |
| isl_int_fdiv_r(r_row[1], r_row[1], tab->mat->row[row][0]); |
| isl_int_neg(r_row[1], r_row[1]); |
| if (tab->M) |
| isl_int_set_si(r_row[2], 0); |
| for (i = 0; i < tab->n_param; ++i) { |
| if (tab->var[i].is_row) |
| continue; |
| col = tab->var[i].index; |
| isl_int_neg(r_row[off + col], tab->mat->row[row][off + col]); |
| isl_int_fdiv_r(r_row[off + col], r_row[off + col], |
| tab->mat->row[row][0]); |
| isl_int_neg(r_row[off + col], r_row[off + col]); |
| } |
| for (i = 0; i < tab->n_div; ++i) { |
| if (tab->var[tab->n_var - tab->n_div + i].is_row) |
| continue; |
| col = tab->var[tab->n_var - tab->n_div + i].index; |
| isl_int_neg(r_row[off + col], tab->mat->row[row][off + col]); |
| isl_int_fdiv_r(r_row[off + col], r_row[off + col], |
| tab->mat->row[row][0]); |
| isl_int_neg(r_row[off + col], r_row[off + col]); |
| } |
| for (i = 0; i < tab->n_col; ++i) { |
| if (tab->col_var[i] >= 0 && |
| (tab->col_var[i] < tab->n_param || |
| tab->col_var[i] >= tab->n_var - tab->n_div)) |
| continue; |
| isl_int_fdiv_r(r_row[off + i], |
| tab->mat->row[row][off + i], tab->mat->row[row][0]); |
| } |
| if (tab->var[tab->n_var - tab->n_div + d].is_row) { |
| isl_int gcd; |
| int d_row = tab->var[tab->n_var - tab->n_div + d].index; |
| isl_int_init(gcd); |
| isl_int_gcd(gcd, tab->mat->row[d_row][0], r_row[0]); |
| isl_int_divexact(r_row[0], r_row[0], gcd); |
| isl_int_divexact(gcd, tab->mat->row[d_row][0], gcd); |
| isl_seq_combine(r_row + 1, gcd, r_row + 1, |
| r_row[0], tab->mat->row[d_row] + 1, |
| off - 1 + tab->n_col); |
| isl_int_mul(r_row[0], r_row[0], tab->mat->row[d_row][0]); |
| isl_int_clear(gcd); |
| } else { |
| col = tab->var[tab->n_var - tab->n_div + d].index; |
| isl_int_set(r_row[off + col], tab->mat->row[row][0]); |
| } |
| |
| tab->con[r].is_nonneg = 1; |
| if (isl_tab_push_var(tab, isl_tab_undo_nonneg, &tab->con[r]) < 0) |
| return -1; |
| if (tab->row_sign) |
| tab->row_sign[tab->con[r].index] = isl_tab_row_neg; |
| |
| isl_vec_free(div); |
| |
| row = tab->con[r].index; |
| |
| if (d >= n && context->op->detect_equalities(context, tab) < 0) |
| return -1; |
| |
| return row; |
| } |
| |
| /* Construct a tableau for bmap that can be used for computing |
| * the lexicographic minimum (or maximum) of bmap. |
| * If not NULL, then dom is the domain where the minimum |
| * should be computed. In this case, we set up a parametric |
| * tableau with row signs (initialized to "unknown"). |
| * If M is set, then the tableau will use a big parameter. |
| * If max is set, then a maximum should be computed instead of a minimum. |
| * This means that for each variable x, the tableau will contain the variable |
| * x' = M - x, rather than x' = M + x. This in turn means that the coefficient |
| * of the variables in all constraints are negated prior to adding them |
| * to the tableau. |
| */ |
| static struct isl_tab *tab_for_lexmin(struct isl_basic_map *bmap, |
| struct isl_basic_set *dom, unsigned M, int max) |
| { |
| int i; |
| struct isl_tab *tab; |
| |
| tab = isl_tab_alloc(bmap->ctx, 2 * bmap->n_eq + bmap->n_ineq + 1, |
| isl_basic_map_total_dim(bmap), M); |
| if (!tab) |
| return NULL; |
| |
| tab->rational = ISL_F_ISSET(bmap, ISL_BASIC_MAP_RATIONAL); |
| if (dom) { |
| tab->n_param = isl_basic_set_total_dim(dom) - dom->n_div; |
| tab->n_div = dom->n_div; |
| tab->row_sign = isl_calloc_array(bmap->ctx, |
| enum isl_tab_row_sign, tab->mat->n_row); |
| if (!tab->row_sign) |
| goto error; |
| } |
| if (ISL_F_ISSET(bmap, ISL_BASIC_MAP_EMPTY)) { |
| if (isl_tab_mark_empty(tab) < 0) |
| goto error; |
| return tab; |
| } |
| |
| for (i = tab->n_param; i < tab->n_var - tab->n_div; ++i) { |
| tab->var[i].is_nonneg = 1; |
| tab->var[i].frozen = 1; |
| } |
| for (i = 0; i < bmap->n_eq; ++i) { |
| if (max) |
| isl_seq_neg(bmap->eq[i] + 1 + tab->n_param, |
| bmap->eq[i] + 1 + tab->n_param, |
| tab->n_var - tab->n_param - tab->n_div); |
| tab = add_lexmin_valid_eq(tab, bmap->eq[i]); |
| if (max) |
| isl_seq_neg(bmap->eq[i] + 1 + tab->n_param, |
| bmap->eq[i] + 1 + tab->n_param, |
| tab->n_var - tab->n_param - tab->n_div); |
| if (!tab || tab->empty) |
| return tab; |
| } |
| if (bmap->n_eq && restore_lexmin(tab) < 0) |
| goto error; |
| for (i = 0; i < bmap->n_ineq; ++i) { |
| if (max) |
| isl_seq_neg(bmap->ineq[i] + 1 + tab->n_param, |
| bmap->ineq[i] + 1 + tab->n_param, |
| tab->n_var - tab->n_param - tab->n_div); |
| tab = add_lexmin_ineq(tab, bmap->ineq[i]); |
| if (max) |
| isl_seq_neg(bmap->ineq[i] + 1 + tab->n_param, |
| bmap->ineq[i] + 1 + tab->n_param, |
| tab->n_var - tab->n_param - tab->n_div); |
| if (!tab || tab->empty) |
| return tab; |
| } |
| return tab; |
| error: |
| isl_tab_free(tab); |
| return NULL; |
| } |
| |
| /* Given a main tableau where more than one row requires a split, |
| * determine and return the "best" row to split on. |
| * |
| * Given two rows in the main tableau, if the inequality corresponding |
| * to the first row is redundant with respect to that of the second row |
| * in the current tableau, then it is better to split on the second row, |
| * since in the positive part, both row will be positive. |
| * (In the negative part a pivot will have to be performed and just about |
| * anything can happen to the sign of the other row.) |
| * |
| * As a simple heuristic, we therefore select the row that makes the most |
| * of the other rows redundant. |
| * |
| * Perhaps it would also be useful to look at the number of constraints |
| * that conflict with any given constraint. |
| */ |
| static int best_split(struct isl_tab *tab, struct isl_tab *context_tab) |
| { |
| struct isl_tab_undo *snap; |
| int split; |
| int row; |
| int best = -1; |
| int best_r; |
| |
| if (isl_tab_extend_cons(context_tab, 2) < 0) |
| return -1; |
| |
| snap = isl_tab_snap(context_tab); |
| |
| for (split = tab->n_redundant; split < tab->n_row; ++split) { |
| struct isl_tab_undo *snap2; |
| struct isl_vec *ineq = NULL; |
| int r = 0; |
| int ok; |
| |
| if (!isl_tab_var_from_row(tab, split)->is_nonneg) |
| continue; |
| if (tab->row_sign[split] != isl_tab_row_any) |
| continue; |
| |
| ineq = get_row_parameter_ineq(tab, split); |
| if (!ineq) |
| return -1; |
| ok = isl_tab_add_ineq(context_tab, ineq->el) >= 0; |
| isl_vec_free(ineq); |
| if (!ok) |
| return -1; |
| |
| snap2 = isl_tab_snap(context_tab); |
| |
| for (row = tab->n_redundant; row < tab->n_row; ++row) { |
| struct isl_tab_var *var; |
| |
| if (row == split) |
| continue; |
| if (!isl_tab_var_from_row(tab, row)->is_nonneg) |
| continue; |
| if (tab->row_sign[row] != isl_tab_row_any) |
| continue; |
| |
| ineq = get_row_parameter_ineq(tab, row); |
| if (!ineq) |
| return -1; |
| ok = isl_tab_add_ineq(context_tab, ineq->el) >= 0; |
| isl_vec_free(ineq); |
| if (!ok) |
| return -1; |
| var = &context_tab->con[context_tab->n_con - 1]; |
| if (!context_tab->empty && |
| !isl_tab_min_at_most_neg_one(context_tab, var)) |
| r++; |
| if (isl_tab_rollback(context_tab, snap2) < 0) |
| return -1; |
| } |
| if (best == -1 || r > best_r) { |
| best = split; |
| best_r = r; |
| } |
| if (isl_tab_rollback(context_tab, snap) < 0) |
| return -1; |
| } |
| |
| return best; |
| } |
| |
| static struct isl_basic_set *context_lex_peek_basic_set( |
| struct isl_context *context) |
| { |
| struct isl_context_lex *clex = (struct isl_context_lex *)context; |
| if (!clex->tab) |
| return NULL; |
| return isl_tab_peek_bset(clex->tab); |
| } |
| |
| static struct isl_tab *context_lex_peek_tab(struct isl_context *context) |
| { |
| struct isl_context_lex *clex = (struct isl_context_lex *)context; |
| return clex->tab; |
| } |
| |
| static void context_lex_add_eq(struct isl_context *context, isl_int *eq, |
| int check, int update) |
| { |
| struct isl_context_lex *clex = (struct isl_context_lex *)context; |
| if (isl_tab_extend_cons(clex->tab, 2) < 0) |
| goto error; |
| if (add_lexmin_eq(clex->tab, eq) < 0) |
| goto error; |
| if (check) { |
| int v = tab_has_valid_sample(clex->tab, eq, 1); |
| if (v < 0) |
| goto error; |
| if (!v) |
| clex->tab = check_integer_feasible(clex->tab); |
| } |
| if (update) |
| clex->tab = check_samples(clex->tab, eq, 1); |
| return; |
| error: |
| isl_tab_free(clex->tab); |
| clex->tab = NULL; |
| } |
| |
| static void context_lex_add_ineq(struct isl_context *context, isl_int *ineq, |
| int check, int update) |
| { |
| struct isl_context_lex *clex = (struct isl_context_lex *)context; |
| if (isl_tab_extend_cons(clex->tab, 1) < 0) |
| goto error; |
| clex->tab = add_lexmin_ineq(clex->tab, ineq); |
| if (check) { |
| int v = tab_has_valid_sample(clex->tab, ineq, 0); |
| if (v < 0) |
| goto error; |
| if (!v) |
| clex->tab = check_integer_feasible(clex->tab); |
| } |
| if (update) |
| clex->tab = check_samples(clex->tab, ineq, 0); |
| return; |
| error: |
| isl_tab_free(clex->tab); |
| clex->tab = NULL; |
| } |
| |
| static int context_lex_add_ineq_wrap(void *user, isl_int *ineq) |
| { |
| struct isl_context *context = (struct isl_context *)user; |
| context_lex_add_ineq(context, ineq, 0, 0); |
| return context->op->is_ok(context) ? 0 : -1; |
| } |
| |
| /* Check which signs can be obtained by "ineq" on all the currently |
| * active sample values. See row_sign for more information. |
| */ |
| static enum isl_tab_row_sign tab_ineq_sign(struct isl_tab *tab, isl_int *ineq, |
| int strict) |
| { |
| int i; |
| int sgn; |
| isl_int tmp; |
| enum isl_tab_row_sign res = isl_tab_row_unknown; |
| |
| isl_assert(tab->mat->ctx, tab->samples, return isl_tab_row_unknown); |
| isl_assert(tab->mat->ctx, tab->samples->n_col == 1 + tab->n_var, |
| return isl_tab_row_unknown); |
| |
| isl_int_init(tmp); |
| for (i = tab->n_outside; i < tab->n_sample; ++i) { |
| isl_seq_inner_product(tab->samples->row[i], ineq, |
| 1 + tab->n_var, &tmp); |
| sgn = isl_int_sgn(tmp); |
| if (sgn > 0 || (sgn == 0 && strict)) { |
| if (res == isl_tab_row_unknown) |
| res = isl_tab_row_pos; |
| if (res == isl_tab_row_neg) |
| res = isl_tab_row_any; |
| } |
| if (sgn < 0) { |
| if (res == isl_tab_row_unknown) |
| res = isl_tab_row_neg; |
| if (res == isl_tab_row_pos) |
| res = isl_tab_row_any; |
| } |
| if (res == isl_tab_row_any) |
| break; |
| } |
| isl_int_clear(tmp); |
| |
| return res; |
| } |
| |
| static enum isl_tab_row_sign context_lex_ineq_sign(struct isl_context *context, |
| isl_int *ineq, int strict) |
| { |
| struct isl_context_lex *clex = (struct isl_context_lex *)context; |
| return tab_ineq_sign(clex->tab, ineq, strict); |
| } |
| |
| /* Check whether "ineq" can be added to the tableau without rendering |
| * it infeasible. |
| */ |
| static int context_lex_test_ineq(struct isl_context *context, isl_int *ineq) |
| { |
| struct isl_context_lex *clex = (struct isl_context_lex *)context; |
| struct isl_tab_undo *snap; |
| int feasible; |
| |
| if (!clex->tab) |
| return -1; |
| |
| if (isl_tab_extend_cons(clex->tab, 1) < 0) |
| return -1; |
| |
| snap = isl_tab_snap(clex->tab); |
| if (isl_tab_push_basis(clex->tab) < 0) |
| return -1; |
| clex->tab = add_lexmin_ineq(clex->tab, ineq); |
| clex->tab = check_integer_feasible(clex->tab); |
| if (!clex->tab) |
| return -1; |
| feasible = !clex->tab->empty; |
| if (isl_tab_rollback(clex->tab, snap) < 0) |
| return -1; |
| |
| return feasible; |
| } |
| |
| static int context_lex_get_div(struct isl_context *context, struct isl_tab *tab, |
| struct isl_vec *div) |
| { |
| return get_div(tab, context, div); |
| } |
| |
| /* Add a div specified by "div" to the context tableau and return |
| * 1 if the div is obviously non-negative. |
| * context_tab_add_div will always return 1, because all variables |
| * in a isl_context_lex tableau are non-negative. |
| * However, if we are using a big parameter in the context, then this only |
| * reflects the non-negativity of the variable used to _encode_ the |
| * div, i.e., div' = M + div, so we can't draw any conclusions. |
| */ |
| static int context_lex_add_div(struct isl_context *context, struct isl_vec *div) |
| { |
| struct isl_context_lex *clex = (struct isl_context_lex *)context; |
| int nonneg; |
| nonneg = context_tab_add_div(clex->tab, div, |
| context_lex_add_ineq_wrap, context); |
| if (nonneg < 0) |
| return -1; |
| if (clex->tab->M) |
| return 0; |
| return nonneg; |
| } |
| |
| static int context_lex_detect_equalities(struct isl_context *context, |
| struct isl_tab *tab) |
| { |
| return 0; |
| } |
| |
| static int context_lex_best_split(struct isl_context *context, |
| struct isl_tab *tab) |
| { |
| struct isl_context_lex *clex = (struct isl_context_lex *)context; |
| struct isl_tab_undo *snap; |
| int r; |
| |
| snap = isl_tab_snap(clex->tab); |
| if (isl_tab_push_basis(clex->tab) < 0) |
| return -1; |
| r = best_split(tab, clex->tab); |
| |
| if (r >= 0 && isl_tab_rollback(clex->tab, snap) < 0) |
| return -1; |
| |
| return r; |
| } |
| |
| static int context_lex_is_empty(struct isl_context *context) |
| { |
| struct isl_context_lex *clex = (struct isl_context_lex *)context; |
| if (!clex->tab) |
| return -1; |
| return clex->tab->empty; |
| } |
| |
| static void *context_lex_save(struct isl_context *context) |
| { |
| struct isl_context_lex *clex = (struct isl_context_lex *)context; |
| struct isl_tab_undo *snap; |
| |
| snap = isl_tab_snap(clex->tab); |
| if (isl_tab_push_basis(clex->tab) < 0) |
| return NULL; |
| if (isl_tab_save_samples(clex->tab) < 0) |
| return NULL; |
| |
| return snap; |
| } |
| |
| static void context_lex_restore(struct isl_context *context, void *save) |
| { |
| struct isl_context_lex *clex = (struct isl_context_lex *)context; |
| if (isl_tab_rollback(clex->tab, (struct isl_tab_undo *)save) < 0) { |
