Merge pull request #167 from peastman/cpu

Created optimized CPU platform

CMakeLists.txt

@@ -374,6 +374,13 @@ IF(OPENMM_BUILD_OPENCL_LIB)
     ADD_SUBDIRECTORY(platforms/opencl)
 ENDIF(OPENMM_BUILD_OPENCL_LIB)
 
+# Optimized CPU platform
+
+SET(OPENMM_BUILD_CPU_LIB ON CACHE BOOL "Build optimized CPU platform")
+IF(OPENMM_BUILD_CPU_LIB)
+   ADD_SUBDIRECTORY(platforms/cpu)
+ENDIF(OPENMM_BUILD_CPU_LIB)
+
 # Amoeba plugin
 
 SET(OPENMM_BUILD_AMOEBA_PLUGIN ON CACHE BOOL "Build Amoeba plugin")

openmmapi/include/openmm/internal/hardware.h

+#ifndef OPENMM_HARDWARE_H_
+#define OPENMM_HARDWARE_H_
+
+/* -------------------------------------------------------------------------- *
+ *                                   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) 2013 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 file defines a collection of functions for querying the specific hardware being used.
+ */
+
+/**
+ * Get the number of CPU cores available.
+ */
+#ifdef __APPLE__
+   #include <sys/sysctl.h>
+   #include <dlfcn.h>
+#else
+   #ifdef WIN32
+      #include <windows.h>
+   #else
+      #include <dlfcn.h>
+      #include <unistd.h>
+   #endif
+#endif
+
+static int getNumProcessors() {
+#ifdef __APPLE__
+    int ncpu;
+    size_t len = 4;
+    if (sysctlbyname("hw.logicalcpu", &ncpu, &len, NULL, 0) == 0)
+       return ncpu;
+    else
+       return 1;
+#else
+#ifdef WIN32
+    SYSTEM_INFO siSysInfo;
+    int ncpu;
+    GetSystemInfo(&siSysInfo);
+    ncpu = siSysInfo.dwNumberOfProcessors;
+    if (ncpu < 1)
+        ncpu = 1;
+    return ncpu;
+#else
+    long nProcessorsOnline = sysconf(_SC_NPROCESSORS_ONLN);
+    if (nProcessorsOnline == -1)
+        return 1;
+    else
+        return (int) nProcessorsOnline;
+#endif
+#endif
+}
+
+/**
+ * Get a description of the CPU's capabilities.
+ */
+#ifdef _WIN32
+#define cpuid __cpuid
+#else
+static void cpuid(int cpuInfo[4], int infoType){
+#ifdef __LP64__
+    __asm__ __volatile__ (
+        "cpuid":
+        "=a" (cpuInfo[0]),
+        "=b" (cpuInfo[1]),
+        "=c" (cpuInfo[2]),
+        "=d" (cpuInfo[3]) :
+        "a" (infoType)
+    );
+#else
+    __asm__ __volatile__ (
+        "pushl %%ebx\n"
+        "cpuid\n"
+        "movl %%ebx, %1\n"
+        "popl %%ebx\n" :
+        "=a" (cpuInfo[0]),
+        "=r" (cpuInfo[1]),
+        "=c" (cpuInfo[2]),
+        "=d" (cpuInfo[3]) :
+        "a" (infoType)
+    );
+#endif
+}
+#endif
+
+#endif // OPENMM_HARDWARE_H_

platforms/cpu/CMakeLists.txt

+#---------------------------------------------------
+# OpenMM CPU Platform
+#
+# Creates OpenMM library, base name=OpenMMCPU.
+# Default libraries are shared & optimized. Variants
+# are created for static (_static) and debug (_d).
+#
+# Windows:
+#   OpenMMCPU[_d].dll
+#   OpenMMCPU[_d].lib
+#   OpenMMCPU_static[_d].lib
+# Unix:
+#   libOpenMMCPU[_d].so
+#   libOpenMMCPU_static[_d].a
+#----------------------------------------------------
+
+IF (APPLE)
+    SET (CMAKE_OSX_DEPLOYMENT_TARGET "10.6")
+ENDIF (APPLE)
+
+SUBDIRS (tests)
+
+# The source is organized into subdirectories, but we handle them all from
+# this CMakeLists file rather than letting CMake visit them as SUBDIRS.
+SET(OPENMM_SOURCE_SUBDIRS .)
+
+
+# Collect up information about the version of the OpenMM library we're building
+# and make it available to the code so it can be built into the binaries.
+
+SET(OPENMMCPU_LIBRARY_NAME OpenMMCPU)
+
+SET(SHARED_TARGET ${OPENMMCPU_LIBRARY_NAME})
+SET(STATIC_TARGET ${OPENMMCPU_LIBRARY_NAME}_static)
+
+
+# Ensure that debug libraries have "_d" appended to their names.
+# CMake gets this right on Windows automatically with this definition.
+IF (${CMAKE_GENERATOR} MATCHES "Visual Studio")
+    SET(CMAKE_DEBUG_POSTFIX "_d" CACHE INTERNAL "" FORCE)
+ENDIF (${CMAKE_GENERATOR} MATCHES "Visual Studio")
+
+# But on Unix or Cygwin we have to add the suffix manually
+IF (UNIX AND CMAKE_BUILD_TYPE MATCHES Debug)
+    SET(SHARED_TARGET ${SHARED_TARGET}_d)
+    SET(STATIC_TARGET ${STATIC_TARGET}_d)
+ENDIF (UNIX AND CMAKE_BUILD_TYPE MATCHES Debug)
+
+
+# These are all the places to search for header files which are
+# to be part of the API.
+SET(API_INCLUDE_DIRS) # start empty
+FOREACH(subdir ${OPENMM_SOURCE_SUBDIRS})
+    # append
+    SET(API_INCLUDE_DIRS ${API_INCLUDE_DIRS}
+                         ${CMAKE_CURRENT_SOURCE_DIR}/${subdir}/include
+                         ${CMAKE_CURRENT_SOURCE_DIR}/${subdir}/include/internal)
+ENDFOREACH(subdir)
+
+# We'll need both *relative* path names, starting with their API_INCLUDE_DIRS,
+# and absolute pathnames.
+SET(API_REL_INCLUDE_FILES)   # start these out empty
+SET(API_ABS_INCLUDE_FILES)
+
+FOREACH(dir ${API_INCLUDE_DIRS})
+    FILE(GLOB fullpaths ${dir}/*.h)	# returns full pathnames
+    SET(API_ABS_INCLUDE_FILES ${API_ABS_INCLUDE_FILES} ${fullpaths})
+
+    FOREACH(pathname ${fullpaths})
+        GET_FILENAME_COMPONENT(filename ${pathname} NAME)
+        SET(API_REL_INCLUDE_FILES ${API_REL_INCLUDE_FILES} ${dir}/${filename})
+    ENDFOREACH(pathname)
+ENDFOREACH(dir)
+
+# collect up source files
+SET(SOURCE_FILES) # empty
+SET(SOURCE_INCLUDE_FILES)
+
+FOREACH(subdir ${OPENMM_SOURCE_SUBDIRS})
+    FILE(GLOB_RECURSE src_files  ${CMAKE_CURRENT_SOURCE_DIR}/${subdir}/src/*.cpp ${CMAKE_CURRENT_SOURCE_DIR}/${subdir}/src/*.c)
+    FILE(GLOB incl_files ${CMAKE_CURRENT_SOURCE_DIR}/${subdir}/src/*.h)
+    SET(SOURCE_FILES         ${SOURCE_FILES}         ${src_files})   #append
+    IF(MSVC)
+         FILE(GLOB_RECURSE kernel_files ${CMAKE_CURRENT_SOURCE_DIR}/${subdir}/src/kernels/*.cu)
+         SET(SOURCE_FILES ${SOURCE_FILES} ${kernel_files})
+    ENDIF(MSVC)
+    SET(SOURCE_INCLUDE_FILES ${SOURCE_INCLUDE_FILES} ${incl_files})
+    INCLUDE_DIRECTORIES(BEFORE ${CMAKE_CURRENT_SOURCE_DIR}/${subdir}/include)
+ENDFOREACH(subdir)
+
+INCLUDE_DIRECTORIES(BEFORE ${CMAKE_CURRENT_SOURCE_DIR}/src)
+
+# Install headers
+
+FILE(GLOB CORE_HEADERS include/*.h)
+INSTALL_FILES(/include/openmm/cpu FILES ${CORE_HEADERS})
+
+SUBDIRS (sharedTarget)

platforms/cpu/include/CpuKernelFactory.h

+#ifndef OPENMM_CPUKERNELFACTORY_H_
+#define OPENMM_CPUKERNELFACTORY_H_
+
+/* -------------------------------------------------------------------------- *
+ *                                   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) 2013 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.                                     *
+ * -------------------------------------------------------------------------- */
+
+#include "openmm/KernelFactory.h"
+
+namespace OpenMM {
+
+/**
+ * This KernelFactory creates all kernels for CpuPlatform.
+ */
+
+class CpuKernelFactory : public KernelFactory {
+public:
+    KernelImpl* createKernelImpl(std::string name, const Platform& platform, ContextImpl& context) const;
+};
+
+} // namespace OpenMM
+
+#endif /*OPENMM_CPUKERNELFACTORY_H_*/

platforms/cpu/include/CpuKernels.h

+#ifndef OPENMM_CPUKERNELS_H_
+#define OPENMM_CPUKERNELS_H_
+
+/* -------------------------------------------------------------------------- *
+ *                                   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) 2013 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.                                     *
+ * -------------------------------------------------------------------------- */
+
+#include "CpuPlatform.h"
+#include "CpuNeighborList.h"
+#include "CpuNonbondedForce.h"
+#include "openmm/kernels.h"
+#include "openmm/System.h"
+
+namespace OpenMM {
+
+/**
+ * This kernel is invoked by NonbondedForce to calculate the forces acting on the system.
+ */
+class CpuCalcNonbondedForceKernel : public CalcNonbondedForceKernel {
+public:
+    CpuCalcNonbondedForceKernel(std::string name, const Platform& platform) : CalcNonbondedForceKernel(name, platform),
+            bonded14IndexArray(NULL), bonded14ParamArray(NULL), hasInitializedPme(false) {
+    }
+    ~CpuCalcNonbondedForceKernel();
+    /**
+     * Initialize the kernel.
+     *
+     * @param system     the System this kernel will be applied to
+     * @param force      the NonbondedForce this kernel will be used for
+     */
+    void initialize(const System& system, const NonbondedForce& force);
+    /**
+     * Execute the kernel to calculate the forces and/or energy.
+     *
+     * @param context        the context in which to execute this kernel
+     * @param includeForces  true if forces should be calculated
+     * @param includeEnergy  true if the energy should be calculated
+     * @param includeDirect  true if direct space interactions should be included
+     * @param includeReciprocal  true if reciprocal space interactions should be included
+     * @return the potential energy due to the force
+     */
+    double execute(ContextImpl& context, bool includeForces, bool includeEnergy, bool includeDirect, bool includeReciprocal);
+    /**
+     * Copy changed parameters over to a context.
+     *
+     * @param context    the context to copy parameters to
+     * @param force      the NonbondedForce to copy the parameters from
+     */
+    void copyParametersToContext(ContextImpl& context, const NonbondedForce& force);
+private:
+    class PmeIO;
+    int numParticles, num14;
+    int **bonded14IndexArray;
+    double **bonded14ParamArray;
+    double nonbondedCutoff, switchingDistance, rfDielectric, ewaldAlpha, ewaldSelfEnergy, dispersionCoefficient;
+    int kmax[3], gridSize[3];
+    bool useSwitchingFunction, useOptimizedPme, hasInitializedPme;
+    std::vector<std::set<int> > exclusions;
+    std::vector<std::pair<float, float> > particleParams;
+    std::vector<float> posq;
+    std::vector<float> forces;
+    std::vector<RealVec> lastPositions;
+    NonbondedMethod nonbondedMethod;
+    CpuNeighborList neighborList;
+    CpuNonbondedForce nonbonded;
+    Kernel optimizedPme;
+};
+
+} // namespace OpenMM
+
+#endif /*OPENMM_CPUKERNELS_H_*/
+

platforms/cpu/include/CpuNeighborList.h

+#ifndef OPENMM_CPU_NEIGHBORLIST_H_
+#define OPENMM_CPU_NEIGHBORLIST_H_
+
+#include "windowsExportCpu.h"
+#include <pthread.h>
+#include <set>
+#include <utility>
+#include <vector>
+
+namespace OpenMM {
+    
+class OPENMM_EXPORT_CPU CpuNeighborList {
+public:
+    class ThreadData;
+    class VoxelHash;
+    CpuNeighborList();
+    ~CpuNeighborList();
+    void computeNeighborList(int numAtoms, const std::vector<float>& atomLocations, const std::vector<std::set<int> >& exclusions,
+            const float* periodicBoxSize, bool usePeriodic, float maxDistance);
+    const std::vector<std::pair<int, int> >& getNeighbors();
+    /**
+     * This routine contains the code executed by each thread.
+     */
+    void runThread(int index, std::vector<std::pair<int, int> >& threadNeighbors);
+private:
+    bool isDeleted;
+    int numThreads, waitCount;
+    std::vector<std::pair<int, int> > neighbors;
+    std::vector<pthread_t> thread;
+    std::vector<ThreadData*> threadData;
+    pthread_cond_t startCondition, endCondition;
+    pthread_mutex_t lock;
+    // The following variables are used to make information accessible to the individual threads.
+    VoxelHash* voxelHash;
+    const std::vector<std::set<int> >* exclusions;
+    const float* atomLocations;
+    const float* periodicBoxSize;
+    int numAtoms;
+    bool usePeriodic;
+    float maxDistance;
+};
+
+} // namespace OpenMM
+
+#endif // OPENMM_REFERENCE_NEIGHBORLIST_H_

