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/*
* Copyright 2011 INRIA Saclay
* Copyright 2012 Ecole Normale Superieure
* Copyright 2020 Cerebras Systems
*
* Use of this software is governed by the MIT 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
* and Cerebras Systems, 175 S San Antonio Rd, Los Altos, CA, USA
*/
#include <isl_pw_macro.h>
/* Given a function "cmp" that returns the set of elements where
* "el1" is "better" than "el2", return this set.
*/
static __isl_give isl_set *FN(PW,better)(__isl_keep EL *el1, __isl_keep EL *el2,
__isl_give isl_set *(*cmp)(__isl_take EL *el1, __isl_take EL *el2))
{
return cmp(FN(EL,copy)(el1), FN(EL,copy)(el2));
}
/* Return a list containing the domains of the pieces of "pw".
*/
static __isl_give isl_set_list *FN(PW,extract_domains)(__isl_keep PW *pw)
{
int i;
isl_ctx *ctx;
isl_set_list *list;
if (!pw)
return NULL;
ctx = FN(PW,get_ctx)(pw);
list = isl_set_list_alloc(ctx, pw->n);
for (i = 0; i < pw->n; ++i)
list = isl_set_list_add(list, isl_set_copy(pw->p[i].set));
return list;
}
/* Given sets B ("set"), C ("better") and A' ("out"), return
*
* (B \cap C) \cup ((B \setminus C) \setminus A')
*/
static __isl_give isl_set *FN(PW,better_or_out)(__isl_take isl_set *set,
__isl_take isl_set *better, __isl_take isl_set *out)
{
isl_set *set_better, *set_out;
set_better = isl_set_intersect(isl_set_copy(set), isl_set_copy(better));
set_out = isl_set_subtract(isl_set_subtract(set, better), out);
return isl_set_union(set_better, set_out);
}
/* Given sets A ("set"), C ("better") and B' ("out"), return
*
* (A \setminus C) \cup ((A \cap C) \setminus B')
*/
static __isl_give isl_set *FN(PW,worse_or_out)(__isl_take isl_set *set,
__isl_take isl_set *better, __isl_take isl_set *out)
{
isl_set *set_worse, *set_out;
set_worse = isl_set_subtract(isl_set_copy(set), isl_set_copy(better));
set_out = isl_set_subtract(isl_set_intersect(set, better), out);
return isl_set_union(set_worse, set_out);
}
/* Internal data structure used by isl_pw_*_union_opt_cmp
* that keeps track of a piecewise expression with updated cells.
* "pw" holds the original piecewise expression.
* "list" holds the updated cells.
*/
S(PW,union_opt_cmp_data) {
PW *pw;
isl_set_list *cell;
};
/* Free all memory allocated for "data".
*/
static void FN(PW,union_opt_cmp_data_clear)(S(PW,union_opt_cmp_data) *data)
{
isl_set_list_free(data->cell);
FN(PW,free)(data->pw);
}
/* Given (potentially) updated cells "i" of data_i->pw and "j" of data_j->pw and
* a set "better" where the piece from data_j->pw is better
* than the piece from data_i->pw,
* (further) update the specified cells such that only the better elements
* remain on the (non-empty) intersection.
*
* Let C be the set "better".
* Let A be the cell data_i->cell[i] and B the cell data_j->cell[j].
*
* The elements in C need to be removed from A, except for those parts
* that lie outside of B. That is,
*
* A <- (A \setminus C) \cup ((A \cap C) \setminus B')
*
* Conversely, the elements in B need to be restricted to C, except
* for those parts that lie outside of A. That is
*
* B <- (B \cap C) \cup ((B \setminus C) \setminus A')
*
* Since all pairs of pieces are considered, the domains are updated
* several times. A and B refer to these updated domains
* (kept track of in data_i->cell[i] and data_j->cell[j]), while A' and B' refer
* to the original domains of the pieces. It is safe to use these
* original domains because the difference between, say, A' and A is
* the domains of pw2-pieces that have been removed before and
* those domains are disjoint from B. A' is used instead of A
* because the continued updating of A may result in this domain
* getting broken up into more disjuncts.
