Параллельное программирование с использованием технологии МПИ

Fhkdh\kdbc]hkm^Zjkl\_ggucmgb\_jkbl_lbfF...

Author: Антонов А.С.

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ISBN 5-211-04907-1

2

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Bg^_dkihnmgdpbyf03,....................................................................................... 4 Hkgh\gu_ihgylby................................................................................................... 5 H[sb_ijhp_^mju03,........................................................................................... 8 AZ^Zgby................................................................................................................ 11 I_j_^ZqZijb_fkhh[s_gbcf_`^mhl^_evgufbijhp_kkZfb ......................... 11 I_j_^ZqZijb_fkhh[s_gbck[ehdbjh\dhc ................................................... 12 I_j_^ZqZijb_fkhh[s_gbc[_a[ehdbjh\db.................................................. 21 Hleh`_ggu_aZijhkugZ\aZbfh^_ckl\b_ ....................................................... 30 Lmibdh\u_kblmZpbbdeadlock) ....................................................................... 32 AZ^Zgby................................................................................................................ 34 Dhee_dlb\gu_\aZbfh^_ckl\byijhp_kkh\ ......................................................... 36 AZ^Zgby................................................................................................................ 47 =jmiiubdhffmgbdZlhju .................................................................................... 48 Hi_jZpbbk]jmiiZfbijhp_kkh\...................................................................... 48 Hi_jZpbbkdhffmgbdZlhjZfb ......................................................................... 52 AZ^Zgby................................................................................................................ 55 _dZjlh\Z lhiheh]by ......................................................................................... 56 Lhiheh]by ]jZnZ ................................................................................................ 60 AZ^Zgby................................................................................................................ 62 I_j_kuedZjZaghlbiguo^Zgguo ......................................................................... 63 Ijhba\h^gu_lbiu^Zgguo............................................................................... 63 MiZdh\dZ^Zgguo ............................................................................................... 68 AZ^Zgby................................................................................................................ 70 Ebl_jZlmjZ ............................................................................................................. 71

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Bg^_dkihnmgdpbyf03, MPI_ADDRESS ................ 66 MPI_ALLGATHER .............. 42 MPI_ALLGATHERV ............. 42 MPI_ALLREDUCE .............. 45 MPI_ALLTOALL ............... 42 MPI_ALLTOALLV .............. 43 MPI_BARRIER ................ 36 MPI_BCAST .................. 38 MPI_BSEND .................. 14 MPI_BSEND_INIT ............. 30 MPI_BUFFER_ATTACH .......... 15 MPI_BUFFER_DETACH .......... 15 MPI_CART_COORDS ............ 58 MPI_CART_CREATE ............ 56 MPI_CART_GET ............... 59 MPI_CART_RANK .............. 58 MPI_CART_SHIFT ............. 59 MPI_CART_SUB ............... 58 MPI_CARTDIM_GET ............ 58 MPI_COMM_CREATE ............ 53 MPI_COMM_DUP ............... 53 MPI_COMM_FREE .............. 54 MPI_COMM_GROUP ............. 49 MPI_COMM_RANK ............... 9 MPI_COMM_SIZE ............... 9 MPI_COMM_SPLIT ............. 54 MPI_DIMS_CREATE ............ 57 MPI_FINALIZE ................ 8 MPI_GATHER ................. 39 MPI_GATHERV ................ 40 MPI_GET_COUNT .............. 19 MPI_GET_PROCESSOR_NAME ..... 10 MPI_GRAPH_CREATE ........... 60 MPI_GRAPH_GET .............. 61 MPI_GRAPH_NEIGHBORS ........ 61 MPI_GRAPH_NEIGHBORS_COUNT .. 61 MPI_GRAPHDIMS_GET .......... 61 MPI_GROUP_COMPARE .......... 51 MPI_GROUP_DIFFERENCE ....... 50 MPI_GROUP_EXCL ............. 49 MPI_GROUP_FREE ............. 51 MPI_GROUP_INCL ............. 49 MPI_GROUP_INTERSECTION ..... 50 MPI_GROUP_RANK ............. 50 MPI_GROUP_SIZE ............. 50 MPI_GROUP_TRANSLATE_RANKS .. 51 MPI_GROUP_UNION ............ 50 MPI_IBSEND ................. 23 MPI_INIT .................... 8 MPI_INITIALIZED ............. 9 MPI_IPROBE ................. 23

MPI_IRECV .................. 23 MPI_IRSEND ................. 23 MPI_ISEND .................. 22 MPI_ISSEND ................. 23 MPI_OP_CREATE .............. 46 MPI_OP_FREE ................ 46 MPI_PACK ................... 69 MPI_PACK_SIZE .............. 69 MPI_PROBE .................. 19 MPI_RECV ................... 16 MPI_RECV_INIT .............. 30 MPI_REDUCE ................. 43 MPI_REDUCE_SCATTER ......... 45 MPI_REQUEST_FREE ........... 31 MPI_RSEND .................. 14 MPI_RSEND_INIT ............. 30 MPI_SCAN ................... 46 MPI_SCATTER ................ 40 MPI_SCATTERV ............... 41 MPI_SEND ................... 12 MPI_SEND_INIT .............. 30 MPI_SENDRECV ............... 33 MPI_SENDRECV_REPLACE ....... 34 MPI_SSEND .................. 14 MPI_SSEND_INIT ............. 30 MPI_START .................. 31 MPI_STARTALL ............... 31 MPI_TEST ................... 27 MPI_TESTALL ................ 27 MPI_TESTANY ................ 27 MPI_TESTSOME ............... 28 MPI_TOPO_TEST .............. 56 MPI_TYPE_COMMIT ............ 66 MPI_TYPE_CONTIGUOUS ........ 64 MPI_TYPE_EXTENT ............ 67 MPI_TYPE_FREE .............. 66 MPI_TYPE_HINDEXED .......... 65 MPI_TYPE_HVECTOR ........... 65 MPI_TYPE_INDEXED ........... 65 MPI_TYPE_LB ................ 67 MPI_TYPE_SIZE .............. 66 MPI_TYPE_STRUCT ............ 65 MPI_TYPE_UB ................ 67 MPI_TYPE_VECTOR ............ 64 MPI_UNPACK ................. 69 MPI_WAIT ................... 23 MPI_WAITALL ................ 24 MPI_WAITANY ................ 25 MPI_WAITSOME ............... 25 MPI_WTICK .................. 10 MPI_WTIME .................. 10 4

Hkgh\gu_ihgylby GZb[he__jZkijhkljZg_gghcl_ogheh]b_cijh]jZffbjh\Zgby^eyiZjZee_evguo dhfivxl_jh\ k jZkij_^_e_gghc iZfylvx \ gZklhys__ \j_fy y\ey_lky 03, Hkgh\guf kihkh[hf \aZbfh^_ckl\by iZjZee_evguo ijhp_kkh\ \ lZdbo kbkl_fZoy\ey_lkyi_j_^ZqZkhh[s_gbc^jm]^jm]mWlhbhljZ`_gh\gZa\Zgbb ^Zgghc l_ogheh]bb — 0HVVDJH 3DVVLQJ ,QWHUIDFH bgl_jn_ck i_j_^Zqb khh[s_gbc KlZg^Zjl MPI nbdkbjm_l bgl_jn_ck dhlhjuc ^he`_g kh[ex^Zlvky dZd kbkl_fhc ijh]jZffbjh\Zgby gZ dZ`^hc \uqbkebl_evghc ieZlnhjf_lZdbihevah\Zl_e_fijbkha^Zgbbk\hboijh]jZffKh\j_f_ggu_ j_ZebaZpbb qZs_ \k_]hkhhl\_lkl\mxlklZg^Zjlm03,\_jkbb <— ]h^Zo ihy\beky klZg^Zjl 03,- agZqbl_evgh jZkrbjb\rbc nmgdpbhgZevghklvij_^u^ms_c\_jkbbH^gZdh^hkboihjwlhl\ZjbZglMPI g_ihemqberbjhdh]hjZkijhkljZg_gbyb\iheghfh[t_f_g_j_Zebah\Zggb gZ h^ghc kbkl_f_ <_a^_ ^Ze__ _keb bgh]h g_ h]h\hj_gh fu [m^_f bf_lv ^_ehkhklZg^ZjlhfMPI-1.1. 03, ih^^_j`b\Z_l jZ[hlm k yaudZfb NhjljZg b Kb < ^Zgghf ihkh[bb ijbf_jubhibkZgby\k_oijhp_^mj[m^ml^Zgukbkihevah\Zgb_fyaudZNhjljZg H^gZdh wlh kh\_jr_ggh g_ y\ey_lky ijbgpbibZevguf ihkdhevdm hkgh\gu_ b^_b 03, b ijZ\beZ hnhjfe_gby hl^_evguo dhgkljmdpbc ^ey wlbo yaudh\\hfgh]hfkoh`bIhegZy\_jkbybgl_jn_ckZkh^_j`blhibkZgb_[he__ ijhp_^mj b nmgdpbcGZrZaZ^ZqZ — h[tykgblvb^_xl_ogheh]bbb ihfhqv hk\hblv g_h[oh^bfu_ gZ ijZdlbd_ dhfihg_glu >hihegbl_evgmx bgnhjfZpbx h[ bgl_jn_ck_ MPI fh`gh gZclb gZ l_fZlbq_kdhc kljZgbp_ BgnhjfZpbhggh-ZgZeblbq_kdh]h p_gljZ ih iZjZee_evguf \uqbke_gbyf \ k_lbBgl_jg_lhttp://parallel.ru/tech/tech_dev/mpi.html. Bgl_jn_ck MPI ih^^_j`b\Z_l kha^Zgb_ iZjZee_evguo ijh]jZff \ klbe_ MIMD (Multiple Instruction Multiple Data qlh ih^jZamf_\Z_l h[t_^bg_gb_ ijhp_kkh\kjZaebqgufbbkoh^gufbl_dklZfbH^gZdhibkZlvbhleZ`b\Zlv lZdb_ijh]jZffuhq_gvkeh`ghihwlhfmgZijZdlbd_ijh]jZffbklu]hjZa^h qZs_bkihevamxlSPMD-fh^_evSingle Program Multiple Data)iZjZee_evgh]h ijh]jZffbjh\Zgby \ jZfdZo dhlhjhc ^ey \k_o iZjZee_evguo ijhp_kkh\ bkihevam_lkyh^bgblhl`_dh^
name^eyihemqZ_fh]h\uihegbfh]hnZceZihmfheqZgbx\uihegbfucnZce gZau\Z_lkya.outgZijbf_j mpif77 -o program program.f

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]^_ N - qbkeh ijhp_kkh\ dhlhjh_ ^he`gh [ulv g_ [he__ jZaj_r_ggh]h \ ^Zgghckbkl_f_qbkeZijhp_kkh\^eyh^ghcaZ^ZqbIhke_aZimkdZh^gZblZ `_ijh]jZffZ[m^_l\uihegylvky\k_fbaZims_ggufbijhp_kkZfbj_amevlZl \uiheg_gby \ aZ\bkbfhklb hl kbkl_fu [m^_l \u^Z\Zlvky gZ l_jfbgZe beb aZibku\Zlvky\nZcekij_^hij_^_e_ggufbf_g_f ey ehdZebaZpbb \aZbfh^_ckl\by iZjZee_evguo ijhp_kkh\ ijh]jZffu fh`gh kha^Z\Zlv ]jmiiu ijhp_kkh\ ij_^hklZ\eyy bf hl^_evgmx kj_^m ^ey h[s_gby — dhffmgbdZlhj KhklZ\ h[jZam_fuo ]jmii ijhba\he_g =jmiiu fh]ml iheghklvx kh\iZ^Zlv \oh^blv h^gZ \ ^jm]mx g_ i_j_k_dZlvky beb i_j_k_dZlvky qZklbqgh Ijhp_kku fh]ml \aZbfh^_ckl\h\Zlv lhevdh \gmljb g_dhlhjh]h dhffmgbdZlhjZ khh[s_gby hlijZ\e_ggu_ \ jZaguo dhffmgbdZlhjZog_i_j_k_dZxlkybg_f_rZxl^jm]^jm]mDhffmgbdZlhju bf_xl \ yaud_ NhjljZg lbi INTEGER \ yaud_ Kb – ij_^hij_^_e_gguc lbi MPI_Comm). 6

IjbklZjl_ijh]jZffu\k_]^ZkqblZ_lkyqlh\k_ihjh`^_ggu_ijhp_kkujZ[hlZxl \ jZfdZo \k_h[t_fexs_]h dhffmgbdZlhjZ bf_xs_]h ij_^hij_^_e_ggh_bfyMPI_COMM_WORLDWlhldhffmgbdZlhjkms_kl\m_l\k_]^Zbkem`bl ^ey \aZbfh^_ckl\by \k_o aZims_gguo ijhp_kkh\ MPI-ijh]jZffu Djhf_ g_]h ijb klZjl_ ijh]jZffu bf__lky dhffmgbdZlhj MPI_COMM_SELF, kh^_j`Zsbc lhevdh h^bg l_dmsbc ijhp_kk Z lZd`_ dhffmgbdZlhj MPI_COMM_NULL g_ kh^_j`Zsbc gb h^gh]h ijhp_kkZ ey jZ[hlu k Zljb[mlZfb khh[s_gbc \\_^_g fZkkb\ \ yaud_ Kb – kljmdlmjZ we_f_glu dhlhjh]h^Zxl^hklmidboagZq_gbyf < ihke_^g_f Zj]mf_gl_ \ yaud_ Kb – \ \ha\jZsZ_fhf agZq_gbb nmgdpbb [hevrbgkl\hijhp_^mj03,\ha\jZsZxlbgnhjfZpbxh[mki_rghklbaZ\_jr_gby < kemqZ_ mki_rgh]h \uiheg_gby \ha\jZsZ_lky agZq_gb_ MPI_SUCCESSbgZq_ – dh^hrb[db
7

H[sb_ijhp_^mju03, <^ZgghfjZa^_e_fuhklZgh\bfkygZh[sboijhp_^mjZoMPIg_k\yaZgguok i_j_kuedhc ^Zgguo ;hevrbgkl\h ijhp_^mj wlh]h jZa^_eZ g_h[oh^bfu ijZdlbq_kdb\dZ`^hckh^_j`Zl_evghciZjZee_evghcijh]jZff_ MPI_INIT(IERR) INTEGER IERR

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#include “mpi.h” main(int argc, char **argv) { … MPI_Init(&argc, &argv); … MPI_Finalize(); … }

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KljhdZ khhl\_lkl\mxsZy \uah\m ijhp_^mju print[m^_l\u\_^_gZklhevdh jZa kdhevdh ijhp_kkh\ [ueh ihjh`^_gh ijb aZimkd_ ijh]jZffu Ihjy^hd ihy\e_gbykljhdaZjZg__g_hij_^_e_gbfh`_l[ulv\hh[s_]h\hjyex[uf =ZjZglbjm_lkylhevdhlhqlhkh^_j`bfh_hl^_evguokljhdg_[m^_li_j_f_rZgh^jm]k^jm]hf DOUBLE PRECISION MPI_WTIME(IERR) INTEGER IERR

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ihfhsvx wlhc ijhp_^mju fh`gh hij_^_eblv gZ dZdb_ bf_ggh nbabq_kdb_ ijhp_kkhju[uebkieZgbjh\Zguijhp_kkuMPI-ijbeh`_gby

< ke_^mxs_c ijh]jZff_ gZ dZ`^hf ijhp_kk_ hij_^_eyxlky ^\_ oZjZdl_jbklbdbkbkl_fgh]hlZcf_jZ_]hjZaj_r_gb_b\j_fylj_[m_fh_gZaZf_j\j_f_gb ^ey mkj_^g_gby ihemqZ_fh]h agZq_gby \uihegy_lky NTIMES aZf_jh\ LZd`_ \ ^Zgghf ijbf_j_ ihdZaZgh bkihevah\Zgb_ ijhp_^mju MPI_GET_PROCESSOR_NAME.

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program example3 include 'mpif.h' integer ierr, rank, len, i, NTIMES parameter (NTIMES = 100) character*(MPI_MAX_PROCESSOR_NAME) name double precision time_start, time_finish, tick call MPI_INIT(ierr) call MPI_COMM_RANK(MPI_COMM_WORLD, rank, ierr) call MPI_GET_PROCESSOR_NAME(name, len, ierr) tick = MPI_WTICK(ierr) time_start = MPI_WTIME(ierr) do i = 1, NTIMES time_finish = MPI_WTIME(ierr) end do call MPI_COMM_RANK(MPI_COMM_WORLD, rank, ierr) print *, 'processor ', name(1:len), & ', process ', rank, ': tick = ', tick, & ', time = ', (time_finish-time_start)/NTIMES call MPI_FINALIZE(ierr) end

AZ^Zgby • Hldhfibebjh\Zlvbijh\_jblvwnn_dlb\ghklv\uiheg_gbyijh]jZffu \uqbke_gby qbkeZ Ib gZ jZaebqghf qbke_ ijhp_kkhjh\ ijh]jZffZ h[uqgh\oh^bl\dZq_kl\_l_klh\h]hijbf_jZ\dhfie_dlihklZ\dbMPI b fh`_l gZoh^blvky gZijbf_j \ nZceZo /usr/local/examples/mpi/fpi.f beb cpi.c). • Fh`gh eb \ ijhp_kk_ jZ[hlu 03,-ijh]jZffu ihjh`^Zlv gh\u_ ijhp_kku_keb\dZdhc-lhfhf_glihy\bebkvk\h[h^gu_ijhp_kkhju" • Fh`_l eb 03,-ijh]jZffZ ijh^he`Zlv jZ[hlm ihke_ Z\Zjbcgh]h aZ\_jr_gbyh^gh]hbaijhp_kkh\" • Hij_^_eblvkdhevdhijhp_kkh\\uihegyxll_dklijh]jZffu^h\uah\Z ijhp_^mjuMPI_INITbihke_\uah\Zijhp_^mjuMPI_FINALIZE. • Hij_^_eblv kbgojhgbah\Zgu eb lZcf_ju jZaguo ijhp_kkh\ dhgdj_lghckbkl_fu

I_j_^ZqZijb_fkhh[s_gbcf_`^mhl^_evgufb ijhp_kkZfb IjZdlbq_kdb\k_ijh]jZffugZibkZggu_kbkihevah\Zgb_fdhffmgbdZpbhgghcl_ogheh]bbMPI^he`gukh^_j`Zlvkj_^kl\Zg_lhevdh^eyihjh`^_gby baZ\_jr_gbyiZjZee_evguoijhp_kkh\ghb^ey\aZbfh^_ckl\byaZims_gguo

