ComputeNonbondedUtil.C

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/*
   Common operations for ComputeNonbonded classes
*/

#ifdef WIN32
extern "C" {
  double erfc(double);
}
#endif

#include "InfoStream.h"
#include "ComputeNonbondedUtil.h"
#include "SimParameters.h"
#include "Node.h"
#include "Molecule.h"
#include "LJTable.h"
#include "ReductionMgr.h"
#include "Parameters.h"
#include <stdio.h>

#ifdef NAMD_CUDA
  void build_cuda_force_table();
#endif

Bool            ComputeNonbondedUtil::commOnly;
Bool            ComputeNonbondedUtil::fixedAtomsOn;
BigReal         ComputeNonbondedUtil::cutoff;
BigReal         ComputeNonbondedUtil::cutoff2;
BigReal         ComputeNonbondedUtil::dielectric_1;
const LJTable*  ComputeNonbondedUtil::ljTable = 0;
const Molecule* ComputeNonbondedUtil::mol;
BigReal         ComputeNonbondedUtil::r2_delta;
BigReal         ComputeNonbondedUtil::r2_delta_1;
int             ComputeNonbondedUtil::r2_delta_exp;
int             ComputeNonbondedUtil::rowsize;
int             ComputeNonbondedUtil::columnsize;
BigReal*        ComputeNonbondedUtil::table_alloc = 0;
BigReal*                ComputeNonbondedUtil::table_ener = 0;
BigReal*        ComputeNonbondedUtil::table_short;
BigReal*        ComputeNonbondedUtil::table_noshort;
BigReal*        ComputeNonbondedUtil::fast_table;
BigReal*        ComputeNonbondedUtil::scor_table;
BigReal*        ComputeNonbondedUtil::slow_table;
BigReal*        ComputeNonbondedUtil::corr_table;
BigReal*        ComputeNonbondedUtil::full_table;
BigReal*        ComputeNonbondedUtil::vdwa_table;
BigReal*        ComputeNonbondedUtil::vdwb_table;
BigReal*        ComputeNonbondedUtil::r2_table;
BigReal         ComputeNonbondedUtil::scaling;
BigReal         ComputeNonbondedUtil::scale14;
BigReal         ComputeNonbondedUtil::switchOn;
BigReal         ComputeNonbondedUtil::switchOn_1;
BigReal         ComputeNonbondedUtil::switchOn2;
BigReal         ComputeNonbondedUtil::c0;
BigReal         ComputeNonbondedUtil::c1;
BigReal         ComputeNonbondedUtil::c3;
BigReal         ComputeNonbondedUtil::c5;
BigReal         ComputeNonbondedUtil::c6;
BigReal         ComputeNonbondedUtil::c7;
BigReal         ComputeNonbondedUtil::c8;
// BigReal         ComputeNonbondedUtil::d0;
// fepb
Bool      ComputeNonbondedUtil::alchFepOn;
Bool      ComputeNonbondedUtil::alchThermIntOn;
BigReal   ComputeNonbondedUtil::alchLambda;
BigReal   ComputeNonbondedUtil::alchLambda2;
BigReal   ComputeNonbondedUtil::alchVdwShiftCoeff;
BigReal   ComputeNonbondedUtil::alchVdwLambdaEnd;
BigReal   ComputeNonbondedUtil::alchElecLambdaStart;
Bool      ComputeNonbondedUtil::alchDecouple;
//fepe
Bool      ComputeNonbondedUtil::lesOn;
int       ComputeNonbondedUtil::lesFactor;
BigReal   ComputeNonbondedUtil::lesScaling;

BigReal*        ComputeNonbondedUtil::lambda_table = 0;

Bool            ComputeNonbondedUtil::pairInteractionOn;
Bool            ComputeNonbondedUtil::pairInteractionSelf;

Bool            ComputeNonbondedUtil::pressureProfileOn;
int             ComputeNonbondedUtil::pressureProfileSlabs;
int             ComputeNonbondedUtil::pressureProfileAtomTypes;
BigReal         ComputeNonbondedUtil::pressureProfileThickness;
BigReal         ComputeNonbondedUtil::pressureProfileMin;

BigReal         ComputeNonbondedUtil::ewaldcof;
BigReal         ComputeNonbondedUtil::pi_ewaldcof;

void (*ComputeNonbondedUtil::calcPair)(nonbonded *);
void (*ComputeNonbondedUtil::calcPairEnergy)(nonbonded *);
void (*ComputeNonbondedUtil::calcSelf)(nonbonded *);
void (*ComputeNonbondedUtil::calcSelfEnergy)(nonbonded *);

void (*ComputeNonbondedUtil::calcFullPair)(nonbonded *);
void (*ComputeNonbondedUtil::calcFullPairEnergy)(nonbonded *);
void (*ComputeNonbondedUtil::calcFullSelf)(nonbonded *);
void (*ComputeNonbondedUtil::calcFullSelfEnergy)(nonbonded *);

void (*ComputeNonbondedUtil::calcMergePair)(nonbonded *);
void (*ComputeNonbondedUtil::calcMergePairEnergy)(nonbonded *);
void (*ComputeNonbondedUtil::calcMergeSelf)(nonbonded *);
void (*ComputeNonbondedUtil::calcMergeSelfEnergy)(nonbonded *);

void (*ComputeNonbondedUtil::calcSlowPair)(nonbonded *);
void (*ComputeNonbondedUtil::calcSlowPairEnergy)(nonbonded *);
void (*ComputeNonbondedUtil::calcSlowSelf)(nonbonded *);
void (*ComputeNonbondedUtil::calcSlowSelfEnergy)(nonbonded *);

