| /* |
| * Copyright 2008-2009 Katholieke Universiteit Leuven |
| * Copyright 2010 INRIA Saclay |
| * Copyright 2016-2017 Sven Verdoolaege |
| * |
| * Use of this software is governed by the MIT license |
| * |
| * Written by Sven Verdoolaege, K.U.Leuven, Departement |
| * Computerwetenschappen, Celestijnenlaan 200A, B-3001 Leuven, Belgium |
| * and 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_vec_private.h> |
| #include <isl_aff_private.h> |
| #include <isl_constraint_private.h> |
| #include <isl_options_private.h> |
| #include <isl_config.h> |
| |
| #include <bset_to_bmap.c> |
| |
| /* |
| * 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); |
| /* insert div "div" to context at "pos" and return non-negativity */ |
| isl_bool (*insert_div)(struct isl_context *context, int pos, |
| __isl_keep 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 *); |
| /* discard saved context */ |
| void (*discard)(void *); |
| /* invalidate context */ |
| void (*invalidate)(struct isl_context *context); |
| /* free context */ |
| __isl_null struct isl_context *(*free)(struct isl_context *context); |
| }; |
| |
| /* Shared parts of context representation. |
| * |
| * "n_unknown" is the number of final unknown integer divisions |
| * in the input domain. |
| */ |
| struct isl_context { |
| struct isl_context_op *op; |
| int n_unknown; |
| }; |
| |
| struct isl_context_lex { |
| struct isl_context context; |
| struct isl_tab *tab; |
| }; |
| |
| /* A stack (linked list) of solutions of subtrees of the search space. |
| * |
| * "ma" describes the solution as a function of "dom". |
| * In particular, the domain space of "ma" is equal to the space of "dom". |
| * |
| * If "ma" is NULL, then there is no solution on "dom". |
| */ |
| struct isl_partial_sol { |
| int level; |
| struct isl_basic_set *dom; |
| isl_multi_aff *ma; |
| |
| 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, the function "add" is called |
| * on the isl_sol passed to find_solutions_main. In a state where |
| * the tableau is empty, "add_empty" is called instead. |
| * "free" is called to free the implementation specific fields, if any. |
| * |
| * "error" is set if some error has occurred. This flag invalidates |
| * the remainder of the data structure. |
| * If "rational" is set, then a rational optimization is being performed. |
| * "level" is the current level in the tree with nodes for each |
| * split in the context. |
| * If "max" is set, then a maximization problem is being solved, rather than |
| * a minimization problem, which means that the variables in the |
| * tableau have value "M - x" rather than "M + x". |
| * "n_out" is the number of output dimensions in the input. |
| * "space" is the space in which the solution (and also the input) lives. |
| * |
| * 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_pma, which collects an isl_pw_multi_aff instead. |
| */ |
| struct isl_sol { |
| int error; |
| int rational; |
| int level; |
| int max; |
| int n_out; |
| isl_space *space; |
| struct isl_context *context; |
| struct isl_partial_sol *partial; |
| void (*add)(struct isl_sol *sol, |
| __isl_take isl_basic_set *dom, __isl_take isl_multi_aff *ma); |
| 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_multi_aff_free(partial->ma); |
| free(partial); |
| } |
| isl_space_free(sol->space); |
| if (sol->context) |
| sol->context->op->free(sol->context); |
| sol->free(sol); |
| free(sol); |
| } |
| |
| /* Push a partial solution represented by a domain and function "ma" |
| * onto the stack of partial solutions. |
| * If "ma" is NULL, then "dom" represents a part of the domain |
| * with no solution. |
| */ |
| static void sol_push_sol(struct isl_sol *sol, |
| __isl_take isl_basic_set *dom, __isl_take isl_multi_aff *ma) |
| { |
| 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->ma = ma; |
| partial->next = sol->partial; |
| |
| sol->partial = partial; |
| |
| return; |
| error: |
| isl_basic_set_free(dom); |
| isl_multi_aff_free(ma); |
| sol->error = 1; |
| } |
| |
| /* Check that the final columns of "M", starting at "first", are zero. |
| */ |
| static isl_stat check_final_columns_are_zero(__isl_keep isl_mat *M, |
| unsigned first) |
| { |
| int i; |
| unsigned rows, cols, n; |
| |
| if (!M) |
| return isl_stat_error; |
| rows = isl_mat_rows(M); |
| cols = isl_mat_cols(M); |
| n = cols - first; |
| for (i = 0; i < rows; ++i) |
| if (isl_seq_first_non_zero(M->row[i] + first, n) != -1) |
| isl_die(isl_mat_get_ctx(M), isl_error_internal, |
| "final columns should be zero", |
| return isl_stat_error); |
| return isl_stat_ok; |
| } |
| |
| /* Set the affine expressions in "ma" according to the rows in "M", which |
| * are defined over the local space "ls". |
| * The matrix "M" may have extra (zero) columns beyond the number |
| * of variables in "ls". |
| */ |
| static __isl_give isl_multi_aff *set_from_affine_matrix( |
| __isl_take isl_multi_aff *ma, __isl_take isl_local_space *ls, |
| __isl_take isl_mat *M) |
| { |
| int i, dim; |
| isl_aff *aff; |
| |
| if (!ma || !ls || !M) |
| goto error; |
| |
| dim = isl_local_space_dim(ls, isl_dim_all); |
| if (check_final_columns_are_zero(M, 1 + dim) < 0) |
| goto error; |
| 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], 1 + dim); |
| } |
| aff = isl_aff_normalize(aff); |
| ma = isl_multi_aff_set_aff(ma, i - 1, aff); |
| } |
| isl_local_space_free(ls); |
| isl_mat_free(M); |
| |
| return ma; |
| error: |
| isl_local_space_free(ls); |
| isl_mat_free(M); |
| isl_multi_aff_free(ma); |
| return NULL; |
| } |
| |
| /* Push a partial solution represented by a domain and mapping M |
| * onto the stack of partial solutions. |
| * |
| * The affine matrix "M" maps the dimensions of the context |
| * to the output variables. Convert it into an isl_multi_aff and |
| * then call sol_push_sol. |
| * |
| * Note that the description of the initial context may have involved |
| * existentially quantified variables, in which case they also appear |
| * in "dom". These need to be removed before creating the affine |
| * expression because an affine expression cannot be defined in terms |
| * of existentially quantified variables without a known representation. |
| * Since newly added integer divisions are inserted before these |
| * existentially quantified variables, they are still in the final |
| * positions and the corresponding final columns of "M" are zero |
| * because align_context_divs adds the existentially quantified |
| * variables of the context to the main tableau without any constraints and |
| * any equality constraints that are added later on can only serve |
| * to eliminate these existentially quantified variables. |
| */ |
| static void sol_push_sol_mat(struct isl_sol *sol, |
| __isl_take isl_basic_set *dom, __isl_take isl_mat *M) |
| { |
| isl_local_space *ls; |
| isl_multi_aff *ma; |
| int n_div, n_known; |
| |
| n_div = isl_basic_set_dim(dom, isl_dim_div); |
| n_known = n_div - sol->context->n_unknown; |
| |
| ma = isl_multi_aff_alloc(isl_space_copy(sol->space)); |
| ls = isl_basic_set_get_local_space(dom); |
| ls = isl_local_space_drop_dims(ls, isl_dim_div, |
| n_known, n_div - n_known); |
| ma = set_from_affine_matrix(ma, ls, M); |
| |
| if (!ma) |
| dom = isl_basic_set_free(dom); |
| sol_push_sol(sol, dom, ma); |
| } |
| |
| /* 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->ma) |
| sol->add(sol, partial->dom, partial->ma); |
| 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 affine expressions. |
| */ |
| static isl_bool same_solution(struct isl_partial_sol *s1, |
| struct isl_partial_sol *s2) |
| { |
| if (!s1->ma != !s2->ma) |
| return isl_bool_false; |
| if (!s1->ma) |
| return isl_bool_true; |
| |
| return isl_multi_aff_plain_is_equal(s1->ma, s2->ma); |
| } |
| |
| /* Swap the initial two partial solutions in "sol". |
| * |
| * That is, go from |
| * |
| * sol->partial = p1; p1->next = p2; p2->next = p3 |
| * |
| * to |
| * |
| * sol->partial = p2; p2->next = p1; p1->next = p3 |
| */ |
| static void swap_initial(struct isl_sol *sol) |
| { |
| struct isl_partial_sol *partial; |
| |
| partial = sol->partial; |
