X-Git-Url: http://review.tizen.org/git/?a=blobdiff_plain;f=isl_equalities.c;h=4447d9b15c83baecdc8e2fbd4d7a26f2081bef75;hb=de51a9bc4da5dd3f1f9f57c2362da6f9752c44e0;hp=1f0c69815ec40b8561396fcc64124e8f6f351008;hpb=246abfb0f42edc80a2e61827a939c699b8e24e54;p=platform%2Fupstream%2Fisl.git

diff --git a/isl_equalities.c b/isl_equalities.c
index 1f0c698..4447d9b 100644
--- a/isl_equalities.c
+++ b/isl_equalities.c
@@ -1,5 +1,14 @@
-#include "isl_mat.h"
-#include "isl_seq.h"
+/*
+ * Copyright 2008-2009 Katholieke Universiteit Leuven
+ *
+ * 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
+ */
+
+#include <isl_mat_private.h>
+#include <isl/seq.h>
 #include "isl_map_private.h"
 #include "isl_equalities.h"
 
@@ -49,8 +58,7 @@
  * then the constraints admit no integer solution and
  * a zero-column matrix is returned.
  */
-static struct isl_mat *particular_solution(struct isl_ctx *ctx,
-			struct isl_mat *B, struct isl_vec *d)
+static struct isl_mat *particular_solution(struct isl_mat *B, struct isl_vec *d)
 {
 	int i, j;
 	struct isl_mat *M = NULL;
@@ -60,8 +68,8 @@ static struct isl_mat *particular_solution(struct isl_ctx *ctx,
 	struct isl_mat *cst = NULL;
 	struct isl_mat *T = NULL;
 
-	M = isl_mat_alloc(ctx, B->n_row, B->n_row + B->n_col - 1);
-	C = isl_mat_alloc(ctx, 1 + B->n_row, 1);
+	M = isl_mat_alloc(B->ctx, B->n_row, B->n_row + B->n_col - 1);
+	C = isl_mat_alloc(B->ctx, 1 + B->n_row, 1);
 	if (!M || !C)
 		goto error;
 	isl_int_set_si(C->row[0][0], 1);
@@ -74,12 +82,12 @@ static struct isl_mat *particular_solution(struct isl_ctx *ctx,
 			isl_int_fdiv_r(M->row[i][B->n_row + j],
 					B->row[i][1 + j], M->row[i][i]);
 	}
-	M = isl_mat_left_hermite(ctx, M, 0, &U, NULL);
+	M = isl_mat_left_hermite(M, 0, &U, NULL);
 	if (!M || !U)
 		goto error;
-	H = isl_mat_sub_alloc(ctx, M->row, 0, B->n_row, 0, B->n_row);
-	H = isl_mat_lin_to_aff(ctx, H);
-	C = isl_mat_inverse_product(ctx, H, C);
+	H = isl_mat_sub_alloc(M, 0, B->n_row, 0, B->n_row);
+	H = isl_mat_lin_to_aff(H);
+	C = isl_mat_inverse_product(H, C);
 	if (!C)
 		goto error;
 	for (i = 0; i < B->n_row; ++i) {
@@ -88,19 +96,113 @@ static struct isl_mat *particular_solution(struct isl_ctx *ctx,
 		isl_int_divexact(C->row[1+i][0], C->row[1+i][0], C->row[0][0]);
 	}
 	if (i < B->n_row)
-		cst = isl_mat_alloc(ctx, B->n_row, 0);
+		cst = isl_mat_alloc(B->ctx, B->n_row, 0);
 	else
-		cst = isl_mat_sub_alloc(ctx, C->row, 1, B->n_row, 0, 1);
-	T = isl_mat_sub_alloc(ctx, U->row, B->n_row, B->n_col - 1, 0, B->n_row);
-	cst = isl_mat_product(ctx, T, cst);
-	isl_mat_free(ctx, M);
-	isl_mat_free(ctx, C);
-	isl_mat_free(ctx, U);
+		cst = isl_mat_sub_alloc(C, 1, B->n_row, 0, 1);
+	T = isl_mat_sub_alloc(U, B->n_row, B->n_col - 1, 0, B->n_row);
+	cst = isl_mat_product(T, cst);
+	isl_mat_free(M);
+	isl_mat_free(C);
+	isl_mat_free(U);
 	return cst;
 error:
-	isl_mat_free(ctx, M);
-	isl_mat_free(ctx, C);
-	isl_mat_free(ctx, U);
+	isl_mat_free(M);
+	isl_mat_free(C);
+	isl_mat_free(U);
+	return NULL;
+}
+
+/* Compute and return the matrix
+ *
+ *		U_1^{-1} diag(d_1, 1, ..., 1)
+ *
+ * with U_1 the unimodular completion of the first (and only) row of B.
