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Commit aa96846e authored by Peter Eastman's avatar Peter Eastman
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Created OpenCL implementation of Ewald

parent 014f3406
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platforms/opencl/src/OpenCLKernels.cpp
View file @ aa96846e
...@@ -29,6 +29,7 @@ ...@@ -29,6 +29,7 @@
#include "openmm/LangevinIntegrator.h" #include "openmm/LangevinIntegrator.h"
#include "openmm/Context.h" #include "openmm/Context.h"
#include "openmm/internal/ContextImpl.h" #include "openmm/internal/ContextImpl.h"
#include "openmm/internal/NonbondedForceImpl.h"
#include "OpenCLIntegrationUtilities.h" #include "OpenCLIntegrationUtilities.h"
#include "OpenCLNonbondedUtilities.h" #include "OpenCLNonbondedUtilities.h"
#include <cmath> #include <cmath>
...@@ -42,6 +43,19 @@ static const double AVOGADRO = 6.0221367e23; // () ...@@ -42,6 +43,19 @@ static const double AVOGADRO = 6.0221367e23; // ()
static const double RGAS = BOLTZMANN*AVOGADRO; // (J/(mol K)) static const double RGAS = BOLTZMANN*AVOGADRO; // (J/(mol K))
static const double BOLTZ = (RGAS/KILO); // (kJ/(mol K)) static const double BOLTZ = (RGAS/KILO); // (kJ/(mol K))
static string doubleToString(double value) {
stringstream s;
s.precision(8);
s << scientific << value << "f";
return s.str();
}
static string intToString(int value) {
stringstream s;
s << value;
return s.str();
}
void OpenCLCalcForcesAndEnergyKernel::initialize(const System& system) { void OpenCLCalcForcesAndEnergyKernel::initialize(const System& system) {
} }
...@@ -522,12 +536,14 @@ void OpenCLCalcNonbondedForceKernel::initialize(const System& system, const Nonb ...@@ -522,12 +536,14 @@ void OpenCLCalcNonbondedForceKernel::initialize(const System& system, const Nonb
OpenCLArray<mm_float4>& posq = cl.getPosq(); OpenCLArray<mm_float4>& posq = cl.getPosq();
vector<mm_float2> sigmaEpsilonVector(numParticles); vector<mm_float2> sigmaEpsilonVector(numParticles);
vector<vector<int> > exclusionList(numParticles); vector<vector<int> > exclusionList(numParticles);
double sumSquaredCharges = 0.0;
for (int i = 0; i < numParticles; i++) { for (int i = 0; i < numParticles; i++) {
double charge, sigma, epsilon; double charge, sigma, epsilon;
force.getParticleParameters(i, charge, sigma, epsilon); force.getParticleParameters(i, charge, sigma, epsilon);
posq[i].w = (float) charge; posq[i].w = (float) charge;
sigmaEpsilonVector[i] = (mm_float2) {(float) (0.5*sigma), (float) (2.0*sqrt(epsilon))}; sigmaEpsilonVector[i] = (mm_float2) {(float) (0.5*sigma), (float) (2.0*sqrt(epsilon))};
exclusionList[i].push_back(i); exclusionList[i].push_back(i);
sumSquaredCharges += charge*charge;
} }
for (int i = 0; i < (int) exclusions.size(); i++) { for (int i = 0; i < (int) exclusions.size(); i++) {
exclusionList[exclusions[i].first].push_back(exclusions[i].second); exclusionList[exclusions[i].first].push_back(exclusions[i].second);
...@@ -537,68 +553,56 @@ void OpenCLCalcNonbondedForceKernel::initialize(const System& system, const Nonb ...@@ -537,68 +553,56 @@ void OpenCLCalcNonbondedForceKernel::initialize(const System& system, const Nonb
sigmaEpsilon->upload(sigmaEpsilonVector); sigmaEpsilon->upload(sigmaEpsilonVector);
bool useCutoff = (force.getNonbondedMethod() != NonbondedForce::NoCutoff); bool useCutoff = (force.getNonbondedMethod() != NonbondedForce::NoCutoff);
bool usePeriodic = (force.getNonbondedMethod() != NonbondedForce::NoCutoff && force.getNonbondedMethod() != NonbondedForce::CutoffNonPeriodic); bool usePeriodic = (force.getNonbondedMethod() != NonbondedForce::NoCutoff && force.getNonbondedMethod() != NonbondedForce::CutoffNonPeriodic);
Vec3 boxVectors[3];
system.getPeriodicBoxVectors(boxVectors[0], boxVectors[1], boxVectors[2]);
map<string, string> defines; map<string, string> defines;
if (useCutoff) { if (useCutoff) {
// Compute the reaction field constants.
double reactionFieldK = pow(force.getCutoffDistance(), -3.0)*(force.getReactionFieldDielectric()-1.0)/(2.0*force.getReactionFieldDielectric()+1.0); double reactionFieldK = pow(force.getCutoffDistance(), -3.0)*(force.getReactionFieldDielectric()-1.0)/(2.0*force.getReactionFieldDielectric()+1.0);
double reactionFieldC = (1.0 / force.getCutoffDistance())*(3.0*force.getReactionFieldDielectric())/(2.0*force.getReactionFieldDielectric()+1.0); double reactionFieldC = (1.0 / force.getCutoffDistance())*(3.0*force.getReactionFieldDielectric())/(2.0*force.getReactionFieldDielectric()+1.0);
stringstream k, c; defines["REACTION_FIELD_K"] = doubleToString(reactionFieldK);
k.precision(8); defines["REACTION_FIELD_C"] = doubleToString(reactionFieldC);
c.precision(8);
k << scientific << reactionFieldK << "f";
c << scientific << reactionFieldC << "f";
defines["REACTION_FIELD_K"] = k.str();
defines["REACTION_FIELD_C"] = c.str();
} }
// if (force.getNonbondedMethod() != NonbondedForce::NoCutoff) { if (force.getNonbondedMethod() == NonbondedForce::Ewald) {
// method = CUTOFF; // Compute the Ewald parameters.
// }
// if (force.getNonbondedMethod() == NonbondedForce::CutoffPeriodic) { double alpha;
// method = PERIODIC; int kmaxx, kmaxy, kmaxz;
// } NonbondedForceImpl::calcEwaldParameters(system, force, alpha, kmaxx, kmaxy, kmaxz);
// if (force.getNonbondedMethod() == NonbondedForce::Ewald || force.getNonbondedMethod() == NonbondedForce::PME) { defines["EWALD_ALPHA"] = doubleToString(alpha);
// double ewaldErrorTol = force.getEwaldErrorTolerance(); defines["TWO_OVER_SQRT_PI"] = doubleToString(2.0/sqrt(M_PI));
// double alpha = (1.0/force.getCutoffDistance())*std::sqrt(-std::log(ewaldErrorTol)); defines["USE_EWALD"] = "1";
// double mx = boxVectors[0][0]/force.getCutoffDistance(); double selfEnergyScale = 138.935485*alpha/std::sqrt(M_PI);
// double my = boxVectors[1][1]/force.getCutoffDistance(); ewaldSelfEnergy = - 138.935485*alpha*sumSquaredCharges/std::sqrt(M_PI);
// double mz = boxVectors[2][2]/force.getCutoffDistance();
// double pi = 3.1415926535897932385; // Create the reciprocal space kernels.
// int kmaxx = (int)std::ceil(-(mx/pi)*std::log(ewaldErrorTol));
// int kmaxy = (int)std::ceil(-(my/pi)*std::log(ewaldErrorTol)); map<string, string> replacements;
// int kmaxz = (int)std::ceil(-(mz/pi)*std::log(ewaldErrorTol)); replacements["NUM_ATOMS"] = intToString(numParticles);
// if (force.getNonbondedMethod() == NonbondedForce::Ewald) { replacements["KMAX_X"] = intToString(kmaxx);
// if (kmaxx%2 == 0) replacements["KMAX_Y"] = intToString(kmaxy);
// kmaxx++; replacements["KMAX_Z"] = intToString(kmaxz);
// if (kmaxy%2 == 0) replacements["RECIPROCAL_BOX_SIZE_X"] = doubleToString(2.0*M_PI/boxVectors[0][0]);
// kmaxy++; replacements["RECIPROCAL_BOX_SIZE_Y"] = doubleToString(2.0*M_PI/boxVectors[1][1]);
// if (kmaxz%2 == 0) replacements["RECIPROCAL_BOX_SIZE_Z"] = doubleToString(2.0*M_PI/boxVectors[2][2]);
// kmaxz++; replacements["RECIPROCAL_COEFFICIENT"] = doubleToString(138.935485*4*M_PI/(boxVectors[0][0]*boxVectors[1][1]*boxVectors[2][2]));
// gpuSetEwaldParameters(gpu, (float) alpha, kmaxx, kmaxy, kmaxz); replacements["EXP_COEFFICIENT"] = doubleToString(-1.0/(4.0*alpha*alpha));
// method = EWALD; cl::Program program = cl.createProgram(cl.loadSourceFromFile("ewald.cl"), replacements);
// } ewaldSumsKernel = cl::Kernel(program, "calculateEwaldCosSinSums");
// else { ewaldForcesKernel = cl::Kernel(program, "calculateEwaldForces");
// int gridSizeX = -0.5*kmaxx*std::log(ewaldErrorTol); cosSinSums = new OpenCLArray<mm_float2>(cl, (2*kmaxx-1)*(2*kmaxy-1)*(2*kmaxz-1), "cosSinSums");
// int gridSizeY = -0.5*kmaxy*std::log(ewaldErrorTol); }
// int gridSizeZ = -0.5*kmaxz*std::log(ewaldErrorTol); else
// gpuSetPMEParameters(gpu, (float) alpha, gridSizeX, gridSizeY, gridSizeZ); ewaldSelfEnergy = 0.0;
// method = PARTICLE_MESH_EWALD;
// } // Add the interaction to the default nonbonded kernel.
