-#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"
* 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;
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);
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) {
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;
}
* The columns of this matrix generate the lattice that satisfies
* the single (linear) modulo constraint.
*/
-static struct isl_mat *parameter_compression_1(struct isl_ctx *ctx,
+static struct isl_mat *parameter_compression_1(
struct isl_mat *B, struct isl_vec *d)
{
struct isl_mat *U;
- U = isl_mat_alloc(ctx, B->n_col - 1, B->n_col - 1);
+ 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(ctx, U, 1);
- U = isl_mat_right_inverse(ctx, U);
+ 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(ctx, U);
+ U = isl_mat_lin_to_aff(U);
return U;
-error:
- isl_mat_free(ctx, U);
- return NULL;
}
/* Compute a common lattice of solutions to the linear modulo
* 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_ctx *ctx,
+static struct isl_mat *parameter_compression_multi(
struct isl_mat *B, struct isl_vec *d)
{
int i, j, k;
- int ok;
isl_int D;
struct isl_mat *A = NULL, *U = NULL;
struct isl_mat *T;
isl_int_init(D);
- isl_vec_lcm(ctx, d, &D);
+ isl_vec_lcm(d, &D);
size = B->n_col - 1;
- A = isl_mat_alloc(ctx, size, B->n_row * size);
- U = isl_mat_alloc(ctx, size, size);
+ 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(ctx, U, 1);
+ U = isl_mat_unimodular_complete(U, 1);
if (!U)
goto error;
isl_int_divexact(D, D, d->block.data[i]);
isl_int_mul(A->row[k][i*size+j],
D, U->row[j][k]);
}
- A = isl_mat_left_hermite(ctx, A, 0, NULL, NULL);
- T = isl_mat_sub_alloc(ctx, A->row, 0, A->n_row, 0, A->n_row);
- T = isl_mat_lin_to_aff(ctx, T);
+ 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(ctx, T);
- isl_assert(ctx, isl_int_is_one(T->row[0][0]), goto error);
- T = isl_mat_transpose(ctx, T);
- isl_mat_free(ctx, A);
- isl_mat_free(ctx, U);
+ 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(ctx, A);
- isl_mat_free(ctx, U);
+ isl_mat_free(A);
+ isl_mat_free(U);
isl_int_clear(D);
return NULL;
}
* 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, the G is the identity matrix. Otherwise,
+ * 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.
* 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;
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;
}
isl_int_init(D);
if (isl_int_is_one(D))
continue;
if (isl_int_is_zero(D)) {
- B = isl_mat_drop_rows(ctx, B, i, 1);
- d = isl_vec_cow(ctx, 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,
i--;
continue;
}
- B = isl_mat_cow(ctx, B);
+ 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(ctx, d);
+ 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(ctx, B->n_col);
+ T = isl_mat_identity(B->ctx, B->n_col);
else if (B->n_row == 1)
- T = parameter_compression_1(ctx, B, d);
+ T = parameter_compression_1(B, d);
else
- T = parameter_compression_multi(ctx, B, d);
- T = isl_mat_left_hermite(ctx, T, 0, NULL, NULL);
+ T = parameter_compression_multi(B, d);
+ T = isl_mat_left_hermite(T, 0, NULL, NULL);
if (!T)
goto error;
- isl_mat_sub_copy(ctx, T->row + 1, cst->row, cst->n_row, 0, 0, 1);
- 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, 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;
}
*
* 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'].
*
*
* 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
*/
-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;
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 + dim, 0);
}
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;
* 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;
*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(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;
bset = isl_basic_set_gauss(bset, NULL);
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);
/* 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)
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;
}
projects / platform / upstream / isl.git / blobdiff