+ * The columns of this matrix generate the lattice that satisfies
+ * the single (linear) modulo constraint.
+ */
+static struct isl_mat *parameter_compression_1(
+			struct isl_mat *B, struct isl_vec *d)
+{
+	struct isl_mat *U;
+
+	U = isl_mat_alloc(B->ctx, B->n_col - 1, B->n_col - 1);
+	if (!U)
+		return NULL;
+	isl_seq_cpy(U->row[0], B->row[0] + 1, B->n_col - 1);
+	U = isl_mat_unimodular_complete(U, 1);
+	U = isl_mat_right_inverse(U);
+	if (!U)
+		return NULL;
+	isl_mat_col_mul(U, 0, d->block.data[0], 0);
+	U = isl_mat_lin_to_aff(U);
+	return U;
+}
+
+/* Compute a common lattice of solutions to the linear modulo
+ * constraints specified by B and d.
+ * See also the documentation of isl_mat_parameter_compression.
+ * We put the matrix
+ * 
+ *		A = [ L_1^{-T} L_2^{-T} ... L_k^{-T} ]
+ *
+ * on a common denominator.  This denominator D is the lcm of modulos d.
+ * Since L_i = U_i^{-1} diag(d_i, 1, ... 1), we have
+ * L_i^{-T} = U_i^T diag(d_i, 1, ... 1)^{-T} = U_i^T diag(1/d_i, 1, ..., 1).
+ * Putting this on the common denominator, we have
+ * D * L_i^{-T} = U_i^T diag(D/d_i, D, ..., D).
+ */
+static struct isl_mat *parameter_compression_multi(
+			struct isl_mat *B, struct isl_vec *d)
+{
+	int i, j, k;
+	isl_int D;
+	struct isl_mat *A = NULL, *U = NULL;
+	struct isl_mat *T;
+	unsigned size;
+
+	isl_int_init(D);
+
+	isl_vec_lcm(d, &D);
+
+	size = B->n_col - 1;
+	A = isl_mat_alloc(B->ctx, size, B->n_row * size);
+	U = isl_mat_alloc(B->ctx, size, size);
+	if (!U || !A)
+		goto error;
+	for (i = 0; i < B->n_row; ++i) {
+		isl_seq_cpy(U->row[0], B->row[i] + 1, size);
+		U = isl_mat_unimodular_complete(U, 1);
+		if (!U)
+			goto error;
+		isl_int_divexact(D, D, d->block.data[i]);
+		for (k = 0; k < U->n_col; ++k)
+			isl_int_mul(A->row[k][i*size+0], D, U->row[0][k]);
+		isl_int_mul(D, D, d->block.data[i]);
+		for (j = 1; j < U->n_row; ++j)
+			for (k = 0; k < U->n_col; ++k)
+				isl_int_mul(A->row[k][i*size+j],
+						D, U->row[j][k]);
+	}
+	A = isl_mat_left_hermite(A, 0, NULL, NULL);
+	T = isl_mat_sub_alloc(A, 0, A->n_row, 0, A->n_row);
+	T = isl_mat_lin_to_aff(T);
+	if (!T)
+		goto error;
+	isl_int_set(T->row[0][0], D);
+	T = isl_mat_right_inverse(T);
+	if (!T)
+		goto error;
+	isl_assert(T->ctx, isl_int_is_one(T->row[0][0]), goto error);
+	T = isl_mat_transpose(T);
+	isl_mat_free(A);
+	isl_mat_free(U);
+
+	isl_int_clear(D);
+	return T;
+error:
+	isl_mat_free(A);
+	isl_mat_free(U);
+	isl_int_clear(D);
 	return NULL;
 }
 
@@ -115,9 +217,16 @@ error:
  * that bijectively maps the integer vectors y' to integer
  * vectors y that satisfy the modulo constraints.
