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g(:)f(:)h(:)f(:)h(:)f(:)h(:)g(:)f(:)h(:)f(:)h(:)f(:)h(:)g(:)f(:)h(:)f(:)h(:)f (:)h(:)g(:)f(:)h(:)84 b Fx(42)465 3251 y(6.2.5)94 b(INDEPENDENT)27 b(assertion)f(-)i(k)n(ernel)f(EP)22 b Fs(:)42 b(:)g(:)f(:)h(:)f(:)h(:)f(:)h (:)g(:)f(:)h(:)f(:)h(:)f(:)h(:)g(:)f(:)h(:)84 b Fx(42)465 3351 y(6.2.6)94 b(Non-elemen)n(tal)27 b(in)n(trinsic)g(functions)h(-)g(k)n(ernel)e (RD)48 b Fs(:)41 b(:)h(:)f(:)h(:)g(:)f(:)h(:)f(:)h(:)f(:)h(:)g(:)f(:)h(:)84 b Fx(42)465 3450 y(6.2.7)94 b(P)n(assing)24 b(distributed)i(arra)n(ys)d(as)i (subprograms')f(argumen)n(ts)g(-)h(k)n(ernels)g(AS,)h(IT,)731 3550 y(IM)i(and)f(EI)f Fs(:)42 b(:)f(:)h(:)g(:)f(:)h(:)f(:)h(:)f(:)h(:)g(:)f (:)h(:)f(:)h(:)f(:)h(:)g(:)f(:)h(:)f(:)h(:)f(:)h(:)g(:)f(:)h(:)f(:)h(:)f(:)h (:)g(:)f(:)h(:)84 b Fx(42)275 3650 y(6.3)f(Summary)67 b Fs(:)42 b(:)f(:)h(:)f(:)h(:)f(:)h(:)g(:)f(:)h(:)f(:)h(:)f(:)h(:)g(:)f(:)h(:)f(:)h(:)f (:)h(:)g(:)f(:)h(:)f(:)h(:)f(:)h(:)g(:)f(:)h(:)f(:)h(:)f(:)h(:)g(:)f(:)h(:)84 b Fx(43)150 3832 y Ft(7)77 b(Conclusions)2661 b(44)150 4015 y(Bibliograph)m(y)2747 b(45)150 4198 y(App)s(endix)2873 b(48)150 4380 y(A)53 b(Compact)32 b(Applications)i(Submission)d(F)-8 b(orm)1476 b(48)150 4563 y(B)57 b(Sample)32 b(Xnetlib/PDS)h(Screens)1925 b(52)1817 5428 y Fx(2)p eop PNP restore PNEP %%Page: ? 3 0.6303 -612.00 PNLS /PNP save def 12.6922 89.4750 translate 4 bop 150 935 a Fr(Chapter)66 b(1)150 1350 y Fu(In)-7 b(tro)7 b(duction)1460 1287 y Fq(\003)150 1832 y Fp(1.1)137 b(Bac)l(kground)46 b(and)g(Ob)8 b(jectiv)l(es)150 2013 y Fx(The)30 b Fo(P)-7 b(ARKBENCH)30 b Fx(\(P)-7 b(ARallel)30 b(Kernels)f(and)h(BENCHmarks\))f(committee,)i (originally)d(called)i(the)150 2113 y(P)n(arallel)38 b(Benc)n(hmark)h(W)-7 b(orking)39 b(Group,)k(PBW)n(G,)d(w)n(as)f(founded)i(at)f(Sup)r (ercomputing'92)g(in)g(Min-)150 2213 y(neap)r(olis,)32 b(when)f(a)g(group)f (of)h(ab)r(out)g(50)f(p)r(eople)h(in)n(terested)g(in)h(computer)e(b)r(enc)n (hmarking)h(met)g(under)150 2312 y(the)23 b(join)n(t)g(initiativ)n(e)g(of)f (T)-7 b(on)n(y)22 b(Hey)h(\(Univ)n(ersit)n(y)f(of)h(Southampton,)g(UK\))g (and)g(Jac)n(k)e(Dongarra)g(\(Univ)n(er-)150 2412 y(sit)n(y)g(of)g(T)-7 b(ennessee/Oak)19 b(Ridge)i(National)f(Lab)r(oratory\).)33 b(Most)20 b(of)h(the)h(k)n(ey)e(pla)n(y)n(ers)f(w)n(ere)i(presen)n(t,)g(from) 150 2511 y(the)28 b(Univ)n(ersities,)e(Lab)r(oratories)f(and)i(industries,)g (represen)n(ting)f(b)r(oth)i(computer)e(man)n(ufacturers)g(and)150 2611 y(computer)g(users)g(from)g(b)r(oth)h(sides)f(of)g(the)h(A)n(tlan)n (tic.)37 b(Roger)25 b(Ho)r(c)n(kney)h(\(Univ)n(ersit)n(y)f(of)i (Southampton\))150 2711 y(c)n(haired)g(the)g(meeting,)h(and)g(the)g(ob)5 b(jectiv)n(es)26 b(of)i(the)g(group)e(w)n(ere:)251 2893 y(1.)42 b(T)-7 b(o)31 b(establish)h(a)g(comprehensiv)n(e)f(set)h(of)g(parallel)f(b)r (enc)n(hmarks)g(that)i(is)f(generally)e(accepted)i(b)n(y)358 2993 y(b)r(oth)c(users)e(and)i(v)n(endors)e(of)h(parallel)g(system.)251 3159 y(2.)42 b(T)-7 b(o)28 b(pro)n(vide)h(a)g(fo)r(cus)g(for)g(parallel)f(b)r (enc)n(hmark)g(activities)h(and)h(a)n(v)n(oid)d(unnecessary)h(duplication)358 3259 y(of)f(e\013ort)g(and)h(proliferation)e(of)i(b)r(enc)n(hmarks.)251 3425 y(3.)42 b(T)-7 b(o)33 b(set)h(standards)f(for)h(b)r(enc)n(hmarking)f (metho)r(dology)g(and)g(result-rep)r(orting)g(together)g(with)h(a)358 3524 y(con)n(trol)26 b(database/rep)r(ository)e(for)j(b)r(oth)h(the)g(b)r (enc)n(hmarks)f(and)g(the)h(results.)251 3690 y(4.)42 b(T)-7 b(o)27 b(mak)n(e)g(the)h(b)r(enc)n(hmarks)e(and)i(results)f(freely)g(a)n(v)-5 b(ailable)26 b(in)i(the)g(public)g(domain.)275 3873 y(The)f(\014rst)h(y)n (ear's)e(w)n(ork)g(w)n(as)h(to)h(pro)r(duce)f(a)h(rep)r(ort)f(and)g(an)h (initial)g(set)g(of)f(b)r(enc)n(hmarks)g(for)g(release)150 3973 y(at)j(Sup)r(ercomputing'93)g(in)h(P)n(ortland,)e(Oregon,)h(No)n(v)n(em) n(b)r(er)f(1993.)44 b(The)31 b(committee)f(has)g(met)h(at)g(the)150 4072 y(Univ)n(ersit)n(y)26 b(of)h(T)-7 b(ennessee)27 b(Kno)n(xville)e(on)i (Marc)n(h)f(1{2,)g(1993,)f(Ma)n(y)h(24,)h(1993)e(and)i(August)g(23,)f(1993)f (to)150 4172 y(discuss)j(the)g(ev)n(olving)f(draft)h(of)g(this)g(rep)r(ort.) 38 b(The)28 b(do)r(cumen)n(t)g(repro)r(duced)f(here)h(is)g(the)g(\014nal)g (result)g(of)150 4272 y(these)h(meetings,)h(and)f(is)g(the)h(\014rst)f (o\016cial)f(publication)i(of)f(the)h Fo(P)-7 b(ARKBENCH)29 b Fx(committee.)42 b(It)30 b(w)n(as)150 4371 y(distributed)h(at)f(a)g(public) g Fn(Bir)l(ds)j(of)h(a)e(F)-6 b(e)l(ather)31 b Fx(meeting)f(at)g(Sup)r (ercomputing'93,)g(P)n(ortland,)g(on)g(17th)150 4471 y(No)n(v)n(em)n(b)r(er)c (1993,)g(together)h(with)h(the)g(\014rst)f(release)f(of)i(the)g Fo(P)-7 b(ARKBENCH)30 b Fx(parallel)c(b)r(enc)n(hmarks.)275 4570 y(The)19 b(initial)h(fo)r(cus)f(of)h(the)g(parallel)e(b)r(enc)n(hmarks)h (is)g(on)g(the)h(new)g(generation)e(of)i(scalable)e(distributed-)150 4670 y(memory)g(message-passing)f(arc)n(hitectures)g(for)i(whic)n(h)g(there)g (is)g(a)g(notable)g(lac)n(k)f(of)h(existing)g(b)r(enc)n(hmarks.)150 4770 y(F)-7 b(or)22 b(this)g(reason)f(the)i(initial)f(b)r(enc)n(hmark)g (release)f(concen)n(trates)g(on)h(F)-7 b(ortran77)20 b(message-passing)g(co)r (des)150 4869 y(using)28 b(the)g(widely)g(a)n(v)-5 b(ailable)27 b(PVM)h([1)o(])h(message)d(passing)h(in)n(terface)g(for)h(p)r(ortabilit)n(y) -7 b(.)38 b(F)-7 b(uture)28 b(v)n(ersions)150 4969 y(will)23 b(undoubtedly)h(adopt)e(the)i(prop)r(osed)e(MPI)h([2)o(])g(in)n(terface,)h (when)f(this)h(is)e(fully)i(de\014ned)g(and)e(b)r(ecomes)p 150 5043 1350 4 v 241 5096 a Fm(\003)277 5120 y Fl(written)i(b)n(y)g(Roger)g (Ho)r(c)n(kney)h(for)e(whole)h(committee)1817 5428 y Fx(3)p eop PNP restore /PNP save def 628.2618 89.4750 translate 5 bop 150 312 a Fx(generally)28 b(accepted.)43 b(The)30 b(committee's)f(aim,) i(ho)n(w)n(ev)n(er,)d(is)h(to)h(co)n(v)n(er)e(all)h(parallel)f(arc)n (hitectures,)h(and)150 412 y(this)24 b(is)h(exp)r(ected)f(to)g(b)r(e)h(ac)n (hiev)n(ed)e(b)n(y)h(pro)r(ducing)f(v)n(ersions)g(of)h(the)g(b)r(enc)n(hmark) g(co)r(des)f(using)h(F)-7 b(ortran90)150 511 y(and)34 b(High)g(P)n (erformance)e(F)-7 b(ortran)33 b(\(HPF\).)h(Man)n(y)g(shared-memory)d(arc)n (hitectures)i(pro)n(vide)g(e\016cien)n(t)150 611 y(nativ)n(e)26 b(implemen)n(tations)g(of)g(PVM)g(message-passing)d(and)j(are)f(planning)h (HPF)g(compilers.)36 b(They)26 b(will)150 711 y(b)r(e)i(co)n(v)n(ered)e(b)n (y)h(these)h(routes.)150 982 y Fp(1.2)137 b(Pro)t(cedures)150 1163 y Fx(The)35 b Fo(P)-7 b(ARKBENCH)29 b Fx(committee)35 b(has)f(agreed)g(to)g(divide)h(its)g(w)n(ork)e(b)r(et)n(w)n(een)h(\014v)n(e)h (sub)r(committees,)150 1263 y(corresp)r(onding)f(to)i(the)g(\014v)n(e)g (substan)n(tiv)n(e)f(c)n(hapters)g(in)h(the)h(rep)r(ort,)g(eac)n(h)e(with)i (a)e(leader)g(\(sho)n(wn)h(in)150 1363 y(paren)n(theses\))24 b(who)g(is)h(resp)r(onsible)f(for)g(assem)n(bling)f(the)i(con)n(ten)n(ts)f (of)h(his)g(c)n(hapter)f(and)g(its)h(b)r(enc)n(hmarks)150 1462 y(for)i(the)h(committee's)g(appro)n(v)-5 b(al.)251 1624 y(1.)42 b(Metho)r(dology)26 b(\(Da)n(vid)i(Bailey\):)251 1782 y(2.)42 b(Lo)n(w-lev)n(el)25 b(b)r(enc)n(hmarks)i(\(Roger)g(Ho)r(c)n(kney\):)251 1939 y(3.)42 b(Kernel)26 b(b)r(enc)n(hmarks)h(\(T)-7 b(on)n(y)27 b(Hey\):)251 2097 y(4.)42 b(Compact)27 b(applications)f(\(Da)n(vid)i(W)-7 b(alk)n(er\):)251 2255 y(5.)42 b(Compiler)27 b(b)r(enc)n(hmarks)f(\(T)-7 b(om)28 b(Haupt\):)275 2416 y(In)21 b(order)g(to)g(facilitate)h(discussion)f (and)h(exc)n(hange)e(of)h(information,)i(the)f(follo)n(wing)f(e-mail)g (addresses)150 2516 y(w)n(ere)27 b(set)g(up.)251 2678 y(1.)42 b Fk(pbwg-comm@cs.ut)o(k.e)o(du)21 b Fx(for)27 b(the)h(Whole)g(committee)251 2835 y(2.)42 b Fk(pbwg-method@cs.)o(utk)o(.e)o(du)21 b Fx(for)27 b(the)h(Metho)r(dology)f(sub)r(committee)251 2993 y(3.)42 b Fk(pbwg-lowlevel@c)o(s.u)o(tk)o(.e)o(du)21 b Fx(for)27 b(the)h(Lo)n(w)f(lev)n (el)g(sub)r(committee)251 3151 y(4.)42 b Fk(pbwg-kernel@cs.)o(utk)o(.e)o(du) 21 b Fx(for)27 b(the)h(Kernel)f(sub)r(committee)251 3308 y(5.)42 b Fk(pbwg-compactapp)o(@cs)o(.u)o(tk)o(.ed)o(u)21 b Fx(for)28 b(the)g(Compact)f(applications)f(sub)r(committee)275 3470 y(Recen)n(t)20 b(practice,)h(ho)n(w)n(ev)n(er,)f(has)g(b)r(een)h(to)f(send)h(all)f(mail)g (to)h(pb)n(wg-comm)e(so)h(that)h(all)f(mem)n(b)r(ers)g(ma)n(y)150 3569 y(see)27 b(it.)37 b(All)27 b(mail)g(is)g(b)r(eing)g(collected)g(and)f (can)h(b)r(e)g(retriev)n(ed)f(b)n(y)h(sending)g(email)f(to)h Fk(netlib@ornl.gov)150 3669 y Fx(and)g(in)h(the)g(mail)g(message)e(t)n (yping:)251 3831 y(1.)42 b(send)27 b(comm.arc)n(hiv)n(e)f(from)h(pb)n(wg)251 3988 y(2.)42 b(send)27 b(lo)n(wlev)n(el.arc)n(hiv)n(e)e(from)i(pb)n(wg)251 4146 y(3.)42 b(send)27 b(compactapp.arc)n(hiv)n(e)e(from)j(pb)n(wg)251 4304 y(4.)42 b(send)27 b(metho)r(d.arc)n(hiv)n(e)g(from)g(pb)n(wg)251 4461 y(5.)42 b(send)27 b(k)n(ernel.arc)n(hiv)n(e)e(from)i(pb)n(wg)251 4619 y(6.)42 b(send)27 b(index)h(from)f(pb)n(wg)275 4781 y(W)-7 b(e)36 b(ha)n(v)n(e)e(setup)i(a)f(mail)h(re\015ector)e(for)h(corresp)r (ondence,)h(it)g(is)g(called)f Fk(pbwg-comm@cs.utk.)o(ed)o(u)p Fx(.)150 4880 y(Mail)30 b(to)g(that)h(address)e(will)i(b)r(e)f(sen)n(t)h(to)f (the)h(mailing)e(list)i(and)f(also)f(collected)i(in)f Fk(netlib@ornl.gov)p Fx(.)150 4980 y(All)f Fo(P)-7 b(ARKBENCH)29 b Fx(corresp)r(ondence)e(and)h(b) r(enc)n(hmarks)g(ma)n(y)f(b)r(e)i(retriev)n(ed)e(via)h(anon)n(ymous)f(ftp)i (to)150 5080 y Fk(netlib2.cs.utk.e)o(du)p Fx(.)42 b(Alternativ)n(ely)-7 b(,)32 b(one)f(can)g(collect)g Fo(P)-7 b(ARKBENCH)30 b Fx(mail)h(b)n(y)g (sending)g(email)150 5179 y(to)c Fk(netlib@ornl.gov)22 b Fx(and)27 b(in)h(the)g(mail)g(message)e(t)n(yp)r(e:)1817 5428 y(4)p eop PNP restore PNEP %%Page: ? 4 0.6303 -612.00 PNLS /PNP save def 12.6922 89.4750 translate 6 bop 358 312 a Fx(send)27 b(comm.arc)n(hiv)n(e)f(from)h(pb)n(wg)275 478 y(The)h Fo(P)-7 b(ARKBENCH)29 b Fx(committee)g(is)e(op)r(en)h(without)h (c)n(harge)d(to)i(an)n(y)n(one)f(in)n(terested)g(in)h(computer)150 578 y(b)r(enc)n(hmarking)d(and)h(op)r(erates)f(similarly)g(to)h(the)h(HPFF)f (\(High)g(P)n(erformance)e(F)-7 b(ortran)25 b(F)-7 b(orum\).)36 b(An)n(y-)150 677 y(one)24 b(in)n(terested)f(in)i(joining)f(in)g(the)g (discussion)g(or)f(preparing)f(b)r(enc)n(hmarks)h(should)h(send)g(e-mail)g (to)g(that)150 777 y(e\013ect)k(to:)358 943 y Fk(dongarra@cs.utk)o(.ed)o(u) 150 1109 y Fo(P)-7 b(ARKBENCH)30 b Fx(is)21 b(op)r(erating)f(in)i(a)f(v)n (ery)f(tigh)n(t)h(budget)h(\(in)g(realit)n(y)-7 b(,)21 b(it)h(has)f(no)g (budget)g(at)h(all\).)34 b(Sev)n(eral)150 1209 y(participan)n(ts)22 b(are)f(supp)r(orted)h(b)n(y)h(the)f(companies)g(they)h(represen)n(t,)f(and)g (supp)r(ort)h(for)f(sev)n(eral)e(Europ)r(ean)150 1308 y(participan)n(ts)27 b(is)g(b)r(eing)h(pro)n(vided)e(b)n(y)i(ESPRIT.)150 1583 y Fp(1.3)137 b(V)-11 b(endor's)46 b(Commitmen)l(t)150 1765 y Fx(The)38 b Fo(P)-7 b(ARKBENCH)29 b Fx(committee)38 b(is)g(anxious)e(that)i (its)g(parallel)e(b)r(enc)n(hmarks)h(do)g(not)g(put)i(undue)150 1864 y(demands)f(on)g(computer)g(v)n(endors)f(b)n(y)h(w)n(a)n(y)f(of)i(man)f (p)r(o)n(w)n(er)f(and)h(resources,)h(in)g(a)f(w)n(a)n(y)f(that)i(w)n(ould)150 1964 y(prejudice)c(the)h(wide)f(acceptance)f(and)h(use)g(of)g(the)h(b)r(enc)n (hmarks.)58 b(Initially)36 b(it)f(is)g(felt)h(reasonable)d(to)150 2064 y(exp)r(ect)40 b(that)g(most)g(v)n(endors)e(should)h(ha)n(v)n(e)g (little)i(di\016cult)n(y)f(in)g(running)f(the)h(lo)n(w-lev)n(el)e(and)i(k)n (ernel)150 2163 y(b)r(enc)n(hmarks,)26 b(since)h(these)g(either)f(in)n(v)n (olv)n(e)g(basic)g(hardw)n(are)f(and)h(soft)n(w)n(are)f(tests)i(\(suc)n(h)g (as)f(COMMS1\))150 2263 y(that)f(v)n(endors)f(w)n(ould)g(wish)h(to)g(p)r (erform)g(in)g(an)n(y)f(case,)h(or)f(in)n(v)n(olv)n(e)f(scien)n(ti\014c)i (library)f(subroutines)g(\(suc)n(h)150 2363 y(as)i(FFT\))h(that)f(they)h(w)n (ould)f(b)r(e)g(required)g(to)g(pro)r(duce)g(and)g(optimise.)36 b(In)27 b(the)f(latter)g(case,)g(they)h(w)n(ould)150 2462 y(no)f(doubt)g(b)r (e)h(pleased)e(to)h(sho)n(w)f(the)i(sup)r(erior)e(p)r(erformance)g(of)h (their)g(library)f(routine)h(compared)f(with)150 2562 y(that)j(of)f(the)h (standard)f(F)-7 b(ortran)26 b(pro)n(vided)h(in)h(the)g Fo(P)-7 b(ARKBENCH)29 b Fx(b)r(enc)n(hmark)e(suite.)275 2661 y(The)41 b(case)f(of)h(compact)f(applications)g(is)h(more)f(di\016cult,)45 b(b)r(ecause)c(these)g(co)r(des)f(migh)n(t)h(require)150 2761 y(substan)n(tial)26 b(e\013ort)h(to)g(optimise,)h(and)e(in)i(some)e(cases)g (ev)n(en)h(to)g(run)g(satisfactorily)-7 b(.)35 b(F)-7 b(or)27 b(these)g(reasons,)150 2861 y(it)22 b(is)g(not)g(exp)r(ected)g(that)g(v)n (endors)e(w)n(ould)i(initially)f(run)h(all)g(these)f(co)r(des,)i(or)e(indeed) h(an)n(y)f(of)h(them.)35 b(They)150 2960 y(migh)n(t,)22 b(ho)n(w)n(ev)n(er,)e (c)n(ho)r(ose)f(to)i(run)f(a)g(selection)h(of)f(them)h(from)g(sub)5 b(ject)20 b(areas)f(of)i(in)n(terest)f(to)g(their)h(curren)n(t)150 3060 y(p)r(oten)n(tial)34 b(customers,)h(in)f(order)f(to)h(demonstrate)f (their)h(computer's)f(capabilit)n(y)h(on)g(some)f(standard)150 3160 y(and)22 b(relev)-5 b(an)n(t)22 b(tests.)36 b(In)22 b(this)h(w)n(a)n(y) -7 b(,)23 b(and)f(o)n(v)n(er)f(a)h(p)r(erio)r(d)h(of)f(time,)i(it)f(is)g(hop) r(ed)g(that)g(most)f(of)h(the)g(compact)150 3259 y(applications)k(w)n(ould)g (b)r(e)h(run)f(in)h(a)f(natural)g(w)n(a)n(y)f(and)i(without)g(extra)f (e\013ort.)1817 5428 y(5)p eop PNP restore /PNP save def 628.2618 89.4750 translate 7 bop 150 935 a Fr(Chapter)66 b(2)150 1350 y Fu(Metho)7 b(dology)1515 1287 y Fq(\003)150 1832 y Fp(2.1)137 b(Philosoph)l(y)150 2013 y Fx(One)34 b(migh)n(t)h(ask)e(wh)n(y)i(an)n(y)n(one)e(should)h(care)g(ab)r (out)g(dev)n(eloping)g(a)g(standardized,)h(rigorous)d(and)j(sci-)150 2113 y(en)n(ti\014cally)c(tenable)g(metho)r(dology)f(for)g(studying)h(the)h (p)r(erformance)e(of)h(high-p)r(erformance)e(computer)150 2213 y(systems.)36 b(There)27 b(are)g(sev)n(eral)f(reasons)g(wh)n(y)h(this)h(is)f (an)h(imp)r(ortan)n(t)f(undertaking:)251 2388 y(1.)42 b(T)-7 b(o)27 b(establish)g(and)g(main)n(tain)h(high)f(standards)g(of)g(honest)n(y)g (and)g(in)n(tegrit)n(y)g(in)h(our)f(profession.)251 2551 y(2.)42 b(T)-7 b(o)35 b(impro)n(v)n(e)f(the)j(status)e(of)h(sup)r(ercomputer)f(p)r (erformance)g(analysis)f(as)h(a)h(rigorous)d(scien)n(ti\014c)358 2651 y(discipline.)251 2814 y(3.)42 b(T)-7 b(o)27 b(reduce)g(confusion)g(in)h (the)g(high-p)r(erformance)e(computing)h(literature.)251 2977 y(4.)42 b(T)-7 b(o)33 b(increase)g(understanding)h(of)g(these)g(systems,)h(b) r(oth)f(at)g(a)g(lo)n(w-lev)n(el)f(hardw)n(are)f(or)h(soft)n(w)n(are)358 3076 y(lev)n(el)27 b(and)g(at)h(a)f(high-lev)n(el,)f(total)i(system)f(p)r (erformance)g(lev)n(el.)251 3239 y(5.)42 b(T)-7 b(o)25 b(assist)g(the)i(purc) n(hasers)d(of)i(high-p)r(erformance)e(computing)i(equipmen)n(t)h(in)f (selecting)g(systems)358 3339 y(b)r(est)i(suited)g(to)f(their)h(needs.)251 3502 y(6.)42 b(T)-7 b(o)39 b(reduce)h(the)h(amoun)n(t)e(of)h(time)h(and)f (resources)e(v)n(endors)h(m)n(ust)h(exp)r(end)g(in)h(implemen)n(ting)358 3602 y(m)n(ultiple,)28 b(redundan)n(t)f(b)r(enc)n(hmarks.)251 3765 y(7.)42 b(T)-7 b(o)26 b(pro)n(vide)g(v)-5 b(aluable)26 b(feedbac)n(k)g(to)h(v)n(endors)e(on)i(b)r(ottlenec)n(ks)g(that)g(can)f(b)r (e)h(alleviated)g(in)g(future)358 3865 y(pro)r(ducts.)275 4040 y(It)19 b(is)h(imp)r(ortan)n(t)f(to)h(note)f(that)h(researc)n(hers)d(in)i (man)n(y)g(scien)n(ti\014c)h(disciplines)g(ha)n(v)n(e)e(found)i(it)g (necessary)150 4139 y(to)26 b(establish)f(and)h(re\014ne)f(standards)g(for)g (p)r(erforming)g(exp)r(erimen)n(ts)g(and)h(rep)r(orting)f(the)h(results.)36 b(Man)n(y)150 4239 y(scien)n(tists)21 b(ha)n(v)n(e)e(learned)h(the)i(imp)r (ortance)e(of)h(standard)f(terminology)f(and)i(notation.)34 b(Chemists,)23 b(ph)n(ysi-)150 4339 y(cists)28 b(and)h(biologists)e(long)h (ago)g(disco)n(v)n(ered)e(the)j(imp)r(ortance)f(of)h Fn(c)l(ontr)l(ols)g Fx(in)g(their)f(exp)r(erimen)n(ts.)40 b(The)150 4438 y(issue)21 b(of)h(rep)r(eatabilit)n(y)f(pro)n(v)n(ed)g(crucial)g(in)h(the)g(recen)n(t)f Fn(c)l(old)26 b(fusion)c Fx(episo)r(de.)35 b(Medical)21 b(researc)n(hers)e (ha)n(v)n(e)150 4538 y(found)k(it)g(necessary)e(to)i(p)r(erform)f Fn(double-blind)j Fx(exp)r(erimen)n(ts)d(in)h(their)g(\014eld.)36 b(Psyc)n(hologists)20 b(and)i(so)r(ciol-)150 4638 y(ogists)27 b(ha)n(v)n(e)g(dev)n(elop)r(ed)h(highly)g(re\014ned)h(exp)r(erimen)n(tal)e (metho)r(dologies)h(and)g(adv)-5 b(anced)28 b(data)f(analysis)150 4737 y(tec)n(hniques.)36 b(P)n(olitical)23 b(scien)n(tists)g(ha)n(v)n(e)g (found)i(that)g(subtle)f(di\013erences)g(in)h(the)f(phrasing)f(of)i(a)e (question)150 4837 y(can)35 b(a\013ect)h(the)f(results)g(of)h(a)f(p)r(oll.)60 b(Researc)n(hers)34 b(in)h(man)n(y)g(\014elds)h(ha)n(v)n(e)e(found)i(that)f (en)n(vironmen)n(tal)150 4936 y(factors)30 b(in)g(their)h(exp)r(erimen)n(ts)f (can)g(signi\014can)n(tly)g(in\015uence)h(the)g(measured)f(results;)h(th)n (us)g(they)g(m)n(ust)150 5036 y(carefully)c(rep)r(ort)g(all)g(suc)n(h)g (factors)g(in)h(their)f(pap)r(ers.)p 150 5102 1350 4 v 241 5156 a Fm(\003)277 5179 y Fl(assem)n(bled)c(b)n(y)h(Da)n(vid)g(Bailey)f(for)g (metho)r(dology)i(sub)r(committee)1817 5428 y Fx(6)p eop PNP restore PNEP %%Page: ? 5 0.6303 -612.00 PNLS /PNP save def 12.6922 89.4750 translate 8 bop 275 312 a Fx(If)28 b(sup)r(ercomputer)f(p)r(erformance)f(analysis)h (and)g(b)r(enc)n(hmarking)g(is)g(ev)n(er)g(to)g(b)r(e)h(tak)n(en)g(seriously) e(as)150 412 y(a)34 b(scien)n(ti\014c)h(discipline,)i(certainly)d(its)h (practitioners)f(should)g(b)r(e)i(exp)r(ected)f(to)g(adhere)f(to)g(standards) 150 511 y(that)27 b(prev)-5 b(ail)26 b(in)h(other)f(disciplines.)36 b(This)27 b(do)r(cumen)n(t)g(is)f(dedicated)h(to)f(promoting)g(these)g (standards)g(in)150 611 y(our)h(\014eld.)150 886 y Fp(2.2)137 b(F)-11 b(undamen)l(tal)47 b(Metrics)150 1067 y Fx(The)33 b(conclusions)f (dra)n(wn)h(from)f(a)h(b)r(enc)n(hmark)g(study)g(of)g(computer)g(p)r (erformance)f(dep)r(end)i(not)f(only)150 1167 y(on)26 b(the)h(basic)f(timing) h(results)f(obtained,)g(but)h(also)f(on)g(the)h(w)n(a)n(y)e(these)i(are)e(in) n(terpreted)h(and)h(con)n(v)n(erted)150 1267 y(in)n(to)40 b(p)r(erformance)f (\014gures.)74 b(The)41 b(c)n(hoice)e(of)h(the)h(p)r(erformance)e(metric,)44 b(ma)n(y)39 b(itself)i(in\015uence)g(the)150 1366 y(conclusions.)55 b(F)-7 b(or)34 b(example,)h(do)f(w)n(e)f(w)n(an)n(t)h(the)g(computer)g(that)g (generates)f(the)h(most)g(mega\015op)f(p)r(er)150 1466 y(second)h(\(or)g(has) f(the)i(highest)f(Sp)r(eedup\),)k(or)33 b(the)i(computer)f(that)h(solv)n(es)d (the)j(problem)f(in)h(the)f(least)150 1566 y(time?)65 b(It)37 b(is)g(no)n(w)f(w)n(ell)h(kno)n(wn)f(that)h(high)g(v)-5 b(alues)36 b(of)h(the)g(\014rst)g(metrics)f(do)h(not)g(necessarily)e(imply)150 1665 y(the)30 b(second)e(prop)r(ert)n(y)-7 b(.)41 b(This)29 b(confusion)g(can)f(b)r(e)i(a)n(v)n(oided)e(b)n(y)h(c)n(ho)r(osing)e(a)i (more)g(suitable)g(metric)g(that)150 1765 y(re\015ects)37 b(solution)g(time)h (directly)-7 b(,)40 b(for)d(example)g(either)h(the)g(T)-7 b(emp)r(oral,)39 b(Sim)n(ulation)f(or)e(Benc)n(hmark)150 1864 y(p)r(erformance,)19 b(de\014ned)g(b)r(elo)n(w.)34 b(This)18 b(issue)g(of)g(the)h(sensible)f(c)n (hoice)g(of)g(p)r(erformance)g(metric)g(is)g(b)r(ecoming)150 1964 y(increasing)j(imp)r(ortan)n(t)g(with)i(the)f(adv)n(en)n(t)g(of)g (massiv)n(ely)e(parallel)h(computers)h(whic)n(h)g(ha)n(v)n(e)f(the)h(p)r (oten)n(tial)150 2064 y(of)j(v)n(ery)f(high)i(mega\015op)e(rates,)h(but)h(ha) n(v)n(e)e(m)n(uc)n(h)h(more)g(limited)h(p)r(oten)n(tial)f(for)g(reducing)g (solution)g(time.)150 2338 y Fp(2.3)137 b(Time)45 b(Measuremen)l(t)150 2520 y Fx(Before)21 b(other)h(issues)g(can)g(b)r(e)g(considered,)h(w)n(e)f(m) n(ust)g(discuss)g(the)h(measuremen)n(t)e(of)h(run)h(time.)35 b(In)23 b(recen)n(t)150 2620 y(y)n(ears)i(a)h(consensus)g(has)g(b)r(een)h (reac)n(hed)f(among)g(man)n(y)g(scien)n(tists)g(in)h(the)g(\014eld)g(that)g (the)g(most)g(relev)-5 b(an)n(t)150 2719 y(measure)28 b(of)h(run)g(time)g(is) g(actual)f(w)n(all-clo)r(c)n(k)f(elapsed)i(time.)41 b(This)29 b(measure)f(of)h(time)h(will)f(b)r(e)g(required)150 2819 y(for)e(all)g Fo(P)-7 b(ARKBENCH)30 b Fx(results)d(that)h(are)f(p)r(osted)g(to)h(the)g (database.)275 2919 y(Elapsed)c(w)n(all-clo)r(c)n(k)f(time)i(means)g(the)g (time)h(that)f(w)n(ould)f(b)r(e)i(measured)e(on)h(an)f(external)h(clo)r(c)n (k)f(that)150 3018 y(records)31 b(the)i(time-of-da)n(y)e(or)g(ev)n(en)h(Co)r (ordinated)g(Univ)n(ersal)f(Time)i(\(UTC\),)g(b)r(et)n(w)n(een)g(the)f(start) g(and)150 3118 y(\014nish)37 b(of)f(the)h(b)r(enc)n(hmark.)64 b(W)-7 b(e)37 b(are)e(not)i(concerned)f(with)h(the)g(origin)e(of)i(the)g (time)g(measuremen)n(t,)150 3218 y(since)e(w)n(e)g(are)g(taking)g(a)g (di\013erence,)i(but)f(it)g(is)g(imp)r(ortan)n(t)f(that)g(the)h(time)g (measured)f(w)n(ould)g(b)r(e)h(the)150 3317 y(same)29 b(as)g(that)h(giv)n(en) f(b)n(y)g(a)g(di\013erence)h(b)r(et)n(w)n(een)f(t)n(w)n(o)g(measuremen)n(ts)g (of)g(UTC,)h(if)g(it)g(w)n(ere)f(p)r(ossible)g(to)150 3417 y(mak)n(e)f(them.)41 b(It)29 b(is)g(imp)r(ortan)n(t)g(to)f(b)r(e)i(clear)d (ab)r(out)i(this,)h(b)r(ecause)e(man)n(y)g(computer)h(clo)r(c)n(ks)f(\(e.g.,) h(Sun)150 3516 y(Unix)i(function)g(ETIME\))e(measure)h(elapsed)f(CPU)h(time,) i(whic)n(h)e(is)g(the)h(total)f(time)h(that)g(the)f(pro)r(cess)150 3616 y(or)f(job)i(whic)n(h)f(calls)f(it)i(has)e(b)r(een)i(executing)f(in)g (the)h(CPU.)f(Suc)n(h)g(a)g(clo)r(c)n(k)f(do)r(es)h(not)g(record)f(time)i (\(i.e.)150 3716 y(it)f(stops)f(tic)n(king\))h(when)g(the)g(job)f(is)h(sw)n (app)r(ed)f(out)h(of)f(the)h(CPU.)g(It)g(do)r(es)f(not)h(record,)f (therefore,)g(an)n(y)150 3815 y(w)n(ait)h(time)h(whic)n(h)f(m)n(ust)h(b)r(e)g (included)g(if)g(w)n(e)f(are)f(to)i(assess)e(correctly)g(the)h(p)r (erformance)g(of)g(a)g(parallel)150 3915 y(program.)57 b(On)34 b(some)h(systems,)h(scien)n(tists)e(ha)n(v)n(e)g(found)h(that)g(ev)n(en)g (for)f(programs)f(that)i(p)r(erform)f(no)150 4015 y(explicit)26 b(I/O,)g(considerable)e Fn(system)j Fx(time)f(is)g(nonetheless)g(in)n(v)n (olv)n(ed,)f(for)g(example)h(in)h(fetc)n(hing)f(certain)150 4114 y(library)g(routines)h(or)g(other)g(data.)275 4214 y(Only)35 b(timings)g(actually)g(measured)f(ma)n(y)h(b)r(e)g(cited)h(for)f Fo(P)-7 b(ARKBENCH)30 b Fx(b)r(enc)n(hmarks)k(\(and)h(w)n(e)150 4313 y(strongly)28 b(recommend)g(this)i(practice)e(for)g(other)h(b)r(enc)n (hmarks)f(as)g(w)n(ell\).)42 b(Extrap)r(olations)27 b(and)h(pro)5 b(jec-)150 4413 y(tions,)26 b(for)g(instance)g(to)g(a)f(larger)g(n)n(um)n(b)r (er)g(of)i(no)r(des,)f(ma)n(y)f(not)h(b)r(e)h(emplo)n(y)n(ed)e(for)h(an)n(y)f (reason.)35 b(Also,)26 b(in)150 4513 y(the)k(in)n(terests)f(of)h(rep)r (eatabilit)n(y)f(it)h(is)f(highly)h(recommended)f(that)h(timing)g(runs)f(b)r (e)h(rep)r(eated,)g(sev)n(eral)150 4612 y(times)e(if)g(p)r(ossible.)275 4712 y(Tw)n(o)f(lo)n(w-lev)n(el)f(b)r(enc)n(hmarks)h(are)h(pro)n(vided)f(in)h (the)g Fo(P)-7 b(ARKBENCH)30 b Fx(suite)e(to)g(test)h(the)f(precision)150 4812 y(and)g(accuracy)e(of)i(the)h(clo)r(c)n(k)e(that)i(is)e(to)h(b)r(e)h (used)f(in)g(the)h(b)r(enc)n(hmarking.)37 b(These)28 b(should)g(b)r(e)g(run)g (\014rst,)150 4911 y(b)r(efore)f(an)n(y)g(b)r(enc)n(hmark)g(measuremen)n(ts)f (are)h(made.)37 b(They)27 b(are:)251 5077 y(1.)42 b(TICK1)34 b(-)h(measures)e(the)j(precision)e(of)h(the)g(clo)r(c)n(k)g(b)n(y)g (measuring)f(the)h(time)h(in)n(terv)-5 b(al)34 b(b)r(et)n(w)n(een)358 5177 y(tic)n(ks)27 b(of)g(the)h(clo)r(c)n(k.)36 b(A)28 b(clo)r(c)n(k)f(is)h (said)f(to)g(tic)n(k)h(when)g(it)g(c)n(hanges)e(its)h(v)-5 b(alue.)1817 5428 y(7)p eop PNP restore /PNP save def 628.2618 89.4750 translate 9 bop 251 312 a Fx(2.)42 b(TICK2)19 b(-)h(measures)f(the)i(accuracy)e(of)h (the)h(clo)r(c)n(k)f(b)n(y)g(comparing)f(a)h(giv)n(en)f(time)i(in)n(terv)-5 b(al)20 b(measured)358 412 y(b)n(y)33 b(an)h(external)g(w)n(all-clo)r(c)n(k)e (\(the)j(b)r(enc)n(hmark)n(er's)d(wrist)i(w)n(atc)n(h)g(is)g(adequate\))f (with)i(the)g(same)358 511 y(in)n(terv)-5 b(al)34 b(measured)g(b)n(y)g(the)h (computer)g(clo)r(c)n(k.)57 b(This)35 b(tests)g(the)g(scale)f(factor)g(used)h (to)g(con)n(v)n(ert)358 611 y(computer)29 b(clo)r(c)n(k)f(tic)n(ks)h(to)h (seconds,)f(and)g(immediately)g(detects)h(if)g(a)f(CPU-clo)r(c)n(k)f(is)h (incorrectly)358 711 y(b)r(eing)e(used.)275 867 y(The)j(fundamen)n(tal)g (measuremen)n(t)f(made)h(in)g(an)n(y)f(b)r(enc)n(hmark)h(is)g(the)g(elapsed)f (w)n(all-clo)r(c)n(k)g(time)h(to)150 967 y(complete)23 b(some)g(sp)r (eci\014ed)h(task.)35 b(All)24 b(other)e(p)r(erformance)h(\014gures)f(are)h (deriv)n(ed)f(from)h(this)h(basic)f(timing)150 1066 y(measuremen)n(t.)42 b(The)29 b(b)r(enc)n(hmark)g(time,)i Fs(T)12 b Fx(\()p Fs(N)d Fx(;)14 b Fs(p)p Fx(\),)29 b(will)g(b)r(e)h(a)f(function)h(of)g(the)g (problem)f(size,)g Fs(N)9 b Fx(,)30 b(and)150 1166 y(the)e(n)n(um)n(b)r(er)g (of)g(pro)r(cessors,)d Fs(p)p Fx(.)38 b(Here,)28 b(the)g(problem)g(size)f(is) h(represen)n(ted)f(b)n(y)g(the)i(v)n(ector)d(v)-5 b(ariable,)27 b Fs(N)9 b Fx(,)150 1265 y(whic)n(h)29 b(stands)g(for)f(a)h(set)g(of)g (parameters)e(c)n(haracterising)g(the)i(size)g(of)g(the)h(problem:)39 b(e.g.)i(the)29 b(n)n(um)n(b)r(er)150 1365 y(of)f(mesh)g(p)r(oin)n(ts)g(in)g (eac)n(h)g(dimension,)g(and)g(the)g(n)n(um)n(b)r(er)g(of)g(particles)f(in)i (a)e(particle-mesh)h(sim)n(ulation.)150 1465 y(Benc)n(hmark)21 b(problems)g(of)h(di\013eren)n(t)g(sizes)g(can)f(b)r(e)i(created)e(b)n(y)h(m) n(ultiplying)g(all)g(the)g(size)g(parameters)e(b)n(y)150 1564 y(suitable)29 b(p)r(o)n(w)n(ers)f(of)h(a)f(single)h(scale)f(factor,)h(thereb) n(y)f(increasing)g(the)h(spatial)g(and)g(particle)f(resolution)150 1664 y(in)g(a)f(sensible)g(w)n(a)n(y)-7 b(,)27 b(and)g(reducing)g(the)h(size) g(parameters)d(to)j(a)f(single)g(size)g(factor)g(\(usually)h(called)f Fs(\013)p Fx(\).)275 1764 y(W)-7 b(e)19 b(b)r(eliev)n(e)f(that)h(it)g(is)f (most)h(imp)r(ortan)n(t)f(to)g(regard)f(execution)h(time)h(and)g(p)r (erformance)e(as)h(a)h(function)150 1863 y(of)j(at)g(least)f(the)h(t)n(w)n(o) g(v)-5 b(ariables)20 b(\()p Fs(N)t(;)14 b(p)p Fx(\),)24 b(whic)n(h)e (de\014ne)g(a)f(parameter)g(plane.)34 b(Muc)n(h)22 b(confusion)g(has)f (arisen)150 1963 y(in)32 b(the)g(past)f(b)n(y)h(attempts)g(to)f(treat)g(p)r (erformance)g(as)g(a)g(function)h(of)g(a)f(single)g(v)-5 b(ariable,)32 b(b)n(y)f(taking)g(a)150 2062 y(particular)25 b(path)i(through)f(this)h (plane,)g(and)g(not)g(stating)f(what)h(path)g(is)f(tak)n(en.)36 b(Man)n(y)26 b(di\013eren)n(t)h(paths)150 2162 y(ma)n(y)e(b)r(e)g(tak)n(en,)h (and)f(hence)g(man)n(y)g(di\013eren)n(t)g(conclusions)g(can)g(b)r(e)g(dra)n (wn.)35 b(It)26 b(is)f(imp)r(ortan)n(t,)h(therefore,)150 2262 y(alw)n(a)n(ys)21 b(to)h(de\014ne)h(the)g(path)g(through)f(the)h(p)r (erformance)e(plane,)j(or)e(b)r(etter)h(as)f(w)n(e)g(do)g(here,)h(to)g(study) g(the)150 2361 y(shap)r(e)j(of)h(the)f(t)n(w)n(o-dimensional)f(p)r (erformance)g(hill.)37 b(In)27 b(some)f(cases)f(there)h(ma)n(y)g(ev)n(en)g(b) r(e)h(an)f(optim)n(um)150 2461 y(path)i(up)g(this)g(hill.)37 b(The)27 b(follo)n(wing)g(discussion)g(of)g(units)h(and)g(metrics)f(is)h (based)f(on)g(that)h(of)f([11)o(].)150 2733 y Fp(2.4)137 b(Units)47 b(and)f(Sym)l(b)t(ols)150 2915 y Fx(A)23 b(rational)f(set)h(of)g(units)h(and) f(sym)n(b)r(ols)f(is)h(essen)n(tial)f(for)h(an)n(y)f(n)n(umerate)g(science)h (including)g(b)r(enc)n(hmark-)150 3015 y(ing.)53 b(The)33 b(follo)n(wing)f (extension)g(of)h(the)g(in)n(ternationally)f(agreed)f(SI)j(system)e(of)h(ph)n (ysical)f(units)i([3)o(])f(is)150 3115 y(made)27 b(to)h(accommo)r(date)e(the) i(needs)g(of)f(computer)h(b)r(enc)n(hmarking.)275 3214 y(The)f(v)-5 b(alue)27 b(of)g(a)g(v)-5 b(ariable)27 b(comprises)f(a)h(pure)g(n)n(um)n(b)r (er)g(stating)g(the)g(n)n(um)n(b)r(er)g(of)h(units)f(whic)n(h)h(equal)150 3314 y(the)h(v)-5 b(alue)28 b(of)h(the)g(v)-5 b(ariable,)28 b(follo)n(w)n(ed)f(b)n(y)i(a)f(unit)h(sym)n(b)r(ol)f(sp)r(ecifying)h(the)g (unit)g(in)g(whic)n(h)f(the)h(v)-5 b(ariable)150 3413 y(is)41 b(b)r(eing)h(measured.)77 b(A)42 b(new)f(unit)i(is)e(required)f(whenev)n(er)h (a)g(quan)n(tit)n(y)g(of)g(a)g(new)h(nature)e(arises,)150 3513 y(suc)n(h)c(as)f(the)h(\014rst)g(app)r(earance)f(of)h(v)n(ector)f(op)r (erations,)h(or)g(message)e(sends.)62 b(Generally)35 b(sp)r(eaking)g(a)150 3613 y(unit)f(sym)n(b)r(ol)e(should)h(b)r(e)g(as)f(short)h(as)f(p)r(ossible,) i(consisten)n(t)e(with)i(b)r(eing)f(easily)f(recognised)f(and)i(not)150 3712 y(already)e(used.)53 b(The)32 b(follo)n(wing)g(ha)n(v)n(e)g(b)r(een)h (found)g(necessary)e(in)i(the)g(c)n(haracterisation)d(of)i(computer)150 3812 y(and)20 b(b)r(enc)n(hmark)g(p)r(erformance)f(in)i(science)f(and)h (engineering.)33 b(No)20 b(doubt)h(more)f(will)g(ha)n(v)n(e)f(to)i(b)r(e)g (de\014ned)150 3912 y(as)27 b(b)r(enc)n(hmarking)g(en)n(ters)f(new)i(areas.) 275 4056 y(New)f(unit)i(sym)n(b)r(ols)d(and)i(their)f(meaning:)251 4212 y(1.)42 b(\015op)o(:)37 b(\015oating-p)r(oin)n(t)27 b(op)r(eration)f ([latex)i Fk(\\)p Fx(\015op])251 4373 y(2.)42 b(inst:)37 b(instruction)27 b(of)h(an)n(y)f(kind)g([latex)h Fk(\\)p Fx(inst])251 4535 y(3.)42 b(in)n(top)o(:)37 b(in)n(teger)27 b(op)r(eration)g([latex)g Fk(\\)p Fx(inop])251 4696 y(4.)42 b(v)n(ecop)n(:)37 b(v)n(ector)27 b(op)r(eration)f([latex)i Fk(\\)p Fx(v)n(ecop])251 4857 y(5.)42 b(send)o(:)37 b(message)27 b(send)g(op)r(eration)g([latex)g Fk(\\)p Fx(send])251 5018 y(6.)42 b(iter)o(:)37 b(iteration)27 b(of)h(lo)r(op)f([latex)g Fk(\\)p Fx(iter])251 5179 y(7.)42 b(mref:)36 b(memory)27 b(reference)g(\(read)g(or)g(write\))g([latex)h Fk(\\)p Fx(mref)6 b(])1817 5428 y(8)p eop PNP restore PNEP %%Page: ? 