platforms/cpu/include/CpuNonbondedForce.h

+
+/* Portions copyright (c) 2006-2013 Stanford University and Simbios.
+ * Contributors: Pande Group
+ *
+ * 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.
+ */
+
+#ifndef OPENMM_CPU_NONBONDED_FORCE_H__
+#define OPENMM_CPU_NONBONDED_FORCE_H__
+
+#include "ReferencePairIxn.h"
+#include <pthread.h>
+#include <set>
+#include <utility>
+#include <vector>
+#include <smmintrin.h>
+// ---------------------------------------------------------------------------------------
+
+class CpuNonbondedForce {
+    public:
+        class ThreadData;
+
+      /**---------------------------------------------------------------------------------------
+      
+         Constructor
+      
+         --------------------------------------------------------------------------------------- */
+
+       CpuNonbondedForce();
+
+      /**---------------------------------------------------------------------------------------
+      
+         Destructor
+      
+         --------------------------------------------------------------------------------------- */
+
+       ~CpuNonbondedForce();
+
+      /**---------------------------------------------------------------------------------------
+      
+         Set the force to use a cutoff.
+      
+         @param distance            the cutoff distance
+         @param neighbors           the neighbor list to use
+         @param solventDielectric   the dielectric constant of the bulk solvent
+      
+         --------------------------------------------------------------------------------------- */
+      
+      void setUseCutoff(float distance, const std::vector<std::pair<int, int> >& neighbors, float solventDielectric);
+
+      /**---------------------------------------------------------------------------------------
+      
+         Set the force to use a switching function on the Lennard-Jones interaction.
+      
+         @param distance            the switching distance
+      
+         --------------------------------------------------------------------------------------- */
+      
+      void setUseSwitchingFunction(float distance);
+      
+      /**---------------------------------------------------------------------------------------
+      
+         Set the force to use periodic boundary conditions.  This requires that a cutoff has
+         already been set, and the smallest side of the periodic box is at least twice the cutoff
+         distance.
+      
+         @param boxSize             the X, Y, and Z widths of the periodic box
+      
+         --------------------------------------------------------------------------------------- */
+      
+      void setPeriodic(float* periodicBoxSize);
+       
+      /**---------------------------------------------------------------------------------------
+      
+         Set the force to use Ewald summation.
+      
+         @param alpha  the Ewald separation parameter
+         @param kmaxx  the largest wave vector in the x direction
+         @param kmaxy  the largest wave vector in the y direction
+         @param kmaxz  the largest wave vector in the z direction
+      
+         --------------------------------------------------------------------------------------- */
+      
+      void setUseEwald(float alpha, int kmaxx, int kmaxy, int kmaxz);
+
+     
+      /**---------------------------------------------------------------------------------------
+      
+         Set the force to use Particle-Mesh Ewald (PME) summation.
+      
+         @param alpha    the Ewald separation parameter
+         @param gridSize the dimensions of the mesh
+      
+         --------------------------------------------------------------------------------------- */
+      
+      void setUsePME(float alpha, int meshSize[3]);
+
+      /**---------------------------------------------------------------------------------------
+      
+         Calculate Ewald ixn
+      
+         @param numberOfAtoms    number of atoms
+         @param posq             atom coordinates and charges
+         @param atomCoordinates  atom coordinates (in format needed by PME)
+         @param atomParameters   atom parameters (sigma/2, 2*sqrt(epsilon))
+         @param exclusions       atom exclusion indices
+                                 exclusions[atomIndex] contains the list of exclusions for that atom
+         @param forces           force array (forces added)
+         @param totalEnergy      total energy
+            
+         --------------------------------------------------------------------------------------- */
+          
+      void calculateReciprocalIxn(int numberOfAtoms, float* posq, std::vector<OpenMM::RealVec>& atomCoordinates,
+                            const std::vector<std::pair<float, float> >& atomParameters, const std::vector<std::set<int> >& exclusions,
+                            std::vector<OpenMM::RealVec>& forces, float* totalEnergy) const;
+      
+      /**---------------------------------------------------------------------------------------
+      
+         Calculate LJ Coulomb pair ixn
+      
+         @param numberOfAtoms    number of atoms
+         @param posq             atom coordinates and charges
+         @param atomParameters   atom parameters (sigma/2, 2*sqrt(epsilon))
+         @param exclusions       atom exclusion indices
+                                 exclusions[atomIndex] contains the list of exclusions for that atom
+         @param forces           force array (forces added)
+         @param totalEnergy      total energy
+      
+         --------------------------------------------------------------------------------------- */
+          
+      void calculateDirectIxn(int numberOfAtoms, float* posq, const std::vector<std::pair<float, float> >& atomParameters,
+            const std::vector<std::set<int> >& exclusions, float* forces, float* totalEnergy);
+
+    /**
+     * This routine contains the code executed by each thread.
+     */
+    void runThread(int index, std::vector<float>& threadForce, double& threadEnergy);
+
+private:
+        bool cutoff;
+        bool useSwitch;
+        bool periodic;
+        bool ewald;
+        bool pme;
+        const std::vector<std::pair<int, int> >* neighborList;
+        float periodicBoxSize[3];
+        float cutoffDistance, switchingDistance;
+        float krf, crf;
+        float alphaEwald;
+        int numRx, numRy, numRz;
+        int meshDim[3];
+        std::vector<float> ewaldScaleX, ewaldScaleY, ewaldScaleDeriv;
+        float ewaldDX, ewaldDXInv;
+        __m128 boxSize, invBoxSize, half;
+        bool isDeleted;
+        int numThreads, waitCount;
+        std::vector<pthread_t> thread;
+        std::vector<ThreadData*> threadData;
+        pthread_cond_t startCondition, endCondition;
+        pthread_mutex_t lock;
+        // The following variables are used to make information accessible to the individual threads.
+        int numberOfAtoms;
+        float* posq;
+        std::pair<float, float> const* atomParameters;        
+        std::set<int> const* exclusions;
+        bool includeEnergy;
+
+        static const float TWO_OVER_SQRT_PI;
+        static const int NUM_TABLE_POINTS;
+            
+      /**---------------------------------------------------------------------------------------
+      
+         Calculate LJ Coulomb pair ixn between two atoms
+      
+         @param atom1            the index of the first atom
+         @param atom2            the index of the second atom
+         @param forces           force array (forces added)
+         @param totalEnergy      total energy
+            
+         --------------------------------------------------------------------------------------- */
+          
+      void calculateOneIxn(int atom1, int atom2, float* forces, double* totalEnergy);
+            
+      /**---------------------------------------------------------------------------------------
+      
+         Calculate LJ Coulomb pair ixn between two atoms
+      
+         @param atom1            the index of the first atom
+         @param atom2            the index of the second atom
+         @param forces           force array (forces added)
+         @param totalEnergy      total energy
+            
+         --------------------------------------------------------------------------------------- */
+          
+      void calculateOneEwaldIxn(int atom1, int atom2, float* forces, double* totalEnergy);
+
+      /**
+       * Compute the displacement and squared distance between two points, optionally using
+       * periodic boundary conditions.
+       */
+      void getDeltaR(const __m128& posI, const __m128& posJ, __m128& deltaR, float& r2, bool periodic) const;
+
+      /**
+       * Compute a fast approximation to erfc(x).
+       */
+      static float erfcApprox(float x);
+
+      /**
+       * Create a lookup table for the scale factor used with Ewald and PME.
+       */
+      void tabulateEwaldScaleFactor();
+      
+      /**
+       * Evaluate the scale factor used with Ewald and PME: erfc(alpha*r) + 2*alpha*r*exp(-alpha*alpha*r*r)/sqrt(PI)
+       */
+      float ewaldScaleFunction(float x);
+};
+
+// ---------------------------------------------------------------------------------------
+
+#endif // OPENMM_CPU_NONBONDED_FORCE_H__

platforms/cpu/include/CpuPlatform.h

+#ifndef OPENMM_CPUPLATFORM_H_
+#define OPENMM_CPUPLATFORM_H_
+
+/* -------------------------------------------------------------------------- *
+ *                                   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) 2013 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.                                     *
+ * -------------------------------------------------------------------------- */
+
+#include "ReferencePlatform.h"
+#include "windowsExportCpu.h"
+
+namespace OpenMM {
+    
+/**
+ * This Platform subclass uses CPU implementations of the OpenMM kernels.
+ */
+
+class OPENMM_EXPORT_CPU CpuPlatform : public ReferencePlatform {
+public:
+    CpuPlatform();
+    const std::string& getName() const {
+        static const std::string name = "CPU";
+        return name;
+    }
+    double getSpeed() const;
+    bool supportsDoublePrecision() const;
+};
+
+} // namespace OpenMM
+
+#endif /*OPENMM_CPUPLATFORM_H_*/

platforms/cpu/include/windowsExportCpu.h

+#ifndef OPENMM_WINDOWSEXPORTCPU_H_
+#define OPENMM_WINDOWSEXPORTCPU_H_
+
+/*
+ * Shared libraries are messy in Visual Studio. We have to distinguish three
+ * cases:
+ *   (1) this header is being used to build the OpenMM shared library
+ *       (dllexport)
+ *   (2) this header is being used by a *client* of the OpenMM shared
+ *       library (dllimport)
+ *   (3) we are building the OpenMM static library, or the client is
+ *       being compiled with the expectation of linking with the
+ *       OpenMM static library (nothing special needed)
+ * In the CMake script for building this library, we define one of the symbols
+ *     OPENMM_CPU_BUILDING_{SHARED|STATIC}_LIBRARY
+ * Client code normally has no special symbol defined, in which case we'll
+ * assume it wants to use the shared library. However, if the client defines
+ * the symbol OPENMM_USE_STATIC_LIBRARIES we'll suppress the dllimport so
+ * that the client code can be linked with static libraries. Note that
+ * the client symbol is not library dependent, while the library symbols
+ * affect only the OpenMM library, meaning that other libraries can
+ * be clients of this one. However, we are assuming all-static or all-shared.
+ */
+
+#ifdef _MSC_VER
+    // We don't want to hear about how sprintf is "unsafe".
+    #pragma warning(disable:4996)
+    // Keep MS VC++ quiet about lack of dll export of private members.
+    #pragma warning(disable:4251)
+    #if defined(OPENMM_CPU_BUILDING_SHARED_LIBRARY)
+        #define OPENMM_EXPORT_CPU __declspec(dllexport)
+    #elif defined(OPENMM_CPU_BUILDING_STATIC_LIBRARY) || defined(OPENMM_CPU_USE_STATIC_LIBRARIES)
+        #define OPENMM_EXPORT_CPU
+    #else
+        #define OPENMM_EXPORT_CPU __declspec(dllimport)   // i.e., a client of a shared library
+    #endif
+#else
+    #define OPENMM_EXPORT_CPU // Linux, Mac
+#endif
+
+#endif // OPENMM_WINDOWSEXPORTCPU_H_

platforms/cpu/sharedTarget/CMakeLists.txt

+SET_SOURCE_FILES_PROPERTIES(${SOURCE_FILES} PROPERTIES COMPILE_FLAGS "-msse4.1")
+ADD_LIBRARY(${SHARED_TARGET} SHARED ${SOURCE_FILES} ${SOURCE_INCLUDE_FILES} ${API_ABS_INCLUDE_FILES})
+
+IF (UNIX AND CMAKE_BUILD_TYPE MATCHES Debug)
+    SET(MAIN_OPENMM_LIB ${OPENMM_LIBRARY_NAME}_d)
+ELSE (UNIX AND CMAKE_BUILD_TYPE MATCHES Debug)
+    SET(MAIN_OPENMM_LIB ${OPENMM_LIBRARY_NAME})
+ENDIF (UNIX AND CMAKE_BUILD_TYPE MATCHES Debug)
+TARGET_LINK_LIBRARIES(${SHARED_TARGET} ${MAIN_OPENMM_LIB} ${PTHREADS_LIB})
+SET_TARGET_PROPERTIES(${SHARED_TARGET} PROPERTIES COMPILE_FLAGS "-DOPENMM_CPU_BUILDING_SHARED_LIBRARY")
+
+INSTALL_TARGETS(/lib/plugins RUNTIME_DIRECTORY /lib/plugins ${SHARED_TARGET})

platforms/cpu/src/CpuKernelFactory.cpp

+/* -------------------------------------------------------------------------- *
+ *                                   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) 2013 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.                                     *
+ * -------------------------------------------------------------------------- */
+
+#include "CpuKernelFactory.h"
+#include "CpuKernels.h"
+#include "CpuPlatform.h"
+#include "openmm/internal/ContextImpl.h"
+#include "openmm/OpenMMException.h"
+
+using namespace OpenMM;
+
+KernelImpl* CpuKernelFactory::createKernelImpl(std::string name, const Platform& platform, ContextImpl& context) const {
+    ReferencePlatform::PlatformData& data = *static_cast<ReferencePlatform::PlatformData*>(context.getPlatformData());
+    if (name == CalcNonbondedForceKernel::Name())
+        return new CpuCalcNonbondedForceKernel(name, platform);
+    throw OpenMMException((std::string("Tried to create kernel with illegal kernel name '") + name + "'").c_str());
+}