  *
- * The implementation closely follows the description in Section 2.5.3
+ * This function is inspired by Section 2.5.3
  * of B. Meister, "Stating and Manipulating Periodicity in the Polytope
  * Model.  Applications to Program Analysis and Optimization".
+ * However, the implementation only follows the algorithm of that
+ * section for computing a particular solution and not for computing
+ * a general homogeneous solution.  The latter is incomplete and
+ * may remove some valid solutions.
+ * Instead, we use an adaptation of the algorithm in Section 7 of
+ * B. Meister, S. Verdoolaege, "Polynomial Approximations in the Polytope
+ * Model: Bringing the Power of Quasi-Polynomials to the Masses".
  *
  * The input is given as a matrix B = [ c A ] and a vector d.
  * Each element of the vector d corresponds to a row in B.
@@ -132,14 +241,57 @@ error:
  *
  *		A y = 0 mod d
  *
- * Let K be the right kernel of A, then any y = K y'' is a solution.
- * Any multiple of a unit vector s_j e_j such that for each row i,
- * we have that s_j a_{i,j} is a multiple of d_i, is also a generator
- * for the set of solutions.  The smallest such s_j can be obtained
- * by taking the lcm of all the a_{i,j}/gcd(a_{i,j},d).
- * That is, y = K y'' + S y''', with S = diag s is the general solution.
- * To obtain a minimal representation we compute the Hermite normal
- * form [ G 0 ] of [ S K ].
+ * That is we want to compute G such that
+ *
+ *		y = G y''
+ *
+ * with y'' integer, describes the set of solutions.
+ *
+ * We first remove the common factors of each row.
+ * In particular if gcd(A_i,d_i) != 1, then we divide the whole
+ * row i (including d_i) by this common factor.  If afterwards gcd(A_i) != 1,
+ * then we divide this row of A by the common factor, unless gcd(A_i) = 0.
+ * In the later case, we simply drop the row (in both A and d).
+ *
+ * If there are no rows left in A, then G is the identity matrix. Otherwise,
+ * for each row i, we now determine the lattice of integer vectors
+ * that satisfies this row.  Let U_i be the unimodular extension of the
+ * row A_i.  This unimodular extension exists because gcd(A_i) = 1.
+ * The first component of
+ *
+ *		y' = U_i y
+ *
+ * needs to be a multiple of d_i.  Let y' = diag(d_i, 1, ..., 1) y''.
+ * Then,
+ *
+ *		y = U_i^{-1} diag(d_i, 1, ..., 1) y''
+ *
+ * for arbitrary integer vectors y''.  That is, y belongs to the lattice
+ * generated by the columns of L_i = U_i^{-1} diag(d_i, 1, ..., 1).
+ * If there is only one row, then G = L_1.
+ *
+ * If there is more than one row left, we need to compute the intersection
+ * of the lattices.  That is, we need to compute an L such that
+ *
+ *		L = L_i L_i'	for all i
+ *
+ * with L_i' some integer matrices.  Let A be constructed as follows
+ *
+ *		A = [ L_1^{-T} L_2^{-T} ... L_k^{-T} ]
+ *
+ * and computed the Hermite Normal Form of A = [ H 0 ] U
+ * Then,
+ *
+ *		L_i^{-T} = H U_{1,i}
+ *
+ * or
+ *
+ *		H^{-T} = L_i U_{1,i}^T
+ *
+ * In other words G = L = H^{-T}.
+ * To ensure that G is lower triangular, we compute and use its Hermite
+ * normal form.
+ *
  * The affine transformation matrix returned is then
  *
  *		[  1   0  ]
@@ -148,72 +300,75 @@ error:
  * as any y = y_0 + G y' with y' integer is a solution to the original
  * modulo constraints.
