text: /*
   * This file is part of the GROMACS molecular simulation package.
   *
   * Copyright (c) 1991-2000, University of Groningen, The Netherlands.
   * Copyright (c) 2001-2004, The GROMACS development team,
   * check out http://www.gromacs.org for more information.
   * Copyright (c) 2012,2013, by the GROMACS development team, led by
   * David van der Spoel, Berk Hess, Erik Lindahl, and including many
   * others, as listed in the AUTHORS file in the top-level source
   * directory and at http://www.gromacs.org.
   *
   * GROMACS is free software; you can redistribute it and/or
   * modify it under the terms of the GNU Lesser General Public License
   * as published by the Free Software Foundation; either version 2.1
   * of the License, or (at your option) any later version.
   *
   * GROMACS is distributed in the hope that it will be useful,
   * but WITHOUT ANY WARRANTY; without even the implied warranty of
   * MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE.  See the GNU
   * Lesser General Public License for more details.
   *
   * You should have received a copy of the GNU Lesser General Public
   * License along with GROMACS; if not, see
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   * Inc., 51 Franklin Street, Fifth Floor, Boston, MA  02110-1301  USA.
   *
   * If you want to redistribute modifications to GROMACS, please
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   * derived work must not be called official GROMACS. Details are found
   * in the README & COPYING files - if they are missing, get the
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   *
   * To help us fund GROMACS development, we humbly ask that you cite
   * the research papers on the package. Check out http://www.gromacs.org.
   */
  #ifdef HAVE_CONFIG_H
  #include <config.h>
  #endif
  
  #include <math.h>
  #include <assert.h>
  #include "physics.h"
  #include "vec.h"
  #include "maths.h"
  #include "txtdump.h"
  #include "bondf.h"
  #include "smalloc.h"
  #include "pbc.h"
  #include "ns.h"
  #include "macros.h"
  #include "names.h"
  #include "gmx_fatal.h"
  #include "mshift.h"
  #include "main.h"
  #include "disre.h"
  #include "orires.h"
  #include "force.h"
  #include "nonbonded.h"
  
  /* Include the SIMD macro file and then check for support */
  #include "gmx_simd_macros.h"
  #if defined GMX_HAVE_SIMD_MACROS && defined GMX_SIMD_HAVE_TRIGONOMETRIC
  #define SIMD_BONDEDS
  #include "gmx_simd_vec.h"
  #endif
  
  /* Find a better place for this? */
  const int cmap_coeff_matrix[] = {
      1, 0, -3,  2, 0, 0,  0,  0, -3,  0,  9, -6,  2,  0, -6,  4,
      0, 0,  0,  0, 0, 0,  0,  0,  3,  0, -9,  6, -2,  0,  6, -4,
      0, 0,  0,  0, 0, 0,  0,  0,  0,  0,  9, -6,  0,  0, -6,  4,
      0, 0,  3, -2, 0, 0,  0,  0,  0,  0, -9,  6,  0,  0,  6, -4,
      0, 0,  0,  0, 1, 0, -3,  2, -2,  0,  6, -4,  1,  0, -3,  2,
      0, 0,  0,  0, 0, 0,  0,  0, -1,  0,  3, -2,  1,  0, -3,  2,
      0, 0,  0,  0, 0, 0,  0,  0,  0,  0, -3,  2,  0,  0,  3, -2,
      0, 0,  0,  0, 0, 0,  3, -2,  0,  0, -6,  4,  0,  0,  3, -2,
      0, 1, -2,  1, 0, 0,  0,  0,  0, -3,  6, -3,  0,  2, -4,  2,
      0, 0,  0,  0, 0, 0,  0,  0,  0,  3, -6,  3,  0, -2,  4, -2,
      0, 0,  0,  0, 0, 0,  0,  0,  0,  0, -3,  3,  0,  0,  2, -2,
      0, 0, -1,  1, 0, 0,  0,  0,  0,  0,  3, -3,  0,  0, -2,  2,
      0, 0,  0,  0, 0, 1, -2,  1,  0, -2,  4, -2,  0,  1, -2,  1,
      0, 0,  0,  0, 0, 0,  0,  0,  0, -1,  2, -1,  0,  1, -2,  1,
      0, 0,  0,  0, 0, 0,  0,  0,  0,  0,  1, -1,  0,  0, -1,  1,
      0, 0,  0,  0, 0, 0, -1,  1,  0,  0,  2, -2,  0,  0, -1,  1
  };
  
  
  
  int glatnr(int *global_atom_index, int i)
  {
      int atnr;
  
      if (global_atom_index == NULL)
      {
          atnr = i + 1;
      }
      else
      {
          atnr = global_atom_index[i] + 1;
      }
  
      return atnr;
  }
  
  static int pbc_rvec_sub(const t_pbc *pbc, const rvec xi, const rvec xj, rvec dx)
  {
      if (pbc)
      {
          return pbc_dx_aiuc(pbc, xi, xj, dx);
      }
      else
      {
          rvec_sub(xi, xj, dx);
          return CENTRAL;
      }
  }
  
  #ifdef SIMD_BONDEDS
  
  /* SIMD PBC data structure, containing 1/boxdiag and the box vectors */
  typedef struct {
      gmx_mm_pr inv_bzz;
      gmx_mm_pr inv_byy;
      gmx_mm_pr inv_bxx;
      gmx_mm_pr bzx;
      gmx_mm_pr bzy;
      gmx_mm_pr bzz;
      gmx_mm_pr byx;
      gmx_mm_pr byy;
      gmx_mm_pr bxx;
  } pbc_simd_t;
  
  /* Set the SIMD pbc data from a normal t_pbc struct */
  static void set_pbc_simd(const t_pbc *pbc, pbc_simd_t *pbc_simd)
  {
      rvec inv_bdiag;
      int  d;
  
      /* Setting inv_bdiag to 0 effectively turns off PBC */
      clear_rvec(inv_bdiag);
      if (pbc != NULL)
      {
          for (d = 0; d < pbc->ndim_ePBC; d++)
          {
              inv_bdiag[d] = 1.0/pbc->box[d][d];
          }
      }
  
      pbc_simd->inv_bzz = gmx_set1_pr(inv_bdiag[ZZ]);
      pbc_simd->inv_byy = gmx_set1_pr(inv_bdiag[YY]);
      pbc_simd->inv_bxx = gmx_set1_pr(inv_bdiag[XX]);
  
      if (pbc != NULL)
      {
          pbc_simd->bzx = gmx_set1_pr(pbc->box[ZZ][XX]);
          pbc_simd->bzy = gmx_set1_pr(pbc->box[ZZ][YY]);
          pbc_simd->bzz = gmx_set1_pr(pbc->box[ZZ][ZZ]);
          pbc_simd->byx = gmx_set1_pr(pbc->box[YY][XX]);
          pbc_simd->byy = gmx_set1_pr(pbc->box[YY][YY]);
          pbc_simd->bxx = gmx_set1_pr(pbc->box[XX][XX]);
      }
      else
      {
          pbc_simd->bzx = gmx_setzero_pr();
          pbc_simd->bzy = gmx_setzero_pr();
          pbc_simd->bzz = gmx_setzero_pr();
          pbc_simd->byx = gmx_setzero_pr();
          pbc_simd->byy = gmx_setzero_pr();
          pbc_simd->bxx = gmx_setzero_pr();
      }
  }
  
  /* Correct distance vector *dx,*dy,*dz for PBC using SIMD */
  static gmx_inline void
  pbc_dx_simd(gmx_mm_pr *dx, gmx_mm_pr *dy, gmx_mm_pr *dz,
              const pbc_simd_t *pbc)
  {
      gmx_mm_pr sh;
  
      sh  = gmx_round_pr(gmx_mul_pr(*dz, pbc->inv_bzz));
      *dx = gmx_nmsub_pr(sh, pbc->bzx, *dx);
      *dy = gmx_nmsub_pr(sh, pbc->bzy, *dy);
      *dz = gmx_nmsub_pr(sh, pbc->bzz, *dz);
  
      sh  = gmx_round_pr(gmx_mul_pr(*dy, pbc->inv_byy));
      *dx = gmx_nmsub_pr(sh, pbc->byx, *dx);
      *dy = gmx_nmsub_pr(sh, pbc->byy, *dy);
  
      sh  = gmx_round_pr(gmx_mul_pr(*dx, pbc->inv_bxx));
      *dx = gmx_nmsub_pr(sh, pbc->bxx, *dx);
  }
  
  #endif /* SIMD_BONDEDS */
  
  /*
   * Morse potential bond by Frank Everdij
   *
   * Three parameters needed:
   *
   * b0 = equilibrium distance in nm
   * be = beta in nm^-1 (actually, it's nu_e*Sqrt(2*pi*pi*mu/D_e))
   * cb = well depth in kJ/mol
   *
   * Note: the potential is referenced to be +cb at infinite separation
   *       and zero at the equilibrium distance!
   */
  
  real morse_bonds(int nbonds,
                   const t_iatom forceatoms[], const t_iparams forceparams[],
                   const rvec x[], rvec f[], rvec fshift[],
                   const t_pbc *pbc, const t_graph *g,
                   real lambda, real *dvdlambda,
                   const t_mdatoms *md, t_fcdata *fcd,
                   int *global_atom_index)
  {
      const real one = 1.0;
      const real two = 2.0;
      real       dr, dr2, temp, omtemp, cbomtemp, fbond, vbond, fij, vtot;
      real       b0, be, cb, b0A, beA, cbA, b0B, beB, cbB, L1;
      rvec       dx;
      int        i, m, ki, type, ai, aj;
      ivec       dt;
  
      vtot = 0.0;
      for (i = 0; (i < nbonds); )
      {
          type = forceatoms[i++];
          ai   = forceatoms[i++];
          aj   = forceatoms[i++];
  
          b0A   = forceparams[type].morse.b0A;
          beA   = forceparams[type].morse.betaA;
          cbA   = forceparams[type].morse.cbA;
  
          b0B   = forceparams[type].morse.b0B;
          beB   = forceparams[type].morse.betaB;
          cbB   = forceparams[type].morse.cbB;
  
          L1 = one-lambda;                            /* 1 */
          b0 = L1*b0A + lambda*b0B;                   /* 3 */
          be = L1*beA + lambda*beB;                   /* 3 */
          cb = L1*cbA + lambda*cbB;                   /* 3 */
  
          ki   = pbc_rvec_sub(pbc, x[ai], x[aj], dx); /*   3          */
          dr2  = iprod(dx, dx);                       /*   5          */
          dr   = dr2*gmx_invsqrt(dr2);                /*  10          */
          temp = exp(-be*(dr-b0));                    /*  12          */
  
          if (temp == one)
          {
              /* bonds are constrainted. This may _not_ include bond constraints if they are lambda dependent */
              *dvdlambda += cbB-cbA;
              continue;
          }
  
          omtemp    = one-temp;                                                                                        /*   1          */
          cbomtemp  = cb*omtemp;                                                                                       /*   1          */
          vbond     = cbomtemp*omtemp;                                                                                 /*   1          */
          fbond     = -two*be*temp*cbomtemp*gmx_invsqrt(dr2);                                                          /*   9          */
          vtot     += vbond;                                                                                           /*   1          */
  
          *dvdlambda += (cbB - cbA) * omtemp * omtemp - (2-2*omtemp)*omtemp * cb * ((b0B-b0A)*be - (beB-beA)*(dr-b0)); /* 15 */
  
          if (g)
          {
              ivec_sub(SHIFT_IVEC(g, ai), SHIFT_IVEC(g, aj), dt);
              ki = IVEC2IS(dt);
          }
  
          for (m = 0; (m < DIM); m++)                    /*  15          */
          {
              fij                 = fbond*dx[m];
              f[ai][m]           += fij;
              f[aj][m]           -= fij;
              fshift[ki][m]      += fij;
              fshift[CENTRAL][m] -= fij;
          }
      }                                         /*  83 TOTAL    */
      return vtot;
  }
  
  real cubic_bonds(int nbonds,
                   const t_iatom forceatoms[], const t_iparams forceparams[],
                   const rvec x[], rvec f[], rvec fshift[],
                   const t_pbc *pbc, const t_graph *g,
                   real lambda, real *dvdlambda,
                   const t_mdatoms *md, t_fcdata *fcd,
                   int *global_atom_index)
  {
      const real three = 3.0;
      const real two   = 2.0;
      real       kb, b0, kcub;
      real       dr, dr2, dist, kdist, kdist2, fbond, vbond, fij, vtot;
      rvec       dx;
      int        i, m, ki, type, ai, aj;
      ivec       dt;
  
      vtot = 0.0;
      for (i = 0; (i < nbonds); )
      {
          type = forceatoms[i++];
          ai   = forceatoms[i++];
          aj   = forceatoms[i++];
  
          b0   = forceparams[type].cubic.b0;
          kb   = forceparams[type].cubic.kb;
          kcub = forceparams[type].cubic.kcub;
  
          ki   = pbc_rvec_sub(pbc, x[ai], x[aj], dx);     /*   3          */
          dr2  = iprod(dx, dx);                           /*   5          */
  
          if (dr2 == 0.0)
          {
              continue;
          }
  
          dr         = dr2*gmx_invsqrt(dr2);                  /*  10          */
          dist       = dr-b0;
          kdist      = kb*dist;
          kdist2     = kdist*dist;
  
          vbond      = kdist2 + kcub*kdist2*dist;
          fbond      = -(two*kdist + three*kdist2*kcub)/dr;
  
          vtot      += vbond;   /* 21 */
  
          if (g)
          {
              ivec_sub(SHIFT_IVEC(g, ai), SHIFT_IVEC(g, aj), dt);
              ki = IVEC2IS(dt);
          }
          for (m = 0; (m < DIM); m++)                    /*  15          */
          {
              fij                 = fbond*dx[m];
              f[ai][m]           += fij;
              f[aj][m]           -= fij;
              fshift[ki][m]      += fij;
              fshift[CENTRAL][m] -= fij;
          }
      }                                         /*  54 TOTAL    */
      return vtot;
  }
  
  real FENE_bonds(int nbonds,
                  const t_iatom forceatoms[], const t_iparams forceparams[],
                  const rvec x[], rvec f[], rvec fshift[],
                  const t_pbc *pbc, const t_graph *g,
                  real lambda, real *dvdlambda,
                  const t_mdatoms *md, t_fcdata *fcd,
                  int *global_atom_index)
  {
      const real half = 0.5;
      const real one  = 1.0;
      real       bm, kb;
      real       dr, dr2, bm2, omdr2obm2, fbond, vbond, fij, vtot;
      rvec       dx;
      int        i, m, ki, type, ai, aj;
      ivec       dt;
  
      vtot = 0.0;
      for (i = 0; (i < nbonds); )
      {
          type = forceatoms[i++];
          ai   = forceatoms[i++];
          aj   = forceatoms[i++];
  
          bm   = forceparams[type].fene.bm;
          kb   = forceparams[type].fene.kb;
  
          ki   = pbc_rvec_sub(pbc, x[ai], x[aj], dx);     /*   3          */
          dr2  = iprod(dx, dx);                           /*   5          */
  
          if (dr2 == 0.0)
          {
              continue;
          }
  
          bm2 = bm*bm;
  
          if (dr2 >= bm2)
          {
              gmx_fatal(FARGS,
                        "r^2 (%f) >= bm^2 (%f) in FENE bond between atoms %d and %d",
                        dr2, bm2,
                        glatnr(global_atom_index, ai),
                        glatnr(global_atom_index, aj));
          }
  
          omdr2obm2  = one - dr2/bm2;
  
          vbond      = -half*kb*bm2*log(omdr2obm2);
          fbond      = -kb/omdr2obm2;
  
          vtot      += vbond;   /* 35 */
  
          if (g)
          {
              ivec_sub(SHIFT_IVEC(g, ai), SHIFT_IVEC(g, aj), dt);
              ki = IVEC2IS(dt);
          }
          for (m = 0; (m < DIM); m++)                    /*  15          */
          {
              fij                 = fbond*dx[m];
              f[ai][m]           += fij;
              f[aj][m]           -= fij;
              fshift[ki][m]      += fij;
              fshift[CENTRAL][m] -= fij;
          }
      }                                         /*  58 TOTAL    */
      return vtot;
  }
  
  real harmonic(real kA, real kB, real xA, real xB, real x, real lambda,
                real *V, real *F)
  {
      const real half = 0.5;
      real       L1, kk, x0, dx, dx2;
      real       v, f, dvdlambda;
  
      L1    = 1.0-lambda;
      kk    = L1*kA+lambda*kB;
      x0    = L1*xA+lambda*xB;
  
      dx    = x-x0;
      dx2   = dx*dx;
  
      f          = -kk*dx;
      v          = half*kk*dx2;
      dvdlambda  = half*(kB-kA)*dx2 + (xA-xB)*kk*dx;
  
      *F    = f;
      *V    = v;
  
      return dvdlambda;
  
      /* That was 19 flops */
  }
  
  
  real bonds(int nbonds,
             const t_iatom forceatoms[], const t_iparams forceparams[],
             const rvec x[], rvec f[], rvec fshift[],
             const t_pbc *pbc, const t_graph *g,
             real lambda, real *dvdlambda,
             const t_mdatoms *md, t_fcdata *fcd,
             int *global_atom_index)
  {
      int  i, m, ki, ai, aj, type;
      real dr, dr2, fbond, vbond, fij, vtot;
      rvec dx;
      ivec dt;
  
      vtot = 0.0;
      for (i = 0; (i < nbonds); )
      {
          type = forceatoms[i++];
          ai   = forceatoms[i++];
          aj   = forceatoms[i++];
  
          ki   = pbc_rvec_sub(pbc, x[ai], x[aj], dx); /*   3      */
          dr2  = iprod(dx, dx);                       /*   5		*/
          dr   = dr2*gmx_invsqrt(dr2);                /*  10		*/
  
          *dvdlambda += harmonic(forceparams[type].harmonic.krA,
                                 forceparams[type].harmonic.krB,
                                 forceparams[type].harmonic.rA,
                                 forceparams[type].harmonic.rB,
                                 dr, lambda, &vbond, &fbond); /*  19  */
  
          if (dr2 == 0.0)
          {
              continue;
          }
  
  
          vtot  += vbond;            /* 1*/
          fbond *= gmx_invsqrt(dr2); /*   6		*/
  #ifdef DEBUG
          if (debug)
          {
              fprintf(debug, "BONDS: dr = %10g  vbond = %10g  fbond = %10g\n",
                      dr, vbond, fbond);
          }
  #endif
          if (g)
          {
              ivec_sub(SHIFT_IVEC(g, ai), SHIFT_IVEC(g, aj), dt);
              ki = IVEC2IS(dt);
          }
          for (m = 0; (m < DIM); m++)     /*  15		*/
          {
              fij                 = fbond*dx[m];
              f[ai][m]           += fij;
              f[aj][m]           -= fij;
              fshift[ki][m]      += fij;
              fshift[CENTRAL][m] -= fij;
          }
      }               /* 59 TOTAL	*/
      return vtot;
  }
  
  real restraint_bonds(int nbonds,
                       const t_iatom forceatoms[], const t_iparams forceparams[],
                       const rvec x[], rvec f[], rvec fshift[],
                       const t_pbc *pbc, const t_graph *g,
                       real lambda, real *dvdlambda,
                       const t_mdatoms *md, t_fcdata *fcd,
                       int *global_atom_index)
  {
      int  i, m, ki, ai, aj, type;
      real dr, dr2, fbond, vbond, fij, vtot;
      real L1;
      real low, dlow, up1, dup1, up2, dup2, k, dk;
      real drh, drh2;
      rvec dx;
      ivec dt;
  
