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solver.c
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#include <stdio.h>
#include <stdlib.h>
#include <math.h>
#include <string.h>
#include <malloc.h>
#include "image.h"
#include "solver.h"
#include <xmmintrin.h>
typedef __v4sf v4sf;
//THIS IS A SLOW VERSION BUT READABLE
//Perform n iterations of the sor_coupled algorithm
//du and dv are used as initial guesses
//The system form is the same as in opticalflow.c
void sor_coupled_slow_but_readable(image_t *du, image_t *dv, const image_t *a11, const image_t *a12, const image_t *a22, const image_t *b1, const image_t *b2, const image_t *dpsis_horiz, const image_t *dpsis_vert, const int iterations, const float omega){
int i,j,iter;
float sigma_u,sigma_v,sum_dpsis,A11,A22,A12,B1,B2,det;
for(iter = 0 ; iter<iterations ; iter++){
for(j=0 ; j<du->height ; j++){
for(i=0 ; i<du->width ; i++){
sigma_u = 0.0f;
sigma_v = 0.0f;
sum_dpsis = 0.0f;
if(j>0){
sigma_u -= dpsis_vert->data[(j-1)*du->stride+i]*du->data[(j-1)*du->stride+i];
sigma_v -= dpsis_vert->data[(j-1)*du->stride+i]*dv->data[(j-1)*du->stride+i];
sum_dpsis += dpsis_vert->data[(j-1)*du->stride+i];
}
if(i>0){
sigma_u -= dpsis_horiz->data[j*du->stride+i-1]*du->data[j*du->stride+i-1];
sigma_v -= dpsis_horiz->data[j*du->stride+i-1]*dv->data[j*du->stride+i-1];
sum_dpsis += dpsis_horiz->data[j*du->stride+i-1];
}
if(j<du->height-1){
sigma_u -= dpsis_vert->data[j*du->stride+i]*du->data[(j+1)*du->stride+i];
sigma_v -= dpsis_vert->data[j*du->stride+i]*dv->data[(j+1)*du->stride+i];
sum_dpsis += dpsis_vert->data[j*du->stride+i];
}
if(i<du->width-1){
sigma_u -= dpsis_horiz->data[j*du->stride+i]*du->data[j*du->stride+i+1];
sigma_v -= dpsis_horiz->data[j*du->stride+i]*dv->data[j*du->stride+i+1];
sum_dpsis += dpsis_horiz->data[j*du->stride+i];
}
A11 = a11->data[j*du->stride+i]+sum_dpsis;
A12 = a12->data[j*du->stride+i];
A22 = a22->data[j*du->stride+i]+sum_dpsis;
det = A11*A22-A12*A12;
B1 = b1->data[j*du->stride+i]-sigma_u;
B2 = b2->data[j*du->stride+i]-sigma_v;
du->data[j*du->stride+i] = (1.0f-omega)*du->data[j*du->stride+i] +omega*( A22*B1-A12*B2)/det;
dv->data[j*du->stride+i] = (1.0f-omega)*dv->data[j*du->stride+i] +omega*(-A12*B1+A11*B2)/det;
}
}
}
}
// THIS IS A FASTER VERSION BUT UNREADABLE
// the first iteration is separated from the other to compute the inverse of the 2x2 block diagonal
// each iteration is split in two first line / middle lines / last line, and the left block is computed separately on each line
