nexmon – Rev 1
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/*
* Copyright 2008-2009 Katholieke Universiteit Leuven
*
* Use of this software is governed by the GNU LGPLv2.1 license
*
* Written by Sven Verdoolaege, K.U.Leuven, Departement
* Computerwetenschappen, Celestijnenlaan 200A, B-3001 Leuven, Belgium
*/
#include <strings.h>
#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>
static void swap_equality(struct 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(struct 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;
}
}
static void constraint_drop_vars(isl_int *c, unsigned n, unsigned rem)
{
isl_seq_cpy(c, c + n, rem);
isl_seq_clr(c + rem, n);
}
/* Drop n dimensions starting at first.
*
* In principle, this frees up some extra variables as the number
* of columns remains constant, but we would have to extend
* the div array too as the number of rows in this array is assumed
* to be equal to extra.
*/
struct isl_basic_set *isl_basic_set_drop_dims(
struct isl_basic_set *bset, unsigned first, unsigned n)
{
int i;
if (!bset)
goto error;
isl_assert(bset->ctx, first + n <= bset->dim->n_out, goto error);
if (n == 0 && !isl_space_get_tuple_name(bset->dim, isl_dim_set))
return bset;
bset = isl_basic_set_cow(bset);
if (!bset)
return NULL;
for (i = 0; i < bset->n_eq; ++i)
constraint_drop_vars(bset->eq[i]+1+bset->dim->nparam+first, n,
(bset->dim->n_out-first-n)+bset->extra);
for (i = 0; i < bset->n_ineq; ++i)
constraint_drop_vars(bset->ineq[i]+1+bset->dim->nparam+first, n,
(bset->dim->n_out-first-n)+bset->extra);
for (i = 0; i < bset->n_div; ++i)
constraint_drop_vars(bset->div[i]+1+1+bset->dim->nparam+first, n,
(bset->dim->n_out-first-n)+bset->extra);
bset->dim = isl_space_drop_outputs(bset->dim, first, n);
if (!bset->dim)
goto error;
ISL_F_CLR(bset, ISL_BASIC_SET_NORMALIZED);
bset = isl_basic_set_simplify(bset);
return isl_basic_set_finalize(bset);
error:
isl_basic_set_free(bset);
return NULL;
}
struct isl_set *isl_set_drop_dims(
struct isl_set *set, unsigned first, unsigned n)
{
int i;
if (!set)
goto error;
isl_assert(set->ctx, first + n <= set->dim->n_out, goto error);
if (n == 0 && !isl_space_get_tuple_name(set->dim, isl_dim_set))
return set;
set = isl_set_cow(set);
if (!set)
goto error;
set->dim = isl_space_drop_outputs(set->dim, first, n);
if (!set->dim)
goto error;
for (i = 0; i < set->n; ++i) {
set->p[i] = isl_basic_set_drop_dims(set->p[i], first, n);
if (!set->p[i])
goto error;
}
ISL_F_CLR(set, ISL_SET_NORMALIZED);
return set;
error:
isl_set_free(set);
return NULL;
}
/* Move "n" divs starting at "first" to the end of the list of divs.
*/
static struct isl_basic_map *move_divs_last(struct isl_basic_map *bmap,
unsigned first, unsigned n)
{
isl_int **div;
int i;
if (first + n == bmap->n_div)
return bmap;
div = isl_alloc_array(bmap->ctx, isl_int *, n);
if (!div)
goto error;
for (i = 0; i < n; ++i)
div[i] = bmap->div[first + i];
for (i = 0; i < bmap->n_div - first - n; ++i)
bmap->div[first + i] = bmap->div[first + n + i];
for (i = 0; i < n; ++i)
bmap->div[bmap->n_div - n + i] = div[i];
free(div);
return bmap;
error:
isl_basic_map_free(bmap);
return NULL;
}
/* Drop "n" dimensions of type "type" starting at "first".
*
* In principle, this frees up some extra variables as the number
* of columns remains constant, but we would have to extend
* the div array too as the number of rows in this array is assumed
* to be equal to extra.
*/
struct isl_basic_map *isl_basic_map_drop(struct isl_basic_map *bmap,
enum isl_dim_type type, unsigned first, unsigned n)
{
int i;
unsigned dim;
unsigned offset;
unsigned left;
if (!bmap)
goto error;
dim = isl_basic_map_dim(bmap, type);
isl_assert(bmap->ctx, first + n <= dim, goto error);
if (n == 0 && !isl_space_is_named_or_nested(bmap->dim, type))
return bmap;
bmap = isl_basic_map_cow(bmap);
if (!bmap)
return NULL;
offset = isl_basic_map_offset(bmap, type) + first;
left = isl_basic_map_total_dim(bmap) - (offset - 1) - n;
for (i = 0; i < bmap->n_eq; ++i)
constraint_drop_vars(bmap->eq[i]+offset, n, left);
for (i = 0; i < bmap->n_ineq; ++i)
constraint_drop_vars(bmap->ineq[i]+offset, n, left);
for (i = 0; i < bmap->n_div; ++i)
constraint_drop_vars(bmap->div[i]+1+offset, n, left);
if (type == isl_dim_div) {
bmap = move_divs_last(bmap, first, n);
if (!bmap)
goto error;
isl_basic_map_free_div(bmap, n);
} else
bmap->dim = isl_space_drop_dims(bmap->dim, type, first, n);
if (!bmap->dim)
goto error;
ISL_F_CLR(bmap, ISL_BASIC_MAP_NORMALIZED);
bmap = isl_basic_map_simplify(bmap);
return isl_basic_map_finalize(bmap);
error:
isl_basic_map_free(bmap);
return NULL;
}
__isl_give isl_basic_set *isl_basic_set_drop(__isl_take isl_basic_set *bset,
enum isl_dim_type type, unsigned first, unsigned n)
{
return (isl_basic_set *)isl_basic_map_drop((isl_basic_map *)bset,
type, first, n);
}
struct isl_basic_map *isl_basic_map_drop_inputs(
struct isl_basic_map *bmap, unsigned first, unsigned n)
{
return isl_basic_map_drop(bmap, isl_dim_in, first, n);
}
struct isl_map *isl_map_drop(struct isl_map *map,
enum isl_dim_type type, unsigned first, unsigned n)
{
int i;
if (!map)
goto error;
isl_assert(map->ctx, first + n <= isl_map_dim(map, type), goto error);
if (n == 0 && !isl_space_get_tuple_name(map->dim, type))
return map;
map = isl_map_cow(map);
if (!map)
goto error;
map->dim = isl_space_drop_dims(map->dim, type, first, n);
if (!map->dim)
goto error;
for (i = 0; i < map->n; ++i) {
map->p[i] = isl_basic_map_drop(map->p[i], type, first, n);
if (!map->p[i])
goto error;
}
ISL_F_CLR(map, ISL_MAP_NORMALIZED);
return map;
error:
isl_map_free(map);
return NULL;
}
struct isl_set *isl_set_drop(struct isl_set *set,
enum isl_dim_type type, unsigned first, unsigned n)
{
return (isl_set *)isl_map_drop((isl_map *)set, type, first, n);
}
struct isl_map *isl_map_drop_inputs(
struct isl_map *map, unsigned first, unsigned n)
{
return isl_map_drop(map, isl_dim_in, first, n);
}
/*
* We don't cow, as the div is assumed to be redundant.
