mirror of
https://github.com/ioacademy-jikim/debugging
synced 2025-06-08 00:16:11 +00:00
347 lines
8.5 KiB
C
347 lines
8.5 KiB
C
/** Compute the matrix inverse via Gauss-Jordan elimination.
|
|
* This program uses OpenMP separate computation steps but no
|
|
* mutexes. It is an example of a race-free program on which no data races
|
|
* are reported by the happens-before algorithm (drd), but a lot of data races
|
|
* (all false positives) are reported by the Eraser-algorithm (helgrind).
|
|
*/
|
|
|
|
|
|
#define _GNU_SOURCE
|
|
|
|
/***********************/
|
|
/* Include directives. */
|
|
/***********************/
|
|
|
|
#include <assert.h>
|
|
#include <math.h>
|
|
#include <omp.h>
|
|
#include <stdio.h>
|
|
#include <stdlib.h>
|
|
#include <unistd.h> // getopt()
|
|
|
|
|
|
/*********************/
|
|
/* Type definitions. */
|
|
/*********************/
|
|
|
|
typedef double elem_t;
|
|
|
|
|
|
/********************/
|
|
/* Local variables. */
|
|
/********************/
|
|
|
|
static int s_trigger_race;
|
|
|
|
|
|
/*************************/
|
|
/* Function definitions. */
|
|
/*************************/
|
|
|
|
/** Allocate memory for a matrix with the specified number of rows and
|
|
* columns.
|
|
*/
|
|
static elem_t* new_matrix(const int rows, const int cols)
|
|
{
|
|
assert(rows > 0);
|
|
assert(cols > 0);
|
|
return malloc(rows * cols * sizeof(elem_t));
|
|
}
|
|
|
|
/** Free the memory that was allocated for a matrix. */
|
|
static void delete_matrix(elem_t* const a)
|
|
{
|
|
free(a);
|
|
}
|
|
|
|
/** Fill in some numbers in a matrix. */
|
|
static void init_matrix(elem_t* const a, const int rows, const int cols)
|
|
{
|
|
int i, j;
|
|
for (i = 0; i < rows; i++)
|
|
{
|
|
for (j = 0; j < rows; j++)
|
|
{
|
|
a[i * cols + j] = 1.0 / (1 + abs(i-j));
|
|
}
|
|
}
|
|
}
|
|
|
|
/** Print all elements of a matrix. */
|
|
void print_matrix(const char* const label,
|
|
const elem_t* const a, const int rows, const int cols)
|
|
{
|
|
int i, j;
|
|
printf("%s:\n", label);
|
|
for (i = 0; i < rows; i++)
|
|
{
|
|
for (j = 0; j < cols; j++)
|
|
{
|
|
printf("%g ", a[i * cols + j]);
|
|
}
|
|
printf("\n");
|
|
}
|
|
}
|
|
|
|
/** Copy a subset of the elements of a matrix into another matrix. */
|
|
static void copy_matrix(const elem_t* const from,
|
|
const int from_rows,
|
|
const int from_cols,
|
|
const int from_row_first,
|
|
const int from_row_last,
|
|
const int from_col_first,
|
|
const int from_col_last,
|
|
elem_t* const to,
|
|
const int to_rows,
|
|
const int to_cols,
|
|
const int to_row_first,
|
|
const int to_row_last,
|
|
const int to_col_first,
|
|
const int to_col_last)
|
|
{
|
|
int i, j;
|
|
|
|
assert(from_row_last - from_row_first == to_row_last - to_row_first);
|
|
assert(from_col_last - from_col_first == to_col_last - to_col_first);
|
|
|
|
for (i = from_row_first; i < from_row_last; i++)
|
|
{
|
|
assert(i < from_rows);
|
|
assert(i - from_row_first + to_row_first < to_rows);
|
|
for (j = from_col_first; j < from_col_last; j++)
|
|
{
|
|
assert(j < from_cols);
|
|
assert(j - from_col_first + to_col_first < to_cols);
|
|
to[(i - from_row_first + to_col_first) * to_cols