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ijhp_kkh\ f_`^m kh[hc LZdh_ \aZbfh^_ckl\b_ hkms_kl\ey_lky \ MPI ihkj_^kl\hfy\ghcihkuedbkhh[s_gbc BUF(*) INTEGER COUNT, DATATYPE, DEST, MSGTAG, COMM, IERR ;ehdbjmxsZy ihkuedZ fZkkb\Z BUF k b^_glbnbdZlhjhf MSGTAG khklhys_]h ba COUNTwe_f_glh\lbiZ DATATYPEijhp_kkmkghf_jhf DEST\dhffmgbdZlhj_COMM
pbZebabjh\ZgZ khhl\_lkl\mxsZy ijhp_^mjZ ijb_fZ Ijb wlhf khh[s_gb_ fh`_l [ulv kdhibjh\Zgh dZd g_ihkj_^kl\_ggh \ [mn_j ijb_fZ lZd b ihf_s_gh\g_dhlhjuckbkl_fguc[mn_j_kebwlhij_^mkfhlj_gh\MPI AgZq_gb_ COUNT fh`_l[ulvgme_fIjhp_kkmjZaj_rZ_lkyi_j_^Z\Zlvkhh[s_gb_ 12

kZfhfmk_[_h^gZdhwlhg_[_ahiZkghbfh`_lijb\_klbd\hagbdgh\_gbxlmibdh\hckblmZpbbIZjZf_lj DATATYPEbf__l\yaud_NhjljZglbi INTEGER \yaud_Kb–ij_^hij_^_e_gguclbiMPI_Datatype Lbii_j_^Z\Z_fuowe_f_glh\ ^he`_g mdZau\Zlvky k ihfhsvx ij_^hij_^_e_gguo dhgklZgl lbiZ i_j_qbke_gguo^eyyaudZNhjljZg\ke_^mxs_clZ[ebp_ Lbi^Zgguo\MPI

Lbi^Zgguo\NhjljZg_

MPI_INTEGER MPI_REAL MPI_DOUBLE_PRECISION MPI_COMPLEX MPI_LOGICAL MPI_CHARACTER MPI_BYTE

INTEGER REAL DOUBLE PRECISION COMPLEX LOGICAL CHARACTER(1) [blbkihevam_lky^eyi_j_^Zqb g_lbibabjh\Zgguo^Zgguo lbi^eymiZdh\Zgguo^Zgguo

MPI_PACKED

?keb bkihevam_fuc k MPI [Zah\uc yaud bf__l ^hihegbl_evgu_ lbiu ^Zgguo lh khhl\_lkl\mxsb_ lbiu ^he`gu [ulv h[_ki_q_gu b \ MPI. Iheguc kibkhd ij_^hij_^_e_gguo bf_g lbih\ ^Zgguo i_j_qbke_g \ nZce_ mpif.h (mpi.h). Ijb i_j_kued_ khh[s_gbc fh`gh bkihevah\Zlv ki_pbZevgh_ agZq_gb_ MPI_PROC_NULL ^ey g_kms_kl\mxs_]h ijhp_kkZ Hi_jZpbb k lZdbf ijhp_kkhf aZ\_jrZxlky g_f_^e_ggh k dh^hf aZ\_jr_gby MPI_SUCCESS. GZijbf_j^eyi_j_kuedbkhh[s_gbyijhp_kkmkghf_jhfgZ_^bgbpm[hevr_ fh`gh\hkihevah\Zlvkyke_^mxsbfnjZ]f_glhf call MPI_COMM_SIZE(MPI_COMM_WORLD, size, ierr) call MPI_COMM_RANK(MPI_COMM_WORLD, rank, ierr) next = rank+1 if(next .eq. size) next = MPI_PROC_NULL call MPI_SEND(buf, 1, MPI_REAL, next, & 5, MPI_COMM_WORLD, ierr)

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Ke_^m_lki_pbZevghhlf_lblvqlh\ha\jZlbaijhp_^mju MPI_SEND g_hagZqZ_lgblh]hqlhkhh[s_gb_ihemq_ghijhp_kkhf DESTgblh]hqlhkhh[s_gb_ihdbgmehijhp_kkhjgucwe_f_glgZdhlhjhf\uihegy_lkyijhp_kk\uihegb\rbc ^Zgguc \uah\ Ij_^hklZ\ey_lky lhevdh ]ZjZglby [_ahiZkgh]h baf_g_gby i_j_f_gguo bkihevah\Zgguo \ \uah\_ ^Zgghc ijhp_^mju Ih^h[gZy g_hij_^_e_gghklv ^Ze_dh g_ \k_]^Z mkljZb\Z_l ihevah\Zl_ey Qlh[u jZkrbjblv \hafh`ghklb i_j_^Zqb khh[s_gbc \ MPI \\_^_gu ^hihegbl_evgu_ ljb ijhp_^mju Zgghcijhp_^mjhc fh`ghihevah\Zlvkylhevdh\lhfkemqZ__kebijhp_kk-ihemqZl_evm`_ bgbpbbjh\Zeijb_fkhh[s_gby
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Ihevah\Zl_ev^he`_ggZagZqblvgZihkueZxs_fijhp_kk_ki_pbZevgucfZkkb\dhlhjuc[m^_lbkihevah\Zlvky^ey[mn_jbaZpbbkhh[s_gbcijb\uah\_ ijhp_^mjuMPI_BSEND. MPI_BUFFER_ATTACH(BUF, SIZE, IERR) BUF(*) INTEGER SIZE, IERR GZagZq_gb_fZkkb\Z BUFjZaf_jZ SIZE^eybkihevah\Zgbyijbihkued_khh[-

s_gbc k [mn_jbaZpb_c < dZ`^hf ijhp_kk_ fh`_l [ulv lhevdh h^bg lZdhc [mn_j :kkhpbbjh\Zgguc k [mn_jhffZkkb\g_ke_^m_lbkihevah\Zlv\ijh]jZff_ ^ey ^jm]bo p_e_c JZaf_j fZkkb\Z \u^_ey_fh]h ^ey [mn_jbaZpbb ^he`_g ij_\hkoh^blv h[sbc jZaf_j khh[s_gby dZd fbgbfmf gZ \_ebqbgm hij_^_ey_fmxdhgklZglhcMPI_BSEND_OVERHEAD. MPI_BUFFER_DETACH(BUF, SIZE, IERR) BUF(*) INTEGER SIZE, IERR

Hk\h[h`^_gb_\u^_e_ggh]h[mn_jgh]hfZkkb\Z^ey_]hbkihevah\Zgby\^jm]bop_eyoIjhp_^mjZ\ha\jZsZ_l\Zj]mf_glZoBUFbSIZEZ^j_kbjZaf_jhk\h[h`^Z_fh]h fZkkb\Z ey[mn_jbaZpbb\u^_ey_lkyfZkkb\ bufihke_aZ\_jr_gbyi_j_kuedb hg hk\h[h`^Z_lky JZaf_j g_h[oh^bfh]h [mn_jZ hij_^_ey_lky jZaf_jhfkhh[s_gbyh^ghp_eh_qbkeh–[ZclZ iexkagZq_gb_dhgklZglu MPI_BSEND_OVERHEAD.

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program example4 include 'mpif.h' integer BUFSIZE parameter (BUFSIZE = 4 + MPI_BSEND_OVERHEAD) byte buf(BUFSIZE) integer rank, ierr, ibufsize, rbuf integer status(MPI_STATUS_SIZE) call MPI_INIT(ierr) call MPI_COMM_RANK(MPI_COMM_WORLD, rank, ierr) if(rank .eq. 0) then call MPI_BUFFER_ATTACH(buf, BUFSIZE, ierr) call MPI_BSEND(rank, 1, MPI_INTEGER, 1, 5, & MPI_COMM_WORLD, ierr) call MPI_BUFFER_DETACH(buf, ibufsize, ierr) end if if(rank .eq. 1) then call MPI_RECV(rbuf, 1, MPI_INTEGER, 0, 5, & MPI_COMM_WORLD, status, ierr) print *, 'Process 1 received ', rbuf, ' from process ', & status(MPI_SOURCE) end if call MPI_FINALIZE(ierr) end MPI_RECV(BUF, COUNT, DATATYPE, SOURCE, MSGTAG, COMM, STATUS, IERR) BUF(*) INTEGER COUNT, DATATYPE, SOURCE, MSGTAG, COMM, IERR, STATUS(MPI_STATUS_SIZE) ;ehdbjmxsbcijb_f\[mn_j BUFg_[he__ COUNTwe_f_glh\khh[s_gbylbiZ DATATYPEkb^_glbnbdZlhjhf MSGTAG hlijhp_kkZkghf_jhf SOURCE\dhffmgbdZlhj_ COMMkaZiheg_gb_ffZkkb\ZZljb[mlh\ijboh^ys_]hkhh[s_gby STATUS?kebqbkehj_Zevghijbgyluowe_f_glh\f_gvr_agZq_gby COUNTlh ]ZjZglbjm_lky qlh \ [mn_j_ BUF baf_gylky lhevdh we_f_glu

khhl\_lkl\mxsb_ we_f_glZf ijbgylh]h khh[s_gby ?keb dhebq_kl\h we_f_glh\\ijbgbfZ_fhfkhh[s_gbb[hevr_agZq_gby COUNTlh\hagbdZ_l hrb[dZ i_j_iheg_gby Qlh[u ba[_`Zlv wlh]h fh`gh kgZqZeZ hij_^_eblv kljmdlmjm ijboh^ys_]h khh[s_gby ijb ihfhsb ijhp_^mju MPI_PROBE (MPI_IPROBE ?keb gm`gh magZlv lhqgh_ qbkeh we_f_glh\ \ ijbgbfZ_fhf khh[s_gbb lh fh`gh \hkihevah\Zlvky ijhp_^mjhc MPI_GET_COUNT. ;ehdbjh\dZ ]ZjZglbjm_l qlh ihke_ \ha\jZlZ ba ijhp_^mju MPI_RECV \k_ we_f_glukhh[s_gbym`_[m^mlijbgylubjZkiheh`_gu\[mn_j_BUF. Gb`_ijb\_^_gijbf_jijh]jZffu\dhlhjhcgme_\hcijhp_kkihkueZ_lkhh[s_gb_ ijhp_kkm k ghf_jhf h^bg b `^_l hl g_]h hl\_lZ ?keb ijh]jZffZ [m^_l aZims_gZ k [hevrbf qbkehf ijhp_kkh\ lh j_Zevgh \uihegylv i_j_kuedb\k_jZ\ghklZgmllhevdhgme_\hcbi_j\ucijhp_kkuHklZevgu_ijhp_kkuihke_bobgbpbZebaZpbbijhp_^mjhc MPI_INITgZi_qZlZxlgZqZevgu_ 16

agZq_gby i_j_f_gguo a b b ihke_ q_]h aZ\_jrZlky \uihegb\ ijhp_^mjm MPI_FINALIZE. program example5 include 'mpif.h' integer ierr, size, rank real a, b integer status(MPI_STATUS_SIZE) call MPI_INIT(ierr) call MPI_COMM_SIZE(MPI_COMM_WORLD, size, ierr) call MPI_COMM_RANK(MPI_COMM_WORLD, rank, ierr) a = 0.0 b = 0.0 if(rank .eq. 0) then b = 1.0 call MPI_SEND(b, 1, MPI_REAL, 1, 5, & MPI_COMM_WORLD, ierr); call MPI_RECV(a, 1, MPI_REAL, 1, 5, & MPI_COMM_WORLD, status, ierr); else if(rank .eq. 1) then a = 2.0 call MPI_RECV(b, 1, MPI_REAL, 0, 5, & MPI_COMM_WORLD, status, ierr); call MPI_SEND(a, 1, MPI_REAL, 0, 5, & MPI_COMM_WORLD, ierr); end if end if print *, 'process ', rank,' a = ', a, ', b = ', b call MPI_FINALIZE(ierr) end

hihegbl_evgh ihklZ\e_gZ ijh\_jdZ ^ey ijhp_kkZ k fZdkbfZevguf ghf_jhf qlh[u hg g_ ihkeZe khh[s_gb_ g_kms_kl\mxs_fm ijhp_kkm AgZq_gby i_j_f_gghc b baf_gylky lhevdhgZijhp_kkZokg_q_lgufbghf_jZfb program example6 include 'mpif.h' integer ierr, size, rank, a, b integer status(MPI_STATUS_SIZE) call MPI_INIT(ierr) call MPI_COMM_SIZE(MPI_COMM_WORLD, size, ierr) call MPI_COMM_RANK(MPI_COMM_WORLD, rank, ierr) a = rank b = -1 if(mod(rank, 2) .eq. 0) then if(rank+1 .lt. size) then &ihkueZxl\k_ijhp_kkudjhf_ihke_^g_]h call MPI_Send(a, 1, MPI_INTEGER, rank+1, 5, 17

&

MPI_COMM_WORLD, ierr);

end if else call MPI_Recv(b, 1, MPI_INTEGER, rank-1, 5, & MPI_COMM_WORLD, status, ierr); end if print *, 'process ', rank,' a = ', a, ', b = ', b call MPI_FINALIZE(ierr) end

Ijbijb_f_khh[s_gby\f_klhZj]mf_glh\ SOURCEb MSGTAGfh`ghbkihevah\Zlvke_^mxsb_ij_^hij_^_e_ggu_dhgklZglu • MPI_ANY_SOURCE — ijbagZd lh]h qlh ih^oh^bl khh[s_gb_ hl ex[h]h ijhp_kkZ • MPI_ANY_TAG — ijbagZd lh]h qlh ih^oh^bl khh[s_gb_ k ex[uf b^_glbnbdZlhjhf Ijbh^gh\j_f_gghfbkihevah\Zgbbwlbo^\modhgklZgl[m^_lijbgylhkhh[s_gb_kex[ufb^_glbnbdZlhjhfhlex[h]hijhp_kkZ J_Zevgu_ Zljb[mlu ijbgylh]h khh[s_gby \k_]^Z fh`gh hij_^_eblv ih khhl\_lkl\mxsbf we_f_glZf fZkkb\Z status < NhjljZg_ iZjZf_lj status y\ey_lky p_ehqbke_gguf fZkkb\hf jZaf_jZ MPI_STATUS_SIZE. DhgklZglu MPI_SOURCE, MPI_TAGbMPI_ERRORy\eyxlkybg^_dkZfbih^ZgghfmfZkkb\m ^ey^hklmiZdagZq_gbyfkhhl\_lkl\mxsboihe_c • status(MPI_SOURCE) — ghf_jijhp_kkZ-hlijZ\bl_eykhh[s_gby • status(MPI_TAG) — b^_glbnbdZlhjkhh[s_gby • status(MPI_ERROR) — dh^ hrb[db. < yaud_ Kb iZjZf_lj status y\ey_lky kljmdlmjhc ij_^hij_^_e_ggh]h lbiZ MPI_StatuskiheyfbMPI_SOURCE, MPI_TAGbMPI_ERROR. H[jZlbf \gbfZgb_ gZ g_dhlhjmx g_kbff_ljbqghklv hi_jZpbc ihkuedb b ijb_fZ khh[s_gbc K ihfhsvx dhgklZglu MPI_ANY_SOURCE fh`gh ijbgylv khh[s_gb_hlex[h]hijhp_kkZH^gZdh\kemqZ_ihkuedb^Zgguolj_[m_lky y\ghmdZaZlvghf_jijbgbfZxs_]hijhp_kkZ
MPI_GET_COUNT(STATUS, DATATYPE, COUNT, IERR) INTEGER COUNT, DATATYPE, IERR, STATUS(MPI_STATUS_SIZE) IhagZq_gbxiZjZf_ljZ STATUSijhp_^mjZhij_^_ey_lqbkeh COUNTm`_ijbgyluoihke_h[jZs_gbyd MPI_RECV bebijbgbfZ_fuoihke_h[jZs_gbyd MPI_PROBE beb MPI_IPROBE we_f_glh\ khh[s_gby lbiZ DATATYPE >ZggZy

ijhp_^mjZ \ qZklghklb g_h[oh^bfZ ^ey hij_^_e_gby jZaf_jZ h[eZklb iZfylb\u^_ey_fhc^eyojZg_gbyijbgbfZ_fh]hkhh[s_gby

MPI_PROBE(SOURCE, MSGTAG, COMM, STATUS, IERR) INTEGER SOURCE, MSGTAG, COMM, IERR, STATUS(MPI_STATUS_SIZE) Ihemq_gb_ \ fZkkb\_ STATUS bgnhjfZpbb h kljmdlmj_ h`b^Z_fh]h khh[s_gby k b^_glbnbdZlhjhf MSGTAG hl ijhp_kkZ k ghf_jhf SOURCE \ dhffmgbdZlhj_ COMM k [ehdbjh\dhc
^h l_o ihj ihdZ khh[s_gb_ k ih^oh^ysbf b^_glbnbdZlhjhf b ghf_jhf ijhp_kkZ-hlijZ\bl_ey g_ [m^_l ^hklmigh ^ey ihemq_gby Ke_^m_l hkh[h h[jZlblv \gbfZgb_ gZ lh qlh ijhp_^mjZ hij_^_ey_l lhevdh nZdl ijboh^Z khh[s_gby gh j_Zevgh _]h g_ ijbgbfZ_l ?keb ihke_ \uah\Z MPI_PROBE \uau\Z_lky MPI_RECV k lZdbfb `_ iZjZf_ljZfb lh [m^_l ijbgylh lh `_ kZfh_khh[s_gb_bgnhjfZpbyhdhlhjhf[ueZihemq_gZkihfhsvx\uah\Z ijhp_^mjuMPI_PROBE. Ke_^mxsbc ijbf_j ^_fhgkljbjm_l ijbf_g_gb_ ijhp_^mju MPI_PROBE ^ey hij_^_e_gbykljmdlmjuijboh^ys_]hkhh[s_gbyIjhp_kk0`^_lkhh[s_gby hlex[h]hbaijhp_kkh\ 1b 2kh^gbfbl_f`_l_]hfH^gZdhihkueZ_fu_ wlbfbijhp_kkZfb^Zggu_bf_xljZaguclbi>eylh]hqlh[uhij_^_eblv\ dZdmx i_j_f_ggmx ihf_sZlv ijboh^ys__ khh[s_gb_ ijhp_kk kgZqZeZ ijb ihfhsb\uah\Z MPI_PROBEhij_^_ey_lhldh]h`_bf_gghihklmibehwlhkhh[s_gb_Ke_^mxsbcg_ihkj_^kl\_gghihke_ MPI_PROBE\uah\ MPI_RECV]ZjZglbjh\Zgghijbf_lgm`gh_khh[s_gb_ihke_q_]hijbgbfZ_lkykhh[s_gb_ hl^jm]h]hijhp_kkZ program example7 include 'mpif.h' integer rank, ierr, ibuf, status(MPI_STATUS_SIZE) real rbuf call MPI_INIT(ierr) call MPI_COMM_RANK(MPI_COMM_WORLD, rank, ierr) ibuf = rank rbuf = 1.0 * rank if(rank .eq. 1) call MPI_SEND(ibuf, 1, MPI_INTEGER, 0, 5, & MPI_COMM_WORLD, ierr) if(rank .eq. 2) call MPI_SEND(rbuf, 1, MPI_REAL, 0, 5, & MPI_COMM_WORLD, ierr) if(rank .eq. 0) then call MPI_PROBE(MPI_ANY_SOURCE, 5, MPI_COMM_WORLD, & status, ierr) 19

if(status(MPI_SOURCE) .EQ. 1) then call MPI_RECV(ibuf, 1, MPI_INTEGER, 1, 5, & MPI_COMM_WORLD, status, ierr) call MPI_RECV(rbuf, 1, MPI_REAL, 2, 5, & MPI_COMM_WORLD, status, ierr) else if(status(MPI_SOURCE) .EQ. 2) then call MPI_RECV(rbuf, 1, MPI_REAL, 2, 5, & MPI_COMM_WORLD, status, ierr) call MPI_RECV(ibuf, 1, MPI_INTEGER, 1, 5, & MPI_COMM_WORLD, status, ierr) end if end if print *, 'Process 0 recv ', ibuf, ' from process 1, ', & rbuf, ' from process 2' end if call MPI_FINALIZE(ierr) end

do i = 1, NTIMES if(rank .eq. 0) then call MPI_SEND(a, n, MPI_DOUBLE_PRECISION, 1, 1, & MPI_COMM_WORLD, ierr) call MPI_RECV(a, n, MPI_DOUBLE_PRECISION, 1, 1, & MPI_COMM_WORLD, status, ierr) end if if(rank .eq. 1) then call MPI_RECV(a, n, MPI_DOUBLE_PRECISION, 0, 1, & MPI_COMM_WORLD, status, ierr) call MPI_SEND(a, n, MPI_DOUBLE_PRECISION, 0, 1, & MPI_COMM_WORLD, ierr) end if enddo time = (MPI_WTIME(ierr)-time_start)/2/NTIMES bandwidth = (8*n*1.d0/(2**20))/time if(max .lt. bandwidth) then max = bandwidth lmax = 8*n end if if(rank .eq. 0) then if(n .eq. 0) then print *, 'latency = ', time, ' seconds' else print *, 8*n, ' bytes, bandwidth =', bandwidth, & ' Mb/s' end if end if if(n .eq. 0) then n = 1 else n = 2*n end if end do if(rank .eq. 0) then print *, 'max bandwidth =', max, ' Mb/s , length =', & lmax, ' bytes' end if call MPI_FINALIZE(ierr) end

