nexmon – Rev 1
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/*
* Copyright 2010 INRIA Saclay
*
* Use of this software is governed by the GNU LGPLv2.1 license
*
* Written by Sven Verdoolaege, INRIA Saclay - Ile-de-France,
* Parc Club Orsay Universite, ZAC des vignes, 4 rue Jacques Monod,
* 91893 Orsay, France
*/
#define ISL_DIM_H
#include <isl_map_private.h>
#include <isl_union_map_private.h>
#include <isl_polynomial_private.h>
#include <isl_point_private.h>
#include <isl_space_private.h>
#include <isl/lp.h>
#include <isl/seq.h>
#include <isl_mat_private.h>
#include <isl_config.h>
enum isl_fold isl_fold_type_negate(enum isl_fold type)
{
switch (type) {
case isl_fold_min:
return isl_fold_max;
case isl_fold_max:
return isl_fold_min;
case isl_fold_list:
return isl_fold_list;
}
isl_die(NULL, isl_error_internal, "unhandled isl_fold type", abort());
}
static __isl_give isl_qpolynomial_fold *qpolynomial_fold_alloc(
enum isl_fold type, __isl_take isl_space *dim, int n)
{
isl_qpolynomial_fold *fold;
if (!dim)
goto error;
isl_assert(dim->ctx, n >= 0, goto error);
fold = isl_calloc(dim->ctx, struct isl_qpolynomial_fold,
sizeof(struct isl_qpolynomial_fold) +
(n - 1) * sizeof(struct isl_qpolynomial *));
if (!fold)
goto error;
fold->ref = 1;
fold->size = n;
fold->n = 0;
fold->type = type;
fold->dim = dim;
return fold;
error:
isl_space_free(dim);
return NULL;
}
isl_ctx *isl_qpolynomial_fold_get_ctx(__isl_keep isl_qpolynomial_fold *fold)
{
return fold ? fold->dim->ctx : NULL;
}
__isl_give isl_space *isl_qpolynomial_fold_get_domain_space(
__isl_keep isl_qpolynomial_fold *fold)
{
return fold ? isl_space_copy(fold->dim) : NULL;
}
__isl_give isl_space *isl_qpolynomial_fold_get_space(
__isl_keep isl_qpolynomial_fold *fold)
{
isl_space *space;
if (!fold)
return NULL;
space = isl_space_copy(fold->dim);
space = isl_space_from_domain(space);
space = isl_space_add_dims(space, isl_dim_out, 1);
return space;
}
__isl_give isl_qpolynomial_fold *isl_qpolynomial_fold_reset_domain_space(
__isl_take isl_qpolynomial_fold *fold, __isl_take isl_space *dim)
{
int i;
fold = isl_qpolynomial_fold_cow(fold);
if (!fold || !dim)
goto error;
for (i = 0; i < fold->n; ++i) {
fold->qp[i] = isl_qpolynomial_reset_domain_space(fold->qp[i],
isl_space_copy(dim));
if (!fold->qp[i])
goto error;
}
isl_space_free(fold->dim);
fold->dim = dim;
return fold;
error:
isl_qpolynomial_fold_free(fold);
isl_space_free(dim);
return NULL;
}
/* Reset the space of "fold". This function is called from isl_pw_templ.c
* and doesn't know if the space of an element object is represented
* directly or through its domain. It therefore passes along both.
*/
__isl_give isl_qpolynomial_fold *isl_qpolynomial_fold_reset_space_and_domain(
__isl_take isl_qpolynomial_fold *fold, __isl_take isl_space *space,
__isl_take isl_space *domain)
{
isl_space_free(space);
return isl_qpolynomial_fold_reset_domain_space(fold, domain);
}
int isl_qpolynomial_fold_involves_dims(__isl_keep isl_qpolynomial_fold *fold,
enum isl_dim_type type, unsigned first, unsigned n)
{
int i;
if (!fold)
return -1;
if (fold->n == 0 || n == 0)
return 0;
for (i = 0; i < fold->n; ++i) {
int involves = isl_qpolynomial_involves_dims(fold->qp[i],
type, first, n);
if (involves < 0 || involves)
return involves;
}
return 0;
}
__isl_give isl_qpolynomial_fold *isl_qpolynomial_fold_set_dim_name(
__isl_take isl_qpolynomial_fold *fold,
enum isl_dim_type type, unsigned pos, const char *s)
{
int i;
fold = isl_qpolynomial_fold_cow(fold);
if (!fold)
return NULL;
fold->dim = isl_space_set_dim_name(fold->dim, type, pos, s);
if (!fold->dim)
goto error;
for (i = 0; i < fold->n; ++i) {
fold->qp[i] = isl_qpolynomial_set_dim_name(fold->qp[i],
type, pos, s);
if (!fold->qp[i])
goto error;
}
return fold;
error:
isl_qpolynomial_fold_free(fold);
return NULL;
}
__isl_give isl_qpolynomial_fold *isl_qpolynomial_fold_drop_dims(
__isl_take isl_qpolynomial_fold *fold,
enum isl_dim_type type, unsigned first, unsigned n)
{
int i;
enum isl_dim_type set_type;
if (!fold)
return NULL;
if (n == 0)
return fold;
set_type = type == isl_dim_in ? isl_dim_set : type;
fold = isl_qpolynomial_fold_cow(fold);
if (!fold)
return NULL;
fold->dim = isl_space_drop_dims(fold->dim, set_type, first, n);
if (!fold->dim)
goto error;
for (i = 0; i < fold->n; ++i) {
fold->qp[i] = isl_qpolynomial_drop_dims(fold->qp[i],
type, first, n);
if (!fold->qp[i])
goto error;
}
return fold;
error:
isl_qpolynomial_fold_free(fold);
return NULL;
}
__isl_give isl_qpolynomial_fold *isl_qpolynomial_fold_insert_dims(
__isl_take isl_qpolynomial_fold *fold,
enum isl_dim_type type, unsigned first, unsigned n)
{
int i;
if (!fold)
return NULL;
if (n == 0 && !isl_space_is_named_or_nested(fold->dim, type))
return fold;
fold = isl_qpolynomial_fold_cow(fold);
if (!fold)
return NULL;
fold->dim = isl_space_insert_dims(fold->dim, type, first, n);
if (!fold->dim)
goto error;
for (i = 0; i < fold->n; ++i) {
fold->qp[i] = isl_qpolynomial_insert_dims(fold->qp[i],
type, first, n);
if (!fold->qp[i])
goto error;
}
return fold;
error:
isl_qpolynomial_fold_free(fold);
return NULL;
}
static int isl_qpolynomial_cst_sign(__isl_keep isl_qpolynomial *qp)
{
struct isl_upoly_cst *cst;
cst = isl_upoly_as_cst(qp->upoly);
if (!cst)
return 0;
return isl_int_sgn(cst->n) < 0 ? -1 : 1;
}
static int isl_qpolynomial_aff_sign(__isl_keep isl_set *set,
__isl_keep isl_qpolynomial *qp)
{
enum isl_lp_result res;
isl_vec *aff;
isl_int opt;
int sgn = 0;
aff = isl_qpolynomial_extract_affine(qp);
if (!aff)
return 0;
isl_int_init(opt);
res = isl_set_solve_lp(set, 0, aff->el + 1, aff->el[0],
&opt, NULL, NULL);
if (res == isl_lp_error)
goto done;
if (res == isl_lp_empty ||
(res == isl_lp_ok && !isl_int_is_neg(opt))) {
sgn = 1;
goto done;
}
res = isl_set_solve_lp(set, 1, aff->el + 1, aff->el[0],
&opt, NULL, NULL);
if (res == isl_lp_ok && !isl_int_is_pos(opt))
sgn = -1;
done:
isl_int_clear(opt);
isl_vec_free(aff);
return sgn;
}
/* Determine, if possible, the sign of the quasipolynomial "qp" on
* the domain "set".