  */
-struct isl_mat *isl_mat_parameter_compression(struct isl_ctx *ctx,
+struct isl_mat *isl_mat_parameter_compression(
 			struct isl_mat *B, struct isl_vec *d)
 {
-	int i, j;
+	int i;
 	struct isl_mat *cst = NULL;
-	struct isl_mat *K = NULL;
-	struct isl_mat *M = NULL;
-	struct isl_mat *T;
-	isl_int v;
+	struct isl_mat *T = NULL;
+	isl_int D;
 
 	if (!B || !d)
 		goto error;
-	isl_assert(ctx, B->n_row == d->size, goto error);
-	cst = particular_solution(ctx, B, d);
+	isl_assert(B->ctx, B->n_row == d->size, goto error);
+	cst = particular_solution(B, d);
 	if (!cst)
 		goto error;
 	if (cst->n_col == 0) {
-		T = isl_mat_alloc(ctx, B->n_col, 0);
-		isl_mat_free(ctx, cst);
-		isl_mat_free(ctx, B);
-		isl_vec_free(ctx, d);
+		T = isl_mat_alloc(B->ctx, B->n_col, 0);
+		isl_mat_free(cst);
+		isl_mat_free(B);
+		isl_vec_free(d);
 		return T;
 	}
-	T = isl_mat_sub_alloc(ctx, B->row, 0, B->n_row, 1, B->n_col - 1);
-	K = isl_mat_right_kernel(ctx, T);
-	if (!K)
-		goto error;
-	M = isl_mat_alloc(ctx, B->n_col - 1, B->n_col - 1 + K->n_col);
-	if (!M)
-		goto error;
-	isl_mat_sub_copy(ctx, M->row, K->row, M->n_row,
-				B->n_col - 1, 0, K->n_col);
-	for (i = 0; i < M->n_row; ++i) {
-		isl_seq_clr(M->row[i], B->n_col - 1);
-		isl_int_set_si(M->row[i][i], 1);
-	}
-	isl_int_init(v);
-	for (i = 0; i < B->n_row; ++i)
-		for (j = 0; j < B->n_col - 1; ++j) {
-			isl_int_gcd(v, B->row[i][1+j], d->block.data[i]);
-			isl_int_divexact(v, d->block.data[i], v);
-			isl_int_lcm(M->row[j][j], M->row[j][j], v);
+	isl_int_init(D);
+	/* Replace a*g*row = 0 mod g*m by row = 0 mod m */
+	for (i = 0; i < B->n_row; ++i) {
+		isl_seq_gcd(B->row[i] + 1, B->n_col - 1, &D);
+		if (isl_int_is_one(D))
+			continue;
+		if (isl_int_is_zero(D)) {
+			B = isl_mat_drop_rows(B, i, 1);
+			d = isl_vec_cow(d);
+			if (!B || !d)
+				goto error2;
+			isl_seq_cpy(d->block.data+i, d->block.data+i+1,
+							d->size - (i+1));
+			d->size--;
+			i--;
+			continue;
 		}
-	isl_int_clear(v);
-	M = isl_mat_left_hermite(ctx, M, 0, NULL, NULL);
-	if (!M)
-		goto error;
-	T = isl_mat_alloc(ctx, 1 + B->n_col - 1, B->n_col);
+		B = isl_mat_cow(B);
+		if (!B)
+			goto error2;
+		isl_seq_scale_down(B->row[i] + 1, B->row[i] + 1, D, B->n_col-1);
+		isl_int_gcd(D, D, d->block.data[i]);
+		d = isl_vec_cow(d);
+		if (!d)
+			goto error2;
+		isl_int_divexact(d->block.data[i], d->block.data[i], D);
+	}
+	isl_int_clear(D);
+	if (B->n_row == 0)
+		T = isl_mat_identity(B->ctx, B->n_col);
+	else if (B->n_row == 1)
+		T = parameter_compression_1(B, d);