*/
static isl_stat FN(PW,union_opt_cmp_split)(S(PW,union_opt_cmp_data) *data_i,
int i, S(PW,union_opt_cmp_data) *data_j, int j,
__isl_take isl_set *better)
{
isl_set *set_i, *set_j;
set_i = isl_set_list_get_set(data_i->cell, i);
set_j = FN(PW,get_domain_at)(data_j->pw, j);
set_i = FN(PW,worse_or_out)(set_i, isl_set_copy(better), set_j);
data_i->cell = isl_set_list_set_set(data_i->cell, i, set_i);
set_i = FN(PW,get_domain_at)(data_i->pw, i);
set_j = isl_set_list_get_set(data_j->cell, j);
set_j = FN(PW,better_or_out)(set_j, better, set_i);
data_j->cell = isl_set_list_set_set(data_j->cell, j, set_j);
return isl_stat_ok;
}
/* Given (potentially) updated cells "i" of data_i->pw and "j" of data_j->pw and
* a function "cmp" that returns the set of elements where
* "el1" is "better" than "el2",
* (further) update the specified cells such that only the "better" elements
* remain on the (non-empty) intersection.
*/
static isl_stat FN(PW,union_opt_cmp_pair)(S(PW,union_opt_cmp_data) *data_i,
int i, S(PW,union_opt_cmp_data) *data_j, int j,
__isl_give isl_set *(*cmp)(__isl_take EL *el1, __isl_take EL *el2))
{
isl_set *better;
EL *el_i, *el_j;
el_i = FN(PW,peek_base_at)(data_i->pw, i);
el_j = FN(PW,peek_base_at)(data_j->pw, j);
better = FN(PW,better)(el_j, el_i, cmp);
return FN(PW,union_opt_cmp_split)(data_i, i, data_j, j, better);
}
/* Given (potentially) updated cells "i" of data_i->pw and "j" of data_j->pw and
* a function "cmp" that returns the set of elements where
* "el1" is "better" than "el2",
* (further) update the specified cells such that only the "better" elements
* remain on the (non-empty) intersection.
*
* The base computation is performed by isl_pw_*_union_opt_cmp_pair,
* which splits the cells according to the set of elements
* where the piece from data_j->pw is better than the piece from data_i->pw.
*
* In some cases, there may be a subset of the intersection
* where both pieces have the same value and can therefore
* both be considered to be "better" than the other.
* This can result in unnecessary splitting on this subset.
* Avoid some of these cases by checking whether
* data_i->pw is always better than data_j->pw on the intersection.
* In particular, do this for the special case where this intersection
* is equal to the cell "j" and data_i->pw is better on its entire cell.
*
* Similarly, if data_i->pw is never better than data_j->pw,
* then no splitting will occur and there is no need to check
* where data_j->pw is better than data_i->pw.
*/
static isl_stat FN(PW,union_opt_cmp_two)(S(PW,union_opt_cmp_data) *data_i,
int i, S(PW,union_opt_cmp_data) *data_j, int j,
__isl_give isl_set *(*cmp)(__isl_take EL *el1, __isl_take EL *el2))
{
isl_bool is_subset, is_empty;
isl_set *better, *set_i, *set_j;
EL *el_i, *el_j;
set_i = FN(PW,peek_domain_at)(data_i->pw, i);
set_j = FN(PW,peek_domain_at)(data_j->pw, j);
is_subset = isl_set_is_subset(set_j, set_i);
if (is_subset < 0)
return isl_stat_error;
if (!is_subset)
return FN(PW,union_opt_cmp_pair)(data_i, i, data_j, j, cmp);
el_i = FN(PW,peek_base_at)(data_i->pw, i);
el_j = FN(PW,peek_base_at)(data_j->pw, j);
better = FN(PW,better)(el_i, el_j, cmp);
is_empty = isl_set_is_empty(better);
if (is_empty >= 0 && is_empty)
return FN(PW,union_opt_cmp_split)(data_j, j, data_i, i, better);
is_subset = isl_set_is_subset(set_i, better);
if (is_subset >= 0 && is_subset)
return FN(PW,union_opt_cmp_split)(data_j, j, data_i, i, better);
isl_set_free(better);
if (is_empty < 0 || is_subset < 0)
return isl_stat_error;
return FN(PW,union_opt_cmp_pair)(data_i, i, data_j, j, cmp);
}
/* Given two piecewise expressions data1->pw and data2->pw, replace
* their domains
* by the sets in data1->cell and data2->cell and combine the results into
* a single piecewise expression.
* The pieces of data1->pw and data2->pw are assumed to have been sorted
* according to the function value expressions.
* The pieces of the result are also sorted in this way.
*
* Run through the pieces of data1->pw and data2->pw in order until they
* have both been exhausted, picking the piece from data1->pw or data2->pw
* depending on which should come first, together with the corresponding
* domain from data1->cell or data2->cell. In cases where the next pieces
* in both data1->pw and data2->pw have the same function value expression,
* construct only a single piece in the result with as domain
* the union of the domains in data1->cell and data2->cell.