*
* If qp is a constant, then the problem is trivial.
* If qp is linear, then we check if the minimum of the corresponding
* affine constraint is non-negative or if the maximum is non-positive.
*
* Otherwise, we check if the outermost variable "v" has a lower bound "l"
* in "set". If so, we write qp(v,v') as
*
* q(v,v') * (v - l) + r(v')
*
* if q(v,v') and r(v') have the same known sign, then the original
* quasipolynomial has the same sign as well.
*
* Return
* -1 if qp <= 0
* 1 if qp >= 0
* 0 if unknown
*/
static int isl_qpolynomial_sign(__isl_keep isl_set *set,
__isl_keep isl_qpolynomial *qp)
{
int d;
int i;
int is;
struct isl_upoly_rec *rec;
isl_vec *v;
isl_int l;
enum isl_lp_result res;
int sgn = 0;
is = isl_qpolynomial_is_cst(qp, NULL, NULL);
if (is < 0)
return 0;
if (is)
return isl_qpolynomial_cst_sign(qp);
is = isl_qpolynomial_is_affine(qp);
if (is < 0)
return 0;
if (is)
return isl_qpolynomial_aff_sign(set, qp);
if (qp->div->n_row > 0)
return 0;
rec = isl_upoly_as_rec(qp->upoly);
if (!rec)
return 0;
d = isl_space_dim(qp->dim, isl_dim_all);
v = isl_vec_alloc(set->ctx, 2 + d);
if (!v)
return 0;
isl_seq_clr(v->el + 1, 1 + d);
isl_int_set_si(v->el[0], 1);
isl_int_set_si(v->el[2 + qp->upoly->var], 1);
isl_int_init(l);
res = isl_set_solve_lp(set, 0, v->el + 1, v->el[0], &l, NULL, NULL);
if (res == isl_lp_ok) {
isl_qpolynomial *min;
isl_qpolynomial *base;
isl_qpolynomial *r, *q;
isl_qpolynomial *t;
min = isl_qpolynomial_cst_on_domain(isl_space_copy(qp->dim), l);
base = isl_qpolynomial_var_pow_on_domain(isl_space_copy(qp->dim),
qp->upoly->var, 1);
r = isl_qpolynomial_alloc(isl_space_copy(qp->dim), 0,
isl_upoly_copy(rec->p[rec->n - 1]));
q = isl_qpolynomial_copy(r);
for (i = rec->n - 2; i >= 0; --i) {
r = isl_qpolynomial_mul(r, isl_qpolynomial_copy(min));
t = isl_qpolynomial_alloc(isl_space_copy(qp->dim), 0,
isl_upoly_copy(rec->p[i]));
r = isl_qpolynomial_add(r, t);
if (i == 0)
break;
q = isl_qpolynomial_mul(q, isl_qpolynomial_copy(base));
q = isl_qpolynomial_add(q, isl_qpolynomial_copy(r));
}
if (isl_qpolynomial_is_zero(q))
sgn = isl_qpolynomial_sign(set, r);
else if (isl_qpolynomial_is_zero(r))
sgn = isl_qpolynomial_sign(set, q);
else {
int sgn_q, sgn_r;
sgn_r = isl_qpolynomial_sign(set, r);
sgn_q = isl_qpolynomial_sign(set, q);
if (sgn_r == sgn_q)
sgn = sgn_r;
}
isl_qpolynomial_free(min);
isl_qpolynomial_free(base);
isl_qpolynomial_free(q);
isl_qpolynomial_free(r);
}
isl_int_clear(l);
isl_vec_free(v);
return sgn;
}
__isl_give isl_qpolynomial_fold *isl_qpolynomial_fold_fold_on_domain(
__isl_keep isl_set *set,
__isl_take isl_qpolynomial_fold *fold1,
__isl_take isl_qpolynomial_fold *fold2)
{
int i, j;
int n1;
struct isl_qpolynomial_fold *res = NULL;
int better;
if (!fold1 || !fold2)
goto error;
isl_assert(fold1->dim->ctx, fold1->type == fold2->type, goto error);
isl_assert(fold1->dim->ctx, isl_space_is_equal(fold1->dim, fold2->dim),
goto error);
better = fold1->type == isl_fold_max ? -1 : 1;
if (isl_qpolynomial_fold_is_empty(fold1)) {
isl_qpolynomial_fold_free(fold1);
return fold2;
}
if (isl_qpolynomial_fold_is_empty(fold2)) {
isl_qpolynomial_fold_free(fold2);
return fold1;
}
res = qpolynomial_fold_alloc(fold1->type, isl_space_copy(fold1->dim),
fold1->n + fold2->n);
if (!res)
goto error;
for (i = 0; i < fold1->n; ++i) {
res->qp[res->n] = isl_qpolynomial_copy(fold1->qp[i]);
if (!res->qp[res->n])
goto error;
res->n++;
}
n1 = res->n;
for (i = 0; i < fold2->n; ++i) {
for (j = n1 - 1; j >= 0; --j) {
isl_qpolynomial *d;
int sgn;
d = isl_qpolynomial_sub(
isl_qpolynomial_copy(res->qp[j]),
isl_qpolynomial_copy(fold2->qp[i]));
sgn = isl_qpolynomial_sign(set, d);
isl_qpolynomial_free(d);
if (sgn == 0)
continue;
if (sgn != better)
break;
isl_qpolynomial_free(res->qp[j]);
if (j != n1 - 1)
res->qp[j] = res->qp[n1 - 1];
n1--;
if (n1 != res->n - 1)
res->qp[n1] = res->qp[res->n - 1];
res->n--;
}
if (j >= 0)
continue;
res->qp[res->n] = isl_qpolynomial_copy(fold2->qp[i]);
if (!res->qp[res->n])
goto error;
res->n++;
}
isl_qpolynomial_fold_free(fold1);
isl_qpolynomial_fold_free(fold2);
return res;
error:
isl_qpolynomial_fold_free(res);