I_j_^ZqZijb_fkhh[s_gbc[_a[ehdbjh\db < MPI ij_^mkfhlj_g gZ[hj ijhp_^mj ^ey hkms_kl\e_gby Zkbgojhgghc i_j_^Zqb^Zgguo
21

< ijbgpbi_ ^ZggZy \hafh`ghklv bkdexqbl_evgh ihe_agZ ^ey kha^Zgby wnn_dlb\guo ijh]jZff < kZfhf ^_e_ ijh]jZffbkl agZ_l qlh \ g_dhlhjuc fhf_gl_fmihlj_[m_lkyfZkkb\dhlhjuc\uqbkey_l^jm]hcijhp_kkHgaZjZg__ \uklZ\ey_l \ ijh]jZff_ Zkbgojhgguc aZijhk gZ ihemq_gb_ ^Zggh]h fZkkb\ZZ^hlh]hfhf_glZdh]^ZfZkkb\j_Zevghihlj_[m_lkyhgfh`_l\uihegylv ex[mx ^jm]mx ihe_agmx jZ[hlm Hiylv `_ \h fgh]bo kemqZyo kh\_jr_gghg_h[yaZl_evgh^h`b^ZlvkyhdhgqZgbyihkuedbkhh[s_gby^ey\uiheg_gby ihke_^mxsbo \uqbke_gbc >ey aZ\_jr_gby Zkbgojhggh]h h[f_gZ lj_[m_lky \uah\ ^hihegbl_evghc ijhp_^mju dhlhjZy ijh\_jy_l aZ\_jrbeZkvebhi_jZpbybeb^h`b^Z_lky__aZ\_jr_gbyLhevdhihke_wlh]hfh`gh bkihevah\Zlv [mn_j ihkuedb ^ey ^jm]bo p_e_c [_a hiZk_gby aZihjlblv hlijZ\ey_fh_khh[s_gb_ ?keb _klv \hafh`ghklv hi_jZpbb ijb_fZi_j_^Zqb khh[s_gbc kdjulv gZ nhg_\uqbke_gbclhwlbf\jh^_[ugZ^h[_ah]h\hjhqghihevah\ZlvkyH^gZdh gZ ijZdlbd_ g_ \k_ \k_]^Z kh]eZkm_lky k l_hjb_c Fgh]h_ aZ\bkbl hl dhgdj_lghcj_ZebaZpbbDkh`Ze_gbx^Ze_dhg_\k_]^ZZkbgojhggu_hi_jZpbb wnn_dlb\gh ih^^_j`b\Zxlky ZiiZjZlmjhc b kbkl_fguf hdjm`_gb_f Ihwlhfm g_ klhbl m^b\eylvky _keb wnn_dl hl \uiheg_gby \uqbke_gbc gZ nhg_ i_j_kuehd hdZ`_lky gme_\uf beb kh\k_f g_[hevrbf K^_eZggu_ aZf_qZgby dZkZxlky lhevdh \hijhkh\ wnn_dlb\ghklb < hlghr_gbb ij_^hklZ\ey_fhc nmgdpbhgZevghklb Zkbgojhggu_ hi_jZpbb bkdexqbl_evgh ihe_agu ihwlhfm hgb ijbkmlkl\mxl ijZdlbq_kdb \ dZ`^hc j_Zevghc ijh]jZff_ MPI_ISEND(BUF, COUNT, DATATYPE, DEST, MSGTAG, COMM, REQUEST, IERR) BUF(*) INTEGER COUNT, DATATYPE, DEST, MSGTAG, COMM, REQUEST, IERR G_[ehdbjmxsZy ihkuedZ ba [mn_jZ BUF COUNT we_f_glh\ khh[s_gby lbiZ DATATYPE k b^_glbnbdZlhjhf MSGTAG ijhp_kkm DEST dhffmgbdZlhjZ COMM.

• MPI_IBSEND — g_[ehdbjmxsZyi_j_^ZqZkhh[s_gbyk[mn_jbaZpb_c • MPI_ISSEND — g_[ehdbjmxsZyi_j_^ZqZkhh[s_gbykkbgojhgbaZpb_c • MPI_IRSEND — g_[ehdbjmxsZyi_j_^ZqZkhh[s_gbyih]hlh\ghklb Dbaeh`_gghc\ur_k_fZglbd_jZ[hluwlboijhp_^mj^h[Z\ey_lkyhlkmlkl\b_ [ehdbjh\db MPI_IRECV(BUF, COUNT, DATATYPE, SOURCE, MSGTAG, COMM, REQUEST, IERR) BUF(*) INTEGER COUNT, DATATYPE, SOURCE, MSGTAG, COMM, REQUEST, IERR G_[ehdbjmxsbc ijb_f \ [mn_j BUF g_ [he__ COUNT we_f_glh\ khh[s_gby lbiZ DATATYPEkb^_glbnbdZlhjhf MSGTAG hlijhp_kkZkghf_jhf SOURCE\ dhffmgbdZlhj_ COMM k aZiheg_gb_f fZkkb\Z STATUS < hlebqb_ hl [ehdb-

jmxs_]hijb_fZ\ha\jZlbaijhp_^mjuijhbkoh^blkjZamihke_bgbpbZebaZpbbijhp_kkZijb_fZ[_ah`b^Zgbyihemq_gby\k_]hkhh[s_gbyb_]haZibkb \[mn_j_BUFHdhgqZgb_ijhp_kkZijb_fZfh`ghhij_^_eblvkihfhsvxiZjZf_ljZREQUESTbijhp_^mjk_f_ckl\MPI_WAIT bMPI_TEST.

Khh[s_gb_hlijZ\e_ggh_ex[hcbaijhp_^mjMPI_SEND, MPI_ISENDbex[hc balj_obofh^bnbdZpbcfh`_l[ulvijbgylhex[hcbaijhp_^mj MPI_RECV bMPI_IRECV. H[jZlbf hkh[h_ \gbfZgb_ gZ lh qlh ^h aZ\_jr_gby g_[ehdbjmxs_c hi_jZpbbg_ke_^m_laZibku\Zlv\bkihevam_fucfZkkb\^Zgguo MPI_IPROBE(SOURCE, MSGTAG, COMM, FLAG, STATUS, IERR) LOGICAL FLAG INTEGER SOURCE, MSGTAG, COMM, IERR, STATUS(MPI_STATUS_SIZE) Ihemq_gb_ \ fZkkb\_ STATUS bgnhjfZpbb h kljmdlmj_ h`b^Z_fh]h khh[s_gby k b^_glbnbdZlhjhf MSGTAG hl ijhp_kkZ k ghf_jhf SOURCE \ dhffmgbdZlhj_ COMM [_a [ehdbjh\db < iZjZf_lj_ FLAG \ha\jZsZ_lky agZq_gb_ .TRUE. _keb khh[s_gb_ k ih^oh^ysbfb Zljb[mlZfb m`_ fh`_l

[ulv ijbgylh \ wlhf kemqZ_ ^_ckl\b_ ijhp_^mju iheghklvx ZgZeh]bqgh MPI_PROBE bagZq_gb_ .FALSE._kebkhh[s_gbykmdZaZggufbZljb[mlZfb _s_g_l MPI_WAIT(REQUEST, STATUS, IERR) INTEGER REQUEST, IERR, STATUS(MPI_STATUS_SIZE)

H`b^Zgb_aZ\_jr_gbyZkbgojhgghchi_jZpbbZkkhpbbjh\Zgghckb^_glbnbdZlhjhf REQUEST b aZims_gghc \uah\hf ijhp_^mju MPI_ISEND beb MPI_IRECVIhdZZkbgojhggZyhi_jZpbyg_[m^_laZ\_jr_gZijhp_kk\uihegb\rbc ijhp_^mjm MPI_WAIT [m^_l aZ[ehdbjh\Zg >ey hi_jZpbb g_[ehdbjmxs_]hijb_fZhij_^_ey_lkyiZjZf_lj STATUSIhke_\uiheg_gby 23

ijhp_^mju b^_glbnbdZlhj g_[ehdbjmxs_c mklZgZ\eb\Z_lky\agZq_gb_MPI_REQUEST_NULL.

hi_jZpbb

REQUEST

MPI_WAITALL(COUNT, REQUESTS, STATUSES, IERR) INTEGER COUNT, REQUESTS(*), STATUSES(MPI_STATUS_SIZE,*), IERR H`b^Zgb_ aZ\_jr_gby COUNT Zkbgojhgguo hi_jZpbc Zkkhpbbjh\Zgguo k b^_glbnbdZlhjZfb fZkkb\Z REQUESTS >ey hi_jZpbc g_[ehdbjmxsbo ijb_fh\ hij_^_eyxlky khhl\_lkl\mxsb_ iZjZf_lju \ fZkkb\_ STATUSES.

?keb\h\j_fyh^ghcbebg_kdhevdbohi_jZpbch[f_gZ\hagbdebhrb[dblh ihe_ hrb[db \ we_f_glZo fZkkb\Z STATUSES [m^_l mklZgh\e_gh \ khhl\_lkl\mxs__agZq_gb_Ihke_\uiheg_gbyijhp_^mjukhhl\_lkl\mxsb_ REQUESTS we_f_glu iZjZf_ljZ mklZgZ\eb\Zxlky \ agZq_gb_ MPI_REQUEST_NULL. Gb`_ihdZaZgijbf_jnjZ]f_glZijh]jZffu\dhlhjhc\k_ijhp_kkuh[f_gb\Zxlky khh[s_gbyfb k [eb`Zcrbfb khk_^yfb \ khhl\_lkl\bb k lhiheh]b_cdhevpZijbihfhsbg_[ehdbjmxsbohi_jZpbcAZf_lbfqlhbkihevah\Zgb_^eywlbop_e_c[ehdbjmxsbohi_jZpbcfh]ehijb\_klbd\hagbdgh\_gbxlmibdh\hckblmZpbb program example9 include 'mpif.h' integer ierr, rank, size, prev, next, reqs(4), buf(2) integer stats(MPI_STATUS_SIZE, 4) call MPI_INIT(ierr) call MPI_COMM_SIZE(MPI_COMM_WORLD, size, ierr) call MPI_COMM_RANK(MPI_COMM_WORLD, rank, ierr) prev = rank - 1 next = rank + 1 if (rank .eq. 0) prev = size - 1 if (rank .eq. size - 1) next = 0 call MPI_IRECV(buf(1), 1, MPI_INTEGER, prev, 5, & MPI_COMM_WORLD, reqs(1), ierr) call MPI_IRECV(buf(2), 1, MPI_INTEGER, next, 6, & MPI_COMM_WORLD, reqs(2), ierr) call MPI_ISEND(rank, 1, MPI_INTEGER, prev, 6, & MPI_COMM_WORLD, reqs(3), ierr) call MPI_ISEND(rank, 1, MPI_INTEGER, next, 5, & MPI_COMM_WORLD, reqs(4), ierr) call MPI_WAITALL(4, reqs, stats, ierr); print *, ‘process ’, rank, & ‘ prev=’, buf(1), ‘ next=’, buf(2) call MPI_FINALIZE(ierr) end MPI_WAITANY(COUNT, REQUESTS, INDEX, STATUS, IERR) INTEGER COUNT, REQUESTS(*), INDEX, STATUS(MPI_STATUS_SIZE), IERR H`b^Zgb_ aZ\_jr_gby h^ghc ba COUNT Zkbgojhgguo hi_jZpbc Zkkhpbbjh\Zgguokb^_glbnbdZlhjZfb REQUESTS?kebdfhf_glm\uah\ZaZ\_jrbebkv 24

g_kdhevdh ba h`b^Z_fuo hi_jZpbc lh kemqZcguf h[jZahf [m^_l \u[jZgZ h^gZbagboIZjZf_lj INDEX kh^_j`blghf_jwe_f_glZ\fZkkb\_ REQUESTS, kh^_j`Zs_]h b^_glbnbdZlhj aZ\_jr_gghc hi_jZpbb >ey g_[ehdbjmxs_]h ijb_fZ hij_^_ey_lky iZjZf_lj STATUS Ihke_ \uiheg_gby ijhp_^mju khhl\_lkl\mxsbc we_f_gl iZjZf_ljZ REQUESTS mklZgZ\eb\Z_lky \ agZq_gb_ MPI_REQUEST_NULL. MPI_WAITSOME(INCOUNT, REQUESTS, OUTCOUNT, INDEXES, STATUSES, IERR) INTEGER INCOUNT, REQUESTS(*), OUTCOUNT, INDEXES(*), IERR, STATUSES(MPI_STATUS_SIZE,*) H`b^Zgb_aZ\_jr_gbyohly[uh^ghcbaINCOUNTZkbgojhgguohi_jZpbcZkkhpbbjh\Zgguo k b^_glbnbdZlhjZfb REQUESTS IZjZf_lj OUTCOUNT kh^_j`bl qbkeh aZ\_jr_gguo hi_jZpbc Z i_j\u_ OUTCOUNT we_f_glh\ fZkkb\Z INDEXES kh^_j`Zl ghf_jZ we_f_glh\ fZkkb\Z REQUESTS k bo b^_glbnbdZlhjZfb I_j\u_ OUTCOUNT we_f_glh\ fZkkb\Z STATUSES kh^_j`Zl iZjZf_lju

aZ\_jr_gguo hi_jZpbc ^ey g_[ehdbjmxsbo ijb_fh\ Ihke_ \uiheg_gby ijhp_^mju khhl\_lkl\mxsb_ we_f_glu iZjZf_ljZ REQUESTS mklZgZ\eb\Zxlky\agZq_gb_MPI_REQUEST_NULL.