| isl_tab_free(clex->tab); |
| clex->tab = NULL; |
| } |
| } |
| |
| static int context_lex_is_ok(struct isl_context *context) |
| { |
| struct isl_context_lex *clex = (struct isl_context_lex *)context; |
| return !!clex->tab; |
| } |
| |
| /* For each variable in the context tableau, check if the variable can |
| * only attain non-negative values. If so, mark the parameter as non-negative |
| * in the main tableau. This allows for a more direct identification of some |
| * cases of violated constraints. |
| */ |
| static struct isl_tab *tab_detect_nonnegative_parameters(struct isl_tab *tab, |
| struct isl_tab *context_tab) |
| { |
| int i; |
| struct isl_tab_undo *snap; |
| struct isl_vec *ineq = NULL; |
| struct isl_tab_var *var; |
| int n; |
| |
| if (context_tab->n_var == 0) |
| return tab; |
| |
| ineq = isl_vec_alloc(tab->mat->ctx, 1 + context_tab->n_var); |
| if (!ineq) |
| goto error; |
| |
| if (isl_tab_extend_cons(context_tab, 1) < 0) |
| goto error; |
| |
| snap = isl_tab_snap(context_tab); |
| |
| n = 0; |
| isl_seq_clr(ineq->el, ineq->size); |
| for (i = 0; i < context_tab->n_var; ++i) { |
| isl_int_set_si(ineq->el[1 + i], 1); |
| if (isl_tab_add_ineq(context_tab, ineq->el) < 0) |
| goto error; |
| var = &context_tab->con[context_tab->n_con - 1]; |
| if (!context_tab->empty && |
| !isl_tab_min_at_most_neg_one(context_tab, var)) { |
| int j = i; |
| if (i >= tab->n_param) |
| j = i - tab->n_param + tab->n_var - tab->n_div; |
| tab->var[j].is_nonneg = 1; |
| n++; |
| } |
| isl_int_set_si(ineq->el[1 + i], 0); |
| if (isl_tab_rollback(context_tab, snap) < 0) |
| goto error; |
| } |
| |
| if (context_tab->M && n == context_tab->n_var) { |
| context_tab->mat = isl_mat_drop_cols(context_tab->mat, 2, 1); |
| context_tab->M = 0; |
| } |
| |
| isl_vec_free(ineq); |
| return tab; |
| error: |
| isl_vec_free(ineq); |
| isl_tab_free(tab); |
| return NULL; |
| } |
| |
| static struct isl_tab *context_lex_detect_nonnegative_parameters( |
| struct isl_context *context, struct isl_tab *tab) |
| { |
| struct isl_context_lex *clex = (struct isl_context_lex *)context; |
| struct isl_tab_undo *snap; |
| |
| if (!tab) |
| return NULL; |
| |
| snap = isl_tab_snap(clex->tab); |
| if (isl_tab_push_basis(clex->tab) < 0) |
| goto error; |
| |
| tab = tab_detect_nonnegative_parameters(tab, clex->tab); |
| |
| if (isl_tab_rollback(clex->tab, snap) < 0) |
| goto error; |
| |
| return tab; |
| error: |
| isl_tab_free(tab); |
| return NULL; |
| } |
| |
| static void context_lex_invalidate(struct isl_context *context) |
| { |
| struct isl_context_lex *clex = (struct isl_context_lex *)context; |
| isl_tab_free(clex->tab); |
| clex->tab = NULL; |
| } |
| |
| static void context_lex_free(struct isl_context *context) |
| { |
| struct isl_context_lex *clex = (struct isl_context_lex *)context; |
| isl_tab_free(clex->tab); |
| free(clex); |
| } |
| |
| struct isl_context_op isl_context_lex_op = { |
| context_lex_detect_nonnegative_parameters, |
| context_lex_peek_basic_set, |
| context_lex_peek_tab, |
| context_lex_add_eq, |
| context_lex_add_ineq, |
| context_lex_ineq_sign, |
| context_lex_test_ineq, |
| context_lex_get_div, |
| context_lex_add_div, |
| context_lex_detect_equalities, |
| context_lex_best_split, |
| context_lex_is_empty, |
| context_lex_is_ok, |
| context_lex_save, |
| context_lex_restore, |
| context_lex_invalidate, |
| context_lex_free, |
| }; |
| |
| static struct isl_tab *context_tab_for_lexmin(struct isl_basic_set *bset) |
| { |
| struct isl_tab *tab; |
| |
| bset = isl_basic_set_cow(bset); |
| if (!bset) |
| return NULL; |
| tab = tab_for_lexmin((struct isl_basic_map *)bset, NULL, 1, 0); |
| if (!tab) |
| goto error; |
| if (isl_tab_track_bset(tab, bset) < 0) |
| goto error; |
| tab = isl_tab_init_samples(tab); |
| return tab; |
| error: |
| isl_basic_set_free(bset); |
| return NULL; |
| } |
| |
| static struct isl_context *isl_context_lex_alloc(struct isl_basic_set *dom) |
| { |
| struct isl_context_lex *clex; |
| |
| if (!dom) |
| return NULL; |
| |
| clex = isl_alloc_type(dom->ctx, struct isl_context_lex); |
| if (!clex) |
| return NULL; |
| |
| clex->context.op = &isl_context_lex_op; |
| |
| clex->tab = context_tab_for_lexmin(isl_basic_set_copy(dom)); |
| if (restore_lexmin(clex->tab) < 0) |
| goto error; |
| clex->tab = check_integer_feasible(clex->tab); |
| if (!clex->tab) |
| goto error; |
| |
| return &clex->context; |
| error: |
| clex->context.op->free(&clex->context); |
| return NULL; |
| } |
| |
| struct isl_context_gbr { |
| struct isl_context context; |
| struct isl_tab *tab; |
| struct isl_tab *shifted; |
| struct isl_tab *cone; |
| }; |
| |
| static struct isl_tab *context_gbr_detect_nonnegative_parameters( |
| struct isl_context *context, struct isl_tab *tab) |
| { |
| struct isl_context_gbr *cgbr = (struct isl_context_gbr *)context; |
| if (!tab) |
| return NULL; |
| return tab_detect_nonnegative_parameters(tab, cgbr->tab); |
| } |
| |
| static struct isl_basic_set *context_gbr_peek_basic_set( |
| struct isl_context *context) |
| { |
| struct isl_context_gbr *cgbr = (struct isl_context_gbr *)context; |
| if (!cgbr->tab) |
| return NULL; |
| return isl_tab_peek_bset(cgbr->tab); |
| } |
| |
| static struct isl_tab *context_gbr_peek_tab(struct isl_context *context) |
| { |
| struct isl_context_gbr *cgbr = (struct isl_context_gbr *)context; |
| return cgbr->tab; |
| } |
| |
| /* Initialize the "shifted" tableau of the context, which |
| * contains the constraints of the original tableau shifted |
| * by the sum of all negative coefficients. This ensures |
| * that any rational point in the shifted tableau can |
| * be rounded up to yield an integer point in the original tableau. |
| */ |
| static void gbr_init_shifted(struct isl_context_gbr *cgbr) |
| { |
| int i, j; |
| struct isl_vec *cst; |
| struct isl_basic_set *bset = isl_tab_peek_bset(cgbr->tab); |
| unsigned dim = isl_basic_set_total_dim(bset); |
| |
| cst = isl_vec_alloc(cgbr->tab->mat->ctx, bset->n_ineq); |
| if (!cst) |
| return; |
| |
| for (i = 0; i < bset->n_ineq; ++i) { |
| isl_int_set(cst->el[i], bset->ineq[i][0]); |
| for (j = 0; j < dim; ++j) { |
| if (!isl_int_is_neg(bset->ineq[i][1 + j])) |
| continue; |
| isl_int_add(bset->ineq[i][0], bset->ineq[i][0], |
| bset->ineq[i][1 + j]); |
| } |
| } |
| |
| cgbr->shifted = isl_tab_from_basic_set(bset); |
| |
| for (i = 0; i < bset->n_ineq; ++i) |
| isl_int_set(bset->ineq[i][0], cst->el[i]); |
| |
| isl_vec_free(cst); |
| } |
| |
| /* Check if the shifted tableau is non-empty, and if so |
| * use the sample point to construct an integer point |
| * of the context tableau. |
| */ |
| static struct isl_vec *gbr_get_shifted_sample(struct isl_context_gbr *cgbr) |
| { |
| struct isl_vec *sample; |
| |
| if (!cgbr->shifted) |
| gbr_init_shifted(cgbr); |
| if (!cgbr->shifted) |
| return NULL; |
| if (cgbr->shifted->empty) |
| return isl_vec_alloc(cgbr->tab->mat->ctx, 0); |
| |
| sample = isl_tab_get_sample_value(cgbr->shifted); |
| sample = isl_vec_ceil(sample); |
| |
| return sample; |
| } |
| |
| static struct isl_basic_set *drop_constant_terms(struct isl_basic_set *bset) |
| { |
| int i; |
| |
| if (!bset) |
| return NULL; |
| |
| for (i = 0; i < bset->n_eq; ++i) |
| isl_int_set_si(bset->eq[i][0], 0); |
| |
| for (i = 0; i < bset->n_ineq; ++i) |
| isl_int_set_si(bset->ineq[i][0], 0); |
| |
| return bset; |
| } |
| |
| static int use_shifted(struct isl_context_gbr *cgbr) |
| { |
| return cgbr->tab->bmap->n_eq == 0 && cgbr->tab->bmap->n_div == 0; |
| } |
| |
| static struct isl_vec *gbr_get_sample(struct isl_context_gbr *cgbr) |
| { |
| struct isl_basic_set *bset; |
| struct isl_basic_set *cone; |
| |
| if (isl_tab_sample_is_integer(cgbr->tab)) |
| return isl_tab_get_sample_value(cgbr->tab); |
| |
| if (use_shifted(cgbr)) { |
| struct isl_vec *sample; |
| |
| sample = gbr_get_shifted_sample(cgbr); |
| if (!sample || sample->size > 0) |
| return sample; |
| |
| isl_vec_free(sample); |
| } |
| |
| if (!cgbr->cone) { |
| bset = isl_tab_peek_bset(cgbr->tab); |
| cgbr->cone = isl_tab_from_recession_cone(bset, 0); |
| if (!cgbr->cone) |
| return NULL; |
| if (isl_tab_track_bset(cgbr->cone, isl_basic_set_dup(bset)) < 0) |
| return NULL; |
| } |
| if (isl_tab_detect_implicit_equalities(cgbr->cone) < 0) |
| return NULL; |
| |
| if (cgbr->cone->n_dead == cgbr->cone->n_col) { |
| struct isl_vec *sample; |
| struct isl_tab_undo *snap; |
| |
| if (cgbr->tab->basis) { |
| if (cgbr->tab->basis->n_col != 1 + cgbr->tab->n_var) { |
| isl_mat_free(cgbr->tab->basis); |
| cgbr->tab->basis = NULL; |
| } |
| cgbr->tab->n_zero = 0; |
| cgbr->tab->n_unbounded = 0; |
| } |
| |
| snap = isl_tab_snap(cgbr->tab); |
| |
| sample = isl_tab_sample(cgbr->tab); |
| |
| if (isl_tab_rollback(cgbr->tab, snap) < 0) { |
| isl_vec_free(sample); |
| return NULL; |
| } |
| |
| return sample; |
| } |
| |
| cone = isl_basic_set_dup(isl_tab_peek_bset(cgbr->cone)); |
| cone = drop_constant_terms(cone); |
| cone = isl_basic_set_update_from_tab(cone, cgbr->cone); |
| cone = isl_basic_set_underlying_set(cone); |
| cone = isl_basic_set_gauss(cone, NULL); |
| |
| bset = isl_basic_set_dup(isl_tab_peek_bset(cgbr->tab)); |
| bset = isl_basic_set_update_from_tab(bset, cgbr->tab); |
| bset = isl_basic_set_underlying_set(bset); |
| bset = isl_basic_set_gauss(bset, NULL); |
| |
| return isl_basic_set_sample_with_cone(bset, cone); |
| } |
| |
| static void check_gbr_integer_feasible(struct isl_context_gbr *cgbr) |
| { |
| struct isl_vec *sample; |
| |
| if (!cgbr->tab) |
| return; |
| |
| if (cgbr->tab->empty) |
| return; |
| |
| sample = gbr_get_sample(cgbr); |
| if (!sample) |
| goto error; |
| |
| if (sample->size == 0) { |
| isl_vec_free(sample); |
| if (isl_tab_mark_empty(cgbr->tab) < 0) |
| goto error; |
| return; |
| } |
| |
| cgbr->tab = isl_tab_add_sample(cgbr->tab, sample); |
| |
| return; |
| error: |
| isl_tab_free(cgbr->tab); |
| cgbr->tab = NULL; |
| } |
| |
| static struct isl_tab *add_gbr_eq(struct isl_tab *tab, isl_int *eq) |
| { |
| if (!tab) |
| return NULL; |
| |
| if (isl_tab_extend_cons(tab, 2) < 0) |
| goto error; |
| |
| if (isl_tab_add_eq(tab, eq) < 0) |
| goto error; |
| |
| return tab; |
| error: |
| isl_tab_free(tab); |
| return NULL; |
| } |
| |
| static void context_gbr_add_eq(struct isl_context *context, isl_int *eq, |
| int check, int update) |
| { |
| struct isl_context_gbr *cgbr = (struct isl_context_gbr *)context; |
| |
| cgbr->tab = add_gbr_eq(cgbr->tab, eq); |
| |
| if (cgbr->cone && cgbr->cone->n_col != cgbr->cone->n_dead) { |
| if (isl_tab_extend_cons(cgbr->cone, 2) < 0) |
| goto error; |
| if (isl_tab_add_eq(cgbr->cone, eq) < 0) |
| goto error; |
| } |
| |
| if (check) { |
| int v = tab_has_valid_sample(cgbr->tab, eq, 1); |
| if (v < 0) |
| goto error; |
| if (!v) |
| check_gbr_integer_feasible(cgbr); |
| } |
| if (update) |
| cgbr->tab = check_samples(cgbr->tab, eq, 1); |
| return; |
| error: |
| isl_tab_free(cgbr->tab); |
| cgbr->tab = NULL; |
| } |
| |
| static void add_gbr_ineq(struct isl_context_gbr *cgbr, isl_int *ineq) |
| { |
| if (!cgbr->tab) |
| return; |
| |
| if (isl_tab_extend_cons(cgbr->tab, 1) < 0) |
| goto error; |
| |
| if (isl_tab_add_ineq(cgbr->tab, ineq) < 0) |
| goto error; |
| |
| if (cgbr->shifted && !cgbr->shifted->empty && use_shifted(cgbr)) { |
| int i; |
| unsigned dim; |
| dim = isl_basic_map_total_dim(cgbr->tab->bmap); |
| |
| if (isl_tab_extend_cons(cgbr->shifted, 1) < 0) |
| goto error; |
| |
| for (i = 0; i < dim; ++i) { |
| if (!isl_int_is_neg(ineq[1 + i])) |
| continue; |
| isl_int_add(ineq[0], ineq[0], ineq[1 + i]); |
| } |
| |
| if (isl_tab_add_ineq(cgbr->shifted, ineq) < 0) |
| goto error; |
| |
| for (i = 0; i < dim; ++i) { |
| if (!isl_int_is_neg(ineq[1 + i])) |
| continue; |
| isl_int_sub(ineq[0], ineq[0], ineq[1 + i]); |
| } |
| } |
| |
| if (cgbr->cone && cgbr->cone->n_col != cgbr->cone->n_dead) { |
| if (isl_tab_extend_cons(cgbr->cone, 1) < 0) |
| goto error; |
| if (isl_tab_add_ineq(cgbr->cone, ineq) < 0) |
| goto error; |
| } |
| |
| return; |
| error: |
| isl_tab_free(cgbr->tab); |
| cgbr->tab = NULL; |
| } |
| |
| static void context_gbr_add_ineq(struct isl_context *context, isl_int *ineq, |
| int check, int update) |
| { |
| struct isl_context_gbr *cgbr = (struct isl_context_gbr *)context; |
| |
| add_gbr_ineq(cgbr, ineq); |
| if (!cgbr->tab) |
| return; |
| |
| if (check) { |
| int v = tab_has_valid_sample(cgbr->tab, ineq, 0); |
| if (v < 0) |
| goto error; |
| if (!v) |
| check_gbr_integer_feasible(cgbr); |
| } |
| if (update) |
| cgbr->tab = check_samples(cgbr->tab, ineq, 0); |
| return; |
| error: |
| isl_tab_free(cgbr->tab); |
| cgbr->tab = NULL; |
| } |
| |
| static int context_gbr_add_ineq_wrap(void *user, isl_int *ineq) |
| { |
| struct isl_context *context = (struct isl_context *)user; |
| context_gbr_add_ineq(context, ineq, 0, 0); |
| return context->op->is_ok(context) ? 0 : -1; |
| } |
| |
| static enum isl_tab_row_sign context_gbr_ineq_sign(struct isl_context *context, |
| isl_int *ineq, int strict) |
| { |
| struct isl_context_gbr *cgbr = (struct isl_context_gbr *)context; |
| return tab_ineq_sign(cgbr->tab, ineq, strict); |
| } |
| |
| /* Check whether "ineq" can be added to the tableau without rendering |
| * it infeasible. |
| */ |
| static int context_gbr_test_ineq(struct isl_context *context, isl_int *ineq) |
| { |
| struct isl_context_gbr *cgbr = (struct isl_context_gbr *)context; |
| struct isl_tab_undo *snap; |
| struct isl_tab_undo *shifted_snap = NULL; |
| struct isl_tab_undo *cone_snap = NULL; |
| int feasible; |
| |
| if (!cgbr->tab) |
| return -1; |
| |
