/**
* clay_util_relation_negate_row function:
* Negate the line at `row' (doesn't affect the e/i column)
* \param[in,out] statement
* \param[in] row row to negate
*/
void clay_util_relation_negate_row(osl_relation_p r, int row) {
int i;
int precision = r->precision;
for (i = 1 ; i < r->nb_columns ; i++) {
osl_int_oppose(precision,
&r->m[row][i],
r->m[row][i]);
}
osl_int_decrement(precision,
&r->m[row][r->nb_columns-1],
r->m[row][r->nb_columns-1]);
}
// Converts relation into ``input form'': coefficients on the input side of the
// relation matrix are set to 1 whenever possible.
int clay_relation_input_form(osl_relation_p relation) {
int i, j, col_i;
clay_array_p row_indices = clay_array_malloc();
clay_relation_alpha_equation_rows(row_indices, relation);
if (row_indices->size != relation->nb_input_dims) {
CLAY_debug("Relation defined by an overdetermined matrix");
return -1;
}
// Forward iteration (triangularization).
for (i = 0; i < row_indices->size; ++i) {
col_i = 1 + relation->nb_output_dims + i;
for (j = i + 1; j < row_indices->size; ++j) {
clay_relation_zero_coefficient(relation, row_indices->data[i],
row_indices->data[j], col_i);
}
}
// Reverse iteration (diagonalization).
for (i = row_indices->size - 1; i >= 0; --i) {
col_i = 1 + relation->nb_output_dims + i;
for (j = i - 1; j >= 0; --j) {
clay_relation_zero_coefficient(relation, row_indices->data[i],
row_indices->data[j], col_i);
}
}
// Change signs on the diagonal.
for (i = 0; i < row_indices->size; ++i) {
col_i = 1 + relation->nb_output_dims + i;
if (osl_int_neg(relation->precision, relation->m[row_indices->data[i]][col_i])) {
for (j = 1; j < relation->nb_columns; j++) {
osl_int_oppose(relation->precision,
&relation->m[row_indices->data[i]][j],
relation->m[row_indices->data[i]][j]);
}
}
}
clay_array_free(row_indices);
return 0;
}
int main(int argc, char** argv)
{
if (argc > 1) { printf("argv are ignored\n"); }
unsigned int nb_fail = 0;
#ifdef OSL_GMP_IS_HERE
int i;
for (i = SCHAR_MIN; i <= SCHAR_MAX; ++i) {
osl_int_t a_sp; osl_int_init_set_si(OSL_PRECISION_SP, &a_sp, i);
osl_int_t a_dp; osl_int_init_set_si(OSL_PRECISION_DP, &a_dp, i);
osl_int_t a_mp; osl_int_init_set_si(OSL_PRECISION_MP, &a_mp, i);
int j;
for (j = SCHAR_MIN; j <= SCHAR_MAX; ++j) {
int error = 0;
osl_int_t b_sp; osl_int_init_set_si(OSL_PRECISION_SP, &b_sp, j);
osl_int_t b_dp; osl_int_init_set_si(OSL_PRECISION_DP, &b_dp, j);
osl_int_t b_mp; osl_int_init_set_si(OSL_PRECISION_MP, &b_mp, j);
osl_int_t c_sp; osl_int_init(OSL_PRECISION_SP, &c_sp);
osl_int_t c_dp; osl_int_init(OSL_PRECISION_DP, &c_dp);
osl_int_t c_mp; osl_int_init(OSL_PRECISION_MP, &c_mp);
int const a_sp_i = osl_int_get_si(OSL_PRECISION_SP, a_sp);
