__m128d test_mm_div_sd(__m128d A, __m128d B) {
// DAG-LABEL: test_mm_div_sd
// DAG: fdiv double
//
// ASM-LABEL: test_mm_div_sd
// ASM: divsd
return _mm_div_sd(A, B);
}
void CalcGravity(int sp, PSpot* allSpot,int* length)
{
__m128d force1 = _mm_set1_pd(0);
__m128d force2 = _mm_set1_pd(0);
PSpot* spotSp = &allSpot[sp];
for(int i=0;i<sp;i++)
{
__m128d diff1 = _mm_sub_pd(allSpot[i].pos1, spotSp->pos1);
__m128d diff2 = _mm_sub_sd(allSpot[i].pos2, spotSp->pos2);
__m128d r = Length(diff1, diff2);
if (r.m128d_f64[0]*2 < (spotSp->qmass + allSpot[i].qmass))
{
if (allSpot[i].mass > spotSp->mass)
{
allSpot[i].heading1 =
_mm_add_pd(
allSpot[i].heading1,
_mm_mul_pd(
_mm_sub_pd(spotSp->heading1, allSpot[i].heading1),
_mm_set1_pd(spotSp->mass / (spotSp->mass + allSpot[i].mass))
)
);
allSpot[i].heading2 =
_mm_add_sd(
allSpot[i].heading2,
_mm_mul_sd(
_mm_sub_sd(spotSp->heading2, allSpot[i].heading2),
_mm_set1_pd(spotSp->mass / (spotSp->mass + allSpot[i].mass))
)
);
allSpot[i].mass += spotSp->mass;
allSpot[i].qmass = pow(allSpot[i].mass, 0.33333);
spotSp->mass = 0;
(*length)--;
PSpot temp;
temp = allSpot[sp];
allSpot[sp] = allSpot[*length];
allSpot[*length] = temp;
return;
}
else
{
spotSp->heading1 =
_mm_add_pd(
spotSp->heading1,
_mm_mul_pd(
_mm_sub_pd(allSpot[i].heading1, spotSp->heading1),
_mm_set1_pd(allSpot[i].mass / (spotSp->mass + allSpot[i].mass))
)
);
spotSp->heading2 =
_mm_add_sd(
spotSp->heading2,
_mm_mul_sd(
_mm_sub_sd(allSpot[i].heading2, spotSp->heading2),
_mm_set1_pd(allSpot[i].mass / (spotSp->mass + allSpot[i].mass))
)
);
spotSp->mass += allSpot[i].mass;
spotSp->qmass = pow(spotSp->mass, 0.33333);
allSpot[i].mass = 0;
(*length)--;
PSpot temp;
temp = allSpot[i];
allSpot[i] = allSpot[*length];
allSpot[*length] = temp;
return;
}
}
//float f = (G * spotSp->mass * allSpot[i].mass) / (r.m128d_f64[0] * r.m128d_f64[0] * r.m128d_f64[0]);
__m128d r1 = r;
r1.m128d_f64[1] = G;
__m128d r2 = r;
r2.m128d_f64[1] = spotSp->mass;
__m128d r3 = r;
r3.m128d_f64[1] = allSpot[i].mass;
__m128d r4 = _mm_mul_pd(_mm_mul_pd(r1, r2), r3);
__m128d r5 = _mm_shuffle_pd(r4, r4, 3);
r4 = _mm_shuffle_pd(r4, r4, 0);
__m128d r6 = _mm_div_pd(r5, r4);
force1 = _mm_add_pd(force1,_mm_mul_pd(diff1, r6));
force2 = _mm_add_sd(force2,_mm_mul_sd(diff2, r6));
}
for(int i=sp+1;i<*length;i++)
{
__m128d diff1 = _mm_sub_pd(allSpot[i].pos1, spotSp->pos1);
__m128d diff2 = _mm_sub_sd(allSpot[i].pos2, spotSp->pos2);
__m128d r = Length(diff1, diff2);
if (r.m128d_f64[0]*2 < (spotSp->qmass + allSpot[i].qmass))
{
if (allSpot[i].mass > spotSp->mass)
{
allSpot[i].heading1 =
_mm_add_pd(
allSpot[i].heading1,
_mm_mul_pd(
_mm_sub_pd(spotSp->heading1, allSpot[i].heading1),
_mm_set1_pd(spotSp->mass / (spotSp->mass + allSpot[i].mass))
)
);