// }
// data.nonbondedMethod = method;
// gpuSetCoulombParameters(gpu, 138.935485f, particle, c6, c12, q, symbol, exclusionList, method);
string source = cl.loadSourceFromFile("coulombLennardJones.cl", defines); string source = cl.loadSourceFromFile("coulombLennardJones.cl", defines);
cl.getNonbondedUtilities().addInteraction(useCutoff, usePeriodic, true, force.getCutoffDistance(), exclusionList, source); cl.getNonbondedUtilities().addInteraction(useCutoff, usePeriodic, true, force.getCutoffDistance(), exclusionList, source);
cl.getNonbondedUtilities().addParameter(OpenCLNonbondedUtilities::ParameterInfo("sigmaEpsilon", "float2", sizeof(cl_float2), sigmaEpsilon->getDeviceBuffer())); cl.getNonbondedUtilities().addParameter(OpenCLNonbondedUtilities::ParameterInfo("sigmaEpsilon", "float2", sizeof(cl_float2), sigmaEpsilon->getDeviceBuffer()));
cutoffSquared = force.getCutoffDistance()*force.getCutoffDistance(); cutoffSquared = force.getCutoffDistance()*force.getCutoffDistance();
// Compute the Ewald self energy.
ewaldSelfEnergy = 0.0;
if (force.getNonbondedMethod() == NonbondedForce::Ewald || force.getNonbondedMethod() == NonbondedForce::PME) {
// double selfEnergyScale = gpu->sim.epsfac*gpu->sim.alphaEwald/std::sqrt(PI);
// for (int i = 0; i < numParticles; i++)
// ewaldSelfEnergy -= selfEnergyScale*q[i]*q[i];
}
// Initialize the exceptions. // Initialize the exceptions.
int numExceptions = exceptions.size(); int numExceptions = exceptions.size();
...@@ -645,6 +649,16 @@ void OpenCLCalcNonbondedForceKernel::executeForces(ContextImpl& context) { ...@@ -645,6 +649,16 @@ void OpenCLCalcNonbondedForceKernel::executeForces(ContextImpl& context) {
exceptionsKernel.setArg<cl::Buffer>(8, exceptionIndices->getDeviceBuffer()); exceptionsKernel.setArg<cl::Buffer>(8, exceptionIndices->getDeviceBuffer());
cl.executeKernel(exceptionsKernel, numExceptions); cl.executeKernel(exceptionsKernel, numExceptions);
} }
if (cosSinSums != NULL) {
ewaldSumsKernel.setArg<cl::Buffer>(0, cl.getEnergyBuffer().getDeviceBuffer());
ewaldSumsKernel.setArg<cl::Buffer>(1, cl.getPosq().getDeviceBuffer());
ewaldSumsKernel.setArg<cl::Buffer>(2, cosSinSums->getDeviceBuffer());
cl.executeKernel(ewaldSumsKernel, cosSinSums->getSize());
ewaldForcesKernel.setArg<cl::Buffer>(0, cl.getForceBuffers().getDeviceBuffer());
ewaldForcesKernel.setArg<cl::Buffer>(1, cl.getPosq().getDeviceBuffer());
ewaldForcesKernel.setArg<cl::Buffer>(2, cosSinSums->getDeviceBuffer());
cl.executeKernel(ewaldForcesKernel, cl.getNumAtoms());
}
} }
double OpenCLCalcNonbondedForceKernel::executeEnergy(ContextImpl& context) { double OpenCLCalcNonbondedForceKernel::executeEnergy(ContextImpl& context) {
......
platforms/opencl/src/OpenCLKernels.h
View file @ aa96846e
...@@ -328,7 +328,10 @@ private: ...@@ -328,7 +328,10 @@ private:
OpenCLArray<mm_float2>* sigmaEpsilon; OpenCLArray<mm_float2>* sigmaEpsilon;
OpenCLArray<mm_float4>* exceptionParams; OpenCLArray<mm_float4>* exceptionParams;
OpenCLArray<mm_int4>* exceptionIndices; OpenCLArray<mm_int4>* exceptionIndices;
OpenCLArray<mm_float2>* cosSinSums;
cl::Kernel exceptionsKernel; cl::Kernel exceptionsKernel;
cl::Kernel ewaldSumsKernel;
cl::Kernel ewaldForcesKernel;
double cutoffSquared, ewaldSelfEnergy; double cutoffSquared, ewaldSelfEnergy;
}; };
......
platforms/opencl/src/kernels/coulombLennardJones.cl
View file @ aa96846e
#if USE_EWALD
if (r2 < CUTOFF_SQUARED) {
bool needCorrection = isExcluded && atom1 != atom2 && atom1 < NUM_ATOMS && atom2 < NUM_ATOMS;
if (!isExcluded || needCorrection) {
const float prefactor = 138.935485f*posq1.w*posq2.w*invR;
float alphaR = EWALD_ALPHA*r;
float erfcAlphaR = erfc(alphaR);
float tempForce;
if (needCorrection) {
// Subtract off the part of this interaction that was included in the reciprocal space contribution.
tempForce = -prefactor*((1.0f-erfcAlphaR)-alphaR*exp(-alphaR*alphaR)*TWO_OVER_SQRT_PI);
tempEnergy += -prefactor*(1.0f-erfcAlphaR);
}
else {
float sig = sigmaEpsilon1.x + sigmaEpsilon2.x;
float sig2 = invR*sig;
sig2 *= sig2;
float sig6 = sig2*sig2*sig2;
float eps = sigmaEpsilon1.y*sigmaEpsilon2.y;
tempForce = eps*(12.0f*sig6 - 6.0f)*sig6 + prefactor*(erfcAlphaR+alphaR*exp(-alphaR*alphaR)*TWO_OVER_SQRT_PI);
tempEnergy += eps*(sig6 - 1.0f)*sig6 + prefactor*erfcAlphaR;
}
dEdR += tempForce*invR*invR;
}
}
#else
#ifdef USE_CUTOFF #ifdef USE_CUTOFF
if (!isExcluded && r2 < CUTOFF_SQUARED) { if (!isExcluded && r2 < CUTOFF_SQUARED) {
#else #else
...@@ -10,13 +37,15 @@ if (!isExcluded) { ...@@ -10,13 +37,15 @@ if (!isExcluded) {
float eps = sigmaEpsilon1.y*sigmaEpsilon2.y; float eps = sigmaEpsilon1.y*sigmaEpsilon2.y;
float tempForce = eps*(12.0f*sig6 - 6.0f)*sig6; float tempForce = eps*(12.0f*sig6 - 6.0f)*sig6;
tempEnergy += eps*(sig6 - 1.0f)*sig6; tempEnergy += eps*(sig6 - 1.0f)*sig6;
const float EpsilonFactor = 138.935485f;
#ifdef USE_CUTOFF #ifdef USE_CUTOFF
tempForce += EpsilonFactor*posq1.w*posq2.w*(invR - 2.0f*REACTION_FIELD_K*r2); const float prefactor = 138.935485f*posq1.w*posq2.w;
tempEnergy += EpsilonFactor*posq1.w*posq2.w*(invR + REACTION_FIELD_K*r2 - REACTION_FIELD_C); tempForce += prefactor*(invR - 2.0f*REACTION_FIELD_K*r2);
tempEnergy += prefactor*(invR + REACTION_FIELD_K*r2 - REACTION_FIELD_C);
#else #else
tempForce += EpsilonFactor*posq1.w*posq2.w*invR; const float prefactor = 138.935485f*posq1.w*posq2.w*invR;
tempEnergy += EpsilonFactor*posq1.w*posq2.w*invR; tempForce += prefactor;
tempEnergy += prefactor;
#endif #endif
dEdR += tempForce*invR*invR; dEdR += tempForce*invR*invR;
} }
#endif
\ No newline at end of file
platforms/opencl/src/kernels/ewald.cl 0 → 100644
View file @ aa96846e
float2 multofFloat2(float2 a, float2 b) {
return (float2) (a.x*b.x - a.y*b.y, a.x*b.y + a.y*b.x);
}
/**
* Precompute the cosine and sine sums which appear in each force term.
*/
__kernel void calculateEwaldCosSinSums(__global float* energyBuffer, __global float4* posq, __global float2* cosSinSum) {
const unsigned int ksizex = 2*KMAX_X-1;
const unsigned int ksizey = 2*KMAX_Y-1;
const unsigned int ksizez = 2*KMAX_Z-1;
const unsigned int totalK = ksizex*ksizey*ksizez;
unsigned int index = get_global_id(0);
float energy = 0.0f;
while (index < (KMAX_Y-1)*ksizez+KMAX_Z)
index += get_global_size(0);
while (index < totalK) {
// Find the wave vector (kx, ky, kz) this index corresponds to.
int rx = index/(ksizey*ksizez);
int remainder = index - rx*ksizey*ksizez;
int ry = remainder/ksizez;
int rz = remainder - ry*ksizez - KMAX_Z + 1;
ry += -KMAX_Y + 1;
float kx = rx*RECIPROCAL_BOX_SIZE_X;
float ky = ry*RECIPROCAL_BOX_SIZE_Y;
float kz = rz*RECIPROCAL_BOX_SIZE_Z;
// Compute the sum for this wave vector.
float2 sum = 0.0f;
for (int atom = 0; atom < NUM_ATOMS; atom++) {
float4 apos = posq[atom];
float phase = apos.x*kx;
float2 structureFactor = (float2) (cos(phase), sin(phase));
phase = apos.y*ky;
structureFactor = multofFloat2(structureFactor, (float2) (cos(phase), sin(phase)));
phase = apos.z*kz;
structureFactor = multofFloat2(structureFactor, (float2) (cos(phase), sin(phase)));
sum += apos.w*structureFactor;
}
cosSinSum[index] = sum;
// Compute the contribution to the energy.
float k2 = kx*kx + ky*ky + kz*kz;
float ak = exp(k2*EXP_COEFFICIENT) / k2;
energy += RECIPROCAL_COEFFICIENT*ak*(sum.x*sum.x + sum.y*sum.y);
index += get_global_size(0);
}
energyBuffer[get_global_id(0)] += energy;
}
/**
* Compute the reciprocal space part of the Ewald force, using the precomputed sums from the
* previous routine.
*/
__kernel void calculateEwaldForces(__global float4* forceBuffers, __global float4* posq, __global float2* cosSinSum) {
unsigned int atom = get_global_id(0);
while (atom < NUM_ATOMS) {
float4 force = forceBuffers[atom];
float4 apos = posq[atom];
// Loop over all wave vectors.
int lowry = 0;
int lowrz = 1;
for (int rx = 0; rx < KMAX_X; rx++) {
float kx = rx*RECIPROCAL_BOX_SIZE_X;
for (int ry = lowry; ry < KMAX_Y; ry++) {
float ky = ry*RECIPROCAL_BOX_SIZE_Y;
float phase = apos.x*kx;
float2 tab_xy = (float2) (cos(phase), sin(phase));
phase = apos.y*ky;
tab_xy = multofFloat2(tab_xy, (float2) (cos(phase), sin(phase)));
for (int rz = lowrz; rz < KMAX_Z; rz++) {
float kz = rz*RECIPROCAL_BOX_SIZE_Z;
// Compute the force contribution of this wave vector.
int index = rx*(KMAX_Y*2-1)*(KMAX_Z*2-1) + (ry+KMAX_Y-1)*(KMAX_Z*2-1) + (rz+KMAX_Z-1);
float k2 = kx*kx + ky*ky + kz*kz;
float ak = exp(k2*EXP_COEFFICIENT)/k2;
phase = apos.z*kz;
float2 structureFactor = multofFloat2(tab_xy, (float2) (cos(phase), sin(phase)));
float2 sum = cosSinSum[index];
float dEdR = 2*RECIPROCAL_COEFFICIENT*ak*apos.w*(sum.x*structureFactor.y - sum.y*structureFactor.x);
force.x += dEdR*kx;
force.y += dEdR*ky;
force.z += dEdR*kz;
lowrz = 1 - KMAX_Z;
}
lowry = 1 - KMAX_Y;
}
}
// Record the force on the atom.
forceBuffers[atom] = force;
atom += get_global_size(0);
}
}
platforms/opencl/tests/TestOpenCLEwald.cpp 0 → 100644
View file @ aa96846e
/* -------------------------------------------------------------------------- *
* OpenMM *
* -------------------------------------------------------------------------- *
* This is part of the OpenMM molecular simulation toolkit originating from *
* Simbios, the NIH National Center for Physics-Based Simulation of *
* Biological Structures at Stanford, funded under the NIH Roadmap for *
* Medical Research, grant U54 GM072970. See https://simtk.org. *
* *
* Portions copyright (c) 2008-2009 Stanford University and the Authors. *
* Authors: Peter Eastman *
* Contributors: *
* *
* 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 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, CONTRIBUTORS 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. *
* -------------------------------------------------------------------------- */
/**
* This tests the Ewald summation method OpenCL implementation of NonbondedForce.
