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43 #include "gromacs/math/functions.h"
44 #include "gromacs/math/utilities.h"
45 #include "gromacs/math/vec.h"
46 #include "gromacs/mdlib/nbnxn_consts.h"
47 #include "gromacs/mdlib/nbnxn_search.h"
48 #include "gromacs/mdtypes/commrec.h"
49 #include "gromacs/mdtypes/inputrec.h"
50 #include "gromacs/mdtypes/md_enums.h"
51 #include "gromacs/simd/simd.h"
52 #include "gromacs/topology/ifunc.h"
53 #include "gromacs/topology/topology.h"
54 #include "gromacs/utility/fatalerror.h"
56 /* Computational cost of bonded, non-bonded and PME calculations.
57 * This will be machine dependent.
58 * The numbers are only used for estimating the relative cost of PME vs PP,
59 * so only relative numbers matter.
60 * The numbers here are accurate cycle counts for Haswell in single precision
61 * compiled with gcc5.2. A correction factor for other architectures is given
62 * by simd_cycle_factor().
63 * In double precision PME mesh is slightly cheaper, although not so much
64 * that the numbers need to be adjusted.
67 /* Cost of a pair interaction in the "group" cut-off scheme */
68 static const double c_group_fq = 18.0;
69 static const double c_group_qlj_cut = 18.0;
70 static const double c_group_qlj_tab = 24.0;
71 static const double c_group_lj_cut = 12.0;
72 static const double c_group_lj_tab = 21.0;
73 /* Cost of 1 water with one Q/LJ atom */
74 static const double c_group_qljw_cut = 24.0;
75 static const double c_group_qljw_tab = 27.0;
76 /* Cost of 1 water with one Q atom or with 1/3 water (LJ negligible) */
77 static const double c_group_qw = 21.0;
79 /* Cost of a pair interaction in the "Verlet" cut-off scheme, QEXP is Ewald */
80 static const double c_nbnxn_lj = 2.5;
81 static const double c_nbnxn_qrf_lj = 2.9;
82 static const double c_nbnxn_qrf = 2.4;
83 static const double c_nbnxn_qexp_lj = 4.2;
84 static const double c_nbnxn_qexp = 3.8;
85 /* Extra cost for expensive LJ interaction, e.g. pot-switch or LJ-PME */
86 static const double c_nbnxn_ljexp_add = 1.0;
88 /* Cost of the different components of PME. */
89 /* Cost of particle reordering and redistribution (no SIMD correction).
90 * This will be zero without MPI and can be very high with load imbalance.
91 * Thus we use an approximate value for medium parallelization.
93 static const double c_pme_redist = 100.0;
94 /* Cost of q spreading and force interpolation per charge. This part almost
95 * doesn't accelerate with SIMD, so we don't use SIMD correction.
97 static const double c_pme_spread = 5.0;
98 /* Cost of fft's, will be multiplied with 2 N log2(N) (no SIMD correction)
99 * Without MPI the number is 2-3, depending on grid factors and thread count.
100 * We take the high limit to be on the safe side and account for some MPI
101 * communication cost, which will dominate at high parallelization.
103 static const double c_pme_fft = 3.0;
104 /* Cost of pme_solve, will be multiplied with N */
105 static const double c_pme_solve = 9.0;
107 /* Cost of a bonded interaction divided by the number of distances calculations
108 * required in one interaction. The actual cost is nearly propotional to this.
110 static const double c_bond = 25.0;
113 #if GMX_SIMD_HAVE_REAL
114 static const gmx_bool bHaveSIMD = TRUE;
116 static const gmx_bool bHaveSIMD = FALSE;
119 /* Gives a correction factor for the currently compiled SIMD implementations
120 * versus the reference used for the coefficients above (8-wide SIMD with FMA).
121 * bUseSIMD sets if we asking for plain-C (FALSE) or SIMD (TRUE) code.
123 static double simd_cycle_factor(gmx_bool bUseSIMD)
125 /* The (average) ratio of the time taken by plain-C force calculations
126 * relative to SIMD versions, for the reference platform Haswell:
127 * 8-wide SIMD with FMA, factor: sqrt(2*8)*1.25 = 5.
128 * This factor is used for normalization in simd_cycle_factor().
130 const double simd_cycle_no_simd = 5.0;
133 #if GMX_SIMD_HAVE_REAL
136 /* We never get full speed-up of a factor GMX_SIMD_REAL_WIDTH.
137 * The actual speed-up depends very much on gather+scatter overhead,
138 * which is different for different bonded and non-bonded kernels.
139 * As a rough, but actually not bad, approximation we use a sqrt
140 * dependence on the width which gives a factor 4 for width=8.