|
|
+ (j - from_col_first + to_col_first)]
|
|
= from[i * from_cols + j];
|
|
}
|
|
}
|
|
}
|
|
|
|
/** Compute the matrix product of a1 and a2. */
|
|
static elem_t* multiply_matrices(const elem_t* const a1,
|
|
const int rows1,
|
|
const int cols1,
|
|
const elem_t* const a2,
|
|
const int rows2,
|
|
const int cols2)
|
|
{
|
|
int i, j, k;
|
|
elem_t* prod;
|
|
|
|
assert(cols1 == rows2);
|
|
|
|
prod = new_matrix(rows1, cols2);
|
|
for (i = 0; i < rows1; i++)
|
|
{
|
|
for (j = 0; j < cols2; j++)
|
|
{
|
|
prod[i * cols2 + j] = 0;
|
|
for (k = 0; k < cols1; k++)
|
|
{
|
|
prod[i * cols2 + j] += a1[i * cols1 + k] * a2[k * cols2 + j];
|
|
}
|
|
}
|
|
}
|
|
return prod;
|
|
}
|
|
|
|
/** Apply the Gauss-Jordan elimination algorithm on the matrix p->a starting
|
|
* at row r0 and up to but not including row r1. It is assumed that as many
|
|
* threads execute this function concurrently as the count barrier p->b was
|
|
* initialized with. If the matrix p->a is nonsingular, and if matrix p->a
|
|
* has at least as many columns as rows, the result of this algorithm is that
|
|
* submatrix p->a[0..p->rows-1,0..p->rows-1] is the identity matrix.
|
|
* @see http://en.wikipedia.org/wiki/Gauss-Jordan_elimination
|
|
*/
|
|
static void gj(elem_t* const a, const int rows, const int cols)
|
|
{
|
|
int i, j, k;
|
|
|
|
for (i = 0; i < rows; i++)
|
|
{
|
|
{
|
|
// Pivoting.
|
|
j = i;
|
|
for (k = i + 1; k < rows; k++)
|
|
{
|
|
if (a[k * cols + i] > a[j * cols + i])
|
|
{
|
|
j = k;
|
|
}
|
|
}
|
|
if (j != i)
|
|
{
|
|
for (k = 0; k < cols; k++)
|
|
{
|
|
const elem_t t = a[i * cols + k];
|
|
a[i * cols + k] = a[j * cols + k];
|
|
a[j * cols + k] = t;
|
|
}
|
|
}
|
|
// Normalize row i.
|
|
if (a[i * cols + i] != 0)
|
|
{
|
|
for (k = cols - 1; k >= 0; k--)
|
|
{
|
|
a[i * cols + k] /= a[i * cols + i];
|
|
}
|
|
}
|
|
}
|
|
|
|
// Reduce all rows j != i.
|
|
|
|
if (s_trigger_race)
|
|
{
|
|
# pragma omp parallel for private(j)
|
|
for (j = 0; j < rows; j++)
|
|
{
|
|
if (i != j)
|
|
{
|
|
const elem_t factor = a[j * cols + i];
|
|
for (k = 0; k < cols; k++)
|
|
{
|
|
a[j * cols + k] -= a[i * cols + k] * factor;
|
|
}
|
|
}
|
|
}
|
|
}
|
|
else
|
|
{
|
|
# pragma omp parallel for private(j, k)
|
|
for (j = 0; j < rows; j++)
|
|
{
|
|
if (i != j)
|
|
{
|
|
const elem_t factor = a[j * cols + i];
|
|
for (k = 0; k < cols; k++)
|
|
{
|
|
a[j * cols + k] -= a[i * cols + k] * factor;
|
|
}
|
|
}
|
|
}
|
|
}
|
|
}
|
|
}
|
|
|
|
/** Matrix inversion via the Gauss-Jordan algorithm. */
|
|
static elem_t* invert_matrix(const elem_t* const a, const int n)
|
|
{
|
|
int i, j;
|
|
elem_t* const inv = new_matrix(n, n);
|
|
elem_t* const tmp = new_matrix(n, 2*n);
|
|
copy_matrix(a, n, n, 0, n, 0, n, tmp, n, 2 * n, 0, n, 0, n);
|
|
for (i = 0; i < n; i++)
|
|
for (j = 0; j < n; j++)
|
|
tmp[i * 2 * n + n + j] = (i == j);
|
|
gj(tmp, n, 2*n);
|
|
copy_matrix(tmp, n, 2*n, 0, n, n, 2*n, inv, n, n, 0, n, 0, n);
|
|
delete_matrix(tmp);
|
|
return inv;
|
|
}
|
|
|
|
/** Compute the average square error between the identity matrix and the
|
|
* product of matrix a with its inverse matrix.