      L1   = 1.0 - lambda;
  
      vtot = 0.0;
      for (i = 0; (i < nbonds); )
      {
          type = forceatoms[i++];
          ai   = forceatoms[i++];
          aj   = forceatoms[i++];
  
          ki   = pbc_rvec_sub(pbc, x[ai], x[aj], dx); /*   3      */
          dr2  = iprod(dx, dx);                       /*   5		*/
          dr   = dr2*gmx_invsqrt(dr2);                /*  10		*/
  
          low  = L1*forceparams[type].restraint.lowA + lambda*forceparams[type].restraint.lowB;
          dlow =   -forceparams[type].restraint.lowA +        forceparams[type].restraint.lowB;
          up1  = L1*forceparams[type].restraint.up1A + lambda*forceparams[type].restraint.up1B;
          dup1 =   -forceparams[type].restraint.up1A +        forceparams[type].restraint.up1B;
          up2  = L1*forceparams[type].restraint.up2A + lambda*forceparams[type].restraint.up2B;
          dup2 =   -forceparams[type].restraint.up2A +        forceparams[type].restraint.up2B;
          k    = L1*forceparams[type].restraint.kA   + lambda*forceparams[type].restraint.kB;
          dk   =   -forceparams[type].restraint.kA   +        forceparams[type].restraint.kB;
          /* 24 */
  
          if (dr < low)
          {
              drh         = dr - low;
              drh2        = drh*drh;
              vbond       = 0.5*k*drh2;
              fbond       = -k*drh;
              *dvdlambda += 0.5*dk*drh2 - k*dlow*drh;
          } /* 11 */
          else if (dr <= up1)
          {
              vbond = 0;
              fbond = 0;
          }
          else if (dr <= up2)
          {
              drh         = dr - up1;
              drh2        = drh*drh;
              vbond       = 0.5*k*drh2;
              fbond       = -k*drh;
              *dvdlambda += 0.5*dk*drh2 - k*dup1*drh;
          } /* 11	*/
          else
          {
              drh         = dr - up2;
              vbond       = k*(up2 - up1)*(0.5*(up2 - up1) + drh);
              fbond       = -k*(up2 - up1);
              *dvdlambda += dk*(up2 - up1)*(0.5*(up2 - up1) + drh)
                  + k*(dup2 - dup1)*(up2 - up1 + drh)
                  - k*(up2 - up1)*dup2;
          }
  
          if (dr2 == 0.0)
          {
              continue;
          }
  
          vtot  += vbond;            /* 1*/
          fbond *= gmx_invsqrt(dr2); /*   6		*/
  #ifdef DEBUG
          if (debug)
          {
              fprintf(debug, "BONDS: dr = %10g  vbond = %10g  fbond = %10g\n",
                      dr, vbond, fbond);
          }
  #endif
          if (g)
          {
              ivec_sub(SHIFT_IVEC(g, ai), SHIFT_IVEC(g, aj), dt);
              ki = IVEC2IS(dt);
          }
          for (m = 0; (m < DIM); m++)             /*  15		*/
          {
              fij                 = fbond*dx[m];
              f[ai][m]           += fij;
              f[aj][m]           -= fij;
              fshift[ki][m]      += fij;
              fshift[CENTRAL][m] -= fij;
          }
      }                   /* 59 TOTAL	*/
  
      return vtot;
  }
  
  real polarize(int nbonds,
                const t_iatom forceatoms[], const t_iparams forceparams[],
                const rvec x[], rvec f[], rvec fshift[],
                const t_pbc *pbc, const t_graph *g,
                real lambda, real *dvdlambda,
                const t_mdatoms *md, t_fcdata *fcd,
                int *global_atom_index)
  {
      int  i, m, ki, ai, aj, type;
      real dr, dr2, fbond, vbond, fij, vtot, ksh;
      rvec dx;
      ivec dt;
  
      vtot = 0.0;
      for (i = 0; (i < nbonds); )
      {
          type = forceatoms[i++];
          ai   = forceatoms[i++];
          aj   = forceatoms[i++];
          ksh  = sqr(md->chargeA[aj])*ONE_4PI_EPS0/forceparams[type].polarize.alpha;
          if (debug)
          {
              fprintf(debug, "POL: local ai = %d aj = %d ksh = %.3f\n", ai, aj, ksh);
          }
  
          ki   = pbc_rvec_sub(pbc, x[ai], x[aj], dx);                         /*   3      */
          dr2  = iprod(dx, dx);                                               /*   5		*/
          dr   = dr2*gmx_invsqrt(dr2);                                        /*  10		*/
  
          *dvdlambda += harmonic(ksh, ksh, 0, 0, dr, lambda, &vbond, &fbond); /*  19  */
  
          if (dr2 == 0.0)
          {
              continue;
          }
  
          vtot  += vbond;            /* 1*/
          fbond *= gmx_invsqrt(dr2); /*   6		*/
  
          if (g)
          {
              ivec_sub(SHIFT_IVEC(g, ai), SHIFT_IVEC(g, aj), dt);
              ki = IVEC2IS(dt);
          }
          for (m = 0; (m < DIM); m++)     /*  15		*/
          {
              fij                 = fbond*dx[m];
              f[ai][m]           += fij;
              f[aj][m]           -= fij;
              fshift[ki][m]      += fij;
              fshift[CENTRAL][m] -= fij;
          }
      }               /* 59 TOTAL	*/
      return vtot;
  }
  
  real anharm_polarize(int nbonds,
                       const t_iatom forceatoms[], const t_iparams forceparams[],
                       const rvec x[], rvec f[], rvec fshift[],
                       const t_pbc *pbc, const t_graph *g,
                       real lambda, real *dvdlambda,
                       const t_mdatoms *md, t_fcdata *fcd,
                       int *global_atom_index)
  {
      int  i, m, ki, ai, aj, type;
      real dr, dr2, fbond, vbond, fij, vtot, ksh, khyp, drcut, ddr, ddr3;
      rvec dx;
      ivec dt;
  
      vtot = 0.0;
      for (i = 0; (i < nbonds); )
      {
          type  = forceatoms[i++];
          ai    = forceatoms[i++];
          aj    = forceatoms[i++];
          ksh   = sqr(md->chargeA[aj])*ONE_4PI_EPS0/forceparams[type].anharm_polarize.alpha; /* 7*/
          khyp  = forceparams[type].anharm_polarize.khyp;
          drcut = forceparams[type].anharm_polarize.drcut;
          if (debug)
          {
              fprintf(debug, "POL: local ai = %d aj = %d ksh = %.3f\n", ai, aj, ksh);
          }
  
          ki   = pbc_rvec_sub(pbc, x[ai], x[aj], dx);                         /*   3      */
          dr2  = iprod(dx, dx);                                               /*   5		*/
          dr   = dr2*gmx_invsqrt(dr2);                                        /*  10		*/
  
          *dvdlambda += harmonic(ksh, ksh, 0, 0, dr, lambda, &vbond, &fbond); /*  19  */
  
          if (dr2 == 0.0)
          {
              continue;
          }
  
          if (dr > drcut)
          {
              ddr    = dr-drcut;
              ddr3   = ddr*ddr*ddr;
              vbond += khyp*ddr*ddr3;
              fbond -= 4*khyp*ddr3;
          }
          fbond *= gmx_invsqrt(dr2); /*   6		*/
          vtot  += vbond;            /* 1*/
  
          if (g)
          {
              ivec_sub(SHIFT_IVEC(g, ai), SHIFT_IVEC(g, aj), dt);
              ki = IVEC2IS(dt);
          }
          for (m = 0; (m < DIM); m++)     /*  15		*/
          {
              fij                 = fbond*dx[m];
              f[ai][m]           += fij;
              f[aj][m]           -= fij;
              fshift[ki][m]      += fij;
              fshift[CENTRAL][m] -= fij;
          }
      }               /* 72 TOTAL	*/
      return vtot;
  }
  
  real water_pol(int nbonds,
                 const t_iatom forceatoms[], const t_iparams forceparams[],
                 const rvec x[], rvec f[], rvec fshift[],
                 const t_pbc *pbc, const t_graph *g,
                 real lambda, real *dvdlambda,
                 const t_mdatoms *md, t_fcdata *fcd,
                 int *global_atom_index)
  {
      /* This routine implements anisotropic polarizibility for water, through
       * a shell connected to a dummy with spring constant that differ in the
       * three spatial dimensions in the molecular frame.
       */
      int  i, m, aO, aH1, aH2, aD, aS, type, type0;
      rvec dOH1, dOH2, dHH, dOD, dDS, nW, kk, dx, kdx, proj;
  #ifdef DEBUG
      rvec df;
  #endif
      real vtot, fij, r_HH, r_OD, r_nW, tx, ty, tz, qS;
  
      vtot = 0.0;
      if (nbonds > 0)
      {
          type0  = forceatoms[0];
          aS     = forceatoms[5];
          qS     = md->chargeA[aS];
          kk[XX] = sqr(qS)*ONE_4PI_EPS0/forceparams[type0].wpol.al_x;
          kk[YY] = sqr(qS)*ONE_4PI_EPS0/forceparams[type0].wpol.al_y;
          kk[ZZ] = sqr(qS)*ONE_4PI_EPS0/forceparams[type0].wpol.al_z;
          r_HH   = 1.0/forceparams[type0].wpol.rHH;
          r_OD   = 1.0/forceparams[type0].wpol.rOD;
          if (debug)
          {
              fprintf(debug, "WPOL: qS  = %10.5f aS = %5d\n", qS, aS);
              fprintf(debug, "WPOL: kk  = %10.3f        %10.3f        %10.3f\n",
                      kk[XX], kk[YY], kk[ZZ]);
              fprintf(debug, "WPOL: rOH = %10.3f  rHH = %10.3f  rOD = %10.3f\n",
                      forceparams[type0].wpol.rOH,
                      forceparams[type0].wpol.rHH,
                      forceparams[type0].wpol.rOD);
          }
          for (i = 0; (i < nbonds); i += 6)
          {
              type = forceatoms[i];
              if (type != type0)
              {
                  gmx_fatal(FARGS, "Sorry, type = %d, type0 = %d, file = %s, line = %d",
                            type, type0, __FILE__, __LINE__);
              }
              aO   = forceatoms[i+1];
              aH1  = forceatoms[i+2];
              aH2  = forceatoms[i+3];
              aD   = forceatoms[i+4];
              aS   = forceatoms[i+5];
  
              /* Compute vectors describing the water frame */
              rvec_sub(x[aH1], x[aO], dOH1);
              rvec_sub(x[aH2], x[aO], dOH2);
              rvec_sub(x[aH2], x[aH1], dHH);
              rvec_sub(x[aD], x[aO], dOD);
              rvec_sub(x[aS], x[aD], dDS);
              cprod(dOH1, dOH2, nW);
  
              /* Compute inverse length of normal vector
               * (this one could be precomputed, but I'm too lazy now)
               */
              r_nW = gmx_invsqrt(iprod(nW, nW));
              /* This is for precision, but does not make a big difference,
               * it can go later.
               */
              r_OD = gmx_invsqrt(iprod(dOD, dOD));
  
              /* Normalize the vectors in the water frame */
              svmul(r_nW, nW, nW);
              svmul(r_HH, dHH, dHH);
              svmul(r_OD, dOD, dOD);
  
              /* Compute displacement of shell along components of the vector */
              dx[ZZ] = iprod(dDS, dOD);
              /* Compute projection on the XY plane: dDS - dx[ZZ]*dOD */
              for (m = 0; (m < DIM); m++)
              {
                  proj[m] = dDS[m]-dx[ZZ]*dOD[m];
              }
  
              /*dx[XX] = iprod(dDS,nW);
                 dx[YY] = iprod(dDS,dHH);*/
              dx[XX] = iprod(proj, nW);
              for (m = 0; (m < DIM); m++)
              {
                  proj[m] -= dx[XX]*nW[m];
              }
              dx[YY] = iprod(proj, dHH);
              /*#define DEBUG*/
  #ifdef DEBUG
              if (debug)
              {
                  fprintf(debug, "WPOL: dx2=%10g  dy2=%10g  dz2=%10g  sum=%10g  dDS^2=%10g\n",
                          sqr(dx[XX]), sqr(dx[YY]), sqr(dx[ZZ]), iprod(dx, dx), iprod(dDS, dDS));
                  fprintf(debug, "WPOL: dHH=(%10g,%10g,%10g)\n", dHH[XX], dHH[YY], dHH[ZZ]);
                  fprintf(debug, "WPOL: dOD=(%10g,%10g,%10g), 1/r_OD = %10g\n",
                          dOD[XX], dOD[YY], dOD[ZZ], 1/r_OD);
                  fprintf(debug, "WPOL: nW =(%10g,%10g,%10g), 1/r_nW = %10g\n",
                          nW[XX], nW[YY], nW[ZZ], 1/r_nW);
                  fprintf(debug, "WPOL: dx  =%10g, dy  =%10g, dz  =%10g\n",
                          dx[XX], dx[YY], dx[ZZ]);
                  fprintf(debug, "WPOL: dDSx=%10g, dDSy=%10g, dDSz=%10g\n",
                          dDS[XX], dDS[YY], dDS[ZZ]);
              }
  #endif
              /* Now compute the forces and energy */
              kdx[XX] = kk[XX]*dx[XX];
              kdx[YY] = kk[YY]*dx[YY];
              kdx[ZZ] = kk[ZZ]*dx[ZZ];
              vtot   += iprod(dx, kdx);
              for (m = 0; (m < DIM); m++)
              {
                  /* This is a tensor operation but written out for speed */
                  tx        =  nW[m]*kdx[XX];
                  ty        = dHH[m]*kdx[YY];
                  tz        = dOD[m]*kdx[ZZ];
                  fij       = -tx-ty-tz;
  #ifdef DEBUG
                  df[m] = fij;
  #endif
                  f[aS][m] += fij;
                  f[aD][m] -= fij;
              }
  #ifdef DEBUG
              if (debug)
              {
                  fprintf(debug, "WPOL: vwpol=%g\n", 0.5*iprod(dx, kdx));
                  fprintf(debug, "WPOL: df = (%10g, %10g, %10g)\n", df[XX], df[YY], df[ZZ]);
              }
  #endif
          }
      }
      return 0.5*vtot;
  }
  
  static real do_1_thole(const rvec xi, const rvec xj, rvec fi, rvec fj,
                         const t_pbc *pbc, real qq,
                         rvec fshift[], real afac)
  {
      rvec r12;
      real r12sq, r12_1, r12n, r12bar, v0, v1, fscal, ebar, fff;
      int  m, t;
  
      t      = pbc_rvec_sub(pbc, xi, xj, r12);                      /*  3 */
  
      r12sq  = iprod(r12, r12);                                     /*  5 */
      r12_1  = gmx_invsqrt(r12sq);                                  /*  5 */
      r12bar = afac/r12_1;                                          /*  5 */
      v0     = qq*ONE_4PI_EPS0*r12_1;                               /*  2 */
      ebar   = exp(-r12bar);                                        /*  5 */
      v1     = (1-(1+0.5*r12bar)*ebar);                             /*  4 */
      fscal  = ((v0*r12_1)*v1 - v0*0.5*afac*ebar*(r12bar+1))*r12_1; /* 9 */
      if (debug)
      {
          fprintf(debug, "THOLE: v0 = %.3f v1 = %.3f r12= % .3f r12bar = %.3f fscal = %.3f  ebar = %.3f\n", v0, v1, 1/r12_1, r12bar, fscal, ebar);
      }
  
      for (m = 0; (m < DIM); m++)
      {
          fff                 = fscal*r12[m];
          fi[m]              += fff;
          fj[m]              -= fff;
          fshift[t][m]       += fff;
          fshift[CENTRAL][m] -= fff;
      }             /* 15 */
  
      return v0*v1; /* 1 */
      /* 54 */
  }
  
  real thole_pol(int nbonds,
                 const t_iatom forceatoms[], const t_iparams forceparams[],
                 const rvec x[], rvec f[], rvec fshift[],
                 const t_pbc *pbc, const t_graph *g,
                 real lambda, real *dvdlambda,
                 const t_mdatoms *md, t_fcdata *fcd,
                 int *global_atom_index)
  {
      /* Interaction between two pairs of particles with opposite charge */
      int  i, type, a1, da1, a2, da2;
      real q1, q2, qq, a, al1, al2, afac;
      real V = 0;
  
      for (i = 0; (i < nbonds); )
      {
          type  = forceatoms[i++];
          a1    = forceatoms[i++];
          da1   = forceatoms[i++];
          a2    = forceatoms[i++];
          da2   = forceatoms[i++];
          q1    = md->chargeA[da1];
          q2    = md->chargeA[da2];
          a     = forceparams[type].thole.a;
          al1   = forceparams[type].thole.alpha1;
          al2   = forceparams[type].thole.alpha2;
          qq    = q1*q2;
          afac  = a*pow(al1*al2, -1.0/6.0);
          V    += do_1_thole(x[a1], x[a2], f[a1], f[a2], pbc, qq, fshift, afac);
          V    += do_1_thole(x[da1], x[a2], f[da1], f[a2], pbc, -qq, fshift, afac);
          V    += do_1_thole(x[a1], x[da2], f[a1], f[da2], pbc, -qq, fshift, afac);
          V    += do_1_thole(x[da1], x[da2], f[da1], f[da2], pbc, qq, fshift, afac);
      }
      /* 290 flops */
      return V;
  }
  
  real bond_angle(const rvec xi, const rvec xj, const rvec xk, const t_pbc *pbc,
                  rvec r_ij, rvec r_kj, real *costh,
                  int *t1, int *t2)
  /* Return value is the angle between the bonds i-j and j-k */
  {
      /* 41 FLOPS */
      real th;
  
      *t1 = pbc_rvec_sub(pbc, xi, xj, r_ij); /*  3		*/
      *t2 = pbc_rvec_sub(pbc, xk, xj, r_kj); /*  3		*/
  
      *costh = cos_angle(r_ij, r_kj);        /* 25		*/
      th     = acos(*costh);                 /* 10		*/
      /* 41 TOTAL	*/
      return th;
  }
  
  real angles(int nbonds,
              const t_iatom forceatoms[], const t_iparams forceparams[],
              const rvec x[], rvec f[], rvec fshift[],
              const t_pbc *pbc, const t_graph *g,
              real lambda, real *dvdlambda,
              const t_mdatoms *md, t_fcdata *fcd,
              int *global_atom_index)
  {
      int  i, ai, aj, ak, t1, t2, type;
      rvec r_ij, r_kj;
      real cos_theta, cos_theta2, theta, dVdt, va, vtot;
      ivec jt, dt_ij, dt_kj;
  
      vtot = 0.0;
      for (i = 0; i < nbonds; )
      {
          type = forceatoms[i++];
          ai   = forceatoms[i++];
          aj   = forceatoms[i++];
          ak   = forceatoms[i++];
  
          theta  = bond_angle(x[ai], x[aj], x[ak], pbc,
                              r_ij, r_kj, &cos_theta, &t1, &t2);  /*  41		*/
  
          *dvdlambda += harmonic(forceparams[type].harmonic.krA,
                                 forceparams[type].harmonic.krB,
                                 forceparams[type].harmonic.rA*DEG2RAD,
                                 forceparams[type].harmonic.rB*DEG2RAD,
                                 theta, lambda, &va, &dVdt);  /*  21  */
          vtot += va;
  
          cos_theta2 = sqr(cos_theta);
          if (cos_theta2 < 1)
          {
              int  m;
              real st, sth;
              real cik, cii, ckk;
              real nrkj2, nrij2;
              real nrkj_1, nrij_1;
              rvec f_i, f_j, f_k;
  
              st  = dVdt*gmx_invsqrt(1 - cos_theta2); /*  12		*/
              sth = st*cos_theta;                     /*   1		*/
  #ifdef DEBUG
              if (debug)
              {
                  fprintf(debug, "ANGLES: theta = %10g  vth = %10g  dV/dtheta = %10g\n",
                          theta*RAD2DEG, va, dVdt);
              }
  #endif
              nrij2 = iprod(r_ij, r_ij);      /*   5		*/
              nrkj2 = iprod(r_kj, r_kj);      /*   5		*/
  
              nrij_1 = gmx_invsqrt(nrij2);    /*  10		*/
              nrkj_1 = gmx_invsqrt(nrkj2);    /*  10		*/
  
              cik = st*nrij_1*nrkj_1;         /*   2		*/
              cii = sth*nrij_1*nrij_1;        /*   2		*/
              ckk = sth*nrkj_1*nrkj_1;        /*   2		*/
  
              for (m = 0; m < DIM; m++)
              {           /*  39		*/
                  f_i[m]    = -(cik*r_kj[m] - cii*r_ij[m]);
                  f_k[m]    = -(cik*r_ij[m] - ckk*r_kj[m]);
                  f_j[m]    = -f_i[m] - f_k[m];
                  f[ai][m] += f_i[m];
                  f[aj][m] += f_j[m];
                  f[ak][m] += f_k[m];
              }
              if (g != NULL)
              {
                  copy_ivec(SHIFT_IVEC(g, aj), jt);
  
                  ivec_sub(SHIFT_IVEC(g, ai), jt, dt_ij);
                  ivec_sub(SHIFT_IVEC(g, ak), jt, dt_kj);
                  t1 = IVEC2IS(dt_ij);
                  t2 = IVEC2IS(dt_kj);
              }
              rvec_inc(fshift[t1], f_i);
              rvec_inc(fshift[CENTRAL], f_j);
              rvec_inc(fshift[t2], f_k);
          }                                           /* 161 TOTAL	*/
      }
  
      return vtot;
  }
  
  #ifdef SIMD_BONDEDS
  
  /* As angles, but using SIMD to calculate many dihedrals at once.
   * This routines does not calculate energies and shift forces.
   */
  static gmx_inline void
  angles_noener_simd(int nbonds,
                     const t_iatom forceatoms[], const t_iparams forceparams[],
                     const rvec x[], rvec f[],
                     const t_pbc *pbc, const t_graph *g,
                     real lambda,
                     const t_mdatoms *md, t_fcdata *fcd,
                     int *global_atom_index)
  {
  #define UNROLL GMX_SIMD_WIDTH_HERE
      const int      nfa1 = 4;
      int            i, iu, s, m;
      int            type, ai[UNROLL], aj[UNROLL], ak[UNROLL];
      real           coeff_array[2*UNROLL+UNROLL], *coeff;
      real           dr_array[2*DIM*UNROLL+UNROLL], *dr;
      real           f_buf_array[6*UNROLL+UNROLL], *f_buf;
      gmx_mm_pr      k_S, theta0_S;
      gmx_mm_pr      rijx_S, rijy_S, rijz_S;
      gmx_mm_pr      rkjx_S, rkjy_S, rkjz_S;
      gmx_mm_pr      one_S;
      gmx_mm_pr      min_one_plus_eps_S;
      gmx_mm_pr      rij_rkj_S;
      gmx_mm_pr      nrij2_S, nrij_1_S;
      gmx_mm_pr      nrkj2_S, nrkj_1_S;
      gmx_mm_pr      cos_S, invsin_S;
      gmx_mm_pr      theta_S;
      gmx_mm_pr      st_S, sth_S;
      gmx_mm_pr      cik_S, cii_S, ckk_S;
      gmx_mm_pr      f_ix_S, f_iy_S, f_iz_S;
      gmx_mm_pr      f_kx_S, f_ky_S, f_kz_S;
      pbc_simd_t     pbc_simd;
  