142 speedup = std::sqrt(2.0*GMX_SIMD_REAL_WIDTH);
143 #if GMX_SIMD_HAVE_FMA
144 /* FMA tends to give a bit more speedup */
155 gmx_incons("gmx_cycle_factor() compiled without SIMD called with bUseSIMD=TRUE");
157 /* No SIMD, no speedup */
161 /* Return speed compared to the reference (Haswell).
162 * For x86 SIMD, the nbnxn kernels are relatively much slower on
163 * Sandy/Ivy Bridge than Haswell, but that only leads to a too high
164 * PME load estimate on SB/IB, which is erring on the safe side.
166 return simd_cycle_no_simd/speedup;
169 void count_bonded_distances(const gmx_mtop_t *mtop, const t_inputrec *ir,
170 double *ndistance_c, double *ndistance_simd)
173 double nonsimd_step_frac;
175 double ndtot_c, ndtot_simd;
176 #if GMX_SIMD_HAVE_REAL
177 gmx_bool bSimdBondeds = TRUE;
179 gmx_bool bSimdBondeds = FALSE;
182 bExcl = (ir->cutoff_scheme == ecutsGROUP && inputrecExclForces(ir)
183 && !EEL_FULL(ir->coulombtype));
187 /* We only have SIMD versions of these bondeds without energy and
188 * without shift-forces, we take that into account here.
190 if (ir->nstcalcenergy > 0)
192 nonsimd_step_frac = 1.0/ir->nstcalcenergy;
196 nonsimd_step_frac = 0;
198 if (ir->epc != epcNO && 1.0/ir->nstpcouple > nonsimd_step_frac)
200 nonsimd_step_frac = 1.0/ir->nstpcouple;
205 nonsimd_step_frac = 1;
208 /* Count the number of pbc_rvec_sub calls required for bonded interactions.
209 * This number is also roughly proportional to the computational cost.
213 for (const gmx_molblock_t &molb : mtop->molblock)
215 const gmx_moltype_t *molt = &mtop->moltype[molb.type];
216 for (ftype = 0; ftype < F_NRE; ftype++)
220 if (interaction_function[ftype].flags & IF_BOND)
222 double nd_c, nd_simd;
226 /* For all interactions, except for the three exceptions
227 * in the switch below, #distances = #atoms - 1.
237 /* These bonded potentially use SIMD */
242 nd_c = nonsimd_step_frac *(NRAL(ftype) - 1);
243 nd_simd = (1 - nonsimd_step_frac)*(NRAL(ftype) - 1);
246 nd_c = NRAL(ftype) - 1;
249 nbonds = molb.nmol*molt->ilist[ftype].size()/(1 + NRAL(ftype));
250 ndtot_c += nbonds*nd_c;
251 ndtot_simd += nbonds*nd_simd;
256 ndtot_c += molb.nmol*(molt->excls.nra - molt->atoms.nr)/2.;
262 fprintf(debug, "nr. of distance calculations in bondeds: C %.1f SIMD %.1f\n", ndtot_c, ndtot_simd);
265 if (ndistance_c != nullptr)
267 *ndistance_c = ndtot_c;
269 if (ndistance_simd != nullptr)
271 *ndistance_simd = ndtot_simd;
275 static void pp_group_load(const gmx_mtop_t *mtop, const t_inputrec *ir,
277 int *nq_tot, int *nlj_tot,
279 gmx_bool *bChargePerturbed, gmx_bool *bTypePerturbed)
281 int atnr, cg, a0, ncqlj, ncq, nclj;
282 gmx_bool bBHAM, bLJcut, bWater, bQ, bLJ;
283 int nw, nqlj, nq, nlj;
284 double fq, fqlj, flj, fqljw, fqw;
287 bBHAM = (mtop->ffparams.functype[0] == F_BHAM);
289 bLJcut = ((ir->vdwtype == evdwCUT) && !bBHAM);
291 /* Computational cost of bonded, non-bonded and PME calculations.
292 * This will be machine dependent.
293 * The numbers here are accurate for Intel Core2 and AMD Athlon 64
294 * in single precision. In double precision PME mesh is slightly cheaper,
295 * although not so much that the numbers need to be adjusted.