| sol->partial = partial->next; |
| partial->next = partial->next->next; |
| sol->partial->next = partial; |
| } |
| |
| /* Combine the initial two partial solution of "sol" into |
| * a partial solution with the current context domain of "sol" and |
| * the function description of the second partial solution in the list. |
| * The level of the new partial solution is set to the current level. |
| * |
| * That is, the first two partial solutions (D1,M1) and (D2,M2) are |
| * replaced by (D,M2), where D is the domain of "sol", which is assumed |
| * to be the union of D1 and D2, while M1 is assumed to be equal to M2 |
| * (at least on D1). |
| */ |
| static isl_stat combine_initial_into_second(struct isl_sol *sol) |
| { |
| struct isl_partial_sol *partial; |
| isl_basic_set *bset; |
| |
| partial = sol->partial; |
| |
| bset = sol_domain(sol); |
| isl_basic_set_free(partial->next->dom); |
| partial->next->dom = bset; |
| partial->next->level = sol->level; |
| |
| if (!bset) |
| return isl_stat_error; |
| |
| sol->partial = partial->next; |
| isl_basic_set_free(partial->dom); |
| isl_multi_aff_free(partial->ma); |
| free(partial); |
| |
| return isl_stat_ok; |
| } |
| |
| /* Are "ma1" and "ma2" equal to each other on "dom"? |
| * |
| * Combine "ma1" and "ma2" with "dom" and check if the results are the same. |
| * "dom" may have existentially quantified variables. Eliminate them first |
| * as otherwise they would have to be eliminated twice, in a more complicated |
| * context. |
| */ |
| static isl_bool equal_on_domain(__isl_keep isl_multi_aff *ma1, |
| __isl_keep isl_multi_aff *ma2, __isl_keep isl_basic_set *dom) |
| { |
| isl_set *set; |
| isl_pw_multi_aff *pma1, *pma2; |
| isl_bool equal; |
| |
| set = isl_basic_set_compute_divs(isl_basic_set_copy(dom)); |
| pma1 = isl_pw_multi_aff_alloc(isl_set_copy(set), |
| isl_multi_aff_copy(ma1)); |
| pma2 = isl_pw_multi_aff_alloc(set, isl_multi_aff_copy(ma2)); |
| equal = isl_pw_multi_aff_is_equal(pma1, pma2); |
| isl_pw_multi_aff_free(pma1); |
| isl_pw_multi_aff_free(pma2); |
| |
| return equal; |
| } |
| |
| /* The initial two partial solutions of "sol" are known to be at |
| * the same level. |
| * If they represent the same solution (on different parts of the domain), |
| * then combine them into a single solution at the current level. |
| * Otherwise, pop them both. |
| * |
| * Even if the two partial solution are not obviously the same, |
| * one may still be a simplification of the other over its own domain. |
| * Also check if the two sets of affine functions are equal when |
| * restricted to one of the domains. If so, combine the two |
| * using the set of affine functions on the other domain. |
| * That is, for two partial solutions (D1,M1) and (D2,M2), |
| * if M1 = M2 on D1, then the pair of partial solutions can |
| * be replaced by (D1+D2,M2) and similarly when M1 = M2 on D2. |
| */ |
| static isl_stat combine_initial_if_equal(struct isl_sol *sol) |
| { |
| struct isl_partial_sol *partial; |
| isl_bool same; |
| |
| partial = sol->partial; |
| |
| same = same_solution(partial, partial->next); |
| if (same < 0) |
| return isl_stat_error; |
| if (same) |
| return combine_initial_into_second(sol); |
| if (partial->ma && partial->next->ma) { |
| same = equal_on_domain(partial->ma, partial->next->ma, |
| partial->dom); |
| if (same < 0) |
| return isl_stat_error; |
| if (same) |
| return combine_initial_into_second(sol); |
| same = equal_on_domain(partial->ma, partial->next->ma, |
| partial->next->dom); |
| if (same) { |
| swap_initial(sol); |
| return combine_initial_into_second(sol); |
| } |
| } |
| |
| sol_pop_one(sol); |
| sol_pop_one(sol); |
| |
| return isl_stat_ok; |
| } |
| |
| /* 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. |
| * If the outer level (0) has been reached, then all partial solutions |
| * at the current level are also popped off. |
| */ |
| static void sol_pop(struct isl_sol *sol) |
| { |
| struct isl_partial_sol *partial; |
| |
| if (sol->error) |
| return; |
| |
| partial = sol->partial; |
| if (!partial) |
| return; |
| |
| if (partial->level == 0 && sol->level == 0) { |
| for (partial = sol->partial; partial; partial = sol->partial) |
| sol_pop_one(sol); |
| return; |
| } |
| |
| if (partial->level <= sol->level) |
| return; |
| |
| if (partial->next && partial->next->level == partial->level) { |
| if (combine_initial_if_equal(sol) < 0) |
| goto error; |
| } else |
| sol_pop_one(sol); |
| |
| if (sol->level == 0) { |
| for (partial = sol->partial; partial; partial = sol->partial) |
| sol_pop_one(sol); |
| return; |
| } |
| |
| if (0) |
| error: sol->error = 1; |
| } |
| |
| static void sol_dec_level(struct isl_sol *sol) |
| { |
| if (sol->error) |
| return; |
| |
| sol->level--; |
| |
| sol_pop(sol); |
| } |
| |
| static isl_stat 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 ? isl_stat_error : isl_stat_ok; |
| } |
| |
| /* 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; |
| if (sol->context->op->is_empty(sol->context)) |
| 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_mat(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 *sol) |
| { |
| struct isl_sol_map *sol_map = (struct isl_sol_map *) sol; |
| isl_map_free(sol_map->map); |
| isl_set_free(sol_map->empty); |
| } |
| |
| /* 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 || !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 set "dom" that represents the context and a tuple of |
| * affine expressions "ma" defined over this domain, construct a basic map |
| * that expresses this function on the domain. |
| */ |
| static void sol_map_add(struct isl_sol_map *sol, |
| __isl_take isl_basic_set *dom, __isl_take isl_multi_aff *ma) |
| { |
| isl_basic_map *bmap; |
| |
| if (sol->sol.error || !dom || !ma) |
| goto error; |
| |
| bmap = isl_basic_map_from_multi_aff2(ma, sol->sol.rational); |
| bmap = isl_basic_map_intersect_domain(bmap, dom); |
| sol->map = isl_map_grow(sol->map, 1); |
| sol->map = isl_map_add_basic_map(sol->map, bmap); |
| if (!sol->map) |
| sol->sol.error = 1; |
| return; |
| error: |
| isl_basic_set_free(dom); |
| isl_multi_aff_free(ma); |
| sol->sol.error = 1; |
| } |
| |
| static void sol_map_add_wrap(struct isl_sol *sol, |
| __isl_take isl_basic_set *dom, __isl_take isl_multi_aff *ma) |
| { |
| sol_map_add((struct isl_sol_map *)sol, dom, ma); |
| } |
| |
| |
| /* 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; |
| } |
| |
| /* Normalize a div expression of the form |
| * |
| * [(g*f(x) + c)/(g * m)] |
| * |
| * with c the constant term and f(x) the remaining coefficients, to |
| * |
| * [(f(x) + [c/g])/m] |
| */ |
| static void normalize_div(__isl_keep isl_vec *div) |
| { |
| isl_ctx *ctx = isl_vec_get_ctx(div); |
| int len = div->size - 2; |
| |
| isl_seq_gcd(div->el + 2, len, &ctx->normalize_gcd); |
| isl_int_gcd(ctx->normalize_gcd, ctx->normalize_gcd, div->el[0]); |
| |
| if (isl_int_is_one(ctx->normalize_gcd)) |
| return; |
| |
| isl_int_divexact(div->el[0], div->el[0], ctx->normalize_gcd); |
| isl_int_fdiv_q(div->el[1], div->el[1], ctx->normalize_gcd); |
| isl_seq_scale_down(div->el + 2, div->el + 2, ctx->normalize_gcd, len); |
| } |
| |
| /* Return an 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); |
| isl_seq_neg(div->el + 1, div->el + 1, div->size - 1); |
| normalize_div(div); |
| isl_seq_fdiv_r(div->el + 1, div->el + 1, div->el[0], div->size - 1); |
| |
| return div; |
| } |
| |
| /* Return an 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); |
| normalize_div(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 __isl_give isl_vec *ineq_for_div(__isl_keep 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, then 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; |
| } |
| |
| /* Does the index into the tab->var or tab->con array "index" |
| * correspond to a variable in the context tableau? |
| * In particular, it needs to be an index into the tab->var array and |
| * it needs to refer to either one of the first tab->n_param variables or |
| * one of the last tab->n_div variables. |
| */ |
| static int is_parameter_var(struct isl_tab *tab, int index) |
| { |
| if (index < 0) |
