nexmon – Rev 1
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/*
* Copyright 2011 INRIA Saclay
* Copyright 2011 Sven Verdoolaege
* Copyright 2012 Ecole Normale Superieure
*
* 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
* and Ecole Normale Superieure, 45 rue d’Ulm, 75230 Paris, France
*/
#include <isl_ctx_private.h>
#define ISL_DIM_H
#include <isl_map_private.h>
#include <isl_union_map_private.h>
#include <isl_aff_private.h>
#include <isl_space_private.h>
#include <isl_local_space_private.h>
#include <isl_mat_private.h>
#include <isl_list_private.h>
#include <isl/constraint.h>
#include <isl/seq.h>
#include <isl/set.h>
#include <isl_config.h>
__isl_give isl_aff *isl_aff_alloc_vec(__isl_take isl_local_space *ls,
__isl_take isl_vec *v)
{
isl_aff *aff;
if (!ls || !v)
goto error;
aff = isl_calloc_type(v->ctx, struct isl_aff);
if (!aff)
goto error;
aff->ref = 1;
aff->ls = ls;
aff->v = v;
return aff;
error:
isl_local_space_free(ls);
isl_vec_free(v);
return NULL;
}
__isl_give isl_aff *isl_aff_alloc(__isl_take isl_local_space *ls)
{
isl_ctx *ctx;
isl_vec *v;
unsigned total;
if (!ls)
return NULL;
ctx = isl_local_space_get_ctx(ls);
if (!isl_local_space_divs_known(ls))
isl_die(ctx, isl_error_invalid, "local space has unknown divs",
goto error);
if (!isl_local_space_is_set(ls))
isl_die(ctx, isl_error_invalid,
"domain of affine expression should be a set",
goto error);
total = isl_local_space_dim(ls, isl_dim_all);
v = isl_vec_alloc(ctx, 1 + 1 + total);
return isl_aff_alloc_vec(ls, v);
error:
isl_local_space_free(ls);
return NULL;
}
__isl_give isl_aff *isl_aff_zero_on_domain(__isl_take isl_local_space *ls)
{
isl_aff *aff;
aff = isl_aff_alloc(ls);
if (!aff)
return NULL;
isl_int_set_si(aff->v->el[0], 1);
isl_seq_clr(aff->v->el + 1, aff->v->size - 1);
return aff;
}
__isl_give isl_aff *isl_aff_copy(__isl_keep isl_aff *aff)
{
if (!aff)
return NULL;
aff->ref++;
return aff;
}
__isl_give isl_aff *isl_aff_dup(__isl_keep isl_aff *aff)
{
if (!aff)
return NULL;
return isl_aff_alloc_vec(isl_local_space_copy(aff->ls),
isl_vec_copy(aff->v));
}
__isl_give isl_aff *isl_aff_cow(__isl_take isl_aff *aff)
{
if (!aff)
return NULL;
if (aff->ref == 1)
return aff;
aff->ref--;
return isl_aff_dup(aff);
}
void *isl_aff_free(__isl_take isl_aff *aff)
{
if (!aff)
return NULL;
if (--aff->ref > 0)
return NULL;
isl_local_space_free(aff->ls);
isl_vec_free(aff->v);
free(aff);
return NULL;
}
isl_ctx *isl_aff_get_ctx(__isl_keep isl_aff *aff)
{
return aff ? isl_local_space_get_ctx(aff->ls) : NULL;
}
/* Externally, an isl_aff has a map space, but internally, the
* ls field corresponds to the domain of that space.
*/
int isl_aff_dim(__isl_keep isl_aff *aff, enum isl_dim_type type)
{
if (!aff)
return 0;
if (type == isl_dim_out)
return 1;
if (type == isl_dim_in)
type = isl_dim_set;
return isl_local_space_dim(aff->ls, type);
}
__isl_give isl_space *isl_aff_get_domain_space(__isl_keep isl_aff *aff)
{
return aff ? isl_local_space_get_space(aff->ls) : NULL;
}
__isl_give isl_space *isl_aff_get_space(__isl_keep isl_aff *aff)
{
isl_space *space;
if (!aff)
return NULL;
space = isl_local_space_get_space(aff->ls);
space = isl_space_from_domain(space);
space = isl_space_add_dims(space, isl_dim_out, 1);
return space;
}
__isl_give isl_local_space *isl_aff_get_domain_local_space(
__isl_keep isl_aff *aff)
{
return aff ? isl_local_space_copy(aff->ls) : NULL;
}
__isl_give isl_local_space *isl_aff_get_local_space(__isl_keep isl_aff *aff)
{
isl_local_space *ls;
if (!aff)
return NULL;
ls = isl_local_space_copy(aff->ls);
ls = isl_local_space_from_domain(ls);
ls = isl_local_space_add_dims(ls, isl_dim_out, 1);
return ls;
}
/* Externally, an isl_aff has a map space, but internally, the
* ls field corresponds to the domain of that space.
*/
const char *isl_aff_get_dim_name(__isl_keep isl_aff *aff,
enum isl_dim_type type, unsigned pos)
{
if (!aff)
return NULL;
if (type == isl_dim_out)
return NULL;
if (type == isl_dim_in)
type = isl_dim_set;
return isl_local_space_get_dim_name(aff->ls, type, pos);
}
__isl_give isl_aff *isl_aff_reset_domain_space(__isl_take isl_aff *aff,
__isl_take isl_space *dim)
{
aff = isl_aff_cow(aff);
if (!aff || !dim)
goto error;
aff->ls = isl_local_space_reset_space(aff->ls, dim);
if (!aff->ls)
return isl_aff_free(aff);
return aff;
error:
isl_aff_free(aff);
isl_space_free(dim);
return NULL;
}
/* Reset the space of "aff". 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_aff *isl_aff_reset_space_and_domain(__isl_take isl_aff *aff,
__isl_take isl_space *space, __isl_take isl_space *domain)
{
isl_space_free(space);
return isl_aff_reset_domain_space(aff, domain);
}
/* Reorder the coefficients of the affine expression based
* on the given reodering.
* The reordering r is assumed to have been extended with the local
* variables.
*/
static __isl_give isl_vec *vec_reorder(__isl_take isl_vec *vec,
__isl_take isl_reordering *r, int n_div)
{
isl_vec *res;
int i;
if (!vec || !r)
goto error;
res = isl_vec_alloc(vec->ctx,
2 + isl_space_dim(r->dim, isl_dim_all) + n_div);
isl_seq_cpy(res->el, vec->el, 2);
isl_seq_clr(res->el + 2, res->size - 2);
for (i = 0; i < r->len; ++i)
isl_int_set(res->el[2 + r->pos[i]], vec->el[2 + i]);
isl_reordering_free(r);
isl_vec_free(vec);
return res;
error:
isl_vec_free(vec);
isl_reordering_free(r);
return NULL;
}
/* Reorder the dimensions of the domain of "aff" according
* to the given reordering.
*/
__isl_give isl_aff *isl_aff_realign_domain(__isl_take isl_aff *aff,
__isl_take isl_reordering *r)
{
aff = isl_aff_cow(aff);
if (!aff)
goto error;
r = isl_reordering_extend(r, aff->ls->div->n_row);
aff->v = vec_reorder(aff->v, isl_reordering_copy(r),
aff->ls->div->n_row);
aff->ls = isl_local_space_realign(aff->ls, r);
if (!aff->v || !aff->ls)
return isl_aff_free(aff);
return aff;
error:
isl_aff_free(aff);
isl_reordering_free(r);
return NULL;
}
__isl_give isl_aff *isl_aff_align_params(__isl_take isl_aff *aff,
__isl_take isl_space *model)
{
if (!aff || !model)
goto error;
if (!isl_space_match(aff->ls->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(aff->ls->dim, model);
exp = isl_reordering_extend_space(exp,
isl_aff_get_domain_space(aff));
aff = isl_aff_realign_domain(aff, exp);
}
isl_space_free(model);
return aff;
error:
isl_space_free(model);
isl_aff_free(aff);
return NULL;
}
int isl_aff_plain_is_zero(__isl_keep isl_aff *aff)
{
if (!aff)
return -1;
return isl_seq_first_non_zero(aff->v->el + 1, aff->v->size - 1) < 0;
}
int isl_aff_plain_is_equal(__isl_keep isl_aff *aff1, __isl_keep isl_aff *aff2)
{
int equal;
if (!aff1 || !aff2)
return -1;
equal = isl_local_space_is_equal(aff1->ls, aff2->ls);
if (equal < 0 || !equal)
return equal;
return isl_vec_is_equal(aff1->v, aff2->v);
}
int isl_aff_get_denominator(__isl_keep isl_aff *aff, isl_int *v)
{
if (!aff)
return -1;
isl_int_set(*v, aff->v->el[0]);
return 0;
}
int isl_aff_get_constant(__isl_keep isl_aff *aff, isl_int *v)
{
if (!aff)
return -1;
isl_int_set(*v, aff->v->el[1]);
return 0;
}
int isl_aff_get_coefficient(__isl_keep isl_aff *aff,
enum isl_dim_type type, int pos, isl_int *v)
{
if (!aff)
return -1;
if (type == isl_dim_out)
isl_die(aff->v->ctx, isl_error_invalid,
"output/set dimension does not have a coefficient",
return -1);
if (type == isl_dim_in)
type = isl_dim_set;
if (pos >= isl_local_space_dim(aff->ls, type))
isl_die(aff->v->ctx, isl_error_invalid,
"position out of bounds", return -1);
pos += isl_local_space_offset(aff->ls, type);
isl_int_set(*v, aff->v->el[1 + pos]);
return 0;
}
__isl_give isl_aff *isl_aff_set_denominator(__isl_take isl_aff *aff, isl_int v)
{
aff = isl_aff_cow(aff);
if (!aff)
return NULL;
aff->v = isl_vec_cow(aff->v);
if (!aff->v)
return isl_aff_free(aff);
isl_int_set(aff->v->el[0], v);
return aff;
}
__isl_give isl_aff *isl_aff_set_constant(__isl_take isl_aff *aff, isl_int v)
{
aff = isl_aff_cow(aff);
if (!aff)
return NULL;
aff->v = isl_vec_cow(aff->v);
if (!aff->v)
return isl_aff_free(aff);
isl_int_set(aff->v->el[1], v);
return aff;
}
__isl_give isl_aff *isl_aff_add_constant(__isl_take isl_aff *aff, isl_int v)
{
if (isl_int_is_zero(v))
return aff;
aff = isl_aff_cow(aff);
if (!aff)
return NULL;
aff->v = isl_vec_cow(aff->v);
if (!aff->v)
return isl_aff_free(aff);
isl_int_addmul(aff->v->el[1], aff->v->el[0], v);
return aff;
}
__isl_give isl_aff *isl_aff_add_constant_si(__isl_take isl_aff *aff, int v)
{
isl_int t;
isl_int_init(t);
isl_int_set_si(t, v);
aff = isl_aff_add_constant(aff, t);
isl_int_clear(t);
return aff;
}
__isl_give isl_aff *isl_aff_set_constant_si(__isl_take isl_aff *aff, int v)
{
aff = isl_aff_cow(aff);
if (!aff)
return NULL;
aff->v = isl_vec_cow(aff->v);
if (!aff->v)
return isl_aff_free(aff);
isl_int_set_si(aff->v->el[1], v);
return aff;
}
__isl_give isl_aff *isl_aff_set_coefficient(__isl_take isl_aff *aff,
enum isl_dim_type type, int pos, isl_int v)
{
if (!aff)
return NULL;
if (type == isl_dim_out)
isl_die(aff->v->ctx, isl_error_invalid,
"output/set dimension does not have a coefficient",
return isl_aff_free(aff));
if (type == isl_dim_in)
type = isl_dim_set;
if (pos >= isl_local_space_dim(aff->ls, type))
isl_die(aff->v->ctx, isl_error_invalid,
"position out of bounds", return isl_aff_free(aff));
aff = isl_aff_cow(aff);
if (!aff)
return NULL;
aff->v = isl_vec_cow(aff->v);
if (!aff->v)
return isl_aff_free(aff);
pos += isl_local_space_offset(aff->ls, type);
isl_int_set(aff->v->el[1 + pos], v);
return aff;
}
__isl_give isl_aff *isl_aff_set_coefficient_si(__isl_take isl_aff *aff,
enum isl_dim_type type, int pos, int v)
{
if (!aff)
return NULL;
if (type == isl_dim_out)
isl_die(aff->v->ctx, isl_error_invalid,
"output/set dimension does not have a coefficient",
return isl_aff_free(aff));
if (type == isl_dim_in)
type = isl_dim_set;
if (pos >= isl_local_space_dim(aff->ls, type))
isl_die(aff->v->ctx, isl_error_invalid,
"position out of bounds", return isl_aff_free(aff));
aff = isl_aff_cow(aff);
if (!aff)
return NULL;
aff->v = isl_vec_cow(aff->v);
if (!aff->v)
return isl_aff_free(aff);
pos += isl_local_space_offset(aff->ls, type);
isl_int_set_si(aff->v->el[1 + pos], v);
return aff;
}
__isl_give isl_aff *isl_aff_add_coefficient(__isl_take isl_aff *aff,
enum isl_dim_type type, int pos, isl_int v)
{
if (!aff)
return NULL;
if (type == isl_dim_out)
isl_die(aff->v->ctx, isl_error_invalid,
"output/set dimension does not have a coefficient",
return isl_aff_free(aff));
if (type == isl_dim_in)
type = isl_dim_set;
if (pos >= isl_local_space_dim(aff->ls, type))
isl_die(aff->v->ctx, isl_error_invalid,
"position out of bounds", return isl_aff_free(aff));
aff = isl_aff_cow(aff);
if (!aff)
return NULL;
aff->v = isl_vec_cow(aff->v);
if (!aff->v)
return isl_aff_free(aff);
pos += isl_local_space_offset(aff->ls, type);
isl_int_addmul(aff->v->el[1 + pos], aff->v->el[0], v);
return aff;
}
__isl_give isl_aff *isl_aff_add_coefficient_si(__isl_take isl_aff *aff,
enum isl_dim_type type, int pos, int v)
{
isl_int t;
isl_int_init(t);
isl_int_set_si(t, v);
aff = isl_aff_add_coefficient(aff, type, pos, t);
isl_int_clear(t);
return aff;
}
__isl_give isl_aff *isl_aff_get_div(__isl_keep isl_aff *aff, int pos)
{
if (!aff)
return NULL;
return isl_local_space_get_div(aff->ls, pos);
}
__isl_give isl_aff *isl_aff_neg(__isl_take isl_aff *aff)
{
aff = isl_aff_cow(aff);
if (!aff)
return NULL;
aff->v = isl_vec_cow(aff->v);
if (!aff->v)
return isl_aff_free(aff);
isl_seq_neg(aff->v->el + 1, aff->v->el + 1, aff->v->size - 1);
return aff;
}
/* Remove divs from the local space that do not appear in the affine
* expression.
