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
*/
#include <stdlib.h>
#define ISL_DIM_H
#include <isl_ctx_private.h>
#include <isl_map_private.h>
#include <isl_factorization.h>
#include <isl/lp.h>
#include <isl/seq.h>
#include <isl_union_map_private.h>
#include <isl_constraint_private.h>
#include <isl_polynomial_private.h>
#include <isl_point_private.h>
#include <isl_space_private.h>
#include <isl_mat_private.h>
#include <isl_range.h>
#include <isl_local_space_private.h>
#include <isl_aff_private.h>
#include <isl_config.h>
static unsigned pos(__isl_keep isl_space *dim, enum isl_dim_type type)
{
switch (type) {
case isl_dim_param: return 0;
case isl_dim_in: return dim->nparam;
case isl_dim_out: return dim->nparam + dim->n_in;
default: return 0;
}
}
int isl_upoly_is_cst(__isl_keep struct isl_upoly *up)
{
if (!up)
return -1;
return up->var < 0;
}
__isl_keep struct isl_upoly_cst *isl_upoly_as_cst(__isl_keep struct isl_upoly *up)
{
if (!up)
return NULL;
isl_assert(up->ctx, up->var < 0, return NULL);
return (struct isl_upoly_cst *)up;
}
__isl_keep struct isl_upoly_rec *isl_upoly_as_rec(__isl_keep struct isl_upoly *up)
{
if (!up)
return NULL;
isl_assert(up->ctx, up->var >= 0, return NULL);
return (struct isl_upoly_rec *)up;
}
int isl_upoly_is_equal(__isl_keep struct isl_upoly *up1,
__isl_keep struct isl_upoly *up2)
{
int i;
struct isl_upoly_rec *rec1, *rec2;
if (!up1 || !up2)
return -1;
if (up1 == up2)
return 1;
if (up1->var != up2->var)
return 0;
if (isl_upoly_is_cst(up1)) {
struct isl_upoly_cst *cst1, *cst2;
cst1 = isl_upoly_as_cst(up1);
cst2 = isl_upoly_as_cst(up2);
if (!cst1 || !cst2)
return -1;
return isl_int_eq(cst1->n, cst2->n) &&
isl_int_eq(cst1->d, cst2->d);
}
rec1 = isl_upoly_as_rec(up1);
rec2 = isl_upoly_as_rec(up2);
if (!rec1 || !rec2)
return -1;
if (rec1->n != rec2->n)
return 0;
for (i = 0; i < rec1->n; ++i) {
int eq = isl_upoly_is_equal(rec1->p[i], rec2->p[i]);
if (eq < 0 || !eq)
return eq;
}
return 1;
}
int isl_upoly_is_zero(__isl_keep struct isl_upoly *up)
{
struct isl_upoly_cst *cst;
if (!up)
return -1;
if (!isl_upoly_is_cst(up))
return 0;
cst = isl_upoly_as_cst(up);
if (!cst)
return -1;
return isl_int_is_zero(cst->n) && isl_int_is_pos(cst->d);
}
int isl_upoly_sgn(__isl_keep struct isl_upoly *up)
{
struct isl_upoly_cst *cst;
if (!up)
return 0;
if (!isl_upoly_is_cst(up))
return 0;
cst = isl_upoly_as_cst(up);
if (!cst)
return 0;
return isl_int_sgn(cst->n);
}
int isl_upoly_is_nan(__isl_keep struct isl_upoly *up)
{
struct isl_upoly_cst *cst;
if (!up)
return -1;
if (!isl_upoly_is_cst(up))
return 0;
cst = isl_upoly_as_cst(up);
if (!cst)
return -1;
return isl_int_is_zero(cst->n) && isl_int_is_zero(cst->d);
}
int isl_upoly_is_infty(__isl_keep struct isl_upoly *up)
{
struct isl_upoly_cst *cst;
if (!up)
return -1;
if (!isl_upoly_is_cst(up))
return 0;
cst = isl_upoly_as_cst(up);
if (!cst)
return -1;
return isl_int_is_pos(cst->n) && isl_int_is_zero(cst->d);
}
int isl_upoly_is_neginfty(__isl_keep struct isl_upoly *up)
{
struct isl_upoly_cst *cst;
if (!up)
return -1;
if (!isl_upoly_is_cst(up))
return 0;
cst = isl_upoly_as_cst(up);
if (!cst)
return -1;
return isl_int_is_neg(cst->n) && isl_int_is_zero(cst->d);
}
int isl_upoly_is_one(__isl_keep struct isl_upoly *up)
{
struct isl_upoly_cst *cst;
if (!up)
return -1;
if (!isl_upoly_is_cst(up))
return 0;
cst = isl_upoly_as_cst(up);
if (!cst)
return -1;
return isl_int_eq(cst->n, cst->d) && isl_int_is_pos(cst->d);
}
int isl_upoly_is_negone(__isl_keep struct isl_upoly *up)
{
struct isl_upoly_cst *cst;
if (!up)
return -1;
if (!isl_upoly_is_cst(up))
return 0;
cst = isl_upoly_as_cst(up);
if (!cst)
return -1;
return isl_int_is_negone(cst->n) && isl_int_is_one(cst->d);
}
__isl_give struct isl_upoly_cst *isl_upoly_cst_alloc(struct isl_ctx *ctx)
{
struct isl_upoly_cst *cst;
cst = isl_alloc_type(ctx, struct isl_upoly_cst);
if (!cst)
return NULL;
cst->up.ref = 1;
cst->up.ctx = ctx;
isl_ctx_ref(ctx);
cst->up.var = -1;
isl_int_init(cst->n);
isl_int_init(cst->d);
return cst;
}
__isl_give struct isl_upoly *isl_upoly_zero(struct isl_ctx *ctx)
{
struct isl_upoly_cst *cst;
cst = isl_upoly_cst_alloc(ctx);
if (!cst)
return NULL;
isl_int_set_si(cst->n, 0);
isl_int_set_si(cst->d, 1);
return &cst->up;
}
__isl_give struct isl_upoly *isl_upoly_one(struct isl_ctx *ctx)
{
struct isl_upoly_cst *cst;
cst = isl_upoly_cst_alloc(ctx);
if (!cst)
return NULL;
isl_int_set_si(cst->n, 1);
isl_int_set_si(cst->d, 1);
return &cst->up;
}
__isl_give struct isl_upoly *isl_upoly_infty(struct isl_ctx *ctx)
{
struct isl_upoly_cst *cst;
cst = isl_upoly_cst_alloc(ctx);
if (!cst)
return NULL;
isl_int_set_si(cst->n, 1);
isl_int_set_si(cst->d, 0);
return &cst->up;
}
__isl_give struct isl_upoly *isl_upoly_neginfty(struct isl_ctx *ctx)
{
struct isl_upoly_cst *cst;
cst = isl_upoly_cst_alloc(ctx);
if (!cst)
return NULL;
isl_int_set_si(cst->n, -1);
isl_int_set_si(cst->d, 0);
return &cst->up;
}
__isl_give struct isl_upoly *isl_upoly_nan(struct isl_ctx *ctx)
{
struct isl_upoly_cst *cst;
cst = isl_upoly_cst_alloc(ctx);
if (!cst)
return NULL;
isl_int_set_si(cst->n, 0);
isl_int_set_si(cst->d, 0);
return &cst->up;
}
__isl_give struct isl_upoly *isl_upoly_rat_cst(struct isl_ctx *ctx,
isl_int n, isl_int d)
{
struct isl_upoly_cst *cst;
cst = isl_upoly_cst_alloc(ctx);
if (!cst)
return NULL;
isl_int_set(cst->n, n);
isl_int_set(cst->d, d);
return &cst->up;
}
__isl_give struct isl_upoly_rec *isl_upoly_alloc_rec(struct isl_ctx *ctx,
int var, int size)
{
struct isl_upoly_rec *rec;
isl_assert(ctx, var >= 0, return NULL);
isl_assert(ctx, size >= 0, return NULL);
rec = isl_calloc(ctx, struct isl_upoly_rec,
sizeof(struct isl_upoly_rec) +
size * sizeof(struct isl_upoly *));
if (!rec)
return NULL;
rec->up.ref = 1;
rec->up.ctx = ctx;
isl_ctx_ref(ctx);
rec->up.var = var;
rec->n = 0;
rec->size = size;
return rec;
}
__isl_give isl_qpolynomial *isl_qpolynomial_reset_domain_space(
__isl_take isl_qpolynomial *qp, __isl_take isl_space *dim)
{
qp = isl_qpolynomial_cow(qp);
if (!qp || !dim)
goto error;
isl_space_free(qp->dim);
qp->dim = dim;
return qp;
error:
isl_qpolynomial_free(qp);
isl_space_free(dim);
return NULL;
}
/* Reset the space of "qp". 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 *isl_qpolynomial_reset_space_and_domain(
__isl_take isl_qpolynomial *qp, __isl_take isl_space *space,
__isl_take isl_space *domain)
{
isl_space_free(space);
return isl_qpolynomial_reset_domain_space(qp, domain);
}
isl_ctx *isl_qpolynomial_get_ctx(__isl_keep isl_qpolynomial *qp)
{
return qp ? qp->dim->ctx : NULL;
}
__isl_give isl_space *isl_qpolynomial_get_domain_space(
__isl_keep isl_qpolynomial *qp)
{
return qp ? isl_space_copy(qp->dim) : NULL;
}
__isl_give isl_space *isl_qpolynomial_get_space(__isl_keep isl_qpolynomial *qp)
{
isl_space *space;
if (!qp)
return NULL;
space = isl_space_copy(qp->dim);
space = isl_space_from_domain(space);
space = isl_space_add_dims(space, isl_dim_out, 1);
return space;
}
/* Externally, an isl_qpolynomial has a map space, but internally, the
* ls field corresponds to the domain of that space.
*/
unsigned isl_qpolynomial_dim(__isl_keep isl_qpolynomial *qp,
enum isl_dim_type type)
{
if (!qp)
return 0;
if (type == isl_dim_out)
return 1;
if (type == isl_dim_in)
type = isl_dim_set;
return isl_space_dim(qp->dim, type);
}
int isl_qpolynomial_is_zero(__isl_keep isl_qpolynomial *qp)
{
return qp ? isl_upoly_is_zero(qp->upoly) : -1;
}
int isl_qpolynomial_is_one(__isl_keep isl_qpolynomial *qp)
{
return qp ? isl_upoly_is_one(qp->upoly) : -1;
}
int isl_qpolynomial_is_nan(__isl_keep isl_qpolynomial *qp)
{
return qp ? isl_upoly_is_nan(qp->upoly) : -1;
}
int isl_qpolynomial_is_infty(__isl_keep isl_qpolynomial *qp)
{
return qp ? isl_upoly_is_infty(qp->upoly) : -1;
}
int isl_qpolynomial_is_neginfty(__isl_keep isl_qpolynomial *qp)
{
return qp ? isl_upoly_is_neginfty(qp->upoly) : -1;
}
int isl_qpolynomial_sgn(__isl_keep isl_qpolynomial *qp)
{
return qp ? isl_upoly_sgn(qp->upoly) : 0;
}
static void upoly_free_cst(__isl_take struct isl_upoly_cst *cst)
{
isl_int_clear(cst->n);
isl_int_clear(cst->d);
}
static void upoly_free_rec(__isl_take struct isl_upoly_rec *rec)
{
int i;
for (i = 0; i < rec->n; ++i)
isl_upoly_free(rec->p[i]);
}
__isl_give struct isl_upoly *isl_upoly_copy(__isl_keep struct isl_upoly *up)
{
if (!up)
return NULL;
up->ref++;
return up;
}
__isl_give struct isl_upoly *isl_upoly_dup_cst(__isl_keep struct isl_upoly *up)
{
struct isl_upoly_cst *cst;
struct isl_upoly_cst *dup;
cst = isl_upoly_as_cst(up);
if (!cst)
return NULL;
dup = isl_upoly_as_cst(isl_upoly_zero(up->ctx));
if (!dup)
return NULL;
isl_int_set(dup->n, cst->n);
isl_int_set(dup->d, cst->d);
return &dup->up;
}
__isl_give struct isl_upoly *isl_upoly_dup_rec(__isl_keep struct isl_upoly *up)
{
int i;
struct isl_upoly_rec *rec;
struct isl_upoly_rec *dup;
rec = isl_upoly_as_rec(up);
if (!rec)
return NULL;
dup = isl_upoly_alloc_rec(up->ctx, up->var, rec->n);
if (!dup)
return NULL;
for (i = 0; i < rec->n; ++i) {
dup->p[i] = isl_upoly_copy(rec->p[i]);
if (!dup->p[i])
goto error;
dup->n++;
}
return &dup->up;
error:
isl_upoly_free(&dup->up);
return NULL;
}
__isl_give struct isl_upoly *isl_upoly_dup(__isl_keep struct isl_upoly *up)
{
if (!up)
return NULL;
if (isl_upoly_is_cst(up))
return isl_upoly_dup_cst(up);
else
return isl_upoly_dup_rec(up);
}
__isl_give struct isl_upoly *isl_upoly_cow(__isl_take struct isl_upoly *up)
{
if (!up)
return NULL;
if (up->ref == 1)
return up;
up->ref--;
return isl_upoly_dup(up);
}
void isl_upoly_free(__isl_take struct isl_upoly *up)
{
if (!up)
return;
if (--up->ref > 0)
return;
if (up->var < 0)
upoly_free_cst((struct isl_upoly_cst *)up);
else
upoly_free_rec((struct isl_upoly_rec *)up);
isl_ctx_deref(up->ctx);
free(up);
}
static void isl_upoly_cst_reduce(__isl_keep struct isl_upoly_cst *cst)
{
isl_int gcd;
isl_int_init(gcd);
isl_int_gcd(gcd, cst->n, cst->d);
if (!isl_int_is_zero(gcd) && !isl_int_is_one(gcd)) {
isl_int_divexact(cst->n, cst->n, gcd);
isl_int_divexact(cst->d, cst->d, gcd);
}
isl_int_clear(gcd);
}
__isl_give struct isl_upoly *isl_upoly_sum_cst(__isl_take struct isl_upoly *up1,
__isl_take struct isl_upoly *up2)
{
struct isl_upoly_cst *cst1;
struct isl_upoly_cst *cst2;
up1 = isl_upoly_cow(up1);
if (!up1 || !up2)
goto error;
cst1 = isl_upoly_as_cst(up1);
cst2 = isl_upoly_as_cst(up2);
if (isl_int_eq(cst1->d, cst2->d))
isl_int_add(cst1->n, cst1->n, cst2->n);
else {
isl_int_mul(cst1->n, cst1->n, cst2->d);
isl_int_addmul(cst1->n, cst2->n, cst1->d);
isl_int_mul(cst1->d, cst1->d, cst2->d);
}
isl_upoly_cst_reduce(cst1);
isl_upoly_free(up2);
return up1;
error:
isl_upoly_free(up1);
