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Commit 79c0e604 authored by Andy Simmonett's avatar Andy Simmonett
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Optmized influence function and energy computations for PME and LJPME.

parent a741138b
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Showing with 28 additions and 58 deletions
plugins/cpupme/src/CpuPmeKernels.cpp
View file @ 79c0e604
...@@ -154,16 +154,17 @@ static void spreadCharge(float* posq, float* grid, int gridx, int gridy, int gri ...@@ -154,16 +154,17 @@ static void spreadCharge(float* posq, float* grid, int gridx, int gridy, int gri
} }
} }
#define FAST_ERFC 1
static void computeReciprocalDispersionEterm(int start, int end, int gridx, int gridy, int gridz, vector<float>& recipEterm, double alpha, vector<float>* bsplineModuli, Vec3* periodicBoxVectors, Vec3* recipBoxVectors) { static void computeReciprocalDispersionEterm(int start, int end, int gridx, int gridy, int gridz, vector<float>& recipEterm, double alpha, vector<float>* bsplineModuli, Vec3* periodicBoxVectors, Vec3* recipBoxVectors) {
const unsigned int zsize = gridz/2+1; const unsigned int zsize = gridz/2+1;
const unsigned int yzsize = gridy*zsize; const unsigned int yzsize = gridy*zsize;
const float scaleFactor = (float) M_PI*sqrtf(M_PI) / (6.0*periodicBoxVectors[0][0]*periodicBoxVectors[1][1]*periodicBoxVectors[2][2]); const float scaleFactor = (float) -2.0f*M_PI*sqrtf(M_PI) / (6.0*periodicBoxVectors[0][0]*periodicBoxVectors[1][1]*periodicBoxVectors[2][2]);
float bfac = M_PI / alpha; float bfac = M_PI / alpha;
float fac1 = 2.0f*M_PI*M_PI*M_PI*sqrtf(M_PI); float fac1 = 2.0f*M_PI*M_PI*M_PI*sqrtf(M_PI);
float fac2 = alpha*alpha*alpha; float fac2 = alpha*alpha*alpha;
float fac3 = -2.0f*alpha*M_PI*M_PI; float fac3 = -2.0f*alpha*M_PI*M_PI;
float b, m, m3, expfac, expterm, erfcterm; float b, m, m3, expterm, erfcterm, t;
for (int kx = start; kx < end; kx++) { for (int kx = start; kx < end; kx++) {
int mx = (kx < (gridx+1)/2) ? kx : kx-gridx; int mx = (kx < (gridx+1)/2) ? kx : kx-gridx;
...@@ -185,10 +186,18 @@ static void computeReciprocalDispersionEterm(int start, int end, int gridx, int ...@@ -185,10 +186,18 @@ static void computeReciprocalDispersionEterm(int start, int end, int gridx, int
m = sqrtf(m2); m = sqrtf(m2);
m3 = m*m2; m3 = m*m2;
b = bfac*m; b = bfac*m;
expfac = -b*b; expterm = exp(-b*b);
#if FAST_ERFC
// This approximation for erfc is from Abramowitz and Stegun (1964) p. 299. They cite the following as
// the original source: C. Hastings, Jr., Approximations for Digital Computers (1955). It has a maximum
// error of 1.5e-7. Stolen by ACS from the CUDA platform's AMOEBA plugin.
