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51 /* Margin for setting up the DD grid */
52 #define DD_GRID_MARGIN_PRES_SCALE 1.05
54 static int factorize(int n, int **fac, int **mfac)
60 gmx_fatal(FARGS, "Can only factorize positive integers.");
63 /* Decompose n in factors */
72 if (ndiv == 0 || (*fac)[ndiv-1] != d)
86 static gmx_bool largest_divisor(int n)
88 int ndiv, *div, *mdiv, ldiv;
90 ndiv = factorize(n, &div, &mdiv);
98 static int lcd(int n1, int n2)
103 for (i = 2; (i <= n1 && i <= n2); i++)
105 if (n1 % i == 0 && n2 % i == 0)
114 static gmx_bool fits_pme_ratio(int nnodes, int npme, float ratio)
116 return ((double)npme/(double)nnodes > 0.95*ratio);
119 static gmx_bool fits_pp_pme_perf(int nnodes, int npme, float ratio)
121 int ndiv, *div, *mdiv, ldiv;
122 int npp_root3, npme_root2;
124 ndiv = factorize(nnodes-npme, &div, &mdiv);
129 npp_root3 = (int)(pow(nnodes-npme, 1.0/3.0) + 0.5);
130 npme_root2 = (int)(sqrt(npme) + 0.5);
132 /* The check below gives a reasonable division:
133 * factor 5 allowed at 5 or more PP nodes,
134 * factor 7 allowed at 49 or more PP nodes.
136 if (ldiv > 3 + npp_root3)
141 /* Check if the number of PP and PME nodes have a reasonable sized
142 * denominator in common, such that we can use 2D PME decomposition
143 * when required (which requires nx_pp == nx_pme).
144 * The factor of 2 allows for a maximum ratio of 2^2=4
145 * between nx_pme and ny_pme.
147 if (lcd(nnodes-npme, npme)*2 < npme_root2)
152 /* Does this division gives a reasonable PME load? */
153 return fits_pme_ratio(nnodes, npme, ratio);
156 static int guess_npme(FILE *fplog, gmx_mtop_t *mtop, t_inputrec *ir, matrix box,
163 ratio = pme_load_estimate(mtop, ir, box);
167 fprintf(fplog, "Guess for relative PME load: %.2f\n", ratio);
170 /* We assume the optimal node ratio is close to the load ratio.
171 * The communication load is neglected,
172 * but (hopefully) this will balance out between PP and PME.
175 if (!fits_pme_ratio(nnodes, nnodes/2, ratio))
177 /* We would need more than nnodes/2 PME only nodes,
178 * which is not possible. Since the PME load is very high,
179 * we will not loose much performance when all nodes do PME.
185 /* First try to find npme as a factor of nnodes up to nnodes/3.
186 * We start with a minimum PME node fraction of 1/16
187 * and avoid ratios which lead to large prime factors in nnodes-npme.
189 npme = (nnodes + 15)/16;
190 while (npme <= nnodes/3)
192 if (nnodes % npme == 0)
194 /* Note that fits_perf might change the PME grid,
195 * in the current implementation it does not.
197 if (fits_pp_pme_perf(nnodes, npme, ratio))
206 /* Try any possible number for npme */
208 while (npme <= nnodes/2)
210 /* Note that fits_perf may change the PME grid */
211 if (fits_pp_pme_perf(nnodes, npme, ratio))
220 gmx_fatal(FARGS, "Could not find an appropriate number of separate PME nodes. i.e. >= %5f*#nodes (%d) and <= #nodes/2 (%d) and reasonable performance wise (grid_x=%d, grid_y=%d).\n"
221 "Use the -npme option of mdrun or change the number of processors or the PME grid dimensions, see the manual for details.",
222 ratio, (int)(0.95*ratio*nnodes+0.5), nnodes/2, ir->nkx, ir->nky);
223 /* Keep the compiler happy */
231 "Will use %d particle-particle and %d PME only nodes\n"
232 "This is a guess, check the performance at the end of the log file\n",
236 "Will use %d particle-particle and %d PME only nodes\n"
237 "This is a guess, check the performance at the end of the log file\n",
244 static int div_up(int n, int f)
246 return (n + f - 1)/f;
249 real comm_box_frac(ivec dd_nc, real cutoff, gmx_ddbox_t *ddbox)
255 for (i = 0; i < DIM; i++)
257 bt[i] = ddbox->box_size[i]*ddbox->skew_fac[i];
258 nw[i] = dd_nc[i]*cutoff/bt[i];
263 for (i = 0; i < DIM; i++)
269 for (j = i+1; j < DIM; j++)
273 comm_vol += nw[i]*nw[j]*M_PI/4;
274 for (k = j+1; k < DIM; k++)
278 comm_vol += nw[i]*nw[j]*nw[k]*M_PI/6;
289 static gmx_bool inhomogeneous_z(const t_inputrec *ir)
291 return ((EEL_PME(ir->coulombtype) || ir->coulombtype == eelEWALD) &&
292 ir->ePBC == epbcXYZ && ir->ewald_geometry == eewg3DC);
295 /* Avoid integer overflows */
296 static float comm_pme_cost_vol(int npme, int a, int b, int c)
302 comm_vol *= div_up(a, npme);
303 comm_vol *= div_up(b, npme);
308 static float comm_cost_est(real limit, real cutoff,
309 matrix box, gmx_ddbox_t *ddbox,
310 int natoms, t_inputrec *ir,
312 int npme_tot, ivec nc)
314 ivec npme = {1, 1, 1};
315 int i, j, k, nk, overlap;
317 float comm_vol, comm_vol_xf, comm_pme, cost_pbcdx;
318 /* This is the cost of a pbc_dx call relative to the cost
319 * of communicating the coordinate and force of an atom.