      /* Ensure register memory alignment */
      coeff = gmx_simd_align_real(coeff_array);
      dr    = gmx_simd_align_real(dr_array);
      f_buf = gmx_simd_align_real(f_buf_array);
  
      set_pbc_simd(pbc,&pbc_simd);
  
      one_S = gmx_set1_pr(1.0);
  
      /* The smallest number > -1 */
      min_one_plus_eps_S = gmx_set1_pr(-1.0 + 2*GMX_REAL_EPS);
  
      /* nbonds is the number of angles times nfa1, here we step UNROLL angles */
      for (i = 0; (i < nbonds); i += UNROLL*nfa1)
      {
          /* Collect atoms for UNROLL angles.
           * iu indexes into forceatoms, we should not let iu go beyond nbonds.
           */
          iu = i;
          for (s = 0; s < UNROLL; s++)
          {
              type  = forceatoms[iu];
              ai[s] = forceatoms[iu+1];
              aj[s] = forceatoms[iu+2];
              ak[s] = forceatoms[iu+3];
  
              coeff[s]        = forceparams[type].harmonic.krA;
              coeff[UNROLL+s] = forceparams[type].harmonic.rA*DEG2RAD;
  
              /* If you can't use pbc_dx_simd below for PBC, e.g. because
               * you can't round in SIMD, use pbc_rvec_sub here.
               */
              /* Store the non PBC corrected distances packed and aligned */
              for (m = 0; m < DIM; m++)
              {
                  dr[s +      m *UNROLL] = x[ai[s]][m] - x[aj[s]][m];
                  dr[s + (DIM+m)*UNROLL] = x[ak[s]][m] - x[aj[s]][m];
              }
  
              /* At the end fill the arrays with identical entries */
              if (iu + nfa1 < nbonds)
              {
                  iu += nfa1;
              }
          }
  
          k_S       = gmx_load_pr(coeff);
          theta0_S  = gmx_load_pr(coeff+UNROLL);
  
          rijx_S    = gmx_load_pr(dr + 0*UNROLL);
          rijy_S    = gmx_load_pr(dr + 1*UNROLL);
          rijz_S    = gmx_load_pr(dr + 2*UNROLL);
          rkjx_S    = gmx_load_pr(dr + 3*UNROLL);
          rkjy_S    = gmx_load_pr(dr + 4*UNROLL);
          rkjz_S    = gmx_load_pr(dr + 5*UNROLL);
  
          pbc_dx_simd(&rijx_S, &rijy_S, &rijz_S, &pbc_simd);
          pbc_dx_simd(&rkjx_S, &rkjy_S, &rkjz_S, &pbc_simd);
  
          rij_rkj_S = gmx_iprod_pr(rijx_S, rijy_S, rijz_S,
                                   rkjx_S, rkjy_S, rkjz_S);
  
          nrij2_S   = gmx_norm2_pr(rijx_S, rijy_S, rijz_S);
          nrkj2_S   = gmx_norm2_pr(rkjx_S, rkjy_S, rkjz_S);
  
          nrij_1_S  = gmx_invsqrt_pr(nrij2_S);
          nrkj_1_S  = gmx_invsqrt_pr(nrkj2_S);
  
          cos_S     = gmx_mul_pr(rij_rkj_S, gmx_mul_pr(nrij_1_S, nrkj_1_S));
  
          /* To allow for 180 degrees, we take the max of cos and -1 + 1bit,
           * so we can safely get the 1/sin from 1/sqrt(1 - cos^2).
           * This also ensures that rounding errors would cause the argument
           * of gmx_acos_pr to be < -1.
           * Note that we do not take precautions for cos(0)=1, so the outer
           * atoms in an angle should not be on top of each other.
           */
          cos_S     = gmx_max_pr(cos_S, min_one_plus_eps_S);
  
          theta_S   = gmx_acos_pr(cos_S);
  
          invsin_S  = gmx_invsqrt_pr(gmx_sub_pr(one_S, gmx_mul_pr(cos_S, cos_S)));
  
          st_S      = gmx_mul_pr(gmx_mul_pr(k_S, gmx_sub_pr(theta0_S, theta_S)),
                                 invsin_S);
          sth_S     = gmx_mul_pr(st_S, cos_S);
  
          cik_S     = gmx_mul_pr(st_S,  gmx_mul_pr(nrij_1_S, nrkj_1_S));
          cii_S     = gmx_mul_pr(sth_S, gmx_mul_pr(nrij_1_S, nrij_1_S));
          ckk_S     = gmx_mul_pr(sth_S, gmx_mul_pr(nrkj_1_S, nrkj_1_S));
  
          f_ix_S    = gmx_mul_pr(cii_S, rijx_S);
          f_ix_S    = gmx_nmsub_pr(cik_S, rkjx_S, f_ix_S);
          f_iy_S    = gmx_mul_pr(cii_S, rijy_S);
          f_iy_S    = gmx_nmsub_pr(cik_S, rkjy_S, f_iy_S);
          f_iz_S    = gmx_mul_pr(cii_S, rijz_S);
          f_iz_S    = gmx_nmsub_pr(cik_S, rkjz_S, f_iz_S);
          f_kx_S    = gmx_mul_pr(ckk_S, rkjx_S);
          f_kx_S    = gmx_nmsub_pr(cik_S, rijx_S, f_kx_S);
          f_ky_S    = gmx_mul_pr(ckk_S, rkjy_S);
          f_ky_S    = gmx_nmsub_pr(cik_S, rijy_S, f_ky_S);
          f_kz_S    = gmx_mul_pr(ckk_S, rkjz_S);
          f_kz_S    = gmx_nmsub_pr(cik_S, rijz_S, f_kz_S);
  
          gmx_store_pr(f_buf + 0*UNROLL, f_ix_S);
          gmx_store_pr(f_buf + 1*UNROLL, f_iy_S);
          gmx_store_pr(f_buf + 2*UNROLL, f_iz_S);
          gmx_store_pr(f_buf + 3*UNROLL, f_kx_S);
          gmx_store_pr(f_buf + 4*UNROLL, f_ky_S);
          gmx_store_pr(f_buf + 5*UNROLL, f_kz_S);
  
          iu = i;
          s  = 0;
          do
          {
              for (m = 0; m < DIM; m++)
              {
                  f[ai[s]][m] += f_buf[s + m*UNROLL];
                  f[aj[s]][m] -= f_buf[s + m*UNROLL] + f_buf[s + (DIM+m)*UNROLL];
                  f[ak[s]][m] += f_buf[s + (DIM+m)*UNROLL];
              }
              s++;
              iu += nfa1;
          }
          while (s < UNROLL && iu < nbonds);
      }
  #undef UNROLL
  }
  
  #endif /* SIMD_BONDEDS */
  
  real linear_angles(int nbonds,
                     const t_iatom forceatoms[], const t_iparams forceparams[],
                     const rvec x[], rvec f[], rvec fshift[],
                     const t_pbc *pbc, const t_graph *g,
                     real lambda, real *dvdlambda,
                     const t_mdatoms *md, t_fcdata *fcd,
                     int *global_atom_index)
  {
      int  i, m, ai, aj, ak, t1, t2, type;
      rvec f_i, f_j, f_k;
      real L1, kA, kB, aA, aB, dr, dr2, va, vtot, a, b, klin;
      ivec jt, dt_ij, dt_kj;
      rvec r_ij, r_kj, r_ik, dx;
  
      L1   = 1-lambda;
      vtot = 0.0;
      for (i = 0; (i < nbonds); )
      {
          type = forceatoms[i++];
          ai   = forceatoms[i++];
          aj   = forceatoms[i++];
          ak   = forceatoms[i++];
  
          kA   = forceparams[type].linangle.klinA;
          kB   = forceparams[type].linangle.klinB;
          klin = L1*kA + lambda*kB;
  
          aA   = forceparams[type].linangle.aA;
          aB   = forceparams[type].linangle.aB;
          a    = L1*aA+lambda*aB;
          b    = 1-a;
  
          t1 = pbc_rvec_sub(pbc, x[ai], x[aj], r_ij);
          t2 = pbc_rvec_sub(pbc, x[ak], x[aj], r_kj);
          rvec_sub(r_ij, r_kj, r_ik);
  
          dr2 = 0;
          for (m = 0; (m < DIM); m++)
          {
              dr        = -a * r_ij[m] - b * r_kj[m];
              dr2      += dr*dr;
              dx[m]     = dr;
              f_i[m]    = a*klin*dr;
              f_k[m]    = b*klin*dr;
              f_j[m]    = -(f_i[m]+f_k[m]);
              f[ai][m] += f_i[m];
              f[aj][m] += f_j[m];
              f[ak][m] += f_k[m];
          }
          va          = 0.5*klin*dr2;
          *dvdlambda += 0.5*(kB-kA)*dr2 + klin*(aB-aA)*iprod(dx, r_ik);
  
          vtot += va;
  
          if (g)
          {
              copy_ivec(SHIFT_IVEC(g, aj), jt);
  
              ivec_sub(SHIFT_IVEC(g, ai), jt, dt_ij);
              ivec_sub(SHIFT_IVEC(g, ak), jt, dt_kj);
              t1 = IVEC2IS(dt_ij);
              t2 = IVEC2IS(dt_kj);
          }
          rvec_inc(fshift[t1], f_i);
          rvec_inc(fshift[CENTRAL], f_j);
          rvec_inc(fshift[t2], f_k);
      }                                         /* 57 TOTAL	*/
      return vtot;
  }
  
  real urey_bradley(int nbonds,
                    const t_iatom forceatoms[], const t_iparams forceparams[],
                    const rvec x[], rvec f[], rvec fshift[],
                    const t_pbc *pbc, const t_graph *g,
                    real lambda, real *dvdlambda,
                    const t_mdatoms *md, t_fcdata *fcd,
                    int *global_atom_index)
  {
      int  i, m, ai, aj, ak, t1, t2, type, ki;
      rvec r_ij, r_kj, r_ik;
      real cos_theta, cos_theta2, theta;
      real dVdt, va, vtot, dr, dr2, vbond, fbond, fik;
      real kthA, th0A, kUBA, r13A, kthB, th0B, kUBB, r13B;
      ivec jt, dt_ij, dt_kj, dt_ik;
  
      vtot = 0.0;
      for (i = 0; (i < nbonds); )
      {
          type  = forceatoms[i++];
          ai    = forceatoms[i++];
          aj    = forceatoms[i++];
          ak    = forceatoms[i++];
          th0A  = forceparams[type].u_b.thetaA*DEG2RAD;
          kthA  = forceparams[type].u_b.kthetaA;
          r13A  = forceparams[type].u_b.r13A;
          kUBA  = forceparams[type].u_b.kUBA;
          th0B  = forceparams[type].u_b.thetaB*DEG2RAD;
          kthB  = forceparams[type].u_b.kthetaB;
          r13B  = forceparams[type].u_b.r13B;
          kUBB  = forceparams[type].u_b.kUBB;
  
          theta  = bond_angle(x[ai], x[aj], x[ak], pbc,
                              r_ij, r_kj, &cos_theta, &t1, &t2);                     /*  41		*/
  
          *dvdlambda += harmonic(kthA, kthB, th0A, th0B, theta, lambda, &va, &dVdt); /*  21  */
          vtot       += va;
  
          ki   = pbc_rvec_sub(pbc, x[ai], x[ak], r_ik);                               /*   3      */
          dr2  = iprod(r_ik, r_ik);                                                   /*   5		*/
          dr   = dr2*gmx_invsqrt(dr2);                                                /*  10		*/
  
          *dvdlambda += harmonic(kUBA, kUBB, r13A, r13B, dr, lambda, &vbond, &fbond); /*  19  */
  
          cos_theta2 = sqr(cos_theta);                                                /*   1		*/
          if (cos_theta2 < 1)
          {
              real st, sth;
              real cik, cii, ckk;
              real nrkj2, nrij2;
              rvec f_i, f_j, f_k;
  
              st  = dVdt*gmx_invsqrt(1 - cos_theta2); /*  12		*/
              sth = st*cos_theta;                     /*   1		*/
  #ifdef DEBUG
              if (debug)
              {
                  fprintf(debug, "ANGLES: theta = %10g  vth = %10g  dV/dtheta = %10g\n",
                          theta*RAD2DEG, va, dVdt);
              }
  #endif
              nrkj2 = iprod(r_kj, r_kj);  /*   5		*/
              nrij2 = iprod(r_ij, r_ij);
  
              cik = st*gmx_invsqrt(nrkj2*nrij2); /*  12		*/
              cii = sth/nrij2;                   /*  10		*/
              ckk = sth/nrkj2;                   /*  10		*/
  
              for (m = 0; (m < DIM); m++)        /*  39		*/
              {
                  f_i[m]    = -(cik*r_kj[m]-cii*r_ij[m]);
                  f_k[m]    = -(cik*r_ij[m]-ckk*r_kj[m]);
                  f_j[m]    = -f_i[m]-f_k[m];
                  f[ai][m] += f_i[m];
                  f[aj][m] += f_j[m];
                  f[ak][m] += f_k[m];
              }
              if (g)
              {
                  copy_ivec(SHIFT_IVEC(g, aj), jt);
  
                  ivec_sub(SHIFT_IVEC(g, ai), jt, dt_ij);
                  ivec_sub(SHIFT_IVEC(g, ak), jt, dt_kj);
                  t1 = IVEC2IS(dt_ij);
                  t2 = IVEC2IS(dt_kj);
              }
              rvec_inc(fshift[t1], f_i);
              rvec_inc(fshift[CENTRAL], f_j);
              rvec_inc(fshift[t2], f_k);
          }                                       /* 161 TOTAL	*/
          /* Time for the bond calculations */
          if (dr2 == 0.0)
          {
              continue;
          }
  
          vtot  += vbond;            /* 1*/
          fbond *= gmx_invsqrt(dr2); /*   6		*/
  
          if (g)
          {
              ivec_sub(SHIFT_IVEC(g, ai), SHIFT_IVEC(g, ak), dt_ik);
              ki = IVEC2IS(dt_ik);
          }
          for (m = 0; (m < DIM); m++)     /*  15		*/
          {
              fik                 = fbond*r_ik[m];
              f[ai][m]           += fik;
              f[ak][m]           -= fik;
              fshift[ki][m]      += fik;
              fshift[CENTRAL][m] -= fik;
          }
      }
      return vtot;
  }
  
  real quartic_angles(int nbonds,
                      const t_iatom forceatoms[], const t_iparams forceparams[],
                      const rvec x[], rvec f[], rvec fshift[],
                      const t_pbc *pbc, const t_graph *g,
                      real lambda, real *dvdlambda,
                      const t_mdatoms *md, t_fcdata *fcd,
                      int *global_atom_index)
  {
      int  i, j, ai, aj, ak, t1, t2, type;
      rvec r_ij, r_kj;
      real cos_theta, cos_theta2, theta, dt, dVdt, va, dtp, c, vtot;
      ivec jt, dt_ij, dt_kj;
  
      vtot = 0.0;
      for (i = 0; (i < nbonds); )
      {
          type = forceatoms[i++];
          ai   = forceatoms[i++];
          aj   = forceatoms[i++];
          ak   = forceatoms[i++];
  
          theta  = bond_angle(x[ai], x[aj], x[ak], pbc,
                              r_ij, r_kj, &cos_theta, &t1, &t2); /*  41		*/
  
          dt = theta - forceparams[type].qangle.theta*DEG2RAD;   /* 2          */
  
          dVdt = 0;
          va   = forceparams[type].qangle.c[0];
          dtp  = 1.0;
          for (j = 1; j <= 4; j++)
          {
              c     = forceparams[type].qangle.c[j];
              dVdt -= j*c*dtp;
              dtp  *= dt;
              va   += c*dtp;
          }
          /* 20 */
  
          vtot += va;
  
          cos_theta2 = sqr(cos_theta);            /*   1		*/
          if (cos_theta2 < 1)
          {
              int  m;
              real st, sth;
              real cik, cii, ckk;
              real nrkj2, nrij2;
              rvec f_i, f_j, f_k;
  
              st  = dVdt*gmx_invsqrt(1 - cos_theta2); /*  12		*/
              sth = st*cos_theta;                     /*   1		*/
  #ifdef DEBUG
              if (debug)
              {
                  fprintf(debug, "ANGLES: theta = %10g  vth = %10g  dV/dtheta = %10g\n",
                          theta*RAD2DEG, va, dVdt);
              }
  #endif
              nrkj2 = iprod(r_kj, r_kj);  /*   5		*/
              nrij2 = iprod(r_ij, r_ij);
  
              cik = st*gmx_invsqrt(nrkj2*nrij2); /*  12		*/
              cii = sth/nrij2;                   /*  10		*/
              ckk = sth/nrkj2;                   /*  10		*/
  
              for (m = 0; (m < DIM); m++)        /*  39		*/
              {
                  f_i[m]    = -(cik*r_kj[m]-cii*r_ij[m]);
                  f_k[m]    = -(cik*r_ij[m]-ckk*r_kj[m]);
                  f_j[m]    = -f_i[m]-f_k[m];
                  f[ai][m] += f_i[m];
                  f[aj][m] += f_j[m];
                  f[ak][m] += f_k[m];
              }
              if (g)
              {
                  copy_ivec(SHIFT_IVEC(g, aj), jt);
  
                  ivec_sub(SHIFT_IVEC(g, ai), jt, dt_ij);
                  ivec_sub(SHIFT_IVEC(g, ak), jt, dt_kj);
                  t1 = IVEC2IS(dt_ij);
                  t2 = IVEC2IS(dt_kj);
              }
              rvec_inc(fshift[t1], f_i);
              rvec_inc(fshift[CENTRAL], f_j);
              rvec_inc(fshift[t2], f_k);
          }                                       /* 153 TOTAL	*/
      }
      return vtot;
  }
  
  real dih_angle(const rvec xi, const rvec xj, const rvec xk, const rvec xl,
                 const t_pbc *pbc,
                 rvec r_ij, rvec r_kj, rvec r_kl, rvec m, rvec n,
                 real *sign, int *t1, int *t2, int *t3)
  {
      real ipr, phi;
  
      *t1 = pbc_rvec_sub(pbc, xi, xj, r_ij); /*  3        */
      *t2 = pbc_rvec_sub(pbc, xk, xj, r_kj); /*  3		*/
      *t3 = pbc_rvec_sub(pbc, xk, xl, r_kl); /*  3		*/
  
      cprod(r_ij, r_kj, m);                  /*  9        */
      cprod(r_kj, r_kl, n);                  /*  9		*/
      phi     = gmx_angle(m, n);             /* 49 (assuming 25 for atan2) */
      ipr     = iprod(r_ij, n);              /*  5        */
      (*sign) = (ipr < 0.0) ? -1.0 : 1.0;
      phi     = (*sign)*phi;                 /*  1		*/
      /* 82 TOTAL	*/
      return phi;
  }
  