* We currently only remove divs at the end.
* Some intermediate divs may also not appear directly in the affine
* expression, but we would also need to check that no other divs are
* defined in terms of them.
*/
__isl_give isl_aff *isl_aff_remove_unused_divs( __isl_take isl_aff *aff)
{
int pos;
int off;
int n;
if (!aff)
return NULL;
n = isl_local_space_dim(aff->ls, isl_dim_div);
off = isl_local_space_offset(aff->ls, isl_dim_div);
pos = isl_seq_last_non_zero(aff->v->el + 1 + off, n) + 1;
if (pos == n)
return aff;
aff = isl_aff_cow(aff);
if (!aff)
return NULL;
aff->ls = isl_local_space_drop_dims(aff->ls, isl_dim_div, pos, n - pos);
aff->v = isl_vec_drop_els(aff->v, 1 + off + pos, n - pos);
if (!aff->ls || !aff->v)
return isl_aff_free(aff);
return aff;
}
__isl_give isl_aff *isl_aff_normalize(__isl_take isl_aff *aff)
{
if (!aff)
return NULL;
aff->v = isl_vec_normalize(aff->v);
if (!aff->v)
return isl_aff_free(aff);
aff = isl_aff_remove_unused_divs(aff);
return aff;
}
/* Given f, return floor(f).
* If f is an integer expression, then just return f.
* If f is a constant, then return the constant floor(f).
* Otherwise, if f = g/m, write g = q m + r,
* create a new div d = [r/m] and return the expression q + d.
* The coefficients in r are taken to lie between -m/2 and m/2.
*/
__isl_give isl_aff *isl_aff_floor(__isl_take isl_aff *aff)
{
int i;
int size;
isl_ctx *ctx;
isl_vec *div;
if (!aff)
return NULL;
if (isl_int_is_one(aff->v->el[0]))
return aff;
aff = isl_aff_cow(aff);
if (!aff)
return NULL;
aff->v = isl_vec_cow(aff->v);
if (!aff->v)
return isl_aff_free(aff);
if (isl_aff_is_cst(aff)) {
isl_int_fdiv_q(aff->v->el[1], aff->v->el[1], aff->v->el[0]);
isl_int_set_si(aff->v->el[0], 1);
return aff;
}
div = isl_vec_copy(aff->v);
div = isl_vec_cow(div);
if (!div)
return isl_aff_free(aff);
ctx = isl_aff_get_ctx(aff);
isl_int_fdiv_q(aff->v->el[0], aff->v->el[0], ctx->two);
for (i = 1; i < aff->v->size; ++i) {
isl_int_fdiv_r(div->el[i], div->el[i], div->el[0]);
isl_int_fdiv_q(aff->v->el[i], aff->v->el[i], div->el[0]);
if (isl_int_gt(div->el[i], aff->v->el[0])) {
isl_int_sub(div->el[i], div->el[i], div->el[0]);
isl_int_add_ui(aff->v->el[i], aff->v->el[i], 1);
}
}
aff->ls = isl_local_space_add_div(aff->ls, div);
if (!aff->ls)
return isl_aff_free(aff);
size = aff->v->size;
aff->v = isl_vec_extend(aff->v, size + 1);
if (!aff->v)
return isl_aff_free(aff);
isl_int_set_si(aff->v->el[0], 1);
isl_int_set_si(aff->v->el[size], 1);
return aff;
}
/* Compute
*
* aff mod m = aff - m * floor(aff/m)
*/
__isl_give isl_aff *isl_aff_mod(__isl_take isl_aff *aff, isl_int m)
{
isl_aff *res;
res = isl_aff_copy(aff);
aff = isl_aff_scale_down(aff, m);
aff = isl_aff_floor(aff);
aff = isl_aff_scale(aff, m);
res = isl_aff_sub(res, aff);
return res;
}
/* Compute
*
* pwaff mod m = pwaff - m * floor(pwaff/m)
*/
__isl_give isl_pw_aff *isl_pw_aff_mod(__isl_take isl_pw_aff *pwaff, isl_int m)
{
isl_pw_aff *res;
res = isl_pw_aff_copy(pwaff);
pwaff = isl_pw_aff_scale_down(pwaff, m);
pwaff = isl_pw_aff_floor(pwaff);
pwaff = isl_pw_aff_scale(pwaff, m);
res = isl_pw_aff_sub(res, pwaff);
return res;
}
/* Given f, return ceil(f).
* If f is an integer expression, then just return f.
* Otherwise, create a new div d = [-f] and return the expression -d.
*/
__isl_give isl_aff *isl_aff_ceil(__isl_take isl_aff *aff)
{
if (!aff)
return NULL;
if (isl_int_is_one(aff->v->el[0]))
return aff;
aff = isl_aff_neg(aff);
aff = isl_aff_floor(aff);
aff = isl_aff_neg(aff);
return aff;
}
/* Apply the expansion computed by isl_merge_divs.
* The expansion itself is given by "exp" while the resulting
* list of divs is given by "div".
*/
__isl_give isl_aff *isl_aff_expand_divs( __isl_take isl_aff *aff,
__isl_take isl_mat *div, int *exp)
{
int i, j;
int old_n_div;
int new_n_div;
int offset;
aff = isl_aff_cow(aff);
if (!aff || !div)
goto error;
old_n_div = isl_local_space_dim(aff->ls, isl_dim_div);
new_n_div = isl_mat_rows(div);
if (new_n_div < old_n_div)
isl_die(isl_mat_get_ctx(div), isl_error_invalid,
"not an expansion", goto error);
aff->v = isl_vec_extend(aff->v, aff->v->size + new_n_div - old_n_div);
if (!aff->v)
goto error;
offset = 1 + isl_local_space_offset(aff->ls, isl_dim_div);
j = old_n_div - 1;
for (i = new_n_div - 1; i >= 0; --i) {
if (j >= 0 && exp[j] == i) {
if (i != j)
isl_int_swap(aff->v->el[offset + i],
aff->v->el[offset + j]);
j--;
} else
isl_int_set_si(aff->v->el[offset + i], 0);
}
aff->ls = isl_local_space_replace_divs(aff->ls, isl_mat_copy(div));
if (!aff->ls)
goto error;
isl_mat_free(div);
return aff;
error:
isl_aff_free(aff);
isl_mat_free(div);
return NULL;
}
/* Add two affine expressions that live in the same local space.
*/
static __isl_give isl_aff *add_expanded(__isl_take isl_aff *aff1,
__isl_take isl_aff *aff2)
{
isl_int gcd, f;
aff1 = isl_aff_cow(aff1);
if (!aff1 || !aff2)
goto error;
aff1->v = isl_vec_cow(aff1->v);
if (!aff1->v)
goto error;
isl_int_init(gcd);
isl_int_init(f);
isl_int_gcd(gcd, aff1->v->el[0], aff2->v->el[0]);
isl_int_divexact(f, aff2->v->el[0], gcd);
isl_seq_scale(aff1->v->el + 1, aff1->v->el + 1, f, aff1->v->size - 1);
isl_int_divexact(f, aff1->v->el[0], gcd);
isl_seq_addmul(aff1->v->el + 1, f, aff2->v->el + 1, aff1->v->size - 1);
isl_int_divexact(f, aff2->v->el[0], gcd);
isl_int_mul(aff1->v->el[0], aff1->v->el[0], f);
isl_int_clear(f);
isl_int_clear(gcd);
isl_aff_free(aff2);
return aff1;
error:
isl_aff_free(aff1);
isl_aff_free(aff2);
return NULL;
}
__isl_give isl_aff *isl_aff_add(__isl_take isl_aff *aff1,
__isl_take isl_aff *aff2)
{
isl_ctx *ctx;
int *exp1 = NULL;
int *exp2 = NULL;
isl_mat *div;
if (!aff1 || !aff2)
goto error;
ctx = isl_aff_get_ctx(aff1);
if (!isl_space_is_equal(aff1->ls->dim, aff2->ls->dim))
isl_die(ctx, isl_error_invalid,
"spaces don't match", goto error);
if (aff1->ls->div->n_row == 0 && aff2->ls->div->n_row == 0)
return add_expanded(aff1, aff2);
exp1 = isl_alloc_array(ctx, int, aff1->ls->div->n_row);
exp2 = isl_alloc_array(ctx, int, aff2->ls->div->n_row);
if (!exp1 || !exp2)
goto error;
div = isl_merge_divs(aff1->ls->div, aff2->ls->div, exp1, exp2);
aff1 = isl_aff_expand_divs(aff1, isl_mat_copy(div), exp1);
aff2 = isl_aff_expand_divs(aff2, div, exp2);
free(exp1);
free(exp2);
return add_expanded(aff1, aff2);
error:
free(exp1);
free(exp2);
isl_aff_free(aff1);
isl_aff_free(aff2);
return NULL;
}
__isl_give isl_aff *isl_aff_sub(__isl_take isl_aff *aff1,
__isl_take isl_aff *aff2)
{
return isl_aff_add(aff1, isl_aff_neg(aff2));
}
__isl_give isl_aff *isl_aff_scale(__isl_take isl_aff *aff, isl_int f)
{
isl_int gcd;
if (isl_int_is_one(f))
return aff;
aff = isl_aff_cow(aff);
if (!aff)
return NULL;
aff->v = isl_vec_cow(aff->v);
if (!aff->v)
return isl_aff_free(aff);
isl_int_init(gcd);
isl_int_gcd(gcd, aff->v->el[0], f);
isl_int_divexact(aff->v->el[0], aff->v->el[0], gcd);
isl_int_divexact(gcd, f, gcd);
isl_seq_scale(aff->v->el + 1, aff->v->el + 1, gcd, aff->v->size - 1);
isl_int_clear(gcd);
return aff;
}
__isl_give isl_aff *isl_aff_scale_down(__isl_take isl_aff *aff, isl_int f)
{
isl_int gcd;
if (isl_int_is_one(f))
return aff;
aff = isl_aff_cow(aff);
if (!aff)
return NULL;
aff->v = isl_vec_cow(aff->v);
if (!aff->v)
return isl_aff_free(aff);
isl_int_init(gcd);
isl_seq_gcd(aff->v->el + 1, aff->v->size - 1, &gcd);
isl_int_gcd(gcd, gcd, f);
isl_seq_scale_down(aff->v->el + 1, aff->v->el + 1, gcd, aff->v->size - 1);
isl_int_divexact(gcd, f, gcd);
isl_int_mul(aff->v->el[0], aff->v->el[0], gcd);
isl_int_clear(gcd);
return aff;
}
__isl_give isl_aff *isl_aff_scale_down_ui(__isl_take isl_aff *aff, unsigned f)
{
isl_int v;
if (f == 1)
return aff;
isl_int_init(v);
isl_int_set_ui(v, f);
aff = isl_aff_scale_down(aff, v);
isl_int_clear(v);
return aff;
}
__isl_give isl_aff *isl_aff_set_dim_name(__isl_take isl_aff *aff,
enum isl_dim_type type, unsigned pos, const char *s)
{
aff = isl_aff_cow(aff);
if (!aff)
return NULL;
if (type == isl_dim_out)
isl_die(aff->v->ctx, isl_error_invalid,
"cannot set name of output/set dimension",
return isl_aff_free(aff));
if (type == isl_dim_in)
type = isl_dim_set;
aff->ls = isl_local_space_set_dim_name(aff->ls, type, pos, s);
if (!aff->ls)
return isl_aff_free(aff);
return aff;
}
__isl_give isl_aff *isl_aff_set_dim_id(__isl_take isl_aff *aff,
enum isl_dim_type type, unsigned pos, __isl_take isl_id *id)
{
aff = isl_aff_cow(aff);
if (!aff)
return isl_id_free(id);
if (type == isl_dim_out)
isl_die(aff->v->ctx, isl_error_invalid,
"cannot set name of output/set dimension",
goto error);
if (type == isl_dim_in)
type = isl_dim_set;
aff->ls = isl_local_space_set_dim_id(aff->ls, type, pos, id);
if (!aff->ls)
return isl_aff_free(aff);
return aff;
error:
isl_id_free(id);
isl_aff_free(aff);
return NULL;
}
/* Exploit the equalities in "eq" to simplify the affine expression
* and the expressions of the integer divisions in the local space.