| return 0; |
| if (index < tab->n_param) |
| return 1; |
| if (index >= tab->n_var - tab->n_div) |
| return 1; |
| return 0; |
| } |
| |
| /* Does column "col" of "tab" refer to a variable in the context tableau? |
| */ |
| static int col_is_parameter_var(struct isl_tab *tab, int col) |
| { |
| return is_parameter_var(tab, tab->col_var[col]); |
| } |
| |
| /* Does row "row" of "tab" refer to a variable in the context tableau? |
| */ |
| static int row_is_parameter_var(struct isl_tab *tab, int row) |
| { |
| return is_parameter_var(tab, tab->row_var[row]); |
| } |
| |
| /* 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 (col_is_parameter_var(tab, j)) |
| 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 (col_is_parameter_var(tab, col)) |
| 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 it represents a constraint) and all constraint columns with |
| * non-zero (and therefore negative) coefficients. |
| */ |
| 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 (col_is_parameter_var(tab, j)) |
| 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. |
| * |
| * This function assumes that at least two more rows and at least |
| * two more elements in the constraint array are available in the tableau. |
| */ |
| 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; |
| } |
| |
| /* Is the given row a parametric constant? |
| * That is, does it only involve variables that also appear in the context? |
| */ |
| static int is_parametric_constant(struct isl_tab *tab, int row) |
| { |
| unsigned off = 2 + tab->M; |
| int col; |
| |
| for (col = tab->n_dead; col < tab->n_col; ++col) { |
| if (col_is_parameter_var(tab, col)) |
| continue; |
| if (isl_int_is_zero(tab->mat->row[row][off + col])) |
| continue; |
| return 0; |
| } |
| |
| return 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. |
| * |
| * This function assumes that at least two more rows and at least |
| * two more elements in the constraint array are available in the tableau. |
| */ |
| 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. |
| * |
| * This function assumes that at least one more row and at least |
| * one more element in the constraint array are available in the tableau. |
| */ |
| 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 (col_is_parameter_var(tab, i)) |
| 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; |
| } |
| |
| #define CUT_ALL 1 |
| #define CUT_ONE 0 |
| |
| /* 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. |
| * The parameter cutting_strategy controls the strategy used when adding cuts |
| * to remove non-integer points. CUT_ALL adds all possible cuts |
| * before continuing the search. CUT_ONE adds only one cut at a time. |
| */ |
| static struct isl_tab *cut_to_integer_lexmin(struct isl_tab *tab, |
| int cutting_strategy) |
| { |
| 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; |
| if (cutting_strategy == CUT_ONE) |
| break; |
| } 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, CUT_ALL); |
| if (!tab) |
| goto error; |
| |
| if (!tab->empty && sample_is_finite(tab)) { |
| struct isl_vec *sample; |
| |
| sample = isl_tab_get_sample_value(tab); |
| |
| if (isl_tab_add_sample(tab, sample) < 0) |
| goto error; |
| } |
| |
| 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; |
| } |
| |
| /* Insert a div specified by "div" to the tableau "tab" at position "pos" and |
| * return isl_bool_true if the div is obviously non-negative. |
| */ |
| static isl_bool context_tab_insert_div(struct isl_tab *tab, int pos, |
| __isl_keep isl_vec *div, |
| isl_stat (*add_ineq)(void *user, isl_int *), void *user) |
| { |
| int i; |
| int r; |
| struct isl_mat *samples; |
| int nonneg; |
| |
| r = isl_tab_insert_div(tab, pos, div, add_ineq, user); |
| if (r < 0) |
| return isl_bool_error; |
| 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 isl_bool_error; |
| 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]); |
| } |
| tab->samples = isl_mat_move_cols(tab->samples, 1 + pos, |
| 1 + tab->n_var - 1, 1); |
| if (!tab->samples) |
| return isl_bool_error; |
| |
| 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. |
| * |
| * The new integer division is added before any unknown integer |
| * divisions in the context to ensure that it does not get |
| * equated to some linear combination involving unknown integer |
| * divisions. |
| */ |
| static int add_div(struct isl_tab *tab, struct isl_context *context, |
| __isl_keep isl_vec *div) |
| { |
| int r; |
| int pos; |
| isl_bool nonneg; |
| struct isl_tab *context_tab = context->op->peek_tab(context); |
| |
| if (!tab || !context_tab) |
| goto error; |
| |
| pos = context_tab->n_var - context->n_unknown; |
| if ((nonneg = context->op->insert_div(context, pos, div)) < 0) |
| goto error; |
| |
| if (!context->op->is_ok(context)) |
| goto error; |
| |
| pos = tab->n_var - context->n_unknown; |
| if (isl_tab_extend_vars(tab, 1) < 0) |
| goto error; |
| r = isl_tab_insert_var(tab, pos); |
| 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 - context->n_unknown; |
| 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 given 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 - context->n_unknown; |
| d = context->op->get_div(context, tab, div); |
| isl_vec_free(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; |
| |
| 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 __isl_give struct isl_tab *tab_for_lexmin(__isl_keep isl_basic_map *bmap, |
| __isl_keep isl_basic_set *dom, unsigned M, int max) |
| { |
| int i; |
| struct isl_tab *tab; |
| unsigned n_var; |
| unsigned o_var; |
| |
| 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->mat->n_row && !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; |
| } |
| o_var = 1 + tab->n_param; |
| n_var = tab->n_var - tab->n_param - tab->n_div; |
| for (i = 0; i < bmap->n_eq; ++i) { |
| if (max) |
| isl_seq_neg(bmap->eq[i] + o_var, |
| bmap->eq[i] + o_var, n_var); |
| tab = add_lexmin_valid_eq(tab, bmap->eq[i]); |
| if (max) |
| isl_seq_neg(bmap->eq[i] + o_var, |
| bmap->eq[i] + o_var, n_var); |
| 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] + o_var, |
| bmap->ineq[i] + o_var, n_var); |
| tab = add_lexmin_ineq(tab, bmap->ineq[i]); |
| if (max) |
| isl_seq_neg(bmap->ineq[i] + o_var, |
| bmap->ineq[i] + o_var, n_var); |
| 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. |
| * |
| * If any of the rows requiring a split only involves |
| * variables that also appear in the context tableau, |
| * then the negative part is guaranteed not to have a solution. |
| * It is therefore best to split on any of these rows first. |
| * |
| * Otherwise, |
| * 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 rows 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. |
| * |
| * best is the best row so far (-1 when we have not found any row yet). |
| * best_r is the number of other rows made redundant by row best. |
| * When best is still -1, bset_r is meaningless, but it is initialized |
| * to some arbitrary value (0) anyway. Without this redundant initialization |
| * valgrind may warn about uninitialized memory accesses when isl |
| * is compiled with some versions of gcc. |
| */ |
| 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 = 0; |
| |
| 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; |
| |
| if (is_parametric_constant(tab, split)) |
| return split; |
| |
| 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 isl_stat 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) ? isl_stat_ok : isl_stat_error; |
| } |
| |
| /* 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); |
| } |
| |
| /* Insert a div specified by "div" to the context tableau at position "pos" and |
| * return isl_bool_true if the div is obviously non-negative. |
| * context_tab_add_div will always return isl_bool_true, 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 isl_bool context_lex_insert_div(struct isl_context *context, int pos, |
| __isl_keep isl_vec *div) |
| { |
| struct isl_context_lex *clex = (struct isl_context_lex *)context; |
| isl_bool nonneg; |
| nonneg = context_tab_insert_div(clex->tab, pos, div, |