< ke_^mxs_f ijbf_j_ ^_fhgkljbjm_lky ko_fZ bkihevah\Zgby ijhp_^mju MPI_WAITSOME^eyhj]ZgbaZpbbdhffmgbdZpbhgghcko_fu³master-slave´\k_ ijhp_kku h[sZxlky k h^gbf \u^_e_gguf ijhp_kkhf eyijbr_^rbokhh[s_gbcijhp_kk0\uau\Z_lijhp_^mjmh[jZ[hldb masterihke_q_]hkgh\Z\uklZ\ey_lg_[ehdbjmxsb_ijb_fuLZdbf h[jZahf ijhp_kk 0 h[jZ[Zlu\Z_l l_ ihjpbb ^Zgguo dhlhju_ ]hlh\u gZ ^Zgguc fhf_gl Ijb wlhf ^ey dhjj_dlghklb jZ[hlu ijh]jZffu gm`gh h[_ki_qblvqlh[uijhp_kk 0mki_\Zeh[jZ[hlZlvijboh^ysb_khh[s_gbylh _klv qlh[u ijhp_^mjZ slave jZ[hlZeZ agZqbl_evgh ^hevr_ ijhp_^mju master\ijhlb\ghfkemqZ_bjZkiZjZee_eb\Zgb_g_bf__lhkh[h]hkfukeZ Djhf_lh]h\ijbf_j_gZibkZg[_kdhg_qgucpbdeihwlhfm^eydhgdj_lghc ijh]jZffugm`ghij_^mkfhlj_lvmkeh\b_aZ\_jr_gby

25

program example10 include 'mpif.h' integer rank, size, ierr, N, MAXPROC parameter(N = 1000, MAXPROC = 128) integer req(MAXPROC), num, indexes(MAXPROC) integer statuses(MPI_STATUS_SIZE, MAXPROC) double precision a(N, MAXPROC) call MPI_INIT(ierr) call MPI_COMM_SIZE(MPI_COMM_WORLD, size, ierr) call MPI_COMM_RANK(MPI_COMM_WORLD, rank, ierr) if(rank .ne. 0) then do while(.TRUE.) call slave(a, N) call MPI_SEND(a, N, MPI_DOUBLE_PRECISION, 0, 5, & MPI_COMM_WORLD, ierr) end do else do i = 1, size-1 call MPI_IRECV(a(1, i), N, MPI_DOUBLE_PRECISION, i, & 5, MPI_COMM_WORLD, req(i), ierr) end do do while(.TRUE.) call MPI_WAITSOME(size-1, req, num, indexes, & statuses, ierr) do i = 1, num call master(a(1, indexes(i)), N) call MPI_IRECV(a(1, indexes(i)), N, & MPI_DOUBLE_PRECISION, & indexes(i), 5, MPI_COMM_WORLD, & req(indexes(i)), ierr) end do end do end if call MPI_FINALIZE(ierr) end subroutine slave(a, n) double precision a integer n &h[jZ[hldZehdZevghcqZklbfZkkb\ZD end subroutine master(a, n) double precision a integer n &h[jZ[hldZfZkkb\ZD End

26

MPI_TEST(REQUEST, FLAG, STATUS, IERR) LOGICAL FLAG INTEGER REQUEST, IERR, STATUS(MPI_STATUS_SIZE) Ijh\_jdZ aZ\_jr_gghklb Zkbgojhgghchi_jZpbb MPI_ISENDbeb MPI_IRECV, Zkkhpbbjh\Zgghckb^_glbnbdZlhjhf REQUEST
p_^mjZ ijb_fZ lh Zljb[mlu b ^ebgm ihemq_ggh]h khh[s_gby fh`gh hij_^_eblv h[uqguf h[jZahf k ihfhsvx iZjZf_ljZ STATUS Ihke_ \uiheg_gby ijhp_^mju khhl\_lkl\mxsbc we_f_gl iZjZf_ljZ REQUEST mklZgZ\eb\Z_lky\agZq_gb_MPI_REQUEST_NULL. MPI_TESTALL(COUNT, REQUESTS, FLAG, STATUSES, IERR) LOGICAL FLAG INTEGER COUNT, REQUESTS(*), STATUSES(MPI_STATUS_SIZE,*), IERR Ijh\_jdZ aZ\_jr_gghklb COUNT Zkbgojhgguo hi_jZpbc Zkkhpbbjh\Zgguok b^_glbnbdZlhjZfb REQUESTS < iZjZf_lj_ FLAG ijhp_^mjZ \ha\jZsZ_l agZq_gb_ .TRUE. \ yaud_ Kb – 1 _keb \k_ hi_jZpbb Zkkhpbbjh\Zggu_ k mdZ-

aZggufb b^_glbnbdZlhjZfb aZ\_jr_gu < wlhf kemqZ_ iZjZf_lju khh[s_gbc[m^mlmdZaZgu\fZkkb\_ STATUSES?kebdZdZy-eb[hbahi_jZpbc g_aZ\_jrbeZkvlh\ha\jZsZ_lky.FALSE.\yaud_Kb– 0 bhij_^_e_gghklv we_f_glh\ fZkkb\Z STATUSES g_ ]ZjZglbjm_lky Ihke_ \uiheg_gby REQUESTS ijhp_^mju khhl\_lkl\mxsb_ we_f_glu iZjZf_ljZ mklZgZ\eb\Zxlky\agZq_gb_MPI_REQUEST_NULL. MPI_TESTANY(COUNT, REQUESTS, INDEX, FLAG, STATUS, IERR) LOGICAL FLAG INTEGER COUNT, REQUESTS(*), INDEX, STATUS(MPI_STATUS_SIZE), IERR

Ijh\_jdZaZ\_jr_gghklbohly[uh^ghcZkbgojhgghchi_jZpbbZkkhpbbjh\Zgghckb^_glbnbdZlhjhfbafZkkb\ZREQUESTS
27

MPI_TESTSOME(INCOUNT, REQUESTS, OUTCOUNT, INDEXES, STATUSES, IERR) INTEGER INCOUNT, REQUESTS(*), OUTCOUNT, INDEXES(*), IERR, STATUSES(MPI_STATUS_SIZE,*) :gZeh]ijhp_^mju MPI_WAITSOMEgh\ha\jZlijhbkoh^blg_f_^e_ggh?keb

gbh^gZbal_klbjm_fuohi_jZpbcdfhf_glm\uah\Zg_aZ\_jrbeZkvlhagZq_gb_OUTCOUNT[m^_ljZ\ghgmex

Ke_^mxsbc ijbf_j ^_fhgkljbjm_l ijbf_g_gb_ g_[ehdbjmxsbo hi_jZpbc ^eyj_ZebaZpbbljZgkihgbjh\Zgbyd\Z^jZlghcfZljbpujZkij_^_e_gghcf_`^m ijhp_kkZfb ih kljhdZf KgZqZeZ dZ`^uc ijhp_kk ehdZevgh hij_^_ey_l nlkljhdfZkkb\ZaAZl_fijbihfhsbg_[ehdbjmxsbohi_jZpbcMPI_ISEND b MPI_IRECVbgbpbZebabjmxlky\k_g_h[oh^bfu_^eyljZgkihgbjh\Zgbyh[f_gu ^Zggufb GZ nhg_ gZqbgZxsboky h[f_gh\ dZ`^uc ijhp_kk ljZgkihgbjm_l k\hx ehdZevgmx qZklv fZkkb\Z a Ihke_ wlh]h ijhp_kk ijb ihfhsb \uah\Z ijhp_^mju MPI_WAITANY ^h`b^Z_lky ijboh^Z khh[s_gby hl ex[h]h ^jm]h]h ijhp_kkZ b ljZgkihgbjm_l ihemq_ggmx hl ^Zggh]h ijhp_kkZ qZklv fZkkb\Z a H[jZ[hldZ ijh^he`Z_lky ^h l_o ihj ihdZ g_ [m^ml ihemq_gu khh[s_gby hl \k_o ijhp_kkh\ < dhgp_ bkoh^guc fZkkb\ a b ljZgkihgbjh\ZggucfZkkb\bjZki_qZlu\Zxlky program example11 include 'mpif.h' integer ierr, rank, size, N, nl, i, j parameter (N = 9) double precision a(N, N), b(N, N) call MPI_INIT(ierr) call MPI_COMM_SIZE(MPI_COMM_WORLD, size, ierr) call MPI_COMM_RANK(MPI_COMM_WORLD, rank, ierr) nl = (N-1)/size+1 call work(a, b, N, nl, size, rank) call MPI_FINALIZE(ierr) end subroutine work(a, b, n, nl, size, rank) include 'mpif.h' integer ierr, rank, size, n, MAXPROC, nl, i, j, ii, jj, ir parameter (MAXPROC = 64) double precision a(nl, n), b(nl, n), c integer irr, status(MPI_STATUS_SIZE), req(MAXPROC*2) do i = 1, nl do j = 1, n ii = i+rank*nl if(ii .le. n) a(i, j) = 100*ii+j end do end do do ir = 0, size-1 if(ir .ne. rank) & call MPI_IRECV(b(1, ir*nl+1), nl*nl, 28

& & &

MPI_DOUBLE_PRECISION, ir, MPI_ANY_TAG, MPI_COMM_WORLD, req(ir+1), ierr) end do req(rank+1) = MPI_REQUEST_NULL

do ir = 0, size-1 if(ir .ne. rank) & call MPI_ISEND(a(1, ir*nl+1), nl*nl, & MPI_DOUBLE_PRECISION, ir, & 1, MPI_COMM_WORLD, & req(ir+1+size), ierr) end do ir = rank do i = 1, nl ii = i+ir*nl do j = i+1, nl jj = j+ir*nl b(i, jj) = a(j, ii) b(j, ii) = a(i, jj) end do b(i, ii) = a(i, ii) end do do irr = 1, size-1 call MPI_WAITANY(size, req, ir, status, ierr) ir = ir-1 do i = 1, nl ii = i+ir*nl do j = i+1, nl jj = j+ir*nl c = b(i, jj) b(i, jj) = b(j, ii) b(j, ii) = c end do end do end do do i = 1, nl do j = 1, N ii = i+rank*nl if(ii .le. n) print *, 'process ', rank, & ': a(', ii, ', ', j, ') =', a(i,j), & ', b(', ii, ', ', j, ') =', b(i,j) end do end do end

29

Hleh`_ggu_aZijhkugZ\aZbfh^_ckl\b_ Ijhp_^mju ^Zgghc ]jmiiu iha\heyxl kgbablv gZdeZ^gu_ jZkoh^u \hagbdZxsb_\jZfdZoh^gh]hijhp_kkhjZijbh[jZ[hld_ijb_fZi_j_^Zqbbi_j_f_s_gbbg_h[oh^bfhcbgnhjfZpbbf_`^mijhp_kkhfbk_l_\ufdhgljhee_jhf QZklh \ ijh]jZff_ ijboh^blky fgh]hdjZlgh \uihegylv h[f_gu k h^bgZdh\ufbiZjZf_ljZfbgZijbf_j\pbde_ BUF(*) INTEGER COUNT, DATATYPE, DEST, MSGTAG, COMM, REQUEST, IERR

Nhjfbjh\Zgb_hleh`_ggh]haZijhkZgZihkuedmkhh[s_gbyKZfZhi_jZpby i_j_kuedbijbwlhfg_gZqbgZ_lky :gZeh]bqgh lj_f fh^bnbdZpbyf ijhp_^mj MPI_SEND b MPI_ISEND ij_^mkfhlj_guljb^hihegbl_evguo\ZjbZglZijhp_^mjuMPI_SEND_INIT: • MPI_BSEND_INIT — nhjfbjh\Zgb_ hleh`_ggh]h aZijhkZ gZ i_j_^Zqm khh[s_gbyk[mn_jbaZpb_c • MPI_SSEND_INIT — nhjfbjh\Zgb_ hleh`_ggh]h aZijhkZ gZ i_j_^Zqm khh[s_gbykkbgojhgbaZpb_c • MPI_RSEND_INIT — nhjfbjh\Zgb_ hleh`_ggh]h aZijhkZ gZ i_j_^Zqm khh[s_gbyih]hlh\ghklb MPI_RECV_INIT(BUF, COUNT, DATATYPE, SOURCE, MSGTAG, COMM, REQUEST, IERR) BUF(*) INTEGER COUNT, DATATYPE, SOURCE, MSGTAG, COMM, REQUEST, IERR

Nhjfbjh\Zgb_ hleh`_ggh]h aZijhkZ gZ ijb_f khh[s_gby KZfZ hi_jZpby ijb_fZijbwlhfg_gZqbgZ_lky

30

MPI_START(REQUEST, IERR) INTEGER REQUEST, IERR

BgbpbZebaZpbyhleh`_ggh]haZijhkZgZ\uiheg_gb_hi_jZpbbh[f_gZkhhl\_lkl\mxs_c agZq_gbx iZjZf_ljZ REQUEST Hi_jZpby aZimkdZ_lky dZd g_[ehdbjmxsZy MPI_STARTALL(COUNT, REQUESTS, IERR) INTEGER COUNT, REQUESTS, IERR BgbpbZebaZpby COUNT hleh`_gguo aZijhkh\ gZ \uiheg_gb_ hi_jZpbc h[f_gZ khhl\_lkl\mxsbo agZq_gbyf i_j\uo COUNT we_f_glh\ fZkkb\Z REQUESTSHi_jZpbbaZimkdZxlkydZdg_[ehdbjmxsb_

< hlebqb_ hl g_[ehdbjmxsbo hi_jZpbc ih aZ\_jr_gbb \uiheg_gby hi_jZpbbaZims_gghcijbihfhsbhleh`_ggh]haZijhkZgZ\aZbfh^_ckl\b_ agZq_gb_iZjZf_ljZREQUEST (REQUESTS khojZgy_lkybfh`_lbkihevah\Zlvky \^Zevg_cr_f MPI_REQUEST_FREE(REQUEST, IERR) INTEGER REQUEST, IERR

>ZggZy ijhp_^mjZ m^Zey_l kljmdlmju ^Zgguo k\yaZggu_ k iZjZf_ljhf REQUESTIhke___\uiheg_gbyiZjZf_ljREQUESTmklZgZ\eb\Z_lky\agZq_gb_ MPI_REQUEST_NULL ?keb hi_jZpby k\yaZggZy k wlbf aZijhkhf m`_ \uihegy_lkylhhgZ[m^_laZ\_jr_gZ
call call call call

MPI_REQUEST_FREE(reqs(1), MPI_REQUEST_FREE(reqs(2), MPI_REQUEST_FREE(reqs(3), MPI_REQUEST_FREE(reqs(4),

ierr) ierr) ierr) ierr)

Lmibdh\u_kblmZpbbGHDGORFN Bkihevah\Zgb_[ehdbjmxsboijhp_^mjijb_fZbihkuedbk\yaZghk\hafh`guf\hagbdgh\_gb_flmibdh\hckblmZpbbIj_^iheh`bfqlhjZ[hlZxl^\Z iZjZee_evguoijhp_kkZbhgb^he`guh[f_gylvky^Zggufb;ueh[u\iheg_ _kl_kl\_ggh \ dZ`^hf ijhp_kk_ kgZqZeZ \hkihevah\Zlvky ijhp_^mjhc MPI_SENDZaZl_fijhp_^mjhcMPI_RECV.Ghbf_gghwlh]hbg_klhbl^_eZlv >_eh \ lhfqlhfuaZjZg__g_agZ_fdZdj_Zebah\ZgZijhp_^mjZ MPI_SEND. ?keb jZajZ[hlqbdb ^ey ]ZjZglbb dhjj_dlgh]h ih\lhjgh]h bkihevah\Zgby [mn_jZ ihkuedb aZeh`beb ko_fm ijb dhlhjhc ihkueZxsbc ijhp_kk `^_l gZqZeZijb_fZlh\hagbdg_ldeZkkbq_kdbclmibdI_j\ucijhp_kkg_fh`_l \_jgmlvky ba ijhp_^mju ihkuedb ihkdhevdm \lhjhc g_ gZqbgZ_l ijb_f khh[s_gby:\lhjhcijhp_kkg_fh`_lgZqZlvijb_fkhh[s_gbyihkdhevdm kZfihihoh`_cijbqbg_aZkljyegZihkued_ ?s_om`_kblmZpbydh]^Zh[Zijhp_kkZkgZqZeZihiZ^ZxlgZ[ehdbjmxsmx ijhp_^mjm ijb_fZ MPI_RECV Z ebrv aZl_f gZ ihkuedm ^Zgguo < lZdhf kemqZ_lmibd\hagbdg_lg_aZ\bkbfhhlkihkh[Zj_ZebaZpbbijhp_^mjijb_fZ bihkuedb^Zgguo ijhp_kk0:

ijhp_kk1:

MPI_RECVhlijhp_kkZ MPI_SENDijhp_kkm

MPI_RECVhlijhp_kkZ MPI_SENDijhp_kkm

ijhp_kk0:

ijhp_kk1:

MPI_SENDijhp_kkm MPI_RECVhlijhp_kkZ

MPI_SENDijhp_kkm MPI_RECVhlijhp_kkZ

Fh`_l \hagbdgmlv lmibd

JZkkfhljbfjZaebqgu_kihkh[ujZaj_r_gbylmibdh\uokblmZpbc 1. Ijhkl_crbf\ZjbZglhfjZaj_r_gbylmibdh\hckblmZpbb[m^_lbaf_g_gb_ ihjy^dZ ke_^h\Zgby ijhp_^mj ihkuedb b ijb_fZ khh[s_gby gZ hghf ba ijhp_kkh\dZdihdZaZghgb`_ ijhp_kk0:

ijhp_kk1:

MPI_SENDijhp_kkm MPI_RECVhlijhp_kkZ

MPI_RECVhlijhp_kkZ MPI_SENDijhp_kkm

32

Lmibd g_\hagbdZ_l

2. >jm]bf \ZjbZglhf jZaj_r_gby lmibdh\hc kblmZpbb fh`_l [ulv bkihevah\Zgb_ g_[ehdbjmxsbo hi_jZpbc AZf_gbf \uah\ ijhp_^mju ijb_fZkhh[s_gbyk[ehdbjh\dhcgZ\uah\ijhp_^mju MPI_IRECVJZkiheh`bf _]h i_j_^ \uah\hf ijhp_^mju MPI_SEND l_ ij_h[jZam_f njZ]f_glke_^mxsbfh[jZahf Ijhp_kk0:

ijhp_kk1:

MPI_SENDijhp_kkm MPI_RECVhlijhp_kkZ

MPI_IRECVhlijhp_kkZ MPI_SENDijhp_kkm MPI_WAIT

Lmibd g_\hagbdZ_l

< lZdhc kblmZpbb lmibd ]ZjZglbjh\Zggh g_ \hagbdg_l ihkdhevdm d fhf_glm\uah\Zijhp_^mjuMPI_SEND aZijhkgZijb_fkhh[s_gbym`_[m^_l \uklZ\e_g Z agZqbl i_j_^ZqZ ^Zgguo fh`_l gZqZlvky Ijb wlhf j_dhf_g^m_lky\uklZ\eylvijhp_^mjm MPI_IRECV\ijh]jZff_dZdfh`gh jZgvr_ qlh[u jZgvr_ ij_^hklZ\blv \hafh`ghklv gZqZeZ i_j_kuedb b fZdkbfZevghbkihevah\Zlvij_bfms_kl\ZZkbgojhgghklb 3. Lj_lvbf \ZjbZglhf jZaj_r_gby lmibdh\hc kblmZpbb fh`_l [ulv bkihevah\Zgb_ijhp_^mjuMPI_SENDRECV. MPI_SENDRECV(SBUF, SCOUNT, STYPE, DEST, STAG, RBUF, RCOUNT, RTYPE, SOURCE, RTAG, COMM, STATUS, IERR) SBUF(*), RBUF(*) INTEGER SCOUNT, STYPE, DEST, STAG, RCOUNT, RTYPE, SOURCE, RTAG, COMM, STATUS(MPI_STATUS_SIZE), IERR

Ijhp_^mjZ \uihegy_l kh\f_s_ggu_ ijb_f b i_j_^Zqm khh[s_gbc k [ehdbjh\dhc Ih \uah\m ^Zgghc ijhp_^mju hkms_kl\ey_lky ihkuedZ SCOUNT we_f_glh\ lbiZ STYPE ba fZkkb\Z SBUF k l_]hf STAG ijhp_kkm k ghf_jhf DEST \ dhffmgbdZlhj_ COMM b ijb_f \ fZkkb\ RBUF g_ [he__ RCOUNTwe_f_glh\lbiZRTYPE kl_]hfRTAGhlijhp_kkZkghf_jhfSOURCE \ dhffmgbdZlhj_ COMM >ey ijbgbfZ_fh]h khh[s_gby aZihegy_lky iZjZf_lj STATUS IjbgbfZxsbc b hlijZ\eyxsbc ijhp_kku fh]ml y\eylvky h^gbf b l_f `_ ijhp_kkhf ;mn_ju i_j_^Zqb b ijb_fZ ^Zgguo g_ ^he`gu i_j_k_dZlvky =ZjZglbjm_lky qlh ijb wlhf lmibdh\hc kblmZpbb g_ \hagbdZ_l Khh[s_gb_ hlijZ\e_ggh_ hi_jZpb_c MPI_SENDRECV fh`_l [ulv ijbgylh h[uqguf h[jZahf b hi_jZpby MPI_SENDRECV fh`_l ijbgylv khh[s_gb_ hlijZ\e_ggh_ h[uqghc hi_jZpb_c