platforms/cpu/src/CpuKernels.cpp

+/* -------------------------------------------------------------------------- *
+ *                                   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) 2013 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.                                     *
+ * -------------------------------------------------------------------------- */
+
+#include "CpuKernels.h"
+#include "ReferenceBondForce.h"
+#include "ReferenceLJCoulomb14.h"
+#include "openmm/Context.h"
+#include "openmm/OpenMMException.h"
+#include "openmm/internal/ContextImpl.h"
+#include "openmm/internal/NonbondedForceImpl.h"
+#include "RealVec.h"
+
+using namespace OpenMM;
+using namespace std;
+
+static vector<RealVec>& extractPositions(ContextImpl& context) {
+    ReferencePlatform::PlatformData* data = reinterpret_cast<ReferencePlatform::PlatformData*>(context.getPlatformData());
+    return *((vector<RealVec>*) data->positions);
+}
+
+static vector<RealVec>& extractVelocities(ContextImpl& context) {
+    ReferencePlatform::PlatformData* data = reinterpret_cast<ReferencePlatform::PlatformData*>(context.getPlatformData());
+    return *((vector<RealVec>*) data->velocities);
+}
+
+static vector<RealVec>& extractForces(ContextImpl& context) {
+    ReferencePlatform::PlatformData* data = reinterpret_cast<ReferencePlatform::PlatformData*>(context.getPlatformData());
+    return *((vector<RealVec>*) data->forces);
+}
+
+static RealVec& extractBoxSize(ContextImpl& context) {
+    ReferencePlatform::PlatformData* data = reinterpret_cast<ReferencePlatform::PlatformData*>(context.getPlatformData());
+    return *(RealVec*) data->periodicBoxSize;
+}
+
+class CpuCalcNonbondedForceKernel::PmeIO : public CalcPmeReciprocalForceKernel::IO {
+public:
+    PmeIO(float* posq, float* force, int numParticles) : posq(posq), force(force), numParticles(numParticles) {
+    }
+    float* getPosq() {
+        return posq;
+    }
+    void setForce(float* f) {
+        for (int i = 0; i < numParticles; i++) {
+            force[4*i] += f[4*i];
+            force[4*i+1] += f[4*i+1];
+            force[4*i+2] += f[4*i+2];
+        }
+    }
+private:
+    float* posq;
+    float* force;
+    int numParticles;
+};
+
+CpuCalcNonbondedForceKernel::~CpuCalcNonbondedForceKernel() {
+    if (bonded14ParamArray != NULL) {
+        for (int i = 0; i < num14; i++) {
+            delete[] bonded14IndexArray[i];
+            delete[] bonded14ParamArray[i];
+        }
+        delete bonded14IndexArray;
+        delete bonded14ParamArray;
+    }
+}
+
+void CpuCalcNonbondedForceKernel::initialize(const System& system, const NonbondedForce& force) {
+
+    // Identify which exceptions are 1-4 interactions.
+
+    numParticles = force.getNumParticles();
+    posq.resize(4*numParticles, 0);
+    forces.resize(4*numParticles, 0);
+    exclusions.resize(numParticles);
+    vector<int> nb14s;
+    for (int i = 0; i < force.getNumExceptions(); i++) {
+        int particle1, particle2;
+        double chargeProd, sigma, epsilon;
+        force.getExceptionParameters(i, particle1, particle2, chargeProd, sigma, epsilon);
+        exclusions[particle1].insert(particle2);
+        exclusions[particle2].insert(particle1);
+        if (chargeProd != 0.0 || epsilon != 0.0)
+            nb14s.push_back(i);
+    }
+
+    // Record the particle parameters.
+
+    num14 = nb14s.size();
+    bonded14IndexArray = new int*[num14];
+    for (int i = 0; i < num14; i++)
+        bonded14IndexArray[i] = new int[2];
+    bonded14ParamArray = new double*[num14];
+    for (int i = 0; i < num14; i++)
+        bonded14ParamArray[i] = new double[3];
+    particleParams.resize(numParticles);
+    double sumSquaredCharges = 0.0;
+    for (int i = 0; i < numParticles; ++i) {
+        double charge, radius, depth;
+        force.getParticleParameters(i, charge, radius, depth);
+        posq[4*i+3] = (float) charge;
+        particleParams[i] = make_pair((float) (0.5*radius), (float) (2.0*sqrt(depth)));
+        sumSquaredCharges += charge*charge;
+    }
+    
+    // Recorded exception parameters.
+    
+    for (int i = 0; i < num14; ++i) {
+        int particle1, particle2;
+        double charge, radius, depth;
+        force.getExceptionParameters(nb14s[i], particle1, particle2, charge, radius, depth);
+        bonded14IndexArray[i][0] = particle1;
+        bonded14IndexArray[i][1] = particle2;
+        bonded14ParamArray[i][0] = static_cast<RealOpenMM>(radius);
+        bonded14ParamArray[i][1] = static_cast<RealOpenMM>(4.0*depth);
+        bonded14ParamArray[i][2] = static_cast<RealOpenMM>(charge);
+    }
+    
+    // Record other parameters.
+    
+    nonbondedMethod = CalcNonbondedForceKernel::NonbondedMethod(force.getNonbondedMethod());
+    nonbondedCutoff = force.getCutoffDistance();
+    if (nonbondedMethod == NoCutoff)
+        useSwitchingFunction = false;
+    else {
+        useSwitchingFunction = force.getUseSwitchingFunction();
+        switchingDistance = force.getSwitchingDistance();
+    }
+    if (nonbondedMethod == Ewald) {
+        double alpha;
+        NonbondedForceImpl::calcEwaldParameters(system, force, alpha, kmax[0], kmax[1], kmax[2]);
+        ewaldAlpha = alpha;
+    }
+    else if (nonbondedMethod == PME) {
+        double alpha;
+        NonbondedForceImpl::calcPMEParameters(system, force, alpha, gridSize[0], gridSize[1], gridSize[2]);
+        ewaldAlpha = alpha;
+    }
+    if (nonbondedMethod == Ewald || nonbondedMethod == PME)
+        ewaldSelfEnergy = -ONE_4PI_EPS0*ewaldAlpha*sumSquaredCharges/sqrt(M_PI);
+    else
+        ewaldSelfEnergy = 0.0;
+    rfDielectric = force.getReactionFieldDielectric();
+    if (force.getUseDispersionCorrection())
+        dispersionCoefficient = NonbondedForceImpl::calcDispersionCorrection(system, force);
+    else
+        dispersionCoefficient = 0.0;
+    lastPositions.resize(numParticles, Vec3(1e10, 1e10, 1e10));
+}
+
+double CpuCalcNonbondedForceKernel::execute(ContextImpl& context, bool includeForces, bool includeEnergy, bool includeDirect, bool includeReciprocal) {
+    if (!hasInitializedPme) {
+        hasInitializedPme = true;
+        useOptimizedPme = false;
+        if (nonbondedMethod == PME) {
+            // If available, use the optimized PME implementation.
+
+            try {
+                optimizedPme = getPlatform().createKernel(CalcPmeReciprocalForceKernel::Name(), context);
+                optimizedPme.getAs<CalcPmeReciprocalForceKernel>().initialize(gridSize[0], gridSize[1], gridSize[2], numParticles, ewaldAlpha);
+                useOptimizedPme = true;
+            }
+            catch (OpenMMException& ex) {
+                // The CPU PME plugin isn't available.
+            }
+        }
+    }
+    vector<RealVec>& posData = extractPositions(context);
+    vector<RealVec>& forceData = extractForces(context);
+    RealVec boxSize = extractBoxSize(context);
+    float floatBoxSize[3] = {(float) boxSize[0], (float) boxSize[1], (float) boxSize[2]};
+    double energy = ewaldSelfEnergy;
+    bool periodic = (nonbondedMethod == CutoffPeriodic);
+    bool ewald  = (nonbondedMethod == Ewald);
+    bool pme  = (nonbondedMethod == PME);
+    
+    // Convert the positions to single precision.
+    
+    if (periodic)
+        for (int i = 0; i < numParticles; i++)
+            for (int j = 0; j < 3; j++) {
+                RealOpenMM x = posData[i][j];
+                double base = floor(x/boxSize[j]+0.5)*boxSize[j];
+                posq[4*i+j] = (float) (x-base);
+            }
+    else
+        for (int i = 0; i < numParticles; i++) {
+            posq[4*i] = (float) posData[i][0];
+            posq[4*i+1] = (float) posData[i][1];
+            posq[4*i+2] = (float) posData[i][2];
+        }
+    for (int i = 0; i < 4*numParticles; i++)
+        forces[i] = 0.0f;
+    if (nonbondedMethod != NoCutoff) {
+        // Determine whether we need to recompute the neighbor list.
+        
+        double padding = 0.1*nonbondedCutoff;
+        bool needRecompute = false;
+        for (int i = 0; i < numParticles; i++) {
+            RealVec delta = posData[i]-lastPositions[i];
+            if (delta.dot(delta) > 0.25*padding*padding) {
+                needRecompute = true;
+                break;
+            }
+        }
+        if (needRecompute) {
+            neighborList.computeNeighborList(numParticles, posq, exclusions, floatBoxSize, periodic || ewald || pme, nonbondedCutoff+padding);
+            lastPositions = posData;
+        }
+        nonbonded.setUseCutoff(nonbondedCutoff, neighborList.getNeighbors(), rfDielectric);
+    }
+    if (periodic || ewald || pme) {
+        double minAllowedSize = 1.999999*nonbondedCutoff;
+        if (boxSize[0] < minAllowedSize || boxSize[1] < minAllowedSize || boxSize[2] < minAllowedSize)
+            throw OpenMMException("The periodic box size has decreased to less than twice the nonbonded cutoff.");
+        nonbonded.setPeriodic(floatBoxSize);
+    }
+    if (ewald)
+        nonbonded.setUseEwald(ewaldAlpha, kmax[0], kmax[1], kmax[2]);
+    if (pme)
+        nonbonded.setUsePME(ewaldAlpha, gridSize);
+    if (useSwitchingFunction)
+        nonbonded.setUseSwitchingFunction(switchingDistance);
+    float nonbondedEnergy = 0;
+    if (includeDirect)
+        nonbonded.calculateDirectIxn(numParticles, &posq[0], particleParams, exclusions, &forces[0], includeEnergy ? &nonbondedEnergy : NULL);
+    if (includeReciprocal) {
+        if (useOptimizedPme) {
+            PmeIO io(&posq[0], &forces[0], numParticles);
+            Vec3 periodicBoxSize(boxSize[0], boxSize[1], boxSize[2]);
+            optimizedPme.getAs<CalcPmeReciprocalForceKernel>().beginComputation(io, periodicBoxSize, includeEnergy);
+            optimizedPme.getAs<CalcPmeReciprocalForceKernel>().finishComputation(io);
+        }
+        else
+            nonbonded.calculateReciprocalIxn(numParticles, &posq[0], posData, particleParams, exclusions, forceData, includeEnergy ? &nonbondedEnergy : NULL);
+    }
+    energy += nonbondedEnergy;
+    for (int i = 0; i < numParticles; i++) {
+        forceData[i][0] += forces[4*i];
+        forceData[i][1] += forces[4*i+1];
+        forceData[i][2] += forces[4*i+2];
+    }
+    if (includeDirect) {
+        ReferenceBondForce refBondForce;
+        ReferenceLJCoulomb14 nonbonded14;
+        refBondForce.calculateForce(num14, bonded14IndexArray, posData, bonded14ParamArray, forceData, includeEnergy ? &energy : NULL, nonbonded14);
+        if (periodic || ewald || pme)
+            energy += dispersionCoefficient/(boxSize[0]*boxSize[1]*boxSize[2]);
+    }
+    return energy;
+}
+
+void CpuCalcNonbondedForceKernel::copyParametersToContext(ContextImpl& context, const NonbondedForce& force) {
+    if (force.getNumParticles() != numParticles)
+        throw OpenMMException("updateParametersInContext: The number of particles has changed");
+    vector<int> nb14s;
+    for (int i = 0; i < force.getNumExceptions(); i++) {
+        int particle1, particle2;
+        double chargeProd, sigma, epsilon;
+        force.getExceptionParameters(i, particle1, particle2, chargeProd, sigma, epsilon);
+        if (chargeProd != 0.0 || epsilon != 0.0)
+            nb14s.push_back(i);
+    }
+    if (nb14s.size() != num14)
+        throw OpenMMException("updateParametersInContext: The number of non-excluded exceptions has changed");
+
+    // Record the values.
+
+    double sumSquaredCharges = 0.0;
+    for (int i = 0; i < numParticles; ++i) {
+        double charge, radius, depth;
+        force.getParticleParameters(i, charge, radius, depth);
+        posq[4*i+3] = (float) charge;
+        particleParams[i] = make_pair((float) (0.5*radius), (float) (2.0*sqrt(depth)));
+        sumSquaredCharges += charge*charge;
+    }
+    if (nonbondedMethod == Ewald || nonbondedMethod == PME)
+        ewaldSelfEnergy = -ONE_4PI_EPS0*ewaldAlpha*sumSquaredCharges/sqrt(M_PI);
+    else
+        ewaldSelfEnergy = 0.0;
+    for (int i = 0; i < num14; ++i) {
+        int particle1, particle2;
+        double charge, radius, depth;
+        force.getExceptionParameters(nb14s[i], particle1, particle2, charge, radius, depth);
+        bonded14IndexArray[i][0] = particle1;
+        bonded14IndexArray[i][1] = particle2;
+        bonded14ParamArray[i][0] = static_cast<RealOpenMM>(radius);
+        bonded14ParamArray[i][1] = static_cast<RealOpenMM>(4.0*depth);
+        bonded14ParamArray[i][2] = static_cast<RealOpenMM>(charge);
+    }
+    
+    // Recompute the coefficient for the dispersion correction.
+
+    NonbondedForce::NonbondedMethod method = force.getNonbondedMethod();
+    if (force.getUseDispersionCorrection() && (method == NonbondedForce::CutoffPeriodic || method == NonbondedForce::Ewald || method == NonbondedForce::PME))
+        dispersionCoefficient = NonbondedForceImpl::calcDispersionCorrection(context.getSystem(), force);
+}