| context_lex_add_ineq_wrap, context); |
| if (nonneg < 0) |
| return isl_bool_error; |
| if (clex->tab->M) |
| return isl_bool_false; |
| 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 void context_lex_discard(void *save) |
| { |
| } |
| |
| 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 __isl_null struct isl_context *context_lex_free( |
| struct isl_context *context) |
| { |
| struct isl_context_lex *clex = (struct isl_context_lex *)context; |
| isl_tab_free(clex->tab); |
| free(clex); |
| |
| return NULL; |
| } |
| |
| 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_insert_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_discard, |
| context_lex_invalidate, |
| context_lex_free, |
| }; |
| |
| static struct isl_tab *context_tab_for_lexmin(__isl_take isl_basic_set *bset) |
| { |
| struct isl_tab *tab; |
| |
| if (!bset) |
| return NULL; |
| tab = tab_for_lexmin(bset_to_bmap(bset), NULL, 1, 0); |
| if (isl_tab_track_bset(tab, bset) < 0) |
| goto error; |
| tab = isl_tab_init_samples(tab); |
| return tab; |
| error: |
| isl_tab_free(tab); |
| 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; |
| } |
| |
| /* Representation of the context when using generalized basis reduction. |
| * |
| * "shifted" contains the offsets of the unit hypercubes that lie inside the |
| * context. Any rational point in "shifted" can therefore be rounded |
| * up to an integer point in the context. |
| * If the context is constrained by any equality, then "shifted" is not used |
| * as it would be empty. |
| */ |
| 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, 0); |
| |
| 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 __isl_give isl_basic_set *drop_constant_terms( |
| __isl_take 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) |
| { |
| if (!cgbr->tab) |
| return 0; |
| 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_copy(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 (!sample || 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; |
| } |
| |
| if (isl_tab_add_sample(cgbr->tab, sample) < 0) |
| goto error; |
| |
| 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; |
| } |
| |
| /* Add the equality described by "eq" to the context. |
| * If "check" is set, then we check if the context is empty after |
| * adding the equality. |
| * If "update" is set, then we check if the samples are still valid. |
| * |
| * We do not explicitly add shifted copies of the equality to |
| * cgbr->shifted since they would conflict with each other. |
| * Instead, we directly mark cgbr->shifted empty. |
| */ |
| 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->shifted && !cgbr->shifted->empty && use_shifted(cgbr)) { |
| if (isl_tab_mark_empty(cgbr->shifted) < 0) |
| goto error; |
| } |
| |
| 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 isl_stat 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) ? isl_stat_ok : isl_stat_error; |
| } |
| |
| 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. |
| * This tentative addition of equality constraints turns |
| * on the undo facility of the tableau. Turn it off again |
| * at the end, assuming it was turned off to begin with. |
| * |
| * Return 0 on success and -1 on failure. |
| */ |
| static int propagate_equalities(struct isl_context_gbr *cgbr, |
| struct isl_tab *tab, unsigned first) |
| { |
| int i; |
| struct isl_vec *eq = NULL; |
| isl_bool needs_undo; |
| |
| needs_undo = isl_tab_need_undo(tab); |
| if (needs_undo < 0) |
| goto error; |
| 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; |
| } |
| |
| if (!needs_undo) |
| isl_tab_clear_undo(tab); |
| isl_vec_free(eq); |
| |
| return 0; |
| error: |
| isl_vec_free(eq); |
| isl_tab_free(cgbr->tab); |
| cgbr->tab = NULL; |
| return -1; |
| } |
| |
| static int context_gbr_detect_equalities(struct isl_context *context, |
| struct isl_tab *tab) |
| { |
| struct isl_context_gbr *cgbr = (struct isl_context_gbr *)context; |
| unsigned n_ineq; |
| |
| 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_copy(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) |
| return -1; |
| if (cgbr->tab->bmap->n_ineq > n_ineq && |
| propagate_equalities(cgbr, tab, n_ineq) < 0) |
| return -1; |
| |
| 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 isl_bool context_gbr_insert_div(struct isl_context *context, int pos, |
| __isl_keep isl_vec *div) |
| { |
| struct isl_context_gbr *cgbr = (struct isl_context_gbr *)context; |
| if (cgbr->cone) { |
| int r, n_div, o_div; |
| |
| n_div = isl_basic_map_dim(cgbr->cone->bmap, isl_dim_div); |
| o_div = cgbr->cone->n_var - n_div; |
| |
| if (isl_tab_extend_cons(cgbr->cone, 3) < 0) |
| return isl_bool_error; |
| if (isl_tab_extend_vars(cgbr->cone, 1) < 0) |
| return isl_bool_error; |
| if ((r = isl_tab_insert_var(cgbr->cone, pos)) <0) |
| return isl_bool_error; |
| |
| cgbr->cone->bmap = isl_basic_map_insert_div(cgbr->cone->bmap, |
| r - o_div, div); |
| if (!cgbr->cone->bmap) |
| return isl_bool_error; |
| if (isl_tab_push_var(cgbr->cone, isl_tab_undo_bmap_div, |
| &cgbr->cone->var[r]) < 0) |
| return isl_bool_error; |
| } |
| return context_tab_insert_div(cgbr->tab, pos, 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; |
| |
| if (!cgbr->tab) |
| return NULL; |
| |
| 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) |
| goto error; |
| |
| 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 void context_gbr_discard(void *save) |
| { |
| struct isl_gbr_tab_undo *snap = (struct isl_gbr_tab_undo *)save; |
| free(snap); |
| } |
| |
| 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 __isl_null struct isl_context *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); |
| |
| return NULL; |
| } |
| |
| 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_insert_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_discard, |
| context_gbr_invalidate, |
| context_gbr_free, |
| }; |
| |
| static struct isl_context *isl_context_gbr_alloc(__isl_keep 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, 1); |
| cgbr->tab = isl_tab_init_samples(cgbr->tab); |
| if (!cgbr->tab) |
| goto error; |
| check_gbr_integer_feasible(cgbr); |
| |
| return &cgbr->context; |
| error: |
| cgbr->context.op->free(&cgbr->context); |
| return NULL; |
| } |
| |
| /* Allocate a context corresponding to "dom". |
| * The representation specific fields are initialized by |
| * isl_context_lex_alloc or isl_context_gbr_alloc. |
| * The shared "n_unknown" field is initialized to the number |
| * of final unknown integer divisions in "dom". |
| */ |
| static struct isl_context *isl_context_alloc(__isl_keep isl_basic_set *dom) |
| { |
| struct isl_context *context; |
| int first; |
| |
| if (!dom) |
| return NULL; |
| |
| if (dom->ctx->opt->context == ISL_CONTEXT_LEXMIN) |
| context = isl_context_lex_alloc(dom); |
| else |
| context = isl_context_gbr_alloc(dom); |
| |
| if (!context) |
| return NULL; |
| |
| first = isl_basic_set_first_unknown_div(dom); |
| if (first < 0) |
| return context->op->free(context); |
| context->n_unknown = isl_basic_set_dim(dom, isl_dim_div) - first; |
| |
| return context; |
| } |
| |
| /* Initialize some common fields of "sol", which keeps track |
| * of the solution of an optimization problem on "bmap" over |
| * the domain "dom". |
| * If "max" is set, then a maximization problem is being solved, rather than |
| * a minimization problem, which means that the variables in the |
| * tableau have value "M - x" rather than "M + x". |
| */ |
| static isl_stat sol_init(struct isl_sol *sol, __isl_keep isl_basic_map *bmap, |
| __isl_keep isl_basic_set *dom, int max) |
| { |
| sol->rational = ISL_F_ISSET(bmap, ISL_BASIC_MAP_RATIONAL); |
| sol->dec_level.callback.run = &sol_dec_level_wrap; |
| sol->dec_level.sol = sol; |
| sol->max = max; |
| sol->n_out = isl_basic_map_dim(bmap, isl_dim_out); |
| sol->space = isl_basic_map_get_space(bmap); |
| |
| sol->context = isl_context_alloc(dom); |
| if (!sol->space || !sol->context) |
| return isl_stat_error; |
| |
| return isl_stat_ok; |
| } |
| |
| /* 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(__isl_keep isl_basic_map *bmap, |
| __isl_take isl_basic_set *dom, int track_empty, int max) |