|
|
*/
|
|
static double identity_error(const elem_t* const a, const int n)
|
|
{
|
|
int i, j;
|
|
elem_t e = 0;
|
|
for (i = 0; i < n; i++)
|
|
{
|
|
for (j = 0; j < n; j++)
|
|
{
|
|
const elem_t d = a[i * n + j] - (i == j);
|
|
e += d * d;
|
|
}
|
|
}
|
|
return sqrt(e / (n * n));
|
|
}
|
|
|
|
/** Compute epsilon for the numeric type elem_t. Epsilon is defined as the
|
|
* smallest number for which the sum of one and that number is different of
|
|
* one. It is assumed that the underlying representation of elem_t uses
|
|
* base two.
|
|
*/
|
|
static elem_t epsilon()
|
|
{
|
|
elem_t eps;
|
|
for (eps = 1; 1 + eps != 1; eps /= 2)
|
|
;
|
|
return 2 * eps;
|
|
}
|
|
|
|
static void usage(const char* const exe)
|
|
{
|
|
printf("Usage: %s [-h] [-q] [-r] [-t<n>] <m>\n"
|
|
"-h: display this information.\n"
|
|
"-q: quiet mode -- do not print computed error.\n"
|
|
"-r: trigger a race condition.\n"
|
|
"-t<n>: use <n> threads.\n"
|
|
"<m>: matrix size.\n",
|
|
exe);
|
|
}
|
|
|
|
int main(int argc, char** argv)
|
|
{
|
|
int matrix_size;
|
|
int nthread = 1;
|
|
int silent = 0;
|
|
int optchar;
|
|
elem_t *a, *inv, *prod;
|
|
elem_t eps;
|
|
double error;
|
|
double ratio;
|
|
|
|
while ((optchar = getopt(argc, argv, "hqrt:")) != EOF)
|
|
{
|
|
switch (optchar)
|
|
{
|
|
case 'h': usage(argv[0]); return 1;
|
|
case 'q': silent = 1; break;
|
|
case 'r': s_trigger_race = 1; break;
|
|
case 't': nthread = atoi(optarg); break;
|
|
default:
|
|
return 1;
|
|
}
|
|
}
|
|
|
|
if (optind + 1 != argc)
|
|
{
|
|
fprintf(stderr, "Error: wrong number of arguments.\n");
|
|
return 1;
|
|
}
|
|
matrix_size = atoi(argv[optind]);
|
|
|
|
/* Error checking. */
|
|
assert(matrix_size >= 1);
|
|
assert(nthread >= 1);
|
|
|
|
omp_set_num_threads(nthread);
|
|
omp_set_dynamic(0);
|
|
|
|
eps = epsilon();
|
|
a = new_matrix(matrix_size, matrix_size);
|
|
init_matrix(a, matrix_size, matrix_size);
|
|
inv = invert_matrix(a, matrix_size);
|
|
prod = multiply_matrices(a, matrix_size, matrix_size,
|
|
inv, matrix_size, matrix_size);
|
|
error = identity_error(prod, matrix_size);
|
|
ratio = error / (eps * matrix_size);
|
|
if (! silent)
|
|
{
|
|
printf("error = %g; epsilon = %g; error / (epsilon * n) = %g\n",
|
|
error, eps, ratio);
|
|
}
|
|
if (isfinite(ratio) && ratio < 100)
|
|
printf("Error within bounds.\n");
|
|
else
|
|
printf("Error out of bounds.\n");
|
|
delete_matrix(prod);
|
|
delete_matrix(inv);
|
|
delete_matrix(a);
|
|
|
|
return 0;
|
|
}
|