+	else
+		T = parameter_compression_multi(B, d);
+	T = isl_mat_left_hermite(T, 0, NULL, NULL);
 	if (!T)
 		goto error;
-	isl_int_set_si(T->row[0][0], 1);
-	isl_seq_clr(T->row[0] + 1, T->n_col - 1);
-	isl_mat_sub_copy(ctx, T->row + 1, cst->row, cst->n_row, 0, 0, 1);
-	isl_mat_sub_copy(ctx, T->row + 1, M->row, M->n_row, 1, 0, T->n_col - 1);
-	isl_mat_free(ctx, K);
-	isl_mat_free(ctx, M);
-	isl_mat_free(ctx, cst);
-	isl_mat_free(ctx, B);
-	isl_vec_free(ctx, d);
+	isl_mat_sub_copy(T->ctx, T->row + 1, cst->row, cst->n_row, 0, 0, 1);
+	isl_mat_free(cst);
+	isl_mat_free(B);
+	isl_vec_free(d);
 	return T;
+error2:
+	isl_int_clear(D);
 error:
-	isl_mat_free(ctx, K);
-	isl_mat_free(ctx, M);
-	isl_mat_free(ctx, cst);
-	isl_mat_free(ctx, B);
-	isl_vec_free(ctx, d);
+	isl_mat_free(cst);
+	isl_mat_free(B);
+	isl_vec_free(d);
 	return NULL;
 }
 
@@ -221,12 +376,12 @@ error:
  *
  *		M x - c = 0
  *
- * this function computes unimodular transformation from a lower-dimensional
+ * this function computes a unimodular transformation from a lower-dimensional
  * space to the original space that bijectively maps the integer points x'
  * in the lower-dimensional space to the integer points x in the original
  * space that satisfy the equalities.
  *
- * The input is given as a matrix B = [ -c M ] and the out is a
+ * The input is given as a matrix B = [ -c M ] and the output is a
  * matrix that maps [1 x'] to [1 x].
  * If T2 is not NULL, then *T2 is set to a matrix mapping [1 x] to [1 x'].
  *
@@ -249,7 +404,7 @@ error:
  *
  * If any of the c' is non-integer, then the original set has no
  * integer solutions (since the x' are a unimodular transformation
- * of the x).
+ * of the x) and a zero-column matrix is returned.
  * Otherwise, the transformation is given by
  *
  *		x = U1 H1^{-1} c + U2 x2'
@@ -258,8 +413,8 @@ error:
  *
  *		x2' = Q2 x
  */
-struct isl_mat *isl_mat_variable_compression(struct isl_ctx *ctx,
-			struct isl_mat *B, struct isl_mat **T2)
+struct isl_mat *isl_mat_variable_compression(struct isl_mat *B,
+	struct isl_mat **T2)
 {
 	int i;
 	struct isl_mat *H = NULL, *C = NULL, *H1, *U = NULL, *U1, *U2, *TC;
@@ -271,61 +426,61 @@ struct isl_mat *isl_mat_variable_compression(struct isl_ctx *ctx,
 		goto error;
 
 	dim = B->n_col - 1;
-	H = isl_mat_sub_alloc(ctx, B->row, 0, B->n_row, 1, dim);
-	H = isl_mat_left_hermite(ctx, H, 0, &U, T2);
+	H = isl_mat_sub_alloc(B, 0, B->n_row, 1, dim);
+	H = isl_mat_left_hermite(H, 0, &U, T2);
 	if (!H || !U || (T2 && !*T2))
 		goto error;