| if (isl_tab_extend_cons(cgbr->tab, 1) < 0) |
| return -1; |
| |
| snap = isl_tab_snap(cgbr->tab); |
| if (cgbr->shifted) |
| shifted_snap = isl_tab_snap(cgbr->shifted); |
| if (cgbr->cone) |
| cone_snap = isl_tab_snap(cgbr->cone); |
| add_gbr_ineq(cgbr, ineq); |
| check_gbr_integer_feasible(cgbr); |
| if (!cgbr->tab) |
| return -1; |
| feasible = !cgbr->tab->empty; |
| if (isl_tab_rollback(cgbr->tab, snap) < 0) |
| return -1; |
| if (shifted_snap) { |
| if (isl_tab_rollback(cgbr->shifted, shifted_snap)) |
| return -1; |
| } else if (cgbr->shifted) { |
| isl_tab_free(cgbr->shifted); |
| cgbr->shifted = NULL; |
| } |
| if (cone_snap) { |
| if (isl_tab_rollback(cgbr->cone, cone_snap)) |
| return -1; |
| } else if (cgbr->cone) { |
| isl_tab_free(cgbr->cone); |
| cgbr->cone = NULL; |
| } |
| |
| return feasible; |
| } |
| |
| /* Return the column of the last of the variables associated to |
| * a column that has a non-zero coefficient. |
| * This function is called in a context where only coefficients |
| * of parameters or divs can be non-zero. |
| */ |
| static int last_non_zero_var_col(struct isl_tab *tab, isl_int *p) |
| { |
| int i; |
| int col; |
| |
| if (tab->n_var == 0) |
| return -1; |
| |
| for (i = tab->n_var - 1; i >= 0; --i) { |
| if (i >= tab->n_param && i < tab->n_var - tab->n_div) |
| continue; |
| if (tab->var[i].is_row) |
| continue; |
| col = tab->var[i].index; |
| if (!isl_int_is_zero(p[col])) |
| return col; |
| } |
| |
| return -1; |
| } |
| |
| /* Look through all the recently added equalities in the context |
| * to see if we can propagate any of them to the main tableau. |
| * |
| * The newly added equalities in the context are encoded as pairs |
| * of inequalities starting at inequality "first". |
| * |
| * We tentatively add each of these equalities to the main tableau |
| * and if this happens to result in a row with a final coefficient |
| * that is one or negative one, we use it to kill a column |
| * in the main tableau. Otherwise, we discard the tentatively |
| * added row. |
| */ |
| static void propagate_equalities(struct isl_context_gbr *cgbr, |
| struct isl_tab *tab, unsigned first) |
| { |
| int i; |
| struct isl_vec *eq = NULL; |
| |
| eq = isl_vec_alloc(tab->mat->ctx, 1 + tab->n_var); |
| if (!eq) |
| goto error; |
| |
| if (isl_tab_extend_cons(tab, (cgbr->tab->bmap->n_ineq - first)/2) < 0) |
| goto error; |
| |
| isl_seq_clr(eq->el + 1 + tab->n_param, |
| tab->n_var - tab->n_param - tab->n_div); |
| for (i = first; i < cgbr->tab->bmap->n_ineq; i += 2) { |
| int j; |
| int r; |
| struct isl_tab_undo *snap; |
| snap = isl_tab_snap(tab); |
| |
| isl_seq_cpy(eq->el, cgbr->tab->bmap->ineq[i], 1 + tab->n_param); |
| isl_seq_cpy(eq->el + 1 + tab->n_var - tab->n_div, |
| cgbr->tab->bmap->ineq[i] + 1 + tab->n_param, |
| tab->n_div); |
| |
| r = isl_tab_add_row(tab, eq->el); |
| if (r < 0) |
| goto error; |
| r = tab->con[r].index; |
| j = last_non_zero_var_col(tab, tab->mat->row[r] + 2 + tab->M); |
| if (j < 0 || j < tab->n_dead || |
| !isl_int_is_one(tab->mat->row[r][0]) || |
| (!isl_int_is_one(tab->mat->row[r][2 + tab->M + j]) && |
| !isl_int_is_negone(tab->mat->row[r][2 + tab->M + j]))) { |
| if (isl_tab_rollback(tab, snap) < 0) |
| goto error; |
| continue; |
| } |
| if (isl_tab_pivot(tab, r, j) < 0) |
| goto error; |
| if (isl_tab_kill_col(tab, j) < 0) |
| goto error; |
| |
| if (restore_lexmin(tab) < 0) |
| goto error; |
| } |
| |
| isl_vec_free(eq); |
| |
| return; |
| error: |
| isl_vec_free(eq); |
| isl_tab_free(cgbr->tab); |
| cgbr->tab = NULL; |
| } |
| |
| static int context_gbr_detect_equalities(struct isl_context *context, |
| struct isl_tab *tab) |
| { |
| struct isl_context_gbr *cgbr = (struct isl_context_gbr *)context; |
| struct isl_ctx *ctx; |
| unsigned n_ineq; |
| |
| ctx = cgbr->tab->mat->ctx; |
| |
| if (!cgbr->cone) { |
| struct isl_basic_set *bset = isl_tab_peek_bset(cgbr->tab); |
| cgbr->cone = isl_tab_from_recession_cone(bset, 0); |
| if (!cgbr->cone) |
| goto error; |
| if (isl_tab_track_bset(cgbr->cone, isl_basic_set_dup(bset)) < 0) |
| goto error; |
| } |
| if (isl_tab_detect_implicit_equalities(cgbr->cone) < 0) |
| goto error; |
| |
| n_ineq = cgbr->tab->bmap->n_ineq; |
| cgbr->tab = isl_tab_detect_equalities(cgbr->tab, cgbr->cone); |
| if (cgbr->tab && cgbr->tab->bmap->n_ineq > n_ineq) |
| propagate_equalities(cgbr, tab, n_ineq); |
| |
| return 0; |
| error: |
| isl_tab_free(cgbr->tab); |
| cgbr->tab = NULL; |
| return -1; |
| } |
| |
| static int context_gbr_get_div(struct isl_context *context, struct isl_tab *tab, |
| struct isl_vec *div) |
| { |
| return get_div(tab, context, div); |
| } |
| |
| static int context_gbr_add_div(struct isl_context *context, struct isl_vec *div) |
| { |
| struct isl_context_gbr *cgbr = (struct isl_context_gbr *)context; |
| if (cgbr->cone) { |
| int k; |
| |
| if (isl_tab_extend_cons(cgbr->cone, 3) < 0) |
| return -1; |
| if (isl_tab_extend_vars(cgbr->cone, 1) < 0) |
| return -1; |
| if (isl_tab_allocate_var(cgbr->cone) <0) |
| return -1; |
| |
| cgbr->cone->bmap = isl_basic_map_extend_space(cgbr->cone->bmap, |
| isl_basic_map_get_space(cgbr->cone->bmap), 1, 0, 2); |
| k = isl_basic_map_alloc_div(cgbr->cone->bmap); |
| if (k < 0) |
| return -1; |
| isl_seq_cpy(cgbr->cone->bmap->div[k], div->el, div->size); |
| if (isl_tab_push(cgbr->cone, isl_tab_undo_bmap_div) < 0) |
| return -1; |
| } |
| return context_tab_add_div(cgbr->tab, div, |
| context_gbr_add_ineq_wrap, context); |
| } |
| |
| static int context_gbr_best_split(struct isl_context *context, |
| struct isl_tab *tab) |
| { |
| struct isl_context_gbr *cgbr = (struct isl_context_gbr *)context; |
| struct isl_tab_undo *snap; |
| int r; |
| |
| snap = isl_tab_snap(cgbr->tab); |
| r = best_split(tab, cgbr->tab); |
| |
| if (r >= 0 && isl_tab_rollback(cgbr->tab, snap) < 0) |
| return -1; |
| |
| return r; |
| } |
| |
| static int context_gbr_is_empty(struct isl_context *context) |
| { |
| struct isl_context_gbr *cgbr = (struct isl_context_gbr *)context; |
| if (!cgbr->tab) |
| return -1; |
| return cgbr->tab->empty; |
| } |
| |
| struct isl_gbr_tab_undo { |
| struct isl_tab_undo *tab_snap; |
| struct isl_tab_undo *shifted_snap; |
| struct isl_tab_undo *cone_snap; |
| }; |
| |
| static void *context_gbr_save(struct isl_context *context) |
| { |
| struct isl_context_gbr *cgbr = (struct isl_context_gbr *)context; |
| struct isl_gbr_tab_undo *snap; |
| |
| snap = isl_alloc_type(cgbr->tab->mat->ctx, struct isl_gbr_tab_undo); |
| if (!snap) |
| return NULL; |
| |
| snap->tab_snap = isl_tab_snap(cgbr->tab); |
| if (isl_tab_save_samples(cgbr->tab) < 0) |
| goto error; |
| |
| if (cgbr->shifted) |
| snap->shifted_snap = isl_tab_snap(cgbr->shifted); |
| else |
| snap->shifted_snap = NULL; |
| |
| if (cgbr->cone) |
| snap->cone_snap = isl_tab_snap(cgbr->cone); |
| else |
| snap->cone_snap = NULL; |
| |
| return snap; |
| error: |
| free(snap); |
| return NULL; |
| } |
| |
| static void context_gbr_restore(struct isl_context *context, void *save) |
| { |
| struct isl_context_gbr *cgbr = (struct isl_context_gbr *)context; |
| struct isl_gbr_tab_undo *snap = (struct isl_gbr_tab_undo *)save; |
| if (!snap) |
| goto error; |
| if (isl_tab_rollback(cgbr->tab, snap->tab_snap) < 0) { |
| isl_tab_free(cgbr->tab); |
| cgbr->tab = NULL; |
| } |
| |
| if (snap->shifted_snap) { |
| if (isl_tab_rollback(cgbr->shifted, snap->shifted_snap) < 0) |
| goto error; |
| } else if (cgbr->shifted) { |
| isl_tab_free(cgbr->shifted); |
| cgbr->shifted = NULL; |
| } |
| |
| if (snap->cone_snap) { |
| if (isl_tab_rollback(cgbr->cone, snap->cone_snap) < 0) |
| goto error; |
| } else if (cgbr->cone) { |
| isl_tab_free(cgbr->cone); |
| cgbr->cone = NULL; |
| } |
| |
| free(snap); |
| |
| return; |
| error: |
| free(snap); |
| isl_tab_free(cgbr->tab); |
| cgbr->tab = NULL; |
| } |
| |
| static int context_gbr_is_ok(struct isl_context *context) |
| { |
| struct isl_context_gbr *cgbr = (struct isl_context_gbr *)context; |
| return !!cgbr->tab; |
| } |
| |
| static void context_gbr_invalidate(struct isl_context *context) |
| { |
| struct isl_context_gbr *cgbr = (struct isl_context_gbr *)context; |
| isl_tab_free(cgbr->tab); |
| cgbr->tab = NULL; |
| } |
| |
| static void context_gbr_free(struct isl_context *context) |
| { |
| struct isl_context_gbr *cgbr = (struct isl_context_gbr *)context; |
| isl_tab_free(cgbr->tab); |
| isl_tab_free(cgbr->shifted); |
| isl_tab_free(cgbr->cone); |
| free(cgbr); |
| } |
| |
| struct isl_context_op isl_context_gbr_op = { |
| context_gbr_detect_nonnegative_parameters, |
| context_gbr_peek_basic_set, |
| context_gbr_peek_tab, |
| context_gbr_add_eq, |
| context_gbr_add_ineq, |
| context_gbr_ineq_sign, |
| context_gbr_test_ineq, |
| context_gbr_get_div, |
| context_gbr_add_div, |
| context_gbr_detect_equalities, |
| context_gbr_best_split, |
| context_gbr_is_empty, |
| context_gbr_is_ok, |
| context_gbr_save, |
| context_gbr_restore, |
| context_gbr_invalidate, |
| context_gbr_free, |
| }; |
| |
| static struct isl_context *isl_context_gbr_alloc(struct isl_basic_set *dom) |
| { |
| struct isl_context_gbr *cgbr; |
| |
| if (!dom) |
| return NULL; |
| |
| cgbr = isl_calloc_type(dom->ctx, struct isl_context_gbr); |
| if (!cgbr) |
| return NULL; |
| |
| cgbr->context.op = &isl_context_gbr_op; |
| |
| cgbr->shifted = NULL; |
| cgbr->cone = NULL; |
| cgbr->tab = isl_tab_from_basic_set(dom); |
| cgbr->tab = isl_tab_init_samples(cgbr->tab); |
| if (!cgbr->tab) |
| goto error; |
| if (isl_tab_track_bset(cgbr->tab, |
| isl_basic_set_cow(isl_basic_set_copy(dom))) < 0) |
| goto error; |
| check_gbr_integer_feasible(cgbr); |
| |
| return &cgbr->context; |
| error: |
| cgbr->context.op->free(&cgbr->context); |
| return NULL; |
| } |
| |
| static struct isl_context *isl_context_alloc(struct isl_basic_set *dom) |
| { |
| if (!dom) |
| return NULL; |
| |
| if (dom->ctx->opt->context == ISL_CONTEXT_LEXMIN) |
| return isl_context_lex_alloc(dom); |
| else |
| return isl_context_gbr_alloc(dom); |
| } |
| |
| /* Construct an isl_sol_map structure for accumulating the solution. |
| * If track_empty is set, then we also keep track of the parts |
| * of the context where there is no solution. |
| * If max is set, then we are solving a maximization, rather than |
| * a minimization problem, which means that the variables in the |
| * tableau have value "M - x" rather than "M + x". |
| */ |
| static struct isl_sol *sol_map_init(struct isl_basic_map *bmap, |
| struct isl_basic_set *dom, int track_empty, int max) |
| { |
| struct isl_sol_map *sol_map = NULL; |
| |
| if (!bmap) |
| goto error; |
| |
| sol_map = isl_calloc_type(bmap->ctx, struct isl_sol_map); |
| if (!sol_map) |
| goto error; |
| |
| sol_map->sol.rational = ISL_F_ISSET(bmap, ISL_BASIC_MAP_RATIONAL); |
| sol_map->sol.dec_level.callback.run = &sol_dec_level_wrap; |
| sol_map->sol.dec_level.sol = &sol_map->sol; |
| sol_map->sol.max = max; |
| sol_map->sol.n_out = isl_basic_map_dim(bmap, isl_dim_out); |
| sol_map->sol.add = &sol_map_add_wrap; |
| sol_map->sol.add_empty = track_empty ? &sol_map_add_empty_wrap : NULL; |
| sol_map->sol.free = &sol_map_free_wrap; |
| sol_map->map = isl_map_alloc_space(isl_basic_map_get_space(bmap), 1, |
| ISL_MAP_DISJOINT); |
| if (!sol_map->map) |
| goto error; |
| |
| sol_map->sol.context = isl_context_alloc(dom); |
| if (!sol_map->sol.context) |
| goto error; |
| |
| if (track_empty) { |
| sol_map->empty = isl_set_alloc_space(isl_basic_set_get_space(dom), |
| 1, ISL_SET_DISJOINT); |
| if (!sol_map->empty) |
| goto error; |
| } |
| |
| isl_basic_set_free(dom); |
| return &sol_map->sol; |
| error: |
| isl_basic_set_free(dom); |
| sol_map_free(sol_map); |
| return NULL; |
| } |
| |
| /* Check whether all coefficients of (non-parameter) variables |
| * are non-positive, meaning that no pivots can be performed on the row. |
| */ |
| static int is_critical(struct isl_tab *tab, int row) |
| { |
| int j; |
| unsigned off = 2 + tab->M; |
| |
| for (j = tab->n_dead; j < tab->n_col; ++j) { |
| if (tab->col_var[j] >= 0 && |
| (tab->col_var[j] < tab->n_param || |
| tab->col_var[j] >= tab->n_var - tab->n_div)) |
| continue; |
| |
| if (isl_int_is_pos(tab->mat->row[row][off + j])) |
| return 0; |
| } |
| |
| return 1; |
| } |
| |
| /* Check whether the inequality represented by vec is strict over the integers, |
| * i.e., there are no integer values satisfying the constraint with |
| * equality. This happens if the gcd of the coefficients is not a divisor |
| * of the constant term. If so, scale the constraint down by the gcd |
| * of the coefficients. |
| */ |
| static int is_strict(struct isl_vec *vec) |
| { |
| isl_int gcd; |
| int strict = 0; |
| |
| isl_int_init(gcd); |
| isl_seq_gcd(vec->el + 1, vec->size - 1, &gcd); |
| if (!isl_int_is_one(gcd)) { |
| strict = !isl_int_is_divisible_by(vec->el[0], gcd); |
| isl_int_fdiv_q(vec->el[0], vec->el[0], gcd); |
| isl_seq_scale_down(vec->el + 1, vec->el + 1, gcd, vec->size-1); |
| } |
| isl_int_clear(gcd); |
| |
| return strict; |
| } |
| |
| /* Determine the sign of the given row of the main tableau. |
| * The result is one of |
| * isl_tab_row_pos: always non-negative; no pivot needed |
| * isl_tab_row_neg: always non-positive; pivot |
| * isl_tab_row_any: can be both positive and negative; split |
| * |
| * We first handle some simple cases |
| * - the row sign may be known already |
| * - the row may be obviously non-negative |
| * - the parametric constant may be equal to that of another row |
| * for which we know the sign. This sign will be either "pos" or |
| * "any". If it had been "neg" then we would have pivoted before. |
| * |
