1. PARALLEL IMPLEMENTATION OF PARTON STRING MODEL EVENT GENERATOR A.Asryan, G.Feofilov, S.Nemnyugin, P.Naumenko, V.Solodkov, V.Vechernin, A.Zarochencev, V.Zolotarev Saint-Petersburg State University, Russian Federation

2. Table of contents  Problem (what is the matter?)  Model  PSM event generator  Why parallel?  Parallel PSM event generator  Performance tests  Results of simulation

3. Keywords of the report: software Monte-Carlo event generator PSM (Parton String Model)

4. The method of simulation is based on the Parton String model with strings fusion taken into account.

5. The modified model has been suggested by M.A.Braun (Saint-Petersburg State University) and C.Pajares (University Santiago de Compostela). The model was realized as PSM Monte Carlo event generator by N.Amelin (JINR, Dubna). M.A.Braun, C.Pajares, Phys. Lett. B287 (1992) 154; Nucl. Phys. B390 (1993) 542, 549. N.S. Amelin, M.A.Braun, C.Pajares, Phys. Lett. B306 (1993) 312; Z.Phys. C63 (1994) 507.

6. PSM PROGRAM GENERATOR SHORT DESCRIPTION: FIRST VERSION IS WRITTEN BY DR. N. AMELIN FROM THE JOINT INSTITUTE FOR NUCLEAR RESEARCH (DUBNA, RUSSIA) PURPOSE  TO SIMULATE NUCLEON-NUCLEON, NUCLEON-NUCLEUS AND NUCLEUS- NUCLEUS COLLISIONS AT ULTRA-RELATIVISTIC ENERGIES MODEL  PARTON STRING MODEL See N. Armesto, M. A. Braun, E. G. Ferreiro and C. Pajares, Phys. Lett. B344 (1995) 301 SOME MODEL DETAILS: GLUON RADIATION AND HARD GLUON RESCATTERINGS ARE INCLUDED BEAM AND TARGET MAY BE: N, P, anti-P, D, He, Be, B, C, O, Al, Si, S, Ar, Ca, Cu, Ag, Xe, W, Au, Pb, U RANGE OF ENERGIES (in Gev): 10 < E cm / NUCLEON < 15 000 IMPACT PARAMETER: FIXED OR RANDOM NUMBER OF EVENTS: > 1 STRING FUSION: MAY BE INCLUDED GLUON RESCATTERING: MAY BE INCLUDED BUT IS EXTREMELY TIME CONSUMING IT IS POSSIBLE TO SIMULATE  +,  –, K +, K – INDUCED REACTIONS METHOD OF SIMULATION: MONTE CARLO METHOD

7. PSM PROGRAM GENERATOR Long-range correlations Features of installation taken into account

8. WHY PARALLEL? A lot of statistics (10 4 - 10 6 of simulated events) is required in a Monte Carlo simulation to get statistically reliable results.

9. WHY PARALLEL? Simulation is time consuming if all options of the model are turned on:  hard gluon rescattering;  string fusion;  resonances decay;  rescattering of secondaries (sourced from string breaking) + secondaries and spectators (!).

10. WHY PARALLEL? 13.5 secs/event on 600 MHz CPU with all options of the model turned on. Time-consuming? -> supercomputing/parallel programming should be applied.

11. SIMULATION WITH THE PSM MONTE CARLO GENERATOR 1. Getting “raw” output data with the PSM Monte Carlo generator 2. Processing of the output file by the PERL program (new). The result is a correlation diagram as the Postscript file

12. Parallel algorithms of PSM modeling have been developed and tested on parallel clusters of Saint Petersburg State University. Parallel version of the PSM Monte-Carlo generator is realized with MPICH library (version 1.2.4)

13. PROBLEMS TO BE SOLVED 1.Effective parallelization of the PSM Monte Carlo generator: configuration of cluster is important 2.Effective output operations: 25 000 events ~ 1 Gbyte output file 500 000 events ~ 20 Gbytes output file 3.Pseudorandom number generator: parallel, long enough period, good statistical properties (low correlations) etc.

14. PARALLEL PSM GENERATOR FOR CLUSTER WITH LARGE LOCAL DISKS Master-slave model of parallel programming.  Distribution of events to be simulated between nodes of the parallel cluster.  Master process coordinates work of other (slave) processes.  Master process broadcasts (scatters) input data.  Results of modeling are saved in local files (/tmp directory of a hosts).

15. PARALLEL PSM GENERATOR FOR CLUSTER WITH LARGE LOCAL DISKS  After completion of the PSM program local files are sent to the “master” host.  The program (Perl) of statistical data processing is started.  Result (correlation diagram) is saved in the file in Postscript-format.