320 * This will be machine dependent.
321 * These factors are for x86 with SMP or Infiniband.
323 float pbcdx_rect_fac = 0.1;
324 float pbcdx_tric_fac = 0.2;
327 /* Check the DD algorithm restrictions */
328 if ((ir->ePBC == epbcXY && ir->nwall < 2 && nc[ZZ] > 1) ||
329 (ir->ePBC == epbcSCREW && (nc[XX] == 1 || nc[YY] > 1 || nc[ZZ] > 1)))
334 if (inhomogeneous_z(ir) && nc[ZZ] > 1)
339 assert(ddbox->npbcdim <= DIM);
341 /* Check if the triclinic requirements are met */
342 for (i = 0; i < DIM; i++)
344 for (j = i+1; j < ddbox->npbcdim; j++)
346 if (box[j][i] != 0 || ir->deform[j][i] != 0 ||
347 (ir->epc != epcNO && ir->compress[j][i] != 0))
349 if (nc[j] > 1 && nc[i] == 1)
357 for (i = 0; i < DIM; i++)
359 bt[i] = ddbox->box_size[i]*ddbox->skew_fac[i];
361 /* Without PBC there are no cell size limits with 2 cells */
362 if (!(i >= ddbox->npbcdim && nc[i] <= 2) && bt[i] < nc[i]*limit)
370 /* The following choices should match those
371 * in init_domain_decomposition in domdec.c.
373 if (nc[XX] == 1 && nc[YY] > 1)
378 else if (nc[YY] == 1)
385 /* Will we use 1D or 2D PME decomposition? */
386 npme[XX] = (npme_tot % nc[XX] == 0) ? nc[XX] : npme_tot;
387 npme[YY] = npme_tot/npme[XX];
391 /* When two dimensions are (nearly) equal, use more cells
392 * for the smallest index, so the decomposition does not
393 * depend sensitively on the rounding of the box elements.
395 for (i = 0; i < DIM; i++)
397 for (j = i+1; j < DIM; j++)
399 /* Check if the box size is nearly identical,
400 * in that case we prefer nx > ny and ny > nz.
402 if (fabs(bt[j] - bt[i]) < 0.01*bt[i] && nc[j] > nc[i])
404 /* The XX/YY check is a bit compact. If nc[YY]==npme[YY]
405 * this means the swapped nc has nc[XX]==npme[XX],
406 * and we can also swap X and Y for PME.
408 /* Check if dimension i and j are equivalent for PME.
409 * For x/y: if nc[YY]!=npme[YY], we can not swap x/y
410 * For y/z: we can not have PME decomposition in z
413 !((i == XX && j == YY && nc[YY] != npme[YY]) ||
414 (i == YY && j == ZZ && npme[YY] > 1)))
422 /* This function determines only half of the communication cost.
423 * All PP, PME and PP-PME communication is symmetric
424 * and the "back"-communication cost is identical to the forward cost.
