/* * 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 #include #include #include "isl_map_private.h" #include "isl_equalities.h" #include /* 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. */ __isl_give isl_mat *isl_mat_parameter_compression(__isl_take isl_mat *B, __isl_take 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., * * 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); } /* Return a compression matrix that indicates that there are no solutions * to the original constraints. In particular, return a zero-column * matrix with 1 + dim rows. If "T2" is not NULL, then assign *T2 * the inverse of this matrix. *T2 may already have been assigned * matrix, so free it first. * "free1", "free2" and "free3" are temporary matrices that are * not useful when an empty compression is returned. They are * simply freed. */ static __isl_give isl_mat *empty_compression(isl_ctx *ctx, unsigned dim, __isl_give isl_mat **T2, __isl_take isl_mat *free1, __isl_take isl_mat *free2, __isl_take isl_mat *free3) { isl_mat_free(free1); isl_mat_free(free2); isl_mat_free(free3); if (T2) { isl_mat_free(*T2); *T2 = isl_mat_alloc(ctx, 0, 1 + dim); } return isl_mat_alloc(ctx, 1 + dim, 0); } /* Given a matrix that maps a (possibly) parametric domain to * a parametric domain, add in rows that map the "nparam" parameters onto * themselves. */ static __isl_give isl_mat *insert_parameter_rows(__isl_take isl_mat *mat, unsigned nparam) { int i; if (nparam == 0) return mat; if (!mat) return NULL; mat = isl_mat_insert_rows(mat, 1, nparam); if (!mat) return NULL; for (i = 0; i < nparam; ++i) { isl_seq_clr(mat->row[1 + i], mat->n_col); isl_int_set(mat->row[1 + i][1 + i], mat->row[0][0]); } return mat; } /* Given a set of equalities * * -C(y) + M x = 0 * * 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]. * The number of equality constraints in B is assumed to be smaller than * or equal to the number of variables x. * "first" is the position of the first x variable. * The preceding variables are considered to be y-variables. * 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 * M = H Q = [H1 0] [Q1] * [Q2] * * with U, Q unimodular, Q = U^{-1} (and H lower triangular). * Define the transformed variables as * * x = [U1 U2] [ x1' ] = [U1 U2] [Q1] x * [ x2' ] [Q2] * * The equalities then become * * -C(y) + H1 x1' = 0 or x1' = H1^{-1} C(y) = C'(y) * * If the denominator of the constant term does not divide the * the common denominator of the coefficients of y, then every * integer point is mapped to a non-integer point and then the original set * has no integer solutions (since the x' are a unimodular transformation * of the x). In this case, a zero-column matrix is returned. * Otherwise, the transformation is given by * * x = U1 H1^{-1} C(y) + U2 x2' * * The inverse transformation is simply * * x2' = Q2 x */ __isl_give isl_mat *isl_mat_final_variable_compression(__isl_take isl_mat *B, int first, __isl_give isl_mat **T2) { int i, n; isl_ctx *ctx; isl_mat *H = NULL, *C, *H1, *U = NULL, *U1, *U2; unsigned dim; if (T2) *T2 = NULL; if (!B) goto error; ctx = isl_mat_get_ctx(B); dim = B->n_col - 1; n = dim - first; if (n < B->n_row) isl_die(ctx, isl_error_invalid, "too many equality constraints", goto error); H = isl_mat_sub_alloc(B, 0, B->n_row, 1 + first, n); H = isl_mat_left_hermite(H, 0, &U, T2); if (!H || !U || (T2 && !*T2)) goto error; if (T2) { *T2 = isl_mat_drop_rows(*T2, 0, B->n_row); *T2 = isl_mat_diagonal(isl_mat_identity(ctx, 1 + first), *T2); if (!*T2) goto error; } C = isl_mat_alloc(ctx, 1 + B->n_row, 1 + first); if (!C) goto error; isl_int_set_si(C->row[0][0], 1); isl_seq_clr(C->row[0] + 1, first); isl_mat_sub_neg(ctx, C->row + 1, B->row, B->n_row, 0, 0, 1 + first); 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); if (!C) goto error; isl_mat_free(H); if (!isl_int_is_one(C->row[0][0])) { isl_int g; isl_int_init(g); for (i = 0; i < B->n_row; ++i) { isl_seq_gcd(C->row[1 + i] + 1, first, &g); isl_int_gcd(g, g, C->row[0][0]); if (!isl_int_is_divisible_by(C->row[1 + i][0], g)) break; } isl_int_clear(g); if (i < B->n_row) return empty_compression(ctx, dim, T2, B, C, U); C = isl_mat_normalize(C); } 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); C = isl_mat_product(U1, C); C = isl_mat_aff_direct_sum(C, U2); C = insert_parameter_rows(C, first); isl_mat_free(B); return