isl_upoly_free(up2);
return NULL;
}
static __isl_give struct isl_upoly *replace_by_zero(
__isl_take struct isl_upoly *up)
{
struct isl_ctx *ctx;
if (!up)
return NULL;
ctx = up->ctx;
isl_upoly_free(up);
return isl_upoly_zero(ctx);
}
static __isl_give struct isl_upoly *replace_by_constant_term(
__isl_take struct isl_upoly *up)
{
struct isl_upoly_rec *rec;
struct isl_upoly *cst;
if (!up)
return NULL;
rec = isl_upoly_as_rec(up);
if (!rec)
goto error;
cst = isl_upoly_copy(rec->p[0]);
isl_upoly_free(up);
return cst;
error:
isl_upoly_free(up);
return NULL;
}
__isl_give struct isl_upoly *isl_upoly_sum(__isl_take struct isl_upoly *up1,
__isl_take struct isl_upoly *up2)
{
int i;
struct isl_upoly_rec *rec1, *rec2;
if (!up1 || !up2)
goto error;
if (isl_upoly_is_nan(up1)) {
isl_upoly_free(up2);
return up1;
}
if (isl_upoly_is_nan(up2)) {
isl_upoly_free(up1);
return up2;
}
if (isl_upoly_is_zero(up1)) {
isl_upoly_free(up1);
return up2;
}
if (isl_upoly_is_zero(up2)) {
isl_upoly_free(up2);
return up1;
}
if (up1->var < up2->var)
return isl_upoly_sum(up2, up1);
if (up2->var < up1->var) {
struct isl_upoly_rec *rec;
if (isl_upoly_is_infty(up2) || isl_upoly_is_neginfty(up2)) {
isl_upoly_free(up1);
return up2;
}
up1 = isl_upoly_cow(up1);
rec = isl_upoly_as_rec(up1);
if (!rec)
goto error;
rec->p[0] = isl_upoly_sum(rec->p[0], up2);
if (rec->n == 1)
up1 = replace_by_constant_term(up1);
return up1;
}
if (isl_upoly_is_cst(up1))
return isl_upoly_sum_cst(up1, up2);
rec1 = isl_upoly_as_rec(up1);
rec2 = isl_upoly_as_rec(up2);
if (!rec1 || !rec2)
goto error;
if (rec1->n < rec2->n)
return isl_upoly_sum(up2, up1);
up1 = isl_upoly_cow(up1);
rec1 = isl_upoly_as_rec(up1);
if (!rec1)
goto error;
for (i = rec2->n - 1; i >= 0; --i) {
rec1->p[i] = isl_upoly_sum(rec1->p[i],
isl_upoly_copy(rec2->p[i]));
if (!rec1->p[i])
goto error;
if (i == rec1->n - 1 && isl_upoly_is_zero(rec1->p[i])) {
isl_upoly_free(rec1->p[i]);
rec1->n--;
}
}
if (rec1->n == 0)
up1 = replace_by_zero(up1);
else if (rec1->n == 1)
up1 = replace_by_constant_term(up1);
isl_upoly_free(up2);
return up1;
error:
isl_upoly_free(up1);
isl_upoly_free(up2);
return NULL;
}
__isl_give struct isl_upoly *isl_upoly_cst_add_isl_int(
__isl_take struct isl_upoly *up, isl_int v)
{
struct isl_upoly_cst *cst;
up = isl_upoly_cow(up);
if (!up)
return NULL;
cst = isl_upoly_as_cst(up);
isl_int_addmul(cst->n, cst->d, v);
return up;
}
__isl_give struct isl_upoly *isl_upoly_add_isl_int(
__isl_take struct isl_upoly *up, isl_int v)
{
struct isl_upoly_rec *rec;
if (!up)
return NULL;
if (isl_upoly_is_cst(up))
return isl_upoly_cst_add_isl_int(up, v);
up = isl_upoly_cow(up);
rec = isl_upoly_as_rec(up);
if (!rec)
goto error;
rec->p[0] = isl_upoly_add_isl_int(rec->p[0], v);
if (!rec->p[0])
goto error;
return up;
error:
isl_upoly_free(up);
return NULL;
}
__isl_give struct isl_upoly *isl_upoly_cst_mul_isl_int(
__isl_take struct isl_upoly *up, isl_int v)
{
struct isl_upoly_cst *cst;
if (isl_upoly_is_zero(up))
return up;
up = isl_upoly_cow(up);
if (!up)
return NULL;
cst = isl_upoly_as_cst(up);
isl_int_mul(cst->n, cst->n, v);
return up;
}
__isl_give struct isl_upoly *isl_upoly_mul_isl_int(
__isl_take struct isl_upoly *up, isl_int v)
{
int i;
struct isl_upoly_rec *rec;
if (!up)
return NULL;
if (isl_upoly_is_cst(up))
return isl_upoly_cst_mul_isl_int(up, v);
up = isl_upoly_cow(up);
rec = isl_upoly_as_rec(up);
if (!rec)
goto error;
for (i = 0; i < rec->n; ++i) {
rec->p[i] = isl_upoly_mul_isl_int(rec->p[i], v);
if (!rec->p[i])
goto error;
}
return up;
error:
isl_upoly_free(up);
return NULL;
}
__isl_give struct isl_upoly *isl_upoly_mul_cst(__isl_take struct isl_upoly *up1,
__isl_take struct isl_upoly *up2)
{
struct isl_upoly_cst *cst1;
struct isl_upoly_cst *cst2;
up1 = isl_upoly_cow(up1);
if (!up1 || !up2)
goto error;
cst1 = isl_upoly_as_cst(up1);
cst2 = isl_upoly_as_cst(up2);
isl_int_mul(cst1->n, cst1->n, cst2->n);
isl_int_mul(cst1->d, cst1->d, cst2->d);
isl_upoly_cst_reduce(cst1);
isl_upoly_free(up2);
return up1;
error:
isl_upoly_free(up1);
isl_upoly_free(up2);
return NULL;
}
__isl_give struct isl_upoly *isl_upoly_mul_rec(__isl_take struct isl_upoly *up1,
__isl_take struct isl_upoly *up2)
{
struct isl_upoly_rec *rec1;
struct isl_upoly_rec *rec2;
struct isl_upoly_rec *res = NULL;
int i, j;
int size;
rec1 = isl_upoly_as_rec(up1);
rec2 = isl_upoly_as_rec(up2);
if (!rec1 || !rec2)
goto error;
size = rec1->n + rec2->n - 1;
res = isl_upoly_alloc_rec(up1->ctx, up1->var, size);
if (!res)
goto error;
for (i = 0; i < rec1->n; ++i) {
res->p[i] = isl_upoly_mul(isl_upoly_copy(rec2->p[0]),
isl_upoly_copy(rec1->p[i]));
if (!res->p[i])
goto error;
res->n++;
}
for (; i < size; ++i) {
res->p[i] = isl_upoly_zero(up1->ctx);
if (!res->p[i])
goto error;
res->n++;
}
for (i = 0; i < rec1->n; ++i) {
for (j = 1; j < rec2->n; ++j) {
struct isl_upoly *up;
up = isl_upoly_mul(isl_upoly_copy(rec2->p[j]),
isl_upoly_copy(rec1->p[i]));
res->p[i + j] = isl_upoly_sum(res->p[i + j], up);
if (!res->p[i + j])
goto error;
}
}
isl_upoly_free(up1);
isl_upoly_free(up2);
return &res->up;
error:
isl_upoly_free(up1);
isl_upoly_free(up2);
isl_upoly_free(&res->up);
return NULL;
}
__isl_give struct isl_upoly *isl_upoly_mul(__isl_take struct isl_upoly *up1,
__isl_take struct isl_upoly *up2)
{
if (!up1 || !up2)
goto error;
if (isl_upoly_is_nan(up1)) {
isl_upoly_free(up2);
return up1;
}
if (isl_upoly_is_nan(up2)) {
isl_upoly_free(up1);
return up2;
}
if (isl_upoly_is_zero(up1)) {
isl_upoly_free(up2);
return up1;
}
if (isl_upoly_is_zero(up2)) {
isl_upoly_free(up1);
return up2;
}
if (isl_upoly_is_one(up1)) {
isl_upoly_free(up1);
return up2;
}
if (isl_upoly_is_one(up2)) {
isl_upoly_free(up2);
return up1;
}
if (up1->var < up2->var)
return isl_upoly_mul(up2, up1);
if (up2->var < up1->var) {
int i;
struct isl_upoly_rec *rec;
if (isl_upoly_is_infty(up2) || isl_upoly_is_neginfty(up2)) {
isl_ctx *ctx = up1->ctx;
isl_upoly_free(up1);
isl_upoly_free(up2);
return isl_upoly_nan(ctx);
}
up1 = isl_upoly_cow(up1);
rec = isl_upoly_as_rec(up1);
if (!rec)
goto error;
for (i = 0; i < rec->n; ++i) {
rec->p[i] = isl_upoly_mul(rec->p[i],
isl_upoly_copy(up2));
if (!rec->p[i])
goto error;
}
isl_upoly_free(up2);
return up1;
}
if (isl_upoly_is_cst(up1))
return isl_upoly_mul_cst(up1, up2);
return isl_upoly_mul_rec(up1, up2);
error:
isl_upoly_free(up1);
isl_upoly_free(up2);
return NULL;
}
__isl_give struct isl_upoly *isl_upoly_pow(__isl_take struct isl_upoly *up,
unsigned power)
{
struct isl_upoly *res;
if (!up)
return NULL;
if (power == 1)
return up;
if (power % 2)
res = isl_upoly_copy(up);
else
res = isl_upoly_one(up->ctx);
while (power >>= 1) {
up = isl_upoly_mul(up, isl_upoly_copy(up));
if (power % 2)
res = isl_upoly_mul(res, isl_upoly_copy(up));
}
isl_upoly_free(up);
return res;
}
__isl_give isl_qpolynomial *isl_qpolynomial_alloc(__isl_take isl_space *dim,
unsigned n_div, __isl_take struct isl_upoly *up)
{
struct isl_qpolynomial *qp = NULL;
unsigned total;
if (!dim || !up)
goto error;
if (!isl_space_is_set(dim))
isl_die(isl_space_get_ctx(dim), isl_error_invalid,
"domain of polynomial should be a set", goto error);
total = isl_space_dim(dim, isl_dim_all);
qp = isl_calloc_type(dim->ctx, struct isl_qpolynomial);
if (!qp)
goto error;
qp->ref = 1;
qp->div = isl_mat_alloc(dim->ctx, n_div, 1 + 1 + total + n_div);
if (!qp->div)
goto error;
qp->dim = dim;
qp->upoly = up;
return qp;
error:
isl_space_free(dim);
isl_upoly_free(up);
isl_qpolynomial_free(qp);
return NULL;
}
__isl_give isl_qpolynomial *isl_qpolynomial_copy(__isl_keep isl_qpolynomial *qp)
{
if (!qp)
return NULL;
qp->ref++;
return qp;
}
__isl_give isl_qpolynomial *isl_qpolynomial_dup(__isl_keep isl_qpolynomial *qp)
{
struct isl_qpolynomial *dup;
if (!qp)
return NULL;
dup = isl_qpolynomial_alloc(isl_space_copy(qp->dim), qp->div->n_row,
isl_upoly_copy(qp->upoly));
if (!dup)
return NULL;
isl_mat_free(dup->div);
dup->div = isl_mat_copy(qp->div);
if (!dup->div)
goto error;
return dup;
error:
isl_qpolynomial_free(dup);
return NULL;
}
__isl_give isl_qpolynomial *isl_qpolynomial_cow(__isl_take isl_qpolynomial *qp)
{
if (!qp)
return NULL;
if (qp->ref == 1)
return qp;
qp->ref--;
return isl_qpolynomial_dup(qp);
}
void *isl_qpolynomial_free(__isl_take isl_qpolynomial *qp)
{
if (!qp)
return NULL;
if (--qp->ref > 0)
return NULL;
isl_space_free(qp->dim);
isl_mat_free(qp->div);
isl_upoly_free(qp->upoly);
free(qp);
return NULL;
}
__isl_give struct isl_upoly *isl_upoly_var_pow(isl_ctx *ctx, int pos, int power)
{
int i;
struct isl_upoly_rec *rec;
struct isl_upoly_cst *cst;
rec = isl_upoly_alloc_rec(ctx, pos, 1 + power);
if (!rec)
return NULL;
for (i = 0; i < 1 + power; ++i) {
rec->p[i] = isl_upoly_zero(ctx);
if (!rec->p[i])
goto error;
rec->n++;
}
cst = isl_upoly_as_cst(rec->p[power]);
isl_int_set_si(cst->n, 1);
return &rec->up;
error:
isl_upoly_free(&rec->up);
return NULL;
}
/* r array maps original positions to new positions.
*/
static __isl_give struct isl_upoly *reorder(__isl_take struct isl_upoly *up,
int *r)
{
int i;
struct isl_upoly_rec *rec;
struct isl_upoly *base;
struct isl_upoly *res;
if (isl_upoly_is_cst(up))
return up;
rec = isl_upoly_as_rec(up);
if (!rec)
goto error;
isl_assert(up->ctx, rec->n >= 1, goto error);
base = isl_upoly_var_pow(up->ctx, r[up->var], 1);
res = reorder(isl_upoly_copy(rec->p[rec->n - 1]), r);
for (i = rec->n - 2; i >= 0; --i) {
res = isl_upoly_mul(res, isl_upoly_copy(base));
res = isl_upoly_sum(res, reorder(isl_upoly_copy(rec->p[i]), r));
}
isl_upoly_free(base);
isl_upoly_free(up);
return res;
error:
isl_upoly_free(up);
return NULL;
}
static int compatible_divs(__isl_keep isl_mat *div1, __isl_keep isl_mat *div2)
{
int n_row, n_col;
int equal;
isl_assert(div1->ctx, div1->n_row >= div2->n_row &&
div1->n_col >= div2->n_col, return -1);
if (div1->n_row == div2->n_row)
return isl_mat_is_equal(div1, div2);
n_row = div1->n_row;
n_col = div1->n_col;
div1->n_row = div2->n_row;
div1->n_col = div2->n_col;
equal = isl_mat_is_equal(div1, div2);
div1->n_row = n_row;
div1->n_col = n_col;
return equal;
}
static int cmp_row(__isl_keep isl_mat *div, int i, int j)
{
int li, lj;
li = isl_seq_last_non_zero(div->row[i], div->n_col);
lj = isl_seq_last_non_zero(div->row[j], div->n_col);
if (li != lj)
return li - lj;
return isl_seq_cmp(div->row[i], div->row[j], div->n_col);
}
struct isl_div_sort_info {
isl_mat *div;
int row;
};
static int div_sort_cmp(const void *p1, const void *p2)
{
const struct isl_div_sort_info *i1, *i2;
i1 = (const struct isl_div_sort_info *) p1;
i2 = (const struct isl_div_sort_info *) p2;
return cmp_row(i1->div, i1->row, i2->row);
}
/* Sort divs and remove duplicates.