*/
static __isl_give PW *FN(PW,merge)(S(PW,union_opt_cmp_data) *data1,
S(PW,union_opt_cmp_data) *data2)
{
int i, j;
PW *res;
PW *pw1 = data1->pw;
PW *pw2 = data2->pw;
isl_set_list *list1 = data1->cell;
isl_set_list *list2 = data2->cell;
if (!pw1 || !pw2)
return NULL;
res = FN(PW,alloc_size)(isl_space_copy(pw1->dim), pw1->n + pw2->n);
i = 0; j = 0;
while (i < pw1->n || j < pw2->n) {
int cmp;
isl_set *set;
EL *el;
if (i < pw1->n && j < pw2->n)
cmp = FN(EL,plain_cmp)(pw1->p[i].FIELD,
pw2->p[j].FIELD);
else
cmp = i < pw1->n ? -1 : 1;
if (cmp < 0) {
set = isl_set_list_get_set(list1, i);
el = FN(EL,copy)(pw1->p[i].FIELD);
++i;
} else if (cmp > 0) {
set = isl_set_list_get_set(list2, j);
el = FN(EL,copy)(pw2->p[j].FIELD);
++j;
} else {
set = isl_set_union(isl_set_list_get_set(list1, i),
isl_set_list_get_set(list2, j));
el = FN(EL,copy)(pw1->p[i].FIELD);
++i;
++j;
}
res = FN(PW,add_piece)(res, set, el);
}
return res;
}
/* Given a function "cmp" that returns the set of elements where
* "el1" is "better" than "el2", return a piecewise
* expression defined on the union of the definition domains
* of "pw1" and "pw2" that maps to the "best" of "pw1" and
* "pw2" on each cell. If only one of the two input functions
* is defined on a given cell, then it is considered the best.
*
* Run through all pairs of pieces in "pw1" and "pw2".
* If the domains of these pieces intersect, then the intersection
* needs to be distributed over the two pieces based on "cmp".
*
* After the updated domains have been computed, the result is constructed
* from "pw1", "pw2", data[0].cell and data[1].cell. If there are any pieces
* in "pw1" and "pw2" with the same function value expression, then
* they are combined into a single piece in the result.
* In order to be able to do this efficiently, the pieces of "pw1" and
* "pw2" are first sorted according to their function value expressions.
*/
static __isl_give PW *FN(PW,union_opt_cmp)(
__isl_take PW *pw1, __isl_take PW *pw2,
__isl_give isl_set *(*cmp)(__isl_take EL *el1, __isl_take EL *el2))
{
S(PW,union_opt_cmp_data) data[2] = { { pw1, NULL }, { pw2, NULL } };
int i, j;
isl_size n1, n2;
PW *res = NULL;
isl_ctx *ctx;
if (!pw1 || !pw2)
goto error;
ctx = isl_space_get_ctx(pw1->dim);
if (!isl_space_is_equal(pw1->dim, pw2->dim))
isl_die(ctx, isl_error_invalid,
"arguments should live in the same space", goto error);
if (FN(PW,is_empty)(pw1)) {
FN(PW,free)(pw1);
return pw2;
}
if (FN(PW,is_empty)(pw2)) {
FN(PW,free)(pw2);
return pw1;
}
for (i = 0; i < 2; ++i) {
data[i].pw = FN(PW,sort)(data[i].pw);
data[i].cell = FN(PW,extract_domains)(data[i].pw);
}
n1 = FN(PW,n_piece)(data[0].pw);
n2 = FN(PW,n_piece)(data[1].pw);
if (n1 < 0 || n2 < 0)
goto error;
for (i = 0; i < n1; ++i) {
for (j = 0; j < n2; ++j) {
isl_bool disjoint;
isl_set *set_i, *set_j;
set_i = FN(PW,peek_domain_at)(data[0].pw, i);
set_j = FN(PW,peek_domain_at)(data[1].pw, j);
disjoint = isl_set_is_disjoint(set_i, set_j);
if (disjoint < 0)
goto error;
if (disjoint)
continue;
if (FN(PW,union_opt_cmp_two)(&data[0], i,
&data[1], j, cmp) < 0)
goto error;
}
}
res = FN(PW,merge)(&data[0], &data[1]);
for (i = 0; i < 2; ++i)
FN(PW,union_opt_cmp_data_clear)(&data[i]);
return res;
error:
for (i = 0; i < 2; ++i)
FN(PW,union_opt_cmp_data_clear)(&data[i]);
return FN(PW,free)(res);
}
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