427 comm_vol = comm_box_frac(nc, cutoff, ddbox);
430 for (i = 0; i < 2; i++)
432 /* Determine the largest volume for PME x/f redistribution */
433 if (nc[i] % npme[i] != 0)
437 comm_vol_xf = (npme[i] == 2 ? 1.0/3.0 : 0.5);
441 comm_vol_xf = 1.0 - lcd(nc[i], npme[i])/(double)npme[i];
443 comm_pme += 3*natoms*comm_vol_xf;
446 /* Grid overlap communication */
449 nk = (i == 0 ? ir->nkx : ir->nky);
450 overlap = (nk % npme[i] == 0 ? ir->pme_order-1 : ir->pme_order);
458 /* Old line comm_pme += npme[i]*overlap*ir->nkx*ir->nky*ir->nkz/nk; */
462 /* PME FFT communication volume.
463 * This only takes the communication into account and not imbalance
464 * in the calculation. But the imbalance in communication and calculation
465 * are similar and therefore these formulas also prefer load balance
466 * in the FFT and pme_solve calculation.
468 comm_pme += comm_pme_cost_vol(npme[YY], ir->nky, ir->nkz, ir->nkx);
469 comm_pme += comm_pme_cost_vol(npme[XX], ir->nkx, ir->nky, ir->nkz);
471 /* Add cost of pbc_dx for bondeds */
473 if ((nc[XX] == 1 || nc[YY] == 1) || (nc[ZZ] == 1 && ir->ePBC != epbcXY))
475 if ((ddbox->tric_dir[XX] && nc[XX] == 1) ||
476 (ddbox->tric_dir[YY] && nc[YY] == 1))
478 cost_pbcdx = pbcdxr*pbcdx_tric_fac;
482 cost_pbcdx = pbcdxr*pbcdx_rect_fac;
489 "nc %2d %2d %2d %2d %2d vol pp %6.4f pbcdx %6.4f pme %9.3e tot %9.3e\n",
490 nc[XX], nc[YY], nc[ZZ], npme[XX], npme[YY],
491 comm_vol, cost_pbcdx, comm_pme,
492 3*natoms*(comm_vol + cost_pbcdx) + comm_pme);
495 return 3*natoms*(comm_vol + cost_pbcdx) + comm_pme;
498 static void assign_factors(gmx_domdec_t *dd,
499 real limit, real cutoff,
500 matrix box, gmx_ddbox_t *ddbox,
501 int natoms, t_inputrec *ir,
502 float pbcdxr, int npme,
503 int ndiv, int *div, int *mdiv, ivec ir_try, ivec opt)
510 ce = comm_cost_est(limit, cutoff, box, ddbox,
511 natoms, ir, pbcdxr, npme, ir_try);
512 if (ce >= 0 && (opt[XX] == 0 ||
513 ce < comm_cost_est(limit, cutoff, box, ddbox,
517 copy_ivec(ir_try, opt);
523 for (x = mdiv[0]; x >= 0; x--)
525 for (i = 0; i < x; i++)
527 ir_try[XX] *= div[0];
529 for (y = mdiv[0]-x; y >= 0; y--)
531 for (i = 0; i < y; i++)
533 ir_try[YY] *= div[0];
535 for (i = 0; i < mdiv[0]-x-y; i++)
537 ir_try[ZZ] *= div[0];
541 assign_factors(dd, limit, cutoff, box, ddbox, natoms, ir, pbcdxr, npme,
542 ndiv-1, div+1, mdiv+1, ir_try, opt);
544 for (i = 0; i < mdiv[0]-x-y; i++)
546 ir_try[ZZ] /= div[0];
548 for (i = 0; i < y; i++)
550 ir_try[YY] /= div[0];
553 for (i = 0; i < x; i++)
555 ir_try[XX] /= div[0];
560 static real optimize_ncells(FILE *fplog,
561 int nnodes_tot, int npme_only,
562 gmx_bool bDynLoadBal, real dlb_scale,
563 gmx_mtop_t *mtop, matrix box, gmx_ddbox_t *ddbox,
566 real cellsize_limit, real cutoff,
567 gmx_bool bInterCGBondeds,
570 int npp, npme, ndiv, *div, *mdiv, d, nmax;
571 gmx_bool bExcl_pbcdx;
576 limit = cellsize_limit;
582 npp = nnodes_tot - npme_only;
583 if (EEL_PME(ir->coulombtype))
585 npme = (npme_only > 0 ? npme_only : npp);
594 /* For Ewald exclusions pbc_dx is not called */
596 (IR_EXCL_FORCES(*ir) && !EEL_FULL(ir->coulombtype));
597 pbcdxr = (double)n_bonded_dx(mtop, bExcl_pbcdx)/(double)mtop->natoms;
601 /* Every molecule is a single charge group: no pbc required */
604 /* Add a margin for DLB and/or pressure scaling */
607 if (dlb_scale >= 1.0)