*/
static __isl_give isl_qpolynomial *sort_divs(__isl_take isl_qpolynomial *qp)
{
int i;
int skip;
int len;
struct isl_div_sort_info *array = NULL;
int *pos = NULL, *at = NULL;
int *reordering = NULL;
unsigned div_pos;
if (!qp)
return NULL;
if (qp->div->n_row <= 1)
return qp;
div_pos = isl_space_dim(qp->dim, isl_dim_all);
array = isl_alloc_array(qp->div->ctx, struct isl_div_sort_info,
qp->div->n_row);
pos = isl_alloc_array(qp->div->ctx, int, qp->div->n_row);
at = isl_alloc_array(qp->div->ctx, int, qp->div->n_row);
len = qp->div->n_col - 2;
reordering = isl_alloc_array(qp->div->ctx, int, len);
if (!array || !pos || !at || !reordering)
goto error;
for (i = 0; i < qp->div->n_row; ++i) {
array[i].div = qp->div;
array[i].row = i;
pos[i] = i;
at[i] = i;
}
qsort(array, qp->div->n_row, sizeof(struct isl_div_sort_info),
div_sort_cmp);
for (i = 0; i < div_pos; ++i)
reordering[i] = i;
for (i = 0; i < qp->div->n_row; ++i) {
if (pos[array[i].row] == i)
continue;
qp->div = isl_mat_swap_rows(qp->div, i, pos[array[i].row]);
pos[at[i]] = pos[array[i].row];
at[pos[array[i].row]] = at[i];
at[i] = array[i].row;
pos[array[i].row] = i;
}
skip = 0;
for (i = 0; i < len - div_pos; ++i) {
if (i > 0 &&
isl_seq_eq(qp->div->row[i - skip - 1],
qp->div->row[i - skip], qp->div->n_col)) {
qp->div = isl_mat_drop_rows(qp->div, i - skip, 1);
isl_mat_col_add(qp->div, 2 + div_pos + i - skip - 1,
2 + div_pos + i - skip);
qp->div = isl_mat_drop_cols(qp->div,
2 + div_pos + i - skip, 1);
skip++;
}
reordering[div_pos + array[i].row] = div_pos + i - skip;
}
qp->upoly = reorder(qp->upoly, reordering);
if (!qp->upoly || !qp->div)
goto error;
free(at);
free(pos);
free(array);
free(reordering);
return qp;
error:
free(at);
free(pos);
free(array);
free(reordering);
isl_qpolynomial_free(qp);
return NULL;
}
static __isl_give struct isl_upoly *expand(__isl_take struct isl_upoly *up,
int *exp, int first)
{
int i;
struct isl_upoly_rec *rec;
if (isl_upoly_is_cst(up))
return up;
if (up->var < first)
return up;
if (exp[up->var - first] == up->var - first)
return up;
up = isl_upoly_cow(up);
if (!up)
goto error;
up->var = exp[up->var - first] + first;
rec = isl_upoly_as_rec(up);
if (!rec)
goto error;
for (i = 0; i < rec->n; ++i) {
rec->p[i] = expand(rec->p[i], exp, first);
if (!rec->p[i])
goto error;
}
return up;
error:
isl_upoly_free(up);
return NULL;
}
static __isl_give isl_qpolynomial *with_merged_divs(
__isl_give isl_qpolynomial *(*fn)(__isl_take isl_qpolynomial *qp1,
__isl_take isl_qpolynomial *qp2),
__isl_take isl_qpolynomial *qp1, __isl_take isl_qpolynomial *qp2)
{
int *exp1 = NULL;
int *exp2 = NULL;
isl_mat *div = NULL;
qp1 = isl_qpolynomial_cow(qp1);
qp2 = isl_qpolynomial_cow(qp2);
if (!qp1 || !qp2)
goto error;
isl_assert(qp1->div->ctx, qp1->div->n_row >= qp2->div->n_row &&
qp1->div->n_col >= qp2->div->n_col, goto error);
exp1 = isl_alloc_array(qp1->div->ctx, int, qp1->div->n_row);
exp2 = isl_alloc_array(qp2->div->ctx, int, qp2->div->n_row);
if (!exp1 || !exp2)
goto error;
div = isl_merge_divs(qp1->div, qp2->div, exp1, exp2);
if (!div)
goto error;
isl_mat_free(qp1->div);
qp1->div = isl_mat_copy(div);
isl_mat_free(qp2->div);
qp2->div = isl_mat_copy(div);
qp1->upoly = expand(qp1->upoly, exp1, div->n_col - div->n_row - 2);
qp2->upoly = expand(qp2->upoly, exp2, div->n_col - div->n_row - 2);
if (!qp1->upoly || !qp2->upoly)
goto error;
isl_mat_free(div);
free(exp1);
free(exp2);
return fn(qp1, qp2);
error:
isl_mat_free(div);
free(exp1);
free(exp2);
isl_qpolynomial_free(qp1);
isl_qpolynomial_free(qp2);
return NULL;
}
__isl_give isl_qpolynomial *isl_qpolynomial_add(__isl_take isl_qpolynomial *qp1,
__isl_take isl_qpolynomial *qp2)
{
qp1 = isl_qpolynomial_cow(qp1);
if (!qp1 || !qp2)
goto error;
if (qp1->div->n_row < qp2->div->n_row)
return isl_qpolynomial_add(qp2, qp1);
isl_assert(qp1->dim->ctx, isl_space_is_equal(qp1->dim, qp2->dim), goto error);
if (!compatible_divs(qp1->div, qp2->div))
return with_merged_divs(isl_qpolynomial_add, qp1, qp2);
qp1->upoly = isl_upoly_sum(qp1->upoly, isl_upoly_copy(qp2->upoly));
if (!qp1->upoly)
goto error;
isl_qpolynomial_free(qp2);
return qp1;
error:
isl_qpolynomial_free(qp1);
isl_qpolynomial_free(qp2);
return NULL;
}
__isl_give isl_qpolynomial *isl_qpolynomial_add_on_domain(
__isl_keep isl_set *dom,
__isl_take isl_qpolynomial *qp1,
__isl_take isl_qpolynomial *qp2)
{
qp1 = isl_qpolynomial_add(qp1, qp2);
qp1 = isl_qpolynomial_gist(qp1, isl_set_copy(dom));
return qp1;
}
__isl_give isl_qpolynomial *isl_qpolynomial_sub(__isl_take isl_qpolynomial *qp1,
__isl_take isl_qpolynomial *qp2)
{
return isl_qpolynomial_add(qp1, isl_qpolynomial_neg(qp2));
}
__isl_give isl_qpolynomial *isl_qpolynomial_add_isl_int(
__isl_take isl_qpolynomial *qp, isl_int v)
{
if (isl_int_is_zero(v))
return qp;
qp = isl_qpolynomial_cow(qp);
if (!qp)
return NULL;
qp->upoly = isl_upoly_add_isl_int(qp->upoly, v);
if (!qp->upoly)
goto error;
return qp;
error:
isl_qpolynomial_free(qp);
return NULL;
}
__isl_give isl_qpolynomial *isl_qpolynomial_neg(__isl_take isl_qpolynomial *qp)
{
if (!qp)
return NULL;
return isl_qpolynomial_mul_isl_int(qp, qp->dim->ctx->negone);
}
__isl_give isl_qpolynomial *isl_qpolynomial_mul_isl_int(
__isl_take isl_qpolynomial *qp, isl_int v)
{
if (isl_int_is_one(v))
return qp;
if (qp && isl_int_is_zero(v)) {
isl_qpolynomial *zero;
zero = isl_qpolynomial_zero_on_domain(isl_space_copy(qp->dim));
isl_qpolynomial_free(qp);
return zero;
}
qp = isl_qpolynomial_cow(qp);
if (!qp)
return NULL;
qp->upoly = isl_upoly_mul_isl_int(qp->upoly, v);
if (!qp->upoly)
goto error;
return qp;
error:
isl_qpolynomial_free(qp);
return NULL;
}
__isl_give isl_qpolynomial *isl_qpolynomial_scale(
__isl_take isl_qpolynomial *qp, isl_int v)
{
return isl_qpolynomial_mul_isl_int(qp, v);
}
__isl_give isl_qpolynomial *isl_qpolynomial_mul(__isl_take isl_qpolynomial *qp1,
__isl_take isl_qpolynomial *qp2)
{
qp1 = isl_qpolynomial_cow(qp1);
if (!qp1 || !qp2)
goto error;
if (qp1->div->n_row < qp2->div->n_row)
return isl_qpolynomial_mul(qp2, qp1);
isl_assert(qp1->dim->ctx, isl_space_is_equal(qp1->dim, qp2->dim), goto error);
if (!compatible_divs(qp1->div, qp2->div))
return with_merged_divs(isl_qpolynomial_mul, qp1, qp2);
qp1->upoly = isl_upoly_mul(qp1->upoly, isl_upoly_copy(qp2->upoly));
if (!qp1->upoly)
goto error;
isl_qpolynomial_free(qp2);
return qp1;
error:
isl_qpolynomial_free(qp1);
isl_qpolynomial_free(qp2);
return NULL;
}
__isl_give isl_qpolynomial *isl_qpolynomial_pow(__isl_take isl_qpolynomial *qp,
unsigned power)
{
qp = isl_qpolynomial_cow(qp);
if (!qp)
return NULL;
qp->upoly = isl_upoly_pow(qp->upoly, power);
if (!qp->upoly)
goto error;
return qp;
error:
isl_qpolynomial_free(qp);
return NULL;
}
__isl_give isl_pw_qpolynomial *isl_pw_qpolynomial_pow(
__isl_take isl_pw_qpolynomial *pwqp, unsigned power)
{
int i;
if (power == 1)
return pwqp;
pwqp = isl_pw_qpolynomial_cow(pwqp);
if (!pwqp)
return NULL;
for (i = 0; i < pwqp->n; ++i) {
pwqp->p[i].qp = isl_qpolynomial_pow(pwqp->p[i].qp, power);
if (!pwqp->p[i].qp)
return isl_pw_qpolynomial_free(pwqp);
}
return pwqp;
}
__isl_give isl_qpolynomial *isl_qpolynomial_zero_on_domain(
__isl_take isl_space *dim)
{
if (!dim)
return NULL;
return isl_qpolynomial_alloc(dim, 0, isl_upoly_zero(dim->ctx));
}
__isl_give isl_qpolynomial *isl_qpolynomial_one_on_domain(
__isl_take isl_space *dim)
{
if (!dim)
return NULL;
return isl_qpolynomial_alloc(dim, 0, isl_upoly_one(dim->ctx));
}
__isl_give isl_qpolynomial *isl_qpolynomial_infty_on_domain(
__isl_take isl_space *dim)
{
if (!dim)
return NULL;
return isl_qpolynomial_alloc(dim, 0, isl_upoly_infty(dim->ctx));
}
__isl_give isl_qpolynomial *isl_qpolynomial_neginfty_on_domain(
__isl_take isl_space *dim)
{
if (!dim)
return NULL;
return isl_qpolynomial_alloc(dim, 0, isl_upoly_neginfty(dim->ctx));
}
__isl_give isl_qpolynomial *isl_qpolynomial_nan_on_domain(
__isl_take isl_space *dim)
{
if (!dim)
return NULL;
return isl_qpolynomial_alloc(dim, 0, isl_upoly_nan(dim->ctx));
}
__isl_give isl_qpolynomial *isl_qpolynomial_cst_on_domain(
__isl_take isl_space *dim,
isl_int v)
{
struct isl_qpolynomial *qp;
struct isl_upoly_cst *cst;
if (!dim)
return NULL;
qp = isl_qpolynomial_alloc(dim, 0, isl_upoly_zero(dim->ctx));
if (!qp)
return NULL;
cst = isl_upoly_as_cst(qp->upoly);
isl_int_set(cst->n, v);
return qp;
}
int isl_qpolynomial_is_cst(__isl_keep isl_qpolynomial *qp,
isl_int *n, isl_int *d)
{
struct isl_upoly_cst *cst;
if (!qp)
return -1;
if (!isl_upoly_is_cst(qp->upoly))
return 0;
cst = isl_upoly_as_cst(qp->upoly);
if (!cst)
return -1;
if (n)
isl_int_set(*n, cst->n);
if (d)
isl_int_set(*d, cst->d);
return 1;
}
int isl_upoly_is_affine(__isl_keep struct isl_upoly *up)
{
int is_cst;
struct isl_upoly_rec *rec;
if (!up)
return -1;
if (up->var < 0)
return 1;
rec = isl_upoly_as_rec(up);
if (!rec)
return -1;
if (rec->n > 2)
return 0;
isl_assert(up->ctx, rec->n > 1, return -1);
is_cst = isl_upoly_is_cst(rec->p[1]);
if (is_cst < 0)
return -1;
if (!is_cst)
return 0;
return isl_upoly_is_affine(rec->p[0]);
}
int isl_qpolynomial_is_affine(__isl_keep isl_qpolynomial *qp)
{
if (!qp)
return -1;
if (qp->div->n_row > 0)
return 0;
return isl_upoly_is_affine(qp->upoly);
}
static void update_coeff(__isl_keep isl_vec *aff,
__isl_keep struct isl_upoly_cst *cst, int pos)
{
isl_int gcd;
isl_int f;
if (isl_int_is_zero(cst->n))
return;
isl_int_init(gcd);
isl_int_init(f);
isl_int_gcd(gcd, cst->d, aff->el[0]);
isl_int_divexact(f, cst->d, gcd);
isl_int_divexact(gcd, aff->el[0], gcd);
isl_seq_scale(aff->el, aff->el, f, aff->size);
isl_int_mul(aff->el[1 + pos], gcd, cst->n);
isl_int_clear(gcd);
isl_int_clear(f);
}
int isl_upoly_update_affine(__isl_keep struct isl_upoly *up,
__isl_keep isl_vec *aff)
{
struct isl_upoly_cst *cst;
struct isl_upoly_rec *rec;
if (!up || !aff)
return -1;
if (up->var < 0) {
struct isl_upoly_cst *cst;
cst = isl_upoly_as_cst(up);
if (!cst)
return -1;
update_coeff(aff, cst, 0);
return 0;
}
rec = isl_upoly_as_rec(up);
if (!rec)
return -1;
isl_assert(up->ctx, rec->n == 2, return -1);
cst = isl_upoly_as_cst(rec->p[1]);
if (!cst)
return -1;
update_coeff(aff, cst, 1 + up->var);
return isl_upoly_update_affine(rec->p[0], aff);
}
__isl_give isl_vec *isl_qpolynomial_extract_affine(
__isl_keep isl_qpolynomial *qp)
{
isl_vec *aff;
unsigned d;
if (!qp)
return NULL;
d = isl_space_dim(qp->dim, isl_dim_all);
aff = isl_vec_alloc(qp->div->ctx, 2 + d + qp->div->n_row);
if (!aff)
return NULL;
isl_seq_clr(aff->el + 1, 1 + d + qp->div->n_row);
isl_int_set_si(aff->el[0], 1);
if (isl_upoly_update_affine(qp->upoly, aff) < 0)
goto error;
return aff;
error:
isl_vec_free(aff);
return NULL;
}
int isl_qpolynomial_plain_is_equal(__isl_keep isl_qpolynomial *qp1,
__isl_keep isl_qpolynomial *qp2)
{
int equal;
if (!qp1 || !qp2)
return -1;
equal = isl_space_is_equal(qp1->dim, qp2->dim);
if (equal < 0 || !equal)
return equal;
equal = isl_mat_is_equal(qp1->div, qp2->div);
if (equal < 0 || !equal)
return equal;
return isl_upoly_is_equal(qp1->upoly, qp2->upoly);
}
static void upoly_update_den(__isl_keep struct isl_upoly *up, isl_int *d)
{
int i;
struct isl_upoly_rec *rec;
if (isl_upoly_is_cst(up)) {
struct isl_upoly_cst *cst;
cst = isl_upoly_as_cst(up);
if (!cst)
return;
isl_int_lcm(*d, *d, cst->d);
return;
}
rec = isl_upoly_as_rec(up);
if (!rec)
return;
for (i = 0; i < rec->n; ++i)
upoly_update_den(rec->p[i], d);
}
void isl_qpolynomial_get_den(__isl_keep isl_qpolynomial *qp, isl_int *d)
{
isl_int_set_si(*d, 1);
if (!qp)
return;
upoly_update_den(qp->upoly, d);
}
__isl_give isl_qpolynomial *isl_qpolynomial_var_pow_on_domain(
__isl_take isl_space *dim, int pos, int power)
{
struct isl_ctx *ctx;
if (!dim)
return NULL;
ctx = dim->ctx;
return isl_qpolynomial_alloc(dim, 0, isl_upoly_var_pow(ctx, pos, power));
}
__isl_give isl_qpolynomial *isl_qpolynomial_var_on_domain(__isl_take isl_space *dim,
enum isl_dim_type type, unsigned pos)
{
if (!dim)
return NULL;
isl_assert(dim->ctx, isl_space_dim(dim, isl_dim_in) == 0, goto error);
isl_assert(dim->ctx, pos < isl_space_dim(dim, type), goto error);
if (type == isl_dim_set)
pos += isl_space_dim(dim, isl_dim_param);
return isl_qpolynomial_var_pow_on_domain(dim, pos, 1);
error:
isl_space_free(dim);
return NULL;
}
__isl_give struct isl_upoly *isl_upoly_subs(__isl_take struct isl_upoly *up,
unsigned first, unsigned n, __isl_keep struct isl_upoly **subs)
{
int i;
struct isl_upoly_rec *rec;
struct isl_upoly *base, *res;
if (!up)
return NULL;
if (isl_upoly_is_cst(up))
return up;
if (up->var < first)
return up;
rec = isl_upoly_as_rec(up);
if (!rec)
goto error;
isl_assert(up->ctx, rec->n >= 1, goto error);
if (up->var >= first + n)
base = isl_upoly_var_pow(up->ctx, up->var, 1);
else
base = isl_upoly_copy(subs[up->var - first]);
res = isl_upoly_subs(isl_upoly_copy(rec->p[rec->n - 1]), first, n, subs);
for (i = rec->n - 2; i >= 0; --i) {
struct isl_upoly *t;
t = isl_upoly_subs(isl_upoly_copy(rec->p[i]), first, n, subs);
res = isl_upoly_mul(res, isl_upoly_copy(base));
res = isl_upoly_sum(res, t);
}
isl_upoly_free(base);
isl_upoly_free(up);
return res;
error:
isl_upoly_free(up);
return NULL;
}
__isl_give struct isl_upoly *isl_upoly_from_affine(isl_ctx *ctx, isl_int *f,
isl_int denom, unsigned len)
{
int i;
struct isl_upoly *up;
isl_assert(ctx, len >= 1, return NULL);
up = isl_upoly_rat_cst(ctx, f[0], denom);
for (i = 0; i < len - 1; ++i) {
struct isl_upoly *t;
struct isl_upoly *c;
if (isl_int_is_zero(f[1 + i]))
continue;
c = isl_upoly_rat_cst(ctx, f[1 + i], denom);
t = isl_upoly_var_pow(ctx, i, 1);
t = isl_upoly_mul(c, t);
up = isl_upoly_sum(up, t);
}
return up;
}
/* Remove common factor of non-constant terms and denominator.
*/
static void normalize_div(__isl_keep isl_qpolynomial *qp, int div)
{
isl_ctx *ctx = qp->div->ctx;
unsigned total = qp->div->n_col - 2;
isl_seq_gcd(qp->div->row[div] + 2, total, &ctx->normalize_gcd);
isl_int_gcd(ctx->normalize_gcd,
ctx->normalize_gcd, qp->div->row[div][0]);
if (isl_int_is_one(ctx->normalize_gcd))
return;
isl_seq_scale_down(qp->div->row[div] + 2, qp->div->row[div] + 2,
ctx->normalize_gcd, total);
isl_int_divexact(qp->div->row[div][0], qp->div->row[div][0],
ctx->normalize_gcd);
isl_int_fdiv_q(qp->div->row[div][1], qp->div->row[div][1],
ctx->normalize_gcd);
}
/* Replace the integer division identified by "div" by the polynomial "s".
* The integer division is assumed not to appear in the definition
* of any other integer divisions.