// define splitting function
#define SPLIT_NONE      1
#define SPLIT_SHIFT     2
#define SPLIT_C1        3
#define SPLIT_XPLOR     4
#define SPLIT_C2        5

void ComputeNonbondedUtil::submitReductionData(BigReal *data, SubmitReduction *reduction)
{
  reduction->item(REDUCTION_EXCLUSION_CHECKSUM) += data[exclChecksumIndex];
  reduction->item(REDUCTION_PAIRLIST_WARNINGS) += data[pairlistWarningIndex];
  reduction->item(REDUCTION_ELECT_ENERGY) += data[electEnergyIndex];
  reduction->item(REDUCTION_ELECT_ENERGY_SLOW) += data[fullElectEnergyIndex];
  reduction->item(REDUCTION_LJ_ENERGY) += data[vdwEnergyIndex];
//fepb
  reduction->item(REDUCTION_ELECT_ENERGY_F) += data[electEnergyIndex_s];
  reduction->item(REDUCTION_ELECT_ENERGY_SLOW_F) += data[fullElectEnergyIndex_s];
  reduction->item(REDUCTION_LJ_ENERGY_F) += data[vdwEnergyIndex_s];

  reduction->item(REDUCTION_ELECT_ENERGY_TI_1) += data[electEnergyIndex_ti_1];
  reduction->item(REDUCTION_ELECT_ENERGY_SLOW_TI_1) += data[fullElectEnergyIndex_ti_1];
  reduction->item(REDUCTION_LJ_ENERGY_TI_1) += data[vdwEnergyIndex_ti_1];
  reduction->item(REDUCTION_ELECT_ENERGY_TI_2) += data[electEnergyIndex_ti_2];
  reduction->item(REDUCTION_ELECT_ENERGY_SLOW_TI_2) += data[fullElectEnergyIndex_ti_2];
  reduction->item(REDUCTION_LJ_ENERGY_TI_2) += data[vdwEnergyIndex_ti_2];
//fepe
  ADD_TENSOR(reduction,REDUCTION_VIRIAL_NBOND,data,virialIndex);
  ADD_TENSOR(reduction,REDUCTION_VIRIAL_SLOW,data,fullElectVirialIndex);
  ADD_VECTOR(reduction,REDUCTION_PAIR_VDW_FORCE,data,pairVDWForceIndex);
  ADD_VECTOR(reduction,REDUCTION_PAIR_ELECT_FORCE,data,pairElectForceIndex);
  reduction->item(REDUCTION_COMPUTE_CHECKSUM) += 1.;
}

void ComputeNonbondedUtil::submitPressureProfileData(BigReal *data,
  SubmitReduction *reduction)
{
  if (!reduction) return;
  int numAtomTypes = pressureProfileAtomTypes;
  // For ease of calculation we stored interactions between types
  // i and j in (ni+j).  For efficiency now we coalesce the
  // cross interactions so that just i<=j are stored.
  const int arraysize = 3*pressureProfileSlabs;
  size_t nelems = arraysize*(numAtomTypes*(numAtomTypes+1))/2;
  BigReal *arr = new BigReal[nelems];
  memset(arr, 0, nelems*sizeof(BigReal));

  int i, j;
  for (i=0; i<numAtomTypes; i++) {
    for (j=0; j<numAtomTypes; j++) {
      int ii=i;
      int jj=j;
      if (ii > jj) { int tmp=ii; ii=jj; jj=tmp; }
      const int reductionOffset = (ii*numAtomTypes - (ii*(ii+1))/2 + jj)*arraysize;
      for (int k=0; k<arraysize; k++) {
        arr[reductionOffset+k] += data[k];
      }
      data += arraysize;
    }
  }
  // copy into reduction
  reduction->add(nelems, arr);
  delete [] arr;
}
  
void ComputeNonbondedUtil::calc_error(nonbonded *) {
  NAMD_bug("Tried to call missing nonbonded compute routine.");
}
  
void ComputeNonbondedUtil::select(void)
{
  if ( CkMyRank() ) return;

  // These defaults die cleanly if nothing appropriate is assigned.
  ComputeNonbondedUtil::calcPair = calc_error;
  ComputeNonbondedUtil::calcPairEnergy = calc_error;
  ComputeNonbondedUtil::calcSelf = calc_error;
  ComputeNonbondedUtil::calcSelfEnergy = calc_error;
  ComputeNonbondedUtil::calcFullPair = calc_error;
  ComputeNonbondedUtil::calcFullPairEnergy = calc_error;
  ComputeNonbondedUtil::calcFullSelf = calc_error;
  ComputeNonbondedUtil::calcFullSelfEnergy = calc_error;
  ComputeNonbondedUtil::calcMergePair = calc_error;
  ComputeNonbondedUtil::calcMergePairEnergy = calc_error;
  ComputeNonbondedUtil::calcMergeSelf = calc_error;
  ComputeNonbondedUtil::calcMergeSelfEnergy = calc_error;
  ComputeNonbondedUtil::calcSlowPair = calc_error;
  ComputeNonbondedUtil::calcSlowPairEnergy = calc_error;
  ComputeNonbondedUtil::calcSlowSelf = calc_error;
  ComputeNonbondedUtil::calcSlowSelfEnergy = calc_error;

  SimParameters * simParams = Node::Object()->simParameters;
  Parameters * params = Node::Object()->parameters;

  table_ener = params->table_ener;
  rowsize = params->rowsize;
  columnsize = params->columnsize;

  commOnly = simParams->commOnly;
  fixedAtomsOn = ( simParams->fixedAtomsOn && ! simParams->fixedAtomsForces );

  cutoff = simParams->cutoff;
  cutoff2 = cutoff*cutoff;