void sor_coupled(image_t *du, image_t *dv, image_t *a11, image_t *a12, image_t *a22, const image_t *b1, const image_t *b2, const image_t *dpsis_horiz, const image_t *dpsis_vert, const int iterations, const float omega){
//sor_coupled_slow(du,dv,a11,a12,a22,b1,b2,dpsis_horiz,dpsis_vert,iterations,omega); return; printf("test\n");
if(du->width<2 || du->height<2 || iterations < 1){
sor_coupled_slow_but_readable(du,dv,a11,a12,a22,b1,b2,dpsis_horiz,dpsis_vert,iterations,omega);
return;
}
const int stride = du->stride, width = du->width;
const int iterheight = du->height-1, iterline = (stride)/4, width_minus_1_sizeoffloat = sizeof(float)*(width-1);
int j,iter,i,k;
float *floatarray = (float*) memalign(16, stride*sizeof(float)*3);
if(floatarray==NULL){
fprintf(stderr, "error in sor_coupled(): not enough memory\n");
exit(1);
}
float *f1 = floatarray;
float *f2 = f1+stride;
float *f3 = f2+stride;
f1[0] = 0.0f;
memset(&f1[width], 0, sizeof(float)*(stride-width));
memset(&f2[width-1], 0, sizeof(float)*(stride-width+1));
memset(&f3[width-1], 0, sizeof(float)*(stride-width+1));
{ // first iteration
v4sf *a11p = (v4sf*) a11->data, *a12p = (v4sf*) a12->data, *a22p = (v4sf*) a22->data, *b1p = (v4sf*) b1->data, *b2p = (v4sf*) b2->data, *hp = (v4sf*) dpsis_horiz->data, *vp = (v4sf*) dpsis_vert->data;
float *du_ptr = du->data, *dv_ptr = dv->data;
v4sf *dub = (v4sf*) (du_ptr+stride), *dvb = (v4sf*) (dv_ptr+stride);
{ // first iteration - first line
memcpy(f1+1, ((float*) hp), width_minus_1_sizeoffloat);
memcpy(f2, du_ptr+1, width_minus_1_sizeoffloat);
memcpy(f3, dv_ptr+1, width_minus_1_sizeoffloat);
v4sf* hpl = (v4sf*) f1, *dur = (v4sf*) f2, *dvr = (v4sf*) f3;
{ // left block
// reverse 2x2 diagonal block
const v4sf dpsis = (*hpl) + (*hp) + (*vp);
const v4sf A11 = (*a22p)+dpsis, A22 = (*a11p)+dpsis;
const v4sf det = A11*A22 - (*a12p)*(*a12p);
*a11p = A11/det;
*a22p = A22/det;
*a12p /= -det;
// do one iteration
const v4sf s1 = (*hp)*(*dur) + (*vp)*(*dub) + (*b1p);
const v4sf s2 = (*hp)*(*dvr) + (*vp)*(*dvb) + (*b2p);
du_ptr[0] += omega*( a11p[0][0]*s1[0] + a12p[0][0]*s2[0] - du_ptr[0] );
dv_ptr[0] += omega*( a12p[0][0]*s1[0] + a22p[0][0]*s2[0] - dv_ptr[0] );
for(k=1;k<4;k++){
const float B1 = hpl[0][k]*du_ptr[k-1] + s1[k];
const float B2 = hpl[0][k]*dv_ptr[k-1] + s2[k];
du_ptr[k] += omega*( a11p[0][k]*B1 + a12p[0][k]*B2 - du_ptr[k] );
dv_ptr[k] += omega*( a12p[0][k]*B1 + a22p[0][k]*B2 - dv_ptr[k] );
}
// increment pointer
hpl+=1; hp+=1; vp+=1; a11p+=1; a12p+=1; a22p+=1;