*/
#include "../../../tests/AssertionUtilities.h"
#include "openmm/Context.h"
#include "OpenCLPlatform.h"
#include "ReferencePlatform.h"
#include "openmm/NonbondedForce.h"
#include "openmm/System.h"
#include "openmm/LangevinIntegrator.h"
#include "openmm/VerletIntegrator.h"
#include "openmm/internal/ContextImpl.h"
#include "../src/SimTKUtilities/SimTKOpenMMRealType.h"
#include "../src/sfmt/SFMT.h"
#include <iostream>
#include <vector>
using namespace OpenMM;
using namespace std;
const double TOL = 1e-5;
void testEwaldPME() {
// Use amorphous NaCl system for the tests
const int numParticles = 894;
const double cutoff = 1.2;
const double boxSize = 3.00646;
double tol = 1e-5;
OpenCLPlatform cl;
ReferencePlatform reference;
System system;
VerletIntegrator integrator(0.01);
NonbondedForce* nonbonded = new NonbondedForce();
nonbonded->setNonbondedMethod(NonbondedForce::Ewald);
nonbonded->setCutoffDistance(cutoff);
nonbonded->setEwaldErrorTolerance(tol);
for (int i = 0; i < numParticles/2; i++)
system.addParticle(22.99);
for (int i = 0; i < numParticles/2; i++)
system.addParticle(35.45);
for (int i = 0; i < numParticles/2; i++)
nonbonded->addParticle(1.0, 1.0,0.0);
for (int i = 0; i < numParticles/2; i++)
nonbonded->addParticle(-1.0, 1.0,0.0);
system.setPeriodicBoxVectors(Vec3(boxSize, 0, 0), Vec3(0, boxSize, 0), Vec3(0, 0, boxSize));
system.addForce(nonbonded);
vector<Vec3> positions(numParticles);
#include "nacl_amorph.dat"
// (1) Check whether the Reference and OpenCL platforms agree when using Ewald Method
Context clContext(system, integrator, cl);
Context referenceContext(system, integrator, reference);
clContext.setPositions(positions);
referenceContext.setPositions(positions);
State clState = clContext.getState(State::Forces | State::Energy);
State referenceState = referenceContext.getState(State::Forces | State::Energy);
tol = 1e-2;
for (int i = 0; i < numParticles; i++) {
ASSERT_EQUAL_VEC(referenceState.getForces()[i], clState.getForces()[i], tol);
}
tol = 1e-5;
ASSERT_EQUAL_TOL(referenceState.getPotentialEnergy(), clState.getPotentialEnergy(), tol);
// (2) Check whether Ewald method in OpenCL is self-consistent
double norm = 0.0;
for (int i = 0; i < numParticles; ++i) {
Vec3 f = clState.getForces()[i];
norm += f[0]*f[0] + f[1]*f[1] + f[2]*f[2];
}
norm = std::sqrt(norm);
const double delta = 1e-3;
double step = delta/norm;
for (int i = 0; i < numParticles; ++i) {
Vec3 p = positions[i];
Vec3 f = clState.getForces()[i];
positions[i] = Vec3(p[0]-f[0]*step, p[1]-f[1]*step, p[2]-f[2]*step);
}
Context clContext2(system, integrator, cl);
clContext2.setPositions(positions);
tol = 1e-3;
State clState2 = clContext2.getState(State::Energy);
ASSERT_EQUAL_TOL(norm, (clState2.getPotentialEnergy()-clState.getPotentialEnergy())/delta, tol)
// (3) Check whether the Reference and OpenCL platforms agree when using PME
/*
nonbonded->setNonbondedMethod(NonbondedForce::PME);
clContext.reinitialize();
referenceContext.reinitialize();
clContext.setPositions(positions);
referenceContext.setPositions(positions);
clState = clContext.getState(State::Forces | State::Energy);
referenceState = referenceContext.getState(State::Forces | State::Energy);
tol = 1e-2;
for (int i = 0; i < numParticles; i++) {
ASSERT_EQUAL_VEC(referenceState.getForces()[i], clState.getForces()[i], tol);
}
tol = 1e-5;
ASSERT_EQUAL_TOL(referenceState.getPotentialEnergy(), clState.getPotentialEnergy(), tol);
// (4) Check whether PME method in OpenCL is self-consistent
norm = 0.0;
for (int i = 0; i < numParticles; ++i) {
Vec3 f = clState.getForces()[i];
norm += f[0]*f[0] + f[1]*f[1] + f[2]*f[2];
}
norm = std::sqrt(norm);
step = delta/norm;
for (int i = 0; i < numParticles; ++i) {
Vec3 p = positions[i];
Vec3 f = clState.getForces()[i];
positions[i] = Vec3(p[0]-f[0]*step, p[1]-f[1]*step, p[2]-f[2]*step);
}
Context clContext3(system, integrator, cl);
clContext3.setPositions(positions);
tol = 1e-3;
State clState3 = clContext3.getState(State::Energy);
ASSERT_EQUAL_TOL(norm, (clState3.getPotentialEnergy()-clState.getPotentialEnergy())/delta, tol)*/
}
void testEwald2Ions() {
OpenCLPlatform platform;
System system;
system.addParticle(1.0);
system.addParticle(1.0);
VerletIntegrator integrator(0.01);
NonbondedForce* nonbonded = new NonbondedForce();
nonbonded->addParticle(1.0, 1, 0);
nonbonded->addParticle(-1.0, 1, 0);
nonbonded->setNonbondedMethod(NonbondedForce::Ewald);
const double cutoff = 2.0;
nonbonded->setCutoffDistance(cutoff);
nonbonded->setEwaldErrorTolerance(TOL);
system.setPeriodicBoxVectors(Vec3(6, 0, 0), Vec3(0, 6, 0), Vec3(0, 0, 6));
system.addForce(nonbonded);
Context context(system, integrator, platform);
vector<Vec3> positions(2);
positions[0] = Vec3(3.048000,2.764000,3.156000);
positions[1] = Vec3(2.809000,2.888000,2.571000);
context.setPositions(positions);
State state = context.getState(State::Forces | State::Energy);
const vector<Vec3>& forces = state.getForces();
ASSERT_EQUAL_VEC(Vec3(-123.711, 64.1877, -302.716), forces[0], 10*TOL);
ASSERT_EQUAL_VEC(Vec3( 123.711, -64.1877, 302.716), forces[1], 10*TOL);
ASSERT_EQUAL_TOL(-217.276, state.getPotentialEnergy(), 0.01/*10*TOL*/);
}
void testErrorTolerance(NonbondedForce::NonbondedMethod method) {
// Create a cloud of random point charges.
const int numParticles = 51;
const double boxWidth = 5.0;
System system;
system.setPeriodicBoxVectors(Vec3(boxWidth, 0, 0), Vec3(0, boxWidth, 0), Vec3(0, 0, boxWidth));
NonbondedForce* force = new NonbondedForce();
system.addForce(force);
vector<Vec3> positions(numParticles);
init_gen_rand(0);
for (int i = 0; i < numParticles; i++) {
system.addParticle(1.0);
force->addParticle(-1.0+i*2.0/(numParticles-1), 1.0, 0.0);
positions[i] = Vec3(boxWidth*genrand_real2(), boxWidth*genrand_real2(), boxWidth*genrand_real2());
}
force->setNonbondedMethod(method);
OpenCLPlatform platform;
VerletIntegrator integrator(0.01);
// For various values of the cutoff and error tolerance, see if the actual error is reasonable.
for (double cutoff = 1.0; cutoff < boxWidth/2; cutoff += 0.2) {
force->setCutoffDistance(cutoff);
vector<Vec3> refForces;
double norm = 0.0;
for (double tol = 5e-5; tol < 1e-3; tol *= 2.0) {
force->setEwaldErrorTolerance(tol);
Context context(system, integrator, platform);
context.setPositions(positions);
State state = context.getState(State::Forces);
if (refForces.size() == 0) {
refForces = state.getForces();
for (int i = 0; i < numParticles; i++)
norm += refForces[i].dot(refForces[i]);
norm = sqrt(norm);
}
else {
double diff = 0.0;
for (int i = 0; i < numParticles; i++) {
Vec3 delta = refForces[i]-state.getForces()[i];
diff += delta.dot(delta);
}
diff = sqrt(diff)/norm;
ASSERT(diff < 5*tol);
}
}
}
}
int main() {
try {
testEwaldPME();
// testEwald2Ions();
testErrorTolerance(NonbondedForce::Ewald);
// testErrorTolerance(NonbondedForce::PME);
}
catch(const exception& e) {
cout << "exception: " << e.what() << endl;
return 1;
}
cout << "Done" << endl;
return 0;
}
platforms/opencl/tests/nacl_amorph.dat 0 → 100644
View file @ aa96846e
positions[0] = Vec3(1.066000,1.628000,0.835000);
positions[1] = Vec3(1.072000,0.428000,0.190000);
positions[2] = Vec3(0.524000,1.442000,1.160000);
positions[3] = Vec3(2.383000,1.524000,1.119000);
positions[4] = Vec3(0.390000,1.441000,0.575000);
positions[5] = Vec3(0.618000,0.399000,0.819000);
positions[6] = Vec3(1.003000,1.257000,1.543000);
positions[7] = Vec3(2.933000,1.569000,0.642000);
positions[8] = Vec3(0.849000,0.739000,0.089000);
positions[9] = Vec3(0.060000,0.794000,0.766000);
positions[10] = Vec3(1.652000,1.405000,1.010000);
positions[11] = Vec3(2.843000,1.533000,1.781000);
positions[12] = Vec3(0.952000,1.309000,0.996000);
positions[13] = Vec3(1.847000,1.402000,0.313000);
positions[14] = Vec3(2.674000,0.083000,1.691000);
positions[15] = Vec3(1.763000,2.104000,0.728000);
positions[16] = Vec3(0.914000,0.574000,0.982000);
positions[17] = Vec3(0.514000,0.078000,0.891000);
positions[18] = Vec3(0.538000,0.766000,1.110000);
positions[19] = Vec3(0.808000,0.676000,0.570000);
positions[20] = Vec3(0.178000,0.014000,0.628000);
positions[21] = Vec3(1.329000,1.333000,0.339000);
positions[22] = Vec3(1.029000,1.678000,0.503000);
positions[23] = Vec3(1.423000,1.767000,1.104000);
positions[24] = Vec3(1.966000,1.051000,0.282000);
positions[25] = Vec3(1.596000,1.971000,0.194000);
positions[26] = Vec3(1.025000,1.043000,2.809000);
positions[27] = Vec3(1.628000,2.614000,0.088000);
positions[28] = Vec3(0.440000,0.606000,0.141000);
positions[29] = Vec3(1.050000,2.821000,2.517000);
positions[30] = Vec3(0.644000,1.604000,0.770000);
positions[31] = Vec3(0.637000,0.917000,0.392000);
positions[32] = Vec3(0.611000,2.768000,0.013000);
positions[33] = Vec3(1.892000,0.660000,0.473000);
positions[34] = Vec3(1.052000,2.081000,0.982000);