| * If none of these cases hold, we check the value of the row for each |
| * of the currently active samples. Based on the signs of these values |
| * we make an initial determination of the sign of the row. |
| * |
| * all zero -> unk(nown) |
| * all non-negative -> pos |
| * all non-positive -> neg |
| * both negative and positive -> all |
| * |
| * If we end up with "all", we are done. |
| * Otherwise, we perform a check for positive and/or negative |
| * values as follows. |
| * |
| * samples neg unk pos |
| * <0 ? Y N Y N |
| * pos any pos |
| * >0 ? Y N Y N |
| * any neg any neg |
| * |
| * There is no special sign for "zero", because we can usually treat zero |
| * as either non-negative or non-positive, whatever works out best. |
| * However, if the row is "critical", meaning that pivoting is impossible |
| * then we don't want to limp zero with the non-positive case, because |
| * then we we would lose the solution for those values of the parameters |
| * where the value of the row is zero. Instead, we treat 0 as non-negative |
| * ensuring a split if the row can attain both zero and negative values. |
| * The same happens when the original constraint was one that could not |
| * be satisfied with equality by any integer values of the parameters. |
| * In this case, we normalize the constraint, but then a value of zero |
| * for the normalized constraint is actually a positive value for the |
| * original constraint, so again we need to treat zero as non-negative. |
| * In both these cases, we have the following decision tree instead: |
| * |
| * all non-negative -> pos |
| * all negative -> neg |
| * both negative and non-negative -> all |
| * |
| * samples neg pos |
| * <0 ? Y N |
| * any pos |
| * >=0 ? Y N |
| * any neg |
| */ |
| static enum isl_tab_row_sign row_sign(struct isl_tab *tab, |
| struct isl_sol *sol, int row) |
| { |
| struct isl_vec *ineq = NULL; |
| enum isl_tab_row_sign res = isl_tab_row_unknown; |
| int critical; |
| int strict; |
| int row2; |
| |
| if (tab->row_sign[row] != isl_tab_row_unknown) |
| return tab->row_sign[row]; |
| if (is_obviously_nonneg(tab, row)) |
| return isl_tab_row_pos; |
| for (row2 = tab->n_redundant; row2 < tab->n_row; ++row2) { |
| if (tab->row_sign[row2] == isl_tab_row_unknown) |
| continue; |
| if (identical_parameter_line(tab, row, row2)) |
| return tab->row_sign[row2]; |
| } |
| |
| critical = is_critical(tab, row); |
| |
| ineq = get_row_parameter_ineq(tab, row); |
| if (!ineq) |
| goto error; |
| |
| strict = is_strict(ineq); |
| |
| res = sol->context->op->ineq_sign(sol->context, ineq->el, |
| critical || strict); |
| |
| if (res == isl_tab_row_unknown || res == isl_tab_row_pos) { |
| /* test for negative values */ |
| int feasible; |
| isl_seq_neg(ineq->el, ineq->el, ineq->size); |
| isl_int_sub_ui(ineq->el[0], ineq->el[0], 1); |
| |
| feasible = sol->context->op->test_ineq(sol->context, ineq->el); |
| if (feasible < 0) |
| goto error; |
| if (!feasible) |
| res = isl_tab_row_pos; |
| else |
| res = (res == isl_tab_row_unknown) ? isl_tab_row_neg |
| : isl_tab_row_any; |
| if (res == isl_tab_row_neg) { |
| isl_seq_neg(ineq->el, ineq->el, ineq->size); |
| isl_int_sub_ui(ineq->el[0], ineq->el[0], 1); |
| } |
| } |
| |
| if (res == isl_tab_row_neg) { |
| /* test for positive values */ |
| int feasible; |
| if (!critical && !strict) |
| isl_int_sub_ui(ineq->el[0], ineq->el[0], 1); |
| |
| feasible = sol->context->op->test_ineq(sol->context, ineq->el); |
| if (feasible < 0) |
| goto error; |
| if (feasible) |
| res = isl_tab_row_any; |
| } |
| |
| isl_vec_free(ineq); |
| return res; |
| error: |
| isl_vec_free(ineq); |
| return isl_tab_row_unknown; |
| } |
| |
| static void find_solutions(struct isl_sol *sol, struct isl_tab *tab); |
| |
| /* Find solutions for values of the parameters that satisfy the given |
| * inequality. |
| * |
| * We currently take a snapshot of the context tableau that is reset |
| * when we return from this function, while we make a copy of the main |
| * tableau, leaving the original main tableau untouched. |
| * These are fairly arbitrary choices. Making a copy also of the context |
| * tableau would obviate the need to undo any changes made to it later, |
| * while taking a snapshot of the main tableau could reduce memory usage. |
| * If we were to switch to taking a snapshot of the main tableau, |
| * we would have to keep in mind that we need to save the row signs |
| * and that we need to do this before saving the current basis |
| * such that the basis has been restore before we restore the row signs. |
| */ |
| static void find_in_pos(struct isl_sol *sol, struct isl_tab *tab, isl_int *ineq) |
| { |
| void *saved; |
| |
| if (!sol->context) |
| goto error; |
| saved = sol->context->op->save(sol->context); |
| |
| tab = isl_tab_dup(tab); |
| if (!tab) |
| goto error; |
| |
| sol->context->op->add_ineq(sol->context, ineq, 0, 1); |
| |
| find_solutions(sol, tab); |
| |
| if (!sol->error) |
| sol->context->op->restore(sol->context, saved); |
| return; |
| error: |
| sol->error = 1; |
| } |
| |
| /* Record the absence of solutions for those values of the parameters |
| * that do not satisfy the given inequality with equality. |
| */ |
| static void no_sol_in_strict(struct isl_sol *sol, |
| struct isl_tab *tab, struct isl_vec *ineq) |
| { |
| int empty; |
| void *saved; |
| |
| if (!sol->context || sol->error) |
| goto error; |
| saved = sol->context->op->save(sol->context); |
| |
| isl_int_sub_ui(ineq->el[0], ineq->el[0], 1); |
| |
| sol->context->op->add_ineq(sol->context, ineq->el, 1, 0); |
| if (!sol->context) |
| goto error; |
| |
| empty = tab->empty; |
| tab->empty = 1; |
| sol_add(sol, tab); |
| tab->empty = empty; |
| |
| isl_int_add_ui(ineq->el[0], ineq->el[0], 1); |
| |
| sol->context->op->restore(sol->context, saved); |
| return; |
| error: |
| sol->error = 1; |
| } |
| |
| /* Compute the lexicographic minimum of the set represented by the main |
| * tableau "tab" within the context "sol->context_tab". |
| * On entry the sample value of the main tableau is lexicographically |
| * less than or equal to this lexicographic minimum. |
| * Pivots are performed until a feasible point is found, which is then |
| * necessarily equal to the minimum, or until the tableau is found to |
| * be infeasible. Some pivots may need to be performed for only some |
| * feasible values of the context tableau. If so, the context tableau |
| * is split into a part where the pivot is needed and a part where it is not. |
| * |
| * Whenever we enter the main loop, the main tableau is such that no |
| * "obvious" pivots need to be performed on it, where "obvious" means |
| * that the given row can be seen to be negative without looking at |
| * the context tableau. In particular, for non-parametric problems, |
| * no pivots need to be performed on the main tableau. |
| * The caller of find_solutions is responsible for making this property |
| * hold prior to the first iteration of the loop, while restore_lexmin |
| * is called before every other iteration. |
| * |
| * Inside the main loop, we first examine the signs of the rows of |
| * the main tableau within the context of the context tableau. |
| * If we find a row that is always non-positive for all values of |
| * the parameters satisfying the context tableau and negative for at |
| * least one value of the parameters, we perform the appropriate pivot |
| * and start over. An exception is the case where no pivot can be |
| * performed on the row. In this case, we require that the sign of |
| * the row is negative for all values of the parameters (rather than just |
| * non-positive). This special case is handled inside row_sign, which |
| * will say that the row can have any sign if it determines that it can |
| * attain both negative and zero values. |
| * |
| * If we can't find a row that always requires a pivot, but we can find |
| * one or more rows that require a pivot for some values of the parameters |
| * (i.e., the row can attain both positive and negative signs), then we split |
| * the context tableau into two parts, one where we force the sign to be |
| * non-negative and one where we force is to be negative. |
| * The non-negative part is handled by a recursive call (through find_in_pos). |
| * Upon returning from this call, we continue with the negative part and |
| * perform the required pivot. |
| * |
| * If no such rows can be found, all rows are non-negative and we have |
| * found a (rational) feasible point. If we only wanted a rational point |
| * then we are done. |
| * Otherwise, we check if all values of the sample point of the tableau |
| * are integral for the variables. If so, we have found the minimal |
| * integral point and we are done. |
| * If the sample point is not integral, then we need to make a distinction |
| * based on whether the constant term is non-integral or the coefficients |
| * of the parameters. Furthermore, in order to decide how to handle |
| * the non-integrality, we also need to know whether the coefficients |
| * of the other columns in the tableau are integral. This leads |
| * to the following table. The first two rows do not correspond |
| * to a non-integral sample point and are only mentioned for completeness. |
| * |
| * constant parameters other |
| * |
| * int int int | |
| * int int rat | -> no problem |
| * |
| * rat int int -> fail |
| * |
| * rat int rat -> cut |
| * |
| * int rat rat | |
| * rat rat rat | -> parametric cut |
| * |
| * int rat int | |
| * rat rat int | -> split context |
| * |
| * If the parametric constant is completely integral, then there is nothing |
| * to be done. If the constant term is non-integral, but all the other |
| * coefficient are integral, then there is nothing that can be done |
| * and the tableau has no integral solution. |
| * If, on the other hand, one or more of the other columns have rational |
| * coefficients, but the parameter coefficients are all integral, then |
| * we can perform a regular (non-parametric) cut. |
| * Finally, if there is any parameter coefficient that is non-integral, |
| * then we need to involve the context tableau. There are two cases here. |
| * If at least one other column has a rational coefficient, then we |
| * can perform a parametric cut in the main tableau by adding a new |
| * integer division in the context tableau. |
| * If all other columns have integral coefficients, then we need to |
| * enforce that the rational combination of parameters (c + \sum a_i y_i)/m |
| * is always integral. We do this by introducing an integer division |
| * q = floor((c + \sum a_i y_i)/m) and stipulating that its argument should |
| * always be integral in the context tableau, i.e., m q = c + \sum a_i y_i. |
| * Since q is expressed in the tableau as |
| * c + \sum a_i y_i - m q >= 0 |
| * -c - \sum a_i y_i + m q + m - 1 >= 0 |
| * it is sufficient to add the inequality |
| * -c - \sum a_i y_i + m q >= 0 |
| * In the part of the context where this inequality does not hold, the |
| * main tableau is marked as being empty. |
| */ |
| static void find_solutions(struct isl_sol *sol, struct isl_tab *tab) |
| { |
| struct isl_context *context; |
| int r; |
| |
| if (!tab || sol->error) |
| goto error; |
| |
| context = sol->context; |
| |
| if (tab->empty) |
| goto done; |
| if (context->op->is_empty(context)) |
| goto done; |
| |
| for (r = 0; r >= 0 && tab && !tab->empty; r = restore_lexmin(tab)) { |
| int flags; |
| int row; |
| enum isl_tab_row_sign sgn; |
| int split = -1; |
| int n_split = 0; |
| |
| for (row = tab->n_redundant; row < tab->n_row; ++row) { |
| if (!isl_tab_var_from_row(tab, row)->is_nonneg) |
| continue; |
| sgn = row_sign(tab, sol, row); |
| if (!sgn) |
| goto error; |
| tab->row_sign[row] = sgn; |
| if (sgn == isl_tab_row_any) |
| n_split++; |
| if (sgn == isl_tab_row_any && split == -1) |
| split = row; |
| if (sgn == isl_tab_row_neg) |
| break; |
| } |
| if (row < tab->n_row) |
| continue; |
| if (split != -1) { |
| struct isl_vec *ineq; |
| if (n_split != 1) |
| split = context->op->best_split(context, tab); |
| if (split < 0) |
| goto error; |
| ineq = get_row_parameter_ineq(tab, split); |
| if (!ineq) |
| goto error; |
| is_strict(ineq); |
| for (row = tab->n_redundant; row < tab->n_row; ++row) { |
| if (!isl_tab_var_from_row(tab, row)->is_nonneg) |
| continue; |
| if (tab->row_sign[row] == isl_tab_row_any) |
| tab->row_sign[row] = isl_tab_row_unknown; |
| } |
| tab->row_sign[split] = isl_tab_row_pos; |
| sol_inc_level(sol); |
| find_in_pos(sol, tab, ineq->el); |
| tab->row_sign[split] = isl_tab_row_neg; |
| row = split; |
| isl_seq_neg(ineq->el, ineq->el, ineq->size); |
| isl_int_sub_ui(ineq->el[0], ineq->el[0], 1); |
| if (!sol->error) |
| context->op->add_ineq(context, ineq->el, 0, 1); |
| isl_vec_free(ineq); |
| if (sol->error) |
| goto error; |
| continue; |
| } |
| if (tab->rational) |
| break; |
| row = first_non_integer_row(tab, &flags); |
| if (row < 0) |
| break; |
| if (ISL_FL_ISSET(flags, I_PAR)) { |
| if (ISL_FL_ISSET(flags, I_VAR)) { |
| if (isl_tab_mark_empty(tab) < 0) |
| goto error; |
| break; |
| } |
| row = add_cut(tab, row); |
| } else if (ISL_FL_ISSET(flags, I_VAR)) { |
| struct isl_vec *div; |
| struct isl_vec *ineq; |
| int d; |
| div = get_row_split_div(tab, row); |
| if (!div) |
| goto error; |
| d = context->op->get_div(context, tab, div); |
| isl_vec_free(div); |
| if (d < 0) |
| goto error; |
| ineq = ineq_for_div(context->op->peek_basic_set(context), d); |
| if (!ineq) |
| goto error; |
| sol_inc_level(sol); |
| no_sol_in_strict(sol, tab, ineq); |
| isl_seq_neg(ineq->el, ineq->el, ineq->size); |