298 fqlj = (bLJcut ? c_group_qlj_cut : c_group_qlj_tab);
299 flj = (bLJcut ? c_group_lj_cut : c_group_lj_tab);
300 /* Cost of 1 water with one Q/LJ atom */
301 fqljw = (bLJcut ? c_group_qljw_cut : c_group_qljw_tab);
302 /* Cost of 1 water with one Q atom or with 1/3 water (LJ negligible) */
305 iparams = mtop->ffparams.iparams;
306 atnr = mtop->ffparams.atnr;
311 *bChargePerturbed = FALSE;
312 *bTypePerturbed = FALSE;
313 for (const gmx_molblock_t &molb : mtop->molblock)
315 const gmx_moltype_t *molt = &mtop->moltype[molb.type];
316 const t_atom *atom = molt->atoms.atom;
318 for (cg = 0; cg < molt->cgs.nr; cg++)
325 while (a < molt->cgs.index[cg+1])
327 bQ = (atom[a].q != 0 || atom[a].qB != 0);
328 bLJ = (iparams[(atnr+1)*atom[a].type].lj.c6 != 0 ||
329 iparams[(atnr+1)*atom[a].type].lj.c12 != 0);
330 if (atom[a].q != atom[a].qB)
332 *bChargePerturbed = TRUE;
334 if (atom[a].type != atom[a].typeB)
336 *bTypePerturbed = TRUE;
338 /* This if this atom fits into water optimization */
339 if (!((a == a0 && bQ && bLJ) ||
340 (a == a0+1 && bQ && !bLJ) ||
341 (a == a0+2 && bQ && !bLJ && atom[a].q == atom[a-1].q) ||
342 (a == a0+3 && !bQ && bLJ)))
369 nqlj += molb.nmol*ncqlj;
371 nlj += molb.nmol*nclj;
376 *nq_tot = nq + nqlj + nw*3;
377 *nlj_tot = nlj + nqlj + nw;
381 fprintf(debug, "nw %d nqlj %d nq %d nlj %d\n", nw, nqlj, nq, nlj);
384 /* For the PP non-bonded cost it is (unrealistically) assumed
385 * that all atoms are distributed homogeneously in space.
386 * Factor 3 is used because a water molecule has 3 atoms
387 * (and TIP4P effectively has 3 interactions with (water) atoms)).
389 *cost_pp = 0.5*(fqljw*nw*nqlj +
390 fqw *nw*(3*nw + nq) +
392 fq *nq*(3*nw + nqlj + nq) +
393 flj *nlj*(nw + nqlj + nlj))
394 *4/3*M_PI*ir->rlist*ir->rlist*ir->rlist/det(box);
396 *cost_pp *= simd_cycle_factor(bHaveSIMD);
399 static void pp_verlet_load(const gmx_mtop_t *mtop, const t_inputrec *ir,
401 int *nq_tot, int *nlj_tot,
403 gmx_bool *bChargePerturbed, gmx_bool *bTypePerturbed)
405 int atnr, a, nqlj, nq, nlj;
409 double c_qlj, c_q, c_lj;
412 /* Conversion factor for reference vs SIMD kernel performance.
413 * The factor is about right for SSE2/4, but should be 2 higher for AVX256.
416 const real nbnxn_refkernel_fac = 4.0;
418 const real nbnxn_refkernel_fac = 8.0;
421 bQRF = (EEL_RF(ir->coulombtype) || ir->coulombtype == eelCUT);
423 iparams = mtop->ffparams.iparams;
424 atnr = mtop->ffparams.atnr;
427 *bChargePerturbed = FALSE;
428 *bTypePerturbed = FALSE;
429 for (const gmx_molblock_t &molb : mtop->molblock)
431 const gmx_moltype_t *molt = &mtop->moltype[molb.type];
432 const t_atom *atom = molt->atoms.atom;
433 for (a = 0; a < molt->atoms.nr; a++)
435 if (atom[a].q != 0 || atom[a].qB != 0)
437 if (iparams[(atnr+1)*atom[a].type].lj.c6 != 0 ||
438 iparams[(atnr+1)*atom[a].type].lj.c12 != 0)
447 if (atom[a].q != atom[a].qB)
449 *bChargePerturbed = TRUE;
451 if (atom[a].type != atom[a].typeB)
453 *bTypePerturbed = TRUE;
458 nlj = mtop->natoms - nqlj - nq;
461 *nlj_tot = nqlj + nlj;
463 /* Effective cut-off for cluster pair list of 4x4 or 4x8 atoms.
464 * This choice should match the one of pick_nbnxn_kernel_cpu().
465 * TODO: Make this function use pick_nbnxn_kernel_cpu().
