__m128d test_mm_max_sd(__m128d A, __m128d B) {
// DAG-LABEL: test_mm_max_sd
// DAG: call <2 x double> @llvm.x86.sse2.max.sd(<2 x double> %{{.*}}, <2 x double> %{{.*}})
//
// ASM-LABEL: test_mm_max_sd
// ASM: maxsd
return _mm_max_sd(A, B);
}
DBL AVXFMA4Noise(const Vector3d& EPoint, int noise_generator)
{
DBL x, y, z;
DBL *mp;
int ix, iy, iz;
int ixiy_hash, ixjy_hash, jxiy_hash, jxjy_hash;
DBL sum;
// TODO FIXME - global statistics reference
// Stats[Calls_To_Noise]++;
if (noise_generator==kNoiseGen_Perlin)
{
// The 1.59 and 0.985 are to correct for some biasing problems with
// the random # generator used to create the noise tables. Final
// range of values is about 5.0e-4 below 0.0 and above 1.0. Mean
// value is 0.49 (ideally it would be 0.5).
sum = 0.5 * (1.59 * SolidNoise(EPoint) + 0.985);
// Clamp final value to 0-1 range
if (sum < 0.0) sum = 0.0;
if (sum > 1.0) sum = 1.0;
return sum;
}
x = EPoint[X];
y = EPoint[Y];
z = EPoint[Z];
/* its equivalent integer lattice point. */
/* ix = (int)x; iy = (int)y; iz = (long)z; */
/* JB fix for the range problem */
__m128d xy = _mm_setr_pd(x, y);
__m128d zn = _mm_set_sd(z);
__m128d epsy = _mm_set1_pd(1.0 - EPSILON);
__m128d xy_e = _mm_sub_pd(xy, epsy);
__m128d zn_e = _mm_sub_sd(zn, epsy);
__m128i tmp_xy = _mm_cvttpd_epi32(_mm_blendv_pd(xy, xy_e, xy));
__m128i tmp_zn = _mm_cvttpd_epi32(_mm_blendv_pd(zn, zn_e, zn));
__m128i noise_min_xy = _mm_setr_epi32(NOISE_MINX, NOISE_MINY, 0, 0);
__m128i noise_min_zn = _mm_set1_epi32(NOISE_MINZ);
__m128d xy_ixy = _mm_sub_pd(xy, _mm_cvtepi32_pd(tmp_xy));
__m128d zn_izn = _mm_sub_sd(zn, _mm_cvtepi32_pd(tmp_zn));
const __m128i fff = _mm_set1_epi32(0xfff);
__m128i i_xy = _mm_and_si128(_mm_sub_epi32(tmp_xy, noise_min_xy), fff);
__m128i i_zn = _mm_and_si128(_mm_sub_epi32(tmp_zn, noise_min_zn), fff);
ix = _mm_extract_epi32(i_xy, 0);
iy = _mm_extract_epi32(i_xy, 1);
iz = _mm_extract_epi32(i_zn, 0);
ixiy_hash = Hash2d(ix, iy);
jxiy_hash = Hash2d(ix + 1, iy);
ixjy_hash = Hash2d(ix, iy + 1);
jxjy_hash = Hash2d(ix + 1, iy + 1);
mp = &RTable[Hash1dRTableIndex(ixiy_hash, iz)];
DBL *mp2 = &RTable[Hash1dRTableIndex(ixjy_hash, iz)];
DBL *mp3 = &RTable[Hash1dRTableIndex(ixiy_hash, iz + 1)];
DBL *mp4 = &RTable[Hash1dRTableIndex(ixjy_hash, iz + 1)];
DBL *mp5 = &RTable[Hash1dRTableIndex(jxiy_hash, iz)];
DBL *mp6 = &RTable[Hash1dRTableIndex(jxjy_hash, iz)];
DBL *mp7 = &RTable[Hash1dRTableIndex(jxiy_hash, iz + 1)];
DBL *mp8 = &RTable[Hash1dRTableIndex(jxjy_hash, iz + 1)];
const __m128d three = _mm_set1_pd(3.0);
const __m128d two = _mm_set1_pd(2.0);
const __m128d one = _mm_set1_pd(1.0);
__m128d ix_mm = _mm_unpacklo_pd(xy_ixy, xy_ixy);
__m128d iy_mm = _mm_unpackhi_pd(xy_ixy, xy_ixy);
__m128d iz_mm = _mm_unpacklo_pd(zn_izn, zn_izn);
__m128d jx_mm = _mm_sub_pd(ix_mm, one);
__m128d jy_mm = _mm_sub_pd(iy_mm, one);
__m128d jz_mm = _mm_sub_pd(iz_mm, one);
__m128d mm_sxy = _mm_mul_pd(_mm_mul_pd(xy_ixy, xy_ixy), _mm_nmacc_pd(two, xy_ixy, three));
__m128d mm_sz = _mm_mul_pd(_mm_mul_pd(iz_mm, iz_mm), _mm_nmacc_pd(two, iz_mm, three));
__m128d mm_tz = _mm_sub_pd(one, mm_sz);
__m128d mm_txy = _mm_sub_pd(one, mm_sxy);
__m128d mm_tysy = _mm_unpackhi_pd(mm_txy, mm_sxy);
__m128d mm_txty_txsy = _mm_mul_pd(_mm_unpacklo_pd(mm_txy, mm_txy), mm_tysy);
__m128d mm_sxty_sxsy = _mm_mul_pd(_mm_unpacklo_pd(mm_sxy, mm_sxy), mm_tysy);
__m128d y_mm = _mm_unpacklo_pd(iy_mm, jy_mm);
__m128d mp_t1, mp_t2, mp1_mm, mp2_mm, mp4_mm, mp6_mm, sum_p, s_mm;
__m128d int_sum1 = _mm_setzero_pd();
s_mm = _mm_mul_pd(mm_txty_txsy, mm_tz);
INCRSUMP2(mp, mp2, s_mm, ix_mm, y_mm, iz_mm, int_sum1);
s_mm = _mm_mul_pd(mm_txty_txsy, mm_sz);
INCRSUMP2(mp3, mp4, s_mm, ix_mm, y_mm, jz_mm, int_sum1);
s_mm = _mm_mul_pd(mm_sxty_sxsy, mm_tz);
INCRSUMP2(mp5, mp6, s_mm, jx_mm, y_mm, iz_mm, int_sum1);
s_mm = _mm_mul_pd(mm_sxty_sxsy, mm_sz);
INCRSUMP2(mp7, mp8, s_mm, jx_mm, y_mm, jz_mm, int_sum1);
int_sum1 = _mm_hadd_pd(int_sum1, int_sum1);
if(noise_generator==kNoiseGen_RangeCorrected)
{
/* details of range here:
Min, max: -1.05242, 0.988997
Mean: -0.0191481, Median: -0.535493, Std Dev: 0.256828
We want to change it to as close to [0,1] as possible.
*/
const __m128d r2 = _mm_set_sd(0.48985582);
const __m128d r1r2 = _mm_set_sd(1.05242*0.48985582);
int_sum1 = _mm_macc_sd(int_sum1, r2, r1r2);
}
else
{
int_sum1 = _mm_add_sd(int_sum1, _mm_set_sd(0.5));
}
int_sum1 = _mm_min_sd(one, int_sum1);
int_sum1 = _mm_max_sd(_mm_setzero_pd(), int_sum1);
_mm_store_sd(&sum, int_sum1);
return (sum);
}
test (__m128d s1, __m128d s2)
{
return _mm_max_sd (s1, s2);
}
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
}
