/*
* 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"