//fepb
  alchFepOn = simParams->alchFepOn;
  alchThermIntOn = simParams->alchThermIntOn;
  alchLambda = alchLambda2 = 0;
  lesOn = simParams->lesOn;
  lesScaling = lesFactor = 0;
  Bool tabulatedEnergies = simParams->tabulatedEnergies;
  alchVdwShiftCoeff = simParams->alchVdwShiftCoeff;
  alchVdwLambdaEnd = simParams->alchVdwLambdaEnd;
  alchElecLambdaStart = simParams->alchElecLambdaStart;

  alchDecouple = simParams->alchDecouple;

  delete [] lambda_table;
  lambda_table = 0;

  pairInteractionOn = simParams->pairInteractionOn;
  pairInteractionSelf = simParams->pairInteractionSelf;
  pressureProfileOn = simParams->pressureProfileOn;

  if ( alchFepOn ) {
    alchLambda = simParams->alchLambda;
    alchLambda2 = simParams->alchLambda2;
    ComputeNonbondedUtil::calcPair = calc_pair_energy_fep;
    ComputeNonbondedUtil::calcPairEnergy = calc_pair_energy_fep;
    ComputeNonbondedUtil::calcSelf = calc_self_energy_fep;
    ComputeNonbondedUtil::calcSelfEnergy = calc_self_energy_fep;
    ComputeNonbondedUtil::calcFullPair = calc_pair_energy_fullelect_fep;
    ComputeNonbondedUtil::calcFullPairEnergy = calc_pair_energy_fullelect_fep;
    ComputeNonbondedUtil::calcFullSelf = calc_self_energy_fullelect_fep;
    ComputeNonbondedUtil::calcFullSelfEnergy = calc_self_energy_fullelect_fep;
    ComputeNonbondedUtil::calcMergePair = calc_pair_energy_merge_fullelect_fep;
    ComputeNonbondedUtil::calcMergePairEnergy = calc_pair_energy_merge_fullelect_fep;
    ComputeNonbondedUtil::calcMergeSelf = calc_self_energy_merge_fullelect_fep;
    ComputeNonbondedUtil::calcMergeSelfEnergy = calc_self_energy_merge_fullelect_fep;
    ComputeNonbondedUtil::calcSlowPair = calc_pair_energy_slow_fullelect_fep;
    ComputeNonbondedUtil::calcSlowPairEnergy = calc_pair_energy_slow_fullelect_fep;
    ComputeNonbondedUtil::calcSlowSelf = calc_self_energy_slow_fullelect_fep;
    ComputeNonbondedUtil::calcSlowSelfEnergy = calc_self_energy_slow_fullelect_fep;
  }  else if ( alchThermIntOn ) {
    alchLambda = simParams->alchLambda;
    ComputeNonbondedUtil::calcPair = calc_pair_ti;
    ComputeNonbondedUtil::calcPairEnergy = calc_pair_energy_ti;
    ComputeNonbondedUtil::calcSelf = calc_self_ti;
    ComputeNonbondedUtil::calcSelfEnergy = calc_self_energy_ti;
    ComputeNonbondedUtil::calcFullPair = calc_pair_fullelect_ti;
    ComputeNonbondedUtil::calcFullPairEnergy = calc_pair_energy_fullelect_ti;
    ComputeNonbondedUtil::calcFullSelf = calc_self_fullelect_ti;
    ComputeNonbondedUtil::calcFullSelfEnergy = calc_self_energy_fullelect_ti;
    ComputeNonbondedUtil::calcMergePair = calc_pair_merge_fullelect_ti;
    ComputeNonbondedUtil::calcMergePairEnergy = calc_pair_energy_merge_fullelect_ti;
    ComputeNonbondedUtil::calcMergeSelf = calc_self_merge_fullelect_ti;
    ComputeNonbondedUtil::calcMergeSelfEnergy = calc_self_energy_merge_fullelect_ti;
    ComputeNonbondedUtil::calcSlowPair = calc_pair_slow_fullelect_ti;
    ComputeNonbondedUtil::calcSlowPairEnergy = calc_pair_energy_slow_fullelect_ti;
    ComputeNonbondedUtil::calcSlowSelf = calc_self_slow_fullelect_ti;
    ComputeNonbondedUtil::calcSlowSelfEnergy = calc_self_energy_slow_fullelect_ti;
  } else if ( lesOn ) {
    lesFactor = simParams->lesFactor;
    lesScaling = 1.0 / (double)lesFactor;
    lambda_table = new BigReal[(lesFactor+1)*(lesFactor+1)];
    for ( int ip=0; ip<=lesFactor; ++ip ) {
      for ( int jp=0; jp<=lesFactor; ++jp ) {
        BigReal lambda_pair = 1.0;
        if (ip || jp ) {
          if (ip && jp && ip != jp) {
            lambda_pair = 0.0;
          } else {
            lambda_pair = lesScaling;
          }
        }
        lambda_table[(lesFactor+1)*ip+jp] = lambda_pair;
      }
    }
    ComputeNonbondedUtil::calcPair = calc_pair_les;
    ComputeNonbondedUtil::calcPairEnergy = calc_pair_energy_les;
    ComputeNonbondedUtil::calcSelf = calc_self_les;
    ComputeNonbondedUtil::calcSelfEnergy = calc_self_energy_les;
    ComputeNonbondedUtil::calcFullPair = calc_pair_fullelect_les;
    ComputeNonbondedUtil::calcFullPairEnergy = calc_pair_energy_fullelect_les;
    ComputeNonbondedUtil::calcFullSelf = calc_self_fullelect_les;
    ComputeNonbondedUtil::calcFullSelfEnergy = calc_self_energy_fullelect_les;
    ComputeNonbondedUtil::calcMergePair = calc_pair_merge_fullelect_les;
    ComputeNonbondedUtil::calcMergePairEnergy = calc_pair_energy_merge_fullelect_les;
    ComputeNonbondedUtil::calcMergeSelf = calc_self_merge_fullelect_les;
    ComputeNonbondedUtil::calcMergeSelfEnergy = calc_self_energy_merge_fullelect_les;
    ComputeNonbondedUtil::calcSlowPair = calc_pair_slow_fullelect_les;
    ComputeNonbondedUtil::calcSlowPairEnergy = calc_pair_energy_slow_fullelect_les;
    ComputeNonbondedUtil::calcSlowSelf = calc_self_slow_fullelect_les;
    ComputeNonbondedUtil::calcSlowSelfEnergy = calc_self_energy_slow_fullelect_les;
  } else if ( pressureProfileOn) {
    pressureProfileSlabs = simParams->pressureProfileSlabs;
    pressureProfileAtomTypes = simParams->pressureProfileAtomTypes;