isl_qpolynomial_fold_free(fold1);
isl_qpolynomial_fold_free(fold2);
return NULL;
}
__isl_give isl_qpolynomial_fold *isl_qpolynomial_fold_add_qpolynomial(
__isl_take isl_qpolynomial_fold *fold, __isl_take isl_qpolynomial *qp)
{
int i;
if (!fold || !qp)
goto error;
if (isl_qpolynomial_is_zero(qp)) {
isl_qpolynomial_free(qp);
return fold;
}
fold = isl_qpolynomial_fold_cow(fold);
if (!fold)
goto error;
for (i = 0; i < fold->n; ++i) {
fold->qp[i] = isl_qpolynomial_add(fold->qp[i],
isl_qpolynomial_copy(qp));
if (!fold->qp[i])
goto error;
}
isl_qpolynomial_free(qp);
return fold;
error:
isl_qpolynomial_fold_free(fold);
isl_qpolynomial_free(qp);
return NULL;
}
__isl_give isl_qpolynomial_fold *isl_qpolynomial_fold_add_on_domain(
__isl_keep isl_set *dom,
__isl_take isl_qpolynomial_fold *fold1,
__isl_take isl_qpolynomial_fold *fold2)
{
int i;
isl_qpolynomial_fold *res = NULL;
if (!fold1 || !fold2)
goto error;
if (isl_qpolynomial_fold_is_empty(fold1)) {
isl_qpolynomial_fold_free(fold1);
return fold2;
}
if (isl_qpolynomial_fold_is_empty(fold2)) {
isl_qpolynomial_fold_free(fold2);
return fold1;
}
if (fold1->n == 1 && fold2->n != 1)
return isl_qpolynomial_fold_add_on_domain(dom, fold2, fold1);
if (fold2->n == 1) {
res = isl_qpolynomial_fold_add_qpolynomial(fold1,
isl_qpolynomial_copy(fold2->qp[0]));
isl_qpolynomial_fold_free(fold2);
return res;
}
res = isl_qpolynomial_fold_add_qpolynomial(
isl_qpolynomial_fold_copy(fold1),
isl_qpolynomial_copy(fold2->qp[0]));
for (i = 1; i < fold2->n; ++i) {
isl_qpolynomial_fold *res_i;
res_i = isl_qpolynomial_fold_add_qpolynomial(
isl_qpolynomial_fold_copy(fold1),
isl_qpolynomial_copy(fold2->qp[i]));
res = isl_qpolynomial_fold_fold_on_domain(dom, res, res_i);
}
isl_qpolynomial_fold_free(fold1);
isl_qpolynomial_fold_free(fold2);
return res;
error:
isl_qpolynomial_fold_free(res);
isl_qpolynomial_fold_free(fold1);
isl_qpolynomial_fold_free(fold2);
return NULL;
}
__isl_give isl_qpolynomial_fold *isl_qpolynomial_fold_substitute_equalities(
__isl_take isl_qpolynomial_fold *fold, __isl_take isl_basic_set *eq)
{
int i;
if (!fold || !eq)
goto error;
fold = isl_qpolynomial_fold_cow(fold);
if (!fold)
return NULL;
for (i = 0; i < fold->n; ++i) {
fold->qp[i] = isl_qpolynomial_substitute_equalities(fold->qp[i],
isl_basic_set_copy(eq));
if (!fold->qp[i])
goto error;
}
isl_basic_set_free(eq);
return fold;
error:
isl_basic_set_free(eq);
isl_qpolynomial_fold_free(fold);
return NULL;
}
__isl_give isl_qpolynomial_fold *isl_qpolynomial_fold_gist(
__isl_take isl_qpolynomial_fold *fold, __isl_take isl_set *context)
{
int i;
if (!fold || !context)
goto error;
fold = isl_qpolynomial_fold_cow(fold);
if (!fold)
return NULL;
for (i = 0; i < fold->n; ++i) {
fold->qp[i] = isl_qpolynomial_gist(fold->qp[i],
isl_set_copy(context));
if (!fold->qp[i])
goto error;
}
isl_set_free(context);
return fold;
error:
isl_set_free(context);
isl_qpolynomial_fold_free(fold);
return NULL;
}
__isl_give isl_qpolynomial_fold *isl_qpolynomial_fold_gist_params(
__isl_take isl_qpolynomial_fold *fold, __isl_take isl_set *context)
{
isl_space *space = isl_qpolynomial_fold_get_domain_space(fold);
isl_set *dom_context = isl_set_universe(space);
dom_context = isl_set_intersect_params(dom_context, context);
return isl_qpolynomial_fold_gist(fold, dom_context);
}
#define HAS_TYPE
#undef PW
#define PW isl_pw_qpolynomial_fold
#undef EL
#define EL isl_qpolynomial_fold
#undef EL_IS_ZERO
#define EL_IS_ZERO is_empty
#undef ZERO
#define ZERO zero
#undef IS_ZERO
#define IS_ZERO is_zero
#undef FIELD
#define FIELD fold
#undef DEFAULT_IS_ZERO
#define DEFAULT_IS_ZERO 1
#define NO_NEG
#include <isl_pw_templ.c>
#undef UNION
#define UNION isl_union_pw_qpolynomial_fold
#undef PART
#define PART isl_pw_qpolynomial_fold
#undef PARTS
#define PARTS pw_qpolynomial_fold
#define ALIGN_DOMAIN
#include <isl_union_templ.c>
__isl_give isl_qpolynomial_fold *isl_qpolynomial_fold_empty(enum isl_fold type,
__isl_take isl_space *dim)
{
return qpolynomial_fold_alloc(type, dim, 0);
}
__isl_give isl_qpolynomial_fold *isl_qpolynomial_fold_alloc(
enum isl_fold type, __isl_take isl_qpolynomial *qp)