467 #if GMX_SIMD_HAVE_REAL && ((GMX_SIMD_REAL_WIDTH == 8 && defined GMX_SIMD_HAVE_FMA) || GMX_SIMD_REAL_WIDTH > 8)
472 r_eff = ir->rlist + nbnxn_get_rlist_effective_inc(j_cluster_size, mtop->natoms/det(box));
474 /* The average number of pairs per atom */
475 nppa = 0.5*4/3*M_PI*r_eff*r_eff*r_eff*mtop->natoms/det(box);
479 fprintf(debug, "nqlj %d nq %d nlj %d rlist %.3f r_eff %.3f pairs per atom %.1f\n",
480 nqlj, nq, nlj, ir->rlist, r_eff, nppa);
483 /* Determine the cost per pair interaction */
484 c_qlj = (bQRF ? c_nbnxn_qrf_lj : c_nbnxn_qexp_lj);
485 c_q = (bQRF ? c_nbnxn_qrf : c_nbnxn_qexp);
487 if (ir->vdw_modifier == eintmodPOTSWITCH || EVDW_PME(ir->vdwtype))
489 c_qlj += c_nbnxn_ljexp_add;
490 c_lj += c_nbnxn_ljexp_add;
492 if (EVDW_PME(ir->vdwtype) && ir->ljpme_combination_rule == eljpmeLB)
494 /* We don't have LJ-PME LB comb. rule kernels, we use slow kernels */
495 c_qlj *= nbnxn_refkernel_fac;
496 c_q *= nbnxn_refkernel_fac;
497 c_lj *= nbnxn_refkernel_fac;
500 /* For the PP non-bonded cost it is (unrealistically) assumed
501 * that all atoms are distributed homogeneously in space.
503 *cost_pp = (nqlj*c_qlj + nq*c_q + nlj*c_lj)*nppa;
505 *cost_pp *= simd_cycle_factor(bHaveSIMD);
508 float pme_load_estimate(const gmx_mtop_t *mtop, const t_inputrec *ir,
512 gmx_bool bChargePerturbed, bTypePerturbed;
513 double ndistance_c, ndistance_simd;
514 double cost_bond, cost_pp, cost_redist, cost_spread, cost_fft, cost_solve, cost_pme;
517 /* Computational cost of bonded, non-bonded and PME calculations.
518 * This will be machine dependent.
519 * The numbers here are accurate for Intel Core2 and AMD Athlon 64
520 * in single precision. In double precision PME mesh is slightly cheaper,
521 * although not so much that the numbers need to be adjusted.
524 count_bonded_distances(mtop, ir, &ndistance_c, &ndistance_simd);
525 /* C_BOND is the cost for bonded interactions with SIMD implementations,
526 * so we need to scale the number of bonded interactions for which there
527 * are only C implementations to the number of SIMD equivalents.
529 cost_bond = c_bond*(ndistance_c *simd_cycle_factor(FALSE) +
530 ndistance_simd*simd_cycle_factor(bHaveSIMD));
532 if (ir->cutoff_scheme == ecutsGROUP)
534 pp_group_load(mtop, ir, box,
535 &nq_tot, &nlj_tot, &cost_pp,
536 &bChargePerturbed, &bTypePerturbed);
540 pp_verlet_load(mtop, ir, box,
541 &nq_tot, &nlj_tot, &cost_pp,
542 &bChargePerturbed, &bTypePerturbed);
550 int gridNkzFactor = int{
553 if (EEL_PME(ir->coulombtype))
555 double grid = ir->nkx*ir->nky*gridNkzFactor;
557 int f = ((ir->efep != efepNO && bChargePerturbed) ? 2 : 1);
558 cost_redist += c_pme_redist*nq_tot;
559 cost_spread += f*c_pme_spread*nq_tot*gmx::power3(ir->pme_order);
560 cost_fft += f*c_pme_fft*grid*std::log(grid)/std::log(2.0);
561 cost_solve += f*c_pme_solve*grid*simd_cycle_factor(bHaveSIMD);
564 if (EVDW_PME(ir->vdwtype))
566 double grid = ir->nkx*ir->nky*gridNkzFactor;
568 int f = ((ir->efep != efepNO && bTypePerturbed) ? 2 : 1);
569 if (ir->ljpme_combination_rule == eljpmeLB)
571 /* LB combination rule: we have 7 mesh terms */
574 cost_redist += c_pme_redist*nlj_tot;
575 cost_spread += f*c_pme_spread*nlj_tot*gmx::power3(ir->pme_order);
576 cost_fft += f*c_pme_fft*2*grid*std::log(grid)/std::log(2.0);
577 cost_solve += f*c_pme_solve*grid*simd_cycle_factor(bHaveSIMD);
580 cost_pme = cost_redist + cost_spread + cost_fft + cost_solve;
582 ratio = cost_pme/(cost_bond + cost_pp + cost_pme);
593 cost_bond, cost_pp, cost_redist, cost_spread, cost_fft, cost_solve);
595 fprintf(debug, "Estimate for relative PME load: %.3f\n", ratio);