| { |
| struct isl_sol_map *sol_map = NULL; |
| isl_space *space; |
| |
| if (!bmap) |
| goto error; |
| |
| sol_map = isl_calloc_type(bmap->ctx, struct isl_sol_map); |
| if (!sol_map) |
| goto error; |
| |
| sol_map->sol.free = &sol_map_free; |
| if (sol_init(&sol_map->sol, bmap, dom, max) < 0) |
| goto error; |
| sol_map->sol.add = &sol_map_add_wrap; |
| sol_map->sol.add_empty = track_empty ? &sol_map_add_empty_wrap : NULL; |
| space = isl_space_copy(sol_map->sol.space); |
| sol_map->map = isl_map_alloc_space(space, 1, ISL_MAP_DISJOINT); |
| if (!sol_map->map) |
| 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_free(&sol_map->sol); |
| 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 (col_is_parameter_var(tab, j)) |
| 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); |
| else |
| sol->context->op->discard(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; |
| } |
| |
| /* Reset all row variables that are marked to have a sign that may |
| * be both positive and negative to have an unknown sign. |
| */ |
| static void reset_any_to_unknown(struct isl_tab *tab) |
| { |
| int 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[row] == isl_tab_row_any) |
| tab->row_sign[row] = isl_tab_row_unknown; |
| } |
| } |
| |
| /* 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); |
| reset_any_to_unknown(tab); |
| 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; |
| 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; |
| } |
| |
| /* Does "sol" contain a pair of partial solutions that could potentially |
| * be merged? |
| * |
| * We currently only check that "sol" is not in an error state |
| * and that there are at least two partial solutions of which the final two |
| * are defined at the same level. |
| */ |
| static int sol_has_mergeable_solutions(struct isl_sol *sol) |
| { |
| if (sol->error) |
| return 0; |
| if (!sol->partial) |
| return 0; |
| if (!sol->partial->next) |
| return 0; |
| return sol->partial->level == sol->partial->next->level; |
| } |
| |
| /* 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. |
| * |
| * Before we embark on the actual computation, we save a copy |
| * of the context. When we return, we check if there are any |
| * partial solutions that can potentially be merged. If so, |
| * we perform a rollback to the initial state of the context. |
| * The merging of partial solutions happens inside calls to |
| * sol_dec_level that are pushed onto the undo stack of the context. |
| * If there are no partial solutions that can potentially be merged |
| * then the rollback is skipped as it would just be wasted effort. |
| */ |
| static void find_solutions_main(struct isl_sol *sol, struct isl_tab *tab) |
| { |
| int row; |
| void *saved; |
| |
| if (!tab) |
| goto error; |
| |
| sol->level = 0; |
| |
| for (row = tab->n_redundant; row < tab->n_row; ++row) { |
| int p; |
| struct isl_vec *eq; |
| |
| if (!row_is_parameter_var(tab, row)) |
| 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; |
| } |
| |
| saved = sol->context->op->save(sol->context); |
| |
| find_solutions(sol, tab); |
| |
| if (sol_has_mergeable_solutions(sol)) |
| sol->context->op->restore(sol->context, saved); |
| else |
| sol->context->op->discard(saved); |
| |
| 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 __isl_give isl_basic_map *align_context_divs( |
| __isl_take isl_basic_map *bmap, __isl_keep 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. |
| * Furthermore, make sure that the known integer divisions |
| * appear before any unknown integer division because the solution |
| * may depend on the known integer divisions, while anything that |
| * depends on any variable starting from the first unknown integer |
| * division is ignored in sol_pma_add. |
| */ |
| static struct isl_sol *basic_map_partial_lexopt_base_sol( |
| __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_sort_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_sol and extract the results. |
| */ |
| static __isl_give isl_map *basic_map_partial_lexopt_base( |
| __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_sol(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; |
| } |
| |
| /* Return a count of the number of occurrences of the "n" first |
| * variables in the inequality constraints of "bmap". |
| */ |
| static __isl_give int *count_occurrences(__isl_keep isl_basic_map *bmap, |
| int n) |
| { |
| int i, j; |
| isl_ctx *ctx; |
| int *occurrences; |
| |
| if (!bmap) |
| return NULL; |
| ctx = isl_basic_map_get_ctx(bmap); |
| occurrences = isl_calloc_array(ctx, int, n); |
| if (!occurrences) |
| return NULL; |
| |
| for (i = 0; i < bmap->n_ineq; ++i) { |
| for (j = 0; j < n; ++j) { |
| if (!isl_int_is_zero(bmap->ineq[i][1 + j])) |
| occurrences[j]++; |
| } |
| } |
| |
| return occurrences; |
| } |
| |
| /* Do all of the "n" variables with non-zero coefficients in "c" |
| * occur in exactly a single constraint. |
| * "occurrences" is an array of length "n" containing the number |
| * of occurrences of each of the variables in the inequality constraints. |
| */ |
| static int single_occurrence(int n, isl_int *c, int *occurrences) |
| { |
| int i; |
| |
| for (i = 0; i < n; ++i) { |
| if (isl_int_is_zero(c[i])) |
| continue; |
| if (occurrences[i] != 1) |
| return 0; |
| } |
| |
| return 1; |
| } |
| |
| /* Do all of the "n" initial variables that occur in inequality constraint |
| * "ineq" of "bmap" only occur in that constraint? |
| */ |
| static int all_single_occurrence(__isl_keep isl_basic_map *bmap, int ineq, |
| int n) |
| { |
| int i, j; |
| |
| for (i = 0; i < n; ++i) { |
| if (isl_int_is_zero(bmap->ineq[ineq][1 + i])) |
| continue; |
| for (j = 0; j < bmap->n_ineq; ++j) { |
| if (j == ineq) |
| continue; |
| if (!isl_int_is_zero(bmap->ineq[j][1 + i])) |
| return 0; |
| } |
| } |
| |
| return 1; |
| } |
| |
| /* 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 { |
| 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. |
| * Furthermore, check that each of the input variables that occur |
| * in those constraints does not occur in any other constraint. |
| * If so, return true and return the row indices of the two constraints |
| * in *first and *second. |
| */ |
| static isl_bool parallel_constraints(__isl_keep isl_basic_map *bmap, |
| int *first, int *second) |
| { |
| int i; |
| isl_ctx *ctx; |
| int *occurrences = NULL; |
| 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); |
| occurrences = count_occurrences(bmap, info.n_in); |
| if (info.n_in && !occurrences) |
| goto error; |
| 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; |
| if (!single_occurrence(info.n_in, bmap->ineq[i] + 1, |
| occurrences)) |
| 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); |
| free(occurrences); |
| |
| return i < bmap->n_ineq; |
| error: |
| isl_hash_table_free(ctx, table); |
| free(occurrences); |
| return isl_bool_error; |
| } |
| |
| /* 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_set *set = NULL; |
| |
| if (!dim || !var) |
| goto error; |
| |
| 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 isl_bool 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 isl_bool_true; |
| |
| for (i = 0; i < bmap->n_eq; ++i) |
| if (!isl_int_is_zero(bmap->eq[i][1 + pos])) |
| return isl_bool_true; |
| |
| 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 isl_bool_true; |
| if (isl_seq_first_non_zero(bmap->ineq[i] + 1 + pos + 1, |
| total - pos - 1) >= 0) |
| return isl_bool_true; |
| |
| 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 isl_bool_true; |
| } |
| |
| return isl_bool_false; |
| } |
| |
| /* 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 isl_bool need_split_basic_set(__isl_keep isl_basic_set *bset, |
| __isl_keep isl_mat *cst) |
| { |
| return need_split_basic_map(bset_to_bmap(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 isl_bool need_split_set(__isl_keep isl_set *set, __isl_keep isl_mat *cst) |
| { |
| int i; |
| |
| for (i = 0; i < set->n; ++i) { |
| isl_bool split; |
| |
| split = need_split_basic_set(set->p[i], cst); |
| if (split < 0 || split) |
| return split; |
| } |
| |