*/
static __isl_give isl_qpolynomial *substitute_div(
__isl_take isl_qpolynomial *qp,
int div, __isl_take struct isl_upoly *s)
{
int i;
int total;
int *reordering;
if (!qp || !s)
goto error;
qp = isl_qpolynomial_cow(qp);
if (!qp)
goto error;
total = isl_space_dim(qp->dim, isl_dim_all);
qp->upoly = isl_upoly_subs(qp->upoly, total + div, 1, &s);
if (!qp->upoly)
goto error;
reordering = isl_alloc_array(qp->dim->ctx, int, total + qp->div->n_row);
if (!reordering)
goto error;
for (i = 0; i < total + div; ++i)
reordering[i] = i;
for (i = total + div + 1; i < total + qp->div->n_row; ++i)
reordering[i] = i - 1;
qp->div = isl_mat_drop_rows(qp->div, div, 1);
qp->div = isl_mat_drop_cols(qp->div, 2 + total + div, 1);
qp->upoly = reorder(qp->upoly, reordering);
free(reordering);
if (!qp->upoly || !qp->div)
goto error;
isl_upoly_free(s);
return qp;
error:
isl_qpolynomial_free(qp);
isl_upoly_free(s);
return NULL;
}
/* Replace all integer divisions [e/d] that turn out to not actually be integer
* divisions because d is equal to 1 by their definition, i.e., e.
*/
static __isl_give isl_qpolynomial *substitute_non_divs(
__isl_take isl_qpolynomial *qp)
{
int i, j;
int total;
struct isl_upoly *s;
if (!qp)
return NULL;
total = isl_space_dim(qp->dim, isl_dim_all);
for (i = 0; qp && i < qp->div->n_row; ++i) {
if (!isl_int_is_one(qp->div->row[i][0]))
continue;
for (j = i + 1; j < qp->div->n_row; ++j) {
if (isl_int_is_zero(qp->div->row[j][2 + total + i]))
continue;
isl_seq_combine(qp->div->row[j] + 1,
qp->div->ctx->one, qp->div->row[j] + 1,
qp->div->row[j][2 + total + i],
qp->div->row[i] + 1, 1 + total + i);
isl_int_set_si(qp->div->row[j][2 + total + i], 0);
normalize_div(qp, j);
}
s = isl_upoly_from_affine(qp->dim->ctx, qp->div->row[i] + 1,
qp->div->row[i][0], qp->div->n_col - 1);
qp = substitute_div(qp, i, s);
--i;
}
return qp;
}
/* Reduce the coefficients of div "div" to lie in the interval [0, d-1],
* with d the denominator. When replacing the coefficient e of x by
* d * frac(e/d) = e - d * floor(e/d), we are subtracting d * floor(e/d) * x
* inside the division, so we need to add floor(e/d) * x outside.
* That is, we replace q by q' + floor(e/d) * x and we therefore need
* to adjust the coefficient of x in each later div that depends on the
* current div "div" and also in the affine expression "aff"
* (if it too depends on "div").
*/
static void reduce_div(__isl_keep isl_qpolynomial *qp, int div,
__isl_keep isl_vec *aff)
{
int i, j;
isl_int v;
unsigned total = qp->div->n_col - qp->div->n_row - 2;
isl_int_init(v);
for (i = 0; i < 1 + total + div; ++i) {
if (isl_int_is_nonneg(qp->div->row[div][1 + i]) &&
isl_int_lt(qp->div->row[div][1 + i], qp->div->row[div][0]))
continue;
isl_int_fdiv_q(v, qp->div->row[div][1 + i], qp->div->row[div][0]);
isl_int_fdiv_r(qp->div->row[div][1 + i],
qp->div->row[div][1 + i], qp->div->row[div][0]);
if (!isl_int_is_zero(aff->el[1 + total + div]))
isl_int_addmul(aff->el[i], v, aff->el[1 + total + div]);
for (j = div + 1; j < qp->div->n_row; ++j) {
if (isl_int_is_zero(qp->div->row[j][2 + total + div]))
continue;
isl_int_addmul(qp->div->row[j][1 + i],
v, qp->div->row[j][2 + total + div]);
}
}
isl_int_clear(v);
}
/* Check if the last non-zero coefficient is bigger that half of the
* denominator. If so, we will invert the div to further reduce the number
* of distinct divs that may appear.
* If the last non-zero coefficient is exactly half the denominator,
* then we continue looking for earlier coefficients that are bigger
* than half the denominator.
*/
static int needs_invert(__isl_keep isl_mat *div, int row)
{
int i;
int cmp;
for (i = div->n_col - 1; i >= 1; --i) {
if (isl_int_is_zero(div->row[row][i]))
continue;
isl_int_mul_ui(div->row[row][i], div->row[row][i], 2);
cmp = isl_int_cmp(div->row[row][i], div->row[row][0]);
isl_int_divexact_ui(div->row[row][i], div->row[row][i], 2);
if (cmp)
return cmp > 0;
if (i == 1)
return 1;
}
return 0;
}
/* Replace div "div" q = [e/d] by -[(-e+(d-1))/d].
* We only invert the coefficients of e (and the coefficient of q in
* later divs and in "aff"). After calling this function, the
* coefficients of e should be reduced again.
*/
static void invert_div(__isl_keep isl_qpolynomial *qp, int div,
__isl_keep isl_vec *aff)
{
unsigned total = qp->div->n_col - qp->div->n_row - 2;
isl_seq_neg(qp->div->row[div] + 1,
qp->div->row[div] + 1, qp->div->n_col - 1);
isl_int_sub_ui(qp->div->row[div][1], qp->div->row[div][1], 1);
isl_int_add(qp->div->row[div][1],
qp->div->row[div][1], qp->div->row[div][0]);
if (!isl_int_is_zero(aff->el[1 + total + div]))
isl_int_neg(aff->el[1 + total + div], aff->el[1 + total + div]);
isl_mat_col_mul(qp->div, 2 + total + div,
qp->div->ctx->negone, 2 + total + div);
}
/* Assuming "qp" is a monomial, reduce all its divs to have coefficients
* in the interval [0, d-1], with d the denominator and such that the
* last non-zero coefficient that is not equal to d/2 is smaller than d/2.
*
* After the reduction, some divs may have become redundant or identical,
* so we call substitute_non_divs and sort_divs. If these functions
* eliminate divs or merge two or more divs into one, the coefficients
* of the enclosing divs may have to be reduced again, so we call
* ourselves recursively if the number of divs decreases.
*/
static __isl_give isl_qpolynomial *reduce_divs(__isl_take isl_qpolynomial *qp)
{
int i;
isl_vec *aff = NULL;
struct isl_upoly *s;
unsigned n_div;
if (!qp)
return NULL;
aff = isl_vec_alloc(qp->div->ctx, qp->div->n_col - 1);
aff = isl_vec_clr(aff);
if (!aff)
goto error;
isl_int_set_si(aff->el[1 + qp->upoly->var], 1);
for (i = 0; i < qp->div->n_row; ++i) {
normalize_div(qp, i);
reduce_div(qp, i, aff);
if (needs_invert(qp->div, i)) {
invert_div(qp, i, aff);
reduce_div(qp, i, aff);
}
}
s = isl_upoly_from_affine(qp->div->ctx, aff->el,
qp->div->ctx->one, aff->size);
qp->upoly = isl_upoly_subs(qp->upoly, qp->upoly->var, 1, &s);
isl_upoly_free(s);
if (!qp->upoly)
goto error;
isl_vec_free(aff);
n_div = qp->div->n_row;
qp = substitute_non_divs(qp);
qp = sort_divs(qp);
if (qp && qp->div->n_row < n_div)
return reduce_divs(qp);
return qp;
error:
isl_qpolynomial_free(qp);
isl_vec_free(aff);
return NULL;
}
__isl_give isl_qpolynomial *isl_qpolynomial_rat_cst_on_domain(
__isl_take isl_space *dim, const isl_int n, const isl_int d)
{
struct isl_qpolynomial *qp;
struct isl_upoly_cst *cst;
if (!dim)
return NULL;
qp = isl_qpolynomial_alloc(dim, 0, isl_upoly_zero(dim->ctx));
if (!qp)
return NULL;
cst = isl_upoly_as_cst(qp->upoly);
isl_int_set(cst->n, n);
isl_int_set(cst->d, d);
return qp;
}
static int up_set_active(__isl_keep struct isl_upoly *up, int *active, int d)
{
struct isl_upoly_rec *rec;
int i;
if (!up)
return -1;
if (isl_upoly_is_cst(up))
return 0;
if (up->var < d)
active[up->var] = 1;
rec = isl_upoly_as_rec(up);
for (i = 0; i < rec->n; ++i)
if (up_set_active(rec->p[i], active, d) < 0)
return -1;
return 0;
}
static int set_active(__isl_keep isl_qpolynomial *qp, int *active)
{
int i, j;
int d = isl_space_dim(qp->dim, isl_dim_all);
if (!qp || !active)
return -1;
for (i = 0; i < d; ++i)
for (j = 0; j < qp->div->n_row; ++j) {
if (isl_int_is_zero(qp->div->row[j][2 + i]))
continue;
active[i] = 1;
break;
}
return up_set_active(qp->upoly, active, d);
}
int isl_qpolynomial_involves_dims(__isl_keep isl_qpolynomial *qp,
enum isl_dim_type type, unsigned first, unsigned n)
{
int i;
int *active = NULL;
int involves = 0;
if (!qp)
return -1;
if (n == 0)
return 0;
isl_assert(qp->dim->ctx,
first + n <= isl_qpolynomial_dim(qp, type), return -1);
isl_assert(qp->dim->ctx, type == isl_dim_param ||
type == isl_dim_in, return -1);
active = isl_calloc_array(qp->dim->ctx, int,
isl_space_dim(qp->dim, isl_dim_all));
if (set_active(qp, active) < 0)
goto error;
if (type == isl_dim_in)
first += isl_space_dim(qp->dim, isl_dim_param);
for (i = 0; i < n; ++i)
if (active[first + i]) {
involves = 1;
break;
}
free(active);
return involves;
error:
free(active);
return -1;
}
/* Remove divs that do not appear in the quasi-polynomial, nor in any
* of the divs that do appear in the quasi-polynomial.
*/
static __isl_give isl_qpolynomial *remove_redundant_divs(
__isl_take isl_qpolynomial *qp)
{
int i, j;
int d;
int len;
int skip;
int *active = NULL;
int *reordering = NULL;
int redundant = 0;
int n_div;
isl_ctx *ctx;
if (!qp)
return NULL;
if (qp->div->n_row == 0)
return qp;
d = isl_space_dim(qp->dim, isl_dim_all);
len = qp->div->n_col - 2;
ctx = isl_qpolynomial_get_ctx(qp);
active = isl_calloc_array(ctx, int, len);
if (!active)
goto error;
if (up_set_active(qp->upoly, active, len) < 0)
goto error;
for (i = qp->div->n_row - 1; i >= 0; --i) {
if (!active[d + i]) {
redundant = 1;
continue;
}
for (j = 0; j < i; ++j) {
if (isl_int_is_zero(qp->div->row[i][2 + d + j]))
continue;
active[d + j] = 1;
break;
}
}
if (!redundant) {
free(active);
return qp;
}
reordering = isl_alloc_array(qp->div->ctx, int, len);
if (!reordering)
goto error;
for (i = 0; i < d; ++i)
reordering[i] = i;
skip = 0;
n_div = qp->div->n_row;
for (i = 0; i < n_div; ++i) {
if (!active[d + i]) {
qp->div = isl_mat_drop_rows(qp->div, i - skip, 1);
qp->div = isl_mat_drop_cols(qp->div,
2 + d + i - skip, 1);
skip++;
}
reordering[d + i] = d + i - skip;
}
qp->upoly = reorder(qp->upoly, reordering);
if (!qp->upoly || !qp->div)
goto error;
free(active);
free(reordering);
return qp;
error:
free(active);
free(reordering);
isl_qpolynomial_free(qp);
return NULL;
}
__isl_give struct isl_upoly *isl_upoly_drop(__isl_take struct isl_upoly *up,
unsigned first, unsigned n)
{
int i;
struct isl_upoly_rec *rec;
if (!up)
return NULL;
if (n == 0 || up->var < 0 || up->var < first)
return up;
if (up->var < first + n) {
up = replace_by_constant_term(up);
return isl_upoly_drop(up, first, n);
}
up = isl_upoly_cow(up);
if (!up)
return NULL;
up->var -= n;
rec = isl_upoly_as_rec(up);
if (!rec)
goto error;
for (i = 0; i < rec->n; ++i) {
rec->p[i] = isl_upoly_drop(rec->p[i], first, n);
if (!rec->p[i])
goto error;
}
return up;
error:
isl_upoly_free(up);
return NULL;
}
__isl_give isl_qpolynomial *isl_qpolynomial_set_dim_name(
__isl_take isl_qpolynomial *qp,
enum isl_dim_type type, unsigned pos, const char *s)
{
qp = isl_qpolynomial_cow(qp);
if (!qp)
return NULL;
qp->dim = isl_space_set_dim_name(qp->dim, type, pos, s);
if (!qp->dim)
goto error;
return qp;
error:
isl_qpolynomial_free(qp);
return NULL;
}
__isl_give isl_qpolynomial *isl_qpolynomial_drop_dims(
__isl_take isl_qpolynomial *qp,
enum isl_dim_type type, unsigned first, unsigned n)
{
if (!qp)
return NULL;
if (type == isl_dim_out)
isl_die(qp->dim->ctx, isl_error_invalid,
"cannot drop output/set dimension",
goto error);
if (type == isl_dim_in)
type = isl_dim_set;
if (n == 0 && !isl_space_is_named_or_nested(qp->dim, type))
return qp;
qp = isl_qpolynomial_cow(qp);
if (!qp)
return NULL;
isl_assert(qp->dim->ctx, first + n <= isl_space_dim(qp->dim, type),
goto error);
isl_assert(qp->dim->ctx, type == isl_dim_param ||
type == isl_dim_set, goto error);
qp->dim = isl_space_drop_dims(qp->dim, type, first, n);
if (!qp->dim)
goto error;
if (type == isl_dim_set)
first += isl_space_dim(qp->dim, isl_dim_param);
qp->div = isl_mat_drop_cols(qp->div, 2 + first, n);
if (!qp->div)
goto error;
qp->upoly = isl_upoly_drop(qp->upoly, first, n);
if (!qp->upoly)
goto error;
return qp;
error:
isl_qpolynomial_free(qp);
return NULL;
}
/* Project the domain of the quasi-polynomial onto its parameter space.
* The quasi-polynomial may not involve any of the domain dimensions.
*/
__isl_give isl_qpolynomial *isl_qpolynomial_project_domain_on_params(
__isl_take isl_qpolynomial *qp)
{
isl_space *space;
unsigned n;
int involves;
n = isl_qpolynomial_dim(qp, isl_dim_in);
involves = isl_qpolynomial_involves_dims(qp, isl_dim_in, 0, n);
if (involves < 0)
return isl_qpolynomial_free(qp);
if (involves)
isl_die(isl_qpolynomial_get_ctx(qp), isl_error_invalid,
"polynomial involves some of the domain dimensions",
return isl_qpolynomial_free(qp));
qp = isl_qpolynomial_drop_dims(qp, isl_dim_in, 0, n);
space = isl_qpolynomial_get_domain_space(qp);
space = isl_space_params(space);
qp = isl_qpolynomial_reset_domain_space(qp, space);
return qp;
}
static __isl_give isl_qpolynomial *isl_qpolynomial_substitute_equalities_lifted(
__isl_take isl_qpolynomial *qp, __isl_take isl_basic_set *eq)
{
int i, j, k;
isl_int denom;
unsigned total;
unsigned n_div;
struct isl_upoly *up;
if (!eq)
goto error;
if (eq->n_eq == 0) {
isl_basic_set_free(eq);
return qp;
}
qp = isl_qpolynomial_cow(qp);
if (!qp)
goto error;
qp->div = isl_mat_cow(qp->div);
if (!qp->div)
goto error;
total = 1 + isl_space_dim(eq->dim, isl_dim_all);
n_div = eq->n_div;
isl_int_init(denom);
for (i = 0; i < eq->n_eq; ++i) {
j = isl_seq_last_non_zero(eq->eq[i], total + n_div);
if (j < 0 || j == 0 || j >= total)
continue;
for (k = 0; k < qp->div->n_row; ++k) {
if (isl_int_is_zero(qp->div->row[k][1 + j]))
continue;
isl_seq_elim(qp->div->row[k] + 1, eq->eq[i], j, total,
&qp->div->row[k][0]);
normalize_div(qp, k);
}
if (isl_int_is_pos(eq->eq[i][j]))
isl_seq_neg(eq->eq[i], eq->eq[i], total);
isl_int_abs(denom, eq->eq[i][j]);
isl_int_set_si(eq->eq[i][j], 0);
up = isl_upoly_from_affine(qp->dim->ctx,
eq->eq[i], denom, total);
qp->upoly = isl_upoly_subs(qp->upoly, j - 1, 1, &up);
isl_upoly_free(up);
}
isl_int_clear(denom);
if (!qp->upoly)
goto error;
isl_basic_set_free(eq);
qp = substitute_non_divs(qp);
qp = sort_divs(qp);
return qp;
error:
isl_basic_set_free(eq);
isl_qpolynomial_free(qp);
return NULL;
}
/* Exploit the equalities in "eq" to simplify the quasi-polynomial.