positions[35] = Vec3(1.508000,2.300000,0.439000);
positions[36] = Vec3(2.617000,0.328000,1.099000);
positions[37] = Vec3(0.910000,0.040000,0.259000);
positions[38] = Vec3(1.195000,1.494000,1.202000);
positions[39] = Vec3(2.657000,0.997000,0.564000);
positions[40] = Vec3(1.465000,1.580000,0.648000);
positions[41] = Vec3(0.154000,2.538000,1.331000);
positions[42] = Vec3(0.849000,1.476000,1.365000);
positions[43] = Vec3(0.898000,0.987000,1.178000);
positions[44] = Vec3(0.958000,0.656000,1.358000);
positions[45] = Vec3(1.067000,0.934000,0.211000);
positions[46] = Vec3(1.030000,0.319000,1.281000);
positions[47] = Vec3(2.709000,0.807000,0.240000);
positions[48] = Vec3(0.837000,1.362000,0.588000);
positions[49] = Vec3(2.080000,0.791000,2.947000);
positions[50] = Vec3(0.200000,0.266000,1.474000);
positions[51] = Vec3(0.848000,0.379000,1.625000);
positions[52] = Vec3(0.637000,1.071000,0.821000);
positions[53] = Vec3(1.324000,0.757000,2.951000);
positions[54] = Vec3(2.666000,0.935000,1.373000);
positions[55] = Vec3(1.584000,1.025000,1.703000);
positions[56] = Vec3(1.699000,0.636000,0.038000);
positions[57] = Vec3(1.099000,1.644000,1.879000);
positions[58] = Vec3(2.897000,1.302000,1.522000);
positions[59] = Vec3(1.753000,0.949000,2.885000);
positions[60] = Vec3(2.502000,1.321000,0.752000);
positions[61] = Vec3(0.545000,0.193000,1.959000);
positions[62] = Vec3(1.098000,2.646000,1.706000);
positions[63] = Vec3(0.001000,1.205000,0.670000);
positions[64] = Vec3(2.997000,0.061000,1.040000);
positions[65] = Vec3(0.662000,0.828000,1.535000);
positions[66] = Vec3(1.252000,1.246000,0.780000);
positions[67] = Vec3(1.173000,0.472000,0.810000);
positions[68] = Vec3(0.124000,0.622000,2.992000);
positions[69] = Vec3(1.036000,0.883000,0.848000);
positions[70] = Vec3(1.423000,2.146000,1.340000);
positions[71] = Vec3(2.391000,1.136000,1.165000);
positions[72] = Vec3(1.189000,2.961000,0.425000);
positions[73] = Vec3(1.584000,2.500000,0.782000);
positions[74] = Vec3(0.565000,1.122000,1.240000);
positions[75] = Vec3(1.733000,1.716000,1.763000);
positions[76] = Vec3(1.548000,1.522000,0.041000);
positions[77] = Vec3(1.485000,0.561000,0.369000);
positions[78] = Vec3(0.350000,1.661000,0.928000);
positions[79] = Vec3(1.653000,1.223000,0.578000);
positions[80] = Vec3(0.648000,1.349000,0.253000);
positions[81] = Vec3(0.340000,1.820000,0.483000);
positions[82] = Vec3(2.926000,0.119000,1.421000);
positions[83] = Vec3(1.512000,1.084000,0.156000);
positions[84] = Vec3(1.600000,2.115000,1.792000);
positions[85] = Vec3(1.089000,0.934000,1.584000);
positions[86] = Vec3(1.276000,1.104000,1.230000);
positions[87] = Vec3(0.485000,0.305000,0.428000);
positions[88] = Vec3(1.317000,1.261000,1.795000);
positions[89] = Vec3(0.039000,1.413000,1.085000);
positions[90] = Vec3(0.453000,0.701000,0.605000);
positions[91] = Vec3(1.283000,1.937000,0.752000);
positions[92] = Vec3(0.212000,1.416000,1.447000);
positions[93] = Vec3(0.203000,0.358000,0.723000);
positions[94] = Vec3(0.556000,0.445000,1.364000);
positions[95] = Vec3(1.436000,0.861000,0.911000);
positions[96] = Vec3(0.358000,0.966000,0.176000);
positions[97] = Vec3(1.478000,2.715000,0.427000);
positions[98] = Vec3(1.581000,0.575000,0.809000);
positions[99] = Vec3(1.007000,2.153000,2.887000);
positions[100] = Vec3(2.343000,0.663000,2.513000);
positions[101] = Vec3(2.105000,0.649000,1.635000);
positions[102] = Vec3(0.875000,0.743000,2.459000);
positions[103] = Vec3(0.229000,1.315000,1.879000);
positions[104] = Vec3(0.285000,0.935000,1.700000);
positions[105] = Vec3(2.269000,1.284000,2.234000);
positions[106] = Vec3(1.406000,1.149000,2.767000);
positions[107] = Vec3(1.076000,0.220000,1.849000);
positions[108] = Vec3(2.001000,1.532000,2.881000);
positions[109] = Vec3(2.893000,0.485000,1.860000);
positions[110] = Vec3(1.621000,1.786000,2.624000);
positions[111] = Vec3(0.500000,0.616000,1.818000);
positions[112] = Vec3(0.938000,2.978000,2.104000);
positions[113] = Vec3(0.550000,2.081000,0.454000);
positions[114] = Vec3(1.121000,0.685000,2.196000);
positions[115] = Vec3(1.088000,1.385000,2.184000);
positions[116] = Vec3(1.122000,2.705000,2.080000);
positions[117] = Vec3(0.918000,1.767000,2.861000);
positions[118] = Vec3(2.748000,0.232000,2.126000);
positions[119] = Vec3(1.238000,2.766000,0.109000);
positions[120] = Vec3(1.380000,0.785000,1.961000);
positions[121] = Vec3(1.236000,1.757000,0.150000);
positions[122] = Vec3(1.339000,2.187000,2.592000);
positions[123] = Vec3(1.414000,0.342000,2.714000);
positions[124] = Vec3(1.310000,0.770000,2.589000);
positions[125] = Vec3(1.686000,0.765000,2.321000);
positions[126] = Vec3(1.659000,1.367000,2.780000);
positions[127] = Vec3(0.141000,0.095000,1.903000);
positions[128] = Vec3(2.084000,1.002000,2.520000);
positions[129] = Vec3(2.819000,1.286000,2.626000);
positions[130] = Vec3(1.257000,1.044000,2.401000);
positions[131] = Vec3(1.064000,0.546000,2.839000);
positions[132] = Vec3(0.078000,1.246000,0.010000);
positions[133] = Vec3(1.506000,0.420000,2.223000);
positions[134] = Vec3(1.778000,0.699000,1.920000);
positions[135] = Vec3(1.315000,1.721000,2.733000);
positions[136] = Vec3(0.114000,0.281000,0.279000);
positions[137] = Vec3(1.082000,1.421000,2.596000);
positions[138] = Vec3(3.001000,0.592000,2.276000);
positions[139] = Vec3(1.384000,2.227000,2.992000);
positions[140] = Vec3(1.353000,0.044000,1.985000);
positions[141] = Vec3(1.367000,1.832000,2.383000);
positions[142] = Vec3(0.853000,1.119000,2.230000);
positions[143] = Vec3(1.675000,1.482000,2.295000);
positions[144] = Vec3(1.334000,1.890000,1.904000);
positions[145] = Vec3(1.630000,0.140000,2.939000);
positions[146] = Vec3(0.195000,1.290000,2.300000);
positions[147] = Vec3(2.178000,1.173000,3.001000);
positions[148] = Vec3(0.637000,0.655000,2.126000);
positions[149] = Vec3(0.993000,1.796000,2.529000);
positions[150] = Vec3(0.910000,0.701000,1.845000);
positions[151] = Vec3(0.191000,2.128000,0.355000);
positions[152] = Vec3(0.692000,1.163000,2.578000);
positions[153] = Vec3(1.154000,1.052000,1.974000);
positions[154] = Vec3(1.682000,0.335000,2.509000);
positions[155] = Vec3(0.569000,1.032000,1.895000);
positions[156] = Vec3(1.800000,2.796000,1.295000);
positions[157] = Vec3(2.517000,2.347000,2.878000);
positions[158] = Vec3(0.639000,2.470000,1.678000);
positions[159] = Vec3(0.634000,2.006000,1.829000);
positions[160] = Vec3(0.892000,0.215000,0.566000);
positions[161] = Vec3(1.800000,2.143000,1.491000);
positions[162] = Vec3(1.898000,0.226000,2.765000);
positions[163] = Vec3(0.791000,1.738000,0.260000);
positions[164] = Vec3(0.437000,1.740000,2.048000);
positions[165] = Vec3(1.687000,2.438000,1.166000);
positions[166] = Vec3(1.337000,2.304000,1.643000);
positions[167] = Vec3(1.270000,2.397000,1.033000);
positions[168] = Vec3(0.702000,2.429000,0.591000);
positions[169] = Vec3(0.842000,1.976000,0.724000);
positions[170] = Vec3(1.965000,0.095000,1.206000);
positions[171] = Vec3(0.355000,2.710000,0.618000);
positions[172] = Vec3(0.745000,1.434000,2.781000);
positions[173] = Vec3(0.707000,2.171000,1.502000);
positions[174] = Vec3(1.294000,2.696000,0.847000);
positions[175] = Vec3(1.143000,2.075000,0.276000);
positions[176] = Vec3(1.111000,2.474000,0.312000);
positions[177] = Vec3(1.144000,2.316000,0.633000);
positions[178] = Vec3(1.335000,0.292000,0.515000);
positions[179] = Vec3(1.926000,2.813000,2.703000);
positions[180] = Vec3(0.559000,2.314000,2.904000);
positions[181] = Vec3(1.308000,1.605000,1.534000);
positions[182] = Vec3(0.773000,2.913000,1.217000);
positions[183] = Vec3(1.612000,0.082000,1.027000);
positions[184] = Vec3(1.510000,0.287000,1.787000);
positions[185] = Vec3(0.716000,1.424000,1.843000);
positions[186] = Vec3(1.267000,0.685000,1.160000);
positions[187] = Vec3(0.306000,1.653000,1.717000);
positions[188] = Vec3(0.349000,0.020000,1.275000);
positions[189] = Vec3(0.166000,1.979000,0.804000);
positions[190] = Vec3(1.523000,2.992000,0.711000);
positions[191] = Vec3(1.998000,2.146000,0.088000);
positions[192] = Vec3(0.047000,2.513000,0.642000);
positions[193] = Vec3(0.501000,1.793000,1.438000);
positions[194] = Vec3(1.099000,2.010000,1.626000);
positions[195] = Vec3(2.580000,2.854000,1.328000);
positions[196] = Vec3(1.080000,2.779000,1.190000);
positions[197] = Vec3(0.901000,2.561000,0.948000);
positions[198] = Vec3(0.920000,2.990000,0.844000);
positions[199] = Vec3(0.819000,2.924000,1.711000);
positions[200] = Vec3(0.434000,1.516000,0.063000);
positions[201] = Vec3(1.470000,0.058000,0.231000);
positions[202] = Vec3(0.530000,3.005000,1.550000);
positions[203] = Vec3(0.447000,2.330000,1.277000);
positions[204] = Vec3(1.632000,2.683000,1.593000);
positions[205] = Vec3(0.885000,1.835000,2.072000);
positions[206] = Vec3(0.868000,2.601000,1.425000);