int const a_dp_i = osl_int_get_si(OSL_PRECISION_DP, a_dp);
int const a_mp_i = osl_int_get_si(OSL_PRECISION_MP, a_mp);
int const b_sp_i = osl_int_get_si(OSL_PRECISION_SP, b_sp);
int const b_dp_i = osl_int_get_si(OSL_PRECISION_DP, b_dp);
int const b_mp_i = osl_int_get_si(OSL_PRECISION_MP, b_mp);
// osl_int_init_set_si & osl_int_init & osl_int_get_si
if (!error) {
int c_sp_i = osl_int_get_si(OSL_PRECISION_SP, c_sp);
int c_dp_i = osl_int_get_si(OSL_PRECISION_DP, c_dp);
int c_mp_i = osl_int_get_si(OSL_PRECISION_MP, c_mp);
if (a_sp_i != a_dp_i || a_sp_i != a_mp_i) {
error++; printf("Error osl_int_init_set_si or osl_int_get_si\n");
}
if (b_sp_i != b_dp_i || b_sp_i != b_mp_i) {
error++; printf("Error osl_int_init_set_si or osl_int_get_si\n");
}
if (c_sp_i != c_dp_i || c_sp_i != c_mp_i || c_sp_i != 0) {
error++; printf("Error osl_int_init or osl_int_get_si\n");
}
}
// osl_int_assign
if (!error) {
osl_int_assign(OSL_PRECISION_SP, &c_sp, b_sp);
osl_int_assign(OSL_PRECISION_DP, &c_dp, b_dp);
osl_int_assign(OSL_PRECISION_MP, &c_mp, b_mp);
if (osl_int_ne(OSL_PRECISION_SP, c_sp, b_sp)) {
error++; printf("Error osl_int_assign\n");
}
if (osl_int_ne(OSL_PRECISION_DP, c_dp, b_dp)) {
error++; printf("Error osl_int_assign\n");
}
if (osl_int_ne(OSL_PRECISION_MP, c_mp, b_mp)) {
error++; printf("Error osl_int_assign\n");
}
}
// osl_int_swap
// osl_int_increment
if (!error) {
osl_int_increment(OSL_PRECISION_SP, &c_sp, a_sp);
osl_int_increment(OSL_PRECISION_DP, &c_dp, a_dp);
osl_int_increment(OSL_PRECISION_MP, &c_mp, a_mp);
int c_sp_i = osl_int_get_si(OSL_PRECISION_SP, c_sp);
int c_dp_i = osl_int_get_si(OSL_PRECISION_DP, c_dp);
int c_mp_i = osl_int_get_si(OSL_PRECISION_MP, c_mp);
if (c_sp_i != c_dp_i || c_sp_i != c_mp_i || c_sp_i != a_sp_i + 1) {
error++; printf("Error osl_int_increment\n");
}
}
// osl_int_decrement
if (!error) {
osl_int_decrement(OSL_PRECISION_SP, &c_sp, a_sp);
osl_int_decrement(OSL_PRECISION_DP, &c_dp, a_dp);
osl_int_decrement(OSL_PRECISION_MP, &c_mp, a_mp);
int c_sp_i = osl_int_get_si(OSL_PRECISION_SP, c_sp);
int c_dp_i = osl_int_get_si(OSL_PRECISION_DP, c_dp);
int c_mp_i = osl_int_get_si(OSL_PRECISION_MP, c_mp);
if (c_sp_i != c_dp_i || c_sp_i != c_mp_i || c_sp_i != a_sp_i - 1) {
error++; printf("Error osl_int_decrement\n");
}
}
// osl_int_add
if (!error) {
osl_int_add(OSL_PRECISION_SP, &c_sp, a_sp, b_sp);
osl_int_add(OSL_PRECISION_DP, &c_dp, a_dp, b_dp);
osl_int_add(OSL_PRECISION_MP, &c_mp, a_mp, b_mp);
int c_sp_i = osl_int_get_si(OSL_PRECISION_SP, c_sp);
int c_dp_i = osl_int_get_si(OSL_PRECISION_DP, c_dp);
int c_mp_i = osl_int_get_si(OSL_PRECISION_MP, c_mp);