*/
__isl_give isl_qpolynomial *isl_qpolynomial_substitute_equalities(
__isl_take isl_qpolynomial *qp, __isl_take isl_basic_set *eq)
{
if (!qp || !eq)
goto error;
if (qp->div->n_row > 0)
eq = isl_basic_set_add(eq, isl_dim_set, qp->div->n_row);
return isl_qpolynomial_substitute_equalities_lifted(qp, eq);
error:
isl_basic_set_free(eq);
isl_qpolynomial_free(qp);
return NULL;
}
static __isl_give isl_basic_set *add_div_constraints(
__isl_take isl_basic_set *bset, __isl_take isl_mat *div)
{
int i;
unsigned total;
if (!bset || !div)
goto error;
bset = isl_basic_set_extend_constraints(bset, 0, 2 * div->n_row);
if (!bset)
goto error;
total = isl_basic_set_total_dim(bset);
for (i = 0; i < div->n_row; ++i)
if (isl_basic_set_add_div_constraints_var(bset,
total - div->n_row + i, div->row[i]) < 0)
goto error;
isl_mat_free(div);
return bset;
error:
isl_mat_free(div);
isl_basic_set_free(bset);
return NULL;
}
/* Look for equalities among the variables shared by context and qp
* and the integer divisions of qp, if any.
* The equalities are then used to eliminate variables and/or integer
* divisions from qp.
*/
__isl_give isl_qpolynomial *isl_qpolynomial_gist(
__isl_take isl_qpolynomial *qp, __isl_take isl_set *context)
{
isl_basic_set *aff;
if (!qp)
goto error;
if (qp->div->n_row > 0) {
isl_basic_set *bset;
context = isl_set_add_dims(context, isl_dim_set,
qp->div->n_row);
bset = isl_basic_set_universe(isl_set_get_space(context));
bset = add_div_constraints(bset, isl_mat_copy(qp->div));
context = isl_set_intersect(context,
isl_set_from_basic_set(bset));
}
aff = isl_set_affine_hull(context);
return isl_qpolynomial_substitute_equalities_lifted(qp, aff);
error:
isl_qpolynomial_free(qp);
isl_set_free(context);
return NULL;
}
__isl_give isl_qpolynomial *isl_qpolynomial_gist_params(
__isl_take isl_qpolynomial *qp, __isl_take isl_set *context)
{
isl_space *space = isl_qpolynomial_get_domain_space(qp);
isl_set *dom_context = isl_set_universe(space);
dom_context = isl_set_intersect_params(dom_context, context);
return isl_qpolynomial_gist(qp, dom_context);
}
__isl_give isl_pw_qpolynomial *isl_pw_qpolynomial_from_qpolynomial(
__isl_take isl_qpolynomial *qp)
{
isl_set *dom;
if (!qp)
return NULL;
if (isl_qpolynomial_is_zero(qp)) {
isl_space *dim = isl_qpolynomial_get_space(qp);
isl_qpolynomial_free(qp);
return isl_pw_qpolynomial_zero(dim);
}
dom = isl_set_universe(isl_qpolynomial_get_domain_space(qp));
return isl_pw_qpolynomial_alloc(dom, qp);
}
#undef PW
#define PW isl_pw_qpolynomial
#undef EL
#define EL isl_qpolynomial
#undef EL_IS_ZERO
#define EL_IS_ZERO is_zero
#undef ZERO
#define ZERO zero
#undef IS_ZERO
#define IS_ZERO is_zero
#undef FIELD
#define FIELD qp
#undef DEFAULT_IS_ZERO
#define DEFAULT_IS_ZERO 1
#include <isl_pw_templ.c>
#undef UNION
#define UNION isl_union_pw_qpolynomial
#undef PART
#define PART isl_pw_qpolynomial
#undef PARTS
#define PARTS pw_qpolynomial
#define ALIGN_DOMAIN
#include <isl_union_templ.c>
int isl_pw_qpolynomial_is_one(__isl_keep isl_pw_qpolynomial *pwqp)
{
if (!pwqp)
return -1;
if (pwqp->n != -1)
return 0;
if (!isl_set_plain_is_universe(pwqp->p[0].set))
return 0;
return isl_qpolynomial_is_one(pwqp->p[0].qp);
}
__isl_give isl_pw_qpolynomial *isl_pw_qpolynomial_add(
__isl_take isl_pw_qpolynomial *pwqp1,
__isl_take isl_pw_qpolynomial *pwqp2)
{
return isl_pw_qpolynomial_union_add_(pwqp1, pwqp2);
}
__isl_give isl_pw_qpolynomial *isl_pw_qpolynomial_mul(
__isl_take isl_pw_qpolynomial *pwqp1,
__isl_take isl_pw_qpolynomial *pwqp2)
{
int i, j, n;
struct isl_pw_qpolynomial *res;
if (!pwqp1 || !pwqp2)
goto error;
isl_assert(pwqp1->dim->ctx, isl_space_is_equal(pwqp1->dim, pwqp2->dim),
goto error);
if (isl_pw_qpolynomial_is_zero(pwqp1)) {
isl_pw_qpolynomial_free(pwqp2);
return pwqp1;
}
if (isl_pw_qpolynomial_is_zero(pwqp2)) {
isl_pw_qpolynomial_free(pwqp1);
return pwqp2;
}
if (isl_pw_qpolynomial_is_one(pwqp1)) {
isl_pw_qpolynomial_free(pwqp1);
return pwqp2;
}
if (isl_pw_qpolynomial_is_one(pwqp2)) {
isl_pw_qpolynomial_free(pwqp2);
return pwqp1;
}
n = pwqp1->n * pwqp2->n;
res = isl_pw_qpolynomial_alloc_size(isl_space_copy(pwqp1->dim), n);
for (i = 0; i < pwqp1->n; ++i) {
for (j = 0; j < pwqp2->n; ++j) {
struct isl_set *common;
struct isl_qpolynomial *prod;
common = isl_set_intersect(isl_set_copy(pwqp1->p[i].set),
isl_set_copy(pwqp2->p[j].set));
if (isl_set_plain_is_empty(common)) {
isl_set_free(common);
continue;
}
prod = isl_qpolynomial_mul(
isl_qpolynomial_copy(pwqp1->p[i].qp),
isl_qpolynomial_copy(pwqp2->p[j].qp));
res = isl_pw_qpolynomial_add_piece(res, common, prod);
}
}
isl_pw_qpolynomial_free(pwqp1);
isl_pw_qpolynomial_free(pwqp2);
return res;
error:
isl_pw_qpolynomial_free(pwqp1);
isl_pw_qpolynomial_free(pwqp2);
return NULL;
}
__isl_give struct isl_upoly *isl_upoly_eval(
__isl_take struct isl_upoly *up, __isl_take isl_vec *vec)
{
int i;
struct isl_upoly_rec *rec;
struct isl_upoly *res;
struct isl_upoly *base;
if (isl_upoly_is_cst(up)) {
isl_vec_free(vec);
return up;
}
rec = isl_upoly_as_rec(up);
if (!rec)
goto error;
isl_assert(up->ctx, rec->n >= 1, goto error);
base = isl_upoly_rat_cst(up->ctx, vec->el[1 + up->var], vec->el[0]);
res = isl_upoly_eval(isl_upoly_copy(rec->p[rec->n - 1]),
isl_vec_copy(vec));
for (i = rec->n - 2; i >= 0; --i) {
res = isl_upoly_mul(res, isl_upoly_copy(base));
res = isl_upoly_sum(res,
isl_upoly_eval(isl_upoly_copy(rec->p[i]),
isl_vec_copy(vec)));
}
isl_upoly_free(base);
isl_upoly_free(up);
isl_vec_free(vec);
return res;
error:
isl_upoly_free(up);
isl_vec_free(vec);
return NULL;
}
__isl_give isl_qpolynomial *isl_qpolynomial_eval(
__isl_take isl_qpolynomial *qp, __isl_take isl_point *pnt)
{
isl_vec *ext;
struct isl_upoly *up;
isl_space *dim;
if (!qp || !pnt)
goto error;
isl_assert(pnt->dim->ctx, isl_space_is_equal(pnt->dim, qp->dim), goto error);
if (qp->div->n_row == 0)
ext = isl_vec_copy(pnt->vec);
else {
int i;
unsigned dim = isl_space_dim(qp->dim, isl_dim_all);
ext = isl_vec_alloc(qp->dim->ctx, 1 + dim + qp->div->n_row);
if (!ext)
goto error;
isl_seq_cpy(ext->el, pnt->vec->el, pnt->vec->size);
for (i = 0; i < qp->div->n_row; ++i) {
isl_seq_inner_product(qp->div->row[i] + 1, ext->el,
1 + dim + i, &ext->el[1+dim+i]);
isl_int_fdiv_q(ext->el[1+dim+i], ext->el[1+dim+i],
qp->div->row[i][0]);
}
}
up = isl_upoly_eval(isl_upoly_copy(qp->upoly), ext);
if (!up)
goto error;
dim = isl_space_copy(qp->dim);
isl_qpolynomial_free(qp);
isl_point_free(pnt);
return isl_qpolynomial_alloc(dim, 0, up);
error:
isl_qpolynomial_free(qp);
isl_point_free(pnt);
return NULL;
}
int isl_upoly_cmp(__isl_keep struct isl_upoly_cst *cst1,
__isl_keep struct isl_upoly_cst *cst2)
{
int cmp;
isl_int t;
isl_int_init(t);
isl_int_mul(t, cst1->n, cst2->d);
isl_int_submul(t, cst2->n, cst1->d);
cmp = isl_int_sgn(t);
isl_int_clear(t);
return cmp;
}
int isl_qpolynomial_le_cst(__isl_keep isl_qpolynomial *qp1,
__isl_keep isl_qpolynomial *qp2)
{
struct isl_upoly_cst *cst1, *cst2;
if (!qp1 || !qp2)
return -1;
isl_assert(qp1->dim->ctx, isl_upoly_is_cst(qp1->upoly), return -1);
isl_assert(qp2->dim->ctx, isl_upoly_is_cst(qp2->upoly), return -1);
if (isl_qpolynomial_is_nan(qp1))
return -1;
if (isl_qpolynomial_is_nan(qp2))
return -1;
cst1 = isl_upoly_as_cst(qp1->upoly);
cst2 = isl_upoly_as_cst(qp2->upoly);
return isl_upoly_cmp(cst1, cst2) <= 0;
}
__isl_give isl_qpolynomial *isl_qpolynomial_min_cst(
__isl_take isl_qpolynomial *qp1, __isl_take isl_qpolynomial *qp2)
{
struct isl_upoly_cst *cst1, *cst2;
int cmp;
if (!qp1 || !qp2)
goto error;
isl_assert(qp1->dim->ctx, isl_upoly_is_cst(qp1->upoly), goto error);
isl_assert(qp2->dim->ctx, isl_upoly_is_cst(qp2->upoly), goto error);
cst1 = isl_upoly_as_cst(qp1->upoly);
cst2 = isl_upoly_as_cst(qp2->upoly);
cmp = isl_upoly_cmp(cst1, cst2);
if (cmp <= 0) {
isl_qpolynomial_free(qp2);
} else {
isl_qpolynomial_free(qp1);
qp1 = qp2;
}
return qp1;
error:
isl_qpolynomial_free(qp1);
isl_qpolynomial_free(qp2);
return NULL;
}
__isl_give isl_qpolynomial *isl_qpolynomial_max_cst(
__isl_take isl_qpolynomial *qp1, __isl_take isl_qpolynomial *qp2)
{
struct isl_upoly_cst *cst1, *cst2;
int cmp;
if (!qp1 || !qp2)
goto error;
isl_assert(qp1->dim->ctx, isl_upoly_is_cst(qp1->upoly), goto error);
isl_assert(qp2->dim->ctx, isl_upoly_is_cst(qp2->upoly), goto error);
cst1 = isl_upoly_as_cst(qp1->upoly);
cst2 = isl_upoly_as_cst(qp2->upoly);
cmp = isl_upoly_cmp(cst1, cst2);
if (cmp >= 0) {
isl_qpolynomial_free(qp2);
} else {
isl_qpolynomial_free(qp1);
qp1 = qp2;
}
return qp1;
error:
isl_qpolynomial_free(qp1);
isl_qpolynomial_free(qp2);
return NULL;
}
__isl_give isl_qpolynomial *isl_qpolynomial_insert_dims(
__isl_take isl_qpolynomial *qp, enum isl_dim_type type,
unsigned first, unsigned n)
{
unsigned total;
unsigned g_pos;
int *exp;
if (!qp)
return NULL;
if (type == isl_dim_out)
isl_die(qp->div->ctx, isl_error_invalid,
"cannot insert output/set dimensions",
goto error);
if (type == isl_dim_in)
type = isl_dim_set;
if (n == 0 && !isl_space_is_named_or_nested(qp->dim, type))
return qp;
qp = isl_qpolynomial_cow(qp);
if (!qp)
return NULL;
isl_assert(qp->div->ctx, first <= isl_space_dim(qp->dim, type),
goto error);
g_pos = pos(qp->dim, type) + first;
qp->div = isl_mat_insert_zero_cols(qp->div, 2 + g_pos, n);
if (!qp->div)
goto error;
total = qp->div->n_col - 2;
if (total > g_pos) {
int i;
exp = isl_alloc_array(qp->div->ctx, int, total - g_pos);
if (!exp)
goto error;
for (i = 0; i < total - g_pos; ++i)
exp[i] = i + n;
qp->upoly = expand(qp->upoly, exp, g_pos);
free(exp);
if (!qp->upoly)
goto error;
}
qp->dim = isl_space_insert_dims(qp->dim, type, first, n);
if (!qp->dim)
goto error;
return qp;
error:
isl_qpolynomial_free(qp);
return NULL;
}
__isl_give isl_qpolynomial *isl_qpolynomial_add_dims(
__isl_take isl_qpolynomial *qp, enum isl_dim_type type, unsigned n)
{
unsigned pos;
pos = isl_qpolynomial_dim(qp, type);
return isl_qpolynomial_insert_dims(qp, type, pos, n);
}
__isl_give isl_pw_qpolynomial *isl_pw_qpolynomial_add_dims(
__isl_take isl_pw_qpolynomial *pwqp,
enum isl_dim_type type, unsigned n)
{
unsigned pos;
pos = isl_pw_qpolynomial_dim(pwqp, type);
return isl_pw_qpolynomial_insert_dims(pwqp, type, pos, n);
}
static int *reordering_move(isl_ctx *ctx,
unsigned len, unsigned dst, unsigned src, unsigned n)
{
int i;
int *reordering;
reordering = isl_alloc_array(ctx, int, len);
if (!reordering)
return NULL;
if (dst <= src) {
for (i = 0; i < dst; ++i)
reordering[i] = i;
for (i = 0; i < n; ++i)
reordering[src + i] = dst + i;
for (i = 0; i < src - dst; ++i)
reordering[dst + i] = dst + n + i;
for (i = 0; i < len - src - n; ++i)
reordering[src + n + i] = src + n + i;
} else {
for (i = 0; i < src; ++i)
reordering[i] = i;
for (i = 0; i < n; ++i)
reordering[src + i] = dst + i;
for (i = 0; i < dst - src; ++i)
reordering[src + n + i] = src + i;
for (i = 0; i < len - dst - n; ++i)
reordering[dst + n + i] = dst + n + i;
}
return reordering;
}
__isl_give isl_qpolynomial *isl_qpolynomial_move_dims(
__isl_take isl_qpolynomial *qp,
enum isl_dim_type dst_type, unsigned dst_pos,
enum isl_dim_type src_type, unsigned src_pos, unsigned n)
{
unsigned g_dst_pos;
unsigned g_src_pos;
int *reordering;
qp = isl_qpolynomial_cow(qp);
if (!qp)
return NULL;
if (dst_type == isl_dim_out || src_type == isl_dim_out)
isl_die(qp->dim->ctx, isl_error_invalid,
"cannot move output/set dimension",
goto error);
if (dst_type == isl_dim_in)
dst_type = isl_dim_set;
if (src_type == isl_dim_in)
src_type = isl_dim_set;
isl_assert(qp->dim->ctx, src_pos + n <= isl_space_dim(qp->dim, src_type),
goto error);
g_dst_pos = pos(qp->dim, dst_type) + dst_pos;
g_src_pos = pos(qp->dim, src_type) + src_pos;
if (dst_type > src_type)
g_dst_pos -= n;
qp->div = isl_mat_move_cols(qp->div, 2 + g_dst_pos, 2 + g_src_pos, n);
if (!qp->div)
goto error;
qp = sort_divs(qp);
if (!qp)
goto error;
reordering = reordering_move(qp->dim->ctx,
qp->div->n_col - 2, g_dst_pos, g_src_pos, n);
if (!reordering)
goto error;
qp->upoly = reorder(qp->upoly, reordering);
free(reordering);
if (!qp->upoly)
goto error;
qp->dim = isl_space_move_dims(qp->dim, dst_type, dst_pos, src_type, src_pos, n);
if (!qp->dim)
goto error;
return qp;
error:
isl_qpolynomial_free(qp);
return NULL;
}
__isl_give isl_qpolynomial *isl_qpolynomial_from_affine(__isl_take isl_space *dim,
isl_int *f, isl_int denom)
{
struct isl_upoly *up;
dim = isl_space_domain(dim);
if (!dim)
return NULL;
up = isl_upoly_from_affine(dim->ctx, f, denom,
1 + isl_space_dim(dim, isl_dim_all));
return isl_qpolynomial_alloc(dim, 0, up);
}
__isl_give isl_qpolynomial *isl_qpolynomial_from_aff(__isl_take isl_aff *aff)
{
isl_ctx *ctx;
struct isl_upoly *up;
isl_qpolynomial *qp;
if (!aff)
return NULL;
ctx = isl_aff_get_ctx(aff);
up = isl_upoly_from_affine(ctx, aff->v->el + 1, aff->v->el[0],
aff->v->size - 1);
qp = isl_qpolynomial_alloc(isl_aff_get_domain_space(aff),
aff->ls->div->n_row, up);
if (!qp)
goto error;
isl_mat_free(qp->div);
qp->div = isl_mat_copy(aff->ls->div);
qp->div = isl_mat_cow(qp->div);
if (!qp->div)
goto error;
isl_aff_free(aff);
qp = reduce_divs(qp);
qp = remove_redundant_divs(qp);
return qp;
error:
isl_aff_free(aff);
return NULL;
}
__isl_give isl_pw_qpolynomial *isl_pw_qpolynomial_from_pw_aff(
__isl_take isl_pw_aff *pwaff)
{
int i;
isl_pw_qpolynomial *pwqp;
if (!pwaff)
return NULL;
pwqp = isl_pw_qpolynomial_alloc_size(isl_pw_aff_get_space(pwaff),
pwaff->n);
for (i = 0; i < pwaff->n; ++i) {
isl_set *dom;
isl_qpolynomial *qp;
dom = isl_set_copy(pwaff->p[i].set);
qp = isl_qpolynomial_from_aff(isl_aff_copy(pwaff->p[i].aff));
pwqp = isl_pw_qpolynomial_add_piece(pwqp, dom, qp);
}
isl_pw_aff_free(pwaff);
return pwqp;
}
__isl_give isl_qpolynomial *isl_qpolynomial_from_constraint(
__isl_take isl_constraint *c, enum isl_dim_type type, unsigned pos)
{
isl_aff *aff;
aff = isl_constraint_get_bound(c, type, pos);
isl_constraint_free(c);
return isl_qpolynomial_from_aff(aff);
}
/* For each 0 <= i < "n", replace variable "first" + i of type "type"
* in "qp" by subs[i].