{
isl_qpolynomial_fold *fold;
if (!qp)
return NULL;
fold = qpolynomial_fold_alloc(type, isl_space_copy(qp->dim), 1);
if (!fold)
goto error;
fold->qp[0] = qp;
fold->n++;
return fold;
error:
isl_qpolynomial_fold_free(fold);
isl_qpolynomial_free(qp);
return NULL;
}
__isl_give isl_qpolynomial_fold *isl_qpolynomial_fold_copy(
__isl_keep isl_qpolynomial_fold *fold)
{
if (!fold)
return NULL;
fold->ref++;
return fold;
}
__isl_give isl_qpolynomial_fold *isl_qpolynomial_fold_dup(
__isl_keep isl_qpolynomial_fold *fold)
{
int i;
isl_qpolynomial_fold *dup;
if (!fold)
return NULL;
dup = qpolynomial_fold_alloc(fold->type,
isl_space_copy(fold->dim), fold->n);
if (!dup)
return NULL;
dup->n = fold->n;
for (i = 0; i < fold->n; ++i) {
dup->qp[i] = isl_qpolynomial_copy(fold->qp[i]);
if (!dup->qp[i])
goto error;
}
return dup;
error:
isl_qpolynomial_fold_free(dup);
return NULL;
}
__isl_give isl_qpolynomial_fold *isl_qpolynomial_fold_cow(
__isl_take isl_qpolynomial_fold *fold)
{
if (!fold)
return NULL;
if (fold->ref == 1)
return fold;
fold->ref--;
return isl_qpolynomial_fold_dup(fold);
}
void isl_qpolynomial_fold_free(__isl_take isl_qpolynomial_fold *fold)
{
int i;
if (!fold)
return;
if (--fold->ref > 0)
return;
for (i = 0; i < fold->n; ++i)
isl_qpolynomial_free(fold->qp[i]);
isl_space_free(fold->dim);
free(fold);
}
int isl_qpolynomial_fold_is_empty(__isl_keep isl_qpolynomial_fold *fold)
{
if (!fold)
return -1;
return fold->n == 0;
}
__isl_give isl_qpolynomial_fold *isl_qpolynomial_fold_fold(
__isl_take isl_qpolynomial_fold *fold1,
__isl_take isl_qpolynomial_fold *fold2)
{
int i;
struct isl_qpolynomial_fold *res = NULL;
if (!fold1 || !fold2)
goto error;
isl_assert(fold1->dim->ctx, fold1->type == fold2->type, goto error);
isl_assert(fold1->dim->ctx, isl_space_is_equal(fold1->dim, fold2->dim),
goto error);
if (isl_qpolynomial_fold_is_empty(fold1)) {
isl_qpolynomial_fold_free(fold1);
return fold2;
}
if (isl_qpolynomial_fold_is_empty(fold2)) {
isl_qpolynomial_fold_free(fold2);
return fold1;
}
res = qpolynomial_fold_alloc(fold1->type, isl_space_copy(fold1->dim),
fold1->n + fold2->n);
if (!res)
goto error;
for (i = 0; i < fold1->n; ++i) {
res->qp[res->n] = isl_qpolynomial_copy(fold1->qp[i]);
if (!res->qp[res->n])
goto error;
res->n++;
}
for (i = 0; i < fold2->n; ++i) {
res->qp[res->n] = isl_qpolynomial_copy(fold2->qp[i]);
if (!res->qp[res->n])
goto error;
res->n++;
}
isl_qpolynomial_fold_free(fold1);
isl_qpolynomial_fold_free(fold2);
return res;
error:
isl_qpolynomial_fold_free(res);
isl_qpolynomial_fold_free(fold1);
isl_qpolynomial_fold_free(fold2);
return NULL;
}
__isl_give isl_pw_qpolynomial_fold *isl_pw_qpolynomial_fold_fold(
__isl_take isl_pw_qpolynomial_fold *pw1,
__isl_take isl_pw_qpolynomial_fold *pw2)
{
int i, j, n;
struct isl_pw_qpolynomial_fold *res;
isl_set *set;
if (!pw1 || !pw2)
goto error;
isl_assert(pw1->dim->ctx, isl_space_is_equal(pw1->dim, pw2->dim), goto error);
if (isl_pw_qpolynomial_fold_is_zero(pw1)) {
isl_pw_qpolynomial_fold_free(pw1);
return pw2;
}
if (isl_pw_qpolynomial_fold_is_zero(pw2)) {
isl_pw_qpolynomial_fold_free(pw2);
return pw1;
}
if (pw1->type != pw2->type)
isl_die(pw1->dim->ctx, isl_error_invalid,
"fold types don't match", goto error);
n = (pw1->n + 1) * (pw2->n + 1);
res = isl_pw_qpolynomial_fold_alloc_size(isl_space_copy(pw1->dim),
pw1->type, n);
for (i = 0; i < pw1->n; ++i) {
set = isl_set_copy(pw1->p[i].set);
for (j = 0; j < pw2->n; ++j) {
struct isl_set *common;
isl_qpolynomial_fold *sum;
set = isl_set_subtract(set,
isl_set_copy(pw2->p[j].set));
common = isl_set_intersect(isl_set_copy(pw1->p[i].set),
isl_set_copy(pw2->p[j].set));
if (isl_set_plain_is_empty(common)) {
isl_set_free(common);
continue;
}
sum = isl_qpolynomial_fold_fold_on_domain(common,
isl_qpolynomial_fold_copy(pw1->p[i].fold),
isl_qpolynomial_fold_copy(pw2->p[j].fold));
res = isl_pw_qpolynomial_fold_add_piece(res, common, sum);
}
res = isl_pw_qpolynomial_fold_add_piece(res, set,
isl_qpolynomial_fold_copy(pw1->p[i].fold));
}
for (j = 0; j < pw2->n; ++j) {
set = isl_set_copy(pw2->p[j].set);
for (i = 0; i < pw1->n; ++i)
