You can not select more than 25 topics
Topics must start with a letter or number, can include dashes ('-') and can be up to 35 characters long.
424 lines
8.8 KiB
424 lines
8.8 KiB
/*
|
|
* Copyright © 2012 Collabora, Ltd.
|
|
*
|
|
* Permission is hereby granted, free of charge, to any person obtaining
|
|
* a copy of this software and associated documentation files (the
|
|
* "Software"), to deal in the Software without restriction, including
|
|
* without limitation the rights to use, copy, modify, merge, publish,
|
|
* distribute, sublicense, and/or sell copies of the Software, and to
|
|
* permit persons to whom the Software is furnished to do so, subject to
|
|
* the following conditions:
|
|
*
|
|
* The above copyright notice and this permission notice (including the
|
|
* next paragraph) shall be included in all copies or substantial
|
|
* portions of the Software.
|
|
*
|
|
* THE SOFTWARE IS PROVIDED "AS IS", WITHOUT WARRANTY OF ANY KIND,
|
|
* EXPRESS OR IMPLIED, INCLUDING BUT NOT LIMITED TO THE WARRANTIES OF
|
|
* MERCHANTABILITY, FITNESS FOR A PARTICULAR PURPOSE AND
|
|
* NONINFRINGEMENT. IN NO EVENT SHALL THE AUTHORS OR COPYRIGHT HOLDERS
|
|
* BE LIABLE FOR ANY CLAIM, DAMAGES OR OTHER LIABILITY, WHETHER IN AN
|
|
* ACTION OF CONTRACT, TORT OR OTHERWISE, ARISING FROM, OUT OF OR IN
|
|
* CONNECTION WITH THE SOFTWARE OR THE USE OR OTHER DEALINGS IN THE
|
|
* SOFTWARE.
|
|
*/
|
|
|
|
#include "config.h"
|
|
|
|
#include <stdio.h>
|
|
#include <stdlib.h>
|
|
#include <math.h>
|
|
#include <unistd.h>
|
|
#include <signal.h>
|
|
#include <time.h>
|
|
|
|
#include <libweston/matrix.h>
|
|
|
|
struct inverse_matrix {
|
|
double LU[16]; /* column-major */
|
|
unsigned perm[4]; /* permutation */
|
|
};
|
|
|
|
static struct timespec begin_time;
|
|
|
|
static void
|
|
reset_timer(void)
|
|
{
|
|
clock_gettime(CLOCK_MONOTONIC, &begin_time);
|
|
}
|
|
|
|
static double
|
|
read_timer(void)
|
|
{
|
|
struct timespec t;
|
|
|
|
clock_gettime(CLOCK_MONOTONIC, &t);
|
|
return (double)(t.tv_sec - begin_time.tv_sec) +
|
|
1e-9 * (t.tv_nsec - begin_time.tv_nsec);
|
|
}
|
|
|
|
static double
|
|
det3x3(const float *c0, const float *c1, const float *c2)
|
|
{
|
|
return (double)
|
|
c0[0] * c1[1] * c2[2] +
|
|
c1[0] * c2[1] * c0[2] +
|
|
c2[0] * c0[1] * c1[2] -
|
|
c0[2] * c1[1] * c2[0] -
|
|
c1[2] * c2[1] * c0[0] -
|
|
c2[2] * c0[1] * c1[0];
|
|
}
|
|
|
|
static double
|
|
determinant(const struct weston_matrix *m)
|
|
{
|
|
double det = 0;
|
|
#if 1
|
|
/* develop on last row */
|
|