*/
__isl_give isl_qpolynomial *isl_qpolynomial_substitute(
__isl_take isl_qpolynomial *qp,
enum isl_dim_type type, unsigned first, unsigned n,
__isl_keep isl_qpolynomial **subs)
{
int i;
struct isl_upoly **ups;
if (n == 0)
return qp;
qp = isl_qpolynomial_cow(qp);
if (!qp)
return NULL;
if (type == isl_dim_out)
isl_die(qp->dim->ctx, isl_error_invalid,
"cannot substitute output/set dimension",
goto error);
if (type == isl_dim_in)
type = isl_dim_set;
for (i = 0; i < n; ++i)
if (!subs[i])
goto error;
isl_assert(qp->dim->ctx, first + n <= isl_space_dim(qp->dim, type),
goto error);
for (i = 0; i < n; ++i)
isl_assert(qp->dim->ctx, isl_space_is_equal(qp->dim, subs[i]->dim),
goto error);
isl_assert(qp->dim->ctx, qp->div->n_row == 0, goto error);
for (i = 0; i < n; ++i)
isl_assert(qp->dim->ctx, subs[i]->div->n_row == 0, goto error);
first += pos(qp->dim, type);
ups = isl_alloc_array(qp->dim->ctx, struct isl_upoly *, n);
if (!ups)
goto error;
for (i = 0; i < n; ++i)
ups[i] = subs[i]->upoly;
qp->upoly = isl_upoly_subs(qp->upoly, first, n, ups);
free(ups);
if (!qp->upoly)
goto error;
return qp;
error:
isl_qpolynomial_free(qp);
return NULL;
}
/* Extend "bset" with extra set dimensions for each integer division
* in "qp" and then call "fn" with the extended bset and the polynomial
* that results from replacing each of the integer divisions by the
* corresponding extra set dimension.
*/
int isl_qpolynomial_as_polynomial_on_domain(__isl_keep isl_qpolynomial *qp,
__isl_keep isl_basic_set *bset,
int (*fn)(__isl_take isl_basic_set *bset,
__isl_take isl_qpolynomial *poly, void *user), void *user)
{
isl_space *dim;
isl_mat *div;
isl_qpolynomial *poly;
if (!qp || !bset)
goto error;
if (qp->div->n_row == 0)
return fn(isl_basic_set_copy(bset), isl_qpolynomial_copy(qp),
user);
div = isl_mat_copy(qp->div);
dim = isl_space_copy(qp->dim);
dim = isl_space_add_dims(dim, isl_dim_set, qp->div->n_row);
poly = isl_qpolynomial_alloc(dim, 0, isl_upoly_copy(qp->upoly));
bset = isl_basic_set_copy(bset);
bset = isl_basic_set_add(bset, isl_dim_set, qp->div->n_row);
bset = add_div_constraints(bset, div);
return fn(bset, poly, user);
error:
return -1;
}
/* Return total degree in variables first (inclusive) up to last (exclusive).
*/
int isl_upoly_degree(__isl_keep struct isl_upoly *up, int first, int last)
{
int deg = -1;
int i;
struct isl_upoly_rec *rec;
if (!up)
return -2;
if (isl_upoly_is_zero(up))
return -1;
if (isl_upoly_is_cst(up) || up->var < first)
return 0;
rec = isl_upoly_as_rec(up);
if (!rec)
return -2;
for (i = 0; i < rec->n; ++i) {
int d;
if (isl_upoly_is_zero(rec->p[i]))
continue;
d = isl_upoly_degree(rec->p[i], first, last);
if (up->var < last)
d += i;
if (d > deg)
deg = d;
}
return deg;
}
/* Return total degree in set variables.
*/
int isl_qpolynomial_degree(__isl_keep isl_qpolynomial *poly)
{
unsigned ovar;
unsigned nvar;
if (!poly)
return -2;
ovar = isl_space_offset(poly->dim, isl_dim_set);
nvar = isl_space_dim(poly->dim, isl_dim_set);
return isl_upoly_degree(poly->upoly, ovar, ovar + nvar);
}
__isl_give struct isl_upoly *isl_upoly_coeff(__isl_keep struct isl_upoly *up,
unsigned pos, int deg)
{
int i;
struct isl_upoly_rec *rec;
if (!up)
return NULL;
if (isl_upoly_is_cst(up) || up->var < pos) {
if (deg == 0)
return isl_upoly_copy(up);
else
return isl_upoly_zero(up->ctx);
}
rec = isl_upoly_as_rec(up);
if (!rec)
return NULL;
if (up->var == pos) {
if (deg < rec->n)
return isl_upoly_copy(rec->p[deg]);
else
return isl_upoly_zero(up->ctx);
}
up = isl_upoly_copy(up);
up = isl_upoly_cow(up);
rec = isl_upoly_as_rec(up);
if (!rec)
goto error;
for (i = 0; i < rec->n; ++i) {
struct isl_upoly *t;
t = isl_upoly_coeff(rec->p[i], pos, deg);
if (!t)
goto error;
isl_upoly_free(rec->p[i]);
rec->p[i] = t;
}
return up;
error:
isl_upoly_free(up);
return NULL;
}
/* Return coefficient of power "deg" of variable "t_pos" of type "type".
*/
__isl_give isl_qpolynomial *isl_qpolynomial_coeff(
__isl_keep isl_qpolynomial *qp,
enum isl_dim_type type, unsigned t_pos, int deg)
{
unsigned g_pos;
struct isl_upoly *up;
isl_qpolynomial *c;
if (!qp)
return NULL;
if (type == isl_dim_out)
isl_die(qp->div->ctx, isl_error_invalid,
"output/set dimension does not have a coefficient",
return NULL);
if (type == isl_dim_in)
type = isl_dim_set;
isl_assert(qp->div->ctx, t_pos < isl_space_dim(qp->dim, type),
return NULL);
g_pos = pos(qp->dim, type) + t_pos;
up = isl_upoly_coeff(qp->upoly, g_pos, deg);
c = isl_qpolynomial_alloc(isl_space_copy(qp->dim), qp->div->n_row, up);
if (!c)
return NULL;
isl_mat_free(c->div);
c->div = isl_mat_copy(qp->div);
if (!c->div)
goto error;
return c;
error:
isl_qpolynomial_free(c);
return NULL;
}
/* Homogenize the polynomial in the variables first (inclusive) up to
* last (exclusive) by inserting powers of variable first.
* Variable first is assumed not to appear in the input.
*/
__isl_give struct isl_upoly *isl_upoly_homogenize(
__isl_take struct isl_upoly *up, int deg, int target,
int first, int last)
{
int i;
struct isl_upoly_rec *rec;
if (!up)
return NULL;
if (isl_upoly_is_zero(up))
return up;
if (deg == target)
return up;
if (isl_upoly_is_cst(up) || up->var < first) {
struct isl_upoly *hom;
hom = isl_upoly_var_pow(up->ctx, first, target - deg);
if (!hom)
goto error;
rec = isl_upoly_as_rec(hom);
rec->p[target - deg] = isl_upoly_mul(rec->p[target - deg], up);
return hom;
}
up = isl_upoly_cow(up);
rec = isl_upoly_as_rec(up);
if (!rec)
goto error;
for (i = 0; i < rec->n; ++i) {
if (isl_upoly_is_zero(rec->p[i]))
continue;
rec->p[i] = isl_upoly_homogenize(rec->p[i],
up->var < last ? deg + i : i, target,
first, last);
if (!rec->p[i])
goto error;
}
return up;
error:
isl_upoly_free(up);
return NULL;
}
/* Homogenize the polynomial in the set variables by introducing
* powers of an extra set variable at position 0.
*/
__isl_give isl_qpolynomial *isl_qpolynomial_homogenize(
__isl_take isl_qpolynomial *poly)
{
unsigned ovar;
unsigned nvar;
int deg = isl_qpolynomial_degree(poly);
if (deg < -1)
goto error;
poly = isl_qpolynomial_insert_dims(poly, isl_dim_in, 0, 1);
poly = isl_qpolynomial_cow(poly);
if (!poly)
goto error;
ovar = isl_space_offset(poly->dim, isl_dim_set);
nvar = isl_space_dim(poly->dim, isl_dim_set);
poly->upoly = isl_upoly_homogenize(poly->upoly, 0, deg,
ovar, ovar + nvar);
if (!poly->upoly)
goto error;
return poly;
error:
isl_qpolynomial_free(poly);
return NULL;
}
__isl_give isl_term *isl_term_alloc(__isl_take isl_space *dim,
__isl_take isl_mat *div)
{
isl_term *term;
int n;
if (!dim || !div)
goto error;
n = isl_space_dim(dim, isl_dim_all) + div->n_row;
term = isl_calloc(dim->ctx, struct isl_term,
sizeof(struct isl_term) + (n - 1) * sizeof(int));
if (!term)
goto error;
term->ref = 1;
term->dim = dim;
term->div = div;
isl_int_init(term->n);
isl_int_init(term->d);
return term;
error:
isl_space_free(dim);
isl_mat_free(div);
return NULL;
}
__isl_give isl_term *isl_term_copy(__isl_keep isl_term *term)
{
if (!term)
return NULL;
term->ref++;
return term;
}
__isl_give isl_term *isl_term_dup(__isl_keep isl_term *term)
{
int i;
isl_term *dup;
unsigned total;
if (!term)
return NULL;
total = isl_space_dim(term->dim, isl_dim_all) + term->div->n_row;
dup = isl_term_alloc(isl_space_copy(term->dim), isl_mat_copy(term->div));
if (!dup)
return NULL;
isl_int_set(dup->n, term->n);
isl_int_set(dup->d, term->d);
for (i = 0; i < total; ++i)
dup->pow[i] = term->pow[i];
return dup;
}
__isl_give isl_term *isl_term_cow(__isl_take isl_term *term)
{
if (!term)
return NULL;
if (term->ref == 1)
return term;
term->ref--;
return isl_term_dup(term);
}
void isl_term_free(__isl_take isl_term *term)
{
if (!term)
return;
if (--term->ref > 0)
return;
isl_space_free(term->dim);
isl_mat_free(term->div);
isl_int_clear(term->n);
isl_int_clear(term->d);
free(term);
}
unsigned isl_term_dim(__isl_keep isl_term *term, enum isl_dim_type type)
{
if (!term)
return 0;
switch (type) {
case isl_dim_param:
case isl_dim_in:
case isl_dim_out: return isl_space_dim(term->dim, type);
case isl_dim_div: return term->div->n_row;
case isl_dim_all: return isl_space_dim(term->dim, isl_dim_all) +
term->div->n_row;
default: return 0;
}
}
isl_ctx *isl_term_get_ctx(__isl_keep isl_term *term)
{
return term ? term->dim->ctx : NULL;
}
void isl_term_get_num(__isl_keep isl_term *term, isl_int *n)
{
if (!term)
return;
isl_int_set(*n, term->n);
}
void isl_term_get_den(__isl_keep isl_term *term, isl_int *d)
{
if (!term)
return;
isl_int_set(*d, term->d);
}
int isl_term_get_exp(__isl_keep isl_term *term,
enum isl_dim_type type, unsigned pos)
{
if (!term)
return -1;
isl_assert(term->dim->ctx, pos < isl_term_dim(term, type), return -1);
if (type >= isl_dim_set)
pos += isl_space_dim(term->dim, isl_dim_param);
if (type >= isl_dim_div)
pos += isl_space_dim(term->dim, isl_dim_set);
return term->pow[pos];
}
__isl_give isl_aff *isl_term_get_div(__isl_keep isl_term *term, unsigned pos)
{
isl_local_space *ls;
isl_aff *aff;
if (!term)
return NULL;
isl_assert(term->dim->ctx, pos < isl_term_dim(term, isl_dim_div),
return NULL);
ls = isl_local_space_alloc_div(isl_space_copy(term->dim),
isl_mat_copy(term->div));
aff = isl_aff_alloc(ls);
if (!aff)
return NULL;
isl_seq_cpy(aff->v->el, term->div->row[pos], aff->v->size);
aff = isl_aff_normalize(aff);
return aff;
}
__isl_give isl_term *isl_upoly_foreach_term(__isl_keep struct isl_upoly *up,
int (*fn)(__isl_take isl_term *term, void *user),
__isl_take isl_term *term, void *user)
{
int i;
struct isl_upoly_rec *rec;
if (!up || !term)
goto error;
if (isl_upoly_is_zero(up))
return term;
isl_assert(up->ctx, !isl_upoly_is_nan(up), goto error);
isl_assert(up->ctx, !isl_upoly_is_infty(up), goto error);
isl_assert(up->ctx, !isl_upoly_is_neginfty(up), goto error);
if (isl_upoly_is_cst(up)) {
struct isl_upoly_cst *cst;
cst = isl_upoly_as_cst(up);
if (!cst)
goto error;
term = isl_term_cow(term);
if (!term)
goto error;
isl_int_set(term->n, cst->n);
isl_int_set(term->d, cst->d);
if (fn(isl_term_copy(term), user) < 0)
goto error;
return term;
}
rec = isl_upoly_as_rec(up);
if (!rec)
goto error;
for (i = 0; i < rec->n; ++i) {
term = isl_term_cow(term);
if (!term)
goto error;
term->pow[up->var] = i;
term = isl_upoly_foreach_term(rec->p[i], fn, term, user);
if (!term)
goto error;
}
term->pow[up->var] = 0;
return term;
error:
isl_term_free(term);
return NULL;
}
int isl_qpolynomial_foreach_term(__isl_keep isl_qpolynomial *qp,
int (*fn)(__isl_take isl_term *term, void *user), void *user)
{
isl_term *term;
if (!qp)
return -1;
term = isl_term_alloc(isl_space_copy(qp->dim), isl_mat_copy(qp->div));
if (!term)
return -1;
term = isl_upoly_foreach_term(qp->upoly, fn, term, user);
isl_term_free(term);
return term ? 0 : -1;
}
__isl_give isl_qpolynomial *isl_qpolynomial_from_term(__isl_take isl_term *term)
{
struct isl_upoly *up;
isl_qpolynomial *qp;
int i, n;
if (!term)
return NULL;
n = isl_space_dim(term->dim, isl_dim_all) + term->div->n_row;
up = isl_upoly_rat_cst(term->dim->ctx, term->n, term->d);
for (i = 0; i < n; ++i) {
if (!term->pow[i])
continue;
up = isl_upoly_mul(up,
isl_upoly_var_pow(term->dim->ctx, i, term->pow[i]));
}
qp = isl_qpolynomial_alloc(isl_space_copy(term->dim), term->div->n_row, up);
if (!qp)
goto error;
isl_mat_free(qp->div);
qp->div = isl_mat_copy(term->div);
if (!qp->div)
goto error;
isl_term_free(term);
return qp;
error:
isl_qpolynomial_free(qp);
isl_term_free(term);
return NULL;
}
__isl_give isl_qpolynomial *isl_qpolynomial_lift(__isl_take isl_qpolynomial *qp,
__isl_take isl_space *dim)
{
int i;
int extra;
unsigned total;
if (!qp || !dim)
goto error;
if (isl_space_is_equal(qp->dim, dim)) {
isl_space_free(dim);
return qp;
}
qp = isl_qpolynomial_cow(qp);
if (!qp)
goto error;
extra = isl_space_dim(dim, isl_dim_set) -
isl_space_dim(qp->dim, isl_dim_set);
total = isl_space_dim(qp->dim, isl_dim_all);
if (qp->div->n_row) {
int *exp;
exp = isl_alloc_array(qp->div->ctx, int, qp->div->n_row);
if (!exp)
goto error;
for (i = 0; i < qp->div->n_row; ++i)
exp[i] = extra + i;
qp->upoly = expand(qp->upoly, exp, total);
free(exp);
if (!qp->upoly)
goto error;
}
qp->div = isl_mat_insert_cols(qp->div, 2 + total, extra);
if (!qp->div)
goto error;
for (i = 0; i < qp->div->n_row; ++i)
isl_seq_clr(qp->div->row[i] + 2 + total, extra);
isl_space_free(qp->dim);
qp->dim = dim;
return qp;
error:
isl_space_free(dim);
isl_qpolynomial_free(qp);
return NULL;
}
/* For each parameter or variable that does not appear in qp,
* first eliminate the variable from all constraints and then set it to zero.