33

MPI_SENDRECV_REPLACE(BUF, COUNT, DATATYPE, DEST, STAG, SOURCE, RTAG, COMM, STATUS, IERR) BUF(*) INTEGER COUNT, DATATYPE, DEST, STAG, SOURCE, RTAG, COMM, STATUS(MPI_STATUS_SIZE), IERR

Kh\f_s_ggu_ ijb_f b i_j_^ZqZ khh[s_gbc k [ehdbjh\dhc q_j_a h[sbc [mn_jBUFIjbgbfZ_fh_khh[s_gb_g_^he`ghij_\urZlvihjZaf_jmhlijZ\ey_fh_ khh[s_gb_ Z i_j_^Z\Z_fu_ b ijbgbfZ_fu_ ^Zggu_ ^he`gu [ulvh^gh]hlbiZ
AZ^Zgby • DZdbfbZljb[mlZfbh[eZ^Z_l\MPIdZ`^h_ihkueZ_fh_khh[s_gb_" • Fh`ghebkhh[s_gb_hlijZ\e_ggh_kihfhsvx[ehdbjmxs_chi_jZpbbihkuedbijbgylvg_[ehdbjmxs_chi_jZpb_cijb_fZ" • Qlh]ZjZglbjm_l[ehdbjh\dZijbhlijZ\d_ijb_f_khh[s_gbc" • Fh`gh eb \ dZq_kl\_ l_]h\ ijb ihkued_ jZaebqguo khh[s_gbc \ ijh]jZff_\k_]^Zbkihevah\Zlvh^ghblh`_qbkeh" • DZdijbgylvex[h_khh[s_gb_hlex[h]hijhp_kkZ"

34

• DZd ijbgbfZxsbc ijhp_kk fh`_l hij_^_eblv ^ebgm ihemq_ggh]h khh[s_gby" • Fh`gh eb ijb ihkued_ khh[s_gby bkihevah\Zlv dhgklZglu MPI_ANY_SOURCEbMPI_ANY_TAG? • Fh`ghebg_ijbgbfZykhh[s_gbyhij_^_eblv_]hZljb[mlu" • ;m^_lebdhjj_dlgZijh]jZffZ\dhlhjhcihkueZxsbcijhp_kkmdZau\Z_l \ dZq_kl\_ ^ebgu [mn_jZ qbkeh 10 Z ijbgbfZxsbc ijhp_kk qbkeh 20" ?keb ^Z lh kdhevdh we_f_glh\ fZkkb\Z [m^_l j_Zevgh i_j_keZghf_`^mijhp_kkZfb" • KjZ\gblvwnn_dlb\ghklvj_ZebaZpbbjZaebqguo\b^h\i_j_kuehd^Zgguok[ehdbjh\dhcMPI_SEND, MPI_BSEND, MPI_SSEND, MPI_RSEND f_`^m^\mfy\u^_e_ggufbijhp_kkhjZfb • Qlh hagZqZ_l aZ\_jr_gb_ hi_jZpbb ^ey jZaebqguo \b^h\ i_j_kuedb ^Zgguok[ehdbjh\dhc" • Hij_^_eblv fZdkbfZevgh ^himklbfmx ^ebgm ihkueZ_fh]h khh[s_gby \^Zgghcj_ZebaZpbbMPI. • J_Zebah\ZlvkdZeyjgh_ijhba\_^_gb_jZkij_^_e_gguof_`^mijhp_kkhjZfb\_dlhjh\ • KjZ\gblv wnn_dlb\ghklv j_ZebaZpbb i_j_kuehd ^Zgguo f_`^m ^\mfy \u^_e_ggufbijhp_kkhjZfbk[ehdbjh\dhcb[_a[ehdbjh\db • Hij_^_eblv \hafh`gh eb \ ^Zgghc j_ZebaZpbb MPI kh\f_s_gb_ Zkbgojhgguo i_j_kuehd ^Zgguo b \uiheg_gby Zjbnf_lbq_kdbo hi_jZpbc • DZd k ihfhsvx ijhp_^mju MPI_TEST kfh^_ebjh\Zlv nmgdpbhgZevghklvijhp_^mjuMPI_WAIT? • < q_f khklhyl jZaebqby \ bkihevah\Zgbb ijhp_^mj MPI_WAITALL, MPI_WAITANY b MPI_WAITSOME" DZd kfh^_ebjh\Zlv bo nmgdpbhgZevghklvijbihfhsbijhp_^mjuMPI_WAIT? • Qlh ijhbahc^_l ijb hkms_kl\e_gbb h[f_gZ ^Zggufb k ijhp_kkhf MPI_PROC_NULL? • J_Zebah\Zlv ijb ihfhsb ihkuedb khh[s_gbc lbiZ lhqdZ-lhqdZ ke_^mxsb_ko_fudhffmgbdZpbbijhp_kkh\ o i_j_^ZqZ^Zgguoihdhevpm^\Z\ZjbZglZwklZn_lgZyiZehqdZ hq_j_^ghc ijhp_kk ^h`b^Z_lky khh[s_gby hl ij_^u^ms_]h b ihlhfihkueZ_lke_^mxs_fm bk^\b]h^gh\j_f_ggu_ihkuedZ bijb_fkhh[s_gbc o master-VODYH \k_ ijhp_kku h[sZxlky k h^gbf \u^_e_gguf ijhp_kkhf o i_j_kuedZ^ZgguohldZ`^h]hijhp_kkZdZ`^hfm • Bkke_^h\Zlvwnn_dlb\ghklvdhffmgbdZpbhgguoko_fbaij_^u^ms_]h aZ^Zgby \ aZ\bkbfhklb hl qbkeZ bkihevah\Zgguo ijhp_kkh\ b h[t_fZ i_j_kueZ_fuo^Zgguobamqblv\hafh`ghklbhilbfbaZpbb

35

• Hij_^_eblv\ub]jurdhlhjucfh`ghihemqblvijbbkihevah\Zgbbhleh`_gguoaZijhkh\gZ\aZbfh^_ckl\b_ • KjZ\gblv wnn_dlb\ghklv j_ZebaZpbb nmgdpbb MPI_SENDRECV k fh^_ebjh\Zgb_f lhc `_ nmgdpbhgZevghklb ijb ihfhsb g_[ehdbjmxsbohi_jZpbc

Dhee_dlb\gu_\aZbfh^_ckl\byijhp_kkh\ < hi_jZpbyo dhee_dlb\gh]h \aZbfh^_ckl\by ijhp_kkh\ mqZkl\mxl \k_ ijhp_kku dhffmgbdZlhjZ Khhl\_lkl\mxsZy ijhp_^mjZ ^he`gZ [ulv \ua\ZgZ dZ`^uf ijhp_kkhf [ulv fh`_l kh k\hbf gZ[hjhf iZjZf_ljh\
Ijhp_^mjZ bkihevam_lky ^ey [Zjv_jghc kbgojhgbaZpbb ijhp_kkh\ JZ[hlZ ijhp_kkh\ [ehdbjm_lky ^h l_o ihj ihdZ \k_ hklZ\rb_ky ijhp_kku dhffmgbdZlhjZ COMM g_ \uihegyl wlm ijhp_^mjm Lhevdh ihke_ lh]h dZd ihke_^gbc ijhp_kk dhffmgbdZlhjZ \uihegbl ^Zggmx ijhp_^mjm \k_ ijhp_kku [m^ml jZa[ehdbjh\Zgu b ijh^he`Zl \uiheg_gb_ ^Zevr_ >ZggZy ijhp_^mjZ y\ey_lky dhee_dlb\ghc
MPI_BARRIER ohly j_Zevgh bkiheg_ggu_ \uah\u jZaebqgufb ijhp_kkZfb

dhffmgbdZlhjZfh]ml[ulvjZkiheh`_gu\jZaguof_klZoijh]jZffu

< ke_^mxs_f ijbf_j_ nmgdpbhgZevghklv ijhp_^mju MPI_BARRIER fh^_ebjm_lky ijb ihfhsb hleh`_gguo aZijhkh\ gZ \aZbfh^_ckl\b_ >ey mkj_^g_gby j_amevlZlh\ ijhba\h^blky NTIMES hi_jZpbc h[f_gZ \ jZfdZo dZ`^hcbagbo\k_ijhp_kku^he`guihkeZlvkhh[s_gb_ijhp_kkmkghf_jhf 0 ihke_ q_]h ihemqblv hl g_]h hl\_lguc kb]gZe hagZqZxsbc qlh \k_ ijhp_kku ^hreb ^h wlhc lhqdb \ ijh]jZff_ Bkihevah\Zgb_ hleh`_gguo aZijhkh\ iha\hey_l bgbpbZebabjh\Zlv ihkuedm ^Zgguo lhevdh h^bg jZa Z aZl_f bkihevah\Zlv gZ dZ`^hc bl_jZpbb pbdeZ >Ze__ \j_fy gZ fh^_ebjh\Zgb_ kjZ\gb\Z_lky kh \j_f_g_f gZ kbgojhgbaZpbx ijb ihfhsb kZfhcklZg^Zjlghcijhp_^mjuMPI_BARRIER. program example13 include 'mpif.h' integer ierr, rank, size, MAXPROC, NTIMES, i, it parameter (MAXPROC = 128, NTIMES = 10000) integer ibuf(MAXPROC) double precision time_start, time_finish integer req(2*MAXPROC), statuses(MPI_STATUS_SIZE, MAXPROC) call MPI_INIT(ierr) call MPI_COMM_SIZE(MPI_COMM_WORLD, size, ierr) call MPI_COMM_RANK(MPI_COMM_WORLD, rank, ierr) if(rank .eq. 0) then do i = 1, size-1 call MPI_RECV_INIT(ibuf(i), 0, MPI_INTEGER, i, 5, & MPI_COMM_WORLD, req(i), ierr) call MPI_SEND_INIT(rank, 0, MPI_INTEGER, i, 6, & MPI_COMM_WORLD, req(size+i), & ierr) end do time_start = MPI_WTIME(ierr) do it = 1, NTIMES call MPI_STARTALL(size-1, req, ierr) call MPI_WAITALL(size-1, req, statuses, ierr) call MPI_STARTALL(size-1, req(size+1), ierr) call MPI_WAITALL(size-1, req(size+1), statuses, & ierr) end do else call MPI_RECV_INIT(ibuf(1), 0, MPI_INTEGER, 0, 6, & MPI_COMM_WORLD, req(1), ierr) call MPI_SEND_INIT(rank, 0, MPI_INTEGER, 0, 5, & MPI_COMM_WORLD, req(2), ierr) time_start = MPI_WTIME(ierr) do it = 1, NTIMES call MPI_START(req(2), ierr) call MPI_WAIT(req(2), statuses, ierr) call MPI_START(req(1), ierr) 37

call MPI_WAIT(req(1), statuses, ierr) end do end if time_finish = MPI_WTIME(ierr)-time_start print *, 'rank = ', rank, ' all time = ', & (time_finish)/NTIMES time_start = MPI_WTIME(ierr) do it = 1, NTIMES call MPI_BARRIER(MPI_COMM_WORLD,ierr) enddo time_finish = MPI_WTIME(ierr)-time_start print *, 'rank = ', rank, ' barrier time = ', & (time_finish)/NTIMES call MPI_FINALIZE(ierr) end MPI_BCAST(BUF, COUNT, DATATYPE, ROOT, COMM, IERR) BUF(*) INTEGER COUNT, DATATYPE, ROOT, COMM, IERR JZkkuedZCOUNTwe_f_glh\^ZgguolbiZDATATYPEbafZkkb\ZBUFhlijhp_kkZ ROOT \k_f ijhp_kkZf ^Zggh]h dhffmgbdZlhjZ COMM, \dexqZy kZf jZkkueZxsbcijhp_kkIjb\ha\jZl_baijhp_^mjukh^_j`bfh_[mn_jZ BUF ijhp_kkZ ROOT [m^_l kdhibjh\Zgh \ ehdZevguc [mn_j dZ`^h]h ijhp_kkZ dhffmgbdZlhjZ COMM AgZq_gby iZjZf_ljh\ COUNT, DATATYPE, ROOT b COMM

^he`gu[ulvh^bgZdh\ufbm\k_oijhp_kkh\

Ke_^mxsZy ko_fZ beexkljbjm_l ^_ckl\b_ ijhp_^mju MPI_BCAST A^_kv lZd`_ dZd b \ ^Zevg_crbo ko_fZo ih \_jlbdZeb bah[jZ`Zxlky jZagu_ ijhp_kkumqZkl\mxsb_\dhee_dlb\ghchi_jZpbbZih]hjbahglZeb–jZkiheh`_ggu_gZgbo[ehdb^Zgguo

GZijbf_j^eylh]hqlh[ui_j_keZlvhlijhp_kkZ 2\k_fhklZevgufijhp_kkZfijbeh`_gbyfZkkb\ bufba 100p_ehqbke_gguowe_f_glh\gm`ghqlh[u \h\k_oijhp_kkZo\klj_lbekyke_^mxsbc\uah\ 38

call MPI_BCAST(buf, 100, MPI_INTEGER, & 2, MPI_COMM_WORLD, ierr) MPI_GATHER(SBUF, SCOUNT, STYPE, RBUF, RCOUNT, RTYPE, ROOT, COMM, IERR) SBUF(*), RBUF(*) INTEGER SCOUNT, STYPE, RCOUNT, RTYPE, ROOT, COMM, IERR K[hjdZ SCOUNTwe_f_glh\^ZgguolbiZ STYPEbafZkkb\h\ SBUFkh\k_oijhp_kkh\dhffmgbdZlhjZ COMM\[mn_j_ RBUFijhp_kkZ ROOTDZ`^ucijhp_kk \dexqZy ROOTihkueZ_lkh^_j`bfh_k\h_]h[mn_jZ SBUF ijhp_kkm ROOTKh[bjZxsbcijhp_kkkhojZgy_l^Zggu_\[mn_j_RBUFjZkiheZ]Zybo\ihjy^d_

\hajZklZgbyghf_jh\ijhp_kkh\

GZijhp_kk_ ROOTkms_kl\_ggufby\eyxlkyagZq_gby\k_oiZjZf_ljh\ZgZ hklZevguo ijhp_kkZo — lhevdh agZq_gby iZjZf_ljh\ SBUF, SCOUNT, STYPE, ROOTb COMMAgZq_gbyiZjZf_ljh\ ROOTbCOMM^he`gu[ulvh^bgZdh\ufbm \k_oijhp_kkh\IZjZf_lj RCOUNTmijhp_kkZ ROOTh[hagZqZ_lqbkehwe_f_glh\ lbiZ RTYPE ijbgbfZ_fuo g_ hl \k_o ijhp_kkh\ \ kmff_ Z hl dZ`^h]h ijhp_kkZ Ke_^mxsZyko_fZbeexkljbjm_l^_ckl\b_ijhp_^mjuMPI_GATHER.

GZijbf_j^eylh]hqlh[uijhp_kk2kh[jZe\fZkkb\rbufih10p_ehqbke_gguowe_f_glh\fZkkb\h\bufkh\k_oijhp_kkh\ijbeh`_gbygm`ghqlh[u\h \k_oijhp_kkZo\klj_lbekyke_^mxsbc\uah\ call MPI_GATHER(buf, 10, MPI_INTEGER, rbuf, 10, MPI_INTEGER, 2, MPI_COMM_WORLD, ierr)

& &

MPI_GATHERV(SBUF, SCOUNT, STYPE, RBUF, RCOUNTS, DISPLS, RTYPE, ROOT, COMM, IERR) SBUF(*), RBUF(*) 39

INTEGER SCOUNT, STYPE, RCOUNTS(*), DISPLS(*), RTYPE, ROOT, COMM, IERR K[hjdZjZaebqgh]hdhebq_kl\Z^ZgguobafZkkb\h\ SBUFIhjy^hdjZkiheh`_gby^Zgguo\j_amevlbjmxs_f[mn_j_RBUFaZ^Z_lfZkkb\DISPLS. RCOUNTS –p_ehqbke_ggucfZkkb\kh^_j`Zsbcdhebq_kl\hwe_f_glh\i_j_-

^Z\Z_fuohldZ`^h]hijhp_kkZbg^_dkjZ\_gjZg]mihkueZxs_]hijhp_kkZ jZaf_jfZkkb\ZjZ\_gqbkemijhp_kkh\\dhffmgbdZlhj_COMM).

DISPLS – p_ehqbke_gguc fZkkb\ kh^_j`Zsbc kf_s_gby hlghkbl_evgh gZqZeZ fZkkb\Z RBUF bg^_dk jZ\_g jZg]m ihkueZxs_]h ijhp_kkZ jZaf_j fZkkb\ZjZ\_gqbkemijhp_kkh\\dhffmgbdZlhj_COMM).

>Zggu_ihkeZggu_ijhp_kkhf J-1jZaf_sZxlky\ J-hf[ehd_[mn_jZ RBUF gZijhp_kk_ROOTdhlhjucgZqbgZ_lkykhkf_s_gb_f\DISPLS(J)we_f_glh\ lbiZRTYPEkgZqZeZ[mn_jZ MPI_SCATTER(SBUF, SCOUNT, STYPE, RBUF, RCOUNT, RTYPE, ROOT, COMM, IERR) SBUF(*), RBUF(*) INTEGER SCOUNT, STYPE, RCOUNT, RTYPE, ROOT, COMM, IERR Ijhp_^mjZ MPI_SCATTER ih k\h_fm ^_ckl\bx y\ey_lky h[jZlghc d MPI_GATHERHgZhkms_kl\ey_ljZkkuedmih SCOUNTwe_f_glh\^ZgguolbiZ STYPEbafZkkb\ZSBUFijhp_kkZROOT\fZkkb\uRBUF\k_oijhp_kkh\dhffmgbdZlhjZ COMM\dexqZykZfijhp_kk ROOTFh`ghkqblZlvqlhfZkkb\ SBUF

^_eblkygZjZ\gu_qZklbihqbkemijhp_kkh\dZ`^Zybadhlhjuokhklhblba SCOUNT we_f_glh\ lbiZ STYPE ihke_ q_]h I-y qZklv ihkueZ_lky I-1)-fm ijhp_kkm GZijhp_kk_ ROOTkms_kl\_ggufby\eyxlkyagZq_gby\k_oiZjZf_ljh\ZgZ \k_o hklZevguo ijhp_kkZo — lhevdh agZq_gby iZjZf_ljh\ RBUF, RCOUNT, RTYPE, SOURCE b COMM AgZq_gby iZjZf_ljh\ SOURCE b COMM ^he`gu [ulv h^bgZdh\ufbm\k_oijhp_kkh\ Ke_^mxsZyko_fZbeexkljbjm_l^_ckl\b_ijhp_^mjuMPI_SCATTER.