  
  #ifdef SIMD_BONDEDS
  
  /* As dih_angle above, but calculates 4 dihedral angles at once using SIMD,
   * also calculates the pre-factor required for the dihedral force update.
   * Note that bv and buf should be register aligned.
   */
  static gmx_inline void
  dih_angle_simd(const rvec *x,
                 const int *ai, const int *aj, const int *ak, const int *al,
                 const pbc_simd_t *pbc,
                 real *dr,
                 gmx_mm_pr *phi_S,
                 gmx_mm_pr *mx_S, gmx_mm_pr *my_S, gmx_mm_pr *mz_S,
                 gmx_mm_pr *nx_S, gmx_mm_pr *ny_S, gmx_mm_pr *nz_S,
                 gmx_mm_pr *nrkj_m2_S,
                 gmx_mm_pr *nrkj_n2_S,
                 real *p,
                 real *q)
  {
  #define UNROLL GMX_SIMD_WIDTH_HERE
      int       s, m;
      gmx_mm_pr rijx_S, rijy_S, rijz_S;
      gmx_mm_pr rkjx_S, rkjy_S, rkjz_S;
      gmx_mm_pr rklx_S, rkly_S, rklz_S;
      gmx_mm_pr cx_S, cy_S, cz_S;
      gmx_mm_pr cn_S;
      gmx_mm_pr s_S;
      gmx_mm_pr ipr_S;
      gmx_mm_pr iprm_S, iprn_S;
      gmx_mm_pr nrkj2_S, nrkj_1_S, nrkj_2_S, nrkj_S;
      gmx_mm_pr toler_S;
      gmx_mm_pr p_S, q_S;
      gmx_mm_pr nrkj2_min_S;
      gmx_mm_pr real_eps_S;
  
      /* Used to avoid division by zero.
       * We take into acount that we multiply the result by real_eps_S.
       */
      nrkj2_min_S = gmx_set1_pr(GMX_REAL_MIN/(2*GMX_REAL_EPS));
  
      /* The value of the last significant bit (GMX_REAL_EPS is half of that) */
      real_eps_S  = gmx_set1_pr(2*GMX_REAL_EPS);
  
      for (s = 0; s < UNROLL; s++)
      {
          /* If you can't use pbc_dx_simd below for PBC, e.g. because
           * you can't round in SIMD, use pbc_rvec_sub here.
           */
          for (m = 0; m < DIM; m++)
          {
              dr[s + (0*DIM + m)*UNROLL] = x[ai[s]][m] - x[aj[s]][m];
              dr[s + (1*DIM + m)*UNROLL] = x[ak[s]][m] - x[aj[s]][m];
              dr[s + (2*DIM + m)*UNROLL] = x[ak[s]][m] - x[al[s]][m];
          }
      }
  
      rijx_S = gmx_load_pr(dr + 0*UNROLL);
      rijy_S = gmx_load_pr(dr + 1*UNROLL);
      rijz_S = gmx_load_pr(dr + 2*UNROLL);
      rkjx_S = gmx_load_pr(dr + 3*UNROLL);
      rkjy_S = gmx_load_pr(dr + 4*UNROLL);
      rkjz_S = gmx_load_pr(dr + 5*UNROLL);
      rklx_S = gmx_load_pr(dr + 6*UNROLL);
      rkly_S = gmx_load_pr(dr + 7*UNROLL);
      rklz_S = gmx_load_pr(dr + 8*UNROLL);
  
      pbc_dx_simd(&rijx_S, &rijy_S, &rijz_S, pbc);
      pbc_dx_simd(&rkjx_S, &rkjy_S, &rkjz_S, pbc);
      pbc_dx_simd(&rklx_S, &rkly_S, &rklz_S, pbc);
  
      gmx_cprod_pr(rijx_S, rijy_S, rijz_S,
                   rkjx_S, rkjy_S, rkjz_S,
                   mx_S, my_S, mz_S);
  
      gmx_cprod_pr(rkjx_S, rkjy_S, rkjz_S,
                   rklx_S, rkly_S, rklz_S,
                   nx_S, ny_S, nz_S);
  
      gmx_cprod_pr(*mx_S, *my_S, *mz_S,
                   *nx_S, *ny_S, *nz_S,
                   &cx_S, &cy_S, &cz_S);
  
      cn_S       = gmx_sqrt_pr(gmx_norm2_pr(cx_S, cy_S, cz_S));
  
      s_S        = gmx_iprod_pr(*mx_S, *my_S, *mz_S, *nx_S, *ny_S, *nz_S);
  
      /* Determine the dihedral angle, the sign might need correction */
      *phi_S     = gmx_atan2_pr(cn_S, s_S);
  
      ipr_S      = gmx_iprod_pr(rijx_S, rijy_S, rijz_S,
                                *nx_S, *ny_S, *nz_S);
  
      iprm_S     = gmx_norm2_pr(*mx_S, *my_S, *mz_S);
      iprn_S     = gmx_norm2_pr(*nx_S, *ny_S, *nz_S);
  
      nrkj2_S    = gmx_norm2_pr(rkjx_S, rkjy_S, rkjz_S);
  
      /* Avoid division by zero. When zero, the result is multiplied by 0
       * anyhow, so the 3 max below do not affect the final result.
       */
      nrkj2_S    = gmx_max_pr(nrkj2_S, nrkj2_min_S);
      nrkj_1_S   = gmx_invsqrt_pr(nrkj2_S);
      nrkj_2_S   = gmx_mul_pr(nrkj_1_S, nrkj_1_S);
      nrkj_S     = gmx_mul_pr(nrkj2_S, nrkj_1_S);
  
      toler_S    = gmx_mul_pr(nrkj2_S, real_eps_S);
  
      /* Here the plain-C code uses a conditional, but we can't do that in SIMD.
       * So we take a max with the tolerance instead. Since we multiply with
       * m or n later, the max does not affect the results.
       */
      iprm_S     = gmx_max_pr(iprm_S, toler_S);
      iprn_S     = gmx_max_pr(iprn_S, toler_S);
      *nrkj_m2_S = gmx_mul_pr(nrkj_S, gmx_inv_pr(iprm_S));
      *nrkj_n2_S = gmx_mul_pr(nrkj_S, gmx_inv_pr(iprn_S));
  
      /* Set sign of phi_S with the sign of ipr_S; phi_S is currently positive */
      *phi_S     = gmx_cpsgn_nonneg_pr(ipr_S, *phi_S);
  
      p_S        = gmx_iprod_pr(rijx_S, rijy_S, rijz_S,
                                rkjx_S, rkjy_S, rkjz_S);
      p_S        = gmx_mul_pr(p_S, nrkj_2_S);
  
      q_S        = gmx_iprod_pr(rklx_S, rkly_S, rklz_S,
                                rkjx_S, rkjy_S, rkjz_S);
      q_S        = gmx_mul_pr(q_S, nrkj_2_S);
  
      gmx_store_pr(p, p_S);
      gmx_store_pr(q, q_S);
  #undef UNROLL
  }
  
  #endif /* SIMD_BONDEDS */
  
  
  void do_dih_fup(int i, int j, int k, int l, real ddphi,
                  rvec r_ij, rvec r_kj, rvec r_kl,
                  rvec m, rvec n, rvec f[], rvec fshift[],
                  const t_pbc *pbc, const t_graph *g,
                  const rvec x[], int t1, int t2, int t3)
  {
      /* 143 FLOPS */
      rvec f_i, f_j, f_k, f_l;
      rvec uvec, vvec, svec, dx_jl;
      real iprm, iprn, nrkj, nrkj2, nrkj_1, nrkj_2;
      real a, b, p, q, toler;
      ivec jt, dt_ij, dt_kj, dt_lj;
  
      iprm  = iprod(m, m);       /*  5    */
      iprn  = iprod(n, n);       /*  5	*/
      nrkj2 = iprod(r_kj, r_kj); /*  5	*/
      toler = nrkj2*GMX_REAL_EPS;
      if ((iprm > toler) && (iprn > toler))
      {
          nrkj_1 = gmx_invsqrt(nrkj2); /* 10	*/
          nrkj_2 = nrkj_1*nrkj_1;      /*  1	*/
          nrkj   = nrkj2*nrkj_1;       /*  1	*/
          a      = -ddphi*nrkj/iprm;   /* 11	*/
          svmul(a, m, f_i);            /*  3	*/
          b     = ddphi*nrkj/iprn;     /* 11	*/
          svmul(b, n, f_l);            /*  3  */
          p     = iprod(r_ij, r_kj);   /*  5	*/
          p    *= nrkj_2;              /*  1	*/
          q     = iprod(r_kl, r_kj);   /*  5	*/
          q    *= nrkj_2;              /*  1	*/
          svmul(p, f_i, uvec);         /*  3	*/
          svmul(q, f_l, vvec);         /*  3	*/
          rvec_sub(uvec, vvec, svec);  /*  3	*/
          rvec_sub(f_i, svec, f_j);    /*  3	*/
          rvec_add(f_l, svec, f_k);    /*  3	*/
          rvec_inc(f[i], f_i);         /*  3	*/
          rvec_dec(f[j], f_j);         /*  3	*/
          rvec_dec(f[k], f_k);         /*  3	*/
          rvec_inc(f[l], f_l);         /*  3	*/
  
          if (g)
          {
              copy_ivec(SHIFT_IVEC(g, j), jt);
              ivec_sub(SHIFT_IVEC(g, i), jt, dt_ij);
              ivec_sub(SHIFT_IVEC(g, k), jt, dt_kj);
              ivec_sub(SHIFT_IVEC(g, l), jt, dt_lj);
              t1 = IVEC2IS(dt_ij);
              t2 = IVEC2IS(dt_kj);
              t3 = IVEC2IS(dt_lj);
          }
          else if (pbc)
          {
              t3 = pbc_rvec_sub(pbc, x[l], x[j], dx_jl);
          }
          else
          {
              t3 = CENTRAL;
          }
  
          rvec_inc(fshift[t1], f_i);
          rvec_dec(fshift[CENTRAL], f_j);
          rvec_dec(fshift[t2], f_k);
          rvec_inc(fshift[t3], f_l);
      }
      /* 112 TOTAL    */
  }
  
  /* As do_dih_fup above, but without shift forces */
  static void
  do_dih_fup_noshiftf(int i, int j, int k, int l, real ddphi,
                      rvec r_ij, rvec r_kj, rvec r_kl,
                      rvec m, rvec n, rvec f[])
  {
      rvec f_i, f_j, f_k, f_l;
      rvec uvec, vvec, svec, dx_jl;
      real iprm, iprn, nrkj, nrkj2, nrkj_1, nrkj_2;
      real a, b, p, q, toler;
      ivec jt, dt_ij, dt_kj, dt_lj;
  
      iprm  = iprod(m, m);       /*  5    */
      iprn  = iprod(n, n);       /*  5	*/
      nrkj2 = iprod(r_kj, r_kj); /*  5	*/
      toler = nrkj2*GMX_REAL_EPS;
      if ((iprm > toler) && (iprn > toler))
      {
          nrkj_1 = gmx_invsqrt(nrkj2); /* 10	*/
          nrkj_2 = nrkj_1*nrkj_1;      /*  1	*/
          nrkj   = nrkj2*nrkj_1;       /*  1	*/
          a      = -ddphi*nrkj/iprm;   /* 11	*/
          svmul(a, m, f_i);            /*  3	*/
          b     = ddphi*nrkj/iprn;     /* 11	*/
          svmul(b, n, f_l);            /*  3  */
          p     = iprod(r_ij, r_kj);   /*  5	*/
          p    *= nrkj_2;              /*  1	*/
          q     = iprod(r_kl, r_kj);   /*  5	*/
          q    *= nrkj_2;              /*  1	*/
          svmul(p, f_i, uvec);         /*  3	*/
          svmul(q, f_l, vvec);         /*  3	*/
          rvec_sub(uvec, vvec, svec);  /*  3	*/
          rvec_sub(f_i, svec, f_j);    /*  3	*/
          rvec_add(f_l, svec, f_k);    /*  3	*/
          rvec_inc(f[i], f_i);         /*  3	*/
          rvec_dec(f[j], f_j);         /*  3	*/
          rvec_dec(f[k], f_k);         /*  3	*/
          rvec_inc(f[l], f_l);         /*  3	*/
      }
  }
  
  /* As do_dih_fup_noshiftf above, but with pre-calculated pre-factors */
  static gmx_inline void
  do_dih_fup_noshiftf_precalc(int i, int j, int k, int l,
                              real p, real q,
                              real f_i_x, real f_i_y, real f_i_z,
                              real mf_l_x, real mf_l_y, real mf_l_z,
                              rvec f[])
  {
      rvec f_i, f_j, f_k, f_l;
      rvec uvec, vvec, svec;
  
      f_i[XX] = f_i_x;
      f_i[YY] = f_i_y;
      f_i[ZZ] = f_i_z;
      f_l[XX] = -mf_l_x;
      f_l[YY] = -mf_l_y;
      f_l[ZZ] = -mf_l_z;
      svmul(p, f_i, uvec);
      svmul(q, f_l, vvec);
      rvec_sub(uvec, vvec, svec);
      rvec_sub(f_i, svec, f_j);
      rvec_add(f_l, svec, f_k);
      rvec_inc(f[i], f_i);
      rvec_dec(f[j], f_j);
      rvec_dec(f[k], f_k);
      rvec_inc(f[l], f_l);
  }
  
  
  real dopdihs(real cpA, real cpB, real phiA, real phiB, int mult,
               real phi, real lambda, real *V, real *F)
  {
      real v, dvdlambda, mdphi, v1, sdphi, ddphi;
      real L1   = 1.0 - lambda;
      real ph0  = (L1*phiA + lambda*phiB)*DEG2RAD;
      real dph0 = (phiB - phiA)*DEG2RAD;
      real cp   = L1*cpA + lambda*cpB;
  
      mdphi =  mult*phi - ph0;
      sdphi = sin(mdphi);
      ddphi = -cp*mult*sdphi;
      v1    = 1.0 + cos(mdphi);
      v     = cp*v1;
  
      dvdlambda  = (cpB - cpA)*v1 + cp*dph0*sdphi;
  
      *V = v;
      *F = ddphi;
  
      return dvdlambda;
  
      /* That was 40 flops */
  }
  
  static void
  dopdihs_noener(real cpA, real cpB, real phiA, real phiB, int mult,
                 real phi, real lambda, real *F)
  {
      real mdphi, sdphi, ddphi;
      real L1   = 1.0 - lambda;
      real ph0  = (L1*phiA + lambda*phiB)*DEG2RAD;
      real cp   = L1*cpA + lambda*cpB;
  
      mdphi = mult*phi - ph0;
      sdphi = sin(mdphi);
      ddphi = -cp*mult*sdphi;
  
      *F = ddphi;
  
      /* That was 20 flops */
  }
  
  static void
  dopdihs_mdphi(real cpA, real cpB, real phiA, real phiB, int mult,
                real phi, real lambda, real *cp, real *mdphi)
  {
      real L1   = 1.0 - lambda;
      real ph0  = (L1*phiA + lambda*phiB)*DEG2RAD;
  
      *cp    = L1*cpA + lambda*cpB;
  
      *mdphi = mult*phi - ph0;
  }
  
  static real dopdihs_min(real cpA, real cpB, real phiA, real phiB, int mult,
                          real phi, real lambda, real *V, real *F)
  /* similar to dopdihs, except for a minus sign  *
   * and a different treatment of mult/phi0       */
  {
      real v, dvdlambda, mdphi, v1, sdphi, ddphi;
      real L1   = 1.0 - lambda;
      real ph0  = (L1*phiA + lambda*phiB)*DEG2RAD;
      real dph0 = (phiB - phiA)*DEG2RAD;
      real cp   = L1*cpA + lambda*cpB;
  
      mdphi = mult*(phi-ph0);
      sdphi = sin(mdphi);
      ddphi = cp*mult*sdphi;
      v1    = 1.0-cos(mdphi);
      v     = cp*v1;
  
      dvdlambda  = (cpB-cpA)*v1 + cp*dph0*sdphi;
  
      *V = v;
      *F = ddphi;
  
      return dvdlambda;
  
      /* That was 40 flops */
  }
  
  real pdihs(int nbonds,
             const t_iatom forceatoms[], const t_iparams forceparams[],
             const rvec x[], rvec f[], rvec fshift[],
             const t_pbc *pbc, const t_graph *g,
             real lambda, real *dvdlambda,
             const t_mdatoms *md, t_fcdata *fcd,
             int *global_atom_index)
  {
      int  i, type, ai, aj, ak, al;
      int  t1, t2, t3;
      rvec r_ij, r_kj, r_kl, m, n;
      real phi, sign, ddphi, vpd, vtot;
  
      vtot = 0.0;
  
      for (i = 0; (i < nbonds); )
      {
          type = forceatoms[i++];
          ai   = forceatoms[i++];
          aj   = forceatoms[i++];
          ak   = forceatoms[i++];
          al   = forceatoms[i++];
  
          phi = dih_angle(x[ai], x[aj], x[ak], x[al], pbc, r_ij, r_kj, r_kl, m, n,
                          &sign, &t1, &t2, &t3);  /*  84      */
          *dvdlambda += dopdihs(forceparams[type].pdihs.cpA,
                                forceparams[type].pdihs.cpB,
                                forceparams[type].pdihs.phiA,
                                forceparams[type].pdihs.phiB,
                                forceparams[type].pdihs.mult,
                                phi, lambda, &vpd, &ddphi);
  
          vtot += vpd;
          do_dih_fup(ai, aj, ak, al, ddphi, r_ij, r_kj, r_kl, m, n,
                     f, fshift, pbc, g, x, t1, t2, t3); /* 112		*/
  
  #ifdef DEBUG
          fprintf(debug, "pdih: (%d,%d,%d,%d) phi=%g\n",
                  ai, aj, ak, al, phi);
  #endif
      } /* 223 TOTAL  */
  
      return vtot;
  }
  
  void make_dp_periodic(real *dp)  /* 1 flop? */
  {
      /* dp cannot be outside (-pi,pi) */
      if (*dp >= M_PI)
      {
          *dp -= 2*M_PI;
      }
      else if (*dp < -M_PI)
      {
          *dp += 2*M_PI;
      }
      return;
  }
  
  /* As pdihs above, but without calculating energies and shift forces */
  static void
  pdihs_noener(int nbonds,
               const t_iatom forceatoms[], const t_iparams forceparams[],
               const rvec x[], rvec f[],
               const t_pbc *pbc, const t_graph *g,
               real lambda,
               const t_mdatoms *md, t_fcdata *fcd,
               int *global_atom_index)
  {
      int  i, type, ai, aj, ak, al;
      int  t1, t2, t3;
      rvec r_ij, r_kj, r_kl, m, n;
      real phi, sign, ddphi_tot, ddphi;
  
      for (i = 0; (i < nbonds); )
      {
          ai   = forceatoms[i+1];
          aj   = forceatoms[i+2];
          ak   = forceatoms[i+3];
          al   = forceatoms[i+4];
  
          phi = dih_angle(x[ai], x[aj], x[ak], x[al], pbc, r_ij, r_kj, r_kl, m, n,
                          &sign, &t1, &t2, &t3);
  
          ddphi_tot = 0;
  
          /* Loop over dihedrals working on the same atoms,
           * so we avoid recalculating angles and force distributions.
           */
          do
          {
              type = forceatoms[i];
              dopdihs_noener(forceparams[type].pdihs.cpA,
                             forceparams[type].pdihs.cpB,
                             forceparams[type].pdihs.phiA,
                             forceparams[type].pdihs.phiB,
                             forceparams[type].pdihs.mult,
                             phi, lambda, &ddphi);
              ddphi_tot += ddphi;
  
              i += 5;
          }
          while (i < nbonds &&
                 forceatoms[i+1] == ai &&
                 forceatoms[i+2] == aj &&
                 forceatoms[i+3] == ak &&
                 forceatoms[i+4] == al);
  
          do_dih_fup_noshiftf(ai, aj, ak, al, ddphi_tot, r_ij, r_kj, r_kl, m, n, f);
      }
  }
  
  
  #ifdef SIMD_BONDEDS
  
  /* As pdihs_noner above, but using SIMD to calculate many dihedrals at once */
  static void
  pdihs_noener_simd(int nbonds,
                    const t_iatom forceatoms[], const t_iparams forceparams[],
                    const rvec x[], rvec f[],
                    const t_pbc *pbc, const t_graph *g,
                    real lambda,
                    const t_mdatoms *md, t_fcdata *fcd,
                    int *global_atom_index)
  {
  #define UNROLL GMX_SIMD_WIDTH_HERE
      const int      nfa1 = 5;
      int            i, iu, s;
      int            type, ai[UNROLL], aj[UNROLL], ak[UNROLL], al[UNROLL];
      int            t1[UNROLL], t2[UNROLL], t3[UNROLL];
      real           ddphi;
      real           dr_array[3*DIM*UNROLL+UNROLL], *dr;
      real           buf_array[7*UNROLL+UNROLL], *buf;
      real           *cp, *phi0, *mult, *phi, *p, *q, *sf_i, *msf_l;
      gmx_mm_pr      phi0_S, phi_S;
      gmx_mm_pr      mx_S, my_S, mz_S;
      gmx_mm_pr      nx_S, ny_S, nz_S;
      gmx_mm_pr      nrkj_m2_S, nrkj_n2_S;
      gmx_mm_pr      cp_S, mdphi_S, mult_S;
      gmx_mm_pr      sin_S, cos_S;
      gmx_mm_pr      mddphi_S;
      gmx_mm_pr      sf_i_S, msf_l_S;
      pbc_simd_t     pbc_simd;
  