positions[207] = Vec3(0.720000,2.242000,0.907000);
positions[208] = Vec3(1.194000,0.144000,1.065000);
positions[209] = Vec3(0.448000,2.485000,0.959000);
positions[210] = Vec3(1.377000,2.694000,1.352000);
positions[211] = Vec3(1.305000,2.928000,2.713000);
positions[212] = Vec3(1.784000,2.456000,1.981000);
positions[213] = Vec3(0.354000,2.136000,1.563000);
positions[214] = Vec3(0.489000,2.000000,1.108000);
positions[215] = Vec3(1.884000,2.221000,0.461000);
positions[216] = Vec3(1.860000,2.540000,0.306000);
positions[217] = Vec3(1.753000,2.335000,2.768000);
positions[218] = Vec3(1.536000,2.441000,2.344000);
positions[219] = Vec3(0.531000,0.025000,2.235000);
positions[220] = Vec3(0.809000,0.011000,2.834000);
positions[221] = Vec3(0.289000,2.614000,2.879000);
positions[222] = Vec3(0.613000,1.891000,2.337000);
positions[223] = Vec3(0.507000,0.037000,2.694000);
positions[224] = Vec3(0.882000,2.185000,2.583000);
positions[225] = Vec3(0.503000,2.051000,2.615000);
positions[226] = Vec3(1.907000,1.956000,2.831000);
positions[227] = Vec3(2.833000,2.769000,1.644000);
positions[228] = Vec3(1.141000,0.113000,2.945000);
positions[229] = Vec3(0.600000,1.338000,2.200000);
positions[230] = Vec3(0.904000,2.360000,1.952000);
positions[231] = Vec3(0.738000,1.568000,2.437000);
positions[232] = Vec3(1.136000,2.535000,2.805000);
positions[233] = Vec3(1.430000,2.767000,2.321000);
positions[234] = Vec3(1.078000,2.470000,2.385000);
positions[235] = Vec3(0.296000,2.376000,2.560000);
positions[236] = Vec3(0.719000,0.300000,0.075000);
positions[237] = Vec3(0.518000,1.911000,0.080000);
positions[238] = Vec3(0.381000,1.570000,2.450000);
positions[239] = Vec3(0.716000,2.581000,2.697000);
positions[240] = Vec3(1.473000,2.617000,1.936000);
positions[241] = Vec3(0.421000,2.449000,0.229000);
positions[242] = Vec3(0.425000,2.817000,1.910000);
positions[243] = Vec3(1.312000,2.294000,2.057000);
positions[244] = Vec3(1.239000,0.007000,1.539000);
positions[245] = Vec3(0.822000,0.379000,2.086000);
positions[246] = Vec3(0.560000,2.562000,2.227000);
positions[247] = Vec3(0.863000,2.417000,0.050000);
positions[248] = Vec3(1.263000,0.151000,2.332000);
positions[249] = Vec3(0.237000,0.208000,2.336000);
positions[250] = Vec3(0.437000,2.370000,1.910000);
positions[251] = Vec3(1.119000,2.058000,2.207000);
positions[252] = Vec3(1.960000,1.749000,0.118000);
positions[253] = Vec3(2.415000,0.870000,2.757000);
positions[254] = Vec3(1.781000,0.342000,0.366000);
positions[255] = Vec3(2.172000,1.279000,1.421000);
positions[256] = Vec3(1.986000,0.715000,1.301000);
positions[257] = Vec3(1.657000,1.804000,0.810000);
positions[258] = Vec3(2.405000,1.202000,0.416000);
positions[259] = Vec3(1.932000,1.457000,0.786000);
positions[260] = Vec3(1.901000,1.271000,1.207000);
positions[261] = Vec3(1.864000,0.301000,0.810000);
positions[262] = Vec3(1.658000,0.673000,1.558000);
positions[263] = Vec3(2.637000,2.247000,0.396000);
positions[264] = Vec3(1.353000,0.369000,1.438000);
positions[265] = Vec3(0.530000,2.688000,1.346000);
positions[266] = Vec3(0.237000,0.485000,1.047000);
positions[267] = Vec3(2.806000,0.601000,0.822000);
positions[268] = Vec3(1.617000,2.018000,2.136000);
positions[269] = Vec3(2.000000,2.898000,0.022000);
positions[270] = Vec3(2.049000,1.883000,1.001000);
positions[271] = Vec3(2.477000,0.355000,1.786000);
positions[272] = Vec3(1.646000,0.983000,1.266000);
positions[273] = Vec3(1.683000,2.097000,1.114000);
positions[274] = Vec3(2.161000,0.921000,1.065000);
positions[275] = Vec3(2.099000,0.463000,1.942000);
positions[276] = Vec3(2.561000,1.638000,0.572000);
positions[277] = Vec3(2.205000,0.395000,1.005000);
positions[278] = Vec3(2.836000,0.203000,0.698000);
positions[279] = Vec3(2.662000,0.909000,0.966000);
positions[280] = Vec3(0.334000,0.350000,2.767000);
positions[281] = Vec3(2.241000,2.934000,1.248000);
positions[282] = Vec3(2.599000,2.953000,0.921000);
positions[283] = Vec3(2.219000,0.262000,0.058000);
positions[284] = Vec3(0.274000,0.656000,1.456000);
positions[285] = Vec3(1.814000,1.008000,0.882000);
positions[286] = Vec3(2.793000,1.395000,0.316000);
positions[287] = Vec3(0.773000,1.753000,1.639000);
positions[288] = Vec3(2.321000,0.994000,1.591000);
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positions[290] = Vec3(0.178000,1.342000,0.327000);
positions[291] = Vec3(1.623000,1.756000,1.426000);
positions[292] = Vec3(2.252000,0.109000,0.375000);
positions[293] = Vec3(3.003000,1.895000,1.895000);
positions[294] = Vec3(0.407000,0.831000,2.756000);
positions[295] = Vec3(2.193000,0.956000,0.632000);
positions[296] = Vec3(2.405000,0.641000,1.107000);
positions[297] = Vec3(2.361000,0.958000,0.162000);
positions[298] = Vec3(2.173000,1.544000,0.528000);
positions[299] = Vec3(1.565000,1.380000,1.428000);
positions[300] = Vec3(2.342000,0.538000,0.253000);
positions[301] = Vec3(1.910000,0.701000,0.954000);
positions[302] = Vec3(2.910000,0.288000,2.938000);
positions[303] = Vec3(0.257000,1.189000,0.958000);
positions[304] = Vec3(0.134000,1.775000,1.243000);
positions[305] = Vec3(2.476000,1.583000,1.956000);
positions[306] = Vec3(1.838000,1.791000,2.354000);
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positions[311] = Vec3(0.082000,2.857000,0.020000);
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positions[314] = Vec3(2.327000,1.717000,2.350000);
positions[315] = Vec3(2.928000,0.810000,1.582000);
positions[316] = Vec3(2.150000,0.336000,0.576000);
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positions[318] = Vec3(2.851000,0.670000,1.174000);
positions[319] = Vec3(1.954000,1.013000,1.975000);
positions[320] = Vec3(2.474000,1.542000,1.545000);
positions[321] = Vec3(2.826000,0.455000,1.490000);
positions[322] = Vec3(2.140000,2.826000,0.558000);
positions[323] = Vec3(2.151000,1.684000,1.780000);
positions[324] = Vec3(0.174000,0.673000,0.397000);
positions[325] = Vec3(0.066000,1.708000,0.160000);
positions[326] = Vec3(2.158000,0.303000,2.582000);
positions[327] = Vec3(2.602000,1.611000,2.632000);
positions[328] = Vec3(2.566000,1.138000,2.465000);
positions[329] = Vec3(2.026000,1.443000,2.477000);
positions[330] = Vec3(2.365000,0.309000,2.255000);
positions[331] = Vec3(1.636000,1.107000,2.058000);
positions[332] = Vec3(2.522000,2.584000,2.399000);
positions[333] = Vec3(2.537000,2.900000,2.158000);
positions[334] = Vec3(2.660000,0.537000,2.577000);
positions[335] = Vec3(2.679000,1.158000,1.724000);
positions[336] = Vec3(0.220000,1.894000,2.498000);
positions[337] = Vec3(2.266000,1.248000,1.837000);
positions[338] = Vec3(0.055000,1.656000,2.128000);
positions[339] = Vec3(2.899000,1.902000,2.823000);
positions[340] = Vec3(0.085000,2.994000,2.720000);
positions[341] = Vec3(0.013000,0.889000,2.468000);
positions[342] = Vec3(1.804000,0.372000,1.636000);
positions[343] = Vec3(0.201000,1.616000,2.824000);
positions[344] = Vec3(0.369000,1.273000,2.699000);
positions[345] = Vec3(2.996000,0.355000,2.596000);
positions[346] = Vec3(2.867000,1.314000,2.107000);
positions[347] = Vec3(2.611000,0.563000,2.140000);
positions[348] = Vec3(2.676000,2.954000,2.955000);
positions[349] = Vec3(0.256000,0.848000,2.062000);
positions[350] = Vec3(2.530000,0.028000,2.528000);
positions[351] = Vec3(0.537000,1.273000,1.596000);
positions[352] = Vec3(0.004000,1.004000,0.401000);
positions[353] = Vec3(1.676000,1.060000,2.463000);
positions[354] = Vec3(2.622000,1.473000,2.257000);
positions[355] = Vec3(2.917000,2.991000,2.316000);
positions[356] = Vec3(0.672000,1.123000,2.984000);
positions[357] = Vec3(2.229000,1.806000,2.673000);
positions[358] = Vec3(0.463000,0.951000,2.383000);
positions[359] = Vec3(2.126000,0.049000,2.037000);
positions[360] = Vec3(2.868000,0.876000,2.015000);
positions[361] = Vec3(2.720000,2.582000,0.079000);
positions[362] = Vec3(1.966000,0.693000,2.624000);
positions[363] = Vec3(1.971000,0.398000,2.318000);
positions[364] = Vec3(0.337000,0.630000,2.458000);
positions[365] = Vec3(2.562000,1.044000,2.040000);
positions[366] = Vec3(2.817000,1.485000,2.963000);
positions[367] = Vec3(2.514000,0.621000,2.992000);
positions[368] = Vec3(3.000000,1.551000,2.496000);
positions[369] = Vec3(0.698000,2.167000,2.180000);
positions[370] = Vec3(2.693000,0.849000,2.389000);
positions[371] = Vec3(2.092000,2.565000,2.986000);
positions[372] = Vec3(2.010000,3.001000,0.819000);
positions[373] = Vec3(2.392000,2.622000,1.636000);
positions[374] = Vec3(2.086000,2.325000,1.340000);
positions[375] = Vec3(2.578000,2.971000,0.502000);
positions[376] = Vec3(1.871000,2.789000,2.225000);
positions[377] = Vec3(2.230000,2.985000,1.594000);
positions[378] = Vec3(2.860000,2.788000,0.729000);
positions[379] = Vec3(2.051000,1.928000,1.472000);
positions[380] = Vec3(2.307000,2.219000,1.067000);
positions[381] = Vec3(2.369000,2.572000,1.289000);