609 gmx_fatal(FARGS, "The value for option -dds should be smaller than 1");
613 fprintf(fplog, "Scaling the initial minimum size with 1/%g (option -dds) = %g\n", dlb_scale, 1/dlb_scale);
617 else if (ir->epc != epcNO)
621 fprintf(fplog, "To account for pressure scaling, scaling the initial minimum size with %g\n", DD_GRID_MARGIN_PRES_SCALE);
622 limit *= DD_GRID_MARGIN_PRES_SCALE;
628 fprintf(fplog, "Optimizing the DD grid for %d cells with a minimum initial size of %.3f nm\n", npp, limit);
630 if (inhomogeneous_z(ir))
632 fprintf(fplog, "Ewald_geometry=%s: assuming inhomogeneous particle distribution in z, will not decompose in z.\n", eewg_names[ir->ewald_geometry]);
637 fprintf(fplog, "The maximum allowed number of cells is:");
638 for (d = 0; d < DIM; d++)
640 nmax = (int)(ddbox->box_size[d]*ddbox->skew_fac[d]/limit);
641 if (d >= ddbox->npbcdim && nmax < 2)
645 if (d == ZZ && inhomogeneous_z(ir))
649 fprintf(fplog, " %c %d", 'X' + d, nmax);
651 fprintf(fplog, "\n");
657 fprintf(debug, "Average nr of pbc_dx calls per atom %.2f\n", pbcdxr);
660 /* Decompose npp in factors */
661 ndiv = factorize(npp, &div, &mdiv);
667 assign_factors(dd, limit, cutoff, box, ddbox, mtop->natoms, ir, pbcdxr,
668 npme, ndiv, div, mdiv, itry, nc);
676 real dd_choose_grid(FILE *fplog,
677 t_commrec *cr, gmx_domdec_t *dd, t_inputrec *ir,
678 gmx_mtop_t *mtop, matrix box, gmx_ddbox_t *ddbox,
679 gmx_bool bDynLoadBal, real dlb_scale,
680 real cellsize_limit, real cutoff_dd,
681 gmx_bool bInterCGBondeds)
683 gmx_int64_t nnodes_div, ldiv;
688 nnodes_div = cr->nnodes;
689 if (EEL_PME(ir->coulombtype))
691 if (cr->npmenodes > 0)
696 "Can not have separate PME nodes with 2 or less nodes");
698 if (cr->npmenodes >= cr->nnodes)
701 "Can not have %d separate PME nodes with just %d total nodes",
702 cr->npmenodes, cr->nnodes);
705 /* If the user purposely selected the number of PME nodes,
706 * only check for large primes in the PP node count.
708 nnodes_div -= cr->npmenodes;
718 ldiv = largest_divisor(nnodes_div);
719 /* Check if the largest divisor is more than nnodes^2/3 */
720 if (ldiv*ldiv*ldiv > nnodes_div*nnodes_div)
722 gmx_fatal(FARGS, "The number of nodes you selected (%d) contains a large prime factor %d. In most cases this will lead to bad performance. Choose a number with smaller prime factors or set the decomposition (option -dd) manually.",
727 if (EEL_PME(ir->coulombtype))
729 if (cr->npmenodes < 0)
731 /* Use PME nodes when the number of nodes is more than 16 */
732 if (cr->nnodes <= 18)
737 fprintf(fplog, "Using %d separate PME nodes, as there are too few total\n nodes for efficient splitting\n", cr->npmenodes);
742 cr->npmenodes = guess_npme(fplog, mtop, ir, box, cr->nnodes);
745 fprintf(fplog, "Using %d separate PME nodes, as guessed by mdrun\n", cr->npmenodes);
753 fprintf(fplog, "Using %d separate PME nodes, per user request\n", cr->npmenodes);
758 limit = optimize_ncells(fplog, cr->nnodes, cr->npmenodes,
759 bDynLoadBal, dlb_scale,
760 mtop, box, ddbox, ir, dd,
761 cellsize_limit, cutoff_dd,
769 /* Communicate the information set by the master to all nodes */
770 gmx_bcast(sizeof(dd->nc), dd->nc, cr);
771 if (EEL_PME(ir->coulombtype))
773 gmx_bcast(sizeof(ir->nkx), &ir->nkx, cr);
774 gmx_bcast(sizeof(ir->nky), &ir->nky, cr);
775 gmx_bcast(sizeof(cr->npmenodes), &cr->npmenodes, cr);