      /* Ensure SIMD register alignment */
      dr  = gmx_simd_align_real(dr_array);
      buf = gmx_simd_align_real(buf_array);
  
      /* Extract aligned pointer for parameters and variables */
      cp    = buf + 0*UNROLL;
      phi0  = buf + 1*UNROLL;
      mult  = buf + 2*UNROLL;
      p     = buf + 3*UNROLL;
      q     = buf + 4*UNROLL;
      sf_i  = buf + 5*UNROLL;
      msf_l = buf + 6*UNROLL;
  
      set_pbc_simd(pbc, &pbc_simd);
  
      /* nbonds is the number of dihedrals times nfa1, here we step UNROLL dihs */
      for (i = 0; (i < nbonds); i += UNROLL*nfa1)
      {
          /* Collect atoms quadruplets for UNROLL dihedrals.
           * iu indexes into forceatoms, we should not let iu go beyond nbonds.
           */
          iu = i;
          for (s = 0; s < UNROLL; s++)
          {
              type  = forceatoms[iu];
              ai[s] = forceatoms[iu+1];
              aj[s] = forceatoms[iu+2];
              ak[s] = forceatoms[iu+3];
              al[s] = forceatoms[iu+4];
  
              cp[s]   = forceparams[type].pdihs.cpA;
              phi0[s] = forceparams[type].pdihs.phiA*DEG2RAD;
              mult[s] = forceparams[type].pdihs.mult;
  
              /* At the end fill the arrays with identical entries */
              if (iu + nfa1 < nbonds)
              {
                  iu += nfa1;
              }
          }
  
          /* Caclulate UNROLL dihedral angles at once */
          dih_angle_simd(x, ai, aj, ak, al, &pbc_simd,
                         dr,
                         &phi_S,
                         &mx_S, &my_S, &mz_S,
                         &nx_S, &ny_S, &nz_S,
                         &nrkj_m2_S,
                         &nrkj_n2_S,
                         p, q);
  
          cp_S     = gmx_load_pr(cp);
          phi0_S   = gmx_load_pr(phi0);
          mult_S   = gmx_load_pr(mult);
  
          mdphi_S  = gmx_sub_pr(gmx_mul_pr(mult_S, phi_S), phi0_S);
  
          /* Calculate UNROLL sines at once */
          gmx_sincos_pr(mdphi_S, &sin_S, &cos_S);
          mddphi_S = gmx_mul_pr(gmx_mul_pr(cp_S, mult_S), sin_S);
          sf_i_S   = gmx_mul_pr(mddphi_S, nrkj_m2_S);
          msf_l_S  = gmx_mul_pr(mddphi_S, nrkj_n2_S);
  
          /* After this m?_S will contain f[i] */
          mx_S     = gmx_mul_pr(sf_i_S, mx_S);
          my_S     = gmx_mul_pr(sf_i_S, my_S);
          mz_S     = gmx_mul_pr(sf_i_S, mz_S);
  
          /* After this m?_S will contain -f[l] */
          nx_S     = gmx_mul_pr(msf_l_S, nx_S);
          ny_S     = gmx_mul_pr(msf_l_S, ny_S);
          nz_S     = gmx_mul_pr(msf_l_S, nz_S);
  
          gmx_store_pr(dr + 0*UNROLL, mx_S);
          gmx_store_pr(dr + 1*UNROLL, my_S);
          gmx_store_pr(dr + 2*UNROLL, mz_S);
          gmx_store_pr(dr + 3*UNROLL, nx_S);
          gmx_store_pr(dr + 4*UNROLL, ny_S);
          gmx_store_pr(dr + 5*UNROLL, nz_S);
  
          iu = i;
          s  = 0;
          do
          {
              do_dih_fup_noshiftf_precalc(ai[s], aj[s], ak[s], al[s],
                                          p[s], q[s],
                                          dr[     XX *UNROLL+s],
                                          dr[     YY *UNROLL+s],
                                          dr[     ZZ *UNROLL+s],
                                          dr[(DIM+XX)*UNROLL+s],
                                          dr[(DIM+YY)*UNROLL+s],
                                          dr[(DIM+ZZ)*UNROLL+s],
                                          f);
              s++;
              iu += nfa1;
          }
          while (s < UNROLL && iu < nbonds);
      }
  #undef UNROLL
  }
  
  #endif /* SIMD_BONDEDS */
  
  
  real idihs(int nbonds,
             const t_iatom forceatoms[], const t_iparams forceparams[],
             const rvec x[], rvec f[], rvec fshift[],
             const t_pbc *pbc, const t_graph *g,
             real lambda, real *dvdlambda,
             const t_mdatoms *md, t_fcdata *fcd,
             int *global_atom_index)
  {
      int  i, type, ai, aj, ak, al;
      int  t1, t2, t3;
      real phi, phi0, dphi0, ddphi, sign, vtot;
      rvec r_ij, r_kj, r_kl, m, n;
      real L1, kk, dp, dp2, kA, kB, pA, pB, dvdl_term;
  
      L1        = 1.0-lambda;
      dvdl_term = 0;
      vtot      = 0.0;
      for (i = 0; (i < nbonds); )
      {
          type = forceatoms[i++];
          ai   = forceatoms[i++];
          aj   = forceatoms[i++];
          ak   = forceatoms[i++];
          al   = forceatoms[i++];
  
          phi = dih_angle(x[ai], x[aj], x[ak], x[al], pbc, r_ij, r_kj, r_kl, m, n,
                          &sign, &t1, &t2, &t3);  /*  84		*/
  
          /* phi can jump if phi0 is close to Pi/-Pi, which will cause huge
           * force changes if we just apply a normal harmonic.
           * Instead, we first calculate phi-phi0 and take it modulo (-Pi,Pi).
           * This means we will never have the periodicity problem, unless
           * the dihedral is Pi away from phiO, which is very unlikely due to
           * the potential.
           */
          kA = forceparams[type].harmonic.krA;
          kB = forceparams[type].harmonic.krB;
          pA = forceparams[type].harmonic.rA;
          pB = forceparams[type].harmonic.rB;
  
          kk    = L1*kA + lambda*kB;
          phi0  = (L1*pA + lambda*pB)*DEG2RAD;
          dphi0 = (pB - pA)*DEG2RAD;
  
          dp = phi-phi0;
  
          make_dp_periodic(&dp);
  
          dp2 = dp*dp;
  
          vtot += 0.5*kk*dp2;
          ddphi = -kk*dp;
  
          dvdl_term += 0.5*(kB - kA)*dp2 - kk*dphi0*dp;
  
          do_dih_fup(ai, aj, ak, al, (real)(-ddphi), r_ij, r_kj, r_kl, m, n,
                     f, fshift, pbc, g, x, t1, t2, t3); /* 112		*/
          /* 218 TOTAL	*/
  #ifdef DEBUG
          if (debug)
          {
              fprintf(debug, "idih: (%d,%d,%d,%d) phi=%g\n",
                      ai, aj, ak, al, phi);
          }
  #endif
      }
  
      *dvdlambda += dvdl_term;
      return vtot;
  }
  
  
  real posres(int nbonds,
              const t_iatom forceatoms[], const t_iparams forceparams[],
              const rvec x[], rvec f[], rvec vir_diag,
              t_pbc *pbc,
              real lambda, real *dvdlambda,
              int refcoord_scaling, int ePBC, rvec comA, rvec comB)
  {
      int              i, ai, m, d, type, ki, npbcdim = 0;
      const t_iparams *pr;
      real             L1;
      real             vtot, kk, fm;
      real             posA, posB, ref = 0;
      rvec             comA_sc, comB_sc, rdist, dpdl, pos, dx;
      gmx_bool         bForceValid = TRUE;
  
      if ((f == NULL) || (vir_diag == NULL))    /* should both be null together! */
      {
          bForceValid = FALSE;
      }
  
      npbcdim = ePBC2npbcdim(ePBC);
  
      if (refcoord_scaling == erscCOM)
      {
          clear_rvec(comA_sc);
          clear_rvec(comB_sc);
          for (m = 0; m < npbcdim; m++)
          {
              for (d = m; d < npbcdim; d++)
              {
                  comA_sc[m] += comA[d]*pbc->box[d][m];
                  comB_sc[m] += comB[d]*pbc->box[d][m];
              }
          }
      }
  
      L1 = 1.0 - lambda;
  
      vtot = 0.0;
      for (i = 0; (i < nbonds); )
      {
          type = forceatoms[i++];
          ai   = forceatoms[i++];
          pr   = &forceparams[type];
  
          for (m = 0; m < DIM; m++)
          {
              posA = forceparams[type].posres.pos0A[m];
              posB = forceparams[type].posres.pos0B[m];
              if (m < npbcdim)
              {
                  switch (refcoord_scaling)
                  {
                      case erscNO:
                          ref      = 0;
                          rdist[m] = L1*posA + lambda*posB;
                          dpdl[m]  = posB - posA;
                          break;
                      case erscALL:
                          /* Box relative coordinates are stored for dimensions with pbc */
                          posA *= pbc->box[m][m];
                          posB *= pbc->box[m][m];
                          for (d = m+1; d < npbcdim; d++)
                          {
                              posA += forceparams[type].posres.pos0A[d]*pbc->box[d][m];
                              posB += forceparams[type].posres.pos0B[d]*pbc->box[d][m];
                          }
                          ref      = L1*posA + lambda*posB;
                          rdist[m] = 0;
                          dpdl[m]  = posB - posA;
                          break;
                      case erscCOM:
                          ref      = L1*comA_sc[m] + lambda*comB_sc[m];
                          rdist[m] = L1*posA       + lambda*posB;
                          dpdl[m]  = comB_sc[m] - comA_sc[m] + posB - posA;
                          break;
                      default:
                          gmx_fatal(FARGS, "No such scaling method implemented");
                  }
              }
              else
              {
                  ref      = L1*posA + lambda*posB;
                  rdist[m] = 0;
                  dpdl[m]  = posB - posA;
              }
  
              /* We do pbc_dx with ref+rdist,
               * since with only ref we can be up to half a box vector wrong.
               */
              pos[m] = ref + rdist[m];
          }
  
          if (pbc)
          {
              pbc_dx(pbc, x[ai], pos, dx);
          }
          else
          {
              rvec_sub(x[ai], pos, dx);
          }
  
          for (m = 0; (m < DIM); m++)
          {
              kk          = L1*pr->posres.fcA[m] + lambda*pr->posres.fcB[m];
              fm          = -kk*dx[m];
              vtot       += 0.5*kk*dx[m]*dx[m];
              *dvdlambda +=
                  0.5*(pr->posres.fcB[m] - pr->posres.fcA[m])*dx[m]*dx[m]
                  -fm*dpdl[m];
  
              /* Here we correct for the pbc_dx which included rdist */
              if (bForceValid)
              {
                  f[ai][m]    += fm;
                  vir_diag[m] -= 0.5*(dx[m] + rdist[m])*fm;
              }
          }
      }
  
      return vtot;
  }
  
  static real low_angres(int nbonds,
                         const t_iatom forceatoms[], const t_iparams forceparams[],
                         const rvec x[], rvec f[], rvec fshift[],
                         const t_pbc *pbc, const t_graph *g,
                         real lambda, real *dvdlambda,
                         gmx_bool bZAxis)
  {
      int  i, m, type, ai, aj, ak, al;
      int  t1, t2;
      real phi, cos_phi, cos_phi2, vid, vtot, dVdphi;
      rvec r_ij, r_kl, f_i, f_k = {0, 0, 0};
      real st, sth, nrij2, nrkl2, c, cij, ckl;
  
      ivec dt;
      t2 = 0; /* avoid warning with gcc-3.3. It is never used uninitialized */
  
      vtot = 0.0;
      ak   = al = 0; /* to avoid warnings */
      for (i = 0; i < nbonds; )
      {
          type = forceatoms[i++];
          ai   = forceatoms[i++];
          aj   = forceatoms[i++];
          t1   = pbc_rvec_sub(pbc, x[aj], x[ai], r_ij);       /*  3		*/
          if (!bZAxis)
          {
              ak   = forceatoms[i++];
              al   = forceatoms[i++];
              t2   = pbc_rvec_sub(pbc, x[al], x[ak], r_kl);  /*  3		*/
          }
          else
          {
              r_kl[XX] = 0;
              r_kl[YY] = 0;
              r_kl[ZZ] = 1;
          }
  
          cos_phi = cos_angle(r_ij, r_kl); /* 25		*/
          phi     = acos(cos_phi);         /* 10           */
  
          *dvdlambda += dopdihs_min(forceparams[type].pdihs.cpA,
                                    forceparams[type].pdihs.cpB,
                                    forceparams[type].pdihs.phiA,
                                    forceparams[type].pdihs.phiB,
                                    forceparams[type].pdihs.mult,
                                    phi, lambda, &vid, &dVdphi); /*  40  */
  
          vtot += vid;
  
          cos_phi2 = sqr(cos_phi);                /*   1		*/
          if (cos_phi2 < 1)
          {
              st    = -dVdphi*gmx_invsqrt(1 - cos_phi2); /*  12		*/
              sth   = st*cos_phi;                        /*   1		*/
              nrij2 = iprod(r_ij, r_ij);                 /*   5		*/
              nrkl2 = iprod(r_kl, r_kl);                 /*   5          */
  
              c   = st*gmx_invsqrt(nrij2*nrkl2);         /*  11		*/
              cij = sth/nrij2;                           /*  10		*/
              ckl = sth/nrkl2;                           /*  10		*/
  
              for (m = 0; m < DIM; m++)                  /*  18+18       */
              {
                  f_i[m]    = (c*r_kl[m]-cij*r_ij[m]);
                  f[ai][m] += f_i[m];
                  f[aj][m] -= f_i[m];
                  if (!bZAxis)
                  {
                      f_k[m]    = (c*r_ij[m]-ckl*r_kl[m]);
                      f[ak][m] += f_k[m];
                      f[al][m] -= f_k[m];
                  }
              }
  
              if (g)
              {
                  ivec_sub(SHIFT_IVEC(g, ai), SHIFT_IVEC(g, aj), dt);
                  t1 = IVEC2IS(dt);
              }
              rvec_inc(fshift[t1], f_i);
              rvec_dec(fshift[CENTRAL], f_i);
              if (!bZAxis)
              {
                  if (g)
                  {
                      ivec_sub(SHIFT_IVEC(g, ak), SHIFT_IVEC(g, al), dt);
                      t2 = IVEC2IS(dt);
                  }
                  rvec_inc(fshift[t2], f_k);
                  rvec_dec(fshift[CENTRAL], f_k);
              }
          }
      }
  
      return vtot; /*  184 / 157 (bZAxis)  total  */
  }
  
  real angres(int nbonds,
              const t_iatom forceatoms[], const t_iparams forceparams[],
              const rvec x[], rvec f[], rvec fshift[],
              const t_pbc *pbc, const t_graph *g,
              real lambda, real *dvdlambda,
              const t_mdatoms *md, t_fcdata *fcd,
              int *global_atom_index)
  {
      return low_angres(nbonds, forceatoms, forceparams, x, f, fshift, pbc, g,
                        lambda, dvdlambda, FALSE);
  }
  
  real angresz(int nbonds,
               const t_iatom forceatoms[], const t_iparams forceparams[],
               const rvec x[], rvec f[], rvec fshift[],
               const t_pbc *pbc, const t_graph *g,
               real lambda, real *dvdlambda,
               const t_mdatoms *md, t_fcdata *fcd,
               int *global_atom_index)
  {
      return low_angres(nbonds, forceatoms, forceparams, x, f, fshift, pbc, g,
                        lambda, dvdlambda, TRUE);
  }
  
  real dihres(int nbonds,
              const t_iatom forceatoms[], const t_iparams forceparams[],
              const rvec x[], rvec f[], rvec fshift[],
              const t_pbc *pbc, const t_graph *g,
              real lambda, real *dvdlambda,
              const t_mdatoms *md, t_fcdata *fcd,
              int *global_atom_index)
  {
      real vtot = 0;
      int  ai, aj, ak, al, i, k, type, t1, t2, t3;
      real phi0A, phi0B, dphiA, dphiB, kfacA, kfacB, phi0, dphi, kfac;
      real phi, ddphi, ddp, ddp2, dp, sign, d2r, fc, L1;
      rvec r_ij, r_kj, r_kl, m, n;
  
      L1 = 1.0-lambda;
  
      d2r = DEG2RAD;
      k   = 0;
  
      for (i = 0; (i < nbonds); )
      {
          type = forceatoms[i++];
          ai   = forceatoms[i++];
          aj   = forceatoms[i++];
          ak   = forceatoms[i++];
          al   = forceatoms[i++];
  
          phi0A  = forceparams[type].dihres.phiA*d2r;
          dphiA  = forceparams[type].dihres.dphiA*d2r;
          kfacA  = forceparams[type].dihres.kfacA;
  
          phi0B  = forceparams[type].dihres.phiB*d2r;
          dphiB  = forceparams[type].dihres.dphiB*d2r;
          kfacB  = forceparams[type].dihres.kfacB;
  
          phi0  = L1*phi0A + lambda*phi0B;
          dphi  = L1*dphiA + lambda*dphiB;
          kfac  = L1*kfacA + lambda*kfacB;
  
          phi = dih_angle(x[ai], x[aj], x[ak], x[al], pbc, r_ij, r_kj, r_kl, m, n,
                          &sign, &t1, &t2, &t3);
          /* 84 flops */
  
          if (debug)
          {
              fprintf(debug, "dihres[%d]: %d %d %d %d : phi=%f, dphi=%f, kfac=%f\n",
                      k++, ai, aj, ak, al, phi0, dphi, kfac);
          }
          /* phi can jump if phi0 is close to Pi/-Pi, which will cause huge
           * force changes if we just apply a normal harmonic.
           * Instead, we first calculate phi-phi0 and take it modulo (-Pi,Pi).
           * This means we will never have the periodicity problem, unless
           * the dihedral is Pi away from phiO, which is very unlikely due to
           * the potential.
           */
          dp = phi-phi0;
          make_dp_periodic(&dp);
  
          if (dp > dphi)
          {
              ddp = dp-dphi;
          }
          else if (dp < -dphi)
          {
              ddp = dp+dphi;
          }
          else
          {
              ddp = 0;
          }
  
          if (ddp != 0.0)
          {
              ddp2  = ddp*ddp;
              vtot += 0.5*kfac*ddp2;
              ddphi = kfac*ddp;
  
              *dvdlambda += 0.5*(kfacB - kfacA)*ddp2;
              /* lambda dependence from changing restraint distances */
              if (ddp > 0)
              {
                  *dvdlambda -= kfac*ddp*((dphiB - dphiA)+(phi0B - phi0A));
              }
              else if (ddp < 0)
              {
                  *dvdlambda += kfac*ddp*((dphiB - dphiA)-(phi0B - phi0A));
              }
              do_dih_fup(ai, aj, ak, al, ddphi, r_ij, r_kj, r_kl, m, n,
                         f, fshift, pbc, g, x, t1, t2, t3);      /* 112		*/
          }
      }
      return vtot;
  }
  
  
  real unimplemented(int nbonds,
                     const t_iatom forceatoms[], const t_iparams forceparams[],
                     const rvec x[], rvec f[], rvec fshift[],
                     const t_pbc *pbc, const t_graph *g,
                     real lambda, real *dvdlambda,
                     const t_mdatoms *md, t_fcdata *fcd,
                     int *global_atom_index)
  {
      gmx_impl("*** you are using a not implemented function");
  
      return 0.0; /* To make the compiler happy */
  }
  
  real rbdihs(int nbonds,
              const t_iatom forceatoms[], const t_iparams forceparams[],
              const rvec x[], rvec f[], rvec fshift[],
              const t_pbc *pbc, const t_graph *g,
              real lambda, real *dvdlambda,
              const t_mdatoms *md, t_fcdata *fcd,
              int *global_atom_index)
  {
      const real c0 = 0.0, c1 = 1.0, c2 = 2.0, c3 = 3.0, c4 = 4.0, c5 = 5.0;
      int        type, ai, aj, ak, al, i, j;
      int        t1, t2, t3;
      rvec       r_ij, r_kj, r_kl, m, n;
      real       parmA[NR_RBDIHS];
      real       parmB[NR_RBDIHS];
      real       parm[NR_RBDIHS];
      real       cos_phi, phi, rbp, rbpBA;
      real       v, sign, ddphi, sin_phi;
      real       cosfac, vtot;
      real       L1        = 1.0-lambda;
      real       dvdl_term = 0;
  
      vtot = 0.0;
      for (i = 0; (i < nbonds); )
      {
          type = forceatoms[i++];
          ai   = forceatoms[i++];
          aj   = forceatoms[i++];
          ak   = forceatoms[i++];
          al   = forceatoms[i++];
  
          phi = dih_angle(x[ai], x[aj], x[ak], x[al], pbc, r_ij, r_kj, r_kl, m, n,
                          &sign, &t1, &t2, &t3);  /*  84		*/
  