platforms/cpu/src/CpuNeighborList.cpp

+#include "CpuNeighborList.h"
+#include "openmm/internal/hardware.h"
+#include <set>
+#include <map>
+#include <cmath>
+#include <smmintrin.h>
+
+using namespace std;
+
+namespace OpenMM {
+
+class VoxelIndex 
+{
+public:
+    VoxelIndex(int xx, int yy, int zz) : x(xx), y(yy), z(zz) {
+    }
+
+    // operator<() needed for map
+    bool operator<(const VoxelIndex& other) const {
+        if      (x < other.x) return true;
+        else if (x > other.x) return false;
+        else if (y < other.y) return true;
+        else if (y > other.y) return false;
+        else if (z < other.z) return true;
+        else return false;
+    }
+    
+    int x;
+    int y;
+    int z;
+};
+
+typedef pair<const float*, int> VoxelItem;
+typedef vector< VoxelItem > Voxel;
+
+class CpuNeighborList::VoxelHash {
+public:
+    VoxelHash(float vsx, float vsy, float vsz, const float* periodicBoxSize, bool usePeriodic) :
+            voxelSizeX(vsx), voxelSizeY(vsy), voxelSizeZ(vsz), periodicBoxSize(periodicBoxSize), usePeriodic(usePeriodic) {
+        if (usePeriodic) {
+            nx = (int) floorf(periodicBoxSize[0]/voxelSizeX+0.5f);
+            ny = (int) floorf(periodicBoxSize[1]/voxelSizeY+0.5f);
+            nz = (int) floorf(periodicBoxSize[2]/voxelSizeZ+0.5f);
+            voxelSizeX = periodicBoxSize[0]/nx;
+            voxelSizeY = periodicBoxSize[1]/ny;
+            voxelSizeZ = periodicBoxSize[2]/nz;
+        }
+    }
+
+    void insert(const int& item, const float* location) {
+        VoxelIndex voxelIndex = getVoxelIndex(location);
+        if (voxelMap.find(voxelIndex) == voxelMap.end())
+            voxelMap[voxelIndex] = Voxel(); 
+        Voxel& voxel = voxelMap.find(voxelIndex)->second;
+        voxel.push_back(VoxelItem(location, item));
+    }
+    
+
+    VoxelIndex getVoxelIndex(const float* location) const {
+        float xperiodic, yperiodic, zperiodic;
+        if (!usePeriodic) {
+            xperiodic = location[0];
+            yperiodic = location[1];
+            zperiodic = location[2];
+        }
+        else {
+            xperiodic = location[0]-periodicBoxSize[0]*floorf(location[0]/periodicBoxSize[0]);
+            yperiodic = location[1]-periodicBoxSize[1]*floorf(location[1]/periodicBoxSize[1]);
+            zperiodic = location[2]-periodicBoxSize[2]*floorf(location[2]/periodicBoxSize[2]);
+        }
+        int x = int(floorf(xperiodic / voxelSizeX));
+        int y = int(floorf(yperiodic / voxelSizeY));
+        int z = int(floorf(zperiodic / voxelSizeZ));
+        
+        return VoxelIndex(x, y, z);
+    }
+
+    void getNeighbors(vector<pair<int, int> >& neighbors, const VoxelItem& referencePoint, const vector<set<int> >& exclusions, float maxDistance) const {
+
+        // Loop over neighboring voxels
+        // TODO use more clever selection of neighboring voxels
+
+        const int atomI = referencePoint.second;
+        const float* locationI = referencePoint.first;
+        __m128 posI = _mm_loadu_ps(locationI);
+        __m128 boxSize = _mm_set_ps(0, periodicBoxSize[2], periodicBoxSize[1], periodicBoxSize[0]);
+        __m128 invBoxSize = _mm_set_ps(0, (1/periodicBoxSize[2]), (1/periodicBoxSize[1]), (1/periodicBoxSize[0]));
+        __m128 half = _mm_set1_ps(0.5);
+        
+        float maxDistanceSquared = maxDistance * maxDistance;
+
+        int dIndexX = int(maxDistance / voxelSizeX) + 1; // How may voxels away do we have to look?
+        int dIndexY = int(maxDistance / voxelSizeY) + 1;
+        int dIndexZ = int(maxDistance / voxelSizeZ) + 1;
+        VoxelIndex centerVoxelIndex = getVoxelIndex(locationI);
+        int lastx = centerVoxelIndex.x+dIndexX;
+        int lasty = centerVoxelIndex.y+dIndexY;
+        int lastz = centerVoxelIndex.z+dIndexZ;
+        if (usePeriodic) {
+            lastx = min(lastx, centerVoxelIndex.x-dIndexX+nx-1);
+            lasty = min(lasty, centerVoxelIndex.y-dIndexY+ny-1);
+            lastz = min(lastz, centerVoxelIndex.z-dIndexZ+nz-1);
+        }
+        VoxelIndex voxelIndex(0, 0, 0);
+        for (int x = centerVoxelIndex.x - dIndexX; x <= lastx; ++x) {
+            voxelIndex.x = x;
+            if (usePeriodic)
+                voxelIndex.x = (x < 0 ? x+nx : (x >= nx ? x-nx : x));
+            for (int y = centerVoxelIndex.y - dIndexY; y <= lasty; ++y) {
+                voxelIndex.y = y;
+                if (usePeriodic)
+                    voxelIndex.y = (y < 0 ? y+ny : (y >= ny ? y-ny : y));
+                for (int z = centerVoxelIndex.z - dIndexZ; z <= lastz; ++z) {
+                    voxelIndex.z = z;
+                    if (usePeriodic)
+                        voxelIndex.z = (z < 0 ? z+nz : (z >= nz ? z-nz : z));
+                    const map<VoxelIndex, Voxel>::const_iterator voxelEntry = voxelMap.find(voxelIndex);
+                    if (voxelEntry == voxelMap.end())
+                        continue; // no such voxel; skip
+                    const Voxel& voxel = voxelEntry->second;
+                    for (Voxel::const_iterator itemIter = voxel.begin(); itemIter != voxel.end(); ++itemIter) {
+                        const int atomJ = itemIter->second;
+
+                        // Avoid duplicate entries.
+                        if (atomJ >= atomI)
+                            break;
+                        
+                        __m128 posJ = _mm_loadu_ps(itemIter->first);
+                        __m128 delta = _mm_sub_ps(posJ, posI);
+                        if (usePeriodic) {
+                            __m128 base = _mm_mul_ps(_mm_floor_ps(_mm_add_ps(_mm_mul_ps(delta, invBoxSize), half)), boxSize);
+                            delta = _mm_sub_ps(delta, base);
+                        }
+                        float dSquared = _mm_cvtss_f32(_mm_dp_ps(delta, delta, 0x71));
+                        if (dSquared > maxDistanceSquared)
+                            continue;
+                        
+                        // Ignore exclusions.
+                        if (exclusions[atomI].find(atomJ) != exclusions[atomI].end())
+                            continue;
+
+                        neighbors.push_back(make_pair(atomI, atomJ));
+                    }
+                }
+            }
+        }
+    }
+
+private:
+    float voxelSizeX, voxelSizeY, voxelSizeZ;
+    int nx, ny, nz;
+    const float* periodicBoxSize;
+    const bool usePeriodic;
+    map<VoxelIndex, Voxel> voxelMap;
+};
+
+class CpuNeighborList::ThreadData {
+public:
+    ThreadData(int index, CpuNeighborList& owner) : index(index), owner(owner) {
+    }
+    int index;
+    CpuNeighborList& owner;
+    vector<pair<int, int> > threadNeighbors;
+};
+
+static void* threadBody(void* args) {
+    CpuNeighborList::ThreadData& data = *reinterpret_cast<CpuNeighborList::ThreadData*>(args);
+    data.owner.runThread(data.index, data.threadNeighbors);
+    delete &data;
+    return 0;
+}
+
+CpuNeighborList::CpuNeighborList() {
+    isDeleted = false;
+    numThreads = getNumProcessors();
+    pthread_cond_init(&startCondition, NULL);
+    pthread_cond_init(&endCondition, NULL);
+    pthread_mutex_init(&lock, NULL);
+    thread.resize(numThreads);
+    pthread_mutex_lock(&lock);
+    waitCount = 0;
+    for (int i = 0; i < numThreads; i++) {
+        ThreadData* data = new ThreadData(i, *this);
+        threadData.push_back(data);
+        pthread_create(&thread[i], NULL, threadBody, data);
+    }
+    while (waitCount < numThreads)
+        pthread_cond_wait(&endCondition, &lock);
+    pthread_mutex_unlock(&lock);
+}
+
+CpuNeighborList::~CpuNeighborList() {
+    isDeleted = true;
+    pthread_mutex_lock(&lock);
+    pthread_cond_broadcast(&startCondition);
+    pthread_mutex_unlock(&lock);
+    for (int i = 0; i < (int) thread.size(); i++)
+        pthread_join(thread[i], NULL);
+    pthread_mutex_destroy(&lock);
+    pthread_cond_destroy(&startCondition);
+    pthread_cond_destroy(&endCondition);
+}
+
+void CpuNeighborList::computeNeighborList(int numAtoms, const vector<float>& atomLocations, const vector<set<int> >& exclusions,
+            const float* periodicBoxSize, bool usePeriodic, float maxDistance) {
+    // Build the voxel hash.
+    
+    float edgeSizeX, edgeSizeY, edgeSizeZ;
+    if (!usePeriodic)
+        edgeSizeX = edgeSizeY = edgeSizeZ = maxDistance; // TODO - adjust this as needed
+    else {
+        edgeSizeX = 0.5f*periodicBoxSize[0]/floorf(periodicBoxSize[0]/maxDistance);
+        edgeSizeY = 0.5f*periodicBoxSize[1]/floorf(periodicBoxSize[1]/maxDistance);
+        edgeSizeZ = 0.5f*periodicBoxSize[2]/floorf(periodicBoxSize[2]/maxDistance);
+    }
+    VoxelHash voxelHash(edgeSizeX, edgeSizeY, edgeSizeZ, periodicBoxSize, usePeriodic);
+    for (int i = 0; i < numAtoms; i++)
+        voxelHash.insert(i, &atomLocations[4*i]);
+    
+    // Record the parameters for the threads.
+    
+    this->voxelHash = &voxelHash;
+    this->exclusions = &exclusions;
+    this->atomLocations = &atomLocations[0];
+    this->periodicBoxSize = periodicBoxSize;
+    this->numAtoms = numAtoms;
+    this->usePeriodic = usePeriodic;
+    this->maxDistance = maxDistance;
+    
+    // Signal the threads to start running and wait for them to finish.
+    
+    pthread_mutex_lock(&lock);
+    waitCount = 0;
+    pthread_cond_broadcast(&startCondition);
+    while (waitCount < numThreads)
+        pthread_cond_wait(&endCondition, &lock);
+    pthread_mutex_unlock(&lock);
+    
+    // Combine the results from all the threads.
+    
+    neighbors.clear();
+    for (int i = 0; i < numThreads; i++)
+        neighbors.insert(neighbors.end(), threadData[i]->threadNeighbors.begin(), threadData[i]->threadNeighbors.end());
+}
+
+const vector<pair<int, int> >& CpuNeighborList::getNeighbors() {
+    return neighbors;
+}
+
+void CpuNeighborList::runThread(int index, vector<pair<int, int> >& threadNeighbors) {
+    while (true) {
+        // Wait for the signal to start running.
+        
+        pthread_mutex_lock(&lock);
+        waitCount++;
+        pthread_cond_signal(&endCondition);
+        pthread_cond_wait(&startCondition, &lock);
+        pthread_mutex_unlock(&lock);
+        if (isDeleted)
+            break;
+        
+        // Compute this thread's subset of neighbors.
+        
+        threadNeighbors.clear();
+        for (int i = index; i < numAtoms; i += numThreads)
+            voxelHash->getNeighbors(threadNeighbors, VoxelItem(&atomLocations[4*i], i), *exclusions, maxDistance);
+    }
+}
+
+} // namespace OpenMM