positions[382] = Vec3(2.206000,1.924000,0.693000);
positions[383] = Vec3(1.984000,2.058000,2.005000);
positions[384] = Vec3(2.287000,1.854000,0.317000);
positions[385] = Vec3(2.525000,0.345000,0.686000);
positions[386] = Vec3(2.933000,1.920000,1.053000);
positions[387] = Vec3(0.324000,2.324000,0.601000);
positions[388] = Vec3(2.042000,1.576000,1.277000);
positions[389] = Vec3(0.031000,2.376000,0.949000);
positions[390] = Vec3(2.519000,2.250000,1.465000);
positions[391] = Vec3(0.221000,2.722000,1.652000);
positions[392] = Vec3(2.409000,2.361000,2.051000);
positions[393] = Vec3(2.472000,1.917000,1.673000);
positions[394] = Vec3(0.999000,2.715000,0.562000);
positions[395] = Vec3(1.669000,0.017000,1.508000);
positions[396] = Vec3(1.924000,1.777000,0.542000);
positions[397] = Vec3(2.635000,2.634000,1.905000);
positions[398] = Vec3(2.042000,2.628000,1.025000);
positions[399] = Vec3(2.694000,1.974000,2.009000);
positions[400] = Vec3(2.988000,2.221000,1.333000);
positions[401] = Vec3(1.772000,0.196000,1.978000);
positions[402] = Vec3(2.893000,2.961000,0.283000);
positions[403] = Vec3(2.615000,0.261000,0.245000);
positions[404] = Vec3(2.797000,2.521000,1.412000);
positions[405] = Vec3(0.013000,2.497000,0.246000);
positions[406] = Vec3(1.875000,2.861000,1.801000);
positions[407] = Vec3(2.800000,2.617000,1.049000);
positions[408] = Vec3(2.824000,1.858000,1.487000);
positions[409] = Vec3(2.434000,1.868000,1.275000);
positions[410] = Vec3(2.814000,0.526000,0.384000);
positions[411] = Vec3(2.844000,2.545000,2.246000);
positions[412] = Vec3(1.896000,2.587000,0.719000);
positions[413] = Vec3(0.350000,0.055000,0.076000);
positions[414] = Vec3(2.686000,1.784000,0.222000);
positions[415] = Vec3(2.724000,1.604000,0.989000);
positions[416] = Vec3(0.807000,1.761000,1.122000);
positions[417] = Vec3(2.120000,2.382000,2.226000);
positions[418] = Vec3(2.058000,1.587000,2.067000);
positions[419] = Vec3(2.904000,2.571000,2.686000);
positions[420] = Vec3(2.228000,2.910000,2.410000);
positions[421] = Vec3(2.797000,2.142000,0.114000);
positions[422] = Vec3(2.905000,1.875000,0.480000);
positions[423] = Vec3(1.881000,2.565000,2.469000);
positions[424] = Vec3(2.404000,1.929000,2.999000);
positions[425] = Vec3(2.389000,2.814000,2.782000);
positions[426] = Vec3(2.520000,0.301000,2.815000);
positions[427] = Vec3(2.726000,1.907000,2.339000);
positions[428] = Vec3(2.880000,2.273000,2.500000);
positions[429] = Vec3(2.574000,2.045000,2.716000);
positions[430] = Vec3(2.988000,2.288000,2.001000);
positions[431] = Vec3(0.011000,2.341000,2.904000);
positions[432] = Vec3(0.215000,2.265000,2.257000);
positions[433] = Vec3(2.268000,2.311000,0.234000);
positions[434] = Vec3(2.462000,2.621000,0.550000);
positions[435] = Vec3(1.530000,2.540000,2.728000);
positions[436] = Vec3(2.162000,2.306000,2.687000);
positions[437] = Vec3(2.748000,2.301000,1.734000);
positions[438] = Vec3(2.334000,1.976000,2.041000);
positions[439] = Vec3(1.981000,2.076000,2.443000);
positions[440] = Vec3(2.301000,1.367000,2.665000);
positions[441] = Vec3(2.399000,2.164000,2.403000);
positions[442] = Vec3(0.244000,2.713000,2.257000);
positions[443] = Vec3(0.683000,0.488000,2.781000);
positions[444] = Vec3(2.194000,2.711000,1.993000);
positions[445] = Vec3(2.947000,2.848000,2.001000);
positions[446] = Vec3(0.223000,1.981000,2.913000);
positions[447] = Vec3(0.010000,1.226000,0.917000);
positions[448] = Vec3(1.911000,0.426000,0.582000);
positions[449] = Vec3(2.204000,0.015000,0.136000);
positions[450] = Vec3(0.927000,0.138000,1.645000);
positions[451] = Vec3(0.155000,0.885000,1.479000);
positions[452] = Vec3(1.550000,1.933000,1.261000);
positions[453] = Vec3(1.304000,0.407000,0.287000);
positions[454] = Vec3(0.270000,1.384000,2.910000);
positions[455] = Vec3(0.516000,1.817000,1.695000);
positions[456] = Vec3(1.458000,2.879000,1.523000);
positions[457] = Vec3(1.702000,1.670000,0.593000);
positions[458] = Vec3(1.974000,1.380000,0.534000);
positions[459] = Vec3(2.835000,1.185000,0.479000);
positions[460] = Vec3(0.548000,2.979000,1.126000);
positions[461] = Vec3(1.202000,2.174000,1.466000);
positions[462] = Vec3(1.237000,1.701000,0.653000);
positions[463] = Vec3(2.939000,0.761000,0.349000);
positions[464] = Vec3(1.667000,2.119000,0.377000);
positions[465] = Vec3(1.196000,0.552000,1.372000);
positions[466] = Vec3(1.416000,0.901000,1.178000);
positions[467] = Vec3(0.519000,1.577000,2.227000);
positions[468] = Vec3(1.214000,1.281000,1.063000);
positions[469] = Vec3(0.822000,0.433000,1.375000);
positions[470] = Vec3(0.095000,2.760000,0.604000);
positions[471] = Vec3(1.325000,2.144000,1.848000);
positions[472] = Vec3(0.681000,0.896000,1.285000);
positions[473] = Vec3(0.406000,2.936000,0.717000);
positions[474] = Vec3(0.565000,1.852000,0.349000);
positions[475] = Vec3(0.597000,1.651000,1.020000);
positions[476] = Vec3(1.236000,0.170000,1.335000);
positions[477] = Vec3(0.586000,0.441000,1.980000);
positions[478] = Vec3(1.443000,1.208000,1.575000);
positions[479] = Vec3(0.247000,0.243000,0.502000);
positions[480] = Vec3(1.386000,1.564000,0.236000);
positions[481] = Vec3(0.871000,1.063000,0.930000);
positions[482] = Vec3(0.136000,0.992000,0.621000);
positions[483] = Vec3(0.889000,0.986000,0.010000);
positions[484] = Vec3(1.107000,2.731000,1.452000);
positions[485] = Vec3(0.942000,2.471000,0.517000);
positions[486] = Vec3(0.989000,0.652000,0.747000);
positions[487] = Vec3(0.899000,1.235000,2.707000);
positions[488] = Vec3(1.105000,0.684000,0.068000);
positions[489] = Vec3(1.660000,1.235000,2.276000);
positions[490] = Vec3(1.593000,1.883000,1.915000);
positions[491] = Vec3(1.528000,1.613000,0.920000);
positions[492] = Vec3(0.459000,1.046000,1.011000);
positions[493] = Vec3(0.213000,0.612000,0.644000);
positions[494] = Vec3(0.078000,1.392000,1.676000);
positions[495] = Vec3(0.605000,0.491000,0.574000);
positions[496] = Vec3(0.990000,1.586000,1.076000);
positions[497] = Vec3(0.297000,1.434000,1.028000);
positions[498] = Vec3(1.101000,1.471000,1.443000);
positions[499] = Vec3(0.072000,0.139000,1.653000);
positions[500] = Vec3(0.633000,0.884000,0.645000);
positions[501] = Vec3(0.352000,2.841000,1.463000);
positions[502] = Vec3(0.418000,0.774000,0.350000);
positions[503] = Vec3(2.641000,0.198000,0.869000);
positions[504] = Vec3(0.608000,1.341000,0.695000);
positions[505] = Vec3(1.778000,1.151000,1.830000);
positions[506] = Vec3(1.669000,0.342000,2.768000);
positions[507] = Vec3(1.256000,0.994000,0.798000);
positions[508] = Vec3(1.068000,0.375000,1.036000);
positions[509] = Vec3(0.910000,0.758000,1.589000);
positions[510] = Vec3(0.243000,2.452000,0.805000);
positions[511] = Vec3(1.018000,0.764000,1.122000);
positions[512] = Vec3(2.464000,1.089000,1.404000);
positions[513] = Vec3(0.670000,0.564000,0.034000);
positions[514] = Vec3(0.030000,1.296000,1.310000);
positions[515] = Vec3(1.210000,1.785000,1.691000);
positions[516] = Vec3(0.022000,0.620000,0.974000);
positions[517] = Vec3(1.499000,1.277000,2.986000);
positions[518] = Vec3(1.227000,1.896000,1.006000);
positions[519] = Vec3(0.528000,1.022000,1.635000);
positions[520] = Vec3(1.887000,2.670000,0.089000);
positions[521] = Vec3(1.661000,0.825000,0.793000);
positions[522] = Vec3(0.831000,1.494000,0.374000);
positions[523] = Vec3(1.356000,0.613000,0.930000);
positions[524] = Vec3(0.667000,0.600000,0.968000);
positions[525] = Vec3(1.154000,1.702000,2.925000);
positions[526] = Vec3(1.420000,1.581000,1.289000);
positions[527] = Vec3(1.383000,0.041000,0.932000);
positions[528] = Vec3(1.727000,0.140000,1.725000);
positions[529] = Vec3(0.711000,1.215000,2.004000);
positions[530] = Vec3(1.061000,1.067000,1.366000);
positions[531] = Vec3(0.377000,0.597000,1.224000);
positions[532] = Vec3(0.274000,0.719000,1.842000);
positions[533] = Vec3(0.840000,1.658000,1.874000);
positions[534] = Vec3(0.877000,0.290000,0.311000);
positions[535] = Vec3(2.130000,1.153000,1.196000);
positions[536] = Vec3(1.028000,1.379000,0.747000);
positions[537] = Vec3(1.107000,2.450000,2.079000);
positions[538] = Vec3(1.419000,1.333000,0.585000);
positions[539] = Vec3(0.430000,1.305000,1.369000);
positions[540] = Vec3(0.775000,1.363000,1.596000);
positions[541] = Vec3(1.522000,2.009000,0.736000);
positions[542] = Vec3(0.857000,1.722000,0.696000);
positions[543] = Vec3(0.722000,2.831000,1.478000);
positions[544] = Vec3(0.411000,1.673000,0.681000);
positions[545] = Vec3(1.511000,0.456000,0.597000);
positions[546] = Vec3(2.684000,0.820000,2.996000);
positions[547] = Vec3(1.593000,1.713000,2.369000);
positions[548] = Vec3(1.113000,0.803000,1.958000);
positions[549] = Vec3(1.267000,1.095000,0.254000);
positions[550] = Vec3(2.120000,0.540000,2.477000);
positions[551] = Vec3(0.566000,1.409000,2.588000);
positions[552] = Vec3(0.261000,0.872000,2.546000);
