nexmon – Rev 1
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/*
* Copyright 2008-2009 Katholieke Universiteit Leuven
* Copyright 2010 INRIA Saclay
*
* Use of this software is governed by the GNU LGPLv2.1 license
*
* Written by Sven Verdoolaege, K.U.Leuven, Departement
* Computerwetenschappen, Celestijnenlaan 200A, B-3001 Leuven, Belgium
* and INRIA Saclay - Ile-de-France, Parc Club Orsay Universite,
* ZAC des vignes, 4 rue Jacques Monod, 91893 Orsay, France
*/
#include <isl_ctx_private.h>
#include "isl_map_private.h"
#include <isl/seq.h>
#include "isl_tab.h"
#include "isl_sample.h"
#include <isl_mat_private.h>
#include <isl_aff_private.h>
#include <isl_options_private.h>
#include <isl_config.h>
/*
* The implementation of parametric integer linear programming in this file
* was inspired by the paper "Parametric Integer Programming" and the
* report "Solving systems of affine (in)equalities" by Paul Feautrier
* (and others).
*
* The strategy used for obtaining a feasible solution is different
* from the one used in isl_tab.c. In particular, in isl_tab.c,
* upon finding a constraint that is not yet satisfied, we pivot
* in a row that increases the constant term of the row holding the
* constraint, making sure the sample solution remains feasible
* for all the constraints it already satisfied.
* Here, we always pivot in the row holding the constraint,
* choosing a column that induces the lexicographically smallest
* increment to the sample solution.
*
* By starting out from a sample value that is lexicographically
* smaller than any integer point in the problem space, the first
* feasible integer sample point we find will also be the lexicographically
* smallest. If all variables can be assumed to be non-negative,
* then the initial sample value may be chosen equal to zero.
* However, we will not make this assumption. Instead, we apply
* the "big parameter" trick. Any variable x is then not directly
* used in the tableau, but instead it is represented by another
* variable x' = M + x, where M is an arbitrarily large (positive)
* value. x' is therefore always non-negative, whatever the value of x.
* Taking as initial sample value x' = 0 corresponds to x = -M,
* which is always smaller than any possible value of x.
*
* The big parameter trick is used in the main tableau and
* also in the context tableau if isl_context_lex is used.
* In this case, each tableaus has its own big parameter.
* Before doing any real work, we check if all the parameters
* happen to be non-negative. If so, we drop the column corresponding
* to M from the initial context tableau.
* If isl_context_gbr is used, then the big parameter trick is only
* used in the main tableau.
*/
struct isl_context;
struct isl_context_op {
/* detect nonnegative parameters in context and mark them in tab */
struct isl_tab *(*detect_nonnegative_parameters)(
struct isl_context *context, struct isl_tab *tab);
/* return temporary reference to basic set representation of context */
struct isl_basic_set *(*peek_basic_set)(struct isl_context *context);
/* return temporary reference to tableau representation of context */
struct isl_tab *(*peek_tab)(struct isl_context *context);
/* add equality; check is 1 if eq may not be valid;
* update is 1 if we may want to call ineq_sign on context later.
*/
void (*add_eq)(struct isl_context *context, isl_int *eq,
int check, int update);
/* add inequality; check is 1 if ineq may not be valid;
* update is 1 if we may want to call ineq_sign on context later.
*/
void (*add_ineq)(struct isl_context *context, isl_int *ineq,
int check, int update);
/* check sign of ineq based on previous information.
* strict is 1 if saturation should be treated as a positive sign.
*/
enum isl_tab_row_sign (*ineq_sign)(struct isl_context *context,
isl_int *ineq, int strict);
/* check if inequality maintains feasibility */
int (*test_ineq)(struct isl_context *context, isl_int *ineq);
/* return index of a div that corresponds to "div" */
int (*get_div)(struct isl_context *context, struct isl_tab *tab,
struct isl_vec *div);
/* add div "div" to context and return non-negativity */
int (*add_div)(struct isl_context *context, struct isl_vec *div);
int (*detect_equalities)(struct isl_context *context,
struct isl_tab *tab);
/* return row index of "best" split */
int (*best_split)(struct isl_context *context, struct isl_tab *tab);
/* check if context has already been determined to be empty */
int (*is_empty)(struct isl_context *context);
/* check if context is still usable */
int (*is_ok)(struct isl_context *context);
/* save a copy/snapshot of context */
void *(*save)(struct isl_context *context);
/* restore saved context */
void (*restore)(struct isl_context *context, void *);
/* invalidate context */
void (*invalidate)(struct isl_context *context);
/* free context */
void (*free)(struct isl_context *context);
};
struct isl_context {
struct isl_context_op *op;
};
struct isl_context_lex {
struct isl_context context;
struct isl_tab *tab;
};
struct isl_partial_sol {
int level;
struct isl_basic_set *dom;
struct isl_mat *M;
struct isl_partial_sol *next;
};
struct isl_sol;
struct isl_sol_callback {
struct isl_tab_callback callback;
struct isl_sol *sol;
};
/* isl_sol is an interface for constructing a solution to
* a parametric integer linear programming problem.
* Every time the algorithm reaches a state where a solution
* can be read off from the tableau (including cases where the tableau
* is empty), the function "add" is called on the isl_sol passed
* to find_solutions_main.
*
* The context tableau is owned by isl_sol and is updated incrementally.
*
* There are currently two implementations of this interface,
* isl_sol_map, which simply collects the solutions in an isl_map
* and (optionally) the parts of the context where there is no solution
* in an isl_set, and
* isl_sol_for, which calls a user-defined function for each part of
* the solution.
*/
struct isl_sol {
int error;
int rational;
int level;
int max;
int n_out;
struct isl_context *context;
struct isl_partial_sol *partial;
void (*add)(struct isl_sol *sol,
struct isl_basic_set *dom, struct isl_mat *M);
void (*add_empty)(struct isl_sol *sol, struct isl_basic_set *bset);
void (*free)(struct isl_sol *sol);
struct isl_sol_callback dec_level;
};
static void sol_free(struct isl_sol *sol)
{
struct isl_partial_sol *partial, *next;
if (!sol)
return;
for (partial = sol->partial; partial; partial = next) {
next = partial->next;
isl_basic_set_free(partial->dom);
isl_mat_free(partial->M);
free(partial);
}
sol->free(sol);
}
/* Push a partial solution represented by a domain and mapping M
* onto the stack of partial solutions.
*/
static void sol_push_sol(struct isl_sol *sol,
struct isl_basic_set *dom, struct isl_mat *M)
{
struct isl_partial_sol *partial;
if (sol->error || !dom)
goto error;
partial = isl_alloc_type(dom->ctx, struct isl_partial_sol);
if (!partial)
goto error;
partial->level = sol->level;
partial->dom = dom;
partial->M = M;
partial->next = sol->partial;
sol->partial = partial;
return;
error:
isl_basic_set_free(dom);
sol->error = 1;
}
/* Pop one partial solution from the partial solution stack and
* pass it on to sol->add or sol->add_empty.
*/
static void sol_pop_one(struct isl_sol *sol)
{
struct isl_partial_sol *partial;
partial = sol->partial;
sol->partial = partial->next;
if (partial->M)
sol->add(sol, partial->dom, partial->M);
else
sol->add_empty(sol, partial->dom);
free(partial);
}
/* Return a fresh copy of the domain represented by the context tableau.
*/
static struct isl_basic_set *sol_domain(struct isl_sol *sol)
{
struct isl_basic_set *bset;
if (sol->error)
return NULL;
bset = isl_basic_set_dup(sol->context->op->peek_basic_set(sol->context));
bset = isl_basic_set_update_from_tab(bset,
sol->context->op->peek_tab(sol->context));
return bset;
}
/* Check whether two partial solutions have the same mapping, where n_div
* is the number of divs that the two partial solutions have in common.
*/
static int same_solution(struct isl_partial_sol *s1, struct isl_partial_sol *s2,
unsigned n_div)
{
int i;
unsigned dim;
if (!s1->M != !s2->M)
return 0;
if (!s1->M)
return 1;
dim = isl_basic_set_total_dim(s1->dom) - s1->dom->n_div;
for (i = 0; i < s1->M->n_row; ++i) {
if (isl_seq_first_non_zero(s1->M->row[i]+1+dim+n_div,
s1->M->n_col-1-dim-n_div) != -1)
return 0;
if (isl_seq_first_non_zero(s2->M->row[i]+1+dim+n_div,
s2->M->n_col-1-dim-n_div) != -1)
return 0;
if (!isl_seq_eq(s1->M->row[i], s2->M->row[i], 1+dim+n_div))
return 0;
}
return 1;
}
/* Pop all solutions from the partial solution stack that were pushed onto
* the stack at levels that are deeper than the current level.
* If the two topmost elements on the stack have the same level
* and represent the same solution, then their domains are combined.
* This combined domain is the same as the current context domain
* as sol_pop is called each time we move back to a higher level.
*/
static void sol_pop(struct isl_sol *sol)
{
struct isl_partial_sol *partial;
unsigned n_div;
if (sol->error)
return;
if (sol->level == 0) {
for (partial = sol->partial; partial; partial = sol->partial)
sol_pop_one(sol);
return;
}
partial = sol->partial;
if (!partial)
return;
if (partial->level <= sol->level)
return;
if (partial->next && partial->next->level == partial->level) {
n_div = isl_basic_set_dim(
sol->context->op->peek_basic_set(sol->context),
isl_dim_div);
if (!same_solution(partial, partial->next, n_div)) {
sol_pop_one(sol);
sol_pop_one(sol);
} else {
struct isl_basic_set *bset;
bset = sol_domain(sol);
isl_basic_set_free(partial->next->dom);
partial->next->dom = bset;
partial->next->level = sol->level;
sol->partial = partial->next;
isl_basic_set_free(partial->dom);
isl_mat_free(partial->M);
free(partial);
}
} else
sol_pop_one(sol);
}
static void sol_dec_level(struct isl_sol *sol)
{
if (sol->error)
return;
sol->level--;
sol_pop(sol);
}
static int sol_dec_level_wrap(struct isl_tab_callback *cb)
{
struct isl_sol_callback *callback = (struct isl_sol_callback *)cb;
sol_dec_level(callback->sol);
return callback->sol->error ? -1 : 0;
}
/* Move down to next level and push callback onto context tableau
* to decrease the level again when it gets rolled back across
* the current state. That is, dec_level will be called with
* the context tableau in the same state as it is when inc_level
* is called.
*/
static void sol_inc_level(struct isl_sol *sol)
{
struct isl_tab *tab;
if (sol->error)
return;
sol->level++;
tab = sol->context->op->peek_tab(sol->context);
if (isl_tab_push_callback(tab, &sol->dec_level.callback) < 0)
sol->error = 1;
}
static void scale_rows(struct isl_mat *mat, isl_int m, int n_row)
{
int i;
if (isl_int_is_one(m))
return;
for (i = 0; i < n_row; ++i)
isl_seq_scale(mat->row[i], mat->row[i], m, mat->n_col);
}
/* Add the solution identified by the tableau and the context tableau.
*
* The layout of the variables is as follows.
* tab->n_var is equal to the total number of variables in the input
* map (including divs that were copied from the context)
* + the number of extra divs constructed
* Of these, the first tab->n_param and the last tab->n_div variables
* correspond to the variables in the context, i.e.,
* tab->n_param + tab->n_div = context_tab->n_var
* tab->n_param is equal to the number of parameters and input
* dimensions in the input map
* tab->n_div is equal to the number of divs in the context
*
* If there is no solution, then call add_empty with a basic set
* that corresponds to the context tableau. (If add_empty is NULL,
* then do nothing).
*
* If there is a solution, then first construct a matrix that maps
* all dimensions of the context to the output variables, i.e.,
* the output dimensions in the input map.
* The divs in the input map (if any) that do not correspond to any
* div in the context do not appear in the solution.
* The algorithm will make sure that they have an integer value,
* but these values themselves are of no interest.
* We have to be careful not to drop or rearrange any divs in the
* context because that would change the meaning of the matrix.
*
* To extract the value of the output variables, it should be noted
* that we always use a big parameter M in the main tableau and so
* the variable stored in this tableau is not an output variable x itself, but
* x' = M + x (in case of minimization)
* or
* x' = M - x (in case of maximization)
* If x' appears in a column, then its optimal value is zero,
* which means that the optimal value of x is an unbounded number
* (-M for minimization and M for maximization).
* We currently assume that the output dimensions in the original map
* are bounded, so this cannot occur.
* Similarly, when x' appears in a row, then the coefficient of M in that
* row is necessarily 1.
* If the row in the tableau represents
* d x' = c + d M + e(y)
* then, in case of minimization, the corresponding row in the matrix
* will be
* a c + a e(y)
* with a d = m, the (updated) common denominator of the matrix.
* In case of maximization, the row will be
* -a c - a e(y)
*/
static void sol_add(struct isl_sol *sol, struct isl_tab *tab)
{
struct isl_basic_set *bset = NULL;
struct isl_mat *mat = NULL;
unsigned off;
int row;
isl_int m;
if (sol->error || !tab)
goto error;
if (tab->empty && !sol->add_empty)
return;
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(sol, bset, mat);
return;
error2:
isl_int_clear(m);
error:
isl_basic_set_free(bset);
isl_mat_free(mat);
sol->error = 1;
}
struct isl_sol_map {
struct isl_sol sol;
struct isl_map *map;
struct isl_set *empty;
};
static void sol_map_free(struct isl_sol_map *sol_map)
{
if (!sol_map)
return;
if (sol_map->sol.context)
sol_map->sol.context->op->free(sol_map->sol.context);
isl_map_free(sol_map->map);
isl_set_free(sol_map->empty);
free(sol_map);
}
static void sol_map_free_wrap(struct isl_sol *sol)
{
sol_map_free((struct isl_sol_map *)sol);
}
/* This function is called for parts of the context where there is
* no solution, with "bset" corresponding to the context tableau.
* Simply add the basic set to the set "empty".
*/
static void sol_map_add_empty(struct isl_sol_map *sol,
struct isl_basic_set *bset)
{
if (!bset)
goto error;
isl_assert(bset->ctx, sol->empty, goto error);
sol->empty = isl_set_grow(sol->empty, 1);
bset = isl_basic_set_simplify(bset);
bset = isl_basic_set_finalize(bset);
sol->empty = isl_set_add_basic_set(sol->empty, isl_basic_set_copy(bset));
if (!sol->empty)
goto error;
isl_basic_set_free(bset);
return;
error:
isl_basic_set_free(bset);
sol->sol.error = 1;
}
static void sol_map_add_empty_wrap(struct isl_sol *sol,
struct isl_basic_set *bset)
{
sol_map_add_empty((struct isl_sol_map *)sol, bset);
}
/* Given a basic map "dom" that represents the context and an affine
* matrix "M" that maps the dimensions of the context to the
* output variables, construct a basic map with the same parameters
* and divs as the context, the dimensions of the context as input
* dimensions and a number of output dimensions that is equal to
* the number of output dimensions in the input map.
*
* The constraints and divs of the context are simply copied
* from "dom". For each row
* x = c + e(y)
* an equality
* c + e(y) - d x = 0
* is added, with d the common denominator of M.
*/
static void sol_map_add(struct isl_sol_map *sol,
struct isl_basic_set *dom, struct isl_mat *M)
{
int i;
struct isl_basic_map *bmap = NULL;
unsigned n_eq;
unsigned n_ineq;
unsigned nparam;
unsigned total;
unsigned n_div;
unsigned n_out;
if (sol->sol.error || !dom || !M)
goto error;
n_out = sol->sol.n_out;
n_eq = dom->n_eq + n_out;
n_ineq = dom->n_ineq;
n_div = dom->n_div;
nparam = isl_basic_set_total_dim(dom) - n_div;
total = isl_map_dim(sol->map, isl_dim_all);
bmap = isl_basic_map_alloc_space(isl_map_get_space(sol->map),
n_div, n_eq, 2 * n_div + n_ineq);
if (!bmap)
goto error;
if (sol->sol.rational)
ISL_F_SET(bmap, ISL_BASIC_MAP_RATIONAL);
for (i = 0; i < dom->n_div; ++i) {
int k = isl_basic_map_alloc_div(bmap);
if (k < 0)
goto error;
isl_seq_cpy(bmap->div[k], dom->div[i], 1 + 1 + nparam);
isl_seq_clr(bmap->div[k] + 1 + 1 + nparam, total - nparam);
isl_seq_cpy(bmap->div[k] + 1 + 1 + total,
dom->div[i] + 1 + 1 + nparam, i);
}
for (i = 0; i < dom->n_eq; ++i) {
int k = isl_basic_map_alloc_equality(bmap);
if (k < 0)
goto error;
isl_seq_cpy(bmap->eq[k], dom->eq[i], 1 + nparam);
isl_seq_clr(bmap->eq[k] + 1 + nparam, total - nparam);
isl_seq_cpy(bmap->eq[k] + 1 + total,
dom->eq[i] + 1 + nparam, n_div);
}
for (i = 0; i < dom->n_ineq; ++i) {
int k = isl_basic_map_alloc_inequality(bmap);
if (k < 0)
goto error;
isl_seq_cpy(bmap->ineq[k], dom->ineq[i], 1 + nparam);
isl_seq_clr(bmap->ineq[k] + 1 + nparam, total - nparam);
isl_seq_cpy(bmap->ineq[k] + 1 + total,
dom->ineq[i] + 1 + nparam, n_div);
}
for (i = 0; i < M->n_row - 1; ++i) {
int k = isl_basic_map_alloc_equality(bmap);
if (k < 0)
goto error;
isl_seq_cpy(bmap->eq[k], M->row[1 + i], 1 + nparam);
isl_seq_clr(bmap->eq[k] + 1 + nparam, n_out);
isl_int_neg(bmap->eq[k][1 + nparam + i], M->row[0][0]);
isl_seq_cpy(bmap->eq[k] + 1 + nparam + n_out,
M->row[1 + i] + 1 + nparam, n_div);
}
bmap = isl_basic_map_simplify(bmap);
bmap = isl_basic_map_finalize(bmap);
sol->map = isl_map_grow(sol->map, 1);
sol->map = isl_map_add_basic_map(sol->map, bmap);
isl_basic_set_free(dom);
isl_mat_free(M);
if (!sol->map)
sol->sol.error = 1;
return;
error:
isl_basic_set_free(dom);
isl_mat_free(M);
isl_basic_map_free(bmap);
sol->sol.error = 1;
}
static void sol_map_add_wrap(struct isl_sol *sol,
struct isl_basic_set *dom, struct isl_mat *M)
{
sol_map_add((struct isl_sol_map *)sol, dom, M);
}
/* Store the "parametric constant" of row "row" of tableau "tab" in "line",
* i.e., the constant term and the coefficients of all variables that
* appear in the context tableau.
* Note that the coefficient of the big parameter M is NOT copied.
* The context tableau may not have a big parameter and even when it
* does, it is a different big parameter.
*/
static void get_row_parameter_line(struct isl_tab *tab, int row, isl_int *line)
{
int i;
unsigned off = 2 + tab->M;
isl_int_set(line[0], tab->mat->row[row][1]);
for (i = 0; i < tab->n_param; ++i) {
if (tab->var[i].is_row)
isl_int_set_si(line[1 + i], 0);
else {
int col = tab->var[i].index;
isl_int_set(line[1 + i], tab->mat->row[row][off + col]);
}
}
for (i = 0; i < tab->n_div; ++i) {
if (tab->var[tab->n_var - tab->n_div + i].is_row)
isl_int_set_si(line[1 + tab->n_param + i], 0);
else {
int col = tab->var[tab->n_var - tab->n_div + i].index;
isl_int_set(line[1 + tab->n_param + i],
tab->mat->row[row][off + col]);
}
}
}
/* Check if rows "row1" and "row2" have identical "parametric constants",
* as explained above.
* In this case, we also insist that the coefficients of the big parameter
* be the same as the values of the constants will only be the same
* if these coefficients are also the same.
*/
static int identical_parameter_line(struct isl_tab *tab, int row1, int row2)
{
int i;
unsigned off = 2 + tab->M;
if (isl_int_ne(tab->mat->row[row1][1], tab->mat->row[row2][1]))
return 0;
if (tab->M && isl_int_ne(tab->mat->row[row1][2],
tab->mat->row[row2][2]))
return 0;
for (i = 0; i < tab->n_param + tab->n_div; ++i) {
int pos = i < tab->n_param ? i :
tab->n_var - tab->n_div + i - tab->n_param;
int col;
if (tab->var[pos].is_row)
continue;
col = tab->var[pos].index;
if (isl_int_ne(tab->mat->row[row1][off + col],
tab->mat->row[row2][off + col]))
return 0;
}
return 1;
}
/* Return an inequality that expresses that the "parametric constant"
* should be non-negative.