dur+=1; dvr+=1; dub+=1; dvb +=1; b1p+=1; b2p+=1;
du_ptr += 4; dv_ptr += 4;
}
for(i=iterline;--i;){
// reverse 2x2 diagonal block
const v4sf dpsis = (*hpl) + (*hp) + (*vp);
const v4sf A11 = (*a22p)+dpsis, A22 = (*a11p)+dpsis;
const v4sf det = A11*A22 - (*a12p)*(*a12p);
*a11p = A11/det;
*a22p = A22/det;
*a12p /= -det;
// do one iteration
const v4sf s1 = (*hp)*(*dur) + (*vp)*(*dub) + (*b1p);
const v4sf s2 = (*hp)*(*dvr) + (*vp)*(*dvb) + (*b2p);
for(k=0;k<4;k++){
const float B1 = hpl[0][k]*du_ptr[k-1] + s1[k];
const float B2 = hpl[0][k]*dv_ptr[k-1] + s2[k];
du_ptr[k] += omega*( a11p[0][k]*B1 + a12p[0][k]*B2 - du_ptr[k] );
dv_ptr[k] += omega*( a12p[0][k]*B1 + a22p[0][k]*B2 - dv_ptr[k] );
}
// increment pointer
hpl+=1; hp+=1; vp+=1; a11p+=1; a12p+=1; a22p+=1;
dur+=1; dvr+=1; dub+=1; dvb +=1; b1p+=1; b2p+=1;
du_ptr += 4; dv_ptr += 4;
}
}
v4sf *vpt = (v4sf*) dpsis_vert->data;
v4sf *dut = (v4sf*) du->data, *dvt = (v4sf*) dv->data;
for(j=iterheight;--j;){ // first iteration - middle lines
memcpy(f1+1, ((float*) hp), width_minus_1_sizeoffloat);
memcpy(f2, du_ptr+1, width_minus_1_sizeoffloat);
memcpy(f3, dv_ptr+1, width_minus_1_sizeoffloat);
v4sf* hpl = (v4sf*) f1, *dur = (v4sf*) f2, *dvr = (v4sf*) f3;
{ // left block
// reverse 2x2 diagonal block
const v4sf dpsis = (*hpl) + (*hp) + (*vpt) + (*vp);
const v4sf A11 = (*a22p)+dpsis, A22 = (*a11p)+dpsis;
const v4sf det = A11*A22 - (*a12p)*(*a12p);
*a11p = A11/det;
*a22p = A22/det;
*a12p /= -det;
// do one iteration
const v4sf s1 = (*hp)*(*dur) + (*vpt)*(*dut) + (*vp)*(*dub) + (*b1p);
const v4sf s2 = (*hp)*(*dvr) + (*vpt)*(*dvt) + (*vp)*(*dvb) + (*b2p);
du_ptr[0] += omega*( a11p[0][0]*s1[0] + a12p[0][0]*s2[0] - du_ptr[0] );
dv_ptr[0] += omega*( a12p[0][0]*s1[0] + a22p[0][0]*s2[0] - dv_ptr[0] );
for(k=1;k<4;k++){
const float B1 = hpl[0][k]*du_ptr[k-1] + s1[k];
const float B2 = hpl[0][k]*dv_ptr[k-1] + s2[k];
du_ptr[k] += omega*( a11p[0][k]*B1 + a12p[0][k]*B2 - du_ptr[k] );
dv_ptr[k] += omega*( a12p[0][k]*B1 + a22p[0][k]*B2 - dv_ptr[k] );
}
// increment pointer
hpl+=1; hp+=1; vpt+=1; vp+=1; a11p+=1; a12p+=1; a22p+=1;
dur+=1; dvr+=1; dut+=1; dvt+=1; dub+=1; dvb +=1; b1p+=1; b2p+=1;
du_ptr += 4; dv_ptr += 4;
}
for(i=iterline;--i;){
// reverse 2x2 diagonal block
const v4sf dpsis = (*hpl) + (*hp) + (*vpt) + (*vp);
const v4sf A11 = (*a22p)+dpsis, A22 = (*a11p)+dpsis;
const v4sf det = A11*A22 - (*a12p)*(*a12p);
*a11p = A11/det;
*a22p = A22/det;
*a12p /= -det;
// do one iteration
const v4sf s1 = (*hp)*(*dur) + (*vpt)*(*dut) + (*vp)*(*dub) + (*b1p);
