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/*
* Copyright 2008-2009 Katholieke Universiteit Leuven
* Copyright 2012-2013 Ecole Normale Superieure
* Copyright 2014-2015 INRIA Rocquencourt
* Copyright 2016 Sven Verdoolaege
*
* Use of this software is governed by the MIT license
*
* Written by Sven Verdoolaege, K.U.Leuven, Departement
* Computerwetenschappen, Celestijnenlaan 200A, B-3001 Leuven, Belgium
* and Ecole Normale Superieure, 45 rue d’Ulm, 75230 Paris, France
* and Inria Paris - Rocquencourt, Domaine de Voluceau - Rocquencourt,
* B.P. 105 - 78153 Le Chesnay, France
*/
#include <isl_ctx_private.h>
#include <isl_map_private.h>
#include "isl_equalities.h"
#include <isl/map.h>
#include <isl_seq.h>
#include "isl_tab.h"
#include <isl_space_private.h>
#include <isl_mat_private.h>
#include <isl_vec_private.h>
#include <bset_to_bmap.c>
#include <bset_from_bmap.c>
#include <set_to_map.c>
#include <set_from_map.c>
static void swap_equality(__isl_keep isl_basic_map *bmap, int a, int b)
{
isl_int *t = bmap->eq[a];
bmap->eq[a] = bmap->eq[b];
bmap->eq[b] = t;
}
static void swap_inequality(__isl_keep isl_basic_map *bmap, int a, int b)
{
if (a != b) {
isl_int *t = bmap->ineq[a];
bmap->ineq[a] = bmap->ineq[b];
bmap->ineq[b] = t;
}
}
__isl_give isl_basic_map *isl_basic_map_normalize_constraints(
__isl_take isl_basic_map *bmap)
{
int i;
isl_int gcd;
isl_size total = isl_basic_map_dim(bmap, isl_dim_all);
if (total < 0)
return isl_basic_map_free(bmap);
isl_int_init(gcd);
for (i = bmap->n_eq - 1; i >= 0; --i) {
isl_seq_gcd(bmap->eq[i]+1, total, &gcd);
if (isl_int_is_zero(gcd)) {
if (!isl_int_is_zero(bmap->eq[i][0])) {
bmap = isl_basic_map_set_to_empty(bmap);
break;
}
if (isl_basic_map_drop_equality(bmap, i) < 0)
goto error;
continue;
}
if (ISL_F_ISSET(bmap, ISL_BASIC_MAP_RATIONAL))
isl_int_gcd(gcd, gcd, bmap->eq[i][0]);
if (isl_int_is_one(gcd))
continue;
if (!isl_int_is_divisible_by(bmap->eq[i][0], gcd)) {
bmap = isl_basic_map_set_to_empty(bmap);
break;
}
isl_seq_scale_down(bmap->eq[i], bmap->eq[i], gcd, 1+total);
}
for (i = bmap->n_ineq - 1; i >= 0; --i) {
isl_seq_gcd(bmap->ineq[i]+1, total, &gcd);
if (isl_int_is_zero(gcd)) {
if (isl_int_is_neg(bmap->ineq[i][0])) {
bmap = isl_basic_map_set_to_empty(bmap);
break;
}
if (isl_basic_map_drop_inequality(bmap, i) < 0)
goto error;
continue;
}
if (ISL_F_ISSET(bmap, ISL_BASIC_MAP_RATIONAL))
isl_int_gcd(gcd, gcd, bmap->ineq[i][0]);
if (isl_int_is_one(gcd))
continue;
isl_int_fdiv_q(bmap->ineq[i][0], bmap->ineq[i][0], gcd);
isl_seq_scale_down(bmap->ineq[i]+1, bmap->ineq[i]+1, gcd, total);
}
isl_int_clear(gcd);
return bmap;
error:
isl_int_clear(gcd);
isl_basic_map_free(bmap);
return NULL;
}
__isl_give isl_basic_set *isl_basic_set_normalize_constraints(
__isl_take isl_basic_set *bset)
{
isl_basic_map *bmap = bset_to_bmap(bset);
return bset_from_bmap(isl_basic_map_normalize_constraints(bmap));
}
/* Reduce the coefficient of the variable at position "pos"
* in integer division "div", such that it lies in the half-open
* interval (1/2,1/2], extracting any excess value from this integer division.
* "pos" is as determined by isl_basic_map_offset, i.e., pos == 0
* corresponds to the constant term.
*
* That is, the integer division is of the form
*
* floor((... + (c * d + r) * x_pos + ...)/d)
*
* with -d < 2 * r <= d.
* Replace it by
*
* floor((... + r * x_pos + ...)/d) + c * x_pos
*
* If 2 * ((c * d + r) % d) <= d, then c = floor((c * d + r)/d).
* Otherwise, c = floor((c * d + r)/d) + 1.
*
* This is the same normalization that is performed by isl_aff_floor.
*/
static __isl_give isl_basic_map *reduce_coefficient_in_div(
__isl_take isl_basic_map *bmap, int div, int pos)
{
isl_int shift;
int add_one;
isl_int_init(shift);
isl_int_fdiv_r(shift, bmap->div[div][1 + pos], bmap->div[div][0]);
isl_int_mul_ui(shift, shift, 2);
add_one = isl_int_gt(shift, bmap->div[div][0]);
isl_int_fdiv_q(shift, bmap->div[div][1 + pos], bmap->div[div][0]);
if (add_one)
isl_int_add_ui(shift, shift, 1);
isl_int_neg(shift, shift);
bmap = isl_basic_map_shift_div(bmap, div, pos, shift);
isl_int_clear(shift);
return bmap;
}
/* Does the coefficient of the variable at position "pos"
* in integer division "div" need to be reduced?
* That is, does it lie outside the half-open interval (1/2,1/2]?
* The coefficient c/d lies outside this interval if abs(2 * c) >= d and
* 2 * c != d.
*/
static isl_bool needs_reduction(__isl_keep isl_basic_map *bmap, int div,
int pos)
{
isl_bool r;
if (isl_int_is_zero(bmap->div[div][1 + pos]))
return isl_bool_false;
isl_int_mul_ui(bmap->div[div][1 + pos], bmap->div[div][1 + pos], 2);
r = isl_int_abs_ge(bmap->div[div][1 + pos], bmap->div[div][0]) &&
!isl_int_eq(bmap->div[div][1 + pos], bmap->div[div][0]);
isl_int_divexact_ui(bmap->div[div][1 + pos],
bmap->div[div][1 + pos], 2);
return r;
}
/* Reduce the coefficients (including the constant term) of
* integer division "div", if needed.
* In particular, make sure all coefficients lie in
* the half-open interval (1/2,1/2].
*/
static __isl_give isl_basic_map *reduce_div_coefficients_of_div(
__isl_take isl_basic_map *bmap, int div)
{
int i;
isl_size total;
total = isl_basic_map_dim(bmap, isl_dim_all);
if (total < 0)
return isl_basic_map_free(bmap);
for (i = 0; i < 1 + total; ++i) {
isl_bool reduce;
reduce = needs_reduction(bmap, div, i);
if (reduce < 0)
return isl_basic_map_free(bmap);
if (!reduce)
continue;
bmap = reduce_coefficient_in_div(bmap, div, i);
if (!bmap)
break;
}
return bmap;
}
/* Reduce the coefficients (including the constant term) of
* the known integer divisions, if needed
* In particular, make sure all coefficients lie in
* the half-open interval (1/2,1/2].
*/
static __isl_give isl_basic_map *reduce_div_coefficients(
__isl_take isl_basic_map *bmap)
{
int i;
if (!bmap)
return NULL;
if (bmap->n_div == 0)
return bmap;
for (i = 0; i < bmap->n_div; ++i) {
if (isl_int_is_zero(bmap->div[i][0]))
continue;
bmap = reduce_div_coefficients_of_div(bmap, i);
if (!bmap)
break;
}
return bmap;
}
/* Remove any common factor in numerator and denominator of the div expression,
* not taking into account the constant term.
* That is, if the div is of the form
*
* floor((a + m f(x))/(m d))
*
* then replace it by
*
* floor((floor(a/m) + f(x))/d)
*
* The difference {a/m}/d in the argument satisfies 0 <= {a/m}/d < 1/d
* and can therefore not influence the result of the floor.
*/
static __isl_give isl_basic_map *normalize_div_expression(
__isl_take isl_basic_map *bmap, int div)
{
isl_size total = isl_basic_map_dim(bmap, isl_dim_all);
isl_ctx *ctx = bmap->ctx;
if (total < 0)
return isl_basic_map_free(bmap);
if (isl_int_is_zero(bmap->div[div][0]))
return bmap;
isl_seq_gcd(bmap->div[div] + 2, total, &ctx->normalize_gcd);
isl_int_gcd(ctx->normalize_gcd, ctx->normalize_gcd, bmap->div[div][0]);
if (isl_int_is_one(ctx->normalize_gcd))
return bmap;
isl_int_fdiv_q(bmap->div[div][1], bmap->div[div][1],
ctx->normalize_gcd);
isl_int_divexact(bmap->div[div][0], bmap->div[div][0],
ctx->normalize_gcd);
isl_seq_scale_down(bmap->div[div] + 2, bmap->div[div] + 2,
ctx->normalize_gcd, total);
return bmap;
}
/* Remove any common factor in numerator and denominator of a div expression,
* not taking into account the constant term.
* That is, look for any div of the form
*
* floor((a + m f(x))/(m d))
*
* and replace it by
*
* floor((floor(a/m) + f(x))/d)
*
* The difference {a/m}/d in the argument satisfies 0 <= {a/m}/d < 1/d
* and can therefore not influence the result of the floor.
*/
static __isl_give isl_basic_map *normalize_div_expressions(
__isl_take isl_basic_map *bmap)
{
int i;
if (!bmap)
return NULL;
if (bmap->n_div == 0)
return bmap;
for (i = 0; i < bmap->n_div; ++i)
bmap = normalize_div_expression(bmap, i);
return bmap;
}
/* Assumes divs have been ordered if keep_divs is set.
*/
static __isl_give isl_basic_map *eliminate_var_using_equality(
__isl_take isl_basic_map *bmap,
unsigned pos, isl_int *eq, int keep_divs, int *progress)
{
isl_size total;
isl_size v_div;
int k;
int last_div;
total = isl_basic_map_dim(bmap, isl_dim_all);
v_div = isl_basic_map_var_offset(bmap, isl_dim_div);
if (total < 0 || v_div < 0)
return isl_basic_map_free(bmap);
last_div = isl_seq_last_non_zero(eq + 1 + v_div, bmap->n_div);
for (k = 0; k < bmap->n_eq; ++k) {
if (bmap->eq[k] == eq)
continue;
if (isl_int_is_zero(bmap->eq[k][1+pos]))
continue;
if (progress)
*progress = 1;
isl_seq_elim(bmap->eq[k], eq, 1+pos, 1+total, NULL);
isl_seq_normalize(bmap->ctx, bmap->eq[k], 1 + total);
}
for (k = 0; k < bmap->n_ineq; ++k) {
if (isl_int_is_zero(bmap->ineq[k][1+pos]))
continue;
if (progress)
*progress = 1;
isl_seq_elim(bmap->ineq[k], eq, 1+pos, 1+total, NULL);
isl_seq_normalize(bmap->ctx, bmap->ineq[k], 1 + total);
ISL_F_CLR(bmap, ISL_BASIC_MAP_NO_REDUNDANT);
ISL_F_CLR(bmap, ISL_BASIC_MAP_SORTED);
}
for (k = 0; k < bmap->n_div; ++k) {
if (isl_int_is_zero(bmap->div[k][0]))
continue;
if (isl_int_is_zero(bmap->div[k][1+1+pos]))
continue;
if (progress)
*progress = 1;
/* We need to be careful about circular definitions,
* so for now we just remove the definition of div k
* if the equality contains any divs.
* If keep_divs is set, then the divs have been ordered
* and we can keep the definition as long as the result
* is still ordered.
*/
if (last_div == -1 || (keep_divs && last_div < k)) {
isl_seq_elim(bmap->div[k]+1, eq,
1+pos, 1+total, &bmap->div[k][0]);
bmap = normalize_div_expression(bmap, k);
if (!bmap)
return NULL;
} else
isl_seq_clr(bmap->div[k], 1 + total);
}
return bmap;
}
/* Assumes divs have been ordered if keep_divs is set.
*/
static __isl_give isl_basic_map *eliminate_div(__isl_take isl_basic_map *bmap,
isl_int *eq, unsigned div, int keep_divs)
{
isl_size v_div;
unsigned pos;
v_div = isl_basic_map_var_offset(bmap, isl_dim_div);
if (v_div < 0)
return isl_basic_map_free(bmap);
pos = v_div + div;
bmap = eliminate_var_using_equality(bmap, pos, eq, keep_divs, NULL);
bmap = isl_basic_map_drop_div(bmap, div);
return bmap;
}
/* Check if elimination of div "div" using equality "eq" would not
* result in a div depending on a later div.
*/
static isl_bool ok_to_eliminate_div(__isl_keep isl_basic_map *bmap, isl_int *eq,
unsigned div)
{
int k;
int last_div;
isl_size v_div;
unsigned pos;
v_div = isl_basic_map_var_offset(bmap, isl_dim_div);
if (v_div < 0)
return isl_bool_error;
pos = v_div + div;
last_div = isl_seq_last_non_zero(eq + 1 + v_div, bmap->n_div);
if (last_div < 0 || last_div <= div)
return isl_bool_true;
for (k = 0; k <= last_div; ++k) {
if (isl_int_is_zero(bmap->div[k][0]))
continue;
if (!isl_int_is_zero(bmap->div[k][1 + 1 + pos]))
return isl_bool_false;
}
return isl_bool_true;
}
/* Eliminate divs based on equalities
*/
static __isl_give isl_basic_map *eliminate_divs_eq(
__isl_take isl_basic_map *bmap, int *progress)
{
int d;
int i;
int modified = 0;
unsigned off;
bmap = isl_basic_map_order_divs(bmap);
if (!bmap)
return NULL;
off = isl_basic_map_offset(bmap, isl_dim_div);
for (d = bmap->n_div - 1; d >= 0 ; --d) {
for (i = 0; i < bmap->n_eq; ++i) {
isl_bool ok;
if (!isl_int_is_one(bmap->eq[i][off + d]) &&
!isl_int_is_negone(bmap->eq[i][off + d]))
continue;
ok = ok_to_eliminate_div(bmap, bmap->eq[i], d);
if (ok < 0)
return isl_basic_map_free(bmap);
if (!ok)
continue;
modified = 1;
*progress = 1;
bmap = eliminate_div(bmap, bmap->eq[i], d, 1);
if (isl_basic_map_drop_equality(bmap, i) < 0)
return isl_basic_map_free(bmap);
break;
}
}
if (modified)
return eliminate_divs_eq(bmap, progress);
return bmap;
}
/* Eliminate divs based on inequalities
*/
static __isl_give isl_basic_map *eliminate_divs_ineq(
__isl_take isl_basic_map *bmap, int *progress)
{
int d;
int i;
unsigned off;
struct isl_ctx *ctx;
if (!bmap)
return NULL;
ctx = bmap->ctx;
off = isl_basic_map_offset(bmap, isl_dim_div);
for (d = bmap->n_div - 1; d >= 0 ; --d) {
for (i = 0; i < bmap->n_eq; ++i)
if (!isl_int_is_zero(bmap->eq[i][off + d]))
break;
if (i < bmap->n_eq)
continue;
for (i = 0; i < bmap->n_ineq; ++i)
if (isl_int_abs_gt(bmap->ineq[i][off + d], ctx->one))
break;
if (i < bmap->n_ineq)
continue;
*progress = 1;
bmap = isl_basic_map_eliminate_vars(bmap, (off-1)+d, 1);
if (!bmap || ISL_F_ISSET(bmap, ISL_BASIC_MAP_EMPTY))
break;
bmap = isl_basic_map_drop_div(bmap, d);
if (!bmap)
break;
}
return bmap;
}
/* Does the equality constraint at position "eq" in "bmap" involve
* any local variables in the range [first, first + n)
* that are not marked as having an explicit representation?
*/
static isl_bool bmap_eq_involves_unknown_divs(__isl_keep isl_basic_map *bmap,
int eq, unsigned first, unsigned n)
{
unsigned o_div;
int i;
if (!bmap)
return isl_bool_error;
o_div = isl_basic_map_offset(bmap, isl_dim_div);
for (i = 0; i < n; ++i) {
isl_bool unknown;
if (isl_int_is_zero(bmap->eq[eq][o_div + first + i]))
continue;
unknown = isl_basic_map_div_is_marked_unknown(bmap, first + i);
if (unknown < 0)
return isl_bool_error;
if (unknown)
return isl_bool_true;
}
return isl_bool_false;
}
/* The last local variable involved in the equality constraint
* at position "eq" in "bmap" is the local variable at position "div".
* It can therefore be used to extract an explicit representation
* for that variable.
* Do so unless the local variable already has an explicit representation or
* the explicit representation would involve any other local variables
* that in turn do not have an explicit representation.
* An equality constraint involving local variables without an explicit
* representation can be used in isl_basic_map_drop_redundant_divs
* to separate out an independent local variable. Introducing
* an explicit representation here would block this transformation,
* while the partial explicit representation in itself is not very useful.
* Set *progress if anything is changed.
*
* The equality constraint is of the form
*
* f(x) + n e >= 0
*
* with n a positive number. The explicit representation derived from
* this constraint is
*
* floor((-f(x))/n)
*/
static __isl_give isl_basic_map *set_div_from_eq(__isl_take isl_basic_map *bmap,
int div, int eq, int *progress)
{
isl_size total;
unsigned o_div;
isl_bool involves;
if (!bmap)
return NULL;
if (!isl_int_is_zero(bmap->div[div][0]))
return bmap;
involves = bmap_eq_involves_unknown_divs(bmap, eq, 0, div);
if (involves < 0)
return isl_basic_map_free(bmap);
if (involves)
return bmap;
total = isl_basic_map_dim(bmap, isl_dim_all);
if (total < 0)
return isl_basic_map_free(bmap);
o_div = isl_basic_map_offset(bmap, isl_dim_div);
isl_seq_neg(bmap->div[div] + 1, bmap->eq[eq], 1 + total);
isl_int_set_si(bmap->div[div][1 + o_div + div], 0);
isl_int_set(bmap->div[div][0], bmap->eq[eq][o_div + div]);
if (progress)
*progress = 1;
return bmap;
}
/* Perform fangcheng (Gaussian elimination) on the equality
* constraints of "bmap".
* That is, put them into row-echelon form, starting from the last column
* backward and use them to eliminate the corresponding coefficients
* from all constraints.
*
* If "progress" is not NULL, then it gets set if the elimination
* results in any changes.
* The elimination process may result in some equality constraints
* getting interchanged or removed.
* If "swap" or "drop" are not NULL, then they get called when
* two equality constraints get interchanged or
* when a number of final equality constraints get removed.
* As a special case, if the input turns out to be empty,
* then drop gets called with the number of removed equality
* constraints set to the total number of equality constraints.
* If "swap" or "drop" are not NULL, then the local variables (if any)
* are assumed to be in a valid order.
*/
__isl_give isl_basic_map *isl_basic_map_gauss5(__isl_take isl_basic_map *bmap,
int *progress,
isl_stat (*swap)(unsigned a, unsigned b, void *user),
isl_stat (*drop)(unsigned n, void *user), void *user)
{
int k;
int done;
int last_var;
unsigned total_var;
isl_size total;
unsigned n_drop;
if (!swap && !drop)
bmap = isl_basic_map_order_divs(bmap);
total = isl_basic_map_dim(bmap, isl_dim_all);
if (total < 0)
return isl_basic_map_free(bmap);
total_var = total - bmap->n_div;
last_var = total - 1;
for (done = 0; done < bmap->n_eq; ++done) {
for (; last_var >= 0; --last_var) {
for (k = done; k < bmap->n_eq; ++k)
if (!isl_int_is_zero(bmap->eq[k][1+last_var]))
break;
if (k < bmap->n_eq)
break;
}
if (last_var < 0)
break;
if (k != done) {
swap_equality(bmap, k, done);
if (swap && swap(k, done, user) < 0)
return isl_basic_map_free(bmap);
}
if (isl_int_is_neg(bmap->eq[done][1+last_var]))
isl_seq_neg(bmap->eq[done], bmap->eq[done], 1+total);
bmap = eliminate_var_using_equality(bmap, last_var,
bmap->eq[done], 1, progress);
if (last_var >= total_var)
bmap = set_div_from_eq(bmap, last_var - total_var,
done, progress);
if (!bmap)
return NULL;
}
if (done == bmap->n_eq)
return bmap;
for (k = done; k < bmap->n_eq; ++k) {
if (isl_int_is_zero(bmap->eq[k][0]))
continue;
if (drop && drop(bmap->n_eq, user) < 0)
return isl_basic_map_free(bmap);
return isl_basic_map_set_to_empty(bmap);
}
n_drop = bmap->n_eq - done;
bmap = isl_basic_map_free_equality(bmap, n_drop);
if (drop && drop(n_drop, user) < 0)
return isl_basic_map_free(bmap);
return bmap;
}
__isl_give isl_basic_map *isl_basic_map_gauss(__isl_take isl_basic_map *bmap,
int *progress)
{
return isl_basic_map_gauss5(bmap, progress, NULL, NULL, NULL);
}
__isl_give isl_basic_set *isl_basic_set_gauss(
__isl_take isl_basic_set *bset, int *progress)
{
return bset_from_bmap(isl_basic_map_gauss(bset_to_bmap(bset),
progress));
}
static unsigned int round_up(unsigned int v)
{
int old_v = v;
while (v) {
old_v = v;
v ^= v & -v;
}
return old_v << 1;
}
/* Hash table of inequalities in a basic map.
* "index" is an array of addresses of inequalities in the basic map, some
* of which are NULL. The inequalities are hashed on the coefficients
* except the constant term.
* "size" is the number of elements in the array and is always a power of two
* "bits" is the number of bits need to represent an index into the array.
* "total" is the total dimension of the basic map.