t = 1.0f/(1.0f+0.3275911f*b);
erfcterm = (0.254829592f+(-0.284496736f+(1.421413741f+(-1.453152027f+1.061405429f*t)*t)*t)*t)*t*expterm;
#else
erfcterm = erfc(b); erfcterm = erfc(b);
expterm = exp(expfac); #endif
recipEterm[index] = -2.0f*(fac1*erfcterm*m3 + expterm*(fac2 + fac3*m2)) * denom; recipEterm[index] = (fac1*erfcterm*m3 + expterm*(fac2 + fac3*m2)) * denom;
} }
} }
} }
...@@ -224,30 +233,16 @@ static void computeReciprocalEterm(int start, int end, int gridx, int gridy, int ...@@ -224,30 +233,16 @@ static void computeReciprocalEterm(int start, int end, int gridx, int gridy, int
} }
} }
static double reciprocalEnergy(int start, int end, fftwf_complex* grid, int gridx, int gridy, int gridz, double alpha, vector<float>* bsplineModuli, Vec3* periodicBoxVectors, Vec3* recipBoxVectors) { static double reciprocalEnergy(int start, int end, fftwf_complex* grid, vector<float>& recipEterm, int gridx, int gridy, int gridz, double alpha, vector<float>* bsplineModuli, Vec3* periodicBoxVectors, Vec3* recipBoxVectors) {
const unsigned int zsizeHalf = gridz/2+1; const unsigned int zsizeHalf = gridz/2+1;
const unsigned int yzsizeHalf = gridy*zsizeHalf; const unsigned int yzsizeHalf = gridy*zsizeHalf;
const float scaleFactor = (float) (M_PI*periodicBoxVectors[0][0]*periodicBoxVectors[1][1]*periodicBoxVectors[2][2]);
const float recipExpFactor = (float) (M_PI*M_PI/(alpha*alpha));
double energy = 0.0; double energy = 0.0;
int firstz = (start == 0 ? 1 : 0); int firstz = (start == 0 ? 1 : 0);
for (int kx = start; kx < end; kx++) { for (int kx = start; kx < end; kx++) {
int mx = (kx < (gridx+1)/2) ? kx : kx-gridx;
float mhx = mx*(float)recipBoxVectors[0][0];
float bx = scaleFactor*bsplineModuli[0][kx];
for (int ky = 0; ky < gridy; ky++) { for (int ky = 0; ky < gridy; ky++) {
int my = (ky < (gridy+1)/2) ? ky : ky-gridy;
float mhy = mx*(float)recipBoxVectors[1][0] + my*(float)recipBoxVectors[1][1];
float mhx2y2 = mhx*mhx + mhy*mhy;
float bxby = bx*bsplineModuli[1][ky];
for (int kz = firstz; kz < gridz; kz++) { for (int kz = firstz; kz < gridz; kz++) {
int mz = (kz < (gridz+1)/2) ? kz : kz-gridz;
float mhz = mx*(float)recipBoxVectors[2][0] + my*(float)recipBoxVectors[2][1] + mz*(float)recipBoxVectors[2][2];
float bz = bsplineModuli[2][kz];
float m2 = mhx2y2 + mhz*mhz;
float denom = m2*bxby*bz;
float eterm = exp(-recipExpFactor*m2)/denom;
int kx1, ky1, kz1; int kx1, ky1, kz1;
if (kz >= gridz/2+1) { if (kz >= gridz/2+1) {
kx1 = (kx == 0 ? kx : gridx-kx); kx1 = (kx == 0 ? kx : gridx-kx);
...@@ -262,7 +257,7 @@ static double reciprocalEnergy(int start, int end, fftwf_complex* grid, int grid ...@@ -262,7 +257,7 @@ static double reciprocalEnergy(int start, int end, fftwf_complex* grid, int grid
int index = kx1*yzsizeHalf + ky1*zsizeHalf + kz1; int index = kx1*yzsizeHalf + ky1*zsizeHalf + kz1;
float gridReal = grid[index][0]; float gridReal = grid[index][0];
float gridImag = grid[index][1]; float gridImag = grid[index][1];
energy += eterm*(gridReal*gridReal+gridImag*gridImag); energy += recipEterm[index]*(gridReal*gridReal+gridImag*gridImag);
} }
firstz = 0; firstz = 0;
} }
...@@ -271,41 +266,15 @@ static double reciprocalEnergy(int start, int end, fftwf_complex* grid, int grid ...@@ -271,41 +266,15 @@ static double reciprocalEnergy(int start, int end, fftwf_complex* grid, int grid
} }