set = isl_set_subtract(set, isl_set_copy(pw1->p[i].set));
res = isl_pw_qpolynomial_fold_add_piece(res, set,
isl_qpolynomial_fold_copy(pw2->p[j].fold));
}
isl_pw_qpolynomial_fold_free(pw1);
isl_pw_qpolynomial_fold_free(pw2);
return res;
error:
isl_pw_qpolynomial_fold_free(pw1);
isl_pw_qpolynomial_fold_free(pw2);
return NULL;
}
__isl_give isl_union_pw_qpolynomial_fold *isl_union_pw_qpolynomial_fold_fold_pw_qpolynomial_fold(
__isl_take isl_union_pw_qpolynomial_fold *u,
__isl_take isl_pw_qpolynomial_fold *part)
{
uint32_t hash;
struct isl_hash_table_entry *entry;
u = isl_union_pw_qpolynomial_fold_cow(u);
if (!part || !u)
goto error;
isl_assert(u->dim->ctx, isl_space_match(part->dim, isl_dim_param, u->dim,
isl_dim_param), goto error);
hash = isl_space_get_hash(part->dim);
entry = isl_hash_table_find(u->dim->ctx, &u->table, hash,
&has_dim, part->dim, 1);
if (!entry)
goto error;
if (!entry->data)
entry->data = part;
else {
entry->data = isl_pw_qpolynomial_fold_fold(entry->data,
isl_pw_qpolynomial_fold_copy(part));
if (!entry->data)
goto error;
isl_pw_qpolynomial_fold_free(part);
}
return u;
error:
isl_pw_qpolynomial_fold_free(part);
isl_union_pw_qpolynomial_fold_free(u);
return NULL;
}
static int fold_part(__isl_take isl_pw_qpolynomial_fold *part, void *user)
{
isl_union_pw_qpolynomial_fold **u;
u = (isl_union_pw_qpolynomial_fold **)user;
*u = isl_union_pw_qpolynomial_fold_fold_pw_qpolynomial_fold(*u, part);
return 0;
}
__isl_give isl_union_pw_qpolynomial_fold *isl_union_pw_qpolynomial_fold_fold(
__isl_take isl_union_pw_qpolynomial_fold *u1,
__isl_take isl_union_pw_qpolynomial_fold *u2)
{
u1 = isl_union_pw_qpolynomial_fold_cow(u1);
if (!u1 || !u2)
goto error;
if (isl_union_pw_qpolynomial_fold_foreach_pw_qpolynomial_fold(u2,
&fold_part, &u1) < 0)
goto error;
isl_union_pw_qpolynomial_fold_free(u2);
return u1;
error:
isl_union_pw_qpolynomial_fold_free(u1);
isl_union_pw_qpolynomial_fold_free(u2);
return NULL;
}
__isl_give isl_pw_qpolynomial_fold *isl_pw_qpolynomial_fold_from_pw_qpolynomial(
enum isl_fold type, __isl_take isl_pw_qpolynomial *pwqp)
{
int i;
isl_pw_qpolynomial_fold *pwf;
if (!pwqp)
return NULL;
pwf = isl_pw_qpolynomial_fold_alloc_size(isl_space_copy(pwqp->dim),
type, pwqp->n);
for (i = 0; i < pwqp->n; ++i)
pwf = isl_pw_qpolynomial_fold_add_piece(pwf,
isl_set_copy(pwqp->p[i].set),
isl_qpolynomial_fold_alloc(type,
isl_qpolynomial_copy(pwqp->p[i].qp)));
isl_pw_qpolynomial_free(pwqp);
return pwf;
}
__isl_give isl_pw_qpolynomial_fold *isl_pw_qpolynomial_fold_add(
__isl_take isl_pw_qpolynomial_fold *pwf1,
__isl_take isl_pw_qpolynomial_fold *pwf2)
{
return isl_pw_qpolynomial_fold_union_add_(pwf1, pwf2);
}
int isl_qpolynomial_fold_plain_is_equal(__isl_keep isl_qpolynomial_fold *fold1,
__isl_keep isl_qpolynomial_fold *fold2)
{
int i;
if (!fold1 || !fold2)
return -1;
if (fold1->n != fold2->n)
return 0;
/* We probably want to sort the qps first... */
for (i = 0; i < fold1->n; ++i) {
int eq = isl_qpolynomial_plain_is_equal(fold1->qp[i], fold2->qp[i]);
if (eq < 0 || !eq)
return eq;
}
return 1;
}
__isl_give isl_qpolynomial *isl_qpolynomial_fold_eval(
__isl_take isl_qpolynomial_fold *fold, __isl_take isl_point *pnt)
{
isl_qpolynomial *qp;
if (!fold || !pnt)
goto error;
isl_assert(pnt->dim->ctx, isl_space_is_equal(pnt->dim, fold->dim), goto error);
isl_assert(pnt->dim->ctx,
fold->type == isl_fold_max || fold->type == isl_fold_min,
goto error);
if (fold->n == 0)
qp = isl_qpolynomial_zero_on_domain(isl_space_copy(fold->dim));
else {
int i;
qp = isl_qpolynomial_eval(isl_qpolynomial_copy(fold->qp[0]),
isl_point_copy(pnt));
for (i = 1; i < fold->n; ++i) {
isl_qpolynomial *qp_i;
qp_i = isl_qpolynomial_eval(
isl_qpolynomial_copy(fold->qp[i]),
isl_point_copy(pnt));
if (fold->type == isl_fold_max)
qp = isl_qpolynomial_max_cst(qp, qp_i);
else
qp = isl_qpolynomial_min_cst(qp, qp_i);
}
}
isl_qpolynomial_fold_free(fold);
isl_point_free(pnt);
return qp;
error:
isl_qpolynomial_fold_free(fold);
isl_point_free(pnt);
return NULL;
}
size_t isl_pw_qpolynomial_fold_size(__isl_keep isl_pw_qpolynomial_fold *pwf)
{
int i;
size_t n = 0;
for (i = 0; i < pwf->n; ++i)