| context->op->add_ineq(context, ineq->el, 1, 1); |
| isl_vec_free(ineq); |
| if (sol->error || !context->op->is_ok(context)) |
| goto error; |
| tab = set_row_cst_to_div(tab, row, d); |
| if (context->op->is_empty(context)) |
| break; |
| } else |
| row = add_parametric_cut(tab, row, context); |
| if (row < 0) |
| goto error; |
| } |
| if (r < 0) |
| goto error; |
| done: |
| sol_add(sol, tab); |
| isl_tab_free(tab); |
| return; |
| error: |
| isl_tab_free(tab); |
| sol->error = 1; |
| } |
| |
| /* Compute the lexicographic minimum of the set represented by the main |
| * tableau "tab" within the context "sol->context_tab". |
| * |
| * As a preprocessing step, we first transfer all the purely parametric |
| * equalities from the main tableau to the context tableau, i.e., |
| * parameters that have been pivoted to a row. |
| * These equalities are ignored by the main algorithm, because the |
| * corresponding rows may not be marked as being non-negative. |
| * In parts of the context where the added equality does not hold, |
| * the main tableau is marked as being empty. |
| */ |
| static void find_solutions_main(struct isl_sol *sol, struct isl_tab *tab) |
| { |
| int row; |
| |
| if (!tab) |
| goto error; |
| |
| sol->level = 0; |
| |
| for (row = tab->n_redundant; row < tab->n_row; ++row) { |
| int p; |
| struct isl_vec *eq; |
| |
| if (tab->row_var[row] < 0) |
| continue; |
| if (tab->row_var[row] >= tab->n_param && |
| tab->row_var[row] < tab->n_var - tab->n_div) |
| continue; |
| if (tab->row_var[row] < tab->n_param) |
| p = tab->row_var[row]; |
| else |
| p = tab->row_var[row] |
| + tab->n_param - (tab->n_var - tab->n_div); |
| |
| eq = isl_vec_alloc(tab->mat->ctx, 1+tab->n_param+tab->n_div); |
| if (!eq) |
| goto error; |
| get_row_parameter_line(tab, row, eq->el); |
| isl_int_neg(eq->el[1 + p], tab->mat->row[row][0]); |
| eq = isl_vec_normalize(eq); |
| |
| sol_inc_level(sol); |
| no_sol_in_strict(sol, tab, eq); |
| |
| isl_seq_neg(eq->el, eq->el, eq->size); |
| sol_inc_level(sol); |
| no_sol_in_strict(sol, tab, eq); |
| isl_seq_neg(eq->el, eq->el, eq->size); |
| |
| sol->context->op->add_eq(sol->context, eq->el, 1, 1); |
| |
| isl_vec_free(eq); |
| |
| if (isl_tab_mark_redundant(tab, row) < 0) |
| goto error; |
| |
| if (sol->context->op->is_empty(sol->context)) |
| break; |
| |
| row = tab->n_redundant - 1; |
| } |
| |
| find_solutions(sol, tab); |
| |
| sol->level = 0; |
| sol_pop(sol); |
| |
| return; |
| error: |
| isl_tab_free(tab); |
| sol->error = 1; |
| } |
| |
| /* Check if integer division "div" of "dom" also occurs in "bmap". |
| * If so, return its position within the divs. |
| * If not, return -1. |
| */ |
| static int find_context_div(struct isl_basic_map *bmap, |
| struct isl_basic_set *dom, unsigned div) |
| { |
| int i; |
| unsigned b_dim = isl_space_dim(bmap->dim, isl_dim_all); |
| unsigned d_dim = isl_space_dim(dom->dim, isl_dim_all); |
| |
| if (isl_int_is_zero(dom->div[div][0])) |
| return -1; |
| if (isl_seq_first_non_zero(dom->div[div] + 2 + d_dim, dom->n_div) != -1) |
| return -1; |
| |
| for (i = 0; i < bmap->n_div; ++i) { |
| if (isl_int_is_zero(bmap->div[i][0])) |
| continue; |
| if (isl_seq_first_non_zero(bmap->div[i] + 2 + d_dim, |
| (b_dim - d_dim) + bmap->n_div) != -1) |
| continue; |
| if (isl_seq_eq(bmap->div[i], dom->div[div], 2 + d_dim)) |
| return i; |
| } |
| return -1; |
| } |
| |
| /* The correspondence between the variables in the main tableau, |
| * the context tableau, and the input map and domain is as follows. |
| * The first n_param and the last n_div variables of the main tableau |
| * form the variables of the context tableau. |
| * In the basic map, these n_param variables correspond to the |
| * parameters and the input dimensions. In the domain, they correspond |
| * to the parameters and the set dimensions. |
| * The n_div variables correspond to the integer divisions in the domain. |
| * To ensure that everything lines up, we may need to copy some of the |
| * integer divisions of the domain to the map. These have to be placed |
| * in the same order as those in the context and they have to be placed |
| * after any other integer divisions that the map may have. |
| * This function performs the required reordering. |
| */ |
| static struct isl_basic_map *align_context_divs(struct isl_basic_map *bmap, |
| struct isl_basic_set *dom) |
| { |
| int i; |
| int common = 0; |
| int other; |
| |
| for (i = 0; i < dom->n_div; ++i) |
| if (find_context_div(bmap, dom, i) != -1) |
| common++; |
| other = bmap->n_div - common; |
| if (dom->n_div - common > 0) { |
| bmap = isl_basic_map_extend_space(bmap, isl_space_copy(bmap->dim), |
| dom->n_div - common, 0, 0); |
| if (!bmap) |
| return NULL; |
| } |
| for (i = 0; i < dom->n_div; ++i) { |
| int pos = find_context_div(bmap, dom, i); |
| if (pos < 0) { |
| pos = isl_basic_map_alloc_div(bmap); |
| if (pos < 0) |
| goto error; |
| isl_int_set_si(bmap->div[pos][0], 0); |
| } |
| if (pos != other + i) |
| isl_basic_map_swap_div(bmap, pos, other + i); |
| } |
| return bmap; |
| error: |
| isl_basic_map_free(bmap); |
| return NULL; |
| } |
| |
| /* Base case of isl_tab_basic_map_partial_lexopt, after removing |
| * some obvious symmetries. |
| * |
| * We make sure the divs in the domain are properly ordered, |
| * because they will be added one by one in the given order |
| * during the construction of the solution map. |
| */ |
| static struct isl_sol *basic_map_partial_lexopt_base( |
| __isl_take isl_basic_map *bmap, __isl_take isl_basic_set *dom, |
| __isl_give isl_set **empty, int max, |
| struct isl_sol *(*init)(__isl_keep isl_basic_map *bmap, |
| __isl_take isl_basic_set *dom, int track_empty, int max)) |
| { |
| struct isl_tab *tab; |
| struct isl_sol *sol = NULL; |
| struct isl_context *context; |
| |
| if (dom->n_div) { |
| dom = isl_basic_set_order_divs(dom); |
| bmap = align_context_divs(bmap, dom); |
| } |
| sol = init(bmap, dom, !!empty, max); |
| if (!sol) |
| goto error; |
| |
| context = sol->context; |
| if (isl_basic_set_plain_is_empty(context->op->peek_basic_set(context))) |
| /* nothing */; |
| else if (isl_basic_map_plain_is_empty(bmap)) { |
| if (sol->add_empty) |
| sol->add_empty(sol, |
| isl_basic_set_copy(context->op->peek_basic_set(context))); |
| } else { |
| tab = tab_for_lexmin(bmap, |
| context->op->peek_basic_set(context), 1, max); |
| tab = context->op->detect_nonnegative_parameters(context, tab); |
| find_solutions_main(sol, tab); |
| } |
| if (sol->error) |
| goto error; |
| |
| isl_basic_map_free(bmap); |
| return sol; |
| error: |
| sol_free(sol); |
| isl_basic_map_free(bmap); |
| return NULL; |
| } |
| |
| /* Base case of isl_tab_basic_map_partial_lexopt, after removing |
| * some obvious symmetries. |
| * |
| * We call basic_map_partial_lexopt_base and extract the results. |
| */ |
| static __isl_give isl_map *basic_map_partial_lexopt_base_map( |
| __isl_take isl_basic_map *bmap, __isl_take isl_basic_set *dom, |
| __isl_give isl_set **empty, int max) |
| { |
| isl_map *result = NULL; |
| struct isl_sol *sol; |
| struct isl_sol_map *sol_map; |
| |
| sol = basic_map_partial_lexopt_base(bmap, dom, empty, max, |
| &sol_map_init); |
| if (!sol) |
| return NULL; |
| sol_map = (struct isl_sol_map *) sol; |
| |
| result = isl_map_copy(sol_map->map); |
| if (empty) |
| *empty = isl_set_copy(sol_map->empty); |
| sol_free(&sol_map->sol); |
| return result; |
| } |
| |
| /* Structure used during detection of parallel constraints. |
| * n_in: number of "input" variables: isl_dim_param + isl_dim_in |
| * n_out: number of "output" variables: isl_dim_out + isl_dim_div |
| * val: the coefficients of the output variables |
| */ |
| struct isl_constraint_equal_info { |
| isl_basic_map *bmap; |
| unsigned n_in; |
| unsigned n_out; |
| isl_int *val; |
| }; |
| |
| /* Check whether the coefficients of the output variables |
| * of the constraint in "entry" are equal to info->val. |
| */ |
| static int constraint_equal(const void *entry, const void *val) |
| { |
| isl_int **row = (isl_int **)entry; |
| const struct isl_constraint_equal_info *info = val; |
| |
| return isl_seq_eq((*row) + 1 + info->n_in, info->val, info->n_out); |
| } |
| |
| /* Check whether "bmap" has a pair of constraints that have |
| * the same coefficients for the output variables. |
| * Note that the coefficients of the existentially quantified |
| * variables need to be zero since the existentially quantified |
| * of the result are usually not the same as those of the input. |
| * the isl_dim_out and isl_dim_div dimensions. |
| * If so, return 1 and return the row indices of the two constraints |
| * in *first and *second. |
| */ |
| static int parallel_constraints(__isl_keep isl_basic_map *bmap, |
| int *first, int *second) |
| { |
| int i; |
| isl_ctx *ctx = isl_basic_map_get_ctx(bmap); |
| struct isl_hash_table *table = NULL; |
| struct isl_hash_table_entry *entry; |
| struct isl_constraint_equal_info info; |
| unsigned n_out; |
| unsigned n_div; |
| |
| ctx = isl_basic_map_get_ctx(bmap); |
| table = isl_hash_table_alloc(ctx, bmap->n_ineq); |
| if (!table) |
| goto error; |
| |
| info.n_in = isl_basic_map_dim(bmap, isl_dim_param) + |
| isl_basic_map_dim(bmap, isl_dim_in); |
| info.bmap = bmap; |
| n_out = isl_basic_map_dim(bmap, isl_dim_out); |
| n_div = isl_basic_map_dim(bmap, isl_dim_div); |
| info.n_out = n_out + n_div; |
| for (i = 0; i < bmap->n_ineq; ++i) { |
| uint32_t hash; |
| |
| info.val = bmap->ineq[i] + 1 + info.n_in; |
| if (isl_seq_first_non_zero(info.val, n_out) < 0) |
| continue; |
| if (isl_seq_first_non_zero(info.val + n_out, n_div) >= 0) |
| continue; |
| hash = isl_seq_get_hash(info.val, info.n_out); |
| entry = isl_hash_table_find(ctx, table, hash, |
| constraint_equal, &info, 1); |
| if (!entry) |
| goto error; |
| if (entry->data) |
| break; |
| entry->data = &bmap->ineq[i]; |
| } |
| |
| if (i < bmap->n_ineq) { |
| *first = ((isl_int **)entry->data) - bmap->ineq; |
| *second = i; |
| } |
| |
| isl_hash_table_free(ctx, table); |
| |
| return i < bmap->n_ineq; |
| error: |
| isl_hash_table_free(ctx, table); |
| return -1; |
| } |
| |
| /* Given a set of upper bounds in "var", add constraints to "bset" |
| * that make the i-th bound smallest. |
| * |
| * In particular, if there are n bounds b_i, then add the constraints |
| * |
| * b_i <= b_j for j > i |
| * b_i < b_j for j < i |
| */ |
| static __isl_give isl_basic_set *select_minimum(__isl_take isl_basic_set *bset, |
| __isl_keep isl_mat *var, int i) |
| { |
| isl_ctx *ctx; |
| int j, k; |
| |
| ctx = isl_mat_get_ctx(var); |
| |
| for (j = 0; j < var->n_row; ++j) { |
| if (j == i) |
| continue; |
| k = isl_basic_set_alloc_inequality(bset); |
| if (k < 0) |
| goto error; |
| isl_seq_combine(bset->ineq[k], ctx->one, var->row[j], |
| ctx->negone, var->row[i], var->n_col); |
| isl_int_set_si(bset->ineq[k][var->n_col], 0); |
| if (j < i) |
| isl_int_sub_ui(bset->ineq[k][0], bset->ineq[k][0], 1); |
| } |
| |
| bset = isl_basic_set_finalize(bset); |
| |
| return bset; |
| error: |
| isl_basic_set_free(bset); |
| return NULL; |
| } |
| |
| /* Given a set of upper bounds on the last "input" variable m, |
| * construct a set that assigns the minimal upper bound to m, i.e., |
| * construct a set that divides the space into cells where one |
| * of the upper bounds is smaller than all the others and assign |
| * this upper bound to m. |
| * |
| * In particular, if there are n bounds b_i, then the result |
| * consists of n basic sets, each one of the form |
| * |
| * m = b_i |
| * b_i <= b_j for j > i |
| * b_i < b_j for j < i |
| */ |
| static __isl_give isl_set *set_minimum(__isl_take isl_space *dim, |
| __isl_take isl_mat *var) |
| { |
| int i, k; |
| isl_basic_set *bset = NULL; |
| isl_ctx *ctx; |
| isl_set *set = NULL; |
| |
| if (!dim || !var) |
| goto error; |
| |
| ctx = isl_space_get_ctx(dim); |
| set = isl_set_alloc_space(isl_space_copy(dim), |
| var->n_row, ISL_SET_DISJOINT); |
| |
| for (i = 0; i < var->n_row; ++i) { |
| bset = isl_basic_set_alloc_space(isl_space_copy(dim), 0, |
| 1, var->n_row - 1); |
| k = isl_basic_set_alloc_equality(bset); |
| if (k < 0) |
| goto error; |
| isl_seq_cpy(bset->eq[k], var->row[i], var->n_col); |
| isl_int_set_si(bset->eq[k][var->n_col], -1); |
| bset = select_minimum(bset, var, i); |
| set = isl_set_add_basic_set(set, bset); |
| } |
| |
| isl_space_free(dim); |
| isl_mat_free(var); |
| return set; |
| error: |
| isl_basic_set_free(bset); |
| isl_set_free(set); |
| isl_space_free(dim); |
| isl_mat_free(var); |
| return NULL; |
| } |
| |
| /* Given that the last input variable of "bmap" represents the minimum |
| * of the bounds in "cst", check whether we need to split the domain |
| * based on which bound attains the minimum. |
| * |
| * A split is needed when the minimum appears in an integer division |
| * or in an equality. Otherwise, it is only needed if it appears in |
| * an upper bound that is different from the upper bounds on which it |
| * is defined. |
| */ |
| static int need_split_basic_map(__isl_keep isl_basic_map *bmap, |
| __isl_keep isl_mat *cst) |
| { |
| int i, j; |
| unsigned total; |
| unsigned pos; |
| |
| pos = cst->n_col - 1; |
| total = isl_basic_map_dim(bmap, isl_dim_all); |
| |
| for (i = 0; i < bmap->n_div; ++i) |
| if (!isl_int_is_zero(bmap->div[i][2 + pos])) |
| return 1; |
| |
| for (i = 0; i < bmap->n_eq; ++i) |
| if (!isl_int_is_zero(bmap->eq[i][1 + pos])) |
| return 1; |
| |
| for (i = 0; i < bmap->n_ineq; ++i) { |
| if (isl_int_is_nonneg(bmap->ineq[i][1 + pos])) |
| continue; |
| if (!isl_int_is_negone(bmap->ineq[i][1 + pos])) |