C; error: isl_mat_free(B); isl_mat_free(H); isl_mat_free(U); if (T2) { isl_mat_free(*T2); *T2 = NULL; } return NULL; } /* Given a set of equalities * * M x - c = 0 * * 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]. * The number of equality constraints in B is assumed to be smaller than * or equal to the number of variables x. * If T2 is not NULL, then *T2 is set to a matrix mapping [1 x] to [1 x']. */ __isl_give isl_mat *isl_mat_variable_compression(__isl_take isl_mat *B, __isl_give isl_mat **T2) { return isl_mat_final_variable_compression(B, 0, T2); } /* Return "bset" and set *T and *T2 to the identity transformation * on "bset" (provided T and T2 are not NULL). */ static __isl_give isl_basic_set *return_with_identity( __isl_take isl_basic_set *bset, __isl_give isl_mat **T, __isl_give isl_mat **T2) { unsigned dim; isl_mat *id; if (!bset) return NULL; if (!T && !T2) return bset; dim = isl_basic_set_dim(bset, isl_dim_set); id = isl_mat_identity(isl_basic_map_get_ctx(bset), 1 + dim); if (T) *T = isl_mat_copy(id); if (T2) *T2 = isl_mat_copy(id); isl_mat_free(id); return bset; } /* 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 return_with_identity(bset, T, 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(TC); if (T2) { isl_mat_free(*T2); *T2 = NULL; } bset = isl_basic_set_set_to_empty(bset); return return_with_identity(bset, T, T2); } 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; } struct isl_basic_set *isl_basic_set_remove_equalities( struct isl_basic_set *bset, struct isl_mat **T, struct isl_mat **T2) { if (T) *T = NULL; if (T2) *T2 = NULL; if (!bset) return NULL; isl_assert(bset->ctx, isl_basic_set_n_param(bset) == 0, goto error); bset = isl_basic_set_gauss(bset, NULL); if (ISL_F_ISSET(bset, ISL_BASIC_SET_EMPTY)) return return_with_identity(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. */ isl_stat isl_basic_set_dim_residue_class(__isl_keep isl_basic_set *bset, int pos, isl_int *modulo, isl_int *residue) { isl_bool fixed; struct isl_ctx *ctx; struct isl_mat *H = NULL, *U = NULL, *C, *H1, *U1; unsigned total; unsigned nparam; if (!bset || !modulo || !residue) return isl_stat_error; fixed = isl_basic_set_plain_dim_is_fixed(bset, pos, residue); if (fixed < 0) return isl_stat_error; if (fixed) { isl_int_set_si(*modulo, 0); return isl_stat_ok; } ctx = isl_basic_set_get_ctx(bset); total = isl_basic_set_total_dim(bset); nparam = isl_basic_set_n_param(bset); H = isl_mat_sub_alloc6(ctx, bset->eq, 0, bset->n_eq, 1, total); H = isl_mat_left_hermite(H, 0, &U, NULL); if (!H) return isl_stat_error; 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 isl_stat_ok; } C = isl_mat_alloc(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(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) return isl_stat_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 isl_stat_ok; } isl_int_divexact(*residue, C->row[1][0], C->row[0][0]); isl_int_fdiv_r(*residue, *residue, *modulo); isl_mat_free(C); return isl_stat_ok; error: isl_mat_free(H); isl_mat_free(U); return isl_stat_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. */ isl_stat isl_set_dim_residue_class(__isl_keep isl_set *set, int pos, isl_int *modulo, isl_int *residue) { isl_int m; isl_int r; int i; if (!set || !modulo || !residue) return isl_stat_error; if (set->n == 0) { isl_int_set_si(*modulo, 0); isl_int_set_si(*residue, 0); return isl_stat_ok; } if (isl_basic_set_dim_residue_class(set->p[0], pos, modulo, residue)<0) return isl_stat_error; if (set->n == 1) return isl_stat_ok; if (isl_int_is_one(*modulo)) return isl_stat_ok; 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 isl_stat_ok; error: isl_int_clear(m); isl_int_clear(r); return isl_stat_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. */ isl_stat isl_set_dim_residue_class_val(__isl_keep isl_set *set, int pos, __isl_give isl_val **modulo, __isl_give isl_val **residue) { *modulo = NULL; *residue = NULL; if (!set) return isl_stat_error; *modulo = isl_val_alloc(isl_set_get_ctx(set)); *residue = isl_val_alloc(isl_set_get_ctx(set)); if (!*modulo || !*residue) goto error; if (isl_set_dim_residue_class(set, pos, &(*modulo)->n, &(*residue)->n) < 0) goto error; isl_int_set_si((*modulo)->d, 1); isl_int_set_si((*residue)->d, 1); return isl_stat_ok; error: isl_val_free(*modulo); isl_val_free(*residue); return isl_stat_error; }