moldyn.c

   1 /*
   2  * moldyn.c - molecular dynamics library main file
   3  *
   4  * author: Frank Zirkelbach <frank.zirkelbach@physik.uni-augsburg.de>
   5  *
   6  */
   7
   8 #define _GNU_SOURCE
   9 #include <stdio.h>
  10 #include <stdlib.h>
  11 #include <string.h>
  12 #include <sys/types.h>
  13 #include <sys/stat.h>
  14 #include <fcntl.h>
  15 #include <unistd.h>
  16 #include <math.h>
  17
  18 #include "moldyn.h"
  19
  20 #include "math/math.h"
  21 #include "init/init.h"
  22 #include "random/random.h"
  23 #include "visual/visual.h"
  24 #include "list/list.h"
  25
  26 int moldyn_usage(char **argv) {
  27
  28         printf("\n%s usage:\n\n",argv[0]);
  29         printf("--- general options ---\n");
  30         printf("-E <steps> <file> (log total energy)\n");
  31         printf("-M <steps> <file> (log total momentum)\n");
  32         printf("-D <steps> <file> (dump total information)\n");
  33         printf("-S <steps> <filebase> (single save file)\n");
  34         printf("-V <steps> <filebase> (rasmol file)\n");
  35         printf("--- physics options ---\n");
  36         printf("-T <temperature> [K] (%f)\n",MOLDYN_TEMP);
  37         printf("-t <timestep tau> [s] (%.15f)\n",MOLDYN_TAU);
  38         printf("-C <cutoff radius> [m] (%.15f)\n",MOLDYN_CUTOFF);
  39         printf("-R <runs> (%d)\n",MOLDYN_RUNS);
  40         printf(" -- integration algo --\n");
  41         printf("  -I <number> (%d)\n",MOLDYN_INTEGRATE_DEFAULT);
  42         printf("     0: velocity verlet\n");
  43         printf(" -- potential --\n");
  44         printf("  -P <number> <param1 param2 ...>\n");
  45         printf("     0: harmonic oscillator\n");
  46         printf("        param1: spring constant\n");
  47         printf("        param2: equilibrium distance\n");
  48         printf("     1: lennard jones\n");
  49         printf("        param1: epsilon\n");
  50         printf("        param2: sigma\n");
  51         printf("\n");
  52
  53         return 0;
  54 }
  55
  56 int moldyn_parse_argv(t_moldyn *moldyn,int argc,char **argv) {
  57
  58         int i;
  59         t_ho_params hop;
  60         t_lj_params ljp;
  61         t_tersoff_params tp;
  62         double s,e;
  63
  64         memset(moldyn,0,sizeof(t_moldyn));
  65
  66         /* default values */
  67         moldyn->t=MOLDYN_TEMP;
  68         moldyn->tau=MOLDYN_TAU;
  69         moldyn->time_steps=MOLDYN_RUNS;
  70         moldyn->integrate=velocity_verlet;
  71         moldyn->potential_force_function=lennard_jones;
  72
  73         /* parse argv */
  74         for(i=1;i<argc;i++) {
  75                 if(argv[i][0]=='-') {
  76                         switch(argv[i][1]){
  77                                 case 'E':
  78                                         moldyn->ewrite=atoi(argv[++i]);
  79                                         strncpy(moldyn->efb,argv[++i],64);
  80                                         break;
  81                                 case 'M':
  82                                         moldyn->mwrite=atoi(argv[++i]);
  83                                         strncpy(moldyn->mfb,argv[++i],64);
  84                                         break;
  85                                 case 'S':
  86                                         moldyn->swrite=atoi(argv[++i]);
  87                                         strncpy(moldyn->sfb,argv[++i],64);
  88                                         break;
  89                                 case 'V':
  90                                         moldyn->vwrite=atoi(argv[++i]);
  91                                         strncpy(moldyn->vfb,argv[++i],64);
  92                                         break;
  93                                 case 'T':
  94                                         moldyn->t=atof(argv[++i]);
  95                                         break;
  96                                 case 't':
  97                                         moldyn->tau=atof(argv[++i]);
  98                                         break;
  99                                 case 'C':
 100                                         moldyn->cutoff=atof(argv[++i]);
 101                                         break;
 102                                 case 'R':
 103                                         moldyn->time_steps=atoi(argv[++i]);
 104                                         break;
 105                                 case 'I':
 106         /* integration algorithm */
 107         switch(atoi(argv[++i])) {
 108                 case MOLDYN_INTEGRATE_VERLET:
 109                         moldyn->integrate=velocity_verlet;
 110                         break;
 111                 default:
 112                         printf("unknown integration algo %s\n",argv[i]);
 113                         moldyn_usage(argv);
 114                         return -1;
 115         }
 116
 117                                 case 'P':
 118         /* potential + params */
 119         switch(atoi(argv[++i])) {
 120                 case MOLDYN_POTENTIAL_HO:
 121                         hop.spring_constant=atof(argv[++i]);
 122                         hop.equilibrium_distance=atof(argv[++i]);
 123                         moldyn->pot_params=malloc(sizeof(t_ho_params));
 124                         memcpy(moldyn->pot_params,&hop,sizeof(t_ho_params));
 125                         moldyn->potential_force_function=harmonic_oscillator;
 126                         break;
 127                 case MOLDYN_POTENTIAL_LJ:
 128                         e=atof(argv[++i]);
 129                         s=atof(argv[++i]);
 130                         ljp.epsilon4=4*e;
 131                         ljp.sigma6=s*s*s*s*s*s;
 132                         ljp.sigma12=ljp.sigma6*ljp.sigma6;
 133                         moldyn->pot_params=malloc(sizeof(t_lj_params));
 134                         memcpy(moldyn->pot_params,&ljp,sizeof(t_lj_params));
 135                         moldyn->potential_force_function=lennard_jones;
 136                         break;
 137                 default:
 138                         printf("unknown potential %s\n",argv[i]);
 139                         moldyn_usage(argv);
 140                         return -1;
 141         }
 142
 143                                 default:
 144                                         printf("unknown option %s\n",argv[i]);
 145                                         moldyn_usage(argv);
 146                                         return -1;
 147                         }
 148                 } else {
 149                         moldyn_usage(argv);
 150                         return -1;
 151                 }
 152         }
 153
 154         return 0;
 155 }
 156
 157 int moldyn_log_init(t_moldyn *moldyn) {