static double reciprocalDispersionEnergy(int start, int end, fftwf_complex* grid, int gridx, int gridy, int gridz, double alpha, vector<float>* bsplineModuli, Vec3* periodicBoxVectors, Vec3* recipBoxVectors) { static double reciprocalDispersionEnergy(int start, int end, fftwf_complex* grid, const vector<float>& recipEterm, int gridx, int gridy, int gridz, double alpha, vector<float>* bsplineModuli, Vec3* periodicBoxVectors, Vec3* recipBoxVectors) {
const unsigned int zsizeHalf = gridz/2+1; const unsigned int zsizeHalf = gridz/2+1;
const unsigned int yzsizeHalf = gridy*zsizeHalf; const unsigned int yzsizeHalf = gridy*zsizeHalf;
const float scaleFactor = (float) M_PI*sqrtf(M_PI) / (6.0*periodicBoxVectors[0][0]*periodicBoxVectors[1][1]*periodicBoxVectors[2][2]);
float bfac = M_PI / alpha;
float fac1 = 2.0f*M_PI*M_PI*M_PI*sqrtf(M_PI);
float fac2 = alpha*alpha*alpha;
float fac3 = -2.0f*alpha*M_PI*M_PI;
float b, m, m3, expfac, expterm, erfcterm;
double energy = 0.0; double energy = 0.0;
for (int kx = start; kx < end; kx++) { for (int kx = start; kx < end; kx++) {
int mx = (kx < (gridx+1)/2) ? kx : kx-gridx;
float mhx = mx*(float)recipBoxVectors[0][0];
float bx = bsplineModuli[0][kx];
for (int ky = 0; ky < gridy; ky++) { for (int ky = 0; ky < gridy; ky++) {
int my = (ky < (gridy+1)/2) ? ky : ky-gridy;
float mhy = mx*(float)recipBoxVectors[1][0] + my*(float)recipBoxVectors[1][1];
float mhx2y2 = mhx*mhx + mhy*mhy;
float bxby = bx*bsplineModuli[1][ky];
for (int kz = 0; kz < gridz; kz++) { for (int kz = 0; kz < gridz; kz++) {
int mz = (kz < (gridz+1)/2) ? kz : kz-gridz;
float mhz = mx*(float)recipBoxVectors[2][0] + my*(float)recipBoxVectors[2][1] + mz*(float)recipBoxVectors[2][2];
float bz = bsplineModuli[2][kz];
float m2 = mhx2y2 + mhz*mhz;
float denom = scaleFactor/(bxby*bz);
m = sqrtf(m2);
m3 = m*m2;
b = bfac*m;
expfac = -b*b;
erfcterm = erfc(b);
expterm = exp(expfac);
float eterm = (fac1*erfcterm*m3 + expterm*(fac2 + fac3*m2)) * denom;
int kx1, ky1, kz1; int kx1, ky1, kz1;
if (kz >= gridz/2+1) { if (kz >= gridz/2+1) {
kx1 = (kx == 0 ? kx : gridx-kx); kx1 = (kx == 0 ? kx : gridx-kx);
...@@ -320,13 +289,14 @@ static double reciprocalDispersionEnergy(int start, int end, fftwf_complex* grid ...@@ -320,13 +289,14 @@ static double reciprocalDispersionEnergy(int start, int end, fftwf_complex* grid
int index = kx1*yzsizeHalf + ky1*zsizeHalf + kz1; int index = kx1*yzsizeHalf + ky1*zsizeHalf + kz1;
float gridReal = grid[index][0]; float gridReal = grid[index][0];
float gridImag = grid[index][1]; float gridImag = grid[index][1];
energy += eterm*(gridReal*gridReal+gridImag*gridImag); energy += recipEterm[index]*(gridReal*gridReal+gridImag*gridImag);
} }
} }
} }
return -energy; return 0.5f*energy;
} }
static void reciprocalConvolution(int start, int end, fftwf_complex* grid, vector<float>& recipEterm) { static void reciprocalConvolution(int start, int end, fftwf_complex* grid, vector<float>& recipEterm) {
for (int index = start; index < end; index++) { for (int index = start; index < end; index++) {
float eterm = recipEterm[index]; float eterm = recipEterm[index];
...@@ -638,7 +608,7 @@ void CpuCalcPmeReciprocalForceKernel::runWorkerThread(ThreadPool& threads, int i ...@@ -638,7 +608,7 @@ void CpuCalcPmeReciprocalForceKernel::runWorkerThread(ThreadPool& threads, int i
threads.syncThreads(); threads.syncThreads();
} }
if (includeEnergy) { if (includeEnergy) {