*/
static struct isl_basic_map *isl_basic_map_drop_div(
struct isl_basic_map *bmap, unsigned div)
{
int i;
unsigned pos;
if (!bmap)
goto error;
pos = 1 + isl_space_dim(bmap->dim, isl_dim_all) + div;
isl_assert(bmap->ctx, div < bmap->n_div, goto error);
for (i = 0; i < bmap->n_eq; ++i)
constraint_drop_vars(bmap->eq[i]+pos, 1, bmap->extra-div-1);
for (i = 0; i < bmap->n_ineq; ++i) {
if (!isl_int_is_zero(bmap->ineq[i][pos])) {
isl_basic_map_drop_inequality(bmap, i);
--i;
continue;
}
constraint_drop_vars(bmap->ineq[i]+pos, 1, bmap->extra-div-1);
}
for (i = 0; i < bmap->n_div; ++i)
constraint_drop_vars(bmap->div[i]+1+pos, 1, bmap->extra-div-1);
if (div != bmap->n_div - 1) {
int j;
isl_int *t = bmap->div[div];
for (j = div; j < bmap->n_div - 1; ++j)
bmap->div[j] = bmap->div[j+1];
bmap->div[bmap->n_div - 1] = t;
}
ISL_F_CLR(bmap, ISL_BASIC_MAP_NORMALIZED);
isl_basic_map_free_div(bmap, 1);
return bmap;
error:
isl_basic_map_free(bmap);
return NULL;
}
struct isl_basic_map *isl_basic_map_normalize_constraints(
struct isl_basic_map *bmap)
{
int i;
isl_int gcd;
unsigned total = isl_basic_map_total_dim(bmap);
if (!bmap)
return NULL;
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;
}
isl_basic_map_drop_equality(bmap, i);
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;
}
isl_basic_map_drop_inequality(bmap, i);
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;
}
struct isl_basic_set *isl_basic_set_normalize_constraints(
struct isl_basic_set *bset)
{
return (struct isl_basic_set *)isl_basic_map_normalize_constraints(
(struct isl_basic_map *)bset);
}
/* Assumes divs have been ordered if keep_divs is set.
*/
static void eliminate_var_using_equality(struct isl_basic_map *bmap,
unsigned pos, isl_int *eq, int keep_divs, int *progress)
{
unsigned total;
unsigned space_total;
int k;
int last_div;
total = isl_basic_map_total_dim(bmap);
space_total = isl_space_dim(bmap->dim, isl_dim_all);
last_div = isl_seq_last_non_zero(eq + 1 + space_total, 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_NORMALIZED);
}
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]);
else
isl_seq_clr(bmap->div[k], 1 + total);
ISL_F_CLR(bmap, ISL_BASIC_MAP_NORMALIZED);
}
}
/* Assumes divs have been ordered if keep_divs is set.
*/
static void eliminate_div(struct isl_basic_map *bmap, isl_int *eq,
unsigned div, int keep_divs)
{
unsigned pos = isl_space_dim(bmap->dim, isl_dim_all) + div;
eliminate_var_using_equality(bmap, pos, eq, keep_divs, NULL);
isl_basic_map_drop_div(bmap, div);
}
/* Check if elimination of div "div" using equality "eq" would not
* result in a div depending on a later div.