 158
 159         moldyn->lvstat=0;
 160         t_visual *vis;
 161
 162         vis=&(moldyn->vis);
 163
 164         if(moldyn->ewrite) {
 165                 moldyn->efd=open(moldyn->efb,O_WRONLY|O_CREAT|O_TRUNC);
 166                 if(moldyn->efd<0) {
 167                         perror("[moldyn] efd open");
 168                         return moldyn->efd;
 169                 }
 170                 dprintf(moldyn->efd,"# moldyn total energy logfile\n");
 171                 moldyn->lvstat|=MOLDYN_LVSTAT_TOTAL_E;
 172         }
 173
 174         if(moldyn->mwrite) {
 175                 moldyn->mfd=open(moldyn->mfb,O_WRONLY|O_CREAT|O_TRUNC);
 176                 if(moldyn->mfd<0) {
 177                         perror("[moldyn] mfd open");
 178                         return moldyn->mfd;
 179                 }
 180                 dprintf(moldyn->mfd,"# moldyn total momentum logfile\n");
 181                 moldyn->lvstat|=MOLDYN_LVSTAT_TOTAL_M;
 182         }
 183
 184         if(moldyn->swrite)
 185                 moldyn->lvstat|=MOLDYN_LVSTAT_SAVE;
 186
 187         if((moldyn->vwrite)&&(vis)) {
 188                 moldyn->visual=vis;
 189                 visual_init(vis,moldyn->vfb);
 190                 moldyn->lvstat|=MOLDYN_LVSTAT_VISUAL;
 191         }
 192
 193         moldyn->lvstat|=MOLDYN_LVSTAT_INITIALIZED;
 194
 195         return 0;
 196 }
 197
 198 int moldyn_log_shutdown(t_moldyn *moldyn) {
 199
 200         if(moldyn->efd) close(moldyn->efd);
 201         if(moldyn->mfd) close(moldyn->efd);
 202         if(moldyn->dfd) close(moldyn->efd);
 203         if(moldyn->visual) visual_tini(moldyn->visual);
 204
 205         return 0;
 206 }
 207
 208 int moldyn_init(t_moldyn *moldyn,int argc,char **argv) {
 209
 210         int ret;
 211
 212         ret=moldyn_parse_argv(moldyn,argc,argv);
 213         if(ret<0) return ret;
 214
 215         ret=moldyn_log_init(moldyn);
 216         if(ret<0) return ret;
 217
 218         rand_init(&(moldyn->random),NULL,1);
 219         moldyn->random.status|=RAND_STAT_VERBOSE;
 220
 221         moldyn->status=0;
 222
 223         return 0;
 224 }
 225
 226 int moldyn_shutdown(t_moldyn *moldyn) {
 227
 228         moldyn_log_shutdown(moldyn);
 229         rand_close(&(moldyn->random));
 230         free(moldyn->atom);
 231
 232         return 0;
 233 }
 234
 235 int create_lattice(unsigned char type,int element,double mass,double lc,
 236                    int a,int b,int c,t_atom **atom) {
 237
 238         int count;
 239         int ret;
 240         t_3dvec origin;
 241
 242         count=a*b*c;
 243
 244         if(type==FCC) count*=4;
 245         if(type==DIAMOND) count*=8;
 246
 247         *atom=malloc(count*sizeof(t_atom));
 248         if(*atom==NULL) {
 249                 perror("malloc (atoms)");
 250                 return -1;
 251         }
 252
 253         v3_zero(&origin);
 254
 255         switch(type) {
 256                 case FCC:
 257                         ret=fcc_init(a,b,c,lc,*atom,&origin);
 258                         break;
 259                 case DIAMOND:
 260                         ret=diamond_init(a,b,c,lc,*atom,&origin);
 261                         break;
 262                 default:
 263                         printf("unknown lattice type (%02x)\n",type);
 264                         return -1;
 265         }
 266
 267         /* debug */
 268         if(ret!=count) {
 269                 printf("ok, there is something wrong ...\n");
 270                 printf("calculated -> %d atoms\n",count);
 271                 printf("created -> %d atoms\n",ret);
 272                 return -1;
 273         }
 274
 275         while(count) {
 276                 (*atom)[count-1].element=element;
 277                 (*atom)[count-1].mass=mass;
 278                 count-=1;
 279         }
 280
 281         return ret;
 282 }
 283
 284 int destroy_lattice(t_atom *atom) {
 285
 286         if(atom) free(atom);
 287
 288         return 0;
 289 }
 290
 291 int thermal_init(t_moldyn *moldyn) {
 292
 293         /*
 294          * - gaussian distribution of velocities
 295          * - zero total momentum
 296          * - velocity scaling (E = 3/2 N k T), E: kinetic energy
 297          */
 298
 299         int i;
 300         double v,sigma;
 301         t_3dvec p_total,delta;
 302         t_atom *atom;
 303         t_random *random;
 304
 305         atom=moldyn->atom;
 306         random=&(moldyn->random);
 307
 308         /* gaussian distribution of velocities */
 309         v3_zero(&p_total);
 310         for(i=0;i<moldyn->count;i++) {
 311                 sigma=sqrt(2.0*K_BOLTZMANN*moldyn->t/atom[i].mass);
 312                 /* x direction */
 313                 v=sigma*rand_get_gauss(random);
 314                 atom[i].v.x=v;
 315                 p_total.x+=atom[i].mass*v;
 316                 /* y direction */
 317                 v=sigma*rand_get_gauss(random);
 318                 atom[i].v.y=v;
 319                 p_total.y+=atom[i].mass*v;
 320                 /* z direction */
 321                 v=sigma*rand_get_gauss(random);
 322                 atom[i].v.z=v;
 323                 p_total.z+=atom[i].mass*v;
 324         }
 325
 326         /* zero total momentum */
 327         v3_scale(&p_total,&p_total,1.0/moldyn->count);
 328         for(i=0;i<moldyn->count;i++) {
 329                 v3_scale(&delta,&p_total,1.0/atom[i].mass);
 330                 v3_sub(&(atom[i].v),&(atom[i].v),&delta);
 331         }
 332
 333         /* velocity scaling */
 334         scale_velocity(moldyn);
 335
 336         return 0;
 337 }
 338
 339 int scale_velocity(t_moldyn *moldyn) {
 340
 341         int i;
 342         double e,c;
 343         t_atom *atom;
 344
 345         atom=moldyn->atom;
 346
 347         /*
 348          * - velocity scaling (E = 3/2 N k T), E: kinetic energy
 349          */
 350         e=0.0;
 351         for(i=0;i<moldyn->count;i++)
 352                 e+=0.5*atom[i].mass*v3_absolute_square(&(atom[i].v));
 353         c=sqrt((2.0*e)/(3.0*moldyn->count*K_BOLTZMANN*moldyn->t));
 354         for(i=0;i<moldyn->count;i++)
 355                 v3_scale(&(atom[i].v),&(atom[i].v),(1.0/c));
 356
 357         return 0;
 358 }
 359
 360 double get_e_kin(t_atom *atom,int count) {
 361
 362         int i;
 363         double e;
 364
 365         e=0.0;
 366
 367         for(i=0;i<count;i++) {
 368                 e+=0.5*atom[i].mass*v3_absolute_square(&(atom[i].v));
 369         }
 370
 371         return e;
 372 }
 373
 374 double get_e_pot(t_moldyn *moldyn) {
 375
 376         return moldyn->energy;
 377 }
 378
 379 double get_total_energy(t_moldyn *moldyn) {
 380
 381         double e;
 382
 383         e=get_e_kin(moldyn->atom,moldyn->count);
 384         e+=get_e_pot(moldyn);
 385
 386         return e;