| return 1; |
| if (isl_seq_first_non_zero(bmap->ineq[i] + 1 + pos + 1, |
| total - pos - 1) >= 0) |
| return 1; |
| |
| for (j = 0; j < cst->n_row; ++j) |
| if (isl_seq_eq(bmap->ineq[i], cst->row[j], cst->n_col)) |
| break; |
| if (j >= cst->n_row) |
| return 1; |
| } |
| |
| return 0; |
| } |
| |
| /* Given that the last set variable of "bset" represents the minimum |
| * of the bounds in "cst", check whether we need to split the domain |
| * based on which bound attains the minimum. |
| * |
| * We simply call need_split_basic_map here. This is safe because |
| * the position of the minimum is computed from "cst" and not |
| * from "bmap". |
| */ |
| static int need_split_basic_set(__isl_keep isl_basic_set *bset, |
| __isl_keep isl_mat *cst) |
| { |
| return need_split_basic_map((isl_basic_map *)bset, cst); |
| } |
| |
| /* Given that the last set variable of "set" represents the minimum |
| * of the bounds in "cst", check whether we need to split the domain |
| * based on which bound attains the minimum. |
| */ |
| static int need_split_set(__isl_keep isl_set *set, __isl_keep isl_mat *cst) |
| { |
| int i; |
| |
| for (i = 0; i < set->n; ++i) |
| if (need_split_basic_set(set->p[i], cst)) |
| return 1; |
| |
| return 0; |
| } |
| |
| /* Given a set of which the last set variable is the minimum |
| * of the bounds in "cst", split each basic set in the set |
| * in pieces where one of the bounds is (strictly) smaller than the others. |
| * This subdivision is given in "min_expr". |
| * The variable is subsequently projected out. |
| * |
| * We only do the split when it is needed. |
| * For example if the last input variable m = min(a,b) and the only |
| * constraints in the given basic set are lower bounds on m, |
| * i.e., l <= m = min(a,b), then we can simply project out m |
| * to obtain l <= a and l <= b, without having to split on whether |
| * m is equal to a or b. |
| */ |
| static __isl_give isl_set *split(__isl_take isl_set *empty, |
| __isl_take isl_set *min_expr, __isl_take isl_mat *cst) |
| { |
| int n_in; |
| int i; |
| isl_space *dim; |
| isl_set *res; |
| |
| if (!empty || !min_expr || !cst) |
| goto error; |
| |
| n_in = isl_set_dim(empty, isl_dim_set); |
| dim = isl_set_get_space(empty); |
| dim = isl_space_drop_dims(dim, isl_dim_set, n_in - 1, 1); |
| res = isl_set_empty(dim); |
| |
| for (i = 0; i < empty->n; ++i) { |
| isl_set *set; |
| |
| set = isl_set_from_basic_set(isl_basic_set_copy(empty->p[i])); |
| if (need_split_basic_set(empty->p[i], cst)) |
| set = isl_set_intersect(set, isl_set_copy(min_expr)); |
| set = isl_set_remove_dims(set, isl_dim_set, n_in - 1, 1); |
| |
| res = isl_set_union_disjoint(res, set); |
| } |
| |
| isl_set_free(empty); |
| isl_set_free(min_expr); |
| isl_mat_free(cst); |
| return res; |
| error: |
| isl_set_free(empty); |
| isl_set_free(min_expr); |
| isl_mat_free(cst); |
| return NULL; |
| } |
| |
| /* Given a map of which the last input variable is the minimum |
| * of the bounds in "cst", split each basic set in the set |
| * in pieces where one of the bounds is (strictly) smaller than the others. |
| * This subdivision is given in "min_expr". |
| * The variable is subsequently projected out. |
| * |
| * The implementation is essentially the same as that of "split". |
| */ |
| static __isl_give isl_map *split_domain(__isl_take isl_map *opt, |
| __isl_take isl_set *min_expr, __isl_take isl_mat *cst) |
| { |
| int n_in; |
| int i; |
| isl_space *dim; |
| isl_map *res; |
| |
| if (!opt || !min_expr || !cst) |
| goto error; |
| |
| n_in = isl_map_dim(opt, isl_dim_in); |
| dim = isl_map_get_space(opt); |
| dim = isl_space_drop_dims(dim, isl_dim_in, n_in - 1, 1); |
| res = isl_map_empty(dim); |
| |
| for (i = 0; i < opt->n; ++i) { |
| isl_map *map; |
| |
| map = isl_map_from_basic_map(isl_basic_map_copy(opt->p[i])); |
| if (need_split_basic_map(opt->p[i], cst)) |
| map = isl_map_intersect_domain(map, |
| isl_set_copy(min_expr)); |
| map = isl_map_remove_dims(map, isl_dim_in, n_in - 1, 1); |
| |
| res = isl_map_union_disjoint(res, map); |
| } |
| |
| isl_map_free(opt); |
| isl_set_free(min_expr); |
| isl_mat_free(cst); |
| return res; |
| error: |
| isl_map_free(opt); |
| isl_set_free(min_expr); |
| isl_mat_free(cst); |
| return NULL; |
| } |
| |
| static __isl_give isl_map *basic_map_partial_lexopt( |
| __isl_take isl_basic_map *bmap, __isl_take isl_basic_set *dom, |
| __isl_give isl_set **empty, int max); |
| |
| union isl_lex_res { |
| void *p; |
| isl_map *map; |
| isl_pw_multi_aff *pma; |
| }; |
| |
| /* This function is called from basic_map_partial_lexopt_symm. |
| * The last variable of "bmap" and "dom" corresponds to the minimum |
| * of the bounds in "cst". "map_space" is the space of the original |
| * input relation (of basic_map_partial_lexopt_symm) and "set_space" |
| * is the space of the original domain. |
| * |
| * We recursively call basic_map_partial_lexopt and then plug in |
| * the definition of the minimum in the result. |
| */ |
| static __isl_give union isl_lex_res basic_map_partial_lexopt_symm_map_core( |
| __isl_take isl_basic_map *bmap, __isl_take isl_basic_set *dom, |
| __isl_give isl_set **empty, int max, __isl_take isl_mat *cst, |
| __isl_take isl_space *map_space, __isl_take isl_space *set_space) |
| { |
| isl_map *opt; |
| isl_set *min_expr; |
| union isl_lex_res res; |
| |
| min_expr = set_minimum(isl_basic_set_get_space(dom), isl_mat_copy(cst)); |
| |
| opt = basic_map_partial_lexopt(bmap, dom, empty, max); |
| |
| if (empty) { |
| *empty = split(*empty, |
| isl_set_copy(min_expr), isl_mat_copy(cst)); |
| *empty = isl_set_reset_space(*empty, set_space); |
| } |
| |
| opt = split_domain(opt, min_expr, cst); |
| opt = isl_map_reset_space(opt, map_space); |
| |
| res.map = opt; |
| return res; |
| } |
| |
| /* Given a basic map with at least two parallel constraints (as found |
| * by the function parallel_constraints), first look for more constraints |
| * parallel to the two constraint and replace the found list of parallel |
| * constraints by a single constraint with as "input" part the minimum |
| * of the input parts of the list of constraints. Then, recursively call |
| * basic_map_partial_lexopt (possibly finding more parallel constraints) |
| * and plug in the definition of the minimum in the result. |
| * |
| * More specifically, given a set of constraints |
| * |
| * a x + b_i(p) >= 0 |
| * |
| * Replace this set by a single constraint |
| * |
| * a x + u >= 0 |
| * |
| * with u a new parameter with constraints |
| * |
| * u <= b_i(p) |
| * |
| * Any solution to the new system is also a solution for the original system |
| * since |
| * |
| * a x >= -u >= -b_i(p) |
| * |
| * Moreover, m = min_i(b_i(p)) satisfies the constraints on u and can |
| * therefore be plugged into the solution. |
| */ |
| static union isl_lex_res basic_map_partial_lexopt_symm( |
| __isl_take isl_basic_map *bmap, __isl_take isl_basic_set *dom, |
| __isl_give isl_set **empty, int max, int first, int second, |
| __isl_give union isl_lex_res (*core)(__isl_take isl_basic_map *bmap, |
| __isl_take isl_basic_set *dom, |
| __isl_give isl_set **empty, |
| int max, __isl_take isl_mat *cst, |
| __isl_take isl_space *map_space, |
| __isl_take isl_space *set_space)) |
| { |
| int i, n, k; |
| int *list = NULL; |
| unsigned n_in, n_out, n_div; |
| isl_ctx *ctx; |
| isl_vec *var = NULL; |
| isl_mat *cst = NULL; |
| isl_space *map_space, *set_space; |
| union isl_lex_res res; |
| |
| map_space = isl_basic_map_get_space(bmap); |
| set_space = empty ? isl_basic_set_get_space(dom) : NULL; |
| |
| n_in = isl_basic_map_dim(bmap, isl_dim_param) + |
| isl_basic_map_dim(bmap, isl_dim_in); |
| n_out = isl_basic_map_dim(bmap, isl_dim_all) - n_in; |
| |
| ctx = isl_basic_map_get_ctx(bmap); |
| list = isl_alloc_array(ctx, int, bmap->n_ineq); |
| var = isl_vec_alloc(ctx, n_out); |
| if (!list || !var) |
| goto error; |
| |
| list[0] = first; |
| list[1] = second; |
| isl_seq_cpy(var->el, bmap->ineq[first] + 1 + n_in, n_out); |
| for (i = second + 1, n = 2; i < bmap->n_ineq; ++i) { |
| if (isl_seq_eq(var->el, bmap->ineq[i] + 1 + n_in, n_out)) |
| list[n++] = i; |
| } |
| |
| cst = isl_mat_alloc(ctx, n, 1 + n_in); |
| if (!cst) |
| goto error; |
| |
| for (i = 0; i < n; ++i) |
| isl_seq_cpy(cst->row[i], bmap->ineq[list[i]], 1 + n_in); |
| |
| bmap = isl_basic_map_cow(bmap); |
| if (!bmap) |
| goto error; |
| for (i = n - 1; i >= 0; --i) |
| if (isl_basic_map_drop_inequality(bmap, list[i]) < 0) |
| goto error; |
| |
| bmap = isl_basic_map_add(bmap, isl_dim_in, 1); |
| bmap = isl_basic_map_extend_constraints(bmap, 0, 1); |
| k = isl_basic_map_alloc_inequality(bmap); |
| if (k < 0) |
| goto error; |
| isl_seq_clr(bmap->ineq[k], 1 + n_in); |
| isl_int_set_si(bmap->ineq[k][1 + n_in], 1); |
| isl_seq_cpy(bmap->ineq[k] + 1 + n_in + 1, var->el, n_out); |
| bmap = isl_basic_map_finalize(bmap); |
| |
| n_div = isl_basic_set_dim(dom, isl_dim_div); |
| dom = isl_basic_set_add(dom, isl_dim_set, 1); |
| dom = isl_basic_set_extend_constraints(dom, 0, n); |
| for (i = 0; i < n; ++i) { |
| k = isl_basic_set_alloc_inequality(dom); |
| if (k < 0) |
| goto error; |
| isl_seq_cpy(dom->ineq[k], cst->row[i], 1 + n_in); |
| isl_int_set_si(dom->ineq[k][1 + n_in], -1); |
| isl_seq_clr(dom->ineq[k] + 1 + n_in + 1, n_div); |
| } |
| |
| isl_vec_free(var); |
| free(list); |
| |
| return core(bmap, dom, empty, max, cst, map_space, set_space); |
| error: |
| isl_space_free(map_space); |
| isl_space_free(set_space); |
| isl_mat_free(cst); |
| isl_vec_free(var); |
| free(list); |
| isl_basic_set_free(dom); |
| isl_basic_map_free(bmap); |
| res.p = NULL; |
| return res; |
| } |
| |
| static __isl_give isl_map *basic_map_partial_lexopt_symm_map( |
| __isl_take isl_basic_map *bmap, __isl_take isl_basic_set *dom, |
| __isl_give isl_set **empty, int max, int first, int second) |
| { |
| return basic_map_partial_lexopt_symm(bmap, dom, empty, max, |
| first, second, &basic_map_partial_lexopt_symm_map_core).map; |
| } |
| |
| /* Recursive part of isl_tab_basic_map_partial_lexopt, after detecting |
| * equalities and removing redundant constraints. |
| * |
| * We first check if there are any parallel constraints (left). |
| * If not, we are in the base case. |
| * If there are parallel constraints, we replace them by a single |
| * constraint in basic_map_partial_lexopt_symm and then call |
| * this function recursively to look for more parallel constraints. |
| */ |
| static __isl_give isl_map *basic_map_partial_lexopt( |
| __isl_take isl_basic_map *bmap, __isl_take isl_basic_set *dom, |
| __isl_give isl_set **empty, int max) |
| { |
| int par = 0; |
| int first, second; |
| |
| if (!bmap) |
| goto error; |
| |
| if (bmap->ctx->opt->pip_symmetry) |
| par = parallel_constraints(bmap, &first, &second); |
| if (par < 0) |
| goto error; |
| if (!par) |
| return basic_map_partial_lexopt_base_map(bmap, dom, empty, max); |
| |
| return basic_map_partial_lexopt_symm_map(bmap, dom, empty, max, |
| first, second); |
| error: |
| isl_basic_set_free(dom); |
| isl_basic_map_free(bmap); |
| return NULL; |
| } |
| |
| /* Compute the lexicographic minimum (or maximum if "max" is set) |
| * of "bmap" over the domain "dom" and return the result as a map. |
| * If "empty" is not NULL, then *empty is assigned a set that |
| * contains those parts of the domain where there is no solution. |
| * If "bmap" is marked as rational (ISL_BASIC_MAP_RATIONAL), |
| * then we compute the rational optimum. Otherwise, we compute |
| * the integral optimum. |
| * |
| * We perform some preprocessing. As the PILP solver does not |
| * handle implicit equalities very well, we first make sure all |
| * the equalities are explicitly available. |
| * |
| * We also add context constraints to the basic map and remove |
| * redundant constraints. This is only needed because of the |
| * way we handle simple symmetries. In particular, we currently look |
| * for symmetries on the constraints, before we set up the main tableau. |
| * It is then no good to look for symmetries on possibly redundant constraints. |
| */ |
| struct isl_map *isl_tab_basic_map_partial_lexopt( |
| struct isl_basic_map *bmap, struct isl_basic_set *dom, |
| struct isl_set **empty, int max) |
| { |
| if (empty) |
| *empty = NULL; |
| if (!bmap || !dom) |
| goto error; |
| |
| isl_assert(bmap->ctx, |
| isl_basic_map_compatible_domain(bmap, dom), goto error); |
| |
| if (isl_basic_set_dim(dom, isl_dim_all) == 0) |
| return basic_map_partial_lexopt(bmap, dom, empty, max); |
| |
| bmap = isl_basic_map_intersect_domain(bmap, isl_basic_set_copy(dom)); |
| bmap = isl_basic_map_detect_equalities(bmap); |
| bmap = isl_basic_map_remove_redundancies(bmap); |
| |
| return basic_map_partial_lexopt(bmap, dom, empty, max); |
| error: |
| isl_basic_set_free(dom); |
| isl_basic_map_free(bmap); |
| return NULL; |
| } |
| |
| struct isl_sol_for { |
| struct isl_sol sol; |
| int (*fn)(__isl_take isl_basic_set *dom, |
| __isl_take isl_aff_list *list, void *user); |
| void *user; |
| }; |
| |
| static void sol_for_free(struct isl_sol_for *sol_for) |
| { |
| if (sol_for->sol.context) |
| sol_for->sol.context->op->free(sol_for->sol.context); |
| free(sol_for); |
| } |
| |
| static void sol_for_free_wrap(struct isl_sol *sol) |
| { |
| sol_for_free((struct isl_sol_for *)sol); |
| } |
| |
| /* Add the solution identified by the tableau and the context tableau. |
| * |
| * See documentation of sol_add for more details. |
| * |
| * Instead of constructing a basic map, this function calls a user |
| * defined function with the current context as a basic set and |