platforms/cpu/src/CpuNonbondedForce.cpp

+
+/* Portions copyright (c) 2006-2013 Stanford University and Simbios.
+ * Contributors: Pande Group
+ *
+ * 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.
+ */
+
+#include <string.h>
+#include <complex>
+
+#include "SimTKOpenMMCommon.h"
+#include "SimTKOpenMMUtilities.h"
+#include "CpuNonbondedForce.h"
+#include "ReferenceForce.h"
+#include "ReferencePME.h"
+#include "openmm/internal/hardware.h"
+#include "openmm/internal/SplineFitter.h"
+
+// In case we're using some primitive version of Visual Studio this will
+// make sure that erf() and erfc() are defined.
+#include "openmm/internal/MSVC_erfc.h"
+
+using namespace std;
+using namespace OpenMM;
+
+const float CpuNonbondedForce::TWO_OVER_SQRT_PI = (float) (2/sqrt(PI_M));
+const int CpuNonbondedForce::NUM_TABLE_POINTS = 1025;
+
+class CpuNonbondedForce::ThreadData {
+public:
+    ThreadData(int index, CpuNonbondedForce& owner) : index(index), owner(owner) {
+    }
+    int index;
+    CpuNonbondedForce& owner;
+    vector<float> threadForce;
+    double threadEnergy;
+};
+
+static void* threadBody(void* args) {
+    CpuNonbondedForce::ThreadData& data = *reinterpret_cast<CpuNonbondedForce::ThreadData*>(args);
+    data.owner.runThread(data.index, data.threadForce, data.threadEnergy);
+    delete &data;
+    return 0;
+}
+
+/**---------------------------------------------------------------------------------------
+
+   CpuNonbondedForce constructor
+
+   --------------------------------------------------------------------------------------- */
+
+CpuNonbondedForce::CpuNonbondedForce() : cutoff(false), useSwitch(false), periodic(false), ewald(false), pme(false) {
+    isDeleted = false;
+    numThreads = getNumProcessors();
+    pthread_cond_init(&startCondition, NULL);
+    pthread_cond_init(&endCondition, NULL);
+    pthread_mutex_init(&lock, NULL);
+    thread.resize(numThreads);
+    pthread_mutex_lock(&lock);
+    waitCount = 0;
+    for (int i = 0; i < numThreads; i++) {
+        ThreadData* data = new ThreadData(i, *this);
+        threadData.push_back(data);
+        pthread_create(&thread[i], NULL, threadBody, data);
+    }
+    while (waitCount < numThreads)
+        pthread_cond_wait(&endCondition, &lock);
+    pthread_mutex_unlock(&lock);
+}
+
+/**---------------------------------------------------------------------------------------
+
+   CpuNonbondedForce destructor
+
+   --------------------------------------------------------------------------------------- */
+
+CpuNonbondedForce::~CpuNonbondedForce(){
+    isDeleted = true;
+    pthread_mutex_lock(&lock);
+    pthread_cond_broadcast(&startCondition);
+    pthread_mutex_unlock(&lock);
+    for (int i = 0; i < (int) thread.size(); i++)
+        pthread_join(thread[i], NULL);
+    pthread_mutex_destroy(&lock);
+    pthread_cond_destroy(&startCondition);
+    pthread_cond_destroy(&endCondition);
+}
+
+  /**---------------------------------------------------------------------------------------
+
+     Set the force to use a cutoff.
+
+     @param distance            the cutoff distance
+     @param neighbors           the neighbor list to use
+     @param solventDielectric   the dielectric constant of the bulk solvent
+
+     --------------------------------------------------------------------------------------- */
+
+  void CpuNonbondedForce::setUseCutoff(float distance, const vector<pair<int, int> >& neighbors, float solventDielectric) {
+
+    cutoff = true;
+    cutoffDistance = distance;
+    neighborList = &neighbors;
+    krf = pow(cutoffDistance, -3.0f)*(solventDielectric-1.0)/(2.0*solventDielectric+1.0);
+    crf = (1.0/cutoffDistance)*(3.0*solventDielectric)/(2.0*solventDielectric+1.0);
+  }
+
+/**---------------------------------------------------------------------------------------
+
+   Set the force to use a switching function on the Lennard-Jones interaction.
+
+   @param distance            the switching distance
+
+   --------------------------------------------------------------------------------------- */
+
+void CpuNonbondedForce::setUseSwitchingFunction(float distance) {
+    useSwitch = true;
+    switchingDistance = distance;
+}
+
+  /**---------------------------------------------------------------------------------------
+
+     Set the force to use periodic boundary conditions.  This requires that a cutoff has
+     also been set, and the smallest side of the periodic box is at least twice the cutoff
+     distance.
+
+     @param boxSize             the X, Y, and Z widths of the periodic box
+
+     --------------------------------------------------------------------------------------- */
+
+  void CpuNonbondedForce::setPeriodic(float* periodicBoxSize) {
+
+    assert(cutoff);
+    assert(periodicBoxSize[0] >= 2*cutoffDistance);
+    assert(periodicBoxSize[1] >= 2*cutoffDistance);
+    assert(periodicBoxSize[2] >= 2*cutoffDistance);
+    periodic = true;
+    this->periodicBoxSize[0] = periodicBoxSize[0];
+    this->periodicBoxSize[1] = periodicBoxSize[1];
+    this->periodicBoxSize[2] = periodicBoxSize[2];
+    boxSize = _mm_set_ps(0, periodicBoxSize[2], periodicBoxSize[1], periodicBoxSize[0]);
+    invBoxSize = _mm_set_ps(0, (1/periodicBoxSize[2]), (1/periodicBoxSize[1]), (1/periodicBoxSize[0]));
+    half = _mm_set1_ps(0.5);
+  }
+
+  /**---------------------------------------------------------------------------------------
+
+     Set the force to use Ewald summation.
+
+     @param alpha  the Ewald separation parameter
+     @param kmaxx  the largest wave vector in the x direction
+     @param kmaxy  the largest wave vector in the y direction
+     @param kmaxz  the largest wave vector in the z direction
+
+     --------------------------------------------------------------------------------------- */
+
+  void CpuNonbondedForce::setUseEwald(float alpha, int kmaxx, int kmaxy, int kmaxz) {
+      alphaEwald = alpha;
+      numRx = kmaxx;
+      numRy = kmaxy;
+      numRz = kmaxz;
+      ewald = true;
+      tabulateEwaldScaleFactor();
+  }
+
+  /**---------------------------------------------------------------------------------------
+
+     Set the force to use Particle-Mesh Ewald (PME) summation.
+
+     @param alpha  the Ewald separation parameter
+     @param gridSize the dimensions of the mesh
+
+     --------------------------------------------------------------------------------------- */
+
+  void CpuNonbondedForce::setUsePME(float alpha, int meshSize[3]) {
+      alphaEwald = alpha;
+      meshDim[0] = meshSize[0];
+      meshDim[1] = meshSize[1];
+      meshDim[2] = meshSize[2];
+      pme = true;
+      tabulateEwaldScaleFactor();
+  }
+
+  
+void CpuNonbondedForce::tabulateEwaldScaleFactor() {
+    ewaldDX = cutoffDistance/(NUM_TABLE_POINTS-2);
+    ewaldDXInv = 1.0f/ewaldDX;
+    vector<double> x(NUM_TABLE_POINTS);
+    vector<double> y(NUM_TABLE_POINTS);
+    vector<double> deriv;
+    for (int i = 0; i < NUM_TABLE_POINTS; i++) {
+        double r = i*cutoffDistance/(NUM_TABLE_POINTS-2);
+        double alphaR = alphaEwald*r;
+        x[i] = r;
+        y[i] = erfc(alphaR) + TWO_OVER_SQRT_PI*alphaR*exp(-alphaR*alphaR);
+    }
+    SplineFitter::createNaturalSpline(x, y, deriv);
+    ewaldScaleX.resize(NUM_TABLE_POINTS);
+    ewaldScaleY.resize(NUM_TABLE_POINTS);
+    ewaldScaleDeriv.resize(NUM_TABLE_POINTS);
+    for (int i = 0; i < NUM_TABLE_POINTS; i++) {
+        ewaldScaleX[i] = (float) x[i];
+        ewaldScaleY[i] = (float) y[i];
+        ewaldScaleDeriv[i] = (float) (deriv[i]*ewaldDX*ewaldDX/6);
+    }
+}
+  
+void CpuNonbondedForce::calculateReciprocalIxn(int numberOfAtoms, float* posq, vector<RealVec>& atomCoordinates,
+                                             const vector<pair<float, float> >& atomParameters, const vector<set<int> >& exclusions,
+                                             vector<RealVec>& forces, float* totalEnergy) const {
+    typedef std::complex<float> d_complex;
+
+    static const float epsilon     =  1.0;
+
+    int kmax                            = (ewald ? std::max(numRx, std::max(numRy,numRz)) : 0);
+    float factorEwald              = -1 / (4*alphaEwald*alphaEwald);
+    float TWO_PI                   = 2.0 * PI_M;
+    float recipCoeff               = (float)(ONE_4PI_EPS0*4*PI_M/(periodicBoxSize[0] * periodicBoxSize[1] * periodicBoxSize[2]) /epsilon);
+
+    if (pme) {
+        pme_t pmedata;
+        RealOpenMM virial[3][3];
+        pme_init(&pmedata, alphaEwald, numberOfAtoms, meshDim, 5, 1);
+        vector<RealOpenMM> charges(numberOfAtoms);
+        for (int i = 0; i < numberOfAtoms; i++)
+            charges[i] = posq[4*i+3];
+        RealOpenMM boxSize[3] = {periodicBoxSize[0], periodicBoxSize[1], periodicBoxSize[2]};
+        RealOpenMM recipEnergy = 0.0;
+        pme_exec(pmedata, atomCoordinates, forces, charges, boxSize, &recipEnergy, virial);
+        if (totalEnergy)
+            *totalEnergy += recipEnergy;
+        pme_destroy(pmedata);
+    }
+
+    // Ewald method
+
+    else if (ewald) {
+
+        // setup reciprocal box
+
+        float recipBoxSize[3] = { TWO_PI / periodicBoxSize[0], TWO_PI / periodicBoxSize[1], TWO_PI / periodicBoxSize[2]};
+
+
+        // setup K-vectors
+
+        #define EIR(x, y, z) eir[(x)*numberOfAtoms*3+(y)*3+z]
+        vector<d_complex> eir(kmax*numberOfAtoms*3);
+        vector<d_complex> tab_xy(numberOfAtoms);
+        vector<d_complex> tab_qxyz(numberOfAtoms);
+
+        for (int i = 0; (i < numberOfAtoms); i++) {
+            float* pos = posq+4*i;
+            for (int m = 0; (m < 3); m++)
+              EIR(0, i, m) = d_complex(1,0);
+
+            for (int m=0; (m<3); m++)
+              EIR(1, i, m) = d_complex(cos(pos[m]*recipBoxSize[m]),
+                                       sin(pos[m]*recipBoxSize[m]));
+
+            for (int j=2; (j<kmax); j++)
+              for (int m=0; (m<3); m++)
+                EIR(j, i, m) = EIR(j-1, i, m) * EIR(1, i, m);
+        }
+
+        // calculate reciprocal space energy and forces
+
+        int lowry = 0;
+        int lowrz = 1;
+
+        for (int rx = 0; rx < numRx; rx++) {
+            float kx = rx * recipBoxSize[0];
+            for (int ry = lowry; ry < numRy; ry++) {
+                float ky = ry * recipBoxSize[1];
+                if (ry >= 0) {
+                    for (int n = 0; n < numberOfAtoms; n++)
+                      tab_xy[n] = EIR(rx, n, 0) * EIR(ry, n, 1);
+                }
+                else {
+                    for (int n = 0; n < numberOfAtoms; n++)
+                      tab_xy[n]= EIR(rx, n, 0) * conj (EIR(-ry, n, 1));
+                }
+                for (int rz = lowrz; rz < numRz; rz++) {
+                    if (rz >= 0) {
+                        for (int n = 0; n < numberOfAtoms; n++)
+                            tab_qxyz[n] = posq[4*n+3] * (tab_xy[n] * EIR(rz, n, 2));
+                    }
+                    else {
+                        for (int n = 0; n < numberOfAtoms; n++)
+                            tab_qxyz[n] = posq[4*n+3] * (tab_xy[n] * conj(EIR(-rz, n, 2)));
+                    }
+                    float cs = 0.0f;
+                    float ss = 0.0f;
+
+                    for (int n = 0; n < numberOfAtoms; n++) {
+                        cs += tab_qxyz[n].real();
+                        ss += tab_qxyz[n].imag();
+                    }
+
+                    float kz = rz * recipBoxSize[2];
+                    float k2 = kx * kx + ky * ky + kz * kz;
+                    float ak = exp(k2*factorEwald) / k2;
+
+                    for (int n = 0; n < numberOfAtoms; n++) {
+                        float force = ak * (cs * tab_qxyz[n].imag() - ss * tab_qxyz[n].real());
+                        forces[n][0] += 2 * recipCoeff * force * kx;
+                        forces[n][1] += 2 * recipCoeff * force * ky;
+                        forces[n][2] += 2 * recipCoeff * force * kz;
+                    }
+
+                    if (totalEnergy)
+                        *totalEnergy += recipCoeff * ak * (cs * cs + ss * ss);
+
+                    lowrz = 1 - numRz;
+                }
+                lowry = 1 - numRy;
+            }
+        }
+    }
+}
+
+
+void CpuNonbondedForce::calculateDirectIxn(int numberOfAtoms, float* posq, const vector<pair<float, float> >& atomParameters,
+                const vector<set<int> >& exclusions, float* forces, float* totalEnergy) {
+    // Record the parameters for the threads.
+    
+    this->numberOfAtoms = numberOfAtoms;
+    this->posq = posq;
+    this->atomParameters = &atomParameters[0];
+    this->exclusions = &exclusions[0];
+    includeEnergy = (totalEnergy != NULL);
+    
+    // Signal the threads to start running and wait for them to finish.
+    
+    pthread_mutex_lock(&lock);
+    waitCount = 0;
+    pthread_cond_broadcast(&startCondition);
+    while (waitCount < numThreads)
+        pthread_cond_wait(&endCondition, &lock);
+    pthread_mutex_unlock(&lock);
+    
+    // Combine the results from all the threads.
+    
+    double directEnergy = 0;
+    for (int i = 0; i < numThreads; i++)
+        directEnergy += threadData[i]->threadEnergy;
+    for (int i = 0; i < numberOfAtoms; i++) {
+        __m128 f = _mm_loadu_ps(forces+4*i);
+        for (int j = 0; j < numThreads; j++)
+            f = _mm_add_ps(f, _mm_loadu_ps(&threadData[j]->threadForce[4*i]));
+        _mm_storeu_ps(forces+4*i, f);
+    }
+
+    if (ewald || pme) {
+        // Now subtract off the exclusions, since they were implicitly included in the reciprocal space sum.
+
+        for (int i = 0; i < numberOfAtoms; i++)
+            for (set<int>::const_iterator iter = exclusions[i].begin(); iter != exclusions[i].end(); ++iter) {
+                if (*iter > i) {
+                    int ii = i;
+                    int jj = *iter;
+                    __m128 deltaR;
+                    __m128 posI = _mm_loadu_ps(posq+4*ii);
+                    __m128 posJ = _mm_loadu_ps(posq+4*jj);
+                    float r2;
+                    getDeltaR(posJ, posI, deltaR, r2, false);
+                    float r         = sqrtf(r2);
+                    float inverseR  = 1/r;
+                    float chargeProd = ONE_4PI_EPS0*posq[4*ii+3]*posq[4*jj+3];
+                    float dEdR      = (float) (chargeProd * inverseR * inverseR * inverseR);
+                          dEdR      = (float) (dEdR * (1.0f-ewaldScaleFunction(r)));
+                    __m128 result = _mm_mul_ps(deltaR, _mm_set1_ps(dEdR));
+                    _mm_storeu_ps(forces+4*ii, _mm_sub_ps(_mm_loadu_ps(forces+4*ii), result));
+                    _mm_storeu_ps(forces+4*jj, _mm_add_ps(_mm_loadu_ps(forces+4*jj), result));
+                    if (includeEnergy)
+                        directEnergy -= chargeProd*inverseR*(1.0f-erfcApprox(alphaEwald*r));
+                }
+            }
+    }
+    if (totalEnergy != NULL)
+        *totalEnergy += (float) directEnergy;
+}
+
+
+void CpuNonbondedForce::runThread(int index, vector<float>& threadForce, double& threadEnergy) {
+    while (true) {
+        // Wait for the signal to start running.
+        
+        pthread_mutex_lock(&lock);
+        waitCount++;
+        pthread_cond_signal(&endCondition);
+        pthread_cond_wait(&startCondition, &lock);
+        pthread_mutex_unlock(&lock);
+        if (isDeleted)
+            break;
+        
+        // Compute this thread's subset of interactions.
+        
+        threadEnergy = 0;
+        double* energyPtr = (includeEnergy ? &threadEnergy : NULL);
+        threadForce.resize(4*numberOfAtoms, 0.0f);
+        for (int i = 0; i < 4*numberOfAtoms; i++)
+            threadForce[i] = 0.0f;
+        if (ewald || pme) {
+            // Compute the interactions from the neighbor list.
+
+            for (int i = index; i < (int) neighborList->size(); i += numThreads) {
+                pair<int, int> pair = (*neighborList)[i];
+                calculateOneEwaldIxn(pair.first, pair.second, &threadForce[0], energyPtr);
+            }
+        }
+        else if (cutoff) {
+            // Compute the interactions from the neighbor list.
+
+            for (int i = index; i < (int) neighborList->size(); i += numThreads) {
+                pair<int, int> pair = (*neighborList)[i];
+                calculateOneIxn(pair.first, pair.second, &threadForce[0], energyPtr);
+            }
+        }
+        else {
+            // Loop over all atom pairs
+
+            for (int i = index; i < numberOfAtoms; i += numThreads){
+                for (int j = i+1; j < numberOfAtoms; j++)
+                    if (exclusions[j].find(i) == exclusions[j].end())
+                        calculateOneIxn(i, j, &threadForce[0], energyPtr);
+            }
+        }
+    }
+}
+
+void CpuNonbondedForce::calculateOneIxn(int ii, int jj, float* forces, double* totalEnergy) {
+    // get deltaR, R2, and R between 2 atoms
+
+    __m128 deltaR;
+    __m128 posI = _mm_loadu_ps(posq+4*ii);
+    __m128 posJ = _mm_loadu_ps(posq+4*jj);
+    float r2;
+    getDeltaR(posJ, posI, deltaR, r2, periodic);
+    if (cutoff && r2 >= cutoffDistance*cutoffDistance)
+        return;
+    float r = sqrtf(r2);
+    float inverseR = 1/r;
+    float switchValue = 1, switchDeriv = 0;
+    if (useSwitch && r > switchingDistance) {
+        float t = (r-switchingDistance)/(cutoffDistance-switchingDistance);
+        switchValue = 1+t*t*t*(-10+t*(15-t*6));
+        switchDeriv = t*t*(-30+t*(60-t*30))/(cutoffDistance-switchingDistance);
+    }
+    float sig       = atomParameters[ii].first + atomParameters[jj].first;
+    float sig2      = inverseR*sig;
+          sig2     *= sig2;
+    float sig6      = sig2*sig2*sig2;
+
+    float eps       = atomParameters[ii].second*atomParameters[jj].second;
+    float dEdR      = switchValue*eps*(12.0f*sig6 - 6.0f)*sig6;
+    float chargeProd = ONE_4PI_EPS0*posq[4*ii+3]*posq[4*jj+3];
+    if (cutoff)
+        dEdR += (float) (chargeProd*(inverseR-2.0f*krf*r2));
+    else
+        dEdR += (float) (chargeProd*inverseR);
+    dEdR *= inverseR*inverseR;
+    float energy = eps*(sig6-1.0f)*sig6;
+    if (useSwitch) {
+        dEdR -= energy*switchDeriv*inverseR;
+        energy *= switchValue;
+    }
+
+    // accumulate energies
+
+    if (totalEnergy) {
+        if (cutoff)
+            energy += (float) (chargeProd*(inverseR+krf*r2-crf));
+        else
+            energy += (float) (chargeProd*inverseR);
+        *totalEnergy += energy;
+    }
+
+    // accumulate forces
+
+    __m128 result = _mm_mul_ps(deltaR, _mm_set1_ps(dEdR));
+    _mm_storeu_ps(forces+4*ii, _mm_add_ps(_mm_loadu_ps(forces+4*ii), result));
+    _mm_storeu_ps(forces+4*jj, _mm_sub_ps(_mm_loadu_ps(forces+4*jj), result));
+  }
+
+void CpuNonbondedForce::calculateOneEwaldIxn(int ii, int jj, float* forces, double* totalEnergy) {
+    __m128 deltaR;
+    __m128 posI = _mm_loadu_ps(posq+4*ii);
+    __m128 posJ = _mm_loadu_ps(posq+4*jj);
+    float r2;
+    getDeltaR(posJ, posI, deltaR, r2, true);
+    if (r2 >= cutoffDistance*cutoffDistance)
+        return;
+    float r         = sqrtf(r2);
+    float inverseR  = 1/r;
+    float switchValue = 1, switchDeriv = 0;
+    if (useSwitch && r > switchingDistance) {
+        float t = (r-switchingDistance)/(cutoffDistance-switchingDistance);
+        switchValue = 1+t*t*t*(-10+t*(15-t*6));
+        switchDeriv = t*t*(-30+t*(60-t*30))/(cutoffDistance-switchingDistance);
+    }
+    float chargeProd = ONE_4PI_EPS0*posq[4*ii+3]*posq[4*jj+3];
+    float dEdR      = chargeProd*inverseR*ewaldScaleFunction(r);
+    float sig       = atomParameters[ii].first +  atomParameters[jj].first;
+    float sig2      = inverseR*sig;
+          sig2     *= sig2;
+    float sig6      = sig2*sig2*sig2;
+    float eps       = atomParameters[ii].second*atomParameters[jj].second;
+          dEdR     += switchValue*eps*(12.0f*sig6 - 6.0f)*sig6;
+    dEdR *= inverseR*inverseR;
+    float energy = eps*(sig6-1.0f)*sig6;
+    if (useSwitch) {
+        dEdR -= energy*switchDeriv*inverseR;
+        energy *= switchValue;
+    }
+
+    // accumulate forces
+
+    __m128 result = _mm_mul_ps(deltaR, _mm_set1_ps(dEdR));
+    _mm_storeu_ps(forces+4*ii, _mm_add_ps(_mm_loadu_ps(forces+4*ii), result));
+    _mm_storeu_ps(forces+4*jj, _mm_sub_ps(_mm_loadu_ps(forces+4*jj), result));
+
+    // accumulate energies
+
+    if (totalEnergy) {
+        energy += (float) (chargeProd*inverseR*erfcApprox(alphaEwald*r));
+        *totalEnergy += energy;
+    }
+}
+
+void CpuNonbondedForce::getDeltaR(const __m128& posI, const __m128& posJ, __m128& deltaR, float& r2, bool periodic) const {
+    deltaR = _mm_sub_ps(posJ, posI);
+    if (periodic) {
+        __m128 base = _mm_mul_ps(_mm_floor_ps(_mm_add_ps(_mm_mul_ps(deltaR, invBoxSize), half)), boxSize);
+        deltaR = _mm_sub_ps(deltaR, base);
+    }
+    r2 = _mm_cvtss_f32(_mm_dp_ps(deltaR, deltaR, 0x71));
+}
+
+float CpuNonbondedForce::erfcApprox(float x) {
+    // 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 3e-7.
+
+    float t = 1.0f+(0.0705230784f+(0.0422820123f+(0.0092705272f+(0.0001520143f+(0.0002765672f+0.0000430638f*x)*x)*x)*x)*x)*x;
+    t *= t;
+    t *= t;
+    t *= t;
+    return 1.0f/(t*t);
+}
+
+float CpuNonbondedForce::ewaldScaleFunction(float x) {
+    // Compute the tabulated Ewald scale factor: erfc(alpha*r) + 2*alpha*r*exp(-alpha*alpha*r*r)/sqrt(PI)
+
+    int lower = (int) (x*ewaldDXInv);
+    int upper = lower+1;
+    float a = (ewaldScaleX[upper]-x)*ewaldDXInv;
+    float b = 1.0f-a;
+    return a*ewaldScaleY[lower]+b*ewaldScaleY[upper]+((a*a*a-a)*ewaldScaleDeriv[lower] + (b*b*b-b)*ewaldScaleDeriv[upper]);
+}