          /* Change to polymer convention */
          if (phi < c0)
          {
              phi += M_PI;
          }
          else
          {
              phi -= M_PI;    /*   1		*/
  
          }
          cos_phi = cos(phi);
          /* Beware of accuracy loss, cannot use 1-sqrt(cos^2) ! */
          sin_phi = sin(phi);
  
          for (j = 0; (j < NR_RBDIHS); j++)
          {
              parmA[j] = forceparams[type].rbdihs.rbcA[j];
              parmB[j] = forceparams[type].rbdihs.rbcB[j];
              parm[j]  = L1*parmA[j]+lambda*parmB[j];
          }
          /* Calculate cosine powers */
          /* Calculate the energy */
          /* Calculate the derivative */
  
          v            = parm[0];
          dvdl_term   += (parmB[0]-parmA[0]);
          ddphi        = c0;
          cosfac       = c1;
  
          rbp          = parm[1];
          rbpBA        = parmB[1]-parmA[1];
          ddphi       += rbp*cosfac;
          cosfac      *= cos_phi;
          v           += cosfac*rbp;
          dvdl_term   += cosfac*rbpBA;
          rbp          = parm[2];
          rbpBA        = parmB[2]-parmA[2];
          ddphi       += c2*rbp*cosfac;
          cosfac      *= cos_phi;
          v           += cosfac*rbp;
          dvdl_term   += cosfac*rbpBA;
          rbp          = parm[3];
          rbpBA        = parmB[3]-parmA[3];
          ddphi       += c3*rbp*cosfac;
          cosfac      *= cos_phi;
          v           += cosfac*rbp;
          dvdl_term   += cosfac*rbpBA;
          rbp          = parm[4];
          rbpBA        = parmB[4]-parmA[4];
          ddphi       += c4*rbp*cosfac;
          cosfac      *= cos_phi;
          v           += cosfac*rbp;
          dvdl_term   += cosfac*rbpBA;
          rbp          = parm[5];
          rbpBA        = parmB[5]-parmA[5];
          ddphi       += c5*rbp*cosfac;
          cosfac      *= cos_phi;
          v           += cosfac*rbp;
          dvdl_term   += cosfac*rbpBA;
  
          ddphi = -ddphi*sin_phi;         /*  11		*/
  
          do_dih_fup(ai, aj, ak, al, ddphi, r_ij, r_kj, r_kl, m, n,
                     f, fshift, pbc, g, x, t1, t2, t3); /* 112		*/
          vtot += v;
      }
      *dvdlambda += dvdl_term;
  
      return vtot;
  }
  
  int cmap_setup_grid_index(int ip, int grid_spacing, int *ipm1, int *ipp1, int *ipp2)
  {
      int im1, ip1, ip2;
  
      if (ip < 0)
      {
          ip = ip + grid_spacing - 1;
      }
      else if (ip > grid_spacing)
      {
          ip = ip - grid_spacing - 1;
      }
  
      im1 = ip - 1;
      ip1 = ip + 1;
      ip2 = ip + 2;
  
      if (ip == 0)
      {
          im1 = grid_spacing - 1;
      }
      else if (ip == grid_spacing-2)
      {
          ip2 = 0;
      }
      else if (ip == grid_spacing-1)
      {
          ip1 = 0;
          ip2 = 1;
      }
  
      *ipm1 = im1;
      *ipp1 = ip1;
      *ipp2 = ip2;
  
      return ip;
  
  }
  
  real cmap_dihs(int nbonds,
                 const t_iatom forceatoms[], const t_iparams forceparams[],
                 const gmx_cmap_t *cmap_grid,
                 const rvec x[], rvec f[], rvec fshift[],
                 const t_pbc *pbc, const t_graph *g,
                 real lambda, real *dvdlambda,
                 const t_mdatoms *md, t_fcdata *fcd,
                 int *global_atom_index)
  {
      int         i, j, k, n, idx;
      int         ai, aj, ak, al, am;
      int         a1i, a1j, a1k, a1l, a2i, a2j, a2k, a2l;
      int         type, cmapA;
      int         t11, t21, t31, t12, t22, t32;
      int         iphi1, ip1m1, ip1p1, ip1p2;
      int         iphi2, ip2m1, ip2p1, ip2p2;
      int         l1, l2, l3, l4;
      int         pos1, pos2, pos3, pos4, tmp;
  
      real        ty[4], ty1[4], ty2[4], ty12[4], tc[16], tx[16];
      real        phi1, psi1, cos_phi1, sin_phi1, sign1, xphi1;
      real        phi2, psi2, cos_phi2, sin_phi2, sign2, xphi2;
      real        dx, xx, tt, tu, e, df1, df2, ddf1, ddf2, ddf12, vtot;
      real        ra21, rb21, rg21, rg1, rgr1, ra2r1, rb2r1, rabr1;
      real        ra22, rb22, rg22, rg2, rgr2, ra2r2, rb2r2, rabr2;
      real        fg1, hg1, fga1, hgb1, gaa1, gbb1;
      real        fg2, hg2, fga2, hgb2, gaa2, gbb2;
      real        fac;
  
      rvec        r1_ij, r1_kj, r1_kl, m1, n1;
      rvec        r2_ij, r2_kj, r2_kl, m2, n2;
      rvec        f1_i, f1_j, f1_k, f1_l;
      rvec        f2_i, f2_j, f2_k, f2_l;
      rvec        a1, b1, a2, b2;
      rvec        f1, g1, h1, f2, g2, h2;
      rvec        dtf1, dtg1, dth1, dtf2, dtg2, dth2;
      ivec        jt1, dt1_ij, dt1_kj, dt1_lj;
      ivec        jt2, dt2_ij, dt2_kj, dt2_lj;
  
      const real *cmapd;
  
      int         loop_index[4][4] = {
          {0, 4, 8, 12},
          {1, 5, 9, 13},
          {2, 6, 10, 14},
          {3, 7, 11, 15}
      };
  
      /* Total CMAP energy */
      vtot = 0;
  
      for (n = 0; n < nbonds; )
      {
          /* Five atoms are involved in the two torsions */
          type   = forceatoms[n++];
          ai     = forceatoms[n++];
          aj     = forceatoms[n++];
          ak     = forceatoms[n++];
          al     = forceatoms[n++];
          am     = forceatoms[n++];
  
          /* Which CMAP type is this */
          cmapA = forceparams[type].cmap.cmapA;
          cmapd = cmap_grid->cmapdata[cmapA].cmap;
  
          /* First torsion */
          a1i   = ai;
          a1j   = aj;
          a1k   = ak;
          a1l   = al;
  
          phi1  = dih_angle(x[a1i], x[a1j], x[a1k], x[a1l], pbc, r1_ij, r1_kj, r1_kl, m1, n1,
                            &sign1, &t11, &t21, &t31);  /* 84 */
  
          cos_phi1 = cos(phi1);
  
          a1[0] = r1_ij[1]*r1_kj[2]-r1_ij[2]*r1_kj[1];
          a1[1] = r1_ij[2]*r1_kj[0]-r1_ij[0]*r1_kj[2];
          a1[2] = r1_ij[0]*r1_kj[1]-r1_ij[1]*r1_kj[0]; /* 9 */
  
          b1[0] = r1_kl[1]*r1_kj[2]-r1_kl[2]*r1_kj[1];
          b1[1] = r1_kl[2]*r1_kj[0]-r1_kl[0]*r1_kj[2];
          b1[2] = r1_kl[0]*r1_kj[1]-r1_kl[1]*r1_kj[0]; /* 9 */
  
          tmp = pbc_rvec_sub(pbc, x[a1l], x[a1k], h1);
  
          ra21  = iprod(a1, a1);       /* 5 */
          rb21  = iprod(b1, b1);       /* 5 */
          rg21  = iprod(r1_kj, r1_kj); /* 5 */
          rg1   = sqrt(rg21);
  
          rgr1  = 1.0/rg1;
          ra2r1 = 1.0/ra21;
          rb2r1 = 1.0/rb21;
          rabr1 = sqrt(ra2r1*rb2r1);
  
          sin_phi1 = rg1 * rabr1 * iprod(a1, h1) * (-1);
  
          if (cos_phi1 < -0.5 || cos_phi1 > 0.5)
          {
              phi1 = asin(sin_phi1);
  
              if (cos_phi1 < 0)
              {
                  if (phi1 > 0)
                  {
                      phi1 = M_PI - phi1;
                  }
                  else
                  {
                      phi1 = -M_PI - phi1;
                  }
              }
          }
          else
          {
              phi1 = acos(cos_phi1);
  
              if (sin_phi1 < 0)
              {
                  phi1 = -phi1;
              }
          }
  
          xphi1 = phi1 + M_PI; /* 1 */
  
          /* Second torsion */
          a2i   = aj;
          a2j   = ak;
          a2k   = al;
          a2l   = am;
  
          phi2  = dih_angle(x[a2i], x[a2j], x[a2k], x[a2l], pbc, r2_ij, r2_kj, r2_kl, m2, n2,
                            &sign2, &t12, &t22, &t32); /* 84 */
  
          cos_phi2 = cos(phi2);
  
          a2[0] = r2_ij[1]*r2_kj[2]-r2_ij[2]*r2_kj[1];
          a2[1] = r2_ij[2]*r2_kj[0]-r2_ij[0]*r2_kj[2];
          a2[2] = r2_ij[0]*r2_kj[1]-r2_ij[1]*r2_kj[0]; /* 9 */
  
          b2[0] = r2_kl[1]*r2_kj[2]-r2_kl[2]*r2_kj[1];
          b2[1] = r2_kl[2]*r2_kj[0]-r2_kl[0]*r2_kj[2];
          b2[2] = r2_kl[0]*r2_kj[1]-r2_kl[1]*r2_kj[0]; /* 9 */
  
          tmp = pbc_rvec_sub(pbc, x[a2l], x[a2k], h2);
  
          ra22  = iprod(a2, a2);         /* 5 */
          rb22  = iprod(b2, b2);         /* 5 */
          rg22  = iprod(r2_kj, r2_kj);   /* 5 */
          rg2   = sqrt(rg22);
  
          rgr2  = 1.0/rg2;
          ra2r2 = 1.0/ra22;
          rb2r2 = 1.0/rb22;
          rabr2 = sqrt(ra2r2*rb2r2);
  
          sin_phi2 = rg2 * rabr2 * iprod(a2, h2) * (-1);
  
          if (cos_phi2 < -0.5 || cos_phi2 > 0.5)
          {
              phi2 = asin(sin_phi2);
  
              if (cos_phi2 < 0)
              {
                  if (phi2 > 0)
                  {
                      phi2 = M_PI - phi2;
                  }
                  else
                  {
                      phi2 = -M_PI - phi2;
                  }
              }
          }
          else
          {
              phi2 = acos(cos_phi2);
  
              if (sin_phi2 < 0)
              {
                  phi2 = -phi2;
              }
          }
  
          xphi2 = phi2 + M_PI; /* 1 */
  
          /* Range mangling */
          if (xphi1 < 0)
          {
              xphi1 = xphi1 + 2*M_PI;
          }
          else if (xphi1 >= 2*M_PI)
          {
              xphi1 = xphi1 - 2*M_PI;
          }
  
          if (xphi2 < 0)
          {
              xphi2 = xphi2 + 2*M_PI;
          }
          else if (xphi2 >= 2*M_PI)
          {
              xphi2 = xphi2 - 2*M_PI;
          }
  
          /* Number of grid points */
          dx = 2*M_PI / cmap_grid->grid_spacing;
  
          /* Where on the grid are we */
          iphi1 = (int)(xphi1/dx);
          iphi2 = (int)(xphi2/dx);
  
          iphi1 = cmap_setup_grid_index(iphi1, cmap_grid->grid_spacing, &ip1m1, &ip1p1, &ip1p2);
          iphi2 = cmap_setup_grid_index(iphi2, cmap_grid->grid_spacing, &ip2m1, &ip2p1, &ip2p2);
  
          pos1    = iphi1*cmap_grid->grid_spacing+iphi2;
          pos2    = ip1p1*cmap_grid->grid_spacing+iphi2;
          pos3    = ip1p1*cmap_grid->grid_spacing+ip2p1;
          pos4    = iphi1*cmap_grid->grid_spacing+ip2p1;
  
          ty[0]   = cmapd[pos1*4];
          ty[1]   = cmapd[pos2*4];
          ty[2]   = cmapd[pos3*4];
          ty[3]   = cmapd[pos4*4];
  
          ty1[0]   = cmapd[pos1*4+1];
          ty1[1]   = cmapd[pos2*4+1];
          ty1[2]   = cmapd[pos3*4+1];
          ty1[3]   = cmapd[pos4*4+1];
  
          ty2[0]   = cmapd[pos1*4+2];
          ty2[1]   = cmapd[pos2*4+2];
          ty2[2]   = cmapd[pos3*4+2];
          ty2[3]   = cmapd[pos4*4+2];
  
          ty12[0]   = cmapd[pos1*4+3];
          ty12[1]   = cmapd[pos2*4+3];
          ty12[2]   = cmapd[pos3*4+3];
          ty12[3]   = cmapd[pos4*4+3];
  
          /* Switch to degrees */
          dx    = 360.0 / cmap_grid->grid_spacing;
          xphi1 = xphi1 * RAD2DEG;
          xphi2 = xphi2 * RAD2DEG;
  
          for (i = 0; i < 4; i++) /* 16 */
          {
              tx[i]    = ty[i];
              tx[i+4]  = ty1[i]*dx;
              tx[i+8]  = ty2[i]*dx;
              tx[i+12] = ty12[i]*dx*dx;
          }
  
          idx = 0;
          for (i = 0; i < 4; i++) /* 1056 */
          {
              for (j = 0; j < 4; j++)
              {
                  xx = 0;
                  for (k = 0; k < 16; k++)
                  {
                      xx = xx + cmap_coeff_matrix[k*16+idx]*tx[k];
                  }
  
                  idx++;
                  tc[i*4+j] = xx;
              }
          }
  
          tt    = (xphi1-iphi1*dx)/dx;
          tu    = (xphi2-iphi2*dx)/dx;
  
          e     = 0;
          df1   = 0;
          df2   = 0;
          ddf1  = 0;
          ddf2  = 0;
          ddf12 = 0;
  
          for (i = 3; i >= 0; i--)
          {
              l1 = loop_index[i][3];
              l2 = loop_index[i][2];
              l3 = loop_index[i][1];
  
              e     = tt * e    + ((tc[i*4+3]*tu+tc[i*4+2])*tu + tc[i*4+1])*tu+tc[i*4];
              df1   = tu * df1  + (3.0*tc[l1]*tt+2.0*tc[l2])*tt+tc[l3];
              df2   = tt * df2  + (3.0*tc[i*4+3]*tu+2.0*tc[i*4+2])*tu+tc[i*4+1];
              ddf1  = tu * ddf1 + 2.0*3.0*tc[l1]*tt+2.0*tc[l2];
              ddf2  = tt * ddf2 + 2.0*3.0*tc[4*i+3]*tu+2.0*tc[4*i+2];
          }
  
          ddf12 = tc[5] + 2.0*tc[9]*tt + 3.0*tc[13]*tt*tt + 2.0*tu*(tc[6]+2.0*tc[10]*tt+3.0*tc[14]*tt*tt) +
              3.0*tu*tu*(tc[7]+2.0*tc[11]*tt+3.0*tc[15]*tt*tt);
  
          fac     = RAD2DEG/dx;
          df1     = df1   * fac;
          df2     = df2   * fac;
          ddf1    = ddf1  * fac * fac;
          ddf2    = ddf2  * fac * fac;
          ddf12   = ddf12 * fac * fac;
  
          /* CMAP energy */
          vtot += e;
  
          /* Do forces - first torsion */
          fg1       = iprod(r1_ij, r1_kj);
          hg1       = iprod(r1_kl, r1_kj);
          fga1      = fg1*ra2r1*rgr1;
          hgb1      = hg1*rb2r1*rgr1;
          gaa1      = -ra2r1*rg1;
          gbb1      = rb2r1*rg1;
  
          for (i = 0; i < DIM; i++)
          {
              dtf1[i]   = gaa1 * a1[i];
              dtg1[i]   = fga1 * a1[i] - hgb1 * b1[i];
              dth1[i]   = gbb1 * b1[i];
  
              f1[i]     = df1  * dtf1[i];
              g1[i]     = df1  * dtg1[i];
              h1[i]     = df1  * dth1[i];
  
              f1_i[i]   =  f1[i];
              f1_j[i]   = -f1[i] - g1[i];
              f1_k[i]   =  h1[i] + g1[i];
              f1_l[i]   = -h1[i];
  
              f[a1i][i] = f[a1i][i] + f1_i[i];
              f[a1j][i] = f[a1j][i] + f1_j[i]; /* - f1[i] - g1[i] */
              f[a1k][i] = f[a1k][i] + f1_k[i]; /* h1[i] + g1[i] */
              f[a1l][i] = f[a1l][i] + f1_l[i]; /* h1[i] */
          }
  
          /* Do forces - second torsion */
          fg2       = iprod(r2_ij, r2_kj);
          hg2       = iprod(r2_kl, r2_kj);
          fga2      = fg2*ra2r2*rgr2;
          hgb2      = hg2*rb2r2*rgr2;
          gaa2      = -ra2r2*rg2;
          gbb2      = rb2r2*rg2;
  
          for (i = 0; i < DIM; i++)
          {
              dtf2[i]   = gaa2 * a2[i];
              dtg2[i]   = fga2 * a2[i] - hgb2 * b2[i];
              dth2[i]   = gbb2 * b2[i];
  
              f2[i]     = df2  * dtf2[i];
              g2[i]     = df2  * dtg2[i];
              h2[i]     = df2  * dth2[i];
  
              f2_i[i]   =  f2[i];
              f2_j[i]   = -f2[i] - g2[i];
              f2_k[i]   =  h2[i] + g2[i];
              f2_l[i]   = -h2[i];
  
              f[a2i][i] = f[a2i][i] + f2_i[i]; /* f2[i] */
              f[a2j][i] = f[a2j][i] + f2_j[i]; /* - f2[i] - g2[i] */
              f[a2k][i] = f[a2k][i] + f2_k[i]; /* h2[i] + g2[i] */
              f[a2l][i] = f[a2l][i] + f2_l[i]; /* - h2[i] */
          }
  
          /* Shift forces */
          if (g)
          {
              copy_ivec(SHIFT_IVEC(g, a1j), jt1);
              ivec_sub(SHIFT_IVEC(g, a1i),  jt1, dt1_ij);
              ivec_sub(SHIFT_IVEC(g, a1k),  jt1, dt1_kj);
              ivec_sub(SHIFT_IVEC(g, a1l),  jt1, dt1_lj);
              t11 = IVEC2IS(dt1_ij);
              t21 = IVEC2IS(dt1_kj);
              t31 = IVEC2IS(dt1_lj);
  
              copy_ivec(SHIFT_IVEC(g, a2j), jt2);
              ivec_sub(SHIFT_IVEC(g, a2i),  jt2, dt2_ij);
              ivec_sub(SHIFT_IVEC(g, a2k),  jt2, dt2_kj);
              ivec_sub(SHIFT_IVEC(g, a2l),  jt2, dt2_lj);
              t12 = IVEC2IS(dt2_ij);
              t22 = IVEC2IS(dt2_kj);
              t32 = IVEC2IS(dt2_lj);
          }
          else if (pbc)
          {
              t31 = pbc_rvec_sub(pbc, x[a1l], x[a1j], h1);
              t32 = pbc_rvec_sub(pbc, x[a2l], x[a2j], h2);
          }
          else
          {
              t31 = CENTRAL;
              t32 = CENTRAL;
          }
  
          rvec_inc(fshift[t11], f1_i);
          rvec_inc(fshift[CENTRAL], f1_j);
          rvec_inc(fshift[t21], f1_k);
          rvec_inc(fshift[t31], f1_l);
  
          rvec_inc(fshift[t21], f2_i);
          rvec_inc(fshift[CENTRAL], f2_j);
          rvec_inc(fshift[t22], f2_k);
          rvec_inc(fshift[t32], f2_l);
      }
      return vtot;
  }
  
  
  
  /***********************************************************
   *
   *   G R O M O S  9 6   F U N C T I O N S
   *
   ***********************************************************/
  real g96harmonic(real kA, real kB, real xA, real xB, real x, real lambda,
                   real *V, real *F)
  {
      const real half = 0.5;
      real       L1, kk, x0, dx, dx2;
      real       v, f, dvdlambda;
  