allSpot[i].heading2 =
_mm_add_sd(
allSpot[i].heading2,
_mm_mul_sd(
_mm_sub_sd(spotSp->heading2, allSpot[i].heading2),
_mm_set1_pd(spotSp->mass / (spotSp->mass + allSpot[i].mass))
)
);
allSpot[i].mass += spotSp->mass;
allSpot[i].qmass = pow(allSpot[i].mass, 0.33333);
spotSp->mass = 0;
(*length)--;
PSpot temp;
temp = allSpot[sp];
allSpot[sp] = allSpot[*length];
allSpot[*length] = temp;
return;
}
else
{
spotSp->heading1 =
_mm_add_pd(
spotSp->heading1,
_mm_mul_pd(
_mm_sub_pd(allSpot[i].heading1, spotSp->heading1),
_mm_set1_pd(allSpot[i].mass / (spotSp->mass + allSpot[i].mass))
)
);
spotSp->heading2 =
_mm_add_sd(
spotSp->heading2,
_mm_mul_sd(
_mm_sub_sd(allSpot[i].heading2, spotSp->heading2),
_mm_set1_pd(allSpot[i].mass / (spotSp->mass + allSpot[i].mass))
)
);
spotSp->mass += allSpot[i].mass;
spotSp->qmass = pow(spotSp->mass, 0.33333);
allSpot[i].mass = 0;
(*length)--;
PSpot temp;
temp = allSpot[i];
allSpot[i] = allSpot[*length];
allSpot[*length] = temp;
return;
}
}
//float f = (G * spotSp->mass * allSpot[i].mass) / (r.m128d_f64[0] * r.m128d_f64[0] * r.m128d_f64[0]);
__m128d r1 = r;
r1.m128d_f64[1] = G;
__m128d r2 = r;
r2.m128d_f64[1] = spotSp->mass;
__m128d r3 = r;
r3.m128d_f64[1] = allSpot[i].mass;
__m128d r4 = _mm_mul_pd(_mm_mul_pd(r1, r2), r3);
__m128d r5 = _mm_shuffle_pd(r4, r4, 3);
r4 = _mm_shuffle_pd(r4, r4, 0);
__m128d r6 = _mm_div_pd(r5, r4);
force1 = _mm_add_pd(force1,_mm_mul_pd(diff1, r6));
force2 = _mm_add_sd(force2,_mm_mul_sd(diff2, r6));
}
force1 = _mm_div_pd(force1, _mm_set1_pd(spotSp->mass));
force2 = _mm_div_sd(force2, _mm_set1_pd(spotSp->mass));
__m128d forcef = Length(force1, force2);
if (forcef.m128d_f64[0] > 0)
{
double gate = 0.001f;
double step = gate / forcef.m128d_f64[0];
if (spotSp->process + step < 1)
{
spotSp->process += step;
}
else
{
step = 1 - spotSp->process;
spotSp->process = 1;
}
__m128d stepd = _mm_set1_pd(step);
spotSp->heading1 = _mm_add_pd(spotSp->heading1,_mm_mul_pd(force1,stepd));
spotSp->heading2 = _mm_add_sd(spotSp->heading2,_mm_mul_sd(force2,stepd));
spotSp->pos1 = _mm_add_pd(spotSp->pos1, _mm_mul_pd(spotSp->heading1,stepd));
spotSp->pos2 = _mm_add_sd(spotSp->pos2, _mm_mul_sd(spotSp->heading2,stepd));
}
else
{
spotSp->pos1 = _mm_add_pd(spotSp->pos1, spotSp->heading1);
spotSp->pos2 = _mm_add_sd(spotSp->pos2, spotSp->heading2);
spotSp->process = 1;
}
}
void SpringEmbedderFRExact::mainStep_sse3(ArrayGraph &C)
{
//#if (defined(OGDF_ARCH_X86) || defined(OGDF_ARCH_X64)) && !(defined(__GNUC__) && !defined(__SSE3__))
#ifdef OGDF_SSE3_EXTENSIONS
const int n = C.numberOfNodes();
#ifdef _OPENMP
const int work = 256;
const int nThreadsRep = min(omp_get_max_threads(), 1 + n*n/work);
const int nThreadsPrev = min(omp_get_max_threads(), 1 + n /work);
#endif