* This function is only called when the coefficient of the big parameter
* is equal to zero.
*/
static struct isl_vec *get_row_parameter_ineq(struct isl_tab *tab, int row)
{
struct isl_vec *ineq;
ineq = isl_vec_alloc(tab->mat->ctx, 1 + tab->n_param + tab->n_div);
if (!ineq)
return NULL;
get_row_parameter_line(tab, row, ineq->el);
if (ineq)
ineq = isl_vec_normalize(ineq);
return ineq;
}
/* 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 a integer division for use in a parametric cut based on the given row.
* In particular, let the parametric constant of the row be
*
* \sum_i a_i y_i
*
* where y_0 = 1, but none of the y_i corresponds to the big parameter M.
* The div returned is equal to
*
* floor(\sum_i {-a_i} y_i) = floor((\sum_i (-a_i mod d) y_i)/d)
*/
static struct isl_vec *get_row_parameter_div(struct isl_tab *tab, int row)
{
struct isl_vec *div;
div = isl_vec_alloc(tab->mat->ctx, 1 + 1 + tab->n_param + tab->n_div);
if (!div)
return NULL;
isl_int_set(div->el[0], tab->mat->row[row][0]);
get_row_parameter_line(tab, row, div->el + 1);
normalize_div(div);
isl_seq_neg(div->el + 1, div->el + 1, div->size - 1);
isl_seq_fdiv_r(div->el + 1, div->el + 1, div->el[0], div->size - 1);
return div;
}
/* Return a integer division for use in transferring an integrality constraint
* to the context.
* In particular, let the parametric constant of the row be
*
* \sum_i a_i y_i
*
* where y_0 = 1, but none of the y_i corresponds to the big parameter M.
* The the returned div is equal to
*
* floor(\sum_i {a_i} y_i) = floor((\sum_i (a_i mod d) y_i)/d)
*/
static struct isl_vec *get_row_split_div(struct isl_tab *tab, int row)
{
struct isl_vec *div;
div = isl_vec_alloc(tab->mat->ctx, 1 + 1 + tab->n_param + tab->n_div);
if (!div)
return NULL;
isl_int_set(div->el[0], tab->mat->row[row][0]);
get_row_parameter_line(tab, row, div->el + 1);
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 struct isl_vec *ineq_for_div(struct isl_basic_set *bset, unsigned div)
{
unsigned total;
unsigned div_pos;
struct isl_vec *ineq;
if (!bset)
return NULL;
total = isl_basic_set_total_dim(bset);
div_pos = 1 + total - bset->n_div + div;
ineq = isl_vec_alloc(bset->ctx, 1 + total);
if (!ineq)
return NULL;
isl_seq_cpy(ineq->el, bset->div[div] + 1, 1 + total);
isl_int_neg(ineq->el[div_pos], bset->div[div][0]);
return ineq;
}
/* Given a row in the tableau and a div that was created
* using get_row_split_div and that has been constrained to equality, i.e.,
*
* d = floor(\sum_i {a_i} y_i) = \sum_i {a_i} y_i
*
* replace the expression "\sum_i {a_i} y_i" in the row by d,
* i.e., we subtract "\sum_i {a_i} y_i" and add 1 d.
* The coefficients of the non-parameters in the tableau have been
* verified to be integral. We can therefore simply replace coefficient b
* by floor(b). For the coefficients of the parameters we have
* floor(a_i) = a_i - {a_i}, while for the other coefficients, we have
* floor(b) = b.
*/
static struct isl_tab *set_row_cst_to_div(struct isl_tab *tab, int row, int div)
{
isl_seq_fdiv_q(tab->mat->row[row] + 1, tab->mat->row[row] + 1,
tab->mat->row[row][0], 1 + tab->M + tab->n_col);
isl_int_set_si(tab->mat->row[row][0], 1);
if (tab->var[tab->n_var - tab->n_div + div].is_row) {
int drow = tab->var[tab->n_var - tab->n_div + div].index;
isl_assert(tab->mat->ctx,
isl_int_is_one(tab->mat->row[drow][0]), goto error);
isl_seq_combine(tab->mat->row[row] + 1,
tab->mat->ctx->one, tab->mat->row[row] + 1,
tab->mat->ctx->one, tab->mat->row[drow] + 1,
1 + tab->M + tab->n_col);
} else {
int dcol = tab->var[tab->n_var - tab->n_div + div].index;
isl_int_add_ui(tab->mat->row[row][2 + tab->M + dcol],
tab->mat->row[row][2 + tab->M + dcol], 1);
}
return tab;
error:
isl_tab_free(tab);
return NULL;
}
/* Check if the (parametric) constant of the given row is obviously
* negative, meaning that we don't need to consult the context tableau.
* If there is a big parameter and its coefficient is non-zero,
* then this coefficient determines the outcome.
* Otherwise, we check whether the constant is negative and
* all non-zero coefficients of parameters are negative and
* belong to non-negative parameters.
*/
static int is_obviously_neg(struct isl_tab *tab, int row)
{
int i;
int col;
unsigned off = 2 + tab->M;
if (tab->M) {
if (isl_int_is_pos(tab->mat->row[row][2]))
return 0;
if (isl_int_is_neg(tab->mat->row[row][2]))
return 1;
}
if (isl_int_is_nonneg(tab->mat->row[row][1]))
return 0;
for (i = 0; i < tab->n_param; ++i) {
/* Eliminated parameter */
if (tab->var[i].is_row)
continue;
col = tab->var[i].index;
if (isl_int_is_zero(tab->mat->row[row][off + col]))
continue;
if (!tab->var[i].is_nonneg)
return 0;
if (isl_int_is_pos(tab->mat->row[row][off + col]))
return 0;
}
for (i = 0; i < tab->n_div; ++i) {
if (tab->var[tab->n_var - tab->n_div + i].is_row)
continue;
col = tab->var[tab->n_var - tab->n_div + i].index;
if (isl_int_is_zero(tab->mat->row[row][off + col]))
continue;
if (!tab->var[tab->n_var - tab->n_div + i].is_nonneg)
return 0;
if (isl_int_is_pos(tab->mat->row[row][off + col]))
return 0;
}
return 1;
}
/* Check if the (parametric) constant of the given row is obviously
* non-negative, meaning that we don't need to consult the context tableau.
* If there is a big parameter and its coefficient is non-zero,
* then this coefficient determines the outcome.
* Otherwise, we check whether the constant is non-negative and
* all non-zero coefficients of parameters are positive and
* belong to non-negative parameters.
*/
static int is_obviously_nonneg(struct isl_tab *tab, int row)
{
int i;
int col;
unsigned off = 2 + tab->M;
if (tab->M) {
if (isl_int_is_pos(tab->mat->row[row][2]))
return 1;
if (isl_int_is_neg(tab->mat->row[row][2]))
return 0;
}
if (isl_int_is_neg(tab->mat->row[row][1]))
return 0;
for (i = 0; i < tab->n_param; ++i) {
/* Eliminated parameter */
if (tab->var[i].is_row)
continue;
col = tab->var[i].index;
if (isl_int_is_zero(tab->mat->row[row][off + col]))
continue;
if (!tab->var[i].is_nonneg)
return 0;
if (isl_int_is_neg(tab->mat->row[row][off + col]))
return 0;
}
for (i = 0; i < tab->n_div; ++i) {
if (tab->var[tab->n_var - tab->n_div + i].is_row)
continue;
col = tab->var[tab->n_var - tab->n_div + i].index;
if (isl_int_is_zero(tab->mat->row[row][off + col]))
continue;
if (!tab->var[tab->n_var - tab->n_div + i].is_nonneg)
return 0;
if (isl_int_is_neg(tab->mat->row[row][off + col]))
return 0;
}
return 1;
}
/* Given a row r and two columns, return the column that would
* lead to the lexicographically smallest increment in the sample
* solution when leaving the basis in favor of the row.
* Pivoting with column c will increment the sample value by a non-negative
* constant times a_{V,c}/a_{r,c}, with a_{V,c} the elements of column c
* corresponding to the non-parametric variables.
* If variable v appears in a column c_v, the a_{v,c} = 1 iff c = c_v,
* with all other entries in this virtual row equal to zero.
* If variable v appears in a row, then a_{v,c} is the element in column c
* of that row.
*
* Let v be the first variable with a_{v,c1}/a_{r,c1} != a_{v,c2}/a_{r,c2}.
* Then if a_{v,c1}/a_{r,c1} < a_{v,c2}/a_{r,c2}, i.e.,
* a_{v,c2} a_{r,c1} - a_{v,c1} a_{r,c2} > 0, c1 results in the minimal
* increment. Otherwise, it's c2.
*/
static int lexmin_col_pair(struct isl_tab *tab,
int row, int col1, int col2, isl_int tmp)
{
int i;
isl_int *tr;
tr = tab->mat->row[row] + 2 + tab->M;
for (i = tab->n_param; i < tab->n_var - tab->n_div; ++i) {
int s1, s2;
isl_int *r;
if (!tab->var[i].is_row) {
if (tab->var[i].index == col1)
return col2;
if (tab->var[i].index == col2)
return col1;
continue;
}
if (tab->var[i].index == row)
continue;
r = tab->mat->row[tab->var[i].index] + 2 + tab->M;
s1 = isl_int_sgn(r[col1]);
s2 = isl_int_sgn(r[col2]);
if (s1 == 0 && s2 == 0)
continue;
if (s1 < s2)
return col1;
if (s2 < s1)
return col2;
isl_int_mul(tmp, r[col2], tr[col1]);
isl_int_submul(tmp, r[col1], tr[col2]);
if (isl_int_is_pos(tmp))
return col1;
if (isl_int_is_neg(tmp))
return col2;
}
return -1;
}
/* Given a row in the tableau, find and return the column that would
* result in the lexicographically smallest, but positive, increment
* in the sample point.
* If there is no such column, then return tab->n_col.
* If anything goes wrong, return -1.
*/
static int lexmin_pivot_col(struct isl_tab *tab, int row)
{
int j;
int col = tab->n_col;
isl_int *tr;
isl_int tmp;
tr = tab->mat->row[row] + 2 + tab->M;
isl_int_init(tmp);
for (j = tab->n_dead; j < tab->n_col; ++j) {
if (tab->col_var[j] >= 0 &&
(tab->col_var[j] < tab->n_param ||
tab->col_var[j] >= tab->n_var - tab->n_div))
continue;
if (!isl_int_is_pos(tr[j]))
continue;
if (col == tab->n_col)
col = j;
else
col = lexmin_col_pair(tab, row, col, j, tmp);
isl_assert(tab->mat->ctx, col >= 0, goto error);
}
isl_int_clear(tmp);
return col;
error:
isl_int_clear(tmp);
return -1;
}
/* Return the first known violated constraint, i.e., a non-negative
* constraint that currently has an either obviously negative value
* or a previously determined to be negative value.
*
* If any constraint has a negative coefficient for the big parameter,
* if any, then we return one of these first.
*/
static int first_neg(struct isl_tab *tab)
{
int row;
if (tab->M)
for (row = tab->n_redundant; row < tab->n_row; ++row) {
if (!isl_tab_var_from_row(tab, row)->is_nonneg)
continue;
if (!isl_int_is_neg(tab->mat->row[row][2]))
continue;
if (tab->row_sign)
tab->row_sign[row] = isl_tab_row_neg;
return row;
}
for (row = tab->n_redundant; row < tab->n_row; ++row) {
if (!isl_tab_var_from_row(tab, row)->is_nonneg)
continue;
if (tab->row_sign) {
if (tab->row_sign[row] == 0 &&
is_obviously_neg(tab, row))
tab->row_sign[row] = isl_tab_row_neg;
if (tab->row_sign[row] != isl_tab_row_neg)
continue;
} else if (!is_obviously_neg(tab, row))
continue;
return row;
}
return -1;
}
/* Check whether the invariant that all columns are lexico-positive
* is satisfied. This function is not called from the current code
* but is useful during debugging.
*/
static void check_lexpos(struct isl_tab *tab) __attribute__ ((unused));
static void check_lexpos(struct isl_tab *tab)
{
unsigned off = 2 + tab->M;
int col;
int var;
int row;
for (col = tab->n_dead; col < tab->n_col; ++col) {
if (tab->col_var[col] >= 0 &&
(tab->col_var[col] < tab->n_param ||
tab->col_var[col] >= tab->n_var - tab->n_div))
continue;
for (var = tab->n_param; var < tab->n_var - tab->n_div; ++var) {
if (!tab->var[var].is_row) {
if (tab->var[var].index == col)
break;
else
continue;
}
row = tab->var[var].index;
if (isl_int_is_zero(tab->mat->row[row][off + col]))
continue;
if (isl_int_is_pos(tab->mat->row[row][off + col]))
break;
fprintf(stderr, "lexneg column %d (row %d)\n",
col, row);
}
if (var >= tab->n_var - tab->n_div)
fprintf(stderr, "zero column %d\n", col);
}
}
/* Report to the caller that the given constraint is part of an encountered
* conflict.
*/
static int report_conflicting_constraint(struct isl_tab *tab, int con)
{
return tab->conflict(con, tab->conflict_user);
}
/* Given a conflicting row in the tableau, report all constraints
* involved in the row to the caller. That is, the row itself
* (if 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 (tab->col_var[j] >= 0 &&
(tab->col_var[j] < tab->n_param ||
tab->col_var[j] >= tab->n_var - tab->n_div))
continue;
if (!isl_int_is_neg(tr[j]))
continue;
if (tab->col_var[j] < 0 &&
report_conflicting_constraint(tab, ~tab->col_var[j]) < 0)
return -1;
}
return 0;
}
/* Resolve all known or obviously violated constraints through pivoting.
* In particular, as long as we can find any violated constraint, we
* look for a pivoting column that would result in the lexicographically
* smallest increment in the sample point. If there is no such column
* then the tableau is infeasible.
*/
static int restore_lexmin(struct isl_tab *tab) WARN_UNUSED;
static int restore_lexmin(struct isl_tab *tab)
{
int row, col;
if (!tab)
return -1;
if (tab->empty)
return 0;
while ((row = first_neg(tab)) != -1) {
col = lexmin_pivot_col(tab, row);
if (col >= tab->n_col) {
if (report_conflict(tab, row) < 0)
return -1;
if (isl_tab_mark_empty(tab) < 0)
return -1;
return 0;
}
if (col < 0)
return -1;
if (isl_tab_pivot(tab, row, col) < 0)
return -1;
}
return 0;
}
/* Given a row that represents an equality, look for an appropriate
* pivoting column.
* In particular, if there are any non-zero coefficients among
* the non-parameter variables, then we take the last of these
* variables. Eliminating this variable in terms of the other
* variables and/or parameters does not influence the property
* that all column in the initial tableau are lexicographically
* positive. The row corresponding to the eliminated variable
* will only have non-zero entries below the diagonal of the
* initial tableau. That is, we transform
*
* I I
* 1 into a
* I I
*
* If there is no such non-parameter variable, then we are dealing with
* pure parameter equality and we pick any parameter with coefficient 1 or -1
* for elimination. This will ensure that the eliminated parameter
* always has an integer value whenever all the other parameters are integral.
* If there is no such parameter then we return -1.
*/
static int last_var_col_or_int_par_col(struct isl_tab *tab, int row)
{
unsigned off = 2 + tab->M;
int i;
for (i = tab->n_var - tab->n_div - 1; i >= 0 && i >= tab->n_param; --i) {
int col;
if (tab->var[i].is_row)
continue;
col = tab->var[i].index;
if (col <= tab->n_dead)
continue;
if (!isl_int_is_zero(tab->mat->row[row][off + col]))
return col;
}
for (i = tab->n_dead; i < tab->n_col; ++i) {
if (isl_int_is_one(tab->mat->row[row][off + i]))
return i;
if (isl_int_is_negone(tab->mat->row[row][off + i]))
return i;
}
return -1;
}
/* Add an equality that is known to be valid to the tableau.
* We first check if we can eliminate a variable or a parameter.
* If not, we add the equality as two inequalities.
* In this case, the equality was a pure parameter equality and there
* is no need to resolve any constraint violations.
*/
static struct isl_tab *add_lexmin_valid_eq(struct isl_tab *tab, isl_int *eq)
{
int i;
int r;
if (!tab)
return NULL;
r = isl_tab_add_row(tab, eq);
if (r < 0)
goto error;
r = tab->con[r].index;
i = last_var_col_or_int_par_col(tab, r);
if (i < 0) {
tab->con[r].is_nonneg = 1;
if (isl_tab_push_var(tab, isl_tab_undo_nonneg, &tab->con[r]) < 0)
goto error;
isl_seq_neg(eq, eq, 1 + tab->n_var);
r = isl_tab_add_row(tab, eq);
if (r < 0)
goto error;
tab->con[r].is_nonneg = 1;
if (isl_tab_push_var(tab, isl_tab_undo_nonneg, &tab->con[r]) < 0)
goto error;
} else {
if (isl_tab_pivot(tab, r, i) < 0)
goto error;
if (isl_tab_kill_col(tab, i) < 0)
goto error;
tab->n_eq++;
}
return tab;
error:
isl_tab_free(tab);
return NULL;
}
/* Check if the given row is a pure constant.
*/
static int is_constant(struct isl_tab *tab, int row)
{
unsigned off = 2 + tab->M;
return isl_seq_first_non_zero(tab->mat->row[row] + off + tab->n_dead,
tab->n_col - tab->n_dead) == -1;
}
/* Add an equality that may or may not be valid to the tableau.
* If the resulting row is a pure constant, then it must be zero.
* Otherwise, the resulting tableau is empty.
*
* If the row is not a pure constant, then we add two inequalities,
* each time checking that they can be satisfied.
* In the end we try to use one of the two constraints to eliminate
* a column.
*/
static int add_lexmin_eq(struct isl_tab *tab, isl_int *eq) WARN_UNUSED;
static int add_lexmin_eq(struct isl_tab *tab, isl_int *eq)
{
int r1, r2;
int row;
struct isl_tab_undo *snap;
if (!tab)
return -1;
snap = isl_tab_snap(tab);
r1 = isl_tab_add_row(tab, eq);
if (r1 < 0)
return -1;
tab->con[r1].is_nonneg = 1;
if (isl_tab_push_var(tab, isl_tab_undo_nonneg, &tab->con[r1]) < 0)
return -1;
row = tab->con[r1].index;
if (is_constant(tab, row)) {
if (!isl_int_is_zero(tab->mat->row[row][1]) ||
(tab->M && !isl_int_is_zero(tab->mat->row[row][2]))) {
if (isl_tab_mark_empty(tab) < 0)
return -1;
return 0;
}
if (isl_tab_rollback(tab, snap) < 0)
return -1;
return 0;
}
if (restore_lexmin(tab) < 0)
return -1;
if (tab->empty)
return 0;
isl_seq_neg(eq, eq, 1 + tab->n_var);
r2 = isl_tab_add_row(tab, eq);
if (r2 < 0)
return -1;
tab->con[r2].is_nonneg = 1;
if (isl_tab_push_var(tab, isl_tab_undo_nonneg, &tab->con[r2]) < 0)
return -1;
if (restore_lexmin(tab) < 0)
return -1;
if (tab->empty)
return 0;
if (!tab->con[r1].is_row) {
if (isl_tab_kill_col(tab, tab->con[r1].index) < 0)
return -1;
} else if (!tab->con[r2].is_row) {
if (isl_tab_kill_col(tab, tab->con[r2].index) < 0)
return -1;
}
if (tab->bmap) {
tab->bmap = isl_basic_map_add_ineq(tab->bmap, eq);
if (isl_tab_push(tab, isl_tab_undo_bmap_ineq) < 0)
return -1;
isl_seq_neg(eq, eq, 1 + tab->n_var);
tab->bmap = isl_basic_map_add_ineq(tab->bmap, eq);
isl_seq_neg(eq, eq, 1 + tab->n_var);
if (isl_tab_push(tab, isl_tab_undo_bmap_ineq) < 0)
return -1;
if (!tab->bmap)
return -1;
}
return 0;
}
/* Add an inequality to the tableau, resolving violations using
* restore_lexmin.