*/
static __isl_give isl_set *fix_inactive(__isl_take isl_set *set,
__isl_keep isl_qpolynomial *qp)
{
int *active = NULL;
int i;
int d;
unsigned nparam;
unsigned nvar;
if (!set || !qp)
goto error;
d = isl_space_dim(set->dim, isl_dim_all);
active = isl_calloc_array(set->ctx, int, d);
if (set_active(qp, active) < 0)
goto error;
for (i = 0; i < d; ++i)
if (!active[i])
break;
if (i == d) {
free(active);
return set;
}
nparam = isl_space_dim(set->dim, isl_dim_param);
nvar = isl_space_dim(set->dim, isl_dim_set);
for (i = 0; i < nparam; ++i) {
if (active[i])
continue;
set = isl_set_eliminate(set, isl_dim_param, i, 1);
set = isl_set_fix_si(set, isl_dim_param, i, 0);
}
for (i = 0; i < nvar; ++i) {
if (active[nparam + i])
continue;
set = isl_set_eliminate(set, isl_dim_set, i, 1);
set = isl_set_fix_si(set, isl_dim_set, i, 0);
}
free(active);
return set;
error:
free(active);
isl_set_free(set);
return NULL;
}
struct isl_opt_data {
isl_qpolynomial *qp;
int first;
isl_qpolynomial *opt;
int max;
};
static int opt_fn(__isl_take isl_point *pnt, void *user)
{
struct isl_opt_data *data = (struct isl_opt_data *)user;
isl_qpolynomial *val;
val = isl_qpolynomial_eval(isl_qpolynomial_copy(data->qp), pnt);
if (data->first) {
data->first = 0;
data->opt = val;
} else if (data->max) {
data->opt = isl_qpolynomial_max_cst(data->opt, val);
} else {
data->opt = isl_qpolynomial_min_cst(data->opt, val);
}
return 0;
}
__isl_give isl_qpolynomial *isl_qpolynomial_opt_on_domain(
__isl_take isl_qpolynomial *qp, __isl_take isl_set *set, int max)
{
struct isl_opt_data data = { NULL, 1, NULL, max };
if (!set || !qp)
goto error;
if (isl_upoly_is_cst(qp->upoly)) {
isl_set_free(set);
return qp;
}
set = fix_inactive(set, qp);
data.qp = qp;
if (isl_set_foreach_point(set, opt_fn, &data) < 0)
goto error;
if (data.first) {
isl_space *space = isl_qpolynomial_get_domain_space(qp);
data.opt = isl_qpolynomial_zero_on_domain(space);
}
isl_set_free(set);
isl_qpolynomial_free(qp);
return data.opt;
error:
isl_set_free(set);
isl_qpolynomial_free(qp);
isl_qpolynomial_free(data.opt);
return NULL;
}
__isl_give isl_qpolynomial *isl_qpolynomial_morph_domain(
__isl_take isl_qpolynomial *qp, __isl_take isl_morph *morph)
{
int i;
int n_sub;
isl_ctx *ctx;
struct isl_upoly **subs;
isl_mat *mat, *diag;
qp = isl_qpolynomial_cow(qp);
if (!qp || !morph)
goto error;
ctx = qp->dim->ctx;
isl_assert(ctx, isl_space_is_equal(qp->dim, morph->dom->dim), goto error);
n_sub = morph->inv->n_row - 1;
if (morph->inv->n_row != morph->inv->n_col)
n_sub += qp->div->n_row;
subs = isl_calloc_array(ctx, struct isl_upoly *, n_sub);
if (!subs)
goto error;
for (i = 0; 1 + i < morph->inv->n_row; ++i)
subs[i] = isl_upoly_from_affine(ctx, morph->inv->row[1 + i],
morph->inv->row[0][0], morph->inv->n_col);
if (morph->inv->n_row != morph->inv->n_col)
for (i = 0; i < qp->div->n_row; ++i)
subs[morph->inv->n_row - 1 + i] =
isl_upoly_var_pow(ctx, morph->inv->n_col - 1 + i, 1);
qp->upoly = isl_upoly_subs(qp->upoly, 0, n_sub, subs);
for (i = 0; i < n_sub; ++i)
isl_upoly_free(subs[i]);
free(subs);
diag = isl_mat_diag(ctx, 1, morph->inv->row[0][0]);
mat = isl_mat_diagonal(diag, isl_mat_copy(morph->inv));
diag = isl_mat_diag(ctx, qp->div->n_row, morph->inv->row[0][0]);
mat = isl_mat_diagonal(mat, diag);
qp->div = isl_mat_product(qp->div, mat);
isl_space_free(qp->dim);
qp->dim = isl_space_copy(morph->ran->dim);
if (!qp->upoly || !qp->div || !qp->dim)
goto error;
isl_morph_free(morph);
return qp;
error:
isl_qpolynomial_free(qp);
isl_morph_free(morph);
return NULL;
}
static int neg_entry(void **entry, void *user)
{
isl_pw_qpolynomial **pwqp = (isl_pw_qpolynomial **)entry;
*pwqp = isl_pw_qpolynomial_neg(*pwqp);
return *pwqp ? 0 : -1;
}
__isl_give isl_union_pw_qpolynomial *isl_union_pw_qpolynomial_neg(
__isl_take isl_union_pw_qpolynomial *upwqp)
{
upwqp = isl_union_pw_qpolynomial_cow(upwqp);
if (!upwqp)
return NULL;
if (isl_hash_table_foreach(upwqp->dim->ctx, &upwqp->table,
&neg_entry, NULL) < 0)
goto error;
return upwqp;
error:
isl_union_pw_qpolynomial_free(upwqp);
return NULL;
}
__isl_give isl_union_pw_qpolynomial *isl_union_pw_qpolynomial_sub(
__isl_take isl_union_pw_qpolynomial *upwqp1,
__isl_take isl_union_pw_qpolynomial *upwqp2)
{
return isl_union_pw_qpolynomial_add(upwqp1,
isl_union_pw_qpolynomial_neg(upwqp2));
}
__isl_give isl_union_pw_qpolynomial *isl_union_pw_qpolynomial_mul(
__isl_take isl_union_pw_qpolynomial *upwqp1,
__isl_take isl_union_pw_qpolynomial *upwqp2)
{
return match_bin_op(upwqp1, upwqp2, &isl_pw_qpolynomial_mul);
}
/* Reorder the columns of the given div definitions according to the
* given reordering.
*/
static __isl_give isl_mat *reorder_divs(__isl_take isl_mat *div,
__isl_take isl_reordering *r)
{
int i, j;
isl_mat *mat;
int extra;
if (!div || !r)
goto error;
extra = isl_space_dim(r->dim, isl_dim_all) + div->n_row - r->len;
mat = isl_mat_alloc(div->ctx, div->n_row, div->n_col + extra);
if (!mat)
goto error;
for (i = 0; i < div->n_row; ++i) {
isl_seq_cpy(mat->row[i], div->row[i], 2);
isl_seq_clr(mat->row[i] + 2, mat->n_col - 2);
for (j = 0; j < r->len; ++j)
isl_int_set(mat->row[i][2 + r->pos[j]],
div->row[i][2 + j]);
}
isl_reordering_free(r);
isl_mat_free(div);
return mat;
error:
isl_reordering_free(r);
isl_mat_free(div);
return NULL;
}
/* Reorder the dimension of "qp" according to the given reordering.
*/
__isl_give isl_qpolynomial *isl_qpolynomial_realign_domain(
__isl_take isl_qpolynomial *qp, __isl_take isl_reordering *r)
{
qp = isl_qpolynomial_cow(qp);
if (!qp)
goto error;
r = isl_reordering_extend(r, qp->div->n_row);
if (!r)
goto error;
qp->div = reorder_divs(qp->div, isl_reordering_copy(r));
if (!qp->div)
goto error;
qp->upoly = reorder(qp->upoly, r->pos);
if (!qp->upoly)
goto error;
qp = isl_qpolynomial_reset_domain_space(qp, isl_space_copy(r->dim));
isl_reordering_free(r);
return qp;
error:
isl_qpolynomial_free(qp);
isl_reordering_free(r);
return NULL;
}
__isl_give isl_qpolynomial *isl_qpolynomial_align_params(
__isl_take isl_qpolynomial *qp, __isl_take isl_space *model)
{
if (!qp || !model)
goto error;
if (!isl_space_match(qp->dim, isl_dim_param, model, isl_dim_param)) {
isl_reordering *exp;
model = isl_space_drop_dims(model, isl_dim_in,
0, isl_space_dim(model, isl_dim_in));
model = isl_space_drop_dims(model, isl_dim_out,
0, isl_space_dim(model, isl_dim_out));
exp = isl_parameter_alignment_reordering(qp->dim, model);
exp = isl_reordering_extend_space(exp,
isl_qpolynomial_get_domain_space(qp));
qp = isl_qpolynomial_realign_domain(qp, exp);
}
isl_space_free(model);
return qp;
error:
isl_space_free(model);
isl_qpolynomial_free(qp);
return NULL;
}
struct isl_split_periods_data {
int max_periods;
isl_pw_qpolynomial *res;
};
/* Create a slice where the integer division "div" has the fixed value "v".
* In particular, if "div" refers to floor(f/m), then create a slice
*
* m v <= f <= m v + (m - 1)
*
* or
*
* f - m v >= 0
* -f + m v + (m - 1) >= 0
*/
static __isl_give isl_set *set_div_slice(__isl_take isl_space *dim,
__isl_keep isl_qpolynomial *qp, int div, isl_int v)
{
int total;
isl_basic_set *bset = NULL;
int k;
if (!dim || !qp)
goto error;
total = isl_space_dim(dim, isl_dim_all);
bset = isl_basic_set_alloc_space(isl_space_copy(dim), 0, 0, 2);
k = isl_basic_set_alloc_inequality(bset);
if (k < 0)
goto error;
isl_seq_cpy(bset->ineq[k], qp->div->row[div] + 1, 1 + total);
isl_int_submul(bset->ineq[k][0], v, qp->div->row[div][0]);
k = isl_basic_set_alloc_inequality(bset);
if (k < 0)
goto error;
isl_seq_neg(bset->ineq[k], qp->div->row[div] + 1, 1 + total);
isl_int_addmul(bset->ineq[k][0], v, qp->div->row[div][0]);
isl_int_add(bset->ineq[k][0], bset->ineq[k][0], qp->div->row[div][0]);
isl_int_sub_ui(bset->ineq[k][0], bset->ineq[k][0], 1);
isl_space_free(dim);
return isl_set_from_basic_set(bset);
error:
isl_basic_set_free(bset);
isl_space_free(dim);
return NULL;
}
static int split_periods(__isl_take isl_set *set,
__isl_take isl_qpolynomial *qp, void *user);
/* Create a slice of the domain "set" such that integer division "div"
* has the fixed value "v" and add the results to data->res,
* replacing the integer division by "v" in "qp".
*/
static int set_div(__isl_take isl_set *set,
__isl_take isl_qpolynomial *qp, int div, isl_int v,
struct isl_split_periods_data *data)
{
int i;
int total;
isl_set *slice;
struct isl_upoly *cst;
slice = set_div_slice(isl_set_get_space(set), qp, div, v);
set = isl_set_intersect(set, slice);
if (!qp)
goto error;
total = isl_space_dim(qp->dim, isl_dim_all);
for (i = div + 1; i < qp->div->n_row; ++i) {
if (isl_int_is_zero(qp->div->row[i][2 + total + div]))
continue;
isl_int_addmul(qp->div->row[i][1],
qp->div->row[i][2 + total + div], v);
isl_int_set_si(qp->div->row[i][2 + total + div], 0);
}
cst = isl_upoly_rat_cst(qp->dim->ctx, v, qp->dim->ctx->one);
qp = substitute_div(qp, div, cst);
return split_periods(set, qp, data);
error:
isl_set_free(set);
isl_qpolynomial_free(qp);
return -1;
}
/* Split the domain "set" such that integer division "div"
* has a fixed value (ranging from "min" to "max") on each slice
* and add the results to data->res.
*/
static int split_div(__isl_take isl_set *set,
__isl_take isl_qpolynomial *qp, int div, isl_int min, isl_int max,
struct isl_split_periods_data *data)
{
for (; isl_int_le(min, max); isl_int_add_ui(min, min, 1)) {
isl_set *set_i = isl_set_copy(set);
isl_qpolynomial *qp_i = isl_qpolynomial_copy(qp);
if (set_div(set_i, qp_i, div, min, data) < 0)
goto error;
}
isl_set_free(set);
isl_qpolynomial_free(qp);
return 0;
error:
isl_set_free(set);
isl_qpolynomial_free(qp);
return -1;
}
/* If "qp" refers to any integer division
* that can only attain "max_periods" distinct values on "set"
* then split the domain along those distinct values.
* Add the results (or the original if no splitting occurs)
* to data->res.
*/
static int split_periods(__isl_take isl_set *set,
__isl_take isl_qpolynomial *qp, void *user)
{
int i;
isl_pw_qpolynomial *pwqp;
struct isl_split_periods_data *data;
isl_int min, max;
int total;
int r = 0;
data = (struct isl_split_periods_data *)user;
if (!set || !qp)
goto error;
if (qp->div->n_row == 0) {
pwqp = isl_pw_qpolynomial_alloc(set, qp);
data->res = isl_pw_qpolynomial_add_disjoint(data->res, pwqp);
return 0;
}
isl_int_init(min);
isl_int_init(max);
total = isl_space_dim(qp->dim, isl_dim_all);
for (i = 0; i < qp->div->n_row; ++i) {
enum isl_lp_result lp_res;
if (isl_seq_first_non_zero(qp->div->row[i] + 2 + total,
qp->div->n_row) != -1)
continue;
lp_res = isl_set_solve_lp(set, 0, qp->div->row[i] + 1,
set->ctx->one, &min, NULL, NULL);
if (lp_res == isl_lp_error)
goto error2;
if (lp_res == isl_lp_unbounded || lp_res == isl_lp_empty)
continue;
isl_int_fdiv_q(min, min, qp->div->row[i][0]);
lp_res = isl_set_solve_lp(set, 1, qp->div->row[i] + 1,
set->ctx->one, &max, NULL, NULL);
if (lp_res == isl_lp_error)
goto error2;
if (lp_res == isl_lp_unbounded || lp_res == isl_lp_empty)
continue;
isl_int_fdiv_q(max, max, qp->div->row[i][0]);
isl_int_sub(max, max, min);
if (isl_int_cmp_si(max, data->max_periods) < 0) {
isl_int_add(max, max, min);
break;
}
}
if (i < qp->div->n_row) {
r = split_div(set, qp, i, min, max, data);
} else {
pwqp = isl_pw_qpolynomial_alloc(set, qp);
data->res = isl_pw_qpolynomial_add_disjoint(data->res, pwqp);
}
isl_int_clear(max);
isl_int_clear(min);
return r;
error2:
isl_int_clear(max);
isl_int_clear(min);
error:
isl_set_free(set);
isl_qpolynomial_free(qp);
return -1;
}
/* If any quasi-polynomial in pwqp refers to any integer division
* that can only attain "max_periods" distinct values on its domain
* then split the domain along those distinct values.