const double k = m_idealEdgeLength;
const double kSquare = k*k;
const double c_rep = 0.052 * kSquare; // 0.2 = factor for repulsive forces as suggested by Warshal
const double minDist = 10e-6;//100*DBL_EPSILON;
const double minDistSquare = minDist*minDist;
double *disp_x = (double*) System::alignedMemoryAlloc16(n*sizeof(double));
double *disp_y = (double*) System::alignedMemoryAlloc16(n*sizeof(double));
__m128d mm_kSquare = _mm_set1_pd(kSquare);
__m128d mm_minDist = _mm_set1_pd(minDist);
__m128d mm_minDistSquare = _mm_set1_pd(minDistSquare);
__m128d mm_c_rep = _mm_set1_pd(c_rep);
#pragma omp parallel num_threads(nThreadsRep)
{
double tx = m_txNull;
double ty = m_tyNull;
int cF = 1;
for(int i = 1; i <= m_iterations; i++)
{
// repulsive forces
#pragma omp for
for(int v = 0; v < n; ++v)
{
__m128d mm_disp_xv = _mm_setzero_pd();
__m128d mm_disp_yv = _mm_setzero_pd();
__m128d mm_xv = _mm_set1_pd(C.m_x[v]);
__m128d mm_yv = _mm_set1_pd(C.m_y[v]);
int u;
for(u = 0; u+1 < v; u += 2)
{
__m128d mm_delta_x = _mm_sub_pd(mm_xv, _mm_load_pd(&C.m_x[u]));
__m128d mm_delta_y = _mm_sub_pd(mm_yv, _mm_load_pd(&C.m_y[u]));
__m128d mm_distSquare = _mm_max_pd(mm_minDistSquare,
_mm_add_pd(_mm_mul_pd(mm_delta_x,mm_delta_x),_mm_mul_pd(mm_delta_y,mm_delta_y))
);
__m128d mm_t = _mm_div_pd(_mm_load_pd(&C.m_nodeWeight[u]), mm_distSquare);
mm_disp_xv = _mm_add_pd(mm_disp_xv, _mm_mul_pd(mm_delta_x, mm_t));
mm_disp_yv = _mm_add_pd(mm_disp_yv, _mm_mul_pd(mm_delta_y, mm_t));
//mm_disp_xv = _mm_add_pd(mm_disp_xv, _mm_mul_pd(mm_delta_x, _mm_div_pd(mm_kSquare,mm_distSquare)));
//mm_disp_yv = _mm_add_pd(mm_disp_yv, _mm_mul_pd(mm_delta_y, _mm_div_pd(mm_kSquare,mm_distSquare)));
}
int uStart = u+2;
if(u == v) ++u;
if(u < n) {
__m128d mm_delta_x = _mm_sub_sd(mm_xv, _mm_load_sd(&C.m_x[u]));
__m128d mm_delta_y = _mm_sub_sd(mm_yv, _mm_load_sd(&C.m_y[u]));
__m128d mm_distSquare = _mm_max_sd(mm_minDistSquare,
_mm_add_sd(_mm_mul_sd(mm_delta_x,mm_delta_x),_mm_mul_sd(mm_delta_y,mm_delta_y))
);
__m128d mm_t = _mm_div_sd(_mm_load_sd(&C.m_nodeWeight[u]), mm_distSquare);
mm_disp_xv = _mm_add_sd(mm_disp_xv, _mm_mul_sd(mm_delta_x, mm_t));
mm_disp_yv = _mm_add_sd(mm_disp_yv, _mm_mul_sd(mm_delta_y, mm_t));
//mm_disp_xv = _mm_add_sd(mm_disp_xv, _mm_mul_sd(mm_delta_x, _mm_div_sd(mm_kSquare,mm_distSquare)));
//mm_disp_yv = _mm_add_sd(mm_disp_yv, _mm_mul_sd(mm_delta_y, _mm_div_sd(mm_kSquare,mm_distSquare)));
}
for(u = uStart; u < n; u += 2)
{
__m128d mm_delta_x = _mm_sub_pd(mm_xv, _mm_load_pd(&C.m_x[u]));
__m128d mm_delta_y = _mm_sub_pd(mm_yv, _mm_load_pd(&C.m_y[u]));
__m128d mm_distSquare = _mm_max_pd(mm_minDistSquare,
_mm_add_pd(_mm_mul_pd(mm_delta_x,mm_delta_x),_mm_mul_pd(mm_delta_y,mm_delta_y))
);