*/
static struct isl_tab *add_lexmin_ineq(struct isl_tab *tab, isl_int *ineq)
{
int r;
if (!tab)
return NULL;
if (tab->bmap) {
tab->bmap = isl_basic_map_add_ineq(tab->bmap, ineq);
if (isl_tab_push(tab, isl_tab_undo_bmap_ineq) < 0)
goto error;
if (!tab->bmap)
goto error;
}
r = isl_tab_add_row(tab, ineq);
if (r < 0)
goto error;
tab->con[r].is_nonneg = 1;
if (isl_tab_push_var(tab, isl_tab_undo_nonneg, &tab->con[r]) < 0)
goto error;
if (isl_tab_row_is_redundant(tab, tab->con[r].index)) {
if (isl_tab_mark_redundant(tab, tab->con[r].index) < 0)
goto error;
return tab;
}
if (restore_lexmin(tab) < 0)
goto error;
if (!tab->empty && tab->con[r].is_row &&
isl_tab_row_is_redundant(tab, tab->con[r].index))
if (isl_tab_mark_redundant(tab, tab->con[r].index) < 0)
goto error;
return tab;
error:
isl_tab_free(tab);
return NULL;
}
/* Check if the coefficients of the parameters are all integral.
*/
static int integer_parameter(struct isl_tab *tab, int row)
{
int i;
int col;
unsigned off = 2 + tab->M;
for (i = 0; i < tab->n_param; ++i) {
/* Eliminated parameter */
if (tab->var[i].is_row)
continue;
col = tab->var[i].index;
if (!isl_int_is_divisible_by(tab->mat->row[row][off + col],
tab->mat->row[row][0]))
return 0;
}
for (i = 0; i < tab->n_div; ++i) {
if (tab->var[tab->n_var - tab->n_div + i].is_row)
continue;
col = tab->var[tab->n_var - tab->n_div + i].index;
if (!isl_int_is_divisible_by(tab->mat->row[row][off + col],
tab->mat->row[row][0]))
return 0;
}
return 1;
}
/* Check if the coefficients of the non-parameter variables are all integral.
*/
static int integer_variable(struct isl_tab *tab, int row)
{
int i;
unsigned off = 2 + tab->M;
for (i = tab->n_dead; i < tab->n_col; ++i) {
if (tab->col_var[i] >= 0 &&
(tab->col_var[i] < tab->n_param ||
tab->col_var[i] >= tab->n_var - tab->n_div))
continue;
if (!isl_int_is_divisible_by(tab->mat->row[row][off + i],
tab->mat->row[row][0]))
return 0;
}
return 1;
}
/* Check if the constant term is integral.
*/
static int integer_constant(struct isl_tab *tab, int row)
{
return isl_int_is_divisible_by(tab->mat->row[row][1],
tab->mat->row[row][0]);
}
#define I_CST 1 << 0
#define I_PAR 1 << 1
#define I_VAR 1 << 2
/* Check for next (non-parameter) variable after "var" (first if var == -1)
* that is non-integer and therefore requires a cut and return
* the index of the variable.
* For parametric tableaus, there are three parts in a row,
* the constant, the coefficients of the parameters and the rest.
* For each part, we check whether the coefficients in that part
* are all integral and if so, set the corresponding flag in *f.
* If the constant and the parameter part are integral, then the
* current sample value is integral and no cut is required
* (irrespective of whether the variable part is integral).
*/
static int next_non_integer_var(struct isl_tab *tab, int var, int *f)
{
var = var < 0 ? tab->n_param : var + 1;
for (; var < tab->n_var - tab->n_div; ++var) {
int flags = 0;
int row;
if (!tab->var[var].is_row)
continue;
row = tab->var[var].index;
if (integer_constant(tab, row))
ISL_FL_SET(flags, I_CST);
if (integer_parameter(tab, row))
ISL_FL_SET(flags, I_PAR);
if (ISL_FL_ISSET(flags, I_CST) && ISL_FL_ISSET(flags, I_PAR))
continue;
if (integer_variable(tab, row))
ISL_FL_SET(flags, I_VAR);
*f = flags;
return var;
}
return -1;
}
/* Check for first (non-parameter) variable that is non-integer and
* therefore requires a cut and return the corresponding row.
* For parametric tableaus, there are three parts in a row,
* the constant, the coefficients of the parameters and the rest.
* For each part, we check whether the coefficients in that part
* are all integral and if so, set the corresponding flag in *f.
* If the constant and the parameter part are integral, then the
* current sample value is integral and no cut is required
* (irrespective of whether the variable part is integral).
*/
static int first_non_integer_row(struct isl_tab *tab, int *f)
{
int var = next_non_integer_var(tab, -1, f);
return var < 0 ? -1 : tab->var[var].index;
}
/* Add a (non-parametric) cut to cut away the non-integral sample
* value of the given row.
*
* If the row is given by
*
* m r = f + \sum_i a_i y_i
*
* then the cut is
*
* c = - {-f/m} + \sum_i {a_i/m} y_i >= 0
*
* The big parameter, if any, is ignored, since it is assumed to be big
* enough to be divisible by any integer.
* If the tableau is actually a parametric tableau, then this function
* is only called when all coefficients of the parameters are integral.
* The cut therefore has zero coefficients for the parameters.
*
* The current value is known to be negative, so row_sign, if it
* exists, is set accordingly.
*
* Return the row of the cut or -1.
*/
static int add_cut(struct isl_tab *tab, int row)
{
int i;
int r;
isl_int *r_row;
unsigned off = 2 + tab->M;
if (isl_tab_extend_cons(tab, 1) < 0)
return -1;
r = isl_tab_allocate_con(tab);
if (r < 0)
return -1;
r_row = tab->mat->row[tab->con[r].index];
isl_int_set(r_row[0], tab->mat->row[row][0]);
isl_int_neg(r_row[1], tab->mat->row[row][1]);
isl_int_fdiv_r(r_row[1], r_row[1], tab->mat->row[row][0]);
isl_int_neg(r_row[1], r_row[1]);
if (tab->M)
isl_int_set_si(r_row[2], 0);
for (i = 0; i < tab->n_col; ++i)
isl_int_fdiv_r(r_row[off + i],
tab->mat->row[row][off + i], tab->mat->row[row][0]);
tab->con[r].is_nonneg = 1;
if (isl_tab_push_var(tab, isl_tab_undo_nonneg, &tab->con[r]) < 0)
return -1;
if (tab->row_sign)
tab->row_sign[tab->con[r].index] = isl_tab_row_neg;
return tab->con[r].index;
}
#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);
tab = isl_tab_add_sample(tab, sample);
}
if (!tab->empty && isl_tab_rollback(tab, snap) < 0)
goto error;
return tab;
error:
isl_tab_free(tab);
return NULL;
}
/* Check if any of the currently active sample values satisfies
* the inequality "ineq" (an equality if eq is set).
*/
static int tab_has_valid_sample(struct isl_tab *tab, isl_int *ineq, int eq)
{
int i;
isl_int v;
if (!tab)
return -1;
isl_assert(tab->mat->ctx, tab->bmap, return -1);
isl_assert(tab->mat->ctx, tab->samples, return -1);
isl_assert(tab->mat->ctx, tab->samples->n_col == 1 + tab->n_var, return -1);
isl_int_init(v);
for (i = tab->n_outside; i < tab->n_sample; ++i) {
int sgn;
isl_seq_inner_product(ineq, tab->samples->row[i],
1 + tab->n_var, &v);
sgn = isl_int_sgn(v);
if (eq ? (sgn == 0) : (sgn >= 0))
break;
}
isl_int_clear(v);
return i < tab->n_sample;
}
/* Add a div specified by "div" to the tableau "tab" and return
* 1 if the div is obviously non-negative.
*/
static int context_tab_add_div(struct isl_tab *tab, struct isl_vec *div,
int (*add_ineq)(void *user, isl_int *), void *user)
{
int i;
int r;
struct isl_mat *samples;
int nonneg;
r = isl_tab_add_div(tab, div, add_ineq, user);
if (r < 0)
return -1;
nonneg = tab->var[r].is_nonneg;
tab->var[r].frozen = 1;
samples = isl_mat_extend(tab->samples,
tab->n_sample, 1 + tab->n_var);
tab->samples = samples;
if (!samples)
return -1;
for (i = tab->n_outside; i < samples->n_row; ++i) {
isl_seq_inner_product(div->el + 1, samples->row[i],
div->size - 1, &samples->row[i][samples->n_col - 1]);
isl_int_fdiv_q(samples->row[i][samples->n_col - 1],
samples->row[i][samples->n_col - 1], div->el[0]);
}
return nonneg;
}
/* Add a div specified by "div" to both the main tableau and
* the context tableau. In case of the main tableau, we only
* need to add an extra div. In the context tableau, we also
* need to express the meaning of the div.
* Return the index of the div or -1 if anything went wrong.
*/
static int add_div(struct isl_tab *tab, struct isl_context *context,
struct isl_vec *div)
{
int r;
int nonneg;
if ((nonneg = context->op->add_div(context, div)) < 0)
goto error;
if (!context->op->is_ok(context))
goto error;
if (isl_tab_extend_vars(tab, 1) < 0)
goto error;
r = isl_tab_allocate_var(tab);
if (r < 0)
goto error;
if (nonneg)
tab->var[r].is_nonneg = 1;
tab->var[r].frozen = 1;
tab->n_div++;
return tab->n_div - 1;
error:
context->op->invalidate(context);
return -1;
}
static int find_div(struct isl_tab *tab, isl_int *div, isl_int denom)
{
int i;
unsigned total = isl_basic_map_total_dim(tab->bmap);
for (i = 0; i < tab->bmap->n_div; ++i) {
if (isl_int_ne(tab->bmap->div[i][0], denom))
continue;
if (!isl_seq_eq(tab->bmap->div[i] + 1, div, 1 + total))
continue;
return i;
}
return -1;
}
/* Return the index of a div that corresponds to "div".
* We first check if we already have such a div and if not, we create one.
*/
static int get_div(struct isl_tab *tab, struct isl_context *context,
struct isl_vec *div)
{
int d;
struct isl_tab *context_tab = context->op->peek_tab(context);
if (!context_tab)
return -1;
d = find_div(context_tab, div->el + 1, div->el[0]);
if (d != -1)
return d;
return add_div(tab, context, div);
}
/* Add a parametric cut to cut away the non-integral sample value
* of the give row.
* Let a_i be the coefficients of the constant term and the parameters
* and let b_i be the coefficients of the variables or constraints
* in basis of the tableau.
* Let q be the div q = floor(\sum_i {-a_i} y_i).
*
* The cut is expressed as
*
* c = \sum_i -{-a_i} y_i + \sum_i {b_i} x_i + q >= 0
*
* If q did not already exist in the context tableau, then it is added first.
* If q is in a column of the main tableau then the "+ q" can be accomplished
* by setting the corresponding entry to the denominator of the constraint.
* If q happens to be in a row of the main tableau, then the corresponding
* row needs to be added instead (taking care of the denominators).
* Note that this is very unlikely, but perhaps not entirely impossible.
*
* The current value of the cut is known to be negative (or at least
* non-positive), so row_sign is set accordingly.
*
* Return the row of the cut or -1.
*/
static int add_parametric_cut(struct isl_tab *tab, int row,
struct isl_context *context)
{
struct isl_vec *div;
int d;
int i;
int r;
isl_int *r_row;
int col;
int n;
unsigned off = 2 + tab->M;
if (!context)
return -1;
div = get_row_parameter_div(tab, row);
if (!div)
return -1;
n = tab->n_div;
d = context->op->get_div(context, tab, div);
if (d < 0)
return -1;
if (isl_tab_extend_cons(tab, 1) < 0)
return -1;
r = isl_tab_allocate_con(tab);
if (r < 0)
return -1;
r_row = tab->mat->row[tab->con[r].index];
isl_int_set(r_row[0], tab->mat->row[row][0]);
isl_int_neg(r_row[1], tab->mat->row[row][1]);
isl_int_fdiv_r(r_row[1], r_row[1], tab->mat->row[row][0]);
isl_int_neg(r_row[1], r_row[1]);
if (tab->M)
isl_int_set_si(r_row[2], 0);
for (i = 0; i < tab->n_param; ++i) {
if (tab->var[i].is_row)
continue;
col = tab->var[i].index;
isl_int_neg(r_row[off + col], tab->mat->row[row][off + col]);
isl_int_fdiv_r(r_row[off + col], r_row[off + col],
tab->mat->row[row][0]);
isl_int_neg(r_row[off + col], r_row[off + col]);
}
for (i = 0; i < tab->n_div; ++i) {
if (tab->var[tab->n_var - tab->n_div + i].is_row)
continue;
col = tab->var[tab->n_var - tab->n_div + i].index;
isl_int_neg(r_row[off + col], tab->mat->row[row][off + col]);
isl_int_fdiv_r(r_row[off + col], r_row[off + col],
tab->mat->row[row][0]);
isl_int_neg(r_row[off + col], r_row[off + col]);
}
for (i = 0; i < tab->n_col; ++i) {
if (tab->col_var[i] >= 0 &&
(tab->col_var[i] < tab->n_param ||
tab->col_var[i] >= tab->n_var - tab->n_div))
continue;
isl_int_fdiv_r(r_row[off + i],
tab->mat->row[row][off + i], tab->mat->row[row][0]);
}
if (tab->var[tab->n_var - tab->n_div + d].is_row) {
isl_int gcd;
int d_row = tab->var[tab->n_var - tab->n_div + d].index;
isl_int_init(gcd);
isl_int_gcd(gcd, tab->mat->row[d_row][0], r_row[0]);
isl_int_divexact(r_row[0], r_row[0], gcd);
isl_int_divexact(gcd, tab->mat->row[d_row][0], gcd);
isl_seq_combine(r_row + 1, gcd, r_row + 1,
r_row[0], tab->mat->row[d_row] + 1,
off - 1 + tab->n_col);
isl_int_mul(r_row[0], r_row[0], tab->mat->row[d_row][0]);
isl_int_clear(gcd);
} else {
col = tab->var[tab->n_var - tab->n_div + d].index;
isl_int_set(r_row[off + col], tab->mat->row[row][0]);
}
tab->con[r].is_nonneg = 1;
if (isl_tab_push_var(tab, isl_tab_undo_nonneg, &tab->con[r]) < 0)
return -1;
if (tab->row_sign)
tab->row_sign[tab->con[r].index] = isl_tab_row_neg;
isl_vec_free(div);
row = tab->con[r].index;
if (d >= n && context->op->detect_equalities(context, tab) < 0)
return -1;
return row;
}
/* Construct a tableau for bmap that can be used for computing
* the lexicographic minimum (or maximum) of bmap.
* If not NULL, then dom is the domain where the minimum
* should be computed. In this case, we set up a parametric
* tableau with row signs (initialized to "unknown").
* If M is set, then the tableau will use a big parameter.
* If max is set, then a maximum should be computed instead of a minimum.
* This means that for each variable x, the tableau will contain the variable
* x' = M - x, rather than x' = M + x. This in turn means that the coefficient
* of the variables in all constraints are negated prior to adding them
* to the tableau.
*/
static struct isl_tab *tab_for_lexmin(struct isl_basic_map *bmap,
struct isl_basic_set *dom, unsigned M, int max)
{
int i;
struct isl_tab *tab;
tab = isl_tab_alloc(bmap->ctx, 2 * bmap->n_eq + bmap->n_ineq + 1,
isl_basic_map_total_dim(bmap), M);
if (!tab)
return NULL;
tab->rational = ISL_F_ISSET(bmap, ISL_BASIC_MAP_RATIONAL);
if (dom) {
tab->n_param = isl_basic_set_total_dim(dom) - dom->n_div;
tab->n_div = dom->n_div;
tab->row_sign = isl_calloc_array(bmap->ctx,
enum isl_tab_row_sign, tab->mat->n_row);
if (!tab->row_sign)
goto error;
}
if (ISL_F_ISSET(bmap, ISL_BASIC_MAP_EMPTY)) {
if (isl_tab_mark_empty(tab) < 0)
goto error;
return tab;
}
for (i = tab->n_param; i < tab->n_var - tab->n_div; ++i) {
tab->var[i].is_nonneg = 1;
tab->var[i].frozen = 1;
}
for (i = 0; i < bmap->n_eq; ++i) {
if (max)
isl_seq_neg(bmap->eq[i] + 1 + tab->n_param,
bmap->eq[i] + 1 + tab->n_param,
tab->n_var - tab->n_param - tab->n_div);
tab = add_lexmin_valid_eq(tab, bmap->eq[i]);
if (max)
isl_seq_neg(bmap->eq[i] + 1 + tab->n_param,
bmap->eq[i] + 1 + tab->n_param,
tab->n_var - tab->n_param - tab->n_div);
if (!tab || tab->empty)
return tab;
}
if (bmap->n_eq && restore_lexmin(tab) < 0)
goto error;
for (i = 0; i < bmap->n_ineq; ++i) {
if (max)
isl_seq_neg(bmap->ineq[i] + 1 + tab->n_param,
bmap->ineq[i] + 1 + tab->n_param,
tab->n_var - tab->n_param - tab->n_div);
tab = add_lexmin_ineq(tab, bmap->ineq[i]);
if (max)
isl_seq_neg(bmap->ineq[i] + 1 + tab->n_param,
bmap->ineq[i] + 1 + tab->n_param,
tab->n_var - tab->n_param - tab->n_div);
if (!tab || tab->empty)
return tab;
}
return tab;
error:
isl_tab_free(tab);
return NULL;
}
/* Given a main tableau where more than one row requires a split,
* determine and return the "best" row to split on.
*
* Given two rows in the main tableau, if the inequality corresponding
* to the first row is redundant with respect to that of the second row
* in the current tableau, then it is better to split on the second row,
* since in the positive part, both row will be positive.
* (In the negative part a pivot will have to be performed and just about
* anything can happen to the sign of the other row.)
*
* As a simple heuristic, we therefore select the row that makes the most
* of the other rows redundant.
*
* Perhaps it would also be useful to look at the number of constraints
* that conflict with any given constraint.
*/
static int best_split(struct isl_tab *tab, struct isl_tab *context_tab)
{
struct isl_tab_undo *snap;
int split;
int row;
int best = -1;
int best_r;
if (isl_tab_extend_cons(context_tab, 2) < 0)
return -1;
snap = isl_tab_snap(context_tab);
for (split = tab->n_redundant; split < tab->n_row; ++split) {
struct isl_tab_undo *snap2;
struct isl_vec *ineq = NULL;
int r = 0;
int ok;
if (!isl_tab_var_from_row(tab, split)->is_nonneg)
continue;
if (tab->row_sign[split] != isl_tab_row_any)
continue;
ineq = get_row_parameter_ineq(tab, split);
if (!ineq)
return -1;
ok = isl_tab_add_ineq(context_tab, ineq->el) >= 0;
isl_vec_free(ineq);
if (!ok)
return -1;
snap2 = isl_tab_snap(context_tab);
for (row = tab->n_redundant; row < tab->n_row; ++row) {
struct isl_tab_var *var;
if (row == split)
continue;
if (!isl_tab_var_from_row(tab, row)->is_nonneg)
continue;
if (tab->row_sign[row] != isl_tab_row_any)
continue;
ineq = get_row_parameter_ineq(tab, row);
if (!ineq)
return -1;
ok = isl_tab_add_ineq(context_tab, ineq->el) >= 0;
isl_vec_free(ineq);
if (!ok)
return -1;
var = &context_tab->con[context_tab->n_con - 1];
if (!context_tab->empty &&
!isl_tab_min_at_most_neg_one(context_tab, var))
r++;
if (isl_tab_rollback(context_tab, snap2) < 0)
return -1;
}
if (best == -1 || r > best_r) {
best = split;
best_r = r;
}
if (isl_tab_rollback(context_tab, snap) < 0)
return -1;
}
return best;
}
static struct isl_basic_set *context_lex_peek_basic_set(
struct isl_context *context)
{
struct isl_context_lex *clex = (struct isl_context_lex *)context;
if (!clex->tab)
return NULL;
return isl_tab_peek_bset(clex->tab);
}
static struct isl_tab *context_lex_peek_tab(struct isl_context *context)
{
struct isl_context_lex *clex = (struct isl_context_lex *)context;
return clex->tab;
}
static void context_lex_add_eq(struct isl_context *context, isl_int *eq,
int check, int update)
{
struct isl_context_lex *clex = (struct isl_context_lex *)context;
if (isl_tab_extend_cons(clex->tab, 2) < 0)
goto error;
if (add_lexmin_eq(clex->tab, eq) < 0)
goto error;
if (check) {
int v = tab_has_valid_sample(clex->tab, eq, 1);
if (v < 0)
goto error;
if (!v)
clex->tab = check_integer_feasible(clex->tab);
}
if (update)
clex->tab = check_samples(clex->tab, eq, 1);
return;
error:
isl_tab_free(clex->tab);
clex->tab = NULL;
}
static void context_lex_add_ineq(struct isl_context *context, isl_int *ineq,
int check, int update)
{
struct isl_context_lex *clex = (struct isl_context_lex *)context;
if (isl_tab_extend_cons(clex->tab, 1) < 0)
goto error;
clex->tab = add_lexmin_ineq(clex->tab, ineq);
if (check) {
int v = tab_has_valid_sample(clex->tab, ineq, 0);
if (v < 0)
goto error;
if (!v)
clex->tab = check_integer_feasible(clex->tab);
}
if (update)
clex->tab = check_samples(clex->tab, ineq, 0);
return;
error:
isl_tab_free(clex->tab);
clex->tab = NULL;
}
static int context_lex_add_ineq_wrap(void *user, isl_int *ineq)
{
struct isl_context *context = (struct isl_context *)user;
context_lex_add_ineq(context, ineq, 0, 0);
return context->op->is_ok(context) ? 0 : -1;
}
/* Check which signs can be obtained by "ineq" on all the currently
* active sample values. See row_sign for more information.