    ComputeNonbondedUtil::calcPair = calc_pair_pprof;
    ComputeNonbondedUtil::calcPairEnergy = calc_pair_energy_pprof;
    ComputeNonbondedUtil::calcSelf = calc_self_pprof;
    ComputeNonbondedUtil::calcSelfEnergy = calc_self_energy_pprof;
    ComputeNonbondedUtil::calcFullPair = calc_pair_fullelect_pprof;
    ComputeNonbondedUtil::calcFullPairEnergy = calc_pair_energy_fullelect_pprof;
    ComputeNonbondedUtil::calcFullSelf = calc_self_fullelect_pprof;
    ComputeNonbondedUtil::calcFullSelfEnergy = calc_self_energy_fullelect_pprof;
    ComputeNonbondedUtil::calcMergePair = calc_pair_merge_fullelect_pprof;
    ComputeNonbondedUtil::calcMergePairEnergy = calc_pair_energy_merge_fullelect_pprof;
    ComputeNonbondedUtil::calcMergeSelf = calc_self_merge_fullelect_pprof;
    ComputeNonbondedUtil::calcMergeSelfEnergy = calc_self_energy_merge_fullelect_pprof;
    ComputeNonbondedUtil::calcSlowPair = calc_pair_slow_fullelect_pprof;
    ComputeNonbondedUtil::calcSlowPairEnergy = calc_pair_energy_slow_fullelect_pprof;
    ComputeNonbondedUtil::calcSlowSelf = calc_self_slow_fullelect_pprof;
    ComputeNonbondedUtil::calcSlowSelfEnergy = calc_self_energy_slow_fullelect_pprof;
  } else if ( pairInteractionOn ) {
    ComputeNonbondedUtil::calcPairEnergy = calc_pair_energy_int;
    ComputeNonbondedUtil::calcSelfEnergy = calc_self_energy_int;
    ComputeNonbondedUtil::calcFullPairEnergy = calc_pair_energy_fullelect_int;
    ComputeNonbondedUtil::calcFullSelfEnergy = calc_self_energy_fullelect_int;
    ComputeNonbondedUtil::calcMergePairEnergy = calc_pair_energy_merge_fullelect_int;
    ComputeNonbondedUtil::calcMergeSelfEnergy = calc_self_energy_merge_fullelect_int;
  } else if ( tabulatedEnergies ) {
    ComputeNonbondedUtil::calcPair = calc_pair_tabener;
    ComputeNonbondedUtil::calcPairEnergy = calc_pair_energy_tabener;
    ComputeNonbondedUtil::calcSelf = calc_self_tabener;
    ComputeNonbondedUtil::calcSelfEnergy = calc_self_energy_tabener;
    ComputeNonbondedUtil::calcFullPair = calc_pair_fullelect_tabener;
    ComputeNonbondedUtil::calcFullPairEnergy = calc_pair_energy_fullelect_tabener;
    ComputeNonbondedUtil::calcFullSelf = calc_self_fullelect_tabener;
    ComputeNonbondedUtil::calcFullSelfEnergy = calc_self_energy_fullelect_tabener;
    ComputeNonbondedUtil::calcMergePair = calc_pair_merge_fullelect_tabener;
    ComputeNonbondedUtil::calcMergePairEnergy = calc_pair_energy_merge_fullelect_tabener;
    ComputeNonbondedUtil::calcMergeSelf = calc_self_merge_fullelect_tabener;
    ComputeNonbondedUtil::calcMergeSelfEnergy = calc_self_energy_merge_fullelect_tabener;
    ComputeNonbondedUtil::calcSlowPair = calc_pair_slow_fullelect_tabener;
    ComputeNonbondedUtil::calcSlowPairEnergy = calc_pair_energy_slow_fullelect_tabener;
    ComputeNonbondedUtil::calcSlowSelf = calc_self_slow_fullelect_tabener;
    ComputeNonbondedUtil::calcSlowSelfEnergy = calc_self_energy_slow_fullelect_tabener;
  } else {
    ComputeNonbondedUtil::calcPair = calc_pair;
    ComputeNonbondedUtil::calcPairEnergy = calc_pair_energy;
    ComputeNonbondedUtil::calcSelf = calc_self;
    ComputeNonbondedUtil::calcSelfEnergy = calc_self_energy;
    ComputeNonbondedUtil::calcFullPair = calc_pair_fullelect;
    ComputeNonbondedUtil::calcFullPairEnergy = calc_pair_energy_fullelect;
    ComputeNonbondedUtil::calcFullSelf = calc_self_fullelect;
    ComputeNonbondedUtil::calcFullSelfEnergy = calc_self_energy_fullelect;
    ComputeNonbondedUtil::calcMergePair = calc_pair_merge_fullelect;
    ComputeNonbondedUtil::calcMergePairEnergy = calc_pair_energy_merge_fullelect;
    ComputeNonbondedUtil::calcMergeSelf = calc_self_merge_fullelect;
    ComputeNonbondedUtil::calcMergeSelfEnergy = calc_self_energy_merge_fullelect;
    ComputeNonbondedUtil::calcSlowPair = calc_pair_slow_fullelect;
    ComputeNonbondedUtil::calcSlowPairEnergy = calc_pair_energy_slow_fullelect;
    ComputeNonbondedUtil::calcSlowSelf = calc_self_slow_fullelect;
    ComputeNonbondedUtil::calcSlowSelfEnergy = calc_self_energy_slow_fullelect;
  }