 387 }
 388
 389 t_3dvec get_total_p(t_atom *atom, int count) {
 390
 391         t_3dvec p,p_total;
 392         int i;
 393
 394         v3_zero(&p_total);
 395         for(i=0;i<count;i++) {
 396                 v3_scale(&p,&(atom[i].v),atom[i].mass);
 397                 v3_add(&p_total,&p_total,&p);
 398         }
 399
 400         return p_total;
 401 }
 402
 403 double estimate_time_step(t_moldyn *moldyn,double nn_dist,double t) {
 404
 405         double tau;
 406
 407         tau=0.05*nn_dist/(sqrt(3.0*K_BOLTZMANN*t/moldyn->atom[0].mass));
 408         tau*=1.0E-9;
 409         if(tau<moldyn->tau)
 410                 printf("[moldyn] warning: time step  (%f > %.15f)\n",
 411                        moldyn->tau,tau);
 412
 413         return tau;
 414 }
 415
 416 /*
 417  * numerical tricks
 418  */
 419
 420 /* linked list / cell method */
 421
 422 int link_cell_init(t_moldyn *moldyn) {
 423
 424         t_linkcell *lc;
 425         int i;
 426
 427         lc=&(moldyn->lc);
 428
 429         /* list log fd */
 430         lc->listfd=open("/dev/null",O_WRONLY);
 431
 432         /* partitioning the md cell */
 433         lc->nx=moldyn->dim.x/moldyn->cutoff;
 434         lc->x=moldyn->dim.x/lc->nx;
 435         lc->ny=moldyn->dim.y/moldyn->cutoff;
 436         lc->y=moldyn->dim.y/lc->ny;
 437         lc->nz=moldyn->dim.z/moldyn->cutoff;
 438         lc->z=moldyn->dim.z/lc->nz;
 439
 440         lc->cells=lc->nx*lc->ny*lc->nz;
 441         lc->subcell=malloc(lc->cells*sizeof(t_list));
 442
 443         printf("initializing linked cells (%d)\n",lc->cells);
 444
 445         for(i=0;i<lc->cells;i++)
 446                 //list_init(&(lc->subcell[i]),1);
 447                 list_init(&(lc->subcell[i]));
 448
 449         link_cell_update(moldyn);
 450
 451         return 0;
 452 }
 453
 454 int link_cell_update(t_moldyn *moldyn) {
 455
 456         int count,i,j,k;
 457         int nx,ny,nz;
 458         t_atom *atom;
 459         t_linkcell *lc;
 460
 461         atom=moldyn->atom;
 462         lc=&(moldyn->lc);
 463
 464         nx=lc->nx;
 465         ny=lc->ny;
 466         nz=lc->nz;
 467
 468         for(i=0;i<lc->cells;i++)
 469                 list_destroy(&(moldyn->lc.subcell[i]));
 470
 471         for(count=0;count<moedyn->count;count++) {
 472                 i=(atom[count].r.x+(moldyn->dim.x/2))/lc->x;
 473                 j=(atom[count].r.y+(moldyn->dim.y/2))/lc->y;
 474                 k=(atom[count].r.z+(moldyn->dim.z/2))/lc->z;
 475                 list_add_immediate_ptr(&(moldyn->lc.subcell[i+j*nx+k*nx*ny]),
 476                                        &(atom[count]));
 477         }
 478
 479         return 0;
 480 }
 481
 482 int link_cell_neighbour_index(t_moldyn *moldyn,int i,int j,int k,t_list *cell) {
 483
 484         t_linkcell *lc;
 485         int a;
 486         int count1,count2;
 487         int ci,cj,ck;
 488         int nx,ny,nz;
 489         int x,y,z;
 490         unsigned char bx,by,bz;
 491
 492         lc=&(moldyn->lc);
 493         nx=lc->nx;
 494         ny=lc->ny;
 495         nz=lc->nz;
 496         count1=1;
 497         count2=27;
 498         a=nx*ny;
 499
 500
 501         cell[0]=lc->subcell[i+j*nx+k*a];
 502         for(ci=-1;ci<=1;ci++) {
 503                 bx=0;
 504                 x=i+ci;
 505                 if((x<0)||(x>=nx)) {
 506                         x=(x+nx)%nx;
 507                         bx=1;
 508                 }
 509                 for(cj=-1;cj<=1;cj++) {
 510                         by=0;
 511                         y=j+cj;
 512                         if((y<0)||(y>=ny)) {
 513                                 y=(y+ny)%ny;
 514                                 by=1;
 515                         }
 516                         for(ck=-1;ck<=1;ck++) {
 517                                 bz=0;
 518                                 z=k+ck;
 519                                 if((z<0)||(z>=nz)) {
 520                                         z=(z+nz)%nz;
 521                                         bz=1;
 522                                 }
 523                                 if(!(ci|cj|ck)) continue;
 524                                 if(bx|by|bz) {
 525                                         cell[--count2]=lc->subcell[x+y*nx+z*a];
 526                                 }
 527                                 else {
 528                                         cell[count1++]=lc->subcell[x+y*nx+z*a];
 529                                 }
 530                         }
 531                 }
 532         }
 533
 534         lc->dnlc=count2;
 535         lc->countn=27;
 536
 537         return count2;
 538 }
 539
 540 int link_cell_shutdown(t_moldyn *moldyn) {
 541
 542         int i;
 543         t_linkcell *lc;
 544
 545         lc=&(moldyn->lc);
 546
 547         for(i=0;i<lc->nx*lc->ny*lc->nz;i++)
 548                 list_shutdown(&(moldyn->lc.subcell[i]));
 549
 550         if(lc->listfd) close(lc->listfd);
 551
 552         return 0;
 553 }
 554
 555 /*
 556  *
 557  * 'integration of newtons equation' - algorithms
 558  *
 559  */
 560
 561 /* start the integration */
 562
 563 int moldyn_integrate(t_moldyn *moldyn) {
 564
 565         int i;
 566         unsigned int e,m,s,d,v;
 567         t_3dvec p;
 568
 569         int fd;
 570         char fb[128];
 571
 572         /* initialize linked cell method */
 573         link_cell_init(moldyn);
 574
 575         /* logging & visualization */
 576         e=moldyn->ewrite;
 577         m=moldyn->mwrite;
 578         s=moldyn->swrite;
 579         d=moldyn->dwrite;
 580         v=moldyn->vwrite;
 581
 582         if(!(moldyn->lvstat&MOLDYN_LVSTAT_INITIALIZED)) {
 583                 printf("[moldyn] warning, lv system not initialized\n");
 584                 return -1;
 585         }
 586
 587         /* sqaure of some variables */
 588         moldyn->tau_square=moldyn->tau*moldyn->tau;
 589         moldyn->cutoff_square=moldyn->cutoff*moldyn->cutoff;
 590
 591         /* calculate initial forces */
 592         moldyn->potential_force_function(moldyn);
 593
 594         for(i=0;i<moldyn->time_steps;i++) {
 595
 596                 /* integration step */
 597                 moldyn->integrate(moldyn);
 598
 599                 /* check for log & visualization */
 600                 if(e) {
 601                         if(!(i%e))
 602                                 dprintf(moldyn->efd,
 603                                         "%.15f %.45f\n",i*moldyn->tau,
 604                                         get_total_energy(moldyn));
 605                 }
 606                 if(m) {
 607                         if(!(i%m)) {
 608                                 p=get_total_p(moldyn->atom,moldyn->count);
 609                                 dprintf(moldyn->mfd,