6 0.6303 -612.00 PNLS /PNP save def 12.6922 89.4750 translate 10 bop 251 312 a Fx(8.)42 b(barr)n(:)37 b(barrier)26 b(op)r(eration)h([latex) g Fk(\\)p Fx(barr])251 466 y(9.)42 b(b:)37 b(binary)26 b(digit)i(\(bit\))h ([latex)e Fk(\\)p Fx(bit])210 619 y(10.)41 b(B)o(:)c(b)n(yte)28 b(\(groups)e(of)i(8)f(bits\))h([latex)g Fk(\\)p Fx(B])210 773 y(11.)41 b(sol)o(:)c(solution)27 b(or)g(single)g(execution)g(of)h(b)r(enc)n (hmark)e([latex)i Fk(\\)p Fx(sol])210 926 y(12.)41 b(w:)36 b(computer)28 b(w)n(ord.)35 b(Sym)n(b)r(ol)28 b(is)f(lo)n(w)n(er)f(case)h (\(W)h(means)g(w)n(att\))f([latex)h Fk(\\)p Fx(w])150 1067 y(When)g(required)e(a)h(subscript)g(ma)n(y)g(b)r(e)h(used)f(to)g(sho)n(w)g (the)h(n)n(um)n(b)r(er)f(of)g(bits)h(in)n(v)n(olv)n(ed)e(in)h(the)h(unit.)38 b(F)-7 b(or)150 1167 y(example:)49 b(a)34 b(32-bit)f(\015oating-p)r(oin)n(t)g (op)r(eration)g(\015op)1876 1187 y Fj(32)1947 1167 y Fx(,)i(a)f(64-bit)f(w)n (ord)g(w)2599 1179 y Fj(64)2669 1167 y Fx(,)j(also)d(w)n(e)g(ha)n(v)n(e)g(b)h (=)f(w)3465 1179 y Fj(1)3502 1167 y Fx(,)150 1266 y(B)23 b(=)g(w)379 1278 y Fj(8)417 1266 y Fx(,)k(w)527 1278 y Fj(64)621 1266 y Fx(=)22 b(8B.)275 1366 y(Note)41 b(that)g(\015op,)j(mref)d(and)g(other)f(m)n (ulti-letter)h(sym)n(b)r(ols)g(are)f(inseparable)f(four)i(or)f(\014v)n (e-letter)150 1466 y(sym)n(b)r(ols.)35 b(The)26 b(c)n(haracter)d(case)h(is)h (signi\014can)n(t)g(in)g(all)g(unit)h(sym)n(b)r(ols)f(so)f(that)i(e.g.)36 b(Flop,)25 b(Mref,)h Fs(W)3318 1478 y Fj(64)3414 1466 y Fx(are)150 1565 y(incorrect.)48 b(Unit)33 b(sym)n(b)r(ols)e(should)g(alw)n(a)n(ys)f(b)r (e)i(prin)n(ted)g(in)g(roman)f(t)n(yp)r(e,)i(to)f(con)n(trast)e(with)i(v)-5 b(ariables)150 1665 y(names)27 b(whic)n(h)g(are)g(prin)n(ted)g(in)h(italic.) 37 b(T)-7 b(o)27 b(aid)g(in)g(the)h(use)g(of)f(roman)f(t)n(yp)r(e,)i(esp)r (ecially)f(within)h(LaT)-7 b(ex's)150 1764 y(math)40 b(mo)r(de,)k(LaT)-7 b(ex)40 b(commands)f(ha)n(v)n(e)g(b)r(een)i(de\014ned)g(for)e(eac)n(h)h (unit,)k(these)c(commands)g(b)r(eing)g(a)150 1864 y(bac)n(kslash)24 b(follo)n(w)n(ed)h(b)n(y)h(the)h(unit)g(sym)n(b)r(ol)e(\(except)i(for)e(`in)n (top')h(and)g(`b')h(whose)e(names)h(are)f(c)n(hanged)g(in)150 1964 y(the)j(command)f(to)g(a)n(v)n(oid)f(a)g(clash)h(with)h(already)e (de\014ned)h(system)g(commands\).)37 b(Suc)n(h)27 b(commands)g(will)150 2063 y(prin)n(t)g(in)g(roman)f(t)n(yp)r(e)h(wherev)n(er)e(they)i(o)r(ccur.)36 b(Because)26 b(`s')g(is)h(the)g(SI)g(unit)h(for)e(seconds,)g(unit)i(sym)n(b)r (ols)150 2163 y(lik)n(e)e(`sheep')h(do)f(not)h(tak)n(e)f(`s')h(in)f(the)i (plural.)36 b(Th)n(us)26 b(one)g(coun)n(ts:)36 b(one)26 b(\015op,)h(t)n(w)n (o)f(\015op,)h(...,)g(one)f(h)n(undred)150 2263 y(\015op)d(etc.)36 b(This)23 b(is)g(esp)r(ecially)g(imp)r(ortan)n(t)g(when)g(the)h(unit)g(sym)n (b)r(ol)f(is)g(used)g(in)h(ordinary)d(text)j(as)f(a)g(useful)150 2362 y(abbreviation,)j(as)h(often,)h(quite)g(sensibly)-7 b(,)27 b(it)h(is.)275 2499 y(SI)f(pro)n(vides)f(the)i(standard)f(pre\014xes:)251 2640 y(1.)42 b(k)27 b(:)37 b(kilo)27 b(meaning)g(10)1064 2610 y Fj(3)251 2793 y Fx(2.)42 b(M)27 b(:)h(mega)f(meaning)g(10)1145 2763 y Fj(6)251 2947 y Fx(3.)42 b(G)27 b(:)h(giga)e(meaning)h(10)1092 2917 y Fj(9)251 3100 y Fx(4.)42 b(T)27 b(:)h(tera)f(meaning)g(10)1083 3070 y Fj(12)150 3241 y Fx(This)40 b(means)f(that)h(w)n(e)g(cannot)f(use)h(M) g(to)g(mean)f(1024)2016 3211 y Fj(2)2091 3241 y Fx(\(the)i(binary)e(mega\))g (as)g(is)h(often)g(done)g(in)150 3341 y(describing)f(computer)h(memory)g (capacit)n(y)-7 b(,)42 b(e.g.)75 b(256)39 b(MB.)h(W)-7 b(e)40 b(can)g(ho)n(w)n(ev)n(er)e(in)n(tro)r(duce)i(the)h(new)150 3441 y(pre\014x:)251 3582 y(1.)h(K)27 b(:)h(meaning)f(1024,)e(then)k(use)e(a) g(subscript)g(2)h(to)f(indicate)h(the)g(binary)f(v)n(ersions)251 3735 y(2.)42 b(M)434 3747 y Fj(2)499 3735 y Fx(:)37 b(binary)26 b(mega)h(1024)1204 3705 y Fj(2)251 3889 y Fx(3.)42 b(G)423 3901 y Fj(2)488 3889 y Fx(:)37 b(binary)26 b(giga)h(1024)1152 3858 y Fj(3)251 4042 y Fx(4.)42 b(T)418 4054 y Fj(2)482 4042 y Fx(:)37 b(binary)27 b(tera)g(1024)1142 4012 y Fj(4)150 4183 y Fx(In)j(most)g(cases)f(the)h(di\013erence)g(b)r(et)n(w)n(een)g(the)g(mega)f (and)h(the)h(binary)e(mega)g(\(4\045\))h(is)g(probably)f(unim-)150 4283 y(p)r(ortan)n(t,)i(but)g(it)g(is)f(imp)r(ortan)n(t)g(to)g(b)r(e)h(unam)n (biguous.)45 b(In)30 b(this)h(w)n(a)n(y)e(one)h(can)h(con)n(tin)n(ue)f(with)g (existing)150 4382 y(practice)21 b(if)i(the)f(di\013erence)h(do)r(esn't)f (matter,)h(and)f(ha)n(v)n(e)f(an)g(agreed)g(metho)r(d)i(of)f(b)r(eing)g(more) f(exact)h(when)150 4482 y(necessary)-7 b(.)34 b(F)-7 b(or)24 b(example,)h(the)h(ab)r(o)n(v)n(e)d(memory)h(capacit)n(y)g(w)n(as)f(probably) h(in)n(tended)h(to)g(mean)f(256M)3406 4494 y Fj(2)3443 4482 y Fx(B.)275 4581 y(As)36 b(a)f(consequence)g(of)h(the)h(ab)r(o)n(v)n(e,)f(an) g(amoun)n(t)g(of)f(computational)h(w)n(ork)e(in)n(v)n(olving)h(4)p Fs(:)p Fx(5)23 b Fi(\002)h Fx(10)3456 4551 y Fj(12)150 4681 y Fx(\015oating-p)r(oin)n(t)31 b(op)r(erations)g(is)h(correctly)f(written)h (as)g(4.5)f(T\015op.)51 b(Note)32 b(that)h(the)g(unit)g(sym)n(b)r(ol)e (T\015op)150 4781 y(is)i(nev)n(er)e(pluralised)i(with)g(an)f(added)h(`s',)h (and)f(it)g(is)g(therefore)e(incorrect)h(to)h(write)f(the)h(ab)r(o)n(v)n(e)f (as)g(4.5)150 4880 y(T\015ops)j(whic)n(h)h(could)f(b)r(e)h(confused)g(with)g (a)f(rate)g(p)r(er)g(second.)61 b(The)35 b(most)h(frequen)n(tly)f(used)h (unit)g(of)150 4980 y(p)r(erformance,)28 b(millions)h(of)g(\015oating-p)r (oin)n(t)f(op)r(erations)g(p)r(er)g(second)h(is)g(correctly)e(written)i (M\015op/s,)g(in)150 5080 y(analogy)f(to)i(km/s.)42 b(The)30 b(slash)f(is)h(necessary)e(and)i(means)f(`p)r(er',)h(b)r(ecause)g(the)g(`p')g (is)g(an)f(in)n(tegral)g(part)150 5179 y(of)f(the)g(unit)g(sym)n(b)r(ol)f (`\015op')g(and)h(cannot)f(also)g(b)r(e)h(used)f(to)h(mean)f(`p)r(er'.)1817 5428 y(9)p eop PNP restore /PNP save def 628.2618 89.4750 translate 11 bop 150 312 a Fp(2.5)137 b(Floating-P)l(oin)l(t)47 b(Op)t(eration)g(Coun)l (t)150 494 y Fx(Although)31 b(w)n(e)f(discourage)f(the)i(use)f(of)h(millions) g(of)f(\015oating-p)r(oin)n(t)g(op)r(erations)f(p)r(er)i(second)f(as)g(a)g(p) r(er-)150 594 y(formance)24 b(metric,)i(it)g(can)f(b)r(e)g(a)g(useful)h (measure)e(if)i(the)g(n)n(um)n(b)r(er)f(of)g(\015oating-p)r(oin)n(t)f(op)r (erations,)h Fs(F)12 b Fx(\()p Fs(N)d Fx(\),)150 693 y(needed)28 b(to)f(solv)n(e)g(the)h(b)r(enc)n(hmark)e(problem)i(is)f(carefully)g (de\014ned.)275 793 y(F)-7 b(or)24 b(simple)h(problems)f(\(e.g.)36 b(matrix)24 b(m)n(ultiply\))i(it)f(is)g(su\016cien)n(t)g(to)g(use)g(a)f (theoretical)g(v)-5 b(alue)25 b(for)g(the)150 893 y(\015oating-p)r(oin)n(t)f (op)r(eration)h(coun)n(t)g(\(in)h(this)f(case)g(2)p Fs(n)1812 862 y Fj(3)1874 893 y Fx(\015op,)h(for)e(nxn)i(matrices\))f(obtained)g(b)n(y) g(insp)r(ection)150 992 y(of)30 b(the)g(co)r(de)g(or)f(consideration)f(of)i (the)g(arithmetic)g(in)g(the)g(algorithm.)43 b(F)-7 b(or)29 b(more)g(complex)h(problems)150 1092 y(con)n(taining)23 b(data-dep)r(enden)n (t)h(conditional)g(statemen)n(ts,)g(an)g(empirical)g(metho)r(d)g(ma)n(y)g(ha) n(v)n(e)f(to)h(b)r(e)g(used.)150 1191 y(The)33 b(sequen)n(tial)f(v)n(ersion)f (of)h(the)h(b)r(enc)n(hmark)f(co)r(de)h(de\014nes)f(the)h(problem)f(and)h (the)g(algorithm)e(to)i(b)r(e)150 1291 y(used)39 b(to)f(solv)n(e)g(it.)70 b(Coun)n(ters)38 b(can)g(b)r(e)h(inserted)g(in)n(to)f(this)h(co)r(de)g(or)f (a)g(hardw)n(are)f(monitor)h(used)g(to)150 1391 y(coun)n(t)c(the)g(n)n(um)n (b)r(er)f(of)h(\015oating-p)r(oin)n(t)f(op)r(erations.)54 b(The)34 b(latter)g(is)f(the)i(pro)r(cedure)d(follo)n(w)n(ed)h(b)n(y)h(the)150 1490 y Fo(PERFECT)29 b Fx(Club)h([4)o(].)43 b(In)29 b(either)g(case)g(a)g (decision)f(has)h(to)g(b)r(e)h(made)f(regarding)e(the)j(n)n(um)n(b)r(er)f(of) g(\015op)150 1590 y(that)35 b(are)e(to)h(b)r(e)h(credited)f(for)g(di\013eren) n(t)g(t)n(yp)r(es)g(of)h(\015oating-p)r(oin)n(t)e(op)r(erations,)i(and)f(w)n (e)g(see)g(no)g(go)r(o)r(d)150 1690 y(reason)21 b(to)i(deviate)f(from)g (those)g(c)n(hosen)g(b)n(y)g(McMahon)h([5)o(])g(when)g(the)g(M\015op/s)f (measure)f(w)n(as)h(originally)150 1789 y(de\014ned.)37 b(These)28 b(are:)735 1959 y(add,)g(subtract,)f(m)n(ultiply)100 b(1)27 b(\015op)735 2058 y(divide,)h(square-ro)r(ot)256 b(4)27 b(\015op)735 2158 y(exp)r(onen)n(tial,)g(sine)h(etc.)176 b(8)27 b(\015op)h(\(this)g (\014gure)f(will)g(b)r(e)h(adjusted\))735 2257 y Fo(IF\(X)j(.REL.)f(Y\))339 b Fx(1)27 b(\015op)275 2487 y(Some)h(mem)n(b)r(ers)h(of)g(the)h(committee)f (felt)h(that)f(these)g(n)n(um)n(b)r(ers,)g(deriv)n(ed)f(in)i(the)f(1970s,)f (no)g(longer)150 2586 y(correctly)23 b(re\015ected)i(the)g(situation)g(on)f (curren)n(t)g(computers.)35 b(Ho)n(w)n(ev)n(er,)24 b(since)h(these)f(n)n(um)n (b)r(ers)h(are)e(only)150 2686 y(used)d(to)h(calculate)f(a)g(nominal)g(b)r (enc)n(hmark)g(\015op-coun)n(t,)h(it)g(is)f(not)h(so)f(imp)r(ortan)n(t)g (that)h(they)f(b)r(e)h(accurate.)150 2785 y(The)i(imp)r(ortan)n(t)g(thing)h (is)f(that)h(they)f(do)g(not)h(c)n(hange,)f(otherwise)f(all)h(previous)f (\015op-coun)n(ts)g(w)n(ould)h(ha)n(v)n(e)150 2885 y(to)29 b(b)r(e)h(renormalised.)41 b(In)29 b(an)n(y)g(case,)g(it)h(is)f(not)g(p)r (ossible)g(for)g(a)g(single)g(set)h(of)f(ratios)f(to)h(b)r(e)h(v)-5 b(alid)29 b(for)g(all)150 2985 y(computers)j(and)g(library)g(soft)n(w)n(are.) 50 b(I)32 b(\(rwh\))h(suggest)f(the)h(committee)g(sta)n(ys)e(with)i(the)g(ab) r(o)n(v)n(e)e(ratios)150 3084 y(un)n(til)d(suc)n(h)g(time)h(as)e(they)h(b)r (ecome)g(wildly)g(wrong)f(and)h(extensiv)n(e)f(researc)n(h)f(pro)n(vides)h (us)h(with)g(a)g(more)150 3184 y(realistic)f(set.)275 3284 y(W)-7 b(e)25 b(distinguish)g(t)n(w)n(o)g(t)n(yp)r(es)g(of)g(op)r(eration)f (coun)n(t.)36 b(The)25 b(\014rst)g(is)g(the)h(nominal)f(b)r(enc)n(hmark)f (\015oating-)150 3383 y(p)r(oin)n(t)30 b(op)r(eration)e(coun)n(t,)i Fs(F)1049 3395 y Fh(B)1106 3383 y Fx(\()p Fs(N)9 b Fx(\),)31 b(whic)n(h)e(is)g(found)h(in)g(the)g(ab)r(o)n(v)n(e)e(w)n(a)n(y)g(from)h(the) h(de\014ning)f(F)-7 b(ortran77)150 3483 y(sequen)n(tial)23 b(co)r(de.)36 b(The)24 b(other)f(is)h(the)g(actual)g(n)n(um)n(b)r(er)f(of)h (\015oating-p)r(oin)n(t)f(op)r(erations)g(p)r(erformed)g(b)n(y)h(the)150 3582 y(hardw)n(are)e(when)j(executing)f(the)h(distributed)f(m)n(ulti-no)r(de) h(v)n(ersion,)e Fs(F)2424 3594 y Fh(H)2488 3582 y Fx(\()p Fs(N)t(;)14 b(p)p Fx(\),)25 b(whic)n(h)f(ma)n(y)g(b)r(e)h(greater)150 3682 y(than)40 b(the)g(nominal)g(b)r(enc)n(hmark)f(coun)n(t,)j(due)e(to)g(the)g (distributed)g(v)n(ersion)e(p)r(erforming)h(redundan)n(t)150 3782 y(arithmetic)g(op)r(erations.)71 b(Because)38 b(of)i(this,)i(the)e (hardw)n(are)d(\015op)j(coun)n(t)f(ma)n(y)f(also)h(dep)r(end)h(on)f(the)150 3881 y(n)n(um)n(b)r(er)27 b(of)h(pro)r(cessors)d(on)i(whic)n(h)h(the)g(b)r (enc)n(hmark)f(is)g(run,)h(as)f(sho)n(wn)g(in)g(its)h(argumen)n(t)f(list.)150 4156 y Fp(2.6)137 b(P)l(erformance)45 b(Metrics)150 4338 y Fx(Giv)n(en)32 b(the)g(time)h(of)f(execution)g Fs(T)12 b Fx(\()p Fs(N)d Fx(;)14 b Fs(p)p Fx(\))31 b(and)h(the)h(\015op-coun)n(t)e Fs(F)12 b Fx(\()p Fs(N)d Fx(\))33 b(sev)n(eral)d(di\013eren)n(t)i(p)r (erformance)150 4437 y(measures)25 b(can)h(b)r(e)g(de\014ned.)37 b(Eac)n(h)25 b(metric)h(has)g(its)g(o)n(wn)g(uses,)g(and)g(giv)n(es)f (di\013eren)n(t)i(information)e(ab)r(out)150 4537 y(the)30 b(computer)f(and)g(algorithm)f(used)h(in)h(the)f(b)r(enc)n(hmark.)42 b(It)29 b(is)g(imp)r(ortan)n(t)g(therefore)g(to)g(distinguish)150 4637 y(the)e(metrics)f(with)h(di\013eren)n(t)g(names,)g(sym)n(b)r(ols)f(and)g (units,)h(and)g(to)f(understand)h(clearly)e(the)i(di\013erence)150 4736 y(b)r(et)n(w)n(een)e(them.)36 b(Muc)n(h)25 b(confusion)g(and)f(w)n (asted)g(w)n(ork)g(can)g(arise)g(from)g(optimising)h(a)f(b)r(enc)n(hmark)h (with)150 4836 y(resp)r(ect)32 b(to)h(an)f(inappropriate)f(metric.)52 b(The)33 b(principal)f(p)r(erformance)g(metrics)g(are)g(discussed)g(in)h(the) 150 4935 y(follo)n(wing)27 b(subsections.)1796 5428 y(10)p eop PNP restore PNEP %%Page: ? 7 0.6303 -612.00 PNLS /PNP save def 12.6922 89.4750 translate 12 bop 150 312 a Fy(2.6.1)112 b(T)-9 b(emp)s(oral)37 b(P)m(erformance)150 465 y Fx(If)31 b(w)n(e)g(are)e(in)n(terested)i(in)g(comparing)e(the)i(p)r (erformance)f(of)g(di\013eren)n(t)h(algorithms)f(for)g(the)h(solution)f(of) 150 565 y(the)f(same)f(problem,)h(then)g(the)g(correct)e(p)r(erformance)h (metric)h(to)f(use)h(is)f(the)h Fn(T)-6 b(emp)l(or)l(al)32 b(Performanc)l(e)p Fx(,)150 665 y Fs(R)213 677 y Fh(T)265 665 y Fx(,)c(whic)n(h)g(is)f(de\014ned)h(as)f(the)h(in)n(v)n(erse)e(of)i(the)g (execution)f(time)1431 847 y Fs(R)1494 859 y Fh(T)1546 847 y Fx(\()p Fs(N)9 b Fx(;)14 b Fs(p)p Fx(\))23 b(=)g Fs(T)1937 813 y Fg(\000)p Fj(1)2025 847 y Fx(\()p Fs(N)9 b Fx(;)14 b Fs(p)p Fx(\))1110 b(\(2.1\))150 1030 y(The)25 b(units)h(of)f(temp)r(oral)g(p) r(erformance)f(are,)h(in)g(general,)g(solutions)f(p)r(er)h(second)g (\(sol/s\),)g(or)f(some)h(more)150 1130 y(appropriate)32 b(absolute)h(unit)h (suc)n(h)f(as)g(timesteps)h(p)r(er)g(second)f(\(tstep/s\).)55 b(With)35 b(this)f(metric)f(w)n(e)g(can)150 1229 y(b)r(e)41 b(sure)e(that)i(the)f(algorithm)g(with)g(the)h(highest)f(p)r(erformance)f (executes)h(in)h(the)f(least)g(time,)k(and)150 1329 y(is)36 b(therefore)g(the)h(b)r(est)g(algorithm.)63 b(W)-7 b(e)37 b(note)f(that)h (the)g(n)n(um)n(b)r(er)f(of)h(\015op)f(do)r(es)h(not)f(app)r(ear)g(in)h(this) 150 1429 y(de\014nition,)25 b(b)r(ecause)d(the)i(ob)5 b(jectiv)n(e)23 b(of)g(algorithm)f(design)h(is)g(not)g(to)g(p)r(erform)g(the)h(most)f (arithmetic)g(p)r(er)150 1528 y(second,)31 b(but)h(rather)e(it)h(is)g(to)g (solv)n(e)f(a)g(giv)n(en)h(problem)f(in)h(the)h(least)e(time,)j(regardless)28 b(of)j(the)h(amoun)n(t)150 1628 y(of)i(arithmetic)g(in)n(v)n(olv)n(ed.)56 b(F)-7 b(or)34 b(this)g(reason)f(the)i(temp)r(oral)e(p)r(erformance)h(is)g (also)f(the)i(metric)f(that)g(a)150 1727 y(computer)e(user)f(should)h(emplo)n (y)f(to)h(select)g(the)h(b)r(est)f(algorithm)f(to)h(solv)n(e)f(his)h (problem,)g(b)r(ecause)g(his)150 1827 y(ob)5 b(jectiv)n(e)39 b(is)g(also)g(to)g(solv)n(e)f(the)i(problem)f(in)h(the)g(least)f(time,)k(and) d(he)f(do)r(es)g(not)h(care)e(ho)n(w)h(m)n(uc)n(h)150 1927 y(arithmetic)28 b(is)f(done)g(to)h(ac)n(hiev)n(e)e(this.)150 2159 y Fy(2.6.2)112 b(Sim)m(ulation)35 b(P)m(erformance)150 2312 y Fx(A)19 b(sp)r(ecial)g(case)f(of)g(temp)r(oral)h(p)r(erformance)f(o)r (ccurs)g(for)g(sim)n(ulation)g(programs)f(in)i(whic)n(h)g(the)g(b)r(enc)n (hmark)150 2412 y(problem)24 b(is)g(de\014ned)g(as)g(the)h(sim)n(ulation)e (of)i(a)e(certain)h(p)r(erio)r(d)g(of)g(ph)n(ysical)g(time,)h(rather)e(than)i (a)f(certain)150 2512 y(n)n(um)n(b)r(er)37 b(of)g(timesteps.)65 b(In)37 b(this)g(case)f(w)n(e)h(sp)r(eak)f(of)h(the)h Fn(Simulation)g (Performanc)l(e)h Fx(and)e(use)g(units)150 2611 y(suc)n(h)31 b(as)f Fn(simulate)l(d)k(days)g(p)l(er)f(day)g Fx(\(written)e(sim-d/d)g(or)f (`d'/d\))i(in)f(w)n(eather)f(forecasting,)h(where)g(the)150 2711 y(ap)r(ostrophe)26 b(is)h(used)g(to)g(indicate)g(`sim)n(ulated';)g(or)f Fn(simulate)l(d)k(pic)l(o-se)l(c)l(onds)h(p)l(er)e(se)l(c)l(ond)f Fx(\(written)f(sim-)150 2810 y(ps/s)h(or)f(`ps'/s\))h(in)h(electronic)f (device)g(sim)n(ulation.)39 b(It)28 b(is)h(imp)r(ortan)n(t)f(to)g(use)g(sim)n (ulation)g(p)r(erformance)150 2910 y(rather)e(than)h(timestep/s)f(if)i(one)e (is)h(comparing)e(di\013eren)n(t)i(sim)n(ulation)f(algorithms)f(whic)n(h)i (ma)n(y)f(require)150 3010 y(di\013eren)n(t)36 b(sizes)f(of)g(timestep)h(for) f(the)h(same)f(accuracy)f(\(for)h(example)g(an)g(implicit)i(sc)n(heme)e(that) g(can)150 3109 y(use)d(a)g(large)f(timestep,)j(compared)d(with)i(an)f (explicit)g(sc)n(heme)g(that)g(requires)f(a)h(m)n(uc)n(h)g(smaller)g(step\).) 150 3209 y(In)k(order)f(to)h(main)n(tain)f(n)n(umerical)g(stabilit)n(y)-7 b(,)38 b(explicit)e(sc)n(hemes)g(also)f(require)f(the)j(use)f(of)f(a)h (smaller)150 3309 y(timestep)k(as)f(the)h(spatial)f(grid)g(is)g(made)h (\014ner.)72 b(F)-7 b(or)39 b(suc)n(h)g(sc)n(hemes)g(the)h(sim)n(ulation)f(p) r(erformance)150 3408 y(falls)e(o\013)g(dramatically)f(as)h(the)g(problem)g (size)g(is)g(increased)f(b)n(y)h(in)n(tro)r(ducing)g(more)f(mesh)i(p)r(oin)n (ts)f(in)150 3508 y(order)g(to)i(re\014ne)f(the)h(spatial)f(resolution:)58 b(the)39 b(doubling)g(of)g(the)g(n)n(um)n(b)r(er)f(of)h(mesh-p)r(oin)n(ts)f (in)h(eac)n(h)150 3607 y(of)32 b(three)g(dimensions)g(can)g(reduce)g(the)g (sim)n(ulation)g(p)r(erformance)f(b)n(y)h(a)g(factor)f(near)h(16)f(b)r (ecause)h(the)150 3707 y(timestep)g(m)n(ust)g(also)f(b)r(e)h(appro)n (ximately)e(halv)n(ed.)48 b(Ev)n(en)31 b(though)g(the)h(larger)e(problem)h (will)h(generate)150 3807 y(more)24 b(Mega\015op)g(p)r(er)h(second,)g(in)g (forecasting,)f(it)h(is)g(the)g(sim)n(ulated)g(da)n(ys)f(p)r(er)h(da)n(y)f (\(i.e.)36 b(the)26 b(sim)n(ulation)150 3906 y(p)r(erformance\))h(and)g(not)h (the)g(M\015op/s,)f(that)h(matter)f(to)g(the)h(user.)275 4006 y(As)22 b(w)n(e)g(see)h(b)r(elo)n(w,)g(b)r(enc)n(hmark)f(p)r(erformance)f(is) i(also)e(measured)h(in)h(terms)f(of)g(the)h(amoun)n(t)f(of)h(arith-)150 4106 y(metic)j(p)r(erformed)g(p)r(er)g(second)g(or)f(M\015op/s.)35 b(Ho)n(w)n(ev)n(er)24 b(it)j(is)f(imp)r(ortan)n(t)g(to)g(realise)e(that)j(it) f(is)g(incorrect)150 4205 y(to)i(compare)e(the)i(M\015op/s)f(ac)n(hiev)n(ed)g (b)n(y)g(t)n(w)n(o)g(algorithms)f(and)i(to)f(conclude)h(that)g(the)g (algorithm)f(with)150 4305 y(the)36 b(highest)g(M\015op/s)f(rating)f(is)i (the)g(b)r(est)g(algorithm.)61 b(This)35 b(is)h(b)r(ecause)f(the)h(t)n(w)n(o) f(algorithms)g(ma)n(y)150 4404 y(b)r(e)27 b(p)r(erforming)e(quite)i (di\013eren)n(t)g(amoun)n(ts)e(of)i(arithmetic)f(during)g(the)h(solution)f (of)g(the)h(same)f(problem.)150 4504 y(The)k(temp)r(oral)f(p)r(erformance)f (metric,)j Fs(R)1503 4516 y Fh(T)1555 4504 y Fx(,)f(de\014ned)g(ab)r(o)n(v)n (e,)f(has)g(b)r(een)h(in)n(tro)r(duced)g(to)f(o)n(v)n(ercome)f(this)150 4604 y(problem,)f(and)g(pro)n(vide)f(a)g(measure)g(that)i(can)e(b)r(e)i(used) f(to)g(compare)f(di\013eren)n(t)h(algorithms)f(for)g(solving)150 4703 y(the)33 b(same)f(problem.)53 b(Ho)n(w)n(ev)n(er,)32 b(it)h(should)g(b)r (e)g(remem)n(b)r(ered)f(that)h(the)g(temp)r(oral)g(p)r(erformance)e(only)150 4803 y(has)23 b(the)h(same)e(meaning)h(within)h(the)g(con\014nes)f(of)g(a)g (\014xed)g(problem,)h(and)f(no)g(meaning)g(can)g(b)r(e)h(attac)n(hed)150 4903 y(to)i(a)f(comparison)f(of)i(the)g(temp)r(oral)f(p)r(erformance)g(on)g (one)g(problem)h(with)g(the)g(temp)r(oral)f(p)r(erformance)150 5002 y(on)i(another.)1796 5428 y(11)p eop PNP restore /PNP save def 628.2618 89.4750 translate 13 bop 150 312 a Fy(2.6.3)112 b(Benc)m(hmark)38 b(P)m(erformance)150 465 y Fx(In)22 b(order)e(to)h(compare)f(the)i(p)r(erformance)e(of)h(a)g (computer)g(on)g(one)g(b)r(enc)n(hmark)g(with)h(its)f(p)r(erformance)f(on)150 565 y(another,)28 b(accoun)n(t)f(m)n(ust)h(b)r(e)h(tak)n(en)f(of)g(the)h (di\013eren)n(t)f(amoun)n(ts)f(of)i(w)n(ork)e(\(measured)g(in)i(\015op\))f (that)h(the)150 665 y(di\013eren)n(t)d(problems)f(require)g(for)g(their)h (solution.)35 b(Using)26 b(the)g(\015op-coun)n(t)f(for)g(the)i(b)r(enc)n (hmark,)e Fs(F)3304 677 y Fh(B)3362 665 y Fx(\()p Fs(N)9 b Fx(\),)150 764 y(w)n(e)27 b(can)g(de\014ne)h(the)g Fn(Benchmark)j(Performanc) l(e)f Fx(as)1327 926 y Fs(R)1390 938 y Fh(B)1447 926 y Fx(\()p Fs(N)9 b Fx(;)14 b Fs(p)p Fx(\))23 b(=)g Fs(F)1830 938 y Fh(B)1887 926 y Fx(\()p Fs(N)9 b Fx(\))p Fs(=T)j Fx(\()p Fs(N)d Fx(;)14 b Fs(p)p Fx(\))1005 b(\(2.2\))150 1087 y(The)32 b(units)g(of)f(b)r(enc)n (hmark)g(p)r(erformance)g(are)f(M\015op/s)h(\(b)r(enc)n(hmark)h(name\),)g (where)f(w)n(e)h(include)g(the)150 1187 y(name)19 b(of)g(the)h(b)r(enc)n (hmark)e(in)i(paren)n(theses)e(to)h(emphasise)g(that)g(the)h(p)r(erformance)e (ma)n(y)g(dep)r(end)i(strongly)150 1286 y(on)37 b(the)h(problem)f(b)r(eing)h (solv)n(ed,)h(and)f(to)f(emphasise)g(that)h(the)g(v)-5 b(alues)37 b(are)g(based)g(on)g(the)h(nominal)150 1386 y(b)r(enc)n(hmark)27 b(\015op-coun)n(t.)36 b(In)28 b(other)f(con)n(texts)g(suc)n(h)g(p)r (erformance)g(\014gures)f(w)n(ould)i(probably)e(b)r(e)i(quoted)150 1486 y(as)c(examples)g(of)g(the)h(so-called)e Fn(sustaine)l(d)i Fx(p)r(erformance)e(of)i(a)f(computer.)35 b(W)-7 b(e)25 b(feel)g(that)g(the)g (use)f(of)h(this)150 1585 y(term)32 b(is)g(meaningless)g(unless)g(the)g (problem)g(b)r(eing)h(solv)n(ed)e(and)h(the)h(degree)e(of)h(co)r(de)g (optimisation)g(is)150 1685 y(quoted,)c(b)r(ecause)f(the)h(p)r(erformance)f (is)h(so)f(v)-5 b(aried)27 b(across)f(di\013eren)n(t)i(b)r(enc)n(hmarks)f (and)h(di\013eren)n(t)g(lev)n(els)150 1784 y(of)39 b(optimisation.)70 b(Hence)38 b(w)n(e)h(fa)n(v)n(our)e(the)i(quotation)f(of)h(a)f(selection)g (of)h(b)r(enc)n(hmark)f(p)r(erformance)150 1884 y(\014gures,)24 b(rather)e(than)i(a)g(single)f(sustained)h(p)r(erformance,)f(b)r(ecause)h (the)g(latter)g(implies)g(that)g(the)g(quoted)150 1984 y(p)r(erformance)j(is) g(main)n(tained)g(o)n(v)n(er)f(all)h(problems.)275 2083 y(Note)39 b(also)f(that)i(the)g(\015op-coun)n(t)e Fs(F)1466 2095 y Fh(B)1524 2083 y Fx(\()p Fs(N)9 b Fx(\))40 b(is)f(that)h(for)f(the)g(de\014ning)h (sequen)n(tial)e(v)n(ersion)g(of)i(the)150 2183 y(b)r(enc)n(hmark,)h(and)d (that)i(the)f(same)f(coun)n(t)g(is)h(used)g(to)f(calculate)g Fs(R)2418 2195 y Fh(B)2514 2183 y Fx(for)h(the)g(distributed-memory)150 2283 y(\(DM\))31 b(v)n(ersion)c(of)j(the)g(program,)e(ev)n(en)h(though)g(the) h(DM)g(v)n(ersion)d(ma)n(y)i(actually)g(p)r(erform)g(a)g(di\013eren)n(t)150 2382 y(n)n(um)n(b)r(er)37 b(of)h(op)r(erations.)65 b(It)37 b(is)h(usual)f(for)g(DM)h(programs)d(to)i(p)r(erform)g(more)g(arithmetic)g (than)h(the)150 2482 y(de\014ning)31 b(sequen)n(tial)f(v)n(ersion,)h(b)r (ecause)g(often)g(n)n(um)n(b)r(ers)f(are)g(recomputed)h(on)g(the)g(no)r(des)g (in)h(order)d(to)150 2582 y(sa)n(v)n(e)38 b(comm)n(unicating)g(their)i(v)-5 b(alues)39 b(from)g(a)g(master)f(pro)r(cessor.)70 b(Ho)n(w)n(ev)n(er)38 b(suc)n(h)h(calculations)f(are)150 2681 y(redundan)n(t)c(\(they)h(ha)n(v)n(e) e(already)g(b)r(een)i(p)r(erformed)f(on)g(the)h(master\))f(and)g(it)h(w)n (ould)f(b)r(e)h(incorrect)e(to)150 2781 y(credit)27 b(them)i(to)e(the)h (\015op-coun)n(t)f(of)g(the)h(distributed)g(program.)275 2880 y(Using)f(the)g(sequen)n(tial)g(\015op-coun)n(t)f(in)h(the)h(calculation)e (of)h(the)h(DM)g(programs)d(b)r(enc)n(hmark)h(p)r(erfor-)150 2980 y(mance)21 b(has)f(the)h(additional)g(adv)-5 b(an)n(tage)19 b(that)j(it)f(is)g(p)r(ossible)f(to)h(conclude)g(that,)i(for)d(a)h(giv)n(en)f (b)r(enc)n(hmark,)150 3080 y(the)31 b(implemen)n(tation)g(that)g(has)f(the)h (highest)f(b)r(enc)n(hmark)g(p)r(erformance)g(is)g(the)h(b)r(est)g(b)r (ecause)g(it)g(exe-)150 3179 y(cutes)26 b(in)h(the)f(least)g(time.)37 b(This)26 b(w)n(ould)g(not)g(necessarily)f(b)r(e)h(the)h(case)e(if)i(a)e (di\013eren)n(t)i Fs(F)2949 3191 y Fh(B)3006 3179 y Fx(\()p Fs(N)9 b Fx(\))27 b(w)n(ere)e(used)150 3279 y(for)31 b(di\013eren)n(t)g (implemen)n(tations)g(of)g(the)g(b)r(enc)n(hmark.)47 b(F)-7 b(or)30 b(example,)i(the)f(use)g(of)g(a)g(b)r(etter)g(algorithm)150 3379 y(whic)n(h)j(obtains)g(the)g(solution)g(with)h(less)f(than)g Fs(F)1771 3391 y Fh(B)1828 3379 y Fx(\()p Fs(N)9 b Fx(\))35 b(op)r(erations)e(will)h(sho)n(w)g(up)g(as)g(higher)f(b)r(enc)n(h-)150 3478 y(mark)26 b(p)r(erformance.)36 b(F)-7 b(or)27 b(this)g(reason)f(it)h (should)g(cause)g(no)f(surprise)g(if)i(the)g(b)r(enc)n(hmark)e(p)r (erformance)150 3578 y(o)r(ccasionally)c(exceeds)h(the)h(maxim)n(um)g(p)r (ossible)g(hardw)n(are)e(p)r(erformance.)34 b(T)-7 b(o)24 b(this)g(exten)n(t) g(b)r(enc)n(hmark)150 3677 y(p)r(erformance)31 b(M\015op/s)g(m)n(ust)g(b)r(e) i(understo)r(o)r(d)e(to)g(b)r(e)i(nominal)e(v)-5 b(alues,)32 b(and)g(not)g(necessarily)e(exactly)150 3777 y(the)i(n)n(um)n(b)r(er)g(of)g (op)r(erations)f(executed)h(p)r(er)g(second)f(b)n(y)h(the)g(hardw)n(are,)f (whic)n(h)h(is)g(the)h(sub)5 b(ject)32 b(of)g(the)150 3877 y(next)25 b(metric.)36 b(The)26 b(purp)r(ose)e(of)h(b)r(enc)n(hmark)g(p)r (erformance)f(is)h(to)g(compare)f(di\013eren)n(t)h(implemen)n(tations)150 3976 y(and)g(algorithms)f(on)h(di\013eren)n(t)h(computers)f(for)f(the)i (solution)f(of)g(the)h(same)f(problem,)g(on)g(the)h(basis)f(that)150 4076 y(the)f(b)r(est)g(p)r(erformance)f(means)g(the)h(least)f(execution)h (time.)36 b(F)-7 b(or)23 b(this)h(to)f(b)r(e)h(true)g Fs(F)2836 4088 y Fh(B)2893 4076 y Fx(\()p Fs(N)9 b Fx(\))24 b(m)n(ust)g(b)r(e)g(k)n (ept)150 4176 y(the)k(same)f(for)g(all)g(implemen)n(tations)h(and)f (algorithms.)150 4404 y Fy(2.6.4)112 b(Hardw)m(are)38 b(P)m(erformance)150 4558 y Fx(If)28 b(w)n(e)f(wish)g(to)g(compare)f(the)i(observ)n(ed)e(p)r (erformance)g(with)i(the)g(theoretical)e(capabilities)h(of)g(the)h(com-)150 4657 y(puter)g(hardw)n(are,)d(w)n(e)j(m)n(ust)f(compute)h(the)g(actual)f(n)n (um)n(b)r(er)h(of)f(\015oating-p)r(oin)n(t)g(op)r(erations)f(p)r(erformed,) 150 4757 y Fs(F)203 4769 y Fh(H)266 4757 y Fx(\()p Fs(N)9 b Fx(;)14 b Fs(p)p Fx(\),)28 b(and)g(from)f(it)h(the)g(actual)f Fn(Har)l(dwar)l(e)j(Performanc)l(e)1284 4918 y Fs(R)1347 4930 y Fh(H)1410 4918 y Fx(\()p Fs(N)9 b Fx(;)14 b Fs(p)p Fx(\))23 b(=)g Fs(F)1793 4930 y Fh(H)1856 4918 y Fx(\()p Fs(N)t(;)14 b(p)p Fx(\))p Fs(=T)e Fx(\()p Fs(N)d Fx(;)14 b Fs(p)p Fx(\))962 b(\(2.3\))150 5080 y(The)32 b(hardw)n(are)f(p)r(erformance)g(also)g(has)h (the)h(units)g(M\015op/s,)g(and)f(will)h(ha)n(v)n(e)e(the)i(same)f(v)-5 b(alue)32 b(as)g(the)150 5179 y(b)r(enc)n(hmark)27 b(p)r(erformance)f(for)i (the)g(sequen)n(tial)e(v)n(ersion)h(of)g(the)h(b)r(enc)n(hmark.)36 b(Ho)n(w)n(ev)n(er,)26 b(the)i(hardw)n(are)1796 5428 y(12)p eop PNP restore PNEP %%Page: ? 8 0.6303 -612.00 PNLS /PNP save def 12.6922 89.4750 translate 14 bop 150 312 a Fx(p)r(erformance)39 b(ma)n(y)h(b)r(e)h(higher)f(than)g(the) h(b)r(enc)n(hmark)f(p)r(erformance)f(for)h(the)h(distributed)g(v)n(ersion,) 150 412 y(b)r(ecause)28 b(the)g(hardw)n(are)e(p)r(erformance)i(giv)n(es)f (credit)h(for)f(redundan)n(t)h(arithmetic)g(op)r(erations,)f(whereas)150 511 y(the)22 b(b)r(enc)n(hmark)g(p)r(erformance)f(do)r(es)h(not.)35 b(Because)21 b(the)h(hardw)n(are)e(p)r(erformance)h(measures)g(the)i(actual) 150 611 y(\015oating-p)r(oin)n(t)36 b(op)r(erations)g(p)r(erformed)h(p)r(er)g (second,)i(unlik)n(e)e(the)g(b)r(enc)n(hmark)f(p)r(erformance,)j(it)e(can)150 711 y(nev)n(er)27 b(exceed)g(the)h(theoretical)f(p)r(eak)g(p)r(erformance)f (of)i(the)g(computer.)275 810 y(Assuming)36 b(a)h(computer)g(with)g(m)n (ultiple-CPUs)g(eac)n(h)f(with)i(m)n(ultiple)f(arithmetic)g(pip)r(elines,)j (de-)150 910 y(liv)n(ering)f(a)h(maxim)n(um)g(of)h(one)f(\015op)g(p)r(er)g (clo)r(c)n(k)g(p)r(erio)r(d,)j(the)e(theoretical)e(p)r(eak)i(v)-5 b(alue)40 b(of)g(hardw)n(are)150 1010 y(p)r(erformance)27 b(is)1103 1152 y Fs(r)1142 1118 y Fg(\003)1204 1152 y Fx(=)1302 1096 y Fs(f)9 b(l)r(:pt:pipes=C)d(P)12 b(U)p 1302 1133 621 4 v 1392 1209 a(cl)r(ock)s(:per)r(iod)1951 1152 y Fi(\002)18 b Fs(number)n(:C)6 b(P)12 b(U)d(s)781 b Fx(\(2.4\))150 1346 y(with)24 b(units)g(of)f(M\015op/s)g (if)h(the)g(clo)r(c)n(k)e(p)r(erio)r(d)i(is)f(expressed)f(in)i(microseconds.) 