 	if (T2) {
-		*T2 = isl_mat_drop_rows(ctx, *T2, 0, B->n_row);
-		*T2 = isl_mat_lin_to_aff(ctx, *T2);
+		*T2 = isl_mat_drop_rows(*T2, 0, B->n_row);
+		*T2 = isl_mat_lin_to_aff(*T2);
 		if (!*T2)
 			goto error;
 	}
-	C = isl_mat_alloc(ctx, 1+B->n_row, 1);
+	C = isl_mat_alloc(B->ctx, 1+B->n_row, 1);
 	if (!C)
 		goto error;
 	isl_int_set_si(C->row[0][0], 1);
-	isl_mat_sub_neg(ctx, C->row+1, B->row, B->n_row, 0, 0, 1);
-	H1 = isl_mat_sub_alloc(ctx, H->row, 0, H->n_row, 0, H->n_row);
-	H1 = isl_mat_lin_to_aff(ctx, H1);
-	TC = isl_mat_inverse_product(ctx, H1, C);
+	isl_mat_sub_neg(C->ctx, C->row+1, B->row, B->n_row, 0, 0, 1);
+	H1 = isl_mat_sub_alloc(H, 0, H->n_row, 0, H->n_row);
+	H1 = isl_mat_lin_to_aff(H1);
+	TC = isl_mat_inverse_product(H1, C);
 	if (!TC)
 		goto error;
-	isl_mat_free(ctx, H);
+	isl_mat_free(H);
 	if (!isl_int_is_one(TC->row[0][0])) {
 		for (i = 0; i < B->n_row; ++i) {
 			if (!isl_int_is_divisible_by(TC->row[1+i][0], TC->row[0][0])) {
-				isl_mat_free(ctx, B);
-				isl_mat_free(ctx, TC);
-				isl_mat_free(ctx, U);
+				struct isl_ctx *ctx = B->ctx;
+				isl_mat_free(B);
+				isl_mat_free(TC);
+				isl_mat_free(U);
 				if (T2) {
-					isl_mat_free(ctx, *T2);
+					isl_mat_free(*T2);
 					*T2 = NULL;
 				}
-				return isl_mat_alloc(ctx, 1 + B->n_col, 0);
+				return isl_mat_alloc(ctx, 1 + dim, 0);
 			}
 			isl_seq_scale_down(TC->row[1+i], TC->row[1+i], TC->row[0][0], 1);
 		}
 		isl_int_set_si(TC->row[0][0], 1);
 	}
-	U1 = isl_mat_sub_alloc(ctx, U->row, 0, U->n_row, 0, B->n_row);
-	U1 = isl_mat_lin_to_aff(ctx, U1);
-	U2 = isl_mat_sub_alloc(ctx, U->row, 0, U->n_row,
-				B->n_row, U->n_row - B->n_row);
-	U2 = isl_mat_lin_to_aff(ctx, U2);
-	isl_mat_free(ctx, U);
-	TC = isl_mat_product(ctx, U1, TC);
-	TC = isl_mat_aff_direct_sum(ctx, TC, U2);
+	U1 = isl_mat_sub_alloc(U, 0, U->n_row, 0, B->n_row);
+	U1 = isl_mat_lin_to_aff(U1);
+	U2 = isl_mat_sub_alloc(U, 0, U->n_row, B->n_row, U->n_row - B->n_row);
+	U2 = isl_mat_lin_to_aff(U2);
+	isl_mat_free(U);
+	TC = isl_mat_product(U1, TC);
+	TC = isl_mat_aff_direct_sum(TC, U2);
 
-	isl_mat_free(ctx, B);
+	isl_mat_free(B);
 
 	return TC;
 error:
-	isl_mat_free(ctx, B);
-	isl_mat_free(ctx, H);
-	isl_mat_free(ctx, U);
+	isl_mat_free(B);
+	isl_mat_free(H);
+	isl_mat_free(U);
 	if (T2) {
-		isl_mat_free(ctx, *T2);
+		isl_mat_free(*T2);
 		*T2 = NULL;
 	}
 	return NULL;
@@ -338,7 +493,7 @@ error:
  * the new variables x2' back to the original variables x, while T2
  * maps the original variables to the new variables.
