| /* |
| * 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_vec_private.h> |
| #include <isl_seq.h> |
| #include "isl_map_private.h" |
| #include "isl_equalities.h" |
| #include <isl_val_private.h> |
| |
| /* 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 __isl_give isl_mat *particular_solution(__isl_keep isl_mat *B, |
| __isl_keep 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 __isl_take isl_mat *parameter_compression_1(__isl_keep isl_mat *B, |
| __isl_keep 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 __isl_give isl_mat *parameter_compression_multi(__isl_keep isl_mat *B, |
| __isl_keep 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) |
| { |
| isl_size dim; |
| isl_mat *id; |
| |
| dim = isl_basic_set_dim(bset, isl_dim_set); |
| if (dim < 0) |
| return isl_basic_set_free(bset); |
| if (!T && !T2) |
| return bset; |
| |
| 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 __isl_give isl_basic_set *compress_variables( |
| __isl_take isl_basic_set *bset, |
| __isl_give isl_mat **T, __isl_give isl_mat **T2) |
| { |
| struct isl_mat *B, *TC; |
| isl_size dim; |
| |
| if (T) |
| *T = NULL; |
| if (T2) |
| *T2 = NULL; |
| if (isl_basic_set_check_no_params(bset) < 0 || |
| isl_basic_set_check_no_locals(bset) < 0) |
| return isl_basic_set_free(bset); |
| dim = isl_basic_set_dim(bset, isl_dim_set); |
| if (dim < 0) |
| return isl_basic_set_free(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; |
| } |
| |
| __isl_give isl_basic_set *isl_basic_set_remove_equalities( |
| __isl_take isl_basic_set *bset, __isl_give isl_mat **T, |
| __isl_give isl_mat **T2) |
| { |
| if (T) |
| *T = NULL; |
| if (T2) |
| *T2 = NULL; |
| if (isl_basic_set_check_no_params(bset) < 0) |
| return isl_basic_set_free(bset); |
| 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; |
| } |
| |
| /* 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; |
| isl_size total; |
| isl_size 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_dim(bset, isl_dim_all); |
| nparam = isl_basic_set_dim(bset, isl_dim_param); |
| if (total < 0 || nparam < 0) |
| return isl_stat_error; |
| 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; |
| } |