34 b(By)23 b(comparing)f(the)i(mea-)150 1446 y(sured)g(hardw)n(are)f(p)r (erformance,)i Fs(R)1289 1458 y Fh(H)1352 1446 y Fx(\()p Fs(N)9 b Fx(;)14 b Fs(p)p Fx(\),)25 b(with)h(the)f(theoretical)f(p)r(eak)h(p)r (erformance,)f(w)n(e)h(can)g(assess)150 1545 y(the)f(fraction)f(of)h(the)g(a) n(v)-5 b(ailable)23 b(p)r(erformance)f(that)i(is)g(b)r(eing)g(realised)f(b)n (y)g(a)h(particular)e(implemen)n(tation)150 1645 y(of)28 b(the)g(b)r(enc)n (hmark.)150 1877 y Fy(2.6.5)112 b(Sp)s(eedup,)40 b(E\016ciency)c(and)j(P)m (erformance)e(p)s(er)g(No)s(de)150 2030 y Fn(Par)l(al)t(lel)29 b(sp)l(e)l(e)l(dup)24 b Fx(is)g(a)g(p)r(opular)g(metric)g(that)g(has)g(b)r (een)g(used)g(for)g(man)n(y)f(y)n(ears)g(in)h(the)h(study)f(of)g(parallel)150 2130 y(computer)33 b(p)r(erformance.)55 b(Ho)n(w)n(ev)n(er,)33 b(its)h(de\014nition)g(is)g(op)r(en)g(to)f(am)n(biguit)n(y)g(and)h(misuse)f (b)r(ecause)h(it)150 2230 y(alw)n(a)n(ys)26 b(b)r(egs)h(the)h(question)f (\\sp)r(eedup)h(o)n(v)n(er)d(what?")275 2329 y(Sp)r(eedup)j(is)f(usually)h (de\014ned)f(as)1795 2411 y Fs(T)1844 2423 y Fj(1)p 1794 2448 87 4 v 1794 2524 a Fs(T)1843 2536 y Fh(p)3354 2467 y Fx(\(2.5\))150 2663 y(where)20 b Fs(T)432 2675 y Fh(p)491 2663 y Fx(is)g(the)h Fs(p)p Fx(-pro)r(cessor)d(time)j(to)g(p)r(erform)f(some)g(b)r(enc)n(hmark,)h (and)g Fs(T)2562 2675 y Fj(1)2619 2663 y Fx(is)g(the)g(one-pro)r(cessor)d (time.)150 2763 y(There)28 b(is)h(no)g(doubt)g(ab)r(out)g(the)g(meaning)f(of) h Fs(T)1695 2775 y Fh(p)1762 2763 y Fx(|)g(this)g(is)g(the)g(measured)f(time) i Fs(T)12 b Fx(\()p Fs(N)d Fx(;)14 b Fs(p)p Fx(\))28 b(to)h(p)r(erform)150 2862 y(the)37 b(b)r(enc)n(hmark.)63 b(There)36 b(is)g(often)h(considerable)e (dispute)i(o)n(v)n(er)e(the)i(meaning)f(of)h Fs(T)2961 2874 y Fj(1)2997 2862 y Fx(:)55 b(should)37 b(it)g(b)r(e)150 2962 y(the)26 b(time)h(for)e(the)h(parallel)f(co)r(de)h(running)g(on)f(one)h(pro)r (cessor,)e(whic)n(h)i(probably)f(con)n(tains)g(unnecessary)150 3062 y(parallel)31 b(o)n(v)n(erhead,)h(or)f(should)h(it)h(b)r(e)g(the)g(b)r (est)g(serial)e(co)r(de)h(\(p)r(ossibly)g(using)g(a)g(di\013eren)n(t)h (algorithm\))150 3161 y(running)23 b(on)f(one)h(pro)r(cessor?)33 b(Man)n(y)23 b(scien)n(tists)f(feel)i(the)f(latter)g(is)g(a)f(more)h(resp)r (onsible)f(c)n(hoice,)h(but)h(this)150 3261 y(requires)33 b(researc)n(h)f(to) j(determine)f(the)h(b)r(est)g(practical)f(serial)f(algorithm)g(for)h(the)h (giv)n(en)f(application.)150 3361 y(If)h(at)f(a)g(later)f(time)i(a)f(b)r (etter)g(algorithm)g(is)g(found,)i(curren)n(t)d(sp)r(eedup)i(\014gures)e (migh)n(t)h(b)r(e)h(considered)150 3460 y(obsolete.)g(An)24 b(additional)f(di\016cult)n(y)h(with)g(this)g(de\014nition)h(is)e(that)h(ev)n (en)f(if)i(a)e(meaning)g(for)g Fs(T)3149 3472 y Fj(1)3210 3460 y Fx(is)h(agreed)150 3560 y(to,)j(there)g(ma)n(y)g(b)r(e)h(insu\016cien)n(t)f (memory)g(on)g(a)g(single)f(no)r(de)i(to)f(store)f(an)h(en)n(tire)g(large)f (problem.)36 b(Th)n(us)150 3659 y(in)28 b(man)n(y)f(cases)f(it)i(ma)n(y)f(b)r (e)h(imp)r(ossible)g(to)f(measure)g Fs(T)1936 3671 y Fj(1)2000 3659 y Fx(using)g(this)h(de\014nition.)275 3759 y(One)g(principal)g(ob)5 b(jectiv)n(e)28 b(in)h(the)g(\014eld)g(of)g(p)r(erformance)f(analysis)f(is)i (b)r(enc)n(hmarking:)38 b(to)28 b(compare)150 3859 y(the)40 b(p)r(erformance)e(of)h(di\013eren)n(t)g(computers.)71 b(It)39 b(is)g(generally)f(agreed)g(that)h(the)h(b)r(est)f(p)r(erformance)150 3958 y(corresp)r(onds)23 b(to)j(the)f(least)g(w)n(all-clo)r(c)n(k)f (execution)h(time.)36 b(In)26 b(order)e(to)h(adapt)g(the)h(sp)r(eedup)f (statistic)h(for)150 4058 y(b)r(enc)n(hmarking,)31 b(it)h(is)g(th)n(us)f (necessary)f(to)h(de\014ne)h(a)f(single)g(reference)f(v)-5 b(alue)31 b(of)h Fs(T)2823 4070 y Fj(1)2891 4058 y Fx(to)f(b)r(e)h(used)f (for)g(all)150 4158 y(calculations.)48 b(It)33 b(do)r(es)e(not)h(matter)g(ho) n(w)f Fs(T)1588 4170 y Fj(1)1656 4158 y Fx(is)h(de\014ned,)i(or)c(what)i(its) g(v)-5 b(alue)32 b(is,)h(only)e(that)h(the)h(same)150 4257 y(v)-5 b(alue)27 b(of)h Fs(T)508 4269 y Fj(1)572 4257 y Fx(is)g(used)g(to)f (calculate)g(all)g(sp)r(eedup)h(v)-5 b(alues)27 b(used)h(in)g(the)g (comparison.)275 4357 y(Ho)n(w)n(ev)n(er,)f(de\014ning)h Fs(T)997 4369 y Fj(1)1063 4357 y Fx(as)g(a)g(reference)g(time)h(unrelated)g(to)f(the)h (parallel)f(computer)g(b)r(eing)h(b)r(enc)n(h-)150 4456 y(mark)n(ed)e (unfortunately)g(has)h(the)g(consequence)f(that)h(man)n(y)f(prop)r(erties)g (that)h(man)n(y)f(p)r(eople)h(regard)e(as)150 4556 y(essen)n(tial)h(to)g(the) h(concept)g(of)f(parallel)g(sp)r(eedup)h(are)e(lost:)251 4739 y(1.)42 b(It)27 b(is)f(no)g(longer)g(necessarily)f(true)h(that)h(the)g(sp)r (eedup)g(of)g(the)g(parallel)f(co)r(de)g(on)g(one)h(pro)r(cessor)d(is)358 4838 y(unit)n(y)-7 b(.)37 b(It)28 b(ma)n(y)f(b)r(e,)h(but)g(only)f(b)n(y)g(c) n(hance.)251 5004 y(2.)42 b(It)27 b(is)h(no)f(longer)g(true)g(that)h(the)g (maxim)n(um)f(sp)r(eedup)h(using)g Fs(p)p Fx(-pro)r(cessors)c(is)k Fs(p)p Fx(.)1796 5428 y(13)p eop PNP restore /PNP save def 628.2618 89.4750 translate 15 bop 251 312 a Fx(3.)42 b(Because)34 b(of)h(the)h(last)f(item,)j (e\016ciency)e(\014gures)e(computed)i(as)f(sp)r(eedup)h(divided)f(b)n(y)h Fs(p)f Fx(are)f(no)358 412 y(longer)26 b(a)h(meaningful)h(measure)e(of)i(pro) r(cessor)d(utilization.)275 593 y(There)h(are)g(other)g(di\016culties)i(with) f(this)h(form)n(ulation)e(of)g(sp)r(eedup.)38 b(If)27 b(w)n(e)g(use)f Fs(T)2904 605 y Fj(1)2968 593 y Fx(as)g(the)i(run)f(time)150 692 y(on)21 b(a)g(v)n(ery)f(fast)h(single)g(pro)r(cessor)e(\(curren)n(tly)-7 b(,)22 b(sa)n(y)-7 b(,)22 b(a)f(Cra)n(y)e(C90)i(or)f(a)h(NEC)g(SX-3\),)i (then)e(man)n(ufacturers)150 792 y(of)27 b(highly)g(parallel)f(systems)h (will)g(b)r(e)h(reluctan)n(t)e(to)h(quote)g(the)h(sp)r(eedup)f(of)g(their)h (system)e(in)i(the)f(ab)r(o)n(v)n(e)150 892 y(w)n(a)n(y)-7 b(.)37 b(F)-7 b(or)27 b(example,)g(if)i(the)f(sp)r(eedup)g(of)g(a)g(100)e (pro)r(cessor)g(parallel)g(system)i(o)n(v)n(er)e(a)i(single)f(no)r(de)h(of)g (the)150 991 y(same)34 b(system)h(is)f(a)h(resp)r(ectable)f(factor)g(of)h (80,)h(it)f(is)f(lik)n(ely)h(that)g(the)g(sp)r(eedup)g(computed)g(from)g(the) 150 1091 y Fn(standar)l(d)25 b Fs(T)532 1103 y Fj(1)593 1091 y Fx(w)n(ould)f(b)r(e)g(reduced)g(to)g(10)g(or)f(less.)35 b(This)25 b(is)f(b)r(ecause)g(a)f(fast)i(v)n(ector)d(pro)r(cessor)h(is)h(t)n(ypically) 150 1191 y(at)29 b(least)g(ten)g(times)h(faster)e(than)h(the)h(RISC)f(pro)r (cessors)e(used)i(in)g(man)n(y)g(highly)g(parallel)f(systems)g(of)h(a)150 1290 y(comparable)d(generation.)275 1390 y(Th)n(us)32 b(it)h(app)r(ears)e (that)i(if)g(one)f(sharp)r(ens)g(the)h(de\014nition)g(of)f(sp)r(eedup)h(to)g (mak)n(e)f(it)h(an)f(acceptable)150 1489 y(metric)24 b(for)f(comparing)f(the) i(p)r(erformance)f(of)h(di\013eren)n(t)g(computers,)g(one)f(has)h(to)f(thro)n (w)g(a)n(w)n(a)n(y)f(the)i(main)150 1589 y(prop)r(erties)j(that)h(ha)n(v)n(e) e(made)h(the)h(concept)g(of)f(sp)r(eedup)h(useful)g(in)g(the)g(past.)275 1689 y(Accordingly)-7 b(,)26 b(the)i Fo(P)-7 b(ARKBENCH)30 b Fx(committee)e(has)f(decided)g(the)h(follo)n(wing:)251 1870 y(1.)42 b(No)27 b(sp)r(eedup)h(statistic)g(will)f(b)r(e)h(k)n(ept)g(in)g(the) g Fo(P)-7 b(ARKBENCH)29 b Fx(database.)251 2035 y(2.)42 b(Sp)r(eedup)28 b(statistics)f(based)f(on)h Fo(P)-7 b(ARKBENCH)30 b Fx(b)r(enc)n(hmarks)c(m)n (ust)h(nev)n(er)g(b)r(e)g(used)h(as)e(\014gures)358 2135 y(of)i(merit)g(when) h(comparing)e(the)h(p)r(erformance)f(of)i(di\013eren)n(t)f(systems.)39 b(W)-7 b(e)28 b(further)h(recommend)358 2234 y(that)e(sp)r(eedup)g(\014gures) f(based)h(on)g(other)f(b)r(enc)n(hmarks)g(not)h(b)r(e)h(used)f(as)f (\014gures)g(of)h(merit)g(in)g(suc)n(h)358 2334 y(comparisons.)251 2499 y(3.)42 b(Sp)r(eedup)f(statistics)f(ma)n(y)g(b)r(e)h(used)g(in)g(a)f (study)h(of)g(the)g(p)r(erformance)e(c)n(haracteristics)g(of)h(an)358 2599 y(individual)34 b(parallel)e(system.)55 b(But)34 b(the)h(basis)e(for)g (the)h(determination)g(of)f Fs(T)2885 2611 y Fj(1)2956 2599 y Fx(m)n(ust)h(b)r(e)g(clearly)358 2699 y(and)27 b(explicitly)h(stated.)251 2864 y(4.)42 b(The)37 b(v)-5 b(alue)38 b(of)f Fs(T)916 2876 y Fj(1)990 2864 y Fx(should)h(b)r(e)g(based)f(on)g(an)g(e\016cien)n(t)h (unipro)r(cessor)d(implemen)n(tation.)67 b(Co)r(de)358 2964 y(for)33 b(message)g(passing,)i(sync)n(hronization,)f(etc.)57 b(should)34 b(not)g(b)r(e)h(presen)n(t.)56 b(The)34 b(author)f(should)358 3063 y(also)38 b(mak)n(e)i(a)f(reasonable)f(e\013ort)i(to)g(insure)f(that)h (the)h(algorithm)d(used)i(in)h(the)f(unipro)r(cessor)358 3163 y(implemen)n(tation)27 b(is)h(the)g(b)r(est)g(practical)e(serial)h(algorithm) f(for)h(this)h(purp)r(ose.)251 3328 y(5.)42 b(Giv)n(en)34 b(that)h(a)f(large) g(problem)g(frequen)n(tly)g(do)r(es)g(not)h(\014t)g(on)g(a)f(single)g(no)r (de,)j(it)e(is)f(p)r(ermissible)358 3428 y(to)e(cite)h(sp)r(eedup)f (statistics)h(based)f(on)g(the)h(timing)f(of)h(a)f(smaller)f(n)n(um)n(b)r(er) h(of)h(no)r(des.)51 b(In)33 b(other)358 3528 y(w)n(ords,)28 b(it)h(is)g(p)r(ermissible)g(to)f(compute)i(sp)r(eedup)f(as)f Fs(T)2139 3540 y Fh(p)2177 3528 y Fs(=T)2268 3540 y Fh(m)2330 3528 y Fx(,)i(for)e(some)g Fs(m;)40 b Fx(1)24 b Fs(<)h(m)h(<)f(p)p Fx(.)40 b(If)30 b(this)358 3627 y(is)f(done,)h(ho)n(w)n(ev)n(er,)e(this)i (usage)f(m)n(ust)h(b)r(e)g(clearly)f(stated,)h(and)f(full)i(details)e(of)h (the)g(basis)f(of)h(this)358 3727 y(calculation)j(m)n(ust)h(b)r(e)h(presen)n (ted.)56 b(As)34 b(ab)r(o)n(v)n(e,)g(care)f(m)n(ust)i(b)r(e)f(tak)n(en)g(to)g (insure)f(that)i(the)f(unit)358 3826 y(timing)27 b Fs(T)669 3838 y Fh(m)760 3826 y Fx(is)g(based)g(on)h(an)f(e\016cien)n(t)h(implemen)n (tation)f(of)h(appropriate)e(algorithms.)150 4101 y Fp(2.7)137 b(P)l(erformance)45 b(Database)150 4283 y Fx(The)27 b(pro)r(cess)g(of)g (gathering,)f(arc)n(hiving,)g(and)h(distributing)h(computer)f(b)r(enc)n (hmark)f(data)h(is)h(a)f(cum)n(b)r(er-)150 4382 y(some)f(task)g(usually)h(p)r (erformed)f(b)n(y)g(computer)h(users)e(and)i(v)n(endors)e(with)i(little)h(co) r(ordination.)35 b(Within)150 4482 y(Xnetlib)29 b([6)o(])f(there)g(is)g(a)f (mec)n(hanism)h(to)f(pro)n(vide)g(In)n(ternet-access)f(to)i(a)f(p)r (erformance)g(database)g(serv)n(er)150 4581 y(\(PDS\))f(whic)n(h)f(can)f(b)r (e)i(used)f(to)g(extract)f(curren)n(t)g(b)r(enc)n(hmark)h(data)f(and)h (literature.)36 b(PDS)25 b([7)o(])h(pro)n(vides)150 4681 y(an)g(on-line)g (catalog)f(of)h(public-domain)g(computer)g(b)r(enc)n(hmarks)f(suc)n(h)h(as)g (the)h(LINP)-7 b(A)n(CK)25 b(Benc)n(hmark)150 4781 y([8],)34 b(P)n(erfect)e(Benc)n(hmarks)f([4],)j(and)f(the)g(NAS)h(P)n(arallel)c(Benc)n (hmarks)i([9)o(].)53 b(PDS)33 b(do)r(es)f(not)h(reformat)150 4880 y(or)h(presen)n(t)h(the)h(b)r(enc)n(hmark)e(data)h(in)h(an)n(y)e(w)n(a)n (y)g(that)i(con\015icts)f(with)h(the)f(original)f(metho)r(dology)g(of)150 4980 y(an)n(y)e(particular)f(b)r(enc)n(hmark;)j(it)f(is)f(thereb)n(y)g(dev)n (oid)g(of)g(an)n(y)g(sub)5 b(jectiv)n(e)32 b(in)n(terpretations)f(of)i(mac)n (hine)150 5080 y(p)r(erformance.)i(PDS)25 b(is)f(pro)n(viding)f(a)i(more)e (manageable)g(approac)n(h)g(to)i(the)g(dev)n(elopmen)n(t)f(and)g(supp)r(ort) 150 5179 y(of)k(a)f(large)f(dynamic)h(database)g(of)g(published)h(p)r (erformance)f(metrics.)1796 5428 y(14)p eop PNP restore PNEP %%Page: ? 9 0.6303 -612.00 PNLS /PNP save def 12.6922 89.4750 translate 16 bop 275 312 a Fx(The)31 b(PDS)h(system)g(w)n(as)f(dev)n(elop)r(ed)g(at)h (the)g(Univ)n(ersit)n(y)f(of)g(T)-7 b(ennessee)32 b(and)f(Oak)g(Ridge)h (National)150 412 y(Lab)r(oratory)21 b(and)j(is)f(an)h(initial)g(attempt)g (at)g(p)r(erformance)f(data)g(managemen)n(t.)34 b(This)24 b(on-line)f (database)150 511 y(of)41 b(computer)h(b)r(enc)n(hmarks)e(is)i(sp)r (eci\014cally)f(designed)g(to)g(pro)n(vide)g(easy)f(main)n(tenance,)45 b(data)c(secu-)150 611 y(rit)n(y)-7 b(,)35 b(and)f(data)g(in)n(tegrit)n(y)f (in)h(the)h(b)r(enc)n(hmark)e(information)g(con)n(tained)h(in)g(a)g Fn(dynamic)h Fx(p)r(erformance)150 711 y(database.)275 810 y(PDS)28 b(w)n(as)e(designed)i(with)g(a)g(simple)g(tabular)f(format)g(that)i (in)n(v)n(olv)n(es)d(displa)n(ying)h(the)h(data)f(in)i(ro)n(ws)150 910 y(\(mac)n(hine)i(con\014guration\))e(and)i(columns)g(\(n)n(um)n(b)r (ers\).)47 b(Graphical)30 b(represen)n(tations)f(of)h(tabular)h(data,)150 1010 y(suc)n(h)20 b(as)f(the)i(represen)n(tation)d(b)n(y)i(SPEC)f([10)o(])h (with)h(the)f(obsolescen)n(t)f Fn(SPECmarks)p Fx(,)k(are)c(straigh)n(tforw)n (ard.)150 1242 y Fy(2.7.1)112 b(Design)38 b(of)f(a)h(P)m(erformance)f (Database)150 1395 y Fx(Because)30 b(of)h(the)g(complexit)n(y)f(and)h(v)n (olume)f(of)g(the)i(data)e(in)n(v)n(olv)n(ed)f(in)i(a)g(p)r(erformance)f (database,)g(it)h(is)150 1495 y(natural)22 b(to)i(exploit)f(a)g(database)f (managemen)n(t)g(system)h(\(DBMS\))h(to)f(arc)n(hiv)n(e)f(and)h(retriev)n(e)f (b)r(enc)n(hmark)150 1594 y(data.)36 b(A)26 b(DBMS)h(will)f(help)h(not)f (only)f(in)i(managing)d(the)j(data,)f(but)h(also)e(in)h(assuring)e(that)j (the)f(v)-5 b(arious)150 1694 y(b)r(enc)n(hmarks)33 b(are)g(presen)n(ted)h (in)g(some)g(reasonable)e(format)h(for)h(users:)49 b(table)34 b(or)g(spreadsheet)f(where)150 1794 y(mac)n(hines)27 b(are)g Fn(r)l(ows)g Fx(and)h(b)r(enc)n(hmarks)f(are)f Fn(c)l(olumns)p Fx(.)275 1893 y(Of)i(ma)5 b(jor)27 b(concern)g(is)h(the)g(organization)e(of)i (the)h(data.)38 b(It)29 b(seems)e(logical)g(to)h(organize)f(data)g(in)i(the) 150 1993 y(DBMS)j(according)d(to)i(the)h(b)r(enc)n(hmarks)e(themselv)n(es:)44 b(a)31 b(LINP)-7 b(A)n(CK)30 b(table,)i(a)f(P)n(erfect)g(table,)h(etc.)48 b(It)150 2093 y(w)n(ould)32 b(b)r(e)i(nearly)e(imp)r(ossible)g(to)h Fn(for)l(c)l(e)h Fx(these)f(v)n(ery)f(di\013eren)n(t)h(presen)n(tation)e (formats)h(to)h(conform)f(to)150 2192 y(a)g(single)g(presen)n(tation)g (standard)f(just)i(for)f(the)h(sak)n(e)f(of)g(rep)r(orting.)51 b(Individual)33 b(tables)f(preserv)n(e)f(the)150 2292 y(displa)n(y)20 b(c)n(haracteristics)e(of)j(eac)n(h)f(b)r(enc)n(hmark,)h(but)g(the)h(DBMS)f (should)f(allo)n(w)g(users)g(to)g(query)g(all)g(tables)150 2391 y(for)26 b(v)-5 b(arious)25 b(mac)n(hines.)36 b(P)n(arsing)24 b(b)r(enc)n(hmark)h(data)h(in)n(to)g(these)h(tables)f(is)g(straigh)n(tforw)n (ard)d(pro)n(vided)i(a)150 2491 y(customized)i(parser)f(is)i(a)n(v)-5 b(ailable)26 b(for)h(eac)n(h)g(b)r(enc)n(hmark)g(set.)37 b(In)28 b(the)g(parsing)e(pro)r(cess,)h(constructing)f(a)150 2591 y(ra)n(w)31 b(data)g(\014le)h(and)g(building)g(a)g(standard)f(format)g(ASCI)r(I)i(\014le) f(eases)f(the)h(incorp)r(oration)e(of)i(the)h(data)150 2690 y(in)n(to)27 b(the)h(database.)275 2790 y(The)g(functionalit)n(y)h(required)e (b)n(y)h(PDS)h(is)f(not)h(v)n(ery)e(di\013eren)n(t)h(from)h(that)f(of)h(a)f (standard)f(database)150 2890 y(application.)42 b(The)30 b(di\013erence)f (lies)g(in)h(the)g(user)f(in)n(terface.)42 b(Financial)29 b(databases,)g(for) g(example,)g(t)n(ypi-)150 2989 y(cally)e(in)n(v)n(olv)n(e)f(sp)r(eci\014c)i (queries)f(lik)n(e)1060 3172 y(EXTRA)n(CT)g(R)n(O)n(W)h(A)n(CCT)p 1987 3172 25 4 v 30 w(NO)51 b(=)f(R103049)150 3355 y(in)23 b(whic)n(h)g(data)g(p)r(oin)n(ts)g(are)f(usually)g(discrete)h(and)g(the)g (user)g(is)f(v)n(ery)g(familiar)h(with)g(the)h(data.)35 b(The)23 b(user,)150 3454 y(in)d(this)h(case,)g(kno)n(ws)e(exactly)g(what)h(accoun)n (t)f(n)n(um)n(b)r(er)h(to)g(extract,)h(and)f(the)h(format)e(of)h(retriev)n (ed)f(data)h(in)150 3554 y(resp)r(onse)25 b(to)g(queries.)36 b(With)26 b(our)f(p)r(erformance)g(database,)g(ho)n(w)n(ev)n(er,)f(w)n(e)h(w) n(ould)g(exp)r(ect)h(the)g(con)n(trary:)150 3653 y(the)31 b(user)f(do)r(es)g (not)g(really)g(kno)n(w)f(\()p Fs(i)p Fx(\))i(what)f(kind)h(of)f(data)g(is)h (a)n(v)-5 b(ailable,)30 b(\()p Fs(ii)p Fx(\))g(ho)n(w)g(to)g(request/extract) 150 3753 y(the)i(data,)h(and)e(\()p Fs(iii)p Fx(\))g(what)h(form)g(to)f(exp)r (ect)h(the)g(returned)g(data)f(to)h(b)r(e)g(in.)50 b(These)31 b(assumptions)g(are)150 3853 y(based)g(on)h(the)g(curren)n(t)f(lac)n(k)g(of)h (co)r(ordination)e(in)i(\(public-domain\))g(b)r(enc)n(hmark)f(managemen)n(t.) 49 b(The)150 3952 y(n)n(um)n(b)r(er)28 b(of)f(b)r(enc)n(hmarks)g(in)h(use)g (con)n(tin)n(ues)f(to)h(rise)f(with)h(no)g(standard)f(format)g(for)h(presen)n (ting)e(them.)150 4052 y(The)j(n)n(um)n(b)r(er)f(of)h(p)r (erformance-literate)e(users)g(is)i(increasing,)f(but)h(not)g(at)f(a)g(rate)g (su\016cien)n(t)h(to)g(exp)r(ect)150 4152 y(prop)r(er)h(queries)g(from)h(the) g(p)r(erformance)f(database.)45 b(Quite)31 b(often,)h(users)e(just)i(wish)e (to)h(see)g(the)g(b)r(est-)150 4251 y(p)r(erforming)e(mac)n(hines)h(for)f(a)h (particular)f(b)r(enc)n(hmark.)44 b(Hence,)31 b(a)f(simple)g(rank-ordering)d (of)j(the)h Fn(r)l(ows)150 4351 y Fx(of)d(mac)n(hines)e(according)g(to)i(a)f (sp)r(eci\014c)h(b)r(enc)n(hmark)f Fn(c)l(olumn)g Fx(ma)n(y)g(b)r(e)h (su\016cien)n(t)g(for)f(a)g(general)f(user.)275 4450 y(Finally)-7 b(,)27 b(the)h(features)f(of)h(the)g(PDS)f(user)g(in)n(terface)g(should)h (include)150 4616 y Ft(\(1\))42 b Fx(the)27 b(abilit)n(y)h(to)f(extract)g(sp) r(eci\014c)h(mac)n(hine)f(and)g(b)r(enc)n(hmark)g(com)n(binations)g(that)h (are)e(of)i(in)n(terest,)150 4783 y Ft(\(2\))42 b Fx(the)27 b(abilit)n(y)h(to)f(searc)n(h)f(on)i(m)n(ultiple)g(k)n(eyw)n(ords)d(across)h (the)i(en)n(tire)f(dataset,)g(and)150 4949 y Ft(\(3\))42 b Fx(the)20 b(abilit)n(y)h(to)f(view)g(cross-referenced)e(pap)r(ers)i(and)h (bibliographic)e(information)h(ab)r(out)g(the)h(b)r(enc)n(h-)358 5048 y(mark)26 b(itself.)1796 5428 y(15)p eop PNP restore /PNP save def 628.2618 89.4750 translate 17 bop 275 312 a Fx(W)-7 b(e)31 b(include)g(\(3\))g(in)g(the)g(list)g(ab)r(o) n(v)n(e)e(to)i(address)e(the)j(concern)d(of)i(proliferating)e(n)n(um)n(b)r (ers)i(without)150 412 y(an)n(y)24 b(b)r(enc)n(hmark)h(metho)r(dology)f (information.)35 b(PDS)26 b(w)n(ould)f(pro)n(vide)f(abstracts)g(and)h (complete)g(pap)r(ers)150 511 y(related)37 b(to)h(b)r(enc)n(hmarks)g(and)g (thereb)n(y)f(pro)n(vide)g(a)h(needed)g(educational)f(resource)g(without)h (risking)150 611 y(improp)r(er)27 b(in)n(terpretation)f(of)i(retriev)n(ed)e (b)r(enc)n(hmark)h(data.)150 842 y Fy(2.7.2)112 b(PDS)38 b(F)-9 b(eatures)150 996 y Fx(PDS)28 b(pro)n(vides)e(the)i(follo)n(wing)e(retriev)-5 b(al-based)26 b(functions)i(for)f(the)h(user:)150 1156 y Ft(\(1\))42 b Fx(a)g Fn(br)l(owse)h Fx(feature)f(to)h(allo)n(w)e(casual)h(viewing)g(and)h (p)r(oin)n(t-and-clic)n(k)e(na)n(vigation)g(through)h(the)358 1256 y(database,)150 1419 y Ft(\(2\))g Fx(a)27 b Fn(se)l(ar)l(ch)h Fx(feature)f(to)h(p)r(ermit)g(m)n(ultiple)g(k)n(eyw)n(ord)e(searc)n(hes)f (with)k(Bo)r(olean)d(conditions,)150 1582 y Ft(\(3\))42 b Fx(a)27 b Fn(r)l(ank-or)l(dering)h Fx(feature)g(to)f(sort)g(and)g(displa)n(y)g(the)h (results)f(for)g(the)h(user,)f(and)150 1745 y Ft(\(4\))42 b Fx(a)32 b(few)h(additional)g(features)f(that)h(aid)g(the)g(user)g(in)g (acquiring)e(b)r(enc)n(hmark)i(do)r(cumen)n(tation)f(and)358 1845 y(references.)275 2005 y(As)h(discussed)h(in)g([7],)h(the)f Fk(Rank)42 b(Ordering)31 b Fx(option)i(in)i(PDS)e(allo)n(ws)g(the)h(user)f (to)h(view)g(a)f(listing)150 2105 y(of)i(mac)n(hines)f(that)h(ha)n(v)n(e)f(b) r(een)h(rank)n(ed)f(b)n(y)g(a)h(particular)e(p)r(erformance)h(metric)h(suc)n (h)g(as)f(mega\015op/s)150 2204 y(or)g(elapsed)g(CPU)h(time.)59 b(Both)34 b Fk(Rank)42 b(Ordering)32 b Fx(and)i Fk(Papers)f Fx(options)h(are)g(men)n(u-driv)n(en)g(data)g(ac-)150 2304 y(cess)29 b(paths)h(within)h(PDS.)f(With)h(the)g Fk(Browse)d Fx(facilit)n(y)h(in)i(PDS,)f(the)h(user)e(\014rst)h(selects)g(the)g(v)n (endor\(s\))150 2404 y(and)39 b(b)r(enc)n(hmark\(s\))g(of)g(in)n(terest,)j (then)e(selects)e(the)i(large)e Fk(Process)e Fx(button)k(to)f(query)f(the)i (p)r(erfor-)150 2503 y(mance)c(database.)60 b(The)36 b(PDS)g(clien)n(t)g (then)g(op)r(ens)g(a)f(so)r(c)n(k)n(et)g(connection)h(to)f(the)i(serv)n(er)d (and,)j(using)150 2603 y(the)27 b(query)f(language)e(\(rdb\),)j(remotely)f (queries)g(the)h(database.)35 b(The)26 b Fk(Search)e Fx(option)j(in)f(PDS)h (p)r(ermits)150 2703 y(user-sp)r(eci\014ed)i(k)n(eyw)n(ord)e(searc)n(hes)h(o) n(v)n(er)g(the)i(en)n(tire)f(p)r(erformance)f(database.)42 b Fk(Search)27 b Fx(utilizes)j(literal)150 2802 y(case-insensitiv)n(e)g(matc) n(hing)h(along)g(with)h(a)f(mo)r(derate)g(amoun)n(t)g(of)h(aliasing.)48 b(Multiple)33 b(k)n(eyw)n(ords)c(are)150 2902 y(p)r(ermitted,)h(and)f(a)g(Bo) r(olean)f(\015ag)g(is)h(pro)n(vided)f(for)h(more)f(complicated)h(searc)n (hes.)40 b(Using)29 b Fk(Search)p Fx(,)e(the)150 3001 y(user)h(has)g(the)g (option)g(of)h(en)n(tering)e(v)n(endor)g(names,)i(mac)n(hine)e(aliases,)h(b)r (enc)n(hmark)f(names,)h(or)g(sp)r(eci\014c)150 3101 y(strings,)i(or)g(pro)r (ducing)g(a)g(more)f(complicated)h(Bo)r(olean)g(k)n(eyw)n(ord)e(searc)n(h.)44 b(Since)31 b(an)n(y)e(retriev)n(ed)h(data)150 3201 y(will)g(b)r(e)g(displa)n (y)n(ed)f(to)h(the)g(screen)f(\(b)n(y)h(default\),)h(the)f Fk(Save)e Fx(option)i(allo)n(ws)e(the)i(user)f(to)h(store)f(an)n(y)g(re-)150 3300 y(triev)n(ed)23 b(p)r(erformance)f(data)h(to)h(an)f(ASCI)r(I)h(\014le.) 36 b(Finally)-7 b(,)24 b(the)g Fk(Bibliography)19 b Fx(option)k(in)h(PDS)g (pro)n(vides)150 3400 y(a)k(list)g(of)g(relev)-5 b(an)n(t)27 b(man)n(uscripts)g(and)h(other)g(information)f(ab)r(out)h(the)g(b)r(enc)n (hmarks.)37 b(F)-7 b(uture)29 b(enhance-)150 3500 y(men)n(ts)34 b(to)g(PDS)g(include)g(the)g(use)g(of)g(more)f(sophisticated)g(t)n(w)n (o-dimensional)f(graphical)h(displa)n(ys)g(for)150 3599 y(mac)n(hine)20 b(comparisons.)33 b(Additional)21 b(serial)e(and)i(parallel)e(b)r(enc)n (hmarks)h(will)h(b)r(e)g(added)g(to)f(the)h(database)150 3699 y(as)30 b(formal)g(pro)r(cedures)g(for)h(data)f(acquisition)g(are)g (determined.)47 b(The)31 b Fk(Browse)e Fx(and)i Fk(Search)d Fx(facilities)150 3798 y(a)n(v)-5 b(ailable)26 b(in)i(the)g(curren)n(t)f(v)n (ersion)f(of)h(PDS)h(are)f(illustrated)g(in)h(App)r(endix)h(B.)150 4030 y Fy(2.7.3)112 b(PDS)38 b(Av)-6 b(ailabilit)m(y)150 4183 y Fx(T)f(o)27 b(receiv)n(e)f(Xnetlib)h(with)h(PDS)f(supp)r(ort)g(for)g (Unix-based)f(mac)n(hines,)h(send)g(the)g(electronic)g(mail)f(mes-)150 4283 y(sage)e Fn(send)k(xnetlib.shar)h(fr)l(om)f(xnetlib)d Fx(to)h Fk(netlib@ornl.gov)o Fx(.)31 b(Y)-7 b(ou)25 b(can)g Fn(unshar)h Fx(the)f(\014le)h(and)f(compile)150 4382 y(it)34 b(b)n(y)g(answ)n(ering)f(the)h(user-prompted)f(questions)g(up)r(on)i (installation.)55 b(Use)34 b(of)g Fn(shar)h Fx(will)g(install)f(the)150 4482 y(full)27 b(functionalit)n(y)g(of)g(Xnetlib)g(along)e(with)j(the)f (latest)f(PDS)h(clien)n(t)g(to)r(ol.)36 b(Questions)26 b(concerning)f(PDS)150 4581 y(should)j(b)r(e)h(sen)n(t)f(to)g Fk(utpds@cs.utk.ed)o(u.)k Fx(The)c(Univ)n(ersit)n(y)g(of)g(T)-7 b(ennessee)28 b(and)g(Oak)f(Ridge)h (National)150 4681 y(Lab)r(oratory)d(will)i(b)r(e)g(resp)r(onsible)g(for)f (gathering)g(and)h(arc)n(hiving)e(additional)i(\(published\))h(b)r(enc)n (hmark)150 4781 y(data.)275 4880 y(A)n(t)33 b(presen)n(t)f(eac)n(h)g(b)r(enc) n(hmark)g(measuremen)n(t)g(for)g(a)g(particular)f(problem)i(size)f Fs(N)42 b Fx(and)32 b(pro)r(cessor)150 4980 y(n)n(um)n(b)r(er)26 b Fs(p)p Fx(,)h(is)f(represen)n(ted)f(b)n(y)h(one)g(line)h(in)g(the)g (database)e(with)i(v)-5 b(ariable)25 b(length)i(\014elds)f(c)n(hosen)g(b)n(y) g(the)150 5080 y(b)r(enc)n(hmark)f(writer)g(as)g(suitable)g(and)h (comprehensiv)n(e)e(to)i(describ)r(e)f(the)h(conditions)f(of)h(the)g(b)r(enc) n(hmark)150 5179 y(run.)64 b(The)37 b(\014elds)g(separated)f(b)n(y)g(a)h (mark)n(er)e(include,)k(b)r(enc)n(hmark)n(ers)c(name)i(and)g(e-mail,)h (computer)1796 5428 y(16)p eop PNP restore PNEP %%Page: ? 10 0.6303 -612.00 PNLS /PNP save def 12.6922 89.4750 translate 18 bop 150 312 a Fx(lo)r(cation)21 b(and)h(date,)i(hardw)n(are)c(sp)r (eci\014cation,)i(compiler)g(date)g(and)g(optimisation)g(lev)n(el,)g Fs(N)9 b Fx(,)23 b Fs(p)p Fx(,)h Fs(T)12 b Fx(\()p Fs(N)t(;)i(p)p Fx(\),)150 412 y Fs(R)213 424 y Fh(B)270 412 y Fx(\()p Fs(N)t(;)g(P)e Fx(\))24 b(and)f(other)g(metrics)g(as)f(deemed)i(appropriate)d(b)n(y)i(the)h (b)r(enc)n(hmark)f(writer.)34 b(Ideally)-7 b(,)24 b(the)g(line)150 511 y(for)e(the)g(database)f(w)n(ould)h(b)r(e)g(pro)r(duced)g(automatically)f (as)h(output)h(b)n(y)e(the)i(b)r(enc)n(hmark)e(program)g(itself.)150 786 y Fp(2.8)137 b(In)l(teractiv)l(e)47 b(Graphical)g(In)l(terface)150 968 y Fx(The)40 b(Southampton)g(Group)f(has)h(agreed)e(to)i(pro)n(vide)f(an)g (in)n(teractiv)n(e)g(graphical)f(fron)n(t)i(end)g(to)g(the)150 1067 y Fo(P)-7 b(ARKBENCH)30 b Fx(database)d(of)i(p)r(erformance)f(results.) 40 b(T)-7 b(o)29 b(ac)n(hiev)n(e)f(this,)h(the)h(basic)e(data)g(held)i(in)f (the)150 1167 y(P)n(erformance)g(Data)h(Base)g(should)h(b)r(e)g(v)-5 b(alues)30 b(of)h Fs(T)12 b Fx(\()p Fs(N)d Fx(;)14 b Fs(p)p Fx(\))30 b(for)g(at)h(least)g(4)f(v)-5 b(alues)31 b(of)f(problem)h(size)f Fs(N)9 b Fx(,)150 1267 y(eac)n(h)19 b(for)h(su\016cien)n(t)g Fs(p)p Fx(-v)-5 b(alues)19 b(\(sa)n(y)g(5)g(to)h(10\))g(to)g(determine)g(the) g(trend)g(of)g(v)-5 b(ariation)19 b(of)h(p)r(erformance)f(with)150 1366 y(n)n(um)n(b)r(er)24 b(of)h(pro)r(cessors)d(for)j(constan)n(t)f(problem) g(size.)35 b(It)25 b(is)g(imp)r(ortan)n(t)f(that)h(there)g(b)r(e)g(enough)f Fs(p)p Fx(-v)-5 b(alues)150 1466 y(to)35 b(see)f(Amdahl)h(saturation,)h(if)f (presen)n(t,)h(or)e(an)n(y)g(p)r(eak)h(in)g(p)r(erformance)e(follo)n(w)n(ed)h (b)n(y)h(degradation.)150 1566 y(A)e(graphical)f(in)n(terface)g(is)h(really)e (essen)n(tial)h(to)h(allo)n(w)f(this)h(m)n(ultidimensional)g(data)f(to)h(b)r (e)g(view)n(ed)g(in)150 1665 y(an)n(y)28 b(of)g(the)h(metrics)f(de\014ned)h (ab)r(o)n(v)n(e,)e(as)h(c)n(hosen)g(in)n(teractiv)n(ely)f(b)n(y)h(the)h (user.)39 b(The)28 b(user)g(could)g(also)g(b)r(e)150 1765 y(o\013ered)h(\(b)n (y)g(suitable)g(in)n(terp)r(olation\))f(a)h(displa)n(y)f(of)i(the)f(results)g (in)g(v)-5 b(arious)28 b(scaled)g(metrics,)i(in)f(whic)n(h)150 1864 y(the)f(problem)f(size)g(is)h(expanded)f(with)h(the)g(n)n(um)n(b)r(er)g (of)f(pro)r(cessors.)275 1964 y(In)20 b(order)f(to)h(encompass)f(as)h(wide)h (a)f(range)f(of)h(p)r(erformance)f(and)h(n)n(um)n(b)r(er)g(of)h(pro)r (cessors)d(as)h(p)r(ossible,)150 2064 y(a)28 b(log-scale)f(on)i(b)r(oth)g (axes)f(is)g(una)n(v)n(oidable,)g(and)g(the)h(format)g(and)f(scale)g(range)g (should)g(b)r(e)h(k)n(ept)g(\014xed)150 2163 y(as)i(long)g(as)h(p)r(ossible)f (to)h(enable)f(easy)g(comparison)f(b)r(et)n(w)n(een)i(graphs.)48 b(A)33 b(three-cycle)d(b)n(y)i(three-cycle)150 2263 y(log-log)j(graph)h(with) h(range)e(1)i(to)g(1000)e(in)i(b)r(oth)g Fs(p)g Fx(and)g(M\015op/s)f(w)n (ould)g(co)n(v)n(er)f(most)i(needs)g(in)g(the)150 2363 y(immediate)28 b(future.)37 b(Examples)27 b(of)g(suc)n(h)g(graphs)g(are)f(to)i(b)r(e)g (found)g(in)g([11)o(,)f(12)o(].)275 2462 y(A)36 b(log/log)e(graph)h(is)i (also)e(desirable)g(b)r(ecause)h(the)h(size)f(and)g(shap)r(e)g(of)g(the)h (Amdahl)f(saturation)150 2562 y(curv)n(e)29 b(is)h(the)g(same)g(wherev)n(er)e (it)j(is)f(plotted)g(on)g(suc)n(h)g(a)f(graph.)43 b(That)30 b(is)g(to)g(sa)n(y)f(there)h(is)g(a)f(univ)n(ersal)150 2661 y(Amdahl)h(curv)n(e)e(that)i(is)g(in)n(v)-5 b(arian)n(t)28 b(to)h(its)h(p)r(osition)f(on)h(an)n(y)e(log/log)g(graph.)41 b(Amdahl)30 b(saturation)e(is)h(a)150 2761 y(t)n(w)n(o-parameter)f (description)h(of)i(an)n(y)e(of)i(the)f(p)r(erformance)g(metrics,)g Fs(R)q Fx(,)h(as)f(a)g(function)h(of)f Fs(p)g Fx(for)g(\014xed)150 2861 y Fs(N)9 b Fx(,)27 b(whic)n(h)h(can)f(b)r(e)h(expressed)f(b)n(y)1548 2998 y Fs(R)d Fx(=)1858 2942 y Fs(R)1921 2954 y Fg(1)p 1732 2979 385 4 v 1732 3055 a Fx(\(1)18 b(+)g Fs(p)1959 3053 y Ff(1)p 1959 3062 29 4 v 1959 3096 a(2)2002 3055 y Fs(=p)p Fx(\))3354 2998 y(\(2.6\))150 3211 y(where)39 b Fs(R)465 3223 y Fg(1)575 3211 y Fx(is)h(the)g(saturation)f(p)r(erformance)g(approac)n(hed)e(as)j Fs(p)j Fi(!)g(1)d Fx(and)g Fs(p)2851 3209 y Ff(1)p 2850 3218 V 2850 3252 a(2)2893 3211 y Fx(is)f(the)i(n)n(um)n(b)r(er)e(of)150 3311 y(pro)r(cessors)27 b(required)g(to)i(reac)n(h)f(half)h(the)g(saturation) f(p)r(erformance.)40 b(The)29 b(graphical)e(in)n(terface)h(should)150 3411 y(allo)n(w)c(this)i(univ)n(ersal)e(Amdahl)i(curv)n(e)f(to)g(b)r(e)h(mo)n (v)n(ed)e(around)h(the)h(graphical)e(displa)n(y)-7 b(,)25 b(and)g(b)r(e)h (matc)n(hed)150 3510 y(against)k(the)h(p)r(erformance)f(curv)n(es.)45 b(The)31 b(c)n(hanging)e(v)-5 b(alues)31 b(of)g(the)g(t)n(w)n(o)f(parameters) f(\()p Fs(R)3069 3522 y Fg(1)3140 3510 y Fx(,)p Fs(p)3215 3508 y Ff(1)p 3215 3517 V 3215 3551 a(2)3257 3510 y Fx(\)should)150 3610 y(b)r(e)f(displa)n(y)n(ed)f(as)f(the)i(Amdahl)g(curv)n(e)f(is)g(mo)n(v)n (ed.)275 3709 y(As)i(more)g(exp)r(erience)f(is)i(gained)e(with)i(p)r (erformance)f(analysis,)f(that)i(is)f(to)g(sa)n(y)g(the)g(\014tting)h(of)f(p) r(er-)150 3809 y(formance)35 b(data)g(to)h(parameterised)e(form)n(ulae,)i(it) g(is)g(to)g(b)r(e)g(exp)r(ected)g(that)g(the)g(graphical)e(in)n(terface)150 3909 y(will)g(allo)n(w)f(more)g(complicated)g(form)n(ulae)g(to)g(b)r(e)i (compared)d(with)i(the)h(exp)r(erimen)n(tal)e(data,)i(p)r(erhaps)150 4008 y(allo)n(wing)23 b(3)h(to)g(5)g(parameters)e(in)j(the)f(theoretical)g (form)n(ula.)35 b(But,)25 b(as)e(y)n(et,)i(w)n(e)f(do)g(not)g(kno)n(w)g(what) g(these)150 4108 y(for)j(parameterised)f(form)n(ula)h(should)g(b)r(e.)150 4382 y Fp(2.9)137 b(Benc)l(hmarking)46 b(Pro)t(cedure)f(and)i(Co)t(de)f (Optimisation)150 4564 y Fx(Man)n(ufacturers)32 b(will)i(alw)n(a)n(ys)e(feel) i(that)f(an)n(y)g(b)r(enc)n(hmark)g(not)h(tuned)g(sp)r(eci\014cally)f(b)n(y)h (themselv)n(es,)g(is)150 4664 y(an)29 b(unfair)h(test)g(of)f(their)h(hardw)n (are)d(and)j(soft)n(w)n(are.)41 b(This)30 b(is)f(inevitable)h(and)f(from)h (their)f(viewp)r(oin)n(t)h(it)150 4764 y(is)d(true.)37 b(NASA)28 b(ha)n(v)n(e)e(o)n(v)n(ercome)f(this)j(problem)f(b)n(y)g(only)f(sp)r (ecifying)i(the)f(problems)g(\(the)h(NAS)g(pap)r(er-)150 4863 y(and-p)r(encil)33 b(b)r(enc)n(hmarks)f([13)o(]\))i(and)f(lea)n(ving)f(the)h (man)n(ufacturers)f(to)h(write)g(the)g(co)r(de,)i(but)e(in)h(man)n(y)150 4963 y(circumstances)29 b(this)i(w)n(ould)f(require)f(unjusti\014able)i (e\013ort)f(and)g(tak)n(e)g(to)r(o)g(long.)44 b(It)31 b(is)f(also)f(a)h(p)r (erfectly)150 5062 y(v)-5 b(alid)23 b(question)f(to)h(ask)e(ho)n(w)h(a)h (particular)e(parallel)h(computer)g(will)h(p)r(erform)f(on)g(existing)h (parallel)e(co)r(de,)150 5162 y(and)27 b(that)h(is)g(the)g(viewp)r(oin)n(t)f (of)h Fo(P)-7 b(ARKBENCH)29 b Fx(.)1796 5428 y(17)p eop PNP restore /PNP save def 628.2618 89.4750 translate 19 bop 275 312 a Fx(The)31 b(b)r(enc)n(hmarking)f(pro)r(cedure)g(is)i(to)f (run)g(the)h(distributed)f Fo(P)-7 b(ARKBENCH)30 b Fx(suite)h(on)g(an)h Fn(as-is)150 412 y Fx(basis,)25 b(making)g(only)h(suc)n(h)f(non-substan)n (tiv)n(e)g(c)n(hanges)f(that)i(are)f(required)f(to)i(mak)n(e)f(the)h(co)r(de) g(run)f(\(e.g.)150 511 y(c)n(hanging)f(the)i(names)f(of)g(header)g(\014les)g (to)h(a)f(lo)r(cal)g(v)-5 b(arian)n(t\).)35 b(The)26 b(as-is)e(run)h(ma)n(y)g (use)g(the)h(highest)g(lev)n(el)150 611 y(of)31 b(automatic)f(compiler)g (optimisation)g(that)h(w)n(orks,)e(but)j(the)f(lev)n(el)f(used)g(and)h (compiler)f(date)g(should)150 711 y(b)r(e)e(noted)g(in)f(the)h(appropriate)e (section)i(of)f(the)h(p)r(erformance)f(database)f(en)n(try)-7 b(.)275 810 y(After)22 b(completing)f(the)h(as-is)e(run,)j(whic)n(h)f(giv)n (es)e(a)h(base-line)g(result,)i(an)n(y)e(form)g(of)h(optimisation)f(ma)n(y) 150 910 y(b)r(e)j(applied)g(to)g(sho)n(w)f(the)h(particular)e(computer)i(to)g (its)g(b)r(est)g(adv)-5 b(an)n(tage,)23 b(up)h(to)g(completely)f(rethinking) 150 1010 y(the)29 b(algorithm,)f(and)h(rewriting)f(the)h(co)r(de.)40 b(The)29 b(only)f(requiremen)n(t)g(on)h(the)g(b)r(enc)n(hmark)n(er)e(is)i(to) f(state)150 1109 y(what)j(has)f(b)r(een)h(done.)46 b(Ho)n(w)n(ev)n(er,)30 b(remem)n(b)r(er)g(that,)h(ev)n(en)g(if)g(the)g(algorithm)f(is)g(c)n(hanged,) h(the)g(o\016cial)150 1209 y(\015op-coun)n(t,)g Fs(F)620 1221 y Fh(B)677 1209 y Fx(\()p Fs(N)9 b Fx(\))31 b(that)g(is)g(used)g(in)g(the)g (calculation)f(of)g(nominal)h(b)r(enc)n(hmark)f(M\015op/s,)g Fs(R)3230 1221 y Fh(B)3288 1209 y Fx(\()p Fs(N)t(;)14 b(p)p Fx(\),)150 1308 y(do)r(es)27 b(not.)36 b(In)28 b(this)f(w)n(a)n(y)f(a)g(b)r (etter)i(algorithm)d(will)j(sho)n(w)e(up)h(with)g(a)g(higher)f Fs(R)2695 1320 y Fh(B)2753 1308 y Fx(,)h(as)f(w)n(e)h(w)n(ould)f(w)n(an)n(t)h (it)150 1408 y(to,)h(ev)n(en)f(though)g(the)h(hardw)n(are)e(M\015op/s)g(is)i (lik)n(ely)f(to)g(b)r(e)h(little)h(c)n(hanged.)275 1508 y(T)n(ypical)d(steps) i(in)g(optimisation)f(migh)n(t)g(b)r(e:)251 1674 y(1.)42 b(explore)30 b(the)h(e\013ect)h(of)g(di\013eren)n(t)f(compiler)g(optimisations)f(on)h(a)g (single)g(pro)r(cessor,)f(and)h(c)n(ho)r(ose)358 1773 y(the)d(b)r(est)g(for)f (the)h(as-is)e(run.)251 1939 y(2.)42 b(p)r(erform)25 b(the)i(as-is)e(run)h (on)g(m)n(ultiple)g(pro)r(cessors,)e(using)i(enough)g(v)-5 b(alues)25 b(of)i Fs(p)f Fx(to)g(determine)g(an)n(y)358 2039 y(p)r(eak)h(in)h(p)r(erformance)e(or)h(saturation.)251 2205 y(3.)42 b(return)33 b(to)g(single)g(pro)r(cessor)e(and)j(optimise)f(co)r(de)g (for)g(v)n(ectorisation,)h(if)g(a)f(v)n(ector)f(pro)r(cessor)f(is)358 2305 y(b)r(eing)c(used.)37 b(This)28 b(means)f(restructuring)f(lo)r(ops)h(to) h(p)r(ermit)g(v)n(ectorisation.)251 2471 y(4.)42 b(con)n(tin)n(ue)26 b(b)n(y)h(replacemen)n(t)f(of)h(selected)g(lo)r(ops)f(with)h(optimal)g(assem) n(bly)f(co)r(ded)h(library)f(routines)358 2570 y(\(e.g.)36 b(BLAS)28 b([14)o(])g(where)f(appropriate\).)251 2736 y(5.)42 b(replacemen)n(t)23 b(of)g(whole)h(b)r(enc)n(hmark)f(b)n(y)h(a)f(tuned)i (library)d(routine)i(with)g(the)h(same)e(functionalit)n(y)-7 b(.)251 2902 y(6.)42 b(replace)30 b(whole)i(b)r(enc)n(hmark)f(with)i(lo)r (cally)e(written)h(v)n(ersion)e(with)j(the)f(same)g(functionalit)n(y)f(but) 358 3002 y(using)c(p)r(ossibly)g(an)g(en)n(tirely)g(di\013eren)n(t)h (algorithm)e(that)i(is)g(more)f(suited)h(to)f(the)h(arc)n(hitecture.)1796 5428 y(18)p eop PNP restore PNEP %%Page: ? 