*/
__isl_give isl_pw_qpolynomial *isl_pw_qpolynomial_split_periods(
__isl_take isl_pw_qpolynomial *pwqp, int max_periods)
{
struct isl_split_periods_data data;
data.max_periods = max_periods;
data.res = isl_pw_qpolynomial_zero(isl_pw_qpolynomial_get_space(pwqp));
if (isl_pw_qpolynomial_foreach_piece(pwqp, &split_periods, &data) < 0)
goto error;
isl_pw_qpolynomial_free(pwqp);
return data.res;
error:
isl_pw_qpolynomial_free(data.res);
isl_pw_qpolynomial_free(pwqp);
return NULL;
}
/* Construct a piecewise quasipolynomial that is constant on the given
* domain. In particular, it is
* 0 if cst == 0
* 1 if cst == 1
* infinity if cst == -1
*/
static __isl_give isl_pw_qpolynomial *constant_on_domain(
__isl_take isl_basic_set *bset, int cst)
{
isl_space *dim;
isl_qpolynomial *qp;
if (!bset)
return NULL;
bset = isl_basic_set_params(bset);
dim = isl_basic_set_get_space(bset);
if (cst < 0)
qp = isl_qpolynomial_infty_on_domain(dim);
else if (cst == 0)
qp = isl_qpolynomial_zero_on_domain(dim);
else
qp = isl_qpolynomial_one_on_domain(dim);
return isl_pw_qpolynomial_alloc(isl_set_from_basic_set(bset), qp);
}
/* Factor bset, call fn on each of the factors and return the product.
*
* If no factors can be found, simply call fn on the input.
* Otherwise, construct the factors based on the factorizer,
* call fn on each factor and compute the product.
*/
static __isl_give isl_pw_qpolynomial *compressed_multiplicative_call(
__isl_take isl_basic_set *bset,
__isl_give isl_pw_qpolynomial *(*fn)(__isl_take isl_basic_set *bset))
{
int i, n;
isl_space *dim;
isl_set *set;
isl_factorizer *f;
isl_qpolynomial *qp;
isl_pw_qpolynomial *pwqp;
unsigned nparam;
unsigned nvar;
f = isl_basic_set_factorizer(bset);
if (!f)
goto error;
if (f->n_group == 0) {
isl_factorizer_free(f);
return fn(bset);
}
nparam = isl_basic_set_dim(bset, isl_dim_param);
nvar = isl_basic_set_dim(bset, isl_dim_set);
dim = isl_basic_set_get_space(bset);
dim = isl_space_domain(dim);
set = isl_set_universe(isl_space_copy(dim));
qp = isl_qpolynomial_one_on_domain(dim);
pwqp = isl_pw_qpolynomial_alloc(set, qp);
bset = isl_morph_basic_set(isl_morph_copy(f->morph), bset);
for (i = 0, n = 0; i < f->n_group; ++i) {
isl_basic_set *bset_i;
isl_pw_qpolynomial *pwqp_i;
bset_i = isl_basic_set_copy(bset);
bset_i = isl_basic_set_drop_constraints_involving(bset_i,
nparam + n + f->len[i], nvar - n - f->len[i]);
bset_i = isl_basic_set_drop_constraints_involving(bset_i,
nparam, n);
bset_i = isl_basic_set_drop(bset_i, isl_dim_set,
n + f->len[i], nvar - n - f->len[i]);
bset_i = isl_basic_set_drop(bset_i, isl_dim_set, 0, n);
pwqp_i = fn(bset_i);
pwqp = isl_pw_qpolynomial_mul(pwqp, pwqp_i);
n += f->len[i];
}
isl_basic_set_free(bset);
isl_factorizer_free(f);
return pwqp;
error:
isl_basic_set_free(bset);
return NULL;
}
/* Factor bset, call fn on each of the factors and return the product.
* The function is assumed to evaluate to zero on empty domains,
* to one on zero-dimensional domains and to infinity on unbounded domains
* and will not be called explicitly on zero-dimensional or unbounded domains.
*
* We first check for some special cases and remove all equalities.
* Then we hand over control to compressed_multiplicative_call.
*/
__isl_give isl_pw_qpolynomial *isl_basic_set_multiplicative_call(
__isl_take isl_basic_set *bset,
__isl_give isl_pw_qpolynomial *(*fn)(__isl_take isl_basic_set *bset))
{
int bounded;
isl_morph *morph;
isl_pw_qpolynomial *pwqp;
if (!bset)
return NULL;
if (isl_basic_set_plain_is_empty(bset))
return constant_on_domain(bset, 0);
if (isl_basic_set_dim(bset, isl_dim_set) == 0)
return constant_on_domain(bset, 1);
bounded = isl_basic_set_is_bounded(bset);
if (bounded < 0)
goto error;
if (!bounded)
return constant_on_domain(bset, -1);
if (bset->n_eq == 0)
return compressed_multiplicative_call(bset, fn);
morph = isl_basic_set_full_compression(bset);
bset = isl_morph_basic_set(isl_morph_copy(morph), bset);
pwqp = compressed_multiplicative_call(bset, fn);
morph = isl_morph_dom_params(morph);
morph = isl_morph_ran_params(morph);
morph = isl_morph_inverse(morph);
pwqp = isl_pw_qpolynomial_morph_domain(pwqp, morph);
return pwqp;
error:
isl_basic_set_free(bset);
return NULL;
}
/* Drop all floors in "qp", turning each integer division [a/m] into
* a rational division a/m. If "down" is set, then the integer division
* is replaces by (a-(m-1))/m instead.
*/
static __isl_give isl_qpolynomial *qp_drop_floors(
__isl_take isl_qpolynomial *qp, int down)
{
int i;
struct isl_upoly *s;
if (!qp)
return NULL;
if (qp->div->n_row == 0)
return qp;
qp = isl_qpolynomial_cow(qp);
if (!qp)
return NULL;
for (i = qp->div->n_row - 1; i >= 0; --i) {
if (down) {
isl_int_sub(qp->div->row[i][1],
qp->div->row[i][1], qp->div->row[i][0]);
isl_int_add_ui(qp->div->row[i][1],
qp->div->row[i][1], 1);
}
s = isl_upoly_from_affine(qp->dim->ctx, qp->div->row[i] + 1,
qp->div->row[i][0], qp->div->n_col - 1);
qp = substitute_div(qp, i, s);
if (!qp)
return NULL;
}
return qp;
}
/* Drop all floors in "pwqp", turning each integer division [a/m] into
* a rational division a/m.
*/
static __isl_give isl_pw_qpolynomial *pwqp_drop_floors(
__isl_take isl_pw_qpolynomial *pwqp)
{
int i;
if (!pwqp)
return NULL;
if (isl_pw_qpolynomial_is_zero(pwqp))
return pwqp;
pwqp = isl_pw_qpolynomial_cow(pwqp);
if (!pwqp)
return NULL;
for (i = 0; i < pwqp->n; ++i) {
pwqp->p[i].qp = qp_drop_floors(pwqp->p[i].qp, 0);
if (!pwqp->p[i].qp)
goto error;
}
return pwqp;
error:
isl_pw_qpolynomial_free(pwqp);
return NULL;
}
/* Adjust all the integer divisions in "qp" such that they are at least
* one over the given orthant (identified by "signs"). This ensures
* that they will still be non-negative even after subtracting (m-1)/m.
*
* In particular, f is replaced by f' + v, changing f = [a/m]
* to f' = [(a - m v)/m].
* If the constant term k in a is smaller than m,
* the constant term of v is set to floor(k/m) - 1.
* For any other term, if the coefficient c and the variable x have
* the same sign, then no changes are needed.
* Otherwise, if the variable is positive (and c is negative),
* then the coefficient of x in v is set to floor(c/m).
* If the variable is negative (and c is positive),
* then the coefficient of x in v is set to ceil(c/m).
*/
static __isl_give isl_qpolynomial *make_divs_pos(__isl_take isl_qpolynomial *qp,
int *signs)
{
int i, j;
int total;
isl_vec *v = NULL;
struct isl_upoly *s;
qp = isl_qpolynomial_cow(qp);
if (!qp)
return NULL;
qp->div = isl_mat_cow(qp->div);
if (!qp->div)
goto error;
total = isl_space_dim(qp->dim, isl_dim_all);
v = isl_vec_alloc(qp->div->ctx, qp->div->n_col - 1);
for (i = 0; i < qp->div->n_row; ++i) {
isl_int *row = qp->div->row[i];
v = isl_vec_clr(v);
if (!v)
goto error;
if (isl_int_lt(row[1], row[0])) {
isl_int_fdiv_q(v->el[0], row[1], row[0]);
isl_int_sub_ui(v->el[0], v->el[0], 1);
isl_int_submul(row[1], row[0], v->el[0]);
}
for (j = 0; j < total; ++j) {
if (isl_int_sgn(row[2 + j]) * signs[j] >= 0)
continue;
if (signs[j] < 0)
isl_int_cdiv_q(v->el[1 + j], row[2 + j], row[0]);
else
isl_int_fdiv_q(v->el[1 + j], row[2 + j], row[0]);
isl_int_submul(row[2 + j], row[0], v->el[1 + j]);
}
for (j = 0; j < i; ++j) {
if (isl_int_sgn(row[2 + total + j]) >= 0)
continue;
isl_int_fdiv_q(v->el[1 + total + j],
row[2 + total + j], row[0]);
isl_int_submul(row[2 + total + j],
row[0], v->el[1 + total + j]);
}
for (j = i + 1; j < qp->div->n_row; ++j) {
if (isl_int_is_zero(qp->div->row[j][2 + total + i]))
continue;
isl_seq_combine(qp->div->row[j] + 1,
qp->div->ctx->one, qp->div->row[j] + 1,
qp->div->row[j][2 + total + i], v->el, v->size);
}
isl_int_set_si(v->el[1 + total + i], 1);
s = isl_upoly_from_affine(qp->dim->ctx, v->el,
qp->div->ctx->one, v->size);
qp->upoly = isl_upoly_subs(qp->upoly, total + i, 1, &s);
isl_upoly_free(s);
if (!qp->upoly)
goto error;
}
isl_vec_free(v);
return qp;
error:
isl_vec_free(v);
isl_qpolynomial_free(qp);
return NULL;
}
struct isl_to_poly_data {
int sign;
isl_pw_qpolynomial *res;
isl_qpolynomial *qp;
};
/* Appoximate data->qp by a polynomial on the orthant identified by "signs".
* We first make all integer divisions positive and then split the
* quasipolynomials into terms with sign data->sign (the direction
* of the requested approximation) and terms with the opposite sign.
* In the first set of terms, each integer division [a/m] is
* overapproximated by a/m, while in the second it is underapproximated
* by (a-(m-1))/m.
*/
static int to_polynomial_on_orthant(__isl_take isl_set *orthant, int *signs,
void *user)
{
struct isl_to_poly_data *data = user;
isl_pw_qpolynomial *t;
isl_qpolynomial *qp, *up, *down;
qp = isl_qpolynomial_copy(data->qp);
qp = make_divs_pos(qp, signs);
up = isl_qpolynomial_terms_of_sign(qp, signs, data->sign);
up = qp_drop_floors(up, 0);
down = isl_qpolynomial_terms_of_sign(qp, signs, -data->sign);
down = qp_drop_floors(down, 1);
isl_qpolynomial_free(qp);
qp = isl_qpolynomial_add(up, down);
t = isl_pw_qpolynomial_alloc(orthant, qp);
data->res = isl_pw_qpolynomial_add_disjoint(data->res, t);
return 0;
}
/* Approximate each quasipolynomial by a polynomial. If "sign" is positive,
* the polynomial will be an overapproximation. If "sign" is negative,
* it will be an underapproximation. If "sign" is zero, the approximation
* will lie somewhere in between.
*
* In particular, is sign == 0, we simply drop the floors, turning
* the integer divisions into rational divisions.
* Otherwise, we split the domains into orthants, make all integer divisions
* positive and then approximate each [a/m] by either a/m or (a-(m-1))/m,
* depending on the requested sign and the sign of the term in which
* the integer division appears.
*/
__isl_give isl_pw_qpolynomial *isl_pw_qpolynomial_to_polynomial(
__isl_take isl_pw_qpolynomial *pwqp, int sign)
{
int i;
struct isl_to_poly_data data;
if (sign == 0)
return pwqp_drop_floors(pwqp);
if (!pwqp)
return NULL;
data.sign = sign;
data.res = isl_pw_qpolynomial_zero(isl_pw_qpolynomial_get_space(pwqp));
for (i = 0; i < pwqp->n; ++i) {
if (pwqp->p[i].qp->div->n_row == 0) {
isl_pw_qpolynomial *t;
t = isl_pw_qpolynomial_alloc(
isl_set_copy(pwqp->p[i].set),
isl_qpolynomial_copy(pwqp->p[i].qp));
data.res = isl_pw_qpolynomial_add_disjoint(data.res, t);
continue;
}
data.qp = pwqp->p[i].qp;
if (isl_set_foreach_orthant(pwqp->p[i].set,
&to_polynomial_on_orthant, &data) < 0)
goto error;
}
isl_pw_qpolynomial_free(pwqp);
return data.res;
error:
isl_pw_qpolynomial_free(pwqp);
isl_pw_qpolynomial_free(data.res);
return NULL;
}
static int poly_entry(void **entry, void *user)
{
int *sign = user;
isl_pw_qpolynomial **pwqp = (isl_pw_qpolynomial **)entry;
*pwqp = isl_pw_qpolynomial_to_polynomial(*pwqp, *sign);
return *pwqp ? 0 : -1;
}
__isl_give isl_union_pw_qpolynomial *isl_union_pw_qpolynomial_to_polynomial(
__isl_take isl_union_pw_qpolynomial *upwqp, int sign)
{
upwqp = isl_union_pw_qpolynomial_cow(upwqp);
if (!upwqp)
return NULL;
if (isl_hash_table_foreach(upwqp->dim->ctx, &upwqp->table,
&poly_entry, &sign) < 0)
goto error;
return upwqp;
error:
isl_union_pw_qpolynomial_free(upwqp);
return NULL;
}
__isl_give isl_basic_map *isl_basic_map_from_qpolynomial(
__isl_take isl_qpolynomial *qp)
{
int i, k;
isl_space *dim;
isl_vec *aff = NULL;
isl_basic_map *bmap = NULL;
unsigned pos;
unsigned n_div;
if (!qp)
return NULL;
if (!isl_upoly_is_affine(qp->upoly))
isl_die(qp->dim->ctx, isl_error_invalid,
"input quasi-polynomial not affine", goto error);
aff = isl_qpolynomial_extract_affine(qp);
if (!aff)
goto error;
dim = isl_qpolynomial_get_space(qp);
pos = 1 + isl_space_offset(dim, isl_dim_out);
n_div = qp->div->n_row;
bmap = isl_basic_map_alloc_space(dim, n_div, 1, 2 * n_div);
for (i = 0; i < n_div; ++i) {
k = isl_basic_map_alloc_div(bmap);
if (k < 0)
goto error;
isl_seq_cpy(bmap->div[k], qp->div->row[i], qp->div->n_col);
isl_int_set_si(bmap->div[k][qp->div->n_col], 0);
if (isl_basic_map_add_div_constraints(bmap, k) < 0)
goto error;
}
k = isl_basic_map_alloc_equality(bmap);
if (k < 0)
goto error;
isl_int_neg(bmap->eq[k][pos], aff->el[0]);
isl_seq_cpy(bmap->eq[k], aff->el + 1, pos);
isl_seq_cpy(bmap->eq[k] + pos + 1, aff->el + 1 + pos, n_div);
isl_vec_free(aff);
isl_qpolynomial_free(qp);
bmap = isl_basic_map_finalize(bmap);
return bmap;
error:
isl_vec_free(aff);
isl_qpolynomial_free(qp);
isl_basic_map_free(bmap);
return NULL;
}