*/
struct isl_constraint_index {
unsigned int size;
int bits;
isl_int ***index;
isl_size total;
};
/* Fill in the "ci" data structure for holding the inequalities of "bmap".
*/
static isl_stat create_constraint_index(struct isl_constraint_index *ci,
__isl_keep isl_basic_map *bmap)
{
isl_ctx *ctx;
ci->index = NULL;
if (!bmap)
return isl_stat_error;
ci->total = isl_basic_map_dim(bmap, isl_dim_all);
if (ci->total < 0)
return isl_stat_error;
if (bmap->n_ineq == 0)
return isl_stat_ok;
ci->size = round_up(4 * (bmap->n_ineq + 1) / 3 - 1);
ci->bits = ffs(ci->size) - 1;
ctx = isl_basic_map_get_ctx(bmap);
ci->index = isl_calloc_array(ctx, isl_int **, ci->size);
if (!ci->index)
return isl_stat_error;
return isl_stat_ok;
}
/* Free the memory allocated by create_constraint_index.
*/
static void constraint_index_free(struct isl_constraint_index *ci)
{
free(ci->index);
}
/* Return the position in ci->index that contains the address of
* an inequality that is equal to *ineq up to the constant term,
* provided this address is not identical to "ineq".
* If there is no such inequality, then return the position where
* such an inequality should be inserted.
*/
static int hash_index_ineq(struct isl_constraint_index *ci, isl_int **ineq)
{
int h;
uint32_t hash = isl_seq_get_hash_bits((*ineq) + 1, ci->total, ci->bits);
for (h = hash; ci->index[h]; h = (h+1) % ci->size)
if (ineq != ci->index[h] &&
isl_seq_eq((*ineq) + 1, ci->index[h][0]+1, ci->total))
break;
return h;
}
/* Return the position in ci->index that contains the address of
* an inequality that is equal to the k'th inequality of "bmap"
* up to the constant term, provided it does not point to the very
* same inequality.
* If there is no such inequality, then return the position where
* such an inequality should be inserted.
*/
static int hash_index(struct isl_constraint_index *ci,
__isl_keep isl_basic_map *bmap, int k)
{
return hash_index_ineq(ci, &bmap->ineq[k]);
}
static int set_hash_index(struct isl_constraint_index *ci,
__isl_keep isl_basic_set *bset, int k)
{
return hash_index(ci, bset, k);
}
/* Fill in the "ci" data structure with the inequalities of "bset".
*/
static isl_stat setup_constraint_index(struct isl_constraint_index *ci,
__isl_keep isl_basic_set *bset)
{
int k, h;
if (create_constraint_index(ci, bset) < 0)
return isl_stat_error;
for (k = 0; k < bset->n_ineq; ++k) {
h = set_hash_index(ci, bset, k);
ci->index[h] = &bset->ineq[k];
}
return isl_stat_ok;
}
/* Is the inequality ineq (obviously) redundant with respect
* to the constraints in "ci"?
*
* Look for an inequality in "ci" with the same coefficients and then
* check if the contant term of "ineq" is greater than or equal
* to the constant term of that inequality. If so, "ineq" is clearly
* redundant.
*
* Note that hash_index_ineq ignores a stored constraint if it has
* the same address as the passed inequality. It is ok to pass
* the address of a local variable here since it will never be
* the same as the address of a constraint in "ci".
*/
static isl_bool constraint_index_is_redundant(struct isl_constraint_index *ci,
isl_int *ineq)
{
int h;
h = hash_index_ineq(ci, &ineq);
if (!ci->index[h])
return isl_bool_false;
return isl_int_ge(ineq[0], (*ci->index[h])[0]);
}
/* If we can eliminate more than one div, then we need to make
* sure we do it from last div to first div, in order not to
* change the position of the other divs that still need to
* be removed.
*/
static __isl_give isl_basic_map *remove_duplicate_divs(
__isl_take isl_basic_map *bmap, int *progress)
{
unsigned int size;
int *index;
int *elim_for;
int k, l, h;
int bits;
struct isl_blk eq;
isl_size v_div;
unsigned total;
struct isl_ctx *ctx;
bmap = isl_basic_map_order_divs(bmap);
if (!bmap || bmap->n_div <= 1)
return bmap;
v_div = isl_basic_map_var_offset(bmap, isl_dim_div);
if (v_div < 0)
return isl_basic_map_free(bmap);
total = v_div + bmap->n_div;
ctx = bmap->ctx;
for (k = bmap->n_div - 1; k >= 0; --k)
if (!isl_int_is_zero(bmap->div[k][0]))
break;
if (k <= 0)
return bmap;
size = round_up(4 * bmap->n_div / 3 - 1);
if (size == 0)
return bmap;
elim_for = isl_calloc_array(ctx, int, bmap->n_div);
bits = ffs(size) - 1;
index = isl_calloc_array(ctx, int, size);
if (!elim_for || !index)
goto out;
eq = isl_blk_alloc(ctx, 1+total);
if (isl_blk_is_error(eq))
goto out;
isl_seq_clr(eq.data, 1+total);
index[isl_seq_get_hash_bits(bmap->div[k], 2+total, bits)] = k + 1;
for (--k; k >= 0; --k) {
uint32_t hash;
if (isl_int_is_zero(bmap->div[k][0]))
continue;
hash = isl_seq_get_hash_bits(bmap->div[k], 2+total, bits);
for (h = hash; index[h]; h = (h+1) % size)
if (isl_seq_eq(bmap->div[k],
bmap->div[index[h]-1], 2+total))
break;
if (index[h]) {
*progress = 1;
l = index[h] - 1;
elim_for[l] = k + 1;
}
index[h] = k+1;
}
for (l = bmap->n_div - 1; l >= 0; --l) {
if (!elim_for[l])
continue;
k = elim_for[l] - 1;
isl_int_set_si(eq.data[1 + v_div + k], -1);
isl_int_set_si(eq.data[1 + v_div + l], 1);
bmap = eliminate_div(bmap, eq.data, l, 1);
if (!bmap)
break;
isl_int_set_si(eq.data[1 + v_div + k], 0);
isl_int_set_si(eq.data[1 + v_div + l], 0);
}
isl_blk_free(ctx, eq);
out:
free(index);
free(elim_for);
return bmap;
}
static int n_pure_div_eq(__isl_keep isl_basic_map *bmap)
{
int i, j;
isl_size v_div;
v_div = isl_basic_map_var_offset(bmap, isl_dim_div);
if (v_div < 0)
return -1;
for (i = 0, j = bmap->n_div-1; i < bmap->n_eq; ++i) {
while (j >= 0 && isl_int_is_zero(bmap->eq[i][1 + v_div + j]))
--j;
if (j < 0)
break;
if (isl_seq_first_non_zero(bmap->eq[i] + 1 + v_div, j) != -1)
return 0;
}
return i;
}
/* Normalize divs that appear in equalities.
*
* In particular, we assume that bmap contains some equalities
* of the form
*
* a x = m * e_i
*
* and we want to replace the set of e_i by a minimal set and
* such that the new e_i have a canonical representation in terms
* of the vector x.
* If any of the equalities involves more than one divs, then
* we currently simply bail out.
*
* Let us first additionally assume that all equalities involve
* a div. The equalities then express modulo constraints on the
* remaining variables and we can use "parameter compression"
* to find a minimal set of constraints. The result is a transformation
*
* x = T(x') = x_0 + G x'
*
* with G a lower-triangular matrix with all elements below the diagonal
* non-negative and smaller than the diagonal element on the same row.
* We first normalize x_0 by making the same property hold in the affine
* T matrix.
* The rows i of G with a 1 on the diagonal do not impose any modulo
* constraint and simply express x_i = x'_i.
* For each of the remaining rows i, we introduce a div and a corresponding
* equality. In particular
*
* g_ii e_j = x_i - g_i(x')
*
* where each x'_k is replaced either by x_k (if g_kk = 1) or the
* corresponding div (if g_kk != 1).
*
* If there are any equalities not involving any div, then we
* first apply a variable compression on the variables x:
*
* x = C x'' x'' = C_2 x
*
* and perform the above parameter compression on A C instead of on A.
* The resulting compression is then of the form
*
* x'' = T(x') = x_0 + G x'
*
* and in constructing the new divs and the corresponding equalities,
* we have to replace each x'', i.e., the x'_k with (g_kk = 1),
* by the corresponding row from C_2.
*/
static __isl_give isl_basic_map *normalize_divs(__isl_take isl_basic_map *bmap,
int *progress)
{
int i, j, k;
isl_size v_div;
int div_eq;
struct isl_mat *B;
struct isl_vec *d;
struct isl_mat *T = NULL;
struct isl_mat *C = NULL;
struct isl_mat *C2 = NULL;
isl_int v;
int *pos = NULL;
int dropped, needed;
if (!bmap)
return NULL;
if (bmap->n_div == 0)
return bmap;
if (bmap->n_eq == 0)
return bmap;
if (ISL_F_ISSET(bmap, ISL_BASIC_MAP_NORMALIZED_DIVS))
return bmap;
v_div = isl_basic_map_var_offset(bmap, isl_dim_div);
div_eq = n_pure_div_eq(bmap);
if (v_div < 0 || div_eq < 0)
return isl_basic_map_free(bmap);
if (div_eq == 0)
return bmap;
if (div_eq < bmap->n_eq) {
B = isl_mat_sub_alloc6(bmap->ctx, bmap->eq, div_eq,
bmap->n_eq - div_eq, 0, 1 + v_div);
C = isl_mat_variable_compression(B, &C2);
if (!C || !C2)
goto error;
if (C->n_col == 0) {
bmap = isl_basic_map_set_to_empty(bmap);
isl_mat_free(C);
isl_mat_free(C2);
goto done;
}
}
d = isl_vec_alloc(bmap->ctx, div_eq);
if (!d)
goto error;
for (i = 0, j = bmap->n_div-1; i < div_eq; ++i) {
while (j >= 0 && isl_int_is_zero(bmap->eq[i][1 + v_div + j]))
--j;
isl_int_set(d->block.data[i], bmap->eq[i][1 + v_div + j]);
}
B = isl_mat_sub_alloc6(bmap->ctx, bmap->eq, 0, div_eq, 0, 1 + v_div);
if (C) {
B = isl_mat_product(B, C);
C = NULL;
}
T = isl_mat_parameter_compression(B, d);
if (!T)
goto error;
if (T->n_col == 0) {
bmap = isl_basic_map_set_to_empty(bmap);
isl_mat_free(C2);
isl_mat_free(T);
goto done;
}
isl_int_init(v);
for (i = 0; i < T->n_row - 1; ++i) {
isl_int_fdiv_q(v, T->row[1 + i][0], T->row[1 + i][1 + i]);
if (isl_int_is_zero(v))
continue;
isl_mat_col_submul(T, 0, v, 1 + i);
}
isl_int_clear(v);
pos = isl_alloc_array(bmap->ctx, int, T->n_row);
if (!pos)
goto error;
/* We have to be careful because dropping equalities may reorder them */
dropped = 0;
for (j = bmap->n_div - 1; j >= 0; --j) {
for (i = 0; i < bmap->n_eq; ++i)
if (!isl_int_is_zero(bmap->eq[i][1 + v_div + j]))
break;
if (i < bmap->n_eq) {
bmap = isl_basic_map_drop_div(bmap, j);
if (isl_basic_map_drop_equality(bmap, i) < 0)
goto error;
++dropped;
}
}
pos[0] = 0;
needed = 0;
for (i = 1; i < T->n_row; ++i) {
if (isl_int_is_one(T->row[i][i]))
pos[i] = i;
else
needed++;
}
if (needed > dropped) {
bmap = isl_basic_map_extend(bmap, needed, needed, 0);
if (!bmap)
goto error;
}
for (i = 1; i < T->n_row; ++i) {
if (isl_int_is_one(T->row[i][i]))
continue;
k = isl_basic_map_alloc_div(bmap);
pos[i] = 1 + v_div + k;
isl_seq_clr(bmap->div[k] + 1, 1 + v_div + bmap->n_div);
isl_int_set(bmap->div[k][0], T->row[i][i]);
if (C2)
isl_seq_cpy(bmap->div[k] + 1, C2->row[i], 1 + v_div);
else
isl_int_set_si(bmap->div[k][1 + i], 1);
for (j = 0; j < i; ++j) {
if (isl_int_is_zero(T->row[i][j]))
continue;
if (pos[j] < T->n_row && C2)
isl_seq_submul(bmap->div[k] + 1, T->row[i][j],
C2->row[pos[j]], 1 + v_div);
else
isl_int_neg(bmap->div[k][1 + pos[j]],
T->row[i][j]);
}
j = isl_basic_map_alloc_equality(bmap);
isl_seq_neg(bmap->eq[j], bmap->div[k]+1, 1+v_div+bmap->n_div);
isl_int_set(bmap->eq[j][pos[i]], bmap->div[k][0]);
}
free(pos);
isl_mat_free(C2);
isl_mat_free(T);
if (progress)
*progress = 1;
done:
ISL_F_SET(bmap, ISL_BASIC_MAP_NORMALIZED_DIVS);
return bmap;
error:
free(pos);
isl_mat_free(C);
isl_mat_free(C2);
isl_mat_free(T);
isl_basic_map_free(bmap);
return NULL;
}
static __isl_give isl_basic_map *set_div_from_lower_bound(
__isl_take isl_basic_map *bmap, int div, int ineq)
{
unsigned total = isl_basic_map_offset(bmap, isl_dim_div);
isl_seq_neg(bmap->div[div] + 1, bmap->ineq[ineq], total + bmap->n_div);
isl_int_set(bmap->div[div][0], bmap->ineq[ineq][total + div]);
isl_int_add(bmap->div[div][1], bmap->div[div][1], bmap->div[div][0]);
isl_int_sub_ui(bmap->div[div][1], bmap->div[div][1], 1);
isl_int_set_si(bmap->div[div][1 + total + div], 0);
return bmap;
}
/* Check whether it is ok to define a div based on an inequality.
* To avoid the introduction of circular definitions of divs, we
* do not allow such a definition if the resulting expression would refer to
* any other undefined divs or if any known div is defined in
* terms of the unknown div.
*/
static isl_bool ok_to_set_div_from_bound(__isl_keep isl_basic_map *bmap,
int div, int ineq)
{
int j;
unsigned total = isl_basic_map_offset(bmap, isl_dim_div);
/* Not defined in terms of unknown divs */
for (j = 0; j < bmap->n_div; ++j) {
if (div == j)
continue;
if (isl_int_is_zero(bmap->ineq[ineq][total + j]))
continue;
if (isl_int_is_zero(bmap->div[j][0]))
return isl_bool_false;
}
/* No other div defined in terms of this one => avoid loops */
for (j = 0; j < bmap->n_div; ++j) {
if (div == j)
continue;
if (isl_int_is_zero(bmap->div[j][0]))
continue;
if (!isl_int_is_zero(bmap->div[j][1 + total + div]))
return isl_bool_false;
}
return isl_bool_true;
}
/* Would an expression for div "div" based on inequality "ineq" of "bmap"
* be a better expression than the current one?
*
* If we do not have any expression yet, then any expression would be better.
* Otherwise we check if the last variable involved in the inequality
* (disregarding the div that it would define) is in an earlier position
* than the last variable involved in the current div expression.
*/
static isl_bool better_div_constraint(__isl_keep isl_basic_map *bmap,
int div, int ineq)
{
unsigned total = isl_basic_map_offset(bmap, isl_dim_div);
int last_div;
int last_ineq;
if (isl_int_is_zero(bmap->div[div][0]))
return isl_bool_true;
if (isl_seq_last_non_zero(bmap->ineq[ineq] + total + div + 1,
bmap->n_div - (div + 1)) >= 0)
return isl_bool_false;
last_ineq = isl_seq_last_non_zero(bmap->ineq[ineq], total + div);
last_div = isl_seq_last_non_zero(bmap->div[div] + 1,
total + bmap->n_div);
return last_ineq < last_div;
}
/* Given two constraints "k" and "l" that are opposite to each other,
* except for the constant term, check if we can use them
* to obtain an expression for one of the hitherto unknown divs or
* a "better" expression for a div for which we already have an expression.
* "sum" is the sum of the constant terms of the constraints.
* If this sum is strictly smaller than the coefficient of one
* of the divs, then this pair can be used define the div.
* To avoid the introduction of circular definitions of divs, we
* do not use the pair if the resulting expression would refer to
* any other undefined divs or if any known div is defined in
* terms of the unknown div.
*/
static __isl_give isl_basic_map *check_for_div_constraints(
__isl_take isl_basic_map *bmap, int k, int l, isl_int sum,
int *progress)
{
int i;
unsigned total = isl_basic_map_offset(bmap, isl_dim_div);
for (i = 0; i < bmap->n_div; ++i) {
isl_bool set_div;
if (isl_int_is_zero(bmap->ineq[k][total + i]))
continue;
if (isl_int_abs_ge(sum, bmap->ineq[k][total + i]))
continue;
set_div = better_div_constraint(bmap, i, k);
if (set_div >= 0 && set_div)
set_div = ok_to_set_div_from_bound(bmap, i, k);
if (set_div < 0)
return isl_basic_map_free(bmap);
if (!set_div)
break;
if (isl_int_is_pos(bmap->ineq[k][total + i]))
bmap = set_div_from_lower_bound(bmap, i, k);
else
bmap = set_div_from_lower_bound(bmap, i, l);
if (progress)
*progress = 1;
break;
}
return bmap;
}
__isl_give isl_basic_map *isl_basic_map_remove_duplicate_constraints(
__isl_take isl_basic_map *bmap, int *progress, int detect_divs)
{
struct isl_constraint_index ci;
int k, l, h;
isl_size total = isl_basic_map_dim(bmap, isl_dim_all);
isl_int sum;
if (total < 0 || bmap->n_ineq <= 1)
return bmap;
if (create_constraint_index(&ci, bmap) < 0)
return bmap;
h = isl_seq_get_hash_bits(bmap->ineq[0] + 1, total, ci.bits);
ci.index[h] = &bmap->ineq[0];
for (k = 1; k < bmap->n_ineq; ++k) {
h = hash_index(&ci, bmap, k);
if (!ci.index[h]) {
ci.index[h] = &bmap->ineq[k];
continue;
}
if (progress)
*progress = 1;
l = ci.index[h] - &bmap->ineq[0];
if (isl_int_lt(bmap->ineq[k][0], bmap->ineq[l][0]))
swap_inequality(bmap, k, l);
isl_basic_map_drop_inequality(bmap, k);
--k;
}
isl_int_init(sum);
for (k = 0; bmap && k < bmap->n_ineq-1; ++k) {
isl_seq_neg(bmap->ineq[k]+1, bmap->ineq[k]+1, total);
h = hash_index(&ci, bmap, k);
isl_seq_neg(bmap->ineq[k]+1, bmap->ineq[k]+1, total);
if (!ci.index[h])
continue;
l = ci.index[h] - &bmap->ineq[0];
isl_int_add(sum, bmap->ineq[k][0], bmap->ineq[l][0]);
if (isl_int_is_pos(sum)) {
if (detect_divs)
bmap = check_for_div_constraints(bmap, k, l,
sum, progress);
continue;
}
if (isl_int_is_zero(sum)) {
/* We need to break out of the loop after these
* changes since the contents of the hash
* will no longer be valid.
* Plus, we probably we want to regauss first.
*/
if (progress)
*progress = 1;
isl_basic_map_drop_inequality(bmap, l);
isl_basic_map_inequality_to_equality(bmap, k);
} else
bmap = isl_basic_map_set_to_empty(bmap);
break;
}
isl_int_clear(sum);
constraint_index_free(&ci);
return bmap;
}
/* Detect all pairs of inequalities that form an equality.
*
* isl_basic_map_remove_duplicate_constraints detects at most one such pair.
* Call it repeatedly while it is making progress.
*/
__isl_give isl_basic_map *isl_basic_map_detect_inequality_pairs(
__isl_take isl_basic_map *bmap, int *progress)
{
int duplicate;
do {
duplicate = 0;
bmap = isl_basic_map_remove_duplicate_constraints(bmap,
&duplicate, 0);
if (progress && duplicate)
*progress = 1;
} while (duplicate);
return bmap;
}
/* Given a known integer division "div" that is not integral
* (with denominator 1), eliminate it from the constraints in "bmap"
* where it appears with a (positive or negative) unit coefficient.
* If "progress" is not NULL, then it gets set if the elimination
* results in any changes.
*
* That is, replace
*
* floor(e/m) + f >= 0
*
* by
*
* e + m f >= 0
*
* and
*
* -floor(e/m) + f >= 0
*
* by
*
* -e + m f + m - 1 >= 0
*
* The first conversion is valid because floor(e/m) >= -f is equivalent
* to e/m >= -f because -f is an integral expression.
* The second conversion follows from the fact that
*
* -floor(e/m) = ceil(-e/m) = floor((-e + m - 1)/m)
*
*
* Note that one of the div constraints may have been eliminated
* due to being redundant with respect to the constraint that is
* being modified by this function. The modified constraint may
* no longer imply this div constraint, so we add it back to make
* sure we do not lose any information.
*/
static __isl_give isl_basic_map *eliminate_unit_div(
__isl_take isl_basic_map *bmap, int div, int *progress)
{
int j;
isl_size v_div, dim;
isl_ctx *ctx;
v_div = isl_basic_map_var_offset(bmap, isl_dim_div);
dim = isl_basic_map_dim(bmap, isl_dim_all);
if (v_div < 0 || dim < 0)
return isl_basic_map_free(bmap);
ctx = isl_basic_map_get_ctx(bmap);
for (j = 0; j < bmap->n_ineq; ++j) {
int s;
if (!isl_int_is_one(bmap->ineq[j][1 + v_div + div]) &&
!isl_int_is_negone(bmap->ineq[j][1 + v_div + div]))
continue;
if (progress)
*progress = 1;
s = isl_int_sgn(bmap->ineq[j][1 + v_div + div]);
isl_int_set_si(bmap->ineq[j][1 + v_div + div], 0);
if (s < 0)
isl_seq_combine(bmap->ineq[j],
ctx->negone, bmap->div[div] + 1,
bmap->div[div][0], bmap->ineq[j], 1 + dim);
else
isl_seq_combine(bmap->ineq[j],
ctx->one, bmap->div[div] + 1,
bmap->div[div][0], bmap->ineq[j], 1 + dim);
if (s < 0) {
isl_int_add(bmap->ineq[j][0],
bmap->ineq[j][0], bmap->div[div][0]);
isl_int_sub_ui(bmap->ineq[j][0],
bmap->ineq[j][0], 1);
}
bmap = isl_basic_map_extend_constraints(bmap, 0, 1);
bmap = isl_basic_map_add_div_constraint(bmap, div, s);
if (!bmap)
return NULL;
}
return bmap;
}
/* Eliminate selected known divs from constraints where they appear with
* a (positive or negative) unit coefficient.