n += pwf->p[i].fold->n;
return n;
}
__isl_give isl_qpolynomial *isl_qpolynomial_fold_opt_on_domain(
__isl_take isl_qpolynomial_fold *fold, __isl_take isl_set *set, int max)
{
int i;
isl_qpolynomial *opt;
if (!set || !fold)
goto error;
if (fold->n == 0) {
isl_space *dim = isl_space_copy(fold->dim);
isl_set_free(set);
isl_qpolynomial_fold_free(fold);
return isl_qpolynomial_zero_on_domain(dim);
}
opt = isl_qpolynomial_opt_on_domain(isl_qpolynomial_copy(fold->qp[0]),
isl_set_copy(set), max);
for (i = 1; i < fold->n; ++i) {
isl_qpolynomial *opt_i;
opt_i = isl_qpolynomial_opt_on_domain(
isl_qpolynomial_copy(fold->qp[i]),
isl_set_copy(set), max);
if (max)
opt = isl_qpolynomial_max_cst(opt, opt_i);
else
opt = isl_qpolynomial_min_cst(opt, opt_i);
}
isl_set_free(set);
isl_qpolynomial_fold_free(fold);
return opt;
error:
isl_set_free(set);
isl_qpolynomial_fold_free(fold);
return NULL;
}
/* Check whether for each quasi-polynomial in "fold2" there is
* a quasi-polynomial in "fold1" that dominates it on "set".
*/
static int qpolynomial_fold_covers_on_domain(__isl_keep isl_set *set,
__isl_keep isl_qpolynomial_fold *fold1,
__isl_keep isl_qpolynomial_fold *fold2)
{
int i, j;
int covers;
if (!set || !fold1 || !fold2)
return -1;
covers = fold1->type == isl_fold_max ? 1 : -1;
for (i = 0; i < fold2->n; ++i) {
for (j = 0; j < fold1->n; ++j) {
isl_qpolynomial *d;
int sgn;
d = isl_qpolynomial_sub(
isl_qpolynomial_copy(fold1->qp[j]),
isl_qpolynomial_copy(fold2->qp[i]));
sgn = isl_qpolynomial_sign(set, d);
isl_qpolynomial_free(d);
if (sgn == covers)
break;
}
if (j >= fold1->n)
return 0;
}
return 1;
}
/* Check whether "pwf1" dominated "pwf2", i.e., the domain of "pwf1" contains
* that of "pwf2" and on each cell, the corresponding fold from pwf1 dominates
* that of pwf2.
*/
int isl_pw_qpolynomial_fold_covers(__isl_keep isl_pw_qpolynomial_fold *pwf1,
__isl_keep isl_pw_qpolynomial_fold *pwf2)
{
int i, j;
isl_set *dom1, *dom2;
int is_subset;
if (!pwf1 || !pwf2)
return -1;
if (pwf2->n == 0)
return 1;
if (pwf1->n == 0)
return 0;
dom1 = isl_pw_qpolynomial_fold_domain(isl_pw_qpolynomial_fold_copy(pwf1));
dom2 = isl_pw_qpolynomial_fold_domain(isl_pw_qpolynomial_fold_copy(pwf2));
is_subset = isl_set_is_subset(dom2, dom1);
isl_set_free(dom1);
isl_set_free(dom2);
if (is_subset < 0 || !is_subset)
return is_subset;
for (i = 0; i < pwf2->n; ++i) {
for (j = 0; j < pwf1->n; ++j) {
int is_empty;
isl_set *common;
int covers;
common = isl_set_intersect(isl_set_copy(pwf1->p[j].set),
isl_set_copy(pwf2->p[i].set));
is_empty = isl_set_is_empty(common);
if (is_empty < 0 || is_empty) {
isl_set_free(common);
if (is_empty < 0)
return -1;
continue;
}
covers = qpolynomial_fold_covers_on_domain(common,
pwf1->p[j].fold, pwf2->p[i].fold);
isl_set_free(common);
if (covers < 0 || !covers)
return covers;
}
}
return 1;
}
__isl_give isl_qpolynomial_fold *isl_qpolynomial_fold_morph_domain(
__isl_take isl_qpolynomial_fold *fold, __isl_take isl_morph *morph)
{
int i;
isl_ctx *ctx;
if (!fold || !morph)
goto error;
ctx = fold->dim->ctx;
isl_assert(ctx, isl_space_is_equal(fold->dim, morph->dom->dim), goto error);
fold = isl_qpolynomial_fold_cow(fold);
if (!fold)
goto error;
isl_space_free(fold->dim);
fold->dim = isl_space_copy(morph->ran->dim);
if (!fold->dim)
goto error;
for (i = 0; i < fold->n; ++i) {
fold->qp[i] = isl_qpolynomial_morph_domain(fold->qp[i],
isl_morph_copy(morph));
if (!fold->qp[i])
goto error;
}
isl_morph_free(morph);
return fold;
error:
isl_qpolynomial_fold_free(fold);
isl_morph_free(morph);
return NULL;
}
enum isl_fold isl_qpolynomial_fold_get_type(__isl_keep isl_qpolynomial_fold *fold)
{
if (!fold)
return isl_fold_list;
return fold->type;
}
enum isl_fold isl_union_pw_qpolynomial_fold_get_type(
__isl_keep isl_union_pw_qpolynomial_fold *upwf)
{
if (!upwf)
return isl_fold_list;
return upwf->type;
}
__isl_give isl_qpolynomial_fold *isl_qpolynomial_fold_lift(
__isl_take isl_qpolynomial_fold *fold, __isl_take isl_space *dim)
{
int i;
if (!fold || !dim)
goto error;
if (isl_space_is_equal(fold->dim, dim)) {
isl_space_free(dim);
return fold;
}
fold = isl_qpolynomial_fold_cow(fold);