40

1

real sbuf(size, size), rbuf(size) if(rank .eq. 0) then do 1 i = 1, size do 1 j = 1, size sbuf(i, j)=... end if if (numtasks .eq. size) then call MPI_SCATTER(sbuf, size, MPI_REAL, & rbuf, size, MPI_REAL, & 0, MPI_COMM_WORLD, ierr) end if

MPI_SCATTERV(SBUF, SCOUNTS, DISPLS, STYPE, RBUF, RCOUNT, RTYPE, ROOT, COMM, IERR) SBUF(*), RBUF(*) INTEGER SCOUNTS(*), DISPLS(*), STYPE, RCOUNT, RTYPE, ROOT, COMM, IERR JZkkuedZ jZaebqgh]h dhebq_kl\Z ^Zgguo ba fZkkb\Z SBUF GZqZeh ihjpbc jZkkueZ_fuo^ZgguoaZ^Z_lfZkkb\DISPLS. SCOUNTS –p_ehqbke_ggucfZkkb\kh^_j`Zsbcdhebq_kl\hwe_f_glh\i_j_-

^Z\Z_fuo dZ`^hfm ijhp_kkm bg^_dk jZ\_g jZg]m Z^j_kZlZ ^ebgZ jZ\gZ qbkemijhp_kkh\\dhffmgbdZlhj_COMM).

DISPLS – p_ehqbke_gguc fZkkb\ kh^_j`Zsbc kf_s_gby hlghkbl_evgh gZqZeZfZkkb\Z SBUFbg^_dkjZ\_gjZg]mZ^j_kZlZ^ebgZjZ\gZqbkemijhp_kkh\\dhffmgbdZlhj_COMM).

>Zggu_ihkueZ_fu_ijhp_kkhfROOTijhp_kkmJ-1jZaf_s_gu\J-hf[ehd_ [mn_jZSBUFdhlhjucgZqbgZ_lkykhkf_s_gb_f\DISPLS(J)we_f_glh\lbiZ STYPEkgZqZeZ[mn_jZSBUF. 41

MPI_ALLGATHER(SBUF, SCOUNT, STYPE, RBUF, RCOUNT, RTYPE, COMM, IERR) SBUF(*), RBUF(*) INTEGER SCOUNT, STYPE, RCOUNT, RTYPE, COMM, IERR K[hjdZ ^Zgguo ba fZkkb\h\ SBUF kh \k_o ijhp_kkh\ dhffmgbdZlhjZ COMM \ [mn_j_ RBUFdZ`^h]hijhp_kkZ>Zggu_khojZgyxlky\ihjy^d_\hajZklZgby ghf_jh\ijhp_kkh\;ehd^ZgguoihkeZggucijhp_kkhf J-1jZaf_sZ_lky\ J-hf[ehd_[mn_jZRBUFijbgbfZxs_]hijhp_kkZHi_jZpbxfh`ghjZkkfZljb\ZlvdZd MPI_GATHERijbdhlhjhcj_amevlZlihemqZ_lkygZ\k_oijhp_kkZo dhffmgbdZlhjZCOMM.

Ke_^mxsZyko_fZbeexkljbjm_l^_ckl\b_ijhp_^mjuMPI_ALLGATHER.

MPI_ALLGATHERV(SBUF, SCOUNT, STYPE, RBUF, RCOUNTS, DISPLS, RTYPE, COMM, IERR) SBUF(*), RBUF(*) INTEGER SCOUNT, STYPE, RCOUNTS(*), DISPLS(*), RTYPE, COMM, IERR K[hjdZ gZ \k_o ijhp_kkZo dhffmgbdZlhjZ COMM jZaebqgh]h dhebq_kl\Z ^ZgguobafZkkb\h\ SBUFIhjy^hdjZkiheh`_gby^Zgguo\fZkkb\_RBUFaZ^Z_l fZkkb\DISPLS. MPI_ALLTOALL(SBUF, SCOUNT, STYPE, RBUF, RCOUNT, RTYPE, COMM, IERR) SBUF(*), RBUF(*) INTEGER SCOUNT, STYPE, RCOUNT, RTYPE, COMM, IERR JZkkuedZdZ`^ufijhp_kkhfdhffmgbdZlhjZCOMMjZaebqguoihjpbc^Zgguo \k_f^jm]bfijhp_kkZf J-c[ehd^Zgguo[mn_jZ SBUF (I-1)-]hijhp_kkZihiZ^Z_l\I-c[ehd^Zgguo[mn_jZRBUF (J-1)-]hijhp_kkZ

Ke_^mxsZyko_fZbeexkljbjm_l^_ckl\b_ijhp_^mjuMPI_ALLTOALL.

42

MPI_ALLTOALLV(SBUF, SCOUNTS, SDISPLS, STYPE, RBUF, RCOUNTS, RDISPLS, RTYPE, COMM, IERR) SBUF(*), RBUF(*) INTEGER SCOUNTS(*), SDISPLS(*), STYPE, RCOUNTS(*), RDISPLS(*), RTYPE, COMM, IERR JZkkuedZ kh \k_o ijhp_kkh\ dhffmgbdZlhjZ COMM jZaebqgh]h dhebq_kl\Z

^Zgguo \k_f ijhp_kkZf ^Zggh]h dhffmgbdZlhjZ JZaf_s_gb_ ^Zgguo \ [mn_j_ SBUFhlkueZxs_]hijhp_kkZhij_^_ey_lkyfZkkb\hf SDISPLSZjZaf_s_gb_ ^Zgguo \ [mn_j_ RBUF ijbgbfZxs_]h ijhp_kkZ hij_^_ey_lky fZkkb\hfRDISPLS.

MPI_REDUCE(SBUF, RBUF, COUNT, DATATYPE, OP, ROOT, COMM, IERR) SBUF(*), RBUF(*) INTEGER COUNT, DATATYPE, OP, ROOT, COMM, IERR

Djhf_lh]hijh]jZffbklfh`_laZ^Zlvk\hxnmgdpbx^ey\uiheg_gby]eh[Zevghchi_jZpbbijbihfhsbijhp_^mjuMPI_OP_CREATE. < ke_^mxs_f ijbf_j_ hi_jZpby ]eh[Zevgh]h kmffbjh\Zgby fh^_ebjm_lky ijb ihfhsb ko_fu k^\Zb\Zgby k bkihevah\Zgb_f i_j_kuehd ^Zgguo lbiZ lhqdZ-lhqdZWnn_dlb\ghklvlZdh]hfh^_ebjh\ZgbykjZ\gb\Z_lkykbkihevah\Zgb_fdhee_dlb\ghchi_jZpbbMPI_REDUCE. program example14 include 'mpif.h' integer ierr, rank, i, size, n, nproc parameter (n = 1 000 000) double precision time_start, time_finish double precision a(n), b(n), c(n) integer status(MPI_STATUS_SIZE) call MPI_INIT(ierr) call MPI_COMM_SIZE(MPI_COMM_WORLD, size, ierr) call MPI_COMM_RANK(MPI_COMM_WORLD, rank, ierr) nproc = size do i = 1, n a(i) = 1.d0/size end do call MPI_BARRIER(MPI_COMM_WORLD, ierr) time_start = MPI_WTIME(ierr) do i = 1, n c(i) = a(i) end do do while (nproc .gt. 1) if(rank .lt. nproc/2) then call MPI_RECV(b, n, MPI_DOUBLE_PRECISION, & nproc-rank-1, 1, MPI_COMM_WORLD, & status, ierr) do i = 1, n c(i) = c(i) + b(i) end do else if(rank .lt. nproc) then call MPI_SEND(c, n, MPI_DOUBLE_PRECISION, & nproc-rank-1, 1, MPI_COMM_WORLD, ierr) end if nproc = nproc/2 end do do i = 1, n b(i) = c(i) end do time_finish = MPI_WTIME(ierr)-time_start if(rank .eq. 0) print *, 'model b(1)=', b(1) print *, 'rank=', rank, ' model time =', time_finish do i = 1, n a(i) = 1.d0/size end do call MPI_BARRIER(MPI_COMM_WORLD, ierr) 44

time_start = MPI_WTIME(ierr) call MPI_REDUCE(a, b, n, MPI_DOUBLE_PRECISION, MPI_SUM, 0, & MPI_COMM_WORLD, ierr) time_finish = MPI_WTIME(ierr)-time_start if(rank .eq. 0) print *, 'reduce b(1)=', b(1) print *, 'rank=', rank, ' reduce time =', time_finish call MPI_FINALIZE(ierr) end MPI_ALLREDUCE(SBUF, RBUF, COUNT, DATATYPE, OP, COMM, IERR) SBUF(*), RBUF(*) INTEGER COUNT, DATATYPE, OP, COMM, IERR
< ke_^mxs_f ijbf_j_ dZ`^uc ijhp_kk \uqbkey_l ihkljhqgu_ kmffu we_f_glh\ehdZevgh]hfZkkb\Z aihke_q_]hihemq_ggu_kmffukh\k_oijhp_kkh\kdeZ^u\Zxlkyijbihfhsbijhp_^mjuMPI_ALLREDUCEbj_amevlZlihemqZ_lky\fZkkb\_rgZ\k_oijhp_kkZoijbeh`_gby do i = 1, n s(i) = 0.0 end do do i = 1, n do j = 1, m s(i) = s(i)+a(i, j) end do end do call MPI_ALLREDUCE(s, r, n, MPI_REAL, MPI_SUM, & MPI_COMM_WORLD, IERR) MPI_REDUCE_SCATTER(SBUF, RBUF, RCOUNTS, DATATYPE, OP, COMM, IERR) SBUF(*), RBUF(*) INTEGER RCOUNTS(*), DATATYPE, OP, COMM, IERR
lhfm qlh kgZqZeZ \uihegyxlky ]eh[Zevgu_ hi_jZpbb aZl_f j_amevlZl jZkkueZ_lky ih ijhp_kkZf I-uc ijhp_kk ihemqZ_l (I+1)-mx ihjpbx j_amevlZlh\ba RCOUNTS(I+1)we_f_glh\bihf_sZ_l\fZkkb\ RBUFFZkkb\ RCOUNTS ^he`_g[ulvh^bgZdh\ufgZ\k_oijhp_kkZodhffmgbdZlhjZCOMM.

45

MPI_SCAN(SBUF, RBUF, COUNT, DATATYPE, OP, COMM, IERR) SBUF(*), RBUF(*) INTEGER COUNT, DATATYPE, OP, COMM, IERR
Kha^Zgb_ ihevah\Zl_evkdhc ]eh[Zevghc hi_jZpbb OP dhlhjZy [m^_l \uqbkeylvkynmgdpb_c FUNCKha^Z\Z_fZyhi_jZpby^he`gZ[ulvZkkhpbZlb\ghcZ _kebiZjZf_lj COMMUTEjZ\_g .TRUE.lhhgZ^he`gZ[ulvlZd`_bdhffmlZlb\ghc ?keb iZjZf_lj COMMUTE jZ\_g .FALSE. lh ihjy^hd \uiheg_gby ]eh[Zevghc hi_jZpbb kljh]h nbdkbjm_lky kh]eZkgh m\_ebq_gbx ghf_jh\ ijhp_kkh\gZqbgZykijhp_kkZkghf_jhf0. FUNCTION FUNC(INVEC(*), INOUTVEC(*), LEN, TYPE) INVEC(LEN), INOUTVEC(LEN) INTEGER LEN, TYPE

LZdbfh[jZahfaZ^Z_lkybgl_jn_ckihevah\Zl_evkdhcnmgdpbb^eykha^Zgby ]eh[Zevghc hi_jZpbb I_j\uc Zj]mf_gl hi_jZpbb [_j_lky ba iZjZf_ljZ INVEC\lhjhcZj]mf_gl–baiZjZf_ljZINOUTVECZj_amevlZl\ha\jZsZ_lky\ iZjZf_lj_ INOUTVECIZjZf_lj LENaZ^Z_ldhebq_kl\hwe_f_glh\\oh^gh]hb \uoh^gh]hfZkkb\h\ZiZjZf_lj TYPE –lbi\oh^guob\uoh^guo^Zgguo< ihevah\Zl_evkdhc nmgdpbb g_ ^he`gu ijhba\h^blvky gbdZdb_ h[f_gu ^Zggufbkbkihevah\Zgb_f\uah\h\ijhp_^mjMPI. MPI_OP_FREE(OP, IERR) INTEGER OP, IERR

Mgbqlh`_gb_ ihevah\Zl_evkdhc ]eh[Zevghc hi_jZpbb Ih \uiheg_gbb ijhp_^mjui_j_f_gghcOPijbk\Zb\Z_lkyagZq_gb_MPI_OP_NULL. Ke_^mxsbc ijbf_j ^_fhgkljbjm_l aZ^Zgb_ ihevah\Zl_evkdhc nmgdpbb ^ey bkihevah\Zgby \ dZq_kl\_ ]eh[Zevghc hi_jZpbb AZ^Z_lky nmgdpby smod5, \uqbkeyxsZy ihwe_f_glgmx kmffm ih fh^mex 5 \_dlhjh\ p_ehqbke_gguo Zj]mf_glh\>ZggZynmgdpbyh[ty\ey_lky\dZq_kl\_]eh[Zevghchi_jZpbbop \ \uah\_ ijhp_^mju MPI_OP_CREATE aZl_f bkihevam_lky \ ijhp_^mj_ MPI_REDUCE ihke_ q_]h m^Zey_lky k ihfhsvx \uah\Z ijhp_^mju MPI_OP_FREE. program example15 46

include 'mpif.h' integer ierr, rank, i, n parameter (n = 1 000) integer a(n), b(n) integer op external smod5 call MPI_INIT(ierr) call MPI_COMM_RANK(MPI_COMM_WORLD, rank, ierr) do i = 1, n a(i) = i + rank end do print *, 'process ', rank, ' a(1) =', a(1) call MPI_OP_CREATE(smod5, .TRUE., op, ierr) call MPI_REDUCE(a, b, n, MPI_INTEGER, op, 0, & MPI_COMM_WORLD, ierr) call MPI_OP_FREE(op, ierr) if(rank .eq. 0) print *, ' b(1) =', b(1) call MPI_FINALIZE(ierr) end integer function smod5(in, inout, l, type) integer l, type integer in(l), inout(l), i do i = 1, l inout(i) = mod(in(i)+inout(i), 5) end do return end

AZ^Zgby • Q_f dhee_dlb\gu_ hi_jZpbb hlebqZxlky hl \aZbfh^_ckl\bc lbiZ lhqdZ-lhqdZ" • <_jgh eb qlh \ dhee_dlb\guo \aZbfh^_ckl\byo mqZkl\mxl \k_ ijhp_kkuijbeh`_gby? • Fh]mleb\hagbdZlvdhgnebdluf_`^mh[uqgufbkhh[s_gbyfbihkueZ_fufbijhp_kkZfb^jm]^jm]mbkhh[s_gbyfbdhee_dlb\guohi_jZpbc"?keb^ZdZdhgbjZaj_rZxlky" • Fh`gh eb ijb ihfhsb ijhp_^mju MPI_RECV ijbgylv khh[s_gb_ ihkeZggh_ijhp_^mjhcMPI_BCAST? • Kfh^_ebjh\Zlv [Zjv_jgmx kbgojhgbaZpbx ijb ihfhsb i_j_kuehd lhqdZ-lhqdZbkjZ\gblvwnn_dlb\ghklvlZdhcj_ZebaZpbbbklZg^Zjlghc ijhp_^mjuMPI_BARRIER. • < q_f jZaebqb_ \ nmgdpbhgZevghklb ijhp_^mj MPI_BCAST b MPI_SCATTER? • Kfh^_ebjh\Zlv]eh[Zevgh_kmffbjh\Zgb_f_lh^hfk^\Zb\ZgbybkjZ\gblv wnn_dlb\ghklv lZdhc j_ZebaZpbb k bkihevah\Zgb_f klZg^Zjlghc ijhp_^mjuMPI_REDUCE. 47

• Kfh^_ebjh\Zlv ijhp_^mjm MPI_ALLREDUCE ijb ihfhsb ijhp_^mj MPI_REDUCEbMPI_BCAST. • GZibrbl_k\hc\ZjbZglijhp_^mjuMPI_GATHERbkihevamynmgdpbbihkuedbkhh[s_gbclbiZlhqdZ-lhqdZ • Ih^mfZcl_ dZd hj]Zgbah\Zlv dhee_dlb\guc Zkbgojhgguc h[f_g ^ZggufbZgZeh]bqgucnmgdpbbZ MPI_REDUCE[ MPI_ALLTOALL. • Bkke_^h\Zlv fZkrlZ[bjm_fhklv aZ\bkbfhklv \j_f_gb \uiheg_gby hl qbkeZ ijhp_kkh\ jZaebqguo dhee_dlb\guo hi_jZpbc gZ dhgdj_lghc kbkl_f_

=jmiiubdhffmgbdZlhju < MPI kms_kl\mxl rbjhdb_ \hafh`ghklb ^ey hi_jZpbc gZ^ ]jmiiZfb ijhp_kkh\bdhffmgbdZlhjZfbWlh[u\Z_lg_h[oh^bfh\h-i_j\uoqlh[u^Zlv \hafh`ghklv g_dhlhjhc ]jmii_ ijhp_kkh\ jZ[hlZlv gZ^ k\h_c g_aZ\bkbfhc ih^aZ^Zq_c
48

MPI_COMM_GROUP(COMM, GROUP, IERR) INTEGER COMM, GROUP, IERR Ihemq_gb_ ]jmiiu GROUP khhl\_lkl\mxs_c dhffmgbdZlhjm COMM < yaud_ KbiZjZf_lj GROUPbf__lij_^hij_^_e_gguclbi MPI_GroupIhkdhevdmba-

gZqZevgh

kms_kl\m_l _^bgkl\_gguc g_ljb\bZevguc dhffmgbdZlhj MPI_COMM_WORLD kgZqZeZ gm`gh ihemqblv khhl\_lkl\mxsmx _fm ]jmiim ijhp_kkh\Wlhfh`ghk^_eZlvijbihfhsbke_^mxs_]h\uah\Z call MPI_COMM_GROUP(MPI_COMM_WORLD, group, ierr) MPI_GROUP_INCL(GROUP, N, RANKS, NEWGROUP, IERR) INTEGER GROUP, N, RANKS(*), NEWGROUP, IERR Kha^Zgb_]jmiiu NEWGROUPba Nijhp_kkh\ij_`g_c]jmiiu GROUPkjZg]Zfb RANKS(1),…,RANKS(N) ijbq_f jZg]m RANKS(I) \ klZjhc ]jmii_ khhl\_lkl\m_l jZg] I-1 \ gh\hc ]jmii_ Ijb N=0 kha^Z_lky imklZy ]jmiiZ MPI_GROUP_EMPTY
\h]hihjy^dZijhp_kkh\\]jmii_