positions[553] = Vec3(1.878000,1.446000,2.680000);
positions[554] = Vec3(0.878000,1.606000,2.658000);
positions[555] = Vec3(1.564000,0.749000,1.786000);
positions[556] = Vec3(1.412000,1.942000,2.625000);
positions[557] = Vec3(1.660000,1.114000,2.710000);
positions[558] = Vec3(1.118000,0.813000,2.424000);
positions[559] = Vec3(1.482000,0.893000,2.434000);
positions[560] = Vec3(1.093000,1.129000,1.740000);
positions[561] = Vec3(2.163000,0.849000,2.709000);
positions[562] = Vec3(1.201000,1.429000,1.957000);
positions[563] = Vec3(0.235000,2.258000,2.002000);
positions[564] = Vec3(0.413000,1.444000,0.314000);
positions[565] = Vec3(0.164000,0.450000,2.408000);
positions[566] = Vec3(1.551000,0.851000,0.033000);
positions[567] = Vec3(0.659000,0.228000,2.807000);
positions[568] = Vec3(0.741000,0.131000,2.124000);
positions[569] = Vec3(0.455000,0.567000,2.682000);
positions[570] = Vec3(0.729000,0.971000,2.408000);
positions[571] = Vec3(1.487000,2.820000,0.162000);
positions[572] = Vec3(1.855000,0.700000,2.858000);
positions[573] = Vec3(0.305000,1.074000,1.926000);
positions[574] = Vec3(1.300000,0.153000,1.747000);
positions[575] = Vec3(1.272000,1.249000,2.568000);
positions[576] = Vec3(0.431000,0.743000,2.238000);
positions[577] = Vec3(0.493000,0.240000,0.184000);
positions[578] = Vec3(1.734000,0.506000,2.317000);
positions[579] = Vec3(0.874000,0.631000,2.692000);
positions[580] = Vec3(0.473000,2.790000,2.161000);
positions[581] = Vec3(1.310000,0.571000,2.759000);
positions[582] = Vec3(0.677000,0.798000,1.916000);
positions[583] = Vec3(0.944000,0.442000,1.858000);
positions[584] = Vec3(3.006000,2.098000,2.976000);
positions[585] = Vec3(0.864000,0.592000,2.231000);
positions[586] = Vec3(1.366000,0.611000,2.147000);
positions[587] = Vec3(2.871000,1.217000,2.880000);
positions[588] = Vec3(1.674000,2.664000,2.336000);
positions[589] = Vec3(1.757000,0.879000,2.101000);
positions[590] = Vec3(1.293000,2.939000,2.457000);
positions[591] = Vec3(1.108000,1.131000,2.206000);
positions[592] = Vec3(1.207000,1.658000,2.498000);
positions[593] = Vec3(0.850000,1.373000,2.312000);
positions[594] = Vec3(1.413000,1.060000,1.939000);
positions[595] = Vec3(1.138000,0.140000,2.102000);
positions[596] = Vec3(0.752000,1.307000,1.190000);
positions[597] = Vec3(1.254000,0.942000,2.790000);
positions[598] = Vec3(1.544000,1.614000,2.800000);
positions[599] = Vec3(2.128000,0.302000,2.833000);
positions[600] = Vec3(0.300000,1.744000,0.027000);
positions[601] = Vec3(1.878000,2.986000,2.060000);
positions[602] = Vec3(1.528000,0.233000,2.045000);
positions[603] = Vec3(1.146000,1.817000,2.067000);
positions[604] = Vec3(1.037000,2.746000,0.813000);
positions[605] = Vec3(0.524000,0.610000,1.566000);
positions[606] = Vec3(0.945000,2.964000,0.503000);
positions[607] = Vec3(1.788000,2.565000,0.965000);
positions[608] = Vec3(0.471000,2.510000,0.491000);
positions[609] = Vec3(0.512000,2.043000,1.371000);
positions[610] = Vec3(2.316000,2.423000,1.494000);
positions[611] = Vec3(1.575000,2.394000,2.953000);
positions[612] = Vec3(2.845000,2.869000,0.985000);
positions[613] = Vec3(1.016000,2.335000,1.003000);
positions[614] = Vec3(0.998000,2.830000,1.879000);
positions[615] = Vec3(0.624000,2.508000,0.075000);
positions[616] = Vec3(1.362000,2.808000,2.069000);
positions[617] = Vec3(1.747000,0.068000,0.810000);
positions[618] = Vec3(1.768000,2.355000,0.661000);
positions[619] = Vec3(1.535000,2.410000,2.085000);
positions[620] = Vec3(0.844000,2.004000,1.646000);
positions[621] = Vec3(1.124000,0.280000,0.649000);
positions[622] = Vec3(0.689000,2.170000,0.648000);
positions[623] = Vec3(0.849000,2.666000,1.175000);
positions[624] = Vec3(2.975000,1.963000,1.308000);
positions[625] = Vec3(1.074000,2.082000,0.714000);
positions[626] = Vec3(1.284000,2.651000,1.110000);
positions[627] = Vec3(1.669000,0.205000,0.180000);
positions[628] = Vec3(1.716000,0.047000,1.253000);
positions[629] = Vec3(0.501000,2.241000,1.043000);
positions[630] = Vec3(1.038000,1.833000,0.305000);
positions[631] = Vec3(0.646000,2.431000,1.424000);
positions[632] = Vec3(1.383000,2.059000,2.230000);
positions[633] = Vec3(0.370000,2.566000,1.192000);
positions[634] = Vec3(1.355000,2.006000,0.120000);
positions[635] = Vec3(2.113000,0.075000,0.589000);
positions[636] = Vec3(1.850000,0.448000,1.890000);
positions[637] = Vec3(1.215000,2.704000,0.405000);
positions[638] = Vec3(0.575000,2.997000,1.798000);
positions[639] = Vec3(0.967000,2.586000,2.603000);
positions[640] = Vec3(0.276000,1.669000,1.430000);
positions[641] = Vec3(1.483000,2.284000,1.128000);
positions[642] = Vec3(0.983000,3.003000,1.099000);
positions[643] = Vec3(0.539000,2.222000,1.720000);
positions[644] = Vec3(0.648000,2.826000,2.751000);
positions[645] = Vec3(0.803000,1.994000,0.993000);
positions[646] = Vec3(0.451000,0.216000,1.438000);
positions[647] = Vec3(1.604000,2.512000,0.334000);
positions[648] = Vec3(1.980000,2.022000,0.588000);
positions[649] = Vec3(1.843000,2.834000,1.544000);
positions[650] = Vec3(1.835000,3.005000,2.858000);
positions[651] = Vec3(0.679000,2.499000,0.838000);
positions[652] = Vec3(0.012000,2.637000,1.524000);
positions[653] = Vec3(0.314000,2.065000,0.602000);
positions[654] = Vec3(1.157000,0.004000,0.173000);
positions[655] = Vec3(0.736000,1.705000,1.382000);
positions[656] = Vec3(1.511000,2.736000,0.690000);
positions[657] = Vec3(1.330000,2.541000,1.735000);
positions[658] = Vec3(0.744000,0.170000,0.785000);
positions[659] = Vec3(2.593000,2.794000,0.703000);
positions[660] = Vec3(0.275000,1.872000,1.043000);
positions[661] = Vec3(1.624000,2.608000,1.341000);
positions[662] = Vec3(1.382000,0.122000,2.855000);
positions[663] = Vec3(1.326000,2.434000,0.783000);
positions[664] = Vec3(0.117000,0.116000,1.254000);
positions[665] = Vec3(1.045000,2.970000,2.748000);
positions[666] = Vec3(1.341000,2.692000,2.799000);
positions[667] = Vec3(1.797000,2.586000,2.709000);
positions[668] = Vec3(0.890000,2.484000,1.716000);
positions[669] = Vec3(2.373000,2.558000,1.889000);
positions[670] = Vec3(1.566000,2.323000,2.574000);
positions[671] = Vec3(1.257000,2.280000,0.399000);
positions[672] = Vec3(0.679000,2.130000,2.434000);
positions[673] = Vec3(2.016000,2.334000,2.462000);
positions[674] = Vec3(1.077000,2.213000,2.416000);
positions[675] = Vec3(0.581000,1.950000,2.081000);
positions[676] = Vec3(0.805000,2.315000,2.810000);
positions[677] = Vec3(0.844000,1.787000,2.322000);
positions[678] = Vec3(0.980000,2.205000,0.129000);
positions[679] = Vec3(2.468000,0.603000,2.740000);
positions[680] = Vec3(2.366000,2.403000,2.299000);
positions[681] = Vec3(0.337000,2.487000,2.329000);
positions[682] = Vec3(2.007000,2.793000,2.452000);
positions[683] = Vec3(1.072000,2.571000,0.063000);
positions[684] = Vec3(1.217000,2.283000,2.806000);
positions[685] = Vec3(0.459000,2.477000,2.728000);
positions[686] = Vec3(0.958000,1.975000,2.710000);
positions[687] = Vec3(0.914000,2.111000,2.052000);
positions[688] = Vec3(0.768000,2.958000,0.075000);
positions[689] = Vec3(0.474000,1.805000,2.533000);
positions[690] = Vec3(1.313000,2.552000,2.395000);
positions[691] = Vec3(1.853000,2.014000,2.229000);
positions[692] = Vec3(2.405000,2.230000,2.658000);
positions[693] = Vec3(0.727000,1.781000,0.016000);
positions[694] = Vec3(0.974000,2.791000,2.271000);
positions[695] = Vec3(0.438000,0.096000,2.457000);
positions[696] = Vec3(0.652000,2.392000,2.064000);
positions[697] = Vec3(1.972000,2.209000,2.834000);
positions[698] = Vec3(0.333000,0.141000,2.088000);
positions[699] = Vec3(1.813000,1.952000,0.063000);
positions[700] = Vec3(0.166000,2.838000,1.877000);
positions[701] = Vec3(1.772000,0.487000,0.951000);
positions[702] = Vec3(1.924000,1.404000,1.434000);
positions[703] = Vec3(2.734000,0.348000,1.712000);
positions[704] = Vec3(2.874000,0.729000,1.811000);
positions[705] = Vec3(1.841000,0.877000,1.137000);
positions[706] = Vec3(2.327000,1.491000,1.768000);
positions[707] = Vec3(1.916000,1.483000,1.057000);
positions[708] = Vec3(2.783000,0.850000,0.745000);
positions[709] = Vec3(1.829000,1.526000,0.085000);
positions[710] = Vec3(2.426000,1.082000,0.652000);
positions[711] = Vec3(1.645000,1.241000,1.217000);
positions[712] = Vec3(2.286000,0.725000,0.084000);
positions[713] = Vec3(2.755000,0.691000,1.421000);
positions[714] = Vec3(2.651000,0.591000,1.023000);
positions[715] = Vec3(2.040000,0.863000,0.442000);
positions[716] = Vec3(0.035000,0.109000,2.497000);
positions[717] = Vec3(0.127000,1.410000,0.572000);
positions[718] = Vec3(2.174000,0.357000,0.307000);
positions[719] = Vec3(2.705000,1.508000,0.758000);
positions[720] = Vec3(2.223000,1.407000,2.913000);
positions[721] = Vec3(2.528000,1.722000,1.088000);
positions[722] = Vec3(2.860000,0.345000,0.198000);
positions[723] = Vec3(2.580000,1.789000,1.479000);