platforms/cpu/src/CpuPlatform.cpp

+/* -------------------------------------------------------------------------- *
+ *                                   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) 2013 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.                                     *
+ * -------------------------------------------------------------------------- */
+
+#include "CpuPlatform.h"
+#include "CpuKernelFactory.h"
+#include "CpuKernels.h"
+#include "openmm/internal/hardware.h"
+
+using namespace OpenMM;
+
+extern "C" OPENMM_EXPORT_CPU void registerPlatforms() {
+    // Only register this platform if the CPU supports SSE 4.1.
+
+    int cpuInfo[4];
+    cpuid(cpuInfo, 0);
+    if (cpuInfo[0] >= 1) {
+        cpuid(cpuInfo, 1);
+        if ((cpuInfo[2] & ((int) 1 << 19)) != 0)
+            Platform::registerPlatform(new CpuPlatform());
+    }
+}
+
+CpuPlatform::CpuPlatform() {
+    CpuKernelFactory* factory = new CpuKernelFactory();
+    registerKernelFactory(CalcNonbondedForceKernel::Name(), factory);
+}
+
+double CpuPlatform::getSpeed() const {
+    return 10;
+}
+
+bool CpuPlatform::supportsDoublePrecision() const {
+    return false;
+}

platforms/cpu/tests/CMakeLists.txt

+#
+# Testing
+#
+
+ENABLE_TESTING()
+
+SET( INCLUDE_SERIALIZATION FALSE )
+#SET( INCLUDE_SERIALIZATION TRUE )
+
+IF( INCLUDE_SERIALIZATION )
+    INCLUDE_DIRECTORIES(${OPENMM_DIR}/serialization/include)
+    SET( SHARED_OPENMM_SERIALIZATION "OpenMMSerialization" )
+ENDIF( INCLUDE_SERIALIZATION )
+
+# Automatically create tests using files named "Test*.cpp"
+FILE(GLOB TEST_PROGS "*Test*.cpp")
+FOREACH(TEST_PROG ${TEST_PROGS})
+    GET_FILENAME_COMPONENT(TEST_ROOT ${TEST_PROG} NAME_WE)
+
+    # Link with shared library
+    ADD_EXECUTABLE(${TEST_ROOT} ${TEST_PROG})
+    TARGET_LINK_LIBRARIES(${TEST_ROOT} ${SHARED_TARGET})
+    ADD_TEST(${TEST_ROOT} ${EXECUTABLE_OUTPUT_PATH}/${TEST_ROOT} single)
+
+ENDFOREACH(TEST_PROG ${TEST_PROGS})

platforms/cpu/tests/TestCpuEwald.cpp

+/* -------------------------------------------------------------------------- *
+ *                                   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) 2008-2013 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 CPU implementation of NonbondedForce.
+ */
+
+#include "openmm/internal/AssertionUtilities.h"
+#include "openmm/Context.h"
+#include "CpuPlatform.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 "SimTKOpenMMRealType.h"
+#include "sfmt/SFMT.h"
+#include <iostream>
+#include <vector>
+
+using namespace OpenMM;
+using namespace std;
+
+CpuPlatform platform;
+
+const double TOL = 1e-5;
+
+void testEwaldPME(bool includeExceptions) {
+
+//      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;
+
+    ReferencePlatform reference;
+    System system;
+    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.setDefaultPeriodicBoxVectors(Vec3(boxSize, 0, 0), Vec3(0, boxSize, 0), Vec3(0, 0, boxSize));
+    system.addForce(nonbonded);
+
+    vector<Vec3> positions(numParticles);
+    #include "nacl_amorph.dat"
+    if (includeExceptions) {
+        // Add some exclusions.
+
+        for (int i = 0; i < numParticles-1; i++) {
+            Vec3 delta = positions[i]-positions[i+1];
+            if (sqrt(delta.dot(delta)) < 0.5*cutoff)
+                nonbonded->addException(i, i+1, i%2 == 0 ? 0.0 : 0.5, 1.0, 0.0);
+        }
+    }
+
+//    (1)  Check whether the Reference and CPU platforms agree when using Ewald Method
+
+    VerletIntegrator integrator1(0.01);
+    VerletIntegrator integrator2(0.01);
+    Context cpuContext(system, integrator1, platform);
+    Context referenceContext(system, integrator2, reference);
+    cpuContext.setPositions(positions);
+    referenceContext.setPositions(positions);
+    State cpuState = cpuContext.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], cpuState.getForces()[i], tol);
+    }
+    tol = 1e-5;
+    ASSERT_EQUAL_TOL(referenceState.getPotentialEnergy(), cpuState.getPotentialEnergy(), tol);
+
+//    (2) Check whether Ewald method in CPU is self-consistent
+
+    double norm = 0.0;
+    for (int i = 0; i < numParticles; ++i) {
+        Vec3 f = cpuState.getForces()[i];
+        norm += f[0]*f[0] + f[1]*f[1] + f[2]*f[2];
+    }
+
+    norm = std::sqrt(norm);
+    const double delta = 5e-3;
+    double step = delta/norm;
+    for (int i = 0; i < numParticles; ++i) {
+        Vec3 p = positions[i];
+        Vec3 f = cpuState.getForces()[i];
+        positions[i] = Vec3(p[0]-f[0]*step, p[1]-f[1]*step, p[2]-f[2]*step);
+    }
+    VerletIntegrator integrator3(0.01);
+    Context cpuContext2(system, integrator3, platform);
+    cpuContext2.setPositions(positions);
+
+    tol = 1e-2;
+    State cpuState2 = cpuContext2.getState(State::Energy);
+    ASSERT_EQUAL_TOL(norm, (cpuState2.getPotentialEnergy()-cpuState.getPotentialEnergy())/delta, tol)
+
+//    (3)  Check whether the Reference and CPU platforms agree when using PME
+
+    nonbonded->setNonbondedMethod(NonbondedForce::PME);
+    cpuContext.reinitialize();
+    referenceContext.reinitialize();
+    cpuContext.setPositions(positions);
+    referenceContext.setPositions(positions);
+    cpuState = cpuContext.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], cpuState.getForces()[i], tol);
+    }
+    tol = 1e-5;
+    ASSERT_EQUAL_TOL(referenceState.getPotentialEnergy(), cpuState.getPotentialEnergy(), tol);
+
+//    (4) Check whether PME method in CPU is self-consistent
+
+    norm = 0.0;
+    for (int i = 0; i < numParticles; ++i) {
+        Vec3 f = cpuState.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 = cpuState.getForces()[i];
+        positions[i] = Vec3(p[0]-f[0]*step, p[1]-f[1]*step, p[2]-f[2]*step);
+    }
+    VerletIntegrator integrator4(0.01);
+    Context cpuContext3(system, integrator4, platform);
+    cpuContext3.setPositions(positions);
+
+    tol = 1e-2;
+    State cpuState3 = cpuContext3.getState(State::Energy);
+    ASSERT_EQUAL_TOL(norm, (cpuState3.getPotentialEnergy()-cpuState.getPotentialEnergy())/delta, tol)
+}
+
+void testEwald2Ions() {
+    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.setDefaultPeriodicBoxVectors(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.setDefaultPeriodicBoxVectors(Vec3(boxWidth, 0, 0), Vec3(0, boxWidth, 0), Vec3(0, 0, boxWidth));
+    NonbondedForce* force = new NonbondedForce();
+    system.addForce(force);
+    vector<Vec3> positions(numParticles);
+    OpenMM_SFMT::SFMT sfmt;
+    init_gen_rand(0, sfmt);
+
+    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(sfmt), boxWidth*genrand_real2(sfmt), boxWidth*genrand_real2(sfmt));
+    }
+    force->setNonbondedMethod(method);
+
+    // 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 *= 1.2) {
+        force->setCutoffDistance(cutoff);
+        vector<Vec3> refForces;
+        double norm = 0.0;
+        for (double tol = 5e-5; tol < 1e-3; tol *= 2.0) {
+            force->setEwaldErrorTolerance(tol);
+            VerletIntegrator integrator(0.01);
+            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 < 2*tol);
+            }
+        }
+    }
+}
+
+int main(int argc, char* argv[]) {
+    try {
+        testEwaldPME(false);
+        testEwaldPME(true);
+//        testEwald2Ions();
+        testErrorTolerance(NonbondedForce::Ewald);
+        testErrorTolerance(NonbondedForce::PME);
+    }
+    catch(const exception& e) {
+        cout << "exception: " << e.what() << endl;
+        return 1;
+    }
+    cout << "Done" << endl;
+    return 0;
+}

platforms/cpu/tests/TestCpuNeighborList.cpp

+/* -------------------------------------------------------------------------- *
+ *                                   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) 2013 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 all the CPU implementation of neighbor list construction.
+ */
+
+#include "openmm/internal/AssertionUtilities.h"
+#include "CpuNeighborList.h"
+#include "sfmt/SFMT.h"
+#include <iostream>
+#include <set>
+#include <vector>
+
+using namespace OpenMM;
+using namespace std;
+
+void testNeighborList(bool periodic) {
+    const int numParticles = 500;
+    const float cutoff = 2.0f;
+    const float boxSize[3] = {20.0f, 15.0f, 22.0f};
+    OpenMM_SFMT::SFMT sfmt;
+    init_gen_rand(0, sfmt);
+    vector<float> positions(4*numParticles);
+    for (int i = 0; i < 4*numParticles; i++)
+        if (i%4 < 3)
+            positions[i] = boxSize[i%4]*genrand_real2(sfmt);
+    vector<set<int> > exclusions(numParticles);
+    for (int i = 0; i < numParticles; i++) {
+        int num = min(i+1, 10);
+        for (int j = 0; j < num; j++) {
+            exclusions[i].insert(i-j);
+            exclusions[i-j].insert(i);
+        }
+    }
+    CpuNeighborList neighborList;
+    neighborList.computeNeighborList(numParticles, positions, exclusions, boxSize, periodic, cutoff);
+    
+    // Convert the neighbor list to a set for faster lookup.
+    
+    set<pair<int, int> > neighbors;
+    for (int i = 0; i < (int) neighborList.getNeighbors().size(); i++) {
+        pair<int, int> entry = neighborList.getNeighbors()[i];
+        ASSERT(neighbors.find(entry) == neighbors.end() && neighbors.find(make_pair(entry.second, entry.first)) == neighbors.end()); // No duplicates
+        neighbors.insert(entry);
+    }
+    
+    // Check each particle pair and figure out whether they should be in the neighbor list.
+    
+    for (int i = 0; i < numParticles; i++)
+        for (int j = 0; j <= i; j++) {
+            bool shouldInclude = (exclusions[i].find(j) == exclusions[i].end());
+            float dx = positions[4*i]-positions[4*j];
+            float dy = positions[4*i+1]-positions[4*j+1];
+            float dz = positions[4*i+2]-positions[4*j+2];
+            if (periodic) {
+                dx -= floor(dx/boxSize[0]+0.5f)*boxSize[0];
+                dy -= floor(dy/boxSize[1]+0.5f)*boxSize[1];
+                dz -= floor(dz/boxSize[2]+0.5f)*boxSize[2];
+            }
+            if (dx*dx + dy*dy + dz*dz > cutoff*cutoff)
+                shouldInclude = false;
+            bool isIncluded = (neighbors.find(make_pair(i, j)) != neighbors.end() || neighbors.find(make_pair(j, i)) != neighbors.end());
+            ASSERT_EQUAL(shouldInclude, isIncluded);
+        }
+}
+
+int main() {
+    try {
+        testNeighborList(false);
+        testNeighborList(true);
+    }
+    catch(const exception& e) {
+        cout << "exception: " << e.what() << endl;
+        return 1;
+    }
+    cout << "Done" << endl;
+    return 0;
+}