  */
-static struct isl_basic_set *compress_variables(struct isl_ctx *ctx,
+static struct isl_basic_set *compress_variables(
 	struct isl_basic_set *bset, struct isl_mat **T, struct isl_mat **T2)
 {
 	struct isl_mat *B, *TC;
@@ -350,27 +505,27 @@ static struct isl_basic_set *compress_variables(struct isl_ctx *ctx,
 		*T2 = NULL;
 	if (!bset)
 		goto error;
-	isl_assert(ctx, isl_basic_set_n_param(bset) == 0, goto error);
-	isl_assert(ctx, bset->n_div == 0, goto error);
+	isl_assert(bset->ctx, isl_basic_set_n_param(bset) == 0, goto error);
+	isl_assert(bset->ctx, bset->n_div == 0, goto error);
 	dim = isl_basic_set_n_dim(bset);
-	isl_assert(ctx, bset->n_eq <= dim, goto error);
+	isl_assert(bset->ctx, bset->n_eq <= dim, goto error);
 	if (bset->n_eq == 0)
 		return bset;
 
-	B = isl_mat_sub_alloc(ctx, bset->eq, 0, bset->n_eq, 0, 1 + dim);
-	TC = isl_mat_variable_compression(ctx, B, T2);
+	B = isl_mat_sub_alloc6(bset->ctx, bset->eq, 0, bset->n_eq, 0, 1 + dim);
+	TC = isl_mat_variable_compression(B, T2);
 	if (!TC)
 		goto error;
 	if (TC->n_col == 0) {
-		isl_mat_free(ctx, TC);
+		isl_mat_free(TC);
 		if (T2) {
-			isl_mat_free(ctx, *T2);
+			isl_mat_free(*T2);
 			*T2 = NULL;
 		}
 		return isl_basic_set_set_to_empty(bset);
 	}
 
-	bset = isl_basic_set_preimage(ctx, bset, T ? isl_mat_copy(ctx, TC) : TC);
+	bset = isl_basic_set_preimage(bset, T ? isl_mat_copy(TC) : TC);
 	if (T)
 		*T = TC;
 	return bset;
@@ -390,9 +545,9 @@ struct isl_basic_set *isl_basic_set_remove_equalities(
 		return NULL;
 	isl_assert(bset->ctx, isl_basic_set_n_param(bset) == 0, goto error);
 	bset = isl_basic_set_gauss(bset, NULL);
-	if (F_ISSET(bset, ISL_BASIC_SET_EMPTY))
+	if (ISL_F_ISSET(bset, ISL_BASIC_SET_EMPTY))
 		return bset;
-	bset = compress_variables(bset->ctx, bset, T, T2);
+	bset = compress_variables(bset, T, T2);
 	return bset;
 error:
 	isl_basic_set_free(bset);
@@ -403,6 +558,11 @@ error:
 /* Check if dimension dim belongs to a residue class
  *		i_dim \equiv r mod m
  * with m != 1 and if so return m in *modulo and r in *residue.
+ * As a special case, when i_dim has a fixed value v, then
+ * *modulo is set to 0 and *residue to v.
+ *
+ * If i_dim does not belong to such a residue class, then *modulo
+ * is set to 1 and *residue is set to 0.
  */
 int isl_basic_set_dim_residue_class(struct isl_basic_set *bset,
 	int pos, isl_int *modulo, isl_int *residue)
@@ -415,52 +575,118 @@ int isl_basic_set_dim_residue_class(struct isl_basic_set *bset,
 	if (!bset || !modulo || !residue)
 		return -1;
 
+	if (isl_basic_set_plain_dim_is_fixed(bset, pos, residue)) {
+		isl_int_set_si(*modulo, 0);
+		return 0;
+	}
+
 	ctx = bset->ctx;
 	total = isl_basic_set_total_dim(bset);
 	nparam = isl_basic_set_n_param(bset);
-	H = isl_mat_sub_alloc(ctx, bset->eq, 0, bset->n_eq, 1, total);
-	H = isl_mat_left_hermite(ctx, H, 0, &U, NULL);
+	H = isl_mat_sub_alloc6(bset->ctx, bset->eq, 0, bset->n_eq, 1, total);
+	H = isl_mat_left_hermite(H, 0, &U, NULL);
 	if (!H)
 		return -1;
 
 	isl_seq_gcd(U->row[nparam + pos]+bset->n_eq,
 			total-bset->n_eq, modulo);