11 0.6303 -612.00 PNLS /PNP save def 12.6922 89.4750 translate 20 bop 150 935 a Fr(Chapter)66 b(3)150 1350 y Fu(Lo)-7 b(w-Lev)g(el)79 b(Benc)-7 b(hmarks)2552 1287 y Fq(\003)150 1832 y Fp(3.1)137 b(In)l(tro)t(duction)150 2013 y Fx(The)25 b(\014rst)f(step)g(in)h(the)g (assessmen)n(t)e(of)i(the)f(p)r(erformance)g(of)g(a)g(massiv)n(ely)g (parallel)f(computer)h(system)g(is)150 2113 y(to)h(measure)e(the)i(p)r (erformance)f(of)h(a)f(single)g(pro)r(cessing)g(no)r(de)h(of)f(the)h(m)n (ulti-no)r(de)g(system.)36 b(There)24 b(exist)150 2213 y(already)h(man)n(y)h (go)r(o)r(d)h(and)f(w)n(ell-established)g(b)r(enc)n(hmarks)g(for)g(this)h (purp)r(ose,)f(notably)h(the)g(LINP)-7 b(A)n(CK)150 2312 y(b)r(enc)n(hmarks) 35 b(and)h(the)g(Liv)n(ermore)e(Lo)r(ops.)61 b(These)35 b(are)g(not)h(part)f (of)h(the)g Fo(P)-7 b(ARKBENCH)30 b Fx(suite)36 b(of)150 2412 y(programs,)31 b(but)i Fo(P)-7 b(ARKBENCH)29 b Fx(recommends)i(that)i(these)f (b)r(e)g(used)g(to)g(measure)f(single-no)r(de)g(p)r(er-)150 2511 y(formance,)k(in)g(addition)g(to)f(some)g(sp)r(eci\014c)h(lo)n(w-lev)n (el)e(measuremen)n(ts)g(of)i(its)g(o)n(wn)f(\(see)g(Section)h(3.2\).)150 2611 y(There)25 b(follo)n(ws)f(a)h(brief)h(description)f(of)g(existing)g(b)r (enc)n(hmarks)f(that)i(are)f(recommended)f(for)h(measuring)150 2711 y(single-no)r(de)i(p)r(erformance,)f(with)i(a)g(discussion)e(of)i(their) g(v)-5 b(alue.)150 2943 y Fy(3.1.1)112 b(Most)38 b(Rep)s(orted)f(Benc)m (hmark:)50 b(LINP)-9 b(A)m(CKD)35 b(\(n=100\))150 3096 y Fx(This)g(w)n (ell-kno)n(wn)f(standard)g(b)r(enc)n(hmark)g(is)h(a)g(F)-7 b(ortran)34 b(program)f(for)i(the)g(solution)g(of)g(\(100)22 b Fi(\002)h Fx(100\))150 3196 y(dense)30 b(set)h(of)f(linear)g(equations)f(b) n(y)h(Gaussian)g(elimination.)45 b(It)31 b(is)f(distributed)h(b)n(y)f(Jac)n (k)f(Dongarra)f(of)150 3296 y(the)c(Univ)n(ersit)n(y)g(of)g(T)-7 b(ennessee)23 b([8].)35 b(The)25 b(results)e(are)g(quoted)h(in)g(M\015op/s)g (and)f(are)g(regularly)g(published)150 3395 y(and)k(a)n(v)-5 b(ailable)25 b(b)n(y)i(electronic)f(mail.)36 b(The)27 b(main)g(v)-5 b(alue)27 b(of)g(this)g(b)r(enc)n(hmark)f(is)h(that)g(results)f(are)g(kno)n (wn)150 3495 y(for)34 b(more)g(computers)f(than)i(an)n(y)e(other)h(b)r(enc)n (hmark.)57 b(Most)34 b(of)h(the)f(compute)h(time)g(is)f(con)n(tained)g(in)150 3595 y(v)n(ectorisable)19 b(DO-lo)r(ops)g(suc)n(h)i(as)f(the)h(D)n(AXPY)g (\(scalar)e(times)i(v)n(ector)f(plus)g(v)n(ector\))g(and)h(inner)f(pro)r (duct.)150 3694 y(Therefore)25 b(one)h(exp)r(ects)h(v)n(ector)e(computers)h (to)g(p)r(erform)g(w)n(ell)g(on)g(this)h(b)r(enc)n(hmark.)36 b(The)26 b(w)n(eakness)f(of)150 3794 y(the)31 b(b)r(enc)n(hmark)e(is)h(that)g (it)h(tests)f(only)g(a)g(small)f(n)n(um)n(b)r(er)h(of)g(v)n(ector)f(op)r (erations,)h(but)g(it)h(do)r(es)f(include)150 3893 y(the)e(e\013ect)g(of)g (memory)e(access)h(and)g(it)h(is)g(solving)e(a)h(complete)h(\(although)f (small\))h(real)e(problem.)150 4126 y Fy(3.1.2)112 b(P)m(erformance)37 b(Range:)51 b(The)38 b(Liv)m(ermore)e(Lo)s(ops)150 4279 y Fx(These)h(are)f(a) h(set)h(of)f(24)f(F)-7 b(ortran)36 b(DO-lo)r(ops)h(\(The)g(Liv)n(ermore)f(F) -7 b(ortran)36 b(Kernels,)i(LFK\))g(extracted)150 4379 y(from)29 b(op)r(erational)f(co)r(des)g(used)i(at)f(the)g(La)n(wrence)f(Liv)n(ermore)f (National)i(Lab)r(oratory)e([5)o(].)42 b(They)29 b(ha)n(v)n(e)150 4478 y(b)r(een)36 b(used)g(since)f(the)h(early)f(sev)n(en)n(ties)f(to)i (assess)e(the)i(arithmetic)f(p)r(erformance)g(of)g(computers)g(and)150 4578 y(their)24 b(compilers.)35 b(They)24 b(are)f(a)h(mixture)g(of)g(v)n (ectorisable)e(and)i(non-v)n(ectorisable)e(lo)r(ops)i(and)g(test)g(rather)150 4678 y(fully)g(the)h(computational)e(capabilities)g(of)h(the)g(hardw)n(are,)f (and)g(the)i(skill)e(of)h(the)g(soft)n(w)n(are)e(in)i(compiling)150 4777 y(e\016cien)n(t)35 b(co)r(de,)h(and)f(in)g(v)n(ectorisation.)56 b(The)35 b(main)g(v)-5 b(alue)35 b(of)f(the)h(b)r(enc)n(hmark)g(is)f(the)h (range)f(of)g(p)r(er-)150 4877 y(formance)27 b(that)h(it)h(demonstrates,)e (and)h(in)g(this)h(resp)r(ect)f(it)g(complemen)n(ts)g(the)g(limited)h(range)e (of)h(lo)r(ops)150 4976 y(tested)i(in)g(the)f(LINP)-7 b(A)n(CK)29 b(b)r(enc)n(hmark.)42 b(The)29 b(b)r(enc)n(hmark)g(pro)n(vides)f(the)i (individual)g(p)r(erformance)e(of)p 150 5046 1350 4 v 241 5099 a Fm(\003)277 5122 y Fl(assem)n(bled)23 b(b)n(y)h(Roger)g(Ho)r(c)n(kney)h (for)e(Lo)n(w-Lev)n(el)h(sub)r(committee)1796 5428 y Fx(19)p eop PNP restore /PNP save def 628.2618 89.4750 translate 21 bop 150 312 a Fx(eac)n(h)25 b(lo)r(op,)h(together)e(with)i(v)-5 b(arious)25 b(a)n(v)n(erages)d(\(arithmetic,)27 b(geometric,)e(harmonic\))f (and)i(the)g(quartiles)150 412 y(of)i(the)g(distribution.)39 b(Ho)n(w)n(ev)n(er,)26 b(it)i(is)g(di\016cult)h(to)f(giv)n(e)f(a)g(clear)g (meaning)h(to)g(these)g(a)n(v)n(erages,)d(and)j(the)150 511 y(v)-5 b(alue)34 b(of)g(the)g(b)r(enc)n(hmark)g(is)g(more)f(in)h(the)g (distribution)h(itself.)56 b(In)35 b(particular,)f(the)g(maxim)n(um)g(and)150 611 y(minim)n(um)29 b(giv)n(e)f(the)g(range)g(of)g(lik)n(ely)g(p)r (erformance)f(in)i(full)g(applications.)39 b(The)28 b(ratio)g(of)g(maxim)n (um)g(to)150 711 y(minim)n(um)j(p)r(erformance)e(has)g(b)r(een)i(called)e (the)i Fn(instability)g Fx(or)e(the)i Fn(sp)l(e)l(ciality)h Fx([15)o(],)f(and)f(is)f(a)h(measure)150 810 y(of)g(ho)n(w)f(di\016cult)i(it) g(is)f(to)g(obtain)g(go)r(o)r(d)f(p)r(erformance)g(from)h(the)g(computer,)h (and)f(therefore)f(ho)n(w)g(sp)r(e-)150 910 y(cialised)e(it)h(is.)37 b(The)27 b(minim)n(um)i(or)d(w)n(orst)h(p)r(erformance)f(obtained)h(on)h (these)f(lo)r(ops)g(is)g(of)h(sp)r(ecial)f(v)-5 b(alue,)150 1010 y(b)r(ecause)27 b(there)g(is)g(m)n(uc)n(h)g(truth)h(in)g(the)f(sa)n (ying)f(that)i(\\the)f(b)r(est)h(computer)f(to)g(c)n(ho)r(ose)f(is)h(that)h (with)g(the)150 1109 y(b)r(est)g(w)n(orst-p)r(erformance".)150 1384 y Fp(3.2)137 b(Single-Pro)t(cessor)46 b(Benc)l(hmarks)150 1566 y Fx(The)23 b(single-pro)r(cessor)d(lo)n(w-lev)n(el)i(b)r(enc)n(hmarks)g (pro)n(vided)g(b)n(y)h Fo(P)-7 b(ARKBENCH)29 b Fx(,)24 b(aim)f(to)g(measure)f (p)r(er-)150 1665 y(formance)c(parameters)f(that)j(c)n(haracterise)c(the)k (basic)e(arc)n(hitecture)g(of)h(the)g(computer,)i(and)d(the)i(compiler)150 1765 y(soft)n(w)n(are)33 b(through)g(whic)n(h)h(it)h(is)f(used.)57 b(F)-7 b(or)33 b(this)i(reason,)f(suc)n(h)g(b)r(enc)n(hmarks)g(ha)n(v)n(e)f (also)g(b)r(een)h(called)150 1864 y(appropriately)22 b Fn(b)l(asic)28 b(ar)l(chite)l(ctur)l(al)f(b)l(enchmarks)p Fx(.)37 b(F)-7 b(ollo)n(wing)23 b(the)i(metho)r(dology)e(of)h(Eurob)r(en)f([16],)i(the)150 1964 y(aim)33 b(is)g(that)h(these)f(hardw)n(are/compiler)d(parameters)i(will) i(b)r(e)f(used)h(in)f(p)r(erformance)g(form)n(ulae)f(that)150 2064 y(predict)h(the)g(timing)h(and)e(p)r(erformance)g(of)h(the)g(more)g (complex)f(k)n(ernels)g(\(see)h(Chapter)f(4\))h(and)g(com-)150 2163 y(pact)25 b(applications)f(\(see)h(Chapter)f(5\).)36 b(They)25 b(are)f(therefore)g(a)h(set)g(of)g Fn(synthetic)g Fx(b)r(enc)n(hmarks)f(con)n (triv)n(ed)150 2263 y(to)35 b(measure)e(theoretical)h(parameters)f(that)i (describ)r(e)f(the)h(sev)n(erit)n(y)e(of)i(some)f(o)n(v)n(erhead)e(or)i(p)r (oten)n(tial)150 2363 y(b)r(ottlenec)n(k,)i(or)d(the)h(prop)r(erties)f(of)h (some)g(item)h(of)f(hardw)n(are.)54 b(Th)n(us)34 b(RINF1)g(c)n(haracterises)d (the)k(ba-)150 2462 y(sic)c(prop)r(erties)g(of)g(the)h(arithmetic)g(pip)r (elines)g(b)n(y)f(measuring)f(the)i(parameter)f(\()p Fs(r)2806 2474 y Fg(1)2877 2462 y Fx(,)p Fs(n)2960 2460 y Ff(1)p 2959 2469 29 4 v 2959 2503 a(2)3002 2462 y Fx(\),)i(and)e(POL)-7 b(Y1)150 2562 y(and)27 b(POL)-7 b(Y2)26 b(c)n(haracterise)e(the)k(sev)n(erit) n(y)d(of)i(the)h(memory)e(b)r(ottlenec)n(k)h(b)n(y)g(measuring)e(the)j (parameters)150 2661 y(\()t(^)-46 b Fs(r)s Fx(,)p Fs(f)296 2659 y Ff(1)p 296 2668 V 296 2702 a(2)338 2661 y Fx(\).)275 2761 y(The)28 b(fundamen)n(tal)h(measuremen)n(t)f(in)h(an)n(y)f(b)r(enc)n (hmarking)g(is)g(the)h(measuremen)n(t)f(of)h(elapsed)f(w)n(all-)150 2861 y(clo)r(c)n(k)d(time.)37 b(Because)25 b(the)h(computer)g(clo)r(c)n(ks)f (on)h(eac)n(h)f(no)r(de)h(of)g(a)g(m)n(ulti-no)r(de)g(MPP)f(are)g(not)h(sync) n(hro-)150 2960 y(nised,)f(all)g(b)r(enc)n(hmark)e(time)i(measuremen)n(ts)f (m)n(ust)h(b)r(e)g(made)f(with)h(a)f(single)g(clo)r(c)n(k)g(on)g(one)h(no)r (de)f(of)h(the)150 3060 y(system.)58 b(The)34 b(b)r(enc)n(hmarks)g(TICK1)g (and)g(TICK2)g(ha)n(v)n(e,)h(resp)r(ectiv)n(ely)-7 b(,)35 b(b)r(een)g (designed)g(to)f(measure)150 3160 y(the)26 b(resolution)f(and)h(to)g(c)n(hec) n(k)f(the)h(absolute)g(v)-5 b(alue)26 b(of)g(this)g(clo)r(c)n(k.)35 b(These)26 b(b)r(enc)n(hmarks)f(should)h(b)r(e)g(run)150 3259 y(with)i(satisfactory)e(results)h(b)r(efore)g(an)n(y)g(further)h(b)r(enc)n (hmark)f(measuremen)n(ts)f(are)h(made.)150 3492 y Fy(3.2.1)112 b(Timer)36 b(resolution:)49 b(TICK1)150 3645 y Fx(TICK1)32 b(measures)g(the)h(in)n(terv)-5 b(al)32 b(b)r(et)n(w)n(een)h(tic)n(ks)g(of)g (the)g(clo)r(c)n(k)f(b)r(eing)h(used)g(in)g(the)h(b)r(enc)n(hmark)e(mea-)150 3745 y(suremen)n(ts.)67 b(That)38 b(is)g(to)g(sa)n(y)f(the)h(resolution)f(of) h(the)h(clo)r(c)n(k.)67 b(A)39 b(succession)d(of)i(calls)g(to)g(the)g(timer) 150 3844 y(routine)31 b(are)f(inserted)g(in)h(a)g(lo)r(op)g(and)f(executed)h (man)n(y)g(times.)47 b(The)31 b(di\013erences)g(b)r(et)n(w)n(een)f(successiv) n(e)150 3944 y(v)-5 b(alues)24 b(giv)n(en)f(b)n(y)h(the)h(timer)f(are)g(then) g(examined.)36 b(If)25 b(the)f(c)n(hanges)f(in)i(the)f(clo)r(c)n(k)g(v)-5 b(alue)24 b(\(or)g(tic)n(ks\))g(o)r(ccur)150 4043 y(less)30 b(frequen)n(tly)h(than)g(the)g(time)h(tak)n(en)e(to)h(en)n(ter)f(and)h(lea)n (v)n(e)e(the)j(timer)f(routine,)g(then)g(most)g(of)g(these)150 4143 y(di\013erences)26 b(will)g(b)r(e)h(zero.)35 b(When)27 b(a)f(tic)n(k)g(tak)n(es)f(place,)h(ho)n(w)n(ev)n(er,)e(a)i(di\013erence)g (equal)g(to)g(the)g(tic)n(k)g(v)-5 b(alue)150 4243 y(will)32 b(b)r(e)g(recorded,)g(surrounded)e(b)n(y)i(man)n(y)f(zero)g(di\013erences.)49 b(This)32 b(is)g(the)g(case)f(with)h(clo)r(c)n(ks)f(of)h(p)r(o)r(or)150 4342 y(resolution;)e(for)g(example)g(most)g(UNIX)h(clo)r(c)n(ks)e(that)h(tic) n(k)g(t)n(ypically)g(ev)n(ery)f(10)g(ms.)45 b(Suc)n(h)30 b(p)r(o)r(or)f(UNIX) 150 4442 y(clo)r(c)n(ks)f(can)h(still)g(b)r(e)h(used)f(for)g(lo)n(w-lev)n(el) e(b)r(enc)n(hmark)i(measuremen)n(ts)f(if)h(the)h(b)r(enc)n(hmark)e(is)h(rep)r (eated,)150 4542 y(sa)n(y)-7 b(,)27 b(10,000)e(times,)j(and)f(the)h(timer)g (calls)f(are)f(made)i(outside)f(this)h(rep)r(eat)f(lo)r(op.)275 4641 y(With)33 b(some)f(computers,)h(suc)n(h)f(as)f(the)i(CRA)-7 b(Y)33 b(series,)g(the)g(clo)r(c)n(k)e(tic)n(ks)h(ev)n(ery)g(cycle)g(of)g (the)h(com-)150 4741 y(puter,)f(that)f(is)g(to)g(sa)n(y)e(ev)n(ery)h(6ns)h (on)f(the)i(Y-MP)-7 b(.)30 b(The)h(resolution)f(of)h(the)g(CRA)-7 b(Y)32 b(clo)r(c)n(k)e(is)h(therefore)150 4840 y(appro)n(ximately)c(one)i (million)g(times)h(b)r(etter)f(than)h(a)e(UNIX)j(clo)r(c)n(k,)d(and)h(that)h (is)f(quite)g(a)g(di\013erence!)42 b(If)150 4940 y(TICK1)28 b(is)h(used)h(on)f(suc)n(h)g(a)f(computer)h(the)h(di\013erence)f(b)r(et)n(w)n (een)g(successiv)n(e)f(v)-5 b(alues)29 b(of)g(the)h(timer)f(is)g(a)150 5040 y(v)n(ery)h(accurate)g(measure)h(of)g(ho)n(w)g(long)g(it)h(tak)n(es)e (to)h(execute)h(the)g(instructions)f(of)g(the)h(timer)f(routine,)150 5139 y(and)i(therefore)f(is)h(nev)n(er)f(zero.)53 b(TICK1)32 b(tak)n(es)g(the)i(minim)n(um)g(of)f(all)g(suc)n(h)f(di\013erences,)j(and)e (all)g(it)g(is)1796 5428 y(20)p eop PNP restore PNEP %%Page: ? 12 0.6303 -612.00 PNLS /PNP save def 12.6922 89.4750 translate 22 bop 150 312 a Fx(p)r(ossible)30 b(to)h(sa)n(y)e(is)i(that)g(the)g(clo)r(c) n(k)f(tic)n(k)g(is)h(less)f(than)h(or)f(equal)g(to)g(this)h(v)-5 b(alue.)46 b(T)n(ypically)30 b(this)h(mini-)150 412 y(m)n(um)g(will)g(b)r(e)g (sev)n(eral)f(h)n(undreds)g(of)h(clo)r(c)n(k)f(tic)n(ks.)46 b(With)32 b(a)e(clo)r(c)n(k)h(tic)n(king)f(ev)n(ery)g(computer)g(cycle,)h(w)n (e)150 511 y(can)26 b(mak)n(e)g(lo)n(w-lev)n(el)f(b)r(enc)n(hmark)h (measuremen)n(ts)f(without)i(a)f(rep)r(eat)g(lo)r(op.)36 b(Suc)n(h)27 b(measuremen)n(ts)e(can)150 611 y(ev)n(en)33 b(b)r(e)h(made)f(on)g(a)g(busy)h (timeshared)f(system)g(\(where)g(man)n(y)g(users)g(are)f(con)n(tending)h(for) g(memory)150 711 y(access\))27 b(b)n(y)i(taking)e(the)i(min)n(um)n(um)g(time) g(recorded)e(from)h(a)g(sample)g(of,)h(sa)n(y)-7 b(,)27 b(10,000)f(single)i (execution)150 810 y(measuremen)n(ts.)40 b(In)30 b(this)f(case,)g(the)g (minim)n(um)h(can)f(usually)f(b)r(e)i(said)e(to)h(apply)g(to)g(a)g(case)f (when)h(there)150 910 y(w)n(as)e(no)g(memory)g(access)f(dela)n(y)h(caused)g (b)n(y)g(other)g(users.)275 1010 y(TICK1)f(exists)h(and)h(forms)f(part)g(of)h (the)g(Genesis)f(b)r(enc)n(hmarks)f([17].)150 1240 y Fy(3.2.2)112 b(Timer)36 b(v)-6 b(alue:)50 b(TICK2)150 1394 y Fx(TICK2)39 b(con\014rms)g(that)g(the)h(absolute)f(v)-5 b(alues)40 b(returned)f(b)n(y)g (the)h(computer)g(clo)r(c)n(k)e(are)h(correct,)i(b)n(y)150 1493 y(comparing)17 b(its)i(measuremen)n(t)f(of)g(a)h(giv)n(en)e(time)j(in)n (terv)-5 b(al)18 b(with)h(that)g(of)f(an)h(external)f(w)n(all-clo)r(c)n(k)e (\(actually)150 1593 y(the)27 b(b)r(enc)n(hmark)n(er's)d(wrist)n(w)n(atc)n (h\).)35 b(P)n(arallel)24 b(b)r(enc)n(hmark)i(p)r(erformance)f(can)h(only)g (b)r(e)g(measured)f(using)150 1692 y(the)i(elapsed)f(w)n(all-clo)r(c)n(k)f (time,)i(b)r(ecause)g(the)g(ob)5 b(jectiv)n(e)26 b(of)g(parallel)g(execution) g(is)h(to)f(reduce)h(this)g(time.)150 1792 y(Measuremen)n(ts)f(made)h(with)h (a)f(CPU-timer)g(\(whic)n(h)h(only)e(records)g(time)i(when)g(its)f(job)h(is)f (executing)g(in)150 1892 y(the)i(CPU\))g(are)e(clearly)h(incorrect,)g(b)r (ecause)g(the)h(clo)r(c)n(k)f(do)r(es)g(not)h(record)e(w)n(aiting)h(time)h (when)g(the)g(job)150 1991 y(is)h(out)g(of)g(the)g(CPU.)g(TICK2)f(will)h (immediately)h(detect)f(the)g(incorrect)f(use)h(of)g(a)g(CPU-time-for-this-) 150 2091 y(job-only)f(clo)r(c)n(k.)41 b(An)30 b(example)f(of)g(a)g(timer)g (that)h(claims)f(to)g(measure)f(elapsed)h(time)h(but)g(is)f(actually)f(a)150 2191 y(CPU-timer,)d(is)f(the)i(returned)e(v)-5 b(alue)24 b(of)h(the)g(p)r (opular)f(Sun)i(UNIX)f(timer)g(ETIME.)f(TICK2)g(also)f(c)n(hec)n(ks)150 2290 y(that)36 b(the)g(correct)e(m)n(ultiplier)h(is)h(b)r(eing)f(used)h(in)f (the)h(computer)f(system)h(soft)n(w)n(are)d(to)j(con)n(v)n(ert)e(clo)r(c)n(k) 150 2390 y(tic)n(ks)27 b(to)h(true)f(seconds.)275 2489 y(TICK2)f(exists)h (and)h(forms)f(part)g(of)h(release)e(2.2)g(and)i(later)f(of)g(the)h(Genesis)g (b)r(enc)n(hmarks)e([17)o(].)150 2720 y Fy(3.2.3)112 b(Basic)37 b(Arithmetic)d(Op)s(erations:)50 b(RINF1)150 2873 y Fx(This)23 b(b)r(enc)n(hmark)f(tak)n(es)g(a)h(set)g(of)g(common)f(F)-7 b(ortran)22 b(DO-lo)r(ops)g(and)h(analyses)e(their)i(time)g(of)g(execution) 150 2973 y(in)28 b(terms)g(of)g(the)g(t)n(w)n(o)f(parameters)f(\()p Fs(r)1373 2985 y Fg(1)1444 2973 y Fx(,)p Fs(n)1527 2971 y Ff(1)p 1527 2980 29 4 v 1527 3014 a(2)1569 2973 y Fx(\))q([18)o(,)i(19)o(,)g(20)o(,) g(21)o(,)g(22)o(,)g(23)o(].)38 b Fs(r)2499 2985 y Fg(1)2626 2973 y Fx(is)27 b(the)i(asymptotic)e(p)r(erfor-)150 3084 y(mance)f(rate)g(in) g(M\015op/s)f(whic)n(h)i(is)f(approac)n(hed)e(as)i(the)g(lo)r(op)g(\(or)g(v)n (ector\))f(length,)i Fs(n)p Fx(,)f(b)r(ecomes)g(longer.)150 3184 y Fs(n)210 3182 y Ff(1)p 210 3191 V 210 3224 a(2)252 3184 y Fx(\(the)h(half-p)r(erformance)d(length\))j(expresses)d(ho)n(w)i(rapidly)-7 b(,)25 b(in)h(terms)g(increasing)f(v)n(ector)f(length,)j(the)150 3283 y(actual)j(p)r(erformance,)g Fs(r)r Fx(,)i(approac)n(hes)c Fs(r)1465 3295 y Fg(1)1536 3283 y Fx(.)46 b(It)30 b(is)h(de\014ned)f(as)g (the)h(v)n(ector)e(length)i(required)e(to)h(ac)n(hiev)n(e)150 3383 y(a)35 b(p)r(erformance)f(of)h(one)g(half)g(of)g Fs(r)1282 3395 y Fg(1)1353 3383 y Fx(.)60 b(This)35 b(means)g(that)h(the)f(time,)j Fs(t)p Fx(,)f(for)e(a)g(DO-lo)r(op)f(corresp)r(ond-)150 3483 y(ing)c(to)g Fs(q)j Fx(v)n(ector)28 b(op)r(erations)h(\(i.e.)44 b(with)31 b Fs(q)i Fx(\015oating-p)r(oin)n(t)c(op)r(erations)g(p)r(er)h (elemen)n(t)g(p)r(er)g(iteration\))f(is)150 3582 y(appro)n(ximated)d(b)n(y) 1449 3682 y Fs(t)d Fx(=)g Fs(q)e Fi(\003)d Fx(\()p Fs(n)h Fx(+)f Fs(n)1952 3680 y Ff(1)p 1951 3689 V 1951 3722 a(2)1994 3682 y Fx(\))p Fs(=r)2105 3694 y Fg(1)2203 3682 y Fs(:)1128 b Fx(\(3.1\))150 3826 y(Then)28 b(the)g(p)r(erformance)e(rate)h(is)h(giv)n(en)e(b)n(y)1377 4018 y Fs(r)g Fx(=)1537 3962 y Fs(q)c Fi(\003)c Fs(n)p 1537 3999 169 4 v 1607 4075 a(t)1739 4018 y Fx(=)1983 3962 y Fs(r)2020 3974 y Fg(1)p 1836 3999 402 4 v 1836 4075 a Fx(\(1)h(+)f Fs(n)2072 4073 y Ff(1)p 2071 4082 29 4 v 2071 4116 a(2)2114 4075 y Fs(=n)p Fx(\))2275 4018 y Fs(:)1056 b Fx(\(3.2\))150 4260 y(W)-7 b(e)35 b(can)f(see)f(from)h(Eqn.\(3.1\))g(that)g Fs(n)1423 4258 y Ff(1)p 1423 4267 V 1423 4300 a(2)1466 4260 y Fx(is)g(a)g(w)n(a)n(y)f(of)h (measuring)f(the)h(imp)r(ortance)g(of)g(v)n(ector)f(startup)150 4371 y(o)n(v)n(erhead)24 b(\(=)p Fs(n)654 4369 y Ff(1)p 654 4378 V 654 4411 a(2)696 4371 y Fx(/)p Fs(r)775 4383 y Fg(1)846 4371 y Fx(\))j(in)g(terms)f(of)g(quan)n(tities)h(kno)n(wn)f(to)g(the)h (programmer)d(\(lo)r(op)j(or)e(v)n(ector)h(length\).)150 4470 y(In)32 b(the)f(b)r(enc)n(hmark)g(program,)g(the)h(t)n(w)n(o)e(parameters)g (are)g(determined)i(b)n(y)f(a)g(least-squares)e(\014t)j(of)g(the)150 4570 y(data)g(to)h(the)f(straigh)n(t)g(line)h(de\014ned)g(b)n(y)f (Eqn.\(3.1\).)51 b(A)33 b(useful)g(guide)f(to)h(the)f(signi\014cance)g(of)h Fs(n)3321 4568 y Ff(1)p 3320 4577 V 3320 4610 a(2)3363 4570 y Fx(is)f(to)150 4681 y(note)j(from)g(Eqn.\(3.2\))g(that)h(80)e(p)r(ercen)n (t)h(of)g(the)h(asymptotic)f(p)r(erformance)f(is)i(ac)n(hiev)n(ed)e(for)h(v)n (ectors)150 4781 y(of)c(length)h(4)20 b Fi(\002)g Fs(n)713 4779 y Ff(1)p 713 4788 V 713 4821 a(2)756 4781 y Fx(.)47 b(Generally)31 b(sp)r(eaking,)g Fs(n)1636 4779 y Ff(1)p 1636 4788 V 1636 4821 a(2)1678 4781 y Fx(v)-5 b(alues)31 b(of)g(upto)h(ab)r(out)f(50)f(are)h (tolerable,)g(whereas)f(the)150 4880 y(p)r(erformance)25 b(of)h(computers)g (with)h(larger)d(v)-5 b(alues)26 b(of)g Fs(n)1939 4878 y Ff(1)p 1939 4887 V 1939 4921 a(2)1981 4880 y Fx(is)g(sev)n(erely)f(constrained)g(b)n (y)h(the)g(need)h(to)f(k)n(eep)150 4980 y(v)n(ector)c(lengths)h(signi\014can) n(tly)f(longer)g(than)h Fs(n)1628 4978 y Ff(1)p 1628 4987 V 1628 5020 a(2)1670 4980 y Fx(.)35 b(This)23 b(requiremen)n(t)f(mak)n(es)g (the)i(computers)e(di\016cult)i(to)150 5080 y(program)19 b(e\016cien)n(tly)-7 b(,)23 b(and)e(often)h(leads)f(to)g(disapp)r(oin)n(ting)g(p)r(erformance,)g (compared)g(to)g(the)h(asymptotic)150 5179 y(rate)27 b(adv)n(ertised)f(b)n(y) i(the)g(man)n(ufacturer.)1796 5428 y(21)p eop PNP restore /PNP save def 628.2618 89.4750 translate 23 bop 275 312 a Fx(RINF1)24 b(has)h(b)r(een)g(used)f(extensiv)n(ely)g(for)g (ab)r(out)h(ten)g(y)n(ears)e(as)h(part)g(of)h(the)g(Ho)r(c)n(kney)f(and)h (EuroBen)150 412 y(b)r(enc)n(hmarks)i(\(mo)r(dule)h(MOD1A)n(C\))f([24)o(].)37 b(It)28 b(is)g(also)e(included)i(in)g(the)g(Genesis)g(b)r(enc)n(hmarks)e([17) o(].)150 644 y Fy(3.2.4)112 b(Memory-Bottlenec)m(k)36 b(Benc)m(hmarks:)50 b(POL)-9 b(Y1)37 b(and)i(POL)-9 b(Y2)150 797 y Fx(Ev)n(en)39 b(if)h(the)g(v)n(ector)f(lengths)g(are)g(long)g(enough)g(to)h(o)n(v)n(ercome) d(the)j(v)n(ector)f(startup)g(o)n(v)n(erhead,)i(the)150 897 y(p)r(eak)36 b(rate)f(of)h(the)h(arithmetic)f(pip)r(elines)h(ma)n(y)e(not)h (b)r(e)h(realised)e(b)r(ecause)h(of)g(the)g(dela)n(ys)f(asso)r(ciated)150 997 y(with)40 b(obtaining)f(data)h(from)f(the)h(cac)n(he)f(or)g(main)g (memory)g(of)h(the)g(computer.)73 b(The)40 b(POL)-7 b(Y1)38 b(and)150 1096 y(POL)-7 b(Y2)36 b(b)r(enc)n(hmarks)f(quan)n(tify)i(this)g (dep)r(endence)g(of)f(computer)h(p)r(erformance)e(on)h(memory)g(access)150 1196 y(b)r(ottlenec)n(ks.)f(The)21 b(computational)f(in)n(tensit)n(y)-7 b(,)23 b Fs(f)9 b Fx(,)22 b(of)f(a)g(DO-lo)r(op)g(is)g(de\014ned)h(as)e(the)i (n)n(um)n(b)r(er)f(of)g(\015oating-)150 1296 y(p)r(oin)n(t)39 b(op)r(erations)e(\(\015op\))i(p)r(erformed)g(p)r(er)f(memory)g(reference)g (\(mref)6 b(\))40 b(to)e(an)h(elemen)n(t)f(of)h(a)f(v)n(ector)150 1395 y(v)-5 b(ariable)38 b([23)o(].)70 b(The)38 b(asymptotic)h(p)r (erformance,)h Fs(r)1864 1407 y Fg(1)1935 1395 y Fx(,)h(of)e(a)f(computer)g (is)h(observ)n(ed)e(to)h(increase)g(as)150 1495 y(the)30 b(computational)g (in)n(tensit)n(y)g(increases,)f(b)r(ecause)h(as)f(this)h(b)r(ecomes)g (larger,)f(the)i(e\013ects)f(of)g(memory)150 1594 y(access)37 b(dela)n(ys)h(b)r(ecome)h(negligible)f(compared)f(to)i(the)g(time)g(sp)r(en)n (t)g(on)f(arithmetic.)70 b(This)39 b(e\013ect)g(is)150 1694 y(c)n(haracterised)26 b(b)n(y)h(the)i(t)n(w)n(o)e(parameters)f(\()t(^)-46 b Fs(r)s Fx(,)p Fs(f)1644 1692 y Ff(1)p 1644 1701 29 4 v 1644 1735 a(2)1686 1694 y Fx(\),)29 b(where)i(^)-46 b Fs(r)s Fx(is)28 b(the)g(p)r(eak)g(hardw)n(are)e(p)r(erformance)h(of)h(the)150 1794 y(arithmetic)33 b(pip)r(eline,)h(and)f Fs(f)1115 1792 y Ff(1)p 1115 1801 V 1115 1834 a(2)1157 1794 y Fx(is)g(the)g(computational)f (in)n(tensit)n(y)g(required)g(to)g(ac)n(hiev)n(e)g(half)h(this)g(rate.)150 1893 y(That)28 b(is)f(to)h(sa)n(y)e(the)i(asymptotic)f(p)r(erformance)g(is)g (giv)n(en)g(b)n(y:)1522 2115 y Fs(r)1559 2127 y Fg(1)1653 2115 y Fx(=)1931 2058 y(^)-46 b Fs(r)p 1751 2096 392 4 v 1751 2172 a Fx(\(1)18 b(+)g Fs(f)1977 2170 y Ff(1)p 1977 2179 29 4 v 1977 2212 a(2)2019 2172 y Fs(=f)9 b Fx(\))3354 2115 y(\(3.3\))150 2361 y(If)35 b(memory)f(access)f(and)h(arithmetic)h(are)f(not)g(o)n(v)n (erlapp)r(ed,)h(then)g Fs(f)2396 2359 y Ff(1)p 2395 2368 V 2395 2402 a(2)2438 2361 y Fx(can)f(b)r(e)h(sho)n(wn)f(to)g(b)r(e)h(the)g (ratio)150 2472 y(of)30 b(arithmetic)g(sp)r(eed)g(\(in)g(M\015op/s\))f(to)h (memory)f(access)g(sp)r(eed)h(\(in)g(Mw)n(ord/s\))f([23)o(].)44 b(The)30 b(parameter)150 2572 y Fs(f)201 2570 y Ff(1)p 201 2579 V 201 2612 a(2)243 2572 y Fx(,)g(lik)n(e)f Fs(n)510 2570 y Ff(1)p 510 2579 V 510 2612 a(2)552 2572 y Fx(,)h(measures)e(an)h(un)n(w)n (an)n(ted)g(o)n(v)n(erhead)e(and)i(should)g(b)r(e)h(as)e(small)h(as)g(p)r (ossible.)42 b(In)29 b(order)f(to)150 2671 y(v)-5 b(ary)23 b Fs(f)33 b Fx(and)24 b(allo)n(w)f(the)i(p)r(eak)f(p)r(erformance)f(to)h(b)r (e)h(approac)n(hed,)e(w)n(e)h(c)n(ho)r(ose)f(a)g(k)n(ernel)h(lo)r(op)f(that)i (can)f(b)r(e)150 2771 y(computed)29 b(with)f(maxim)n(um)h(e\016ciency)f(on)g (an)n(y)f(hardw)n(are.)37 b(This)29 b(is)f(the)h(ev)-5 b(aluation)27 b(of)i(a)f(p)r(olynomial)150 2871 y(b)n(y)33 b(Horner's)g(rule,)i(in)f(whic)n (h)g(case)f(the)h(computational)f(in)n(tensit)n(y)h(is)f(the)h(order)f(of)h (the)g(p)r(olynomial,)150 2970 y(and)26 b(b)r(oth)h(the)g(m)n(ultiply)f(and)h (add)f(pip)r(elines)h(can)f(b)r(e)g(used)h(in)f(parallel.)35 b(T)-7 b(o)26 b(measure)g Fs(f)3009 2968 y Ff(1)p 3008 2977 V 3008 3011 a(2)3051 2970 y Fx(,)g(the)h(order)e(of)150 3070 y(the)30 b(p)r(olynomial)f(is)h(increased)f(from)g(one)h(to)g(ten,)g(and)g (the)g(measured)f(p)r(erformance)g(for)g(long)h(v)n(ectors)150 3169 y(is)d(\014tted)i(to)e(Eqn.\(3.3\).)275 3269 y(The)33 b(POL)-7 b(Y1)31 b(b)r(enc)n(hmark)i(rep)r(eats)f(the)i(p)r(olynomial)e(ev)-5 b(aluation)32 b(for)h(eac)n(h)f(order)g(t)n(ypically)g(1000)150 3369 y(times)25 b(for)f(v)n(ector)f(lengths)i(upto)f(10,000,)f(whic)n(h)i(w)n (ould)f(normally)f(\014t)i(in)n(to)g(the)g(cac)n(he)e(of)i(a)f(cac)n (he-based)150 3468 y(pro)r(cessor.)33 b(Except)20 b(for)h(the)g(\014rst)g(ev) -5 b(aluation)20 b(the)h(data)g(will)g(therefore)f(b)r(e)h(found)h(in)f(the)g (cac)n(he.)34 b(POL)-7 b(Y1)150 3568 y(is)26 b(therefore)f(an)g Fn(in-c)l(ache)i Fx(test)f(of)g(the)g(memory)f(b)r(ottlenec)n(k)h(b)r(et)n(w) n(een)g(the)g(arithmetic)g(registers)e(of)i(the)150 3668 y(pro)r(cessor)f (and)j(its)g(cac)n(he.)275 3767 y(POL)-7 b(Y2,)20 b(on)f(the)h(other)f(hand,) i(\015ushes)e(the)h(cac)n(he)f(prior)f(to)i(eac)n(h)f(di\013eren)n(t)g(order) f(and)i(then)g(p)r(erforms)150 3867 y(only)35 b(one)h(p)r(olynomial)f(ev)-5 b(aluation,)38 b(for)d(v)n(ector)g(lengths)g(from)h(10,000)d(upto)j(100,000,) g(whic)n(h)g(w)n(ould)150 3966 y(normally)g(exceed)i(the)g(cac)n(he)e(size.) 67 b(Data)37 b(will)h(ha)n(v)n(e)e(to)i(b)r(e)g(brough)n(t)e(from)i(o\013-c)n (hip)f(memory)-7 b(,)39 b(and)150 4066 y(POL)-7 b(Y2)32 b(is)i(an)f Fn(out-of-c)l(ache)i Fx(test)e(of)h(the)g(memory)f(b)r(ottlenec)n(k)g(b)r(et) n(w)n(een)h(o\013-c)n(hip)f(memory)f(and)i(the)150 4166 y(arithmetic)28 b(registers.)275 4265 y(The)23 b(POL)-7 b(Y1)23 b(b)r(enc)n(hmark)f(exists)i (as)f(MOD1G)g(of)h(the)f(EuroBen)g(b)r(enc)n(hmarks)f([24)o(].)36 b(POL)-7 b(Y2)22 b(exists)150 4365 y(as)27 b(part)g(of)h(the)g(Ho)r(c)n(kney) f(b)r(enc)n(hmarks.)150 4640 y Fp(3.3)137 b(Multi-Pro)t(cessor)46 b(Benc)l(hmarks)150 4821 y Fx(The)33 b Fo(P)-7 b(ARKBENCH)29 b Fx(suite)k(of)g(b)r(enc)n(hmark)f(programs)f(pro)n(vide)g(lo)n(w-lev)n(el)h (b)r(enc)n(hmarks)f(to)i(c)n(harac-)150 4921 y(terise)21 b(the)g(basic)g (comm)n(unication)f(prop)r(erties)h(of)g(an)g(MPP)f(b)n(y)h(measuring)f(the)i (parameters)d(\()p Fs(r)3197 4933 y Fg(1)3268 4921 y Fx(,)p Fs(n)3351 4919 y Ff(1)p 3351 4928 V 3351 4961 a(2)3393 4921 y Fx(\))q(for)150 5032 y(comm)n(unication)26 b(\(COMMS1,)h(COMMS2,)f (COMMS3\).)37 b(The)27 b(ratio)e(of)i(arithmetic)g(sp)r(eed)g(to)g(comm)n(u-) 150 5132 y(nication)h(sp)r(eed)g(\(the)h(hardw)n(are+compiler)24 b(parameter)j Fs(f)2059 5130 y Ff(1)p 2059 5139 V 2059 5172 a(2)2101 5132 y Fx(for)g(comm)n(unication\))h(is)g(measured)f(b)n(y)h(the) 1796 5428 y(22)p eop PNP restore PNEP %%Page: ? 