 610                                         "%.15f %.45f\n",i*moldyn->tau,
 611                                         v3_norm(&p));
 612                         }
 613                 }
 614                 if(s) {
 615                         if(!(i%s)) {
 616                                 snprintf(fb,128,"%s-%f-%.15f.save",moldyn->sfb,
 617                                          moldyn->t,i*moldyn->tau);
 618                                 fd=open(fb,O_WRONLY|O_TRUNC|O_CREAT);
 619                                 if(fd<0) perror("[moldyn] save fd open");
 620                                 else {
 621                                         write(fd,moldyn,sizeof(t_moldyn));
 622                                         write(fd,moldyn->atom,
 623                                               moldyn->count*sizeof(t_atom));
 624                                 }
 625                                 close(fd);
 626                         }
 627                 }
 628                 if(v) {
 629                         if(!(i%v)) {
 630                                 visual_atoms(moldyn->visual,i*moldyn->tau,
 631                                              moldyn->atom,moldyn->count);
 632                                 printf("\rsteps: %d",i);
 633                                 fflush(stdout);
 634                         }
 635                 }
 636         }
 637
 638         return 0;
 639 }
 640
 641 /* velocity verlet */
 642
 643 int velocity_verlet(t_moldyn *moldyn) {
 644
 645         int i,count;
 646         double tau,tau_square;
 647         t_3dvec delta;
 648         t_atom *atom;
 649
 650         atom=moldyn->atom;
 651         count=moldyn->count;
 652         tau=moldyn->tau;
 653         tau_square=moldyn->tau_square;
 654
 655         for(i=0;i<count;i++) {
 656                 /* new positions */
 657                 v3_scale(&delta,&(atom[i].v),tau);
 658                 v3_add(&(atom[i].r),&(atom[i].r),&delta);
 659                 v3_scale(&delta,&(atom[i].f),0.5*tau_square/atom[i].mass);
 660                 v3_add(&(atom[i].r),&(atom[i].r),&delta);
 661                 v3_per_bound(&(atom[i].r),&(moldyn->dim));
 662
 663                 /* velocities */
 664                 v3_scale(&delta,&(atom[i].f),0.5*tau/atom[i].mass);
 665                 v3_add(&(atom[i].v),&(atom[i].v),&delta);
 666         }
 667
 668         /* neighbour list update */
 669 printf("list update ...\n");
 670         link_cell_update(moldyn);
 671 printf("done\n");
 672
 673         /* forces depending on chosen potential */
 674 printf("calc potential/force ...\n");
 675         potential_force_calc(moldyn);
 676         //moldyn->potential_force_function(moldyn);
 677 printf("done\n");
 678
 679         for(i=0;i<count;i++) {
 680                 /* again velocities */
 681                 v3_scale(&delta,&(atom[i].f),0.5*tau/atom[i].mass);
 682                 v3_add(&(atom[i].v),&(atom[i].v),&delta);
 683         }
 684
 685         return 0;
 686 }
 687
 688
 689 /*
 690  *
 691  * potentials & corresponding forces
 692  *
 693  */
 694
 695 /* generic potential and force calculation */
 696
 697 int potential_force_calc(t_moldyn *moldyn) {
 698
 699         int i,count;
 700         t_atom *atom;
 701         t_linkcell *lc;
 702         t_list neighbour[27];
 703         t_list *this;
 704         double u;
 705         unsigned char bc,bc3;
 706         int countn,dnlc;
 707
 708         count=moldyn->count;
 709         atom=moldyn->atom;
 710         lc=&(moldyn->lc);
 711
 712         /* reset energy */
 713         moldyn->energy=0.0;
 714
 715         for(i=0;i<count;i++) {
 716
 717                 /* reset force */
 718                 v3_zero(&(atom[i].f));
 719
 720                 /* single particle potential/force */
 721                 if(atom[i].attr&ATOM_ATTR_1BP)
 722                         moldyn->pf_func1b(moldyn,&(atom[i]));
 723
 724                 /* 2 body pair potential/force */
 725                 if(atom[i].attr&(ATOM_ATTR_2BP|ATOM_ATTR_3BP)) {
 726
 727                         link_cell_neighbour_index(moldyn,
 728                                 (atom[i].r.x+moldyn->dim.x/2)/lc->x,
 729                                 (atom[i].r.y+moldyn->dim.y/2)/lc->y,
 730                                 (atom[i].r.z+moldyn->dim.z/2)/lc->z,
 731                                 neighbour);
 732
 733                         countn=lc->countn;
 734                         dnlc=lc->dnlc;
 735
 736                         for(j=0;j<countn;j++) {
 737
 738                                 this=&(neighbour[j]);
 739                                 list_reset(this);
 740
 741                                 if(this->start==NULL)
 742                                         continue;
 743
 744                                 bc=(j<dnlc)?0:1;
 745
 746                                 do {
 747                                         btom=this->current->data;
 748
 749                                         if(btom==&(atom[i]))
 750                                                 continue;
 751
 752                                         if((btom->attr&ATOM_ATTR_2BP)&
 753                                            (atom[i].attr&ATOM_ATTR_2BP))
 754                                                 moldyn->pf_func2b(moldyn,
 755                                                                   &(atom[i]),
 756                                                                   btom,
 757                                                                   bc);
 758
 759                                         /* 3 body potential/force */
 760
 761                                         if(!(atom[i].attr&ATOM_ATTR_3BP)||
 762                                            !(btom->attr&ATOM_ATTR_3BP))
 763                                                 continue;
 764
 765                                         link_cell_neighbour_index(moldyn,
 766                                            (btom->r.x+moldyn->dim.x/2)/lc->x,
 767                                            (btom->r.y+moldyn->dim.y/2)/lc->y,
 768                                            (btom->r.z+moldyn->dim.z/2)/lc->z,
 769                                            neighbourk);
 770
 771                                         for(k=0;k<lc->countn;k++) {
 772
 773                                                 thisk=&(neighbourk[k]);
 774                                                 list_reset(thisk);
 775
 776                                                 if(thisk->start==NULL)
 777                                                         continue;
 778
 779                                                 bck=(k<lc->dnlc)?0:1;
 780
 781                                                 do {
 782