| * a list of affine expressions representing the relation between |
| * the input and output. The space over which the affine expressions |
| * are defined is the same as that of the domain. The number of |
| * affine expressions in the list is equal to the number of output variables. |
| */ |
| static void sol_for_add(struct isl_sol_for *sol, |
| struct isl_basic_set *dom, struct isl_mat *M) |
| { |
| int i; |
| isl_ctx *ctx; |
| isl_local_space *ls; |
| isl_aff *aff; |
| isl_aff_list *list; |
| |
| if (sol->sol.error || !dom || !M) |
| goto error; |
| |
| ctx = isl_basic_set_get_ctx(dom); |
| ls = isl_basic_set_get_local_space(dom); |
| list = isl_aff_list_alloc(ctx, M->n_row - 1); |
| for (i = 1; i < M->n_row; ++i) { |
| aff = isl_aff_alloc(isl_local_space_copy(ls)); |
| if (aff) { |
| isl_int_set(aff->v->el[0], M->row[0][0]); |
| isl_seq_cpy(aff->v->el + 1, M->row[i], M->n_col); |
| } |
| list = isl_aff_list_add(list, aff); |
| } |
| isl_local_space_free(ls); |
| |
| dom = isl_basic_set_finalize(dom); |
| |
| if (sol->fn(isl_basic_set_copy(dom), list, sol->user) < 0) |
| goto error; |
| |
| isl_basic_set_free(dom); |
| isl_mat_free(M); |
| return; |
| error: |
| isl_basic_set_free(dom); |
| isl_mat_free(M); |
| sol->sol.error = 1; |
| } |
| |
| static void sol_for_add_wrap(struct isl_sol *sol, |
| struct isl_basic_set *dom, struct isl_mat *M) |
| { |
| sol_for_add((struct isl_sol_for *)sol, dom, M); |
| } |
| |
| static struct isl_sol_for *sol_for_init(struct isl_basic_map *bmap, int max, |
| int (*fn)(__isl_take isl_basic_set *dom, __isl_take isl_aff_list *list, |
| void *user), |
| void *user) |
| { |
| struct isl_sol_for *sol_for = NULL; |
| isl_space *dom_dim; |
| struct isl_basic_set *dom = NULL; |
| |
| sol_for = isl_calloc_type(bmap->ctx, struct isl_sol_for); |
| if (!sol_for) |
| goto error; |
| |
| dom_dim = isl_space_domain(isl_space_copy(bmap->dim)); |
| dom = isl_basic_set_universe(dom_dim); |
| |
| sol_for->sol.rational = ISL_F_ISSET(bmap, ISL_BASIC_MAP_RATIONAL); |
| sol_for->sol.dec_level.callback.run = &sol_dec_level_wrap; |
| sol_for->sol.dec_level.sol = &sol_for->sol; |
| sol_for->fn = fn; |
| sol_for->user = user; |
| sol_for->sol.max = max; |
| sol_for->sol.n_out = isl_basic_map_dim(bmap, isl_dim_out); |
| sol_for->sol.add = &sol_for_add_wrap; |
| sol_for->sol.add_empty = NULL; |
| sol_for->sol.free = &sol_for_free_wrap; |
| |
| sol_for->sol.context = isl_context_alloc(dom); |
| if (!sol_for->sol.context) |
| goto error; |
| |
| isl_basic_set_free(dom); |
| return sol_for; |
| error: |
| isl_basic_set_free(dom); |
| sol_for_free(sol_for); |
| return NULL; |
| } |
| |
| static void sol_for_find_solutions(struct isl_sol_for *sol_for, |
| struct isl_tab *tab) |
| { |
| find_solutions_main(&sol_for->sol, tab); |
| } |
| |
| int isl_basic_map_foreach_lexopt(__isl_keep isl_basic_map *bmap, int max, |
| int (*fn)(__isl_take isl_basic_set *dom, __isl_take isl_aff_list *list, |
| void *user), |
| void *user) |
| { |
| struct isl_sol_for *sol_for = NULL; |
| |
| bmap = isl_basic_map_copy(bmap); |
| if (!bmap) |
| return -1; |
| |
| bmap = isl_basic_map_detect_equalities(bmap); |
| sol_for = sol_for_init(bmap, max, fn, user); |
| |
| if (isl_basic_map_plain_is_empty(bmap)) |
| /* nothing */; |
| else { |
| struct isl_tab *tab; |
| struct isl_context *context = sol_for->sol.context; |
| tab = tab_for_lexmin(bmap, |
| context->op->peek_basic_set(context), 1, max); |
| tab = context->op->detect_nonnegative_parameters(context, tab); |
| sol_for_find_solutions(sol_for, tab); |
| if (sol_for->sol.error) |
| goto error; |
| } |
| |
| sol_free(&sol_for->sol); |
| isl_basic_map_free(bmap); |
| return 0; |
| error: |
| sol_free(&sol_for->sol); |
| isl_basic_map_free(bmap); |
| return -1; |
| } |
| |
| int isl_basic_set_foreach_lexopt(__isl_keep isl_basic_set *bset, int max, |
| int (*fn)(__isl_take isl_basic_set *dom, __isl_take isl_aff_list *list, |
| void *user), |
| void *user) |
| { |
| return isl_basic_map_foreach_lexopt(bset, max, fn, user); |
| } |
| |
| /* Check if the given sequence of len variables starting at pos |
| * represents a trivial (i.e., zero) solution. |
| * The variables are assumed to be non-negative and to come in pairs, |
| * with each pair representing a variable of unrestricted sign. |
| * The solution is trivial if each such pair in the sequence consists |
| * of two identical values, meaning that the variable being represented |
| * has value zero. |
| */ |
| static int region_is_trivial(struct isl_tab *tab, int pos, int len) |
| { |
| int i; |
| |
| if (len == 0) |
| return 0; |
| |
| for (i = 0; i < len; i += 2) { |
| int neg_row; |
| int pos_row; |
| |
| neg_row = tab->var[pos + i].is_row ? |
| tab->var[pos + i].index : -1; |
| pos_row = tab->var[pos + i + 1].is_row ? |
| tab->var[pos + i + 1].index : -1; |
| |
| if ((neg_row < 0 || |
| isl_int_is_zero(tab->mat->row[neg_row][1])) && |
| (pos_row < 0 || |
| isl_int_is_zero(tab->mat->row[pos_row][1]))) |
| continue; |
| |
| if (neg_row < 0 || pos_row < 0) |
| return 0; |
| if (isl_int_ne(tab->mat->row[neg_row][1], |
| tab->mat->row[pos_row][1])) |
| return 0; |
| } |
| |
| return 1; |
| } |
| |
| /* Return the index of the first trivial region or -1 if all regions |
| * are non-trivial. |
| */ |
| static int first_trivial_region(struct isl_tab *tab, |
| int n_region, struct isl_region *region) |
| { |
| int i; |
| |
| for (i = 0; i < n_region; ++i) { |
| if (region_is_trivial(tab, region[i].pos, region[i].len)) |
| return i; |
| } |
| |
| return -1; |
| } |
| |
| /* Check if the solution is optimal, i.e., whether the first |
| * n_op entries are zero. |
| */ |
| static int is_optimal(__isl_keep isl_vec *sol, int n_op) |
| { |
| int i; |
| |
| for (i = 0; i < n_op; ++i) |
| if (!isl_int_is_zero(sol->el[1 + i])) |
| return 0; |
| return 1; |
| } |
| |
| /* Add constraints to "tab" that ensure that any solution is significantly |
| * better that that represented by "sol". That is, find the first |
| * relevant (within first n_op) non-zero coefficient and force it (along |
| * with all previous coefficients) to be zero. |
| * If the solution is already optimal (all relevant coefficients are zero), |
| * then just mark the table as empty. |
| */ |
| static int force_better_solution(struct isl_tab *tab, |
| __isl_keep isl_vec *sol, int n_op) |
| { |
| int i; |
| isl_ctx *ctx; |
| isl_vec *v = NULL; |
| |
| if (!sol) |
| return -1; |
| |
| for (i = 0; i < n_op; ++i) |
| if (!isl_int_is_zero(sol->el[1 + i])) |
| break; |
| |
| if (i == n_op) { |
| if (isl_tab_mark_empty(tab) < 0) |
| return -1; |
| return 0; |
| } |
| |
| ctx = isl_vec_get_ctx(sol); |
| v = isl_vec_alloc(ctx, 1 + tab->n_var); |
| if (!v) |
| return -1; |
| |
| for (; i >= 0; --i) { |
| v = isl_vec_clr(v); |
| isl_int_set_si(v->el[1 + i], -1); |
| if (add_lexmin_eq(tab, v->el) < 0) |
| goto error; |
| } |
| |
| isl_vec_free(v); |
| return 0; |
| error: |
| isl_vec_free(v); |
| return -1; |
| } |
| |
| struct isl_trivial { |
| int update; |
| int region; |
| int side; |
| struct isl_tab_undo *snap; |
| }; |
| |
| /* Return the lexicographically smallest non-trivial solution of the |
| * given ILP problem. |
| * |
| * All variables are assumed to be non-negative. |
| * |
| * n_op is the number of initial coordinates to optimize. |
| * That is, once a solution has been found, we will only continue looking |
| * for solution that result in significantly better values for those |
| * initial coordinates. That is, we only continue looking for solutions |
| * that increase the number of initial zeros in this sequence. |
| * |
| * A solution is non-trivial, if it is non-trivial on each of the |
| * specified regions. Each region represents a sequence of pairs |
| * of variables. A solution is non-trivial on such a region if |
| * at least one of these pairs consists of different values, i.e., |
| * such that the non-negative variable represented by the pair is non-zero. |
| * |
| * Whenever a conflict is encountered, all constraints involved are |
| * reported to the caller through a call to "conflict". |
| * |
| * We perform a simple branch-and-bound backtracking search. |
| * Each level in the search represents initially trivial region that is forced |
| * to be non-trivial. |
| * At each level we consider n cases, where n is the length of the region. |
| * In terms of the n/2 variables of unrestricted signs being encoded by |
| * the region, we consider the cases |
| * x_0 >= 1 |
| * x_0 <= -1 |
| * x_0 = 0 and x_1 >= 1 |
| * x_0 = 0 and x_1 <= -1 |
| * x_0 = 0 and x_1 = 0 and x_2 >= 1 |
| * x_0 = 0 and x_1 = 0 and x_2 <= -1 |
| * ... |
| * The cases are considered in this order, assuming that each pair |
| * x_i_a x_i_b represents the value x_i_b - x_i_a. |
| * That is, x_0 >= 1 is enforced by adding the constraint |
| * x_0_b - x_0_a >= 1 |
| */ |
| __isl_give isl_vec *isl_tab_basic_set_non_trivial_lexmin( |
| __isl_take isl_basic_set *bset, int n_op, int n_region, |
| struct isl_region *region, |
| int (*conflict)(int con, void *user), void *user) |
| { |
| int i, j; |
| int r; |
| isl_ctx *ctx = isl_basic_set_get_ctx(bset); |
| isl_vec *v = NULL; |
| isl_vec *sol = isl_vec_alloc(ctx, 0); |
| struct isl_tab *tab; |
| struct isl_trivial *triv = NULL; |
| int level, init; |
| |
| tab = tab_for_lexmin(bset, NULL, 0, 0); |
| if (!tab) |
| goto error; |
| tab->conflict = conflict; |
| tab->conflict_user = user; |
| |
| v = isl_vec_alloc(ctx, 1 + tab->n_var); |
| triv = isl_calloc_array(ctx, struct isl_trivial, n_region); |
| if (!v || !triv) |
| goto error; |
| |
| level = 0; |
| init = 1; |
| |
| while (level >= 0) { |
| int side, base; |
| |
| if (init) { |
| tab = cut_to_integer_lexmin(tab); |
| if (!tab) |
| goto error; |
| if (tab->empty) |
| goto backtrack; |
| r = first_trivial_region(tab, n_region, region); |
| if (r < 0) { |
| for (i = 0; i < level; ++i) |
| triv[i].update = 1; |
| isl_vec_free(sol); |
| sol = isl_tab_get_sample_value(tab); |
| if (!sol) |
| goto error; |
| if (is_optimal(sol, n_op)) |
| break; |
| goto backtrack; |
| } |
| if (level >= n_region) |
| isl_die(ctx, isl_error_internal, |
| "nesting level too deep", goto error); |
| if (isl_tab_extend_cons(tab, |
| 2 * region[r].len + 2 * n_op) < 0) |
| goto error; |
| triv[level].region = r; |
| triv[level].side = 0; |
| } |
| |
| r = triv[level].region; |
| side = triv[level].side; |
| base = 2 * (side/2); |
| |
| if (side >= region[r].len) { |
| backtrack: |
| level--; |
| init = 0; |
| if (level >= 0) |
| if (isl_tab_rollback(tab, triv[level].snap) < 0) |
| goto error; |
| continue; |
| } |
| |
| if (triv[level].update) { |
| if (force_better_solution(tab, sol, n_op) < 0) |
| goto error; |
| triv[level].update = 0; |
| } |
| |
| if (side == base && base >= 2) { |
| for (j = base - 2; j < base; ++j) { |
| v = isl_vec_clr(v); |
| isl_int_set_si(v->el[1 + region[r].pos + j], 1); |
| if (add_lexmin_eq(tab, v->el) < 0) |
| goto error; |
| } |
| } |
| |
| triv[level].snap = isl_tab_snap(tab); |
| if (isl_tab_push_basis(tab) < 0) |
| goto error; |
| |
| v = isl_vec_clr(v); |
| isl_int_set_si(v->el[0], -1); |
| isl_int_set_si(v->el[1 + region[r].pos + side], -1); |
| isl_int_set_si(v->el[1 + region[r].pos + (side ^ 1)], 1); |
| tab = add_lexmin_ineq(tab, v->el); |
| |
| triv[level].side++; |
| level++; |
| init = 1; |
| } |
| |
| free(triv); |
| isl_vec_free(v); |
| isl_tab_free(tab); |
| isl_basic_set_free(bset); |
| |
| return sol; |
| error: |
| free(triv); |
| isl_vec_free(v); |
| isl_tab_free(tab); |
| isl_basic_set_free(bset); |
| isl_vec_free(sol); |
| return NULL; |
| } |
| |
| /* Return the lexicographically smallest rational point in "bset", |
| * assuming that all variables are non-negative. |
| * If "bset" is empty, then return a zero-length vector. |
| */ |
| __isl_give isl_vec *isl_tab_basic_set_non_neg_lexmin( |
| __isl_take isl_basic_set *bset) |
| { |
| struct isl_tab *tab; |
| isl_ctx *ctx = isl_basic_set_get_ctx(bset); |
| isl_vec *sol; |
| |
| tab = tab_for_lexmin(bset, NULL, 0, 0); |
| if (!tab) |
| goto error; |
| if (tab->empty) |
| sol = isl_vec_alloc(ctx, 0); |
| else |
| sol = isl_tab_get_sample_value(tab); |
| isl_tab_free(tab); |
| isl_basic_set_free(bset); |
| return sol; |
| error: |
| isl_tab_free(tab); |
| isl_basic_set_free(bset); |
| return NULL; |
| } |
| |
| struct isl_sol_pma { |
| struct isl_sol sol; |
| isl_pw_multi_aff *pma; |
| isl_set *empty; |
| }; |
| |
| static void sol_pma_free(struct isl_sol_pma *sol_pma) |
| { |
| if (!sol_pma) |
| return; |
| if (sol_pma->sol.context) |
| sol_pma->sol.context->op->free(sol_pma->sol.context); |
| isl_pw_multi_aff_free(sol_pma->pma); |
| isl_set_free(sol_pma->empty); |
| free(sol_pma); |
| } |
| |
| /* This function is called for parts of the context where there is |
| * no solution, with "bset" corresponding to the context tableau. |
| * Simply add the basic set to the set "empty". |
| */ |
| static void sol_pma_add_empty(struct isl_sol_pma *sol, |
| __isl_take isl_basic_set *bset) |
| { |
| if (!bset) |
| goto error; |
| isl_assert(bset->ctx, sol->empty, goto error); |
| |
| sol->empty = isl_set_grow(sol->empty, 1); |
| bset = isl_basic_set_simplify(bset); |
| bset = isl_basic_set_finalize(bset); |
| sol->empty = isl_set_add_basic_set(sol->empty, bset); |
| if (!sol->empty) |
| sol->sol.error = 1; |
| return; |
| error: |
| isl_basic_set_free(bset); |
| sol->sol.error = 1; |
| } |
| |
| /* Given a basic map "dom" that represents the context and an affine |
| * matrix "M" that maps the dimensions of the context to the |
| * output variables, construct an isl_pw_multi_aff with a single |