*/
static int ok_to_eliminate_div(struct isl_basic_map *bmap, isl_int *eq,
unsigned div)
{
int k;
int last_div;
unsigned space_total = isl_space_dim(bmap->dim, isl_dim_all);
unsigned pos = space_total + div;
last_div = isl_seq_last_non_zero(eq + 1 + space_total, bmap->n_div);
if (last_div < 0 || last_div <= div)
return 1;
for (k = 0; k <= last_div; ++k) {
if (isl_int_is_zero(bmap->div[k][0]))
return 1;
if (!isl_int_is_zero(bmap->div[k][1 + 1 + pos]))
return 0;
}
return 1;
}
/* Elimininate divs based on equalities
*/
static struct isl_basic_map *eliminate_divs_eq(
struct 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 = 1 + isl_space_dim(bmap->dim, isl_dim_all);
for (d = bmap->n_div - 1; d >= 0 ; --d) {
for (i = 0; i < bmap->n_eq; ++i) {
if (!isl_int_is_one(bmap->eq[i][off + d]) &&
!isl_int_is_negone(bmap->eq[i][off + d]))
continue;
if (!ok_to_eliminate_div(bmap, bmap->eq[i], d))
continue;
modified = 1;
*progress = 1;
eliminate_div(bmap, bmap->eq[i], d, 1);
isl_basic_map_drop_equality(bmap, i);
break;
}
}
if (modified)
return eliminate_divs_eq(bmap, progress);
return bmap;
}
/* Elimininate divs based on inequalities
*/
static struct isl_basic_map *eliminate_divs_ineq(
struct isl_basic_map *bmap, int *progress)
{
int d;
int i;
unsigned off;
struct isl_ctx *ctx;
if (!bmap)
return NULL;
ctx = bmap->ctx;
off = 1 + isl_space_dim(bmap->dim, isl_dim_all);
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;
}
struct isl_basic_map *isl_basic_map_gauss(
struct isl_basic_map *bmap, int *progress)
{
int k;
int done;
int last_var;
unsigned total_var;
unsigned total;
bmap = isl_basic_map_order_divs(bmap);
if (!bmap)
return NULL;
total = isl_basic_map_total_dim(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 (isl_int_is_neg(bmap->eq[done][1+last_var]))
isl_seq_neg(bmap->eq[done], bmap->eq[done], 1+total);
eliminate_var_using_equality(bmap, last_var, bmap->eq[done], 1,
progress);
if (last_var >= total_var &&
isl_int_is_zero(bmap->div[last_var - total_var][0])) {
unsigned div = last_var - total_var;
isl_seq_neg(bmap->div[div]+1, bmap->eq[done], 1+total);
isl_int_set_si(bmap->div[div][1+1+last_var], 0);
isl_int_set(bmap->div[div][0],
bmap->eq[done][1+last_var]);
ISL_F_CLR(bmap, ISL_BASIC_MAP_NORMALIZED);
}
}
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;
return isl_basic_map_set_to_empty(bmap);
}
isl_basic_map_free_equality(bmap, bmap->n_eq-done);
return bmap;
}
struct isl_basic_set *isl_basic_set_gauss(
struct isl_basic_set *bset, int *progress)
{
return (struct isl_basic_set*)isl_basic_map_gauss(
(struct isl_basic_map *)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;
}
static int hash_index(isl_int ***index, unsigned int size, int bits,
struct isl_basic_map *bmap, int k)
{
int h;
unsigned total = isl_basic_map_total_dim(bmap);
uint32_t hash = isl_seq_get_hash_bits(bmap->ineq[k]+1, total, bits);
for (h = hash; index[h]; h = (h+1) % size)
if (&bmap->ineq[k] != index[h] &&
isl_seq_eq(bmap->ineq[k]+1, index[h][0]+1, total))
break;
return h;
}
static int set_hash_index(isl_int ***index, unsigned int size, int bits,
struct isl_basic_set *bset, int k)
{
return hash_index(index, size, bits, (struct isl_basic_map *)bset, k);
}
/* 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 struct isl_basic_map *remove_duplicate_divs(
struct isl_basic_map *bmap, int *progress)
{
unsigned int size;
int *index;
int *elim_for;
int k, l, h;
int bits;
struct isl_blk eq;
unsigned total_var;
unsigned total;
struct isl_ctx *ctx;
if (!bmap || bmap->n_div <= 1)
return bmap;
total_var = isl_space_dim(bmap->dim, isl_dim_all);
total = total_var + 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;
elim_for = isl_calloc_array(ctx, int, bmap->n_div);
size = round_up(4 * bmap->n_div / 3 - 1);
bits = ffs(size) - 1;
index = isl_calloc_array(ctx, int, size);
if (!index)
return bmap;
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+total_var+k], -1);
isl_int_set_si(eq.data[1+total_var+l], 1);
eliminate_div(bmap, eq.data, l, 0);
isl_int_set_si(eq.data[1+total_var+k], 0);
isl_int_set_si(eq.data[1+total_var+l], 0);
}
isl_blk_free(ctx, eq);
out:
free(index);
free(elim_for);
return bmap;
}
static int n_pure_div_eq(struct isl_basic_map *bmap)
{
int i, j;
unsigned total;
total = isl_space_dim(bmap->dim, isl_dim_all);
for (i = 0, j = bmap->n_div-1; i < bmap->n_eq; ++i) {
while (j >= 0 && isl_int_is_zero(bmap->eq[i][1 + total + j]))
--j;
if (j < 0)
break;
if (isl_seq_first_non_zero(bmap->eq[i] + 1 + total, 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 struct isl_basic_map *normalize_divs(
struct isl_basic_map *bmap, int *progress)
{
int i, j, k;
int total;
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;
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;
total = isl_space_dim(bmap->dim, isl_dim_all);
div_eq = n_pure_div_eq(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 + total);
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 + total + j]))
--j;
isl_int_set(d->block.data[i], bmap->eq[i][1 + total + j]);
}
B = isl_mat_sub_alloc6(bmap->ctx, bmap->eq, 0, div_eq, 0, 1 + total);
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 + total + j]))
break;
if (i < bmap->n_eq) {
bmap = isl_basic_map_drop_div(bmap, j);
isl_basic_map_drop_equality(bmap, i);
++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_space(bmap, isl_space_copy(bmap->dim),
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 + total + k;
isl_seq_clr(bmap->div[k] + 1, 1 + total + 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 + total);
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 + total);
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+total+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:
isl_mat_free(C);
isl_mat_free(C2);
isl_mat_free(T);
return bmap;
}
static struct isl_basic_map *set_div_from_lower_bound(
struct isl_basic_map *bmap, int div, int ineq)
{
unsigned total = 1 + isl_space_dim(bmap->dim, isl_dim_all);
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 int ok_to_set_div_from_bound(struct isl_basic_map *bmap,
int div, int ineq)
{
int j;
unsigned total = 1 + isl_space_dim(bmap->dim, isl_dim_all);
/* 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 0;
}
/* 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 0;
}
return 1;
}
/* 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.