platforms/cpu/tests/TestCpuNonbondedForce.cpp

+/* -------------------------------------------------------------------------- *
+ *                                   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) 2008-2013 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 all the different force terms in the CUDA implementation of NonbondedForce.
+ */
+
+#include "openmm/internal/AssertionUtilities.h"
+#include "openmm/Context.h"
+#include "CpuPlatform.h"
+#include "ReferencePlatform.h"
+#include "openmm/HarmonicBondForce.h"
+#include "openmm/NonbondedForce.h"
+#include "openmm/System.h"
+#include "openmm/LangevinIntegrator.h"
+#include "openmm/VerletIntegrator.h"
+#include "openmm/internal/ContextImpl.h"
+#include "SimTKOpenMMRealType.h"
+#include "sfmt/SFMT.h"
+#include <iostream>
+#include <vector>
+
+using namespace OpenMM;
+using namespace std;
+
+CpuPlatform platform;
+
+const double TOL = 1e-5;
+
+void testCoulomb() {
+    System system;
+    system.addParticle(1.0);
+    system.addParticle(1.0);
+    VerletIntegrator integrator(0.01);
+    NonbondedForce* forceField = new NonbondedForce();
+    forceField->addParticle(0.5, 1, 0);
+    forceField->addParticle(-1.5, 1, 0);
+    system.addForce(forceField);
+    Context context(system, integrator, platform);
+    vector<Vec3> positions(2);
+    positions[0] = Vec3(0, 0, 0);
+    positions[1] = Vec3(2, 0, 0);
+    context.setPositions(positions);
+    State state = context.getState(State::Forces | State::Energy);
+    const vector<Vec3>& forces = state.getForces();
+    double force = ONE_4PI_EPS0*(-0.75)/4.0;
+    ASSERT_EQUAL_VEC(Vec3(-force, 0, 0), forces[0], TOL);
+    ASSERT_EQUAL_VEC(Vec3(force, 0, 0), forces[1], TOL);
+    ASSERT_EQUAL_TOL(ONE_4PI_EPS0*(-0.75)/2.0, state.getPotentialEnergy(), TOL);
+}
+
+void testLJ() {
+    System system;
+    system.addParticle(1.0);
+    system.addParticle(1.0);
+    VerletIntegrator integrator(0.01);
+    NonbondedForce* forceField = new NonbondedForce();
+    forceField->addParticle(0, 1.2, 1);
+    forceField->addParticle(0, 1.4, 2);
+    system.addForce(forceField);
+    Context context(system, integrator, platform);
+    vector<Vec3> positions(2);
+    positions[0] = Vec3(0, 0, 0);
+    positions[1] = Vec3(2, 0, 0);
+    context.setPositions(positions);
+    State state = context.getState(State::Forces | State::Energy);
+    const vector<Vec3>& forces = state.getForces();
+    double x = 1.3/2.0;
+    double eps = SQRT_TWO;
+    double force = 4.0*eps*(12*std::pow(x, 12.0)-6*std::pow(x, 6.0))/2.0;
+    ASSERT_EQUAL_VEC(Vec3(-force, 0, 0), forces[0], TOL);
+    ASSERT_EQUAL_VEC(Vec3(force, 0, 0), forces[1], TOL);
+    ASSERT_EQUAL_TOL(4.0*eps*(std::pow(x, 12.0)-std::pow(x, 6.0)), state.getPotentialEnergy(), TOL);
+}
+
+void testExclusionsAnd14() {
+    System system;
+    NonbondedForce* nonbonded = new NonbondedForce();
+    for (int i = 0; i < 5; ++i) {
+        system.addParticle(1.0);
+        nonbonded->addParticle(0, 1.5, 0);
+    }
+    vector<pair<int, int> > bonds;
+    bonds.push_back(pair<int, int>(0, 1));
+    bonds.push_back(pair<int, int>(1, 2));
+    bonds.push_back(pair<int, int>(2, 3));
+    bonds.push_back(pair<int, int>(3, 4));
+    nonbonded->createExceptionsFromBonds(bonds, 0.0, 0.0);
+    int first14, second14;
+    for (int i = 0; i < nonbonded->getNumExceptions(); i++) {
+        int particle1, particle2;
+        double chargeProd, sigma, epsilon;
+        nonbonded->getExceptionParameters(i, particle1, particle2, chargeProd, sigma, epsilon);
+        if ((particle1 == 0 && particle2 == 3) || (particle1 == 3 && particle2 == 0))
+            first14 = i;
+        if ((particle1 == 1 && particle2 == 4) || (particle1 == 4 && particle2 == 1))
+            second14 = i;
+    }
+    system.addForce(nonbonded);
+    VerletIntegrator integrator(0.01);
+    Context context(system, integrator, platform);
+    for (int i = 1; i < 5; ++i) {
+
+        // Test LJ forces
+
+        vector<Vec3> positions(5);
+        const double r = 1.0;
+        for (int j = 0; j < 5; ++j) {
+            nonbonded->setParticleParameters(j, 0, 1.5, 0);
+            positions[j] = Vec3(0, j, 0);
+        }
+        nonbonded->setParticleParameters(0, 0, 1.5, 1);
+        nonbonded->setParticleParameters(i, 0, 1.5, 1);
+        nonbonded->setExceptionParameters(first14, 0, 3, 0, 1.5, i == 3 ? 0.5 : 0.0);
+        nonbonded->setExceptionParameters(second14, 1, 4, 0, 1.5, 0.0);
+        positions[i] = Vec3(r, 0, 0);
+        context.reinitialize();
+        context.setPositions(positions);
+        State state = context.getState(State::Forces | State::Energy);
+        const vector<Vec3>& forces = state.getForces();
+        double x = 1.5/r;
+        double eps = 1.0;
+        double force = 4.0*eps*(12*std::pow(x, 12.0)-6*std::pow(x, 6.0))/r;
+        double energy = 4.0*eps*(std::pow(x, 12.0)-std::pow(x, 6.0));
+        if (i == 3) {
+            force *= 0.5;
+            energy *= 0.5;
+        }
+        if (i < 3) {
+            force = 0;
+            energy = 0;
+        }
+        ASSERT_EQUAL_VEC(Vec3(-force, 0, 0), forces[0], TOL);
+        ASSERT_EQUAL_VEC(Vec3(force, 0, 0), forces[i], TOL);
+        ASSERT_EQUAL_TOL(energy, state.getPotentialEnergy(), TOL);
+
+        // Test Coulomb forces
+
+        nonbonded->setParticleParameters(0, 2, 1.5, 0);
+        nonbonded->setParticleParameters(i, 2, 1.5, 0);
+        nonbonded->setExceptionParameters(first14, 0, 3, i == 3 ? 4/1.2 : 0, 1.5, 0);
+        nonbonded->setExceptionParameters(second14, 1, 4, 0, 1.5, 0);
+        context.reinitialize();
+        context.setPositions(positions);
+        state = context.getState(State::Forces | State::Energy);
+        const vector<Vec3>& forces2 = state.getForces();
+        force = ONE_4PI_EPS0*4/(r*r);
+        energy = ONE_4PI_EPS0*4/r;
+        if (i == 3) {
+            force /= 1.2;
+            energy /= 1.2;
+        }
+        if (i < 3) {
+            force = 0;
+            energy = 0;
+        }
+        ASSERT_EQUAL_VEC(Vec3(-force, 0, 0), forces2[0], TOL);
+        ASSERT_EQUAL_VEC(Vec3(force, 0, 0), forces2[i], TOL);
+        ASSERT_EQUAL_TOL(energy, state.getPotentialEnergy(), TOL);
+    }
+}
+
+void testCutoff() {
+    System system;
+    system.addParticle(1.0);
+    system.addParticle(1.0);
+    system.addParticle(1.0);
+    VerletIntegrator integrator(0.01);
+    NonbondedForce* forceField = new NonbondedForce();
+    forceField->addParticle(1.0, 1, 0);
+    forceField->addParticle(1.0, 1, 0);
+    forceField->addParticle(1.0, 1, 0);
+    forceField->setNonbondedMethod(NonbondedForce::CutoffNonPeriodic);
+    const double cutoff = 2.9;
+    forceField->setCutoffDistance(cutoff);
+    const double eps = 50.0;
+    forceField->setReactionFieldDielectric(eps);
+    system.addForce(forceField);
+    Context context(system, integrator, platform);
+    vector<Vec3> positions(3);
+    positions[0] = Vec3(0, 0, 0);
+    positions[1] = Vec3(0, 2, 0);
+    positions[2] = Vec3(0, 3, 0);
+    context.setPositions(positions);
+    State state = context.getState(State::Forces | State::Energy);
+    const vector<Vec3>& forces = state.getForces();
+    const double krf = (1.0/(cutoff*cutoff*cutoff))*(eps-1.0)/(2.0*eps+1.0);
+    const double crf = (1.0/cutoff)*(3.0*eps)/(2.0*eps+1.0);
+    const double force1 = ONE_4PI_EPS0*(1.0)*(0.25-2.0*krf*2.0);
+    const double force2 = ONE_4PI_EPS0*(1.0)*(1.0-2.0*krf*1.0);
+    ASSERT_EQUAL_VEC(Vec3(0, -force1, 0), forces[0], TOL);
+    ASSERT_EQUAL_VEC(Vec3(0, force1-force2, 0), forces[1], TOL);
+    ASSERT_EQUAL_VEC(Vec3(0, force2, 0), forces[2], TOL);
+    const double energy1 = ONE_4PI_EPS0*(1.0)*(0.5+krf*4.0-crf);
+    const double energy2 = ONE_4PI_EPS0*(1.0)*(1.0+krf*1.0-crf);
+    ASSERT_EQUAL_TOL(energy1+energy2, state.getPotentialEnergy(), TOL);
+}
+
+void testCutoff14() {
+    System system;
+    VerletIntegrator integrator(0.01);
+    NonbondedForce* nonbonded = new NonbondedForce();
+    nonbonded->setNonbondedMethod(NonbondedForce::CutoffNonPeriodic);
+    for (int i = 0; i < 5; ++i) {
+        system.addParticle(1.0);
+        nonbonded->addParticle(0, 1.5, 0);
+    }
+    const double cutoff = 3.5;
+    nonbonded->setCutoffDistance(cutoff);
+    const double eps = 30.0;
+    nonbonded->setReactionFieldDielectric(eps);
+    vector<pair<int, int> > bonds;
+    bonds.push_back(pair<int, int>(0, 1));
+    bonds.push_back(pair<int, int>(1, 2));
+    bonds.push_back(pair<int, int>(2, 3));
+    bonds.push_back(pair<int, int>(3, 4));
+    nonbonded->createExceptionsFromBonds(bonds, 0.0, 0.0);
+    int first14, second14;
+    for (int i = 0; i < nonbonded->getNumExceptions(); i++) {
+        int particle1, particle2;
+        double chargeProd, sigma, epsilon;
+        nonbonded->getExceptionParameters(i, particle1, particle2, chargeProd, sigma, epsilon);
+        if ((particle1 == 0 && particle2 == 3) || (particle1 == 3 && particle2 == 0))
+            first14 = i;
+        if ((particle1 == 1 && particle2 == 4) || (particle1 == 4 && particle2 == 1))
+            second14 = i;
+    }
+    system.addForce(nonbonded);
+    Context context(system, integrator, platform);
+    vector<Vec3> positions(5);
+    positions[0] = Vec3(0, 0, 0);
+    positions[1] = Vec3(1, 0, 0);
+    positions[2] = Vec3(2, 0, 0);
+    positions[3] = Vec3(3, 0, 0);
+    positions[4] = Vec3(4, 0, 0);
+    for (int i = 1; i < 5; ++i) {
+
+        // Test LJ forces
+
+        nonbonded->setParticleParameters(0, 0, 1.5, 1);
+        for (int j = 1; j < 5; ++j)
+            nonbonded->setParticleParameters(j, 0, 1.5, 0);
+        nonbonded->setParticleParameters(i, 0, 1.5, 1);
+        nonbonded->setExceptionParameters(first14, 0, 3, 0, 1.5, i == 3 ? 0.5 : 0.0);
+        nonbonded->setExceptionParameters(second14, 1, 4, 0, 1.5, 0.0);
+        context.reinitialize();
+        context.setPositions(positions);
+        State state = context.getState(State::Forces | State::Energy);
+        const vector<Vec3>& forces = state.getForces();
+        double r = positions[i][0];
+        double x = 1.5/r;
+        double e = 1.0;
+        double force = 4.0*e*(12*std::pow(x, 12.0)-6*std::pow(x, 6.0))/r;
+        double energy = 4.0*e*(std::pow(x, 12.0)-std::pow(x, 6.0));
+        if (i == 3) {
+            force *= 0.5;
+            energy *= 0.5;
+        }
+        if (i < 3 || r > cutoff) {
+            force = 0;
+            energy = 0;
+        }
+        ASSERT_EQUAL_VEC(Vec3(-force, 0, 0), forces[0], TOL);
+        ASSERT_EQUAL_VEC(Vec3(force, 0, 0), forces[i], TOL);
+        ASSERT_EQUAL_TOL(energy, state.getPotentialEnergy(), TOL);
+
+        // Test Coulomb forces
+
+        const double q = 0.7;
+        nonbonded->setParticleParameters(0, q, 1.5, 0);
+        nonbonded->setParticleParameters(i, q, 1.5, 0);
+        nonbonded->setExceptionParameters(first14, 0, 3, i == 3 ? q*q/1.2 : 0, 1.5, 0);
+        nonbonded->setExceptionParameters(second14, 1, 4, 0, 1.5, 0);
+        context.reinitialize();
+        context.setPositions(positions);
+        state = context.getState(State::Forces | State::Energy);
+        const vector<Vec3>& forces2 = state.getForces();
+        force = ONE_4PI_EPS0*q*q/(r*r);
+        energy = ONE_4PI_EPS0*q*q/r;
+        if (i == 3) {
+            force /= 1.2;
+            energy /= 1.2;
+        }
+        if (i < 3 || r > cutoff) {
+            force = 0;
+            energy = 0;
+        }
+        ASSERT_EQUAL_VEC(Vec3(-force, 0, 0), forces2[0], TOL);
+        ASSERT_EQUAL_VEC(Vec3(force, 0, 0), forces2[i], TOL);
+        ASSERT_EQUAL_TOL(energy, state.getPotentialEnergy(), TOL);
+    }
+}
+
+void testPeriodic() {
+    System system;
+    system.addParticle(1.0);
+    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->addParticle(1.0, 1, 0);
+    nonbonded->addException(0, 1, 0.0, 1.0, 0.0);
+    nonbonded->setNonbondedMethod(NonbondedForce::CutoffPeriodic);
+    const double cutoff = 2.0;
+    nonbonded->setCutoffDistance(cutoff);
+    system.setDefaultPeriodicBoxVectors(Vec3(4, 0, 0), Vec3(0, 4, 0), Vec3(0, 0, 4));
+    system.addForce(nonbonded);
+    Context context(system, integrator, platform);
+    vector<Vec3> positions(3);
+    positions[0] = Vec3(0, 0, 0);
+    positions[1] = Vec3(2, 0, 0);
+    positions[2] = Vec3(3, 0, 0);
+    context.setPositions(positions);
+    State state = context.getState(State::Forces | State::Energy);
+    const vector<Vec3>& forces = state.getForces();
+    const double eps = 78.3;
+    const double krf = (1.0/(cutoff*cutoff*cutoff))*(eps-1.0)/(2.0*eps+1.0);
+    const double crf = (1.0/cutoff)*(3.0*eps)/(2.0*eps+1.0);
+    const double force = ONE_4PI_EPS0*(1.0)*(1.0-2.0*krf*1.0);
+    ASSERT_EQUAL_VEC(Vec3(force, 0, 0), forces[0], TOL);
+    ASSERT_EQUAL_VEC(Vec3(-force, 0, 0), forces[1], TOL);
+    ASSERT_EQUAL_VEC(Vec3(0, 0, 0), forces[2], TOL);
+    ASSERT_EQUAL_TOL(2*ONE_4PI_EPS0*(1.0)*(1.0+krf*1.0-crf), state.getPotentialEnergy(), TOL);
+}
+
+
+void testLargeSystem() {
+    const int numMolecules = 600;
+    const int numParticles = numMolecules*2;
+    const double cutoff = 2.0;
+    const double boxSize = 20.0;
+    const double tol = 2e-3;