if (!fold)
goto error;
isl_space_free(fold->dim);
fold->dim = isl_space_copy(dim);
if (!fold->dim)
goto error;
for (i = 0; i < fold->n; ++i) {
fold->qp[i] = isl_qpolynomial_lift(fold->qp[i],
isl_space_copy(dim));
if (!fold->qp[i])
goto error;
}
isl_space_free(dim);
return fold;
error:
isl_qpolynomial_fold_free(fold);
isl_space_free(dim);
return NULL;
}
int isl_qpolynomial_fold_foreach_qpolynomial(
__isl_keep isl_qpolynomial_fold *fold,
int (*fn)(__isl_take isl_qpolynomial *qp, void *user), void *user)
{
int i;
if (!fold)
return -1;
for (i = 0; i < fold->n; ++i)
if (fn(isl_qpolynomial_copy(fold->qp[i]), user) < 0)
return -1;
return 0;
}
__isl_give isl_qpolynomial_fold *isl_qpolynomial_fold_move_dims(
__isl_take isl_qpolynomial_fold *fold,
enum isl_dim_type dst_type, unsigned dst_pos,
enum isl_dim_type src_type, unsigned src_pos, unsigned n)
{
int i;
if (n == 0)
return fold;
fold = isl_qpolynomial_fold_cow(fold);
if (!fold)
return NULL;
fold->dim = isl_space_move_dims(fold->dim, dst_type, dst_pos,
src_type, src_pos, n);
if (!fold->dim)
goto error;
for (i = 0; i < fold->n; ++i) {
fold->qp[i] = isl_qpolynomial_move_dims(fold->qp[i],
dst_type, dst_pos, src_type, src_pos, n);
if (!fold->qp[i])
goto error;
}
return fold;
error:
isl_qpolynomial_fold_free(fold);
return NULL;
}
/* For each 0 <= i < "n", replace variable "first" + i of type "type"
* in fold->qp[k] by subs[i].
*/
__isl_give isl_qpolynomial_fold *isl_qpolynomial_fold_substitute(
__isl_take isl_qpolynomial_fold *fold,
enum isl_dim_type type, unsigned first, unsigned n,
__isl_keep isl_qpolynomial **subs)
{
int i;
if (n == 0)
return fold;
fold = isl_qpolynomial_fold_cow(fold);
if (!fold)
return NULL;
for (i = 0; i < fold->n; ++i) {
fold->qp[i] = isl_qpolynomial_substitute(fold->qp[i],
type, first, n, subs);
if (!fold->qp[i])
goto error;
}
return fold;
error:
isl_qpolynomial_fold_free(fold);
return NULL;
}
static int add_pwqp(__isl_take isl_pw_qpolynomial *pwqp, void *user)
{
isl_ctx *ctx;
isl_pw_qpolynomial_fold *pwf;
isl_union_pw_qpolynomial_fold **upwf;
uint32_t hash;
struct isl_hash_table_entry *entry;
upwf = (isl_union_pw_qpolynomial_fold **)user;
ctx = pwqp->dim->ctx;
hash = isl_space_get_hash(pwqp->dim);
entry = isl_hash_table_find(ctx, &(*upwf)->table,
hash, &has_dim, pwqp->dim, 1);
if (!entry)
goto error;
pwf = isl_pw_qpolynomial_fold_from_pw_qpolynomial((*upwf)->type, pwqp);
if (!entry->data)
entry->data = pwf;
else {
entry->data = isl_pw_qpolynomial_fold_add(entry->data, pwf);
if (!entry->data)
return -1;
if (isl_pw_qpolynomial_fold_is_zero(entry->data)) {
isl_pw_qpolynomial_fold_free(entry->data);
isl_hash_table_remove(ctx, &(*upwf)->table, entry);
}
}
return 0;
error:
isl_pw_qpolynomial_free(pwqp);
return -1;
}
__isl_give isl_union_pw_qpolynomial_fold *isl_union_pw_qpolynomial_fold_add_union_pw_qpolynomial(
__isl_take isl_union_pw_qpolynomial_fold *upwf,
__isl_take isl_union_pw_qpolynomial *upwqp)
{
upwf = isl_union_pw_qpolynomial_fold_align_params(upwf,
isl_union_pw_qpolynomial_get_space(upwqp));
upwqp = isl_union_pw_qpolynomial_align_params(upwqp,
isl_union_pw_qpolynomial_fold_get_space(upwf));
upwf = isl_union_pw_qpolynomial_fold_cow(upwf);
if (!upwf || !upwqp)
goto error;
if (isl_union_pw_qpolynomial_foreach_pw_qpolynomial(upwqp, &add_pwqp,
&upwf) < 0)
goto error;
isl_union_pw_qpolynomial_free(upwqp);
return upwf;
error:
isl_union_pw_qpolynomial_fold_free(upwf);
isl_union_pw_qpolynomial_free(upwqp);
return NULL;
}
static int join_compatible(__isl_keep isl_space *dim1, __isl_keep isl_space *dim2)
{
int m;
m = isl_space_match(dim1, isl_dim_param, dim2, isl_dim_param);
if (m < 0 || !m)
return m;
return isl_space_tuple_match(dim1, isl_dim_out, dim2, isl_dim_in);
}
/* Compute the intersection of the range of the map and the domain
* of the piecewise quasipolynomial reduction and then compute a bound
* on the associated quasipolynomial reduction over all elements
* in this intersection.
*
* We first introduce some unconstrained dimensions in the
* piecewise quasipolynomial, intersect the resulting domain
* with the wrapped map and the compute the sum.