* In particular, only handle those for which "select" returns isl_bool_true.
* If "progress" is not NULL, then it gets set if the elimination
* results in any changes.
*
* We skip integral divs, i.e., those with denominator 1, as we would
* risk eliminating the div from the div constraints. We do not need
* to handle those divs here anyway since the div constraints will turn
* out to form an equality and this equality can then be used to eliminate
* the div from all constraints.
*/
static __isl_give isl_basic_map *eliminate_selected_unit_divs(
__isl_take isl_basic_map *bmap,
isl_bool (*select)(__isl_keep isl_basic_map *bmap, int div),
int *progress)
{
int i;
if (!bmap)
return NULL;
for (i = 0; i < bmap->n_div; ++i) {
isl_bool selected;
if (isl_int_is_zero(bmap->div[i][0]))
continue;
if (isl_int_is_one(bmap->div[i][0]))
continue;
selected = select(bmap, i);
if (selected < 0)
return isl_basic_map_free(bmap);
if (!selected)
continue;
bmap = eliminate_unit_div(bmap, i, progress);
if (!bmap)
return NULL;
}
return bmap;
}
/* eliminate_selected_unit_divs callback that selects every
* integer division.
*/
static isl_bool is_any_div(__isl_keep isl_basic_map *bmap, int div)
{
return isl_bool_true;
}
/* Eliminate known divs from constraints where they appear with
* a (positive or negative) unit coefficient.
* If "progress" is not NULL, then it gets set if the elimination
* results in any changes.
*/
static __isl_give isl_basic_map *eliminate_unit_divs(
__isl_take isl_basic_map *bmap, int *progress)
{
return eliminate_selected_unit_divs(bmap, &is_any_div, progress);
}
/* eliminate_selected_unit_divs callback that selects
* integer divisions that only appear with
* a (positive or negative) unit coefficient
* (outside their div constraints).
*/
static isl_bool is_pure_unit_div(__isl_keep isl_basic_map *bmap, int div)
{
int i;
isl_size v_div, n_ineq;
v_div = isl_basic_map_var_offset(bmap, isl_dim_div);
n_ineq = isl_basic_map_n_inequality(bmap);
if (v_div < 0 || n_ineq < 0)
return isl_bool_error;
for (i = 0; i < n_ineq; ++i) {
isl_bool skip;
if (isl_int_is_zero(bmap->ineq[i][1 + v_div + div]))
continue;
skip = isl_basic_map_is_div_constraint(bmap,
bmap->ineq[i], div);
if (skip < 0)
return isl_bool_error;
if (skip)
continue;
if (!isl_int_is_one(bmap->ineq[i][1 + v_div + div]) &&
!isl_int_is_negone(bmap->ineq[i][1 + v_div + div]))
return isl_bool_false;
}
return isl_bool_true;
}
/* Eliminate known divs from constraints where they appear with
* a (positive or negative) unit coefficient,
* but only if they do not appear in any other constraints
* (other than the div constraints).
*/
__isl_give isl_basic_map *isl_basic_map_eliminate_pure_unit_divs(
__isl_take isl_basic_map *bmap)
{
return eliminate_selected_unit_divs(bmap, &is_pure_unit_div, NULL);
}
__isl_give isl_basic_map *isl_basic_map_simplify(__isl_take isl_basic_map *bmap)
{
int progress = 1;
if (!bmap)
return NULL;
while (progress) {
isl_bool empty;
progress = 0;
empty = isl_basic_map_plain_is_empty(bmap);
if (empty < 0)
return isl_basic_map_free(bmap);
if (empty)
break;
bmap = isl_basic_map_normalize_constraints(bmap);
bmap = reduce_div_coefficients(bmap);
bmap = normalize_div_expressions(bmap);
bmap = remove_duplicate_divs(bmap, &progress);
bmap = eliminate_unit_divs(bmap, &progress);
bmap = eliminate_divs_eq(bmap, &progress);
bmap = eliminate_divs_ineq(bmap, &progress);
bmap = isl_basic_map_gauss(bmap, &progress);
/* requires equalities in normal form */
bmap = normalize_divs(bmap, &progress);
bmap = isl_basic_map_remove_duplicate_constraints(bmap,
&progress, 1);
if (bmap && progress)
ISL_F_CLR(bmap, ISL_BASIC_MAP_REDUCED_COEFFICIENTS);
}
return bmap;
}
__isl_give isl_basic_set *isl_basic_set_simplify(
__isl_take isl_basic_set *bset)
{
return bset_from_bmap(isl_basic_map_simplify(bset_to_bmap(bset)));
}
isl_bool isl_basic_map_is_div_constraint(__isl_keep isl_basic_map *bmap,
isl_int *constraint, unsigned div)
{
unsigned pos;
if (!bmap)
return isl_bool_error;
pos = isl_basic_map_offset(bmap, isl_dim_div) + div;
if (isl_int_eq(constraint[pos], bmap->div[div][0])) {
int neg;
isl_int_sub(bmap->div[div][1],
bmap->div[div][1], bmap->div[div][0]);
isl_int_add_ui(bmap->div[div][1], bmap->div[div][1], 1);
neg = isl_seq_is_neg(constraint, bmap->div[div]+1, pos);
isl_int_sub_ui(bmap->div[div][1], bmap->div[div][1], 1);
isl_int_add(bmap->div[div][1],
bmap->div[div][1], bmap->div[div][0]);
if (!neg)
return isl_bool_false;
if (isl_seq_first_non_zero(constraint+pos+1,
bmap->n_div-div-1) != -1)
return isl_bool_false;
} else if (isl_int_abs_eq(constraint[pos], bmap->div[div][0])) {
if (!isl_seq_eq(constraint, bmap->div[div]+1, pos))
return isl_bool_false;
if (isl_seq_first_non_zero(constraint+pos+1,
bmap->n_div-div-1) != -1)
return isl_bool_false;
} else
return isl_bool_false;
return isl_bool_true;
}
/* If the only constraints a div d=floor(f/m)
* appears in are its two defining constraints
*
* f - m d >=0
* -(f - (m - 1)) + m d >= 0
*
* then it can safely be removed.
*/
static isl_bool div_is_redundant(__isl_keep isl_basic_map *bmap, int div)
{
int i;
isl_size v_div = isl_basic_map_var_offset(bmap, isl_dim_div);
unsigned pos = 1 + v_div + div;
if (v_div < 0)
return isl_bool_error;
for (i = 0; i < bmap->n_eq; ++i)
if (!isl_int_is_zero(bmap->eq[i][pos]))
return isl_bool_false;
for (i = 0; i < bmap->n_ineq; ++i) {
isl_bool red;
if (isl_int_is_zero(bmap->ineq[i][pos]))
continue;
red = isl_basic_map_is_div_constraint(bmap, bmap->ineq[i], div);
if (red < 0 || !red)
return red;
}
for (i = 0; i < bmap->n_div; ++i) {
if (isl_int_is_zero(bmap->div[i][0]))
continue;
if (!isl_int_is_zero(bmap->div[i][1+pos]))
return isl_bool_false;
}
return isl_bool_true;
}
/*
* Remove divs that don't occur in any of the constraints or other divs.
* These can arise when dropping constraints from a basic map or
* when the divs of a basic map have been temporarily aligned
* with the divs of another basic map.
*/
static __isl_give isl_basic_map *remove_redundant_divs(
__isl_take isl_basic_map *bmap)
{
int i;
isl_size v_div;
v_div = isl_basic_map_var_offset(bmap, isl_dim_div);
if (v_div < 0)
return isl_basic_map_free(bmap);
for (i = bmap->n_div-1; i >= 0; --i) {
isl_bool redundant;
redundant = div_is_redundant(bmap, i);
if (redundant < 0)
return isl_basic_map_free(bmap);
if (!redundant)
continue;
bmap = isl_basic_map_drop_constraints_involving(bmap,
v_div + i, 1);
bmap = isl_basic_map_drop_div(bmap, i);
}
return bmap;
}
/* Mark "bmap" as final, without checking for obviously redundant
* integer divisions. This function should be used when "bmap"
* is known not to involve any such integer divisions.
*/
__isl_give isl_basic_map *isl_basic_map_mark_final(
__isl_take isl_basic_map *bmap)
{
if (!bmap)
return NULL;
ISL_F_SET(bmap, ISL_BASIC_SET_FINAL);
return bmap;
}
/* Mark "bmap" as final, after removing obviously redundant integer divisions.
*/
__isl_give isl_basic_map *isl_basic_map_finalize(__isl_take isl_basic_map *bmap)
{
bmap = remove_redundant_divs(bmap);
bmap = isl_basic_map_mark_final(bmap);
return bmap;
}
__isl_give isl_basic_set *isl_basic_set_finalize(
__isl_take isl_basic_set *bset)
{
return bset_from_bmap(isl_basic_map_finalize(bset_to_bmap(bset)));
}
/* Remove definition of any div that is defined in terms of the given variable.
* The div itself is not removed. Functions such as
* eliminate_divs_ineq depend on the other divs remaining in place.
*/
static __isl_give isl_basic_map *remove_dependent_vars(
__isl_take isl_basic_map *bmap, int pos)
{
int i;
if (!bmap)
return NULL;
for (i = 0; i < bmap->n_div; ++i) {
if (isl_int_is_zero(bmap->div[i][0]))
continue;
if (isl_int_is_zero(bmap->div[i][1+1+pos]))
continue;
bmap = isl_basic_map_mark_div_unknown(bmap, i);
if (!bmap)
return NULL;
}
return bmap;
}
/* Eliminate the specified variables from the constraints using
* Fourier-Motzkin. The variables themselves are not removed.
*/
__isl_give isl_basic_map *isl_basic_map_eliminate_vars(
__isl_take isl_basic_map *bmap, unsigned pos, unsigned n)
{
int d;
int i, j, k;
isl_size total;
int need_gauss = 0;
if (n == 0)
return bmap;
total = isl_basic_map_dim(bmap, isl_dim_all);
if (total < 0)
return isl_basic_map_free(bmap);
bmap = isl_basic_map_cow(bmap);
for (d = pos + n - 1; d >= 0 && d >= pos; --d)
bmap = remove_dependent_vars(bmap, d);
if (!bmap)
return NULL;
for (d = pos + n - 1;
d >= 0 && d >= total - bmap->n_div && d >= pos; --d)
isl_seq_clr(bmap->div[d-(total-bmap->n_div)], 2+total);
for (d = pos + n - 1; d >= 0 && d >= pos; --d) {
int n_lower, n_upper;
if (!bmap)
return NULL;
for (i = 0; i < bmap->n_eq; ++i) {
if (isl_int_is_zero(bmap->eq[i][1+d]))
continue;
bmap = eliminate_var_using_equality(bmap, d,
bmap->eq[i], 0, NULL);
if (isl_basic_map_drop_equality(bmap, i) < 0)
return isl_basic_map_free(bmap);
need_gauss = 1;
break;
}
if (i < bmap->n_eq)
continue;
n_lower = 0;
n_upper = 0;
for (i = 0; i < bmap->n_ineq; ++i) {
if (isl_int_is_pos(bmap->ineq[i][1+d]))
n_lower++;
else if (isl_int_is_neg(bmap->ineq[i][1+d]))
n_upper++;
}
bmap = isl_basic_map_extend_constraints(bmap,
0, n_lower * n_upper);
if (!bmap)
goto error;
for (i = bmap->n_ineq - 1; i >= 0; --i) {
int last;
if (isl_int_is_zero(bmap->ineq[i][1+d]))
continue;
last = -1;
for (j = 0; j < i; ++j) {
if (isl_int_is_zero(bmap->ineq[j][1+d]))
continue;
last = j;
if (isl_int_sgn(bmap->ineq[i][1+d]) ==
isl_int_sgn(bmap->ineq[j][1+d]))
continue;
k = isl_basic_map_alloc_inequality(bmap);
if (k < 0)
goto error;
isl_seq_cpy(bmap->ineq[k], bmap->ineq[i],
1+total);
isl_seq_elim(bmap->ineq[k], bmap->ineq[j],
1+d, 1+total, NULL);
}
isl_basic_map_drop_inequality(bmap, i);
i = last + 1;
}
if (n_lower > 0 && n_upper > 0) {
bmap = isl_basic_map_normalize_constraints(bmap);
bmap = isl_basic_map_remove_duplicate_constraints(bmap,
NULL, 0);
bmap = isl_basic_map_gauss(bmap, NULL);
bmap = isl_basic_map_remove_redundancies(bmap);
need_gauss = 0;
if (!bmap)
goto error;
if (ISL_F_ISSET(bmap, ISL_BASIC_MAP_EMPTY))
break;
}
}
if (need_gauss)
bmap = isl_basic_map_gauss(bmap, NULL);
return bmap;
error:
isl_basic_map_free(bmap);
return NULL;
}
__isl_give isl_basic_set *isl_basic_set_eliminate_vars(
__isl_take isl_basic_set *bset, unsigned pos, unsigned n)
{
return bset_from_bmap(isl_basic_map_eliminate_vars(bset_to_bmap(bset),
pos, n));
}
/* Eliminate the specified n dimensions starting at first from the
* constraints, without removing the dimensions from the space.
* If the set is rational, the dimensions are eliminated using Fourier-Motzkin.
* Otherwise, they are projected out and the original space is restored.
*/
__isl_give isl_basic_map *isl_basic_map_eliminate(
__isl_take isl_basic_map *bmap,
enum isl_dim_type type, unsigned first, unsigned n)
{
isl_space *space;
if (!bmap)
return NULL;
if (n == 0)
return bmap;
if (isl_basic_map_check_range(bmap, type, first, n) < 0)
return isl_basic_map_free(bmap);
if (ISL_F_ISSET(bmap, ISL_BASIC_MAP_RATIONAL)) {
first += isl_basic_map_offset(bmap, type) - 1;
bmap = isl_basic_map_eliminate_vars(bmap, first, n);
return isl_basic_map_finalize(bmap);
}
space = isl_basic_map_get_space(bmap);
bmap = isl_basic_map_project_out(bmap, type, first, n);
bmap = isl_basic_map_insert_dims(bmap, type, first, n);
bmap = isl_basic_map_reset_space(bmap, space);
return bmap;
}
__isl_give isl_basic_set *isl_basic_set_eliminate(
__isl_take isl_basic_set *bset,
enum isl_dim_type type, unsigned first, unsigned n)
{
return isl_basic_map_eliminate(bset, type, first, n);
}
/* Remove all constraints from "bmap" that reference any unknown local
* variables (directly or indirectly).
*
* Dropping all constraints on a local variable will make it redundant,
* so it will get removed implicitly by
* isl_basic_map_drop_constraints_involving_dims. Some other local
* variables may also end up becoming redundant if they only appear
* in constraints together with the unknown local variable.
* Therefore, start over after calling
* isl_basic_map_drop_constraints_involving_dims.
*/
__isl_give isl_basic_map *isl_basic_map_drop_constraints_involving_unknown_divs(
__isl_take isl_basic_map *bmap)
{
isl_bool known;
isl_size n_div;
int i, o_div;
known = isl_basic_map_divs_known(bmap);
if (known < 0)
return isl_basic_map_free(bmap);
if (known)
return bmap;
n_div = isl_basic_map_dim(bmap, isl_dim_div);
if (n_div < 0)
return isl_basic_map_free(bmap);
o_div = isl_basic_map_offset(bmap, isl_dim_div) - 1;
for (i = 0; i < n_div; ++i) {
known = isl_basic_map_div_is_known(bmap, i);
if (known < 0)
return isl_basic_map_free(bmap);
if (known)
continue;
bmap = remove_dependent_vars(bmap, o_div + i);
bmap = isl_basic_map_drop_constraints_involving_dims(bmap,
isl_dim_div, i, 1);
n_div = isl_basic_map_dim(bmap, isl_dim_div);
if (n_div < 0)
return isl_basic_map_free(bmap);
i = -1;
}
return bmap;
}
/* Remove all constraints from "bset" that reference any unknown local
* variables (directly or indirectly).
*/
__isl_give isl_basic_set *isl_basic_set_drop_constraints_involving_unknown_divs(
__isl_take isl_basic_set *bset)
{
isl_basic_map *bmap;
bmap = bset_to_bmap(bset);
bmap = isl_basic_map_drop_constraints_involving_unknown_divs(bmap);
return bset_from_bmap(bmap);
}
/* Remove all constraints from "map" that reference any unknown local
* variables (directly or indirectly).
*
* Since constraints may get dropped from the basic maps,
* they may no longer be disjoint from each other.
*/
__isl_give isl_map *isl_map_drop_constraints_involving_unknown_divs(
__isl_take isl_map *map)
{
int i;
isl_bool known;
known = isl_map_divs_known(map);
if (known < 0)
return isl_map_free(map);
if (known)
return map;
map = isl_map_cow(map);
if (!map)
return NULL;
for (i = 0; i < map->n; ++i) {
map->p[i] =
isl_basic_map_drop_constraints_involving_unknown_divs(
map->p[i]);
if (!map->p[i])
return isl_map_free(map);
}
if (map->n > 1)
ISL_F_CLR(map, ISL_MAP_DISJOINT);
return map;
}
/* Don't assume equalities are in order, because align_divs
* may have changed the order of the divs.
*/
static void compute_elimination_index(__isl_keep isl_basic_map *bmap, int *elim,
unsigned len)
{
int d, i;
for (d = 0; d < len; ++d)
elim[d] = -1;
for (i = 0; i < bmap->n_eq; ++i) {
for (d = len - 1; d >= 0; --d) {
if (isl_int_is_zero(bmap->eq[i][1+d]))
continue;
elim[d] = i;
break;
}
}
}
static void set_compute_elimination_index(__isl_keep isl_basic_set *bset,
int *elim, unsigned len)
{
compute_elimination_index(bset_to_bmap(bset), elim, len);
}
static int reduced_using_equalities(isl_int *dst, isl_int *src,
__isl_keep isl_basic_map *bmap, int *elim, unsigned total)
{
int d;
int copied = 0;
for (d = total - 1; d >= 0; --d) {
if (isl_int_is_zero(src[1+d]))
continue;
if (elim[d] == -1)
continue;
if (!copied) {
isl_seq_cpy(dst, src, 1 + total);
copied = 1;
}
isl_seq_elim(dst, bmap->eq[elim[d]], 1 + d, 1 + total, NULL);
}
return copied;
}
static int set_reduced_using_equalities(isl_int *dst, isl_int *src,
__isl_keep isl_basic_set *bset, int *elim, unsigned total)
{
return reduced_using_equalities(dst, src,
bset_to_bmap(bset), elim, total);
}
static __isl_give isl_basic_set *isl_basic_set_reduce_using_equalities(
__isl_take isl_basic_set *bset, __isl_take isl_basic_set *context)
{
int i;
int *elim;
isl_size dim;
if (!bset || !context)
goto error;
if (context->n_eq == 0) {
isl_basic_set_free(context);
return bset;
}
bset = isl_basic_set_cow(bset);
dim = isl_basic_set_dim(bset, isl_dim_set);
if (dim < 0)
goto error;
elim = isl_alloc_array(bset->ctx, int, dim);
if (!elim)
goto error;
set_compute_elimination_index(context, elim, dim);
for (i = 0; i < bset->n_eq; ++i)
set_reduced_using_equalities(bset->eq[i], bset->eq[i],
context, elim, dim);
for (i = 0; i < bset->n_ineq; ++i)
set_reduced_using_equalities(bset->ineq[i], bset->ineq[i],
context, elim, dim);
isl_basic_set_free(context);
free(elim);
bset = isl_basic_set_simplify(bset);
bset = isl_basic_set_finalize(bset);
return bset;
error:
isl_basic_set_free(bset);
isl_basic_set_free(context);
return NULL;
}
/* For each inequality in "ineq" that is a shifted (more relaxed)
* copy of an inequality in "context", mark the corresponding entry
* in "row" with -1.
* If an inequality only has a non-negative constant term, then
* mark it as well.
*/
static isl_stat mark_shifted_constraints(__isl_keep isl_mat *ineq,
__isl_keep isl_basic_set *context, int *row)
{
struct isl_constraint_index ci;
isl_size n_ineq, cols;
unsigned total;
int k;
if (!ineq || !context)
return isl_stat_error;
if (context->n_ineq == 0)
return isl_stat_ok;
if (setup_constraint_index(&ci, context) < 0)
return isl_stat_error;
n_ineq = isl_mat_rows(ineq);
cols = isl_mat_cols(ineq);
if (n_ineq < 0 || cols < 0)
return isl_stat_error;
total = cols - 1;
for (k = 0; k < n_ineq; ++k) {
int l;
isl_bool redundant;
l = isl_seq_first_non_zero(ineq->row[k] + 1, total);
if (l < 0 && isl_int_is_nonneg(ineq->row[k][0])) {
row[k] = -1;
continue;
}
redundant = constraint_index_is_redundant(&ci, ineq->row[k]);
if (redundant < 0)
goto error;
if (!redundant)
continue;
row[k] = -1;
}
constraint_index_free(&ci);
return isl_stat_ok;
error:
constraint_index_free(&ci);
return isl_stat_error;
}
static __isl_give isl_basic_set *remove_shifted_constraints(
__isl_take isl_basic_set *bset, __isl_keep isl_basic_set *context)
{
struct isl_constraint_index ci;
int k;
if (!bset || !context)
return bset;
if (context->n_ineq == 0)
return bset;
if (setup_constraint_index(&ci, context) < 0)
return bset;
for (k = 0; k < bset->n_ineq; ++k) {
isl_bool redundant;
redundant = constraint_index_is_redundant(&ci, bset->ineq[k]);
if (redundant < 0)
goto error;
if (!redundant)
continue;
bset = isl_basic_set_cow(bset);
if (!bset)
goto error;
isl_basic_set_drop_inequality(bset, k);
--k;
}
constraint_index_free(&ci);
return bset;
error:
constraint_index_free(&ci);
return bset;
}
/* Remove constraints from "bmap" that are identical to constraints
* in "context" or that are more relaxed (greater constant term).