 783                         ktom=thisk->current->data;
 784
 785                         if(!(ktom->attr&ATOM_ATTR_3BP))
 786                                 continue;
 787
 788                         if(ktom==btom)
 789                                 continue;
 790
 791                         if(ktom==&(atom[i]))
 792                                 continue;
 793
 794                         moldyn->pf_func3b(moldyn,&(atom[i]),btom,ktom,bck);
 795
 796                                                 } while(list_next(thisk)!=\
 797                                                         L_NO_NEXT_ELEMENT);
 798
 799                                 } while(list_next(this)!=L_NO_NEXT_ELEMENT);
 800                         }
 801                 }
 802         }
 803
 804         return 0;
 805 }
 806
 807 /*
 808  * example potentials
 809  */
 810
 811 /* harmonic oscillator potential and force */
 812
 813 int harmonic_oscillator(t_moldyn *moldyn,t_atom *ai,t_atom *aj,unsigned char bc)) {
 814
 815         t_ho_params *params;
 816         t_atom *atom,*btom;
 817         t_linkcell *lc;
 818         t_list *this,neighbour[27];
 819         int i,j,c;
 820         int count;
 821         t_3dvec force,distance;
 822         double d,u;
 823         double sc,equi_dist;
 824         int ni,nj,nk;
 825
 826         params=moldyn->pot_params;
 827         atom=moldyn->atom;
 828         lc=&(moldyn->lc);
 829         sc=params->spring_constant;
 830         equi_dist=params->equilibrium_distance;
 831         count=moldyn->count;
 832
 833         /* reset energy counter */
 834         u=0.0;
 835
 836         for(i=0;i<count;i++) {
 837                 /* reset force */
 838                 v3_zero(&(atom[i].f));
 839
 840                 /* determine cell + neighbours */
 841                 ni=(atom[i].r.x+(moldyn->dim.x/2))/lc->x;
 842                 nj=(atom[i].r.y+(moldyn->dim.y/2))/lc->y;
 843                 nk=(atom[i].r.z+(moldyn->dim.z/2))/lc->z;
 844                 c=link_cell_neighbour_index(moldyn,ni,nj,nk,neighbour);
 845
 846                 /*
 847                  * processing cell of atom i
 848                  * => no need to check for empty list (1 element at minimum)
 849                  */
 850                 this=&(neighbour[0]);
 851                 list_reset(this);
 852                 do {
 853                         btom=this->current->data;
 854                         if(btom==&(atom[i]))
 855                                 continue;
 856                         v3_sub(&distance,&(atom[i].r),&(btom->r));
 857                         d=v3_norm(&distance);
 858                         if(d<=moldyn->cutoff) {
 859                                 u+=(0.5*sc*(d-equi_dist)*(d-equi_dist));
 860                                 v3_scale(&force,&distance,
 861                                          -sc*(1.0-(equi_dist/d)));
 862                                 v3_add(&(atom[i].f),&(atom[i].f),&force);
 863                         }
 864                 } while(list_next(this)!=L_NO_NEXT_ELEMENT);
 865
 866                 /*
 867                  * direct neighbour cells
 868                  * => no boundary condition check necessary
 869                  */
 870                 for(j=1;j<c;j++) {
 871                         this=&(neighbour[j]);
 872                         list_reset(this); /* there might not be a single atom */
 873                         if(this->start!=NULL) {
 874
 875                         do {
 876                                 btom=this->current->data;
 877                                 v3_sub(&distance,&(atom[i].r),&(btom->r));
 878                                 d=v3_norm(&distance);
 879                                 if(d<=moldyn->cutoff) {
 880                                         u+=(0.5*sc*(d-equi_dist)*(d-equi_dist));
 881                                         v3_scale(&force,&distance,
 882                                                  -sc*(1.0-(equi_dist/d)));
 883                                         v3_add(&(atom[i].f),&(atom[i].f),
 884                                                &force);
 885                                 }
 886                         } while(list_next(this)!=L_NO_NEXT_ELEMENT);
 887
 888                         }
 889                 }
 890
 891                 /*
 892                  * indirect neighbour cells
 893                  * => check boundary conditions
 894                  */
 895                 for(j=c;j<27;j++) {
 896                         this=&(neighbour[j]);
 897                         list_reset(this); /* check boundary conditions */
 898                         if(this->start!=NULL) {
 899
 900                         do {
 901                                 btom=this->current->data;
 902                                 v3_sub(&distance,&(atom[i].r),&(btom->r));
 903                                 v3_per_bound(&distance,&(moldyn->dim));
 904                                 d=v3_norm(&distance);
 905                                 if(d<=moldyn->cutoff) {
 906                                         u+=(0.5*sc*(d-equi_dist)*(d-equi_dist));
 907                                         v3_scale(&force,&distance,
 908                                                  -sc*(1.0-(equi_dist/d)));
 909                                         v3_add(&(atom[i].f),&(atom[i].f),
 910                                                &force);
 911                                 }
 912                         } while(list_next(this)!=L_NO_NEXT_ELEMENT);
 913
 914                         }
 915                 }
 916         }
 917
 918         moldyn->energy=0.5*u;
 919
 920         return 0;
 921 }
 922
 923 /* lennard jones potential & force for one sort of atoms */
 924
 925 int lennard_jones(t_moldyn *moldyn) {
 926
 927         t_lj_params *params;
 928         t_atom *atom,*btom;
 929         t_linkcell *lc;
 930         t_list *this,neighbour[27];
 931         int i,j,c;
 932         int count;
 933         t_3dvec force,distance;
 934         double d,h1,h2,u;
 935         double eps,sig6,sig12;
 936         int ni,nj,nk;
 937
 938         params=moldyn->pot_params;
 939         atom=moldyn->atom;
 940         lc=&(moldyn->lc);
 941         count=moldyn->count;
 942         eps=params->epsilon4;
 943         sig6=params->sigma6;
 944         sig12=params->sigma12;
 945
 946         /* reset energy counter */
 947         u=0.0;
 948
 949         for(i=0;i<count;i++) {
 950                 /* reset force */
 951                 v3_zero(&(atom[i].f));
 952
 953                 /* determine cell + neighbours */
 954                 ni=(atom[i].r.x+(moldyn->dim.x/2))/lc->x;
 955                 nj=(atom[i].r.y+(moldyn->dim.y/2))/lc->y;
 956                 nk=(atom[i].r.z+(moldyn->dim.z/2))/lc->z;