*/
__isl_give isl_pw_qpolynomial_fold *isl_map_apply_pw_qpolynomial_fold(
__isl_take isl_map *map, __isl_take isl_pw_qpolynomial_fold *pwf,
int *tight)
{
isl_ctx *ctx;
isl_set *dom;
isl_space *map_dim;
isl_space *pwf_dim;
unsigned n_in;
int ok;
ctx = isl_map_get_ctx(map);
if (!ctx)
goto error;
map_dim = isl_map_get_space(map);
pwf_dim = isl_pw_qpolynomial_fold_get_space(pwf);
ok = join_compatible(map_dim, pwf_dim);
isl_space_free(map_dim);
isl_space_free(pwf_dim);
if (!ok)
isl_die(ctx, isl_error_invalid, "incompatible dimensions",
goto error);
n_in = isl_map_dim(map, isl_dim_in);
pwf = isl_pw_qpolynomial_fold_insert_dims(pwf, isl_dim_in, 0, n_in);
dom = isl_map_wrap(map);
pwf = isl_pw_qpolynomial_fold_reset_domain_space(pwf,
isl_set_get_space(dom));
pwf = isl_pw_qpolynomial_fold_intersect_domain(pwf, dom);
pwf = isl_pw_qpolynomial_fold_bound(pwf, tight);
return pwf;
error:
isl_map_free(map);
isl_pw_qpolynomial_fold_free(pwf);
return NULL;
}
__isl_give isl_pw_qpolynomial_fold *isl_set_apply_pw_qpolynomial_fold(
__isl_take isl_set *set, __isl_take isl_pw_qpolynomial_fold *pwf,
int *tight)
{
return isl_map_apply_pw_qpolynomial_fold(set, pwf, tight);
}
struct isl_apply_fold_data {
isl_union_pw_qpolynomial_fold *upwf;
isl_union_pw_qpolynomial_fold *res;
isl_map *map;
int tight;
};
static int pw_qpolynomial_fold_apply(__isl_take isl_pw_qpolynomial_fold *pwf,
void *user)
{
isl_space *map_dim;
isl_space *pwf_dim;
struct isl_apply_fold_data *data = user;
int ok;
map_dim = isl_map_get_space(data->map);
pwf_dim = isl_pw_qpolynomial_fold_get_space(pwf);
ok = join_compatible(map_dim, pwf_dim);
isl_space_free(map_dim);
isl_space_free(pwf_dim);
if (ok) {
pwf = isl_map_apply_pw_qpolynomial_fold(isl_map_copy(data->map),
pwf, data->tight ? &data->tight : NULL);
data->res = isl_union_pw_qpolynomial_fold_fold_pw_qpolynomial_fold(
data->res, pwf);
} else
isl_pw_qpolynomial_fold_free(pwf);
return 0;
}
static int map_apply(__isl_take isl_map *map, void *user)
{
struct isl_apply_fold_data *data = user;
int r;
data->map = map;
r = isl_union_pw_qpolynomial_fold_foreach_pw_qpolynomial_fold(
data->upwf, &pw_qpolynomial_fold_apply, data);
isl_map_free(map);
return r;
}
__isl_give isl_union_pw_qpolynomial_fold *isl_union_map_apply_union_pw_qpolynomial_fold(
__isl_take isl_union_map *umap,
__isl_take isl_union_pw_qpolynomial_fold *upwf, int *tight)
{
isl_space *dim;
enum isl_fold type;
struct isl_apply_fold_data data;
upwf = isl_union_pw_qpolynomial_fold_align_params(upwf,
isl_union_map_get_space(umap));
umap = isl_union_map_align_params(umap,
isl_union_pw_qpolynomial_fold_get_space(upwf));
data.upwf = upwf;
data.tight = tight ? 1 : 0;
dim = isl_union_pw_qpolynomial_fold_get_space(upwf);
type = isl_union_pw_qpolynomial_fold_get_type(upwf);
data.res = isl_union_pw_qpolynomial_fold_zero(dim, type);
if (isl_union_map_foreach_map(umap, &map_apply, &data) < 0)
goto error;
isl_union_map_free(umap);
isl_union_pw_qpolynomial_fold_free(upwf);
if (tight)
*tight = data.tight;
return data.res;
error:
isl_union_map_free(umap);
isl_union_pw_qpolynomial_fold_free(upwf);
isl_union_pw_qpolynomial_fold_free(data.res);
return NULL;
}
__isl_give isl_union_pw_qpolynomial_fold *isl_union_set_apply_union_pw_qpolynomial_fold(
__isl_take isl_union_set *uset,
__isl_take isl_union_pw_qpolynomial_fold *upwf, int *tight)
{
return isl_union_map_apply_union_pw_qpolynomial_fold(uset, upwf, tight);
}
/* Reorder the dimension of "fold" according to the given reordering.
*/
__isl_give isl_qpolynomial_fold *isl_qpolynomial_fold_realign_domain(
__isl_take isl_qpolynomial_fold *fold, __isl_take isl_reordering *r)
{
int i;
fold = isl_qpolynomial_fold_cow(fold);
if (!fold || !r)
goto error;
for (i = 0; i < fold->n; ++i) {
fold->qp[i] = isl_qpolynomial_realign_domain(fold->qp[i],
isl_reordering_copy(r));
if (!fold->qp[i])
goto error;
}
fold = isl_qpolynomial_fold_reset_domain_space(fold,
isl_space_copy(r->dim));
isl_reordering_free(r);
return fold;
error:
isl_qpolynomial_fold_free(fold);
isl_reordering_free(r);
return NULL;
}
__isl_give isl_qpolynomial_fold *isl_qpolynomial_fold_mul_isl_int(
__isl_take isl_qpolynomial_fold *fold, isl_int v)
{
int i;
if (isl_int_is_one(v))
return fold;
if (fold && isl_int_is_zero(v)) {
isl_qpolynomial_fold *zero;
isl_space *dim = isl_space_copy(fold->dim);
zero = isl_qpolynomial_fold_empty(fold->type, dim);
isl_qpolynomial_fold_free(fold);
return zero;
}
fold = isl_qpolynomial_fold_cow(fold);
if (!fold)
return NULL;
if (isl_int_is_neg(v))
fold->type = isl_fold_type_negate(fold->type);
for (i = 0; i < fold->n; ++i) {
fold->qp[i] = isl_qpolynomial_mul_isl_int(fold->qp[i], v);
if (!fold->qp[i])
goto error;
}
return fold;
error:
isl_qpolynomial_fold_free(fold);
return NULL;
}
__isl_give isl_qpolynomial_fold *isl_qpolynomial_fold_scale(
__isl_take isl_qpolynomial_fold *fold, isl_int v)
{
return isl_qpolynomial_fold_mul_isl_int(fold, v);
}