13 0.6303 -612.00 PNLS /PNP save def 12.6922 89.4750 translate 24 bop 150 312 a Fx(POL)-7 b(Y3)20 b(b)r(enc)n(hmark.)34 b(The)21 b(abilit)n(y)g(to)g(sync)n(hronise)e(the)i(pro)r(cessors)e(in)i(a)g(large)e (MPP)-7 b(,)21 b(in)g(an)g(acceptable)150 412 y(time,)35 b(is)f(a)f(k)n(ey)f (c)n(haracteristic)g(of)h(suc)n(h)g(computers,)h(and)f(the)h(SYNCH1)g(b)r (enc)n(hmark)f(measures)f(the)150 511 y(n)n(um)n(b)r(er)26 b(of)h(barrier)d(statemen)n(ts)i(that)h(can)f(b)r(e)h(executed)g(p)r(er)f (second)g(as)g(a)g(function)h(of)f(the)h(n)n(um)n(b)r(er)f(of)150 611 y(pro)r(cessors)f(taking)i(part)g(in)h(the)g(barrier.)150 843 y Fy(3.3.1)112 b(Comm)m(unication)35 b(Benc)m(hmarks:)51 b(COMMS1)38 b(and)g(COMMS2)150 996 y Fx(The)28 b(purp)r(ose)f(of)h(the)g (COMMS1,)f(or)g Fn(Pingp)l(ong)p Fx(,)i(b)r(enc)n(hmark)e([25)o(,)h(15)o(])g (is)g(to)g(measure)e(the)j(basic)e(com-)150 1096 y(m)n(unication)22 b(prop)r(erties)f(of)h(a)g(message-passing)d(MIMD)k(computer.)34 b(A)23 b(message)e(of)h(v)-5 b(ariable)21 b(length,)i Fs(n)p Fx(,)150 1196 y(is)g(sen)n(t)g(from)g(a)g(master)f(no)r(de)h(to)g(a)g(sla)n (v)n(e)f(no)r(de.)35 b(The)24 b(sla)n(v)n(e)d(no)r(de)j(receiv)n(es)d(the)j (message)e(in)n(to)g(a)h(F)-7 b(ortran)150 1295 y(data)24 b(arra)n(y)-7 b(,)23 b(and)h(immediately)h(returns)f(it)h(to)f(the)h(master.)35 b(Half)25 b(the)g(time)g(for)f(this)h Fn(message)j(pingp)l(ong)150 1395 y Fx(is)23 b(recorded)e(as)i(the)g(time,)h Fs(t)p Fx(,)g(to)f(send)g(a)g (message)e(of)i(length,)h Fs(n)p Fx(.)35 b(In)23 b(the)h(COMMS2)e(b)r(enc)n (hmark)g(there)h(is)150 1494 y(a)e(message)e(exc)n(hange)h(in)h(whic)n(h)g(t) n(w)n(o)g(no)r(des)f(sim)n(ultaneously)h(send)g(messages)e(to)i(eac)n(h)f (other)h(and)g(return)150 1594 y(them.)37 b(In)24 b(this)h(case)f(adv)-5 b(an)n(tage)24 b(can)g(b)r(e)h(tak)n(en)f(of)h(bidirectional)f(links,)h(and)g (a)f(greater)f(bandwidth)i(can)150 1694 y(b)r(e)30 b(obtained)g(than)g(is)g (p)r(ossible)f(with)i(COMMS1.)43 b(In)30 b(b)r(oth)h(b)r(enc)n(hmarks,)e(the) h(time)h(as)e(a)h(function)g(of)150 1793 y(message)22 b(length)i(is)g (\014tted)h(b)n(y)f(least)f(squares)f(using)i(the)g(parameters)e(\()p Fs(r)2453 1805 y Fg(1)2524 1793 y Fx(,)p Fs(n)2607 1791 y Ff(1)p 2607 1800 29 4 v 2607 1834 a(2)2650 1793 y Fx(\)[20)o(,)i(23)o(])g(to)g(the)g (follo)n(wing)150 1893 y(linear)j(timing)h(mo)r(del:)1533 1993 y Fs(t)c Fx(=)e(\()p Fs(n)d Fx(+)f Fs(n)1918 1991 y Ff(1)p 1918 2000 V 1918 2033 a(2)1960 1993 y Fx(\))p Fs(=r)2071 2005 y Fg(1)3354 1993 y Fx(\(3.4\))150 2140 y(when)28 b(the)g(comm)n(unication)f (rate)f(is)i(giv)n(en)f(b)n(y)1269 2337 y Fs(r)e Fx(=)1543 2281 y Fs(r)1580 2293 y Fg(1)p 1429 2318 337 4 v 1429 2394 a Fx(1)18 b(+)g Fs(n)1632 2392 y Ff(1)p 1632 2401 29 4 v 1632 2434 a(2)1674 2394 y Fs(=n)1798 2337 y Fx(=)23 b Fs(r)1923 2349 y Fg(1)1994 2337 y Fx(pip)r(e\()p Fs(n=n)2332 2335 y Ff(1)p 2332 2344 V 2332 2377 a(2)2374 2337 y Fx(\))948 b(\(3.5\))1258 2633 y(where)276 b(pip)r(e\()p Fs(x)p Fx(\))24 b(=)2250 2576 y(1)p 2134 2614 274 4 v 2134 2690 a(1)18 b(+)g(1)p Fs(=x)3354 2633 y Fx(\(3.6\))150 2824 y(and)27 b(the)h(startup)g(time)g(is)1623 2924 y Fs(t)1653 2936 y Fj(0)1713 2924 y Fx(=)23 b Fs(n)1861 2922 y Ff(1)p 1861 2931 29 4 v 1861 2965 a(2)1903 2924 y Fs(=r)1982 2936 y Fg(1)3354 2924 y Fx(\(3.7\))150 3072 y(In)h(the)g(ab)r(o)n(v)n(e)e (equations,)h Fs(r)1048 3084 y Fg(1)1119 3072 y Fx(is)h(the)f Fn(asymptotic)28 b(b)l(andwidth)d Fx(of)e(comm)n(unication)g(whic)n(h)h(is)f (approac)n(hed)150 3172 y(as)34 b(the)g(message)f(length)h(tends)h(to)f (in\014nit)n(y)h(\(hence)f(the)h(subscript\),)h(and)e Fs(n)2691 3170 y Ff(1)p 2691 3179 V 2691 3212 a(2)2733 3172 y Fx(is)g(the)h(message)e (length)150 3271 y(required)24 b(to)g(ac)n(hiev)n(e)f(half)i(this)g (asymptotic)f(rate.)35 b(Hence)25 b Fs(n)2106 3269 y Ff(1)p 2106 3278 V 2106 3312 a(2)2148 3271 y Fx(is)f(called)h(the)g Fn(half-p)l(erformanc)l(e)k(message)150 3371 y(length)p Fx(.)275 3470 y(The)d(imp)r(ortance)g(of)g(the)h(parameter)e Fs(n)1570 3468 y Ff(1)p 1570 3477 V 1570 3511 a(2)1612 3470 y Fx(is)h(that)h(it)g(pro)n (vides)e(a)h(y)n(ardstic)n(k)f(with)h(whic)n(h)h(to)f(measure)150 3570 y(message-length,)38 b(and)g(thereb)n(y)e(enables)h(one)g(to)h (distinguish)f(the)h(t)n(w)n(o)f(regimes)f(of)i(short)e(and)i(long)150 3670 y(messages.)59 b(F)-7 b(or)35 b(long)g(messages)f(\()p Fs(n)i(>)g(n)1542 3668 y Ff(1)p 1542 3677 V 1542 3710 a(2)1584 3670 y Fx(\),)i(the)e(denominator)f(in)h(equation)f(3.5)f(is)i(appro)n (ximately)150 3769 y(unit)n(y)28 b(and)f(the)h(comm)n(unication)f(rate)g(is)g (appro)n(ximately)f(constan)n(t)h(at)h(its)f(asymptotic)g(rate,)g Fs(r)3261 3781 y Fg(1)1708 3949 y Fs(r)f Fi(\031)d Fs(r)1896 3961 y Fg(1)3354 3949 y Fx(\(3.8\))150 4129 y(F)-7 b(or)31 b(short)g(messages)f(\()p Fs(n)g(<)f(n)1142 4127 y Ff(1)p 1142 4136 V 1142 4170 a(2)1184 4129 y Fx(\),)k(the)f(comm)n(unication)f(rate)g(is) g(b)r(est)h(expressed)f(in)g(the)h(algebraically)150 4229 y(equiv)-5 b(alen)n(t)27 b(form)1552 4345 y Fs(r)f Fx(=)1846 4289 y Fs(\031)1893 4301 y Fj(0)1930 4289 y Fs(n)p 1712 4326 402 4 v 1712 4402 a Fx(\(1)18 b(+)g Fs(n=n)2039 4400 y Ff(1)p 2039 4409 29 4 v 2039 4442 a(2)2081 4402 y Fx(\))3354 4345 y(\(3.9\))1255 4572 y(where)276 b Fs(\031)1791 4584 y Fj(0)1851 4572 y Fx(=)23 b Fs(t)1969 4536 y Fg(\000)p Fj(1)1969 4594 y(0)2081 4572 y Fx(=)g Fs(r)2206 4584 y Fg(1)2277 4572 y Fs(=n)2379 4570 y Ff(1)p 2378 4579 V 2378 4612 a(2)3313 4572 y Fx(\(3.10\))150 4720 y(F)-7 b(or)27 b(short)g(messages,)f(the)i(denominator)e(in)i(equation)f (3.9)g(is)g(appro)n(ximately)f(unit)n(y)-7 b(,)28 b(so)f(that)1560 4900 y Fs(r)f Fi(\031)d Fs(\031)1758 4912 y Fj(0)1795 4900 y Fs(n)g Fx(=)g Fs(n=t)2078 4912 y Fj(0)3313 4900 y Fx(\(3.11\))150 5080 y(In)i(sharp)f(con)n(trast)g(to)g(the)i(appro)n(ximately)d(constan)n(t)h (rate)g(in)h(the)h(long-message)c(limit,)k(the)g(comm)n(uni-)150 5179 y(cation)d(rate)h(in)g(the)g(short)g(message)e(limit)j(is)f(seen)g(to)f (b)r(e)i(appro)n(ximately)d(prop)r(ortional)g(to)i(the)g(message)1796 5428 y(23)p eop PNP restore /PNP save def 628.2618 89.4750 translate 25 bop 150 312 a Fx(length.)37 b(The)27 b(constan)n(t)f(of)h(prop)r (ortionalit)n(y)-7 b(,)26 b Fs(\031)1672 324 y Fj(0)1710 312 y Fx(,)h(is)g(kno)n(wn)f(as)h(the)g Fn(sp)l(e)l(ci\014c)j(p)l(erformanc)l(e)p Fx(,)f(and)e(can)g(b)r(e)150 412 y(expressed)j(con)n(v)n(enien)n(tly)g(in)i (units)g(of)f(kilob)n(yte)g(p)r(er)g(second)g(p)r(er)g(b)n(yte)h(\(kB/s\)/B)e (or)h(`k/s'.)47 b(Unfortu-)150 511 y(nately)26 b(since)f(an)h(SI)g(pre\014x,) f(suc)n(h)h(as)f(k,)h(cannot)f(stand)h(alone)f(without)h(a)f(unit)i(sym)n(b)r (ol,)e(this)i(unit)f(m)n(ust)150 611 y(b)r(e)i(written)g(either)f(as)g(10)975 581 y Fj(3)1011 611 y Fx(/s)g(or)g(as)g(kHz,)h(where)f(Hz)h(is)f(a)g(sp)r (ecial)h(unit)g(name)f(for)g(p)r(er)h(second)f(\()p Fs(s)3309 581 y Fg(\000)p Fj(1)3398 611 y Fx(\).)275 711 y(Th)n(us,)j(in)f(general,)g (w)n(e)h(ma)n(y)f(sa)n(y)f(that)i Fs(r)1592 723 y Fg(1)1663 711 y Fx(c)n(haracterises)d(the)j(long-message)d(p)r(erformance)i(and)g Fs(\031)3487 723 y Fj(0)150 810 y Fx(the)36 b(short-message)c(p)r (erformance.)59 b(The)35 b(COMMS1)g(b)r(enc)n(hmark)g(computes)g(all)g(four)g (of)g(the)g(ab)r(o)n(v)n(e)150 910 y(parameters,)f(\()p Fs(r)680 922 y Fg(1)751 910 y Fs(;)14 b(n)848 908 y Ff(1)p 848 917 29 4 v 848 950 a(2)890 910 y Fs(;)g(t)957 922 y Fj(0)994 910 y Fs(;)g Fx(and)p Fs(\031)1212 922 y Fj(0)1250 910 y Fx(\),)36 b(b)r(ecause)d(eac)n(h)h(emphasises)f(a)h(di\013eren)n(t)g(asp)r(ect)g(of)g (p)r(erformance.)150 1010 y(Ho)n(w)n(ev)n(er)g(only)i(t)n(w)n(o)g(of)g(them)h (are)f(indep)r(enden)n(t.)64 b(In)36 b(the)h(case)e(that)i(there)f(are)f (di\013eren)n(t)i(mo)r(des)f(of)150 1109 y(transmission)d(for)g(messages)g (shorter)f(or)i(longer)e(than)j(a)e(certain)h(length,)h(the)g(b)r(enc)n (hmark)e(can)h(read)150 1209 y(in)d(this)h(breakp)r(oin)n(t)e(and)h(p)r (erform)g(a)f(separate)g(least-squares)f(\014t)i(for)g(the)h(t)n(w)n(o)e (regions.)46 b(An)32 b(example)150 1308 y(is)g(the)g(In)n(tel)g(iPSC/860)e (whic)n(h)h(has)h(a)f(di\013eren)n(t)h(message)f(proto)r(col)f(for)i (messages)e(shorter)g(than)i(and)150 1408 y(longer)26 b(than)i(100)e(b)n (yte.)275 1508 y(Because)c(of)i(the)h(\014nite)f(\(and)g(often)g(large\))f(v) -5 b(alue)24 b(of)g Fs(t)1987 1520 y Fj(0)2024 1508 y Fx(,)h(the)f(ab)r(o)n (v)n(e)f(is)h(a)f Fn(two-p)l(ar)l(ameter)i Fx(description)150 1607 y(of)e(comm)n(unication)f(p)r(erformance.)35 b(It)23 b(is)g(therefore)f (incorrect,)h(and)g(sometimes)f(p)r(ositiv)n(ely)h(misleading,)150 1707 y(to)c(quote)g(only)g(one)g(of)g(the)g(parameters)f(\(e.g.)34 b(just)19 b Fs(r)1806 1719 y Fg(1)1877 1707 y Fx(,)i(as)e(is)g(often)g (done\))h(to)f(describ)r(e)f(the)i(p)r(erformance.)150 1807 y(The)j(most)f(useful)h(pairs)f(of)h(parameters)e(are)g(\()p Fs(r)1663 1819 y Fg(1)1735 1807 y Fx(,)p Fs(n)1818 1805 y Ff(1)p 1817 1814 V 1817 1847 a(2)1860 1807 y Fx(\),)j(\()p Fs(\031)2018 1819 y Fj(0)2056 1807 y Fs(;)14 b(n)2153 1805 y Ff(1)p 2152 1814 V 2152 1847 a(2)2195 1807 y Fx(\))23 b(and)f(\()p Fs(t)2468 1819 y Fj(0)2506 1807 y Fs(;)14 b(r)2580 1819 y Fg(1)2651 1807 y Fx(\),)24 b(dep)r(ending)f(on)f(whether)150 1906 y(one)j(is)g(concerned)g (with)g(long)g(v)n(ectors,)f(short)h(v)n(ectors)f(or)g(a)h(direct)g (comparison)f(with)i(hardw)n(are)d(times.)150 2006 y(Note)39 b(also)f(that,)43 b(although)38 b Fs(n)1175 2004 y Ff(1)p 1175 2013 V 1175 2046 a(2)1257 2006 y Fx(is)h(de\014ned)h(as)e(the)i(message)e (length)h(required)f(to)h(obtain)g(half)h(the)150 2117 y(asymptotic)22 b(rate)f Fs(r)774 2129 y Fg(1)845 2117 y Fx(,)i(the)f(t)n(w)n(o)g(parameters) e(\()p Fs(r)1673 2129 y Fg(1)1744 2117 y Fx(,)p Fs(n)1827 2115 y Ff(1)p 1827 2124 V 1827 2157 a(2)1869 2117 y Fx(\))j(are)e(su\016cien)n(t)h (to)g(calculate)f(the)i(comm)n(unication)150 2217 y(rate)k(for)g(an)n(y)g (message)f(length)i(via)f(equation)g(3.5,)g(or)f(equiv)-5 b(alen)n(tly)27 b(using)h Fs(\031)2637 2229 y Fj(0)2702 2217 y Fx(instead)f(of)h Fs(r)3120 2229 y Fg(1)3191 2217 y Fx(via)f(3.9.)275 2316 y(The)g(COMMS1)g (and)h(COMMS2)f(b)r(enc)n(hmarks)f(exist)i(as)f(part)g(of)g(the)h(Genesis)g (b)r(enc)n(hmarks)e([17)o(].)150 2548 y Fy(3.3.2)112 b(T)-9 b(otal)37 b(Saturation)g(Bandwidth:)50 b(COMMS3)150 2702 y Fx(T)-7 b(o)34 b(complemen)n(t)h(the)g(ab)r(o)n(v)n(e)e(comm)n(unication)h(b) r(enc)n(hmarks,)i(there)e(is)h(a)f(need)h(for)f(a)g(b)r(enc)n(hmark)g(to)150 2801 y(measure)e(the)h(total)f(saturation)g(bandwidth)h(of)g(the)g(complete)f (comm)n(unication)g(system,)i(and)f(to)f(see)150 2901 y(ho)n(w)k(this)i (scales)e(with)h(the)h(n)n(um)n(b)r(er)f(of)g(pro)r(cessors.)63 b(A)37 b(natural)f(generalisation)f(of)i(the)h(COMMS2)150 3000 y(b)r(enc)n(hmark)30 b(is)h(made)g(as)f(follo)n(ws,)h(and)g(called)g(the)g (COMMS3)f(b)r(enc)n(hmark:)43 b(Eac)n(h)30 b(pro)r(cessor)f(of)i(a)g Fs(p)p Fx(-)150 3100 y(pro)r(cessor)25 b(system)i(sends)g(a)f(message)g(of)h (length)g Fs(n)g Fx(to)g(the)g(other)g(\()p Fs(p)17 b Fi(\000)g Fx(1\))27 b(pro)r(cessors.)34 b(Eac)n(h)26 b(pro)r(cessor)150 3200 y(then)20 b(w)n(aits)f(to)h(receiv)n(e)f(the)h(\()p Fs(p)s Fi(\000)s Fx(1\))f(messages)f(directed)h(at)h(it.)35 b(The)20 b(timing)g(of)f(this)i(generalised)d Fn(pingp)l(ong)150 3299 y Fx(ends)24 b(when)g(all)f(messages)f(ha)n(v)n(e)h(b)r(een)h(successfully)f (receiv)n(ed)g(b)n(y)g(all)g(pro)r(cessors;)g(although)g(the)h(pro)r(cess)150 3399 y(will)34 b(b)r(e)h(rep)r(eated)f(man)n(y)f(times)i(to)f(obtain)g(an)g (accurate)f(measuremen)n(t,)i(and)f(the)g(o)n(v)n(erall)e(time)j(will)150 3499 y(b)r(e)e(divided)f(b)n(y)h(the)f(n)n(um)n(b)r(er)h(of)f(rep)r(eats.)51 b(The)32 b(time)h(for)f(the)h(generalised)d(pingp)r(ong)i(is)h(the)f(time)h (to)150 3598 y(send)f Fs(p)p Fx(\()p Fs(p)21 b Fi(\000)g Fx(1\))33 b(messages)d(of)i(length)g Fs(n)g Fx(and)g(can)g(b)r(e)h(analysed)e(in)h(the) h(same)e(w)n(a)n(y)g(as)h(COMMS1)f(and)150 3698 y(COMMS2)e(in)n(to)h(v)-5 b(alues)29 b(of)h(\()p Fs(r)1130 3710 y Fg(1)1201 3698 y Fx(,)p Fs(n)1284 3696 y Ff(1)p 1284 3705 V 1284 3738 a(2)1327 3698 y Fx(\).)44 b(The)29 b(v)-5 b(alue)30 b(obtained)g(for)f Fs(r)2325 3710 y Fg(1)2396 3698 y Fx(is)h(the)g(required)f(total)g(saturation)150 3797 y(bandwidth,)24 b(and)f(w)n(e)f(are)g(in)n(terested)g(in)h(ho)n(w)f (this)i(scales)d(up)i(as)f(the)h(n)n(um)n(b)r(er)g(of)g(pro)r(cessors)d Fs(p)j Fx(increases)150 3897 y(and)k(with)i(it)f(the)g(n)n(um)n(b)r(er)f(of)g (a)n(v)-5 b(ailable)27 b(links)g(in)h(the)g(system.)275 3997 y(COMMS3)f(is)g(a)g(new)h(b)r(enc)n(hmark)f(written)h(sp)r(eci\014cally)f (for)g Fo(P)-7 b(ARKBENCH)29 b Fx(.)150 4229 y Fy(3.3.3)112 b(Comm)m(unication)35 b(Bottlenec)m(k:)49 b(POL)-9 b(Y3)150 4382 y Fx(POL)i(Y3)28 b(assesses)g(the)i(sev)n(erit)n(y)e(of)i(the)g(comm)n (unication)e(b)r(ottlenec)n(k.)43 b(It)30 b(is)f(the)h(same)f(as)g(the)h(POL) -7 b(Y1)150 4482 y(b)r(enc)n(hmark)21 b(except)g(that)h(the)g(data)f(for)g (the)g(p)r(olynomial)g(ev)-5 b(aluation)21 b(is)g(stored)g(on)g(a)g(neigh)n (b)r(ouring)f(pro-)150 4581 y(cessor.)35 b(The)27 b(v)-5 b(alue)27 b(of)g Fs(f)952 4579 y Ff(1)p 951 4588 V 951 4622 a(2)994 4581 y Fx(obtained)f(therefore)g(measures)g(the)h(ratio)f(of)h(arithmetic)g(to)g (comm)n(unication)150 4681 y(p)r(erformance.)35 b(Equation)25 b(3.3)f(sho)n(ws)h(that)h(the)g(computational)e(in)n(tensit)n(y)i(of)f(the)h (calculation)f(m)n(ust)h(b)r(e)150 4781 y(signi\014can)n(tly)g(greater)g (than)h Fs(f)1137 4779 y Ff(1)p 1137 4788 V 1137 4821 a(2)1179 4781 y Fx(\(sa)n(y)g(4)f(times)i(greater\))e(if)h(comm)n(unication)g(is)g (not)g(to)h(b)r(e)f(a)g(b)r(ottlenec)n(k.)150 4880 y(In)e(this)h(case)e(the)h (computational)g(in)n(tensit)n(y)g(is)g(the)g(ratio)f(of)h(arithmetic)g(p)r (erformed)g(on)g(a)f(pro)r(cessor)f(to)150 4980 y(w)n(ords)i(transferred)f (to/from)i(it)g(o)n(v)n(er)e(comm)n(unication)i(links.)36 b(In)26 b(the)h(common)e(case)h(that)g(the)h(amoun)n(t)150 5080 y(of)32 b(arithmetic)h(is)f(prop)r(ortional)f(to)h(the)h(v)n(olume)f(of)h(a)f (region,)g(and)h(the)g(data)f(comm)n(unicated)g(is)g(pro-)150 5179 y(p)r(ortional)d(to)h(the)h(surface)e(of)h(the)h(region,)e(the)i (computational)e(in)n(tensit)n(y)h(is)g(increased)f(as)h(the)g(size)g(of)1796 5428 y(24)p eop PNP restore PNEP %%Page: ? 14 0.6303 -612.00 PNLS /PNP save def 12.6922 89.4750 translate 26 bop 150 312 a Fx(the)28 b(region)f(\(or)g(gran)n(ularit)n(y)e(of)j(the)h (decomp)r(osition\))e(is)h(increased.)36 b(Then)28 b(the)h Fs(f)2811 310 y Ff(1)p 2810 319 29 4 v 2810 353 a(2)2853 312 y Fx(obtained)e(from)h(this)150 412 y(b)r(enc)n(hmark)c(is)h(directly)g (related)f(to)h(the)h(gran)n(ularit)n(y)c(that)j(is)g(required)f(to)h(mak)n (e)f(comm)n(unication)h(time)150 511 y(unimp)r(ortan)n(t.)275 611 y(POL)-7 b(Y3)26 b(is)i(a)f(new)g(b)r(enc)n(hmark)g(written)h(sp)r (eci\014cally)f(for)g Fo(P)-7 b(ARKBENCH)30 b Fx(.)150 842 y Fy(3.3.4)112 b(Sync)m(hronisation)37 b(Benc)m(hmarks:)50 b(SYNCH1)150 996 y Fx(SYNCH1)31 b(measures)f(the)h(time)h(to)f(execute)f(a)h (barrier)e(sync)n(hronisation)g(statemen)n(t)i(as)f(a)h(function)g(of)150 1095 y(the)i(n)n(um)n(b)r(er)g(of)g(pro)r(cesses)f(taking)g(part)h(in)g(the)h (barrier.)51 b(The)33 b(practicabilit)n(y)g(of)g(massiv)n(ely)e(parallel)150 1195 y(computation)e(with)h(thousands)e(or)g(tens)i(of)f(thousands)f(of)h (pro)r(cessors)e(dep)r(ends)j(on)f(this)g(barrier)f(time)150 1295 y(not)22 b(increasing)f(to)r(o)h(fast)g(with)h(the)f(n)n(um)n(b)r(er)g (of)g(pro)r(cessors.)33 b(The)22 b(results)g(are)f(quoted)h(b)r(oth)h(as)e(a) h(barrier)150 1394 y(time,)28 b(and)g(as)f(the)h(n)n(um)n(b)r(er)f(of)g (barrier)f(statemen)n(ts)i(executed)f(p)r(er)h(second)f(\(barr/s\).)275 1494 y(The)g(SYNCH1)h(b)r(enc)n(hmark)f(exists)g(as)g(part)g(of)h(Genesis)f (v2.1.1)f([17)o(].)150 1767 y Fp(3.4)137 b(Summary)45 b(of)g(Benc)l(hmarks) 150 1949 y Fx(T)-7 b(able-3.1)26 b(summarises)g(the)i(curren)n(t)f(lo)n (w-lev)n(el)f(b)r(enc)n(hmarks,)g(and)i(the)g(arc)n(hitectural)e(prop)r (erties)g(and)150 2049 y(parameters)g(that)i(they)g(measure.)337 2303 y(T)-7 b(able)26 b(3.1:)34 b(Curren)n(t)25 b(Lo)n(w-Lev)n(el)e(b)r(enc)n (hmarks)i(and)g(the)g(P)n(arameters)e(they)i(measure.)36 b(Note)337 2402 y(w)n(e)f(abbreviate)g(p)r(erformance)f(\(p)r(erf.\),)k(arithmetic)d (\(arith.\),)j(comm)n(unication)c(\(comms.\),)337 2502 y(op)r(erations)27 b(\(ops.\).)p 638 2534 2375 4 v 687 2598 a Fe(Benc)n(hmark)510 b(Measures)618 b(P)n(arameters)p 638 2720 V 687 2784 a(SINGLE-PR)n(OCESSOR) 687 2876 y(TICK1)654 b(Timer)25 b(resolution)359 b(tic)n(k)25 b(in)n(terv)l(al)687 2967 y(TICK2)654 b(Timer)25 b(v)l(alue)446 b(w)n(all-clo)r(c)n(k)28 b(c)n(hec)n(k)687 3058 y(RINF1)659 b(Basic)27 b(Arith.)34 b(ops.)404 b(\()p Fd(r)2619 3066 y Fm(1)2684 3058 y Fe(,)p Fd(n)2761 3059 y Ff(1)p 2762 3068 29 4 v 2762 3100 a(2)2804 3058 y Fe(\))687 3164 y(POL)-6 b(Y1)640 b(Cac)n(he-b)r (ottlenec)n(k)437 b(\()s(^)-41 b Fd(r)r Fe(,)p Fd(f)2725 3165 y Ff(1)p 2726 3174 V 2726 3206 a(2)2768 3164 y Fe(\))687 3270 y(POL)-6 b(Y2)640 b(Memory-b)r(ottlenec)n(k)361 b(\()s(^)-41 b Fd(r)r Fe(,)p Fd(f)2725 3271 y Ff(1)p 2726 3280 V 2726 3312 a(2)2768 3270 y Fe(\))p 638 3315 2375 4 v 687 3379 a(MUL)-6 b(TI-PR)n(OCESSOR)687 3471 y(COMMS1)554 b(Basic)27 b(Message)h(p)r(erf.)318 b(\()p Fd(r)2619 3479 y Fm(1)2684 3471 y Fe(,)p Fd(n)2761 3472 y Ff(1)p 2762 3481 29 4 v 2762 3513 a(2)2804 3471 y Fe(\))687 3576 y(COMMS2)554 b(Message)28 b(exc)n(h.)33 b(p)r(erf.)318 b(\()p Fd(r)2619 3584 y Fm(1)2684 3576 y Fe(,)p Fd(n)2761 3577 y Ff(1)p 2762 3586 V 2762 3618 a(2)2804 3576 y Fe(\))687 3682 y(COMMS3)554 b(Saturation)26 b(Bandwidth)227 b(\()p Fd(r)2619 3690 y Fm(1)2684 3682 y Fe(,)p Fd(n)2761 3683 y Ff(1)p 2762 3692 V 2762 3724 a(2)2804 3682 y Fe(\))687 3788 y(POL)-6 b(Y3)640 b(Comms.)33 b(Bottlenec)n(k)349 b(\()s(^)-41 b Fd(r)r Fe(,)p Fd(f)2725 3789 y Ff(1)p 2726 3798 V 2726 3830 a(2)2768 3788 y Fe(\))687 3894 y(SYNCH1)580 b(Barrier)27 b(time)e(and)g(rate)292 b(barr/s)p 638 3925 2375 4 v 150 4329 a Fy(3.4.1)112 b(Arithmetic)34 b(Benc)m(hmark)k(Results)150 4482 y Fx(As)24 b(an)f(indication)g(of)h(the)f (t)n(yp)r(e)h(of)g(results)f(giv)n(en)f(b)n(y)h(the)h(prop)r(osed)f(lo)n (w-lev)n(el)f(arithmetic)h(b)r(enc)n(hmarks,)150 4581 y(T)-7 b(able-3.2)30 b(giv)n(es)h(measuremen)n(ts)g(made)h(on)f(a)h(n)n(um)n(b)r(er) g(of)g(w)n(orkstations,)f(and)g(micropro)r(cessor)e(c)n(hips)150 4681 y(that)35 b(are)e(used)i(as)f(pro)r(cessing)f(no)r(des)h(in)h(m)n (ultipro)r(cessor)e(MIMD)i(computers.)58 b(The)34 b(measuremen)n(ts)150 4781 y(sho)n(wn)j(represen)n(t)f(the)i(state)g(of)f(a\013airs)f(on)i(the)g (date)f(of)h(the)g(measuremen)n(ts,)h(and)e(b)r(oth)h(hardw)n(are)150 4880 y(and)f(soft)n(w)n(are)e(impro)n(v)n(emen)n(ts)g(since)i(that)h(time)f (should)g(ha)n(v)n(e)e(signi\014can)n(tly)i(impro)n(v)n(ed)e(the)j(results.) 150 4980 y(They)c(are)e(presen)n(ted)h(here)g(only)h(to)f(illustrate)h(the)g (t)n(yp)r(e)f(of)h(results)f(to)h(b)r(e)g(exp)r(ected)g(from)f(the)h(lo)n(w-) 150 5080 y(lev)n(el)28 b(b)r(enc)n(hmarks.)37 b(They)28 b(should)g(not)g(b)r (e)g(tak)n(en)g(as)f(represen)n(ting)f(the)j(curren)n(t)e(state)h(of)g(comp)r (etitiv)n(e)150 5179 y(p)r(erformance)j(in)h(the)g(v)n(ery)f(rapidly)g(c)n (hanging)f(w)n(orkstation)g(and)h(c)n(hip)h(mark)n(et.)49 b(Suc)n(h)31 b(a)h(comparison)1796 5428 y(25)p eop PNP restore /PNP save def 628.2618 89.4750 translate 27 bop 337 370 a Fx(T)-7 b(able)25 b(3.2:)34 b(Examples)24 b(of)g(lo)n(w-lev)n(el)f(b)r(enc)n(hmark)h(measuremen)n(ts)f(on)h(some)g (common)g(w)n(ork-)337 469 y(stations)32 b(and)g(micropro)r(cessor)d(c)n (hips)i(used)h(in)h(MIMD)f(computers.)50 b(Measuremen)n(ts)31 b(w)n(ere)337 569 y(made)d(with)g(the)f(highest)h(lev)n(el)f(of)g (optimisation)g(that)h(ran,)e(and)i(are)e(in)i(M\015op/s)e(for)h(64-bit)337 669 y(precision.)47 b(The)31 b(units)h(of)f Fs(n)1271 667 y Ff(1)p 1271 676 29 4 v 1271 709 a(2)1313 669 y Fx(are)f(v)n(ector)g(length,)j (and)e Fs(f)2206 667 y Ff(1)p 2205 676 V 2205 709 a(2)2248 669 y Fx(are)f(\015op/mref.)47 b(Results)31 b(are)f(for)337 768 y(the)k(b)r(est)g(generally)e(a)n(v)-5 b(ailable)32 b(compiler)g(on)h (the)h(date)f(sho)n(wn.)53 b(The)34 b(RINF1)f(b)r(enc)n(hmark)337 868 y(giv)n(es)g(v)-5 b(alues)32 b(of)h(the)h(\()p Fs(r)1117 880 y Fg(1)1188 868 y Fx(,)p Fs(n)1271 866 y Ff(1)p 1271 875 V 1271 908 a(2)1313 868 y Fx(\))q(parameters)d(for)i(the)g(k)n(ernel)g(A=B*C) f(\(v)n(ector)g(=)h(v)n(ector)f Fi(\002)337 979 y Fx(v)n(ector\))27 b(for)g(con)n(tiguously)f(stored)h(v)n(ectors.)p 986 1011 1678 4 v 1591 1075 a Fe(In)n(tel)176 b(IBM)26 b(RS/)155 b(DEC)1036 1167 y(Benc)n(hmark)129 b(i860XP)142 b(6000-530)226 b Fd(\013)1548 1258 y Fe(50MHz)173 b(25MHz)139 b(133MHz)p 986 1289 V 1036 1353 a(d/m/y)253 b(12/10/93)126 b(14/6/90)131 b(13/1/93)p 986 1383 V 1036 1447 a(Linpac)n(kd)255 b(14.7)276 b(9.54)261 b(20.7)1036 1539 y(n=100)p 986 1569 V 1036 1633 a(Liv)n(ermore)225 b(28.8)276 b(31.8)261 b(46.6)1036 1725 y(Maxim)n(um)p 986 1755 V 1036 1819 a(Liv)n(ermore)225 b(2.62)276 b(1.34)261 b(4.47)1036 1911 y(Minim)n(um)p 986 1941 V 1036 2005 a(RINF1)1036 2097 y Fd(r)1071 2105 y Fm(1)1600 2097 y Fe(7.64)672 b(26.4)1036 2188 y(\()p Fd(n)1122 2189 y Ff(1)p 1122 2198 29 4 v 1122 2230 a(2)1164 2188 y Fe(\))376 b(\(2.58\))631 b(\(5.6\))p 986 2233 1678 4 v 1036 2297 a(POL)-6 b(Y1)1039 2388 y(^)-41 b Fd(r)509 b Fe(13.50)238 b(25.85)243 b(88.9)1036 2480 y(\()p Fd(f)1113 2481 y Ff(1)p 1113 2490 29 4 v 1113 2522 a(2)1155 2480 y Fe(\))385 b(\(0.44\))216 b(\(0.34\))201 b(\(0.71\))p 986 2525 1678 4 v 1036 2589 a(POL)-6 b(Y2)1039 2680 y(^)-41 b Fd(r)509 b Fe(13.48)238 b(25.65)1036 2772 y(\()p Fd(f)1113 2773 y Ff(1)p 1113 2782 29 4 v 1113 2813 a(2)1155 2772 y Fe(\))385 b(\(1.12\))216 b(\(0.91\))p 986 2817 1678 4 v 986 2837 V 150 3086 a Fx(will)24 b(only)g(b)r(e)h(p)r(ossible)f(if)g (these)g(b)r(enc)n(hmarks)g(are)f(routinely)h(run)g(on)f(new)i(hardw)n(are)d (and)i(soft)n(w)n(are)e(and)150 3185 y(the)j(results)f(stored)f(in)i(the)f Fo(P)-7 b(ARKBENCH)30 b Fx(in)n(teractiv)n(e)23 b(p)r(erformance)h(database,) f(whic)n(h)i(w)n(ould)f(then)150 3285 y(con)n(tain)35 b(an)h(up-to-date)f (comparison)f(of)i(comp)r(etitiv)n(e)g(hardw)n(are)e(and)h(soft)n(w)n(are.)60 b(Not)n(withstanding)150 3385 y(these)22 b(ca)n(v)n(eats,)f(w)n(e)h(feel)h (it)f(is)g(helpful)h(to)f(giv)n(e)f(these)h(examples)f(of)h(lo)n(w-lev)n(el)f (b)r(enc)n(hmark)g(measuremen)n(ts)150 3484 y(that)35 b(happ)r(en)g(to)f(b)r (e)h(a)n(v)-5 b(ailable,)35 b(ev)n(en)f(though)g(some)g(are)f(a)i(few)f(y)n (ears)f(old)h(and)h(therefore)e(probably)150 3584 y(seriously)c(outdated.)43 b(In)30 b(this)h(small)e(table)h(w)n(e)g(ha)n(v)n(e)e(not)i(ro)r(om)f(to)h (giv)n(e)f(the)i(full)f(sp)r(eci\014cation)g(of)g(the)150 3684 y(conditions)i(for)g(eac)n(h)g(measuremen)n(t)g(\(full)i(and)f(exact)f (description)g(hardw)n(are,)g(and)g(of)h(compiler)f(and)150 3783 y(options)27 b(used,)h(etc.\),)g(but)g(this)g(information)f(w)n(ould)g (b)r(e)h(an)g(essen)n(tial)e(and)i(required)e(comp)r(onen)n(t)i(of)f(an)150 3883 y(en)n(try)g(in)n(to)g(the)h Fo(P)-7 b(ARKBENCH)30 b Fx(database)c(of)i (b)r(enc)n(hmark)f(results.)150 4115 y Fy(3.4.2)112 b(Example)37 b(Results)f(for)i(the)f(COMMS1)i(b)s(enc)m(hmark)150 4268 y Fx(W)-7 b(e)44 b(rep)r(ort)f(b)r(elo)n(w)h(results)f(for)g(the)i(COMMS1)e(b)r (enc)n(hmark)g(on)h(the)g Fo(SUPRENUM)29 b Fx(,)48 b(and)c(In)n(tel)150 4368 y(iPSC/860)25 b([15)o(],)j(T)-7 b(ouc)n(hstone)27 b(Delta)h([26)o(],)g (In)n(tel)f(P)n(aragon)e(XP/S)i(and)g(Meik)n(o)g(CS-2)g(computers.)275 4468 y(T)-7 b(able-3.3)31 b(giv)n(es)g(the)i(v)-5 b(alues)33 b(obtained)f(for)g(the)i(comm)n(unication)d(parameters,)i(in)g(the)g(v)n (ersion)e(of)150 4567 y(the)f(b)r(enc)n(hmark)e(using)h(the)h(nativ)n(e)e Fo(SUPRENUM)i Fx(extensions)e(to)i(the)f(F)-7 b(ortran90)27 b(language.)40 b(These)150 4667 y(include)g(a)g(SEND)g(and)g(RECEIVE)f (language)f(statemen)n(t)i(with)g(a)g(syn)n(tax)f(similar)g(to)h(that)g(of)g (the)150 4767 y(F)-7 b(ortran)36 b(READ)h(and)g(WRITE)g(statemen)n(t.)65 b(The)37 b(asymptotic)f(stream)g(rate,)j(or)d(bandwidth,)k(\()p Fs(r)3422 4779 y Fg(1)3493 4767 y Fx(\))150 4866 y(sho)n(ws)27 b(considerable)g(v)-5 b(ariation)28 b(on)g(the)h(Supren)n(um,)g(dep)r(ending) f(on)h(ho)n(w)e(the)i(data)f(to)h(b)r(e)f(transferred)150 4966 y(is)38 b(sp)r(eci\014ed)g(in)g(the)h(I/O)e(list)h(of)g(the)g(SEND)h (statemen)n(t.)68 b(A)38 b(v)-5 b(ariable)37 b(length)h(arra)n(y)e(in)i(F)-7 b(ortran90)150 5065 y(syn)n(tax)23 b(in)i(single)e(precision)h(ac)n(hiev)n (es)e(0.67)h(MB/s,)h(whereas)f(the)i(same)e(statemen)n(t)h(sp)r(eci\014ed)h (in)f(double)150 5165 y(precision)40 b(ac)n(hiev)n(es)f(4.8)h(MB/s.)76 b(This)41 b(double-precision)e(rate)h(is)h(ab)r(out)f(t)n(wice)h(that)g (observ)n(ed)e(on)1796 5428 y(26)p eop PNP restore PNEP %%Page: ? 15 0.6303 -612.00 PNLS /PNP save def 12.6922 89.4750 translate 28 bop 150 312 a Fx(the)33 b(iPSC/860)d(with)k(their)e(CSEND)h(F)-7 b(ortran)32 b(subroutine,)h(whic)n(h)g(sends)f(an)g(arra)n(y)f(whose)g (length)i(is)150 412 y(sp)r(eci\014ed)23 b(in)g(b)n(ytes.)35 b(The)23 b(principal)f(di\013erence)h(b)r(et)n(w)n(een)g(the)g(t)n(w)n(o)f (computers)g(is)h(the)g(magnitude)g(of)g(the)150 511 y(startup)i(time,)i Fs(t)680 523 y Fj(0)717 511 y Fx(,)f(whic)n(h)g(is)f(73)p Fs(\026s)g Fx(on)g(the)h(iPSC/860)e(compared)g(with)i(ab)r(out)g(3ms)f(on)g(the)h (Supren)n(um.)150 611 y(Since)i(the)g(startup)g(time,)g(via)g Fs(\031)1198 623 y Fj(0)1235 611 y Fx(,)g(determines)g(the)g(transfer)f(rate) g(for)h(short)f(messages)f(\(sa)n(y)h Fs(<)c Fx(100B\),)150 711 y(w)n(e)30 b(see)f(that)h(the)h(Supren)n(um)e(is)h(45)f(times)h(slo)n(w)n (er)e(than)i(the)h(iPSC/860)c(for)j(short)f(messages.)42 b(On)30 b(the)150 810 y(other)c(hand)i(the)f(Supren)n(um)g(has)g(almost)f(t)n(wice)h (the)g(stream)g(rate)f(for)h(long)f(messages)f(\(as)i(seen)g(b)n(y)g(the)150 910 y(v)-5 b(alue)28 b(of)g Fs(r)497 922 y Fg(1)568 910 y Fx(\),)h(pro)n (vided)e(the)h(most)g(fa)n(v)n(ourable)f(format)g(\(i.e.)39 b(double)28 b(precision)g(or)f(64-bit\))h(is)g(used)g(in)150 1010 y(the)23 b(I/O)e(list.)35 b(One)22 b(ma)n(y)f(compute)i(from)e(these)i (n)n(um)n(b)r(ers)e(that)i(the)f(iPSC/860)e(is)i(faster)g(at)g(transferring) 150 1109 y(messages)h(for)g(all)h(message)f(lengths)h(less)g(than)g(16,481)e (Byte.)36 b(The)24 b(longer)f(startup)h(time)h(on)f(Supren)n(um)150 1209 y(results)29 b(in)i(larger)d(v)-5 b(alues)29 b(of)h Fs(n)1160 1207 y Ff(1)p 1160 1216 29 4 v 1160 1249 a(2)1202 1209 y Fx(,)h(sho)n(wing)d (that)j(longer)d(messages)g(are)h(needed)h(to)g(ac)n(hiev)n(e)f(an)n(y)g(giv) n(en)150 1308 y(fraction)e(of)h(the)f(asymptotic)h(rate.)275 1408 y(The)k(results)g(for)g(the)g(T)-7 b(ouc)n(hstone)32 b(Delta)g(sho)n(w)g (that)g(this)h(computer)f(has)g(the)g(fastest)h(short)e(and)150 1508 y(long)38 b(message)e(p)r(erformance,)k(judged)f(resp)r(ectiv)n(ely)e(b) n(y)h(the)h(v)-5 b(alues)38 b(of)g Fs(\031)2616 1520 y Fj(0)2692 1508 y Fx(and)g Fs(r)2901 1520 y Fg(1)2972 1508 y Fx(.)69 b(Ho)n(w)n(ev)n(er) 37 b(the)150 1607 y(impro)n(v)n(emen)n(t)j(of)g(short)h(message)e(p)r (erformance)h(o)n(v)n(er)f(the)i(iPSC/860)e(is)i(only)f(marginal,)j(and)e (the)150 1707 y(long)26 b(message)g(p)r(erformance)g(is)h(only)f(ab)r(out)h (one)g(quarter)e(of)i(the)h(adv)n(ertised)d(bandwidth)j(of)f(25MB/s.)150 1807 y(Ho)n(w)n(ev)n(er)17 b(hardw)n(are)g(and)i(soft)n(w)n(are)e(impro)n(v)n (emen)n(ts)g(made)i(since)g(the)g(measuremen)n(ts)f(w)n(ere)g(made)g(should) 150 1906 y(ha)n(v)n(e)26 b(impro)n(v)n(ed)h(the)h(results.)275 2006 y(If)h(w)n(e)g(compare)f(the)h(new)g(generation)f(of)h(pro)r(duction)g (computers,)g(the)g(In)n(tel)h(P)n(aragon)c(XP/S)i(and)150 2105 y(the)40 b(Meik)n(o)e(CS-2,)k(w)n(e)d(\014nd,)k(on)c(the)h(dates)f (stated,)k(the)d(CS-2)e(to)i(ha)n(v)n(e)e(a)h(higher)g(comm)n(unication)150 2205 y(p)r(erformance)d(than)h(the)g(P)n(aragon)d(for)j(b)r(oth)g(short)g(\() p Fs(\031)1970 2217 y Fj(0)2007 2205 y Fx(\))h(and)f(long)f(messages)f(\()p Fs(r)2867 2217 y Fg(1)2938 2205 y Fx(\),)40 b(and)d(therefore)150 2305 y(for)31 b(all)g(message)f(lengths.)48 b(Ho)n(w)n(ev)n(er)29 b(b)r(oth)j(computers)f(are)f(at)h(an)g(early)g(state)g(of)g(the)h(hardw)n (are)d(and)150 2404 y(soft)n(w)n(are)37 b(dev)n(elopmen)n(t,)k(and)d(b)r(oth) h(ha)n(v)n(e)f(considerable)f(dev)n(elopmen)n(t)h(p)r(oten)n(tial.)70 b(The)39 b(COMMS1)150 2504 y(b)r(enc)n(hmark)25 b(will)g(con)n(tin)n(ue)g(to) h(b)r(e)f(used)h(to)f(trac)n(k)f(this)i(comp)r(etition)g(in)f(comm)n (unication)g(p)r(erformance,)150 2604 y(and)h(the)h(success)f(of)g(b)r(oth)h (man)n(ufacturers)e(to)i(ac)n(hiev)n(e)e(a)h(high)g(p)r(erformance)g(for)g(b) r(oth)h(short)e(and)i(long)150 2703 y(messages.)337 2961 y(T)-7 b(able)34 b(3.3:)48 b(V)-7 b(alues)33 b(of)h(\()p Fs(r)1189 2973 y Fg(1)1260 2961 y Fx(,)p Fs(n)1343 2959 y Ff(1)p 1343 2968 V 1343 3002 a(2)1385 2961 y Fx(,)h Fs(t)1473 2973 y Fj(0)1511 2961 y Fx(,)g Fs(\031)1616 2973 y Fj(0)1653 2961 y Fx(\))f(for)f(the)h(comm)n (unication)f(of)h(messages)e(b)r(et)n(w)n(een)337 3061 y(t)n(w)n(o)37 b(no)r(des)f(of)h(the)g(same)f(cluster)h(on)f(the)h(Supren)n(um)g(and)g (neigh)n(b)r(ouring)e(no)r(des)i(on)f(the)337 3161 y(In)n(tel)29 b(iPSC/860,)d(T)-7 b(ouc)n(hstone)28 b(Delta,)g(In)n(tel)h(P)n(aragon)c(and)j (Meik)n(o)g(CS-2)f(computers.)39 b(The)337 3260 y(Delta)31 b(measuremen)n(ts)f(w)n(ere)g(made)g(on)h(17)e(Jan.)46 b(1992,)29 b(and)i(should)f(ha)n(v)n(e)g(b)r(een)h(impro)n(v)n(ed)337 3360 y(b)n(y)f(subsequen)n(t)f(hardw)n(are)e(and)i(soft)n(w)n(are)f(c)n (hanges.)41 b(P)n(aragon)26 b(measuremen)n(ts)i(w)n(ere)h(made)337 3459 y(at)23 b(ORNL)f(25-28)f(Ma)n(y)-7 b(,)22 b(1993,)g(and)g(the)h(CS-2)f (measuremen)n(ts)f(w)n(ere)h(made)g(at)h(Southampton)337 3559 y(Univ)n(ersit)n(y)k(9)g(July)-7 b(,)28 b(1993)p 596 3587 2457 4 v 646 3651 a Fe(Sp)r(eci\014cation)435 b(Range)301 b Fd(r)2051 3659 y Fm(1)2309 3651 y Fd(n)2365 3652 y Ff(1)p 2365 3661 29 4 v 2365 3693 a(2)2610 3651 y Fd(t)2638 3659 y Fc(0)2876 3651 y Fd(\031)2920 3659 y Fc(0)1505 3757 y Fe(B*)372 b(MB/s)170 b(B)209 b(ms)161 b(kHz)p 596 3787 2457 4 v 646 3851 a(SUPRENUM)646 3943 y(sp)26 b(SEND)f(A\(1:N\))780 b(0.67)149 b(2041)140 b(3.05)120 b(0.328)646 4034 y(dp)25 b(SEND)g(A\(1:N\))768 b(4.82)130 b(12740)121 b(2.64)f(0.378)p 596 4065 V 646 4129 a(INTEL)26 b(iPSC/860)646 4220 y(CSEND)g(\(,A,N,,\))306 b Fd(N)30 b(<)21 b Fe(100)206 b(2.36)168 b(179)140 b(0.074)120 b(13.5)1505 4311 y Fd(N)30 b(>)21 b Fe(100)206 b(2.80)168 b(560)140 b(0.200)g(5.0)p 596 4342 V 646 4406 a(INTEL)26 b(Delta)646 4497 y(CSEND)g(\(,A,N,,\))306 b Fd(N)30 b(<)21 b Fe(512)206 b(3.48)168 b(213)140 b(0.061)120 b(16.3)1505 4589 y Fd(N)30 b(>)21 b Fe(512)206 b(6.76)168 b(892)140 b(0.132)120 b(7.57)p 596 4619 V 646 4683 a(INTEL)26 b(P)n(aragon)h(XP/S)646 4775 y(CSEND)f(\(,A,N,,\))306 b Fd(N)30 b(<)21 b Fe(40000)130 b(23.5)149 b(4044)121 b(0.172)f(5.80)p 596 4805 V 646 4869 a(Meik)n(o)27 b(CS-2)646 4960 y(P)-6 b(ARMA)n(CS)474 b Fd(N)30 b(<)21 b Fe(40000)130 b(43.0)149 b(3747)121 b(0.087)f(11.5)p 596 4991 V 646 5055 a(*)26 b(B)g(-)f(b)n(yte)1796 5428 y Fx(27)p eop PNP restore /PNP save def 628.2618 89.4750 translate 29 bop 150 935 a Fr(Chapter)66 b(4)150 1350 y Fu(Kernel)79 b(Benc)-7 b(hmarks)2201 1287 y Fq(\003)150 1832 y Fp(4.1)137 b(In)l(tro)t(duction)48 b(and)e(Rationale)150 2013 y Fx(The)36 b(lo)n(w-lev)n(el)e(b)r(enc)n(hmark)h(co)r(des)g(are)g(designed)g(to)g (measure)g(the)h(basic)f(arc)n(hitectural)f(features)h(of)150 2113 y(parallel)h(mac)n(hines.)66 b(F)-7 b(ull)38 b(application)f(co)r(des)g (ob)n(viously)f(measure)h(the)g(p)r(erformance)g(of)g(a)g(parallel)150 2213 y(system)d(on)h(the)f(full)i(problem)e(and)g(this)h(is)f(ultimately)h (what)g(the)g(user)f(w)n(an)n(ts.)56 b(Ho)n(w)n(ev)n(er,)35 b(in)g(man)n(y)150 2312 y(instances,)29 b(the)h(full)g(application)f(co)r (des)g(are)f(complex,)h(con)n(tain)g(man)n(y)g(100s)f(of)h(thousands)g(of)g (lines)g(of)150 2412 y(F)-7 b(ortran,)26 b(and)h(are)e(not)i(a)n(v)-5 b(ailable)26 b(in)h(a)f(suitable)h(parallel)f(v)n(ersion.)35 b(In)27 b(order)f(to)g(obtain)h(a)f(guide)h(to)g(the)150 2511 y(p)r(erformance)h(of)h(an)n(y)f(giv)n(en)g(parallel)g(system)g(on)h(a)g (particular)e(application)i(something)f(less)h(complex)150 2611 y(than)23 b(the)g(full)g(application)f(is)h(useful.)35 b(A)23 b(pro\014le)f(of)h(the)g(sequen)n(tial)f(v)n(ersion)f(of)i(the)g (application)f(enables)150 2711 y(the)28 b(compute)h(in)n(tensiv)n(e)e(p)r (ortions)h(of)g(the)g(program)e(to)i(b)r(e)h(iden)n(ti\014ed.)38 b(It)29 b(is)f(these)g(compute-in)n(tensiv)n(e)150 2810 y(sections)39 b(of)h(an)g(application)f(that)h(w)n(e)g(wish)f(to)h(mo)r(del)g(with)h(the)f (in)n(tro)r(duction)f(of)h(parallel)f(k)n(ernel)150 2910 y(b)r(enc)n(hmarks.) 