*
* We perform the test for shifted copies on the pure constraints
* in remove_shifted_constraints.
*/
static __isl_give isl_basic_map *isl_basic_map_remove_shifted_constraints(
__isl_take isl_basic_map *bmap, __isl_take isl_basic_map *context)
{
isl_basic_set *bset, *bset_context;
if (!bmap || !context)
goto error;
if (bmap->n_ineq == 0 || context->n_ineq == 0) {
isl_basic_map_free(context);
return bmap;
}
bmap = isl_basic_map_order_divs(bmap);
context = isl_basic_map_align_divs(context, bmap);
bmap = isl_basic_map_align_divs(bmap, context);
bset = isl_basic_map_underlying_set(isl_basic_map_copy(bmap));
bset_context = isl_basic_map_underlying_set(context);
bset = remove_shifted_constraints(bset, bset_context);
isl_basic_set_free(bset_context);
bmap = isl_basic_map_overlying_set(bset, bmap);
return bmap;
error:
isl_basic_map_free(bmap);
isl_basic_map_free(context);
return NULL;
}
/* Does the (linear part of a) constraint "c" involve any of the "len"
* "relevant" dimensions?
*/
static int is_related(isl_int *c, int len, int *relevant)
{
int i;
for (i = 0; i < len; ++i) {
if (!relevant[i])
continue;
if (!isl_int_is_zero(c[i]))
return 1;
}
return 0;
}
/* Drop constraints from "bmap" that do not involve any of
* the dimensions marked "relevant".
*/
static __isl_give isl_basic_map *drop_unrelated_constraints(
__isl_take isl_basic_map *bmap, int *relevant)
{
int i;
isl_size dim;
dim = isl_basic_map_dim(bmap, isl_dim_all);
if (dim < 0)
return isl_basic_map_free(bmap);
for (i = 0; i < dim; ++i)
if (!relevant[i])
break;
if (i >= dim)
return bmap;
for (i = bmap->n_eq - 1; i >= 0; --i)
if (!is_related(bmap->eq[i] + 1, dim, relevant)) {
bmap = isl_basic_map_cow(bmap);
if (isl_basic_map_drop_equality(bmap, i) < 0)
return isl_basic_map_free(bmap);
}
for (i = bmap->n_ineq - 1; i >= 0; --i)
if (!is_related(bmap->ineq[i] + 1, dim, relevant)) {
bmap = isl_basic_map_cow(bmap);
if (isl_basic_map_drop_inequality(bmap, i) < 0)
return isl_basic_map_free(bmap);
}
return bmap;
}
/* Update the groups in "group" based on the (linear part of a) constraint "c".
*
* In particular, for any variable involved in the constraint,
* find the actual group id from before and replace the group
* of the corresponding variable by the minimal group of all
* the variables involved in the constraint considered so far
* (if this minimum is smaller) or replace the minimum by this group
* (if the minimum is larger).
*
* At the end, all the variables in "c" will (indirectly) point
* to the minimal of the groups that they referred to originally.
*/
static void update_groups(int dim, int *group, isl_int *c)
{
int j;
int min = dim;
for (j = 0; j < dim; ++j) {
if (isl_int_is_zero(c[j]))
continue;
while (group[j] >= 0 && group[group[j]] != group[j])
group[j] = group[group[j]];
if (group[j] == min)
continue;
if (group[j] < min) {
if (min >= 0 && min < dim)
group[min] = group[j];
min = group[j];
} else
group[group[j]] = min;
}
}
/* Allocate an array of groups of variables, one for each variable
* in "context", initialized to zero.
*/
static int *alloc_groups(__isl_keep isl_basic_set *context)
{
isl_ctx *ctx;
isl_size dim;
dim = isl_basic_set_dim(context, isl_dim_set);
if (dim < 0)
return NULL;
ctx = isl_basic_set_get_ctx(context);
return isl_calloc_array(ctx, int, dim);
}
/* Drop constraints from "bmap" that only involve variables that are
* not related to any of the variables marked with a "-1" in "group".
*
* We construct groups of variables that collect variables that
* (indirectly) appear in some common constraint of "bmap".
* Each group is identified by the first variable in the group,
* except for the special group of variables that was already identified
* in the input as -1 (or are related to those variables).
* If group[i] is equal to i (or -1), then the group of i is i (or -1),
* otherwise the group of i is the group of group[i].
*
* We first initialize groups for the remaining variables.
* Then we iterate over the constraints of "bmap" and update the
* group of the variables in the constraint by the smallest group.
* Finally, we resolve indirect references to groups by running over
* the variables.
*
* After computing the groups, we drop constraints that do not involve
* any variables in the -1 group.
*/
__isl_give isl_basic_map *isl_basic_map_drop_unrelated_constraints(
__isl_take isl_basic_map *bmap, __isl_take int *group)
{
isl_size dim;
int i;
int last;
dim = isl_basic_map_dim(bmap, isl_dim_all);
if (dim < 0)
return isl_basic_map_free(bmap);
last = -1;
for (i = 0; i < dim; ++i)
if (group[i] >= 0)
last = group[i] = i;
if (last < 0) {
free(group);
return bmap;
}
for (i = 0; i < bmap->n_eq; ++i)
update_groups(dim, group, bmap->eq[i] + 1);
for (i = 0; i < bmap->n_ineq; ++i)
update_groups(dim, group, bmap->ineq[i] + 1);
for (i = 0; i < dim; ++i)
if (group[i] >= 0)
group[i] = group[group[i]];
for (i = 0; i < dim; ++i)
group[i] = group[i] == -1;
bmap = drop_unrelated_constraints(bmap, group);
free(group);
return bmap;
}
/* Drop constraints from "context" that are irrelevant for computing
* the gist of "bset".
*
* In particular, drop constraints in variables that are not related
* to any of the variables involved in the constraints of "bset"
* in the sense that there is no sequence of constraints that connects them.
*
* We first mark all variables that appear in "bset" as belonging
* to a "-1" group and then continue with group_and_drop_irrelevant_constraints.
*/
static __isl_give isl_basic_set *drop_irrelevant_constraints(
__isl_take isl_basic_set *context, __isl_keep isl_basic_set *bset)
{
int *group;
isl_size dim;
int i, j;
dim = isl_basic_set_dim(bset, isl_dim_set);
if (!context || dim < 0)
return isl_basic_set_free(context);
group = alloc_groups(context);
if (!group)
return isl_basic_set_free(context);
for (i = 0; i < dim; ++i) {
for (j = 0; j < bset->n_eq; ++j)
if (!isl_int_is_zero(bset->eq[j][1 + i]))
break;
if (j < bset->n_eq) {
group[i] = -1;
continue;
}
for (j = 0; j < bset->n_ineq; ++j)
if (!isl_int_is_zero(bset->ineq[j][1 + i]))
break;
if (j < bset->n_ineq)
group[i] = -1;
}
return isl_basic_map_drop_unrelated_constraints(context, group);
}
/* Drop constraints from "context" that are irrelevant for computing
* the gist of the inequalities "ineq".
* Inequalities in "ineq" for which the corresponding element of row
* is set to -1 have already been marked for removal and should be ignored.
*
* In particular, drop constraints in variables that are not related
* to any of the variables involved in "ineq"
* in the sense that there is no sequence of constraints that connects them.
*
* We first mark all variables that appear in "bset" as belonging
* to a "-1" group and then continue with group_and_drop_irrelevant_constraints.
*/
static __isl_give isl_basic_set *drop_irrelevant_constraints_marked(
__isl_take isl_basic_set *context, __isl_keep isl_mat *ineq, int *row)
{
int *group;
isl_size dim;
int i, j;
isl_size n;
dim = isl_basic_set_dim(context, isl_dim_set);
n = isl_mat_rows(ineq);
if (dim < 0 || n < 0)
return isl_basic_set_free(context);
group = alloc_groups(context);
if (!group)
return isl_basic_set_free(context);
for (i = 0; i < dim; ++i) {
for (j = 0; j < n; ++j) {
if (row[j] < 0)
continue;
if (!isl_int_is_zero(ineq->row[j][1 + i]))
break;
}
if (j < n)
group[i] = -1;
}
return isl_basic_map_drop_unrelated_constraints(context, group);
}
/* Do all "n" entries of "row" contain a negative value?
*/
static int all_neg(int *row, int n)
{
int i;
for (i = 0; i < n; ++i)
if (row[i] >= 0)
return 0;
return 1;
}
/* Update the inequalities in "bset" based on the information in "row"
* and "tab".
*
* In particular, the array "row" contains either -1, meaning that
* the corresponding inequality of "bset" is redundant, or the index
* of an inequality in "tab".
*
* If the row entry is -1, then drop the inequality.
* Otherwise, if the constraint is marked redundant in the tableau,
* then drop the inequality. Similarly, if it is marked as an equality
* in the tableau, then turn the inequality into an equality and
* perform Gaussian elimination.
*/
static __isl_give isl_basic_set *update_ineq(__isl_take isl_basic_set *bset,
__isl_keep int *row, struct isl_tab *tab)
{
int i;
unsigned n_ineq;
unsigned n_eq;
int found_equality = 0;
if (!bset)
return NULL;
if (tab && tab->empty)
return isl_basic_set_set_to_empty(bset);
n_ineq = bset->n_ineq;
for (i = n_ineq - 1; i >= 0; --i) {
if (row[i] < 0) {
if (isl_basic_set_drop_inequality(bset, i) < 0)
return isl_basic_set_free(bset);
continue;
}
if (!tab)
continue;
n_eq = tab->n_eq;
if (isl_tab_is_equality(tab, n_eq + row[i])) {
isl_basic_map_inequality_to_equality(bset, i);
found_equality = 1;
} else if (isl_tab_is_redundant(tab, n_eq + row[i])) {
if (isl_basic_set_drop_inequality(bset, i) < 0)
return isl_basic_set_free(bset);
}
}
if (found_equality)
bset = isl_basic_set_gauss(bset, NULL);
bset = isl_basic_set_finalize(bset);
return bset;
}
/* Update the inequalities in "bset" based on the information in "row"
* and "tab" and free all arguments (other than "bset").
*/
static __isl_give isl_basic_set *update_ineq_free(
__isl_take isl_basic_set *bset, __isl_take isl_mat *ineq,
__isl_take isl_basic_set *context, __isl_take int *row,
struct isl_tab *tab)
{
isl_mat_free(ineq);
isl_basic_set_free(context);
bset = update_ineq(bset, row, tab);
free(row);
isl_tab_free(tab);
return bset;
}
/* Remove all information from bset that is redundant in the context
* of context.
* "ineq" contains the (possibly transformed) inequalities of "bset",
* in the same order.
* The (explicit) equalities of "bset" are assumed to have been taken
* into account by the transformation such that only the inequalities
* are relevant.
* "context" is assumed not to be empty.
*
* "row" keeps track of the constraint index of a "bset" inequality in "tab".
* A value of -1 means that the inequality is obviously redundant and may
* not even appear in "tab".
*
* We first mark the inequalities of "bset"
* that are obviously redundant with respect to some inequality in "context".
* Then we remove those constraints from "context" that have become
* irrelevant for computing the gist of "bset".
* Note that this removal of constraints cannot be replaced by
* a factorization because factors in "bset" may still be connected
* to each other through constraints in "context".
*
* If there are any inequalities left, we construct a tableau for
* the context and then add the inequalities of "bset".
* Before adding these inequalities, we freeze all constraints such that
* they won't be considered redundant in terms of the constraints of "bset".
* Then we detect all redundant constraints (among the
* constraints that weren't frozen), first by checking for redundancy in the
* the tableau and then by checking if replacing a constraint by its negation
* would lead to an empty set. This last step is fairly expensive
* and could be optimized by more reuse of the tableau.
* Finally, we update bset according to the results.
*/
static __isl_give isl_basic_set *uset_gist_full(__isl_take isl_basic_set *bset,
__isl_take isl_mat *ineq, __isl_take isl_basic_set *context)
{
int i, r;
int *row = NULL;
isl_ctx *ctx;
isl_basic_set *combined = NULL;
struct isl_tab *tab = NULL;
unsigned n_eq, context_ineq;
if (!bset || !ineq || !context)
goto error;
if (bset->n_ineq == 0 || isl_basic_set_plain_is_universe(context)) {
isl_basic_set_free(context);
isl_mat_free(ineq);
return bset;
}
ctx = isl_basic_set_get_ctx(context);
row = isl_calloc_array(ctx, int, bset->n_ineq);
if (!row)
goto error;
if (mark_shifted_constraints(ineq, context, row) < 0)
goto error;
if (all_neg(row, bset->n_ineq))
return update_ineq_free(bset, ineq, context, row, NULL);
context = drop_irrelevant_constraints_marked(context, ineq, row);
if (!context)
goto error;
if (isl_basic_set_plain_is_universe(context))
return update_ineq_free(bset, ineq, context, row, NULL);
n_eq = context->n_eq;
context_ineq = context->n_ineq;
combined = isl_basic_set_cow(isl_basic_set_copy(context));
combined = isl_basic_set_extend_constraints(combined, 0, bset->n_ineq);
tab = isl_tab_from_basic_set(combined, 0);
for (i = 0; i < context_ineq; ++i)
if (isl_tab_freeze_constraint(tab, n_eq + i) < 0)
goto error;
if (isl_tab_extend_cons(tab, bset->n_ineq) < 0)
goto error;
r = context_ineq;
for (i = 0; i < bset->n_ineq; ++i) {
if (row[i] < 0)
continue;
combined = isl_basic_set_add_ineq(combined, ineq->row[i]);
if (isl_tab_add_ineq(tab, ineq->row[i]) < 0)
goto error;
row[i] = r++;
}
if (isl_tab_detect_implicit_equalities(tab) < 0)
goto error;
if (isl_tab_detect_redundant(tab) < 0)
goto error;
for (i = bset->n_ineq - 1; i >= 0; --i) {
isl_basic_set *test;
int is_empty;
if (row[i] < 0)
continue;
r = row[i];
if (tab->con[n_eq + r].is_redundant)
continue;
test = isl_basic_set_dup(combined);
test = isl_inequality_negate(test, r);
test = isl_basic_set_update_from_tab(test, tab);
is_empty = isl_basic_set_is_empty(test);
isl_basic_set_free(test);
if (is_empty < 0)
goto error;
if (is_empty)
tab->con[n_eq + r].is_redundant = 1;
}
bset = update_ineq_free(bset, ineq, context, row, tab);
if (bset) {
ISL_F_SET(bset, ISL_BASIC_SET_NO_IMPLICIT);
ISL_F_SET(bset, ISL_BASIC_SET_NO_REDUNDANT);
}
isl_basic_set_free(combined);
return bset;
error:
free(row);
isl_mat_free(ineq);
isl_tab_free(tab);
isl_basic_set_free(combined);
isl_basic_set_free(context);
isl_basic_set_free(bset);
return NULL;
}
/* Extract the inequalities of "bset" as an isl_mat.
*/
static __isl_give isl_mat *extract_ineq(__isl_keep isl_basic_set *bset)
{
isl_size total;
isl_ctx *ctx;
isl_mat *ineq;
total = isl_basic_set_dim(bset, isl_dim_all);
if (total < 0)
return NULL;
ctx = isl_basic_set_get_ctx(bset);
ineq = isl_mat_sub_alloc6(ctx, bset->ineq, 0, bset->n_ineq,
0, 1 + total);
return ineq;
}
/* Remove all information from "bset" that is redundant in the context
* of "context", for the case where both "bset" and "context" are
* full-dimensional.
*/
static __isl_give isl_basic_set *uset_gist_uncompressed(
__isl_take isl_basic_set *bset, __isl_take isl_basic_set *context)
{
isl_mat *ineq;
ineq = extract_ineq(bset);
return uset_gist_full(bset, ineq, context);
}
/* Replace "bset" by an empty basic set in the same space.
*/
static __isl_give isl_basic_set *replace_by_empty(
__isl_take isl_basic_set *bset)
{
isl_space *space;
space = isl_basic_set_get_space(bset);
isl_basic_set_free(bset);
return isl_basic_set_empty(space);
}
/* Remove all information from "bset" that is redundant in the context
* of "context", for the case where the combined equalities of
* "bset" and "context" allow for a compression that can be obtained
* by preapplication of "T".
* If the compression of "context" is empty, meaning that "bset" and
* "context" do not intersect, then return the empty set.
*
* "bset" itself is not transformed by "T". Instead, the inequalities
* are extracted from "bset" and those are transformed by "T".
* uset_gist_full then determines which of the transformed inequalities
* are redundant with respect to the transformed "context" and removes
* the corresponding inequalities from "bset".
*
* After preapplying "T" to the inequalities, any common factor is
* removed from the coefficients. If this results in a tightening
* of the constant term, then the same tightening is applied to
* the corresponding untransformed inequality in "bset".
* That is, if after plugging in T, a constraint f(x) >= 0 is of the form
*
* g f'(x) + r >= 0
*
* with 0 <= r < g, then it is equivalent to
*
* f'(x) >= 0
*
* This means that f(x) >= 0 is equivalent to f(x) - r >= 0 in the affine
* subspace compressed by T since the latter would be transformed to
*
* g f'(x) >= 0
*/
static __isl_give isl_basic_set *uset_gist_compressed(
__isl_take isl_basic_set *bset, __isl_take isl_basic_set *context,
__isl_take isl_mat *T)
{
isl_ctx *ctx;
isl_mat *ineq;
int i;
isl_size n_row, n_col;
isl_int rem;
ineq = extract_ineq(bset);
ineq = isl_mat_product(ineq, isl_mat_copy(T));
context = isl_basic_set_preimage(context, T);
if (!ineq || !context)
goto error;
if (isl_basic_set_plain_is_empty(context)) {
isl_mat_free(ineq);
isl_basic_set_free(context);
return replace_by_empty(bset);
}
ctx = isl_mat_get_ctx(ineq);
n_row = isl_mat_rows(ineq);
n_col = isl_mat_cols(ineq);
if (n_row < 0 || n_col < 0)
goto error;
isl_int_init(rem);
for (i = 0; i < n_row; ++i) {
isl_seq_gcd(ineq->row[i] + 1, n_col - 1, &ctx->normalize_gcd);
if (isl_int_is_zero(ctx->normalize_gcd))
continue;
if (isl_int_is_one(ctx->normalize_gcd))
continue;
isl_seq_scale_down(ineq->row[i] + 1, ineq->row[i] + 1,
ctx->normalize_gcd, n_col - 1);
isl_int_fdiv_r(rem, ineq->row[i][0], ctx->normalize_gcd);
isl_int_fdiv_q(ineq->row[i][0],
ineq->row[i][0], ctx->normalize_gcd);
if (isl_int_is_zero(rem))
continue;
bset = isl_basic_set_cow(bset);
if (!bset)
break;
isl_int_sub(bset->ineq[i][0], bset->ineq[i][0], rem);
}
isl_int_clear(rem);
return uset_gist_full(bset, ineq, context);
error:
isl_mat_free(ineq);
isl_basic_set_free(context);
isl_basic_set_free(bset);
return NULL;
}
/* Project "bset" onto the variables that are involved in "template".
*/
static __isl_give isl_basic_set *project_onto_involved(
__isl_take isl_basic_set *bset, __isl_keep isl_basic_set *template)
{
int i;
isl_size n;
n = isl_basic_set_dim(template, isl_dim_set);
if (n < 0 || !template)
return isl_basic_set_free(bset);
for (i = 0; i < n; ++i) {
isl_bool involved;
involved = isl_basic_set_involves_dims(template,
isl_dim_set, i, 1);
if (involved < 0)
return isl_basic_set_free(bset);
if (involved)
continue;
bset = isl_basic_set_eliminate_vars(bset, i, 1);
}
return bset;
}
/* Remove all information from bset that is redundant in the context
* of context. In particular, equalities that are linear combinations
* of those in context are removed. Then the inequalities that are
* redundant in the context of the equalities and inequalities of
* context are removed.
*
* First of all, we drop those constraints from "context"
* that are irrelevant for computing the gist of "bset".
* Alternatively, we could factorize the intersection of "context" and "bset".
*
* We first compute the intersection of the integer affine hulls
* of "bset" and "context",
* compute the gist inside this intersection and then reduce
* the constraints with respect to the equalities of the context
* that only involve variables already involved in the input.
* If the intersection of the affine hulls turns out to be empty,
* then return the empty set.
*
* If two constraints are mutually redundant, then uset_gist_full
* will remove the second of those constraints. We therefore first
* sort the constraints so that constraints not involving existentially
* quantified variables are given precedence over those that do.
* We have to perform this sorting before the variable compression,
* because that may effect the order of the variables.