-	if (isl_int_is_zero(*modulo) || isl_int_is_one(*modulo)) {
+	if (isl_int_is_zero(*modulo))
+		isl_int_set_si(*modulo, 1);
+	if (isl_int_is_one(*modulo)) {
 		isl_int_set_si(*residue, 0);
-		isl_mat_free(ctx, H);
-		isl_mat_free(ctx, U);
+		isl_mat_free(H);
+		isl_mat_free(U);
 		return 0;
 	}
 
-	C = isl_mat_alloc(ctx, 1+bset->n_eq, 1);
+	C = isl_mat_alloc(bset->ctx, 1+bset->n_eq, 1);
 	if (!C)
 		goto error;
 	isl_int_set_si(C->row[0][0], 1);
-	isl_mat_sub_neg(ctx, C->row+1, bset->eq, bset->n_eq, 0, 0, 1);
-	H1 = isl_mat_sub_alloc(ctx, H->row, 0, H->n_row, 0, H->n_row);
-	H1 = isl_mat_lin_to_aff(ctx, H1);
-	C = isl_mat_inverse_product(ctx, H1, C);
-	isl_mat_free(ctx, H);
-	U1 = isl_mat_sub_alloc(ctx, U->row, nparam+pos, 1, 0, bset->n_eq);
-	U1 = isl_mat_lin_to_aff(ctx, U1);
-	isl_mat_free(ctx, U);
-	C = isl_mat_product(ctx, U1, C);
+	isl_mat_sub_neg(C->ctx, C->row+1, bset->eq, bset->n_eq, 0, 0, 1);
+	H1 = isl_mat_sub_alloc(H, 0, H->n_row, 0, H->n_row);
+	H1 = isl_mat_lin_to_aff(H1);
+	C = isl_mat_inverse_product(H1, C);
+	isl_mat_free(H);
+	U1 = isl_mat_sub_alloc(U, nparam+pos, 1, 0, bset->n_eq);
+	U1 = isl_mat_lin_to_aff(U1);
+	isl_mat_free(U);
+	C = isl_mat_product(U1, C);
 	if (!C)
 		goto error;
 	if (!isl_int_is_divisible_by(C->row[1][0], C->row[0][0])) {
 		bset = isl_basic_set_copy(bset);
 		bset = isl_basic_set_set_to_empty(bset);
 		isl_basic_set_free(bset);
-		isl_int_set_si(*modulo, 0);
+		isl_int_set_si(*modulo, 1);
 		isl_int_set_si(*residue, 0);
 		return 0;
 	}
 	isl_int_divexact(*residue, C->row[1][0], C->row[0][0]);
 	isl_int_fdiv_r(*residue, *residue, *modulo);
-	isl_mat_free(ctx, C);
+	isl_mat_free(C);
+	return 0;
+error:
+	isl_mat_free(H);
+	isl_mat_free(U);
+	return -1;
+}
+
+/* Check if dimension dim belongs to a residue class
+ *		i_dim \equiv r mod m
+ * with m != 1 and if so return m in *modulo and r in *residue.
+ * As a special case, when i_dim has a fixed value v, then
+ * *modulo is set to 0 and *residue to v.
+ *
+ * If i_dim does not belong to such a residue class, then *modulo
+ * is set to 1 and *residue is set to 0.
+ */
+int isl_set_dim_residue_class(struct isl_set *set,
+	int pos, isl_int *modulo, isl_int *residue)
+{
+	isl_int m;
+	isl_int r;
+	int i;
+
+	if (!set || !modulo || !residue)
+		return -1;
+
+	if (set->n == 0) {
+		isl_int_set_si(*modulo, 0);
+		isl_int_set_si(*residue, 0);
+		return 0;
+	}
+
+	if (isl_basic_set_dim_residue_class(set->p[0], pos, modulo, residue)<0)
+		return -1;
+
+	if (set->n == 1)
+		return 0;
+
+	if (isl_int_is_one(*modulo))
+		return 0;
+
+	isl_int_init(m);
+	isl_int_init(r);
+
+	for (i = 1; i < set->n; ++i) {
+		if (isl_basic_set_dim_residue_class(set->p[i], pos, &m, &r) < 0)
+			goto error;
+		isl_int_gcd(*modulo, *modulo, m);
+		isl_int_sub(m, *residue, r);
+		isl_int_gcd(*modulo, *modulo, m);
+		if (!isl_int_is_zero(*modulo))
+			isl_int_fdiv_r(*residue, *residue, *modulo);
+		if (isl_int_is_one(*modulo))
+			break;
+	}
+
+	isl_int_clear(m);
+	isl_int_clear(r);
+
 	return 0;
 error:
-	isl_mat_free(ctx, H);
-	isl_mat_free(ctx, U);
+	isl_int_clear(m);
+	isl_int_clear(r);
 	return -1;
 }