 957                 c=link_cell_neighbour_index(moldyn,ni,nj,nk,neighbour);
 958
 959                 /* processing cell of atom i */
 960                 this=&(neighbour[0]);
 961                 list_reset(this); /* list has 1 element at minimum */
 962                 do {
 963                         btom=this->current->data;
 964                         if(btom==&(atom[i]))
 965                                 continue;
 966                         v3_sub(&distance,&(atom[i].r),&(btom->r));
 967                         d=v3_absolute_square(&distance);        /* 1/r^2 */
 968                         if(d<=moldyn->cutoff_square) {
 969                                 d=1.0/d;        /* 1/r^2 */
 970                                 h2=d*d;         /* 1/r^4 */
 971                                 h2*=d;          /* 1/r^6 */
 972                                 h1=h2*h2;       /* 1/r^12 */
 973                                 u+=eps*(sig12*h1-sig6*h2);
 974                                 h2*=d;          /* 1/r^8 */
 975                                 h1*=d;          /* 1/r^14 */
 976                                 h2*=6*sig6;
 977                                 h1*=12*sig12;
 978                                 d=+h1-h2;
 979                                 d*=eps;
 980                                 v3_scale(&force,&distance,d);
 981                                 v3_add(&(atom[i].f),&(atom[i].f),&force);
 982                         }
 983                 } while(list_next(this)!=L_NO_NEXT_ELEMENT);
 984
 985                 /* neighbours not doing boundary condition overflow */
 986                 for(j=1;j<c;j++) {
 987                         this=&(neighbour[j]);
 988                         list_reset(this); /* there might not be a single atom */
 989                         if(this->start!=NULL) {
 990
 991                         do {
 992                                 btom=this->current->data;
 993                                 v3_sub(&distance,&(atom[i].r),&(btom->r));
 994                                 d=v3_absolute_square(&distance); /* r^2 */
 995                                 if(d<=moldyn->cutoff_square) {
 996                                         d=1.0/d;        /* 1/r^2 */
 997                                         h2=d*d;         /* 1/r^4 */
 998                                         h2*=d;          /* 1/r^6 */
 999                                         h1=h2*h2;       /* 1/r^12 */
1000                                         u+=eps*(sig12*h1-sig6*h2);
1001                                         h2*=d;          /* 1/r^8 */
1002                                         h1*=d;          /* 1/r^14 */
1003                                         h2*=6*sig6;
1004                                         h1*=12*sig12;
1005                                         d=+h1-h2;
1006                                         d*=eps;
1007                                         v3_scale(&force,&distance,d);
1008                                         v3_add(&(atom[i].f),&(atom[i].f),
1009                                                &force);
1010                                 }
1011                         } while(list_next(this)!=L_NO_NEXT_ELEMENT);
1012
1013                         }
1014                 }
1015
1016                 /* neighbours due to boundary conditions */
1017                 for(j=c;j<27;j++) {
1018                         this=&(neighbour[j]);
1019                         list_reset(this); /* check boundary conditions */
1020                         if(this->start!=NULL) {
1021
1022                         do {
1023                                 btom=this->current->data;
1024                                 v3_sub(&distance,&(atom[i].r),&(btom->r));
1025                                 v3_per_bound(&distance,&(moldyn->dim));
1026                                 d=v3_absolute_square(&distance); /* r^2 */
1027                                 if(d<=moldyn->cutoff_square) {
1028                                         d=1.0/d;        /* 1/r^2 */
1029                                         h2=d*d;         /* 1/r^4 */
1030                                         h2*=d;          /* 1/r^6 */
1031                                         h1=h2*h2;       /* 1/r^12 */
1032                                         u+=eps*(sig12*h1-sig6*h2);
1033                                         h2*=d;          /* 1/r^8 */
1034                                         h1*=d;          /* 1/r^14 */
1035                                         h2*=6*sig6;
1036                                         h1*=12*sig12;
1037                                         d=+h1-h2;
1038                                         d*=eps;
1039                                         v3_scale(&force,&distance,d);
1040                                         v3_add(&(atom[i].f),&(atom[i].f),
1041                                                &force);
1042                                 }
1043                         } while(list_next(this)!=L_NO_NEXT_ELEMENT);
1044
1045                         }
1046                 }
1047         }
1048
1049         moldyn->energy=0.5*u;
1050
1051         return 0;
1052 }
1053
1054 /* tersoff potential & force for 2 sorts of atoms */
1055
1056 int tersoff(t_moldyn *moldyn) {
1057
1058         t_tersoff_params *params;
1059         t_atom *atom,*btom,*ktom;
1060         t_linkcell *lc;
1061         t_list *this,*thisk,neighbour[27],neighbourk[27];
1062         int i,j,k,c,ck;
1063         int count;
1064         double u;
1065         int ni,nj,nk;
1066         int ki,kj,kk;
1067
1068
1069         params=moldyn->pot_params;
1070         atom=moldyn->atom;
1071         lc=&(moldyn->lc);
1072         count=moldyn->count;
1073
1074         /* reset energy counter */
1075         u=0.0;
1076
1077         for(i=0;i<count;i++) {
1078                 /* reset force */
1079                 v3_zero(&(atom[i].f));
1080
1081                 /* determin cell neighbours */
1082                 ni=(atom[i].r.x+(moldyn->dim.x/2))/lc->x;
1083                 nj=(atom[i].r.y+(moldyn->dim.y/2))/lc->y;
1084                 nk=(atom[i].r.z+(moldyn->dim.z/2))/lc->z;
1085                 c=link_cell_neighbour_index(moldyn,ni,nj,nk,neighbour);
1086
1087                 /*
1088                  * processing cell of atom i
1089                  * => no need to check for empty list (1 element at minimum)
1090                  */
1091                 this=&(neighbour[0]);
1092                 list_reset(this);
1093                 do {
1094                         btom=this->current->data;
1095                         if(btom==&(atom[i]))
1096                                 continue;
1097
1098                         /* 2 body stuff */
1099
1100                         /* we need: f_c, df_c, f_r, df_r */