      L1    = 1.0-lambda;
      kk    = L1*kA+lambda*kB;
      x0    = L1*xA+lambda*xB;
  
      dx    = x-x0;
      dx2   = dx*dx;
  
      f          = -kk*dx;
      v          = half*kk*dx2;
      dvdlambda  = half*(kB-kA)*dx2 + (xA-xB)*kk*dx;
  
      *F    = f;
      *V    = v;
  
      return dvdlambda;
  
      /* That was 21 flops */
  }
  
  real g96bonds(int nbonds,
                const t_iatom forceatoms[], const t_iparams forceparams[],
                const rvec x[], rvec f[], rvec fshift[],
                const t_pbc *pbc, const t_graph *g,
                real lambda, real *dvdlambda,
                const t_mdatoms *md, t_fcdata *fcd,
                int *global_atom_index)
  {
      int  i, m, ki, ai, aj, type;
      real dr2, fbond, vbond, fij, vtot;
      rvec dx;
      ivec dt;
  
      vtot = 0.0;
      for (i = 0; (i < nbonds); )
      {
          type = forceatoms[i++];
          ai   = forceatoms[i++];
          aj   = forceatoms[i++];
  
          ki   = pbc_rvec_sub(pbc, x[ai], x[aj], dx); /*   3      */
          dr2  = iprod(dx, dx);                       /*   5		*/
  
          *dvdlambda += g96harmonic(forceparams[type].harmonic.krA,
                                    forceparams[type].harmonic.krB,
                                    forceparams[type].harmonic.rA,
                                    forceparams[type].harmonic.rB,
                                    dr2, lambda, &vbond, &fbond);
  
          vtot  += 0.5*vbond;                         /* 1*/
  #ifdef DEBUG
          if (debug)
          {
              fprintf(debug, "G96-BONDS: dr = %10g  vbond = %10g  fbond = %10g\n",
                      sqrt(dr2), vbond, fbond);
          }
  #endif
  
          if (g)
          {
              ivec_sub(SHIFT_IVEC(g, ai), SHIFT_IVEC(g, aj), dt);
              ki = IVEC2IS(dt);
          }
          for (m = 0; (m < DIM); m++)     /*  15		*/
          {
              fij                 = fbond*dx[m];
              f[ai][m]           += fij;
              f[aj][m]           -= fij;
              fshift[ki][m]      += fij;
              fshift[CENTRAL][m] -= fij;
          }
      }               /* 44 TOTAL	*/
      return vtot;
  }
  
  real g96bond_angle(const rvec xi, const rvec xj, const rvec xk, const t_pbc *pbc,
                     rvec r_ij, rvec r_kj,
                     int *t1, int *t2)
  /* Return value is the angle between the bonds i-j and j-k */
  {
      real costh;
  
      *t1 = pbc_rvec_sub(pbc, xi, xj, r_ij); /*  3		*/
      *t2 = pbc_rvec_sub(pbc, xk, xj, r_kj); /*  3		*/
  
      costh = cos_angle(r_ij, r_kj);         /* 25		*/
      /* 41 TOTAL	*/
      return costh;
  }
  
  real g96angles(int nbonds,
                 const t_iatom forceatoms[], const t_iparams forceparams[],
                 const rvec x[], rvec f[], rvec fshift[],
                 const t_pbc *pbc, const t_graph *g,
                 real lambda, real *dvdlambda,
                 const t_mdatoms *md, t_fcdata *fcd,
                 int *global_atom_index)
  {
      int  i, ai, aj, ak, type, m, t1, t2;
      rvec r_ij, r_kj;
      real cos_theta, dVdt, va, vtot;
      real rij_1, rij_2, rkj_1, rkj_2, rijrkj_1;
      rvec f_i, f_j, f_k;
      ivec jt, dt_ij, dt_kj;
  
      vtot = 0.0;
      for (i = 0; (i < nbonds); )
      {
          type = forceatoms[i++];
          ai   = forceatoms[i++];
          aj   = forceatoms[i++];
          ak   = forceatoms[i++];
  
          cos_theta  = g96bond_angle(x[ai], x[aj], x[ak], pbc, r_ij, r_kj, &t1, &t2);
  
          *dvdlambda += g96harmonic(forceparams[type].harmonic.krA,
                                    forceparams[type].harmonic.krB,
                                    forceparams[type].harmonic.rA,
                                    forceparams[type].harmonic.rB,
                                    cos_theta, lambda, &va, &dVdt);
          vtot    += va;
  
          rij_1    = gmx_invsqrt(iprod(r_ij, r_ij));
          rkj_1    = gmx_invsqrt(iprod(r_kj, r_kj));
          rij_2    = rij_1*rij_1;
          rkj_2    = rkj_1*rkj_1;
          rijrkj_1 = rij_1*rkj_1;                 /* 23 */
  
  #ifdef DEBUG
          if (debug)
          {
              fprintf(debug, "G96ANGLES: costheta = %10g  vth = %10g  dV/dct = %10g\n",
                      cos_theta, va, dVdt);
          }
  #endif
          for (m = 0; (m < DIM); m++)     /*  42	*/
          {
              f_i[m]    = dVdt*(r_kj[m]*rijrkj_1 - r_ij[m]*rij_2*cos_theta);
              f_k[m]    = dVdt*(r_ij[m]*rijrkj_1 - r_kj[m]*rkj_2*cos_theta);
              f_j[m]    = -f_i[m]-f_k[m];
              f[ai][m] += f_i[m];
              f[aj][m] += f_j[m];
              f[ak][m] += f_k[m];
          }
  
          if (g)
          {
              copy_ivec(SHIFT_IVEC(g, aj), jt);
  
              ivec_sub(SHIFT_IVEC(g, ai), jt, dt_ij);
              ivec_sub(SHIFT_IVEC(g, ak), jt, dt_kj);
              t1 = IVEC2IS(dt_ij);
              t2 = IVEC2IS(dt_kj);
          }
          rvec_inc(fshift[t1], f_i);
          rvec_inc(fshift[CENTRAL], f_j);
          rvec_inc(fshift[t2], f_k);          /* 9 */
          /* 163 TOTAL	*/
      }
      return vtot;
  }
  
  real cross_bond_bond(int nbonds,
                       const t_iatom forceatoms[], const t_iparams forceparams[],
                       const rvec x[], rvec f[], rvec fshift[],
                       const t_pbc *pbc, const t_graph *g,
                       real lambda, real *dvdlambda,
                       const t_mdatoms *md, t_fcdata *fcd,
                       int *global_atom_index)
  {
      /* Potential from Lawrence and Skimmer, Chem. Phys. Lett. 372 (2003)
       * pp. 842-847
       */
      int  i, ai, aj, ak, type, m, t1, t2;
      rvec r_ij, r_kj;
      real vtot, vrr, s1, s2, r1, r2, r1e, r2e, krr;
      rvec f_i, f_j, f_k;
      ivec jt, dt_ij, dt_kj;
  
      vtot = 0.0;
      for (i = 0; (i < nbonds); )
      {
          type = forceatoms[i++];
          ai   = forceatoms[i++];
          aj   = forceatoms[i++];
          ak   = forceatoms[i++];
          r1e  = forceparams[type].cross_bb.r1e;
          r2e  = forceparams[type].cross_bb.r2e;
          krr  = forceparams[type].cross_bb.krr;
  
          /* Compute distance vectors ... */
          t1 = pbc_rvec_sub(pbc, x[ai], x[aj], r_ij);
          t2 = pbc_rvec_sub(pbc, x[ak], x[aj], r_kj);
  
          /* ... and their lengths */
          r1 = norm(r_ij);
          r2 = norm(r_kj);
  
          /* Deviations from ideality */
          s1 = r1-r1e;
          s2 = r2-r2e;
  
          /* Energy (can be negative!) */
          vrr   = krr*s1*s2;
          vtot += vrr;
  
          /* Forces */
          svmul(-krr*s2/r1, r_ij, f_i);
          svmul(-krr*s1/r2, r_kj, f_k);
  
          for (m = 0; (m < DIM); m++)     /*  12	*/
          {
              f_j[m]    = -f_i[m] - f_k[m];
              f[ai][m] += f_i[m];
              f[aj][m] += f_j[m];
              f[ak][m] += f_k[m];
          }
  
          /* Virial stuff */
          if (g)
          {
              copy_ivec(SHIFT_IVEC(g, aj), jt);
  
              ivec_sub(SHIFT_IVEC(g, ai), jt, dt_ij);
              ivec_sub(SHIFT_IVEC(g, ak), jt, dt_kj);
              t1 = IVEC2IS(dt_ij);
              t2 = IVEC2IS(dt_kj);
          }
          rvec_inc(fshift[t1], f_i);
          rvec_inc(fshift[CENTRAL], f_j);
          rvec_inc(fshift[t2], f_k);          /* 9 */
          /* 163 TOTAL	*/
      }
      return vtot;
  }
  
  real cross_bond_angle(int nbonds,
                        const t_iatom forceatoms[], const t_iparams forceparams[],
                        const rvec x[], rvec f[], rvec fshift[],
                        const t_pbc *pbc, const t_graph *g,
                        real lambda, real *dvdlambda,
                        const t_mdatoms *md, t_fcdata *fcd,
                        int *global_atom_index)
  {
      /* Potential from Lawrence and Skimmer, Chem. Phys. Lett. 372 (2003)
       * pp. 842-847
       */
      int  i, ai, aj, ak, type, m, t1, t2, t3;
      rvec r_ij, r_kj, r_ik;
      real vtot, vrt, s1, s2, s3, r1, r2, r3, r1e, r2e, r3e, krt, k1, k2, k3;
      rvec f_i, f_j, f_k;
      ivec jt, dt_ij, dt_kj;
  
      vtot = 0.0;
      for (i = 0; (i < nbonds); )
      {
          type = forceatoms[i++];
          ai   = forceatoms[i++];
          aj   = forceatoms[i++];
          ak   = forceatoms[i++];
          r1e  = forceparams[type].cross_ba.r1e;
          r2e  = forceparams[type].cross_ba.r2e;
          r3e  = forceparams[type].cross_ba.r3e;
          krt  = forceparams[type].cross_ba.krt;
  
          /* Compute distance vectors ... */
          t1 = pbc_rvec_sub(pbc, x[ai], x[aj], r_ij);
          t2 = pbc_rvec_sub(pbc, x[ak], x[aj], r_kj);
          t3 = pbc_rvec_sub(pbc, x[ai], x[ak], r_ik);
  
          /* ... and their lengths */
          r1 = norm(r_ij);
          r2 = norm(r_kj);
          r3 = norm(r_ik);
  
          /* Deviations from ideality */
          s1 = r1-r1e;
          s2 = r2-r2e;
          s3 = r3-r3e;
  
          /* Energy (can be negative!) */
          vrt   = krt*s3*(s1+s2);
          vtot += vrt;
  
          /* Forces */
          k1 = -krt*(s3/r1);
          k2 = -krt*(s3/r2);
          k3 = -krt*(s1+s2)/r3;
          for (m = 0; (m < DIM); m++)
          {
              f_i[m] = k1*r_ij[m] + k3*r_ik[m];
              f_k[m] = k2*r_kj[m] - k3*r_ik[m];
              f_j[m] = -f_i[m] - f_k[m];
          }
  
          for (m = 0; (m < DIM); m++)     /*  12	*/
          {
              f[ai][m] += f_i[m];
              f[aj][m] += f_j[m];
              f[ak][m] += f_k[m];
          }
  
          /* Virial stuff */
          if (g)
          {
              copy_ivec(SHIFT_IVEC(g, aj), jt);
  
              ivec_sub(SHIFT_IVEC(g, ai), jt, dt_ij);
              ivec_sub(SHIFT_IVEC(g, ak), jt, dt_kj);
              t1 = IVEC2IS(dt_ij);
              t2 = IVEC2IS(dt_kj);
          }
          rvec_inc(fshift[t1], f_i);
          rvec_inc(fshift[CENTRAL], f_j);
          rvec_inc(fshift[t2], f_k);          /* 9 */
          /* 163 TOTAL	*/
      }
      return vtot;
  }
  
  static real bonded_tab(const char *type, int table_nr,
                         const bondedtable_t *table, real kA, real kB, real r,
                         real lambda, real *V, real *F)
  {
      real k, tabscale, *VFtab, rt, eps, eps2, Yt, Ft, Geps, Heps2, Fp, VV, FF;
      int  n0, nnn;
      real v, f, dvdlambda;
  
      k = (1.0 - lambda)*kA + lambda*kB;
  
      tabscale = table->scale;
      VFtab    = table->data;
  
      rt    = r*tabscale;
      n0    = rt;
      if (n0 >= table->n)
      {
          gmx_fatal(FARGS, "A tabulated %s interaction table number %d is out of the table range: r %f, between table indices %d and %d, table length %d",
                    type, table_nr, r, n0, n0+1, table->n);
      }
      eps   = rt - n0;
      eps2  = eps*eps;
      nnn   = 4*n0;
      Yt    = VFtab[nnn];
      Ft    = VFtab[nnn+1];
      Geps  = VFtab[nnn+2]*eps;
      Heps2 = VFtab[nnn+3]*eps2;
      Fp    = Ft + Geps + Heps2;
      VV    = Yt + Fp*eps;
      FF    = Fp + Geps + 2.0*Heps2;
  
      *F         = -k*FF*tabscale;
      *V         = k*VV;
      dvdlambda  = (kB - kA)*VV;
  
      return dvdlambda;
  
      /* That was 22 flops */
  }
  
  real tab_bonds(int nbonds,
                 const t_iatom forceatoms[], const t_iparams forceparams[],
                 const rvec x[], rvec f[], rvec fshift[],
                 const t_pbc *pbc, const t_graph *g,
                 real lambda, real *dvdlambda,
                 const t_mdatoms *md, t_fcdata *fcd,
                 int *global_atom_index)
  {
      int  i, m, ki, ai, aj, type, table;
      real dr, dr2, fbond, vbond, fij, vtot;
      rvec dx;
      ivec dt;
  
      vtot = 0.0;
      for (i = 0; (i < nbonds); )
      {
          type = forceatoms[i++];
          ai   = forceatoms[i++];
          aj   = forceatoms[i++];
  
          ki   = pbc_rvec_sub(pbc, x[ai], x[aj], dx); /*   3      */
          dr2  = iprod(dx, dx);                       /*   5		*/
          dr   = dr2*gmx_invsqrt(dr2);                /*  10		*/
  
          table = forceparams[type].tab.table;
  
          *dvdlambda += bonded_tab("bond", table,
                                   &fcd->bondtab[table],
                                   forceparams[type].tab.kA,
                                   forceparams[type].tab.kB,
                                   dr, lambda, &vbond, &fbond); /*  22 */
  
          if (dr2 == 0.0)
          {
              continue;
          }
  
  
          vtot  += vbond;            /* 1*/
          fbond *= gmx_invsqrt(dr2); /*   6		*/
  #ifdef DEBUG
          if (debug)
          {
              fprintf(debug, "TABBONDS: dr = %10g  vbond = %10g  fbond = %10g\n",
                      dr, vbond, fbond);
          }
  #endif
          if (g)
          {
              ivec_sub(SHIFT_IVEC(g, ai), SHIFT_IVEC(g, aj), dt);
              ki = IVEC2IS(dt);
          }
          for (m = 0; (m < DIM); m++)     /*  15		*/
          {
              fij                 = fbond*dx[m];
              f[ai][m]           += fij;
              f[aj][m]           -= fij;
              fshift[ki][m]      += fij;
              fshift[CENTRAL][m] -= fij;
          }
      }               /* 62 TOTAL	*/
      return vtot;
  }
  
  real tab_angles(int nbonds,
                  const t_iatom forceatoms[], const t_iparams forceparams[],
                  const rvec x[], rvec f[], rvec fshift[],
                  const t_pbc *pbc, const t_graph *g,
                  real lambda, real *dvdlambda,
                  const t_mdatoms *md, t_fcdata *fcd,
                  int *global_atom_index)
  {
      int  i, ai, aj, ak, t1, t2, type, table;
      rvec r_ij, r_kj;
      real cos_theta, cos_theta2, theta, dVdt, va, vtot;
      ivec jt, dt_ij, dt_kj;
  
      vtot = 0.0;
      for (i = 0; (i < nbonds); )
      {
          type = forceatoms[i++];
          ai   = forceatoms[i++];
          aj   = forceatoms[i++];
          ak   = forceatoms[i++];
  
          theta  = bond_angle(x[ai], x[aj], x[ak], pbc,
                              r_ij, r_kj, &cos_theta, &t1, &t2); /*  41		*/
  
          table = forceparams[type].tab.table;
  
          *dvdlambda += bonded_tab("angle", table,
                                   &fcd->angletab[table],
                                   forceparams[type].tab.kA,
                                   forceparams[type].tab.kB,
                                   theta, lambda, &va, &dVdt); /*  22  */
          vtot += va;
  
          cos_theta2 = sqr(cos_theta);            /*   1		*/
          if (cos_theta2 < 1)
          {
              int  m;
              real snt, st, sth;
              real cik, cii, ckk;
              real nrkj2, nrij2;
              rvec f_i, f_j, f_k;
  
              st  = dVdt*gmx_invsqrt(1 - cos_theta2); /*  12		*/
              sth = st*cos_theta;                     /*   1		*/
  #ifdef DEBUG
              if (debug)
              {
                  fprintf(debug, "ANGLES: theta = %10g  vth = %10g  dV/dtheta = %10g\n",
                          theta*RAD2DEG, va, dVdt);
              }
  #endif
              nrkj2 = iprod(r_kj, r_kj);  /*   5		*/
              nrij2 = iprod(r_ij, r_ij);
  
              cik = st*gmx_invsqrt(nrkj2*nrij2); /*  12		*/
              cii = sth/nrij2;                   /*  10		*/
              ckk = sth/nrkj2;                   /*  10		*/
  
              for (m = 0; (m < DIM); m++)        /*  39		*/
              {
                  f_i[m]    = -(cik*r_kj[m]-cii*r_ij[m]);
                  f_k[m]    = -(cik*r_ij[m]-ckk*r_kj[m]);
                  f_j[m]    = -f_i[m]-f_k[m];
                  f[ai][m] += f_i[m];
                  f[aj][m] += f_j[m];
                  f[ak][m] += f_k[m];
              }
              if (g)
              {
                  copy_ivec(SHIFT_IVEC(g, aj), jt);
  
                  ivec_sub(SHIFT_IVEC(g, ai), jt, dt_ij);
                  ivec_sub(SHIFT_IVEC(g, ak), jt, dt_kj);
                  t1 = IVEC2IS(dt_ij);
                  t2 = IVEC2IS(dt_kj);
              }
              rvec_inc(fshift[t1], f_i);
              rvec_inc(fshift[CENTRAL], f_j);
              rvec_inc(fshift[t2], f_k);
          }                                       /* 169 TOTAL	*/
      }
      return vtot;
  }
  
  real tab_dihs(int nbonds,
                const t_iatom forceatoms[], const t_iparams forceparams[],
                const rvec x[], rvec f[], rvec fshift[],
                const t_pbc *pbc, const t_graph *g,
                real lambda, real *dvdlambda,
                const t_mdatoms *md, t_fcdata *fcd,
                int *global_atom_index)
  {
      int  i, type, ai, aj, ak, al, table;
      int  t1, t2, t3;
      rvec r_ij, r_kj, r_kl, m, n;
      real phi, sign, ddphi, vpd, vtot;
  
      vtot = 0.0;
      for (i = 0; (i < nbonds); )
      {
          type = forceatoms[i++];
          ai   = forceatoms[i++];
          aj   = forceatoms[i++];
          ak   = forceatoms[i++];
          al   = forceatoms[i++];
  
          phi = dih_angle(x[ai], x[aj], x[ak], x[al], pbc, r_ij, r_kj, r_kl, m, n,
                          &sign, &t1, &t2, &t3);  /*  84  */
  
          table = forceparams[type].tab.table;
  
          /* Hopefully phi+M_PI never results in values < 0 */
          *dvdlambda += bonded_tab("dihedral", table,
                                   &fcd->dihtab[table],
                                   forceparams[type].tab.kA,
                                   forceparams[type].tab.kB,
                                   phi+M_PI, lambda, &vpd, &ddphi);
  
          vtot += vpd;
          do_dih_fup(ai, aj, ak, al, -ddphi, r_ij, r_kj, r_kl, m, n,
                     f, fshift, pbc, g, x, t1, t2, t3); /* 112	*/
  