*/
static enum isl_tab_row_sign tab_ineq_sign(struct isl_tab *tab, isl_int *ineq,
int strict)
{
int i;
int sgn;
isl_int tmp;
enum isl_tab_row_sign res = isl_tab_row_unknown;
isl_assert(tab->mat->ctx, tab->samples, return isl_tab_row_unknown);
isl_assert(tab->mat->ctx, tab->samples->n_col == 1 + tab->n_var,
return isl_tab_row_unknown);
isl_int_init(tmp);
for (i = tab->n_outside; i < tab->n_sample; ++i) {
isl_seq_inner_product(tab->samples->row[i], ineq,
1 + tab->n_var, &tmp);
sgn = isl_int_sgn(tmp);
if (sgn > 0 || (sgn == 0 && strict)) {
if (res == isl_tab_row_unknown)
res = isl_tab_row_pos;
if (res == isl_tab_row_neg)
res = isl_tab_row_any;
}
if (sgn < 0) {
if (res == isl_tab_row_unknown)
res = isl_tab_row_neg;
if (res == isl_tab_row_pos)
res = isl_tab_row_any;
}
if (res == isl_tab_row_any)
break;
}
isl_int_clear(tmp);
return res;
}
static enum isl_tab_row_sign context_lex_ineq_sign(struct isl_context *context,
isl_int *ineq, int strict)
{
struct isl_context_lex *clex = (struct isl_context_lex *)context;
return tab_ineq_sign(clex->tab, ineq, strict);
}
/* Check whether "ineq" can be added to the tableau without rendering
* it infeasible.
*/
static int context_lex_test_ineq(struct isl_context *context, isl_int *ineq)
{
struct isl_context_lex *clex = (struct isl_context_lex *)context;
struct isl_tab_undo *snap;
int feasible;
if (!clex->tab)
return -1;
if (isl_tab_extend_cons(clex->tab, 1) < 0)
return -1;
snap = isl_tab_snap(clex->tab);
if (isl_tab_push_basis(clex->tab) < 0)
return -1;
clex->tab = add_lexmin_ineq(clex->tab, ineq);
clex->tab = check_integer_feasible(clex->tab);
if (!clex->tab)
return -1;
feasible = !clex->tab->empty;
if (isl_tab_rollback(clex->tab, snap) < 0)
return -1;
return feasible;
}
static int context_lex_get_div(struct isl_context *context, struct isl_tab *tab,
struct isl_vec *div)
{
return get_div(tab, context, div);
}
/* Add a div specified by "div" to the context tableau and return
* 1 if the div is obviously non-negative.
* context_tab_add_div will always return 1, because all variables
* in a isl_context_lex tableau are non-negative.
* However, if we are using a big parameter in the context, then this only
* reflects the non-negativity of the variable used to _encode_ the
* div, i.e., div' = M + div, so we can't draw any conclusions.
*/
static int context_lex_add_div(struct isl_context *context, struct isl_vec *div)
{
struct isl_context_lex *clex = (struct isl_context_lex *)context;
int nonneg;
nonneg = context_tab_add_div(clex->tab, div,
context_lex_add_ineq_wrap, context);
if (nonneg < 0)
return -1;
if (clex->tab->M)
return 0;
return nonneg;
}
static int context_lex_detect_equalities(struct isl_context *context,
struct isl_tab *tab)
{
return 0;
}
static int context_lex_best_split(struct isl_context *context,
struct isl_tab *tab)
{
struct isl_context_lex *clex = (struct isl_context_lex *)context;
struct isl_tab_undo *snap;
int r;
snap = isl_tab_snap(clex->tab);
if (isl_tab_push_basis(clex->tab) < 0)
return -1;
r = best_split(tab, clex->tab);
if (r >= 0 && isl_tab_rollback(clex->tab, snap) < 0)
return -1;
return r;
}
static int context_lex_is_empty(struct isl_context *context)
{
struct isl_context_lex *clex = (struct isl_context_lex *)context;
if (!clex->tab)
return -1;
return clex->tab->empty;
}
static void *context_lex_save(struct isl_context *context)
{
struct isl_context_lex *clex = (struct isl_context_lex *)context;
struct isl_tab_undo *snap;
snap = isl_tab_snap(clex->tab);
if (isl_tab_push_basis(clex->tab) < 0)
return NULL;
if (isl_tab_save_samples(clex->tab) < 0)
return NULL;
return snap;
}
static void context_lex_restore(struct isl_context *context, void *save)
{
struct isl_context_lex *clex = (struct isl_context_lex *)context;
if (isl_tab_rollback(clex->tab, (struct isl_tab_undo *)save) < 0) {
isl_tab_free(clex->tab);
clex->tab = NULL;
}
}
static int context_lex_is_ok(struct isl_context *context)
{
struct isl_context_lex *clex = (struct isl_context_lex *)context;
return !!clex->tab;
}
/* For each variable in the context tableau, check if the variable can
* only attain non-negative values. If so, mark the parameter as non-negative
* in the main tableau. This allows for a more direct identification of some
* cases of violated constraints.
*/
static struct isl_tab *tab_detect_nonnegative_parameters(struct isl_tab *tab,
struct isl_tab *context_tab)
{
int i;
struct isl_tab_undo *snap;
struct isl_vec *ineq = NULL;
struct isl_tab_var *var;
int n;
if (context_tab->n_var == 0)
return tab;
ineq = isl_vec_alloc(tab->mat->ctx, 1 + context_tab->n_var);
if (!ineq)
goto error;
if (isl_tab_extend_cons(context_tab, 1) < 0)
goto error;
snap = isl_tab_snap(context_tab);
n = 0;
isl_seq_clr(ineq->el, ineq->size);
for (i = 0; i < context_tab->n_var; ++i) {
isl_int_set_si(ineq->el[1 + i], 1);
if (isl_tab_add_ineq(context_tab, ineq->el) < 0)
goto error;
var = &context_tab->con[context_tab->n_con - 1];
if (!context_tab->empty &&
!isl_tab_min_at_most_neg_one(context_tab, var)) {
int j = i;
if (i >= tab->n_param)
j = i - tab->n_param + tab->n_var - tab->n_div;
tab->var[j].is_nonneg = 1;
n++;
}
isl_int_set_si(ineq->el[1 + i], 0);
if (isl_tab_rollback(context_tab, snap) < 0)
goto error;
}
if (context_tab->M && n == context_tab->n_var) {
context_tab->mat = isl_mat_drop_cols(context_tab->mat, 2, 1);
context_tab->M = 0;
}
isl_vec_free(ineq);
return tab;
error:
isl_vec_free(ineq);
isl_tab_free(tab);
return NULL;
}
static struct isl_tab *context_lex_detect_nonnegative_parameters(
struct isl_context *context, struct isl_tab *tab)
{
struct isl_context_lex *clex = (struct isl_context_lex *)context;
struct isl_tab_undo *snap;
if (!tab)
return NULL;
snap = isl_tab_snap(clex->tab);
if (isl_tab_push_basis(clex->tab) < 0)
goto error;
tab = tab_detect_nonnegative_parameters(tab, clex->tab);
if (isl_tab_rollback(clex->tab, snap) < 0)
goto error;
return tab;
error:
isl_tab_free(tab);
return NULL;
}
static void context_lex_invalidate(struct isl_context *context)
{
struct isl_context_lex *clex = (struct isl_context_lex *)context;
isl_tab_free(clex->tab);
clex->tab = NULL;
}
static void context_lex_free(struct isl_context *context)
{
struct isl_context_lex *clex = (struct isl_context_lex *)context;
isl_tab_free(clex->tab);
free(clex);
}
struct isl_context_op isl_context_lex_op = {
context_lex_detect_nonnegative_parameters,
context_lex_peek_basic_set,
context_lex_peek_tab,
context_lex_add_eq,
context_lex_add_ineq,
context_lex_ineq_sign,
context_lex_test_ineq,
context_lex_get_div,
context_lex_add_div,
context_lex_detect_equalities,
context_lex_best_split,
context_lex_is_empty,
context_lex_is_ok,
context_lex_save,
context_lex_restore,
context_lex_invalidate,
context_lex_free,
};
static struct isl_tab *context_tab_for_lexmin(struct isl_basic_set *bset)
{
struct isl_tab *tab;
if (!bset)
return NULL;
tab = tab_for_lexmin((struct isl_basic_map *)bset, NULL, 1, 0);
if (!tab)
goto error;
if (isl_tab_track_bset(tab, bset) < 0)
goto error;
tab = isl_tab_init_samples(tab);
return tab;
error:
isl_basic_set_free(bset);
return NULL;
}
static struct isl_context *isl_context_lex_alloc(struct isl_basic_set *dom)
{
struct isl_context_lex *clex;
if (!dom)
return NULL;
clex = isl_alloc_type(dom->ctx, struct isl_context_lex);
if (!clex)
return NULL;
clex->context.op = &isl_context_lex_op;
clex->tab = context_tab_for_lexmin(isl_basic_set_copy(dom));
if (restore_lexmin(clex->tab) < 0)
goto error;
clex->tab = check_integer_feasible(clex->tab);
if (!clex->tab)
goto error;
return &clex->context;
error:
clex->context.op->free(&clex->context);
return NULL;
}
struct isl_context_gbr {
struct isl_context context;
struct isl_tab *tab;
struct isl_tab *shifted;
struct isl_tab *cone;
};
static struct isl_tab *context_gbr_detect_nonnegative_parameters(
struct isl_context *context, struct isl_tab *tab)
{
struct isl_context_gbr *cgbr = (struct isl_context_gbr *)context;
if (!tab)
return NULL;
return tab_detect_nonnegative_parameters(tab, cgbr->tab);
}
static struct isl_basic_set *context_gbr_peek_basic_set(
struct isl_context *context)
{
struct isl_context_gbr *cgbr = (struct isl_context_gbr *)context;
if (!cgbr->tab)
return NULL;
return isl_tab_peek_bset(cgbr->tab);
}
static struct isl_tab *context_gbr_peek_tab(struct isl_context *context)
{
struct isl_context_gbr *cgbr = (struct isl_context_gbr *)context;
return cgbr->tab;
}
/* Initialize the "shifted" tableau of the context, which
* contains the constraints of the original tableau shifted
* by the sum of all negative coefficients. This ensures
* that any rational point in the shifted tableau can
* be rounded up to yield an integer point in the original tableau.
*/
static void gbr_init_shifted(struct isl_context_gbr *cgbr)
{
int i, j;
struct isl_vec *cst;
struct isl_basic_set *bset = isl_tab_peek_bset(cgbr->tab);
unsigned dim = isl_basic_set_total_dim(bset);
cst = isl_vec_alloc(cgbr->tab->mat->ctx, bset->n_ineq);
if (!cst)
return;
for (i = 0; i < bset->n_ineq; ++i) {
isl_int_set(cst->el[i], bset->ineq[i][0]);
for (j = 0; j < dim; ++j) {
if (!isl_int_is_neg(bset->ineq[i][1 + j]))
continue;
isl_int_add(bset->ineq[i][0], bset->ineq[i][0],
bset->ineq[i][1 + j]);
}
}
cgbr->shifted = isl_tab_from_basic_set(bset, 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 struct isl_basic_set *drop_constant_terms(struct isl_basic_set *bset)
{
int i;
if (!bset)
return NULL;
for (i = 0; i < bset->n_eq; ++i)
isl_int_set_si(bset->eq[i][0], 0);
for (i = 0; i < bset->n_ineq; ++i)
isl_int_set_si(bset->ineq[i][0], 0);
return bset;
}
static int use_shifted(struct isl_context_gbr *cgbr)
{
return cgbr->tab->bmap->n_eq == 0 && cgbr->tab->bmap->n_div == 0;
}
static struct isl_vec *gbr_get_sample(struct isl_context_gbr *cgbr)
{
struct isl_basic_set *bset;
struct isl_basic_set *cone;
if (isl_tab_sample_is_integer(cgbr->tab))
return isl_tab_get_sample_value(cgbr->tab);
if (use_shifted(cgbr)) {
struct isl_vec *sample;
sample = gbr_get_shifted_sample(cgbr);
if (!sample || sample->size > 0)
return sample;
isl_vec_free(sample);
}
if (!cgbr->cone) {
bset = isl_tab_peek_bset(cgbr->tab);
cgbr->cone = isl_tab_from_recession_cone(bset, 0);
if (!cgbr->cone)
return NULL;
if (isl_tab_track_bset(cgbr->cone,
isl_basic_set_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 (isl_tab_rollback(cgbr->tab, snap) < 0) {
isl_vec_free(sample);
return NULL;
}
return sample;
}
cone = isl_basic_set_dup(isl_tab_peek_bset(cgbr->cone));
cone = drop_constant_terms(cone);
cone = isl_basic_set_update_from_tab(cone, cgbr->cone);
cone = isl_basic_set_underlying_set(cone);
cone = isl_basic_set_gauss(cone, NULL);
bset = isl_basic_set_dup(isl_tab_peek_bset(cgbr->tab));
bset = isl_basic_set_update_from_tab(bset, cgbr->tab);
bset = isl_basic_set_underlying_set(bset);
bset = isl_basic_set_gauss(bset, NULL);
return isl_basic_set_sample_with_cone(bset, cone);
}
static void check_gbr_integer_feasible(struct isl_context_gbr *cgbr)
{
struct isl_vec *sample;
if (!cgbr->tab)
return;
if (cgbr->tab->empty)
return;
sample = gbr_get_sample(cgbr);
if (!sample)
goto error;
if (sample->size == 0) {
isl_vec_free(sample);
if (isl_tab_mark_empty(cgbr->tab) < 0)
goto error;
return;
}
cgbr->tab = isl_tab_add_sample(cgbr->tab, sample);
return;
error:
isl_tab_free(cgbr->tab);
cgbr->tab = NULL;
}
static struct isl_tab *add_gbr_eq(struct isl_tab *tab, isl_int *eq)
{
if (!tab)
return NULL;
if (isl_tab_extend_cons(tab, 2) < 0)
goto error;
if (isl_tab_add_eq(tab, eq) < 0)
goto error;
return tab;
error:
isl_tab_free(tab);
return NULL;
}
static void context_gbr_add_eq(struct isl_context *context, isl_int *eq,
int check, int update)
{
struct isl_context_gbr *cgbr = (struct isl_context_gbr *)context;
cgbr->tab = add_gbr_eq(cgbr->tab, eq);
if (cgbr->cone && cgbr->cone->n_col != cgbr->cone->n_dead) {
if (isl_tab_extend_cons(cgbr->cone, 2) < 0)
goto error;
if (isl_tab_add_eq(cgbr->cone, eq) < 0)
goto error;
}
if (check) {
int v = tab_has_valid_sample(cgbr->tab, eq, 1);
if (v < 0)
goto error;
if (!v)
check_gbr_integer_feasible(cgbr);
}
if (update)
cgbr->tab = check_samples(cgbr->tab, eq, 1);
return;
error:
isl_tab_free(cgbr->tab);
cgbr->tab = NULL;
}
static void add_gbr_ineq(struct isl_context_gbr *cgbr, isl_int *ineq)
{
if (!cgbr->tab)
return;
if (isl_tab_extend_cons(cgbr->tab, 1) < 0)
goto error;
if (isl_tab_add_ineq(cgbr->tab, ineq) < 0)
goto error;
if (cgbr->shifted && !cgbr->shifted->empty && use_shifted(cgbr)) {
int i;
unsigned dim;
dim = isl_basic_map_total_dim(cgbr->tab->bmap);
if (isl_tab_extend_cons(cgbr->shifted, 1) < 0)
goto error;
for (i = 0; i < dim; ++i) {
if (!isl_int_is_neg(ineq[1 + i]))
continue;
isl_int_add(ineq[0], ineq[0], ineq[1 + i]);
}
if (isl_tab_add_ineq(cgbr->shifted, ineq) < 0)
goto error;
for (i = 0; i < dim; ++i) {
if (!isl_int_is_neg(ineq[1 + i]))
continue;
isl_int_sub(ineq[0], ineq[0], ineq[1 + i]);
}
}
if (cgbr->cone && cgbr->cone->n_col != cgbr->cone->n_dead) {
if (isl_tab_extend_cons(cgbr->cone, 1) < 0)
goto error;
if (isl_tab_add_ineq(cgbr->cone, ineq) < 0)
goto error;
}
return;
error:
isl_tab_free(cgbr->tab);
cgbr->tab = NULL;
}
static void context_gbr_add_ineq(struct isl_context *context, isl_int *ineq,
int check, int update)
{
struct isl_context_gbr *cgbr = (struct isl_context_gbr *)context;
add_gbr_ineq(cgbr, ineq);
if (!cgbr->tab)
return;
if (check) {
int v = tab_has_valid_sample(cgbr->tab, ineq, 0);
if (v < 0)
goto error;
if (!v)
check_gbr_integer_feasible(cgbr);
}
if (update)
cgbr->tab = check_samples(cgbr->tab, ineq, 0);
return;
error:
isl_tab_free(cgbr->tab);
cgbr->tab = NULL;
}
static int context_gbr_add_ineq_wrap(void *user, isl_int *ineq)
{
struct isl_context *context = (struct isl_context *)user;
context_gbr_add_ineq(context, ineq, 0, 0);
return context->op->is_ok(context) ? 0 : -1;
}
static enum isl_tab_row_sign context_gbr_ineq_sign(struct isl_context *context,
isl_int *ineq, int strict)
{
struct isl_context_gbr *cgbr = (struct isl_context_gbr *)context;
return tab_ineq_sign(cgbr->tab, ineq, strict);
}
/* Check whether "ineq" can be added to the tableau without rendering
* it infeasible.
*/
static int context_gbr_test_ineq(struct isl_context *context, isl_int *ineq)
{
struct isl_context_gbr *cgbr = (struct isl_context_gbr *)context;
struct isl_tab_undo *snap;
struct isl_tab_undo *shifted_snap = NULL;
struct isl_tab_undo *cone_snap = NULL;
int feasible;
if (!cgbr->tab)
return -1;
if (isl_tab_extend_cons(cgbr->tab, 1) < 0)
return -1;
snap = isl_tab_snap(cgbr->tab);
if (cgbr->shifted)
shifted_snap = isl_tab_snap(cgbr->shifted);
if (cgbr->cone)
cone_snap = isl_tab_snap(cgbr->cone);
add_gbr_ineq(cgbr, ineq);
check_gbr_integer_feasible(cgbr);
if (!cgbr->tab)
return -1;
feasible = !cgbr->tab->empty;
if (isl_tab_rollback(cgbr->tab, snap) < 0)
return -1;
if (shifted_snap) {
if (isl_tab_rollback(cgbr->shifted, shifted_snap))
return -1;
} else if (cgbr->shifted) {
isl_tab_free(cgbr->shifted);
cgbr->shifted = NULL;
}
if (cone_snap) {
if (isl_tab_rollback(cgbr->cone, cone_snap))
return -1;
} else if (cgbr->cone) {
isl_tab_free(cgbr->cone);
cgbr->cone = NULL;
}
return feasible;
}
/* Return the column of the last of the variables associated to
* a column that has a non-zero coefficient.