| return isl_bool_false; |
| } |
| |
| /* 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_bool split; |
| isl_set *set; |
| |
| set = isl_set_from_basic_set(isl_basic_set_copy(empty->p[i])); |
| split = need_split_basic_set(empty->p[i], cst); |
| if (split < 0) |
| set = isl_set_free(set); |
| else if (split) |
| 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; |
| isl_bool split; |
| |
| map = isl_map_from_basic_map(isl_basic_map_copy(opt->p[i])); |
| split = need_split_basic_map(opt->p[i], cst); |
| if (split < 0) |
| map = isl_map_free(map); |
| else if (split) |
| 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); |
| |
| /* 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 isl_map *basic_map_partial_lexopt_symm_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; |
| |
| 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); |
| |
| return opt; |
| } |
| |
| /* Extract a domain from "bmap" for the purpose of computing |
| * a lexicographic optimum. |
| * |
| * This function is only called when the caller wants to compute a full |
| * lexicographic optimum, i.e., without specifying a domain. In this case, |
| * the caller is not interested in the part of the domain space where |
| * there is no solution and the domain can be initialized to those constraints |
| * of "bmap" that only involve the parameters and the input dimensions. |
| * This relieves the parametric programming engine from detecting those |
| * inequalities and transferring them to the context. More importantly, |
| * it ensures that those inequalities are transferred first and not |
| * intermixed with inequalities that actually split the domain. |
| * |
| * If the caller does not require the absence of existentially quantified |
| * variables in the result (i.e., if ISL_OPT_QE is not set in "flags"), |
| * then the actual domain of "bmap" can be used. This ensures that |
| * the domain does not need to be split at all just to separate out |
| * pieces of the domain that do not have a solution from piece that do. |
| * This domain cannot be used in general because it may involve |
| * (unknown) existentially quantified variables which will then also |
| * appear in the solution. |
| */ |
| static __isl_give isl_basic_set *extract_domain(__isl_keep isl_basic_map *bmap, |
| unsigned flags) |
| { |
| int n_div; |
| int n_out; |
| |
| n_div = isl_basic_map_dim(bmap, isl_dim_div); |
| n_out = isl_basic_map_dim(bmap, isl_dim_out); |
| bmap = isl_basic_map_copy(bmap); |
| if (ISL_FL_ISSET(flags, ISL_OPT_QE)) { |
| bmap = isl_basic_map_drop_constraints_involving_dims(bmap, |
| isl_dim_div, 0, n_div); |
| bmap = isl_basic_map_drop_constraints_involving_dims(bmap, |
| isl_dim_out, 0, n_out); |
| } |
| return isl_basic_map_domain(bmap); |
| } |
| |
| #undef TYPE |
| #define TYPE isl_map |
| #undef SUFFIX |
| #define SUFFIX |
| #include "isl_tab_lexopt_templ.c" |
| |
| /* Extract the subsequence of the sample value of "tab" |
| * starting at "pos" and of length "len". |
| */ |
| static __isl_give isl_vec *extract_sample_sequence(struct isl_tab *tab, |
| int pos, int len) |
| { |
| int i; |
| isl_ctx *ctx; |
| isl_vec *v; |
| |
| ctx = isl_tab_get_ctx(tab); |
| v = isl_vec_alloc(ctx, len); |
| if (!v) |
| return NULL; |
| for (i = 0; i < len; ++i) { |
| if (!tab->var[pos + i].is_row) { |
| isl_int_set_si(v->el[i], 0); |
| } else { |
| int row; |
| |
| row = tab->var[pos + i].index; |
| isl_int_divexact(v->el[i], tab->mat->row[row][1], |
| tab->mat->row[row][0]); |
| } |
| } |
| |
| return v; |
| } |
| |
| /* Check if the sequence of variables starting at "pos" |
| * represents a trivial solution according to "trivial". |
| * That is, is the result of applying "trivial" to this sequence |
| * equal to the zero vector? |
| */ |
| static isl_bool region_is_trivial(struct isl_tab *tab, int pos, |
| __isl_keep isl_mat *trivial) |
| { |
| int n, len; |
| isl_vec *v; |
| isl_bool is_trivial; |
| |
| if (!trivial) |
| return isl_bool_error; |
| |
| n = isl_mat_rows(trivial); |
| if (n == 0) |
| return isl_bool_false; |
| |
| len = isl_mat_cols(trivial); |
| v = extract_sample_sequence(tab, pos, len); |
| v = isl_mat_vec_product(isl_mat_copy(trivial), v); |
| is_trivial = isl_vec_is_zero(v); |
| isl_vec_free(v); |
| |
| return is_trivial; |
| } |
| |
| /* Global internal data for isl_tab_basic_set_non_trivial_lexmin. |
| * |
| * "n_op" is the number of initial coordinates to optimize, |
| * as passed to isl_tab_basic_set_non_trivial_lexmin. |
| * "region" is the "n_region"-sized array of regions passed |
| * to isl_tab_basic_set_non_trivial_lexmin. |
| * |
| * "tab" is the tableau that corresponds to the ILP problem. |
| * "local" is an array of local data structure, one for each |
| * (potential) level of the backtracking procedure of |
| * isl_tab_basic_set_non_trivial_lexmin. |
| * "v" is a pre-allocated vector that can be used for adding |
| * constraints to the tableau. |
| * |
| * "sol" contains the best solution found so far. |
| * It is initialized to a vector of size zero. |
| */ |
| struct isl_lexmin_data { |
| int n_op; |
| int n_region; |
| struct isl_trivial_region *region; |
| |
| struct isl_tab *tab; |
| struct isl_local_region *local; |
| isl_vec *v; |
| |
| isl_vec *sol; |
| }; |
| |
| /* Return the index of the first trivial region, "n_region" if all regions |
| * are non-trivial or -1 in case of error. |
| */ |
| static int first_trivial_region(struct isl_lexmin_data *data) |
| { |
| int i; |
| |
| for (i = 0; i < data->n_region; ++i) { |
| isl_bool trivial; |
| trivial = region_is_trivial(data->tab, data->region[i].pos, |
| data->region[i].trivial); |
| if (trivial < 0) |
| return -1; |
| if (trivial) |
| return i; |
| } |
| |
| return data->n_region; |
| } |
| |
| /* 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 than 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. |
| * "n_zero" is the number of coefficients that have been forced zero |
| * by previous calls to this function at the same level. |
| * Return the updated number of forced zero coefficients or -1 on error. |
| * |
| * This function assumes that at least 2 * (n_op - n_zero) more rows and |
| * at least 2 * (n_op - n_zero) more elements in the constraint array |
| * are available in the tableau. |
| */ |
| static int force_better_solution(struct isl_tab *tab, |
| __isl_keep isl_vec *sol, int n_op, int n_zero) |
| { |
| int i, n; |
| isl_ctx *ctx; |
| isl_vec *v = NULL; |
| |
| if (!sol) |
| return -1; |
| |
| for (i = n_zero; 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 n_op; |
| } |
| |
| ctx = isl_vec_get_ctx(sol); |
| v = isl_vec_alloc(ctx, 1 + tab->n_var); |
| if (!v) |
| return -1; |
| |
| n = i + 1; |
| for (; i >= n_zero; --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 n; |
| error: |
| isl_vec_free(v); |
| return -1; |
| } |
| |
| /* Fix triviality direction "dir" of the given region to zero. |
| * |
| * This function assumes that at least two more rows and at least |
| * two more elements in the constraint array are available in the tableau. |
| */ |
| static isl_stat fix_zero(struct isl_tab *tab, struct isl_trivial_region *region, |
| int dir, struct isl_lexmin_data *data) |
| { |
| int len; |
| |
| data->v = isl_vec_clr(data->v); |
| if (!data->v) |
| return isl_stat_error; |
| len = isl_mat_cols(region->trivial); |
| isl_seq_cpy(data->v->el + 1 + region->pos, region->trivial->row[dir], |
| len); |
| if (add_lexmin_eq(tab, data->v->el) < 0) |
| return isl_stat_error; |
| |
| return isl_stat_ok; |
| } |
| |
| /* This function selects case "side" for non-triviality region "region", |
| * assuming all the equality constraints have been imposed already. |
| * In particular, the triviality direction side/2 is made positive |
| * if side is even and made negative if side is odd. |
| * |
| * This function assumes that at least one more row and at least |
| * one more element in the constraint array are available in the tableau. |
| */ |
| static struct isl_tab *pos_neg(struct isl_tab *tab, |
| struct isl_trivial_region *region, |
| int side, struct isl_lexmin_data *data) |
| { |
| int len; |
| |