| * cell corresponding to "dom" and affine expressions copied from "M". |
| */ |
| static void sol_pma_add(struct isl_sol_pma *sol, |
| __isl_take isl_basic_set *dom, __isl_take isl_mat *M) |
| { |
| int i; |
| isl_local_space *ls; |
| isl_aff *aff; |
| isl_multi_aff *maff; |
| isl_pw_multi_aff *pma; |
| |
| maff = isl_multi_aff_alloc(isl_pw_multi_aff_get_space(sol->pma)); |
| ls = isl_basic_set_get_local_space(dom); |
| for (i = 1; i < M->n_row; ++i) { |
| aff = isl_aff_alloc(isl_local_space_copy(ls)); |
| if (aff) { |
| isl_int_set(aff->v->el[0], M->row[0][0]); |
| isl_seq_cpy(aff->v->el + 1, M->row[i], M->n_col); |
| } |
| aff = isl_aff_normalize(aff); |
| maff = isl_multi_aff_set_aff(maff, i - 1, aff); |
| } |
| isl_local_space_free(ls); |
| isl_mat_free(M); |
| dom = isl_basic_set_simplify(dom); |
| dom = isl_basic_set_finalize(dom); |
| pma = isl_pw_multi_aff_alloc(isl_set_from_basic_set(dom), maff); |
| sol->pma = isl_pw_multi_aff_add_disjoint(sol->pma, pma); |
| if (!sol->pma) |
| sol->sol.error = 1; |
| } |
| |
| static void sol_pma_free_wrap(struct isl_sol *sol) |
| { |
| sol_pma_free((struct isl_sol_pma *)sol); |
| } |
| |
| static void sol_pma_add_empty_wrap(struct isl_sol *sol, |
| __isl_take isl_basic_set *bset) |
| { |
| sol_pma_add_empty((struct isl_sol_pma *)sol, bset); |
| } |
| |
| static void sol_pma_add_wrap(struct isl_sol *sol, |
| __isl_take isl_basic_set *dom, __isl_take isl_mat *M) |
| { |
| sol_pma_add((struct isl_sol_pma *)sol, dom, M); |
| } |
| |
| /* Construct an isl_sol_pma structure for accumulating the solution. |
| * If track_empty is set, then we also keep track of the parts |
| * of the context where there is no solution. |
| * If max is set, then we are solving a maximization, rather than |
| * a minimization problem, which means that the variables in the |
| * tableau have value "M - x" rather than "M + x". |
| */ |
| static struct isl_sol *sol_pma_init(__isl_keep isl_basic_map *bmap, |
| __isl_take isl_basic_set *dom, int track_empty, int max) |
| { |
| struct isl_sol_pma *sol_pma = NULL; |
| |
| if (!bmap) |
| goto error; |
| |
| sol_pma = isl_calloc_type(bmap->ctx, struct isl_sol_pma); |
| if (!sol_pma) |
| goto error; |
| |
| sol_pma->sol.rational = ISL_F_ISSET(bmap, ISL_BASIC_MAP_RATIONAL); |
| sol_pma->sol.dec_level.callback.run = &sol_dec_level_wrap; |
| sol_pma->sol.dec_level.sol = &sol_pma->sol; |
| sol_pma->sol.max = max; |
| sol_pma->sol.n_out = isl_basic_map_dim(bmap, isl_dim_out); |
| sol_pma->sol.add = &sol_pma_add_wrap; |
| sol_pma->sol.add_empty = track_empty ? &sol_pma_add_empty_wrap : NULL; |
| sol_pma->sol.free = &sol_pma_free_wrap; |
| sol_pma->pma = isl_pw_multi_aff_empty(isl_basic_map_get_space(bmap)); |
| if (!sol_pma->pma) |
| goto error; |
| |
| sol_pma->sol.context = isl_context_alloc(dom); |
| if (!sol_pma->sol.context) |
| goto error; |
| |
| if (track_empty) { |
| sol_pma->empty = isl_set_alloc_space(isl_basic_set_get_space(dom), |
| 1, ISL_SET_DISJOINT); |
| if (!sol_pma->empty) |
| goto error; |
| } |
| |
| isl_basic_set_free(dom); |
| return &sol_pma->sol; |
| error: |
| isl_basic_set_free(dom); |
| sol_pma_free(sol_pma); |
| return NULL; |
| } |
| |
| /* Base case of isl_tab_basic_map_partial_lexopt, after removing |
| * some obvious symmetries. |
| * |
| * We call basic_map_partial_lexopt_base and extract the results. |
| */ |
| static __isl_give isl_pw_multi_aff *basic_map_partial_lexopt_base_pma( |
| __isl_take isl_basic_map *bmap, __isl_take isl_basic_set *dom, |
| __isl_give isl_set **empty, int max) |
| { |
| isl_pw_multi_aff *result = NULL; |
| struct isl_sol *sol; |
| struct isl_sol_pma *sol_pma; |
| |
| sol = basic_map_partial_lexopt_base(bmap, dom, empty, max, |
| &sol_pma_init); |
| if (!sol) |
| return NULL; |
| sol_pma = (struct isl_sol_pma *) sol; |
| |
| result = isl_pw_multi_aff_copy(sol_pma->pma); |
| if (empty) |
| *empty = isl_set_copy(sol_pma->empty); |
| sol_free(&sol_pma->sol); |
| return result; |
| } |
| |
| /* Given that the last input variable of "maff" represents the minimum |
| * of some bounds, check whether we need to plug in the expression |
| * of the minimum. |
| * |
| * In particular, check if the last input variable appears in any |
| * of the expressions in "maff". |
| */ |
| static int need_substitution(__isl_keep isl_multi_aff *maff) |
| { |
| int i; |
| unsigned pos; |
| |
| pos = isl_multi_aff_dim(maff, isl_dim_in) - 1; |
| |
| for (i = 0; i < maff->n; ++i) |
| if (isl_aff_involves_dims(maff->p[i], isl_dim_in, pos, 1)) |
| return 1; |
| |
| return 0; |
| } |
| |
| /* Given a set of upper bounds on the last "input" variable m, |
| * construct a piecewise affine expression that selects |
| * the minimal upper bound to m, i.e., |
| * divide the space into cells where one |
| * of the upper bounds is smaller than all the others and select |
| * this upper bound on that cell. |
| * |
| * In particular, if there are n bounds b_i, then the result |
| * consists of n cell, each one of the form |
| * |
| * b_i <= b_j for j > i |
| * b_i < b_j for j < i |
| * |
| * The affine expression on this cell is |
| * |
| * b_i |
| */ |
| static __isl_give isl_pw_aff *set_minimum_pa(__isl_take isl_space *space, |
| __isl_take isl_mat *var) |
| { |
| int i; |
| isl_aff *aff = NULL; |
| isl_basic_set *bset = NULL; |
| isl_ctx *ctx; |
| isl_pw_aff *paff = NULL; |
| isl_space *pw_space; |
| isl_local_space *ls = NULL; |
| |
| if (!space || !var) |
| goto error; |
| |
| ctx = isl_space_get_ctx(space); |
| ls = isl_local_space_from_space(isl_space_copy(space)); |
| pw_space = isl_space_copy(space); |
| pw_space = isl_space_from_domain(pw_space); |
| pw_space = isl_space_add_dims(pw_space, isl_dim_out, 1); |
| paff = isl_pw_aff_alloc_size(pw_space, var->n_row); |
| |
| for (i = 0; i < var->n_row; ++i) { |
| isl_pw_aff *paff_i; |
| |
| aff = isl_aff_alloc(isl_local_space_copy(ls)); |
| bset = isl_basic_set_alloc_space(isl_space_copy(space), 0, |
| 0, var->n_row - 1); |
| if (!aff || !bset) |
| goto error; |
| isl_int_set_si(aff->v->el[0], 1); |
| isl_seq_cpy(aff->v->el + 1, var->row[i], var->n_col); |
| isl_int_set_si(aff->v->el[1 + var->n_col], 0); |
| bset = select_minimum(bset, var, i); |
| paff_i = isl_pw_aff_alloc(isl_set_from_basic_set(bset), aff); |
| paff = isl_pw_aff_add_disjoint(paff, paff_i); |
| } |
| |
| isl_local_space_free(ls); |
| isl_space_free(space); |
| isl_mat_free(var); |
| return paff; |
| error: |
| isl_aff_free(aff); |
| isl_basic_set_free(bset); |
| isl_pw_aff_free(paff); |
| isl_local_space_free(ls); |
| isl_space_free(space); |
| isl_mat_free(var); |
| return NULL; |
| } |
| |
| /* Given a piecewise multi-affine expression of which the last input variable |
| * is the minimum of the bounds in "cst", plug in the value of the minimum. |
| * This minimum expression is given in "min_expr_pa". |
| * The set "min_expr" contains the same information, but in the form of a set. |
| * The variable is subsequently projected out. |
| * |
| * The implementation is similar to those of "split" and "split_domain". |
| * If the variable appears in a given expression, then minimum expression |
| * is plugged in. Otherwise, if the variable appears in the constraints |
| * and a split is required, then the domain is split. Otherwise, no split |
| * is performed. |
| */ |
| static __isl_give isl_pw_multi_aff *split_domain_pma( |
| __isl_take isl_pw_multi_aff *opt, __isl_take isl_pw_aff *min_expr_pa, |
| __isl_take isl_set *min_expr, __isl_take isl_mat *cst) |
| { |
| int n_in; |
| int i; |
| isl_space *space; |
| isl_pw_multi_aff *res; |
| |
| if (!opt || !min_expr || !cst) |
| goto error; |
| |
| n_in = isl_pw_multi_aff_dim(opt, isl_dim_in); |
| space = isl_pw_multi_aff_get_space(opt); |
| space = isl_space_drop_dims(space, isl_dim_in, n_in - 1, 1); |
| res = isl_pw_multi_aff_empty(space); |
| |
| for (i = 0; i < opt->n; ++i) { |
| isl_pw_multi_aff *pma; |
| |
| pma = isl_pw_multi_aff_alloc(isl_set_copy(opt->p[i].set), |
| isl_multi_aff_copy(opt->p[i].maff)); |
| if (need_substitution(opt->p[i].maff)) |
| pma = isl_pw_multi_aff_substitute(pma, |
| isl_dim_in, n_in - 1, min_expr_pa); |
| else if (need_split_set(opt->p[i].set, cst)) |
| pma = isl_pw_multi_aff_intersect_domain(pma, |
| isl_set_copy(min_expr)); |
| pma = isl_pw_multi_aff_project_out(pma, |
| isl_dim_in, n_in - 1, 1); |
| |
| res = isl_pw_multi_aff_add_disjoint(res, pma); |
| } |
| |
| isl_pw_multi_aff_free(opt); |
| isl_pw_aff_free(min_expr_pa); |
| isl_set_free(min_expr); |
| isl_mat_free(cst); |
| return res; |
| error: |
| isl_pw_multi_aff_free(opt); |
| isl_pw_aff_free(min_expr_pa); |
| isl_set_free(min_expr); |
| isl_mat_free(cst); |
| return NULL; |
| } |
| |
| static __isl_give isl_pw_multi_aff *basic_map_partial_lexopt_pma( |
| __isl_take isl_basic_map *bmap, __isl_take isl_basic_set *dom, |
| __isl_give isl_set **empty, int max); |
| |
| /* This function is called from basic_map_partial_lexopt_symm. |
| * The last variable of "bmap" and "dom" corresponds to the minimum |
| * of the bounds in "cst". "map_space" is the space of the original |
| * input relation (of basic_map_partial_lexopt_symm) and "set_space" |
| * is the space of the original domain. |
| * |
| * We recursively call basic_map_partial_lexopt and then plug in |
| * the definition of the minimum in the result. |
| */ |
| static __isl_give union isl_lex_res basic_map_partial_lexopt_symm_pma_core( |
| __isl_take isl_basic_map *bmap, __isl_take isl_basic_set *dom, |
| __isl_give isl_set **empty, int max, __isl_take isl_mat *cst, |
| __isl_take isl_space *map_space, __isl_take isl_space *set_space) |
| { |
| isl_pw_multi_aff *opt; |
| isl_pw_aff *min_expr_pa; |
| isl_set *min_expr; |
| union isl_lex_res res; |
| |
| min_expr = set_minimum(isl_basic_set_get_space(dom), isl_mat_copy(cst)); |
| min_expr_pa = set_minimum_pa(isl_basic_set_get_space(dom), |
| isl_mat_copy(cst)); |
| |
| opt = basic_map_partial_lexopt_pma(bmap, dom, empty, max); |
| |
| if (empty) { |
| *empty = split(*empty, |
| isl_set_copy(min_expr), isl_mat_copy(cst)); |
| *empty = isl_set_reset_space(*empty, set_space); |
| } |
| |
| opt = split_domain_pma(opt, min_expr_pa, min_expr, cst); |
| opt = isl_pw_multi_aff_reset_space(opt, map_space); |
| |
| res.pma = opt; |
| return res; |
| } |
| |
| static __isl_give isl_pw_multi_aff *basic_map_partial_lexopt_symm_pma( |
| __isl_take isl_basic_map *bmap, __isl_take isl_basic_set *dom, |
| __isl_give isl_set **empty, int max, int first, int second) |
| { |
| return basic_map_partial_lexopt_symm(bmap, dom, empty, max, |
| first, second, &basic_map_partial_lexopt_symm_pma_core).pma; |
| } |
| |
| /* Recursive part of isl_basic_map_partial_lexopt_pw_multi_aff, after detecting |
| * equalities and removing redundant constraints. |
| * |
| * We first check if there are any parallel constraints (left). |
| * If not, we are in the base case. |
| * If there are parallel constraints, we replace them by a single |
| * constraint in basic_map_partial_lexopt_symm_pma and then call |
| * this function recursively to look for more parallel constraints. |
| */ |
| static __isl_give isl_pw_multi_aff *basic_map_partial_lexopt_pma( |
| __isl_take isl_basic_map *bmap, __isl_take isl_basic_set *dom, |
| __isl_give isl_set **empty, int max) |
| { |
| int par = 0; |
| int first, second; |
| |
| if (!bmap) |
| goto error; |
| |
| if (bmap->ctx->opt->pip_symmetry) |
| par = parallel_constraints(bmap, &first, &second); |
| if (par < 0) |
| goto error; |
| if (!par) |
| return basic_map_partial_lexopt_base_pma(bmap, dom, empty, max); |
| |
| return basic_map_partial_lexopt_symm_pma(bmap, dom, empty, max, |
| first, second); |
| error: |
| isl_basic_set_free(dom); |
| isl_basic_map_free(bmap); |
| return NULL; |
| } |
| |
| /* Compute the lexicographic minimum (or maximum if "max" is set) |
| * of "bmap" over the domain "dom" and return the result as a piecewise |
| * multi-affine expression. |
| * If "empty" is not NULL, then *empty is assigned a set that |
| * contains those parts of the domain where there is no solution. |
| * If "bmap" is marked as rational (ISL_BASIC_MAP_RATIONAL), |
| * then we compute the rational optimum. Otherwise, we compute |
| * the integral optimum. |
| * |
| * We perform some preprocessing. As the PILP solver does not |
| * handle implicit equalities very well, we first make sure all |
| * the equalities are explicitly available. |
| * |
| * We also add context constraints to the basic map and remove |
| * redundant constraints. This is only needed because of the |
| * way we handle simple symmetries. In particular, we currently look |
| * for symmetries on the constraints, before we set up the main tableau. |
| * It is then no good to look for symmetries on possibly redundant constraints. |
| */ |
| __isl_give isl_pw_multi_aff *isl_basic_map_partial_lexopt_pw_multi_aff( |
| __isl_take isl_basic_map *bmap, __isl_take isl_basic_set *dom, |
| __isl_give isl_set **empty, int max) |
| { |
| if (empty) |
| *empty = NULL; |
| if (!bmap || !dom) |
| goto error; |
| |
| isl_assert(bmap->ctx, |
| isl_basic_map_compatible_domain(bmap, dom), goto error); |
| |
| if (isl_basic_set_dim(dom, isl_dim_all) == 0) |
| return basic_map_partial_lexopt_pma(bmap, dom, empty, max); |
| |
| bmap = isl_basic_map_intersect_domain(bmap, isl_basic_set_copy(dom)); |
| bmap = isl_basic_map_detect_equalities(bmap); |
| bmap = isl_basic_map_remove_redundancies(bmap); |
| |
| return basic_map_partial_lexopt_pma(bmap, dom, empty, max); |
| error: |
| isl_basic_set_free(dom); |
| isl_basic_map_free(bmap); |
| return NULL; |
| } |