det -= m->d[3 + 0 * 4] * det3x3(&m->d[4], &m->d[8], &m->d[12]);
|
|
det += m->d[3 + 1 * 4] * det3x3(&m->d[0], &m->d[8], &m->d[12]);
|
|
det -= m->d[3 + 2 * 4] * det3x3(&m->d[0], &m->d[4], &m->d[12]);
|
|
det += m->d[3 + 3 * 4] * det3x3(&m->d[0], &m->d[4], &m->d[8]);
|
|
#else
|
|
/* develop on first row */
|
|
det += m->d[0 + 0 * 4] * det3x3(&m->d[5], &m->d[9], &m->d[13]);
|
|
det -= m->d[0 + 1 * 4] * det3x3(&m->d[1], &m->d[9], &m->d[13]);
|
|
det += m->d[0 + 2 * 4] * det3x3(&m->d[1], &m->d[5], &m->d[13]);
|
|
det -= m->d[0 + 3 * 4] * det3x3(&m->d[1], &m->d[5], &m->d[9]);
|
|
#endif
|
|
return det;
|
|
}
|
|
|
|
static void
|
|
print_permutation_matrix(const struct inverse_matrix *m)
|
|
{
|
|
const unsigned *p = m->perm;
|
|
const char *row[4] = {
|
|
"1 0 0 0\n",
|
|
"0 1 0 0\n",
|
|
"0 0 1 0\n",
|
|
"0 0 0 1\n"
|
|
};
|
|
|
|
printf(" P =\n%s%s%s%s", row[p[0]], row[p[1]], row[p[2]], row[p[3]]);
|
|
}
|
|
|
|
static void
|
|
print_LU_decomposition(const struct inverse_matrix *m)
|
|
{
|
|
unsigned r, c;
|
|
|
|
printf(" L "
|
|
" U\n");
|
|
for (r = 0; r < 4; ++r) {
|
|
double v;
|
|
|
|
for (c = 0; c < 4; ++c) {
|
|
if (c < r)
|
|
v = m->LU[r + c * 4];
|
|
else if (c == r)
|
|
v = 1.0;
|
|
else
|
|
v = 0.0;
|
|
printf(" %12.6f", v);
|
|
}
|
|
|
|
printf(" | ");
|
|
|
|
for (c = 0; c < 4; ++c) {
|
|
if (c >= r)
|
|
v = m->LU[r + c * 4];
|
|
else
|
|
v = 0.0;
|
|
printf(" %12.6f", v);
|
|
}
|
|
printf("\n");
|
|
}
|
|
}
|
|
|
|
static void
|
|
print_inverse_data_matrix(const struct inverse_matrix *m)
|
|
{
|
|
unsigned r, c;
|
|
|
|
for (r = 0; r < 4; ++r) {
|
|
for (c = 0; c < 4; ++c)
|
|
printf(" %12.6f", m->LU[r + c * 4]);
|
|
printf("\n");
|
|
}
|
|
|
|
printf("permutation: ");
|
|
for (r = 0; r < 4; ++r)
|
|
printf(" %u", m->perm[r]);
|
|
printf("\n");
|
|
}
|
|
|
|
static void
|
|
print_matrix(const struct weston_matrix *m)
|
|
{
|
|
unsigned r, c;
|
|
|
|
for (r = 0; r < 4; ++r) {
|
|
for (c = 0; c < 4; ++c)
|
|
printf(" %14.6e", m->d[r + c * 4]);
|
|
printf("\n");
|
|
}
|
|
}
|
|
|
|
static double
|
|
frand(void)
|
|
{
|
|
double r = random();
|
|
return r / (double)(RAND_MAX / 2) - 1.0f;
|
|
}
|
|
|
|
static void
|
|
randomize_matrix(struct weston_matrix *m)
|
|
{
|
|
unsigned i;
|
|
for (i = 0; i < 16; ++i)
|
|
#if 1
|
|
m->d[i] = frand() * exp(10.0 * frand());
|
|
#else
|
|
m->d[i] = frand();
|
|
#endif
|
|
}
|
|
|
|
/* Take a matrix, compute inverse, multiply together
|
|
* and subtract the identity matrix to get the error matrix.
|
|
* Return the largest absolute value from the error matrix.