positions[724] = Vec3(2.779000,0.295000,1.295000);
positions[725] = Vec3(0.097000,0.434000,2.826000);
positions[726] = Vec3(2.952000,1.654000,1.091000);
positions[727] = Vec3(0.119000,1.878000,0.343000);
positions[728] = Vec3(1.718000,1.173000,0.327000);
positions[729] = Vec3(2.833000,0.016000,0.527000);
positions[730] = Vec3(2.085000,1.779000,2.888000);
positions[731] = Vec3(2.754000,2.952000,1.485000);
positions[732] = Vec3(2.826000,0.935000,1.162000);
positions[733] = Vec3(1.564000,1.585000,1.615000);
positions[734] = Vec3(2.132000,0.645000,1.093000);
positions[735] = Vec3(2.294000,1.490000,1.350000);
positions[736] = Vec3(0.081000,0.490000,1.479000);
positions[737] = Vec3(2.118000,1.165000,1.642000);
positions[738] = Vec3(2.141000,0.121000,1.390000);
positions[739] = Vec3(2.385000,0.389000,1.196000);
positions[740] = Vec3(0.049000,0.166000,0.817000);
positions[741] = Vec3(1.993000,0.806000,1.814000);
positions[742] = Vec3(0.006000,1.450000,0.171000);
positions[743] = Vec3(2.297000,0.428000,0.764000);
positions[744] = Vec3(2.851000,0.469000,2.114000);
positions[745] = Vec3(1.814000,1.957000,0.945000);
positions[746] = Vec3(0.386000,0.327000,0.902000);
positions[747] = Vec3(2.452000,1.070000,1.807000);
positions[748] = Vec3(2.309000,1.537000,2.159000);
positions[749] = Vec3(2.712000,1.497000,2.007000);
positions[750] = Vec3(1.727000,0.924000,1.503000);
positions[751] = Vec3(0.861000,0.801000,0.344000);
positions[752] = Vec3(1.740000,1.245000,0.819000);
positions[753] = Vec3(0.117000,0.042000,0.197000);
positions[754] = Vec3(2.557000,0.996000,0.317000);
positions[755] = Vec3(2.228000,1.588000,2.548000);
positions[756] = Vec3(2.849000,1.557000,2.708000);
positions[757] = Vec3(0.152000,1.107000,0.219000);
positions[758] = Vec3(2.460000,1.318000,1.002000);
positions[759] = Vec3(2.405000,1.436000,0.528000);
positions[760] = Vec3(2.135000,1.179000,2.046000);
positions[761] = Vec3(1.726000,0.588000,0.286000);
positions[762] = Vec3(2.831000,1.053000,1.538000);
positions[763] = Vec3(1.932000,1.556000,1.833000);
positions[764] = Vec3(2.423000,0.900000,1.064000);
positions[765] = Vec3(3.001000,1.807000,0.709000);
positions[766] = Vec3(0.578000,1.095000,0.223000);
positions[767] = Vec3(2.215000,1.160000,0.252000);
positions[768] = Vec3(2.050000,0.921000,0.835000);
positions[769] = Vec3(2.080000,1.682000,0.738000);
positions[770] = Vec3(2.851000,1.753000,0.027000);
positions[771] = Vec3(0.203000,0.509000,0.202000);
positions[772] = Vec3(1.967000,1.018000,0.018000);
positions[773] = Vec3(1.869000,0.878000,2.472000);
positions[774] = Vec3(1.917000,0.228000,2.507000);
positions[775] = Vec3(0.316000,0.795000,2.991000);
positions[776] = Vec3(2.175000,1.229000,2.472000);
positions[777] = Vec3(2.405000,1.062000,2.931000);
positions[778] = Vec3(2.501000,0.511000,2.369000);
positions[779] = Vec3(2.641000,0.819000,2.141000);
positions[780] = Vec3(0.649000,1.384000,3.006000);
positions[781] = Vec3(1.012000,0.329000,2.963000);
positions[782] = Vec3(2.755000,0.350000,2.718000);
positions[783] = Vec3(2.315000,0.153000,2.454000);
positions[784] = Vec3(2.583000,1.696000,2.389000);
positions[785] = Vec3(0.439000,2.593000,1.776000);
positions[786] = Vec3(2.630000,1.390000,0.116000);
positions[787] = Vec3(2.854000,0.669000,2.478000);
positions[788] = Vec3(2.551000,1.342000,2.621000);
positions[789] = Vec3(2.533000,2.734000,2.987000);
positions[790] = Vec3(2.772000,2.446000,2.875000);
positions[791] = Vec3(2.817000,1.051000,2.498000);
positions[792] = Vec3(2.688000,1.404000,1.621000);
positions[793] = Vec3(0.083000,2.737000,2.775000);
positions[794] = Vec3(2.514000,0.322000,2.041000);
positions[795] = Vec3(2.470000,0.900000,2.504000);
positions[796] = Vec3(2.790000,0.444000,0.624000);
positions[797] = Vec3(0.040000,0.840000,2.202000);
positions[798] = Vec3(0.530000,1.067000,2.764000);
positions[799] = Vec3(0.191000,1.385000,2.541000);
positions[800] = Vec3(2.465000,0.363000,0.051000);
positions[801] = Vec3(1.850000,1.902000,2.592000);
positions[802] = Vec3(1.432000,0.306000,2.449000);
positions[803] = Vec3(2.259000,0.489000,1.753000);
positions[804] = Vec3(2.803000,1.118000,1.956000);
positions[805] = Vec3(2.426000,0.147000,1.636000);
positions[806] = Vec3(2.880000,1.846000,2.133000);
positions[807] = Vec3(2.862000,2.110000,1.867000);
positions[808] = Vec3(0.424000,1.184000,2.299000);
positions[809] = Vec3(2.518000,1.218000,2.228000);
positions[810] = Vec3(2.153000,0.834000,1.468000);
positions[811] = Vec3(0.105000,1.397000,2.088000);
positions[812] = Vec3(2.579000,0.601000,0.316000);
positions[813] = Vec3(2.594000,2.106000,2.968000);
positions[814] = Vec3(0.448000,1.435000,1.783000);
positions[815] = Vec3(2.125000,0.299000,2.132000);
positions[816] = Vec3(2.849000,1.402000,2.356000);
positions[817] = Vec3(2.956000,0.091000,2.078000);
positions[818] = Vec3(0.156000,1.696000,2.357000);
positions[819] = Vec3(1.566000,2.211000,1.557000);
positions[820] = Vec3(2.047000,0.194000,0.985000);
positions[821] = Vec3(1.947000,2.680000,0.488000);
positions[822] = Vec3(2.343000,2.796000,1.447000);
positions[823] = Vec3(2.006000,2.332000,0.265000);
positions[824] = Vec3(2.396000,1.834000,0.546000);
positions[825] = Vec3(2.538000,2.059000,2.207000);
positions[826] = Vec3(0.110000,2.360000,0.447000);
positions[827] = Vec3(2.198000,2.448000,1.136000);
positions[828] = Vec3(2.420000,2.121000,1.271000);
positions[829] = Vec3(0.422000,2.192000,0.260000);
positions[830] = Vec3(2.145000,2.767000,2.839000);
positions[831] = Vec3(2.434000,2.398000,0.421000);
positions[832] = Vec3(2.489000,2.175000,1.718000);
positions[833] = Vec3(2.870000,2.527000,0.814000);
positions[834] = Vec3(2.741000,2.016000,0.337000);
positions[835] = Vec3(1.997000,2.574000,2.107000);
positions[836] = Vec3(0.002000,2.128000,0.932000);
positions[837] = Vec3(2.787000,2.375000,0.234000);
positions[838] = Vec3(2.235000,1.852000,1.620000);
positions[839] = Vec3(2.782000,1.642000,0.422000);
positions[840] = Vec3(2.915000,1.760000,1.699000);
positions[841] = Vec3(2.047000,2.178000,1.549000);
positions[842] = Vec3(1.808000,1.878000,1.556000);
positions[843] = Vec3(2.224000,2.043000,0.913000);
positions[844] = Vec3(2.619000,2.611000,1.237000);
positions[845] = Vec3(2.916000,2.726000,0.168000);
positions[846] = Vec3(2.021000,2.833000,1.176000);
positions[847] = Vec3(2.967000,2.308000,2.258000);
positions[848] = Vec3(2.778000,2.270000,1.477000);
positions[849] = Vec3(2.121000,1.834000,2.002000);
positions[850] = Vec3(2.097000,2.752000,0.808000);
positions[851] = Vec3(1.897000,0.566000,1.501000);
positions[852] = Vec3(0.359000,2.802000,0.036000);
positions[853] = Vec3(2.966000,2.454000,1.186000);
positions[854] = Vec3(2.461000,2.964000,1.132000);
positions[855] = Vec3(2.093000,1.821000,1.243000);
positions[856] = Vec3(1.706000,2.659000,1.841000);
positions[857] = Vec3(2.074000,1.709000,0.342000);
positions[858] = Vec3(2.137000,2.894000,1.813000);
positions[859] = Vec3(0.223000,2.293000,1.417000);
positions[860] = Vec3(2.637000,0.007000,0.197000);
positions[861] = Vec3(1.416000,0.050000,0.483000);
positions[862] = Vec3(1.845000,2.250000,1.251000);
positions[863] = Vec3(2.906000,0.034000,2.896000);
positions[864] = Vec3(2.481000,0.204000,0.474000);
positions[865] = Vec3(2.234000,2.051000,0.158000);
positions[866] = Vec3(0.185000,2.453000,0.055000);
positions[867] = Vec3(2.509000,0.048000,2.786000);
positions[868] = Vec3(2.202000,2.206000,2.027000);
positions[869] = Vec3(0.061000,2.367000,2.656000);
positions[870] = Vec3(3.003000,2.755000,2.241000);
positions[871] = Vec3(0.297000,2.131000,2.463000);
positions[872] = Vec3(1.553000,0.429000,1.573000);
positions[873] = Vec3(2.506000,1.832000,1.911000);
positions[874] = Vec3(2.472000,1.814000,2.759000);
positions[875] = Vec3(1.922000,1.563000,2.278000);
positions[876] = Vec3(2.623000,2.666000,2.169000);
positions[877] = Vec3(0.120000,1.834000,2.723000);
positions[878] = Vec3(0.294000,0.103000,2.826000);
positions[879] = Vec3(2.364000,2.821000,0.417000);
positions[880] = Vec3(2.446000,1.734000,0.153000);
positions[881] = Vec3(2.777000,2.037000,2.565000);
positions[882] = Vec3(2.837000,2.477000,1.924000);
positions[883] = Vec3(2.221000,1.961000,2.443000);
positions[884] = Vec3(2.284000,2.895000,2.157000);
positions[885] = Vec3(2.728000,2.880000,1.861000);
positions[886] = Vec3(0.454000,2.080000,2.868000);
positions[887] = Vec3(2.430000,2.790000,2.524000);
positions[888] = Vec3(1.808000,2.213000,1.899000);
positions[889] = Vec3(2.666000,0.053000,2.309000);
positions[890] = Vec3(2.290000,2.408000,2.995000);
positions[891] = Vec3(2.646000,2.592000,1.625000);
positions[892] = Vec3(2.750000,2.508000,2.489000);
positions[893] = Vec3(0.211000,1.753000,1.939000);
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