275 3010 y(The)21 b(p)r(opular)g(k)n(ernel)f(b)r(enc)n(hmarks)g(that)i(ha)n (v)n(e)e(b)r(een)i(used)f(for)g(traditional)f(v)n(ector)g(sup)r(ercomputers,) 150 3109 y(suc)n(h)25 b(as)g(the)h(Liv)n(ermore)e(Lo)r(ops)50 b([5],)26 b(the)g(LINP)-7 b(A)n(CK)25 b(b)r(enc)n(hmark)50 b([8])26 b(and)f(the)h(original)e(NAS)i(k)n(ernels)150 3209 y([27)o(],)43 b(are)38 b(clearly)h(inappropriate)f(for)h(the)h(p)r (erformance)e(ev)-5 b(aluation)39 b(of)h(highly)f(parallel)g(mac)n(hines.)150 3308 y(First)33 b(of)g(all,)h(the)g(tuning)f(restrictions)f(of)h(these)g(b)r (enc)n(hmarks)g(rule)f(out)h(man)n(y)g(widely)g(used)g(parallel)150 3408 y(extensions.)k(More)27 b(imp)r(ortan)n(tly)-7 b(,)28 b(the)g(computation)g(and)g(memory)f(requiremen)n(ts)g(of)g(these)h(programs) 150 3508 y(do)c(not)g(do)f(justice)i(to)e(the)i(v)-5 b(astly)23 b(increased)g(capabilities)h(of)f(the)i(new)f(parallel)e(mac)n(hines,)j (particularly)150 3607 y(those)e(that)h(will)g(b)r(e)g(a)n(v)-5 b(ailable)22 b(b)n(y)h(the)h(mid)g(1990's.)34 b(F)-7 b(or)23 b(these)g(reasons)f(w)n(e)h(b)r(eliev)n(e)h(that)f(a)h(new,)g(widely)150 3707 y(accepted)37 b(set)g(of)g(k)n(ernel)f(b)r(enc)n(hmarks)h(is)g (desirable)f(as)g(a)h(step)h(on)e(the)i(w)n(a)n(y)e(to)h(more)f(sensible)h (and)150 3807 y(scien)n(ti\014c)27 b(p)r(erformance)g(rep)r(orting)g(of)g (parallel)g(systems.)275 3906 y(The)k(k)n(ernel)g(co)r(des)g(are)f(t)n (ypically)h(up)h(to)g(a)f(few)h(thousand)f(lines)g(of)h(F)-7 b(ortran)30 b(and)i(are)e(su\016cien)n(tly)150 4006 y(simple)40 b(that)f(the)h(p)r(erformance)e(of)i(a)f(giv)n(en)f(parallel)g(mac)n(hine)h (on)g(this)h(program)d(ma)n(y)i(b)r(e)h(related)150 4105 y(to)h(the)g (underlying)f(arc)n(hitectural)f(parameters.)74 b(It)41 b(m)n(ust)g(b)r(e)g (ac)n(kno)n(wledged,)h(ho)n(w)n(ev)n(er,)g(that)f(the)150 4205 y(p)r(erformance)26 b(on)h(k)n(ernels)f(alone)h(is)g(insu\016cien)n(t)h(to)f (completely)g(assess)f(the)i(p)r(erformance)e(p)r(oten)n(tial)h(of)150 4305 y(a)34 b(parallel)f(mac)n(hine)h(on)h(full)g(scien)n(ti\014c)f (applications.)57 b(The)34 b(c)n(hief)h(di\016cult)n(y)g(is)f(that)h(a)f (certain)g(data)150 4404 y(structure)24 b(ma)n(y)f(b)r(e)i(v)n(ery)e (e\016cien)n(t)h(on)g(a)g(certain)g(system)g(for)g(one)f(of)i(the)f(isolated) g(k)n(ernels,)g(and)g(y)n(et)g(this)150 4504 y(data)i(structure)g(w)n(ould)h (b)r(e)g(inappropriate)e(if)i(incorp)r(orated)f(in)n(to)g(a)h(larger)d (application.)36 b(F)-7 b(or)26 b(example,)150 4604 y(the)37 b(p)r(erformance)e(of)i(a)f(real)g(CFD)h(application)f(on)g(a)g(parallel)g (system)g(is)g(critically)g(dep)r(enden)n(t)h(on)150 4703 y(data)29 b(motion)h(b)r(et)n(w)n(een)f(di\013eren)n(t)h(computational)f(k)n(ernels.)42 b(In)29 b(addition,)i(full)f(applications)f(t)n(ypically)150 4803 y(ha)n(v)n(e)h(initialization)g(phases,)h(I/O)f(and)g(so)h(on,)g(so)f (complete)h(repro)r(duction)f(of)g(these)h(features)f(can)h(b)r(e)150 4903 y(of)d(critical)f(imp)r(ortance)g(for)g(a)g(realistic)g(guide)g(to)g(p)r (erformance.)275 5002 y(F)-7 b(or)27 b(these)i(reasons)e(the)i Fo(P)-7 b(ARKBENCH)29 b Fx(suite)g(in)n(tro)r(duces)f(a)g(lev)n(el)g(of)h (complexit)n(y)f(ab)r(o)n(v)n(e)f(k)n(ernel)p 150 5071 1350 4 v 241 5125 a Fm(\003)277 5148 y Fl(assem)n(bled)c(b)n(y)h(T)-6 b(on)n(y)24 b(Hey)g(for)f(Kernel)h(sub)r(committee)1796 5428 y Fx(28)p eop PNP restore PNEP %%Page: ? 16 0.6303 -612.00 PNLS /PNP save def 12.6922 89.4750 translate 30 bop 150 312 a Fx(co)r(des)29 b(whic)n(h)g(is)g(called)g Fn(c)l(omp)l(act)j(applic)l(ations)p Fx(.)45 b(These)29 b(are)f(full)i(but)g (p)r(erhaps)f(simpli\014ed)h(application)150 412 y(co)r(des)d(that)g(con)n (tain)g(all)g(the)h(necessary)d(features)i(of)g(the)h(full)g(problem)e(but)i (are)f(su\016cien)n(tly)g(simple)g(to)150 511 y(run)g(and)h(analyse.)36 b(These)27 b(are)f(describ)r(ed)i(in)g(the)g(Compact)f(Application)g(c)n (hapter)g(of)h(this)g(do)r(cumen)n(t.)150 786 y Fp(4.2)137 b(The)46 b(Kernel)g(Benc)l(hmarks)150 968 y Fx(The)34 b(k)n(ernels)e(attempt) i(to)g(span)f(a)g(reasonably)e(wide)j(range)e(of)i(application)f(areas)f(b)n (y)h(including)h(the)150 1067 y(most)20 b(frequen)n(tly)g(encoun)n(tered)f (computationally)h(in)n(tensiv)n(e)g(t)n(yp)r(es)g(of)g(problems.)34 b(W)-7 b(e)20 b(ha)n(v)n(e)g(ten)n(tativ)n(ely)150 1167 y(group)r(ed)g(them)i (in)n(to)f(four)f(sections.)34 b(Some)21 b(of)g(the)h(b)r(enc)n(hmark)e(co)r (des)g(are)g(tak)n(en)h(from)g(existing)f(parallel)150 1267 y(b)r(enc)n(hmark)f(suites)i(\(NAS)41 b([28)o(],)22 b(Genesis)40 b([12)o(],)22 b(etc\).)35 b(In)20 b(order)f(to)h(a)n(v)n(oid)e(duplication)j (and)f(redundancy)-7 b(,)150 1366 y(w)n(e)28 b(ha)n(v)n(e)g(attempted)h(to)g (list)g(some)f(of)h(the)g(attributes)g(of)f(the)h(parallel)f(system)h(tested) g(b)n(y)f(eac)n(h)g(k)n(ernel)150 1466 y(b)r(enc)n(hmark.)150 1698 y Fy(4.2.1)112 b(Matrix)37 b(b)s(enc)m(hmarks)150 1852 y Fx(F)-7 b(or)29 b(the)i(past)e(15)g(y)n(ears)f(or)h(so,)h(there)g(has)f(b)r (een)i(a)e(great)g(deal)g(of)h(activit)n(y)g(in)g(the)g(area)f(of)g (algorithms)150 1951 y(and)38 b(soft)n(w)n(are)e(for)i(solving)f(linear)g (algebra)g(problems.)67 b(The)39 b(linear)e(algebra)f(comm)n(unit)n(y)i(has)g (long)150 2051 y(recognized)22 b(the)i(need)g(for)g(help)g(in)g(dev)n (eloping)e(algorithms)h(in)n(to)g(soft)n(w)n(are)f(libraries,)h(and)h(sev)n (eral)e(y)n(ears)150 2151 y(ago,)28 b(as)g(a)h(comm)n(unit)n(y)g(e\013ort,)g (put)h(together)e(a)g Fn(de)k(facto)e Fx(standard)e(for)h(iden)n(tifying)g (basic)f(op)r(erations)150 2250 y(required)22 b(in)i(linear)e(algebra)g (algorithms)g(and)h(soft)n(w)n(are.)33 b(The)24 b(hop)r(e)f(w)n(as)f(that)i (the)g(routines)e(making)h(up)150 2350 y(this)h(standard,)f(kno)n(wn)g (collectiv)n(ely)f(as)h(the)h(Basic)f(Linear)f(Algebra)h(Subprograms)e (\(BLAS\),)k(w)n(ould)e(b)r(e)150 2449 y(e\016cien)n(tly)k(implemen)n(ted)h (on)f(adv)-5 b(anced-arc)n(hitecture)25 b(computers)h(b)n(y)h(man)n(y)g(man)n (ufacturers,)f(making)150 2549 y(it)31 b(p)r(ossible)f(to)g(reap)g(the)h(p)r (ortabilit)n(y)f(b)r(ene\014ts)h(of)g(ha)n(ving)e(them)i(e\016cien)n(tly)g (implemen)n(ted)g(on)f(a)g(wide)150 2649 y(range)c(of)i(mac)n(hines.)36 b(This)28 b(goal)e(has)h(b)r(een)h(largely)e(realized.)275 2748 y(The)d(k)n(ey)h(insigh)n(t)f(of)h(this)g(approac)n(h)e(to)i(designing)f (linear)g(algebra)f(algorithms)h(for)g(adv)-5 b(anced)24 b(arc)n(hi-)150 2848 y(tecture)h(computers)e(is)i(that)g(the)g(frequency)f(with)h(whic)n(h)f (data)g(are)g(mo)n(v)n(ed)f(b)r(et)n(w)n(een)i(di\013eren)n(t)f(lev)n(els)g (of)150 2948 y(the)e(memory)e(hierarc)n(h)n(y)f(m)n(ust)i(b)r(e)h(minimized)g (in)f(order)f(to)h(attain)g(high)g(p)r(erformance.)34 b(Th)n(us,)22 b(our)e(main)150 3047 y(algorithmic)i(approac)n(h)f(for)h(exploiting)g(b)r (oth)i(v)n(ectorization)d(and)h(parallelism)g(in)h(our)f(implemen)n(tations) 150 3147 y(is)29 b(the)g(use)g(of)h(blo)r(c)n(k-partitioned)d(algorithms,)h (particularly)g(in)h(conjunction)h(with)f(highly-tuned)g(k)n(er-)150 3246 y(nels)24 b(for)g(p)r(erforming)g(matrix-v)n(ector)e(and)j (matrix-matrix)e(op)r(erations)g(\(the)i(Lev)n(el)f(2)g(and)h(3)f(BLAS\).)h (In)150 3346 y(general,)31 b(the)h(use)f(of)g(blo)r(c)n(k-partitioned)f (algorithms)g(requires)g(data)h(to)g(b)r(e)h(mo)n(v)n(ed)e(as)h(blo)r(c)n (ks,)g(rather)150 3446 y(than)j(as)f(v)n(ectors)g(or)g(scalars,)g(so)h(that)g (although)f(the)i(total)e(amoun)n(t)h(of)g(data)f(mo)n(v)n(ed)g(is)h(unc)n (hanged,)150 3545 y(the)c(latency)f(\(or)f(startup)h(cost\))h(asso)r(ciated)e (with)h(the)h(mo)n(v)n(emen)n(t)f(is)g(greatly)f(reduced)h(b)r(ecause)g(few)n (er)150 3645 y(messages)d(are)h(needed)g(to)h(mo)n(v)n(e)e(the)i(data.)275 3745 y(A)36 b(second)g(k)n(ey)g(idea)g(is)g(that)g(the)h(p)r(erformance)e(of) i(an)f(algorithm)f(can)h(b)r(e)h(tuned)g(b)n(y)f(a)g(user)f(b)n(y)150 3844 y(v)-5 b(arying)34 b(the)h(parameters)f(that)h(sp)r(ecify)h(the)f(data)g (la)n(y)n(out.)58 b(On)35 b(shared)f(memory)g(mac)n(hines,)j(this)e(is)150 3944 y(con)n(trolled)f(b)n(y)i(the)g(blo)r(c)n(k)f(size,)i(while)f(on)f (distributed)h(memory)f(mac)n(hines)g(it)h(is)f(con)n(trolled)f(b)n(y)i(the) 150 4043 y(blo)r(c)n(k)27 b(size)g(and)h(the)g(con\014guration)e(of)h(the)h (logical)f(pro)r(cess)f(mesh.)275 4143 y(The)i(w)n(a)n(y)f(in)h(whic)n(h)g (an)g(algorithm's)f(data)h(are)f(distributed)i(o)n(v)n(er)d(the)j(pro)r (cessors)c(of)k(a)e(concurren)n(t)150 4243 y(computer)j(has)g(a)g(ma)5 b(jor)30 b(impact)g(on)g(the)h(load)f(balance)g(and)g(comm)n(unication)g(c)n (haracteristics)e(of)j(the)150 4342 y(concurren)n(t)40 b(algorithm,)j(and)e (hence)g(largely)e(determines)i(its)g(p)r(erformance)f(and)h(scalabilit)n(y) -7 b(.)76 b(The)150 4442 y(blo)r(c)n(k)24 b(scattered)g(\(or)g(blo)r(c)n(k)g (cyclic\))h(decomp)r(osition)f(pro)n(vides)f(a)h(simple,)h(y)n(et)g (general-purp)r(ose,)e(w)n(a)n(y)g(of)150 4542 y(distributing)28 b(a)g(blo)r(c)n(k-partitioned)f(matrix)h(on)f(distributed)i(memory)e (concurren)n(t)g(computers.)38 b(In)29 b(the)150 4641 y(blo)r(c)n(k)f (scattered)g(decomp)r(osition,)g(describ)r(ed)h(in)g(detail)f(in)h([29)o(],)g (a)g(matrix)f(is)g(partitioned)g(in)n(to)h(blo)r(c)n(ks)150 4741 y(of)36 b(size)g Fs(r)26 b Fi(\002)e Fs(s)p Fx(,)38 b(and)e(blo)r(c)n (ks)f(separated)g(b)n(y)g(a)h(\014xed)g(stride)g(in)g(the)g(column)g(and)g (ro)n(w)f(directions)g(are)150 4840 y(assigned)d(to)h(the)h(same)f(pro)r (cessor.)51 b(If)34 b(the)g(stride)f(in)g(the)h(column)f(and)g(ro)n(w)f (directions)h(is)g Fs(P)45 b Fx(and)33 b Fs(Q)150 4940 y Fx(blo)r(c)n(ks)24 b(resp)r(ectiv)n(ely)-7 b(,)25 b(then)g(w)n(e)g(require)f(that)h Fs(P)h(Q)e Fx(equals)g(the)i(n)n(um)n(b)r(er)e(of)h(pro)r(cessors,)e Fs(N)3060 4952 y Fh(p)3099 4940 y Fx(.)36 b(Th)n(us,)25 b(it)g(is)150 5040 y(useful)j(to)f(imagine)g(the)h(pro)r(cessors)d(arranged)h(as)h(a)g Fs(P)j Fi(\002)18 b Fs(Q)27 b Fx(mesh,)h(or)e(template.)38 b(Then)27 b(the)h(pro)r(cessor)1796 5428 y(29)p eop PNP restore /PNP save def 628.2618 89.4750 translate 31 bop 150 312 a Fx(at)27 b(p)r(osition)h(\()p Fs(p;)14 b(q)s Fx(\))28 b(\(0)23 b Fi(\024)f Fs(p)h(<)g(P)12 b Fx(,)27 b(0)c Fi(\024)g Fs(q)j(<)c(Q)p Fx(\))28 b(in)g(the)g(template)g(is)f(assigned)g (the)h(blo)r(c)n(ks)e(indexed)i(b)n(y)-7 b(,)1518 456 y(\()p Fs(p)18 b Fx(+)g Fs(i)c(P)r(;)28 b(q)22 b Fx(+)c Fs(j)g(Q)p Fx(\))p Fs(;)1197 b Fx(\(4.1\))150 600 y(where)30 b Fs(i)d Fx(=)h(0)p Fs(;)14 b(:)g(:)g(:)f(;)h Fi(b)p Fx(\()p Fs(M)918 612 y Fh(b)971 600 y Fi(\000)20 b Fs(p)g Fi(\000)g Fx(1\))p Fs(=P)12 b Fi(c)p Fx(,)31 b Fs(j)h Fx(=)c(0)p Fs(;)14 b(:)g(:)g(:)f(;)h Fi(b)p Fx(\()p Fs(N)1996 612 y Fh(b)2049 600 y Fi(\000)20 b Fs(q)k Fi(\000)c Fx(1\))p Fs(=Q)p Fi(c)p Fx(,)30 b(and)g Fs(M)2797 612 y Fh(b)2850 600 y Fi(\002)20 b Fs(N)3002 612 y Fh(b)3066 600 y Fx(is)30 b(the)h(size)f(of)150 700 y(the)e(matrix)f(in)h(blo)r(c)n(ks.) 275 800 y(Blo)r(c)n(ks)19 b(are)h(scattered)h(in)g(this)g(w)n(a)n(y)f(so)g (that)h(go)r(o)r(d)f(load)h(balance)f(can)g(b)r(e)i(main)n(tained)e(in)h (algorithms,)150 899 y(suc)n(h)k(as)h(LU)g(factorization)e([30)o(,)i(31)o(],) g(in)g(whic)n(h)g(ro)n(ws)e(and/or)h(columns)g(of)h(blo)r(c)n(ks)f(of)h(a)f (matrix)g(b)r(ecome)150 999 y(eliminated)32 b(as)e(the)i(algorithm)e (progresses.)46 b(Ho)n(w)n(ev)n(er,)31 b(for)f(some)h(of)h(the)f(distributed) h(Lev)n(el)f(3)g(BLAS)150 1098 y(routines)f(a)f(scattered)h(decomp)r(osition) f(do)r(es)h(not)g(impro)n(v)n(e)f(load)h(balance,)g(and)g(ma)n(y)f(result)h (in)h(higher)150 1198 y(concurren)n(t)18 b(o)n(v)n(erhead.)32 b(The)20 b(general)e(matrix-matrix)f(m)n(ultiplication)j(routine)f(xGEMM)g (is)g(an)h(example)150 1298 y(of)32 b(suc)n(h)f(a)h(routine)f(for)h(whic)n(h) f(a)h(pure)f(blo)r(c)n(k)h(\(i.e.,)h(nonscattered\))e(decomp)r(osition)g(is)h (optimal)g(when)150 1397 y(considering)i(the)i(routine)g(in)g(isolation.)60 b(Ho)n(w)n(ev)n(er,)36 b(xGEMM)f(ma)n(y)g(b)r(e)h(used)g(in)g(an)g (application)f(for)150 1497 y(whic)n(h,)28 b(o)n(v)n(erall,)d(a)i(scattered)g (decomp)r(osition)g(is)h(b)r(est.)275 1597 y(The)23 b(underlying)h(concept)f (of)h(the)g(implemen)n(tations)g(w)n(e)g(ha)n(v)n(e)e(c)n(hosen)h(for)h (dense)f(matrix)h(computa-)150 1696 y(tions)i(is)g(the)h(use)f(of)g(blo)r(c)n (k-partitioned)f(algorithms)g(to)i(minimize)f(data)g(mo)n(v)n(emen)n(t)g(b)r (et)n(w)n(een)g(di\013eren)n(t)150 1796 y(lev)n(els)f(in)h(hierarc)n(hical)e (memory)-7 b(.)36 b(The)25 b(ideas)h(discussed)f(here)g(for)h(dense)f(linear) h(algebra)e(computations)150 1895 y(are)c(applicable)g(to)h(an)n(y)f (computer)h(with)g(a)f(hierarc)n(hical)f(memory)h(that)i(\(1\))f(imp)r(oses)f (a)h(su\016cien)n(tly)f(large)150 1995 y(startup)26 b(cost)h(on)f(the)h(mo)n (v)n(emen)n(t)f(of)h(data)f(b)r(et)n(w)n(een)h(di\013eren)n(t)f(lev)n(els)g (in)h(the)g(hierarc)n(h)n(y)-7 b(,)25 b(and)i(for)f(whic)n(h)150 2095 y(\(2\))e(the)g(cost)g(of)g(a)f(con)n(text)h(switc)n(h)f(is)h(to)r(o)g (great)e(to)i(mak)n(e)f(\014ne)h(grain)f(size)h(m)n(ultithreading)f(w)n(orth) n(while.)150 2194 y(These)k(ideas)g(ha)n(v)n(e)f(b)r(een)i(exploited)f(b)n(y) h(the)f(soft)n(w)n(are)f(pac)n(k)-5 b(ages)26 b(LAP)-7 b(A)n(CK)26 b([14)o(])i(and)f(ScaLapac)n(k)f([32)o(].)150 2294 y(The)i Fo(P)-7 b(ARKBENCH)29 b Fx(suite)f(includes)g(\014v)n(e)f(matrix)g(k)n (ernels.)251 2438 y(1.)42 b(Dense)28 b(matrix)f(m)n(ultiply)-7 b(.)38 b(Comm)n(unication)28 b(in)n(v)n(olv)n(es)e(broadcast)g(of)i(data)f (along)g(ro)n(ws)f(of)i(mesh,)358 2538 y(and)f(p)r(erio)r(dic)g(shift)i (along)d(column)i(direction)f(\(or)g(vice)g(v)n(ersa\).)251 2688 y(2.)42 b(T)-7 b(ransp)r(ose.)41 b(Matrix)29 b(transp)r(ose)f(is)i(an)f (imp)r(ortan)n(t)h(b)r(enc)n(hmark)e(b)r(ecause)i(it)g(exercises)e(the)i (com-)358 2788 y(m)n(unications)f(of)h(computer)g(hea)n(vily)f(on)g(a)h (realistic)f(problem)h(where)f(pairs)g(of)h(pro)r(cessors)e(com-)358 2888 y(m)n(unicate)c(with)i(eac)n(h)e(other)g(sim)n(ultaneously)-7 b(.)35 b(It)25 b(is)g(a)f(useful)h(test)h(of)e(the)i(total)e(comm)n (unications)358 2987 y(capacit)n(y)i(of)i(the)g(net)n(w)n(ork.)251 3138 y(3.)42 b(Dense)26 b(LU)h(factorization)e(with)i(partial)e(piv)n(oting.) 36 b(Searc)n(hing)25 b(for)g(a)h(piv)n(ot)g(is)h(basically)e(a)h(reduc-)358 3237 y(tion)32 b(op)r(eration)g(within)h(one)f(column)h(of)f(the)h(pro)r (cessor)e(mesh.)52 b(Exc)n(hange)30 b(of)j(piv)n(ot)f(ro)n(ws)f(is)h(a)358 3337 y(p)r(oin)n(t-to-p)r(oin)n(t)c(comm)n(unication.)40 b(Up)r(date)29 b(phase)f(requires)g(data)g(to)h(b)r(e)g(broadcast)e(along)h(ro)n(ws)358 3437 y(and)f(columns)g(of)h(the)g(pro)r(cessor)d(mesh.)251 3587 y(4.)42 b(QR)21 b(Decomp)r(osition.)35 b(In)22 b(this)g(b)r(enc)n(hmark) f(parallelization)f(is)i(ac)n(hiev)n(ed)e(b)n(y)i(distribution)g(of)g(ro)n (ws)358 3687 y(on)27 b(a)g(logical)f(grid)h(of)h(pro)r(cessors)d(using)i(blo) r(c)n(k)g(in)n(terlea)n(ving.)251 3837 y(5.)42 b(Matrix)27 b(tridiagonalization,)e(for)i(eigen)n(v)-5 b(alue)27 b(computations)g(of)g (symmetric)h(matrices.)275 3982 y(There)22 b(ha)n(v)n(e)f(b)r(een)i(man)n(y)f (implemen)n(tations)h(of)f(matrix)g(m)n(ultiplication)h(algorithms)e(on)i (distributed)150 4081 y(memory)32 b(mac)n(hines)f([33)o(,)i(34)o(,)f(35].)51 b(Man)n(y)32 b(of)g(them)h(are)e(limited)j(in)e(their)h(use)f(since)g(they)h (are)e(imple-)150 4181 y(men)n(ted)c(with)h(a)f(pure)g(blo)r(c)n(k)g (\(non-scattered\))f(distribution,)h(or)g(sp)r(eci\014c)g(\(not)g (general-purp)r(ose\))f(data)150 4280 y(distribution,)32 b(and/or)d(on)h (square)f(pro)r(cessor)g(con\014gurations)f(with)k(a)e(sp)r(eci\014c)h(n)n (um)n(b)r(er)f(of)g(pro)r(cessors)150 4380 y(\(column)h(and/or)d(ro)n(w)i(n)n (um)n(b)r(ers)f(of)i(pro)r(cessors)d(are)h(p)r(o)n(w)n(ers)g(of)h(2\).)45 b(The)31 b(soft)n(w)n(are)d(con)n(tained)i(in)h(this)150 4480 y(b)r(enc)n(hmark)c(eliminates)g(all)h(of)f(these)h(constrain)n(ts.)275 4579 y(Our)g(matrix)g(m)n(ultiplication)h(algorithm)f(is)h(a)f(blo)r(c)n(k)g (scattered)g(v)-5 b(arian)n(t)28 b(of)h(that)g(of)g(F)-7 b(o)n(x,)29 b(Hey)-7 b(,)29 b(and)150 4679 y(Otto)e([33)o(],)h(that)g(deals)f(with)h (arbitrary)e(rectangular)f(pro)r(cessor)h(templates.)275 4779 y(Supp)r(ose)f(the)g(matrix)g Ft(A)g Fx(has)g Fs(M)1330 4791 y Fh(b)1388 4779 y 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y(and)27 b(one)h(for)f(a)g(large)f(3-D)h (FFT.)251 2890 y(1.)42 b(1-D)27 b(FFT.)h(In)g(this)h(k)n(ernel,)e(t)n(w)n(o)g (sequences)g(of)g(in)n(tegers)g Fs(x)2255 2902 y Fh(i)2311 2890 y Fx(and)h Fs(y)2514 2902 y Fh(i)2569 2890 y Fx(are)f(generated,)g(with) h(length)358 2990 y Fs(n)22 b Fx(=)h(2)560 2960 y Fh(m)644 2990 y Fx(and)e(v)-5 b(alues)21 b(in)g(the)h(range)d(0)k Fi(\024)g Fs(x)1686 3002 y Fh(i)1714 2990 y Fs(;)37 b(y)1815 3002 y Fh(i)1865 2990 y Fs(<)23 b(M)9 b Fx(.)34 b(The)21 b(standard)g(v)-5 b(alue)21 b(of)g Fs(M)29 b Fx(is)22 b(1024.)32 b(These)358 3090 y(sequences)h(are)g (generated)g(using)h(the)h(same)e(uniform)h(pseudo-random)f(n)n(um)n(b)r(er)h (generator)e(as)358 3189 y(is)e(used)g(in)h(the)g(3-D)f(FFT)h(k)n(ernel)e (and)h(the)h(em)n(barrassingly)d(parallel)h(k)n(ernel.)44 b(Then)31 b(the)g(linear)358 3289 y(con)n(v)n(olution)e(of)j(these)f(t)n(w)n(o)f (sequences)h(is)g(computed)h(using)e(a)h(complex-n)n(um)n(b)r(er)g(FFT,)g (i.e.)48 b(b)n(y)358 3389 y(padding)27 b Fs(x)h Fx(and)g Fs(y)j Fx(with)d(zero)r(es)f(to)h(length)g(2)p Fs(n)p Fx(,)f(then)i(p)r(erforming)e (a)g(forw)n(ard)f(FFT)j(on)e Fs(x)i Fx(and)e Fs(y)s Fx(,)358 3488 y(m)n(ultiplying)h(the)g(t)n(w)n(o)f(resulting)g(sequences)g(of)h (complex)g(n)n(um)n(b)r(ers,)f(and)h(\014nally)f(p)r(erforming)g(an)358 3588 y(in)n(v)n(erse)i(FFT)i(on)f(the)h(result.)45 b(The)31 b(result)f(sequence)g(should)g(ha)n(v)n(e)f(exclusiv)n(ely)h(in)n(teger)f(v) -5 b(alues,)358 3687 y(whic)n(h)27 b(p)r(ermits)h(a)f(straigh)n(tforw)n(ard)e (v)-5 b(alidit)n(y)27 b(c)n(hec)n(k.)358 3820 y(No)g(restriction)g(is)g (placed)h(on)f(the)h(FFT)g(tec)n(hnique)g(used)f(to)h(p)r(erform)f(this)h (con)n(v)n(olution,)e(except)358 3920 y(that)21 b(it)h(b)r(e)g(based)e(on)h (a)g(complex-n)n(um)n(b)r(er)g(FFT)g(rather)g(than,)h(for)f(example,)h(a)f(n) n(um)n(b)r(er-theoretic)358 4020 y(FFT.)f(It)g(is)g(exp)r(ected,)i(ho)n(w)n (ev)n(er,)d(that)i(e\016cien)n(t)f(implemen)n(tations)g(will)g(emplo)n(y)f (tec)n(hniques,)i(suc)n(h)358 4119 y(as)26 b(Edson's)h(algorithm)f(and)i (real-to-complex)d(FFTs,)j(that)g(tak)n(e)e(adv)-5 b(an)n(tage)26 b(of)i(the)g(purely)f(real)358 4219 y(nature)33 b(of)h(the)g(input)g(and)g (output)g(data)g(to)f(reduce)g(the)i(computational)e(cost.)55 b(The)33 b(usage)g(of)358 4318 y(v)n(endor-supplied)25 b(library)h(FFT)h (routines)g(is)g(p)r(ermitted.)37 b(The)27 b(serial)f(implemen)n(tation)h (program)358 4418 y(includes)33 b(a)g(reasonably)f(e\016cien)n(t)h(1-D)h(FFT) f(suitable)h(for)f(computation)g(on)g(a)g(w)n(orkstation)f(or)358 4518 y(single)27 b(pro)r(cessor)e(v)n(ector)h(system.)251 4684 y(2.)42 b(3-D)28 b(FFT.)h(The)g Fo(P)-7 b(ARKBENCH)30 b Fx(3-D)e(FFT)h(k)n (ernel)f(is)h(the)g Fn(3-D)i(FFT)g(PDE)e Fx(b)r(enc)n(hmark)f(from)358 4783 y(the)h(NAS)h(P)n(arallel)c(Benc)n(hmark)i(suite)h([28)o(].)41 b(It)29 b(p)r(erforms)g(the)g(essence)f(of)h(man)n(y)f Fn(sp)l(e)l(ctr)l(al)i Fx(co)r(des)358 4883 y(and)e(is)g(a)g(rigorous)e(test)i(of)g(long-distance)f (comm)n(unication)h(p)r(erformance.)38 b(A)28 b(brief)h(description)358 4983 y(of)e(this)h(b)r(enc)n(hmark)f(is)g(as)g(follo)n(ws.)1796 5428 y(32)p eop PNP restore PNEP %%Page: ? 18 0.6303 -612.00 PNLS /PNP save def 12.6922 89.4750 translate 34 bop 358 312 a Fx(Consider)26 b(the)i(partial)f(di\013eren)n(tial)g (equation)g(\(PDE\))1495 476 y Fs(@)5 b(u)p Fx(\()p Fs(x;)14 b(t)p Fx(\))p 1495 513 276 4 v 1593 589 a Fs(@)5 b(t)1863 532 y Fx(=)83 b Fs(\013)p Fi(r)2133 497 y Fj(2)2171 532 y Fs(u)p Fx(\()p Fs(x;)14 b(t)p Fx(\))358 758 y(where)29 b Fs(x)i Fx(is)e(a)h(p)r (osition)g(in)g(three-dimensional)f(space.)43 b(When)31 b(a)e(F)-7 b(ourier)29 b(transform)g(is)h(applied)358 857 y(to)d(eac)n(h)g(side,)g(this) h(equation)f(b)r(ecomes)1398 1016 y Fs(@)5 b(v)s Fx(\()p Fs(z)t(;)14 b(t)p Fx(\))p 1398 1053 266 4 v 1492 1129 a Fs(@)5 b(t)1757 1072 y Fx(=)83 b Fi(\000)p Fx(4)p Fs(\013\031)2115 1038 y Fj(2)2152 1072 y Fi(j)p Fs(z)t Fi(j)2241 1038 y Fj(2)2277 1072 y Fs(v)s Fx(\()p Fs(z)t(;)14 b(t)p Fx(\))358 1303 y(where)27 b Fs(v)s Fx(\()p Fs(z)t(;)14 b(t)p Fx(\))27 b(is)h(the)g(F)-7 b(ourier)26 b(transform)h(of)g Fs(u)p Fx(\()p Fs(x;)14 b(t)p Fx(\).)38 b(This)27 b(has)g(the)h(solution)1416 1490 y Fs(v)s Fx(\()p Fs(z)t(;)14 b(t)p Fx(\))83 b(=)f Fs(e)1902 1456 y Fg(\000)p Fj(4)p Fh(\013\031)2071 1430 y Ff(2)2103 1456 y Fg(j)p Fh(z)r Fg(j)2177 1430 y Ff(2)2209 1456 y Fh(t)2238 1490 y Fs(v)s Fx(\()p Fs(z)t(;)14 b Fx(0\))358 1692 y(In)27 b(this)g(b)r(enc)n(hmark)f(problem,)h (one)f(starts)g(with)i(a)e(3-D)h(complex)g(arra)n(y)d Fs(U)9 b Fx(,)27 b(whic)n(h)g(represen)n(ts)e Fs(u)358 1792 y Fx(ab)r(o)n(v)n(e,)f (whic)n(h)h(is)f(\014lled)i(with)f(pseudorandom)f(data)g(generated)g(b)n(y)h (the)g(same)f(sc)n(heme)h(as)f(used)h(in)358 1892 y(the)31 b(em)n(barrassingly)d(parallel)i(k)n(ernel.)46 b(Then)31 b(one)g(computes)g Fs(V)19 b Fx(,)32 b(the)f(result)g(of)g(a)f(forw)n(ard)f(3-D)358 1991 y(FFT)20 b(of)h Fs(U)9 b Fx(.)34 b(F)-7 b(or)19 b(eac)n(h)h(of)g(sev)n (eral)f(iterations,)i(one)e(m)n(ultiplies)i Fs(V)39 b Fx(b)n(y)20 b(the)h(appropriate)e(exp)r(onen)n(tial)358 2091 y(factors)26 b(and)i(p)r(erforms)e(an)i(in)n(v)n(erse)e(3-D)h(FFT)h(on)f(the)h(result.)358 2222 y(An)n(y)i(complex)h(FFT)g(algorithm)f(ma)n(y)g(b)r(e)i(used)f(for)f (the)h(computation)g(of)g(the)g(3-D)g(FFTs)g(men-)358 2321 y(tioned)c(ab)r(o)n(v)n(e,)g(and)g(v)n(endor-supplied)f(library)h(routines)f (ma)n(y)h(b)r(e)h(emplo)n(y)n(ed.)150 2552 y Fy(4.2.3)112 b(PDE)37 b(Kernels)150 2705 y Fx(In)21 b(these)g(PDE)g(k)n(ernels)f(comm)n(unication)g (is)h(basically)f(exc)n(hange)f(with)j(neigh)n(b)r(ors)d(and)i(the)h(con)n(v) n(ergence)150 2805 y(c)n(hec)n(k)30 b(is)h(a)f(reduction.)47 b(A)31 b(v)-5 b(ariet)n(y)30 b(of)h(metho)r(ds)g(and)g(up)r(date)g(stencils)g (ma)n(y)f(b)r(e)h(used.)47 b(The)31 b(follo)n(wing)150 2904 y(t)n(w)n(o)c(PDE)g(solv)n(ers)f(ha)n(v)n(e)g(b)r(een)i(prop)r(osed)f(for)g (inclusion)g(in)h(the)g(parallel)e(b)r(enc)n(hmark)h(suite:)251 3061 y(1.)42 b(Successiv)n(e)35 b(Ov)n(er-Relaxation)f(\(SOR\))j(k)n(ernel.) 63 b(The)36 b Fo(P)-7 b(ARKBENCH)30 b Fx(SOR)36 b(k)n(ernel)g(is)h(based)358 3161 y(on)25 b(the)i(PDE1)e(b)r(enc)n(hmark)g(from)h(the)h(GENESIS)e (distributed)i(memory)e(b)r(enc)n(hmark)h(suite)g([17)o(].)358 3261 y(This)20 b(b)r(enc)n(hmark)f(solv)n(es)f(the)j(P)n(oisson)d(equation)h (on)h(a)f(3-dimensional)g(grid)g(b)n(y)h(parallel)f(red-blac)n(k)358 3360 y(relaxation)h(with)i(Cheb)n(yshev)g(acceleration.)33 b(In)22 b(this)g(metho)r(d)h(the)f(mesh)g(p)r(oin)n(ts)g(are)f(divided)h(in)n (to)358 3460 y(t)n(w)n(o)i(groups)g(according)g(to)h(whether)g(the)h(sum)f (of)h(indices)f(is)g(o)r(dd)h(\(`red'\))g(or)e(ev)n(en)h(\(`blac)n(k'\).)36 b(The)358 3560 y(metho)r(d)21 b(pro)r(ceeds)f(in)h(half)g(iterations,)g (during)f(eac)n(h)g(of)h(whic)n(h)g(only)f(half)h(the)g(p)r(oin)n(ts)g(are)f (adjusted)358 3659 y(\(alternately)i(the)i(`red')g(and)f(`blac)n(k')g(set)h (of)f(p)r(oin)n(ts\).)36 b(Th)n(us)23 b(all)h(the)g(`red')f(p)r(oin)n(ts)h (can)f(b)r(e)h(adjusted)358 3759 y(in)f(parallel)f(during)g(one)h(half)g (iteration,)g(and)g(similarly)f(all)h(the)g(`blac)n(k')g(p)r(oin)n(ts)f(in)i (parallel)e(during)358 3858 y(the)27 b(next)g(half)g(iteration.)36 b(The)27 b(problem)f(is)h(discretized)f(using)h(the)g(ordinary)e(7-p)r(oin)n (t)h(di\013erence)358 3958 y(stencil)32 b(in)g(a)g(regular)e(cubic)i(grid.)50 b(The)32 b(v)-5 b(alue)32 b(of)g(the)g(relaxation)f(factor)g(\()p Fs(!)s Fx(\))h(c)n(hanges)f(at)h(eac)n(h)358 4058 y(half)27 b(iteration)g(according)f(to:)1038 4229 y Fs(!)1093 4195 y Fj(\(0\))1265 4229 y Fx(=)82 b(1)971 4354 y Fs(!)1026 4320 y Fj(\(1)p Fh(=)p Fj(2\))1265 4354 y Fx(=)g(1)p Fs(=)p Fx(\(1)18 b Fi(\000)g Fx(1)p Fs(=)p Fx(2)p Fs(\032)1840 4320 y Fj(2)1875 4354 y Fx(\))895 4478 y Fs(!)950 4444 y Fj(\()p Fh(t)p Fj(+1)p Fh(=)p Fj(2\))1265 4478 y Fx(=)82 b(1)p Fs(=)p Fx(\(1)18 b Fi(\000)g Fx(1)p Fs(=)p Fx(4)p Fs(\032)1840 4444 y Fj(2)1875 4478 y Fs(!)1930 4444 y Fj(\()p Fh(t)p Fj(\))2011 4478 y Fx(\))p Fs(;)251 b(t)23 b Fx(=)f(0)p Fs(;)14 b Fx(1)p Fs(=)p Fx(2)p Fs(;)g Fx(1)p Fs(;)g(:::;)g Fi(1)p Fs(;)364 b Fx(\(4.3\))358 4650 y(where)29 b Fs(\032)i Fx(is)f(the)h(con)n(v)n(ergence)d(factor)i(of)g (the)h(corresp)r(onding)d(Jacobi)i(iteration)f(and)i(the)g(sup)r(er-)358 4750 y(script)c Fs(t)h Fx(designates)f(the)h(iteration)f(n)n(um)n(b)r(er.)37 b(F)-7 b(or)28 b(large)e(n)n(um)n(b)r(er)i(of)f(iterations,)g Fs(!)k Fx(tends)d(to)g(the)358 4849 y(constan)n(t)f(relaxation)f(factor)h (that)h(is)g(used)g(throughout)f(the)h(traditional)f(SOR)h(pro)r(cedure.)37 b(The)358 4949 y(asymptotic)27 b(con)n(v)n(ergence)e(factor)i(is)g(therefore) g(the)h(same)f(for)g(b)r(oth)h(algorithms.)358 5080 y(In)20 b(order)e(to)i(map)g(the)g(problem)g(on)n(to)f(a)g(parallel)g(m)n(ultipro)r (cessor)f(system)i(the)g(3-dimensional)f(grid)358 5179 y(is)25 b(divided)h(in)n(to)f(cub)r(oidal)g(subgrids.)36 b(Eac)n(h)24 b(subgrid)h(is)g(assigned)f(to)i(a)f(no)r(de)g(in)h(suc)n(h)f(a)h(w)n(a)n(y)e (that)1796 5428 y(33)p eop PNP restore /PNP save def 628.2618 89.4750 translate 35 bop 358 312 a Fx(neigh)n(b)r(ouring)31 b(subgrids)h(are)f(mapp)r(ed)i(on)f (neigh)n(b)r(ouring)g(no)r(des.)51 b(The)33 b(grid)f(v)-5 b(ariables)31 b(in)i(eac)n(h)358 412 y(subgrid)24 b(are)g(exclusiv)n(ely)g(computed)h(b)n (y)g(its)g(asso)r(ciated)e(no)r(de.)36 b(A)n(t)26 b(the)f(inner)g(b)r (oundaries)f(of)h(the)358 511 y(subgrid)20 b(the)i(no)r(des)g(need)f(v)-5 b(alues)22 b(at)f(p)r(oin)n(ts)h(whic)n(h)f(are)g(con)n(tained)g(in)g(the)h (neigh)n(b)r(ouring)f(subgrid.)358 611 y(Rather)30 b(then)i(transferring)d (these)i(v)-5 b(alues)31 b(exactly)f(at)h(the)g(time)h(when)f(they)g(are)f (needed)h({)g(this)358 711 y(w)n(ould)f(prev)n(en)n(t)f(v)n(ector)g(pro)r (cessing)g(within)i(the)g(no)r(de)g({)f(they)g(are)g(stored)f(in)i(so-called) e(o)n(v)n(erlap)358 810 y(areas.)45 b(After)31 b(eac)n(h)g(iteration)f(the)h (v)-5 b(alues)31 b(in)g(the)h(o)n(v)n(erlap)d(areas)g(are)h(exc)n(hanged)g (and)h(up)r(dated)358 910 y(via)e(the)h(message-passing)d(comm)n(unication)i (mec)n(hanism.)44 b(The)30 b(in)n(tro)r(duction)f(of)h(o)n(v)n(erlap)e(areas) 358 1010 y(needs)23 b(a)f(strict)h(sync)n(hronization)e(follo)n(wing)h(eac)n (h)h(iteration)f(step)h(in)h(order)e(to)g(ensure)h(the)g(correct)358 1109 y(execution)k(of)g(the)h(b)r(enc)n(hmark.)358 1240 y(Since)22 b(the)i(Cheb)n(yshev)d(SOR)i(metho)r(d)g(requires)f(no)g(extra)g(arithmetic)g (o)n(v)n(er)f(the)i(traditional)f(SOR)358 1339 y(algorithm)31 b(y)n(et)i(has)f(more)g(fa)n(v)n(ourable)e(initial)j(error)e(deca)n(y)h(prop) r(erties,)h(it)g(is)g(one)f(of)h(the)g(most)358 1439 y(e\016cien)n(t)h(PDE)f (k)n(ernels.)55 b(Note,)36 b(ho)n(w)n(ev)n(er,)e(that)g(in)h(this)f(b)r(enc)n (hmark)f(only)h(nearest)f(neigh)n(b)r(our)358 1538 y(in)n(teractions)c(are)h (required)g(and)g(the)i(n)n(um)n(b)r(er)e(of)h(\015oating)f(p)r(oin)n(t)h(op) r(erations)e(p)r(er)i(grid)f(p)r(oin)n(t)h(is)358 1638 y(v)n(ery)26 b(small)h(when)h(compared)e(to)i(more)f(complex)g(PDEs.)251 1799 y(2.)42 b(Multigrid)27 b(k)n(ernel.)358 1929 y(The)22 b Fo(P)-7 b(ARKBENCH)29 b Fx(m)n(ultigrid)22 b(k)n(ernel)f(is)h(the)h(m)n (ultigrid)f(b)r(enc)n(hmark)f(from)h(the)g(NAS)h(P)n(arallel)358 2029 y(Benc)n(hmarks)29 b([28)o(].)48 b(It)31 b(requires)f(highly)h (structured)g(long)f(distance)h(comm)n(unication)f(and)h(tests)358 2129 y(b)r(oth)d(short)e(and)i(long)f(distance)g(data)g(comm)n(unication.)358 2259 y(This)k(k)n(ernel)f(p)r(erforms)h(a)f(V-cycle)h(m)n(ultigrid)g (algorithm)f(to)h(obtain)g(an)g(appro)n(ximate)f(solution)358 2359 y Fs(u)d Fx(to)g(the)h(discrete)f(P)n(oisson)f(problem)1727 2529 y Fi(r)1796 2494 y Fj(2)1834 2529 y Fs(u)82 b Fx(=)h Fs(v)358 2729 y Fx(on)27 b(a)g(256)17 b Fi(\002)h Fx(256)f Fi(\002)h Fx(256)26 b(grid)h(with)h(p)r(erio)r(dic)g(b)r(oundary)f(conditions.)358 2860 y(One)c(starts)f(out)h(with)h(the)g(arra)n(y)d Fs(v)26 b Fx(=)d(0,)h(except)f(at)g(a)g(20)f(particular)g(p)r(oin)n(ts)i(where)e Fs(v)27 b Fx(=)22 b Fi(\006)p Fx(1.)35 b(The)358 2959 y(iterativ)n(e)29 b(solution)h(starts)f(with)i Fs(u)c Fx(=)g(0.)45 b(Eac)n(h)29 b(iteration)h(consists)f(of)i(the)f(follo)n(wing)g(t)n(w)n(o)f(steps,)358 3059 y(where)e Fs(k)f Fx(=)c(8)h(=)f(log)1014 3079 y Fj(2)1051 3059 y Fx(\(256\):)1134 3229 y Fs(r)54 b Fx(=)c Fs(v)f Fi(\000)d Fs(A)28 b(u)248 b Fx(\()p Fs(ev)s(al)r(uate)27 b(r)r(esidual)r Fx(\))1187 3354 y Fs(u)51 b Fx(=)f Fs(u)c Fx(+)f Fs(M)1695 3319 y Fh(k)1763 3354 y Fs(r)169 b Fx(\()p Fs(appl)r(y)30 b(cor)r(r)r(ection) p Fx(\))358 3554 y(Here)d Fs(M)644 3524 y Fh(k)712 3554 y Fx(denotes)g(a)g Fn(V-cycle)h Fx(m)n(ultigrid)f(op)r(erator,)e(and)j Fs(A)f Fx(denotes)g(a)g(trilinear)g(\014nite)h(elemen)n(t)358 3654 y(discretization)e(of)i(the)g(Laplacian)e Fi(r)1556 3624 y Fj(2)1594 3654 y Fx(.)150 3884 y Fy(4.2.4)112 b(Other)251 4038 y Fx(1.)42 b(Em)n(barrassingly)18 b(P)n(arallel.)33 b(The)22 b(P)n(arkb)r(enc)n(h)e Fn(emb)l(arr)l(assingly)26 b(p)l(ar)l(al)t(lel)e Fx(k)n(ernel)d(is)h(tak)n(en)f(from)h(the)358 4137 y(NAS)33 b(P)n(arallel)d(Benc)n(hmarks)g([28)o(].)51 b(It)33 b(pro)n(vides)e(an)h (estimate)g(of)g(the)h(upp)r(er)f(ac)n(hiev)-5 b(able)32 b(limits)358 4237 y(for)g(\015oating)f(p)r(oin)n(t)i(p)r(erformance,)g(i.e.)52 b(the)32 b(p)r(erformance)g(without)h(signi\014can)n(t)f(in)n(terpro)r (cessor)358 4336 y(comm)n(unication.)358 4467 y(In)h(this)h(b)r(enc)n(hmark,) g(one)f(\014rst)g(generates)f(pairs)g(\()p Fs(x)2086 4479 y Fh(j)2122 4467 y Fs(;)46 b(y)2232 4479 y Fh(j)2267 4467 y Fx(\))34 b(of)f(uniformly)g(distributed)h(pseudo-)358 4566 y(random)26 b(\015oating)h(p)r(oin)n(t)h(v)-5 b(alues)27 b(generated)f(using)i(the)g (linear)f(congruen)n(tial)f(generator)1459 4737 y Fs(z)1498 4749 y Fh(k)q Fj(+1)1706 4737 y Fx(=)83 b Fs(az)1937 4749 y Fh(k)2060 4737 y Fx(\(mo)r(d)28 b(2)2321 4702 y Fj(46)2391 4737 y Fx(\))1461 4861 y Fs(r)1498 4873 y Fh(k)q Fj(+1)1706 4861 y Fx(=)83 b(2)1896 4827 y Fg(\000)p Fj(46)2017 4861 y Fs(z)2056 4873 y Fh(k)q Fj(+1)358 5062 y Fx(F)-7 b(or)24 b(eac)n(h)f(pair)h (\()p Fs(x)934 5074 y Fh(j)970 5062 y Fs(;)37 b(y)1071 5074 y Fh(j)1106 5062 y Fx(\),)25 b(one)f(tests)h(to)f(see)h(if)g Fs(t)1860 5074 y Fh(j)1918 5062 y Fx(=)d Fs(x)2052 5032 y Fj(2)2052 5083 y Fh(j)2102 5062 y Fx(+)12 b Fs(y)2223 5032 y Fj(2)2220 5083 y Fh(j)2283 5062 y Fi(\024)23 b Fx(1.)35 b(If)25 b(not,)h(this)e(pair)g (is)h(rejected.)36 b(If)358 5179 y(this)23 b(inequalit)n(y)g(holds,)h(then)f (one)g(sets)g Fs(X)1692 5191 y Fh(k)1756 5179 y Fx(=)g Fs(x)1891 5191 y Fh(j)1926 5110 y Fa(p)p 2009 5110 478 4 v 69 x Fx(\()p Fi(\000)p Fx(2)14 b(log)f Fs(t)2312 5191 y Fh(j)2347 5179 y Fx(\))p Fs(=t)2451 5191 y Fh(j)2509 5179 y Fx(and)23 b Fs(Y)2714 5191 y Fh(k)2779 5179 y Fx(=)f Fs(y)2907 5191 y Fh(j)2942 5110 y Fa(p)p 3025 5110 V 69 x Fx(\()p Fi(\000)p Fx(2)14 b(log)f Fs(t)3328 5191 y Fh(j)3363 5179 y Fx(\))p Fs(=t)3467 5191 y Fh(j)3502 5179 y Fx(.)1796 5428 y(34)p eop PNP restore PNEP %%Page: ? 