* This function is called in a context where only coefficients
* of parameters or divs can be non-zero.
*/
static int last_non_zero_var_col(struct isl_tab *tab, isl_int *p)
{
int i;
int col;
if (tab->n_var == 0)
return -1;
for (i = tab->n_var - 1; i >= 0; --i) {
if (i >= tab->n_param && i < tab->n_var - tab->n_div)
continue;
if (tab->var[i].is_row)
continue;
col = tab->var[i].index;
if (!isl_int_is_zero(p[col]))
return col;
}
return -1;
}
/* Look through all the recently added equalities in the context
* to see if we can propagate any of them to the main tableau.
*
* The newly added equalities in the context are encoded as pairs
* of inequalities starting at inequality "first".
*
* We tentatively add each of these equalities to the main tableau
* and if this happens to result in a row with a final coefficient
* that is one or negative one, we use it to kill a column
* in the main tableau. Otherwise, we discard the tentatively
* added row.
*/
static void propagate_equalities(struct isl_context_gbr *cgbr,
struct isl_tab *tab, unsigned first)
{
int i;
struct isl_vec *eq = NULL;
eq = isl_vec_alloc(tab->mat->ctx, 1 + tab->n_var);
if (!eq)
goto error;
if (isl_tab_extend_cons(tab, (cgbr->tab->bmap->n_ineq - first)/2) < 0)
goto error;
isl_seq_clr(eq->el + 1 + tab->n_param,
tab->n_var - tab->n_param - tab->n_div);
for (i = first; i < cgbr->tab->bmap->n_ineq; i += 2) {
int j;
int r;
struct isl_tab_undo *snap;
snap = isl_tab_snap(tab);
isl_seq_cpy(eq->el, cgbr->tab->bmap->ineq[i], 1 + tab->n_param);
isl_seq_cpy(eq->el + 1 + tab->n_var - tab->n_div,
cgbr->tab->bmap->ineq[i] + 1 + tab->n_param,
tab->n_div);
r = isl_tab_add_row(tab, eq->el);
if (r < 0)
goto error;
r = tab->con[r].index;
j = last_non_zero_var_col(tab, tab->mat->row[r] + 2 + tab->M);
if (j < 0 || j < tab->n_dead ||
!isl_int_is_one(tab->mat->row[r][0]) ||
(!isl_int_is_one(tab->mat->row[r][2 + tab->M + j]) &&
!isl_int_is_negone(tab->mat->row[r][2 + tab->M + j]))) {
if (isl_tab_rollback(tab, snap) < 0)
goto error;
continue;
}
if (isl_tab_pivot(tab, r, j) < 0)
goto error;
if (isl_tab_kill_col(tab, j) < 0)
goto error;
if (restore_lexmin(tab) < 0)
goto error;
}
isl_vec_free(eq);
return;
error:
isl_vec_free(eq);
isl_tab_free(cgbr->tab);
cgbr->tab = NULL;
}
static int context_gbr_detect_equalities(struct isl_context *context,
struct isl_tab *tab)
{
struct isl_context_gbr *cgbr = (struct isl_context_gbr *)context;
struct isl_ctx *ctx;
unsigned n_ineq;
ctx = cgbr->tab->mat->ctx;
if (!cgbr->cone) {
struct isl_basic_set *bset = isl_tab_peek_bset(cgbr->tab);
cgbr->cone = isl_tab_from_recession_cone(bset, 0);
if (!cgbr->cone)
goto error;
if (isl_tab_track_bset(cgbr->cone,
isl_basic_set_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 && cgbr->tab->bmap->n_ineq > n_ineq)
propagate_equalities(cgbr, tab, n_ineq);
return 0;
error:
isl_tab_free(cgbr->tab);
cgbr->tab = NULL;
return -1;
}
static int context_gbr_get_div(struct isl_context *context, struct isl_tab *tab,
struct isl_vec *div)
{
return get_div(tab, context, div);
}
static int context_gbr_add_div(struct isl_context *context, struct isl_vec *div)
{
struct isl_context_gbr *cgbr = (struct isl_context_gbr *)context;
if (cgbr->cone) {
int k;
if (isl_tab_extend_cons(cgbr->cone, 3) < 0)
return -1;
if (isl_tab_extend_vars(cgbr->cone, 1) < 0)
return -1;
if (isl_tab_allocate_var(cgbr->cone) <0)
return -1;
cgbr->cone->bmap = isl_basic_map_extend_space(cgbr->cone->bmap,
isl_basic_map_get_space(cgbr->cone->bmap), 1, 0, 2);
k = isl_basic_map_alloc_div(cgbr->cone->bmap);
if (k < 0)
return -1;
isl_seq_cpy(cgbr->cone->bmap->div[k], div->el, div->size);
if (isl_tab_push(cgbr->cone, isl_tab_undo_bmap_div) < 0)
return -1;
}
return context_tab_add_div(cgbr->tab, div,
context_gbr_add_ineq_wrap, context);
}
static int context_gbr_best_split(struct isl_context *context,
struct isl_tab *tab)
{
struct isl_context_gbr *cgbr = (struct isl_context_gbr *)context;
struct isl_tab_undo *snap;
int r;
snap = isl_tab_snap(cgbr->tab);
r = best_split(tab, cgbr->tab);
if (r >= 0 && isl_tab_rollback(cgbr->tab, snap) < 0)
return -1;
return r;
}
static int context_gbr_is_empty(struct isl_context *context)
{
struct isl_context_gbr *cgbr = (struct isl_context_gbr *)context;
if (!cgbr->tab)
return -1;
return cgbr->tab->empty;
}
struct isl_gbr_tab_undo {
struct isl_tab_undo *tab_snap;
struct isl_tab_undo *shifted_snap;
struct isl_tab_undo *cone_snap;
};
static void *context_gbr_save(struct isl_context *context)
{
struct isl_context_gbr *cgbr = (struct isl_context_gbr *)context;
struct isl_gbr_tab_undo *snap;
snap = isl_alloc_type(cgbr->tab->mat->ctx, struct isl_gbr_tab_undo);
if (!snap)
return NULL;
snap->tab_snap = isl_tab_snap(cgbr->tab);
if (isl_tab_save_samples(cgbr->tab) < 0)
goto error;
if (cgbr->shifted)
snap->shifted_snap = isl_tab_snap(cgbr->shifted);
else
snap->shifted_snap = NULL;
if (cgbr->cone)
snap->cone_snap = isl_tab_snap(cgbr->cone);
else
snap->cone_snap = NULL;
return snap;
error:
free(snap);
return NULL;
}
static void context_gbr_restore(struct isl_context *context, void *save)
{
struct isl_context_gbr *cgbr = (struct isl_context_gbr *)context;
struct isl_gbr_tab_undo *snap = (struct isl_gbr_tab_undo *)save;
if (!snap)
goto error;
if (isl_tab_rollback(cgbr->tab, snap->tab_snap) < 0) {
isl_tab_free(cgbr->tab);
cgbr->tab = NULL;
}
if (snap->shifted_snap) {
if (isl_tab_rollback(cgbr->shifted, snap->shifted_snap) < 0)
goto error;
} else if (cgbr->shifted) {
isl_tab_free(cgbr->shifted);
cgbr->shifted = NULL;
}
if (snap->cone_snap) {
if (isl_tab_rollback(cgbr->cone, snap->cone_snap) < 0)
goto error;
} else if (cgbr->cone) {
isl_tab_free(cgbr->cone);
cgbr->cone = NULL;
}
free(snap);
return;
error:
free(snap);
isl_tab_free(cgbr->tab);
cgbr->tab = NULL;
}
static int context_gbr_is_ok(struct isl_context *context)
{
struct isl_context_gbr *cgbr = (struct isl_context_gbr *)context;
return !!cgbr->tab;
}
static void context_gbr_invalidate(struct isl_context *context)
{
struct isl_context_gbr *cgbr = (struct isl_context_gbr *)context;
isl_tab_free(cgbr->tab);
cgbr->tab = NULL;
}
static void context_gbr_free(struct isl_context *context)
{
struct isl_context_gbr *cgbr = (struct isl_context_gbr *)context;
isl_tab_free(cgbr->tab);
isl_tab_free(cgbr->shifted);
isl_tab_free(cgbr->cone);
free(cgbr);
}
struct isl_context_op isl_context_gbr_op = {
context_gbr_detect_nonnegative_parameters,
context_gbr_peek_basic_set,
context_gbr_peek_tab,
context_gbr_add_eq,
context_gbr_add_ineq,
context_gbr_ineq_sign,
context_gbr_test_ineq,
context_gbr_get_div,
context_gbr_add_div,
context_gbr_detect_equalities,
context_gbr_best_split,
context_gbr_is_empty,
context_gbr_is_ok,
context_gbr_save,
context_gbr_restore,
context_gbr_invalidate,
context_gbr_free,
};
static struct isl_context *isl_context_gbr_alloc(struct isl_basic_set *dom)
{
struct isl_context_gbr *cgbr;
if (!dom)
return NULL;
cgbr = isl_calloc_type(dom->ctx, struct isl_context_gbr);
if (!cgbr)
return NULL;
cgbr->context.op = &isl_context_gbr_op;
cgbr->shifted = NULL;
cgbr->cone = NULL;
cgbr->tab = isl_tab_from_basic_set(dom, 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;
}
static struct isl_context *isl_context_alloc(struct isl_basic_set *dom)
{
if (!dom)
return NULL;
if (dom->ctx->opt->context == ISL_CONTEXT_LEXMIN)
return isl_context_lex_alloc(dom);
else
return isl_context_gbr_alloc(dom);
}
/* Construct an isl_sol_map structure for accumulating the solution.
* If track_empty is set, then we also keep track of the parts
* of the context where there is no solution.
* If max is set, then we are solving a maximization, rather than
* a minimization problem, which means that the variables in the
* tableau have value "M - x" rather than "M + x".
*/
static struct isl_sol *sol_map_init(struct isl_basic_map *bmap,
struct isl_basic_set *dom, int track_empty, int max)
{
struct isl_sol_map *sol_map = NULL;
if (!bmap)
goto error;
sol_map = isl_calloc_type(bmap->ctx, struct isl_sol_map);
if (!sol_map)
goto error;
sol_map->sol.rational = ISL_F_ISSET(bmap, ISL_BASIC_MAP_RATIONAL);
sol_map->sol.dec_level.callback.run = &sol_dec_level_wrap;
sol_map->sol.dec_level.sol = &sol_map->sol;
sol_map->sol.max = max;
sol_map->sol.n_out = isl_basic_map_dim(bmap, isl_dim_out);
sol_map->sol.add = &sol_map_add_wrap;
sol_map->sol.add_empty = track_empty ? &sol_map_add_empty_wrap : NULL;
sol_map->sol.free = &sol_map_free_wrap;
sol_map->map = isl_map_alloc_space(isl_basic_map_get_space(bmap), 1,
ISL_MAP_DISJOINT);
if (!sol_map->map)
goto error;
sol_map->sol.context = isl_context_alloc(dom);
if (!sol_map->sol.context)
goto error;
if (track_empty) {
sol_map->empty = isl_set_alloc_space(isl_basic_set_get_space(dom),
1, ISL_SET_DISJOINT);
if (!sol_map->empty)
goto error;
}
isl_basic_set_free(dom);
return &sol_map->sol;
error:
isl_basic_set_free(dom);
sol_map_free(sol_map);
return NULL;
}
/* Check whether all coefficients of (non-parameter) variables
* are non-positive, meaning that no pivots can be performed on the row.
*/
static int is_critical(struct isl_tab *tab, int row)
{
int j;
unsigned off = 2 + tab->M;
for (j = tab->n_dead; j < tab->n_col; ++j) {
if (tab->col_var[j] >= 0 &&
(tab->col_var[j] < tab->n_param ||
tab->col_var[j] >= tab->n_var - tab->n_div))
continue;
if (isl_int_is_pos(tab->mat->row[row][off + j]))
return 0;
}
return 1;
}
/* Check whether the inequality represented by vec is strict over the integers,
* i.e., there are no integer values satisfying the constraint with
* equality. This happens if the gcd of the coefficients is not a divisor
* of the constant term. If so, scale the constraint down by the gcd
* of the coefficients.
*/
static int is_strict(struct isl_vec *vec)
{
isl_int gcd;
int strict = 0;
isl_int_init(gcd);
isl_seq_gcd(vec->el + 1, vec->size - 1, &gcd);
if (!isl_int_is_one(gcd)) {
strict = !isl_int_is_divisible_by(vec->el[0], gcd);
isl_int_fdiv_q(vec->el[0], vec->el[0], gcd);
isl_seq_scale_down(vec->el + 1, vec->el + 1, gcd, vec->size-1);
}
isl_int_clear(gcd);
return strict;
}
/* Determine the sign of the given row of the main tableau.
* The result is one of
* isl_tab_row_pos: always non-negative; no pivot needed
* isl_tab_row_neg: always non-positive; pivot
* isl_tab_row_any: can be both positive and negative; split
*
* We first handle some simple cases
* - the row sign may be known already
* - the row may be obviously non-negative
* - the parametric constant may be equal to that of another row
* for which we know the sign. This sign will be either "pos" or
* "any". If it had been "neg" then we would have pivoted before.
*
* If none of these cases hold, we check the value of the row for each
* of the currently active samples. Based on the signs of these values
* we make an initial determination of the sign of the row.
*
* all zero -> unk(nown)
* all non-negative -> pos
* all non-positive -> neg
* both negative and positive -> all
*
* If we end up with "all", we are done.
* Otherwise, we perform a check for positive and/or negative
* values as follows.
*
* samples neg unk pos
* <0 ? Y N Y N
* pos any pos
* >0 ? Y N Y N
* any neg any neg
*
* There is no special sign for "zero", because we can usually treat zero
* as either non-negative or non-positive, whatever works out best.
* However, if the row is "critical", meaning that pivoting is impossible
* then we don't want to limp zero with the non-positive case, because
* then we we would lose the solution for those values of the parameters
* where the value of the row is zero. Instead, we treat 0 as non-negative
* ensuring a split if the row can attain both zero and negative values.
* The same happens when the original constraint was one that could not
* be satisfied with equality by any integer values of the parameters.
* In this case, we normalize the constraint, but then a value of zero
* for the normalized constraint is actually a positive value for the
* original constraint, so again we need to treat zero as non-negative.
* In both these cases, we have the following decision tree instead:
*
* all non-negative -> pos
* all negative -> neg
* both negative and non-negative -> all
*
* samples neg pos
* <0 ? Y N
* any pos
* >=0 ? Y N
* any neg
*/
static enum isl_tab_row_sign row_sign(struct isl_tab *tab,
struct isl_sol *sol, int row)
{
struct isl_vec *ineq = NULL;
enum isl_tab_row_sign res = isl_tab_row_unknown;
int critical;
int strict;
int row2;
if (tab->row_sign[row] != isl_tab_row_unknown)
return tab->row_sign[row];
if (is_obviously_nonneg(tab, row))
return isl_tab_row_pos;
for (row2 = tab->n_redundant; row2 < tab->n_row; ++row2) {
if (tab->row_sign[row2] == isl_tab_row_unknown)
continue;
if (identical_parameter_line(tab, row, row2))
return tab->row_sign[row2];
}
critical = is_critical(tab, row);
ineq = get_row_parameter_ineq(tab, row);
if (!ineq)
goto error;
strict = is_strict(ineq);
res = sol->context->op->ineq_sign(sol->context, ineq->el,
critical || strict);
if (res == isl_tab_row_unknown || res == isl_tab_row_pos) {
/* test for negative values */
int feasible;
isl_seq_neg(ineq->el, ineq->el, ineq->size);
isl_int_sub_ui(ineq->el[0], ineq->el[0], 1);
feasible = sol->context->op->test_ineq(sol->context, ineq->el);
if (feasible < 0)
goto error;
if (!feasible)
res = isl_tab_row_pos;
else
res = (res == isl_tab_row_unknown) ? isl_tab_row_neg
: isl_tab_row_any;
if (res == isl_tab_row_neg) {
isl_seq_neg(ineq->el, ineq->el, ineq->size);
isl_int_sub_ui(ineq->el[0], ineq->el[0], 1);
}
}
if (res == isl_tab_row_neg) {
/* test for positive values */
int feasible;
if (!critical && !strict)
isl_int_sub_ui(ineq->el[0], ineq->el[0], 1);
feasible = sol->context->op->test_ineq(sol->context, ineq->el);
if (feasible < 0)
goto error;
if (feasible)
res = isl_tab_row_any;
}
isl_vec_free(ineq);
return res;
error:
isl_vec_free(ineq);
return isl_tab_row_unknown;
}
static void find_solutions(struct isl_sol *sol, struct isl_tab *tab);
/* Find solutions for values of the parameters that satisfy the given
* inequality.
*
* We currently take a snapshot of the context tableau that is reset
* when we return from this function, while we make a copy of the main
* tableau, leaving the original main tableau untouched.
* These are fairly arbitrary choices. Making a copy also of the context
* tableau would obviate the need to undo any changes made to it later,
* while taking a snapshot of the main tableau could reduce memory usage.
* If we were to switch to taking a snapshot of the main tableau,
* we would have to keep in mind that we need to save the row signs
* and that we need to do this before saving the current basis
* such that the basis has been restore before we restore the row signs.
*/
static void find_in_pos(struct isl_sol *sol, struct isl_tab *tab, isl_int *ineq)
{
void *saved;
if (!sol->context)
goto error;
saved = sol->context->op->save(sol->context);
tab = isl_tab_dup(tab);
if (!tab)
goto error;
sol->context->op->add_ineq(sol->context, ineq, 0, 1);
find_solutions(sol, tab);
if (!sol->error)
sol->context->op->restore(sol->context, saved);
return;
error:
sol->error = 1;
}
/* Record the absence of solutions for those values of the parameters
* that do not satisfy the given inequality with equality.
*/
static void no_sol_in_strict(struct isl_sol *sol,
struct isl_tab *tab, struct isl_vec *ineq)
{
int empty;
void *saved;
if (!sol->context || sol->error)
goto error;
saved = sol->context->op->save(sol->context);
isl_int_sub_ui(ineq->el[0], ineq->el[0], 1);
sol->context->op->add_ineq(sol->context, ineq->el, 1, 0);
if (!sol->context)
goto error;
empty = tab->empty;
tab->empty = 1;
sol_add(sol, tab);
tab->empty = empty;
isl_int_add_ui(ineq->el[0], ineq->el[0], 1);
sol->context->op->restore(sol->context, saved);
return;
error:
sol->error = 1;
}
/* Compute the lexicographic minimum of the set represented by the main
* tableau "tab" within the context "sol->context_tab".
* On entry the sample value of the main tableau is lexicographically
* less than or equal to this lexicographic minimum.
* Pivots are performed until a feasible point is found, which is then
* necessarily equal to the minimum, or until the tableau is found to
* be infeasible. Some pivots may need to be performed for only some
* feasible values of the context tableau. If so, the context tableau
* is split into a part where the pivot is needed and a part where it is not.
*
* Whenever we enter the main loop, the main tableau is such that no
* "obvious" pivots need to be performed on it, where "obvious" means
* that the given row can be seen to be negative without looking at
* the context tableau. In particular, for non-parametric problems,
* no pivots need to be performed on the main tableau.
* The caller of find_solutions is responsible for making this property
* hold prior to the first iteration of the loop, while restore_lexmin
* is called before every other iteration.
*
* Inside the main loop, we first examine the signs of the rows of
* the main tableau within the context of the context tableau.
* If we find a row that is always non-positive for all values of
* the parameters satisfying the context tableau and negative for at
* least one value of the parameters, we perform the appropriate pivot
* and start over. An exception is the case where no pivot can be
* performed on the row. In this case, we require that the sign of
* the row is negative for all values of the parameters (rather than just
* non-positive). This special case is handled inside row_sign, which
* will say that the row can have any sign if it determines that it can
* attain both negative and zero values.
*
* If we can't find a row that always requires a pivot, but we can find
* one or more rows that require a pivot for some values of the parameters
* (i.e., the row can attain both positive and negative signs), then we split
* the context tableau into two parts, one where we force the sign to be
* non-negative and one where we force is to be negative.
* The non-negative part is handled by a recursive call (through find_in_pos).