//fepe

  dielectric_1 = 1.0/simParams->dielectric;
  if ( ! ljTable ) ljTable = new LJTable;
  mol = Node::Object()->molecule;
  scaling = simParams->nonbondedScaling;
  if ( simParams->exclude == SCALED14 )
  {
    scale14 = simParams->scale14;
  }
  else
  {
    scale14 = 1.;
  }
  if ( simParams->switchingActive )
  {
    switchOn = simParams->switchingDist;
    switchOn_1 = 1.0/switchOn;
    // d0 = 1.0/(cutoff-switchOn);
    switchOn2 = switchOn*switchOn;
    c0 = 1.0/(cutoff2-switchOn2);
  }
  else
  {
    switchOn = cutoff;
    switchOn_1 = 1.0/switchOn;
    // d0 = 0.;  // avoid division by zero
    switchOn2 = switchOn*switchOn;
    c0 = 0.;  // avoid division by zero
  }
  c1 = c0*c0*c0;
  c3 = 3.0 * (cutoff2 - switchOn2);
  c5 = 0;
  c6 = 0;
  c7 = 0;
  c8 = 0;

  const int PMEOn = simParams->PMEOn;

  if ( PMEOn ) {
    ewaldcof = simParams->PMEEwaldCoefficient;
    BigReal TwoBySqrtPi = 1.12837916709551;
    pi_ewaldcof = TwoBySqrtPi * ewaldcof;
  }

  int splitType = SPLIT_NONE;
  if ( simParams->switchingActive ) splitType = SPLIT_SHIFT;
  if ( simParams->fullDirectOn || simParams->FMAOn || PMEOn ) {
    switch ( simParams->longSplitting ) {
      case C2:
      splitType = SPLIT_C2;
      break;

      case C1:
      splitType = SPLIT_C1;
      break;

      case XPLOR:
      NAMD_die("Sorry, XPLOR splitting not supported.");
      break;

      case SHARP:
      NAMD_die("Sorry, SHARP splitting not supported.");
      break;

      default:
      NAMD_die("Unknown splitting type found!");

    }
  }

  BigReal r2_tol = 0.1;
  
  r2_delta = 1.0;
  r2_delta_exp = 0;
  while ( r2_delta > r2_tol ) { r2_delta /= 2.0; r2_delta_exp += 1; }
  r2_delta_1 = 1.0 / r2_delta;

  if ( ! CkMyPe() ) {
    iout << iINFO << "NONBONDED TABLE R-SQUARED SPACING: " <<
                                r2_delta << "\n" << endi;
  }

  BigReal r2_tmp = 1.0;
  int cutoff2_exp = 0;
  while ( (cutoff2 + r2_delta) > r2_tmp ) { r2_tmp *= 2.0; cutoff2_exp += 1; }

  int i;
  int n = (r2_delta_exp + cutoff2_exp) * 64 + 1;

  if ( ! CkMyPe() ) {
    iout << iINFO << "NONBONDED TABLE SIZE: " <<
                                n << " POINTS\n" << endi;
  }

  if ( table_alloc ) delete [] table_alloc;
  table_alloc = new BigReal[61*n+16];
  BigReal *table_align = table_alloc;
  while ( ((long)table_align) % 128 ) ++table_align;
  table_noshort = table_align;
  table_short = table_align + 16*n;
  slow_table = table_align + 32*n;
  fast_table = table_align + 36*n;
  scor_table = table_align + 40*n;
  corr_table = table_align + 44*n;
  full_table = table_align + 48*n;
  vdwa_table = table_align + 52*n;
  vdwb_table = table_align + 56*n;
  r2_table = table_align + 60*n;
  BigReal *fast_i = fast_table + 4;
  BigReal *scor_i = scor_table + 4;
  BigReal *slow_i = slow_table + 4;
  BigReal *vdwa_i = vdwa_table + 4;
  BigReal *vdwb_i = vdwb_table + 4;
  BigReal *r2_i = r2_table;  *(r2_i++) = r2_delta;
  BigReal r2_limit = simParams->limitDist * simParams->limitDist;
  if ( r2_limit < r2_delta ) r2_limit = r2_delta;
  int r2_delta_i = 0;  // entry for r2 == r2_delta