19 0.6303 -612.00 PNLS /PNP save def 12.6922 89.4750 translate 36 bop 358 312 a Fx(Then)29 b Fs(X)645 324 y Fh(k)716 312 y Fx(and)h Fs(Y)928 324 y Fh(k)998 312 y Fx(are)f(indep)r(enden)n(t)i(Gaussian) e(deviates)g(with)h(mean)g(zero)e(and)i(v)-5 b(ariance)28 b(one.)358 412 y(The)i(b)r(enc)n(hmark)g(problem)h(is)f(to)h(coun)n(t)f(the)h(n)n(um)n (b)r(er)g(of)f(these)h(Gaussian)f(deviates)g(that)h(lie)g(in)358 511 y(v)-5 b(arious)26 b(square)g(ann)n(uli)i(around)e(the)i(origin.)251 677 y(2.)42 b(Large)26 b(In)n(teger)g(Sort.)358 810 y(Although)31 b(sorting)f(has)g(traditionally)g(b)r(een)i(though)n(t)f(of)g(as)f(of)h(imp)r (ortance)g(primarily)f(in)i(non-)358 910 y(scien)n(ti\014c)d(computing,)g (this)h(op)r(eration)e(is)h(increasingly)f(imp)r(ortan)n(t)g(in)i(adv)-5 b(anced)29 b(scien)n(ti\014c)g(ap-)358 1010 y(plications.)59 b(In)36 b Fn(p)l(article)i(metho)l(d)e Fx(\015uid)g(sim)n(ulations,)h(for)e (example,)i(sorting)d(is)i(the)f(dominan)n(t)358 1109 y(cost.)358 1242 y(The)j Fo(P)-7 b(ARKBENCH)30 b Fx(in)n(teger)38 b(sort)g(b)r(enc)n (hmark)g(is)h(tak)n(en)f(from)g(the)i(NAS)f(P)n(arallel)e(Benc)n(h-)358 1342 y(marks)30 b([28)o(].)49 b(The)32 b(k)n(ernel)e(tests)i(b)r(oth)g(in)n (teger)e(computation)i(sp)r(eed)f(and)h(comm)n(unication)e(p)r(er-)358 1441 y(formance.In)d(this)h(b)r(enc)n(hmark,)f(a)g(v)n(ector)g(of)g(in)n (teger)g(data)g(is)h(generated)f(using)g(the)h(same)f(pseu-)358 1541 y(dorandom)34 b(n)n(um)n(b)r(er)i(generator)d(that)k(is)e(used)h(in)g (the)h(em)n(barrassingly)c(parallel)h(k)n(ernel.)61 b(This)358 1641 y(data)23 b(is)g(initially)h(mapp)r(ed)g(according)d(to)j(a)f (particular)f(sc)n(heme.)35 b(The)24 b(b)r(enc)n(hmark)f(problem)g(is)g(to) 358 1740 y(sort)e(this)i(data)e(b)n(y)h(the)h(most)f(e\016cien)n(t)g(sc)n (heme)g(for)g(a)g(particular)f(arc)n(hitecture.)34 b(V)-7 b(endor-supplied) 358 1840 y(sort)26 b(routines)h(ma)n(y)g(b)r(e)h(used)g(to)f(p)r(erform)g (the)h(sort)f(op)r(eration.)251 2006 y(3.)42 b(Input/Output.)47 b(W)-7 b(e)31 b(prop)r(ose)e(a)i Fn(p)l(encil)i(and)g(p)l(ap)l(er)f Fx(st)n(yle)e(b)r(enc)n(hmark)g({)h(not)f(tied)i(to)e(an)n(y)g(par-)358 2105 y(ticular)h(parallel)g(platform)h(or)g(application)f(but)i(just)g (measuring)e(some)h(k)n(ey)g(fundamen)n(tal)g(I/O)358 2205 y(parameters)37 b(of)i(the)g(system.)71 b(A)39 b(standard)f(F)-7 b(ortran-77)37 b(v)n(ersion)g(complemen)n(ts)i(the)g(detailed)358 2305 y(description)27 b(giv)n(en)h(in)h(the)f(individual)h Fk(ReadMe)d Fx(\014le.)39 b(The)29 b(I/O)e(p)r(erformance)g(is)i(tested)f(b)n (y)h(writ-)358 2404 y(ing)35 b(and)g(then)h(reading)e(di\013eren)n(t)i(sized) f(data)g(sets)h(to)f(and)g(from)g(disk.)61 b(The)35 b(read)g(and)g(write)358 2504 y(bu\013er)28 b(sizes)f(are)g(v)-5 b(aried)28 b(so)f(that)h(estimates)g (of)g(disk)g(I/O)f(start-up)g(time,)i(bandwidth)g(and)f(data)358 2604 y(transference)e(times)i(ma)n(y)f(b)r(e)h(made.)150 2878 y Fp(4.3)137 b(Benc)l(hmark)45 b(Implemen)l(tation)150 3060 y Fx(The)26 b Fo(P)-7 b(ARKBENCH)30 b Fx(k)n(ernel)25 b(b)r(enc)n(hmarks)h (are)f(written)h(as)g(far)g(as)f(p)r(ossible)h(in)h(standard)e(F)-7 b(ortran)25 b(77)150 3160 y(using)f(64-bit)h(\015oating)f(p)r(oin)n(t)h (arithmetic)f(\()p Fk(DOUBLE)42 b(PRECISION)21 b Fx(on)j(most)h(systems\),)g (unless)g(otherwise)150 3259 y(stated.)35 b(Both)24 b(PVM/MPI)e([1,)h(2])g (and)h(subset)f(HPF)g(v)n(ersions)f(exist)h(for)g(most)g(of)h(the)g(co)r(des) f(in)g(addition)150 3359 y(to)f(the)g(standard)e(F)-7 b(ortran-77)19 b(v)n(ersions.)33 b(A)22 b(description)f(of)h(eac)n(h)f(b)r(enc)n(hmark)g (and)g(instructions)g(on)h(ho)n(w)150 3459 y(to)31 b(run)h(it)g(are)e(giv)n (en)h(in)g(individual)h Fk(ReadMe)d Fx(\014les.)48 b(They)32 b(also)e(con)n(tain)h(a)g(sp)r(eci\014cation)g(of)g(the)h(three)150 3558 y(problem)g(sizes)f(agreed)g(up)r(on)h(for)g(eac)n(h)f(co)r(de:)46 b(\(1\))32 b(test)g(problem)g(\(2\))g(mo)r(derate)f(size)h(and)g(\(3\))g (grand)150 3658 y(c)n(hallenge)e(size.)47 b(A)31 b(form)n(ula)f(should)h(b)r (e)h(giv)n(en)e(in)h(the)h Fk(ReadMe)c Fx(\014les)j(to)g(pro)r(duce)g(\015op) g(coun)n(ts)f(for)h(the)150 3757 y(k)n(ernel)24 b(b)r(enc)n(hmarks)g(along)g (with)i(precalculated)e(\014gures)g(for)h(eac)n(h)g(standard)f(problem)g (size.)36 b Fk(Make)p Fx(-\014les)150 3857 y(are)27 b(supplied)h(with)g(eac)n (h)e(b)r(enc)n(hmark)h(to)h(handle)f(compilation)g(and)h(linking)f(in)h(a)f (Unix)h(en)n(vironmen)n(t.)150 4132 y Fp(4.4)137 b(Concluding)48 b(Remarks)150 4313 y Fx(The)24 b(con)n(ten)n(ts)g(of)g(the)h Fo(P)-7 b(ARKBENCH)30 b Fx(k)n(ernel)23 b(b)r(enc)n(hmark)h(suite)g(should)g (map)h(reasonably)d(w)n(ell)i(on)n(to)150 4413 y(an)n(y)30 b(parallel)g(library)f(supplied)j(b)n(y)e(the)i(v)n(endors.)45 b(This)31 b(will)g(allo)n(w)f(comparativ)n(e)f(p)r(erformance)h(mea-)150 4513 y(suremen)n(ts)f(across)f(di\013eren)n(t)i(platforms)f(using)g(the)h Fo(P)-7 b(ARKBENCH)30 b Fx(k)n(ernels)e(but)j(also)d(p)r(erformance)150 4612 y(comparisons)23 b(to)i(the)g(functionally)g(similar)f(and)h (highly-optimized)f(library)g(routines)g(on)g(ev)n(ery)g(partic-)150 4712 y(ular)k(parallel)g(system.)40 b(Another)28 b(adv)-5 b(an)n(tage)27 b(of)i(the)g(use)g(of)f(k)n(ernel)g(b)r(enc)n(hmarks)g(is)g(that)h(they)g (should)150 4812 y(not)f(in)n(v)n(olv)n(e)e(an)h(unreasonable)f(amoun)n(t)h (of)g(lab)r(or)g(on)g(the)h(part)g(of)f(v)n(endors.)1796 5428 y(35)p eop PNP restore /PNP save def 628.2618 89.4750 translate 37 bop 150 935 a Fr(Chapter)66 b(5)150 1350 y Fu(Compact)78 b(Applications)2463 1287 y Fq(\003)150 1832 y Fp(5.1)137 b(In)l(tro)t (duction)150 2013 y Fx(While)38 b(k)n(ernel)e(applications,)i(suc)n(h)f(as)g (those)f(describ)r(ed)h(in)h(Chapter)e(3,)j(pro)n(vide)d(a)h(fairly)g (straigh)n(t-)150 2113 y(forw)n(ard)31 b(w)n(a)n(y)h(of)h(assessing)e(the)i (p)r(erformance)f(of)h(parallel)f(systems)g(they)h(are)f(not)h(represen)n (tativ)n(e)e(of)150 2213 y(scien)n(ti\014c)26 b(applications)e(in)i(general)f (since)g(they)h(do)f(not)h(re\015ect)f(certain)g(t)n(yp)r(es)h(of)g(system)f (b)r(eha)n(vior.)35 b(In)150 2312 y(particular,)26 b(man)n(y)h(scien)n (ti\014c)g(applications)f(in)n(v)n(olv)n(e)g(data)h(mo)n(v)n(emen)n(t)f(b)r (et)n(w)n(een)h(phases)g(of)g(an)g(applica-)150 2412 y(tion,)f(and)g(ma)n(y)f (also)f(require)h(signi\014can)n(t)g(amoun)n(ts)g(of)h(I/O.)f(These)g(t)n(yp) r(es)h(of)g(b)r(eha)n(vior)e(are)h(di\016cult)h(to)150 2511 y(gauge)g(using)h(k)n(ernel)g(applications.)275 2611 y(One)k(factor)g(that)h (has)g(hindered)g(the)g(use)g(of)g(full)g(application)f(co)r(des)h(for)f(b)r (enc)n(hmarking)g(parallel)150 2711 y(computers)24 b(in)i(the)f(past)g(is)g (that)g(suc)n(h)g(co)r(des)f(are)g(di\016cult)i(to)f(parallelize)f(and)g(to)h (p)r(ort)g(b)r(et)n(w)n(een)g(target)150 2810 y(arc)n(hitectures.)44 b(In)30 b(addition,)h(full)h(application)d(co)r(des)h(that)h(ha)n(v)n(e)e(b)r (een)i(successfully)f(parallelized)f(are)150 2910 y(often)21 b(proprietary)-7 b(,)21 b(and/or)e(sub)5 b(ject)21 b(to)g(distribution)g (restrictions.)34 b(T)-7 b(o)20 b(minimize)i(the)f(negativ)n(e)f(impact)150 3010 y(of)28 b(these)f(factors)g(w)n(e)g(prop)r(ose)f(to)i(mak)n(e)f(use)g (of)h(compact)f(applications)f(in)i(our)f(b)r(enc)n(hmarking)g(e\013ort.)275 3109 y(Compact)h(applications)h(are)f(t)n(ypical)h(of)g(those)g(found)h(in)f (researc)n(h)e(en)n(vironmen)n(ts)i(\(as)f(opp)r(osed)h(to)150 3209 y(pro)r(duction)d(or)f(engineering)f(en)n(vironmen)n(ts\),)i(and)f (usually)h(consist)f(of)h(up)g(to)g(a)g(few)g(thousand)f(lines)h(of)150 3308 y(source)21 b(co)r(de.)35 b(Compact)21 b(applications)h(are)f(distinct)h (from)g(k)n(ernel)f(applications)h(since)f(they)i(are)e(capable)150 3408 y(of)26 b(pro)r(ducing)g(scien)n(ti\014cally)f(useful)i(results.)36 b(In)26 b(man)n(y)g(cases,)f(compact)h(applications)f(are)h(made)g(up)g(of) 150 3508 y(sev)n(eral)g(k)n(ernels,)g(in)n(tersp)r(ersed)h(with)h(data)f(mo)n (v)n(emen)n(ts)g(and)g(I/O)g(op)r(erations)f(b)r(et)n(w)n(een)i(the)g(k)n (ernels.)275 3607 y(In)22 b(this)h(c)n(hapter)e(the)i(criteria)e(for)h (selecting)g(compact)g(applications)g(for)f(the)i Fo(P)-7 b(ARKBENCH)30 b Fx(suite)150 3707 y(will)d(b)r(e)h(discussed.)36 b(In)27 b(addition,)g(the)h(general)d(researc)n(h)g(areas)g(that)j(will)f(b)r(e)g (represen)n(ted)f(in)h(the)h(suite)150 3807 y(are)f(outlined.)150 4081 y Fp(5.2)137 b(Criteria)46 b(for)f(Selection)150 4263 y Fx(The)25 b(three)g(main)g(criteria)f(for)h(inclusion)g(of)g(a)g(parallel)f (co)r(de)h(in)g(the)h(Compact)f(Applications)g(suite)g(are,)251 4429 y(1.)42 b(The)22 b(co)r(de)g(m)n(ust)h(b)r(e)f(a)g(complete)h (application)e(and)i(b)r(e)f(capable)g(of)g(pro)r(ducing)g(results)g(of)g (researc)n(h)358 4529 y(in)n(terest.)34 b(These)20 b(t)n(w)n(o)g(p)r(oin)n (ts)h(distinguish)g(a)f(compact)h(application)f(from)g(a)h(k)n(ernel.)33 b(F)-7 b(or)20 b(example,)358 4628 y(a)27 b(co)r(de)g(that)h(only)f(solv)n (es)f(a)h(randomly-generated,)e(dense,)i(linear)g(system)g(b)n(y)h(LU)f (factorization)358 4728 y(should)j(b)r(e)h(considered)f(a)g(k)n(ernel.)45 b(Ev)n(en)30 b(though)h(the)g(co)r(de)f(is)h(complete,)g(it)g(do)r(es)g(not)f (pro)r(duce)358 4828 y(results)h(of)g(researc)n(h)f(in)n(terest.)48 b(Ho)n(w)n(ev)n(er,)31 b(if)h(the)g(LU)g(factorization)e(is)h(em)n(b)r(edded) h(in)g(an)f(appli-)358 4927 y(cation)25 b(that)h(uses)f(the)h(b)r(oundary)f (elemen)n(t)h(metho)r(d)g(to)g(solv)n(e,)f(for)g(example,)g(a)h(t)n(w)n (o-dimensional)358 5027 y(elasto)r(dynamics)34 b(problem,)k(then)f(suc)n(h)e (an)h(application)f(could)h(legitimately)g(b)r(e)g(considered)f(a)p 150 5096 1350 4 v 241 5149 a Fm(\003)277 5173 y Fl(assem)n(bled)23 b(b)n(y)h(Da)n(vid)g(W)-6 b(alk)n(er)24 b(for)f(Compact)h(Applications)g(sub) r(committee)1796 5428 y Fx(36)p eop PNP restore PNEP %%Page: ? 20 0.6303 -612.00 PNLS /PNP save def 12.6922 89.4750 translate 38 bop 358 312 a Fx(compact)25 b(application.)36 b(Compact)26 b(applications)g(and)g(full)h(pro)r(duction)f(co)r(des)g(are)f(distinguished) 358 412 y(b)n(y)32 b(their)h(soft)n(w)n(are)f(complexit)n(y)-7 b(,)34 b(whic)n(h)f(is)g(di\016cult)h(to)f(quan)n(tify)-7 b(.)53 b(Soft)n(w)n(are)32 b(complexit)n(y)g(giv)n(es)358 511 y(an)c(indication)g (of)g(ho)n(w)g(hard)g(it)h(is)f(to)g(write,)h(p)r(ort)f(and)g(main)n(tain)g (an)h(application,)f(and)g(ma)n(y)g(b)r(e)358 611 y(gauged)e(v)n(ery)g (roughly)h(b)n(y)g(the)h(length)g(of)g(the)g(source)e(co)r(de.)37 b(Ho)n(w)n(ev)n(er,)26 b(there)h(is)h(no)f(hard)g(upp)r(er)358 711 y(limit)35 b(on)g(the)g(length)g(of)f(a)h(co)r(de)f(in)h(the)g(Compact)g (Applications)f(suite.)59 b(It)35 b(is)g(exp)r(ected)g(that)358 810 y(the)c(source)e(co)r(de)h(\(excluding)h(commen)n(ts)f(and)h(rep)r(eated) f(common)g(blo)r(c)n(ks\))g(for)g(most)h(compact)358 910 y(applications)26 b(will)i(b)r(e)g(b)r(et)n(w)n(een)g(2000)d(and)j(10000)d(lines,)j(but)g(some) f(ma)n(y)g(b)r(e)h(longer.)251 1076 y(2.)42 b(The)26 b(co)r(de)g(m)n(ust)g(b) r(e)h(of)f(high)g(qualit)n(y)-7 b(.)36 b(This)26 b(means)g(it)g(m)n(ust)h(ha) n(v)n(e)e(b)r(een)h(extensiv)n(ely)g(tested)g(and)358 1176 y(v)-5 b(alidated,)25 b(preferably)e(on)i(a)f(wide)h(selection)f(of)h (di\013eren)n(t)g(parallel)e(arc)n(hitectures.)35 b(The)25 b(problem)358 1275 y(size)32 b(and)h(n)n(um)n(b)r(er)g(of)g(pro)r(cessors)d (used)j(m)n(ust)g(not)g(b)r(e)h(hard-co)r(ded)d(in)n(to)i(the)h(application,) f(and)358 1375 y(should)24 b(b)r(e)g(sp)r(eci\014ed)h(at)f(run)n(time)g(as)g (input)h(to)f(the)h(program.)34 b(Ideally)-7 b(,)24 b(the)h(parallel)e(co)r (de)h(should)358 1475 y(not)e(imp)r(ose)h(restrictions)e(on)i(the)g(problem)f (size)h(that)g(are)f(not)g(applicable)h(for)f(the)h(corresp)r(onding)358 1574 y(sequen)n(tial)34 b(co)r(de.)59 b(Th)n(us,)37 b(the)e(parallel)f(co)r (de)h(should)g(not)g(require)f(that)h(the)g(problem)g(size)g(b)r(e)358 1674 y(exactly)f(divisible)h(b)n(y)g(the)h(n)n(um)n(b)r(er)f(of)g(pro)r (cessors,)g(or)g(that)g(the)h(n)n(um)n(b)r(er)f(of)g(pro)r(cessors)e(b)r(e)i (a)358 1773 y(p)r(o)n(w)n(er)18 b(of)i(t)n(w)n(o.)34 b(In)20 b(some)f(cases)g(this)h(latter)g(requiremen)n(t)f(ma)n(y)g(ha)n(v)n(e)g(to)h (b)r(e)g(relaxed.)33 b(F)-7 b(or)19 b(example,)358 1873 y(most)31 b(parallel)f(fast)h(F)-7 b(ourier)31 b(transform)f(routines)h(require)f(the)i (n)n(um)n(b)r(er)f(of)g(pro)r(cessors)e(to)j(b)r(e)f(a)358 1973 y(p)r(o)n(w)n(er)26 b(of)i(t)n(w)n(o.)37 b(It)28 b(is)g(preferable)f (that)h(the)g(co)r(de)g(b)r(e)g(written)g(so)f(that)h(it)h(w)n(orks)d (correctly)g(for)h(an)358 2072 y(arbitrary)17 b(one-to-one)h(mapping)i(b)r (et)n(w)n(een)g(the)g(logical)e(pro)r(cess)h(top)r(ology)f(of)i(the)g (application)f(and)358 2172 y(the)k(hardw)n(are)e(top)r(ology)g(of)i(the)g (parallel)f(computer.)35 b(This)23 b(is)g(desirable)e(so)i(that)g(the)g (assignmen)n(t)358 2272 y(of)e(a)g(lo)r(cation)f(in)i(the)f(logical)f(pro)r (cess)g(top)r(ology)g(to)i(a)e(ph)n(ysical)h(pro)r(cessor)e(can)i(b)r(e)g (easily)g(adjusted)358 2371 y(when)29 b(p)r(orting)f(the)i(application)e(b)r (et)n(w)n(een)h(platforms.)40 b(F)-7 b(or)29 b(example)f(a)h(Gra)n(y)e(co)r (de)i(assignmen)n(t)358 2471 y(ma)n(y)d(b)r(e)i(b)r(est)g(for)g(a)f(h)n(yp)r (ercub)r(e,)g(and)h(a)f(natural)g(ordering)f(for)h(a)g(mesh)h(arc)n (hitecture.)251 2637 y(3.)42 b(The)36 b(application)f(m)n(ust)i(b)r(e)g(w)n (ell)f(do)r(cumen)n(ted.)63 b(The)36 b(source)f(co)r(de)h(itself)h(should)f (con)n(tain)f(an)358 2736 y(adequate)27 b(n)n(um)n(b)r(er)i(of)f(commen)n (ts,)g(and)h(eac)n(h)e(mo)r(dule)i(should)f(b)r(egin)h(with)g(a)f(commen)n(t) g(section)358 2836 y(that)39 b(describ)r(es)f(what)h(the)g(routine)f(do)r (es,)j(and)e(the)g(argumen)n(ts)f(passed)g(to)g(it.)71 b(In)39 b(addition,)358 2936 y(there)28 b(should)g(b)r(e)g(a)g Fn(Users')i(Guide)g Fx(to)e(the)g(application)g(that)g(describ)r(es)g(the)g(input)h(and)f (output,)358 3035 y(the)h(parameterization)f(of)h(the)h(problem)f(size)g(and) g(pro)r(cessor)e(la)n(y)n(out,)i(and)g(details)g(of)g(what)h(the)358 3135 y(application)22 b(do)r(es.)35 b(The)24 b(Users')e(Guide)i(should)f (also)f(con)n(tain)g(a)h(bibliograph)n(y)f(of)h(related)g(pap)r(ers.)275 3301 y(In)33 b(addition,)h(to)f(the)h(three)f(criteria)f(discussed)g(ab)r(o)n (v)n(e,)i(there)f(are)f(a)h(n)n(um)n(b)r(er)f(of)i(other)e(desirable)150 3401 y(features)23 b(that)g(a)g Fo(P)-7 b(ARKBENCH)29 b Fx(Compact)23 b(Application)g(should)g(ha)n(v)n(e.)35 b(These)22 b(are)h(discussed)f(in)i (the)150 3500 y(follo)n(wing)j(subsections.)150 3733 y Fy(5.2.1)112 b(Self)38 b(Chec)m(king)f(Applications)150 3886 y Fx(The)20 b(application)g(should)g(b)r(e)h(self-c)n(hec)n(king.)33 b(That)20 b(is,)i(at)e(the)h(end)g(of)f(the)h(computation)f(the)h(application)150 3986 y(should)32 b(p)r(erform)f(a)g(c)n(hec)n(k)g(to)h(v)-5 b(alidate)32 b(the)g(results)f(of)h(the)g(run.)50 b(The)31 b(application)h(ma)n(y)f(also)g(output)150 4085 y(a)i(summary)f(of)i(p)r (erformance)e(results)h(for)g(the)g(run,)i(suc)n(h)e(as)g(the)g(M\015op)h (rate,)g(and)f(other)g(p)r(ertinen)n(t)150 4185 y(information.)150 4417 y Fy(5.2.2)112 b(Programming)36 b(Languages)150 4570 y Fx(The)26 b(co)r(de)g(should)g(b)r(e)h(written)g(in)f(F)-7 b(ortran)25 b(77,)h(F)-7 b(ortran)25 b(90,)h(High)g(P)n(erformance)e(F)-7 b(ortran,)26 b(or)f(C.)h(Data)150 4670 y(should)31 b(b)r(e)h(passed)e(b)r(et) n(w)n(een)h(pro)r(cessors)e(b)n(y)i(explicit)h(message)e(passing.)47 b Fo(P)-7 b(ARKBENCH)29 b Fx(do)r(es)i(not)150 4770 y(sp)r(ecify)23 b(whic)n(h)g(message)e(passing)h(system)h(should)f(b)r(e)h(used,)h(but)g(one) e(that)h(is)g(a)n(v)-5 b(ailable)22 b(on)g(a)h(n)n(um)n(b)r(er)f(of)150 4869 y(parallel)28 b(platforms)g(is)h(preferable.)39 b(Ev)n(en)n(tually)28 b(it)h(is)g(exp)r(ected)g(that)g(MPI)f(will)i(b)r(ecome)e(the)h(message)150 4969 y(passing)23 b(system)g(of)g(c)n(hoice,)h(but)g(in)g(the)g(mean)n(time)g (p)r(ortable)f(systems)g(suc)n(h)g(as)g(PVM,)h(PICL,)f(Express,)150 5069 y(P)-7 b(ARMA)n(CS,)24 b(and)f(P4)g(are)f(acceptable)h(alternativ)n(es.) 34 b(The)24 b(co)r(des)f(in)h(the)f(Compact)h(Applications)f(suite)1796 5428 y(37)p eop PNP restore /PNP save def 628.2618 89.4750 translate 39 bop 150 312 a Fx(should)38 b(not)f(con)n(tain)h(an)n(y)f(assem)n(bly)f(co) r(ded)i(p)r(ortions,)i(although)d(assem)n(bly)g(co)r(de)h(ma)n(y)f(b)r(e)h (used)g(in)150 412 y(optimized)28 b(v)n(ersions)e(of)h(the)h(co)r(de.)150 686 y Fp(5.3)137 b(Prop)t(osed)46 b(Compact)g(Application)i(Benc)l(hmarks)150 868 y Fx(A)n(t)32 b(the)g(time)f(of)h(writing)f(\(Octob)r(er)g(1993\))f(the)h Fo(P)-7 b(ARKBENCH)30 b Fx(organization)f(is)i(in)h(the)g(pro)r(cess)e(of)150 968 y(soliciting)19 b(submission)h(of)g(applications)f(for)h(inclusion)g(in)g (the)g(Compact)g(Applications)g(suite.)34 b(Th)n(us,)22 b(the)150 1067 y(applications)c(that)g(comprise)g(the)h(suite)f(cannot)g(y)n(et)g(b)r (e)h(listed)g(here.)33 b(Ho)n(w)n(ev)n(er,)19 b(in)f(this)h(section)f(the)h (main)150 1167 y(application)24 b(areas)f(that)h(are)g(exp)r(ected)h(to)f(b)r (e)h(in)g(the)g(suite)f(are)g(outlined.)36 b(The)24 b(in)n(ten)n(tion)h(is)f (that)h(these)150 1267 y(areas)d(should)i(b)r(e)g(represen)n(tativ)n(e)e(of)i (the)g(\014elds)g(in)g(whic)n(h)g(parallel)f(computers)g(are)g(actually)g (used.)36 b(The)150 1366 y(co)r(des)29 b(should)h(exercise)f(a)g(n)n(um)n(b)r (er)h(of)g(di\013eren)n(t)g(algorithms,)f(and)h(p)r(ossess)f(di\013eren)n(t)h (comm)n(unication)150 1466 y(and)25 b(I/O)f(c)n(haracteristics.)34 b(Initially)25 b(the)g(Compact)g(Applications)f(suite)i(will)f(consist)f(of)h (no)g(more)f(than)150 1566 y(ten)k(co)r(des.)37 b(This)28 b(restriction)f(is) g(imp)r(osed)h(so)f(that)h(the)g(resources)e(needed)i(to)g(manage)e(and)i (distribute)150 1665 y(the)h(suite)f(can)g(b)r(e)h(assessed.)37 b(The)29 b(suite)f(ma)n(y)g(b)r(e)g(enlarged)f(in)i(the)g(future)f(if)h(this) g(seems)f(manageable.)150 1765 y(Belo)n(w)22 b(is)h(a)g(list)g(of)g(the)h (application)e(areas)f(that)j(are)e(exp)r(ected)h(to)g(b)r(e)h(represen)n (ted)e(in)h(the)h(suite.)35 b(This)23 b(is)150 1864 y(not)j(mean)n(t)g(to)g (b)r(e)g(an)g(exclusiv)n(e)f(list;)i(submissions)e(from)h(other)f (application)g(areas)f(will)j(b)r(e)f(considered)150 1964 y(for)h(inclusion)g (in)h(the)g(suite.)275 2130 y Fi(\017)41 b Fx(Climate)27 b(and)h (meteorological)d(mo)r(deling)275 2296 y Fi(\017)41 b Fx(Computational)26 b(\015uid)j(dynamics)e(\(CFD\))275 2462 y Fi(\017)41 b Fx(Finance,)27 b(e.g.,)g(p)r(ortfolio)g(optimization)275 2628 y Fi(\017)41 b Fx(Molecular)26 b(dynamics)275 2794 y Fi(\017)41 b Fx(Plasma)26 b(ph)n(ysics)275 2960 y Fi(\017)41 b Fx(Quan)n(tum)27 b(c)n(hemistry)275 3126 y Fi(\017)41 b Fx(Quan)n(tum)27 b(c)n(hromo)r(dynamics)f(\(QCD\))275 3292 y Fi(\017)41 b Fx(Reserv)n(oir)25 b(mo)r(deling)150 3567 y Fp(5.4)137 b(Submitting)48 b(to)e(the)h(Compact)f(Application)i(Suite)150 3749 y Fx(The)27 b(pro)r(cedure)f(for)g(submitting)i(co)r(des)f(to)f(the)i Fo(P)-7 b(ARKBENCH)29 b Fx(Compact)e(Applications)g(suite)g(is)g(as)150 3848 y(follo)n(ws.)251 4015 y(1.)42 b(Complete)58 b(the)h(submission)f(form)g (in)h(App)r(endix)g(A,)67 b(and)58 b(email)h(it)g(to)f(Da)n(vid)g(W)-7 b(alk)n(er)358 4114 y(at)66 b Fk(walker@msr.epm.or)o(nl)o(.go)o(v)p Fx(.)149 b(The)67 b(data)f(on)g(this)i(form)e(will)h(b)r(e)h(review)n(ed)d(b) n(y)358 4214 y(the)54 b Fo(P)-7 b(ARKBENCH)29 b Fx(Compact)53 b(Applications)h(Sub)r(committee,)61 b(and)54 b(the)g(submitter)g(will)358 4313 y(b)r(e)61 b(noti\014ed)h(if)f(the)h(application)e(is)i(to)f(b)r(e)g (considered)f(further)i(for)e(inclusion)h(in)h(the)358 4413 y Fo(P)-7 b(ARKBENCH)29 b Fx(suite.)251 4579 y(2.)42 b(If)30 b Fo(P)-7 b(ARKBENCH)30 b Fx(Compact)g(Applications)g(Sub)r(committee)i (decides)e(to)g(consider)g(the)g(appli-)358 4679 y(cation)36 b(further)i(the)f(submitter)h(will)g(b)r(e)f(ask)n(ed)g(to)g(submit)h(the)g (source)e(co)r(de)h(and)g(input)h(and)358 4778 y(output)23 b(\014les,)h(together)f(with)g(an)n(y)g(do)r(cumen)n(tation)g(and)g(pap)r (ers)f(ab)r(out)i(the)f(application.)35 b(Source)358 4878 y(co)r(de)23 b(and)h(input)h(and)e(output)i(\014les)f(should)f(b)r(e)i(submitted)g(b)n(y)e (email,)i(or)e(ftp,)i(unless)f(the)g(\014les)g(are)358 4978 y(v)n(ery)h(large,)h(in)g(whic)n(h)h(case)f(a)g(tar)g(\014le)h(on)f(a)h(1/4)e (inc)n(h)i(cassette)f(tap)r(e.)36 b(Wherev)n(er)26 b(p)r(ossible)g(email)358 5077 y(submission)i(is)h(preferred)f(for)g(all)h(do)r(cumen)n(ts)g(in)g(man)g (page,)g(Latex)f(and/or)g(P)n(ostscipt)g(format.)1796 5428 y(38)p eop PNP restore PNEP %%Page: ? 21 0.6303 -612.00 PNLS /PNP save def 12.6922 89.4750 translate 40 bop 358 312 a Fx(These)27 b(\014les)h(do)r(cumen)n(ts)g(and)f(pap)r(ers)g (together)g(constitute)h(the)h(application)e(pac)n(k)-5 b(age.)36 b(The)28 b(ap-)358 412 y(plication)19 b(pac)n(k)-5 b(age)18 b(should)h(b)r(e)h(sen)n(t)f(to)h(the)g(follo)n(wing)e(address,)i(and)g(the)g (sub)r(committee)g(will)g(then)358 511 y(mak)n(e)h(a)i(\014nal)f(decision)g (on)g(whether)h(to)f(include)h(the)g(application)f(in)h(the)g Fo(P)-7 b(ARKBENCH)30 b Fx(suite.)358 669 y(Da)n(vid)d(W.)h(W)-7 b(alk)n(er)358 802 y(Oak)26 b(Ridge)i(National)f(Lab)r(oratory)358 935 y(Bldg.)g(6012/MS-6367)358 1068 y(P)-7 b(.)27 b(O.)g(Bo)n(x)g(2008)358 1201 y(Oak)f(Ridge,)i(TN)f(37831-6367)358 1333 y(\(615\))f(574-7401/0680)c (\(phone/fax\))358 1466 y Fk(walker@msr.epm.)o(orn)o(l.)o(go)o(v)251 1632 y Fx(3.)42 b(If)32 b(the)g(application)f(is)g(appro)n(v)n(ed)f(for)h (inclusion)h(in)g(the)g Fo(P)-7 b(ARKBENCH)30 b Fx(suite)i(an)f(authorized) 358 1732 y(p)r(erson)38 b(from)h(the)g(submitting)g(organization)e(will)i(b)r (e)h(ask)n(ed)e(to)h(complete)f(and)h(sign)g(a)f(form)358 1832 y(giving)17 b Fo(P)-7 b(ARKBENCH)30 b Fx(authorit)n(y)17 b(to)h(distribute,)j (and)d(mo)r(dify)h(\(if)g(necessary\),)g(the)g(application)358 1931 y(pac)n(k)-5 b(age.)1796 5428 y(39)p eop PNP restore /PNP save def 628.2618 89.4750 translate 41 bop 150 935 a Fr(Chapter)66 b(6)150 1350 y Fu(HPF)80 b(Compiler)d(Benc)-7 b(hmarks)3037 1287 y Fq(\003)150 1832 y Fp(6.1)137 b(Ob)8 b(jectiv)l(es)150 2013 y Fx(F)-7 b(or)41 b(most)g(users,)j(the)d(p)r(erformance)f(of)i(co)r (des)e(generated)g(b)n(y)h(a)g(compiler)g(is)g(what)g(that)h(actually)150 2113 y(matters.)d(This)29 b(can)f(b)r(e)h(inferred)g(from)f(running)g(HPF)h (v)n(ersion)e(of)h Fo(P)-7 b(ARKBENCH)30 b Fx(co)r(des)e(describ)r(ed)150 2213 y(in)34 b(c)n(hapter)e(4)h(and)h(5.)53 b(F)-7 b(or)33 b(HPF)h(compiler)e(dev)n(elop)r(ers,)i(ho)n(w)n(ev)n(er,)f Fn(an)i(additional)h Fx(b)r(enc)n(hmark)d(suite)150 2312 y(ma)n(y)c(b)r(e)h (v)n(ery)e(useful:)41 b(the)30 b(b)r(enc)n(hmark)e(suite)i(that)g(can)f(ev)-5 b(aluate)29 b(sp)r(eci\014c)g(HPF)h(compilation)f(phases)150 2412 y(and)23 b(the)h(compiler)e(run)n(time)i(supp)r(ort.)35 b(F)-7 b(or)22 b(that)i(purp)r(ose,)g(the)f(relev)-5 b(an)n(t)23 b(metric)g(seems)g(to)g(b)r(e)g(the)h(ratio)150 2511 y(of)f(execution)g (times)h(of)f(compiler)g(generated)f(to)h(hand)h(co)r(ded)f(programs)e(as)i (a)g(function)h(of)f(the)h(problem)150 2611 y(size)j(and)h(n)n(um)n(b)r(er)f (of)h(pro)r(cessors)d(engaged)h(in)i(the)g(computation.)275 2711 y(The)35 b(compilation)f(pro)r(cess)g(can)h(b)r(e)g(logically)f(divided) i(in)n(to)e(sev)n(eral)g(phases,)i(and)f(eac)n(h)f(of)i(them)150 2810 y(in\015uence)22 b(the)g(e\016ciency)f(of)h(the)g(resulting)f(co)r(de.) 35 b(The)21 b(initial)h(stage)f(is)g(parsing)g(of)g(a)g(source)g(co)r(de)g (whic)n(h)150 2910 y(results)28 b(in)g(an)g(in)n(ternal)g(represen)n(tation)e (of)j(the)f(co)r(de.)39 b(It)29 b(is)f(follo)n(w)n(ed)f(compiler)h (transformations,)e(lik)n(e)150 3010 y(data)j(distribution,)g(lo)r(op)g (transformations,)f(computation)h(distribution,)g(comm)n(unication)g (detection,)150 3109 y(sequen)n(tialization,)24 b(insertion)f(of)h(calls)g (to)g(a)f(run)n(time)h(supp)r(ort,)h(and)f(others.)35 b(This)24 b(w)n(e)g(will)g(call)g(a)f(HPF-)150 3209 y(sp)r(eci\014c)33 b(phase)f(of)h(compilation.)53 b(The)33 b(compilation)f(is)h(concluded)g(b)n (y)f(co)r(de)h(generation)e(phase.)53 b(F)-7 b(or)150 3308 y(p)r(ortable)25 b(compilers)f(that)h(outputs)h(f77+message)c(passing)j(co)r (de,)g(the)h(no)r(de)f(compilation)f(is)i(ob)n(viously)150 3408 y(factorized)h(out)g(and)h(the)g(e\016ciency)f(of)h(the)g(no)r(de)f (compiler)g(can)h(b)r(e)g(ev)-5 b(aluated)27 b(separately)-7 b(.)275 3508 y(This)33 b(b)r(enc)n(hmark)f(suite)i(addresses)d(the)j(HPF-sp)r (eci\014c)f(phase)g(only)-7 b(.)53 b(Th)n(us,)34 b(it)g(is)f(w)n(ell)g (suited)h(for)150 3607 y(p)r(erformance)25 b(ev)-5 b(aluation)24 b(of)i(b)r(oth)g(translators)d(\(HPF)j(to)g(F77+message)d(passing\))i(and)g (gen)n(uine)g(HPF)150 3707 y(compilers.)37 b(The)28 b(parsing)e(phase)i(is)g (an)f(elemen)n(t)h(of)g(the)g(con)n(v)n(en)n(tional)e(compiler)i(tec)n (hnology)e(and)i(it)g(is)150 3807 y(not)33 b(of)g(in)n(terest)f(in)h(this)h (con)n(text.)52 b(The)33 b(co)r(de)g(generation)e(phase)i(in)n(v)n(olv)n(es)e (optimization)h(tec)n(hniques)150 3906 y(dev)n(elop)r(ed)40 b(for)f(sequen)n(tial)g(compilers)h(\(in)g(particular,)i(F)-7 b(ortran)39 b(90)g(compilers\))h(as)f(w)n(ell)h(as)f(micro-)150 4006 y(grain)33 b(parallelism)g(or)h(v)n(ectorization.)55 b(The)34 b(ob)5 b(ject)34 b(co)r(des)g(for)g(sp)r(eci\014c)g(platforms)g(ma)n(y)g(b)r (e)g(strongly)150 4105 y(arc)n(hitecture)21 b(dep)r(enden)n(t)j(\(e.g.,)f(ma) n(y)f(b)r(e)i(v)n(ery)d(di\013eren)n(t)i(for)f(pro)r(cessors)e(with)j(v)n (ector)f(capabilities)g(than)150 4205 y(for)27 b(those)h(without)g(it\).)38 b(Ev)-5 b(aluation)27 b(of)h(p)r(erformance)f(of)g(these)h(asp)r(ects)g (require)e(di\013eren)n(t)i(tec)n(hniques)150 4305 y(that)g(these)g(prop)r (osed)e(here.)275 4404 y(It)33 b(is)g(w)n(orth)g(noting,)h(that)f(the)h (HPF-phase)e(strongly)g(a\013ect)i(the)f(p)r(ossibilit)n(y)g(of)g (optimization)g(of)150 4504 y(the)f(no)r(de)f(co)r(des.)48 b(F)-7 b(or)31 b(example,)h(insertions)f(of)g(calls)g(to)h(the)g(comm)n (unication)e(library)g(ma)n(y)h(prohibit)150 4604 y(the)23 b(no)r(de)g(compiler)f(to)h(p)r(erform)f(man)n(y)g(standard)g(optimizations)g (without)i(exp)r(ensiv)n(e)e(in)n(terpro)r(cedural)150 4703 y(analysis.)35 b(Therefore,)26 b(capabilit)n(y)g(to)h(exploit)g(opp)r (ortunities)f(for)g(optimizations)h(at)f(HPF)h(lev)n(el)g(and)f(to)150 4803 y(generate)33 b(the)i(output)g(co)r(de)f(that)h(w)n(a)n(y)e(it)i(can)f (b)r(e)h(further)g(optimized)g(b)n(y)f(the)h(no)r(de)f(compiler)g(is)g(an)150 4903 y(imp)r(ortan)n(t)22 b(elemen)n(t)g(of)g(ev)-5 b(aluation)21 b(of)h(HPF)g(compilers.)34 b(Nev)n(ertheless,)22 b(ev)-5 b(aluation)22 b(of)g(the)g(HPF-phase)150 5002 y(separately)29 b(is)i(v)n(ery)f(v)-5 b(aluable)30 b(since)h(the)g(hand)g(co)r(ded)g(programs)d(face)j(the)g(same)g (problems.)46 b(W)-7 b(e)31 b(will)p 150 5071 1350 4 v 241 5125 a Fm(\003)277 5148 y Fl(assem)n(bled)23 b(b)n(y)h(T)-6 b(om)23 b(Haupt)h(for)f(Compiler)f(Benc)n(hmarks)h(sub)r(committee)1796 5428 y Fx(40)p eop PNP restore PNEP %%Page: ? 