-#include "isl_mat.h"
+/*
+ * Copyright 2008-2009 Katholieke Universiteit Leuven
+ * Copyright 2010 INRIA Saclay
+ *
+ * Use of this software is governed by the MIT license
+ *
+ * Written by Sven Verdoolaege, K.U.Leuven, Departement
+ * Computerwetenschappen, Celestijnenlaan 200A, B-3001 Leuven, Belgium
+ * and INRIA Saclay - Ile-de-France, Parc Club Orsay Universite,
+ * ZAC des vignes, 4 rue Jacques Monod, 91893 Orsay, France
+ */
+
+#include <isl_mat_private.h>
+#include <isl/seq.h>
#include "isl_map_private.h"
#include "isl_equalities.h"
-/* Use the n equalities of bset to unimodularly transform the
- * variables x such that n transformed variables x1' have a constant value
- * and rewrite the constraints of bset in terms of the remaining
- * transformed variables x2'. The matrix pointed to by T maps
- * the new variables x2' back to the original variables x, while T2
- * maps the original variables to the new variables.
+/* Given a set of modulo constraints
+ *
+ * c + A y = 0 mod d
+ *
+ * this function computes a particular solution y_0
+ *
+ * The input is given as a matrix B = [ c A ] and a vector d.
+ *
+ * The output is matrix containing the solution y_0 or
+ * a zero-column matrix if the constraints admit no integer solution.
+ *
+ * The given set of constrains is equivalent to
+ *
+ * c + A y = -D x
+ *
+ * with D = diag d and x a fresh set of variables.
+ * Reducing both c and A modulo d does not change the
+ * value of y in the solution and may lead to smaller coefficients.
+ * Let M = [ D A ] and [ H 0 ] = M U, the Hermite normal form of M.
+ * Then
+ * [ x ]
+ * M [ y ] = - c
+ * and so
+ * [ x ]
+ * [ H 0 ] U^{-1} [ y ] = - c
+ * Let
+ * [ A ] [ x ]
+ * [ B ] = U^{-1} [ y ]
+ * then
+ * H A + 0 B = -c
+ *
+ * so B may be chosen arbitrarily, e.g., B = 0, and then
+ *
+ * [ x ] = [ -c ]
+ * U^{-1} [ y ] = [ 0 ]
+ * or
+ * [ x ] [ -c ]
+ * [ y ] = U [ 0 ]
+ * specifically,
+ *
+ * y = U_{2,1} (-c)
+ *
+ * If any of the coordinates of this y are non-integer
+ * then the constraints admit no integer solution and
+ * a zero-column matrix is returned.
+ */
+static struct isl_mat *particular_solution(struct isl_mat *B, struct isl_vec *d)
+{
+ int i, j;
+ struct isl_mat *M = NULL;
+ struct isl_mat *C = NULL;
+ struct isl_mat *U = NULL;
+ struct isl_mat *H = NULL;
+ struct isl_mat *cst = NULL;
+ struct isl_mat *T = NULL;
+
+ 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);
+ for (i = 0; i < B->n_row; ++i) {
+ isl_seq_clr(M->row[i], B->n_row);
+ isl_int_set(M->row[i][i], d->block.data[i]);
+ isl_int_neg(C->row[1 + i][0], B->row[i][0]);
+ isl_int_fdiv_r(C->row[1+i][0], C->row[1+i][0], M->row[i][i]);
+ for (j = 0; j < B->n_col - 1; ++j)
+ 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(M, 0, &U, NULL);
+ if (!M || !U)
+ goto error;
+ 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) {
+ if (!isl_int_is_divisible_by(C->row[1+i][0], C->row[0][0]))
+ break;
+ 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(B->ctx, B->n_row, 0);
+ else
+ 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(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;
+}
+
+/* Given a set of modulo constraints
+ *
+ * c + A y = 0 mod d
+ *
+ * this function returns an affine transformation T,
+ *
+ * y = T y'
+ *
+ * that bijectively maps the integer vectors y' to integer
+ * vectors y that satisfy the modulo constraints.
+ *
+ * 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.
+ * The output is a lower triangular matrix.
+ * If no integer vector y satisfies the given constraints then
+ * a matrix with zero columns is returned.
+ *
+ * We first compute a particular solution y_0 to the given set of
+ * modulo constraints in particular_solution. If no such solution
+ * exists, then we return a zero-columned transformation matrix.
+ * Otherwise, we compute the generic solution to
+ *
+ * A y = 0 mod d
+ *
+ * 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 ]
+ * [ y_0 G ]
+ *
+ * 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_mat *B, struct isl_vec *d)
+{
+ int i;
+ struct isl_mat *cst = NULL;
+ struct isl_mat *T = NULL;
+ isl_int D;
+
+ if (!B || !d)
+ goto error;
+ 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(B->ctx, B->n_col, 0);
+ isl_mat_free(cst);
+ isl_mat_free(B);
+ isl_vec_free(d);
+ return T;
+ }
+ 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;
+ }
+ 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_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(cst);
+ isl_mat_free(B);
+ isl_vec_free(d);
+ return NULL;
+}
+
+/* Given a set of equalities
+ *
+ * B(y) + A x = 0 (*)
+ *
+ * compute and return an affine transformation T,
+ *
+ * y = T y'
+ *
+ * that bijectively maps the integer vectors y' to integer
+ * vectors y that satisfy the modulo constraints for some value of x.
+ *
+ * Let [H 0] be the Hermite Normal Form of A, i.e.,
*
- * Let the equalities of bset be
+ * A = [H 0] Q
+ *
+ * Then y is a solution of (*) iff
+ *
+ * H^-1 B(y) (= - [I 0] Q x)
+ *
+ * is an integer vector. Let d be the common denominator of H^-1.