*/
static __isl_give isl_basic_set *uset_gist(__isl_take isl_basic_set *bset,
__isl_take isl_basic_set *context)
{
isl_mat *eq;
isl_mat *T;
isl_basic_set *aff;
isl_basic_set *aff_context;
isl_size total;
total = isl_basic_set_dim(bset, isl_dim_all);
if (total < 0 || !context)
goto error;
context = drop_irrelevant_constraints(context, bset);
bset = isl_basic_set_detect_equalities(bset);
aff = isl_basic_set_copy(bset);
aff = isl_basic_set_plain_affine_hull(aff);
context = isl_basic_set_detect_equalities(context);
aff_context = isl_basic_set_copy(context);
aff_context = isl_basic_set_plain_affine_hull(aff_context);
aff = isl_basic_set_intersect(aff, aff_context);
if (!aff)
goto error;
if (isl_basic_set_plain_is_empty(aff)) {
isl_basic_set_free(bset);
isl_basic_set_free(context);
return aff;
}
bset = isl_basic_set_sort_constraints(bset);
if (aff->n_eq == 0) {
isl_basic_set_free(aff);
return uset_gist_uncompressed(bset, context);
}
eq = isl_mat_sub_alloc6(bset->ctx, aff->eq, 0, aff->n_eq, 0, 1 + total);
eq = isl_mat_cow(eq);
T = isl_mat_variable_compression(eq, NULL);
isl_basic_set_free(aff);
if (T && T->n_col == 0) {
isl_mat_free(T);
isl_basic_set_free(context);
return replace_by_empty(bset);
}
aff_context = isl_basic_set_affine_hull(isl_basic_set_copy(context));
aff_context = project_onto_involved(aff_context, bset);
bset = uset_gist_compressed(bset, context, T);
bset = isl_basic_set_reduce_using_equalities(bset, aff_context);
if (bset) {
ISL_F_SET(bset, ISL_BASIC_SET_NO_IMPLICIT);
ISL_F_SET(bset, ISL_BASIC_SET_NO_REDUNDANT);
}
return bset;
error:
isl_basic_set_free(bset);
isl_basic_set_free(context);
return NULL;
}
/* Return the number of equality constraints in "bmap" that involve
* local variables. This function assumes that Gaussian elimination
* has been applied to the equality constraints.
*/
static int n_div_eq(__isl_keep isl_basic_map *bmap)
{
int i;
isl_size total, n_div;
if (!bmap)
return -1;
if (bmap->n_eq == 0)
return 0;
total = isl_basic_map_dim(bmap, isl_dim_all);
n_div = isl_basic_map_dim(bmap, isl_dim_div);
if (total < 0 || n_div < 0)
return -1;
total -= n_div;
for (i = 0; i < bmap->n_eq; ++i)
if (isl_seq_first_non_zero(bmap->eq[i] + 1 + total,
n_div) == -1)
return i;
return bmap->n_eq;
}
/* Construct a basic map in "space" defined by the equality constraints in "eq".
* The constraints are assumed not to involve any local variables.
*/
static __isl_give isl_basic_map *basic_map_from_equalities(
__isl_take isl_space *space, __isl_take isl_mat *eq)
{
int i, k;
isl_size total;
isl_basic_map *bmap = NULL;
total = isl_space_dim(space, isl_dim_all);
if (total < 0 || !eq)
goto error;
if (1 + total != eq->n_col)
isl_die(isl_space_get_ctx(space), isl_error_internal,
"unexpected number of columns", goto error);
bmap = isl_basic_map_alloc_space(isl_space_copy(space),
0, eq->n_row, 0);
for (i = 0; i < eq->n_row; ++i) {
k = isl_basic_map_alloc_equality(bmap);
if (k < 0)
goto error;
isl_seq_cpy(bmap->eq[k], eq->row[i], eq->n_col);
}
isl_space_free(space);
isl_mat_free(eq);
return bmap;
error:
isl_space_free(space);
isl_mat_free(eq);
isl_basic_map_free(bmap);
return NULL;
}
/* Construct and return a variable compression based on the equality
* constraints in "bmap1" and "bmap2" that do not involve the local variables.
* "n1" is the number of (initial) equality constraints in "bmap1"
* that do involve local variables.
* "n2" is the number of (initial) equality constraints in "bmap2"
* that do involve local variables.
* "total" is the total number of other variables.
* This function assumes that Gaussian elimination
* has been applied to the equality constraints in both "bmap1" and "bmap2"
* such that the equality constraints not involving local variables
* are those that start at "n1" or "n2".
*
* If either of "bmap1" and "bmap2" does not have such equality constraints,
* then simply compute the compression based on the equality constraints
* in the other basic map.
* Otherwise, combine the equality constraints from both into a new
* basic map such that Gaussian elimination can be applied to this combination
* and then construct a variable compression from the resulting
* equality constraints.
*/
static __isl_give isl_mat *combined_variable_compression(
__isl_keep isl_basic_map *bmap1, int n1,
__isl_keep isl_basic_map *bmap2, int n2, int total)
{
isl_ctx *ctx;
isl_mat *E1, *E2, *V;
isl_basic_map *bmap;
ctx = isl_basic_map_get_ctx(bmap1);
if (bmap1->n_eq == n1) {
E2 = isl_mat_sub_alloc6(ctx, bmap2->eq,
n2, bmap2->n_eq - n2, 0, 1 + total);
return isl_mat_variable_compression(E2, NULL);
}
if (bmap2->n_eq == n2) {
E1 = isl_mat_sub_alloc6(ctx, bmap1->eq,
n1, bmap1->n_eq - n1, 0, 1 + total);
return isl_mat_variable_compression(E1, NULL);
}
E1 = isl_mat_sub_alloc6(ctx, bmap1->eq,
n1, bmap1->n_eq - n1, 0, 1 + total);
E2 = isl_mat_sub_alloc6(ctx, bmap2->eq,
n2, bmap2->n_eq - n2, 0, 1 + total);
E1 = isl_mat_concat(E1, E2);
bmap = basic_map_from_equalities(isl_basic_map_get_space(bmap1), E1);
bmap = isl_basic_map_gauss(bmap, NULL);
if (!bmap)
return NULL;
E1 = isl_mat_sub_alloc6(ctx, bmap->eq, 0, bmap->n_eq, 0, 1 + total);
V = isl_mat_variable_compression(E1, NULL);
isl_basic_map_free(bmap);
return V;
}
/* Extract the stride constraints from "bmap", compressed
* with respect to both the stride constraints in "context" and
* the remaining equality constraints in both "bmap" and "context".
* "bmap_n_eq" is the number of (initial) stride constraints in "bmap".
* "context_n_eq" is the number of (initial) stride constraints in "context".
*
* Let x be all variables in "bmap" (and "context") other than the local
* variables. First compute a variable compression
*
* x = V x'
*
* based on the non-stride equality constraints in "bmap" and "context".
* Consider the stride constraints of "context",
*
* A(x) + B(y) = 0
*
* with y the local variables and plug in the variable compression,
* resulting in
*
* A(V x') + B(y) = 0
*
* Use these constraints to compute a parameter compression on x'
*
* x' = T x''
*
* Now consider the stride constraints of "bmap"
*
* C(x) + D(y) = 0
*
* and plug in x = V*T x''.
* That is, return A = [C*V*T D].
*/
static __isl_give isl_mat *extract_compressed_stride_constraints(
__isl_keep isl_basic_map *bmap, int bmap_n_eq,
__isl_keep isl_basic_map *context, int context_n_eq)
{
isl_size total, n_div;
isl_ctx *ctx;
isl_mat *A, *B, *T, *V;
total = isl_basic_map_dim(context, isl_dim_all);
n_div = isl_basic_map_dim(context, isl_dim_div);
if (total < 0 || n_div < 0)
return NULL;
total -= n_div;
ctx = isl_basic_map_get_ctx(bmap);
V = combined_variable_compression(bmap, bmap_n_eq,
context, context_n_eq, total);
A = isl_mat_sub_alloc6(ctx, context->eq, 0, context_n_eq, 0, 1 + total);
B = isl_mat_sub_alloc6(ctx, context->eq,
0, context_n_eq, 1 + total, n_div);
A = isl_mat_product(A, isl_mat_copy(V));
T = isl_mat_parameter_compression_ext(A, B);
T = isl_mat_product(V, T);
n_div = isl_basic_map_dim(bmap, isl_dim_div);
if (n_div < 0)
T = isl_mat_free(T);
else
T = isl_mat_diagonal(T, isl_mat_identity(ctx, n_div));
A = isl_mat_sub_alloc6(ctx, bmap->eq,
0, bmap_n_eq, 0, 1 + total + n_div);
A = isl_mat_product(A, T);
return A;
}
/* Remove the prime factors from *g that have an exponent that
* is strictly smaller than the exponent in "c".
* All exponents in *g are known to be smaller than or equal
* to those in "c".
*
* That is, if *g is equal to
*
* p_1^{e_1} p_2^{e_2} ... p_n^{e_n}
*
* and "c" is equal to
*
* p_1^{f_1} p_2^{f_2} ... p_n^{f_n}
*
* then update *g to
*
* p_1^{e_1 * (e_1 = f_1)} p_2^{e_2 * (e_2 = f_2)} ...
* p_n^{e_n * (e_n = f_n)}
*
* If e_i = f_i, then c / *g does not have any p_i factors and therefore
* neither does the gcd of *g and c / *g.
* If e_i < f_i, then the gcd of *g and c / *g has a positive
* power min(e_i, s_i) of p_i with s_i = f_i - e_i among its factors.
* Dividing *g by this gcd therefore strictly reduces the exponent
* of the prime factors that need to be removed, while leaving the
* other prime factors untouched.
* Repeating this process until gcd(*g, c / *g) = 1 therefore
* removes all undesired factors, without removing any others.
*/
static void remove_incomplete_powers(isl_int *g, isl_int c)
{
isl_int t;
isl_int_init(t);
for (;;) {
isl_int_divexact(t, c, *g);
isl_int_gcd(t, t, *g);
if (isl_int_is_one(t))
break;
isl_int_divexact(*g, *g, t);
}
isl_int_clear(t);
}
/* Reduce the "n" stride constraints in "bmap" based on a copy "A"
* of the same stride constraints in a compressed space that exploits
* all equalities in the context and the other equalities in "bmap".
*
* If the stride constraints of "bmap" are of the form
*
* C(x) + D(y) = 0
*
* then A is of the form
*
* B(x') + D(y) = 0
*
* If any of these constraints involves only a single local variable y,
* then the constraint appears as
*
* f(x) + m y_i = 0
*
* in "bmap" and as
*
* h(x') + m y_i = 0
*
* in "A".
*
* Let g be the gcd of m and the coefficients of h.
* Then, in particular, g is a divisor of the coefficients of h and
*
* f(x) = h(x')
*
* is known to be a multiple of g.
* If some prime factor in m appears with the same exponent in g,
* then it can be removed from m because f(x) is already known
* to be a multiple of g and therefore in particular of this power
* of the prime factors.
* Prime factors that appear with a smaller exponent in g cannot
* be removed from m.
* Let g' be the divisor of g containing all prime factors that
* appear with the same exponent in m and g, then
*
* f(x) + m y_i = 0
*
* can be replaced by
*
* f(x) + m/g' y_i' = 0
*
* Note that (if g' != 1) this changes the explicit representation
* of y_i to that of y_i', so the integer division at position i
* is marked unknown and later recomputed by a call to
* isl_basic_map_gauss.
*/
static __isl_give isl_basic_map *reduce_stride_constraints(
__isl_take isl_basic_map *bmap, int n, __isl_keep isl_mat *A)
{
int i;
isl_size total, n_div;
int any = 0;
isl_int gcd;
total = isl_basic_map_dim(bmap, isl_dim_all);
n_div = isl_basic_map_dim(bmap, isl_dim_div);
if (total < 0 || n_div < 0 || !A)
return isl_basic_map_free(bmap);
total -= n_div;
isl_int_init(gcd);
for (i = 0; i < n; ++i) {
int div;
div = isl_seq_first_non_zero(bmap->eq[i] + 1 + total, n_div);
if (div < 0)
isl_die(isl_basic_map_get_ctx(bmap), isl_error_internal,
"equality constraints modified unexpectedly",
goto error);
if (isl_seq_first_non_zero(bmap->eq[i] + 1 + total + div + 1,
n_div - div - 1) != -1)
continue;
if (isl_mat_row_gcd(A, i, &gcd) < 0)
goto error;
if (isl_int_is_one(gcd))
continue;
remove_incomplete_powers(&gcd, bmap->eq[i][1 + total + div]);
if (isl_int_is_one(gcd))
continue;
isl_int_divexact(bmap->eq[i][1 + total + div],
bmap->eq[i][1 + total + div], gcd);
bmap = isl_basic_map_mark_div_unknown(bmap, div);
if (!bmap)
goto error;
any = 1;
}
isl_int_clear(gcd);
if (any)
bmap = isl_basic_map_gauss(bmap, NULL);
return bmap;
error:
isl_int_clear(gcd);
isl_basic_map_free(bmap);
return NULL;
}
/* Simplify the stride constraints in "bmap" based on
* the remaining equality constraints in "bmap" and all equality
* constraints in "context".
* Only do this if both "bmap" and "context" have stride constraints.
*
* First extract a copy of the stride constraints in "bmap" in a compressed
* space exploiting all the other equality constraints and then
* use this compressed copy to simplify the original stride constraints.
*/
static __isl_give isl_basic_map *gist_strides(__isl_take isl_basic_map *bmap,
__isl_keep isl_basic_map *context)
{
int bmap_n_eq, context_n_eq;
isl_mat *A;
if (!bmap || !context)
return isl_basic_map_free(bmap);
bmap_n_eq = n_div_eq(bmap);
context_n_eq = n_div_eq(context);
if (bmap_n_eq < 0 || context_n_eq < 0)
return isl_basic_map_free(bmap);
if (bmap_n_eq == 0 || context_n_eq == 0)
return bmap;
A = extract_compressed_stride_constraints(bmap, bmap_n_eq,
context, context_n_eq);
bmap = reduce_stride_constraints(bmap, bmap_n_eq, A);
isl_mat_free(A);
return bmap;
}
/* Return a basic map that has the same intersection with "context" as "bmap"
* and that is as "simple" as possible.
*
* The core computation is performed on the pure constraints.
* When we add back the meaning of the integer divisions, we need
* to (re)introduce the div constraints. If we happen to have
* discovered that some of these integer divisions are equal to
* some affine combination of other variables, then these div
* constraints may end up getting simplified in terms of the equalities,
* resulting in extra inequalities on the other variables that
* may have been removed already or that may not even have been
* part of the input. We try and remove those constraints of
* this form that are most obviously redundant with respect to
* the context. We also remove those div constraints that are
* redundant with respect to the other constraints in the result.
*
* The stride constraints among the equality constraints in "bmap" are
* also simplified with respecting to the other equality constraints
* in "bmap" and with respect to all equality constraints in "context".
*/
__isl_give isl_basic_map *isl_basic_map_gist(__isl_take isl_basic_map *bmap,
__isl_take isl_basic_map *context)
{
isl_basic_set *bset, *eq;
isl_basic_map *eq_bmap;
isl_size total, n_div, n_div_bmap;
unsigned extra, n_eq, n_ineq;
if (!bmap || !context)
goto error;
if (isl_basic_map_plain_is_universe(bmap)) {
isl_basic_map_free(context);
return bmap;
}
if (isl_basic_map_plain_is_empty(context)) {
isl_space *space = isl_basic_map_get_space(bmap);
isl_basic_map_free(bmap);
isl_basic_map_free(context);
return isl_basic_map_universe(space);
}
if (isl_basic_map_plain_is_empty(bmap)) {
isl_basic_map_free(context);
return bmap;
}
bmap = isl_basic_map_remove_redundancies(bmap);
context = isl_basic_map_remove_redundancies(context);
bmap = isl_basic_map_order_divs(bmap);
context = isl_basic_map_align_divs(context, bmap);
n_div = isl_basic_map_dim(context, isl_dim_div);
total = isl_basic_map_dim(bmap, isl_dim_all);
n_div_bmap = isl_basic_map_dim(bmap, isl_dim_div);
if (n_div < 0 || total < 0 || n_div_bmap < 0)
goto error;
extra = n_div - n_div_bmap;
bset = isl_basic_map_underlying_set(isl_basic_map_copy(bmap));
bset = isl_basic_set_add_dims(bset, isl_dim_set, extra);
bset = uset_gist(bset,
isl_basic_map_underlying_set(isl_basic_map_copy(context)));
bset = isl_basic_set_project_out(bset, isl_dim_set, total, extra);
if (!bset || bset->n_eq == 0 || n_div == 0 ||
isl_basic_set_plain_is_empty(bset)) {
isl_basic_map_free(context);
return isl_basic_map_overlying_set(bset, bmap);
}
n_eq = bset->n_eq;
n_ineq = bset->n_ineq;
eq = isl_basic_set_copy(bset);
eq = isl_basic_set_cow(eq);
eq = isl_basic_set_free_inequality(eq, n_ineq);
bset = isl_basic_set_free_equality(bset, n_eq);
eq_bmap = isl_basic_map_overlying_set(eq, isl_basic_map_copy(bmap));
eq_bmap = gist_strides(eq_bmap, context);
eq_bmap = isl_basic_map_remove_shifted_constraints(eq_bmap, context);
bmap = isl_basic_map_overlying_set(bset, bmap);
bmap = isl_basic_map_intersect(bmap, eq_bmap);
bmap = isl_basic_map_remove_redundancies(bmap);
return bmap;
error:
isl_basic_map_free(bmap);
isl_basic_map_free(context);
return NULL;
}
/*
* Assumes context has no implicit divs.
*/
__isl_give isl_map *isl_map_gist_basic_map(__isl_take isl_map *map,
__isl_take isl_basic_map *context)
{
int i;
if (!map || !context)
goto error;
if (isl_basic_map_plain_is_empty(context)) {
isl_space *space = isl_map_get_space(map);
isl_map_free(map);
isl_basic_map_free(context);
return isl_map_universe(space);
}
context = isl_basic_map_remove_redundancies(context);
map = isl_map_cow(map);
if (isl_map_basic_map_check_equal_space(map, context) < 0)
goto error;
map = isl_map_compute_divs(map);
if (!map)
goto error;
for (i = map->n - 1; i >= 0; --i) {
map->p[i] = isl_basic_map_gist(map->p[i],
isl_basic_map_copy(context));
if (!map->p[i])
goto error;
if (isl_basic_map_plain_is_empty(map->p[i])) {
isl_basic_map_free(map->p[i]);
if (i != map->n - 1)
map->p[i] = map->p[map->n - 1];
map->n--;
}
}
isl_basic_map_free(context);
ISL_F_CLR(map, ISL_MAP_NORMALIZED);
return map;
error:
isl_map_free(map);
isl_basic_map_free(context);
return NULL;
}
/* Drop all inequalities from "bmap" that also appear in "context".
* "context" is assumed to have only known local variables and
* the initial local variables of "bmap" are assumed to be the same
* as those of "context".
* The constraints of both "bmap" and "context" are assumed
* to have been sorted using isl_basic_map_sort_constraints.
*
* Run through the inequality constraints of "bmap" and "context"
* in sorted order.
* If a constraint of "bmap" involves variables not in "context",
* then it cannot appear in "context".
* If a matching constraint is found, it is removed from "bmap".
*/
static __isl_give isl_basic_map *drop_inequalities(
__isl_take isl_basic_map *bmap, __isl_keep isl_basic_map *context)
{
int i1, i2;
isl_size total, bmap_total;
unsigned extra;
total = isl_basic_map_dim(context, isl_dim_all);
bmap_total = isl_basic_map_dim(bmap, isl_dim_all);
if (total < 0 || bmap_total < 0)
return isl_basic_map_free(bmap);
extra = bmap_total - total;
i1 = bmap->n_ineq - 1;
i2 = context->n_ineq - 1;
while (bmap && i1 >= 0 && i2 >= 0) {
int cmp;
if (isl_seq_first_non_zero(bmap->ineq[i1] + 1 + total,
extra) != -1) {
--i1;
continue;
}
cmp = isl_basic_map_constraint_cmp(context, bmap->ineq[i1],
context->ineq[i2]);
if (cmp < 0) {
--i2;
continue;
}
if (cmp > 0) {
--i1;
continue;
}
if (isl_int_eq(bmap->ineq[i1][0], context->ineq[i2][0])) {
bmap = isl_basic_map_cow(bmap);
if (isl_basic_map_drop_inequality(bmap, i1) < 0)
bmap = isl_basic_map_free(bmap);
}
--i1;
--i2;
}
return bmap;
}
/* Drop all equalities from "bmap" that also appear in "context".
* "context" is assumed to have only known local variables and
* the initial local variables of "bmap" are assumed to be the same
* as those of "context".
*
* Run through the equality constraints of "bmap" and "context"
* in sorted order.
* If a constraint of "bmap" involves variables not in "context",
* then it cannot appear in "context".
* If a matching constraint is found, it is removed from "bmap".
*/
static __isl_give isl_basic_map *drop_equalities(
__isl_take isl_basic_map *bmap, __isl_keep isl_basic_map *context)
{
int i1, i2;
isl_size total, bmap_total;
unsigned extra;
total = isl_basic_map_dim(context, isl_dim_all);
bmap_total = isl_basic_map_dim(bmap, isl_dim_all);
if (total < 0 || bmap_total < 0)
return isl_basic_map_free(bmap);
extra = bmap_total - total;
i1 = bmap->n_eq - 1;
i2 = context->n_eq - 1;
while (bmap && i1 >= 0 && i2 >= 0) {
int last1, last2;
if (isl_seq_first_non_zero(bmap->eq[i1] + 1 + total,
extra) != -1)
break;
last1 = isl_seq_last_non_zero(bmap->eq[i1] + 1, total);
last2 = isl_seq_last_non_zero(context->eq[i2] + 1, total);
if (last1 > last2) {
--i2;
continue;
}
if (last1 < last2) {
--i1;
continue;
}
if (isl_seq_eq(bmap->eq[i1], context->eq[i2], 1 + total)) {
bmap = isl_basic_map_cow(bmap);
if (isl_basic_map_drop_equality(bmap, i1) < 0)
bmap = isl_basic_map_free(bmap);
}
--i1;
--i2;
}
return bmap;
}
/* Remove the constraints in "context" from "bmap".
* "context" is assumed to have explicit representations
* for all local variables.
*
* First align the divs of "bmap" to those of "context" and
* sort the constraints. Then drop all constraints from "bmap"
* that appear in "context".