* Upon returning from this call, we continue with the negative part and
* perform the required pivot.
*
* If no such rows can be found, all rows are non-negative and we have
* found a (rational) feasible point. If we only wanted a rational point
* then we are done.
* Otherwise, we check if all values of the sample point of the tableau
* are integral for the variables. If so, we have found the minimal
* integral point and we are done.
* If the sample point is not integral, then we need to make a distinction
* based on whether the constant term is non-integral or the coefficients
* of the parameters. Furthermore, in order to decide how to handle
* the non-integrality, we also need to know whether the coefficients
* of the other columns in the tableau are integral. This leads
* to the following table. The first two rows do not correspond
* to a non-integral sample point and are only mentioned for completeness.
*
* constant parameters other
*
* int int int |
* int int rat | -> no problem
*
* rat int int -> fail
*
* rat int rat -> cut
*
* int rat rat |
* rat rat rat | -> parametric cut
*
* int rat int |
* rat rat int | -> split context
*
* If the parametric constant is completely integral, then there is nothing
* to be done. If the constant term is non-integral, but all the other
* coefficient are integral, then there is nothing that can be done
* and the tableau has no integral solution.
* If, on the other hand, one or more of the other columns have rational
* coefficients, but the parameter coefficients are all integral, then
* we can perform a regular (non-parametric) cut.
* Finally, if there is any parameter coefficient that is non-integral,
* then we need to involve the context tableau. There are two cases here.
* If at least one other column has a rational coefficient, then we
* can perform a parametric cut in the main tableau by adding a new
* integer division in the context tableau.
* If all other columns have integral coefficients, then we need to
* enforce that the rational combination of parameters (c + \sum a_i y_i)/m
* is always integral. We do this by introducing an integer division
* q = floor((c + \sum a_i y_i)/m) and stipulating that its argument should
* always be integral in the context tableau, i.e., m q = c + \sum a_i y_i.
* Since q is expressed in the tableau as
* c + \sum a_i y_i - m q >= 0
* -c - \sum a_i y_i + m q + m - 1 >= 0
* it is sufficient to add the inequality
* -c - \sum a_i y_i + m q >= 0
* In the part of the context where this inequality does not hold, the
* main tableau is marked as being empty.
*/
static void find_solutions(struct isl_sol *sol, struct isl_tab *tab)
{
struct isl_context *context;
int r;
if (!tab || sol->error)
goto error;
context = sol->context;
if (tab->empty)
goto done;
if (context->op->is_empty(context))
goto done;
for (r = 0; r >= 0 && tab && !tab->empty; r = restore_lexmin(tab)) {
int flags;
int row;
enum isl_tab_row_sign sgn;
int split = -1;
int n_split = 0;
for (row = tab->n_redundant; row < tab->n_row; ++row) {
if (!isl_tab_var_from_row(tab, row)->is_nonneg)
continue;
sgn = row_sign(tab, sol, row);
if (!sgn)
goto error;
tab->row_sign[row] = sgn;
if (sgn == isl_tab_row_any)
n_split++;
if (sgn == isl_tab_row_any && split == -1)
split = row;
if (sgn == isl_tab_row_neg)
break;
}
if (row < tab->n_row)
continue;
if (split != -1) {
struct isl_vec *ineq;
if (n_split != 1)
split = context->op->best_split(context, tab);
if (split < 0)
goto error;
ineq = get_row_parameter_ineq(tab, split);
if (!ineq)
goto error;
is_strict(ineq);
for (row = tab->n_redundant; row < tab->n_row; ++row) {
if (!isl_tab_var_from_row(tab, row)->is_nonneg)
continue;
if (tab->row_sign[row] == isl_tab_row_any)
tab->row_sign[row] = isl_tab_row_unknown;
}
tab->row_sign[split] = isl_tab_row_pos;
sol_inc_level(sol);
find_in_pos(sol, tab, ineq->el);
tab->row_sign[split] = isl_tab_row_neg;
row = split;
isl_seq_neg(ineq->el, ineq->el, ineq->size);
isl_int_sub_ui(ineq->el[0], ineq->el[0], 1);
if (!sol->error)
context->op->add_ineq(context, ineq->el, 0, 1);
isl_vec_free(ineq);
if (sol->error)
goto error;
continue;
}
if (tab->rational)
break;
row = first_non_integer_row(tab, &flags);
if (row < 0)
break;
if (ISL_FL_ISSET(flags, I_PAR)) {
if (ISL_FL_ISSET(flags, I_VAR)) {
if (isl_tab_mark_empty(tab) < 0)
goto error;
break;
}
row = add_cut(tab, row);
} else if (ISL_FL_ISSET(flags, I_VAR)) {
struct isl_vec *div;
struct isl_vec *ineq;
int d;
div = get_row_split_div(tab, row);
if (!div)
goto error;
d = context->op->get_div(context, tab, div);
isl_vec_free(div);
if (d < 0)
goto error;
ineq = ineq_for_div(context->op->peek_basic_set(context), d);
if (!ineq)
goto error;
sol_inc_level(sol);
no_sol_in_strict(sol, tab, ineq);
isl_seq_neg(ineq->el, ineq->el, ineq->size);
context->op->add_ineq(context, ineq->el, 1, 1);
isl_vec_free(ineq);
if (sol->error || !context->op->is_ok(context))
goto error;
tab = set_row_cst_to_div(tab, row, d);
if (context->op->is_empty(context))
break;
} else
row = add_parametric_cut(tab, row, context);
if (row < 0)
goto error;
}
if (r < 0)
goto error;
done:
sol_add(sol, tab);
isl_tab_free(tab);
return;
error:
isl_tab_free(tab);
sol->error = 1;
}
/* Compute the lexicographic minimum of the set represented by the main
* tableau "tab" within the context "sol->context_tab".
*
* As a preprocessing step, we first transfer all the purely parametric
* equalities from the main tableau to the context tableau, i.e.,
* parameters that have been pivoted to a row.
* These equalities are ignored by the main algorithm, because the
* corresponding rows may not be marked as being non-negative.
* In parts of the context where the added equality does not hold,
* the main tableau is marked as being empty.
*/
static void find_solutions_main(struct isl_sol *sol, struct isl_tab *tab)
{
int row;
if (!tab)
goto error;
sol->level = 0;
for (row = tab->n_redundant; row < tab->n_row; ++row) {
int p;
struct isl_vec *eq;
if (tab->row_var[row] < 0)
continue;
if (tab->row_var[row] >= tab->n_param &&
tab->row_var[row] < tab->n_var - tab->n_div)
continue;
if (tab->row_var[row] < tab->n_param)
p = tab->row_var[row];
else
p = tab->row_var[row]
+ tab->n_param - (tab->n_var - tab->n_div);
eq = isl_vec_alloc(tab->mat->ctx, 1+tab->n_param+tab->n_div);
if (!eq)
goto error;
get_row_parameter_line(tab, row, eq->el);
isl_int_neg(eq->el[1 + p], tab->mat->row[row][0]);
eq = isl_vec_normalize(eq);
sol_inc_level(sol);
no_sol_in_strict(sol, tab, eq);
isl_seq_neg(eq->el, eq->el, eq->size);
sol_inc_level(sol);
no_sol_in_strict(sol, tab, eq);
isl_seq_neg(eq->el, eq->el, eq->size);
sol->context->op->add_eq(sol->context, eq->el, 1, 1);
isl_vec_free(eq);
if (isl_tab_mark_redundant(tab, row) < 0)
goto error;
if (sol->context->op->is_empty(sol->context))
break;
row = tab->n_redundant - 1;
}
find_solutions(sol, tab);
sol->level = 0;
sol_pop(sol);
return;
error:
isl_tab_free(tab);
sol->error = 1;
}
/* Check if integer division "div" of "dom" also occurs in "bmap".
* If so, return its position within the divs.
* If not, return -1.
*/
static int find_context_div(struct isl_basic_map *bmap,
struct isl_basic_set *dom, unsigned div)
{
int i;
unsigned b_dim = isl_space_dim(bmap->dim, isl_dim_all);
unsigned d_dim = isl_space_dim(dom->dim, isl_dim_all);
if (isl_int_is_zero(dom->div[div][0]))
return -1;
if (isl_seq_first_non_zero(dom->div[div] + 2 + d_dim, dom->n_div) != -1)
return -1;
for (i = 0; i < bmap->n_div; ++i) {
if (isl_int_is_zero(bmap->div[i][0]))
continue;
if (isl_seq_first_non_zero(bmap->div[i] + 2 + d_dim,
(b_dim - d_dim) + bmap->n_div) != -1)
continue;
if (isl_seq_eq(bmap->div[i], dom->div[div], 2 + d_dim))
return i;
}
return -1;
}
/* The correspondence between the variables in the main tableau,
* the context tableau, and the input map and domain is as follows.
* The first n_param and the last n_div variables of the main tableau
* form the variables of the context tableau.
* In the basic map, these n_param variables correspond to the
* parameters and the input dimensions. In the domain, they correspond
* to the parameters and the set dimensions.
* The n_div variables correspond to the integer divisions in the domain.
* To ensure that everything lines up, we may need to copy some of the
* integer divisions of the domain to the map. These have to be placed
* in the same order as those in the context and they have to be placed
* after any other integer divisions that the map may have.
* This function performs the required reordering.
*/
static struct isl_basic_map *align_context_divs(struct isl_basic_map *bmap,
struct isl_basic_set *dom)
{
int i;
int common = 0;
int other;
for (i = 0; i < dom->n_div; ++i)
if (find_context_div(bmap, dom, i) != -1)
common++;
other = bmap->n_div - common;
if (dom->n_div - common > 0) {
bmap = isl_basic_map_extend_space(bmap, isl_space_copy(bmap->dim),
dom->n_div - common, 0, 0);
if (!bmap)
return NULL;
}
for (i = 0; i < dom->n_div; ++i) {
int pos = find_context_div(bmap, dom, i);
if (pos < 0) {
pos = isl_basic_map_alloc_div(bmap);
if (pos < 0)
goto error;
isl_int_set_si(bmap->div[pos][0], 0);
}
if (pos != other + i)
isl_basic_map_swap_div(bmap, pos, other + i);
}
return bmap;
error:
isl_basic_map_free(bmap);
return NULL;
}
/* Base case of isl_tab_basic_map_partial_lexopt, after removing
* some obvious symmetries.
*
* We make sure the divs in the domain are properly ordered,
* because they will be added one by one in the given order
* during the construction of the solution map.
*/
static struct isl_sol *basic_map_partial_lexopt_base(
__isl_take isl_basic_map *bmap, __isl_take isl_basic_set *dom,
__isl_give isl_set **empty, int max,
struct isl_sol *(*init)(__isl_keep isl_basic_map *bmap,
__isl_take isl_basic_set *dom, int track_empty, int max))
{
struct isl_tab *tab;
struct isl_sol *sol = NULL;
struct isl_context *context;
if (dom->n_div) {
dom = isl_basic_set_order_divs(dom);
bmap = align_context_divs(bmap, dom);
}
sol = init(bmap, dom, !!empty, max);
if (!sol)
goto error;
context = sol->context;
if (isl_basic_set_plain_is_empty(context->op->peek_basic_set(context)))
/* nothing */;
else if (isl_basic_map_plain_is_empty(bmap)) {
if (sol->add_empty)
sol->add_empty(sol,
isl_basic_set_copy(context->op->peek_basic_set(context)));
} else {
tab = tab_for_lexmin(bmap,
context->op->peek_basic_set(context), 1, max);
tab = context->op->detect_nonnegative_parameters(context, tab);
find_solutions_main(sol, tab);
}
if (sol->error)
goto error;
isl_basic_map_free(bmap);
return sol;
error:
sol_free(sol);
isl_basic_map_free(bmap);
return NULL;
}
/* Base case of isl_tab_basic_map_partial_lexopt, after removing
* some obvious symmetries.
*
* We call basic_map_partial_lexopt_base and extract the results.
*/
static __isl_give isl_map *basic_map_partial_lexopt_base_map(
__isl_take isl_basic_map *bmap, __isl_take isl_basic_set *dom,
__isl_give isl_set **empty, int max)
{
isl_map *result = NULL;
struct isl_sol *sol;
struct isl_sol_map *sol_map;
sol = basic_map_partial_lexopt_base(bmap, dom, empty, max,
&sol_map_init);
if (!sol)
return NULL;
sol_map = (struct isl_sol_map *) sol;
result = isl_map_copy(sol_map->map);
if (empty)
*empty = isl_set_copy(sol_map->empty);
sol_free(&sol_map->sol);
return result;
}
/* Structure used during detection of parallel constraints.
* n_in: number of "input" variables: isl_dim_param + isl_dim_in
* n_out: number of "output" variables: isl_dim_out + isl_dim_div
* val: the coefficients of the output variables
*/
struct isl_constraint_equal_info {
isl_basic_map *bmap;
unsigned n_in;
unsigned n_out;
isl_int *val;
};
/* Check whether the coefficients of the output variables
* of the constraint in "entry" are equal to info->val.
*/
static int constraint_equal(const void *entry, const void *val)
{
isl_int **row = (isl_int **)entry;
const struct isl_constraint_equal_info *info = val;
return isl_seq_eq((*row) + 1 + info->n_in, info->val, info->n_out);
}
/* Check whether "bmap" has a pair of constraints that have
* the same coefficients for the output variables.
* Note that the coefficients of the existentially quantified
* variables need to be zero since the existentially quantified
* of the result are usually not the same as those of the input.
* the isl_dim_out and isl_dim_div dimensions.
* If so, return 1 and return the row indices of the two constraints
* in *first and *second.
*/
static int parallel_constraints(__isl_keep isl_basic_map *bmap,
int *first, int *second)
{
int i;
isl_ctx *ctx = isl_basic_map_get_ctx(bmap);
struct isl_hash_table *table = NULL;
struct isl_hash_table_entry *entry;
struct isl_constraint_equal_info info;
unsigned n_out;
unsigned n_div;
ctx = isl_basic_map_get_ctx(bmap);
table = isl_hash_table_alloc(ctx, bmap->n_ineq);
if (!table)
goto error;
info.n_in = isl_basic_map_dim(bmap, isl_dim_param) +
isl_basic_map_dim(bmap, isl_dim_in);
info.bmap = bmap;
n_out = isl_basic_map_dim(bmap, isl_dim_out);
n_div = isl_basic_map_dim(bmap, isl_dim_div);
info.n_out = n_out + n_div;
for (i = 0; i < bmap->n_ineq; ++i) {
uint32_t hash;
info.val = bmap->ineq[i] + 1 + info.n_in;
if (isl_seq_first_non_zero(info.val, n_out) < 0)
continue;
if (isl_seq_first_non_zero(info.val + n_out, n_div) >= 0)
continue;
hash = isl_seq_get_hash(info.val, info.n_out);
entry = isl_hash_table_find(ctx, table, hash,
constraint_equal, &info, 1);
if (!entry)
goto error;
if (entry->data)
break;
entry->data = &bmap->ineq[i];
}
if (i < bmap->n_ineq) {
*first = ((isl_int **)entry->data) - bmap->ineq;
*second = i;
}
isl_hash_table_free(ctx, table);
return i < bmap->n_ineq;
error:
isl_hash_table_free(ctx, table);
return -1;
}
/* Given a set of upper bounds in "var", add constraints to "bset"
* that make the i-th bound smallest.
*
* In particular, if there are n bounds b_i, then add the constraints
*
* b_i <= b_j for j > i
* b_i < b_j for j < i
*/
static __isl_give isl_basic_set *select_minimum(__isl_take isl_basic_set *bset,
__isl_keep isl_mat *var, int i)
{
isl_ctx *ctx;
int j, k;
ctx = isl_mat_get_ctx(var);
for (j = 0; j < var->n_row; ++j) {
if (j == i)
continue;
k = isl_basic_set_alloc_inequality(bset);
if (k < 0)
goto error;
isl_seq_combine(bset->ineq[k], ctx->one, var->row[j],
ctx->negone, var->row[i], var->n_col);
isl_int_set_si(bset->ineq[k][var->n_col], 0);
if (j < i)
isl_int_sub_ui(bset->ineq[k][0], bset->ineq[k][0], 1);
}
bset = isl_basic_set_finalize(bset);
return bset;
error:
isl_basic_set_free(bset);
return NULL;
}
/* Given a set of upper bounds on the last "input" variable m,
* construct a set that assigns the minimal upper bound to m, i.e.,
* construct a set that divides the space into cells where one
* of the upper bounds is smaller than all the others and assign
* this upper bound to m.
*
* In particular, if there are n bounds b_i, then the result
* consists of n basic sets, each one of the form
*
* m = b_i
* b_i <= b_j for j > i
* b_i < b_j for j < i
*/
static __isl_give isl_set *set_minimum(__isl_take isl_space *dim,
__isl_take isl_mat *var)
{
int i, k;
isl_basic_set *bset = NULL;
isl_ctx *ctx;
isl_set *set = NULL;
if (!dim || !var)
goto error;
ctx = isl_space_get_ctx(dim);
set = isl_set_alloc_space(isl_space_copy(dim),
var->n_row, ISL_SET_DISJOINT);
for (i = 0; i < var->n_row; ++i) {
bset = isl_basic_set_alloc_space(isl_space_copy(dim), 0,
1, var->n_row - 1);
k = isl_basic_set_alloc_equality(bset);
if (k < 0)
goto error;
isl_seq_cpy(bset->eq[k], var->row[i], var->n_col);
isl_int_set_si(bset->eq[k][var->n_col], -1);
bset = select_minimum(bset, var, i);
set = isl_set_add_basic_set(set, bset);
}
isl_space_free(dim);
isl_mat_free(var);
return set;
error:
isl_basic_set_free(bset);
isl_set_free(set);
isl_space_free(dim);
isl_mat_free(var);
return NULL;
}
/* Given that the last input variable of "bmap" represents the minimum
* of the bounds in "cst", check whether we need to split the domain
* based on which bound attains the minimum.
*
* A split is needed when the minimum appears in an integer division
* or in an equality. Otherwise, it is only needed if it appears in
* an upper bound that is different from the upper bounds on which it
* is defined.
*/
static int need_split_basic_map(__isl_keep isl_basic_map *bmap,
__isl_keep isl_mat *cst)
{
int i, j;
unsigned total;
unsigned pos;
pos = cst->n_col - 1;
total = isl_basic_map_dim(bmap, isl_dim_all);
for (i = 0; i < bmap->n_div; ++i)
if (!isl_int_is_zero(bmap->div[i][2 + pos]))
return 1;
for (i = 0; i < bmap->n_eq; ++i)
if (!isl_int_is_zero(bmap->eq[i][1 + pos]))
return 1;
for (i = 0; i < bmap->n_ineq; ++i) {
if (isl_int_is_nonneg(bmap->ineq[i][1 + pos]))
continue;
if (!isl_int_is_negone(bmap->ineq[i][1 + pos]))
return 1;
if (isl_seq_first_non_zero(bmap->ineq[i] + 1 + pos + 1,
total - pos - 1) >= 0)
return 1;
for (j = 0; j < cst->n_row; ++j)
if (isl_seq_eq(bmap->ineq[i], cst->row[j], cst->n_col))
break;
if (j >= cst->n_row)
return 1;
}
return 0;
}
/* Given that the last set variable of "bset" represents the minimum
* of the bounds in "cst", check whether we need to split the domain
* based on which bound attains the minimum.
*
* We simply call need_split_basic_map here. This is safe because
* the position of the minimum is computed from "cst" and not
* from "bmap".
*/
static int need_split_basic_set(__isl_keep isl_basic_set *bset,
__isl_keep isl_mat *cst)
{
return need_split_basic_map((isl_basic_map *)bset, cst);
}
/* Given that the last set variable of "set" represents the minimum
* of the bounds in "cst", check whether we need to split the domain
* based on which bound attains the minimum.
*/
static int need_split_set(__isl_keep isl_set *set, __isl_keep isl_mat *cst)
{
int i;
for (i = 0; i < set->n; ++i)
if (need_split_basic_set(set->p[i], cst))
return 1;
return 0;
}
/* Given a set of which the last set variable is the minimum
* of the bounds in "cst", split each basic set in the set
* in pieces where one of the bounds is (strictly) smaller than the others.
* This subdivision is given in "min_expr".
* The variable is subsequently projected out.
*
* We only do the split when it is needed.