if (c_sp_i != c_dp_i || c_sp_i != c_mp_i || c_sp_i != a_sp_i + b_sp_i) {
error++; printf("Error osl_int_add\n");
}
}
// osl_int_add_si
// osl_int_sub
if (!error) {
osl_int_sub(OSL_PRECISION_SP, &c_sp, a_sp, b_sp);
osl_int_sub(OSL_PRECISION_DP, &c_dp, a_dp, b_dp);
osl_int_sub(OSL_PRECISION_MP, &c_mp, a_mp, b_mp);
int c_sp_i = osl_int_get_si(OSL_PRECISION_SP, c_sp);
int c_dp_i = osl_int_get_si(OSL_PRECISION_DP, c_dp);
int c_mp_i = osl_int_get_si(OSL_PRECISION_MP, c_mp);
if (c_sp_i != c_dp_i || c_sp_i != c_mp_i || c_sp_i != a_sp_i - b_sp_i) {
error++; printf("Error osl_int_add\n");
}
}
// osl_int_mul
if (!error) {
osl_int_mul(OSL_PRECISION_SP, &c_sp, a_sp, b_sp);
osl_int_mul(OSL_PRECISION_DP, &c_dp, a_dp, b_dp);
osl_int_mul(OSL_PRECISION_MP, &c_mp, a_mp, b_mp);
int c_sp_i = osl_int_get_si(OSL_PRECISION_SP, c_sp);
int c_dp_i = osl_int_get_si(OSL_PRECISION_DP, c_dp);
int c_mp_i = osl_int_get_si(OSL_PRECISION_MP, c_mp);
if (c_sp_i != c_dp_i || c_sp_i != c_mp_i || c_sp_i != a_sp_i * b_sp_i) {
error++; printf("Error osl_int_mul\n");
}
}
// osl_int_mul_si
if (!error) {
osl_int_mul_si(OSL_PRECISION_SP, &c_sp, a_sp, b_sp_i);
osl_int_mul_si(OSL_PRECISION_DP, &c_dp, a_dp, b_dp_i);
osl_int_mul_si(OSL_PRECISION_MP, &c_mp, a_mp, b_mp_i);
int c_sp_i = osl_int_get_si(OSL_PRECISION_SP, c_sp);
int c_dp_i = osl_int_get_si(OSL_PRECISION_DP, c_dp);
int c_mp_i = osl_int_get_si(OSL_PRECISION_MP, c_mp);
if (c_sp_i != c_dp_i || c_sp_i != c_mp_i || c_sp_i != a_sp_i * b_sp_i) {
error++; printf("Error osl_int_mul_si\n");
}
}
// osl_int_div_exact
if (!error && b_sp_i != 0 && a_sp_i % b_sp_i == 0) {
osl_int_div_exact(OSL_PRECISION_SP, &c_sp, a_sp, b_sp);
osl_int_div_exact(OSL_PRECISION_DP, &c_dp, a_dp, b_dp);
osl_int_div_exact(OSL_PRECISION_MP, &c_mp, a_mp, b_mp);
int c_sp_i = osl_int_get_si(OSL_PRECISION_SP, c_sp);
int c_dp_i = osl_int_get_si(OSL_PRECISION_DP, c_dp);
int c_mp_i = osl_int_get_si(OSL_PRECISION_MP, c_mp);
if (c_sp_i != c_dp_i || c_sp_i != c_mp_i || c_sp_i != a_sp_i / b_sp_i) {
error++; printf("Error osl_int_div_exact\n");
}
}
// osl_int_floor_div_q
if (!error && b_sp_i != 0) {
osl_int_floor_div_q(OSL_PRECISION_SP, &c_sp, a_sp, b_sp);
osl_int_floor_div_q(OSL_PRECISION_DP, &c_dp, a_dp, b_dp);
osl_int_floor_div_q(OSL_PRECISION_MP, &c_mp, a_mp, b_mp);
int c_sp_i = osl_int_get_si(OSL_PRECISION_SP, c_sp);
int c_dp_i = osl_int_get_si(OSL_PRECISION_DP, c_dp);
int c_mp_i = osl_int_get_si(OSL_PRECISION_MP, c_mp);
if (c_sp_i != c_dp_i || c_sp_i != c_mp_i) {
error++; printf("Error osl_int_floor_div_q\n");
}
}
// osl_int_floor_div_r
if (!error && b_sp_i != 0) {
osl_int_floor_div_r(OSL_PRECISION_SP, &c_sp, a_sp, b_sp);
osl_int_floor_div_r(OSL_PRECISION_DP, &c_dp, a_dp, b_dp);