  // fill in the table, fix up i==0 (r2==0) below
  for ( i=1; i<n; ++i ) {

    const BigReal r2_base = r2_delta * ( 1 << (i/64) );
    const BigReal r2_del = r2_base / 64.0;
    const BigReal r2 = r2_base - r2_delta + r2_del * (i%64);

    if ( r2 <= r2_limit ) r2_delta_i = i;

    const BigReal r = sqrt(r2);
    const BigReal r_1 = 1.0/r;
    const BigReal r_2 = 1.0/r2;

    // fast_ is defined as (full_ - slow_)
    // corr_ and fast_ are both zero at the cutoff, full_ is not
    // all three are approx 1/r at short distances

    // for actual interpolation, we use fast_ for fast forces and
    // scor_ = slow_ + corr_ - full_ and slow_ for slow forces
    // since these last two are of small magnitude

    BigReal fast_energy, fast_gradient;
    BigReal scor_energy, scor_gradient;
    BigReal slow_energy, slow_gradient;

    // corr_ is PME direct sum, or similar correction term
    // corr_energy is multiplied by r until later
    // corr_gradient is multiplied by -r^2 until later
    BigReal corr_energy, corr_gradient;

    
    if ( PMEOn ) {
      BigReal tmp_a = r * ewaldcof;
      BigReal tmp_b = erfc(tmp_a);
      corr_energy = tmp_b;
      corr_gradient = pi_ewaldcof*exp(-(tmp_a*tmp_a))*r + tmp_b;
    } else {
      corr_energy = corr_gradient = 0;
    }

    switch(splitType) {
      case SPLIT_NONE:
        fast_energy = 1.0/r;
        fast_gradient = -1.0/r2;
        scor_energy = scor_gradient = 0;
        slow_energy = slow_gradient = 0;
        break;
      case SPLIT_SHIFT: {
        BigReal shiftVal = r2/cutoff2 - 1.0;
        shiftVal *= shiftVal;
        BigReal dShiftVal = 2.0 * (r2/cutoff2 - 1.0) * 2.0*r/cutoff2;
        fast_energy = shiftVal/r;
        fast_gradient = dShiftVal/r - shiftVal/r2;
        scor_energy = scor_gradient = 0;
        slow_energy = slow_gradient = 0;
        } 
        break;
      case SPLIT_C1:
        // calculate actual energy and gradient
        slow_energy = 0.5/cutoff * (3.0 - (r2/cutoff2));
        slow_gradient = -1.0/cutoff2 * (r/cutoff);
        // calculate scor from slow and corr
        scor_energy = slow_energy + (corr_energy - 1.0)/r;
        scor_gradient = slow_gradient - (corr_gradient - 1.0)/r2;
        // calculate fast from slow
        fast_energy = 1.0/r - slow_energy;
        fast_gradient = -1.0/r2 - slow_gradient;
        break;
      case SPLIT_C2:
        //
        // Quintic splitting function contributed by
        // Bruce Berne, Ruhong Zhou, and Joe Morrone
        //
        // calculate actual energy and gradient
        slow_energy = r2/(cutoff*cutoff2) * (6.0 * (r2/cutoff2)
            - 15.0*(r/cutoff) + 10.0);
        slow_gradient = r/(cutoff*cutoff2) * (24.0 * (r2/cutoff2)
            - 45.0 *(r/cutoff) + 20.0);
        // calculate scor from slow and corr
        scor_energy = slow_energy + (corr_energy - 1.0)/r;
        scor_gradient = slow_gradient - (corr_gradient - 1.0)/r2;
        // calculate fast from slow
        fast_energy = 1.0/r - slow_energy;
        fast_gradient = -1.0/r2 - slow_gradient;
        break;
    }

    // foo_gradient is calculated as ( d foo_energy / d r )
    // and now divided by 2r to get ( d foo_energy / d r2 )

    fast_gradient *= 0.5 * r_1;
    scor_gradient *= 0.5 * r_1;
    slow_gradient *= 0.5 * r_1;

    // let modf be 1 if excluded, 1-scale14 if modified, 0 otherwise,
    // add scor_ - modf * slow_ to slow terms and
    // add fast_ - modf * fast_ to fast terms.

    BigReal vdwa_energy, vdwa_gradient;
    BigReal vdwb_energy, vdwb_gradient;

    const BigReal r_6 = r_2*r_2*r_2;
    const BigReal r_12 = r_6*r_6;

    // Lennard-Jones switching function
    const BigReal c2 = cutoff2-r2;
    const BigReal c4 = c2*(c3-2.0*c2);
    const BigReal switchVal =         // used for Lennard-Jones
                        ( r2 > switchOn2 ? c2*c4*c1 : 1.0 );
    const BigReal dSwitchVal =        // d switchVal / d r2
                        ( r2 > switchOn2 ? 2*c1*(c2*c2-c4) : 0.0 );

    vdwa_energy = switchVal * r_12;
    vdwb_energy = switchVal * r_6;

    vdwa_gradient = ( dSwitchVal - 6.0 * switchVal * r_2 ) * r_12;
    vdwb_gradient = ( dSwitchVal - 3.0 * switchVal * r_2 ) * r_6;


    *(fast_i++) = fast_energy;
    *(fast_i++) = fast_gradient;
    *(fast_i++) = 0;
    *(fast_i++) = 0;
    *(scor_i++) = scor_energy;
    *(scor_i++) = scor_gradient;
    *(scor_i++) = 0;
    *(scor_i++) = 0;
    *(slow_i++) = slow_energy;
    *(slow_i++) = slow_gradient;
    *(slow_i++) = 0;
    *(slow_i++) = 0;
    *(vdwa_i++) = vdwa_energy;
    *(vdwa_i++) = vdwa_gradient;
    *(vdwa_i++) = 0;
    *(vdwa_i++) = 0;
    *(vdwb_i++) = vdwb_energy;
    *(vdwb_i++) = vdwb_gradient;
    *(vdwb_i++) = 0;
    *(vdwb_i++) = 0;
    *(r2_i++) = r2 + r2_delta;