1101
1102                         v3_sub(&dist_ij,btom,&(atom[i]));
1103                         d_ij=v3_norm(&dist_ij);
1104                         if(d_ij<=S) {
1105
1106                                 /* determine the tersoff parameters */
1107                                 if(atom[i].element!=btom->element) {
1108                                 S=sqrt(TERSOFF_S[e1]*TERSOFF_S[e2]);
1109                                 R=R_m;
1110                                 A=;
1111                                 lambda=;
1112                                 B=;
1113                                 mu=;
1114                                 chi=;
1115                                 beta=;
1116                                 betaN=;
1117
1118                                 if(d_ij<=R) {
1119                                         df_r=-lambda*A*exp(-lambda*d_ij)/d_ij;
1120                                         v3_scale(&force,&dist_ij,df_r);
1121                                         v3_add(&(atom[i].f),&(atom[i].f),
1122                                                 &force);
1123                                 }
1124                                 else {
1125                                         s_r=S-R;
1126                                         arg1=PI*(d_ij-R)/s_r;
1127                                         f_c=0.5+0.5*cos(arg1);
1128                                         df_c=-0.5*sin(arg1)*(PI/(s_r*d_ij));
1129                                         f_r=A*exp(-lambda*d_ij);
1130                                         df_r=-lambda*f_r/d_ij;
1131                                         scale=df_c*f_r+df_r*f_c;
1132                                         v3_scale(&force,&dist_ij,scale);
1133                                         v3_add(&(atom[i].f),&(atom[i].f),
1134                                                &force);
1135                                 }
1136                         }
1137                         else
1138                                 continue;
1139
1140
1141                         /* end 2 body stuff */
1142
1143                         /* determine cell neighbours of btom */
1144                         ki=(btom->r.x+(moldyn->dim.x/2))/lc->x;
1145                         kj=(btom->r.y+(moldyn->dim.y/2))/lc->y;
1146                         kk=(btom->r.z+(moldyn->dim.z/2))/lc->z;
1147                         ck=link_cell_neighbour_index(moldyn,ki,kj,kk,
1148                                                      neighbourk);
1149
1150                         /* go for zeta - 3 body stuff! */
1151                         zeta=0.0;
1152                         d_ij2=d_ij*d_ij;
1153
1154                         /* cell of btom */
1155                         thisk=&(neighbourk[0]);
1156                         list_reset(thisk);
1157                         do {
1158                                 ktom=thisk->current->data;
1159                                 if(ktom==btom)
1160                                         continue;
1161                                 if(ktom==&(atom[i]))
1162                                         continue;
1163
1164                                 /* 3 body stuff (1) */
1165
1166                                 v3_sub(&dist_ik,ktom,&(atom[i]));
1167                                 d_ik=v3_norm(&dist_ik);
1168                                 if(d_ik<=Sik) {
1169
1170                                 Rik=;
1171                                 Sik=;
1172                                 Aik=;
1173                                 lambda_ik=;
1174                                 Bik=;
1175                                 mu_ik=;
1176                                 omega_ik=;
1177                                 c_i=;
1178                                 d_i=;
1179                                 h_i=;
1180
1181
1182                                         if(d_ik<=Rik) {
1183                                                 f_cik=1.0;
1184                                                 df_cik=0.0;
1185                                         }
1186                                         else {
1187                                                 sik_rik=Sik-Rik;
1188                                                 arg1ik=PI*(d_ik-Rik)/sik_rik;
1189                                                 f_cik=0.5+0.5*cos(arg1ik);
1190                                                 df_cik=-0.5*sin(arg1ik)* \
1191                                                        (PI/(sik_rik*d_ik));
1192                                                 f_rik=Aik*exp(-lambda_ik*d_ik);
1193                                                 f_aik=-Bik*exp(-mu_ik*d_ik);
1194                                         }
1195
1196                                         v3_sub(&distance_jk,ktom,btom);
1197                                         cos_theta=(d_ij2+d_ik*d_ik-d_jk*d_jk)/\
1198                                                   (2*d_ij*d_ik);
1199                                         sin_theta=sqrt(1.0/\
1200                                                   (cos_theta*cos_theta));
1201                                         theta=arccos(cos_theta);
1202
1203
1204                                 }
1205                                 else
1206                                         continue;
1207
1208                                 /* end 3 body stuff (1) */
1209
1210
1211                         } while(list_next(thisk)!=L_NO_NEXT_ELEMENT);
1212
1213                         /* direct neighbours of btom cell */
1214                         for(k=1;k<ck;k++) {
1215                                 thisk=&(neighbourk[k]);
1216                                 list_reset(thisk);
1217                                 if(thisk->start!=NULL) {
1218
1219                                 do {
1220                                         ktom=thisk->current->data;
1221                                         if(ktom==&(atom[i]))
1222                                                 continue;
1223
1224                                 /* 3 body stuff (2) */
1225
1226                                 } while(list_next(thisk)!=L_NO_NEXT_ELEMENT);
1227
1228                                 }
1229                         }
1230
1231                         /* indirect neighbours of btom cell */
1232                         for(k=ck;k<27;k++) {
1233                                 thisk=&(neighbourk[k]);
1234                                 list_reset(thisk);
1235                                 if(thisk->start!=NULL) {
1236
1237                                 do {
1238                                         ktom=thisk->current->data;
1239                                         if(ktom==&(atom[i]))
1240                                                 continue;