* "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 struct isl_basic_map *check_for_div_constraints(
struct isl_basic_map *bmap, int k, int l, isl_int sum, int *progress)
{
int i;
unsigned total = 1 + isl_space_dim(bmap->dim, isl_dim_all);
for (i = 0; i < bmap->n_div; ++i) {
if (!isl_int_is_zero(bmap->div[i][0]))
continue;
if (isl_int_is_zero(bmap->ineq[k][total + i]))
continue;
if (isl_int_abs_ge(sum, bmap->ineq[k][total + i]))
continue;
if (!ok_to_set_div_from_bound(bmap, i, k))
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;
}
static struct isl_basic_map *remove_duplicate_constraints(
struct isl_basic_map *bmap, int *progress, int detect_divs)
{
unsigned int size;
isl_int ***index;
int k, l, h;
int bits;
unsigned total = isl_basic_map_total_dim(bmap);
isl_int sum;
isl_ctx *ctx;
if (!bmap || bmap->n_ineq <= 1)
return bmap;
size = round_up(4 * (bmap->n_ineq+1) / 3 - 1);
bits = ffs(size) - 1;
ctx = isl_basic_map_get_ctx(bmap);
index = isl_calloc_array(ctx, isl_int **, size);
if (!index)
return bmap;
index[isl_seq_get_hash_bits(bmap->ineq[0]+1, total, bits)] = &bmap->ineq[0];
for (k = 1; k < bmap->n_ineq; ++k) {
h = hash_index(index, size, bits, bmap, k);
if (!index[h]) {
index[h] = &bmap->ineq[k];
continue;
}
if (progress)
*progress = 1;
l = 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; k < bmap->n_ineq-1; ++k) {
isl_seq_neg(bmap->ineq[k]+1, bmap->ineq[k]+1, total);
h = hash_index(index, size, bits, bmap, k);
isl_seq_neg(bmap->ineq[k]+1, bmap->ineq[k]+1, total);
if (!index[h])
continue;
l = 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);
free(index);
return bmap;
}
struct isl_basic_map *isl_basic_map_simplify(struct isl_basic_map *bmap)
{
int progress = 1;
if (!bmap)
return NULL;
while (progress) {
progress = 0;
bmap = isl_basic_map_normalize_constraints(bmap);
bmap = remove_duplicate_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 = remove_duplicate_constraints(bmap, &progress, 1);
}
return bmap;
}
struct isl_basic_set *isl_basic_set_simplify(struct isl_basic_set *bset)
{
return (struct isl_basic_set *)
isl_basic_map_simplify((struct isl_basic_map *)bset);
}
int isl_basic_map_is_div_constraint(__isl_keep isl_basic_map *bmap,
isl_int *constraint, unsigned div)
{
unsigned pos;
if (!bmap)
return -1;
pos = 1 + isl_space_dim(bmap->dim, isl_dim_all) + 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 0;
if (isl_seq_first_non_zero(constraint+pos+1,
bmap->n_div-div-1) != -1)
return 0;
} else if (isl_int_abs_eq(constraint[pos], bmap->div[div][0])) {
if (!isl_seq_eq(constraint, bmap->div[div]+1, pos))
return 0;
if (isl_seq_first_non_zero(constraint+pos+1,
bmap->n_div-div-1) != -1)
return 0;
} else
return 0;
return 1;
}
int isl_basic_set_is_div_constraint(__isl_keep isl_basic_set *bset,
isl_int *constraint, unsigned div)
{
return isl_basic_map_is_div_constraint(bset, constraint, div);
}
/* 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 int div_is_redundant(struct isl_basic_map *bmap, int div)
{
int i;
unsigned pos = 1 + isl_space_dim(bmap->dim, isl_dim_all) + div;
for (i = 0; i < bmap->n_eq; ++i)
if (!isl_int_is_zero(bmap->eq[i][pos]))
return 0;
for (i = 0; i < bmap->n_ineq; ++i) {
if (isl_int_is_zero(bmap->ineq[i][pos]))
continue;
if (!isl_basic_map_is_div_constraint(bmap, bmap->ineq[i], div))
return 0;
}
for (i = 0; i < bmap->n_div; ++i)
if (!isl_int_is_zero(bmap->div[i][1+pos]))
return 0;
return 1;
}
/*
* Remove divs that don't occur in any of the constraints or other divs.
* These can arise when dropping some of the variables in a quast
* returned by piplib.
*/
static struct isl_basic_map *remove_redundant_divs(struct isl_basic_map *bmap)
{
int i;
if (!bmap)
return NULL;
for (i = bmap->n_div-1; i >= 0; --i) {
if (!div_is_redundant(bmap, i))
continue;
bmap = isl_basic_map_drop_div(bmap, i);
}
return bmap;
}
struct isl_basic_map *isl_basic_map_finalize(struct isl_basic_map *bmap)
{
bmap = remove_redundant_divs(bmap);
if (!bmap)
return NULL;
ISL_F_SET(bmap, ISL_BASIC_SET_FINAL);
return bmap;
}
struct isl_basic_set *isl_basic_set_finalize(struct isl_basic_set *bset)
{
return (struct isl_basic_set *)
isl_basic_map_finalize((struct isl_basic_map *)bset);
}
struct isl_set *isl_set_finalize(struct isl_set *set)
{
int i;
if (!set)
return NULL;
for (i = 0; i < set->n; ++i) {
set->p[i] = isl_basic_set_finalize(set->p[i]);
if (!set->p[i])
goto error;
}
return set;
error:
isl_set_free(set);
return NULL;
}
struct isl_map *isl_map_finalize(struct isl_map *map)
{
int i;
if (!map)
return NULL;
for (i = 0; i < map->n; ++i) {
map->p[i] = isl_basic_map_finalize(map->p[i]);
if (!map->p[i])
goto error;
}
ISL_F_CLR(map, ISL_MAP_NORMALIZED);
return map;
error:
isl_map_free(map);
return NULL;
}
/* 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 struct isl_basic_map *remove_dependent_vars(struct isl_basic_map *bmap,
int pos)
{
int i;
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;
isl_int_set_si(bmap->div[i][0], 0);
}
return bmap;
}
/* Eliminate the specified variables from the constraints using
* Fourier-Motzkin. The variables themselves are not removed.
*/
struct isl_basic_map *isl_basic_map_eliminate_vars(
struct isl_basic_map *bmap, unsigned pos, unsigned n)
{
int d;
int i, j, k;
unsigned total;
int need_gauss = 0;
if (n == 0)
return bmap;
if (!bmap)
return NULL;
total = isl_basic_map_total_dim(bmap);
bmap = isl_basic_map_cow(bmap);
for (d = pos + n - 1; d >= 0 && d >= pos; --d)
bmap = remove_dependent_vars(bmap, d);
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;
eliminate_var_using_equality(bmap, d, bmap->eq[i], 0, NULL);
isl_basic_map_drop_equality(bmap, i);
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 = 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;
}
}
ISL_F_CLR(bmap, ISL_BASIC_MAP_NORMALIZED);
if (need_gauss)
bmap = isl_basic_map_gauss(bmap, NULL);
return bmap;
error:
isl_basic_map_free(bmap);
return NULL;
}
struct isl_basic_set *isl_basic_set_eliminate_vars(
struct isl_basic_set *bset, unsigned pos, unsigned n)
{
return (struct isl_basic_set *)isl_basic_map_eliminate_vars(
(struct isl_basic_map *)bset, pos, n);
}
/* Eliminate the specified n dimensions starting at first from the
* constraints using Fourier-Motzkin. The dimensions themselves
* are not removed.