| data->v = isl_vec_clr(data->v); |
| if (!data->v) |
| goto error; |
| isl_int_set_si(data->v->el[0], -1); |
| len = isl_mat_cols(region->trivial); |
| if (side % 2 == 0) |
| isl_seq_cpy(data->v->el + 1 + region->pos, |
| region->trivial->row[side / 2], len); |
| else |
| isl_seq_neg(data->v->el + 1 + region->pos, |
| region->trivial->row[side / 2], len); |
| return add_lexmin_ineq(tab, data->v->el); |
| error: |
| isl_tab_free(tab); |
| return NULL; |
| } |
| |
| /* Local data at each level of the backtracking procedure of |
| * isl_tab_basic_set_non_trivial_lexmin. |
| * |
| * "update" is set if a solution has been found in the current case |
| * of this level, such that a better solution needs to be enforced |
| * in the next case. |
| * "n_zero" is the number of initial coordinates that have already |
| * been forced to be zero at this level. |
| * "region" is the non-triviality region considered at this level. |
| * "side" is the index of the current case at this level. |
| * "n" is the number of triviality directions. |
| * "snap" is a snapshot of the tableau holding a state that needs |
| * to be satisfied by all subsequent cases. |
| */ |
| struct isl_local_region { |
| int update; |
| int n_zero; |
| int region; |
| int side; |
| int n; |
| struct isl_tab_undo *snap; |
| }; |
| |
| /* Initialize the global data structure "data" used while solving |
| * the ILP problem "bset". |
| */ |
| static isl_stat init_lexmin_data(struct isl_lexmin_data *data, |
| __isl_keep isl_basic_set *bset) |
| { |
| isl_ctx *ctx; |
| |
| ctx = isl_basic_set_get_ctx(bset); |
| |
| data->tab = tab_for_lexmin(bset, NULL, 0, 0); |
| if (!data->tab) |
| return isl_stat_error; |
| |
| data->v = isl_vec_alloc(ctx, 1 + data->tab->n_var); |
| if (!data->v) |
| return isl_stat_error; |
| data->local = isl_calloc_array(ctx, struct isl_local_region, |
| data->n_region); |
| if (data->n_region && !data->local) |
| return isl_stat_error; |
| |
| data->sol = isl_vec_alloc(ctx, 0); |
| |
| return isl_stat_ok; |
| } |
| |
| /* Mark all outer levels as requiring a better solution |
| * in the next cases. |
| */ |
| static void update_outer_levels(struct isl_lexmin_data *data, int level) |
| { |
| int i; |
| |
| for (i = 0; i < level; ++i) |
| data->local[i].update = 1; |
| } |
| |
| /* Initialize "local" to refer to region "region" and |
| * to initiate processing at this level. |
| */ |
| static void init_local_region(struct isl_local_region *local, int region, |
| struct isl_lexmin_data *data) |
| { |
| local->n = isl_mat_rows(data->region[region].trivial); |
| local->region = region; |
| local->side = 0; |
| local->update = 0; |
| local->n_zero = 0; |
| } |
| |
| /* What to do next after entering a level of the backtracking procedure. |
| * |
| * error: some error has occurred; abort |
| * done: an optimal solution has been found; stop search |
| * backtrack: backtrack to the previous level |
| * handle: add the constraints for the current level and |
| * move to the next level |
| */ |
| enum isl_next { |
| isl_next_error = -1, |
| isl_next_done, |
| isl_next_backtrack, |
| isl_next_handle, |
| }; |
| |
| /* Have all cases of the current region been considered? |
| * If there are n directions, then there are 2n cases. |
| * |
| * The constraints in the current tableau are imposed |
| * in all subsequent cases. This means that if the current |
| * tableau is empty, then none of those cases should be considered |
| * anymore and all cases have effectively been considered. |
| */ |
| static int finished_all_cases(struct isl_local_region *local, |
| struct isl_lexmin_data *data) |
| { |
| if (data->tab->empty) |
| return 1; |
| return local->side >= 2 * local->n; |
| } |
| |
| /* Enter level "level" of the backtracking search and figure out |
| * what to do next. "init" is set if the level was entered |
| * from a higher level and needs to be initialized. |
| * Otherwise, the level is entered as a result of backtracking and |
| * the tableau needs to be restored to a position that can |
| * be used for the next case at this level. |
| * The snapshot is assumed to have been saved in the previous case, |
| * before the constraints specific to that case were added. |
| * |
| * In the initialization case, the local region is initialized |
| * to point to the first violated region. |
| * If the constraints of all regions are satisfied by the current |
| * sample of the tableau, then tell the caller to continue looking |
| * for a better solution or to stop searching if an optimal solution |
| * has been found. |
| * |
| * If the tableau is empty or if all cases at the current level |
| * have been considered, then the caller needs to backtrack as well. |
| */ |
| static enum isl_next enter_level(int level, int init, |
| struct isl_lexmin_data *data) |
| { |
| struct isl_local_region *local = &data->local[level]; |
| |
| if (init) { |
| int r; |
| |
| data->tab = cut_to_integer_lexmin(data->tab, CUT_ONE); |
| if (!data->tab) |
| return isl_next_error; |
| if (data->tab->empty) |
| return isl_next_backtrack; |
| r = first_trivial_region(data); |
| if (r < 0) |
| return isl_next_error; |
| if (r == data->n_region) { |
| update_outer_levels(data, level); |
| isl_vec_free(data->sol); |
| data->sol = isl_tab_get_sample_value(data->tab); |
| if (!data->sol) |
| return isl_next_error; |
| if (is_optimal(data->sol, data->n_op)) |
| return isl_next_done; |
| return isl_next_backtrack; |
| } |
| if (level >= data->n_region) |
| isl_die(isl_vec_get_ctx(data->v), isl_error_internal, |
| "nesting level too deep", |
| return isl_next_error); |
| init_local_region(local, r, data); |
| if (isl_tab_extend_cons(data->tab, |
| 2 * local->n + 2 * data->n_op) < 0) |
| return isl_next_error; |
| } else { |
| if (isl_tab_rollback(data->tab, local->snap) < 0) |
| return isl_next_error; |
| } |
| |
| if (finished_all_cases(local, data)) |
| return isl_next_backtrack; |
| return isl_next_handle; |
| } |
| |
| /* If a solution has been found in the previous case at this level |
| * (marked by local->update being set), then add constraints |
| * that enforce a better solution in the present and all following cases. |
| * The constraints only need to be imposed once because they are |
| * included in the snapshot (taken in pick_side) that will be used in |
| * subsequent cases. |
| */ |
| static isl_stat better_next_side(struct isl_local_region *local, |
| struct isl_lexmin_data *data) |
| { |
| if (!local->update) |
| return isl_stat_ok; |
| |
| local->n_zero = force_better_solution(data->tab, |
| data->sol, data->n_op, local->n_zero); |
| if (local->n_zero < 0) |
| return isl_stat_error; |
| |
| local->update = 0; |
| |
| return isl_stat_ok; |
| } |
| |
| /* Add constraints to data->tab that select the current case (local->side) |
| * at the current level. |
| * |
| * If the linear combinations v should not be zero, then the cases are |
| * v_0 >= 1 |
| * v_0 <= -1 |
| * v_0 = 0 and v_1 >= 1 |
| * v_0 = 0 and v_1 <= -1 |
| * v_0 = 0 and v_1 = 0 and v_2 >= 1 |
| * v_0 = 0 and v_1 = 0 and v_2 <= -1 |
| * ... |
| * in this order. |
| * |
| * A snapshot is taken after the equality constraint (if any) has been added |
| * such that the next case can start off from this position. |
| * The rollback to this position is performed in enter_level. |
| */ |
| static isl_stat pick_side(struct isl_local_region *local, |
| struct isl_lexmin_data *data) |
| { |
| struct isl_trivial_region *region; |
| int side, base; |
| |
| region = &data->region[local->region]; |
| side = local->side; |
| base = 2 * (side/2); |
| |
| if (side == base && base >= 2 && |
| fix_zero(data->tab, region, base / 2 - 1, data) < 0) |
| return isl_stat_error; |
| |
| local->snap = isl_tab_snap(data->tab); |
| if (isl_tab_push_basis(data->tab) < 0) |
| return isl_stat_error; |
| |
| data->tab = pos_neg(data->tab, region, side, data); |
| if (!data->tab) |
| return isl_stat_error; |
| return isl_stat_ok; |
| } |
| |
| /* Free the memory associated to "data". |
| */ |
| static void clear_lexmin_data(struct isl_lexmin_data *data) |
| { |
| free(data->local); |
| isl_vec_free(data->v); |