* The integer divisions in this local space are assumed to appear
* as regular dimensions in "eq".
*/
static __isl_give isl_aff *isl_aff_substitute_equalities_lifted(
__isl_take isl_aff *aff, __isl_take isl_basic_set *eq)
{
int i, j;
unsigned total;
unsigned n_div;
if (!eq)
goto error;
if (eq->n_eq == 0) {
isl_basic_set_free(eq);
return aff;
}
aff = isl_aff_cow(aff);
if (!aff)
goto error;
aff->ls = isl_local_space_substitute_equalities(aff->ls,
isl_basic_set_copy(eq));
if (!aff->ls)
goto error;
total = 1 + isl_space_dim(eq->dim, isl_dim_all);
n_div = eq->n_div;
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;
isl_seq_elim(aff->v->el + 1, eq->eq[i], j, total,
&aff->v->el[0]);
}
isl_basic_set_free(eq);
aff = isl_aff_normalize(aff);
return aff;
error:
isl_basic_set_free(eq);
isl_aff_free(aff);
return NULL;
}
/* Exploit the equalities in "eq" to simplify the affine expression
* and the expressions of the integer divisions in the local space.
*/
static __isl_give isl_aff *isl_aff_substitute_equalities(
__isl_take isl_aff *aff, __isl_take isl_basic_set *eq)
{
int n_div;
if (!aff || !eq)
goto error;
n_div = isl_local_space_dim(aff->ls, isl_dim_div);
if (n_div > 0)
eq = isl_basic_set_add(eq, isl_dim_set, n_div);
return isl_aff_substitute_equalities_lifted(aff, eq);
error:
isl_basic_set_free(eq);
isl_aff_free(aff);
return NULL;
}
/* Look for equalities among the variables shared by context and aff
* and the integer divisions of aff, if any.
* The equalities are then used to eliminate coefficients and/or integer
* divisions from aff.
*/
__isl_give isl_aff *isl_aff_gist(__isl_take isl_aff *aff,
__isl_take isl_set *context)
{
isl_basic_set *hull;
int n_div;
if (!aff)
goto error;
n_div = isl_local_space_dim(aff->ls, isl_dim_div);
if (n_div > 0) {
isl_basic_set *bset;
isl_local_space *ls;
context = isl_set_add_dims(context, isl_dim_set, n_div);
ls = isl_aff_get_domain_local_space(aff);
bset = isl_basic_set_from_local_space(ls);
bset = isl_basic_set_lift(bset);
bset = isl_basic_set_flatten(bset);
context = isl_set_intersect(context,
isl_set_from_basic_set(bset));
}
hull = isl_set_affine_hull(context);
return isl_aff_substitute_equalities_lifted(aff, hull);
error:
isl_aff_free(aff);
isl_set_free(context);
return NULL;
}
__isl_give isl_aff *isl_aff_gist_params(__isl_take isl_aff *aff,
__isl_take isl_set *context)
{
isl_set *dom_context = isl_set_universe(isl_aff_get_domain_space(aff));
dom_context = isl_set_intersect_params(dom_context, context);
return isl_aff_gist(aff, dom_context);
}
/* Return a basic set containing those elements in the space
* of aff where it is non-negative.
*/
__isl_give isl_basic_set *isl_aff_nonneg_basic_set(__isl_take isl_aff *aff)
{
isl_constraint *ineq;
isl_basic_set *bset;
ineq = isl_inequality_from_aff(aff);
bset = isl_basic_set_from_constraint(ineq);
bset = isl_basic_set_simplify(bset);
return bset;
}
/* Return a basic set containing those elements in the space
* of aff where it is zero.
*/
__isl_give isl_basic_set *isl_aff_zero_basic_set(__isl_take isl_aff *aff)
{
isl_constraint *ineq;
isl_basic_set *bset;
ineq = isl_equality_from_aff(aff);
bset = isl_basic_set_from_constraint(ineq);
bset = isl_basic_set_simplify(bset);
return bset;
}
/* Return a basic set containing those elements in the shared space
* of aff1 and aff2 where aff1 is greater than or equal to aff2.
*/
__isl_give isl_basic_set *isl_aff_ge_basic_set(__isl_take isl_aff *aff1,
__isl_take isl_aff *aff2)
{
aff1 = isl_aff_sub(aff1, aff2);
return isl_aff_nonneg_basic_set(aff1);
}
/* Return a basic set containing those elements in the shared space
* of aff1 and aff2 where aff1 is smaller than or equal to aff2.
*/
__isl_give isl_basic_set *isl_aff_le_basic_set(__isl_take isl_aff *aff1,
__isl_take isl_aff *aff2)
{
return isl_aff_ge_basic_set(aff2, aff1);
}
__isl_give isl_aff *isl_aff_add_on_domain(__isl_keep isl_set *dom,
__isl_take isl_aff *aff1, __isl_take isl_aff *aff2)
{
aff1 = isl_aff_add(aff1, aff2);
aff1 = isl_aff_gist(aff1, isl_set_copy(dom));
return aff1;
}
int isl_aff_is_empty(__isl_keep isl_aff *aff)
{
if (!aff)
return -1;
return 0;
}
/* Check whether the given affine expression has non-zero coefficient
* for any dimension in the given range or if any of these dimensions
* appear with non-zero coefficients in any of the integer divisions
* involved in the affine expression.
*/
int isl_aff_involves_dims(__isl_keep isl_aff *aff,
enum isl_dim_type type, unsigned first, unsigned n)
{
int i;
isl_ctx *ctx;
int *active = NULL;
int involves = 0;
if (!aff)
return -1;
if (n == 0)
return 0;
ctx = isl_aff_get_ctx(aff);
if (first + n > isl_aff_dim(aff, type))
isl_die(ctx, isl_error_invalid,
"range out of bounds", return -1);
active = isl_local_space_get_active(aff->ls, aff->v->el + 2);
if (!active)
goto error;
first += isl_local_space_offset(aff->ls, type) - 1;
for (i = 0; i < n; ++i)
if (active[first + i]) {
involves = 1;
break;
}
free(active);
return involves;
error:
free(active);
return -1;
}
__isl_give isl_aff *isl_aff_drop_dims(__isl_take isl_aff *aff,
enum isl_dim_type type, unsigned first, unsigned n)
{
isl_ctx *ctx;
if (!aff)
return NULL;
if (type == isl_dim_out)
isl_die(aff->v->ctx, isl_error_invalid,
"cannot drop output/set dimension",
return isl_aff_free(aff));
if (type == isl_dim_in)
type = isl_dim_set;
if (n == 0 && !isl_local_space_is_named_or_nested(aff->ls, type))
return aff;
ctx = isl_aff_get_ctx(aff);
if (first + n > isl_local_space_dim(aff->ls, type))
isl_die(ctx, isl_error_invalid, "range out of bounds",
return isl_aff_free(aff));
aff = isl_aff_cow(aff);
if (!aff)
return NULL;
aff->ls = isl_local_space_drop_dims(aff->ls, type, first, n);
if (!aff->ls)
return isl_aff_free(aff);
first += 1 + isl_local_space_offset(aff->ls, type);
aff->v = isl_vec_drop_els(aff->v, first, n);
if (!aff->v)
return isl_aff_free(aff);
return aff;
}
/* Project the domain of the affine expression onto its parameter space.
* The affine expression may not involve any of the domain dimensions.
*/
__isl_give isl_aff *isl_aff_project_domain_on_params(__isl_take isl_aff *aff)
{
isl_space *space;
unsigned n;
int involves;
n = isl_aff_dim(aff, isl_dim_in);
involves = isl_aff_involves_dims(aff, isl_dim_in, 0, n);
if (involves < 0)
return isl_aff_free(aff);
if (involves)
isl_die(isl_aff_get_ctx(aff), isl_error_invalid,
"affine expression involves some of the domain dimensions",
return isl_aff_free(aff));
aff = isl_aff_drop_dims(aff, isl_dim_in, 0, n);
space = isl_aff_get_domain_space(aff);
space = isl_space_params(space);
aff = isl_aff_reset_domain_space(aff, space);
return aff;
}
__isl_give isl_aff *isl_aff_insert_dims(__isl_take isl_aff *aff,
enum isl_dim_type type, unsigned first, unsigned n)
{
isl_ctx *ctx;
if (!aff)
return NULL;
if (type == isl_dim_out)
isl_die(aff->v->ctx, isl_error_invalid,
"cannot insert output/set dimensions",
return isl_aff_free(aff));
if (type == isl_dim_in)
type = isl_dim_set;
if (n == 0 && !isl_local_space_is_named_or_nested(aff->ls, type))
return aff;
ctx = isl_aff_get_ctx(aff);
if (first > isl_local_space_dim(aff->ls, type))
isl_die(ctx, isl_error_invalid, "position out of bounds",
return isl_aff_free(aff));
aff = isl_aff_cow(aff);
if (!aff)
return NULL;
aff->ls = isl_local_space_insert_dims(aff->ls, type, first, n);
if (!aff->ls)
return isl_aff_free(aff);
first += 1 + isl_local_space_offset(aff->ls, type);
aff->v = isl_vec_insert_zero_els(aff->v, first, n);
if (!aff->v)
return isl_aff_free(aff);
return aff;
}
__isl_give isl_aff *isl_aff_add_dims(__isl_take isl_aff *aff,
enum isl_dim_type type, unsigned n)
{
unsigned pos;
pos = isl_aff_dim(aff, type);
return isl_aff_insert_dims(aff, type, pos, n);
}
__isl_give isl_pw_aff *isl_pw_aff_add_dims(__isl_take isl_pw_aff *pwaff,
enum isl_dim_type type, unsigned n)
{
unsigned pos;
pos = isl_pw_aff_dim(pwaff, type);
return isl_pw_aff_insert_dims(pwaff, type, pos, n);
}
__isl_give isl_pw_aff *isl_pw_aff_from_aff(__isl_take isl_aff *aff)
{
isl_set *dom = isl_set_universe(isl_aff_get_domain_space(aff));
return isl_pw_aff_alloc(dom, aff);
}
#undef PW
#define PW isl_pw_aff
#undef EL
#define EL isl_aff
#undef EL_IS_ZERO
#define EL_IS_ZERO is_empty
#undef ZERO
#define ZERO empty
#undef IS_ZERO
#define IS_ZERO is_empty
#undef FIELD
#define FIELD aff
#undef DEFAULT_IS_ZERO
#define DEFAULT_IS_ZERO 0
#define NO_EVAL
#define NO_OPT
#define NO_MOVE_DIMS
#define NO_LIFT
#define NO_MORPH
#include <isl_pw_templ.c>
static __isl_give isl_set *align_params_pw_pw_set_and(
__isl_take isl_pw_aff *pwaff1, __isl_take isl_pw_aff *pwaff2,
__isl_give isl_set *(*fn)(__isl_take isl_pw_aff *pwaff1,
__isl_take isl_pw_aff *pwaff2))
{
if (!pwaff1 || !pwaff2)
goto error;
if (isl_space_match(pwaff1->dim, isl_dim_param,
pwaff2->dim, isl_dim_param))
return fn(pwaff1, pwaff2);
if (!isl_space_has_named_params(pwaff1->dim) ||
!isl_space_has_named_params(pwaff2->dim))
isl_die(isl_pw_aff_get_ctx(pwaff1), isl_error_invalid,
"unaligned unnamed parameters", goto error);
pwaff1 = isl_pw_aff_align_params(pwaff1, isl_pw_aff_get_space(pwaff2));
pwaff2 = isl_pw_aff_align_params(pwaff2, isl_pw_aff_get_space(pwaff1));
return fn(pwaff1, pwaff2);
error:
isl_pw_aff_free(pwaff1);
isl_pw_aff_free(pwaff2);
return NULL;
}
/* Compute a piecewise quasi-affine expression with a domain that
* is the union of those of pwaff1 and pwaff2 and such that on each
* cell, the quasi-affine expression is the better (according to cmp)
* of those of pwaff1 and pwaff2. If only one of pwaff1 or pwaff2
* is defined on a given cell, then the associated expression
* is the defined one.