*/
__isl_give isl_basic_map *isl_basic_map_eliminate(
__isl_take isl_basic_map *bmap,
enum isl_dim_type type, unsigned first, unsigned n)
{
if (!bmap)
return NULL;
if (n == 0)
return bmap;
if (first + n > isl_basic_map_dim(bmap, type))
isl_die(bmap->ctx, isl_error_invalid,
"index out of bounds", goto error);
first += isl_basic_map_offset(bmap, type) - 1;
bmap = isl_basic_map_eliminate_vars(bmap, first, n);
return isl_basic_map_finalize(bmap);
error:
isl_basic_map_free(bmap);
return NULL;
}
/* Don't assume equalities are in order, because align_divs
* may have changed the order of the divs.
*/
static void compute_elimination_index(struct isl_basic_map *bmap, int *elim)
{
int d, i;
unsigned total;
total = isl_space_dim(bmap->dim, isl_dim_all);
for (d = 0; d < total; ++d)
elim[d] = -1;
for (i = 0; i < bmap->n_eq; ++i) {
for (d = total - 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(struct isl_basic_set *bset, int *elim)
{
compute_elimination_index((struct isl_basic_map *)bset, elim);
}
static int reduced_using_equalities(isl_int *dst, isl_int *src,
struct isl_basic_map *bmap, int *elim)
{
int d;
int copied = 0;
unsigned total;
total = isl_space_dim(bmap->dim, isl_dim_all);
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,
struct isl_basic_set *bset, int *elim)
{
return reduced_using_equalities(dst, src,
(struct isl_basic_map *)bset, elim);
}
static struct isl_basic_set *isl_basic_set_reduce_using_equalities(
struct isl_basic_set *bset, struct isl_basic_set *context)
{
int i;
int *elim;
if (!bset || !context)
goto error;
if (context->n_eq == 0) {
isl_basic_set_free(context);
return bset;
}
bset = isl_basic_set_cow(bset);
if (!bset)
goto error;
elim = isl_alloc_array(bset->ctx, int, isl_basic_set_n_dim(bset));
if (!elim)
goto error;
set_compute_elimination_index(context, elim);
for (i = 0; i < bset->n_eq; ++i)
set_reduced_using_equalities(bset->eq[i], bset->eq[i],
context, elim);
for (i = 0; i < bset->n_ineq; ++i)
set_reduced_using_equalities(bset->ineq[i], bset->ineq[i],
context, elim);
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;
}
static struct isl_basic_set *remove_shifted_constraints(
struct isl_basic_set *bset, struct isl_basic_set *context)
{
unsigned int size;
isl_int ***index;
int bits;
int k, h, l;
isl_ctx *ctx;
if (!bset)
return NULL;
size = round_up(4 * (context->n_ineq+1) / 3 - 1);
bits = ffs(size) - 1;
ctx = isl_basic_set_get_ctx(bset);
index = isl_calloc_array(ctx, isl_int **, size);
if (!index)
return bset;
for (k = 0; k < context->n_ineq; ++k) {
h = set_hash_index(index, size, bits, context, k);
index[h] = &context->ineq[k];
}
for (k = 0; k < bset->n_ineq; ++k) {
h = set_hash_index(index, size, bits, bset, k);
if (!index[h])
continue;
l = index[h] - &context->ineq[0];
if (isl_int_lt(bset->ineq[k][0], context->ineq[l][0]))
continue;
bset = isl_basic_set_cow(bset);
if (!bset)
goto error;
isl_basic_set_drop_inequality(bset, k);
--k;
}
free(index);
return bset;
error:
free(index);
return bset;
}
/* Remove all information from bset that is redundant in the context
* of context. Both bset and context are assumed to be full-dimensional.
*
* We first * remove the inequalities from "bset"
* that are obviously redundant with respect to some inequality 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_basic_set *context)
{
int i, k;
isl_basic_set *combined = NULL;
struct isl_tab *tab = NULL;
unsigned context_ineq;
unsigned total;
if (!bset || !context)
goto error;
if (isl_basic_set_is_universe(bset)) {
isl_basic_set_free(context);
return bset;
}
if (isl_basic_set_is_universe(context)) {
isl_basic_set_free(context);
return bset;
}
bset = remove_shifted_constraints(bset, context);
if (!bset)
goto error;
if (bset->n_ineq == 0)
goto done;
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, i) < 0)
goto error;
tab = isl_tab_extend(tab, bset->n_ineq);
for (i = 0; i < bset->n_ineq; ++i)
if (isl_tab_add_ineq(tab, bset->ineq[i]) < 0)
goto error;
bset = isl_basic_set_add_constraints(combined, bset, 0);
combined = NULL;
if (!bset)
goto error;
if (isl_tab_detect_redundant(tab) < 0)
goto error;
total = isl_basic_set_total_dim(bset);
for (i = context_ineq; i < bset->n_ineq; ++i) {
int is_empty;
if (tab->con[i].is_redundant)
continue;
tab->con[i].is_redundant = 1;
combined = isl_basic_set_dup(bset);
combined = isl_basic_set_update_from_tab(combined, tab);
combined = isl_basic_set_extend_constraints(combined, 0, 1);
k = isl_basic_set_alloc_inequality(combined);
if (k < 0)
goto error;
isl_seq_neg(combined->ineq[k], bset->ineq[i], 1 + total);
isl_int_sub_ui(combined->ineq[k][0], combined->ineq[k][0], 1);
is_empty = isl_basic_set_is_empty(combined);
if (is_empty < 0)
goto error;
isl_basic_set_free(combined);
combined = NULL;
if (!is_empty)
tab->con[i].is_redundant = 0;
}
for (i = 0; i < context_ineq; ++i)
tab->con[i].is_redundant = 1;
bset = isl_basic_set_update_from_tab(bset, tab);
if (bset) {
ISL_F_SET(bset, ISL_BASIC_SET_NO_IMPLICIT);
ISL_F_SET(bset, ISL_BASIC_SET_NO_REDUNDANT);
}
isl_tab_free(tab);
done:
bset = isl_basic_set_simplify(bset);
bset = isl_basic_set_finalize(bset);
isl_basic_set_free(context);
return bset;
error:
isl_tab_free(tab);
isl_basic_set_free(combined);
isl_basic_set_free(context);
isl_basic_set_free(bset);
return NULL;
}
/* 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.