MPI_GROUP_EXCL(GROUP, N, RANKS, NEWGROUP, IERR) INTEGER GROUP, N, RANKS(*), NEWGROUP, IERR Kha^Zgb_]jmiiu NEWGROUPbaijhp_kkh\]jmiiu GROUPbkdexqZyijhp_kku k jZg]Zfb RANKS(1),…,RANKS(N) ijbq_f ihjy^hd hklZ\rboky ijhp_kkh\ \ gh\hc ]jmii_ khhl\_lkl\m_l ihjy^dm ijhp_kkh\ \ klZjhc ]jmii_ Ijb N=0

kha^Z_lky]jmiiZb^_glbqgZyklZjhc]jmii_

< ke_^mxs_f ijbf_j_ kha^Z_lky ^\_ g_i_j_k_dZxsboky ]jmiiu ijhp_kkh\ group1b group2gZhkgh\_ijhp_kkh\]jmiiu group
Ke_^mxsb_ ljb ijhp_^mju hij_^_eyxl hi_jZpbb gZ^ ]jmiiZfb ijhp_kkh\ dZd gZ^fgh`_kl\ZfbBa-aZhkh[_gghkl_cgmf_jZpbbijhp_kkh\gbh[t_^bg_gb_gbi_j_k_q_gb_]jmiig_dhffmlZlb\gughZkkhpbZlb\gu MPI_GROUP_INTERSECTION(GROUP1, GROUP2, NEWGROUP, IERR) INTEGER GROUP1, GROUP2, NEWGROUP, IERR Kha^Zgb_ ]jmiiu NEWGROUP ba i_j_k_q_gby ]jmii GROUP1 b GROUP2 Ihemq_ggZy ]jmiiZ kh^_j`bl \k_ ijhp_kku ]jmiiu GROUP1 \oh^ysb_ lZd`_ \ ]jmiimGROUP2bmihjy^hq_ggu_dZd\i_j\hc]jmii_ 49

MPI_GROUP_UNION(GROUP1, GROUP2, NEWGROUP, IERR) INTEGER GROUP1, GROUP2, NEWGROUP, IERR Kha^Zgb_ ]jmiiu NEWGROUP ba h[t_^bg_gby ]jmii GROUP1 b GROUP2 Ihemq_ggZy]jmiiZkh^_j`bl\k_ijhp_kku]jmiiu GROUP1\ij_`g_fihjy^d_aZ dhlhjufbke_^mxlijhp_kku]jmiiu GROUP2g_\hr_^rb_\]jmiim GROUP1,

lZd`_\ij_`g_fihjy^d_

MPI_GROUP_DIFFERENCE(GROUP1, GROUP2, NEWGROUP, IERR) INTEGER GROUP1, GROUP2, NEWGROUP, IERR Kha^Zgb_]jmiiu NEWGROUPbajZaghklb]jmii GROUP1b GROUP2Ihemq_ggZy ]jmiiZkh^_j`bl\k_we_f_glu]jmiiuGROUP1g_\oh^ysb_\]jmiimGROUP2

bmihjy^hq_ggu_dZd\i_j\hc]jmii_

GZijbf_jimklv\]jmiim gr1\oh^ylijhp_kku 0, 1, 2, 4, 5Z\]jmiim gr2 ijhp_kku 0, 2, 3 gmf_jZpby ijhp_kkh\ aZ^ZgZ \ ]jmii_ khhl\_lkl\mxs_c dhffmgbdZlhjmMPI_COMM_WORLD Lh]^Zihke_\uah\h\ call MPI_GROUP_INTERSECTION(gr1, gr2, newgr1, ierr) call MPI_GROUP_UNION(gr1, gr2, newgr2, ierr) call MPI_GROUP_DIFFERENCE(gr1, gr2, newgr3, ierr)

\]jmiimnewgr1\oh^ylijhp_kku0, 2; \]jmiimnewgr2\oh^ylijhp_kku0, 1, 2, 4, 5, 3; \]jmiimnewgr3\oh^ylijhp_kku1, 4, 5. Ihjy^hdgmf_jZpbbijhp_kkh\\ihemq_gguo]jmiiZokhhl\_lkl\m_lihjy^dm boi_j_qbke_gby MPI_GROUP_SIZE(GROUP, SIZE, IERR) INTEGER GROUP, SIZE, IERR Hij_^_e_gb_dhebq_kl\ZSIZEijhp_kkh\\]jmii_GROUP. MPI_GROUP_RANK(GROUP, RANK, IERR) INTEGER GROUP, RANK, IERR Hij_^_e_gb_ghf_jZijhp_kkZRANK\]jmii_GROUP?keb\ua\Z\rbcijhp_kk g_\oh^bl\]jmiimGROUPlh\ha\jZsZ_lkyagZq_gb_MPI_UNDEFINED. MPI_GROUP_TRANSLATE_RANKS(GROUP1, N, RANKS1, GROUP2, RANKS2, IERR) INTEGER GROUP1, N, RANKS1(*), GROUP2, RANKS2(*), IERR
gm`ghhij_^_eblvjZg]b

MPI_GROUP_COMPARE(GROUP1, GROUP2, RESULT, IERR) INTEGER GROUP1, GROUP2, RESULT, IERR 50

KjZ\g_gb_]jmiiGROUP1bGROUP2?keb]jmiiuGROUP1bGROUP2iheghklvx kh\iZ^Zxl lh \ iZjZf_lj_ RESULT \ha\jZsZ_lky agZq_gb_ MPI_IDENT ?keb ]jmiiu hlebqZxlky lhevdh jZg]Zfb ijhp_kkh\ lh \ha\jZsZ_lky agZq_gb_ MPI_SIMILARBgZq_\ha\jZsZ_lkyagZq_gb_MPI_UNEQUAL. MPI_GROUP_FREE(GROUP, IERR) INTEGER GROUP, IERR Mgbqlh`_gb_ ]jmiiu GROUP. Ihke_ \uiheg_gby ijhp_^mju i_j_f_ggZy GROUPijbgbfZ_lagZq_gb_ MPI_GROUP_NULL?kebkwlhc]jmiihcdfhf_glm

\uah\Z ijhp_^mju m`_ \uihegy_lky dZdZy-lh hi_jZpby lh hgZ [m^_l aZ\_jr_gZ

else call MPI_GROUP_TRANSLATE_RANKS(group2, 1, rank1, & group, rank3, ierr) end if a(1) = rank a(2) = rank1 a(3) = rank2 a(4) = rank3 if (rank3 .ne. MPI_UNDEFINED) then call MPI_SENDRECV(a, 4, MPI_INTEGER, rank3, 1, & b, 4, MPI_INTEGER, rank3, 1, & MPI_COMM_WORLD, status, ierr) end if call MPI_GROUP_FREE(group, ierr) call MPI_GROUP_FREE(group1, ierr) call MPI_GROUP_FREE(group2, ierr) print *, 'process ', rank, ' a=', a, ' b=', b call MPI_FINALIZE(ierr) end

Hi_jZpbbkdhffmgbdZlhjZfb DhffmgbdZlhjij_^hklZ\ey_lhl^_evgucdhgl_dklh[f_gZijhp_kkh\g_dhlhjhc]jmiiuDhgl_dklh[_ki_qb\Z_l\hafh`ghklvg_aZ\bkbfuoh[f_gh\^ZggufbDZ`^hc]jmii_ijhp_kkh\fh`_lkhhl\_lkl\h\Zlvg_kdhevdhdhffmgbdZlhjh\ghdZ`^ucdhffmgbdZlhj\ex[hcfhf_gl\j_f_gbh^ghagZqghkhhl\_lkl\m_llhevdhh^ghc]jmii_ Ke_^mxsb_ dhffmgbdZlhju kha^Zxlky kjZam ihke_ \uah\Z ijhp_^mju MPI_INIT: • MPI_COMM_WORLD –dhffmgbdZlhjh[t_^bgyxsbc\k_ijhp_kkuijbeh`_gby • MPI_COMM_NULL –agZq_gb_bkihevam_fh_^eyhrb[hqgh]hdhffmgbdZlhjZ • MPI_COMM_SELF –dhffmgbdZlhj\dexqZxsbclhevdh\ua\Z\rbcijhp_kk Kha^Zgb_ dhffmgbdZlhjZ y\ey_lky dhee_dlb\ghc hi_jZpb_c b lj_[m_l hi_jZpbb f_`ijhp_kkgh]h h[f_gZ ihwlhfm lZdb_ ijhp_^mju ^he`gu \uau\Zlvky\k_fbijhp_kkZfbg_dhlhjh]hkms_kl\mxs_]hdhffmgbdZlhjZ MPI_COMM_DUP(COMM, NEWCOMM, IERR) INTEGER COMM, NEWCOMM, IERR Kha^Zgb_gh\h]hdhffmgbdZlhjZ NEWCOMMklhc`_]jmiihcijhp_kkh\bZljb[mlZfbqlhbmdhffmgbdZlhjZCOMM. 52

MPI_COMM_CREATE(COMM, GROUP, NEWCOMM, IERR) INTEGER COMM, GROUP, NEWCOMM, IERR Kha^Zgb_ gh\h]h dhffmgbdZlhjZ NEWCOMM ba dhffmgbdZlhjZ COMM ^ey ]jmiiu ijhp_kkh\ GROUP dhlhjZy ^he`gZ y\eylvky ih^fgh`_kl\hf ]jmiiu k\yaZgghc k dhffmgbdZlhjhf COMM
eydZ`^hc gh\hc ]jmiiu kha^Z_lky khhl\_lkl\mxsbc _c dhffmgbdZlhj new_comm b hi_jZpby MPI_ALLREDUCE \uihegy_lky ih hl^_evghklb ^ey ijhp_kkh\ \oh^ysbo\jZagu_]jmiiu call MPI_COMM_GROUP(MPI_COMM_WORLD, group, ierr) do i = 1, size/2 ranks(i) = i-1 end do if (rank .lt. size/2) then call MPI_GROUP_INCL(group, size/2, ranks, & new_group, ierr) else call MPI_GROUP_EXCL(group, size/2, ranks, & new_group, ierr) end if call MPI_COMM_CREATE(MPI_COMM_WORLD, new_group, & new_comm, ierr) call MPI_ALLREDUCE(sbuf, rbuf, 1, MPI_INTEGER, & MPI_SUM, new_comm, ierr) call MPI_GROUP_RANK(new_group, new_rank, ierr) print *, 'rank= ', rank, ' newrank= ', & new_rank, ' rbuf= ', rbuf

53

MPI_COMM_SPLIT(COMM, COLOR, KEY, NEWCOMM, IERR) INTEGER COMM, COLOR, KEY, NEWCOMM, IERR JZa[b_gb_ dhffmgbdZlhjZ COMM gZ g_kdhevdh gh\uo dhffmgbdZlhjh\ ih qbkemagZq_gbciZjZf_ljZ COLOR
ihjy^hdgmf_jZpbbijhp_kkh\\u[bjZ_lkykbkl_fhc

Ijhp_kkudhlhju_g_^he`gu\hclb\gh\u_dhffmgbdZlhjumdZau\Zxl\ dZq_kl\_ iZjZf_ljZ COLOR dhgklZglm MPI_UNDEFINED Bf \ iZjZf_lj_ NEWCOMM\_jg_lkyagZq_gb_MPI_COMM_NULL. < ke_^mxs_f ijbf_j_ dhffmgbdZlhj MPI_COMM_WORLD jZa[b\Z_lky gZ ljb qZklb
&

MPI_COMM_FREE(COMM, IERR) INTEGER COMM, IERR M^Ze_gb_ dhffmgbdZlhjZ COMM Ihke_ \uiheg_gby ijhp_^mju i_j_f_gghc COMMijbk\Zb\Z_lkyagZq_gb_MPI_COMM_NULL?kebkwlbfdhffmgbdZlhjhfd

fhf_glm\uah\Zijhp_^mjum`_\uihegy_lkydZdZy-lhhi_jZpbylhhgZ[m^_l aZ\_jr_gZ
AZ^Zgby • H[yaZgZ eb \bjlmZevgZy lhiheh]by ih\lhjylv nbabq_kdmx lhiheh]bx p_e_\h]hdhfivxl_jZ" • Ex[hcebdhffmgbdZlhjfh`_lh[eZ^Zlv\bjlmZevghclhiheh]b_c" • Fh`_l eb ijhp_kk \oh^blv h^gh\j_f_ggh \ ^_dZjlh\m lhiheh]bx b \ lhiheh]bx]jZnZ" • Fh`gh eb \ua\Zlv ijhp_^mjm MPI_CART_CREATE lhevdh gZ iheh\bg_ ijhp_kkh\dhffmgbdZlhjZ" • G_h[oh^bfhebbkihevah\Zlvijhp_^mjmMPI_DIMS_CREATEi_j_^\uah\hfijhp_^mjuMPI_CART_CREATE? • Fh`ghebbkihevah\Zlvdhhj^bgZluijhp_kkZ\^_dZjlh\hclhiheh]bb \ijhp_^mjZoh[f_gZ^Zggufb" 62

• DZdb_ • • •

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i_j_kuedb ^Zgguo hkms_kl\eyxlky ijhp_^mjhc MPI_CART_SHIFT? DZd hij_^_eblv k dZdbfb ijhp_kkZfb \ lhiheh]bb ]jZnZ k\yaZg ^Zggucijhp_kk" DZdkha^Zlvlhiheh]bx]jZnZ\dhlhjhcdZ`^ucijhp_kkk\yaZgkdZ`^uf" J_Zebah\Zlv jZa[b_gb_ ijhp_kkh\ gZ ^\_ ]jmiiu \ h^ghc ba dhlhjuo hkms_kl\ey_lkyh[f_gihdhevpmijbihfhsbk^\b]Z\h^ghf_jghc^_dZjlh\hclhiheh]bbZ\^jm]hc–dhffmgbdZpbbihko_f_PDVWHU-slave, j_Zebah\Zgghcijbihfhsblhiheh]bb]jZnZ Bkihevah\Zlv^\mf_jgmx^_dZjlh\mlhiheh]bxijhp_kkh\ijbj_ZebaZpbbiZjZee_evghcijh]jZffui_j_fgh`_gbyfZljbp

I_j_kuedZjZaghlbiguo^Zgguo Ih^ khh[s_gb_f \ MPI ihgbfZ_lky fZkkb\ h^ghlbiguo ^Zgguo jZkiheh`_gguo\ihke_^h\Zl_evguoyq_cdZoiZfylbQZklh\ijh]jZffZolj_[mxlky i_j_kuedb[he__keh`guoh[t_dlh\^ZgguokhklhysbobajZaghlbiguowe_f_glh\ beb jZkiheh`_gguo g_ \ ihke_^h\Zl_evguo yq_cdZo iZfylb < wlhf kemqZ_fh`gheb[hihkueZlv^Zggu_g_[hevrbfbihjpbyfbjZkiheh`_gguo ih^jy^we_f_glh\h^gh]hlbiZeb[hbkihevah\Zlvdhibjh\Zgb_^Zgguoi_j_^ hlkuedhc\g_dhlhjucijhf_`mlhqguc[mn_jH[Z\ZjbZglZy\eyxlky^hklZlhqgh g_m^h[gufb b lj_[mxl ^hihegbl_evguo aZljZl dZd \j_f_gb lZd b hi_jZlb\ghciZfylb >eyi_j_kuedbjZaghlbiguo^Zgguo\MPIij_^mkfhlj_gu^\Zki_pbZevguo kihkh[Z • Ijhba\h^gu_lbiu^Zgguo; • MiZdh\dZ^Zgguo. Ijhba\h^gu_lbiu^Zgguo Ijhba\h^gu_lbiu^Zgguokha^Zxlky\h\j_fy\uiheg_gbyijh]jZffukihfhsvxijhp_^mj-dhgkljmdlhjh\gZhkgh\_kms_kl\mxsbodfhf_glm\uah\Z dhgkljmdlhjZlbih\^Zgguo Kha^Zgb_lbiZ^Zgguokhklhblba^\mowlZih\ 1. Dhgkljmbjh\Zgb_lbiZ 2. J_]bkljZpbylbiZ 63