*/
static __isl_give isl_pw_aff *pw_aff_union_opt(__isl_take isl_pw_aff *pwaff1,
__isl_take isl_pw_aff *pwaff2,
__isl_give isl_basic_set *(*cmp)(__isl_take isl_aff *aff1,
__isl_take isl_aff *aff2))
{
int i, j, n;
isl_pw_aff *res;
isl_ctx *ctx;
isl_set *set;
if (!pwaff1 || !pwaff2)
goto error;
ctx = isl_space_get_ctx(pwaff1->dim);
if (!isl_space_is_equal(pwaff1->dim, pwaff2->dim))
isl_die(ctx, isl_error_invalid,
"arguments should live in same space", goto error);
if (isl_pw_aff_is_empty(pwaff1)) {
isl_pw_aff_free(pwaff1);
return pwaff2;
}
if (isl_pw_aff_is_empty(pwaff2)) {
isl_pw_aff_free(pwaff2);
return pwaff1;
}
n = 2 * (pwaff1->n + 1) * (pwaff2->n + 1);
res = isl_pw_aff_alloc_size(isl_space_copy(pwaff1->dim), n);
for (i = 0; i < pwaff1->n; ++i) {
set = isl_set_copy(pwaff1->p[i].set);
for (j = 0; j < pwaff2->n; ++j) {
struct isl_set *common;
isl_set *better;
common = isl_set_intersect(
isl_set_copy(pwaff1->p[i].set),
isl_set_copy(pwaff2->p[j].set));
better = isl_set_from_basic_set(cmp(
isl_aff_copy(pwaff2->p[j].aff),
isl_aff_copy(pwaff1->p[i].aff)));
better = isl_set_intersect(common, better);
if (isl_set_plain_is_empty(better)) {
isl_set_free(better);
continue;
}
set = isl_set_subtract(set, isl_set_copy(better));
res = isl_pw_aff_add_piece(res, better,
isl_aff_copy(pwaff2->p[j].aff));
}
res = isl_pw_aff_add_piece(res, set,
isl_aff_copy(pwaff1->p[i].aff));
}
for (j = 0; j < pwaff2->n; ++j) {
set = isl_set_copy(pwaff2->p[j].set);
for (i = 0; i < pwaff1->n; ++i)
set = isl_set_subtract(set,
isl_set_copy(pwaff1->p[i].set));
res = isl_pw_aff_add_piece(res, set,
isl_aff_copy(pwaff2->p[j].aff));
}
isl_pw_aff_free(pwaff1);
isl_pw_aff_free(pwaff2);
return res;
error:
isl_pw_aff_free(pwaff1);
isl_pw_aff_free(pwaff2);
return NULL;
}
/* Compute a piecewise quasi-affine expression with a domain that
* is the union of those of pwaff1 and pwaff2 and such that on each
* cell, the quasi-affine expression is the maximum of those of pwaff1
* and pwaff2. If only one of pwaff1 or pwaff2 is defined on a given
* cell, then the associated expression is the defined one.
*/
static __isl_give isl_pw_aff *pw_aff_union_max(__isl_take isl_pw_aff *pwaff1,
__isl_take isl_pw_aff *pwaff2)
{
return pw_aff_union_opt(pwaff1, pwaff2, &isl_aff_ge_basic_set);
}
__isl_give isl_pw_aff *isl_pw_aff_union_max(__isl_take isl_pw_aff *pwaff1,
__isl_take isl_pw_aff *pwaff2)
{
return isl_pw_aff_align_params_pw_pw_and(pwaff1, pwaff2,
&pw_aff_union_max);
}
/* Compute a piecewise quasi-affine expression with a domain that
* is the union of those of pwaff1 and pwaff2 and such that on each
* cell, the quasi-affine expression is the minimum of those of pwaff1
* and pwaff2. If only one of pwaff1 or pwaff2 is defined on a given
* cell, then the associated expression is the defined one.
*/
static __isl_give isl_pw_aff *pw_aff_union_min(__isl_take isl_pw_aff *pwaff1,
__isl_take isl_pw_aff *pwaff2)
{
return pw_aff_union_opt(pwaff1, pwaff2, &isl_aff_le_basic_set);
}
__isl_give isl_pw_aff *isl_pw_aff_union_min(__isl_take isl_pw_aff *pwaff1,
__isl_take isl_pw_aff *pwaff2)
{
return isl_pw_aff_align_params_pw_pw_and(pwaff1, pwaff2,
&pw_aff_union_min);
}
__isl_give isl_pw_aff *isl_pw_aff_union_opt(__isl_take isl_pw_aff *pwaff1,
__isl_take isl_pw_aff *pwaff2, int max)
{
if (max)
return isl_pw_aff_union_max(pwaff1, pwaff2);
else
return isl_pw_aff_union_min(pwaff1, pwaff2);
}
/* Construct a map with as domain the domain of pwaff and
* one-dimensional range corresponding to the affine expressions.
*/
static __isl_give isl_map *map_from_pw_aff(__isl_take isl_pw_aff *pwaff)
{
int i;
isl_space *dim;
isl_map *map;
if (!pwaff)
return NULL;
dim = isl_pw_aff_get_space(pwaff);
map = isl_map_empty(dim);
for (i = 0; i < pwaff->n; ++i) {
isl_basic_map *bmap;
isl_map *map_i;
bmap = isl_basic_map_from_aff(isl_aff_copy(pwaff->p[i].aff));
map_i = isl_map_from_basic_map(bmap);
map_i = isl_map_intersect_domain(map_i,
isl_set_copy(pwaff->p[i].set));
map = isl_map_union_disjoint(map, map_i);
}
isl_pw_aff_free(pwaff);
return map;
}
/* Construct a map with as domain the domain of pwaff and
* one-dimensional range corresponding to the affine expressions.
*/
__isl_give isl_map *isl_map_from_pw_aff(__isl_take isl_pw_aff *pwaff)
{
if (!pwaff)
return NULL;
if (isl_space_is_set(pwaff->dim))
isl_die(isl_pw_aff_get_ctx(pwaff), isl_error_invalid,
"space of input is not a map",
return isl_pw_aff_free(pwaff));
return map_from_pw_aff(pwaff);
}
/* Construct a one-dimensional set with as parameter domain
* the domain of pwaff and the single set dimension
* corresponding to the affine expressions.
*/
__isl_give isl_set *isl_set_from_pw_aff(__isl_take isl_pw_aff *pwaff)
{
if (!pwaff)
return NULL;
if (!isl_space_is_set(pwaff->dim))
isl_die(isl_pw_aff_get_ctx(pwaff), isl_error_invalid,
"space of input is not a set",
return isl_pw_aff_free(pwaff));
return map_from_pw_aff(pwaff);
}
/* Return a set containing those elements in the domain
* of pwaff where it is non-negative.
*/
__isl_give isl_set *isl_pw_aff_nonneg_set(__isl_take isl_pw_aff *pwaff)
{
int i;
isl_set *set;
if (!pwaff)
return NULL;
set = isl_set_empty(isl_pw_aff_get_domain_space(pwaff));
for (i = 0; i < pwaff->n; ++i) {
isl_basic_set *bset;
isl_set *set_i;
bset = isl_aff_nonneg_basic_set(isl_aff_copy(pwaff->p[i].aff));
set_i = isl_set_from_basic_set(bset);
set_i = isl_set_intersect(set_i, isl_set_copy(pwaff->p[i].set));
set = isl_set_union_disjoint(set, set_i);
}
isl_pw_aff_free(pwaff);
return set;
}
/* Return a set containing those elements in the domain
* of pwaff where it is zero (if complement is 0) or not zero
* (if complement is 1).
*/
static __isl_give isl_set *pw_aff_zero_set(__isl_take isl_pw_aff *pwaff,
int complement)
{
int i;
isl_set *set;
if (!pwaff)
return NULL;
set = isl_set_empty(isl_pw_aff_get_domain_space(pwaff));
for (i = 0; i < pwaff->n; ++i) {
isl_basic_set *bset;
isl_set *set_i, *zero;
bset = isl_aff_zero_basic_set(isl_aff_copy(pwaff->p[i].aff));
zero = isl_set_from_basic_set(bset);
set_i = isl_set_copy(pwaff->p[i].set);
if (complement)
set_i = isl_set_subtract(set_i, zero);
else
set_i = isl_set_intersect(set_i, zero);
set = isl_set_union_disjoint(set, set_i);
}
isl_pw_aff_free(pwaff);
return set;
}
/* Return a set containing those elements in the domain
* of pwaff where it is zero.
*/
__isl_give isl_set *isl_pw_aff_zero_set(__isl_take isl_pw_aff *pwaff)
{
return pw_aff_zero_set(pwaff, 0);
}
/* Return a set containing those elements in the domain
* of pwaff where it is not zero.
*/
__isl_give isl_set *isl_pw_aff_non_zero_set(__isl_take isl_pw_aff *pwaff)
{
return pw_aff_zero_set(pwaff, 1);
}
/* Return a set containing those elements in the shared domain
* of pwaff1 and pwaff2 where pwaff1 is greater than (or equal) to pwaff2.
*
* We compute the difference on the shared domain and then construct
* the set of values where this difference is non-negative.
* If strict is set, we first subtract 1 from the difference.
* If equal is set, we only return the elements where pwaff1 and pwaff2
* are equal.
*/
static __isl_give isl_set *pw_aff_gte_set(__isl_take isl_pw_aff *pwaff1,
__isl_take isl_pw_aff *pwaff2, int strict, int equal)
{
isl_set *set1, *set2;
set1 = isl_pw_aff_domain(isl_pw_aff_copy(pwaff1));
set2 = isl_pw_aff_domain(isl_pw_aff_copy(pwaff2));
set1 = isl_set_intersect(set1, set2);
pwaff1 = isl_pw_aff_intersect_domain(pwaff1, isl_set_copy(set1));
pwaff2 = isl_pw_aff_intersect_domain(pwaff2, isl_set_copy(set1));
pwaff1 = isl_pw_aff_add(pwaff1, isl_pw_aff_neg(pwaff2));
if (strict) {
isl_space *dim = isl_set_get_space(set1);
isl_aff *aff;
aff = isl_aff_zero_on_domain(isl_local_space_from_space(dim));
aff = isl_aff_add_constant_si(aff, -1);
pwaff1 = isl_pw_aff_add(pwaff1, isl_pw_aff_alloc(set1, aff));
} else
isl_set_free(set1);
if (equal)
return isl_pw_aff_zero_set(pwaff1);
return isl_pw_aff_nonneg_set(pwaff1);
}
/* Return a set containing those elements in the shared domain
* of pwaff1 and pwaff2 where pwaff1 is equal to pwaff2.