const v4sf s2 = (*hp)*(*dvr) + (*vpt)*(*dvt) + (*vp)*(*dvb) + (*b2p);
for(k=0;k<4;k++){
const float B1 = hpl[0][k]*du_ptr[k-1] + s1[k];
const float B2 = hpl[0][k]*dv_ptr[k-1] + s2[k];
du_ptr[k] += omega*( a11p[0][k]*B1 + a12p[0][k]*B2 - du_ptr[k] );
dv_ptr[k] += omega*( a12p[0][k]*B1 + a22p[0][k]*B2 - dv_ptr[k] );
}
// increment pointer
hpl+=1; hp+=1; vpt+=1; vp+=1; a11p+=1; a12p+=1; a22p+=1;
dur+=1; dvr+=1; dut+=1; dvt+=1; dub+=1; dvb +=1; b1p+=1; b2p+=1;
du_ptr += 4; dv_ptr += 4;
}
}
{ // first iteration - last line
memcpy(f1+1, ((float*) hp), width_minus_1_sizeoffloat);
memcpy(f2, du_ptr+1, width_minus_1_sizeoffloat);
memcpy(f3, dv_ptr+1, width_minus_1_sizeoffloat);
v4sf* hpl = (v4sf*) f1, *dur = (v4sf*) f2, *dvr = (v4sf*) f3;
{ // left block
// reverse 2x2 diagonal block
const v4sf dpsis = (*hpl) + (*hp) + (*vpt);
const v4sf A11 = (*a22p)+dpsis, A22 = (*a11p)+dpsis;
const v4sf det = A11*A22 - (*a12p)*(*a12p);
*a11p = A11/det;
*a22p = A22/det;
*a12p /= -det;
// do one iteration
const v4sf s1 = (*hp)*(*dur) + (*vpt)*(*dut) + (*b1p);
const v4sf s2 = (*hp)*(*dvr) + (*vpt)*(*dvt) + (*b2p);
du_ptr[0] += omega*( a11p[0][0]*s1[0] + a12p[0][0]*s2[0] - du_ptr[0] );
dv_ptr[0] += omega*( a12p[0][0]*s1[0] + a22p[0][0]*s2[0] - dv_ptr[0] );
for(k=1;k<4;k++){
const float B1 = hpl[0][k]*du_ptr[k-1] + s1[k];
const float B2 = hpl[0][k]*dv_ptr[k-1] + s2[k];
du_ptr[k] += omega*( a11p[0][k]*B1 + a12p[0][k]*B2 - du_ptr[k] );
dv_ptr[k] += omega*( a12p[0][k]*B1 + a22p[0][k]*B2 - dv_ptr[k] );
}
// increment pointer
hpl+=1; hp+=1; vpt+=1; a11p+=1; a12p+=1; a22p+=1;
dur+=1; dvr+=1; dut+=1; dvt+=1; b1p+=1; b2p+=1;
du_ptr += 4; dv_ptr += 4;
}
for(i=iterline;--i;){
// reverse 2x2 diagonal block
const v4sf dpsis = (*hpl) + (*hp) + (*vpt);
const v4sf A11 = (*a22p)+dpsis, A22 = (*a11p)+dpsis;
const v4sf det = A11*A22 - (*a12p)*(*a12p);
*a11p = A11/det;
*a22p = A22/det;
*a12p /= -det;
// do one iteration
const v4sf s1 = (*hp)*(*dur) + (*vpt)*(*dut) + (*b1p);
const v4sf s2 = (*hp)*(*dvr) + (*vpt)*(*dvt) + (*b2p);
for(k=0;k<4;k++){
const float B1 = hpl[0][k]*du_ptr[k-1] + s1[k];
const float B2 = hpl[0][k]*dv_ptr[k-1] + s2[k];
du_ptr[k] += omega*( a11p[0][k]*B1 + a12p[0][k]*B2 - du_ptr[k] );
dv_ptr[k] += omega*( a12p[0][k]*B1 + a22p[0][k]*B2 - dv_ptr[k] );
}
// increment pointer
hpl+=1; hp+=1; vpt+=1; a11p+=1; a12p+=1; a22p+=1;
dur+=1; dvr+=1; dut+=1; dvt+=1; b1p+=1; b2p+=1;
du_ptr += 4; dv_ptr += 4;
}
}
}
for(iter=iterations;--iter;){ // other iterations