  }

  if ( ! r2_delta_i ) {
    NAMD_bug("Failed to find table entry for r2 == r2_limit\n");
  }
  if ( r2_table[r2_delta_i] > r2_limit + r2_delta ) {
    NAMD_bug("Found bad table entry for r2 == r2_limit\n");
  }

  int j;
  const char *table_name = "XXXX";
  int smooth_short = 0;
  for ( j=0; j<5; ++j ) {
    BigReal *t0 = 0;
    switch (j) {
      case 0: 
        t0 = fast_table;
        table_name = "FAST";
        smooth_short = 1;
      break;
      case 1: 
        t0 = scor_table;
        table_name = "SCOR";
        smooth_short = 0;
      break;
      case 2: 
        t0 = slow_table;
        table_name = "SLOW";
        smooth_short = 0;
      break;
      case 3: 
        t0 = vdwa_table;
        table_name = "VDWA";
        smooth_short = 1;
      break;
      case 4: 
        t0 = vdwb_table;
        table_name = "VDWB";
        smooth_short = 1;
      break;
    }
    // patch up data for i=0
    t0[0] = t0[4] - t0[5] * ( r2_delta / 64.0 );  // energy
    t0[1] = t0[5];  // gradient
    t0[2] = 0;
    t0[3] = 0;
    if ( smooth_short ) {
      BigReal energy0 = t0[4*r2_delta_i];
      BigReal gradient0 = t0[4*r2_delta_i+1];
      BigReal r20 = r2_table[r2_delta_i];
      t0[0] = energy0 - gradient0 * (r20 - r2_table[0]);  // energy
      t0[1] = gradient0;  // gradient
    }
    BigReal *t;
    for ( i=0,t=t0; i<(n-1); ++i,t+=4 ) {
      BigReal x = ( r2_delta * ( 1 << (i/64) ) ) / 64.0;
      if ( r2_table[i+1] != r2_table[i] + x ) {
        NAMD_bug("Bad table delta calculation.\n");
      }
      if ( smooth_short && i+1 < r2_delta_i ) {
        BigReal energy0 = t0[4*r2_delta_i];
        BigReal gradient0 = t0[4*r2_delta_i+1];
        BigReal r20 = r2_table[r2_delta_i];
        t[4] = energy0 - gradient0 * (r20 - r2_table[i+1]);  // energy
        t[5] = gradient0;  // gradient
      }
      BigReal v1 = t[0];
      BigReal g1 = t[1];
      BigReal v2 = t[4];
      BigReal g2 = t[5];
      // explicit formulas for v1 + g1 x + c x^2 + d x^3
      BigReal c = ( 3.0 * (v2 - v1) - x * (2.0 * g1 + g2) ) / ( x * x );
      BigReal d = ( -2.0 * (v2 - v1) + x * (g1 + g2) ) / ( x * x * x );
      // since v2 - v1 is imprecise, we refine c and d numerically
      // important because we need accurate forces (more than energies!)
      for ( int k=0; k < 2; ++k ) {
        BigReal dv = (v1 - v2) + ( ( d * x + c ) * x + g1 ) * x;
        BigReal dg = (g1 - g2) + ( 3.0 * d * x + 2.0 * c ) * x;
        c -= ( 3.0 * dv - x * dg ) / ( x * x );
        d -= ( -2.0 * dv + x * dg ) / ( x * x * x );
      }
      // store in the array;
      t[2] = c;  t[3] = d;
    }

    if ( ! CkMyPe() ) {
    BigReal dvmax = 0;
    BigReal dgmax = 0;
    BigReal dvmax_r = 0;
    BigReal dgmax_r = 0;
    BigReal fdvmax = 0;
    BigReal fdgmax = 0;
    BigReal fdvmax_r = 0;
    BigReal fdgmax_r = 0;
    for ( i=0,t=t0; i<(n-1); ++i,t+=4 ) {
      const BigReal r2_base = r2_delta * ( 1 << (i/64) );
      const BigReal r2_del = r2_base / 64.0;
      const BigReal r2 = r2_base - r2_delta + r2_del * (i%64);
      const BigReal r = sqrt(r2);
      BigReal x = r2_del;
      BigReal dv = ( ( t[3] * x + t[2] ) * x + t[1] ) * x + t[0] - t[4];
      BigReal dg = ( 3.0 * t[3] * x + 2.0 * t[2] ) * x + t[1] - t[5];
      if ( t[4] != 0. && fabs(dv/t[4]) > fdvmax ) {
        fdvmax = fabs(dv/t[4]); fdvmax_r = r;
      }
      if ( fabs(dv) > dvmax ) {
        dvmax = fabs(dv); dvmax_r = r;
      }
      if ( t[5] != 0. && fabs(dg/t[5]) > fdgmax ) {
        fdgmax = fabs(dg/t[5]); fdgmax_r = r;
      }
      if ( fabs(dg) > dgmax ) {
        dgmax = fabs(dg); dgmax_r = r;
      }
#if 0
      if (dv != 0.) CkPrintf("TABLE %d ENERGY ERROR %g AT %g (%d)\n",j,dv,r,i);
      if (dg != 0.) CkPrintf("TABLE %d FORCE ERROR %g AT %g (%d)\n",j,dg,r,i);
#endif
    }
    if ( dvmax != 0.0 ) {
      iout << iINFO << "ABSOLUTE IMPRECISION IN " << table_name <<
        " TABLE ENERGY: " << dvmax << " AT " << dvmax_r << "\n" << endi;
    }
    if ( fdvmax != 0.0 ) {
      iout << iINFO << "RELATIVE IMPRECISION IN " << table_name <<
        " TABLE ENERGY: " << fdvmax << " AT " << fdvmax_r << "\n" << endi;
    }
    if ( dgmax != 0.0 ) {
      iout << iINFO << "ABSOLUTE IMPRECISION IN " << table_name <<
        " TABLE FORCE: " << dgmax << " AT " << dgmax_r << "\n" << endi;
    }
    if ( fdgmax != 0.0 ) {
      iout << iINFO << "RELATIVE IMPRECISION IN " << table_name <<
        " TABLE FORCE: " << fdgmax << " AT " << fdgmax_r << "\n" << endi;
    }
    }