osl_int_floor_div_r(OSL_PRECISION_MP, &c_mp, a_mp, b_mp);
int c_sp_i = osl_int_get_si(OSL_PRECISION_SP, c_sp);
int c_dp_i = osl_int_get_si(OSL_PRECISION_DP, c_dp);
int c_mp_i = osl_int_get_si(OSL_PRECISION_MP, c_mp);
if (c_sp_i != c_dp_i || c_sp_i != c_mp_i) {
error++; printf("Error osl_int_floor_div_r\n");
}
}
// osl_int_floor_div_q_r
if (!error && b_sp_i != 0) {
osl_int_t q_sp; osl_int_init(OSL_PRECISION_SP, &q_sp);
osl_int_t q_dp; osl_int_init(OSL_PRECISION_DP, &q_dp);
osl_int_t q_mp; osl_int_init(OSL_PRECISION_MP, &q_mp);
osl_int_t r_sp; osl_int_init(OSL_PRECISION_SP, &r_sp);
osl_int_t r_dp; osl_int_init(OSL_PRECISION_DP, &r_dp);
osl_int_t r_mp; osl_int_init(OSL_PRECISION_MP, &r_mp);
osl_int_floor_div_q_r(OSL_PRECISION_SP, &q_sp, &r_sp, a_sp, b_sp);
osl_int_floor_div_q_r(OSL_PRECISION_DP, &q_dp, &r_dp, a_dp, b_dp);
osl_int_floor_div_q_r(OSL_PRECISION_MP, &q_mp, &r_mp, a_mp, b_mp);
int q_sp_i = osl_int_get_si(OSL_PRECISION_SP, q_sp);
int q_dp_i = osl_int_get_si(OSL_PRECISION_DP, q_dp);
int q_mp_i = osl_int_get_si(OSL_PRECISION_MP, q_mp);
int r_sp_i = osl_int_get_si(OSL_PRECISION_SP, r_sp);
int r_dp_i = osl_int_get_si(OSL_PRECISION_DP, r_dp);
int r_mp_i = osl_int_get_si(OSL_PRECISION_MP, r_mp);
if (q_sp_i != q_dp_i || q_sp_i != q_mp_i) {
error++; printf("Error osl_int_floor_div_q_r\n");
}
if (r_sp_i != r_dp_i || r_sp_i != r_mp_i) {
error++; printf("Error osl_int_floor_div_q_r\n");
}
}
// osl_int_mod
if (!error && b_sp_i != 0) {
osl_int_mod(OSL_PRECISION_SP, &c_sp, a_sp, b_sp);
osl_int_mod(OSL_PRECISION_DP, &c_dp, a_dp, b_dp);
osl_int_mod(OSL_PRECISION_MP, &c_mp, a_mp, b_mp);
int c_sp_i = osl_int_get_si(OSL_PRECISION_SP, c_sp);
int c_dp_i = osl_int_get_si(OSL_PRECISION_DP, c_dp);
int c_mp_i = osl_int_get_si(OSL_PRECISION_MP, c_mp);
if (c_sp_i != c_dp_i || c_sp_i != c_mp_i) {
error++; printf("Error osl_int_mod\n");
}
}
// osl_int_gcd
if (!error) {
osl_int_gcd(OSL_PRECISION_SP, &c_sp, a_sp, b_sp);
osl_int_gcd(OSL_PRECISION_DP, &c_dp, a_dp, b_dp);
osl_int_gcd(OSL_PRECISION_MP, &c_mp, a_mp, b_mp);
int c_sp_i = osl_int_get_si(OSL_PRECISION_SP, c_sp);
int c_dp_i = osl_int_get_si(OSL_PRECISION_DP, c_dp);
int c_mp_i = osl_int_get_si(OSL_PRECISION_MP, c_mp);
if (c_sp_i != c_dp_i || c_sp_i != c_mp_i) {
error++; printf("Error osl_int_gcd\n");
}
}
// osl_int_oppose
if (!error) {
osl_int_oppose(OSL_PRECISION_SP, &c_sp, b_sp);
osl_int_oppose(OSL_PRECISION_DP, &c_dp, b_dp);
osl_int_oppose(OSL_PRECISION_MP, &c_mp, b_mp);
int c_sp_i = osl_int_get_si(OSL_PRECISION_SP, c_sp);
int c_dp_i = osl_int_get_si(OSL_PRECISION_DP, c_dp);
int c_mp_i = osl_int_get_si(OSL_PRECISION_MP, c_mp);
if (c_sp_i != c_dp_i || c_sp_i != c_mp_i) {