*/
__isl_give isl_basic_map *isl_basic_map_plain_gist(
__isl_take isl_basic_map *bmap, __isl_take isl_basic_map *context)
{
isl_bool done, known;
done = isl_basic_map_plain_is_universe(context);
if (done == isl_bool_false)
done = isl_basic_map_plain_is_universe(bmap);
if (done == isl_bool_false)
done = isl_basic_map_plain_is_empty(context);
if (done == isl_bool_false)
done = isl_basic_map_plain_is_empty(bmap);
if (done < 0)
goto error;
if (done) {
isl_basic_map_free(context);
return bmap;
}
known = isl_basic_map_divs_known(context);
if (known < 0)
goto error;
if (!known)
isl_die(isl_basic_map_get_ctx(bmap), isl_error_invalid,
"context has unknown divs", goto error);
context = isl_basic_map_order_divs(context);
bmap = isl_basic_map_align_divs(bmap, context);
bmap = isl_basic_map_gauss(bmap, NULL);
bmap = isl_basic_map_sort_constraints(bmap);
context = isl_basic_map_sort_constraints(context);
bmap = drop_inequalities(bmap, context);
bmap = drop_equalities(bmap, context);
isl_basic_map_free(context);
bmap = isl_basic_map_finalize(bmap);
return bmap;
error:
isl_basic_map_free(bmap);
isl_basic_map_free(context);
return NULL;
}
/* Replace "map" by the disjunct at position "pos" and free "context".
*/
static __isl_give isl_map *replace_by_disjunct(__isl_take isl_map *map,
int pos, __isl_take isl_basic_map *context)
{
isl_basic_map *bmap;
bmap = isl_basic_map_copy(map->p[pos]);
isl_map_free(map);
isl_basic_map_free(context);
return isl_map_from_basic_map(bmap);
}
/* Remove the constraints in "context" from "map".
* If any of the disjuncts in the result turns out to be the universe,
* then return this universe.
* "context" is assumed to have explicit representations
* for all local variables.
*/
__isl_give isl_map *isl_map_plain_gist_basic_map(__isl_take isl_map *map,
__isl_take isl_basic_map *context)
{
int i;
isl_bool univ, known;
univ = isl_basic_map_plain_is_universe(context);
if (univ < 0)
goto error;
if (univ) {
isl_basic_map_free(context);
return map;
}
known = isl_basic_map_divs_known(context);
if (known < 0)
goto error;
if (!known)
isl_die(isl_map_get_ctx(map), isl_error_invalid,
"context has unknown divs", goto error);
map = isl_map_cow(map);
if (!map)
goto error;
for (i = 0; i < map->n; ++i) {
map->p[i] = isl_basic_map_plain_gist(map->p[i],
isl_basic_map_copy(context));
univ = isl_basic_map_plain_is_universe(map->p[i]);
if (univ < 0)
goto error;
if (univ && map->n > 1)
return replace_by_disjunct(map, i, context);
}
isl_basic_map_free(context);
ISL_F_CLR(map, ISL_MAP_NORMALIZED);
if (map->n > 1)
ISL_F_CLR(map, ISL_MAP_DISJOINT);
return map;
error:
isl_map_free(map);
isl_basic_map_free(context);
return NULL;
}
/* Remove the constraints in "context" from "set".
* If any of the disjuncts in the result turns out to be the universe,
* then return this universe.
* "context" is assumed to have explicit representations
* for all local variables.
*/
__isl_give isl_set *isl_set_plain_gist_basic_set(__isl_take isl_set *set,
__isl_take isl_basic_set *context)
{
return set_from_map(isl_map_plain_gist_basic_map(set_to_map(set),
bset_to_bmap(context)));
}
/* Remove the constraints in "context" from "map".
* If any of the disjuncts in the result turns out to be the universe,
* then return this universe.
* "context" is assumed to consist of a single disjunct and
* to have explicit representations for all local variables.
*/
__isl_give isl_map *isl_map_plain_gist(__isl_take isl_map *map,
__isl_take isl_map *context)
{
isl_basic_map *hull;
hull = isl_map_unshifted_simple_hull(context);
return isl_map_plain_gist_basic_map(map, hull);
}
/* Replace "map" by a universe map in the same space and free "drop".
*/
static __isl_give isl_map *replace_by_universe(__isl_take isl_map *map,
__isl_take isl_map *drop)
{
isl_map *res;
res = isl_map_universe(isl_map_get_space(map));
isl_map_free(map);
isl_map_free(drop);
return res;
}
/* Return a map that has the same intersection with "context" as "map"
* and that is as "simple" as possible.
*
* If "map" is already the universe, then we cannot make it any simpler.
* Similarly, if "context" is the universe, then we cannot exploit it
* to simplify "map"
* If "map" and "context" are identical to each other, then we can
* return the corresponding universe.
*
* If either "map" or "context" consists of multiple disjuncts,
* then check if "context" happens to be a subset of "map",
* in which case all constraints can be removed.
* In case of multiple disjuncts, the standard procedure
* may not be able to detect that all constraints can be removed.
*
* If none of these cases apply, we have to work a bit harder.
* During this computation, we make use of a single disjunct context,
* so if the original context consists of more than one disjunct
* then we need to approximate the context by a single disjunct set.
* Simply taking the simple hull may drop constraints that are
* only implicitly available in each disjunct. We therefore also
* look for constraints among those defining "map" that are valid
* for the context. These can then be used to simplify away
* the corresponding constraints in "map".
*/
__isl_give isl_map *isl_map_gist(__isl_take isl_map *map,
__isl_take isl_map *context)
{
int equal;
int is_universe;
isl_size n_disjunct_map, n_disjunct_context;
isl_bool subset;
isl_basic_map *hull;
is_universe = isl_map_plain_is_universe(map);
if (is_universe >= 0 && !is_universe)
is_universe = isl_map_plain_is_universe(context);
if (is_universe < 0)
goto error;
if (is_universe) {
isl_map_free(context);
return map;
}
isl_map_align_params_bin(&map, &context);
equal = isl_map_plain_is_equal(map, context);
if (equal < 0)
goto error;
if (equal)
return replace_by_universe(map, context);
n_disjunct_map = isl_map_n_basic_map(map);
n_disjunct_context = isl_map_n_basic_map(context);
if (n_disjunct_map < 0 || n_disjunct_context < 0)
goto error;
if (n_disjunct_map != 1 || n_disjunct_context != 1) {
subset = isl_map_is_subset(context, map);
if (subset < 0)
goto error;
if (subset)
return replace_by_universe(map, context);
}
context = isl_map_compute_divs(context);
if (!context)
goto error;
if (n_disjunct_context == 1) {
hull = isl_map_simple_hull(context);
} else {
isl_ctx *ctx;
isl_map_list *list;
ctx = isl_map_get_ctx(map);
list = isl_map_list_alloc(ctx, 2);
list = isl_map_list_add(list, isl_map_copy(context));
list = isl_map_list_add(list, isl_map_copy(map));
hull = isl_map_unshifted_simple_hull_from_map_list(context,
list);
}
return isl_map_gist_basic_map(map, hull);
error:
isl_map_free(map);
isl_map_free(context);
return NULL;
}
__isl_give isl_basic_set *isl_basic_set_gist(__isl_take isl_basic_set *bset,
__isl_take isl_basic_set *context)
{
return bset_from_bmap(isl_basic_map_gist(bset_to_bmap(bset),
bset_to_bmap(context)));
}
__isl_give isl_set *isl_set_gist_basic_set(__isl_take isl_set *set,
__isl_take isl_basic_set *context)
{
return set_from_map(isl_map_gist_basic_map(set_to_map(set),
bset_to_bmap(context)));
}
__isl_give isl_set *isl_set_gist_params_basic_set(__isl_take isl_set *set,
__isl_take isl_basic_set *context)
{
isl_space *space = isl_set_get_space(set);
isl_basic_set *dom_context = isl_basic_set_universe(space);
dom_context = isl_basic_set_intersect_params(dom_context, context);
return isl_set_gist_basic_set(set, dom_context);
}
__isl_give isl_set *isl_set_gist(__isl_take isl_set *set,
__isl_take isl_set *context)
{
return set_from_map(isl_map_gist(set_to_map(set), set_to_map(context)));
}
/* Compute the gist of "bmap" with respect to the constraints "context"
* on the domain.
*/
__isl_give isl_basic_map *isl_basic_map_gist_domain(
__isl_take isl_basic_map *bmap, __isl_take isl_basic_set *context)
{
isl_space *space = isl_basic_map_get_space(bmap);
isl_basic_map *bmap_context = isl_basic_map_universe(space);
bmap_context = isl_basic_map_intersect_domain(bmap_context, context);
return isl_basic_map_gist(bmap, bmap_context);
}
__isl_give isl_map *isl_map_gist_domain(__isl_take isl_map *map,
__isl_take isl_set *context)
{
isl_map *map_context = isl_map_universe(isl_map_get_space(map));
map_context = isl_map_intersect_domain(map_context, context);
return isl_map_gist(map, map_context);
}
__isl_give isl_map *isl_map_gist_range(__isl_take isl_map *map,
__isl_take isl_set *context)
{
isl_map *map_context = isl_map_universe(isl_map_get_space(map));
map_context = isl_map_intersect_range(map_context, context);
return isl_map_gist(map, map_context);
}
__isl_give isl_map *isl_map_gist_params(__isl_take isl_map *map,
__isl_take isl_set *context)
{
isl_map *map_context = isl_map_universe(isl_map_get_space(map));
map_context = isl_map_intersect_params(map_context, context);
return isl_map_gist(map, map_context);
}
__isl_give isl_set *isl_set_gist_params(__isl_take isl_set *set,
__isl_take isl_set *context)
{
return isl_map_gist_params(set, context);
}
/* Quick check to see if two basic maps are disjoint.
* In particular, we reduce the equalities and inequalities of
* one basic map in the context of the equalities of the other
* basic map and check if we get a contradiction.
*/
isl_bool isl_basic_map_plain_is_disjoint(__isl_keep isl_basic_map *bmap1,
__isl_keep isl_basic_map *bmap2)
{
struct isl_vec *v = NULL;
int *elim = NULL;
isl_size total;
int i;
if (isl_basic_map_check_equal_space(bmap1, bmap2) < 0)
return isl_bool_error;
if (bmap1->n_div || bmap2->n_div)
return isl_bool_false;
if (!bmap1->n_eq && !bmap2->n_eq)
return isl_bool_false;
total = isl_space_dim(bmap1->dim, isl_dim_all);
if (total < 0)
return isl_bool_error;
if (total == 0)
return isl_bool_false;
v = isl_vec_alloc(bmap1->ctx, 1 + total);
if (!v)
goto error;
elim = isl_alloc_array(bmap1->ctx, int, total);
if (!elim)
goto error;
compute_elimination_index(bmap1, elim, total);
for (i = 0; i < bmap2->n_eq; ++i) {
int reduced;
reduced = reduced_using_equalities(v->block.data, bmap2->eq[i],
bmap1, elim, total);
if (reduced && !isl_int_is_zero(v->block.data[0]) &&
isl_seq_first_non_zero(v->block.data + 1, total) == -1)
goto disjoint;
}
for (i = 0; i < bmap2->n_ineq; ++i) {
int reduced;
reduced = reduced_using_equalities(v->block.data,
bmap2->ineq[i], bmap1, elim, total);
if (reduced && isl_int_is_neg(v->block.data[0]) &&
isl_seq_first_non_zero(v->block.data + 1, total) == -1)
goto disjoint;
}
compute_elimination_index(bmap2, elim, total);
for (i = 0; i < bmap1->n_ineq; ++i) {
int reduced;
reduced = reduced_using_equalities(v->block.data,
bmap1->ineq[i], bmap2, elim, total);
if (reduced && isl_int_is_neg(v->block.data[0]) &&
isl_seq_first_non_zero(v->block.data + 1, total) == -1)
goto disjoint;
}
isl_vec_free(v);
free(elim);
return isl_bool_false;
disjoint:
isl_vec_free(v);
free(elim);
return isl_bool_true;
error:
isl_vec_free(v);
free(elim);
return isl_bool_error;
}
int isl_basic_set_plain_is_disjoint(__isl_keep isl_basic_set *bset1,
__isl_keep isl_basic_set *bset2)
{
return isl_basic_map_plain_is_disjoint(bset_to_bmap(bset1),
bset_to_bmap(bset2));
}
/* Does "test" hold for all pairs of basic maps in "map1" and "map2"?
*/
static isl_bool all_pairs(__isl_keep isl_map *map1, __isl_keep isl_map *map2,
isl_bool (*test)(__isl_keep isl_basic_map *bmap1,
__isl_keep isl_basic_map *bmap2))
{
int i, j;
if (!map1 || !map2)
return isl_bool_error;
for (i = 0; i < map1->n; ++i) {
for (j = 0; j < map2->n; ++j) {
isl_bool d = test(map1->p[i], map2->p[j]);
if (d != isl_bool_true)
return d;
}
}
return isl_bool_true;
}
/* Are "map1" and "map2" obviously disjoint, based on information
* that can be derived without looking at the individual basic maps?
*
* In particular, if one of them is empty or if they live in different spaces
* (ignoring parameters), then they are clearly disjoint.
*/
static isl_bool isl_map_plain_is_disjoint_global(__isl_keep isl_map *map1,
__isl_keep isl_map *map2)
{
isl_bool disjoint;
isl_bool match;
if (!map1 || !map2)
return isl_bool_error;
disjoint = isl_map_plain_is_empty(map1);
if (disjoint < 0 || disjoint)
return disjoint;
disjoint = isl_map_plain_is_empty(map2);
if (disjoint < 0 || disjoint)
return disjoint;
match = isl_map_tuple_is_equal(map1, isl_dim_in, map2, isl_dim_in);
if (match < 0 || !match)
return match < 0 ? isl_bool_error : isl_bool_true;
match = isl_map_tuple_is_equal(map1, isl_dim_out, map2, isl_dim_out);
if (match < 0 || !match)
return match < 0 ? isl_bool_error : isl_bool_true;
return isl_bool_false;
}
/* Are "map1" and "map2" obviously disjoint?
*
* If one of them is empty or if they live in different spaces (ignoring
* parameters), then they are clearly disjoint.
* This is checked by isl_map_plain_is_disjoint_global.
*
* If they have different parameters, then we skip any further tests.
*
* If they are obviously equal, but not obviously empty, then we will
* not be able to detect if they are disjoint.
*
* Otherwise we check if each basic map in "map1" is obviously disjoint
* from each basic map in "map2".
*/
isl_bool isl_map_plain_is_disjoint(__isl_keep isl_map *map1,
__isl_keep isl_map *map2)
{
isl_bool disjoint;
isl_bool intersect;
isl_bool match;
disjoint = isl_map_plain_is_disjoint_global(map1, map2);
if (disjoint < 0 || disjoint)
return disjoint;
match = isl_map_has_equal_params(map1, map2);
if (match < 0 || !match)
return match < 0 ? isl_bool_error : isl_bool_false;
intersect = isl_map_plain_is_equal(map1, map2);
if (intersect < 0 || intersect)
return intersect < 0 ? isl_bool_error : isl_bool_false;
return all_pairs(map1, map2, &isl_basic_map_plain_is_disjoint);
}
/* Are "map1" and "map2" disjoint?
* The parameters are assumed to have been aligned.
*
* In particular, check whether all pairs of basic maps are disjoint.
*/
static isl_bool isl_map_is_disjoint_aligned(__isl_keep isl_map *map1,
__isl_keep isl_map *map2)
{
return all_pairs(map1, map2, &isl_basic_map_is_disjoint);
}
/* Are "map1" and "map2" disjoint?
*
* They are disjoint if they are "obviously disjoint" or if one of them
* is empty. Otherwise, they are not disjoint if one of them is universal.
* If the two inputs are (obviously) equal and not empty, then they are
* not disjoint.
* If none of these cases apply, then check if all pairs of basic maps
* are disjoint after aligning the parameters.
*/
isl_bool isl_map_is_disjoint(__isl_keep isl_map *map1, __isl_keep isl_map *map2)
{
isl_bool disjoint;
isl_bool intersect;
disjoint = isl_map_plain_is_disjoint_global(map1, map2);
if (disjoint < 0 || disjoint)
return disjoint;
disjoint = isl_map_is_empty(map1);
if (disjoint < 0 || disjoint)
return disjoint;
disjoint = isl_map_is_empty(map2);
if (disjoint < 0 || disjoint)
return disjoint;
intersect = isl_map_plain_is_universe(map1);
if (intersect < 0 || intersect)
return isl_bool_not(intersect);
intersect = isl_map_plain_is_universe(map2);
if (intersect < 0 || intersect)
return isl_bool_not(intersect);
intersect = isl_map_plain_is_equal(map1, map2);
if (intersect < 0 || intersect)
return isl_bool_not(intersect);
return isl_map_align_params_map_map_and_test(map1, map2,
&isl_map_is_disjoint_aligned);
}
/* Are "bmap1" and "bmap2" disjoint?
*
* They are disjoint if they are "obviously disjoint" or if one of them
* is empty. Otherwise, they are not disjoint if one of them is universal.
* If none of these cases apply, we compute the intersection and see if
* the result is empty.
*/
isl_bool isl_basic_map_is_disjoint(__isl_keep isl_basic_map *bmap1,
__isl_keep isl_basic_map *bmap2)
{
isl_bool disjoint;
isl_bool intersect;
isl_basic_map *test;
disjoint = isl_basic_map_plain_is_disjoint(bmap1, bmap2);
if (disjoint < 0 || disjoint)
return disjoint;
disjoint = isl_basic_map_is_empty(bmap1);
if (disjoint < 0 || disjoint)
return disjoint;
disjoint = isl_basic_map_is_empty(bmap2);
if (disjoint < 0 || disjoint)
return disjoint;
intersect = isl_basic_map_plain_is_universe(bmap1);
if (intersect < 0 || intersect)
return isl_bool_not(intersect);
intersect = isl_basic_map_plain_is_universe(bmap2);
if (intersect < 0 || intersect)
return isl_bool_not(intersect);
test = isl_basic_map_intersect(isl_basic_map_copy(bmap1),
isl_basic_map_copy(bmap2));
disjoint = isl_basic_map_is_empty(test);
isl_basic_map_free(test);
return disjoint;
}
/* Are "bset1" and "bset2" disjoint?
*/
isl_bool isl_basic_set_is_disjoint(__isl_keep isl_basic_set *bset1,
__isl_keep isl_basic_set *bset2)
{
return isl_basic_map_is_disjoint(bset1, bset2);
}
isl_bool isl_set_plain_is_disjoint(__isl_keep isl_set *set1,
__isl_keep isl_set *set2)
{
return isl_map_plain_is_disjoint(set_to_map(set1), set_to_map(set2));
}
/* Are "set1" and "set2" disjoint?
*/
isl_bool isl_set_is_disjoint(__isl_keep isl_set *set1, __isl_keep isl_set *set2)
{
return isl_map_is_disjoint(set1, set2);
}
/* Is "v" equal to 0, 1 or -1?
*/
static int is_zero_or_one(isl_int v)
{
return isl_int_is_zero(v) || isl_int_is_one(v) || isl_int_is_negone(v);
}
/* Are the "n" coefficients starting at "first" of inequality constraints
* "i" and "j" of "bmap" opposite to each other?
*/
static int is_opposite_part(__isl_keep isl_basic_map *bmap, int i, int j,
int first, int n)
{
return isl_seq_is_neg(bmap->ineq[i] + first, bmap->ineq[j] + first, n);
}
/* Are inequality constraints "i" and "j" of "bmap" opposite to each other,
* apart from the constant term?
*/
static isl_bool is_opposite(__isl_keep isl_basic_map *bmap, int i, int j)
{
isl_size total;
total = isl_basic_map_dim(bmap, isl_dim_all);
if (total < 0)
return isl_bool_error;
return is_opposite_part(bmap, i, j, 1, total);
}
/* Check if we can combine a given div with lower bound l and upper
* bound u with some other div and if so return that other div.
* Otherwise, return a position beyond the integer divisions.
* Return -1 on error.
*
* We first check that
* - the bounds are opposites of each other (except for the constant
* term)
* - the bounds do not reference any other div
* - no div is defined in terms of this div
*
* Let m be the size of the range allowed on the div by the bounds.
* That is, the bounds are of the form
*
* e <= a <= e + m - 1
*
* with e some expression in the other variables.
* We look for another div b such that no third div is defined in terms
* of this second div b and such that in any constraint that contains
* a (except for the given lower and upper bound), also contains b
* with a coefficient that is m times that of b.
* That is, all constraints (except for the lower and upper bound)
* are of the form
*
* e + f (a + m b) >= 0
*
* Furthermore, in the constraints that only contain b, the coefficient
* of b should be equal to 1 or -1.
* If so, we return b so that "a + m b" can be replaced by
* a single div "c = a + m b".