  }

  for ( i=0; i<4*n; ++i ) {
    corr_table[i] = fast_table[i] + scor_table[i];
    full_table[i] = fast_table[i] + slow_table[i];
  }

#if 0  
  for ( i=0; i<n; ++i ) {
   for ( int j=0; j<4; ++j ) {
    table_short[16*i+6-2*j] = table_noshort[16*i+6-2*j] = vdwa_table[4*i+j];
    table_short[16*i+7-2*j] = table_noshort[16*i+7-2*j] = vdwb_table[4*i+j];
    table_short[16*i+8+3-j] = fast_table[4*i+j];
    table_short[16*i+12+3-j] = scor_table[4*i+j];
    table_noshort[16*i+8+3-j] = corr_table[4*i+j];
    table_noshort[16*i+12+3-j] = full_table[4*i+j];
   }
  }
#endif 

  for ( i=0; i<n; ++i ) {
    table_short[16*i+ 0] = table_noshort[16*i+0] = -6.*vdwa_table[4*i+3];
    table_short[16*i+ 2] = table_noshort[16*i+2] = -6.*vdwb_table[4*i+3];
    table_short[16*i+ 4] = table_noshort[16*i+4] = -2.*vdwa_table[4*i+1];
    table_short[16*i+ 6] = table_noshort[16*i+6] = -2.*vdwb_table[4*i+1];
    
    table_short[16*i+1] = table_noshort[16*i+1] = -4.*vdwa_table[4*i+2];
    table_short[16*i+3] = table_noshort[16*i+3] = -4.*vdwb_table[4*i+2];
    table_short[16*i+5] = table_noshort[16*i+5] = -1.*vdwa_table[4*i+0];
    table_short[16*i+7] = table_noshort[16*i+7] = -1.*vdwb_table[4*i+0];
    
    table_short[16*i+8]  = -6.*fast_table[4*i+3];
    table_short[16*i+9]  = -4.*fast_table[4*i+2];
    table_short[16*i+10] = -2.*fast_table[4*i+1];
    table_short[16*i+11] = -1.*fast_table[4*i+0];

    table_noshort[16*i+8]  = -6.*corr_table[4*i+3];
    table_noshort[16*i+9]  = -4.*corr_table[4*i+2];
    table_noshort[16*i+10] = -2.*corr_table[4*i+1];
    table_noshort[16*i+11] = -1.*corr_table[4*i+0];

    table_short[16*i+12] = -6.*scor_table[4*i+3];
    table_short[16*i+13] = -4.*scor_table[4*i+2];
    table_short[16*i+14] = -2.*scor_table[4*i+1];
    table_short[16*i+15] = -1.*scor_table[4*i+0];

    table_noshort[16*i+12] = -6.*full_table[4*i+3];
    table_noshort[16*i+13] = -4.*full_table[4*i+2];
    table_noshort[16*i+14] = -2.*full_table[4*i+1];
    table_noshort[16*i+15] = -1.*full_table[4*i+0];
  }

#if 0
  char fname[100];
  sprintf(fname,"/tmp/namd.table.pe%d.dat",CkMyPe());
  FILE *f = fopen(fname,"w");
  for ( i=0; i<(n-1); ++i ) {
    const BigReal r2_base = r2_delta * ( 1 << (i/64) );
    const BigReal r2_del = r2_base / 64.0;
    const BigReal r2 = r2_base - r2_delta + r2_del * (i%64);
    BigReal *t;
    if ( r2 + r2_delta != r2_table[i] ) fprintf(f,"r2 error! ");
    fprintf(f,"%g",r2);
    t = fast_table + 4*i;
    fprintf(f,"   %g %g %g %g", t[0], t[1], t[2], t[3]);
    t = scor_table + 4*i;
    fprintf(f,"   %g %g %g %g", t[0], t[1], t[2], t[3]);
    t = slow_table + 4*i;
    fprintf(f,"   %g %g %g %g", t[0], t[1], t[2], t[3]);
    t = corr_table + 4*i;
    fprintf(f,"   %g %g %g %g", t[0], t[1], t[2], t[3]);
    t = full_table + 4*i;
    fprintf(f,"   %g %g %g %g", t[0], t[1], t[2], t[3]);
    t = vdwa_table + 4*i;
    fprintf(f,"   %g %g %g %g", t[0], t[1], t[2], t[3]);
    t = vdwb_table + 4*i;
    fprintf(f,"   %g %g %g %g", t[0], t[1], t[2], t[3]);
    fprintf(f,"\n");
  }
  fclose(f);
#endif

#ifdef NAMD_CUDA
  build_cuda_force_table();
#endif

}

---