*/
static __isl_give isl_set *pw_aff_eq_set(__isl_take isl_pw_aff *pwaff1,
__isl_take isl_pw_aff *pwaff2)
{
return pw_aff_gte_set(pwaff1, pwaff2, 0, 1);
}
__isl_give isl_set *isl_pw_aff_eq_set(__isl_take isl_pw_aff *pwaff1,
__isl_take isl_pw_aff *pwaff2)
{
return align_params_pw_pw_set_and(pwaff1, pwaff2, &pw_aff_eq_set);
}
/* Return a set containing those elements in the shared domain
* of pwaff1 and pwaff2 where pwaff1 is greater than or equal to pwaff2.
*/
static __isl_give isl_set *pw_aff_ge_set(__isl_take isl_pw_aff *pwaff1,
__isl_take isl_pw_aff *pwaff2)
{
return pw_aff_gte_set(pwaff1, pwaff2, 0, 0);
}
__isl_give isl_set *isl_pw_aff_ge_set(__isl_take isl_pw_aff *pwaff1,
__isl_take isl_pw_aff *pwaff2)
{
return align_params_pw_pw_set_and(pwaff1, pwaff2, &pw_aff_ge_set);
}
/* Return a set containing those elements in the shared domain
* of pwaff1 and pwaff2 where pwaff1 is strictly greater than pwaff2.
*/
static __isl_give isl_set *pw_aff_gt_set(__isl_take isl_pw_aff *pwaff1,
__isl_take isl_pw_aff *pwaff2)
{
return pw_aff_gte_set(pwaff1, pwaff2, 1, 0);
}
__isl_give isl_set *isl_pw_aff_gt_set(__isl_take isl_pw_aff *pwaff1,
__isl_take isl_pw_aff *pwaff2)
{
return align_params_pw_pw_set_and(pwaff1, pwaff2, &pw_aff_gt_set);
}
__isl_give isl_set *isl_pw_aff_le_set(__isl_take isl_pw_aff *pwaff1,
__isl_take isl_pw_aff *pwaff2)
{
return isl_pw_aff_ge_set(pwaff2, pwaff1);
}
__isl_give isl_set *isl_pw_aff_lt_set(__isl_take isl_pw_aff *pwaff1,
__isl_take isl_pw_aff *pwaff2)
{
return isl_pw_aff_gt_set(pwaff2, pwaff1);
}
/* Return a set containing those elements in the shared domain
* of the elements of list1 and list2 where each element in list1
* has the relation specified by "fn" with each element in list2.
*/
static __isl_give isl_set *pw_aff_list_set(__isl_take isl_pw_aff_list *list1,
__isl_take isl_pw_aff_list *list2,
__isl_give isl_set *(*fn)(__isl_take isl_pw_aff *pwaff1,
__isl_take isl_pw_aff *pwaff2))
{
int i, j;
isl_ctx *ctx;
isl_set *set;
if (!list1 || !list2)
goto error;
ctx = isl_pw_aff_list_get_ctx(list1);
if (list1->n < 1 || list2->n < 1)
isl_die(ctx, isl_error_invalid,
"list should contain at least one element", goto error);
set = isl_set_universe(isl_pw_aff_get_domain_space(list1->p[0]));
for (i = 0; i < list1->n; ++i)
for (j = 0; j < list2->n; ++j) {
isl_set *set_ij;
set_ij = fn(isl_pw_aff_copy(list1->p[i]),
isl_pw_aff_copy(list2->p[j]));
set = isl_set_intersect(set, set_ij);
}
isl_pw_aff_list_free(list1);
isl_pw_aff_list_free(list2);
return set;
error:
isl_pw_aff_list_free(list1);
isl_pw_aff_list_free(list2);
return NULL;
}
/* Return a set containing those elements in the shared domain
* of the elements of list1 and list2 where each element in list1
* is equal to each element in list2.
*/
__isl_give isl_set *isl_pw_aff_list_eq_set(__isl_take isl_pw_aff_list *list1,
__isl_take isl_pw_aff_list *list2)
{
return pw_aff_list_set(list1, list2, &isl_pw_aff_eq_set);
}
__isl_give isl_set *isl_pw_aff_list_ne_set(__isl_take isl_pw_aff_list *list1,
__isl_take isl_pw_aff_list *list2)
{
return pw_aff_list_set(list1, list2, &isl_pw_aff_ne_set);
}
/* Return a set containing those elements in the shared domain
* of the elements of list1 and list2 where each element in list1
* is less than or equal to each element in list2.
*/
__isl_give isl_set *isl_pw_aff_list_le_set(__isl_take isl_pw_aff_list *list1,
__isl_take isl_pw_aff_list *list2)
{
return pw_aff_list_set(list1, list2, &isl_pw_aff_le_set);
}
__isl_give isl_set *isl_pw_aff_list_lt_set(__isl_take isl_pw_aff_list *list1,
__isl_take isl_pw_aff_list *list2)
{
return pw_aff_list_set(list1, list2, &isl_pw_aff_lt_set);
}
__isl_give isl_set *isl_pw_aff_list_ge_set(__isl_take isl_pw_aff_list *list1,
__isl_take isl_pw_aff_list *list2)
{
return pw_aff_list_set(list1, list2, &isl_pw_aff_ge_set);
}
__isl_give isl_set *isl_pw_aff_list_gt_set(__isl_take isl_pw_aff_list *list1,
__isl_take isl_pw_aff_list *list2)
{
return pw_aff_list_set(list1, list2, &isl_pw_aff_gt_set);
}
/* Return a set containing those elements in the shared domain
* of pwaff1 and pwaff2 where pwaff1 is not equal to pwaff2.
*/
static __isl_give isl_set *pw_aff_ne_set(__isl_take isl_pw_aff *pwaff1,
__isl_take isl_pw_aff *pwaff2)
{
isl_set *set_lt, *set_gt;
set_lt = isl_pw_aff_lt_set(isl_pw_aff_copy(pwaff1),
isl_pw_aff_copy(pwaff2));
set_gt = isl_pw_aff_gt_set(pwaff1, pwaff2);
return isl_set_union_disjoint(set_lt, set_gt);
}
__isl_give isl_set *isl_pw_aff_ne_set(__isl_take isl_pw_aff *pwaff1,
__isl_take isl_pw_aff *pwaff2)
{
return align_params_pw_pw_set_and(pwaff1, pwaff2, &pw_aff_ne_set);
}
__isl_give isl_pw_aff *isl_pw_aff_scale_down(__isl_take isl_pw_aff *pwaff,
isl_int v)
{
int i;
if (isl_int_is_one(v))
return pwaff;
if (!isl_int_is_pos(v))
isl_die(isl_pw_aff_get_ctx(pwaff), isl_error_invalid,
"factor needs to be positive",
return isl_pw_aff_free(pwaff));
pwaff = isl_pw_aff_cow(pwaff);
if (!pwaff)
return NULL;
if (pwaff->n == 0)
return pwaff;
for (i = 0; i < pwaff->n; ++i) {
pwaff->p[i].aff = isl_aff_scale_down(pwaff->p[i].aff, v);
if (!pwaff->p[i].aff)
return isl_pw_aff_free(pwaff);
}
return pwaff;
}
__isl_give isl_pw_aff *isl_pw_aff_floor(__isl_take isl_pw_aff *pwaff)
{
int i;
pwaff = isl_pw_aff_cow(pwaff);
if (!pwaff)
return NULL;
if (pwaff->n == 0)
return pwaff;
for (i = 0; i < pwaff->n; ++i) {
pwaff->p[i].aff = isl_aff_floor(pwaff->p[i].aff);
if (!pwaff->p[i].aff)
return isl_pw_aff_free(pwaff);
}
return pwaff;
}
__isl_give isl_pw_aff *isl_pw_aff_ceil(__isl_take isl_pw_aff *pwaff)
{
int i;
pwaff = isl_pw_aff_cow(pwaff);
if (!pwaff)
return NULL;
if (pwaff->n == 0)
return pwaff;
for (i = 0; i < pwaff->n; ++i) {
pwaff->p[i].aff = isl_aff_ceil(pwaff->p[i].aff);
if (!pwaff->p[i].aff)
return isl_pw_aff_free(pwaff);
}
return pwaff;
}
/* Assuming that "cond1" and "cond2" are disjoint,
* return an affine expression that is equal to pwaff1 on cond1
* and to pwaff2 on cond2.
*/
static __isl_give isl_pw_aff *isl_pw_aff_select(
__isl_take isl_set *cond1, __isl_take isl_pw_aff *pwaff1,
__isl_take isl_set *cond2, __isl_take isl_pw_aff *pwaff2)
{
pwaff1 = isl_pw_aff_intersect_domain(pwaff1, cond1);
pwaff2 = isl_pw_aff_intersect_domain(pwaff2, cond2);
return isl_pw_aff_add_disjoint(pwaff1, pwaff2);
}
/* Return an affine expression that is equal to pwaff_true for elements
* where "cond" is non-zero and to pwaff_false for elements where "cond"
* is zero.
* That is, return cond ? pwaff_true : pwaff_false;
*/
__isl_give isl_pw_aff *isl_pw_aff_cond(__isl_take isl_pw_aff *cond,
__isl_take isl_pw_aff *pwaff_true, __isl_take isl_pw_aff *pwaff_false)
{
isl_set *cond_true, *cond_false;
cond_true = isl_pw_aff_non_zero_set(isl_pw_aff_copy(cond));
cond_false = isl_pw_aff_zero_set(cond);
return isl_pw_aff_select(cond_true, pwaff_true,
cond_false, pwaff_false);
}
int isl_aff_is_cst(__isl_keep isl_aff *aff)
{
if (!aff)
return -1;
return isl_seq_first_non_zero(aff->v->el + 2, aff->v->size - 2) == -1;
}
/* Check whether pwaff is a piecewise constant.