*
* We first compute the integer affine hull of the intersection,
* compute the gist inside this affine hull and then add back
* those equalities that are not implied by the context.
*
* 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, *T2;
isl_basic_set *aff;
isl_basic_set *aff_context;
unsigned total;
if (!bset || !context)
goto error;
bset = isl_basic_set_intersect(bset, isl_basic_set_copy(context));
if (isl_basic_set_plain_is_empty(bset)) {
isl_basic_set_free(context);
return bset;
}
bset = isl_basic_set_sort_constraints(bset);
aff = isl_basic_set_affine_hull(isl_basic_set_copy(bset));
if (!aff)
goto error;
if (isl_basic_set_plain_is_empty(aff)) {
isl_basic_set_free(aff);
isl_basic_set_free(context);
return bset;
}
if (aff->n_eq == 0) {
isl_basic_set_free(aff);
return uset_gist_full(bset, context);
}
total = isl_basic_set_total_dim(bset);
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, &T2);
if (T && T->n_col == 0) {
isl_mat_free(T);
isl_mat_free(T2);
isl_basic_set_free(context);
isl_basic_set_free(aff);
return isl_basic_set_set_to_empty(bset);
}
aff_context = isl_basic_set_affine_hull(isl_basic_set_copy(context));
bset = isl_basic_set_preimage(bset, isl_mat_copy(T));
context = isl_basic_set_preimage(context, T);
bset = uset_gist_full(bset, context);
bset = isl_basic_set_preimage(bset, T2);
bset = isl_basic_set_intersect(bset, aff);
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;
}
/* Normalize the divs in "bmap" in the context of the equalities in "context".
* We simply add the equalities in context to bmap and then do a regular
* div normalizations. Better results can be obtained by normalizing
* only the divs in bmap than do not also appear in context.
* We need to be careful to reduce the divs using the equalities
* so that later calls to isl_basic_map_overlying_set wouldn't introduce
* spurious constraints.
*/
static struct isl_basic_map *normalize_divs_in_context(
struct isl_basic_map *bmap, struct isl_basic_map *context)
{
int i;
unsigned total_context;
int div_eq;
div_eq = n_pure_div_eq(bmap);
if (div_eq == 0)
return bmap;
if (context->n_div > 0)
bmap = isl_basic_map_align_divs(bmap, context);
total_context = isl_basic_map_total_dim(context);
bmap = isl_basic_map_extend_constraints(bmap, context->n_eq, 0);
for (i = 0; i < context->n_eq; ++i) {
int k;
k = isl_basic_map_alloc_equality(bmap);
isl_seq_cpy(bmap->eq[k], context->eq[i], 1 + total_context);
isl_seq_clr(bmap->eq[k] + 1 + total_context,
isl_basic_map_total_dim(bmap) - total_context);
}
bmap = isl_basic_map_gauss(bmap, NULL);
bmap = normalize_divs(bmap, NULL);
bmap = isl_basic_map_gauss(bmap, NULL);
return bmap;
}
struct isl_basic_map *isl_basic_map_gist(struct isl_basic_map *bmap,
struct isl_basic_map *context)
{
struct isl_basic_set *bset;
if (!bmap || !context)
goto error;
if (isl_basic_map_is_universe(bmap)) {
isl_basic_map_free(context);
return bmap;
}
if (isl_basic_map_plain_is_empty(context)) {
isl_basic_map_free(bmap);
return context;
}
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);
if (context->n_eq)
bmap = normalize_divs_in_context(bmap, context);
context = isl_basic_map_align_divs(context, bmap);
bmap = isl_basic_map_align_divs(bmap, context);
bset = uset_gist(isl_basic_map_underlying_set(isl_basic_map_copy(bmap)),
isl_basic_map_underlying_set(context));
return isl_basic_map_overlying_set(bset, 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_map_free(map);
return isl_map_from_basic_map(context);
}
context = isl_basic_map_remove_redundancies(context);
map = isl_map_cow(map);
if (!map || !context)
goto error;;
isl_assert(map->ctx, isl_space_is_equal(map->dim, context->dim), goto error);
map = isl_map_compute_divs(map);
for (i = 0; i < map->n; ++i)
context = isl_basic_map_align_divs(context, map->p[i]);
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;
}
static __isl_give isl_map *map_gist(__isl_take isl_map *map,
__isl_take isl_map *context)
{
context = isl_map_compute_divs(context);
return isl_map_gist_basic_map(map, isl_map_simple_hull(context));
}
__isl_give isl_map *isl_map_gist(__isl_take isl_map *map,
__isl_take isl_map *context)
{
return isl_map_align_params_map_map_and(map, context, &map_gist);
}
struct isl_basic_set *isl_basic_set_gist(struct isl_basic_set *bset,
struct isl_basic_set *context)
{
return (struct isl_basic_set *)isl_basic_map_gist(
(struct isl_basic_map *)bset, (struct isl_basic_map *)context);
}
__isl_give isl_set *isl_set_gist_basic_set(__isl_take isl_set *set,
__isl_take isl_basic_set *context)
{
return (struct isl_set *)isl_map_gist_basic_map((struct isl_map *)set,
(struct isl_basic_map *)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 (struct isl_set *)isl_map_gist((struct isl_map *)set,
(struct isl_map *)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.