1241
1242                                 /* 3 body stuff */
1243
1244                                 } while(list_next(thisk)!=L_NO_NEXT_ELEMENT);
1245
1246                                 }
1247                         }
1248
1249
1250                 } while(list_next(this)!=L_NO_NEXT_ELEMENT);
1251
1252                 /*
1253                  * direct neighbour cells of atom i
1254                  */
1255                 for(j=1;j<c;j++) {
1256                         this=&(neighbour[j]);
1257                         list_reset(this);
1258                         if(this->start!=NULL) {
1259
1260                         do {
1261                                 btom=this->current->data;
1262
1263                                 /* 2 body stuff */
1264
1265
1266                         /* determine cell neighbours of btom */
1267                         ki=(btom->r.x+(moldyn->dim.x/2))/lc->x;
1268                         kj=(btom->r.y+(moldyn->dim.y/2))/lc->y;
1269                         kk=(btom->r.z+(moldyn->dim.z/2))/lc->z;
1270                         ck=link_cell_neighbour_index(moldyn,ki,kj,kk,
1271                                                      neighbourk);
1272
1273                         /* cell of btom */
1274                         thisk=&(neighbourk[0]);
1275                         list_reset(thisk);
1276                         do {
1277                                 ktom=thisk->current->data;
1278                                 if(ktom==btom)
1279                                         continue;
1280                                 if(ktom==&(atom[i]))
1281                                         continue;
1282
1283                                 /* 3 body stuff (1) */
1284
1285                         } while(list_next(thisk)!=L_NO_NEXT_ELEMENT);
1286
1287                         /* direct neighbours of btom cell */
1288                         for(k=1;k<ck;k++) {
1289                                 thisk=&(neighbourk[k]);
1290                                 list_reset(thisk);
1291                                 if(thisk->start!=NULL) {
1292
1293                                 do {
1294                                         ktom=thisk->current->data;
1295                                         if(ktom==&(atom[i]))
1296                                                 continue;
1297
1298                                 /* 3 body stuff (2) */
1299
1300                                 } while(list_next(thisk)!=L_NO_NEXT_ELEMENT);
1301
1302                                 }
1303                         }
1304
1305                         /* indirect neighbours of btom cell */
1306                         for(k=ck;k<27;k++) {
1307                                 thisk=&(neighbourk[k]);
1308                                 list_reset(thisk);
1309                                 if(thisk->start!=NULL) {
1310
1311                                 do {
1312                                         ktom=thisk->current->data;
1313                                         if(ktom==&(atom[i]))
1314                                                 continue;
1315
1316                                 /* 3 body stuff (3) */
1317
1318                                 } while(list_next(thisk)!=L_NO_NEXT_ELEMENT);
1319
1320                                 }
1321                         }
1322
1323
1324                         } while(list_next(this)!=L_NO_NEXT_ELEMENT);
1325
1326                         }
1327                 }
1328
1329                 /*
1330                  * indirect neighbour cells of atom i
1331                  */
1332                 for(j=c;j<27;j++) {
1333                         this=&(neighbour[j]);
1334                         list_reset(this);
1335                         if(this->start!=NULL) {
1336
1337                         do {
1338                                 btom=this->current->data;
1339
1340                                 /* 2 body stuff */
1341
1342
1343                         /* determine cell neighbours of btom */
1344                         ki=(btom->r.x+(moldyn->dim.x/2))/lc->x;
1345                         kj=(btom->r.y+(moldyn->dim.y/2))/lc->y;
1346                         kk=(btom->r.z+(moldyn->dim.z/2))/lc->z;
1347                         ck=link_cell_neighbour_index(moldyn,ki,kj,kk,
1348                                                      neighbourk);
1349
1350                         /* cell of btom */
1351                         thisk=&(neighbourk[0]);
1352                         list_reset(thisk);
1353                         do {
1354                                 ktom=thisk->current->data;
1355                                 if(ktom==btom)
1356                                         continue;
1357                                 if(ktom==&(atom[i]))
1358                                         continue;
1359
1360                                 /* 3 body stuff (1) */
1361
1362                         } while(list_next(thisk)!=L_NO_NEXT_ELEMENT);
1363
1364                         /* direct neighbours of btom cell */
1365                         for(k=1;k<ck;k++) {
1366                                 thisk=&(neighbourk[k]);
1367                                 list_reset(thisk);
1368                                 if(thisk->start!=NULL) {
1369
1370                                 do {
1371                                         ktom=thisk->current->data;
1372                                         if(ktom==&(atom[i]))
1373                                                 continue;
1374
1375                                 /* 3 body stuff (2) */
1376
1377                                 } while(list_next(thisk)!=L_NO_NEXT_ELEMENT);
1378
1379                                 }
1380                         }
1381
1382                         /* indirect neighbours of btom cell */
1383                         for(k=ck;k<27;k++) {
1384                                 thisk=&(neighbourk[k]);
1385                                 list_reset(thisk);
1386                                 if(thisk->start!=NULL) {
1387
1388                                 do {
1389                                         ktom=thisk->current->data;
1390                                         if(ktom==&(atom[i]))
1391                                                 continue;
1392
1393                                 /* 3 body stuff (3) */
1394
1395                                 } while(list_next(thisk)!=L_NO_NEXT_ELEMENT);
1396
1397                                 }
1398                         }
1399
1400
1401                         } while(list_next(this)!=L_NO_NEXT_ELEMENT);
1402
1403                         }
1404                 }
1405
1406         }
1407
1408         moldyn->energy=0.5*u;
1409
1410         return 0;
1411 }
1412