*/
int isl_pw_aff_is_cst(__isl_keep isl_pw_aff *pwaff)
{
int i;
if (!pwaff)
return -1;
for (i = 0; i < pwaff->n; ++i) {
int is_cst = isl_aff_is_cst(pwaff->p[i].aff);
if (is_cst < 0 || !is_cst)
return is_cst;
}
return 1;
}
__isl_give isl_aff *isl_aff_mul(__isl_take isl_aff *aff1,
__isl_take isl_aff *aff2)
{
if (!isl_aff_is_cst(aff2) && isl_aff_is_cst(aff1))
return isl_aff_mul(aff2, aff1);
if (!isl_aff_is_cst(aff2))
isl_die(isl_aff_get_ctx(aff1), isl_error_invalid,
"at least one affine expression should be constant",
goto error);
aff1 = isl_aff_cow(aff1);
if (!aff1 || !aff2)
goto error;
aff1 = isl_aff_scale(aff1, aff2->v->el[1]);
aff1 = isl_aff_scale_down(aff1, aff2->v->el[0]);
isl_aff_free(aff2);
return aff1;
error:
isl_aff_free(aff1);
isl_aff_free(aff2);
return NULL;
}
static __isl_give isl_pw_aff *pw_aff_add(__isl_take isl_pw_aff *pwaff1,
__isl_take isl_pw_aff *pwaff2)
{
return isl_pw_aff_on_shared_domain(pwaff1, pwaff2, &isl_aff_add);
}
__isl_give isl_pw_aff *isl_pw_aff_add(__isl_take isl_pw_aff *pwaff1,
__isl_take isl_pw_aff *pwaff2)
{
return isl_pw_aff_align_params_pw_pw_and(pwaff1, pwaff2, &pw_aff_add);
}
__isl_give isl_pw_aff *isl_pw_aff_union_add(__isl_take isl_pw_aff *pwaff1,
__isl_take isl_pw_aff *pwaff2)
{
return isl_pw_aff_union_add_(pwaff1, pwaff2);
}
static __isl_give isl_pw_aff *pw_aff_mul(__isl_take isl_pw_aff *pwaff1,
__isl_take isl_pw_aff *pwaff2)
{
return isl_pw_aff_on_shared_domain(pwaff1, pwaff2, &isl_aff_mul);
}
__isl_give isl_pw_aff *isl_pw_aff_mul(__isl_take isl_pw_aff *pwaff1,
__isl_take isl_pw_aff *pwaff2)
{
return isl_pw_aff_align_params_pw_pw_and(pwaff1, pwaff2, &pw_aff_mul);
}
static __isl_give isl_pw_aff *pw_aff_min(__isl_take isl_pw_aff *pwaff1,
__isl_take isl_pw_aff *pwaff2)
{
isl_set *le;
isl_set *dom;
dom = isl_set_intersect(isl_pw_aff_domain(isl_pw_aff_copy(pwaff1)),
isl_pw_aff_domain(isl_pw_aff_copy(pwaff2)));
le = isl_pw_aff_le_set(isl_pw_aff_copy(pwaff1),
isl_pw_aff_copy(pwaff2));
dom = isl_set_subtract(dom, isl_set_copy(le));
return isl_pw_aff_select(le, pwaff1, dom, pwaff2);
}
__isl_give isl_pw_aff *isl_pw_aff_min(__isl_take isl_pw_aff *pwaff1,
__isl_take isl_pw_aff *pwaff2)
{
return isl_pw_aff_align_params_pw_pw_and(pwaff1, pwaff2, &pw_aff_min);
}
static __isl_give isl_pw_aff *pw_aff_max(__isl_take isl_pw_aff *pwaff1,
__isl_take isl_pw_aff *pwaff2)
{
isl_set *ge;
isl_set *dom;
dom = isl_set_intersect(isl_pw_aff_domain(isl_pw_aff_copy(pwaff1)),
isl_pw_aff_domain(isl_pw_aff_copy(pwaff2)));
ge = isl_pw_aff_ge_set(isl_pw_aff_copy(pwaff1),
isl_pw_aff_copy(pwaff2));
dom = isl_set_subtract(dom, isl_set_copy(ge));
return isl_pw_aff_select(ge, pwaff1, dom, pwaff2);
}
__isl_give isl_pw_aff *isl_pw_aff_max(__isl_take isl_pw_aff *pwaff1,
__isl_take isl_pw_aff *pwaff2)
{
return isl_pw_aff_align_params_pw_pw_and(pwaff1, pwaff2, &pw_aff_max);
}
static __isl_give isl_pw_aff *pw_aff_list_reduce(
__isl_take isl_pw_aff_list *list,
__isl_give isl_pw_aff *(*fn)(__isl_take isl_pw_aff *pwaff1,
__isl_take isl_pw_aff *pwaff2))
{
int i;
isl_ctx *ctx;
isl_pw_aff *res;
if (!list)
return NULL;
ctx = isl_pw_aff_list_get_ctx(list);
if (list->n < 1)
isl_die(ctx, isl_error_invalid,
"list should contain at least one element",
return isl_pw_aff_list_free(list));
res = isl_pw_aff_copy(list->p[0]);
for (i = 1; i < list->n; ++i)
res = fn(res, isl_pw_aff_copy(list->p[i]));
isl_pw_aff_list_free(list);
return res;
}
/* Return an isl_pw_aff that maps each element in the intersection of the
* domains of the elements of list to the minimal corresponding affine
* expression.
*/
__isl_give isl_pw_aff *isl_pw_aff_list_min(__isl_take isl_pw_aff_list *list)
{
return pw_aff_list_reduce(list, &isl_pw_aff_min);
}
/* Return an isl_pw_aff that maps each element in the intersection of the
* domains of the elements of list to the maximal corresponding affine
* expression.
*/
__isl_give isl_pw_aff *isl_pw_aff_list_max(__isl_take isl_pw_aff_list *list)
{
return pw_aff_list_reduce(list, &isl_pw_aff_max);
}
#undef BASE
#define BASE aff
#include <isl_multi_templ.c>
/* Construct an isl_multi_aff in the given space with value zero in
* each of the output dimensions.
*/
__isl_give isl_multi_aff *isl_multi_aff_zero(__isl_take isl_space *space)
{
int n;
isl_multi_aff *ma;
if (!space)
return NULL;
n = isl_space_dim(space , isl_dim_out);
ma = isl_multi_aff_alloc(isl_space_copy(space));
if (!n)
isl_space_free(space);
else {
int i;
isl_local_space *ls;
isl_aff *aff;
space = isl_space_domain(space);
ls = isl_local_space_from_space(space);
aff = isl_aff_zero_on_domain(ls);
for (i = 0; i < n; ++i)
ma = isl_multi_aff_set_aff(ma, i, isl_aff_copy(aff));
isl_aff_free(aff);
}
return ma;
}
/* Create an isl_pw_multi_aff with the given isl_multi_aff on a universe
* domain.
*/
__isl_give isl_pw_multi_aff *isl_pw_multi_aff_from_multi_aff(
__isl_take isl_multi_aff *ma)
{
isl_set *dom = isl_set_universe(isl_multi_aff_get_domain_space(ma));
return isl_pw_multi_aff_alloc(dom, ma);
}
__isl_give isl_multi_aff *isl_multi_aff_add(__isl_take isl_multi_aff *maff1,
__isl_take isl_multi_aff *maff2)
{
int i;
isl_ctx *ctx;
maff1 = isl_multi_aff_cow(maff1);
if (!maff1 || !maff2)
goto error;
ctx = isl_multi_aff_get_ctx(maff1);
if (!isl_space_is_equal(maff1->space, maff2->space))
isl_die(ctx, isl_error_invalid,
"spaces don't match", goto error);
for (i = 0; i < maff1->n; ++i) {
maff1->p[i] = isl_aff_add(maff1->p[i],
isl_aff_copy(maff2->p[i]));
if (!maff1->p[i])
goto error;
}
isl_multi_aff_free(maff2);
return maff1;
error:
isl_multi_aff_free(maff1);
isl_multi_aff_free(maff2);
return NULL;
}
/* Exploit the equalities in "eq" to simplify the affine expressions.
*/
static __isl_give isl_multi_aff *isl_multi_aff_substitute_equalities(
__isl_take isl_multi_aff *maff, __isl_take isl_basic_set *eq)
{
int i;
maff = isl_multi_aff_cow(maff);
if (!maff || !eq)
goto error;
for (i = 0; i < maff->n; ++i) {
maff->p[i] = isl_aff_substitute_equalities(maff->p[i],
isl_basic_set_copy(eq));
if (!maff->p[i])
goto error;
}
isl_basic_set_free(eq);
return maff;
error:
isl_basic_set_free(eq);
isl_multi_aff_free(maff);
return NULL;
}
__isl_give isl_multi_aff *isl_multi_aff_scale(__isl_take isl_multi_aff *maff,
isl_int f)
{
int i;
maff = isl_multi_aff_cow(maff);
if (!maff)
return NULL;
for (i = 0; i < maff->n; ++i) {
maff->p[i] = isl_aff_scale(maff->p[i], f);
if (!maff->p[i])
return isl_multi_aff_free(maff);
}
return maff;
}
__isl_give isl_multi_aff *isl_multi_aff_add_on_domain(__isl_keep isl_set *dom,
__isl_take isl_multi_aff *maff1, __isl_take isl_multi_aff *maff2)
{
maff1 = isl_multi_aff_add(maff1, maff2);
maff1 = isl_multi_aff_gist(maff1, isl_set_copy(dom));
return maff1;
}
int isl_multi_aff_is_empty(__isl_keep isl_multi_aff *maff)
{
if (!maff)
return -1;
return 0;
}
int isl_multi_aff_plain_is_equal(__isl_keep isl_multi_aff *maff1,
__isl_keep isl_multi_aff *maff2)
{
int i;
int equal;
if (!maff1 || !maff2)
return -1;
if (maff1->n != maff2->n)
return 0;
equal = isl_space_is_equal(maff1->space, maff2->space);
if (equal < 0 || !equal)
return equal;
for (i = 0; i < maff1->n; ++i) {
equal = isl_aff_plain_is_equal(maff1->p[i], maff2->p[i]);
if (equal < 0 || !equal)
return equal;
}
return 1;
}
__isl_give isl_multi_aff *isl_multi_aff_set_dim_name(
__isl_take isl_multi_aff *maff,
enum isl_dim_type type, unsigned pos, const char *s)
{
int i;
maff = isl_multi_aff_cow(maff);
if (!maff)
return NULL;
maff->space = isl_space_set_dim_name(maff->space, type, pos, s);
if (!maff->space)
return isl_multi_aff_free(maff);
for (i = 0; i < maff->n; ++i) {
maff->p[i] = isl_aff_set_dim_name(maff->p[i], type, pos, s);
if (!maff->p[i])
return isl_multi_aff_free(maff);
}
return maff;
}
__isl_give isl_multi_aff *isl_multi_aff_drop_dims(__isl_take isl_multi_aff *maff,
enum isl_dim_type type, unsigned first, unsigned n)
{
int i;
maff = isl_multi_aff_cow(maff);
if (!maff)
return NULL;
maff->space = isl_space_drop_dims(maff->space, type, first, n);
if (!maff->space)
return isl_multi_aff_free(maff);
if (type == isl_dim_out) {
for (i = 0; i < n; ++i)
isl_aff_free(maff->p[first + i]);
for (i = first; i + n < maff->n; ++i)
maff->p[i] = maff->p[i + n];
maff->n -= n;
return maff;
}
for (i = 0; i < maff->n; ++i) {
maff->p[i] = isl_aff_drop_dims(maff->p[i], type, first, n);
if (!maff->p[i])
return isl_multi_aff_free(maff);
}
return maff;
}
#undef PW
#define PW isl_pw_multi_aff
#undef EL
#define EL isl_multi_aff
#undef EL_IS_ZERO
#define EL_IS_ZERO is_empty
#undef ZERO
#define ZERO empty
#undef IS_ZERO
#define IS_ZERO is_empty
#undef FIELD
#define FIELD maff
#undef DEFAULT_IS_ZERO
#define DEFAULT_IS_ZERO 0
#define NO_NEG
#define NO_EVAL
#define NO_OPT
#define NO_INVOLVES_DIMS
#define NO_MOVE_DIMS
#define NO_INSERT_DIMS
#define NO_LIFT
#define NO_MORPH
#include <isl_pw_templ.c>
#undef UNION
#define UNION isl_union_pw_multi_aff
#undef PART
#define PART isl_pw_multi_aff
#undef PARTS
#define PARTS pw_multi_aff
#define ALIGN_DOMAIN
#define NO_EVAL
#include <isl_union_templ.c>
static __isl_give isl_pw_multi_aff *pw_multi_aff_add(
__isl_take isl_pw_multi_aff *pma1, __isl_take isl_pw_multi_aff *pma2)
{
return isl_pw_multi_aff_on_shared_domain(pma1, pma2,
&isl_multi_aff_add);
}
__isl_give isl_pw_multi_aff *isl_pw_multi_aff_add(
__isl_take isl_pw_multi_aff *pma1, __isl_take isl_pw_multi_aff *pma2)
{
return isl_pw_multi_aff_align_params_pw_pw_and(pma1, pma2,
&pw_multi_aff_add);
}
__isl_give isl_pw_multi_aff *isl_pw_multi_aff_union_add(
__isl_take isl_pw_multi_aff *pma1, __isl_take isl_pw_multi_aff *pma2)
{
return isl_pw_multi_aff_union_add_(pma1, pma2);
}
/* Construct a map mapping the domain of the piecewise multi-affine expression
* to its range, with each dimension in the range equated to the
* corresponding affine expression on its cell.
*/
__isl_give isl_map *isl_map_from_pw_multi_aff(__isl_take isl_pw_multi_aff *pma)
{
int i;
isl_map *map;
if (!pma)
return NULL;
map = isl_map_empty(isl_pw_multi_aff_get_space(pma));
for (i = 0; i < pma->n; ++i) {
isl_multi_aff *maff;
isl_basic_map *bmap;
isl_map *map_i;
maff = isl_multi_aff_copy(pma->p[i].maff);
bmap = isl_basic_map_from_multi_aff(maff);
map_i = isl_map_from_basic_map(bmap);
map_i = isl_map_intersect_domain(map_i,
isl_set_copy(pma->p[i].set));
map = isl_map_union_disjoint(map, map_i);
}
isl_pw_multi_aff_free(pma);
return map;
}
__isl_give isl_set *isl_set_from_pw_multi_aff(__isl_take isl_pw_multi_aff *pma)
{
if (!isl_space_is_set(pma->dim))
isl_die(isl_pw_multi_aff_get_ctx(pma), isl_error_invalid,
"isl_pw_multi_aff cannot be converted into an isl_set",
return isl_pw_multi_aff_free(pma));
return isl_map_from_pw_multi_aff(pma);
}
/* Given a basic map with a single output dimension that is defined
* in terms of the parameters and input dimensions using an equality,
* extract an isl_aff that expresses the output dimension in terms
* of the parameters and input dimensions.