|
|
*/
|
|
static double
|
|
test_inverse(struct weston_matrix *m)
|
|
{
|
|
unsigned i;
|
|
struct inverse_matrix q;
|
|
double errsup = 0.0;
|
|
|
|
if (matrix_invert(q.LU, q.perm, m) != 0)
|
|
return INFINITY;
|
|
|
|
for (i = 0; i < 4; ++i)
|
|
inverse_transform(q.LU, q.perm, &m->d[i * 4]);
|
|
|
|
m->d[0] -= 1.0f;
|
|
m->d[5] -= 1.0f;
|
|
m->d[10] -= 1.0f;
|
|
m->d[15] -= 1.0f;
|
|
|
|
for (i = 0; i < 16; ++i) {
|
|
double err = fabs(m->d[i]);
|
|
if (err > errsup)
|
|
errsup = err;
|
|
}
|
|
|
|
return errsup;
|
|
}
|
|
|
|
enum {
|
|
TEST_OK,
|
|
TEST_NOT_INVERTIBLE_OK,
|
|
TEST_FAIL,
|
|
TEST_COUNT
|
|
};
|
|
|
|
static int
|
|
test(void)
|
|
{
|
|
struct weston_matrix m;
|
|
double det, errsup;
|
|
|
|
randomize_matrix(&m);
|
|
det = determinant(&m);
|
|
|
|
errsup = test_inverse(&m);
|
|
if (errsup < 1e-6)
|
|
return TEST_OK;
|
|
|
|
if (fabs(det) < 1e-5 && isinf(errsup))
|
|
return TEST_NOT_INVERTIBLE_OK;
|
|
|
|
printf("test fail, det: %g, error sup: %g\n", det, errsup);
|
|
|
|
return TEST_FAIL;
|
|
}
|
|
|
|
static int running;
|
|
static void
|
|
stopme(int n)
|
|
{
|
|
running = 0;
|
|
}
|
|
|
|
static void
|
|
test_loop_precision(void)
|
|
{
|
|
int counts[TEST_COUNT] = { 0 };
|
|
|
|
printf("\nRunning a test loop for 10 seconds...\n");
|
|
running = 1;
|
|
alarm(10);
|
|
while (running) {
|
|
counts[test()]++;
|
|
}
|
|
|
|
printf("tests: %d ok, %d not invertible but ok, %d failed.\n"
|
|
"Total: %d iterations.\n",
|
|
counts[TEST_OK], counts[TEST_NOT_INVERTIBLE_OK],
|
|
counts[TEST_FAIL],
|
|
counts[TEST_OK] + counts[TEST_NOT_INVERTIBLE_OK] +
|
|
counts[TEST_FAIL]);
|
|
}
|
|
|
|
static void __attribute__((noinline))
|
|
test_loop_speed_matrixvector(void)
|
|
{
|
|
struct weston_matrix m;
|
|
struct weston_vector v = { { 0.5, 0.5, 0.5, 1.0 } };
|
|
unsigned long count = 0;
|
|
double t;
|
|
|
|
printf("\nRunning 3 s test on weston_matrix_transform()...\n");
|
|
|
|
weston_matrix_init(&m);
|
|
|
|
running = 1;
|
|
alarm(3);
|
|
reset_timer();
|
|
while (running) {
|
|
weston_matrix_transform(&m, &v);
|
|
count++;
|
|
}
|
|
t = read_timer();
|
|
|
|
printf("%lu iterations in %f seconds, avg. %.1f ns/iter.\n",
|
|
count, t, 1e9 * t / count);
|
|
}
|
|
|
|
static void __attribute__((noinline))
|
|
test_loop_speed_inversetransform(void)
|
|
{
|
|
struct weston_matrix m;
|
|
struct inverse_matrix inv;
|
|
struct weston_vector v = { { 0.5, 0.5, 0.5, 1.0 } };
|
|
unsigned long count = 0;
|
|
double t;
|
|
|
|
printf("\nRunning 3 s test on inverse_transform()...\n");
|
|
|
|
weston_matrix_init(&m);
|
|
matrix_invert(inv.LU, inv.perm, &m);
|
|
|
|
running = 1;
|
|
alarm(3);
|
|
reset_timer();
|