*/
static int div_find_coalesce(__isl_keep isl_basic_map *bmap, int *pairs,
unsigned div, unsigned l, unsigned u)
{
int i, j;
unsigned n_div;
isl_size v_div;
int coalesce;
isl_bool opp;
n_div = isl_basic_map_dim(bmap, isl_dim_div);
if (n_div <= 1)
return n_div;
v_div = isl_basic_map_var_offset(bmap, isl_dim_div);
if (v_div < 0)
return -1;
if (isl_seq_first_non_zero(bmap->ineq[l] + 1 + v_div, div) != -1)
return n_div;
if (isl_seq_first_non_zero(bmap->ineq[l] + 1 + v_div + div + 1,
n_div - div - 1) != -1)
return n_div;
opp = is_opposite(bmap, l, u);
if (opp < 0 || !opp)
return opp < 0 ? -1 : n_div;
for (i = 0; i < n_div; ++i) {
if (isl_int_is_zero(bmap->div[i][0]))
continue;
if (!isl_int_is_zero(bmap->div[i][1 + 1 + v_div + div]))
return n_div;
}
isl_int_add(bmap->ineq[l][0], bmap->ineq[l][0], bmap->ineq[u][0]);
if (isl_int_is_neg(bmap->ineq[l][0])) {
isl_int_sub(bmap->ineq[l][0],
bmap->ineq[l][0], bmap->ineq[u][0]);
bmap = isl_basic_map_copy(bmap);
bmap = isl_basic_map_set_to_empty(bmap);
isl_basic_map_free(bmap);
return n_div;
}
isl_int_add_ui(bmap->ineq[l][0], bmap->ineq[l][0], 1);
coalesce = n_div;
for (i = 0; i < n_div; ++i) {
if (i == div)
continue;
if (!pairs[i])
continue;
for (j = 0; j < n_div; ++j) {
if (isl_int_is_zero(bmap->div[j][0]))
continue;
if (!isl_int_is_zero(bmap->div[j][1 + 1 + v_div + i]))
break;
}
if (j < n_div)
continue;
for (j = 0; j < bmap->n_ineq; ++j) {
int valid;
if (j == l || j == u)
continue;
if (isl_int_is_zero(bmap->ineq[j][1 + v_div + div])) {
if (is_zero_or_one(bmap->ineq[j][1 + v_div + i]))
continue;
break;
}
if (isl_int_is_zero(bmap->ineq[j][1 + v_div + i]))
break;
isl_int_mul(bmap->ineq[j][1 + v_div + div],
bmap->ineq[j][1 + v_div + div],
bmap->ineq[l][0]);
valid = isl_int_eq(bmap->ineq[j][1 + v_div + div],
bmap->ineq[j][1 + v_div + i]);
isl_int_divexact(bmap->ineq[j][1 + v_div + div],
bmap->ineq[j][1 + v_div + div],
bmap->ineq[l][0]);
if (!valid)
break;
}
if (j < bmap->n_ineq)
continue;
coalesce = i;
break;
}
isl_int_sub_ui(bmap->ineq[l][0], bmap->ineq[l][0], 1);
isl_int_sub(bmap->ineq[l][0], bmap->ineq[l][0], bmap->ineq[u][0]);
return coalesce;
}
/* Internal data structure used during the construction and/or evaluation of
* an inequality that ensures that a pair of bounds always allows
* for an integer value.
*
* "tab" is the tableau in which the inequality is evaluated. It may
* be NULL until it is actually needed.
* "v" contains the inequality coefficients.
* "g", "fl" and "fu" are temporary scalars used during the construction and
* evaluation.
*/
struct test_ineq_data {
struct isl_tab *tab;
isl_vec *v;
isl_int g;
isl_int fl;
isl_int fu;
};
/* Free all the memory allocated by the fields of "data".
*/
static void test_ineq_data_clear(struct test_ineq_data *data)
{
isl_tab_free(data->tab);
isl_vec_free(data->v);
isl_int_clear(data->g);
isl_int_clear(data->fl);
isl_int_clear(data->fu);
}
/* Is the inequality stored in data->v satisfied by "bmap"?
* That is, does it only attain non-negative values?
* data->tab is a tableau corresponding to "bmap".
*/
static isl_bool test_ineq_is_satisfied(__isl_keep isl_basic_map *bmap,
struct test_ineq_data *data)
{
isl_ctx *ctx;
enum isl_lp_result res;
ctx = isl_basic_map_get_ctx(bmap);
if (!data->tab)
data->tab = isl_tab_from_basic_map(bmap, 0);
res = isl_tab_min(data->tab, data->v->el, ctx->one, &data->g, NULL, 0);
if (res == isl_lp_error)
return isl_bool_error;
return res == isl_lp_ok && isl_int_is_nonneg(data->g);
}
/* Given a lower and an upper bound on div i, do they always allow
* for an integer value of the given div?
* Determine this property by constructing an inequality
* such that the property is guaranteed when the inequality is nonnegative.
* The lower bound is inequality l, while the upper bound is inequality u.
* The constructed inequality is stored in data->v.
*
* Let the upper bound be
*
* -n_u a + e_u >= 0
*
* and the lower bound
*
* n_l a + e_l >= 0
*
* Let n_u = f_u g and n_l = f_l g, with g = gcd(n_u, n_l).
* We have
*
* - f_u e_l <= f_u f_l g a <= f_l e_u
*
* Since all variables are integer valued, this is equivalent to
*
* - f_u e_l - (f_u - 1) <= f_u f_l g a <= f_l e_u + (f_l - 1)
*
* If this interval is at least f_u f_l g, then it contains at least
* one integer value for a.
* That is, the test constraint is
*
* f_l e_u + f_u e_l + f_l - 1 + f_u - 1 + 1 >= f_u f_l g
*
* or
*
* f_l e_u + f_u e_l + f_l - 1 + f_u - 1 + 1 - f_u f_l g >= 0
*
* If the coefficients of f_l e_u + f_u e_l have a common divisor g',
* then the constraint can be scaled down by a factor g',
* with the constant term replaced by
* floor((f_l e_{u,0} + f_u e_{l,0} + f_l - 1 + f_u - 1 + 1 - f_u f_l g)/g').
* Note that the result of applying Fourier-Motzkin to this pair
* of constraints is
*
* f_l e_u + f_u e_l >= 0
*
* If the constant term of the scaled down version of this constraint,
* i.e., floor((f_l e_{u,0} + f_u e_{l,0})/g') is equal to the constant
* term of the scaled down test constraint, then the test constraint
* is known to hold and no explicit evaluation is required.
* This is essentially the Omega test.
*
* If the test constraint consists of only a constant term, then
* it is sufficient to look at the sign of this constant term.
*/
static isl_bool int_between_bounds(__isl_keep isl_basic_map *bmap, int i,
int l, int u, struct test_ineq_data *data)
{
unsigned offset;
isl_size n_div;
offset = isl_basic_map_offset(bmap, isl_dim_div);
n_div = isl_basic_map_dim(bmap, isl_dim_div);
if (n_div < 0)
return isl_bool_error;
isl_int_gcd(data->g,
bmap->ineq[l][offset + i], bmap->ineq[u][offset + i]);
isl_int_divexact(data->fl, bmap->ineq[l][offset + i], data->g);
isl_int_divexact(data->fu, bmap->ineq[u][offset + i], data->g);
isl_int_neg(data->fu, data->fu);
isl_seq_combine(data->v->el, data->fl, bmap->ineq[u],
data->fu, bmap->ineq[l], offset + n_div);
isl_int_mul(data->g, data->g, data->fl);
isl_int_mul(data->g, data->g, data->fu);
isl_int_sub(data->g, data->g, data->fl);
isl_int_sub(data->g, data->g, data->fu);
isl_int_add_ui(data->g, data->g, 1);
isl_int_sub(data->fl, data->v->el[0], data->g);
isl_seq_gcd(data->v->el + 1, offset - 1 + n_div, &data->g);
if (isl_int_is_zero(data->g))
return isl_int_is_nonneg(data->fl);
if (isl_int_is_one(data->g)) {
isl_int_set(data->v->el[0], data->fl);
return test_ineq_is_satisfied(bmap, data);
}
isl_int_fdiv_q(data->fl, data->fl, data->g);
isl_int_fdiv_q(data->v->el[0], data->v->el[0], data->g);
if (isl_int_eq(data->fl, data->v->el[0]))
return isl_bool_true;
isl_int_set(data->v->el[0], data->fl);
isl_seq_scale_down(data->v->el + 1, data->v->el + 1, data->g,
offset - 1 + n_div);
return test_ineq_is_satisfied(bmap, data);
}
/* Remove more kinds of divs that are not strictly needed.
* In particular, if all pairs of lower and upper bounds on a div
* are such that they allow at least one integer value of the div,
* then we can eliminate the div using Fourier-Motzkin without
* introducing any spurious solutions.
*
* If at least one of the two constraints has a unit coefficient for the div,
* then the presence of such a value is guaranteed so there is no need to check.
* In particular, the value attained by the bound with unit coefficient
* can serve as this intermediate value.
*/
static __isl_give isl_basic_map *drop_more_redundant_divs(
__isl_take isl_basic_map *bmap, __isl_take int *pairs, int n)
{
isl_ctx *ctx;
struct test_ineq_data data = { NULL, NULL };
unsigned off;
isl_size n_div;
int remove = -1;
isl_int_init(data.g);
isl_int_init(data.fl);
isl_int_init(data.fu);
n_div = isl_basic_map_dim(bmap, isl_dim_div);
if (n_div < 0)
goto error;
ctx = isl_basic_map_get_ctx(bmap);
off = isl_basic_map_offset(bmap, isl_dim_div);
data.v = isl_vec_alloc(ctx, off + n_div);
if (!data.v)
goto error;
while (n > 0) {
int i, l, u;
int best = -1;
isl_bool has_int;
for (i = 0; i < n_div; ++i) {
if (!pairs[i])
continue;
if (best >= 0 && pairs[best] <= pairs[i])
continue;
best = i;
}
i = best;
for (l = 0; l < bmap->n_ineq; ++l) {
if (!isl_int_is_pos(bmap->ineq[l][off + i]))
continue;
if (isl_int_is_one(bmap->ineq[l][off + i]))
continue;
for (u = 0; u < bmap->n_ineq; ++u) {
if (!isl_int_is_neg(bmap->ineq[u][off + i]))
continue;
if (isl_int_is_negone(bmap->ineq[u][off + i]))
continue;
has_int = int_between_bounds(bmap, i, l, u,
&data);
if (has_int < 0)
goto error;
if (data.tab && data.tab->empty)
break;
if (!has_int)
break;
}
if (u < bmap->n_ineq)
break;
}
if (data.tab && data.tab->empty) {
bmap = isl_basic_map_set_to_empty(bmap);
break;
}
if (l == bmap->n_ineq) {
remove = i;
break;
}
pairs[i] = 0;
--n;
}
test_ineq_data_clear(&data);
free(pairs);
if (remove < 0)
return bmap;
bmap = isl_basic_map_remove_dims(bmap, isl_dim_div, remove, 1);
return isl_basic_map_drop_redundant_divs(bmap);
error:
free(pairs);
isl_basic_map_free(bmap);
test_ineq_data_clear(&data);
return NULL;
}
/* Given a pair of divs div1 and div2 such that, except for the lower bound l
* and the upper bound u, div1 always occurs together with div2 in the form
* (div1 + m div2), where m is the constant range on the variable div1
* allowed by l and u, replace the pair div1 and div2 by a single
* div that is equal to div1 + m div2.
*
* The new div will appear in the location that contains div2.
* We need to modify all constraints that contain
* div2 = (div - div1) / m
* The coefficient of div2 is known to be equal to 1 or -1.
* (If a constraint does not contain div2, it will also not contain div1.)
* If the constraint also contains div1, then we know they appear
* as f (div1 + m div2) and we can simply replace (div1 + m div2) by div,
* i.e., the coefficient of div is f.
*
* Otherwise, we first need to introduce div1 into the constraint.
* Let l be
*
* div1 + f >=0
*
* and u
*
* -div1 + f' >= 0
*
* A lower bound on div2
*
* div2 + t >= 0
*
* can be replaced by
*
* m div2 + div1 + m t + f >= 0
*
* An upper bound
*
* -div2 + t >= 0
*
* can be replaced by
*
* -(m div2 + div1) + m t + f' >= 0
*
* These constraint are those that we would obtain from eliminating
* div1 using Fourier-Motzkin.
*
* After all constraints have been modified, we drop the lower and upper
* bound and then drop div1.
* Since the new div is only placed in the same location that used
* to store div2, but otherwise has a different meaning, any possible
* explicit representation of the original div2 is removed.
*/
static __isl_give isl_basic_map *coalesce_divs(__isl_take isl_basic_map *bmap,
unsigned div1, unsigned div2, unsigned l, unsigned u)
{
isl_ctx *ctx;
isl_int m;
isl_size v_div;
unsigned total;
int i;
ctx = isl_basic_map_get_ctx(bmap);
v_div = isl_basic_map_var_offset(bmap, isl_dim_div);
if (v_div < 0)
return isl_basic_map_free(bmap);
total = 1 + v_div + bmap->n_div;
isl_int_init(m);
isl_int_add(m, bmap->ineq[l][0], bmap->ineq[u][0]);
isl_int_add_ui(m, m, 1);
for (i = 0; i < bmap->n_ineq; ++i) {
if (i == l || i == u)
continue;
if (isl_int_is_zero(bmap->ineq[i][1 + v_div + div2]))
continue;
if (isl_int_is_zero(bmap->ineq[i][1 + v_div + div1])) {
if (isl_int_is_pos(bmap->ineq[i][1 + v_div + div2]))
isl_seq_combine(bmap->ineq[i], m, bmap->ineq[i],
ctx->one, bmap->ineq[l], total);
else
isl_seq_combine(bmap->ineq[i], m, bmap->ineq[i],
ctx->one, bmap->ineq[u], total);
}
isl_int_set(bmap->ineq[i][1 + v_div + div2],
bmap->ineq[i][1 + v_div + div1]);
isl_int_set_si(bmap->ineq[i][1 + v_div + div1], 0);
}
isl_int_clear(m);
if (l > u) {
isl_basic_map_drop_inequality(bmap, l);
isl_basic_map_drop_inequality(bmap, u);
} else {
isl_basic_map_drop_inequality(bmap, u);
isl_basic_map_drop_inequality(bmap, l);
}
bmap = isl_basic_map_mark_div_unknown(bmap, div2);
bmap = isl_basic_map_drop_div(bmap, div1);
return bmap;
}
/* First check if we can coalesce any pair of divs and
* then continue with dropping more redundant divs.
*
* We loop over all pairs of lower and upper bounds on a div
* with coefficient 1 and -1, respectively, check if there
* is any other div "c" with which we can coalesce the div
* and if so, perform the coalescing.
*/
static __isl_give isl_basic_map *coalesce_or_drop_more_redundant_divs(
__isl_take isl_basic_map *bmap, int *pairs, int n)
{
int i, l, u;
isl_size v_div;
isl_size n_div;
v_div = isl_basic_map_var_offset(bmap, isl_dim_div);
n_div = isl_basic_map_dim(bmap, isl_dim_div);
if (v_div < 0 || n_div < 0)
return isl_basic_map_free(bmap);
for (i = 0; i < n_div; ++i) {
if (!pairs[i])
continue;
for (l = 0; l < bmap->n_ineq; ++l) {
if (!isl_int_is_one(bmap->ineq[l][1 + v_div + i]))
continue;
for (u = 0; u < bmap->n_ineq; ++u) {
int c;
if (!isl_int_is_negone(bmap->ineq[u][1+v_div+i]))
continue;
c = div_find_coalesce(bmap, pairs, i, l, u);
if (c < 0)
goto error;
if (c >= n_div)
continue;
free(pairs);
bmap = coalesce_divs(bmap, i, c, l, u);
return isl_basic_map_drop_redundant_divs(bmap);
}
}
}
if (ISL_F_ISSET(bmap, ISL_BASIC_MAP_EMPTY)) {
free(pairs);
return bmap;
}
return drop_more_redundant_divs(bmap, pairs, n);
error:
free(pairs);
isl_basic_map_free(bmap);
return NULL;
}
/* Are the "n" coefficients starting at "first" of inequality constraints
* "i" and "j" of "bmap" equal to each other?
*/
static int is_parallel_part(__isl_keep isl_basic_map *bmap, int i, int j,
int first, int n)
{
return isl_seq_eq(bmap->ineq[i] + first, bmap->ineq[j] + first, n);
}
/* Are inequality constraints "i" and "j" of "bmap" equal to each other,
* apart from the constant term and the coefficient at position "pos"?
*/
static isl_bool is_parallel_except(__isl_keep isl_basic_map *bmap, int i, int j,
int pos)
{
isl_size total;
total = isl_basic_map_dim(bmap, isl_dim_all);
if (total < 0)
return isl_bool_error;
return is_parallel_part(bmap, i, j, 1, pos - 1) &&
is_parallel_part(bmap, i, j, pos + 1, total - pos);
}
/* Are inequality constraints "i" and "j" of "bmap" opposite to each other,
* apart from the constant term and the coefficient at position "pos"?
*/
static isl_bool is_opposite_except(__isl_keep isl_basic_map *bmap, int i, int j,
int pos)
{
isl_size total;
total = isl_basic_map_dim(bmap, isl_dim_all);
if (total < 0)
return isl_bool_error;
return is_opposite_part(bmap, i, j, 1, pos - 1) &&
is_opposite_part(bmap, i, j, pos + 1, total - pos);
}
/* Restart isl_basic_map_drop_redundant_divs after "bmap" has
* been modified, simplying it if "simplify" is set.
* Free the temporary data structure "pairs" that was associated
* to the old version of "bmap".
*/
static __isl_give isl_basic_map *drop_redundant_divs_again(
__isl_take isl_basic_map *bmap, __isl_take int *pairs, int simplify)
{
if (simplify)
bmap = isl_basic_map_simplify(bmap);
free(pairs);
return isl_basic_map_drop_redundant_divs(bmap);
}
/* Is "div" the single unknown existentially quantified variable
* in inequality constraint "ineq" of "bmap"?
* "div" is known to have a non-zero coefficient in "ineq".
*/
static isl_bool single_unknown(__isl_keep isl_basic_map *bmap, int ineq,
int div)
{
int i;
isl_size n_div;
unsigned o_div;
isl_bool known;
known = isl_basic_map_div_is_known(bmap, div);
if (known < 0 || known)
return isl_bool_not(known);
n_div = isl_basic_map_dim(bmap, isl_dim_div);
if (n_div < 0)
return isl_bool_error;
if (n_div == 1)
return isl_bool_true;
o_div = isl_basic_map_offset(bmap, isl_dim_div);
for (i = 0; i < n_div; ++i) {
isl_bool known;
if (i == div)
continue;
if (isl_int_is_zero(bmap->ineq[ineq][o_div + i]))
continue;
known = isl_basic_map_div_is_known(bmap, i);
if (known < 0 || !known)
return known;
}
return isl_bool_true;
}
/* Does integer division "div" have coefficient 1 in inequality constraint
* "ineq" of "map"?
*/
static isl_bool has_coef_one(__isl_keep isl_basic_map *bmap, int div, int ineq)
{
unsigned o_div;
o_div = isl_basic_map_offset(bmap, isl_dim_div);
if (isl_int_is_one(bmap->ineq[ineq][o_div + div]))
return isl_bool_true;
return isl_bool_false;
}
/* Turn inequality constraint "ineq" of "bmap" into an equality and
* then try and drop redundant divs again,
* freeing the temporary data structure "pairs" that was associated
* to the old version of "bmap".
*/
static __isl_give isl_basic_map *set_eq_and_try_again(
__isl_take isl_basic_map *bmap, int ineq, __isl_take int *pairs)
{
bmap = isl_basic_map_cow(bmap);
isl_basic_map_inequality_to_equality(bmap, ineq);
return drop_redundant_divs_again(bmap, pairs, 1);
}
/* Drop the integer division at position "div", along with the two
* inequality constraints "ineq1" and "ineq2" in which it appears
* from "bmap" and then try and drop redundant divs again,
* freeing the temporary data structure "pairs" that was associated
* to the old version of "bmap".
*/
static __isl_give isl_basic_map *drop_div_and_try_again(
__isl_take isl_basic_map *bmap, int div, int ineq1, int ineq2,
__isl_take int *pairs)
{
if (ineq1 > ineq2) {
isl_basic_map_drop_inequality(bmap, ineq1);
isl_basic_map_drop_inequality(bmap, ineq2);
} else {
isl_basic_map_drop_inequality(bmap, ineq2);
isl_basic_map_drop_inequality(bmap, ineq1);
}
bmap = isl_basic_map_drop_div(bmap, div);
return drop_redundant_divs_again(bmap, pairs, 0);
}
/* Given two inequality constraints
*
* f(x) + n d + c >= 0, (ineq)
*
* with d the variable at position "pos", and
*
* f(x) + c0 >= 0, (lower)
*
* compute the maximal value of the lower bound ceil((-f(x) - c)/n)
* determined by the first constraint.
* That is, store
*
* ceil((c0 - c)/n)
*
* in *l.
*/
static void lower_bound_from_parallel(__isl_keep isl_basic_map *bmap,
int ineq, int lower, int pos, isl_int *l)
{
isl_int_neg(*l, bmap->ineq[ineq][0]);
isl_int_add(*l, *l, bmap->ineq[lower][0]);
isl_int_cdiv_q(*l, *l, bmap->ineq[ineq][pos]);
}
/* Given two inequality constraints
*
* f(x) + n d + c >= 0, (ineq)
*
* with d the variable at position "pos", and
*
* -f(x) - c0 >= 0, (upper)
*
* compute the minimal value of the lower bound ceil((-f(x) - c)/n)
* determined by the first constraint.
* That is, store
*
* ceil((-c1 - c)/n)
*
* in *u.
*/
static void lower_bound_from_opposite(__isl_keep isl_basic_map *bmap,
int ineq, int upper, int pos, isl_int *u)
{
isl_int_neg(*u, bmap->ineq[ineq][0]);
isl_int_sub(*u, *u, bmap->ineq[upper][0]);
isl_int_cdiv_q(*u, *u, bmap->ineq[ineq][pos]);
}
/* Given a lower bound constraint "ineq" on "div" in "bmap",
* does the corresponding lower bound have a fixed value in "bmap"?
*
* In particular, "ineq" is of the form
*
* f(x) + n d + c >= 0
*
* with n > 0, c the constant term and
* d the existentially quantified variable "div".
* That is, the lower bound is
*
* ceil((-f(x) - c)/n)
*
* Look for a pair of constraints
*
* f(x) + c0 >= 0
* -f(x) + c1 >= 0
*
* i.e., -c1 <= -f(x) <= c0, that fix ceil((-f(x) - c)/n) to a constant value.
* That is, check that
*
* ceil((-c1 - c)/n) = ceil((c0 - c)/n)
*
* If so, return the index of inequality f(x) + c0 >= 0.
* Otherwise, return bmap->n_ineq.
* Return -1 on error.