16. PARALLEL PSM GENERATOR FOR CLUSTER WITH LARGE LOCAL DISKS Pro: Communication network is not overloaded -> maximum scalability, theoretical limit of Ahmdal’s law Contra: A lot of work when merging local output files

18. PARALLEL PSM MONTE CARLO GENERATOR FOR CLUSTER WITH FILE SERVER Master-slave model of parallel programming.  Parallel output in the shared file. It is located on the file server.  Loading of a communication subsystem of the multiprocessor computer grows.

19. PARALLEL PSM MONTE CARLO GENERATOR FOR CLUSTER WITH FILE SERVER Pro: More pleasant “postmortem” life Contra: Communication network is overloaded  > poor scalability

21. PARALLEL PSM MONTE CARLO GENERATOR FOR CLUSTER WITH FILE SERVER Another approach - compromise: not use parallel output operations use gathering operations.

23. HARDWARE* “ALICE” cluster in Saint Petersburg: 7 x 2CPU hosts (2х600 MHz, 512 Mbyte RAM, 2х4,5 Gbyte hard disks) + 1 server (1200 MHz, 256 Mbyte RAM, 40 Gbyte hard disk) --------------------------------------------------- * Before September 2004, now 1 Gbyte RAM, 40 Gbyte hard disks

24. SPEEDUP TEST (1 st approach) Speedup vs Number of processors for different PSM options (speedup=1 CPU time/N CPUs time) – ABCD: A) HARD PART: True/False; B) STRING FUSION; C) RESONANCE DECAY; D) RESCATTERING

25. PERFORMANCE TESTS 1000 events TTTT --------------------------------------------------------------- HOSTs time --------------------------------------------------------------- 1 224m21.353s 2 114m13.243s 3 87m59.043s 4 62m.83.205s 5 54m67.012s 6 48m71.642s 7 44m32.502s

26. PERFORMANCE TESTS 1000 events TTTF --------------------------------------------------------------- HOSTs time --------------------------------------------------------------- 1 14m46.613s 2 7m59.188s 3 5m24.613s 4 4m16.065s 5 3m35.322s 6 3m9.149s 7 2m49.423s

27. PERFORMANCE TESTS 1000 events TTFF --------------------------------------------------------------- HOSTs time --------------------------------------------------------------- 1 14m32.460s 2 7m24.718s 3 4m47.604s 4 3m41.443s 5 3m11.629s 6 2m41.460s 7 2m13.166s

28. PERFORMANCE TESTS 1000 events - TFFF --------------------------------------------------------------- HOSTs time --------------------------------------------------------------- 1 4m35.410s 2 2m20.976s 3 1m35.235s 4 1m10.788s 5 0m58.430s 6 0m46.027s 7 0m41.621s

29. RESULTS OF SIMULATION

31. PSEUDORANDOM NUMBERS GENERATOR Copy of the CERN Library routine RECUSQ Authors: R.Brun, F.Carminati Up to 215 pseudorandom sequences Each sequence has a period of 10**9 numbers – good for 10 4 10 5 statistics, not so good for 10 6 statistics.

32. PSEUDORANDOM NUMBERS GENERATOR SUBROUTINE RANLUX(RVEC,LENV) C Subtract-and-borrow random number generator proposed by C Marsaglia and Zaman, implemented by F. James with the name C RCARRY in 1991, and later improved by Martin Luescher C in 1993 to produce "Luxury Pseudorandom Numbers". C Fortran 77 coded by F. James, 1993 C references: C M. Luscher, Computer Physics Communications 79 (1994) 100 C F. James, Computer Physics Communications 79 (1994) 111 C LUXURY LEVELS. C ------ ------ The available luxury levels are: C level 0 (p=24): equivalent to the original RCARRY of Marsaglia and Zaman, very long period, C but fails many tests. C level 1 (p=48): considerable improvement in quality over level 0, now passes the gap test, C but still fails spectral test. C level 2 (p=97): passes all known tests, but theoretically still defective. C level 3 (p=223): DEFAULT VALUE. Any theoretically possible correlations have very small C chance of being observed. C level 4 (p=389): highest possible luxury, all 24 bits chaotic.

33. CONCLUSIONS/FURTHER PLANS  Parallel PSM event generator is developed.  Parallel PSM event generator works on “ALICE” computing cluster (Saint Petersburg State University).  It is scalable.  Parallelization methods for different cluster configurations are analyzed.  “Compromise” version is under development.  High-performance -> more statistically reliable results + more realistic physical model