X-Git-Url: http://review.tizen.org/git/?a=blobdiff_plain;f=isl_map_simplify.c;h=b797b5ed1a997c0045a762f2f9356105dc1b8266;hb=f67c8d827f8f5d394962bb9cc8f4b6bbb992e1e1;hp=8e6a5e066faf99cc4b4e22445ab2909ce2d74232;hpb=891934ff1dc59be6098a05d64fedba350bb62150;p=platform%2Fupstream%2Fisl.git

diff --git a/isl_map_simplify.c b/isl_map_simplify.c
index 8e6a5e0..b797b5e 100644
--- a/isl_map_simplify.c
+++ b/isl_map_simplify.c
@@ -872,6 +872,92 @@ error:
 	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_dim_total(bmap->dim);
+
+	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_dim_total(bmap->dim);
+
+	/* 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, j;
+	unsigned total = 1 + isl_dim_total(bmap->dim);
+
+	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)
 {
@@ -915,8 +1001,11 @@ static struct isl_basic_map *remove_duplicate_constraints(
 			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 (isl_int_is_pos(sum)) {
+			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
@@ -1720,15 +1809,15 @@ int isl_basic_map_fast_is_disjoint(struct isl_basic_map *bmap1,
 		    isl_seq_first_non_zero(v->block.data + 1, total) == -1)
 			goto disjoint;
 	}
-	isl_vec_free(bmap1->ctx, v);
+	isl_vec_free(v);
 	free(elim);
 	return 0;
 disjoint:
-	isl_vec_free(bmap1->ctx, v);
+	isl_vec_free(v);
 	free(elim);
 	return 1;
 error:
-	isl_vec_free(bmap1->ctx, v);
+	isl_vec_free(v);
 	free(elim);
 	return -1;
 }
@@ -1766,3 +1855,509 @@ int isl_set_fast_is_disjoint(struct isl_set *set1, struct isl_set *set2)
 	return isl_map_fast_is_disjoint((struct isl_map *)set1,
 					(struct isl_map *)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 (expect 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_dim_total(bmap->dim);
+	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]);
+	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_dim_total(bmap->dim);
+
+	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_ctx *ctx = NULL;
+	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;
+
+	ctx = bmap->ctx;
+
+	dim = isl_dim_total(bmap->dim);
+	vec = isl_vec_alloc(ctx, 1 + dim + bmap->n_div);
+	if (!vec)
+		goto error;
+
+	tab = isl_tab_from_basic_map(bmap);
+
+	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(ctx, tab, vec->el,
+						  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(ctx, 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(bmap, isl_dim_div, remove, 1);
+	return isl_basic_map_drop_redundant_divs(bmap);
+error:
+	free(pairs);
+	isl_basic_map_free(bmap);
+	if (ctx) {
+		isl_tab_free(ctx, 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_dim_total(bmap->dim);
+	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_dim_total(bmap->dim);
+
+	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);
+			}
+		}
+	}
+
+	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_dim_total(bmap->dim);
+	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;
+
+		if (!isl_int_is_zero(bmap->div[i][0]))
+			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);
+			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 (!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;
+}