*/
static int lower_bound_is_cst(__isl_keep isl_basic_map *bmap, int div, int ineq)
{
int i;
int lower = -1, upper = -1;
unsigned o_div;
isl_int l, u;
int equal;
o_div = isl_basic_map_offset(bmap, isl_dim_div);
for (i = 0; i < bmap->n_ineq && (lower < 0 || upper < 0); ++i) {
isl_bool par, opp;
if (i == ineq)
continue;
if (!isl_int_is_zero(bmap->ineq[i][o_div + div]))
continue;
par = isl_bool_false;
if (lower < 0)
par = is_parallel_except(bmap, ineq, i, o_div + div);
if (par < 0)
return -1;
if (par) {
lower = i;
continue;
}
opp = isl_bool_false;
if (upper < 0)
opp = is_opposite_except(bmap, ineq, i, o_div + div);
if (opp < 0)
return -1;
if (opp)
upper = i;
}
if (lower < 0 || upper < 0)
return bmap->n_ineq;
isl_int_init(l);
isl_int_init(u);
lower_bound_from_parallel(bmap, ineq, lower, o_div + div, &l);
lower_bound_from_opposite(bmap, ineq, upper, o_div + div, &u);
equal = isl_int_eq(l, u);
isl_int_clear(l);
isl_int_clear(u);
return equal ? lower : bmap->n_ineq;
}
/* Given a lower bound constraint "ineq" on the existentially quantified
* variable "div", such that the corresponding lower bound has
* a fixed value in "bmap", assign this fixed value to the variable and
* then try and drop redundant divs again,
* freeing the temporary data structure "pairs" that was associated
* to the old version of "bmap".
* "lower" determines the constant value for the lower bound.
*
* In particular, "ineq" is of the form
*
* f(x) + n d + c >= 0,
*
* while "lower" is of the form
*
* f(x) + c0 >= 0
*
* The lower bound is ceil((-f(x) - c)/n) and its constant value
* is ceil((c0 - c)/n).
*/
static __isl_give isl_basic_map *fix_cst_lower(__isl_take isl_basic_map *bmap,
int div, int ineq, int lower, int *pairs)
{
isl_int c;
unsigned o_div;
isl_int_init(c);
o_div = isl_basic_map_offset(bmap, isl_dim_div);
lower_bound_from_parallel(bmap, ineq, lower, o_div + div, &c);
bmap = isl_basic_map_fix(bmap, isl_dim_div, div, c);
free(pairs);
isl_int_clear(c);
return isl_basic_map_drop_redundant_divs(bmap);
}
/* Do any of the integer divisions of "bmap" involve integer division "div"?
*
* The integer division "div" could only ever appear in any later
* integer division (with an explicit representation).
*/
static isl_bool any_div_involves_div(__isl_keep isl_basic_map *bmap, int div)
{
int i;
isl_size v_div, n_div;
v_div = isl_basic_map_var_offset(bmap, isl_dim_div);
n_div = isl_basic_map_dim(bmap, isl_dim_div);
if (v_div < 0 || n_div < 0)
return isl_bool_error;
for (i = div + 1; i < n_div; ++i) {
isl_bool unknown;
unknown = isl_basic_map_div_is_marked_unknown(bmap, i);
if (unknown < 0)
return isl_bool_error;
if (unknown)
continue;
if (!isl_int_is_zero(bmap->div[i][1 + 1 + v_div + div]))
return isl_bool_true;
}
return isl_bool_false;
}
/* Remove divs that are not strictly needed based on the inequality
* constraints.
* In particular, if a div only occurs positively (or negatively)
* in constraints, then it can simply be dropped.
* Also, if a div occurs in only two constraints and if moreover
* those two constraints are opposite to each other, except for the constant
* term and if the sum of the constant terms is such that for any value
* of the other values, there is always at least one integer value of the
* div, i.e., if one plus this sum is greater than or equal to
* the (absolute value) of the coefficient of the div in the constraints,
* then we can also simply drop the div.
*
* If an existentially quantified variable does not have an explicit
* representation, appears in only a single lower bound that does not
* involve any other such existentially quantified variables and appears
* in this lower bound with coefficient 1,
* then fix the variable to the value of the lower bound. That is,
* turn the inequality into an equality.
* If for any value of the other variables, there is any value
* for the existentially quantified variable satisfying the constraints,
* then this lower bound also satisfies the constraints.
* It is therefore safe to pick this lower bound.
*
* The same reasoning holds even if the coefficient is not one.
* However, fixing the variable to the value of the lower bound may
* in general introduce an extra integer division, in which case
* it may be better to pick another value.
* If this integer division has a known constant value, then plugging
* in this constant value removes the existentially quantified variable
* completely. In particular, if the lower bound is of the form
* ceil((-f(x) - c)/n) and there are two constraints, f(x) + c0 >= 0 and
* -f(x) + c1 >= 0 such that ceil((-c1 - c)/n) = ceil((c0 - c)/n),
* then the existentially quantified variable can be assigned this
* shared value.
*
* We skip divs that appear in equalities or in the definition of other divs.
* Divs that appear in the definition of other divs usually occur in at least
* 4 constraints, but the constraints may have been simplified.
*
* If any divs are left after these simple checks then we move on
* to more complicated cases in drop_more_redundant_divs.
*/
static __isl_give isl_basic_map *isl_basic_map_drop_redundant_divs_ineq(
__isl_take isl_basic_map *bmap)
{
int i, j;
isl_size off;
int *pairs = NULL;
int n = 0;
isl_size n_ineq;
if (!bmap)
goto error;
if (bmap->n_div == 0)
return bmap;
off = isl_basic_map_var_offset(bmap, isl_dim_div);
if (off < 0)
return isl_basic_map_free(bmap);
pairs = isl_calloc_array(bmap->ctx, int, bmap->n_div);
if (!pairs)
goto error;
n_ineq = isl_basic_map_n_inequality(bmap);
if (n_ineq < 0)
goto error;
for (i = 0; i < bmap->n_div; ++i) {
int pos, neg;
int last_pos, last_neg;
int redundant;
int defined;
isl_bool involves, opp, set_div;
defined = !isl_int_is_zero(bmap->div[i][0]);
involves = any_div_involves_div(bmap, i);
if (involves < 0)
goto error;
if (involves)
continue;
for (j = 0; j < bmap->n_eq; ++j)
if (!isl_int_is_zero(bmap->eq[j][1 + off + i]))
break;
if (j < bmap->n_eq)
continue;
++n;
pos = neg = 0;
for (j = 0; j < bmap->n_ineq; ++j) {
if (isl_int_is_pos(bmap->ineq[j][1 + off + i])) {
last_pos = j;
++pos;
}
if (isl_int_is_neg(bmap->ineq[j][1 + off + i])) {
last_neg = j;
++neg;
}
}
pairs[i] = pos * neg;
if (pairs[i] == 0) {
for (j = bmap->n_ineq - 1; j >= 0; --j)
if (!isl_int_is_zero(bmap->ineq[j][1+off+i]))
isl_basic_map_drop_inequality(bmap, j);
bmap = isl_basic_map_drop_div(bmap, i);
return drop_redundant_divs_again(bmap, pairs, 0);
}
if (pairs[i] != 1)
opp = isl_bool_false;
else
opp = is_opposite(bmap, last_pos, last_neg);
if (opp < 0)
goto error;
if (!opp) {
int lower;
isl_bool single, one;
if (pos != 1)
continue;
single = single_unknown(bmap, last_pos, i);
if (single < 0)
goto error;
if (!single)
continue;
one = has_coef_one(bmap, i, last_pos);
if (one < 0)
goto error;
if (one)
return set_eq_and_try_again(bmap, last_pos,
pairs);
lower = lower_bound_is_cst(bmap, i, last_pos);
if (lower < 0)
goto error;
if (lower < n_ineq)
return fix_cst_lower(bmap, i, last_pos, lower,
pairs);
continue;
}
isl_int_add(bmap->ineq[last_pos][0],
bmap->ineq[last_pos][0], bmap->ineq[last_neg][0]);
isl_int_add_ui(bmap->ineq[last_pos][0],
bmap->ineq[last_pos][0], 1);
redundant = isl_int_ge(bmap->ineq[last_pos][0],
bmap->ineq[last_pos][1+off+i]);
isl_int_sub_ui(bmap->ineq[last_pos][0],
bmap->ineq[last_pos][0], 1);
isl_int_sub(bmap->ineq[last_pos][0],
bmap->ineq[last_pos][0], bmap->ineq[last_neg][0]);
if (redundant)
return drop_div_and_try_again(bmap, i,
last_pos, last_neg, pairs);
if (defined)
set_div = isl_bool_false;
else
set_div = ok_to_set_div_from_bound(bmap, i, last_pos);
if (set_div < 0)
return isl_basic_map_free(bmap);
if (set_div) {
bmap = set_div_from_lower_bound(bmap, i, last_pos);
return drop_redundant_divs_again(bmap, pairs, 1);
}
pairs[i] = 0;
--n;
}
if (n > 0)
return coalesce_or_drop_more_redundant_divs(bmap, pairs, n);
free(pairs);
return bmap;
error:
free(pairs);
isl_basic_map_free(bmap);
return NULL;
}
/* Consider the coefficients at "c" as a row vector and replace
* them with their product with "T". "T" is assumed to be a square matrix.
*/
static isl_stat preimage(isl_int *c, __isl_keep isl_mat *T)
{
isl_size n;
isl_ctx *ctx;
isl_vec *v;
n = isl_mat_rows(T);
if (n < 0)
return isl_stat_error;
if (isl_seq_first_non_zero(c, n) == -1)
return isl_stat_ok;
ctx = isl_mat_get_ctx(T);
v = isl_vec_alloc(ctx, n);
if (!v)
return isl_stat_error;
isl_seq_swp_or_cpy(v->el, c, n);
v = isl_vec_mat_product(v, isl_mat_copy(T));
if (!v)
return isl_stat_error;
isl_seq_swp_or_cpy(c, v->el, n);
isl_vec_free(v);
return isl_stat_ok;
}
/* Plug in T for the variables in "bmap" starting at "pos".
* T is a linear unimodular matrix, i.e., without constant term.
*/
static __isl_give isl_basic_map *isl_basic_map_preimage_vars(
__isl_take isl_basic_map *bmap, unsigned pos, __isl_take isl_mat *T)
{
int i;
isl_size n_row, n_col;
bmap = isl_basic_map_cow(bmap);
n_row = isl_mat_rows(T);
n_col = isl_mat_cols(T);
if (!bmap || n_row < 0 || n_col < 0)
goto error;
if (n_col != n_row)
isl_die(isl_mat_get_ctx(T), isl_error_invalid,
"expecting square matrix", goto error);
if (isl_basic_map_check_range(bmap, isl_dim_all, pos, n_col) < 0)
goto error;
for (i = 0; i < bmap->n_eq; ++i)
if (preimage(bmap->eq[i] + 1 + pos, T) < 0)
goto error;
for (i = 0; i < bmap->n_ineq; ++i)
if (preimage(bmap->ineq[i] + 1 + pos, T) < 0)
goto error;
for (i = 0; i < bmap->n_div; ++i) {
if (isl_basic_map_div_is_marked_unknown(bmap, i))
continue;
if (preimage(bmap->div[i] + 1 + 1 + pos, T) < 0)
goto error;
}
isl_mat_free(T);
return bmap;
error:
isl_basic_map_free(bmap);
isl_mat_free(T);
return NULL;
}
/* Remove divs that are not strictly needed.
*
* First look for an equality constraint involving two or more
* existentially quantified variables without an explicit
* representation. Replace the combination that appears
* in the equality constraint by a single existentially quantified
* variable such that the equality can be used to derive
* an explicit representation for the variable.
* If there are no more such equality constraints, then continue
* with isl_basic_map_drop_redundant_divs_ineq.
*
* In particular, if the equality constraint is of the form
*
* f(x) + \sum_i c_i a_i = 0
*
* with a_i existentially quantified variable without explicit
* representation, then apply a transformation on the existentially
* quantified variables to turn the constraint into
*
* f(x) + g a_1' = 0
*
* with g the gcd of the c_i.
* In order to easily identify which existentially quantified variables
* have a complete explicit representation, i.e., without being defined
* in terms of other existentially quantified variables without
* an explicit representation, the existentially quantified variables
* are first sorted.
*
* The variable transformation is computed by extending the row
* [c_1/g ... c_n/g] to a unimodular matrix, obtaining the transformation
*
* [a_1'] [c_1/g ... c_n/g] [ a_1 ]
* [a_2'] [ a_2 ]
* ... = U ....
* [a_n'] [ a_n ]
*
* with [c_1/g ... c_n/g] representing the first row of U.
* The inverse of U is then plugged into the original constraints.
* The call to isl_basic_map_simplify makes sure the explicit
* representation for a_1' is extracted from the equality constraint.
*/
__isl_give isl_basic_map *isl_basic_map_drop_redundant_divs(
__isl_take isl_basic_map *bmap)
{
int first;
int i;
unsigned o_div;
isl_size n_div;
int l;
isl_ctx *ctx;
isl_mat *T;
if (!bmap)
return NULL;
if (isl_basic_map_divs_known(bmap))
return isl_basic_map_drop_redundant_divs_ineq(bmap);
if (bmap->n_eq == 0)
return isl_basic_map_drop_redundant_divs_ineq(bmap);
bmap = isl_basic_map_sort_divs(bmap);
if (!bmap)
return NULL;
first = isl_basic_map_first_unknown_div(bmap);
if (first < 0)
return isl_basic_map_free(bmap);
o_div = isl_basic_map_offset(bmap, isl_dim_div);
n_div = isl_basic_map_dim(bmap, isl_dim_div);
if (n_div < 0)
return isl_basic_map_free(bmap);
for (i = 0; i < bmap->n_eq; ++i) {
l = isl_seq_first_non_zero(bmap->eq[i] + o_div + first,
n_div - (first));
if (l < 0)
continue;
l += first;
if (isl_seq_first_non_zero(bmap->eq[i] + o_div + l + 1,
n_div - (l + 1)) == -1)
continue;
break;
}
if (i >= bmap->n_eq)
return isl_basic_map_drop_redundant_divs_ineq(bmap);
ctx = isl_basic_map_get_ctx(bmap);
T = isl_mat_alloc(ctx, n_div - l, n_div - l);
if (!T)
return isl_basic_map_free(bmap);
isl_seq_cpy(T->row[0], bmap->eq[i] + o_div + l, n_div - l);
T = isl_mat_normalize_row(T, 0);
T = isl_mat_unimodular_complete(T, 1);
T = isl_mat_right_inverse(T);
for (i = l; i < n_div; ++i)
bmap = isl_basic_map_mark_div_unknown(bmap, i);
bmap = isl_basic_map_preimage_vars(bmap, o_div - 1 + l, T);
bmap = isl_basic_map_simplify(bmap);
return isl_basic_map_drop_redundant_divs(bmap);
}
/* Does "bmap" satisfy any equality that involves more than 2 variables
* and/or has coefficients different from -1 and 1?
*/
static isl_bool has_multiple_var_equality(__isl_keep isl_basic_map *bmap)
{
int i;
isl_size total;
total = isl_basic_map_dim(bmap, isl_dim_all);
if (total < 0)
return isl_bool_error;
for (i = 0; i < bmap->n_eq; ++i) {
int j, k;
j = isl_seq_first_non_zero(bmap->eq[i] + 1, total);
if (j < 0)
continue;
if (!isl_int_is_one(bmap->eq[i][1 + j]) &&
!isl_int_is_negone(bmap->eq[i][1 + j]))
return isl_bool_true;
j += 1;
k = isl_seq_first_non_zero(bmap->eq[i] + 1 + j, total - j);
if (k < 0)
continue;
j += k;
if (!isl_int_is_one(bmap->eq[i][1 + j]) &&
!isl_int_is_negone(bmap->eq[i][1 + j]))
return isl_bool_true;
j += 1;
k = isl_seq_first_non_zero(bmap->eq[i] + 1 + j, total - j);
if (k >= 0)
return isl_bool_true;
}
return isl_bool_false;
}
/* Remove any common factor g from the constraint coefficients in "v".
* The constant term is stored in the first position and is replaced
* by floor(c/g). If any common factor is removed and if this results
* in a tightening of the constraint, then set *tightened.
*/
static __isl_give isl_vec *normalize_constraint(__isl_take isl_vec *v,
int *tightened)
{
isl_ctx *ctx;
if (!v)
return NULL;
ctx = isl_vec_get_ctx(v);
isl_seq_gcd(v->el + 1, v->size - 1, &ctx->normalize_gcd);
if (isl_int_is_zero(ctx->normalize_gcd))
return v;
if (isl_int_is_one(ctx->normalize_gcd))
return v;
v = isl_vec_cow(v);
if (!v)
return NULL;
if (tightened && !isl_int_is_divisible_by(v->el[0], ctx->normalize_gcd))
*tightened = 1;
isl_int_fdiv_q(v->el[0], v->el[0], ctx->normalize_gcd);
isl_seq_scale_down(v->el + 1, v->el + 1, ctx->normalize_gcd,
v->size - 1);
return v;
}
/* If "bmap" is an integer set that satisfies any equality involving
* more than 2 variables and/or has coefficients different from -1 and 1,
* then use variable compression to reduce the coefficients by removing
* any (hidden) common factor.
* In particular, apply the variable compression to each constraint,
* factor out any common factor in the non-constant coefficients and
* then apply the inverse of the compression.
* At the end, we mark the basic map as having reduced constants.
* If this flag is still set on the next invocation of this function,
* then we skip the computation.
*
* Removing a common factor may result in a tightening of some of
* the constraints. If this happens, then we may end up with two
* opposite inequalities that can be replaced by an equality.
* We therefore call isl_basic_map_detect_inequality_pairs,
* which checks for such pairs of inequalities as well as eliminate_divs_eq
* and isl_basic_map_gauss if such a pair was found.
*
* Tightening may also result in some other constraints becoming
* (rationally) redundant with respect to the tightened constraint
* (in combination with other constraints). The basic map may
* therefore no longer be assumed to have no redundant constraints.
*
* Note that this function may leave the result in an inconsistent state.
* In particular, the constraints may not be gaussed.
* Unfortunately, isl_map_coalesce actually depends on this inconsistent state
* for some of the test cases to pass successfully.
* Any potential modification of the representation is therefore only
* performed on a single copy of the basic map.
*/
__isl_give isl_basic_map *isl_basic_map_reduce_coefficients(
__isl_take isl_basic_map *bmap)
{
isl_size total;
isl_bool multi;
isl_ctx *ctx;
isl_vec *v;
isl_mat *eq, *T, *T2;
int i;
int tightened;
if (!bmap)
return NULL;
if (ISL_F_ISSET(bmap, ISL_BASIC_MAP_REDUCED_COEFFICIENTS))
return bmap;
if (isl_basic_map_is_rational(bmap))
return bmap;
if (bmap->n_eq == 0)
return bmap;
multi = has_multiple_var_equality(bmap);
if (multi < 0)
return isl_basic_map_free(bmap);
if (!multi)
return bmap;
total = isl_basic_map_dim(bmap, isl_dim_all);
if (total < 0)
return isl_basic_map_free(bmap);
ctx = isl_basic_map_get_ctx(bmap);
v = isl_vec_alloc(ctx, 1 + total);
if (!v)
return isl_basic_map_free(bmap);
eq = isl_mat_sub_alloc6(ctx, bmap->eq, 0, bmap->n_eq, 0, 1 + total);
T = isl_mat_variable_compression(eq, &T2);
if (!T || !T2)
goto error;
if (T->n_col == 0) {
isl_mat_free(T);
isl_mat_free(T2);
isl_vec_free(v);
return isl_basic_map_set_to_empty(bmap);
}
bmap = isl_basic_map_cow(bmap);
if (!bmap)
goto error;
tightened = 0;
for (i = 0; i < bmap->n_ineq; ++i) {
isl_seq_cpy(v->el, bmap->ineq[i], 1 + total);
v = isl_vec_mat_product(v, isl_mat_copy(T));
v = normalize_constraint(v, &tightened);
v = isl_vec_mat_product(v, isl_mat_copy(T2));
if (!v)
goto error;
isl_seq_cpy(bmap->ineq[i], v->el, 1 + total);
}
isl_mat_free(T);
isl_mat_free(T2);
isl_vec_free(v);
ISL_F_SET(bmap, ISL_BASIC_MAP_REDUCED_COEFFICIENTS);
if (tightened) {
int progress = 0;
ISL_F_CLR(bmap, ISL_BASIC_MAP_NO_REDUNDANT);
bmap = isl_basic_map_detect_inequality_pairs(bmap, &progress);
if (progress) {
bmap = eliminate_divs_eq(bmap, &progress);
bmap = isl_basic_map_gauss(bmap, NULL);
}
}
return bmap;
error:
isl_mat_free(T);
isl_mat_free(T2);
isl_vec_free(v);
return isl_basic_map_free(bmap);
}
/* Shift the integer division at position "div" of "bmap"
* by "shift" times the variable at position "pos".
* "pos" is as determined by isl_basic_map_offset, i.e., pos == 0
* corresponds to the constant term.
*
* That is, if the integer division has the form
*
* floor(f(x)/d)
*
* then replace it by
*
* floor((f(x) + shift * d * x_pos)/d) - shift * x_pos
*/
__isl_give isl_basic_map *isl_basic_map_shift_div(
__isl_take isl_basic_map *bmap, int div, int pos, isl_int shift)
{
int i;
isl_size total, n_div;
if (isl_int_is_zero(shift))
return bmap;
total = isl_basic_map_dim(bmap, isl_dim_all);
n_div = isl_basic_map_dim(bmap, isl_dim_div);
total -= n_div;
if (total < 0 || n_div < 0)
return isl_basic_map_free(bmap);
isl_int_addmul(bmap->div[div][1 + pos], shift, bmap->div[div][0]);
for (i = 0; i < bmap->n_eq; ++i) {
if (isl_int_is_zero(bmap->eq[i][1 + total + div]))
continue;
isl_int_submul(bmap->eq[i][pos],
shift, bmap->eq[i][1 + total + div]);
}
for (i = 0; i < bmap->n_ineq; ++i) {
if (isl_int_is_zero(bmap->ineq[i][1 + total + div]))
continue;
isl_int_submul(bmap->ineq[i][pos],
shift, bmap->ineq[i][1 + total + div]);
}
for (i = 0; i < bmap->n_div; ++i) {
if (isl_int_is_zero(bmap->div[i][0]))
continue;
if (isl_int_is_zero(bmap->div[i][1 + 1 + total + div]))
continue;
isl_int_submul(bmap->div[i][1 + pos],
shift, bmap->div[i][1 + 1 + total + div]);
}
return bmap;
}
|