*/
int 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;
unsigned total;
int i;
if (!bmap1 || !bmap2)
return -1;
isl_assert(bmap1->ctx, isl_space_is_equal(bmap1->dim, bmap2->dim),
return -1);
if (bmap1->n_div || bmap2->n_div)
return 0;
if (!bmap1->n_eq && !bmap2->n_eq)
return 0;
total = isl_space_dim(bmap1->dim, isl_dim_all);
if (total == 0)
return 0;
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);
for (i = 0; i < bmap2->n_eq; ++i) {
int reduced;
reduced = reduced_using_equalities(v->block.data, bmap2->eq[i],
bmap1, elim);
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);
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);
for (i = 0; i < bmap1->n_ineq; ++i) {
int reduced;
reduced = reduced_using_equalities(v->block.data,
bmap1->ineq[i], bmap2, elim);
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 0;
disjoint:
isl_vec_free(v);
free(elim);
return 1;
error:
isl_vec_free(v);
free(elim);
return -1;
}
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((struct isl_basic_map *)bset1,
(struct isl_basic_map *)bset2);
}
int isl_map_plain_is_disjoint(__isl_keep isl_map *map1,
__isl_keep isl_map *map2)
{
int i, j;
if (!map1 || !map2)
return -1;
if (isl_map_plain_is_equal(map1, map2))
return 0;
for (i = 0; i < map1->n; ++i) {
for (j = 0; j < map2->n; ++j) {
int d = isl_basic_map_plain_is_disjoint(map1->p[i],
map2->p[j]);
if (d != 1)
return d;
}
}
return 1;
}
int isl_set_plain_is_disjoint(__isl_keep isl_set *set1,
__isl_keep isl_set *set2)
{
return isl_map_plain_is_disjoint((struct isl_map *)set1,
(struct isl_map *)set2);
}
int isl_set_fast_is_disjoint(__isl_keep isl_set *set1, __isl_keep isl_set *set2)
{
return isl_set_plain_is_disjoint(set1, set2);
}
/* 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 -1.
*
* 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 (execpt for the lower and upper bound)
* are of the form
*
* e + f (a + m b) >= 0
*
* 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(struct isl_basic_map *bmap, int *pairs,
unsigned div, unsigned l, unsigned u)
{
int i, j;
unsigned dim;
int coalesce = -1;
if (bmap->n_div <= 1)
return -1;
dim = isl_space_dim(bmap->dim, isl_dim_all);
if (isl_seq_first_non_zero(bmap->ineq[l] + 1 + dim, div) != -1)
return -1;
if (isl_seq_first_non_zero(bmap->ineq[l] + 1 + dim + div + 1,
bmap->n_div - div - 1) != -1)
return -1;
if (!isl_seq_is_neg(bmap->ineq[l] + 1, bmap->ineq[u] + 1,
dim + bmap->n_div))
return -1;
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 + dim + div]))
return -1;
}
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 -1;
}
isl_int_add_ui(bmap->ineq[l][0], bmap->ineq[l][0], 1);
for (i = 0; i < bmap->n_div; ++i) {
if (i == div)
continue;
if (!pairs[i])
continue;
for (j = 0; j < bmap->n_div; ++j) {
if (isl_int_is_zero(bmap->div[j][0]))
continue;
if (!isl_int_is_zero(bmap->div[j][1 + 1 + dim + i]))
break;
}
if (j < bmap->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 + dim + div]))
continue;
if (isl_int_is_zero(bmap->ineq[j][1 + dim + i]))
break;
isl_int_mul(bmap->ineq[j][1 + dim + div],
bmap->ineq[j][1 + dim + div],
bmap->ineq[l][0]);
valid = isl_int_eq(bmap->ineq[j][1 + dim + div],
bmap->ineq[j][1 + dim + i]);
isl_int_divexact(bmap->ineq[j][1 + dim + div],
bmap->ineq[j][1 + dim + 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;
}
/* Given a lower and an upper bound on div i, construct an inequality
* that when nonnegative ensures that this pair of bounds always allows
* for an integer value of the given div.
* The lower bound is inequality l, while the upper bound is inequality u.
* The constructed inequality is stored in ineq.
* g, fl, fu are temporary scalars.
*
* 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
*/
static void construct_test_ineq(struct isl_basic_map *bmap, int i,
int l, int u, isl_int *ineq, isl_int g, isl_int fl, isl_int fu)
{
unsigned dim;
dim = isl_space_dim(bmap->dim, isl_dim_all);
isl_int_gcd(g, bmap->ineq[l][1 + dim + i], bmap->ineq[u][1 + dim + i]);
isl_int_divexact(fl, bmap->ineq[l][1 + dim + i], g);
isl_int_divexact(fu, bmap->ineq[u][1 + dim + i], g);
isl_int_neg(fu, fu);
isl_seq_combine(ineq, fl, bmap->ineq[u], fu, bmap->ineq[l],
1 + dim + bmap->n_div);
isl_int_add(ineq[0], ineq[0], fl);
isl_int_add(ineq[0], ineq[0], fu);
isl_int_sub_ui(ineq[0], ineq[0], 1);
isl_int_mul(g, g, fl);
isl_int_mul(g, g, fu);
isl_int_sub(ineq[0], ineq[0], g);
}
/* 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,
* the we can eliminate the div using Fourier-Motzkin without
* introducing any spurious solutions.
*/
static struct isl_basic_map *drop_more_redundant_divs(
struct isl_basic_map *bmap, int *pairs, int n)
{
struct isl_tab *tab = NULL;
struct isl_vec *vec = NULL;
unsigned dim;
int remove = -1;
isl_int g, fl, fu;
isl_int_init(g);
isl_int_init(fl);
isl_int_init(fu);
if (!bmap)
goto error;
dim = isl_space_dim(bmap->dim, isl_dim_all);
vec = isl_vec_alloc(bmap->ctx, 1 + dim + bmap->n_div);
if (!vec)
goto error;
tab = isl_tab_from_basic_map(bmap, 0);
while (n > 0) {
int i, l, u;
int best = -1;
enum isl_lp_result res;
for (i = 0; i < bmap->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][1 + dim + i]))
continue;
for (u = 0; u < bmap->n_ineq; ++u) {
if (!isl_int_is_neg(bmap->ineq[u][1 + dim + i]))
continue;
construct_test_ineq(bmap, i, l, u,
vec->el, g, fl, fu);
res = isl_tab_min(tab, vec->el,
bmap->ctx->one, &g, NULL, 0);
if (res == isl_lp_error)
goto error;
if (res == isl_lp_empty) {
bmap = isl_basic_map_set_to_empty(bmap);
break;
}
if (res != isl_lp_ok || isl_int_is_neg(g))
break;
}
if (u < bmap->n_ineq)
break;
}
if (l == bmap->n_ineq) {
remove = i;
break;
}
pairs[i] = 0;
--n;
}
isl_tab_free(tab);
isl_vec_free(vec);
isl_int_clear(g);
isl_int_clear(fl);
isl_int_clear(fu);
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);
isl_tab_free(tab);
isl_vec_free(vec);
isl_int_clear(g);
isl_int_clear(fl);
isl_int_clear(fu);
return NULL;
}
/* Given a pair of divs div1 and div2 such that, expect 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
* (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 the l be
*
* div1 + f >=0
*
* and u
*
* -div1 + f' >= 0
*
* A lower bound on div2
*
* n div2 + t >= 0
*
* can be replaced by
*
* (n * (m div 2 + div1) + m t + n f)/g >= 0
*
* with g = gcd(m,n).