v4sf *a11p = (v4sf*) a11->data, *a12p = (v4sf*) a12->data, *a22p = (v4sf*) a22->data, *b1p = (v4sf*) b1->data, *b2p = (v4sf*) b2->data, *hp = (v4sf*) dpsis_horiz->data, *vp = (v4sf*) dpsis_vert->data;
float *du_ptr = du->data, *dv_ptr = dv->data;
v4sf *dub = (v4sf*) (du_ptr+stride), *dvb = (v4sf*) (dv_ptr+stride);
{ // other iteration - first line
memcpy(f1+1, ((float*) hp), width_minus_1_sizeoffloat);
memcpy(f2, du_ptr+1, width_minus_1_sizeoffloat);
memcpy(f3, dv_ptr+1, width_minus_1_sizeoffloat);
v4sf* hpl = (v4sf*) f1, *dur = (v4sf*) f2, *dvr = (v4sf*) f3;
{ // left block
// do one iteration
const v4sf s1 = (*hp)*(*dur) + (*vp)*(*dub) + (*b1p);
const v4sf s2 = (*hp)*(*dvr) + (*vp)*(*dvb) + (*b2p);
du_ptr[0] += omega*( a11p[0][0]*s1[0] + a12p[0][0]*s2[0] - du_ptr[0] );
dv_ptr[0] += omega*( a12p[0][0]*s1[0] + a22p[0][0]*s2[0] - dv_ptr[0] );
for(k=1;k<4;k++){
const float B1 = hpl[0][k]*du_ptr[k-1] + s1[k];
const float B2 = hpl[0][k]*dv_ptr[k-1] + s2[k];
du_ptr[k] += omega*( a11p[0][k]*B1 + a12p[0][k]*B2 - du_ptr[k] );
dv_ptr[k] += omega*( a12p[0][k]*B1 + a22p[0][k]*B2 - dv_ptr[k] );
}
// increment pointer
hpl+=1; hp+=1; vp+=1; a11p+=1; a12p+=1; a22p+=1;
dur+=1; dvr+=1; dub+=1; dvb +=1; b1p+=1; b2p+=1;
du_ptr += 4; dv_ptr += 4;
}
for(i=iterline;--i;){
// do one iteration
const v4sf s1 = (*hp)*(*dur) + (*vp)*(*dub) + (*b1p);
const v4sf s2 = (*hp)*(*dvr) + (*vp)*(*dvb) + (*b2p);
for(k=0;k<4;k++){
const float B1 = hpl[0][k]*du_ptr[k-1] + s1[k];
const float B2 = hpl[0][k]*dv_ptr[k-1] + s2[k];
du_ptr[k] += omega*( a11p[0][k]*B1 + a12p[0][k]*B2 - du_ptr[k] );
dv_ptr[k] += omega*( a12p[0][k]*B1 + a22p[0][k]*B2 - dv_ptr[k] );
}
// increment pointer
hpl+=1; hp+=1; vp+=1; a11p+=1; a12p+=1; a22p+=1;
dur+=1; dvr+=1; dub+=1; dvb +=1; b1p+=1; b2p+=1;
du_ptr += 4; dv_ptr += 4;
}
}
v4sf *vpt = (v4sf*) dpsis_vert->data;
v4sf *dut = (v4sf*) du->data, *dvt = (v4sf*) dv->data;
for(j=iterheight;--j;){ // other iteration - middle lines
memcpy(f1+1, ((float*) hp), width_minus_1_sizeoffloat);
memcpy(f2, du_ptr+1, width_minus_1_sizeoffloat);
memcpy(f3, dv_ptr+1, width_minus_1_sizeoffloat);
v4sf* hpl = (v4sf*) f1, *dur = (v4sf*) f2, *dvr = (v4sf*) f3;
{ // left block
// do one iteration
const v4sf s1 = (*hp)*(*dur) + (*vpt)*(*dut) + (*vp)*(*dub) + (*b1p);
const v4sf s2 = (*hp)*(*dvr) + (*vpt)*(*dvt) + (*vp)*(*dvb) + (*b2p);
du_ptr[0] += omega*( a11p[0][0]*s1[0] + a12p[0][0]*s2[0] - du_ptr[0] );
dv_ptr[0] += omega*( a12p[0][0]*s1[0] + a22p[0][0]*s2[0] - dv_ptr[0] );
for(k=1;k<4;k++){