|
while (running) {
|
|
inverse_transform(inv.LU, inv.perm, v.f);
|
|
count++;
|
|
}
|
|
t = read_timer();
|
|
|
|
printf("%lu iterations in %f seconds, avg. %.1f ns/iter.\n",
|
|
count, t, 1e9 * t / count);
|
|
}
|
|
|
|
static void __attribute__((noinline))
|
|
test_loop_speed_invert(void)
|
|
{
|
|
struct weston_matrix m;
|
|
struct inverse_matrix inv;
|
|
unsigned long count = 0;
|
|
double t;
|
|
|
|
printf("\nRunning 3 s test on matrix_invert()...\n");
|
|
|
|
weston_matrix_init(&m);
|
|
|
|
running = 1;
|
|
alarm(3);
|
|
reset_timer();
|
|
while (running) {
|
|
matrix_invert(inv.LU, inv.perm, &m);
|
|
count++;
|
|
}
|
|
t = read_timer();
|
|
|
|
printf("%lu iterations in %f seconds, avg. %.1f ns/iter.\n",
|
|
count, t, 1e9 * t / count);
|
|
}
|
|
|
|
static void __attribute__((noinline))
|
|
test_loop_speed_invert_explicit(void)
|
|
{
|
|
struct weston_matrix m;
|
|
unsigned long count = 0;
|
|
double t;
|
|
|
|
printf("\nRunning 3 s test on weston_matrix_invert()...\n");
|
|
|
|
weston_matrix_init(&m);
|
|
|
|
running = 1;
|
|
alarm(3);
|
|
reset_timer();
|
|
while (running) {
|
|
weston_matrix_invert(&m, &m);
|
|
count++;
|
|
}
|
|
t = read_timer();
|
|
|
|
printf("%lu iterations in %f seconds, avg. %.1f ns/iter.\n",
|
|
count, t, 1e9 * t / count);
|
|
}
|
|
|
|
int main(void)
|
|
{
|
|
struct sigaction ding;
|
|
struct weston_matrix M;
|
|
struct inverse_matrix Q;
|
|
int ret;
|
|
double errsup;
|
|
double det;
|
|
|
|
ding.sa_handler = stopme;
|
|
sigemptyset(&ding.sa_mask);
|
|
ding.sa_flags = 0;
|
|
sigaction(SIGALRM, &ding, NULL);
|
|
|
|
srandom(13);
|
|
|
|
M.d[0] = 3.0; M.d[4] = 17.0; M.d[8] = 10.0; M.d[12] = 0.0;
|
|
M.d[1] = 2.0; M.d[5] = 4.0; M.d[9] = -2.0; M.d[13] = 0.0;
|
|
M.d[2] = 6.0; M.d[6] = 18.0; M.d[10] = -12; M.d[14] = 0.0;
|
|
M.d[3] = 0.0; M.d[7] = 0.0; M.d[11] = 0.0; M.d[15] = 1.0;
|
|
|
|
ret = matrix_invert(Q.LU, Q.perm, &M);
|
|
printf("ret = %d\n", ret);
|
|
printf("det = %g\n\n", determinant(&M));
|
|
|
|
if (ret != 0)
|
|
return 1;
|
|
|
|
print_inverse_data_matrix(&Q);
|
|
printf("P * A = L * U\n");
|
|
print_permutation_matrix(&Q);
|
|
print_LU_decomposition(&Q);
|
|
|
|
|
|
printf("a random matrix:\n");
|
|
randomize_matrix(&M);
|
|
det = determinant(&M);
|
|
print_matrix(&M);
|
|
errsup = test_inverse(&M);
|
|
printf("\nThe matrix multiplied by its inverse, error:\n");
|
|
print_matrix(&M);
|
|
printf("max abs error: %g, original determinant %g\n", errsup, det);
|
|
|
|
test_loop_precision();
|
|
test_loop_speed_matrixvector();
|
|
test_loop_speed_inversetransform();
|
|
test_loop_speed_invert();
|
|
test_loop_speed_invert_explicit();
|
|
|
|
return 0;
|
|
}
|
|
|