error++; printf("Error osl_int_oppose\n");
}
}
// osl_int_abs
if (!error) {
osl_int_abs(OSL_PRECISION_SP, &c_sp, b_sp);
osl_int_abs(OSL_PRECISION_DP, &c_dp, b_dp);
osl_int_abs(OSL_PRECISION_MP, &c_mp, b_mp);
int c_sp_i = osl_int_get_si(OSL_PRECISION_SP, c_sp);
int c_dp_i = osl_int_get_si(OSL_PRECISION_DP, c_dp);
int c_mp_i = osl_int_get_si(OSL_PRECISION_MP, c_mp);
if (c_sp_i != c_dp_i || c_sp_i != c_mp_i) {
error++; printf("Error osl_int_abs\n");
}
}
// osl_int_size_in_base_2
if (!error) {
size_t r_sp = osl_int_size_in_base_2(OSL_PRECISION_SP, b_sp);
size_t r_dp = osl_int_size_in_base_2(OSL_PRECISION_DP, b_dp);
size_t r_mp = osl_int_size_in_base_2(OSL_PRECISION_MP, b_mp);
osl_int_set_si(OSL_PRECISION_SP, &c_sp, r_sp);
osl_int_set_si(OSL_PRECISION_DP, &c_dp, r_dp);
osl_int_set_si(OSL_PRECISION_MP, &c_mp, r_mp);
if (r_sp != r_dp || r_sp != r_mp) {
error++; printf("Error osl_int_size_in_base_2\n");
}
}
// osl_int_size_in_base_10
// if (!error) {
// size_t r_sp = osl_int_size_in_base_10(OSL_PRECISION_SP, b_sp);
// size_t r_dp = osl_int_size_in_base_10(OSL_PRECISION_DP, b_dp);
// size_t r_mp = osl_int_size_in_base_10(OSL_PRECISION_MP, b_mp);
//
// osl_int_set_si(OSL_PRECISION_SP, &c_sp, r_sp);
// osl_int_set_si(OSL_PRECISION_DP, &c_dp, r_dp);
// osl_int_set_si(OSL_PRECISION_MP, &c_mp, r_mp);
//
// if (r_sp != r_dp || r_sp != r_mp)
// { error++; printf("Error osl_int_size_in_base_10\n"); }
// }
// osl_int_eq
// osl_int_ne
// osl_int_pos
// osl_int_neg
// osl_int_zero
// osl_int_one
// osl_int_mone
// osl_int_divisible
if (error) {
printf("Error with:\n");
printf("\n");
printf("a_sp = "); osl_int_print(stdout, OSL_PRECISION_SP, a_sp);
printf("\n");
printf("a_dp = "); osl_int_print(stdout, OSL_PRECISION_DP, a_dp);
printf("\n");
printf("a_mp = "); osl_int_print(stdout, OSL_PRECISION_MP, a_mp);
printf("\n");
printf("\n");
printf("b_sp = "); osl_int_print(stdout, OSL_PRECISION_SP, b_sp);
printf("\n");
printf("b_dp = "); osl_int_print(stdout, OSL_PRECISION_DP, b_dp);
printf("\n");
printf("b_mp = "); osl_int_print(stdout, OSL_PRECISION_MP, b_mp);
printf("\n");
printf("\n");
printf("c_sp = "); osl_int_print(stdout, OSL_PRECISION_SP, c_sp);
printf("\n");
printf("c_dp = "); osl_int_print(stdout, OSL_PRECISION_DP, c_dp);
printf("\n");
printf("c_mp = "); osl_int_print(stdout, OSL_PRECISION_MP, c_mp);
printf("\n");
printf("\n");
nb_fail += error;
}
}
}
printf("%s ", argv[0]);
printf("fails = %d\n", nb_fail);
#else
printf("%s ", argv[0]);
printf("works only with GMP\n");
#endif
return nb_fail;
}
// assumes alpha-beta form is preserved, but makes no assumption on the
// (in)equality order of appearance.