*
* Since some applications expect the result of isl_pw_multi_aff_from_map
* to only contain integer affine expressions, we compute the floor
* of the expression before returning.
*
* This function shares some similarities with
* isl_basic_map_has_defining_equality and isl_constraint_get_bound.
*/
static __isl_give isl_aff *extract_isl_aff_from_basic_map(
__isl_take isl_basic_map *bmap)
{
int i;
unsigned offset;
unsigned total;
isl_local_space *ls;
isl_aff *aff;
if (!bmap)
return NULL;
if (isl_basic_map_dim(bmap, isl_dim_out) != 1)
isl_die(isl_basic_map_get_ctx(bmap), isl_error_invalid,
"basic map should have a single output dimension",
goto error);
offset = isl_basic_map_offset(bmap, isl_dim_out);
total = isl_basic_map_total_dim(bmap);
for (i = 0; i < bmap->n_eq; ++i) {
if (isl_int_is_zero(bmap->eq[i][offset]))
continue;
if (isl_seq_first_non_zero(bmap->eq[i] + offset + 1,
1 + total - (offset + 1)) != -1)
continue;
break;
}
if (i >= bmap->n_eq)
isl_die(isl_basic_map_get_ctx(bmap), isl_error_invalid,
"unable to find suitable equality", goto error);
ls = isl_basic_map_get_local_space(bmap);
aff = isl_aff_alloc(isl_local_space_domain(ls));
if (!aff)
goto error;
if (isl_int_is_neg(bmap->eq[i][offset]))
isl_seq_cpy(aff->v->el + 1, bmap->eq[i], offset);
else
isl_seq_neg(aff->v->el + 1, bmap->eq[i], offset);
isl_seq_clr(aff->v->el + 1 + offset, aff->v->size - (1 + offset));
isl_int_abs(aff->v->el[0], bmap->eq[i][offset]);
isl_basic_map_free(bmap);
aff = isl_aff_remove_unused_divs(aff);
aff = isl_aff_floor(aff);
return aff;
error:
isl_basic_map_free(bmap);
return NULL;
}
/* Given a basic map where each output dimension is defined
* in terms of the parameters and input dimensions using an equality,
* extract an isl_multi_aff that expresses the output dimensions in terms
* of the parameters and input dimensions.
*/
static __isl_give isl_multi_aff *extract_isl_multi_aff_from_basic_map(
__isl_take isl_basic_map *bmap)
{
int i;
unsigned n_out;
isl_multi_aff *ma;
if (!bmap)
return NULL;
ma = isl_multi_aff_alloc(isl_basic_map_get_space(bmap));
n_out = isl_basic_map_dim(bmap, isl_dim_out);
for (i = 0; i < n_out; ++i) {
isl_basic_map *bmap_i;
isl_aff *aff;
bmap_i = isl_basic_map_copy(bmap);
bmap_i = isl_basic_map_project_out(bmap_i, isl_dim_out,
i + 1, n_out - (1 + i));
bmap_i = isl_basic_map_project_out(bmap_i, isl_dim_out, 0, i);
aff = extract_isl_aff_from_basic_map(bmap_i);
ma = isl_multi_aff_set_aff(ma, i, aff);
}
isl_basic_map_free(bmap);
return ma;
}
/* Create an isl_pw_multi_aff that is equivalent to
* isl_map_intersect_domain(isl_map_from_basic_map(bmap), domain).
* The given basic map is such that each output dimension is defined
* in terms of the parameters and input dimensions using an equality.
*/
static __isl_give isl_pw_multi_aff *plain_pw_multi_aff_from_map(
__isl_take isl_set *domain, __isl_take isl_basic_map *bmap)
{
isl_multi_aff *ma;
ma = extract_isl_multi_aff_from_basic_map(bmap);
return isl_pw_multi_aff_alloc(domain, ma);
}
/* Try and create an isl_pw_multi_aff that is equivalent to the given isl_map.
* This obivously only works if the input "map" is single-valued.
* If so, we compute the lexicographic minimum of the image in the form
* of an isl_pw_multi_aff. Since the image is unique, it is equal
* to its lexicographic minimum.
* If the input is not single-valued, we produce an error.
*
* As a special case, we first check if all output dimensions are uniquely
* defined in terms of the parameters and input dimensions over the entire
* domain. If so, we extract the desired isl_pw_multi_aff directly
* from the affine hull of "map" and its domain.
*/
__isl_give isl_pw_multi_aff *isl_pw_multi_aff_from_map(__isl_take isl_map *map)
{
int i;
int sv;
isl_pw_multi_aff *pma;
isl_basic_map *hull;
if (!map)
return NULL;
hull = isl_map_affine_hull(isl_map_copy(map));
sv = isl_basic_map_plain_is_single_valued(hull);
if (sv >= 0 && sv)
return plain_pw_multi_aff_from_map(isl_map_domain(map), hull);
isl_basic_map_free(hull);
if (sv < 0)
goto error;
sv = isl_map_is_single_valued(map);
if (sv < 0)
goto error;
if (!sv)
isl_die(isl_map_get_ctx(map), isl_error_invalid,
"map is not single-valued", goto error);
map = isl_map_make_disjoint(map);
if (!map)
return NULL;
pma = isl_pw_multi_aff_empty(isl_map_get_space(map));
for (i = 0; i < map->n; ++i) {
isl_pw_multi_aff *pma_i;
isl_basic_map *bmap;
bmap = isl_basic_map_copy(map->p[i]);
pma_i = isl_basic_map_lexmin_pw_multi_aff(bmap);
pma = isl_pw_multi_aff_add_disjoint(pma, pma_i);
}
isl_map_free(map);
return pma;
error:
isl_map_free(map);
return NULL;
}
__isl_give isl_pw_multi_aff *isl_pw_multi_aff_from_set(__isl_take isl_set *set)
{
return isl_pw_multi_aff_from_map(set);
}
/* Return the piecewise affine expression "set ? 1 : 0".
*/
__isl_give isl_pw_aff *isl_set_indicator_function(__isl_take isl_set *set)
{
isl_pw_aff *pa;
isl_space *space = isl_set_get_space(set);
isl_local_space *ls = isl_local_space_from_space(space);
isl_aff *zero = isl_aff_zero_on_domain(isl_local_space_copy(ls));
isl_aff *one = isl_aff_zero_on_domain(ls);
one = isl_aff_add_constant_si(one, 1);
pa = isl_pw_aff_alloc(isl_set_copy(set), one);
set = isl_set_complement(set);
pa = isl_pw_aff_add_disjoint(pa, isl_pw_aff_alloc(set, zero));
return pa;
}
/* Plug in "subs" for dimension "type", "pos" of "aff".
*
* Let i be the dimension to replace and let "subs" be of the form
*
* f/d
*
* and "aff" of the form
*
* (a i + g)/m
*
* The result is
*
* floor((a f + d g')/(m d))
*
* where g' is the result of plugging in "subs" in each of the integer
* divisions in g.
*/
__isl_give isl_aff *isl_aff_substitute(__isl_take isl_aff *aff,
enum isl_dim_type type, unsigned pos, __isl_keep isl_aff *subs)
{
isl_ctx *ctx;
isl_int v;
aff = isl_aff_cow(aff);
if (!aff || !subs)
return isl_aff_free(aff);
ctx = isl_aff_get_ctx(aff);
if (!isl_space_is_equal(aff->ls->dim, subs->ls->dim))
isl_die(ctx, isl_error_invalid,
"spaces don't match", return isl_aff_free(aff));
if (isl_local_space_dim(subs->ls, isl_dim_div) != 0)
isl_die(ctx, isl_error_unsupported,
"cannot handle divs yet", return isl_aff_free(aff));
aff->ls = isl_local_space_substitute(aff->ls, type, pos, subs);
if (!aff->ls)
return isl_aff_free(aff);
aff->v = isl_vec_cow(aff->v);
if (!aff->v)
return isl_aff_free(aff);
pos += isl_local_space_offset(aff->ls, type);
isl_int_init(v);
isl_int_set(v, aff->v->el[1 + pos]);
isl_int_set_si(aff->v->el[1 + pos], 0);
isl_seq_combine(aff->v->el + 1, subs->v->el[0], aff->v->el + 1,
v, subs->v->el + 1, subs->v->size - 1);
isl_int_mul(aff->v->el[0], aff->v->el[0], subs->v->el[0]);
isl_int_clear(v);
return aff;
}
/* Plug in "subs" for dimension "type", "pos" in each of the affine
* expressions in "maff".
*/
__isl_give isl_multi_aff *isl_multi_aff_substitute(
__isl_take isl_multi_aff *maff, enum isl_dim_type type, unsigned pos,
__isl_keep isl_aff *subs)
{
int i;
maff = isl_multi_aff_cow(maff);
if (!maff || !subs)
return isl_multi_aff_free(maff);
if (type == isl_dim_in)
type = isl_dim_set;
for (i = 0; i < maff->n; ++i) {
maff->p[i] = isl_aff_substitute(maff->p[i], type, pos, subs);
if (!maff->p[i])
return isl_multi_aff_free(maff);
}
return maff;
}
/* Plug in "subs" for dimension "type", "pos" of "pma".
*
* pma is of the form
*
* A_i(v) -> M_i(v)
*
* while subs is of the form
*
* v' = B_j(v) -> S_j
*
* Each pair i,j such that C_ij = A_i \cap B_i is non-empty
* has a contribution in the result, in particular
*
* C_ij(S_j) -> M_i(S_j)
*
* Note that plugging in S_j in C_ij may also result in an empty set
* and this contribution should simply be discarded.
*/
__isl_give isl_pw_multi_aff *isl_pw_multi_aff_substitute(
__isl_take isl_pw_multi_aff *pma, enum isl_dim_type type, unsigned pos,
__isl_keep isl_pw_aff *subs)
{
int i, j, n;
isl_pw_multi_aff *res;
if (!pma || !subs)
return isl_pw_multi_aff_free(pma);
n = pma->n * subs->n;
res = isl_pw_multi_aff_alloc_size(isl_space_copy(pma->dim), n);
for (i = 0; i < pma->n; ++i) {
for (j = 0; j < subs->n; ++j) {
isl_set *common;
isl_multi_aff *res_ij;
common = isl_set_intersect(
isl_set_copy(pma->p[i].set),
isl_set_copy(subs->p[j].set));
common = isl_set_substitute(common,
type, pos, subs->p[j].aff);
if (isl_set_plain_is_empty(common)) {
isl_set_free(common);
continue;
}
res_ij = isl_multi_aff_substitute(
isl_multi_aff_copy(pma->p[i].maff),
type, pos, subs->p[j].aff);
res = isl_pw_multi_aff_add_piece(res, common, res_ij);
}
}
isl_pw_multi_aff_free(pma);
return res;
}
/* Extend the local space of "dst" to include the divs
* in the local space of "src".
*/
__isl_give isl_aff *isl_aff_align_divs(__isl_take isl_aff *dst,
__isl_keep isl_aff *src)
{
isl_ctx *ctx;
int *exp1 = NULL;
int *exp2 = NULL;
isl_mat *div;
if (!src || !dst)
return isl_aff_free(dst);
ctx = isl_aff_get_ctx(src);
if (!isl_space_is_equal(src->ls->dim, dst->ls->dim))
isl_die(ctx, isl_error_invalid,
"spaces don't match", goto error);
if (src->ls->div->n_row == 0)
return dst;
exp1 = isl_alloc_array(ctx, int, src->ls->div->n_row);
exp2 = isl_alloc_array(ctx, int, dst->ls->div->n_row);
if (!exp1 || !exp2)
goto error;
div = isl_merge_divs(src->ls->div, dst->ls->div, exp1, exp2);
dst = isl_aff_expand_divs(dst, div, exp2);
free(exp1);
free(exp2);
return dst;
error:
free(exp1);
free(exp2);
return isl_aff_free(dst);
}
/* Adjust the local spaces of the affine expressions in "maff"
* such that they all have the save divs.