Ihke_ j_]bkljZpbb ijhba\h^guc lbi ^Zgguo fh`gh bkihevah\Zlv gZjy^m k ij_^hij_^_e_ggufblbiZfb\hi_jZpbyoi_j_kuedb\lhfqbke_b\dhee_dlb\guohi_jZpbyoIhke_aZ\_jr_gbyjZ[hlukijhba\h^guflbihf^Zgguo _]hj_dhf_g^m_lkyZggmebjh\ZlvIjbwlhf\k_ijhba\_^_ggu_gZ_]hhkgh\_ gh\u_lbiu^ZgguohklZxlkybfh]mlbkihevah\Zlvky^Zevr_ Ijhba\h^guclbi^ZgguooZjZdl_jbam_lkyihke_^h\Zl_evghklvx[Zah\uolbih\ ^Zgguo b gZ[hjhf p_ehqbke_gguo agZq_gbc kf_s_gby we_f_glh\ lbiZ hlghkbl_evghgZqZeZ[mn_jZh[f_gZKf_s_gbyfh]ml[ulvdZdiheh`bl_evgufblZdbhljbpZl_evgufbg_h[yaZgujZaebqZlvkyg_lj_[m_lkybomihjy^hq_gghklvLZdbfh[jZahfihke_^h\Zl_evghklvwe_f_glh\^Zgguo\ijhba\h^ghf lbi_ fh`_l hlebqZlvky hl ihke_^h\Zl_evghklb bkoh^gh]h lbiZ Z h^bg we_f_gl ^Zgguo fh`_l \klj_qZlvky \ dhgkljmbjm_fhf lbi_ fgh]hdjZlgh MPI_TYPE_CONTIGUOUS(COUNT, TYPE, NEWTYPE, IERR) INTEGER COUNT, TYPE, NEWTYPE, IERR Kha^Zgb_ gh\h]h lbiZ ^Zgguo NEWTYPE khklhys_]h ba COUNT ihke_^h\Zl_evgh jZkiheh`_gguo we_f_glh\ [Zah\h]h lbiZ ^Zgguo TYPE NZdlbq_kdb

kha^Z\Z_fuclbi^Zgguoij_^klZ\ey_lfZkkb\^Zgguo[Zah\h]hlbiZdZdhl^_evguch[t_dl

< ke_^mxs_f ijbf_j_ kha^Z_lky gh\uc lbi ^Zgguo newtype dhlhjuc \ ^Zevg_cr_fihke_j_]bkljZpbblbiZ fh`_lbkihevah\Zlvky^eyi_j_kuedb iylbjZkiheh`_gguoih^jy^p_euoqbk_e call MPI_TYPE_CONTIGUOUS(5, MPI_INTEGER, newtype, ierr) MPI_TYPE_VECTOR(COUNT, BLOCKLEN, STRIDE, TYPE, NEWTYPE, IERR) INTEGER COUNT, BLOCKLEN, STRIDE, TYPE, NEWTYPE, IERR Kha^Zgb_ gh\h]h lbiZ ^Zgguo NEWTYPE khklhys_]h ba COUNT [ehdh\ ih BLOCKLEN we_f_glh\ [Zah\h]h lbiZ ^Zgguo TYPE Ke_^mxsbc [ehd gZqbgZ_lky q_j_a STRIDE we_f_glh\ [Zah\h]h lbiZ ^Zgguo ihke_ gZqZeZ ij_^u^m-

s_]h[ehdZ

64

count = 2 blocklen = 3 stride = 5 call MPI_TYPE_VECTOR(count, blocklen, stride, & MPI_REAL, newtype, ierr) MPI_TYPE_HVECTOR(COUNT, BLOCKLEN, STRIDE, TYPE, NEWTYPE, IERR) INTEGER COUNT, BLOCKLEN, STRIDE, TYPE, NEWTYPE, IERR Kha^Zgb_ gh\h]h lbiZ ^Zgguo NEWTYPE khklhys_]h ba COUNT [ehdh\ ih BLOCKLEN we_f_glh\ [Zah\h]h lbiZ ^Zgguo TYPE Ke_^mxsbc [ehd gZqbgZ_lkyq_j_aSTRIDE[Zclihke_gZqZeZij_^u^ms_]h[ehdZ MPI_TYPE_INDEXED(COUNT, BLOCKLENS, DISPLS, TYPE, NEWTYPE, IERR) INTEGER COUNT, BLOCKLENS(*), DISPLS(*), TYPE, NEWTYPE, IERR Kha^Zgb_ gh\h]h lbiZ ^Zgguo NEWTYPE khklhys_]h ba COUNT [ehdh\ ih BLOCKLENS(I) we_f_glh\ [Zah\h]h lbiZ ^Zgguo I-c [ehd gZqbgZ_lky q_j_a DISPLS(I)we_f_glh\[Zah\h]hlbiZ^ZgguokgZqZeZ[mn_jZihkuedbIhem-

q_gguclbi^Zgguofh`ghkqblZlvh[h[s_gb_f\_dlhjgh]hlbiZ

< ke_^mxs_f ijbf_j_ aZ^Z_lky lbi ^Zgguo newtype ^ey hibkZgby gb`g_lj_m]hevghcfZljbpulbiZ double precision ijbwlhfmqblu\Z_lkyqlh\ yaud_NhjljZgfZkkb\uojZgylkyihklhe[pZf do i = 1, n blocklens(i) = n-i+1 displs(i) = n*(i-1)+i-1 end do call MPI_TYPE_INDEXED(n, blocklens, displs, MPI_DOUBLE_PRECISION, newtype, ierr) MPI_TYPE_HINDEXED(COUNT, BLOCKLENS, DISPLS, TYPE, NEWTYPE, IERR) INTEGER COUNT, BLOCKLENS(*), DISPLS(*), TYPE, NEWTYPE, IERR Kha^Zgb_ gh\h]h lbiZ ^Zgguo NEWTYPE khklhys_]h ba COUNT [ehdh\ ih BLOCKLENS(I) we_f_glh\ [Zah\h]h lbiZ ^Zgguo I-c [ehd gZqbgZ_lky q_j_a DISPLS(I)[ZclkgZqZeZ[mn_jZihkuedb MPI_TYPE_STRUCT(COUNT, BLOCKLENS, DISPLS, TYPES, NEWTYPE, IERR) INTEGER COUNT, BLOCKLENS(*), DISPLS(*), TYPES(*), NEWTYPE, IERR Kha^Zgb_ kljmdlmjgh]h lbiZ ^Zgguo NEWTYPE ba COUNT [ehdh\ ih BLOCKLENS(I) we_f_glh\ lbiZ TYPES(I). I-c [ehd gZqbgZ_lky q_j_a DISPLS(I)[ZclkgZqZeZ[mn_jZihkuedb

(MPI_DOUBLE_PRECISION, 16), (MPI_CHARACTER, 24), (MPI_CHARACTER, 25)} blocklens(1) = 3 blocklens(2) = 2 types(1) = MPI_DOUBLE_PRECISION types(2) = MPI_CHARACTER displs(1) = 0 displs(2) = 24 call MPI_TYPE_STRUCT(2, blocklens, displs, types, & newtype, ierr) MPI_TYPE_COMMIT(DATATYPE, IERR) INTEGER DATATYPE, IERR

J_]bkljZpbykha^Zggh]hijhba\h^gh]hlbiZ^Zgguo DATATYPEIhke_j_]bkljZpbb wlhl lbi ^Zgguo fh`gh bkihevah\Zlv \ hi_jZpbyo h[f_gZ gZjZ\g_ k ij_^hij_^_e_ggufblbiZfb^ZgguoIj_^hij_^_e_ggu_lbiu^Zgguoj_]bkljbjh\Zlvg_gm`gh MPI_TYPE_FREE(DATATYPE, IERR) INTEGER DATATYPE, IERR

:ggmebjh\Zgb_ ijhba\h^gh]h lbiZ ^Zgguo DATATYPE IZjZf_lj DATATYPE mklZgZ\eb\Z_lky \ agZq_gb_ MPI_DATATYPE_NULL =ZjZglbjm_lky qlh ex[hc gZqZluc h[f_g bkihevamxsbc ^Zggu_ Zggmebjm_fh]h lbiZ [m^_l ghjfZevgh aZ\_jr_g Ijb wlhf ijhba\h^gu_ hl DATATYPE lbiu ^Zgguo hklZxlky b fh]ml bkihevah\Zlvky ^Zevr_ Ij_^hij_^_e_ggu_ lbiu ^Zgguo g_fh]ml[ulvZggmebjh\Zgu MPI_TYPE_SIZE(DATATYPE, SIZE, IERR) INTEGER DATATYPE, SIZE, IERR Hij_^_e_gb_jZaf_jZ SIZElbiZ^Zgguo DATATYPE\[ZclZoh[t_fZiZfylb

aZgbfZ_fh]hh^gbfwe_f_glhf^Zggh]hlbiZ

MPI_ADDRESS(LOCATION, ADDRESS, IERR) LOCATION(*) INTEGER ADDRESS, IERR

Hij_^_e_gb_ Z[khexlgh]h [Zcl-Z^j_kZ ADDRESS jZaf_s_gby fZkkb\Z LOCATION \ hi_jZlb\ghc iZfylb dhfivxl_jZ :^j_k hlkqblu\Z_lky hl [Zah\h]h Z^j_kZ agZq_gb_ dhlhjh]h kh^_j`blky \ kbkl_fghc dhgklZgl_ MPI_BOTTOM Ijhp_^mjZ iha\hey_l hij_^_eylv Z[khexlgu_ Z^j_kZ h[t_dlh\ dZd \ yaud_ NhjljZg lZd b \ Kb ohly \ Kb ^ey wlh]h ij_^mkfhlj_gu bgu_ kj_^kl\Z
MPI_ADDRESSI_j_^i_j_kuedhcgh\uclbij_]bkljbjm_lkyijbihfhsb\uah\Zijhp_^mju MPI_TYPE_COMMITAZf_lbfqlhi_j_kueZ_lkyh^bgwe_f_gl

^Zgguo ijhba\h^gh]h lbiZ ohly hg b khklhbl ba ^\mo jZaghlbiguo we_f_glh\ blocklens(1) = 1 blocklens(2) = 1 types(1) = MPI_DOUBLE_PRECISION types(2) = MPI_CHARACTER call MPI_ADDRESS(dat1, address(1), ierr) displs(1) = address(1) call MPI_ADDRESS(dat2, address(2), ierr) displs(2) = address(2) call MPI_TYPE_STRUCT(2, blocklens, displs, types, & newtype, ierr) call MPI_TYPE_COMMIT(newtype, ierr) call MPI_SEND(MPI_BOTTOM, 1, newtype, dest, tag, & MPI_COMM_WORLD, ierr) MPI_TYPE_LB(DATATYPE, DISPL, IERR) INTEGER DATATYPE, DISPL, IERR Hij_^_e_gb_kf_s_gby DISPL\[ZclZogb`g_c]jZgbpuwe_f_glZlbiZ^ZgguoDATATYPEhlgZqZeZ[mn_jZ^Zgguo

MPI_TYPE_UB(DATATYPE, DISPL, IERR) INTEGER DATATYPE, DISPL, IERR Hij_^_e_gb_kf_s_gby DISPL\[ZclZo\_jog_c]jZgbpuwe_f_glZlbiZ^ZgguoDATATYPEhlgZqZeZ[mn_jZ^Zgguo MPI_TYPE_EXTENT(DATATYPE, EXTENT, IERR) INTEGER DATATYPE, EXTENT, IERR Hij_^_e_gb_ ^bZiZahgZ EXTENT jZagbpu f_`^m \_jog_c b gb`g_c ]jZgbpZfbwe_f_glZ^Zggh]hlbiZ lbiZ^ZgguoDATATYPE\[ZclZo

< ke_^mxs_f ijbf_j_ ijhba\h^guc lbi ^Zgguo bkihevam_lky ^ey i_j_klZgh\dbklhe[ph\fZljbpu\h[jZlghfihjy^d_Lbi^Zgguo matr_revkha^Z\Z_fucijhp_^mjhc MPI_TYPE_VECTORhibku\Z_lehdZevgmxqZklvfZljbpu ^Zggh]hijhp_kkZ\i_j_klZ\e_ggufb\h[jZlghfihjy^d_klhe[pZfbIhke_ j_]bkljZpbb wlhl lbi ^Zgguo fh`_l bkihevah\Zlvky ijb i_j_kued_ Ijh]jZffZ jZ[hlZ_l ijZ\bevgh _keb jZaf_j fZljbpu N ^_eblky gZp_eh gZ qbkehijhp_kkh\ijbeh`_gby

67

program example19 include 'mpif.h' integer ierr, rank, size, N, nl parameter (N = 8) double precision a(N, N), b(N, N) call MPI_INIT(ierr) call MPI_COMM_SIZE(MPI_COMM_WORLD, size, ierr) call MPI_COMM_RANK(MPI_COMM_WORLD, rank, ierr) nl = (N-1)/size+1 call work(a, b, N, nl, size, rank) call MPI_FINALIZE(ierr) end subroutine work(a, b, n, nl, size, rank) include 'mpif.h' integer ierr, rank, size, n, nl, ii, matr_rev double precision a(n, nl), b(n, nl) integer i, j, status(MPI_STATUS_SIZE) do j = 1, nl do i = 1, n b(i,j) = 0.d0 ii = j+rank*nl a(i,j) = 100*ii+i enddo enddo call MPI_TYPE_VECTOR(nl, n, -n, MPI_DOUBLE_PRECISION, & matr_rev, ierr) call MPI_TYPE_COMMIT(matr_rev, ierr) call MPI_SENDRECV(a(1, nl), 1, MATR_REV, size-rank-1, 1, & b, nl*n, MPI_DOUBLE_PRECISION, & size-rank-1, 1, MPI_COMM_WORLD, & status, ierr) do j = 1, nl do i = 1, n print *, 'process ', rank, ': ', & j+rank*nl, ' ', i, a(i,j), ' ', b(i,j) enddo enddo end

MiZdh\dZ^Zgguo >eyi_j_kuehdjZaghjh^guo^ZgguogZjy^mkkha^Zgb_fijhba\h^guolbih\ fh`ghbkihevah\Zlvhi_jZpbbmiZdh\dbbjZkiZdh\db^ZgguoJZaghjh^gu_ bebjZkiheh`_ggu_g_\ihke_^h\Zl_evguoyq_cdZoiZfylb^Zggu_ihf_sZxlky\h^bgg_ij_ju\guc[mn_ji_j_kueZ_lkyZihlhfihemq_ggh_khh[s_gb_kgh\ZjZkij_^_ey_lkyihgm`gufyq_cdZfiZfylb

68

MPI_PACK(INBUF, INCOUNT, DATATYPE, OUTBUF, OUTSIZE, POSITION, COMM, IERR) INBUF(*), OUTBUF(*) INTEGER INCOUNT, DATATYPE, OUTSIZE, POSITION, COMM, IERR MiZdh\dZ INCOUNT we_f_glh\ lbiZ DATATYPE ba fZkkb\Z INBUF \ fZkkb\ OUTBUFkhk^\b]hf POSITION[ZclhlgZqZeZfZkkb\Z;mn_j OUTBUF^he`_g kh^_j`ZlvihdjZcg_cf_j_ OUTSIZE[ZclIhke_\uiheg_gbyijhp_^mjuiZjZf_lj POSITIONm\_ebqb\Z_lkygZqbkeh[ZcljZ\gh_jZaf_jmaZibkbIZjZf_lj COMMmdZau\Z_lgZdhffmgbdZlhj\dhlhjhf\^Zevg_cr_f[m^_li_j_-

kueZlvkykhh[s_gb_>eyi_j_kuedbmiZdh\Zgguo^Zgguobkihevam_lkylbi ^ZgguoMPI_PACKED.

MPI_UNPACK(INBUF, INSIZE, POSITION, OUTBUF, OUTCOUNT, DATATYPE, COMM, IERR) INBUF(*), OUTBUF(*) INTEGER INSIZE, POSITION, OUTCOUNT, DATATYPE, COMM, IERR JZkiZdh\dZ OUTCOUNTwe_f_glh\lbiZ DATATYPEbafZkkb\Z INBUFkhk^\b]hf POSITION [Zcl hl gZqZeZ fZkkb\Z \ fZkkb\ OUTBUF FZkkb\ INBUF bf__l jZaf_jg_f_g__INSIZE[Zcl MPI_PACK_SIZE(INCOUNT, DATATYPE, COMM, SIZE, IERR) INTEGER INCOUNT, DATATYPE, COMM, SIZE, IERR Hij_^_e_gb_ g_h[oh^bfh]h h[t_fZ iZfylb SIZE \ [ZclZo ^ey miZdh\db INCOUNT we_f_glh\ lbiZ DATATYPE G_h[oh^bfuc ^ey miZdh\db jZaf_j fh-

`_lij_\urZlvkmffmjZaf_jh\iZdm_fuowe_f_glh\^Zgguo

< ke_^mxs_f ijbf_j_ fZkkb\ bufbkihevam_lky\dZq_kl\_[mn_jZ^eymiZdh\db 10 we_f_glh\ fZkkb\Z a lbiZ real b 10 we_f_glh\ fZkkb\Z b lbiZ character Ihemq_ggh_ khh[s_gb_ i_j_kueZ_lky ijhp_^mjhc MPI_BCAST hl ijhp_kkZ 0\k_fhklZevgufijhp_kkZfihemq_ggh_khh[s_gb_jZkiZdh\u\Z_lkyijbihfhsb\uah\h\ijhp_^mjMPI_UNPACK. program example20 include 'mpif.h' integer ierr, rank, position real a(10) character b(10), buf(100) call MPI_INIT(ierr) call MPI_COMM_RANK(MPI_COMM_WORLD, rank, ierr) do i = 1, 10 a(i) = rank + 1.0 if(rank .eq. 0) then b(i) = 'a' else b(i) = 'b' end if end do position=0 69

if(rank .eq. 0) then call MPI_PACK(a, 10, MPI_REAL, buf, 100, position, & MPI_COMM_WORLD, ierr) call MPI_PACK(b, 10, MPI_CHARACTER, buf, 100, position, & MPI_COMM_WORLD, ierr) call MPI_BCAST(buf, 100, MPI_PACKED, 0, & MPI_COMM_WORLD, ierr) else call MPI_BCAST(buf, 100, MPI_PACKED, 0, & MPI_COMM_WORLD, ierr) position=0 call MPI_UNPACK(buf, 100, position, a, 10, MPI_REAL, & MPI_COMM_WORLD, ierr) call MPI_UNPACK(buf, 100, position, b, 10, & MPI_CHARACTER, MPI_COMM_WORLD, ierr) end if print *, 'procecc ', rank, ' a=', a, ' b=', b call MPI_FINALIZE(ierr) end

AZ^Zgby • Kha^Zlv ijhba\h^guc lbi ^Zgguo ^ey i_j_kuehd ^bZ]hgZevghc fZljbpu • DZdkhhlghkylkyagZq_gby\ha\jZsZ_fu_ijhp_^mjZfbMPI_TYPE_SIZE bMPI_TYPE_EXTENT? • Fh`ghebbkihevah\Zlvijhba\h^gu_lbiu^Zgguo[_a\uah\Zijhp_^mjuMPI_TYPE_COMMIT? • I_j_keZlv gme_\hfm ijhp_kkm hl \k_o ijhp_kkh\ ijbeh`_gby kljmdlmjmkhklhysmxbajZg]Zijhp_kkZbgZa\ZgbymaeZgZdhlhjhf^Zgguc ijhp_kk aZims_g ihemq_ggh]h k ihfhsvx ijhp_^mju MPI_GET_PROCESSOR_NAME). • Ijyfhm]hevgZy fZljbpZ jZkij_^_e_gZ ih ijhp_kkZf ih kljhdZf I_j_klZ\blvkljhdbfZljbpu\h[jZlghfihjy^d_bkihevamy^eyi_j_kuehdijhba\h^guclbi^Zgguo • K^_eZlv ij_^u^msmx aZ^Zqm k bkihevah\Zgb_f i_j_kuehd miZdh\Zgguo^Zgguo •
70

Ebl_jZlmjZ 1. MPI: A Message-Passing Interface Standard (Version 1.1) (http://parallel.ru/docs/Parallel/mpi1.1/mpi-report.html) 2. Zpxd<G@_]meh:BIjh]jZffbjh\Zgb_ fgh]hijhp_kkhjguo\uqbkebl_evguokbkl_fJhklh\-gZ->hgmBa^Zl_evkl\hHHHP<<J 5. RiZdh\kdbc=BK_jbdh\ZG<Ijh]jZffbjh\Zgb_^ey fgh]hijhp_kkhjguokbkl_f\klZg^Zjl_03,Ihkh[b_Fbgkd;=M 2002. 6. G_fgx]bgK:Kl_kbdHEIZjZee_evgh_ijh]jZffbjh\Zgb_^ey fgh]hijhp_kkhjguo\uqbkebl_evguokbkl_fKI[;O<-I_l_j[mj] 2002. 7. Dhjg__\<>IZjZee_evgh_ijh]jZffbjh\Zgb_\03,Gh\hkb[bjkd Ba^-\hKHJ:G

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Параллельное программирование с использованием технологии МПИ

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