__m128d mm_t = _mm_div_pd(_mm_load_pd(&C.m_nodeWeight[u]), mm_distSquare);
mm_disp_xv = _mm_add_pd(mm_disp_xv, _mm_mul_pd(mm_delta_x, mm_t));
mm_disp_yv = _mm_add_pd(mm_disp_yv, _mm_mul_pd(mm_delta_y, mm_t));
//mm_disp_xv = _mm_add_pd(mm_disp_xv, _mm_mul_pd(mm_delta_x, _mm_div_pd(mm_kSquare,mm_distSquare)));
//mm_disp_yv = _mm_add_pd(mm_disp_yv, _mm_mul_pd(mm_delta_y, _mm_div_pd(mm_kSquare,mm_distSquare)));
}
if(u < n) {
__m128d mm_delta_x = _mm_sub_sd(mm_xv, _mm_load_sd(&C.m_x[u]));
__m128d mm_delta_y = _mm_sub_sd(mm_yv, _mm_load_sd(&C.m_y[u]));
__m128d mm_distSquare = _mm_max_sd(mm_minDistSquare,
_mm_add_sd(_mm_mul_sd(mm_delta_x,mm_delta_x),_mm_mul_sd(mm_delta_y,mm_delta_y))
);
__m128d mm_t = _mm_div_sd(_mm_load_sd(&C.m_nodeWeight[u]), mm_distSquare);
mm_disp_xv = _mm_add_sd(mm_disp_xv, _mm_mul_sd(mm_delta_x, mm_t));
mm_disp_yv = _mm_add_sd(mm_disp_yv, _mm_mul_sd(mm_delta_y, mm_t));
//mm_disp_xv = _mm_add_sd(mm_disp_xv, _mm_mul_sd(mm_delta_x, _mm_div_sd(mm_kSquare,mm_distSquare)));
//mm_disp_yv = _mm_add_sd(mm_disp_yv, _mm_mul_sd(mm_delta_y, _mm_div_sd(mm_kSquare,mm_distSquare)));
}
mm_disp_xv = _mm_hadd_pd(mm_disp_xv,mm_disp_xv);
mm_disp_yv = _mm_hadd_pd(mm_disp_yv,mm_disp_yv);
_mm_store_sd(&disp_x[v], _mm_mul_sd(mm_disp_xv, mm_c_rep));
_mm_store_sd(&disp_y[v], _mm_mul_sd(mm_disp_yv, mm_c_rep));
}
// attractive forces
#pragma omp single
for(int e = 0; e < C.numberOfEdges(); ++e)
{
int v = C.m_src[e];
int u = C.m_tgt[e];
double delta_x = C.m_x[v] - C.m_x[u];
double delta_y = C.m_y[v] - C.m_y[u];
double dist = max(minDist, sqrt(delta_x*delta_x + delta_y*delta_y));
disp_x[v] -= delta_x * dist / k;
disp_y[v] -= delta_y * dist / k;
disp_x[u] += delta_x * dist / k;
disp_y[u] += delta_y * dist / k;
}
// limit the maximum displacement to the temperature (m_tx,m_ty)
__m128d mm_tx = _mm_set1_pd(tx);
__m128d mm_ty = _mm_set1_pd(ty);
#pragma omp for nowait
for(int v = 0; v < n-1; v += 2)
{
__m128d mm_disp_xv = _mm_load_pd(&disp_x[v]);
__m128d mm_disp_yv = _mm_load_pd(&disp_y[v]);
__m128d mm_dist = _mm_max_pd(mm_minDist, _mm_sqrt_pd(
_mm_add_pd(_mm_mul_pd(mm_disp_xv,mm_disp_xv),_mm_mul_pd(mm_disp_yv,mm_disp_yv))
));
_mm_store_pd(&C.m_x[v], _mm_add_pd(_mm_load_pd(&C.m_x[v]),
_mm_mul_pd(_mm_div_pd(mm_disp_xv, mm_dist), _mm_min_pd(mm_dist,mm_tx))
));
_mm_store_pd(&C.m_y[v], _mm_add_pd(_mm_load_pd(&C.m_y[v]),
_mm_mul_pd(_mm_div_pd(mm_disp_yv, mm_dist), _mm_min_pd(mm_dist,mm_ty))
));
}
#pragma omp single nowait
{
if(n % 2) {
int v = n-1;
double dist = max(minDist, sqrt(disp_x[v]*disp_x[v] + disp_y[v]*disp_y[v]));
C.m_x[v] += disp_x[v] / dist * min(dist,tx);
C.m_y[v] += disp_y[v] / dist * min(dist,ty);
}
}
cool(tx,ty,cF);
#pragma omp barrier
}
}
System::alignedMemoryFree(disp_x);
System::alignedMemoryFree(disp_y);
#else
mainStep(C);
#endif
}