int clay_relation_output_form(osl_relation_p relation) {
clay_array_p equation_rows;
int i, j, k, row_i, row_j;
int nb_equations, nb_alpha_dims, nb_linearly_dependent_rows;
int nb_steps;
equation_rows = clay_array_malloc();
clay_relation_alpha_equation_rows(equation_rows, relation);
nb_equations = equation_rows->size;
nb_alpha_dims = (relation->nb_output_dims - 1) / 2;
nb_linearly_dependent_rows = 0;
nb_steps = nb_alpha_dims < nb_equations ? nb_alpha_dims : nb_equations;
// Forward pass of integer Gauss elimination: make the alpha-part of the
// relation matrix upper triangular by subtracting lines with coefficients.
// Multiply both lines by the GCD to avoid having fractional coefficients,
// then divide the remaining numbers by their GCD to avoid explosion.
for (i = 0; i < nb_steps; i++) {
for (j = i + 1; j < nb_equations; j++) {
row_i = equation_rows->data[i];
row_j = equation_rows->data[j];
clay_relation_zero_coefficient(relation, row_i, row_j, 2*i + 2);
}
}
// Linearly dependent rows should now contain zeros.
for (i = 0; i < nb_equations; i++) {
row_i = equation_rows->data[i];
if (clay_relation_line_is_zero(relation, row_i, 1,
1 + relation->nb_output_dims)) {
nb_linearly_dependent_rows += 1;
}
}
// Reverse pass of integer Gauss elimination: make the alpha-part of the
// relation matrix diagonal.
for (i = nb_steps - 1; i >= 0; i--) {
for (j = i - 1; j >= 0; j--) {
row_i = equation_rows->data[i];
row_j = equation_rows->data[j];
clay_relation_zero_coefficient(relation, row_i, row_j, 2*i + 2);
}
}
// Flip diagonal elements if necessary.
for (i = 0; i < nb_steps; i++) {
row_i = equation_rows->data[i];
if (!osl_int_neg(relation->precision, relation->m[row_i][2*i + 2])) {
for (k = 1; k < relation->nb_columns; k++) {
if (k < 1 + relation->nb_output_dims && (k % 2) == 1) {
continue; // ignore betas
}
osl_int_oppose(relation->precision, &relation->m[row_i][k],
relation->m[row_i][k]);
}
}
}
if (nb_equations - nb_linearly_dependent_rows > nb_alpha_dims) {
CLAY_debug("relation is defined by overdetermined matrix");
return -1;
} else if (nb_equations - nb_linearly_dependent_rows < nb_alpha_dims) {
// Relation is defined by underdetermined matrix, but this may be okay if
// dimensions are defined implicitly.
}
// Check that diagonal elements are 1. They should be after gcd compression,
// otherwise the corresponding output dimension is invalid (fractional).
for (i = 0; i < nb_equations; i++) {
row_i = equation_rows->data[i];
if (!osl_int_one(relation->precision, relation->m[row_i][2*i + 2])) {
CLAY_debug("output form contains fractional dimension");
return -2;
}
}
clay_array_free(equation_rows);
return 0;
}