const float B1 = hpl[0][k]*du_ptr[k-1] + s1[k];
const float B2 = hpl[0][k]*dv_ptr[k-1] + s2[k];
du_ptr[k] += omega*( a11p[0][k]*B1 + a12p[0][k]*B2 - du_ptr[k] );
dv_ptr[k] += omega*( a12p[0][k]*B1 + a22p[0][k]*B2 - dv_ptr[k] );
}
// increment pointer
hpl+=1; hp+=1; vpt+=1; vp+=1; a11p+=1; a12p+=1; a22p+=1;
dur+=1; dvr+=1; dut+=1; dvt+=1; dub+=1; dvb +=1; b1p+=1; b2p+=1;
du_ptr += 4; dv_ptr += 4;
}
for(i=iterline;--i;){
// do one iteration
const v4sf s1 = (*hp)*(*dur) + (*vpt)*(*dut) + (*vp)*(*dub) + (*b1p);
const v4sf s2 = (*hp)*(*dvr) + (*vpt)*(*dvt) + (*vp)*(*dvb) + (*b2p);
for(k=0;k<4;k++){
const float B1 = hpl[0][k]*du_ptr[k-1] + s1[k];
const float B2 = hpl[0][k]*dv_ptr[k-1] + s2[k];
du_ptr[k] += omega*( a11p[0][k]*B1 + a12p[0][k]*B2 - du_ptr[k] );
dv_ptr[k] += omega*( a12p[0][k]*B1 + a22p[0][k]*B2 - dv_ptr[k] );
}
// increment pointer
hpl+=1; hp+=1; vpt+=1; vp+=1; a11p+=1; a12p+=1; a22p+=1;
dur+=1; dvr+=1; dut+=1; dvt+=1; dub+=1; dvb +=1; b1p+=1; b2p+=1;
du_ptr += 4; dv_ptr += 4;
}
}
{ // other iteration - last line
memcpy(f1+1, ((float*) hp), width_minus_1_sizeoffloat);
memcpy(f2, du_ptr+1, width_minus_1_sizeoffloat);
memcpy(f3, dv_ptr+1, width_minus_1_sizeoffloat);
v4sf* hpl = (v4sf*) f1, *dur = (v4sf*) f2, *dvr = (v4sf*) f3;
{ // left block
// do one iteration
const v4sf s1 = (*hp)*(*dur) + (*vpt)*(*dut) + (*b1p);
const v4sf s2 = (*hp)*(*dvr) + (*vpt)*(*dvt) + (*b2p);
du_ptr[0] += omega*( a11p[0][0]*s1[0] + a12p[0][0]*s2[0] - du_ptr[0] );
dv_ptr[0] += omega*( a12p[0][0]*s1[0] + a22p[0][0]*s2[0] - dv_ptr[0] );
for(k=1;k<4;k++){
const float B1 = hpl[0][k]*du_ptr[k-1] + s1[k];
const float B2 = hpl[0][k]*dv_ptr[k-1] + s2[k];
du_ptr[k] += omega*( a11p[0][k]*B1 + a12p[0][k]*B2 - du_ptr[k] );
dv_ptr[k] += omega*( a12p[0][k]*B1 + a22p[0][k]*B2 - dv_ptr[k] );
}
// increment pointer
hpl+=1; hp+=1; vpt+=1; a11p+=1; a12p+=1; a22p+=1;
dur+=1; dvr+=1; dut+=1; dvt+=1; b1p+=1; b2p+=1;
du_ptr += 4; dv_ptr += 4;
}
for(i=iterline;--i;){
// do one iteration
const v4sf s1 = (*hp)*(*dur) + (*vpt)*(*dut) + (*b1p);
const v4sf s2 = (*hp)*(*dvr) + (*vpt)*(*dvt) + (*b2p);
for(k=0;k<4;k++){
const float B1 = hpl[0][k]*du_ptr[k-1] + s1[k];
const float B2 = hpl[0][k]*dv_ptr[k-1] + s2[k];
du_ptr[k] += omega*( a11p[0][k]*B1 + a12p[0][k]*B2 - du_ptr[k] );
dv_ptr[k] += omega*( a12p[0][k]*B1 + a22p[0][k]*B2 - dv_ptr[k] );
}
// increment pointer
hpl+=1; hp+=1; vpt+=1; a11p+=1; a12p+=1; a22p+=1;
dur+=1; dvr+=1; dut+=1; dvt+=1; b1p+=1; b2p+=1;
du_ptr += 4; dv_ptr += 4;
}
}
}
free(floatarray);
}