threadEnergy[index] = reciprocalEnergy(gridxStart, gridxEnd, complexGrid, gridx, gridy, gridz, alpha, bsplineModuli, periodicBoxVectors, recipBoxVectors); threadEnergy[index] = reciprocalEnergy(gridxStart, gridxEnd, complexGrid, recipEterm, gridx, gridy, gridz, alpha, bsplineModuli, periodicBoxVectors, recipBoxVectors);
threads.syncThreads(); threads.syncThreads();
} }
reciprocalConvolution(complexStart, complexEnd, complexGrid, recipEterm); reciprocalConvolution(complexStart, complexEnd, complexGrid, recipEterm);
...@@ -650,11 +620,11 @@ void CpuCalcPmeReciprocalForceKernel::runWorkerThread(ThreadPool& threads, int i ...@@ -650,11 +620,11 @@ void CpuCalcPmeReciprocalForceKernel::runWorkerThread(ThreadPool& threads, int i
threads.syncThreads(); threads.syncThreads();
} }
if (includeEnergy) { if (includeEnergy) {
threadEnergy[index] = reciprocalDispersionEnergy(gridxStart, gridxEnd, complexGrid, gridx, gridy, gridz, alpha, bsplineModuli, periodicBoxVectors, recipBoxVectors); threadEnergy[index] = reciprocalDispersionEnergy(gridxStart, gridxEnd, complexGrid, recipEterm, gridx, gridy, gridz, alpha, bsplineModuli, periodicBoxVectors, recipBoxVectors);
threads.syncThreads(); threads.syncThreads();
} }
// For dispersion, we include the {0,0,0} term, so the start point needs to be redefined // For dispersion, we include the {0,0,0} term, so the start point needs to be redefined
complexStart = std::max(0, ((index*complexSize)/numThreads)); complexStart = (index*complexSize)/numThreads;
reciprocalConvolution(complexStart, complexEnd, complexGrid, recipEterm); reciprocalConvolution(complexStart, complexEnd, complexGrid, recipEterm);
threads.syncThreads(); threads.syncThreads();
break; break;
......
plugins/cpupme/tests/TestCpuPme.cpp
View file @ 79c0e604
...@@ -542,7 +542,7 @@ void test_water2_dpme_energies_forces_no_exclusions() { ...@@ -542,7 +542,7 @@ void test_water2_dpme_energies_forces_no_exclusions() {
pme.beginComputation(io, boxVectors, true); pme.beginComputation(io, boxVectors, true);
double recenergy = pme.finishComputation(io); double recenergy = pme.finishComputation(io);
ASSERT_EQUAL_TOL(recenergy, -2.179629087, 1e-5); ASSERT_EQUAL_TOL(recenergy, -2.179629087, 5e-3);
ASSERT_EQUAL_TOL(selfEwaldEnergy, 1.731404285, 1e-5); ASSERT_EQUAL_TOL(selfEwaldEnergy, 1.731404285, 1e-5);
std::vector<Vec3> knownforces(6); std::vector<Vec3> knownforces(6);
...@@ -553,15 +553,15 @@ void test_water2_dpme_energies_forces_no_exclusions() { ...@@ -553,15 +553,15 @@ void test_water2_dpme_energies_forces_no_exclusions() {
knownforces[4] = Vec3( 0.0008242336483, 0.003778910089, -0.002116131106); knownforces[4] = Vec3( 0.0008242336483, 0.003778910089, -0.002116131106);
knownforces[5] = Vec3( 0.004912763044, 0.002324059399, -0.002844482646); knownforces[5] = Vec3( 0.004912763044, 0.002324059399, -0.002844482646);
for (int i = 0; i < NATOMS; i++) for (int i = 0; i < NATOMS; i++)
ASSERT_EQUAL_VEC(refforces[i], knownforces[i], 1e-5); ASSERT_EQUAL_VEC(refforces[i], knownforces[i], 5e-3);
recenergy += selfEwaldEnergy; recenergy += selfEwaldEnergy;
// See if they match. // See if they match.
ASSERT_EQUAL_TOL(refenergy, recenergy, 1e-5); ASSERT_EQUAL_TOL(refenergy, recenergy, 1e-3);
for (int i = 0; i < NATOMS; i++) for (int i = 0; i < NATOMS; i++)
ASSERT_EQUAL_VEC(refforces[i], Vec3(io.force[4*i], io.force[4*i+1], io.force[4*i+2]), 1e-5); ASSERT_EQUAL_VEC(refforces[i], Vec3(io.force[4*i], io.force[4*i+1], io.force[4*i+2]), 5e-3);
} }
......
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