+ * We impose
+ *
+ * d H^-1 B(y) = 0 mod d
+ *
+ * and compute the solution using isl_mat_parameter_compression.
+ */
+__isl_give isl_mat *isl_mat_parameter_compression_ext(__isl_take isl_mat *B,
+ __isl_take isl_mat *A)
+{
+ isl_ctx *ctx;
+ isl_vec *d;
+ int n_row, n_col;
+
+ if (!A)
+ return isl_mat_free(B);
+
+ ctx = isl_mat_get_ctx(A);
+ n_row = A->n_row;
+ n_col = A->n_col;
+ A = isl_mat_left_hermite(A, 0, NULL, NULL);
+ A = isl_mat_drop_cols(A, n_row, n_col - n_row);
+ A = isl_mat_lin_to_aff(A);
+ A = isl_mat_right_inverse(A);
+ d = isl_vec_alloc(ctx, n_row);
+ if (A)
+ d = isl_vec_set(d, A->row[0][0]);
+ A = isl_mat_drop_rows(A, 0, 1);
+ A = isl_mat_drop_cols(A, 0, 1);
+ B = isl_mat_product(A, B);
+
+ return isl_mat_parameter_compression(B, d);
+}
+
+/* Given a set of equalities
*
* M x - c = 0
*
- * Compute the (left) Hermite normal form of M,
+ * 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 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'].
+ *
+ * First compute the (left) Hermite normal form of M,
*
* M [U1 U2] = M U = H = [H1 0]
* or
*
* 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'
*
* x2' = Q2 x
*/
-static struct isl_basic_set *compress_variables(struct isl_ctx *ctx,
- struct isl_basic_set *bset, struct isl_mat **T, struct isl_mat **T2)
+__isl_give isl_mat *isl_mat_variable_compression(__isl_take isl_mat *B,
+ __isl_give isl_mat **T2)
{
int i;
struct isl_mat *H = NULL, *C = NULL, *H1, *U = NULL, *U1, *U2, *TC;
+ unsigned dim;
- if (T)
- *T = NULL;
if (T2)
*T2 = NULL;
- if (!bset)
+ if (!B)
goto error;
- isl_assert(ctx, bset->nparam == 0, goto error);
- isl_assert(ctx, bset->n_div == 0, goto error);
- isl_assert(ctx, bset->n_eq <= bset->dim, goto error);
- if (bset->n_eq == 0)
- return bset;
- H = isl_mat_sub_alloc(ctx, bset->eq, 0, bset->n_eq, 1, bset->dim);
- H = isl_mat_left_hermite(ctx, H, 0, &U, T2);
+ dim = B->n_col - 1;
+ 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, bset->n_eq);
- *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+bset->n_eq, 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, 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);
- 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 < bset->n_eq; ++i) {
+ 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, 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_basic_set_set_to_empty(bset);
+ 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, bset->n_eq);
- U1 = isl_mat_lin_to_aff(ctx, U1);
- U2 = isl_mat_sub_alloc(ctx, U->row, 0, U->n_row,
- bset->n_eq, U->n_row - bset->n_eq);
- 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);
- bset = isl_basic_set_preimage(ctx, bset, T ? isl_mat_copy(ctx, TC) : TC);
- if (T)
- *T = TC;
- return bset;
+ 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(B);
+
+ return TC;
error:
- isl_mat_free(ctx, H);
- isl_mat_free(ctx, U);
- if (T2)
- isl_mat_free(ctx, *T2);
- isl_basic_set_free(bset);
+ isl_mat_free(B);
+ isl_mat_free(H);
+ isl_mat_free(U);
+ if (T2) {
+ isl_mat_free(*T2);
+ *T2 = NULL;
+ }
+ return NULL;
+}
+
+/* Use the n equalities of bset to unimodularly transform the
+ * variables x such that n transformed variables x1' have a constant value
+ * and rewrite the constraints of bset in terms of the remaining
+ * transformed variables x2'. The matrix pointed to by T maps
+ * 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_basic_set *bset, struct isl_mat **T, struct isl_mat **T2)
+{
+ struct isl_mat *B, *TC;
+ unsigned dim;
+
if (T)
*T = NULL;
if (T2)
*T2 = NULL;
+ if (!bset)
+ 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(bset->ctx, bset->n_eq <= dim, goto error);
+ if (bset->n_eq == 0)
+ return bset;
+
+ 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(TC);
+ if (T2) {
+ isl_mat_free(*T2);
+ *T2 = NULL;
+ }
+ return isl_basic_set_set_to_empty(bset);
+ }
+
+ bset = isl_basic_set_preimage(bset, T ? isl_mat_copy(TC) : TC);
+ if (T)
+ *T = TC;
+ return bset;
+error:
+ isl_basic_set_free(bset);
return NULL;
}
*T2 = NULL;
if (!bset)
return NULL;
- isl_assert(bset->ctx, bset->nparam == 0, goto error);
+ 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);
*T = NULL;
return NULL;
}
+
+/* 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)
+{
+ struct isl_ctx *ctx;
+ struct isl_mat *H = NULL, *U = NULL, *C, *H1, *U1;
+ unsigned total;
+ unsigned nparam;
+
+ 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_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_set_si(*modulo, 1);
+ if (isl_int_is_one(*modulo)) {
+ isl_int_set_si(*residue, 0);
+ isl_mat_free(H);
+ isl_mat_free(U);
+ return 0;
+ }
+
+ 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(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, 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(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_int_clear(m);
+ isl_int_clear(r);
+ return -1;
+}
projects / platform / upstream / isl.git / blobdiff