  #ifdef DEBUG
          fprintf(debug, "pdih: (%d,%d,%d,%d) phi=%g\n",
                  ai, aj, ak, al, phi);
  #endif
      } /* 227 TOTAL  */
  
      return vtot;
  }
  
  /* Return if this is a potential calculated in bondfree.c,
   * i.e. an interaction that actually calculates a potential and
   * works on multiple atoms (not e.g. a connection or a position restraint).
   */
  static gmx_inline gmx_bool ftype_is_bonded_potential(int ftype)
  {
      return
          (interaction_function[ftype].flags & IF_BOND) &&
          !(ftype == F_CONNBONDS || ftype == F_POSRES) &&
          (ftype < F_GB12 || ftype > F_GB14);
  }
  
  static void divide_bondeds_over_threads(t_idef *idef, int nthreads)
  {
      int ftype;
      int nat1;
      int t;
      int il_nr_thread;
  
      idef->nthreads = nthreads;
  
      if (F_NRE*(nthreads+1) > idef->il_thread_division_nalloc)
      {
          idef->il_thread_division_nalloc = F_NRE*(nthreads+1);
          snew(idef->il_thread_division, idef->il_thread_division_nalloc);
      }
  
      for (ftype = 0; ftype < F_NRE; ftype++)
      {
          if (ftype_is_bonded_potential(ftype))
          {
              nat1 = interaction_function[ftype].nratoms + 1;
  
              for (t = 0; t <= nthreads; t++)
              {
                  /* Divide the interactions equally over the threads.
                   * When the different types of bonded interactions
                   * are distributed roughly equally over the threads,
                   * this should lead to well localized output into
                   * the force buffer on each thread.
                   * If this is not the case, a more advanced scheme
                   * (not implemented yet) will do better.
                   */
                  il_nr_thread = (((idef->il[ftype].nr/nat1)*t)/nthreads)*nat1;
  
                  /* Ensure that distance restraint pairs with the same label
                   * end up on the same thread.
                   * This is slighlty tricky code, since the next for iteration
                   * may have an initial il_nr_thread lower than the final value
                   * in the previous iteration, but this will anyhow be increased
                   * to the approriate value again by this while loop.
                   */
                  while (ftype == F_DISRES &&
                         il_nr_thread > 0 &&
                         il_nr_thread < idef->il[ftype].nr &&
                         idef->iparams[idef->il[ftype].iatoms[il_nr_thread]].disres.label ==
                         idef->iparams[idef->il[ftype].iatoms[il_nr_thread-nat1]].disres.label)
                  {
                      il_nr_thread += nat1;
                  }
  
                  idef->il_thread_division[ftype*(nthreads+1)+t] = il_nr_thread;
              }
          }
      }
  }
  
  static unsigned
  calc_bonded_reduction_mask(const t_idef *idef,
                             int shift,
                             int t, int nt)
  {
      unsigned mask;
      int      ftype, nb, nat1, nb0, nb1, i, a;
  
      mask = 0;
  
      for (ftype = 0; ftype < F_NRE; ftype++)
      {
          if (ftype_is_bonded_potential(ftype))
          {
              nb = idef->il[ftype].nr;
              if (nb > 0)
              {
                  nat1 = interaction_function[ftype].nratoms + 1;
  
                  /* Divide this interaction equally over the threads.
                   * This is not stored: should match division in calc_bonds.
                   */
                  nb0 = idef->il_thread_division[ftype*(nt+1)+t];
                  nb1 = idef->il_thread_division[ftype*(nt+1)+t+1];
  
                  for (i = nb0; i < nb1; i += nat1)
                  {
                      for (a = 1; a < nat1; a++)
                      {
                          mask |= (1U << (idef->il[ftype].iatoms[i+a]>>shift));
                      }
                  }
              }
          }
      }
  
      return mask;
  }
  
  void setup_bonded_threading(t_forcerec   *fr, t_idef *idef)
  {
  #define MAX_BLOCK_BITS 32
      int t;
      int ctot, c, b;
  
  #ifndef NDEBUG
      assert(fr->nthreads >= 1);
  #endif
  
      /* Divide the bonded interaction over the threads */
      divide_bondeds_over_threads(idef, fr->nthreads);
  
      if (fr->nthreads == 1)
      {
          fr->red_nblock = 0;
  
          return;
      }
  
      /* We divide the force array in a maximum of 32 blocks.
       * Minimum force block reduction size is 2^6=64.
       */
      fr->red_ashift = 6;
      while (fr->natoms_force > (int)(MAX_BLOCK_BITS*(1U<<fr->red_ashift)))
      {
          fr->red_ashift++;
      }
      if (debug)
      {
          fprintf(debug, "bonded force buffer block atom shift %d bits\n",
                  fr->red_ashift);
      }
  
      /* Determine to which blocks each thread's bonded force calculation
       * contributes. Store this is a mask for each thread.
       */
  #pragma omp parallel for num_threads(fr->nthreads) schedule(static)
      for (t = 1; t < fr->nthreads; t++)
      {
          fr->f_t[t].red_mask =
              calc_bonded_reduction_mask(idef, fr->red_ashift, t, fr->nthreads);
      }
  
      /* Determine the maximum number of blocks we need to reduce over */
      fr->red_nblock = 0;
      ctot           = 0;
      for (t = 0; t < fr->nthreads; t++)
      {
          c = 0;
          for (b = 0; b < MAX_BLOCK_BITS; b++)
          {
              if (fr->f_t[t].red_mask & (1U<<b))
              {
                  fr->red_nblock = max(fr->red_nblock, b+1);
                  c++;
              }
          }
          if (debug)
          {
              fprintf(debug, "thread %d flags %x count %d\n",
                      t, fr->f_t[t].red_mask, c);
          }
          ctot += c;
      }
      if (debug)
      {
          fprintf(debug, "Number of blocks to reduce: %d of size %d\n",
                  fr->red_nblock, 1<<fr->red_ashift);
          fprintf(debug, "Reduction density %.2f density/#thread %.2f\n",
                  ctot*(1<<fr->red_ashift)/(double)fr->natoms_force,
                  ctot*(1<<fr->red_ashift)/(double)(fr->natoms_force*fr->nthreads));
      }
  }
  
  static void zero_thread_forces(f_thread_t *f_t, int n,
                                 int nblock, int blocksize)
  {
      int b, a0, a1, a, i, j;
  
      if (n > f_t->f_nalloc)
      {
          f_t->f_nalloc = over_alloc_large(n);
          srenew(f_t->f, f_t->f_nalloc);
      }
  
      if (f_t->red_mask != 0)
      {
          for (b = 0; b < nblock; b++)
          {
              if (f_t->red_mask && (1U<<b))
              {
                  a0 = b*blocksize;
                  a1 = min((b+1)*blocksize, n);
                  for (a = a0; a < a1; a++)
                  {
                      clear_rvec(f_t->f[a]);
                  }
              }
          }
      }
      for (i = 0; i < SHIFTS; i++)
      {
          clear_rvec(f_t->fshift[i]);
      }
      for (i = 0; i < F_NRE; i++)
      {
          f_t->ener[i] = 0;
      }
      for (i = 0; i < egNR; i++)
      {
          for (j = 0; j < f_t->grpp.nener; j++)
          {
              f_t->grpp.ener[i][j] = 0;
          }
      }
      for (i = 0; i < efptNR; i++)
      {
          f_t->dvdl[i] = 0;
      }
  }
  
  static void reduce_thread_force_buffer(int n, rvec *f,
                                         int nthreads, f_thread_t *f_t,
                                         int nblock, int block_size)
  {
      /* The max thread number is arbitrary,
       * we used a fixed number to avoid memory management.
       * Using more than 16 threads is probably never useful performance wise.
       */
  #define MAX_BONDED_THREADS 256
      int b;
  
      if (nthreads > MAX_BONDED_THREADS)
      {
          gmx_fatal(FARGS, "Can not reduce bonded forces on more than %d threads",
                    MAX_BONDED_THREADS);
      }
  
      /* This reduction can run on any number of threads,
       * independently of nthreads.
       */
  #pragma omp parallel for num_threads(nthreads) schedule(static)
      for (b = 0; b < nblock; b++)
      {
          rvec *fp[MAX_BONDED_THREADS];
          int   nfb, ft, fb;
          int   a0, a1, a;
  
          /* Determine which threads contribute to this block */
          nfb = 0;
          for (ft = 1; ft < nthreads; ft++)
          {
              if (f_t[ft].red_mask & (1U<<b))
              {
                  fp[nfb++] = f_t[ft].f;
              }
          }
          if (nfb > 0)
          {
              /* Reduce force buffers for threads that contribute */
              a0 =  b   *block_size;
              a1 = (b+1)*block_size;
              a1 = min(a1, n);
              for (a = a0; a < a1; a++)
              {
                  for (fb = 0; fb < nfb; fb++)
                  {
                      rvec_inc(f[a], fp[fb][a]);
                  }
              }
          }
      }
  }
  
  static void reduce_thread_forces(int n, rvec *f, rvec *fshift,
                                   real *ener, gmx_grppairener_t *grpp, real *dvdl,
                                   int nthreads, f_thread_t *f_t,
                                   int nblock, int block_size,
                                   gmx_bool bCalcEnerVir,
                                   gmx_bool bDHDL)
  {
      if (nblock > 0)
      {
          /* Reduce the bonded force buffer */
          reduce_thread_force_buffer(n, f, nthreads, f_t, nblock, block_size);
      }
  
      /* When necessary, reduce energy and virial using one thread only */
      if (bCalcEnerVir)
      {
          int t, i, j;
  
          for (i = 0; i < SHIFTS; i++)
          {
              for (t = 1; t < nthreads; t++)
              {
                  rvec_inc(fshift[i], f_t[t].fshift[i]);
              }
          }
          for (i = 0; i < F_NRE; i++)
          {
              for (t = 1; t < nthreads; t++)
              {
                  ener[i] += f_t[t].ener[i];
              }
          }
          for (i = 0; i < egNR; i++)
          {
              for (j = 0; j < f_t[1].grpp.nener; j++)
              {
                  for (t = 1; t < nthreads; t++)
                  {
  
                      grpp->ener[i][j] += f_t[t].grpp.ener[i][j];
                  }
              }
          }
          if (bDHDL)
          {
              for (i = 0; i < efptNR; i++)
              {
  
                  for (t = 1; t < nthreads; t++)
                  {
                      dvdl[i] += f_t[t].dvdl[i];
                  }
              }
          }
      }
  }
  
  static real calc_one_bond(FILE *fplog, int thread,
                            int ftype, const t_idef *idef,
                            rvec x[], rvec f[], rvec fshift[],
                            t_forcerec *fr,
                            const t_pbc *pbc, const t_graph *g,
                            gmx_grppairener_t *grpp,
                            t_nrnb *nrnb,
                            real *lambda, real *dvdl,
                            const t_mdatoms *md, t_fcdata *fcd,
                            gmx_bool bCalcEnerVir,
                            int *global_atom_index, gmx_bool bPrintSepPot)
  {
      int      nat1, nbonds, efptFTYPE;
      real     v = 0;
      t_iatom *iatoms;
      int      nb0, nbn;
  
      if (IS_RESTRAINT_TYPE(ftype))
      {
          efptFTYPE = efptRESTRAINT;
      }
      else
      {
          efptFTYPE = efptBONDED;
      }
  
      nat1      = interaction_function[ftype].nratoms + 1;
      nbonds    = idef->il[ftype].nr/nat1;
      iatoms    = idef->il[ftype].iatoms;
  
      nb0 = idef->il_thread_division[ftype*(idef->nthreads+1)+thread];
      nbn = idef->il_thread_division[ftype*(idef->nthreads+1)+thread+1] - nb0;
  
      if (!IS_LISTED_LJ_C(ftype))
      {
          if (ftype == F_CMAP)
          {
              v = cmap_dihs(nbn, iatoms+nb0,
                            idef->iparams, &idef->cmap_grid,
                            (const rvec*)x, f, fshift,
                            pbc, g, lambda[efptFTYPE], &(dvdl[efptFTYPE]),
                            md, fcd, global_atom_index);
          }
  #ifdef SIMD_BONDEDS
          else if (ftype == F_ANGLES &&
                   !bCalcEnerVir && fr->efep == efepNO)
          {
              /* No energies, shift forces, dvdl */
              angles_noener_simd(nbn, idef->il[ftype].iatoms+nb0,
                                 idef->iparams,
                                 (const rvec*)x, f,
                                 pbc, g, lambda[efptFTYPE], md, fcd,
                                 global_atom_index);
              v = 0;
          }
  #endif
          else if (ftype == F_PDIHS &&
                   !bCalcEnerVir && fr->efep == efepNO)
          {
              /* No energies, shift forces, dvdl */
  #ifndef SIMD_BONDEDS
              pdihs_noener
  #else
              pdihs_noener_simd
  #endif
                  (nbn, idef->il[ftype].iatoms+nb0,
                   idef->iparams,
                   (const rvec*)x, f,
                   pbc, g, lambda[efptFTYPE], md, fcd,
                   global_atom_index);
              v = 0;
          }
          else
          {
              v = interaction_function[ftype].ifunc(nbn, iatoms+nb0,
                                                    idef->iparams,
                                                    (const rvec*)x, f, fshift,
                                                    pbc, g, lambda[efptFTYPE], &(dvdl[efptFTYPE]),
                                                    md, fcd, global_atom_index);
          }
          if (bPrintSepPot)
          {
              fprintf(fplog, "  %-23s #%4d  V %12.5e  dVdl %12.5e\n",
                      interaction_function[ftype].longname,
                      nbonds, v, lambda[efptFTYPE]);
          }
      }
      else
      {
          v = do_nonbonded_listed(ftype, nbn, iatoms+nb0, idef->iparams, (const rvec*)x, f, fshift,
                                  pbc, g, lambda, dvdl, md, fr, grpp, global_atom_index);
          
          if (bPrintSepPot)
          {
              fprintf(fplog, "  %-5s + %-15s #%4d                  dVdl %12.5e\n",
                      interaction_function[ftype].longname,
                      interaction_function[F_LJ14].longname, nbonds, dvdl[efptVDW]);
              fprintf(fplog, "  %-5s + %-15s #%4d                  dVdl %12.5e\n",
                      interaction_function[ftype].longname,
                      interaction_function[F_COUL14].longname, nbonds, dvdl[efptCOUL]);
          }
      }
  
      if (thread == 0)
      {
          inc_nrnb(nrnb, interaction_function[ftype].nrnb_ind, nbonds);
      }
  
      return v;
  }
  
  void calc_bonds(FILE *fplog, const gmx_multisim_t *ms,
                  const t_idef *idef,
                  rvec x[], history_t *hist,
                  rvec f[], t_forcerec *fr,
                  const t_pbc *pbc, const t_graph *g,
                  gmx_enerdata_t *enerd, t_nrnb *nrnb,
                  real *lambda,
                  const t_mdatoms *md,
                  t_fcdata *fcd, int *global_atom_index,
                  t_atomtypes *atype, gmx_genborn_t *born,
                  int force_flags,
                  gmx_bool bPrintSepPot, gmx_large_int_t step)
  {
      gmx_bool      bCalcEnerVir;
      int           i;
      real          v, dvdl[efptNR], dvdl_dum[efptNR]; /* The dummy array is to have a place to store the dhdl at other values
                                                          of lambda, which will be thrown away in the end*/
      const  t_pbc *pbc_null;
      char          buf[22];
      int           thread;
  
  #ifndef NDEBUG
      assert(fr->nthreads == idef->nthreads);
  #endif
  
      bCalcEnerVir = (force_flags & (GMX_FORCE_VIRIAL | GMX_FORCE_ENERGY));
  
      for (i = 0; i < efptNR; i++)
      {
          dvdl[i] = 0.0;
      }
      if (fr->bMolPBC)
      {
          pbc_null = pbc;
      }
      else
      {
          pbc_null = NULL;
      }
      if (bPrintSepPot)
      {
          fprintf(fplog, "Step %s: bonded V and dVdl for this node\n",
                  gmx_step_str(step, buf));
      }
  
  #ifdef DEBUG
      if (g && debug)
      {
          p_graph(debug, "Bondage is fun", g);
      }
  #endif
  
      /* Do pre force calculation stuff which might require communication */
      if (idef->il[F_ORIRES].nr)
      {
          enerd->term[F_ORIRESDEV] =
              calc_orires_dev(ms, idef->il[F_ORIRES].nr,
                              idef->il[F_ORIRES].iatoms,
                              idef->iparams, md, (const rvec*)x,
                              pbc_null, fcd, hist);
      }
      if (idef->il[F_DISRES].nr)
      {
          calc_disres_R_6(ms, idef->il[F_DISRES].nr,
                          idef->il[F_DISRES].iatoms,
                          idef->iparams, (const rvec*)x, pbc_null,
                          fcd, hist);
      }
  
  #pragma omp parallel for num_threads(fr->nthreads) schedule(static)
      for (thread = 0; thread < fr->nthreads; thread++)
      {
          int                ftype;
          real              *epot, v;
          /* thread stuff */
          rvec              *ft, *fshift;
          real              *dvdlt;
          gmx_grppairener_t *grpp;
  
          if (thread == 0)
          {
              ft     = f;
              fshift = fr->fshift;
              epot   = enerd->term;
              grpp   = &enerd->grpp;
              dvdlt  = dvdl;
          }
          else
          {
              zero_thread_forces(&fr->f_t[thread], fr->natoms_force,
                                 fr->red_nblock, 1<<fr->red_ashift);
  
              ft     = fr->f_t[thread].f;
              fshift = fr->f_t[thread].fshift;
              epot   = fr->f_t[thread].ener;
              grpp   = &fr->f_t[thread].grpp;
              dvdlt  = fr->f_t[thread].dvdl;
          }
          /* Loop over all bonded force types to calculate the bonded forces */
          for (ftype = 0; (ftype < F_NRE); ftype++)
          {
              if (idef->il[ftype].nr > 0 && ftype_is_bonded_potential(ftype))
              {
                  v = calc_one_bond(fplog, thread, ftype, idef, x,
                                    ft, fshift, fr, pbc_null, g, grpp,
                                    nrnb, lambda, dvdlt,
                                    md, fcd, bCalcEnerVir,
                                    global_atom_index, bPrintSepPot);
                  epot[ftype] += v;
              }
          }
      }
      if (fr->nthreads > 1)
      {
          reduce_thread_forces(fr->natoms_force, f, fr->fshift,
                               enerd->term, &enerd->grpp, dvdl,
                               fr->nthreads, fr->f_t,
                               fr->red_nblock, 1<<fr->red_ashift,
                               bCalcEnerVir,
                               force_flags & GMX_FORCE_DHDL);
      }
      if (force_flags & GMX_FORCE_DHDL)
      {
          for (i = 0; i < efptNR; i++)
          {
              enerd->dvdl_nonlin[i] += dvdl[i];
          }
      }
  
      /* Copy the sum of violations for the distance restraints from fcd */
      if (fcd)
      {
          enerd->term[F_DISRESVIOL] = fcd->disres.sumviol;
  
      }
  }
  
  void calc_bonds_lambda(FILE *fplog,
                         const t_idef *idef,
                         rvec x[],
                         t_forcerec *fr,
                         const t_pbc *pbc, const t_graph *g,
                         gmx_grppairener_t *grpp, real *epot, t_nrnb *nrnb,
                         real *lambda,
                         const t_mdatoms *md,
                         t_fcdata *fcd,
                         int *global_atom_index)
  {
      int           i, ftype, nr_nonperturbed, nr;
      real          v;
      real          dvdl_dum[efptNR];
      rvec         *f, *fshift;
      const  t_pbc *pbc_null;
      t_idef       idef_fe;
  
      if (fr->bMolPBC)
      {
          pbc_null = pbc;
      }
      else
      {
          pbc_null = NULL;
      }
  
      /* Copy the whole idef, so we can modify the contents locally */
      idef_fe          = *idef;
      idef_fe.nthreads = 1;
      snew(idef_fe.il_thread_division, F_NRE*(idef_fe.nthreads+1));
  
      /* We already have the forces, so we use temp buffers here */
      snew(f, fr->natoms_force);
      snew(fshift, SHIFTS);
  
      /* Loop over all bonded force types to calculate the bonded energies */
      for (ftype = 0; (ftype < F_NRE); ftype++)
      {
          if (ftype_is_bonded_potential(ftype))
          {
              /* Set the work range of thread 0 to the perturbed bondeds only */
              nr_nonperturbed                       = idef->il[ftype].nr_nonperturbed;
              nr                                    = idef->il[ftype].nr;
              idef_fe.il_thread_division[ftype*2+0] = nr_nonperturbed;
              idef_fe.il_thread_division[ftype*2+1] = nr;
  
              /* This is only to get the flop count correct */
              idef_fe.il[ftype].nr = nr - nr_nonperturbed;
  
              if (nr - nr_nonperturbed > 0)
              {
                  v = calc_one_bond(fplog, 0, ftype, &idef_fe,
                                    x, f, fshift, fr, pbc_null, g,
                                    grpp, nrnb, lambda, dvdl_dum,
                                    md, fcd, TRUE,
                                    global_atom_index, FALSE);
                  epot[ftype] += v;
              }
          }
      }
  
      sfree(fshift);
      sfree(f);
  
      sfree(idef_fe.il_thread_division);
  }
  