* For example if the last input variable m = min(a,b) and the only
* constraints in the given basic set are lower bounds on m,
* i.e., l <= m = min(a,b), then we can simply project out m
* to obtain l <= a and l <= b, without having to split on whether
* m is equal to a or b.
*/
static __isl_give isl_set *split(__isl_take isl_set *empty,
__isl_take isl_set *min_expr, __isl_take isl_mat *cst)
{
int n_in;
int i;
isl_space *dim;
isl_set *res;
if (!empty || !min_expr || !cst)
goto error;
n_in = isl_set_dim(empty, isl_dim_set);
dim = isl_set_get_space(empty);
dim = isl_space_drop_dims(dim, isl_dim_set, n_in - 1, 1);
res = isl_set_empty(dim);
for (i = 0; i < empty->n; ++i) {
isl_set *set;
set = isl_set_from_basic_set(isl_basic_set_copy(empty->p[i]));
if (need_split_basic_set(empty->p[i], cst))
set = isl_set_intersect(set, isl_set_copy(min_expr));
set = isl_set_remove_dims(set, isl_dim_set, n_in - 1, 1);
res = isl_set_union_disjoint(res, set);
}
isl_set_free(empty);
isl_set_free(min_expr);
isl_mat_free(cst);
return res;
error:
isl_set_free(empty);
isl_set_free(min_expr);
isl_mat_free(cst);
return NULL;
}
/* Given a map of which the last input variable is the minimum
* of the bounds in "cst", split each basic set in the set
* in pieces where one of the bounds is (strictly) smaller than the others.
* This subdivision is given in "min_expr".
* The variable is subsequently projected out.
*
* The implementation is essentially the same as that of "split".
*/
static __isl_give isl_map *split_domain(__isl_take isl_map *opt,
__isl_take isl_set *min_expr, __isl_take isl_mat *cst)
{
int n_in;
int i;
isl_space *dim;
isl_map *res;
if (!opt || !min_expr || !cst)
goto error;
n_in = isl_map_dim(opt, isl_dim_in);
dim = isl_map_get_space(opt);
dim = isl_space_drop_dims(dim, isl_dim_in, n_in - 1, 1);
res = isl_map_empty(dim);
for (i = 0; i < opt->n; ++i) {
isl_map *map;
map = isl_map_from_basic_map(isl_basic_map_copy(opt->p[i]));
if (need_split_basic_map(opt->p[i], cst))
map = isl_map_intersect_domain(map,
isl_set_copy(min_expr));
map = isl_map_remove_dims(map, isl_dim_in, n_in - 1, 1);
res = isl_map_union_disjoint(res, map);
}
isl_map_free(opt);
isl_set_free(min_expr);
isl_mat_free(cst);
return res;
error:
isl_map_free(opt);
isl_set_free(min_expr);
isl_mat_free(cst);
return NULL;
}
static __isl_give isl_map *basic_map_partial_lexopt(
__isl_take isl_basic_map *bmap, __isl_take isl_basic_set *dom,
__isl_give isl_set **empty, int max);
union isl_lex_res {
void *p;
isl_map *map;
isl_pw_multi_aff *pma;
};
/* This function is called from basic_map_partial_lexopt_symm.
* The last variable of "bmap" and "dom" corresponds to the minimum
* of the bounds in "cst". "map_space" is the space of the original
* input relation (of basic_map_partial_lexopt_symm) and "set_space"
* is the space of the original domain.
*
* We recursively call basic_map_partial_lexopt and then plug in
* the definition of the minimum in the result.
*/
static __isl_give union isl_lex_res basic_map_partial_lexopt_symm_map_core(
__isl_take isl_basic_map *bmap, __isl_take isl_basic_set *dom,
__isl_give isl_set **empty, int max, __isl_take isl_mat *cst,
__isl_take isl_space *map_space, __isl_take isl_space *set_space)
{
isl_map *opt;
isl_set *min_expr;
union isl_lex_res res;
min_expr = set_minimum(isl_basic_set_get_space(dom), isl_mat_copy(cst));
opt = basic_map_partial_lexopt(bmap, dom, empty, max);
if (empty) {
*empty = split(*empty,
isl_set_copy(min_expr), isl_mat_copy(cst));
*empty = isl_set_reset_space(*empty, set_space);
}
opt = split_domain(opt, min_expr, cst);
opt = isl_map_reset_space(opt, map_space);
res.map = opt;
return res;
}
/* Given a basic map with at least two parallel constraints (as found
* by the function parallel_constraints), first look for more constraints
* parallel to the two constraint and replace the found list of parallel
* constraints by a single constraint with as "input" part the minimum
* of the input parts of the list of constraints. Then, recursively call
* basic_map_partial_lexopt (possibly finding more parallel constraints)
* and plug in the definition of the minimum in the result.
*
* More specifically, given a set of constraints
*
* a x + b_i(p) >= 0
*
* Replace this set by a single constraint
*
* a x + u >= 0
*
* with u a new parameter with constraints
*
* u <= b_i(p)
*
* Any solution to the new system is also a solution for the original system
* since
*
* a x >= -u >= -b_i(p)
*
* Moreover, m = min_i(b_i(p)) satisfies the constraints on u and can
* therefore be plugged into the solution.
*/
static union isl_lex_res basic_map_partial_lexopt_symm(
__isl_take isl_basic_map *bmap, __isl_take isl_basic_set *dom,
__isl_give isl_set **empty, int max, int first, int second,
__isl_give union isl_lex_res (*core)(__isl_take isl_basic_map *bmap,
__isl_take isl_basic_set *dom,
__isl_give isl_set **empty,
int max, __isl_take isl_mat *cst,
__isl_take isl_space *map_space,
__isl_take isl_space *set_space))
{
int i, n, k;
int *list = NULL;
unsigned n_in, n_out, n_div;
isl_ctx *ctx;
isl_vec *var = NULL;
isl_mat *cst = NULL;
isl_space *map_space, *set_space;
union isl_lex_res res;
map_space = isl_basic_map_get_space(bmap);
set_space = empty ? isl_basic_set_get_space(dom) : NULL;
n_in = isl_basic_map_dim(bmap, isl_dim_param) +
isl_basic_map_dim(bmap, isl_dim_in);
n_out = isl_basic_map_dim(bmap, isl_dim_all) - n_in;
ctx = isl_basic_map_get_ctx(bmap);
list = isl_alloc_array(ctx, int, bmap->n_ineq);
var = isl_vec_alloc(ctx, n_out);
if (!list || !var)
goto error;
list[0] = first;
list[1] = second;
isl_seq_cpy(var->el, bmap->ineq[first] + 1 + n_in, n_out);
for (i = second + 1, n = 2; i < bmap->n_ineq; ++i) {
if (isl_seq_eq(var->el, bmap->ineq[i] + 1 + n_in, n_out))
list[n++] = i;
}
cst = isl_mat_alloc(ctx, n, 1 + n_in);
if (!cst)
goto error;
for (i = 0; i < n; ++i)
isl_seq_cpy(cst->row[i], bmap->ineq[list[i]], 1 + n_in);
bmap = isl_basic_map_cow(bmap);
if (!bmap)
goto error;
for (i = n - 1; i >= 0; --i)
if (isl_basic_map_drop_inequality(bmap, list[i]) < 0)
goto error;
bmap = isl_basic_map_add(bmap, isl_dim_in, 1);
bmap = isl_basic_map_extend_constraints(bmap, 0, 1);
k = isl_basic_map_alloc_inequality(bmap);
if (k < 0)
goto error;
isl_seq_clr(bmap->ineq[k], 1 + n_in);
isl_int_set_si(bmap->ineq[k][1 + n_in], 1);
isl_seq_cpy(bmap->ineq[k] + 1 + n_in + 1, var->el, n_out);
bmap = isl_basic_map_finalize(bmap);
n_div = isl_basic_set_dim(dom, isl_dim_div);
dom = isl_basic_set_add(dom, isl_dim_set, 1);
dom = isl_basic_set_extend_constraints(dom, 0, n);
for (i = 0; i < n; ++i) {
k = isl_basic_set_alloc_inequality(dom);
if (k < 0)
goto error;
isl_seq_cpy(dom->ineq[k], cst->row[i], 1 + n_in);
isl_int_set_si(dom->ineq[k][1 + n_in], -1);
isl_seq_clr(dom->ineq[k] + 1 + n_in + 1, n_div);
}
isl_vec_free(var);
free(list);
return core(bmap, dom, empty, max, cst, map_space, set_space);
error:
isl_space_free(map_space);
isl_space_free(set_space);
isl_mat_free(cst);
isl_vec_free(var);
free(list);
isl_basic_set_free(dom);
isl_basic_map_free(bmap);
res.p = NULL;
return res;
}
static __isl_give isl_map *basic_map_partial_lexopt_symm_map(
__isl_take isl_basic_map *bmap, __isl_take isl_basic_set *dom,
__isl_give isl_set **empty, int max, int first, int second)
{
return basic_map_partial_lexopt_symm(bmap, dom, empty, max,
first, second, &basic_map_partial_lexopt_symm_map_core).map;
}
/* Recursive part of isl_tab_basic_map_partial_lexopt, after detecting
* equalities and removing redundant constraints.
*
* We first check if there are any parallel constraints (left).
* If not, we are in the base case.
* If there are parallel constraints, we replace them by a single
* constraint in basic_map_partial_lexopt_symm and then call
* this function recursively to look for more parallel constraints.
*/
static __isl_give isl_map *basic_map_partial_lexopt(
__isl_take isl_basic_map *bmap, __isl_take isl_basic_set *dom,
__isl_give isl_set **empty, int max)
{
int par = 0;
int first, second;
if (!bmap)
goto error;
if (bmap->ctx->opt->pip_symmetry)
par = parallel_constraints(bmap, &first, &second);
if (par < 0)
goto error;
if (!par)
return basic_map_partial_lexopt_base_map(bmap, dom, empty, max);
return basic_map_partial_lexopt_symm_map(bmap, dom, empty, max,
first, second);
error:
isl_basic_set_free(dom);
isl_basic_map_free(bmap);
return NULL;
}
/* Compute the lexicographic minimum (or maximum if "max" is set)
* of "bmap" over the domain "dom" and return the result as a map.
* If "empty" is not NULL, then *empty is assigned a set that
* contains those parts of the domain where there is no solution.
* If "bmap" is marked as rational (ISL_BASIC_MAP_RATIONAL),
* then we compute the rational optimum. Otherwise, we compute
* the integral optimum.
*
* We perform some preprocessing. As the PILP solver does not
* handle implicit equalities very well, we first make sure all
* the equalities are explicitly available.
*
* We also add context constraints to the basic map and remove
* redundant constraints. This is only needed because of the
* way we handle simple symmetries. In particular, we currently look
* for symmetries on the constraints, before we set up the main tableau.
* It is then no good to look for symmetries on possibly redundant constraints.
*/
struct isl_map *isl_tab_basic_map_partial_lexopt(
struct isl_basic_map *bmap, struct isl_basic_set *dom,
struct isl_set **empty, int max)
{
if (empty)
*empty = NULL;
if (!bmap || !dom)
goto error;
isl_assert(bmap->ctx,
isl_basic_map_compatible_domain(bmap, dom), goto error);
if (isl_basic_set_dim(dom, isl_dim_all) == 0)
return basic_map_partial_lexopt(bmap, dom, empty, max);
bmap = isl_basic_map_intersect_domain(bmap, isl_basic_set_copy(dom));
bmap = isl_basic_map_detect_equalities(bmap);
bmap = isl_basic_map_remove_redundancies(bmap);
return basic_map_partial_lexopt(bmap, dom, empty, max);
error:
isl_basic_set_free(dom);
isl_basic_map_free(bmap);
return NULL;
}
struct isl_sol_for {
struct isl_sol sol;
int (*fn)(__isl_take isl_basic_set *dom,
__isl_take isl_aff_list *list, void *user);
void *user;
};
static void sol_for_free(struct isl_sol_for *sol_for)
{
if (sol_for->sol.context)
sol_for->sol.context->op->free(sol_for->sol.context);
free(sol_for);
}
static void sol_for_free_wrap(struct isl_sol *sol)
{
sol_for_free((struct isl_sol_for *)sol);
}
/* Add the solution identified by the tableau and the context tableau.
*
* See documentation of sol_add for more details.
*
* Instead of constructing a basic map, this function calls a user
* defined function with the current context as a basic set and
* a list of affine expressions representing the relation between
* the input and output. The space over which the affine expressions
* are defined is the same as that of the domain. The number of
* affine expressions in the list is equal to the number of output variables.
*/
static void sol_for_add(struct isl_sol_for *sol,
struct isl_basic_set *dom, struct isl_mat *M)
{
int i;
isl_ctx *ctx;
isl_local_space *ls;
isl_aff *aff;
isl_aff_list *list;
if (sol->sol.error || !dom || !M)
goto error;
ctx = isl_basic_set_get_ctx(dom);
ls = isl_basic_set_get_local_space(dom);
list = isl_aff_list_alloc(ctx, M->n_row - 1);
for (i = 1; i < M->n_row; ++i) {
aff = isl_aff_alloc(isl_local_space_copy(ls));
if (aff) {
isl_int_set(aff->v->el[0], M->row[0][0]);
isl_seq_cpy(aff->v->el + 1, M->row[i], M->n_col);
}
aff = isl_aff_normalize(aff);
list = isl_aff_list_add(list, aff);
}
isl_local_space_free(ls);
dom = isl_basic_set_finalize(dom);
if (sol->fn(isl_basic_set_copy(dom), list, sol->user) < 0)
goto error;
isl_basic_set_free(dom);
isl_mat_free(M);
return;
error:
isl_basic_set_free(dom);
isl_mat_free(M);
sol->sol.error = 1;
}
static void sol_for_add_wrap(struct isl_sol *sol,
struct isl_basic_set *dom, struct isl_mat *M)
{
sol_for_add((struct isl_sol_for *)sol, dom, M);
}
static struct isl_sol_for *sol_for_init(struct isl_basic_map *bmap, int max,
int (*fn)(__isl_take isl_basic_set *dom, __isl_take isl_aff_list *list,
void *user),
void *user)
{
struct isl_sol_for *sol_for = NULL;
isl_space *dom_dim;
struct isl_basic_set *dom = NULL;
sol_for = isl_calloc_type(bmap->ctx, struct isl_sol_for);
if (!sol_for)
goto error;
dom_dim = isl_space_domain(isl_space_copy(bmap->dim));
dom = isl_basic_set_universe(dom_dim);
sol_for->sol.rational = ISL_F_ISSET(bmap, ISL_BASIC_MAP_RATIONAL);
sol_for->sol.dec_level.callback.run = &sol_dec_level_wrap;
sol_for->sol.dec_level.sol = &sol_for->sol;
sol_for->fn = fn;
sol_for->user = user;
sol_for->sol.max = max;
sol_for->sol.n_out = isl_basic_map_dim(bmap, isl_dim_out);
sol_for->sol.add = &sol_for_add_wrap;
sol_for->sol.add_empty = NULL;
sol_for->sol.free = &sol_for_free_wrap;
sol_for->sol.context = isl_context_alloc(dom);
if (!sol_for->sol.context)
goto error;
isl_basic_set_free(dom);
return sol_for;
error:
isl_basic_set_free(dom);
sol_for_free(sol_for);
return NULL;
}
static void sol_for_find_solutions(struct isl_sol_for *sol_for,
struct isl_tab *tab)
{
find_solutions_main(&sol_for->sol, tab);
}
int isl_basic_map_foreach_lexopt(__isl_keep isl_basic_map *bmap, int max,
int (*fn)(__isl_take isl_basic_set *dom, __isl_take isl_aff_list *list,
void *user),
void *user)
{
struct isl_sol_for *sol_for = NULL;
bmap = isl_basic_map_copy(bmap);
if (!bmap)
return -1;
bmap = isl_basic_map_detect_equalities(bmap);
sol_for = sol_for_init(bmap, max, fn, user);
if (isl_basic_map_plain_is_empty(bmap))
/* nothing */;
else {
struct isl_tab *tab;
struct isl_context *context = sol_for->sol.context;
tab = tab_for_lexmin(bmap,
context->op->peek_basic_set(context), 1, max);
tab = context->op->detect_nonnegative_parameters(context, tab);
sol_for_find_solutions(sol_for, tab);
if (sol_for->sol.error)
goto error;
}
sol_free(&sol_for->sol);
isl_basic_map_free(bmap);
return 0;
error:
sol_free(&sol_for->sol);
isl_basic_map_free(bmap);
return -1;
}
int isl_basic_set_foreach_lexopt(__isl_keep isl_basic_set *bset, int max,
int (*fn)(__isl_take isl_basic_set *dom, __isl_take isl_aff_list *list,
void *user),
void *user)
{
return isl_basic_map_foreach_lexopt(bset, max, fn, user);
}
/* Check if the given sequence of len variables starting at pos
* represents a trivial (i.e., zero) solution.
* The variables are assumed to be non-negative and to come in pairs,
* with each pair representing a variable of unrestricted sign.
* The solution is trivial if each such pair in the sequence consists
* of two identical values, meaning that the variable being represented
* has value zero.
*/
static int region_is_trivial(struct isl_tab *tab, int pos, int len)
{
int i;
if (len == 0)
return 0;
for (i = 0; i < len; i += 2) {
int neg_row;
int pos_row;
neg_row = tab->var[pos + i].is_row ?
tab->var[pos + i].index : -1;
pos_row = tab->var[pos + i + 1].is_row ?
tab->var[pos + i + 1].index : -1;
if ((neg_row < 0 ||
isl_int_is_zero(tab->mat->row[neg_row][1])) &&
(pos_row < 0 ||
isl_int_is_zero(tab->mat->row[pos_row][1])))
continue;
if (neg_row < 0 || pos_row < 0)
return 0;
if (isl_int_ne(tab->mat->row[neg_row][1],
tab->mat->row[pos_row][1]))
return 0;
}
return 1;
}
/* Return the index of the first trivial region or -1 if all regions
* are non-trivial.
*/
static int first_trivial_region(struct isl_tab *tab,
int n_region, struct isl_region *region)
{
int i;
for (i = 0; i < n_region; ++i) {
if (region_is_trivial(tab, region[i].pos, region[i].len))
return i;
}
return -1;
}
/* Check if the solution is optimal, i.e., whether the first
* n_op entries are zero.
*/
static int is_optimal(__isl_keep isl_vec *sol, int n_op)
{
int i;
for (i = 0; i < n_op; ++i)
if (!isl_int_is_zero(sol->el[1 + i]))
return 0;
return 1;
}
/* Add constraints to "tab" that ensure that any solution is significantly
* better that that represented by "sol". That is, find the first
* relevant (within first n_op) non-zero coefficient and force it (along
* with all previous coefficients) to be zero.
* If the solution is already optimal (all relevant coefficients are zero),
* then just mark the table as empty.
*/
static int force_better_solution(struct isl_tab *tab,
__isl_keep isl_vec *sol, int n_op)
{
int i;
isl_ctx *ctx;
isl_vec *v = NULL;
if (!sol)
return -1;
for (i = 0; i < n_op; ++i)
if (!isl_int_is_zero(sol->el[1 + i]))
break;
if (i == n_op) {
if (isl_tab_mark_empty(tab) < 0)
return -1;
return 0;
}
ctx = isl_vec_get_ctx(sol);
v = isl_vec_alloc(ctx, 1 + tab->n_var);
if (!v)
return -1;
for (; i >= 0; --i) {
v = isl_vec_clr(v);
isl_int_set_si(v->el[1 + i], -1);
if (add_lexmin_eq(tab, v->el) < 0)
goto error;
}
isl_vec_free(v);
return 0;
error:
isl_vec_free(v);
return -1;
}
struct isl_trivial {
int update;
int region;
int side;
struct isl_tab_undo *snap;
};
/* Return the lexicographically smallest non-trivial solution of the
* given ILP problem.
*
* All variables are assumed to be non-negative.
*
* n_op is the number of initial coordinates to optimize.
* That is, once a solution has been found, we will only continue looking
* for solution that result in significantly better values for those
* initial coordinates. That is, we only continue looking for solutions
* that increase the number of initial zeros in this sequence.
*
* A solution is non-trivial, if it is non-trivial on each of the
* specified regions. Each region represents a sequence of pairs
* of variables. A solution is non-trivial on such a region if
* at least one of these pairs consists of different values, i.e.,
* such that the non-negative variable represented by the pair is non-zero.