+    ReferencePlatform reference;
+    System system;
+    for (int i = 0; i < numParticles; i++)
+        system.addParticle(1.0);
+    NonbondedForce* nonbonded = new NonbondedForce();
+    HarmonicBondForce* bonds = new HarmonicBondForce();
+    vector<Vec3> positions(numParticles);
+    vector<Vec3> velocities(numParticles);
+    OpenMM_SFMT::SFMT sfmt;
+    init_gen_rand(0, sfmt);
+
+    for (int i = 0; i < numMolecules; i++) {
+        if (i < numMolecules/2) {
+            nonbonded->addParticle(-1.0, 0.2, 0.1);
+            nonbonded->addParticle(1.0, 0.1, 0.1);
+        }
+        else {
+            nonbonded->addParticle(-1.0, 0.2, 0.2);
+            nonbonded->addParticle(1.0, 0.1, 0.2);
+        }
+        positions[2*i] = Vec3(boxSize*genrand_real2(sfmt), boxSize*genrand_real2(sfmt), boxSize*genrand_real2(sfmt));
+        positions[2*i+1] = Vec3(positions[2*i][0]+1.0, positions[2*i][1], positions[2*i][2]);
+        velocities[2*i] = Vec3(genrand_real2(sfmt), genrand_real2(sfmt), genrand_real2(sfmt));
+        velocities[2*i+1] = Vec3(genrand_real2(sfmt), genrand_real2(sfmt), genrand_real2(sfmt));
+        bonds->addBond(2*i, 2*i+1, 1.0, 0.1);
+        nonbonded->addException(2*i, 2*i+1, 0.0, 0.15, 0.0);
+    }
+
+    // Try with cutoffs but not periodic boundary conditions, and make sure the cl and Reference
+    // platforms agree.
+
+    nonbonded->setNonbondedMethod(NonbondedForce::CutoffNonPeriodic);
+    nonbonded->setCutoffDistance(cutoff);
+    system.addForce(nonbonded);
+    system.addForce(bonds);
+    VerletIntegrator integrator1(0.01);
+    VerletIntegrator integrator2(0.01);
+    Context cuContext(system, integrator1, platform);
+    Context referenceContext(system, integrator2, reference);
+    cuContext.setPositions(positions);
+    cuContext.setVelocities(velocities);
+    referenceContext.setPositions(positions);
+    referenceContext.setVelocities(velocities);
+    State cuState = cuContext.getState(State::Positions | State::Velocities | State::Forces | State::Energy);
+    State referenceState = referenceContext.getState(State::Positions | State::Velocities | State::Forces | State::Energy);
+    for (int i = 0; i < numParticles; i++) {
+        ASSERT_EQUAL_VEC(cuState.getPositions()[i], referenceState.getPositions()[i], tol);
+        ASSERT_EQUAL_VEC(cuState.getVelocities()[i], referenceState.getVelocities()[i], tol);
+        ASSERT_EQUAL_VEC(cuState.getForces()[i], referenceState.getForces()[i], tol);
+    }
+    ASSERT_EQUAL_TOL(cuState.getPotentialEnergy(), referenceState.getPotentialEnergy(), tol);
+
+    // Now do the same thing with periodic boundary conditions.
+
+    nonbonded->setNonbondedMethod(NonbondedForce::CutoffPeriodic);
+    system.setDefaultPeriodicBoxVectors(Vec3(boxSize, 0, 0), Vec3(0, boxSize, 0), Vec3(0, 0, boxSize));
+    cuContext.reinitialize();
+    referenceContext.reinitialize();
+    cuContext.setPositions(positions);
+    cuContext.setVelocities(velocities);
+    referenceContext.setPositions(positions);
+    referenceContext.setVelocities(velocities);
+    cuState = cuContext.getState(State::Positions | State::Velocities | State::Forces | State::Energy);
+    referenceState = referenceContext.getState(State::Positions | State::Velocities | State::Forces | State::Energy);
+    for (int i = 0; i < numParticles; i++) {
+        double dx = cuState.getPositions()[i][0]-referenceState.getPositions()[i][0];
+        double dy = cuState.getPositions()[i][1]-referenceState.getPositions()[i][1];
+        double dz = cuState.getPositions()[i][2]-referenceState.getPositions()[i][2];
+        ASSERT_EQUAL_TOL(fmod(cuState.getPositions()[i][0]-referenceState.getPositions()[i][0], boxSize), 0, tol);
+        ASSERT_EQUAL_TOL(fmod(cuState.getPositions()[i][1]-referenceState.getPositions()[i][1], boxSize), 0, tol);
+        ASSERT_EQUAL_TOL(fmod(cuState.getPositions()[i][2]-referenceState.getPositions()[i][2], boxSize), 0, tol);
+        ASSERT_EQUAL_VEC(cuState.getVelocities()[i], referenceState.getVelocities()[i], tol);
+        ASSERT_EQUAL_VEC(cuState.getForces()[i], referenceState.getForces()[i], tol);
+    }
+    ASSERT_EQUAL_TOL(cuState.getPotentialEnergy(), referenceState.getPotentialEnergy(), tol);
+}
+
+void testDispersionCorrection() {
+    // Create a box full of identical particles.
+
+    int gridSize = 5;
+    int numParticles = gridSize*gridSize*gridSize;
+    double boxSize = gridSize*0.7;
+    double cutoff = boxSize/3;
+    System system;
+    VerletIntegrator integrator(0.01);
+    NonbondedForce* nonbonded = new NonbondedForce();
+    vector<Vec3> positions(numParticles);
+    int index = 0;
+    for (int i = 0; i < gridSize; i++)
+        for (int j = 0; j < gridSize; j++)
+            for (int k = 0; k < gridSize; k++) {
+                system.addParticle(1.0);
+                nonbonded->addParticle(0, 1.1, 0.5);
+                positions[index] = Vec3(i*boxSize/gridSize, j*boxSize/gridSize, k*boxSize/gridSize);
+                index++;
+            }
+    nonbonded->setNonbondedMethod(NonbondedForce::CutoffPeriodic);
+    nonbonded->setCutoffDistance(cutoff);
+    system.setDefaultPeriodicBoxVectors(Vec3(boxSize, 0, 0), Vec3(0, boxSize, 0), Vec3(0, 0, boxSize));
+    system.addForce(nonbonded);
+
+    // See if the correction has the correct value.
+
+    Context context(system, integrator, platform);
+    context.setPositions(positions);
+    double energy1 = context.getState(State::Energy).getPotentialEnergy();
+    nonbonded->setUseDispersionCorrection(false);
+    context.reinitialize();
+    context.setPositions(positions);
+    double energy2 = context.getState(State::Energy).getPotentialEnergy();
+    double term1 = (0.5*pow(1.1, 12)/pow(cutoff, 9))/9;
+    double term2 = (0.5*pow(1.1, 6)/pow(cutoff, 3))/3;
+    double expected = 8*M_PI*numParticles*numParticles*(term1-term2)/(boxSize*boxSize*boxSize);
+    ASSERT_EQUAL_TOL(expected, energy1-energy2, 1e-4);
+
+    // Now modify half the particles to be different, and see if it is still correct.
+
+    int numType2 = 0;
+    for (int i = 0; i < numParticles; i += 2) {
+        nonbonded->setParticleParameters(i, 0, 1, 1);
+        numType2++;
+    }
+    int numType1 = numParticles-numType2;
+    nonbonded->updateParametersInContext(context);
+    energy2 = context.getState(State::Energy).getPotentialEnergy();
+    nonbonded->setUseDispersionCorrection(true);
+    context.reinitialize();
+    context.setPositions(positions);
+    energy1 = context.getState(State::Energy).getPotentialEnergy();
+    term1 = ((numType1*(numType1+1))/2)*(0.5*pow(1.1, 12)/pow(cutoff, 9))/9;
+    term2 = ((numType1*(numType1+1))/2)*(0.5*pow(1.1, 6)/pow(cutoff, 3))/3;
+    term1 += ((numType2*(numType2+1))/2)*(1*pow(1.0, 12)/pow(cutoff, 9))/9;
+    term2 += ((numType2*(numType2+1))/2)*(1*pow(1.0, 6)/pow(cutoff, 3))/3;
+    double combinedSigma = 0.5*(1+1.1);
+    double combinedEpsilon = sqrt(1*0.5);
+    term1 += (numType1*numType2)*(combinedEpsilon*pow(combinedSigma, 12)/pow(cutoff, 9))/9;
+    term2 += (numType1*numType2)*(combinedEpsilon*pow(combinedSigma, 6)/pow(cutoff, 3))/3;
+    term1 /= (numParticles*(numParticles+1))/2;
+    term2 /= (numParticles*(numParticles+1))/2;
+    expected = 8*M_PI*numParticles*numParticles*(term1-term2)/(boxSize*boxSize*boxSize);
+    ASSERT_EQUAL_TOL(expected, energy1-energy2, 1e-4);
+}
+
+void testChangingParameters() {
+    const int numMolecules = 600;
+    const int numParticles = numMolecules*2;
+    const double cutoff = 2.0;
+    const double boxSize = 20.0;
+    const double tol = 2e-3;
+    ReferencePlatform reference;
+    System system;
+    for (int i = 0; i < numParticles; i++)
+        system.addParticle(1.0);
+    NonbondedForce* nonbonded = new NonbondedForce();
+    vector<Vec3> positions(numParticles);
+    OpenMM_SFMT::SFMT sfmt;
+    init_gen_rand(0, sfmt);
+
+    for (int i = 0; i < numMolecules; i++) {
+        if (i < numMolecules/2) {
+            nonbonded->addParticle(-1.0, 0.2, 0.1);
+            nonbonded->addParticle(1.0, 0.1, 0.1);
+        }
+        else {
+            nonbonded->addParticle(-1.0, 0.2, 0.2);
+            nonbonded->addParticle(1.0, 0.1, 0.2);
+        }
+        positions[2*i] = Vec3(boxSize*genrand_real2(sfmt), boxSize*genrand_real2(sfmt), boxSize*genrand_real2(sfmt));
+        positions[2*i+1] = Vec3(positions[2*i][0]+1.0, positions[2*i][1], positions[2*i][2]);
+        system.addConstraint(2*i, 2*i+1, 1.0);
+        nonbonded->addException(2*i, 2*i+1, 0.0, 0.15, 0.0);
+    }
+    nonbonded->setNonbondedMethod(NonbondedForce::PME);
+    nonbonded->setCutoffDistance(cutoff);
+    system.addForce(nonbonded);
+    system.setDefaultPeriodicBoxVectors(Vec3(boxSize, 0, 0), Vec3(0, boxSize, 0), Vec3(0, 0, boxSize));
+    
+    // See if Reference and CPU give the same forces and energies.
+    
+    VerletIntegrator integrator1(0.01);
+    VerletIntegrator integrator2(0.01);
+    Context cuContext(system, integrator1, platform);
+    Context referenceContext(system, integrator2, reference);
+    cuContext.setPositions(positions);
+    referenceContext.setPositions(positions);
+    State cuState = cuContext.getState(State::Forces | State::Energy);
+    State referenceState = referenceContext.getState(State::Forces | State::Energy);
+    for (int i = 0; i < numParticles; i++)
+        ASSERT_EQUAL_VEC(cuState.getForces()[i], referenceState.getForces()[i], tol);
+    ASSERT_EQUAL_TOL(cuState.getPotentialEnergy(), referenceState.getPotentialEnergy(), tol);
+    
+    // Now modify parameters and see if they still agree.
+
+    for (int i = 0; i < numParticles; i += 5) {
+        double charge, sigma, epsilon;
+        nonbonded->getParticleParameters(i, charge, sigma, epsilon);
+        nonbonded->setParticleParameters(i, 1.5*charge, 1.1*sigma, 1.7*epsilon);
+    }
+    nonbonded->updateParametersInContext(cuContext);
+    nonbonded->updateParametersInContext(referenceContext);
+    cuState = cuContext.getState(State::Forces | State::Energy);
+    referenceState = referenceContext.getState(State::Forces | State::Energy);
+    for (int i = 0; i < numParticles; i++)
+        ASSERT_EQUAL_VEC(cuState.getForces()[i], referenceState.getForces()[i], tol);
+    ASSERT_EQUAL_TOL(cuState.getPotentialEnergy(), referenceState.getPotentialEnergy(), tol);
+}
+
+void testSwitchingFunction(NonbondedForce::NonbondedMethod method) {
+    System system;
+    system.setDefaultPeriodicBoxVectors(Vec3(6, 0, 0), Vec3(0, 6, 0), Vec3(0, 0, 6));
+    system.addParticle(1.0);
+    system.addParticle(1.0);
+    VerletIntegrator integrator(0.01);
+    NonbondedForce* nonbonded = new NonbondedForce();
+    nonbonded->addParticle(0, 1.2, 1);
+    nonbonded->addParticle(0, 1.4, 2);
+    nonbonded->setNonbondedMethod(method);
+    nonbonded->setCutoffDistance(2.0);
+    nonbonded->setUseSwitchingFunction(true);
+    nonbonded->setSwitchingDistance(1.5);
+    nonbonded->setUseDispersionCorrection(false);
+    system.addForce(nonbonded);
+    Context context(system, integrator, platform);
+    vector<Vec3> positions(2);
+    positions[0] = Vec3(0, 0, 0);
+    double eps = SQRT_TWO;
+    
+    // Compute the interaction at various distances.
+    
+    for (double r = 1.0; r < 2.5; r += 0.1) {
+        positions[1] = Vec3(r, 0, 0);
+        context.setPositions(positions);
+        State state = context.getState(State::Forces | State::Energy);
+        
+        // See if the energy is correct.
+        
+        double x = 1.3/r;
+        double expectedEnergy = 4.0*eps*(std::pow(x, 12.0)-std::pow(x, 6.0));
+        double switchValue;
+        if (r <= 1.5)
+            switchValue = 1;
+        else if (r >= 2.0)
+            switchValue = 0;
+        else {
+            double t = (r-1.5)/0.5;
+            switchValue = 1+t*t*t*(-10+t*(15-t*6));
+        }
+        ASSERT_EQUAL_TOL(switchValue*expectedEnergy, state.getPotentialEnergy(), TOL);
+        
+        // See if the force is the gradient of the energy.
+        
+        double delta = 1e-3;
+        positions[1] = Vec3(r-delta, 0, 0);
+        context.setPositions(positions);
+        double e1 = context.getState(State::Energy).getPotentialEnergy();
+        positions[1] = Vec3(r+delta, 0, 0);
+        context.setPositions(positions);
+        double e2 = context.getState(State::Energy).getPotentialEnergy();
+        ASSERT_EQUAL_TOL((e2-e1)/(2*delta), state.getForces()[0][0], 1e-3);
+    }
+}
+
+int main(int argc, char* argv[]) {
+    try {
+        testCoulomb();
+        testLJ();
+        testExclusionsAnd14();
+        testCutoff();
+        testCutoff14();
+        testPeriodic();
+        testLargeSystem();
+        testDispersionCorrection();
+        testChangingParameters();
+        testSwitchingFunction(NonbondedForce::CutoffNonPeriodic);
+        testSwitchingFunction(NonbondedForce::PME);
+    }
+    catch(const exception& e) {
+        cout << "exception: " << e.what() << endl;
+        return 1;
+    }
+    cout << "Done" << endl;
+    return 0;
+}

platforms/cpu/tests/nacl_amorph.dat

+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);
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