*/
__isl_give isl_multi_aff *isl_multi_aff_align_divs(
__isl_take isl_multi_aff *maff)
{
int i;
if (!maff)
return NULL;
if (maff->n == 0)
return maff;
maff = isl_multi_aff_cow(maff);
if (!maff)
return NULL;
for (i = 1; i < maff->n; ++i)
maff->p[0] = isl_aff_align_divs(maff->p[0], maff->p[i]);
for (i = 1; i < maff->n; ++i) {
maff->p[i] = isl_aff_align_divs(maff->p[i], maff->p[0]);
if (!maff->p[i])
return isl_multi_aff_free(maff);
}
return maff;
}
__isl_give isl_aff *isl_aff_lift(__isl_take isl_aff *aff)
{
aff = isl_aff_cow(aff);
if (!aff)
return NULL;
aff->ls = isl_local_space_lift(aff->ls);
if (!aff->ls)
return isl_aff_free(aff);
return aff;
}
/* Lift "maff" to a space with extra dimensions such that the result
* has no more existentially quantified variables.
* If "ls" is not NULL, then *ls is assigned the local space that lies
* at the basis of the lifting applied to "maff".
*/
__isl_give isl_multi_aff *isl_multi_aff_lift(__isl_take isl_multi_aff *maff,
__isl_give isl_local_space **ls)
{
int i;
isl_space *space;
unsigned n_div;
if (ls)
*ls = NULL;
if (!maff)
return NULL;
if (maff->n == 0) {
if (ls) {
isl_space *space = isl_multi_aff_get_domain_space(maff);
*ls = isl_local_space_from_space(space);
if (!*ls)
return isl_multi_aff_free(maff);
}
return maff;
}
maff = isl_multi_aff_cow(maff);
maff = isl_multi_aff_align_divs(maff);
if (!maff)
return NULL;
n_div = isl_aff_dim(maff->p[0], isl_dim_div);
space = isl_multi_aff_get_space(maff);
space = isl_space_lift(isl_space_domain(space), n_div);
space = isl_space_extend_domain_with_range(space,
isl_multi_aff_get_space(maff));
if (!space)
return isl_multi_aff_free(maff);
isl_space_free(maff->space);
maff->space = space;
if (ls) {
*ls = isl_aff_get_domain_local_space(maff->p[0]);
if (!*ls)
return isl_multi_aff_free(maff);
}
for (i = 0; i < maff->n; ++i) {
maff->p[i] = isl_aff_lift(maff->p[i]);
if (!maff->p[i])
goto error;
}
return maff;
error:
if (ls)
isl_local_space_free(*ls);
return isl_multi_aff_free(maff);
}
/* Extract an isl_pw_aff corresponding to output dimension "pos" of "pma".
*/
__isl_give isl_pw_aff *isl_pw_multi_aff_get_pw_aff(
__isl_keep isl_pw_multi_aff *pma, int pos)
{
int i;
int n_out;
isl_space *space;
isl_pw_aff *pa;
if (!pma)
return NULL;
n_out = isl_pw_multi_aff_dim(pma, isl_dim_out);
if (pos < 0 || pos >= n_out)
isl_die(isl_pw_multi_aff_get_ctx(pma), isl_error_invalid,
"index out of bounds", return NULL);
space = isl_pw_multi_aff_get_space(pma);
space = isl_space_drop_dims(space, isl_dim_out,
pos + 1, n_out - pos - 1);
space = isl_space_drop_dims(space, isl_dim_out, 0, pos);
pa = isl_pw_aff_alloc_size(space, pma->n);
for (i = 0; i < pma->n; ++i) {
isl_aff *aff;
aff = isl_multi_aff_get_aff(pma->p[i].maff, pos);
pa = isl_pw_aff_add_piece(pa, isl_set_copy(pma->p[i].set), aff);
}
return pa;
}
/* Return an isl_pw_multi_aff with the given "set" as domain and
* an unnamed zero-dimensional range.
*/
__isl_give isl_pw_multi_aff *isl_pw_multi_aff_from_domain(
__isl_take isl_set *set)
{
isl_multi_aff *ma;
isl_space *space;
space = isl_set_get_space(set);
space = isl_space_from_domain(space);
ma = isl_multi_aff_zero(space);
return isl_pw_multi_aff_alloc(set, ma);
}
/* Add an isl_pw_multi_aff with the given "set" as domain and
* an unnamed zero-dimensional range to *user.
*/
static int add_pw_multi_aff_from_domain(__isl_take isl_set *set, void *user)
{
isl_union_pw_multi_aff **upma = user;
isl_pw_multi_aff *pma;
pma = isl_pw_multi_aff_from_domain(set);
*upma = isl_union_pw_multi_aff_add_pw_multi_aff(*upma, pma);
return 0;
}
/* Return an isl_union_pw_multi_aff with the given "uset" as domain and
* an unnamed zero-dimensional range.
*/
__isl_give isl_union_pw_multi_aff *isl_union_pw_multi_aff_from_domain(
__isl_take isl_union_set *uset)
{
isl_space *space;
isl_union_pw_multi_aff *upma;
if (!uset)
return NULL;
space = isl_union_set_get_space(uset);
upma = isl_union_pw_multi_aff_empty(space);
if (isl_union_set_foreach_set(uset,
&add_pw_multi_aff_from_domain, &upma) < 0)
goto error;
isl_union_set_free(uset);
return upma;
error:
isl_union_set_free(uset);
isl_union_pw_multi_aff_free(upma);
return NULL;
}
/* Convert "pma" to an isl_map and add it to *umap.
*/
static int map_from_pw_multi_aff(__isl_take isl_pw_multi_aff *pma, void *user)
{
isl_union_map **umap = user;
isl_map *map;
map = isl_map_from_pw_multi_aff(pma);
*umap = isl_union_map_add_map(*umap, map);
return 0;
}
/* Construct a union map mapping the domain of the union
* piecewise multi-affine expression to its range, with each dimension
* in the range equated to the corresponding affine expression on its cell.
*/
__isl_give isl_union_map *isl_union_map_from_union_pw_multi_aff(
__isl_take isl_union_pw_multi_aff *upma)
{
isl_space *space;
isl_union_map *umap;
if (!upma)
return NULL;
space = isl_union_pw_multi_aff_get_space(upma);
umap = isl_union_map_empty(space);
if (isl_union_pw_multi_aff_foreach_pw_multi_aff(upma,
&map_from_pw_multi_aff, &umap) < 0)
goto error;
isl_union_pw_multi_aff_free(upma);
return umap;
error:
isl_union_pw_multi_aff_free(upma);
isl_union_map_free(umap);
return NULL;
}
/* Local data for bin_entry and the callback "fn".
*/
struct isl_union_pw_multi_aff_bin_data {
isl_union_pw_multi_aff *upma2;
isl_union_pw_multi_aff *res;
isl_pw_multi_aff *pma;
int (*fn)(void **entry, void *user);
};
/* Given an isl_pw_multi_aff from upma1, store it in data->pma
* and call data->fn for each isl_pw_multi_aff in data->upma2.
*/
static int bin_entry(void **entry, void *user)
{
struct isl_union_pw_multi_aff_bin_data *data = user;
isl_pw_multi_aff *pma = *entry;
data->pma = pma;
if (isl_hash_table_foreach(data->upma2->dim->ctx, &data->upma2->table,
data->fn, data) < 0)
return -1;
return 0;
}
/* Call "fn" on each pair of isl_pw_multi_affs in "upma1" and "upma2".
* The isl_pw_multi_aff from upma1 is stored in data->pma (where data is
* passed as user field) and the isl_pw_multi_aff from upma2 is available
* as *entry. The callback should adjust data->res if desired.
*/
static __isl_give isl_union_pw_multi_aff *bin_op(
__isl_take isl_union_pw_multi_aff *upma1,
__isl_take isl_union_pw_multi_aff *upma2,
int (*fn)(void **entry, void *user))
{
isl_space *space;
struct isl_union_pw_multi_aff_bin_data data = { NULL, NULL, NULL, fn };
space = isl_union_pw_multi_aff_get_space(upma2);
upma1 = isl_union_pw_multi_aff_align_params(upma1, space);
space = isl_union_pw_multi_aff_get_space(upma1);
upma2 = isl_union_pw_multi_aff_align_params(upma2, space);
if (!upma1 || !upma2)
goto error;
data.upma2 = upma2;
data.res = isl_union_pw_multi_aff_alloc(isl_space_copy(upma1->dim),
upma1->table.n);
if (isl_hash_table_foreach(upma1->dim->ctx, &upma1->table,
&bin_entry, &data) < 0)
goto error;
isl_union_pw_multi_aff_free(upma1);
isl_union_pw_multi_aff_free(upma2);
return data.res;
error:
isl_union_pw_multi_aff_free(upma1);
isl_union_pw_multi_aff_free(upma2);
isl_union_pw_multi_aff_free(data.res);
return NULL;
}
/* Given two isl_multi_affs A -> B and C -> D,
* construct an isl_multi_aff (A * C) -> (B, D).
*/
__isl_give isl_multi_aff *isl_multi_aff_flat_range_product(
__isl_take isl_multi_aff *ma1, __isl_take isl_multi_aff *ma2)
{
int i, n1, n2;
isl_aff *aff;
isl_space *space;
isl_multi_aff *res;
if (!ma1 || !ma2)
goto error;
space = isl_space_range_product(isl_multi_aff_get_space(ma1),
isl_multi_aff_get_space(ma2));
space = isl_space_flatten_range(space);
res = isl_multi_aff_alloc(space);
n1 = isl_multi_aff_dim(ma1, isl_dim_out);
n2 = isl_multi_aff_dim(ma2, isl_dim_out);
for (i = 0; i < n1; ++i) {
aff = isl_multi_aff_get_aff(ma1, i);
res = isl_multi_aff_set_aff(res, i, aff);
}
for (i = 0; i < n2; ++i) {
aff = isl_multi_aff_get_aff(ma2, i);
res = isl_multi_aff_set_aff(res, n1 + i, aff);
}
isl_multi_aff_free(ma1);
isl_multi_aff_free(ma2);
return res;
error:
isl_multi_aff_free(ma1);
isl_multi_aff_free(ma2);
return NULL;
}
/* Given two aligned isl_pw_multi_affs A -> B and C -> D,
* construct an isl_pw_multi_aff (A * C) -> (B, D).
*/
static __isl_give isl_pw_multi_aff *pw_multi_aff_flat_range_product(
__isl_take isl_pw_multi_aff *pma1, __isl_take isl_pw_multi_aff *pma2)
{
isl_space *space;
space = isl_space_range_product(isl_pw_multi_aff_get_space(pma1),
isl_pw_multi_aff_get_space(pma2));
space = isl_space_flatten_range(space);
return isl_pw_multi_aff_on_shared_domain_in(pma1, pma2, space,
&isl_multi_aff_flat_range_product);
}
/* Given two isl_pw_multi_affs A -> B and C -> D,
* construct an isl_pw_multi_aff (A * C) -> (B, D).
*/
__isl_give isl_pw_multi_aff *isl_pw_multi_aff_flat_range_product(
__isl_take isl_pw_multi_aff *pma1, __isl_take isl_pw_multi_aff *pma2)
{
return isl_pw_multi_aff_align_params_pw_pw_and(pma1, pma2,
&pw_multi_aff_flat_range_product);
}
/* If data->pma and *entry have the same domain space, then compute
* their flat range product and the result to data->res.
*/
static int flat_range_product_entry(void **entry, void *user)
{
struct isl_union_pw_multi_aff_bin_data *data = user;
isl_pw_multi_aff *pma2 = *entry;
if (!isl_space_tuple_match(data->pma->dim, isl_dim_in,
pma2->dim, isl_dim_in))
return 0;
pma2 = isl_pw_multi_aff_flat_range_product(
isl_pw_multi_aff_copy(data->pma),
isl_pw_multi_aff_copy(pma2));
data->res = isl_union_pw_multi_aff_add_pw_multi_aff(data->res, pma2);
return 0;
}
/* Given two isl_union_pw_multi_affs A -> B and C -> D,
* construct an isl_union_pw_multi_aff (A * C) -> (B, D).
*/
__isl_give isl_union_pw_multi_aff *isl_union_pw_multi_aff_flat_range_product(
__isl_take isl_union_pw_multi_aff *upma1,
__isl_take isl_union_pw_multi_aff *upma2)
{
return bin_op(upma1, upma2, &flat_range_product_entry);
}