*
* Whenever a conflict is encountered, all constraints involved are
* reported to the caller through a call to "conflict".
*
* We perform a simple branch-and-bound backtracking search.
* Each level in the search represents initially trivial region that is forced
* to be non-trivial.
* At each level we consider n cases, where n is the length of the region.
* In terms of the n/2 variables of unrestricted signs being encoded by
* the region, we consider the cases
* x_0 >= 1
* x_0 <= -1
* x_0 = 0 and x_1 >= 1
* x_0 = 0 and x_1 <= -1
* x_0 = 0 and x_1 = 0 and x_2 >= 1
* x_0 = 0 and x_1 = 0 and x_2 <= -1
* ...
* The cases are considered in this order, assuming that each pair
* x_i_a x_i_b represents the value x_i_b - x_i_a.
* That is, x_0 >= 1 is enforced by adding the constraint
* x_0_b - x_0_a >= 1
*/
__isl_give isl_vec *isl_tab_basic_set_non_trivial_lexmin(
__isl_take isl_basic_set *bset, int n_op, int n_region,
struct isl_region *region,
int (*conflict)(int con, void *user), void *user)
{
int i, j;
int r;
isl_ctx *ctx = isl_basic_set_get_ctx(bset);
isl_vec *v = NULL;
isl_vec *sol = isl_vec_alloc(ctx, 0);
struct isl_tab *tab;
struct isl_trivial *triv = NULL;
int level, init;
tab = tab_for_lexmin(bset, NULL, 0, 0);
if (!tab)
goto error;
tab->conflict = conflict;
tab->conflict_user = user;
v = isl_vec_alloc(ctx, 1 + tab->n_var);
triv = isl_calloc_array(ctx, struct isl_trivial, n_region);
if (!v || !triv)
goto error;
level = 0;
init = 1;
while (level >= 0) {
int side, base;
if (init) {
tab = cut_to_integer_lexmin(tab, CUT_ONE);
if (!tab)
goto error;
if (tab->empty)
goto backtrack;
r = first_trivial_region(tab, n_region, region);
if (r < 0) {
for (i = 0; i < level; ++i)
triv[i].update = 1;
isl_vec_free(sol);
sol = isl_tab_get_sample_value(tab);
if (!sol)
goto error;
if (is_optimal(sol, n_op))
break;
goto backtrack;
}
if (level >= n_region)
isl_die(ctx, isl_error_internal,
"nesting level too deep", goto error);
if (isl_tab_extend_cons(tab,
2 * region[r].len + 2 * n_op) < 0)
goto error;
triv[level].region = r;
triv[level].side = 0;
}
r = triv[level].region;
side = triv[level].side;
base = 2 * (side/2);
if (side >= region[r].len) {
backtrack:
level--;
init = 0;
if (level >= 0)
if (isl_tab_rollback(tab, triv[level].snap) < 0)
goto error;
continue;
}
if (triv[level].update) {
if (force_better_solution(tab, sol, n_op) < 0)
goto error;
triv[level].update = 0;
}
if (side == base && base >= 2) {
for (j = base - 2; j < base; ++j) {
v = isl_vec_clr(v);
isl_int_set_si(v->el[1 + region[r].pos + j], 1);
if (add_lexmin_eq(tab, v->el) < 0)
goto error;
}
}
triv[level].snap = isl_tab_snap(tab);
if (isl_tab_push_basis(tab) < 0)
goto error;
v = isl_vec_clr(v);
isl_int_set_si(v->el[0], -1);
isl_int_set_si(v->el[1 + region[r].pos + side], -1);
isl_int_set_si(v->el[1 + region[r].pos + (side ^ 1)], 1);
tab = add_lexmin_ineq(tab, v->el);
triv[level].side++;
level++;
init = 1;
}
free(triv);
isl_vec_free(v);
isl_tab_free(tab);
isl_basic_set_free(bset);
return sol;
error:
free(triv);
isl_vec_free(v);
isl_tab_free(tab);
isl_basic_set_free(bset);
isl_vec_free(sol);
return NULL;
}
/* Return the lexicographically smallest rational point in "bset",
* assuming that all variables are non-negative.
* If "bset" is empty, then return a zero-length vector.
*/
__isl_give isl_vec *isl_tab_basic_set_non_neg_lexmin(
__isl_take isl_basic_set *bset)
{
struct isl_tab *tab;
isl_ctx *ctx = isl_basic_set_get_ctx(bset);
isl_vec *sol;
tab = tab_for_lexmin(bset, NULL, 0, 0);
if (!tab)
goto error;
if (tab->empty)
sol = isl_vec_alloc(ctx, 0);
else
sol = isl_tab_get_sample_value(tab);
isl_tab_free(tab);
isl_basic_set_free(bset);
return sol;
error:
isl_tab_free(tab);
isl_basic_set_free(bset);
return NULL;
}
struct isl_sol_pma {
struct isl_sol sol;
isl_pw_multi_aff *pma;
isl_set *empty;
};
static void sol_pma_free(struct isl_sol_pma *sol_pma)
{
if (!sol_pma)
return;
if (sol_pma->sol.context)
sol_pma->sol.context->op->free(sol_pma->sol.context);
isl_pw_multi_aff_free(sol_pma->pma);
isl_set_free(sol_pma->empty);
free(sol_pma);
}
/* This function is called for parts of the context where there is
* no solution, with "bset" corresponding to the context tableau.
* Simply add the basic set to the set "empty".
*/
static void sol_pma_add_empty(struct isl_sol_pma *sol,
__isl_take isl_basic_set *bset)
{
if (!bset)
goto error;
isl_assert(bset->ctx, sol->empty, goto error);
sol->empty = isl_set_grow(sol->empty, 1);
bset = isl_basic_set_simplify(bset);
bset = isl_basic_set_finalize(bset);
sol->empty = isl_set_add_basic_set(sol->empty, bset);
if (!sol->empty)
sol->sol.error = 1;
return;
error:
isl_basic_set_free(bset);
sol->sol.error = 1;
}
/* Given a basic map "dom" that represents the context and an affine
* matrix "M" that maps the dimensions of the context to the
* output variables, construct an isl_pw_multi_aff with a single
* cell corresponding to "dom" and affine expressions copied from "M".
*/
static void sol_pma_add(struct isl_sol_pma *sol,
__isl_take isl_basic_set *dom, __isl_take isl_mat *M)
{
int i;
isl_local_space *ls;
isl_aff *aff;
isl_multi_aff *maff;
isl_pw_multi_aff *pma;
maff = isl_multi_aff_alloc(isl_pw_multi_aff_get_space(sol->pma));
ls = isl_basic_set_get_local_space(dom);
for (i = 1; i < M->n_row; ++i) {
aff = isl_aff_alloc(isl_local_space_copy(ls));
if (aff) {
isl_int_set(aff->v->el[0], M->row[0][0]);
isl_seq_cpy(aff->v->el + 1, M->row[i], M->n_col);
}
aff = isl_aff_normalize(aff);
maff = isl_multi_aff_set_aff(maff, i - 1, aff);
}
isl_local_space_free(ls);
isl_mat_free(M);
dom = isl_basic_set_simplify(dom);
dom = isl_basic_set_finalize(dom);
pma = isl_pw_multi_aff_alloc(isl_set_from_basic_set(dom), maff);
sol->pma = isl_pw_multi_aff_add_disjoint(sol->pma, pma);
if (!sol->pma)
sol->sol.error = 1;
}
static void sol_pma_free_wrap(struct isl_sol *sol)
{
sol_pma_free((struct isl_sol_pma *)sol);
}
static void sol_pma_add_empty_wrap(struct isl_sol *sol,
__isl_take isl_basic_set *bset)
{
sol_pma_add_empty((struct isl_sol_pma *)sol, bset);
}
static void sol_pma_add_wrap(struct isl_sol *sol,
__isl_take isl_basic_set *dom, __isl_take isl_mat *M)
{
sol_pma_add((struct isl_sol_pma *)sol, dom, M);
}
/* Construct an isl_sol_pma structure for accumulating the solution.
* If track_empty is set, then we also keep track of the parts
* of the context where there is no solution.
* If max is set, then we are solving a maximization, rather than
* a minimization problem, which means that the variables in the
* tableau have value "M - x" rather than "M + x".
*/
static struct isl_sol *sol_pma_init(__isl_keep isl_basic_map *bmap,
__isl_take isl_basic_set *dom, int track_empty, int max)
{
struct isl_sol_pma *sol_pma = NULL;
if (!bmap)
goto error;
sol_pma = isl_calloc_type(bmap->ctx, struct isl_sol_pma);
if (!sol_pma)
goto error;
sol_pma->sol.rational = ISL_F_ISSET(bmap, ISL_BASIC_MAP_RATIONAL);
sol_pma->sol.dec_level.callback.run = &sol_dec_level_wrap;
sol_pma->sol.dec_level.sol = &sol_pma->sol;
sol_pma->sol.max = max;
sol_pma->sol.n_out = isl_basic_map_dim(bmap, isl_dim_out);
sol_pma->sol.add = &sol_pma_add_wrap;
sol_pma->sol.add_empty = track_empty ? &sol_pma_add_empty_wrap : NULL;
sol_pma->sol.free = &sol_pma_free_wrap;
sol_pma->pma = isl_pw_multi_aff_empty(isl_basic_map_get_space(bmap));
if (!sol_pma->pma)
goto error;
sol_pma->sol.context = isl_context_alloc(dom);
if (!sol_pma->sol.context)
goto error;
if (track_empty) {
sol_pma->empty = isl_set_alloc_space(isl_basic_set_get_space(dom),
1, ISL_SET_DISJOINT);
if (!sol_pma->empty)
goto error;
}
isl_basic_set_free(dom);
return &sol_pma->sol;
error:
isl_basic_set_free(dom);
sol_pma_free(sol_pma);
return NULL;
}
/* Base case of isl_tab_basic_map_partial_lexopt, after removing
* some obvious symmetries.
*
* We call basic_map_partial_lexopt_base and extract the results.
*/
static __isl_give isl_pw_multi_aff *basic_map_partial_lexopt_base_pma(
__isl_take isl_basic_map *bmap, __isl_take isl_basic_set *dom,
__isl_give isl_set **empty, int max)
{
isl_pw_multi_aff *result = NULL;
struct isl_sol *sol;
struct isl_sol_pma *sol_pma;
sol = basic_map_partial_lexopt_base(bmap, dom, empty, max,
&sol_pma_init);
if (!sol)
return NULL;
sol_pma = (struct isl_sol_pma *) sol;
result = isl_pw_multi_aff_copy(sol_pma->pma);
if (empty)
*empty = isl_set_copy(sol_pma->empty);
sol_free(&sol_pma->sol);
return result;
}
/* Given that the last input variable of "maff" represents the minimum
* of some bounds, check whether we need to plug in the expression
* of the minimum.
*
* In particular, check if the last input variable appears in any
* of the expressions in "maff".
*/
static int need_substitution(__isl_keep isl_multi_aff *maff)
{
int i;
unsigned pos;
pos = isl_multi_aff_dim(maff, isl_dim_in) - 1;
for (i = 0; i < maff->n; ++i)
if (isl_aff_involves_dims(maff->p[i], isl_dim_in, pos, 1))
return 1;
return 0;
}
/* Given a set of upper bounds on the last "input" variable m,
* construct a piecewise affine expression that selects
* the minimal upper bound to m, i.e.,
* divide the space into cells where one
* of the upper bounds is smaller than all the others and select
* this upper bound on that cell.
*
* In particular, if there are n bounds b_i, then the result
* consists of n cell, each one of the form
*
* b_i <= b_j for j > i
* b_i < b_j for j < i
*
* The affine expression on this cell is
*
* b_i
*/
static __isl_give isl_pw_aff *set_minimum_pa(__isl_take isl_space *space,
__isl_take isl_mat *var)
{
int i;
isl_aff *aff = NULL;
isl_basic_set *bset = NULL;
isl_ctx *ctx;
isl_pw_aff *paff = NULL;
isl_space *pw_space;
isl_local_space *ls = NULL;
if (!space || !var)
goto error;
ctx = isl_space_get_ctx(space);
ls = isl_local_space_from_space(isl_space_copy(space));
pw_space = isl_space_copy(space);
pw_space = isl_space_from_domain(pw_space);
pw_space = isl_space_add_dims(pw_space, isl_dim_out, 1);
paff = isl_pw_aff_alloc_size(pw_space, var->n_row);
for (i = 0; i < var->n_row; ++i) {
isl_pw_aff *paff_i;
aff = isl_aff_alloc(isl_local_space_copy(ls));
bset = isl_basic_set_alloc_space(isl_space_copy(space), 0,
0, var->n_row - 1);
if (!aff || !bset)
goto error;
isl_int_set_si(aff->v->el[0], 1);
isl_seq_cpy(aff->v->el + 1, var->row[i], var->n_col);
isl_int_set_si(aff->v->el[1 + var->n_col], 0);
bset = select_minimum(bset, var, i);
paff_i = isl_pw_aff_alloc(isl_set_from_basic_set(bset), aff);
paff = isl_pw_aff_add_disjoint(paff, paff_i);
}
isl_local_space_free(ls);
isl_space_free(space);
isl_mat_free(var);
return paff;
error:
isl_aff_free(aff);
isl_basic_set_free(bset);
isl_pw_aff_free(paff);
isl_local_space_free(ls);
isl_space_free(space);
isl_mat_free(var);
return NULL;
}
/* Given a piecewise multi-affine expression of which the last input variable
* is the minimum of the bounds in "cst", plug in the value of the minimum.
* This minimum expression is given in "min_expr_pa".
* The set "min_expr" contains the same information, but in the form of a set.
* The variable is subsequently projected out.
*
* The implementation is similar to those of "split" and "split_domain".
* If the variable appears in a given expression, then minimum expression
* is plugged in. Otherwise, if the variable appears in the constraints
* and a split is required, then the domain is split. Otherwise, no split
* is performed.
*/
static __isl_give isl_pw_multi_aff *split_domain_pma(
__isl_take isl_pw_multi_aff *opt, __isl_take isl_pw_aff *min_expr_pa,
__isl_take isl_set *min_expr, __isl_take isl_mat *cst)
{
int n_in;
int i;
isl_space *space;
isl_pw_multi_aff *res;
if (!opt || !min_expr || !cst)
goto error;
n_in = isl_pw_multi_aff_dim(opt, isl_dim_in);
space = isl_pw_multi_aff_get_space(opt);
space = isl_space_drop_dims(space, isl_dim_in, n_in - 1, 1);
res = isl_pw_multi_aff_empty(space);
for (i = 0; i < opt->n; ++i) {
isl_pw_multi_aff *pma;
pma = isl_pw_multi_aff_alloc(isl_set_copy(opt->p[i].set),
isl_multi_aff_copy(opt->p[i].maff));
if (need_substitution(opt->p[i].maff))
pma = isl_pw_multi_aff_substitute(pma,
isl_dim_in, n_in - 1, min_expr_pa);
else if (need_split_set(opt->p[i].set, cst))
pma = isl_pw_multi_aff_intersect_domain(pma,
isl_set_copy(min_expr));
pma = isl_pw_multi_aff_project_out(pma,
isl_dim_in, n_in - 1, 1);
res = isl_pw_multi_aff_add_disjoint(res, pma);
}
isl_pw_multi_aff_free(opt);
isl_pw_aff_free(min_expr_pa);
isl_set_free(min_expr);
isl_mat_free(cst);
return res;
error:
isl_pw_multi_aff_free(opt);
isl_pw_aff_free(min_expr_pa);
isl_set_free(min_expr);
isl_mat_free(cst);
return NULL;
}
static __isl_give isl_pw_multi_aff *basic_map_partial_lexopt_pma(
__isl_take isl_basic_map *bmap, __isl_take isl_basic_set *dom,
__isl_give isl_set **empty, int max);
/* This function is called from basic_map_partial_lexopt_symm.
* The last variable of "bmap" and "dom" corresponds to the minimum
* of the bounds in "cst". "map_space" is the space of the original
* input relation (of basic_map_partial_lexopt_symm) and "set_space"
* is the space of the original domain.
*
* We recursively call basic_map_partial_lexopt and then plug in
* the definition of the minimum in the result.
*/
static __isl_give union isl_lex_res basic_map_partial_lexopt_symm_pma_core(
__isl_take isl_basic_map *bmap, __isl_take isl_basic_set *dom,
__isl_give isl_set **empty, int max, __isl_take isl_mat *cst,
__isl_take isl_space *map_space, __isl_take isl_space *set_space)
{
isl_pw_multi_aff *opt;
isl_pw_aff *min_expr_pa;
isl_set *min_expr;
union isl_lex_res res;
min_expr = set_minimum(isl_basic_set_get_space(dom), isl_mat_copy(cst));
min_expr_pa = set_minimum_pa(isl_basic_set_get_space(dom),
isl_mat_copy(cst));
opt = basic_map_partial_lexopt_pma(bmap, dom, empty, max);
if (empty) {
*empty = split(*empty,
isl_set_copy(min_expr), isl_mat_copy(cst));
*empty = isl_set_reset_space(*empty, set_space);
}
opt = split_domain_pma(opt, min_expr_pa, min_expr, cst);
opt = isl_pw_multi_aff_reset_space(opt, map_space);
res.pma = opt;
return res;
}
static __isl_give isl_pw_multi_aff *basic_map_partial_lexopt_symm_pma(
__isl_take isl_basic_map *bmap, __isl_take isl_basic_set *dom,
__isl_give isl_set **empty, int max, int first, int second)
{
return basic_map_partial_lexopt_symm(bmap, dom, empty, max,
first, second, &basic_map_partial_lexopt_symm_pma_core).pma;
}
/* Recursive part of isl_basic_map_partial_lexopt_pw_multi_aff, after detecting
* equalities and removing redundant constraints.
*
* We first check if there are any parallel constraints (left).
* If not, we are in the base case.
* If there are parallel constraints, we replace them by a single
* constraint in basic_map_partial_lexopt_symm_pma and then call
* this function recursively to look for more parallel constraints.
*/
static __isl_give isl_pw_multi_aff *basic_map_partial_lexopt_pma(
__isl_take isl_basic_map *bmap, __isl_take isl_basic_set *dom,
__isl_give isl_set **empty, int max)
{
int par = 0;
int first, second;
if (!bmap)
goto error;
if (bmap->ctx->opt->pip_symmetry)
par = parallel_constraints(bmap, &first, &second);
if (par < 0)
goto error;
if (!par)
return basic_map_partial_lexopt_base_pma(bmap, dom, empty, max);
return basic_map_partial_lexopt_symm_pma(bmap, dom, empty, max,
first, second);
error:
isl_basic_set_free(dom);
isl_basic_map_free(bmap);
return NULL;
}
/* Compute the lexicographic minimum (or maximum if "max" is set)
* of "bmap" over the domain "dom" and return the result as a piecewise
* multi-affine expression.
* If "empty" is not NULL, then *empty is assigned a set that
* contains those parts of the domain where there is no solution.
* If "bmap" is marked as rational (ISL_BASIC_MAP_RATIONAL),
* then we compute the rational optimum. Otherwise, we compute
* the integral optimum.
*
* We perform some preprocessing. As the PILP solver does not
* handle implicit equalities very well, we first make sure all
* the equalities are explicitly available.
*
* We also add context constraints to the basic map and remove
* redundant constraints. This is only needed because of the
* way we handle simple symmetries. In particular, we currently look
* for symmetries on the constraints, before we set up the main tableau.
* It is then no good to look for symmetries on possibly redundant constraints.
*/
__isl_give isl_pw_multi_aff *isl_basic_map_partial_lexopt_pw_multi_aff(
__isl_take isl_basic_map *bmap, __isl_take isl_basic_set *dom,
__isl_give isl_set **empty, int max)
{
if (empty)
*empty = NULL;
if (!bmap || !dom)
goto error;
isl_assert(bmap->ctx,
isl_basic_map_compatible_domain(bmap, dom), goto error);
if (isl_basic_set_dim(dom, isl_dim_all) == 0)
return basic_map_partial_lexopt_pma(bmap, dom, empty, max);
bmap = isl_basic_map_intersect_domain(bmap, isl_basic_set_copy(dom));
bmap = isl_basic_map_detect_equalities(bmap);
bmap = isl_basic_map_remove_redundancies(bmap);
return basic_map_partial_lexopt_pma(bmap, dom, empty, max);
error:
isl_basic_set_free(dom);
isl_basic_map_free(bmap);
return NULL;
}