| isl_tab_free(data->tab); |
| } |
| |
| /* 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 solutions 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 |
| * triviality directions on a sequence of variables that starts |
| * at a given position. A solution is non-trivial on such a region if |
| * at least one of the triviality directions is non-zero |
| * on that sequence of variables. |
| * |
| * 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 an initially trivial region |
| * that is forced to be non-trivial. |
| * At each level we consider 2 * n cases, where n |
| * is the number of triviality directions. |
| * In terms of those n directions v_i, we consider the cases |
| * v_0 >= 1 |
| * v_0 <= -1 |
| * v_0 = 0 and v_1 >= 1 |
| * v_0 = 0 and v_1 <= -1 |
| * v_0 = 0 and v_1 = 0 and v_2 >= 1 |
| * v_0 = 0 and v_1 = 0 and v_2 <= -1 |
| * ... |
| * in this order. |
| */ |
| __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_trivial_region *region, |
| int (*conflict)(int con, void *user), void *user) |
| { |
| struct isl_lexmin_data data = { n_op, n_region, region }; |
| int level, init; |
| |
| if (!bset) |
| return NULL; |
| |
| if (init_lexmin_data(&data, bset) < 0) |
| goto error; |
| data.tab->conflict = conflict; |
| data.tab->conflict_user = user; |
| |
| level = 0; |
| init = 1; |
| |
| while (level >= 0) { |
| enum isl_next next; |
| struct isl_local_region *local = &data.local[level]; |
| |
| next = enter_level(level, init, &data); |
| if (next < 0) |
| goto error; |
| if (next == isl_next_done) |
| break; |
| if (next == isl_next_backtrack) { |
| level--; |
| init = 0; |
| continue; |
| } |
| |
| if (better_next_side(local, &data) < 0) |
| goto error; |
| if (pick_side(local, &data) < 0) |
| goto error; |
| |
| local->side++; |
| level++; |
| init = 1; |
| } |
| |
| clear_lexmin_data(&data); |
| isl_basic_set_free(bset); |
| |
| return data.sol; |
| error: |
| clear_lexmin_data(&data); |
| isl_basic_set_free(bset); |
| isl_vec_free(data.sol); |
| return NULL; |
| } |
| |
| /* Wrapper for a tableau that is used for computing |
| * the lexicographically smallest rational point of a non-negative set. |
| * This point is represented by the sample value of "tab", |
| * unless "tab" is empty. |
| */ |
| struct isl_tab_lexmin { |
| isl_ctx *ctx; |
| struct isl_tab *tab; |
| }; |
| |
| /* Free "tl" and return NULL. |
| */ |
| __isl_null isl_tab_lexmin *isl_tab_lexmin_free(__isl_take isl_tab_lexmin *tl) |
| { |
| if (!tl) |
| return NULL; |
| isl_ctx_deref(tl->ctx); |
| isl_tab_free(tl->tab); |
| free(tl); |
| |
| return NULL; |
| } |
| |
| /* Construct an isl_tab_lexmin for computing |
| * the lexicographically smallest rational point in "bset", |
| * assuming that all variables are non-negative. |
| */ |
| __isl_give isl_tab_lexmin *isl_tab_lexmin_from_basic_set( |
| __isl_take isl_basic_set *bset) |
| { |
| isl_ctx *ctx; |
| isl_tab_lexmin *tl; |
| |
| if (!bset) |
| return NULL; |
| |
| ctx = isl_basic_set_get_ctx(bset); |
| tl = isl_calloc_type(ctx, struct isl_tab_lexmin); |
| if (!tl) |
| goto error; |
| tl->ctx = ctx; |
| isl_ctx_ref(ctx); |
| tl->tab = tab_for_lexmin(bset, NULL, 0, 0); |
| isl_basic_set_free(bset); |
| if (!tl->tab) |
| return isl_tab_lexmin_free(tl); |
| return tl; |
| error: |
| isl_basic_set_free(bset); |
| isl_tab_lexmin_free(tl); |
| return NULL; |
| } |
| |
| /* Return the dimension of the set represented by "tl". |
| */ |
| int isl_tab_lexmin_dim(__isl_keep isl_tab_lexmin *tl) |
| { |
| return tl ? tl->tab->n_var : -1; |
| } |
| |
| /* Add the equality with coefficients "eq" to "tl", updating the optimal |
| * solution if needed. |
| * The equality is added as two opposite inequality constraints. |
| */ |
| __isl_give isl_tab_lexmin *isl_tab_lexmin_add_eq(__isl_take isl_tab_lexmin *tl, |
| isl_int *eq) |
| { |
| unsigned n_var; |
| |
| if (!tl || !eq) |
| return isl_tab_lexmin_free(tl); |
| |
| if (isl_tab_extend_cons(tl->tab, 2) < 0) |
| return isl_tab_lexmin_free(tl); |
| n_var = tl->tab->n_var; |
| isl_seq_neg(eq, eq, 1 + n_var); |
| tl->tab = add_lexmin_ineq(tl->tab, eq); |
| isl_seq_neg(eq, eq, 1 + n_var); |
| tl->tab = add_lexmin_ineq(tl->tab, eq); |
| |
| if (!tl->tab) |
| return isl_tab_lexmin_free(tl); |
| |
| return tl; |
| } |
| |
| /* Add cuts to "tl" until the sample value reaches an integer value or |
| * until the result becomes empty. |
| */ |
| __isl_give isl_tab_lexmin *isl_tab_lexmin_cut_to_integer( |
| __isl_take isl_tab_lexmin *tl) |
| { |
| if (!tl) |
| return NULL; |
| tl->tab = cut_to_integer_lexmin(tl->tab, CUT_ONE); |
| if (!tl->tab) |
| return isl_tab_lexmin_free(tl); |
| return tl; |
| } |
| |
| /* Return the lexicographically smallest rational point in the basic set |
| * from which "tl" was constructed. |
| * If the original input was empty, then return a zero-length vector. |
| */ |
| __isl_give isl_vec *isl_tab_lexmin_get_solution(__isl_keep isl_tab_lexmin *tl) |
| { |
| if (!tl) |
| return NULL; |
| if (tl->tab->empty) |
| return isl_vec_alloc(tl->ctx, 0); |
| else |
| return isl_tab_get_sample_value(tl->tab); |
| } |
| |
| struct isl_sol_pma { |
| struct isl_sol sol; |
| isl_pw_multi_aff *pma; |
| isl_set *empty; |
| }; |
| |
| static void sol_pma_free(struct isl_sol *sol) |
| { |
| struct isl_sol_pma *sol_pma = (struct isl_sol_pma *) sol; |
| isl_pw_multi_aff_free(sol_pma->pma); |
| isl_set_free(sol_pma->empty); |
| } |
| |
| /* 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 || !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 set "dom" that represents the context and a tuple of |
| * affine expressions "maff" defined over this domain, construct |
| * an isl_pw_multi_aff with a single cell corresponding to "dom" and |
| * the affine expressions in "maff". |
| */ |
| static void sol_pma_add(struct isl_sol_pma *sol, |
| __isl_take isl_basic_set *dom, __isl_take isl_multi_aff *maff) |
| { |
| isl_pw_multi_aff *pma; |
| |
| 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_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_multi_aff *ma) |
| { |
| sol_pma_add((struct isl_sol_pma *)sol, dom, ma); |
| } |
| |
| /* 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; |
| isl_space *space; |
| |
| if (!bmap) |
| goto error; |
| |
| sol_pma = isl_calloc_type(bmap->ctx, struct isl_sol_pma); |
| if (!sol_pma) |
| goto error; |
| |
| sol_pma->sol.free = &sol_pma_free; |
| if (sol_init(&sol_pma->sol, bmap, dom, max) < 0) |
| goto error; |
| sol_pma->sol.add = &sol_pma_add_wrap; |
| sol_pma->sol.add_empty = track_empty ? &sol_pma_add_empty_wrap : NULL; |
| space = isl_space_copy(sol_pma->sol.space); |
| sol_pma->pma = isl_pw_multi_aff_empty(space); |
| if (!sol_pma->pma) |
| 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_free(&sol_pma->sol); |
| return NULL; |
| } |
| |
| /* Base case of isl_tab_basic_map_partial_lexopt, after removing |
| * some obvious symmetries. |
| * |
| * We call basic_map_partial_lexopt_base_sol and extract the results. |
| */ |
| static __isl_give isl_pw_multi_aff *basic_map_partial_lexopt_base_pw_multi_aff( |
| __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_sol(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->u.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_pw_aff *paff = NULL; |
| isl_space *pw_space; |
| isl_local_space *ls = NULL; |
| |
| if (!space || !var) |
| goto error; |
| |
| 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 { |
| isl_bool split; |
| split = need_split_set(opt->p[i].set, cst); |
| if (split < 0) |
| pma = isl_pw_multi_aff_free(pma); |
| else if (split) |
| 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_pw_multi_aff( |
| __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 isl_pw_multi_aff * |
| basic_map_partial_lexopt_symm_core_pw_multi_aff( |
| __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; |
| |
| 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_pw_multi_aff(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); |
| |
| return opt; |
| } |
| |
| #undef TYPE |
| #define TYPE isl_pw_multi_aff |
| #undef SUFFIX |
| #define SUFFIX _pw_multi_aff |
| #include "isl_tab_lexopt_templ.c" |