* An upper bound
*
* -n div2 + t >= 0
*
* can be replaced by
*
* (-n * (m div2 + div1) + m t + n f')/g >= 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.
*/
static struct isl_basic_map *coalesce_divs(struct isl_basic_map *bmap,
unsigned div1, unsigned div2, unsigned l, unsigned u)
{
isl_int a;
isl_int b;
isl_int m;
unsigned dim, total;
int i;
dim = isl_space_dim(bmap->dim, isl_dim_all);
total = 1 + dim + bmap->n_div;
isl_int_init(a);
isl_int_init(b);
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 + dim + div2]))
continue;
if (isl_int_is_zero(bmap->ineq[i][1 + dim + div1])) {
isl_int_gcd(b, m, bmap->ineq[i][1 + dim + div2]);
isl_int_divexact(a, m, b);
isl_int_divexact(b, bmap->ineq[i][1 + dim + div2], b);
if (isl_int_is_pos(b)) {
isl_seq_combine(bmap->ineq[i], a, bmap->ineq[i],
b, bmap->ineq[l], total);
} else {
isl_int_neg(b, b);
isl_seq_combine(bmap->ineq[i], a, bmap->ineq[i],
b, bmap->ineq[u], total);
}
}
isl_int_set(bmap->ineq[i][1 + dim + div2],
bmap->ineq[i][1 + dim + div1]);
isl_int_set_si(bmap->ineq[i][1 + dim + div1], 0);
}
isl_int_clear(a);
isl_int_clear(b);
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_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 struct isl_basic_map *coalesce_or_drop_more_redundant_divs(
struct isl_basic_map *bmap, int *pairs, int n)
{
int i, l, u;
unsigned dim;
dim = isl_space_dim(bmap->dim, isl_dim_all);
for (i = 0; i < bmap->n_div; ++i) {
if (!pairs[i])
continue;
for (l = 0; l < bmap->n_ineq; ++l) {
if (!isl_int_is_one(bmap->ineq[l][1 + dim + i]))
continue;
for (u = 0; u < bmap->n_ineq; ++u) {
int c;
if (!isl_int_is_negone(bmap->ineq[u][1+dim+i]))
continue;
c = div_find_coalesce(bmap, pairs, i, l, u);
if (c < 0)
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))
return bmap;
return drop_more_redundant_divs(bmap, pairs, n);
}
/* Remove divs that are not strictly needed.
* In particular, if a div only occurs positively (or negatively)
* in constraints, then it can simply be dropped.
* Also, if a div occurs only occurs in 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 coefficent of the div in the constraints,
* then we can also simply drop the div.
*
* If any divs are left after these simple checks then we move on
* to more complicated cases in drop_more_redundant_divs.
*/
struct isl_basic_map *isl_basic_map_drop_redundant_divs(
struct isl_basic_map *bmap)
{
int i, j;
unsigned off;
int *pairs = NULL;
int n = 0;
if (!bmap)
goto error;
off = isl_space_dim(bmap->dim, isl_dim_all);
pairs = isl_calloc_array(bmap->ctx, int, bmap->n_div);
if (!pairs)
goto error;
for (i = 0; i < bmap->n_div; ++i) {
int pos, neg;
int last_pos, last_neg;
int redundant;
int defined;
defined = !isl_int_is_zero(bmap->div[i][0]);
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);
free(pairs);
return isl_basic_map_drop_redundant_divs(bmap);
}
if (pairs[i] != 1)
continue;
if (!isl_seq_is_neg(bmap->ineq[last_pos] + 1,
bmap->ineq[last_neg] + 1,
off + bmap->n_div))
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) {
if (defined ||
!ok_to_set_div_from_bound(bmap, i, last_pos)) {
pairs[i] = 0;
--n;
continue;
}
bmap = set_div_from_lower_bound(bmap, i, last_pos);
bmap = isl_basic_map_simplify(bmap);
free(pairs);
return isl_basic_map_drop_redundant_divs(bmap);
}
if (last_pos > last_neg) {
isl_basic_map_drop_inequality(bmap, last_pos);
isl_basic_map_drop_inequality(bmap, last_neg);
} else {
isl_basic_map_drop_inequality(bmap, last_neg);
isl_basic_map_drop_inequality(bmap, last_pos);
}
bmap = isl_basic_map_drop_div(bmap, i);
free(pairs);
return isl_basic_map_drop_redundant_divs(bmap);
}
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;
}
struct isl_basic_set *isl_basic_set_drop_redundant_divs(
struct isl_basic_set *bset)
{
return (struct isl_basic_set *)
isl_basic_map_drop_redundant_divs((struct isl_basic_map *)bset);
}
struct isl_map *isl_map_drop_redundant_divs(struct isl_map *map)
{
int i;
if (!map)
return NULL;
for (i = 0; i < map->n; ++i) {
map->p[i] = isl_basic_map_drop_redundant_divs(map->p[i]);
if (!map->p[i])
goto error;
}
ISL_F_CLR(map, ISL_MAP_NORMALIZED);
return map;
error:
isl_map_free(map);
return NULL;
}
struct isl_set *isl_set_drop_redundant_divs(struct isl_set *set)
{
return (struct isl_set *)
isl_map_drop_redundant_divs((struct isl_map *)set);
}