22 0.6303 -612.00 PNLS /PNP save def 12.6922 89.4750 translate 42 bop 150 312 a Fx(address)26 b(these)i(issues)f(in)h(the)g(future)g (releases)e(of)h(the)h(b)r(enc)n(hmark)f(suite.)275 412 y(Compilers)f(for)h (massiv)n(ely)f(parallel)g(and)h(distributed)h(systems)f(are)g(still)g(ob)5 b(ject)28 b(of)f(a)g(researc)n(h)e(and)150 511 y(lab)r(oratory)e(testing)j (rather)e(than)h(commercial)f(pro)r(ducts.)36 b(The)26 b(parallel)e(compiler) h(tec)n(hnology)f(as)g(w)n(ell)150 611 y(as)j(metho)r(ds)h(of)g(ev)-5 b(aluating)27 b(it)h(is)g(not)f(mature)h(y)n(et.)37 b(Nev)n(ertheless,)26 b(the)j(adv)n(en)n(t)d(of)i(the)g(HPF)g(standard)150 711 y(giv)n(es)e(opp)r (ortunit)n(y)i(to)f(dev)n(elop)g(systematic)g(b)r(enc)n(hmarking)g(tec)n (hniques.)275 810 y(The)33 b(curren)n(t)g(de\014nition)h(of)f(HPF)h(cannot)f (b)r(e)h(recognized)e(as)h(an)g(ultimate)h(solution)f(for)g(parallel)150 910 y(computing.)i(Its)24 b(limitations)f(are)f(w)n(ell)i(kno)n(wn,)f(and)g (man)n(y)g(researc)n(hers)e(are)h(w)n(orking)f(on)j(extensions)e(to)150 1010 y(HPF)k(to)g(address)f(a)h(broader)e(class)h(of)i(real)e(life,)i (commercial)e(and)h(scien)n(ti\014c)g(applications.)35 b(W)-7 b(e)27 b(exp)r(ect)150 1109 y(new)j(language)f(features)g(to)h(b)r(e)h(added) f(to)g(the)g(HPF)g(de\014nition)h(in)f(future)h(v)n(ersions)d(of)i(HPF,)g (and)g(w)n(e)150 1209 y(will)23 b(extend)f(the)h(b)r(enc)n(hmark)f(suite)g (accordingly)-7 b(.)33 b(On)23 b(the)f(other)g(hand,)i(new)e(parallel)f (languages)g(based)150 1308 y(on)31 b(languages)e(other)i(than)h(F)-7 b(ortran,)31 b(notably)g(C++,)g(b)r(ecome)g(more)g(and)g(more)g(p)r(opular.) 47 b(Since)32 b(the)150 1408 y(parallelism)26 b(is)i(inheren)n(t)f(in)h(a)f (problem)h(and)f(not)h(its)f(represen)n(tation,)f(w)n(e)i(an)n(ticipate)f (man)n(y)g(common-)150 1508 y(alities)g(in)g(the)g(parallel)f(languages)f (and)i(corresp)r(onding)e(compiler)h(tec)n(hnologies,)g(notably)g(sharing)g (the)150 1607 y(run)n(time)31 b(supp)r(ort.)46 b(Therefore,)30 b(w)n(e)g(decided)h(to)f(address)g(this)h(b)r(enc)n(hmark)f(suite)h(to)f (these)h(asp)r(ects)f(of)150 1707 y(the)24 b(compilation)g(pro)r(cess)f(that) h(are)f(inheren)n(t)h(to)g(parallel)f(pro)r(cessing)g(in)h(general,)g(rather) f(than)h(testing)150 1807 y(syn)n(tactic)j(details)g(of)h(the)g(HPF.)150 2075 y Fp(6.2)137 b(Lo)l(w)46 b(Lev)l(el)f(HPF)g(Compiler)h(Benc)l(hmarks)150 2274 y Fy(6.2.1)112 b(Ov)m(erview)150 2427 y Fx(The)32 b(b)r(enc)n(hmark)g (suite)h(comprises)e(sev)n(eral)f(simple,)k(syn)n(thetic)e(applications)g (whic)n(h)g(test)h(sev)n(eral)d(as-)150 2527 y(p)r(ects)i(of)f(the)g(HPF)h (compilation.)47 b(The)31 b(curren)n(t)g(v)n(ersion)e(of)j(the)f(suite)h (addresses)d(the)j(basic)f(features)150 2626 y(of)c(HPF,)h(and)f(it)g(is)h (designed)f(to)g(measure)f(p)r(erformance)g(of)h(early)g(implemen)n(tations)g (of)g(the)h(compiler.)150 2726 y(They)e(concen)n(trate)g(on)g(testing)h (parallel)e(implemen)n(tation)i(of)f(explicitly)h(parallel)f(statemen)n(ts,)g (i.e.,)h(ar-)150 2826 y(ra)n(y)34 b(assignmen)n(ts,)h(F)n(ORALL)g(statemen)n (ts,)h(INDEPENDENT)f(DO)g(lo)r(ops,)h(and)f(in)n(trinsic)g(functions)150 2925 y(with)i(di\013eren)n(t)f(mapping)g(directiv)n(es.)61 b(In)37 b(addition,)h(the)f(lo)n(w)e(lev)n(el)h(compiler)f(b)r(enc)n(hmarks)g (address)150 3025 y(problem)27 b(of)h(passing)e(distributed)i(arra)n(ys)d(as) i(argumen)n(ts)f(to)i(subprograms.)275 3124 y(The)e(language)f(features)i (not)f(included)i(in)f(the)g(HPF)g(subset)g(are)e(not)i(addressed)f(in)h (this)g(release)e(of)150 3224 y(the)31 b(suite.)47 b(The)31 b(next)h(releases)d(will)i(con)n(tain)f(more)g(k)n(ernels)g(that)h(will)g (address)f(all)h(features)f(of)h(HPF,)150 3324 y(and)c(also)g(they)h(will)g (b)r(e)g(sensitiv)n(e)f(to)g(adv)-5 b(anced)27 b(compiler)g(transformations.) 275 3423 y(The)i(co)r(des)f(included)i(in)f(this)g(suite)g(are)f(either)h (adopted)g(from)f(existing)h(b)r(enc)n(hmark)f(suites,)h(NAS)150 3523 y(suite)c([27)o(],)h(Liv)n(ermore)d(Lo)r(ops)h([5)o(],)i(and)e(the)i (Purdue)e(Set)h([36)o(],)h(or)e(are)f(dev)n(elop)r(ed)i(at)f(Syracuse)g(Univ) n(er-)150 3623 y(sit)n(y)-7 b(.)150 3849 y Fy(6.2.2)112 b(F)m(ORALL)38 b(statemen)m(t)f(-)h(k)m(ernel)e(FL)150 4002 y Fx(F)n(ORALL)41 b(statemen)n(t)g(pro)n(vides)f(an)h(con)n(v)n(enien)n(t)g(syn)n(tax)f(for)h (sim)n(ultaneous)f(assignmen)n(ts)g(to)i(large)150 4102 y(groups)25 b(of)h(arra)n(y)d(elemen)n(ts.)36 b(Suc)n(h)26 b(assignmen)n(ts)f(lie)h(at)g (the)h(heart)e(of)h(the)g(data)g(parallel)f(computations)150 4202 y(that)19 b(HPF)h(is)e(designed)h(to)g(express.)33 b(The)19 b(idea)g(b)r(ehind)h(in)n(tro)r(ducing)e(F)n(ORALL)h(in)h(HPF)f(is)g(to)g (generalize)150 4301 y(F)-7 b(ortran)18 b(90)h(arra)n(y)e(assignmen)n(ts)h (to)i(mak)n(e)e(expressing)g(parallelism)h(easier.)33 b(Kernel)18 b(FL)i(pro)n(vides)e(sev)n(eral)150 4401 y(examples)28 b(of)g(F)n(ORALL)h (statemen)n(ts)f(that)h(are)f(di\016cult)h(or)f(incon)n(v)n(enien)n(t)f(to)i (write)f(using)h(F)-7 b(ortran)27 b(90)150 4500 y(syn)n(tax.)150 4727 y Fy(6.2.3)112 b(Explicit)35 b(template)h(-)h(k)m(ernel)g(TL)150 4880 y Fx(P)n(arallel)23 b(implemen)n(tation)h(of)h(the)g(arra)n(y)d (assignmen)n(ts,)i(including)h(F)n(ORALL)f(statemen)n(ts,)h(is)g(a)f(cen)n (tral)150 4980 y(issue)29 b(for)g(an)f(early)h(HPF)g(compiler.)41 b(Giv)n(en)29 b(a)g(data)f(distribution,)i(the)g(compiler)e(distributes)h (compu-)150 5080 y(tation)g(o)n(v)n(er)e(a)n(v)-5 b(ailable)28 b(pro)r(cessors.)39 b(An)30 b(e\016cien)n(t)f(compiler)g(ac)n(hiev)n(es)e(an) i(optimal)g(load)f(balance)h(with)150 5179 y(minim)n(um)f(in)n(terpro)r (cessor)d(comm)n(unication.)1796 5428 y(41)p eop PNP restore /PNP save def 628.2618 89.4750 translate 43 bop 275 312 a Fx(Sometimes,)27 b(the)g(programmers)e(ma)n(y)i(help)g(the)h (compiler)e(to)h(minimize)h(necessary)e(in)n(terpro)r(cessor)150 412 y(comm)n(unication)34 b(b)n(y)h(suitable)g(data)g(mapping,)i(in)e (particular)f(b)n(y)h(de\014ning)g(a)g(relativ)n(e)e(alignmen)n(t)i(of)150 511 y(di\013eren)n(t)d(data)g(ob)5 b(ject.)51 b(This)33 b(ma)n(y)e(b)r(e)i (ac)n(hiev)n(ed)e(b)n(y)h(aligning)g(the)g(data)g(ob)5 b(jects)32 b(with)h(an)f(explicitly)150 611 y(declared)27 b(template.)37 b(Kernel)27 b(TL)g(pro)n(vides)f(an)i(example)f(of)g(this)h(kind.)150 843 y Fy(6.2.4)112 b(Comm)m(unication)40 b(detection)h(in)h(arra)m(y)g (assignmen)m(ts)g(-)h(k)m(ernels)f(AA,)492 960 y(SH,)c(ST,)g(and)g(IR)150 1113 y Fx(Once)31 b(the)i(data)e(and)g(iteration)h(space)f(is)g(distributed,) j(the)e(next)g(step)g(that)g(strongly)e(in\015uences)i(e\016-)150 1213 y(ciency)26 b(of)g(the)g(resulting)f(co)r(des)h(is)g(comm)n(unication)f (detection)h(and)g(co)r(de)f(generation)g(to)h(execute)g(data)150 1312 y(mo)n(v)n(emen)n(t.)65 b(In)37 b(general,)h(the)g(o\013-pro)r(cessor)d (data)h(elemen)n(ts)h(m)n(ust)h(b)r(e)f(gathered)f(b)r(efore)h(execution)150 1412 y(of)f(an)g(arra)n(y)e(assignmen)n(t,)k(and)e(the)h(results)e(are)h(to)g (b)r(e)h(scattered)e(to)h(destination)h(pro)r(cessors)c(after)150 1511 y(the)g(assignmen)n(t)f(is)h(completed.)53 b(In)33 b(other)f(w)n(ords,)h (some)f(of)h(the)g(arra)n(y)e(assignmen)n(ts)h(ma)n(y)g(require)f(a)150 1611 y(prepro)r(cessing)f(phase)h(to)h(determine)f(whic)n(h)h(o\013-pro)r (cessor)d(data)i(elemen)n(ts)h(are)f(needed)h(and)f(execute)150 1711 y(the)k(gather)e(op)r(eration.)56 b(Similarly)-7 b(,)36 b(they)e(ma)n(y)g(require)f(p)r(ostpro)r(cessing)g(\(scatter\).)57 b(Man)n(y)34 b(di\013eren)n(t)150 1810 y(tec)n(hniques)h(ma)n(y)g(b)r(e)g (used)h(to)f(optimize)g(these)h(op)r(erations.)59 b(T)-7 b(o)35 b(ac)n(hiev)n(e)f(a)h(high)g(e\016ciency)-7 b(,)37 b(it)f(ma)n(y)150 1910 y(b)r(e)27 b(v)n(ery)f(imp)r(ortan)n(t)h(that)g(compiler)g(is)g(able)f (to)h(recognize)f(structured)g(comm)n(unication)h(patterns,)f(lik)n(e)150 2010 y(shift,)42 b(m)n(ulticast,)f(etc.)70 b(Kernels)38 b(AA,)h(SH,)g(and)f (ST)h(in)n(tro)r(duce)f(di\013eren)n(t)h(structured)f(comm)n(unica-)150 2109 y(tion)29 b(patterns,)h(and)f(k)n(ernel)f(IR)h(is)h(an)e(example)h(of)h (an)e(arra)n(y)f(assignmen)n(t)i(that)g(require)f(unstructured)150 2209 y(comm)n(unication)f(\(b)r(ecause)g(of)h(indirections\).)150 2441 y Fy(6.2.5)112 b(INDEPENDENT)34 b(assertion)k(-)f(k)m(ernel)g(EP)150 2594 y Fx(In)32 b(addition)g(to)g(arra)n(y)e(assignmen)n(ts)g(and)i(F)n (ORALL)g(statmen)n(ts,)h(parallelism)e(ma)n(y)g(b)r(e)i(expressed)d(b)n(y)150 2694 y(using)f(INDEPENDENT)f(assertions.)39 b(The)29 b(EP)f(k)n(ernel)g(test) h(p)r(erformance)f(of)g(INDEPENDENT)h(DO)150 2794 y(construct)e(with)h(NEW)g (v)-5 b(ariables.)150 3026 y Fy(6.2.6)112 b(Non-elemen)m(tal)36 b(in)m(trinsic)f(functions)i(-)h(k)m(ernel)f(RD)150 3179 y Fx(F)-7 b(ortran)27 b(90)g(in)n(trinsics)g(and)h(HPF)g(functions)h(o\013er)e (y)n(et)h(another)f(w)n(a)n(y)g(to)h(express)f(parallelism.)37 b(Kernel)150 3279 y(RD)28 b(tests)g(implemen)n(tation)g(of)f(sev)n(eral)f (reduction)h(functions.)150 3511 y Fy(6.2.7)112 b(P)m(assing)26 b(distributed)f(arra)m(ys)h(as)h(subprograms')f(argumen)m(ts)g(-)g(k)m (ernels)492 3628 y(AS,)38 b(IT,)f(IM)g(and)i(EI)150 3781 y Fx(The)24 b(last)f(group)g(of)h(k)n(ernels,)f(demonstrate)g(passing)g (distributed)h(arra)n(ys)e(as)h(subprograms')e(argumen)n(ts.)150 3881 y(They)27 b(represen)n(ts)g(four)g(t)n(ypical)g(cases:)251 4063 y(1.)42 b(a)31 b(kno)n(wn)h(mapping)g(of)g(the)h(actual)f(argumen)n(t)f (is)h(to)h(b)r(e)f(preserv)n(ed)f(b)n(y)h(the)h(dumm)n(y)f(argumen)n(t)358 4163 y(\(AS\).)251 4329 y(2.)42 b(the)27 b(mapping)f(of)h(the)g(dumm)n(y)g (argumen)n(t)e(is)i(to)g(b)r(e)g(inherited)g(from)f(the)h(actual)f(argumen)n (t,)g(th)n(us)358 4428 y(no)h(remapping)g(is)g(necessary)-7 b(.)35 b(The)28 b(mapping)f(is)h(kno)n(wn)f(at)g(compile)h(time)g(\(IT\).)251 4595 y(3.)42 b(the)28 b(mapping)g(of)g(the)g(dumm)n(y)h(argumen)n(t)e(is)g (to)h(b)r(e)h(iden)n(tical)f(to)g(that)g(of)g(the)h(actual)e(argumen)n(t,)358 4694 y(but)h(the)g(mapping)f(is)h(not)f(kno)n(wn)g(at)h(the)f(compile)h(time) g(\(IM\).)251 4860 y(4.)42 b(a)36 b(sp)r(eci\014c)i(mapping)f(of)g(the)g (dumm)n(y)h(argumen)n(t)e(is)h(forced,)i(regardless)c(the)j(mapping)f(of)g (the)358 4960 y(actual)27 b(elemen)n(ts)g(\(EI\).)1796 5428 y(42)p eop PNP restore PNEP %%Page: ? 23 0.6303 -612.00 PNLS /PNP save def 12.6922 89.4750 translate 44 bop 150 312 a Fp(6.3)137 b(Summary)150 494 y Fx(The)19 b(syn)n(thetic)h (compiler)e(b)r(enc)n(hmark)h(suite)g(describ)r(ed)g(here)g(is)g(an)g (addition)g(to)g(the)h(b)r(enc)n(hmark)e(k)n(ernels)150 594 y(and)24 b(applications)f(describ)r(ed)h(in)g(c)n(hapter)f(4)h(and)g(5.)35 b(It)25 b(is)f(not)g(mean)n(t)f(as)h(a)f(to)r(ol)h(to)g(ev)-5 b(aluate)24 b(the)g(o)n(v)n(erall)150 693 y(p)r(erformance)30 b(of)g(the)h(compiler)f(generated)g(co)r(des.)45 b(It)31 b(has)f(b)r(een)h (in)n(tro)r(duced)g(as)f(an)g(aid)h(for)f(compiler)150 793 y(dev)n(elop)r(ers)i(to)g(address)g(some)g(selected)h(asp)r(ect)g(of)g(the)g (HPF)g(compilation)f(pro)r(cess.)52 b(In)33 b(the)g(curren)n(t)150 893 y(v)n(ersion,)41 b(the)f(suite)g(do)r(es)f(not)h(comprise)e(a)i (comprehensiv)n(e)e(sample)h(of)h(HPF)f(co)r(des.)73 b(Actually)-7 b(,)43 b(it)150 992 y(addresses)27 b(only)h(the)h(HPF)g(subset.)39 b(Hop)r(efully)-7 b(,)30 b(this)f(w)n(a)n(y)-7 b(,)27 b(w)n(e)h(will)h(con)n (tribute)f(to)h(establishmen)n(t)f(of)g(a)150 1092 y(systematic)f(compiler)g (b)r(enc)n(hmarking)f(metho)r(dology)-7 b(.)36 b(W)-7 b(e)28 b(in)n(tend)g(to)f(con)n(tin)n(ue)g(our)g(e\013ort)g(to)h(dev)n(elop)150 1191 y(a)f(complete,)h(fully)g(represen)n(tativ)n(e)e(HPF)h(b)r(enc)n(hmark)g (suite.)1796 5428 y(43)p eop PNP restore /PNP save def 628.2618 89.4750 translate 45 bop 150 935 a Fr(Chapter)66 b(7)150 1350 y Fu(Conclusions)1382 1287 y Fq(\003)150 1782 y Fx(The)31 b Fo(P)-7 b(ARKBENCH)29 b Fx(b)r(enc)n(hmark)h(suite)h(comprises)f(co)r(des)g(that)h(v)-5 b(ary)30 b(from)g(lo)n(w-lev)n(el)f(b)r(enc)n(hmarks)150 1881 y(measuring)g(basic)g(mac)n(hine)h(parameters,)f(through)g(imp)r(ortan)n(t)h (application)f(k)n(ernels,)h(to)f(compact)h(re-)150 1981 y(searc)n(h)g (applications.)48 b(This)31 b(hierarc)n(hical)f(structure)h(allo)n(ws)f (information)h(deriv)n(ed)f(from)i(the)f(simpler)150 2081 y(co)r(des)24 b(to)h(b)r(e)g(used)g(in)g(explaining)f(the)h(p)r(erformance)f(c)n (haracteristics)e(of)j(the)g(more)f(complicated)g(co)r(des.)150 2180 y(Th)n(us)37 b(the)g(b)r(enc)n(hmark)g(suite)g(can)g(b)r(e)h(used)f(to)g (ev)-5 b(aluate)36 b(p)r(erformance)g(on)h(a)g(range)f(of)h(lev)n(els)f(from) 150 2280 y(simple)24 b(mac)n(hine)g(parameters)e(to)i(full)g(applications)f (where)h(e\013ects)g(due)g(to)g(non-parallelisable)e(sections)150 2379 y(of)28 b(co)r(de,)f(and)g(memory)-7 b(,)27 b(comm)n(unication)g(or)g (I/O)g(b)r(ottlenec)n(ks)g(ma)n(y)g(b)r(ecome)g(imp)r(ortan)n(t.)150 2654 y Fp(Ac)l(kno)l(wledgemen)l(ts)150 2836 y Fx(Sp)r(ecial)21 b(thanks)f(to)g(all)g(the)h(con)n(tributors)e(to)i(this)f(rep)r(ort:)33 b(Da)n(vid)20 b(Bailey)g(\(NASA)i(Ames)e(Researc)n(h)f(Cen-)150 2935 y(ter\),)33 b(Mic)n(hael)f(Berry)e(\(Univ)n(ersit)n(y)i(of)g(T)-7 b(ennessee\),)33 b(Jac)n(k)d(Dongarra)g(\(Univ)n(ersit)n(y)h(of)h(T)-7 b(ennessee/Oak)150 3035 y(Ridge)22 b(National)f(Lab)r(oratory\),)g(Vladimir)h (Geto)n(v)f(\(Univ)n(ersit)n(y)h(of)g(Southampton\),)h(T)-7 b(om)22 b(Haupt)g(\(Syra-)150 3135 y(cuse)45 b(Univ)n(ersit)n(y\),)j(T)-7 b(on)n(y)44 b(Hey)h(\(Univ)n(ersit)n(y)g(of)f(Southampton\),)50 b(Roger)44 b(Ho)r(c)n(kney)g(\(Univ)n(ersit)n(y)g(of)150 3234 y(Southampton\),)28 b(and)f(Da)n(vid)h(W)-7 b(alk)n(er)26 b(\(Oak)h(Ridge)g (National)g(Lab)r(oratory\).)275 3334 y(The)32 b(follo)n(wing)f Fo(P)-7 b(ARKBENCH)30 b Fx(participan)n(ts)i(w)n(ere)f(instrumen)n(tal)h(in)h (de\014ning/promoting)e(the)150 3434 y(e\013ort,)25 b(attending)g(meetings,)g (and)g(pro)n(viding)e(helpful)j(commen)n(ts)e(and)h(suggestions:)34 b(Ed)24 b(Bro)r(c)n(kleh)n(urst)150 3533 y(\(National)31 b(Ph)n(ysical)f(Lab) r(oratory\),)h(Koushik)f(Ghosh)h(\(Cra)n(y)g(Researc)n(h\),)g(Charles)g (Grassl)f(\(Cra)n(y)g(Re-)150 3633 y(searc)n(h\),)25 b(Ed)g(Kushner)g(\(In)n (tel)h(SSD\),)h(Brian)e(LaRose)g(\(Hewlett)h(P)n(ac)n(k)-5 b(ard\),)25 b(T)-7 b(o)r(dd)25 b(Letsc)n(he)h(\(Univ)n(ersit)n(y)150 3732 y(of)32 b(T)-7 b(ennessee\),)34 b(Da)n(vid)e(Mac)n(k)-5 b(a)n(y)31 b(\(In)n(tel)i(SSD\),)g(Joanne)f(Martin)g(\(IBM\),)h(Ramesh)f (Natara)5 b(jan)31 b(\(IBM,)150 3832 y(Y)-7 b(orkto)n(wn)21 b(Heigh)n(ts\),)j(Bo)r(do)d(P)n(arady)f(\(Sun)j(Microsystems\),)g(Rob)r(ert)f (P)n(ennington)f(\(Pittsburgh)h(Sup)r(er-)150 3932 y(computing)33 b(Cen)n(ter\),)h(Philip)e(T)-7 b(annen)n(baum)33 b(\(NEC\),)g(P)n(earl)e(W)-7 b(ang)33 b(\(George)e(Mason)h(Univ)n(ersit)n(y/US)150 4031 y(Geological)26 b(Surv)n(ey\),)h(and)g(P)n(atric)n(k)f(W)-7 b(orley)27 b(\(Oak)g(Ridge)g(National)g(Lab)r(oratory\).)p 150 5102 1350 4 v 241 5156 a Fm(\003)277 5179 y Fl(assem)n(bled)c(b)n(y)h (Roger)g(Ho)r(c)n(kney)h(for)e(whole)h(committee)1796 5428 y Fx(44)p eop PNP restore PNEP %%Page: ? 24 0.6303 -612.00 PNLS /PNP save def 12.6922 89.4750 translate 46 bop 150 976 a Fu(Bibliograph)-7 b(y)192 1419 y Fx([1])41 b(J.)29 b(Dongarra,)f(A.)i(Geist,)h(R.)f(Manc)n(hek,)g(and)f(V.)h(Sunderam.) 43 b(In)n(tegrated)29 b(p)n(vm)h(framew)n(ork)d(sup-)321 1519 y(p)r(orts)20 b(heterogeneous)e(net)n(w)n(ork)h(computing.)25 b Fn(Computers)e(in)h(Physics)p Fx(,)f(7\(2\):166{175,)18 b(April)j(1993.)192 1685 y([2])41 b(Message)27 b(P)n(assing)g(In)n(terface)i(F)-7 b(orum.)41 b(Do)r(cumen)n(t)30 b(for)e(a)h(Standard)g(Message-P)n(assing)c (In)n(terface.)321 1784 y(Computer)c(Science)g(Dept.)h(Tec)n(hnical)f(Rep)r (ort)g(CS-93-214,)f(Univ)n(ersit)n(y)g(of)h(T)-7 b(ennessee,)22 b(Kno)n(xville,)321 1884 y(T)-7 b(ennessee,)27 b(No)n(v)n(em)n(b)r(er)f (1993.)192 2050 y([3])41 b Fn(Quantities,)29 b(Units)g(and)i(Symb)l(ols)p Fx(.)37 b(The)28 b(Ro)n(y)n(al)e(So)r(ciet)n(y)-7 b(,)27 b(London,)g(1975.) 192 2216 y([4])41 b(M.)30 b(Berry)-7 b(,)28 b(D.)j(Chen,)f(P)-7 b(.)29 b(Koss,)g(D.)h(Kuc)n(k,)g(S.)g(Lo,)f(Y.)h(P)n(ang,)f(L.)h(P)n(oin)n (ter,)e(R.)i(Rolo\013,)g(A.)g(Sameh,)321 2316 y(E.)51 b(Clemen)n(ti,)57 b(S.)52 b(Chin,)57 b(D.)52 b(Sc)n(hneider,)57 b(G.)51 b(F)-7 b(o)n(x,)57 b(P)-7 b(.)51 b(Messina,)57 b(D.)51 b(W)-7 b(alk)n(er,)57 b(C.)51 b(Hsiung,)321 2415 y(J.)36 b(Sc)n(h)n(w)n(arzmeier,)g(K.)g(Lue,)i(S.) f(Orszag,)f(F.)h(Seidl,)i(O.)d(Johnson,)h(R.)g(Go)r(o)r(drum,)h(and)e(J.)g (Mar-)321 2515 y(tin.)d(The)26 b(PERFECT)e(Club)i(Benc)n(hmarks:)34 b(E\013ectiv)n(e)25 b(P)n(erformance)e(Ev)-5 b(aluation)24 b(of)i(Computers.)321 2615 y Fn(Intl.)j(J.)h(Sup)l(er)l(c)l(omputer)f(Appls.) p Fx(,)g(3\(3\):5{40,)d(1989.)192 2781 y([5])41 b(F.)e(H.)g(McMahon.)69 b(The)39 b(Liv)n(ermore)d(F)-7 b(ortran)38 b(Kernels)f(test)i(of)g(the)g (Numerical)f(P)n(erformance)321 2880 y(Range.)44 b(In)31 b(J.)f(L.)h(Martin,) g(editor,)f Fn(Performanc)l(e)k(Evaluation)g(of)f(Sup)l(er)l(c)l(omputers)p Fx(,)e(pages)e(143{)321 2980 y(186.)d(Elsevier)g(Science)i(B.V.,)g (North-Holland,)e(Amsterdam,)i(1988.)192 3146 y([6])41 b(J.)26 b(Dongarra,)f(T.)h(Ro)n(w)n(an,)g(and)g(R.)h(W)-7 b(ade.)35 b(Soft)n(w)n(are)25 b(Distribution)i(Using)g(XNETLIB)f(Database)321 3246 y(Serv)n(er.)49 b(Computer)32 b(Science)h(Dept.)g(Tec)n(hnical)f(Rep)r (ort)g(CS-93-191,)f(Univ)n(ersit)n(y)g(of)i(T)-7 b(ennessee,)321 3345 y(Kno)n(xville,)26 b(T)-7 b(ennessee,)27 b(Marc)n(h)g(1993.)192 3511 y([7])41 b(B.)24 b(H.)i(LaRose.)k(The)25 b(Dev)n(elopmen)n(t)g(and)f (Implemen)n(tation)h(of)g(a)f(P)n(erformance)f(Database)g(Serv)n(er.)321 3611 y(Computer)e(Science)g(Dept.)h(Tec)n(hnical)f(Rep)r(ort)g(CS-93-195,)f (Univ)n(ersit)n(y)g(of)h(T)-7 b(ennessee,)22 b(Kno)n(xville,)321 3711 y(T)-7 b(ennessee,)27 b(August)h(1993.)192 3877 y([8])41 b(J.)d(J.)g(Dongarra.)67 b(P)n(erformance)37 b(of)h(v)-5 b(arious)38 b(Computers)g(using)g(Standard)g(Linear)f(Equations)321 3976 y(Soft)n(w)n(are)30 b(in)j(a)f(F)-7 b(ortran)31 b(En)n(vironmen)n(t.)49 b(Computer)32 b(Science)g(Dept.)h(Tec)n(hnical)f(Rep)r(ort)g(CS-89-)321 4076 y(85,)26 b(Univ)n(ersit)n(y)h(of)h(T)-7 b(ennessee,)27 b(Kno)n(xville,)f(T)-7 b(ennessee,)27 b(Marc)n(h)g(1990.)192 4242 y([9])41 b(D.)24 b(Bailey)-7 b(,)24 b(J.)f(Barton,)h(T.)f(Lasinski,)h (and)f(H.)h(\(editors\))g(Simon.)30 b(The)24 b(NAS)g(parallel)f(b)r(enc)n (hmarks.)321 4342 y(T)-7 b(ec)n(hnical)29 b(Rep)r(ort)h(103863,)e(NASA)j (Ames)f(Researc)n(h)f(Cen)n(ter,)h(Mo\013ett)g(Field,)i(CA)e(94035,)e(July) 321 4441 y(1993.)150 4607 y([10])41 b(Joseph)31 b(Uniejewski.)51 b(SPEC)31 b(Benc)n(hmark)g(Suite:)46 b(Designed)32 b(for)g(To)r(da)n(y's)f (Adv)-5 b(anced)32 b(Systems.)321 4707 y(SPEC)26 b(Newsletter,)i(F)-7 b(all)28 b(1989.)34 b(V)-7 b(olume)28 b(1,)g(Issue)f(1.)150 4873 y([11])41 b(R.)31 b(W.)g(Ho)r(c)n(kney)-7 b(.)45 b(A)31 b(F)-7 b(ramew)n(ork)28 b(for)i(Benc)n(hmark)g(Analysis.)45 b Fn(Sup)l(er)l(c)l(omputer)p Fx(,)31 b(48\(IX-2\):9{22,)321 4973 y(1992.)1796 5428 y(45)p eop PNP restore /PNP save def 628.2618 89.4750 translate 47 bop 150 312 a Fx([12])41 b(C.)i(Addison,)k(J.)c(Allwrigh)n(t,)k(N.)c (Binsted,)48 b(N.)43 b(Bishop,)k(B.)c(Carp)r(en)n(ter,)j(P)-7 b(.)43 b(Dalloz,)j(D.)e(Gee,)321 412 y(V.)23 b(Geto)n(v,)g(A.)g(Hey)-7 b(,)24 b(R.)f(Ho)r(c)n(kney)-7 b(,)23 b(M.)g(Lemk)n(e,)g(J.)g(Merlin,)g(M.)g (Pinc)n(hes,)g(C.)g(Scott,)h(and)e(I.)h(W)-7 b(olton.)321 511 y(The)25 b(Genesis)f(Distributed-Memory)h(Benc)n(hmarks.)e(P)n(art)h(1:)35 b(metho)r(dology)24 b(and)h(general)e(relativ-)321 611 y(it)n(y)30 b(b)r(enc)n(hmark)g(with)h(results)g(for)f(the)h(SUPRENUM)g(computer.)45 b Fn(Concurr)l(ency:)g(Pr)l(actic)l(e)33 b(and)321 711 y(Exp)l(erienc)l(e)p Fx(,)28 b(5\(1\):1{22,)e(1993.)150 876 y([13])41 b(D.)23 b(Bailey)-7 b(,)23 b(E.)f(Barszcz,)g(J.)h(Barton,)g(D.)g(Bro)n(wning,)f(R.)h(Carter,)f (L.)h(Dagum,)h(R.)f(F)-7 b(ato)r(ohi,)23 b(P)-7 b(.)23 b(F)-7 b(red-)321 975 y(eric)n(kson,)29 b(T.)h(Lasinski,)g(R.)h(Sc)n(hreib)r(er,)f (H.)h(Simon,)g(V.)g(V)-7 b(enk)i(atakrishnan,)30 b(and)g(S.)g(W)-7 b(eeratunga.)321 1075 y(The)24 b(NAS)h(parallel)e(b)r(enc)n(hmarks.)30 b Fn(Int.)d(J.)g(of)g(Sup)l(er)l(c)l(omputer)f(Applic)l(ations)p Fx(,)h(5\(3\):63)c({)h(73,)g(1991.)150 1240 y([14])41 b(E.)31 b(Anderson,)i(Z.)f(Bai,)g(C.)h(Bisc)n(hof,)f(J.)g(Demmel,)i(J.)e(Dongarra,)f (J.)g(Du)i(Croz,)f(A.)h(Green)n(baum,)321 1340 y(S.)25 b(Hammarling,)g(A.)h (McKenney)-7 b(,)25 b(S.)h(Ostrouc)n(ho)n(v,)d(and)i(D.)h(Sorensen.)32 b Fn(LAP)-6 b(A)n(CK)27 b(Users')h(Guide)p Fx(.)321 1439 y(SIAM,)g (Philadelphia,)f(P)-7 b(A,)27 b(1992.)150 1604 y([15])41 b(R.)22 b(W.)h(Ho)r(c)n(kney)-7 b(.)28 b(P)n(erformance)20 b(P)n(arameters)g(and)i (Benc)n(hmarking)f(of)h(Sup)r(ercomputers.)28 b Fn(Par)l(al)t(lel)321 1704 y(Computing)p Fx(,)g(17:1111{1130,)22 b(1991.)150 1869 y([16])41 b(A.)26 b(F)-7 b(riedli,)26 b(W.)h(Gen)n(tzsc)n(h,)e(R.)h(Ho)r(c)n (kney)-7 b(,)26 b(and)g(A.)g(v)-5 b(an)26 b(der)f(Steen.)35 b(A)26 b(Europ)r(ean)e(Sup)r(ercomputer)321 1969 y(Benc)n(hmark)i(E\013ort.) 36 b Fn(Sup)l(er)l(c)l(omputer)29 b(34)p Fx(,)g(VI\(6\):14{17,)c(1989.)150 2134 y([17])41 b(A.)j(J.)h(G.)f(Hey)-7 b(.)87 b(The)45 b(Genesis)f (Distributed-Memory)g(Benc)n(hmarks.)85 b Fn(Par)l(al)t(lel)47 b(Computing)p Fx(,)321 2233 y(17:1275{1283,)22 b(1991.)150 2398 y([18])41 b(R.)31 b(W.)g(Ho)r(c)n(kney)-7 b(.)47 b(Sup)r(er-Computer)30 b(Arc)n(hitecture.)47 b(In)31 b(F.)g(Sumner,)h(editor,)f Fn(Infote)l(ch)j (State)e(of)321 2498 y(the)e(A)n(rt)e(Confer)l(enc)l(e:)40 b(F)-6 b(utur)l(e)28 b(Systems)p Fx(,)f(pages)g(277{305.)d(Infotec)n(h,)k (Maidenhead,)f(1977.)150 2663 y([19])41 b(Roger)e(W.)i(Ho)r(c)n(kney)f(and)h (Christopher)e(R.)i(Jesshop)r(e.)75 b Fn(Par)l(al)t(lel)44 b(Computers:)63 b(A)n(r)l(chite)l(ctur)l(e,)321 2763 y(Pr)l(o)l(gr)l(amming) 30 b(and)g(A)n(lgorithms)p Fx(.)38 b(Adam)28 b(Hilger,)f(Bristol,)g(1981.)150 2928 y([20])41 b(R.)e(W.)h(Ho)r(c)n(kney)-7 b(.)72 b(Characterization)37 b(of)j(P)n(arallel)d(Computers)i(and)g(Algorithms.)72 b Fn(Computer)321 3027 y(Physics)31 b(Communic)l(ations)p Fx(,)d(26:285{29,)c(1982.)150 3193 y([21])41 b(R.)28 b(W.)h(Ho)r(c)n(kney)-7 b(.)39 b(Characterizing)26 b(Computers)i(and)g(Optimizing)g(the)h(F)-9 b(A)n(CR\(l\))29 b(P)n(oisson-Solv)n(er)321 3292 y(on)e(P)n(arallel)e(Unicomputers.)37 b Fn(IEEE)31 b(T)-6 b(r)l(ans.)30 b(Comput.)p Fx(,)e(C32:933{941,)c(1983.)150 3457 y([22])41 b(R.)19 b(W.)h(Ho)r(c)n(kney)-7 b(.)23 b(P)n(arametrization)17 b(of)i(computer)g(p)r(erformance.)j Fn(Par)l(al)t(lel)i(Computing)p Fx(,)e(5:97{103,)321 3557 y(1987.)150 3722 y([23])41 b(Roger)32 b(W.)j(Ho)r(c)n(kney)e(and)h(Christopher)f(R.)h(Jesshop)r(e.)56 b Fn(Par)l(al)t(lel)37 b(Computers)f(2:)51 b(A)n(r)l(chite)l(ctur)l(e,)321 3822 y(Pr)l(o)l(gr)l(amming)41 b(and)f(A)n(lgorithms)p Fx(.)72 b(Adam)39 b(Hilger/IOP)e(Publishing,)42 b(Bristol)c(&)h(Philadelphia,)321 3921 y(second)32 b(edition,)i(1988.)50 b(Distributed)33 b(in)g(the)g(USA)g(b) n(y)g(IOP)f(Publ.)g(Inc.,)i(Public)f(Ledger)e(Bldg.,)321 4021 y(Suite)d(1035,)e(Indep)r(endence)i(Square,)f(Philadelphia,)f(P)-7 b(A)28 b(19106.)150 4186 y([24])41 b(A.)36 b(J.)f(v)-5 b(an)35 b(der)g(Steen)h(and)g(P)-7 b(.)35 b(P)-7 b(.)35 b(M.)h(de)f(Rijk.)61 b(Guidelines)36 b(for)f(use)g(of)h(the)g(EuroBen)e(Benc)n(h-)321 4285 y(mark.)d(T)-7 b(ec)n(hnical)24 b(Rep)r(ort)g(TR3,)h(EuroBen,)f(The)h (EuroBen)e(Group,)i(Utrec)n(h)n(t,)g(The)f(Netherlands,)321 4385 y(F)-7 b(ebruary)26 b(1993.)150 4550 y([25])41 b(R.)27 b(W.)g(Ho)r(c)n(kney)-7 b(.)34 b(Sync)n(hronization)25 b(and)i(Comm)n (unication)f(Ov)n(erheads)f(on)h(the)h(LCAP)f(Multiple)321 4650 y(FPS-164)f(Computer)j(System.)37 b Fn(Par)l(al)t(lel)31 b(Computing)p Fx(,)e(9:279{290,)24 b(1988.)150 4815 y([26])41 b(R.)j(W.)g(Ho)r(c)n(kney)g(and)f(E.)h(A.)g(Carmona.)84 b(Comparison)42 b(of)i(Comm)n(unications)f(on)h(the)g(In)n(tel)321 4914 y(iPSC/860)25 b(and)i(T)-7 b(ouc)n(hstone)27 b(Delta.)37 b Fn(Par)l(al)t(lel)32 b(Computing)p Fx(,)c(18:1067{1072,)23 b(1992.)150 5080 y([27])41 b(D.)23 b(Bailey)f(and)h(J.)g(Barton.)28 b(The)23 b(NAS)h(Kernel)e(Benc)n (hmark)g(Program.)k(T)-7 b(ec)n(hnical)23 b(Rep)r(ort)f(86711,)321 5179 y(NASA)28 b(Ames)g(T)-7 b(ec)n(hnical)27 b(Memorandum,)g(1985.)1796 5428 y(46)p eop PNP restore PNEP %%Page: ? 25 0.6303 -612.00 PNLS /PNP save def 12.6922 89.4750 translate 48 bop 150 312 a Fx([28])41 b(D.)31 b(H.)g(Bailey)-7 b(,)31 b(J.)f(Barton,)g(T.)h(Lasinski,)g(and)f(H.)h(\(editors\))g(Simon.)46 b(The)30 b(NAS)i(parallel)d(b)r(enc)n(h-)321 412 y(marks.)43 b(T)-7 b(ec)n(hnical)30 b(Rep)r(ort)g(RNR-91-02,)f(NASA)j(Ames)e(Researc)n(h) f(Cen)n(ter,)h(Mo\013ett)h(Field,)h(CA)321 511 y(94035,)25 b(Jan)n(uary)h(1991.)150 677 y([29])41 b(J.)36 b(Choi,)i(J.)d(J.)h(Dongarra,) g(and)g(D.)h(W.)f(W)-7 b(alk)n(er.)61 b(The)37 b(design)e(of)h(scalable)f (soft)n(w)n(are)g(libraries)321 777 y(for)25 b(distributed)i(memory)f (concurren)n(t)e(computers.)34 b(In)27 b Fn(Pr)l(o)l(c)l(e)l(e)l(dings)i(of)g (Envir)l(onment)g(and)g(To)l(ols)321 877 y(for)i(Par)l(al)t(lel)i (Scienti\014c)d(Computing)h(Workshop,)i(\(Saint)e(Hilair)l(e)g(du)g(T)-6 b(ouvet,)31 b(F)-6 b(r)l(anc)l(e\))p Fx(.)28 b(Elsevier)321 976 y(Science)f(Publishers,)g(Septem)n(b)r(er)h(7-8,)e(1992.)150 1142 y([30])41 b(J.)34 b(Choi,)j(J.)e(J.)g(Dongarra,)f(R.)h(P)n(ozo,)g(and)g (D.)h(W.)f(W)-7 b(alk)n(er.)58 b(ScaLAP)-7 b(A)n(CK:)34 b(A)h(scalable)f (linear)321 1242 y(algebra)28 b(library)h(for)h(distributed)h(memory)e (concurren)n(t)g(computers.)44 b(In)31 b Fn(Pr)l(o)l(c)l(e)l(e)l(dings)i(of)g (Fourth)321 1342 y(Symp)l(osium)21 b(on)h(the)g(F)-6 b(r)l(ontiers)21 b(of)h(Massively)i(Par)l(al)t(lel)f(Computation)g(\(McL)l(e)l(an,)h(Vir)l (ginia\))p Fx(.)c(IEEE)321 1441 y(Computer)27 b(So)r(ciet)n(y)g(Press,)f(Los) h(Alamitos,)h(California,)e(Octob)r(er)h(19-21,)e(1992.)150 1607 y([31])41 b(J.)21 b(J.)g(Dongarra,)f(R.)h(v)-5 b(an)21 b(de)h(Geijn,)h(and)e(D.)g(W)-7 b(alk)n(er.)26 b(A)21 b(lo)r(ok)g(at)g (scalable)f(linear)g(algebra)f(libraries.)321 1707 y(In)k Fn(Pr)l(o)l(c)l(e)l (e)l(dings)j(of)g(the)g(1992)h(Sc)l(alable)f(High)g(Performanc)l(e)h (Computing)f(Confer)l(enc)l(e)p Fx(,)f(pages)d(372{)321 1807 y(379.)k(IEEE)g(Press,)g(1992.)150 1973 y([32])41 b(J.)27 b(Choi,)g(J.)h (Dongarra,)d(R.)j(P)n(ozo,)d(and)j(D.)g(W)-7 b(alk)n(er.)35 b(ScaLAP)-7 b(A)n(CK:)27 b(A)h(Scalable)f(Linear)f(Algebra)321 2072 y(Library)33 b(for)i(Distributed)h(Memory)e(Concurren)n(t)f(Computers.) 59 b(In)35 b(IEEE,)f(editor,)i Fn(Pr)l(o)l(c)l(e)l(e)l(dings)321 2172 y(of)f(the)g(F)-6 b(ourth)35 b(Symp)l(osium)g(on)g(the)g(F)-6 b(r)l(ontiers)35 b(of)g(Massively)i(Par)l(al)t(lel)g(Computation,)g(McL)l(e)l (an)321 2272 y(Vir)l(ginia)p Fx(,)29 b(pages)d(120{127.)e(IEEE)i(Publishers,) h(Octob)r(er)g(1992.)150 2438 y([33])41 b(G.)31 b(C.)f(F)-7 b(o)n(x,)31 b(S.)g(W.)g(Otto,)g(and)g(A.)g(J.)f(G.)h(Hey)-7 b(.)46 b(Matrix)30 b(algorithms)f(on)h(a)g(h)n(yp)r(ercub)r(e)h(I:)g(Matrix) 321 2537 y(m)n(ultiplication.)37 b Fn(Par)l(al)t(lel)31 b(Computing)p Fx(,)e(4:17{31,)c(1987.)150 2703 y([34])41 b(S.)33 b(Huss-Lederman,)g(E.)g (M.)g(Jacobson,)g(A.)g(Tsao,)g(and)g(G.)h(Zhang.)52 b(Matrix)32 b(m)n(ultiplication)h(on)321 2803 y(the)24 b(In)n(tel)g(Touc)n(hstone)f (Delta.)32 b(T)-7 b(ec)n(hnical)23 b(rep)r(ort,)i(Sup)r(ercomputing)f (Researc)n(h)e(Cen)n(ter,)j(1993.)k(in)321 2902 y(preparation.)150 3069 y([35])41 b(C.)28 b(Lin)h(and)f(L.)g(Sn)n(yder.)38 b(A)29 b(matrix)f(pro)r(duct)g(algorithm)f(and)h(its)h(comparativ)n(e)d(p)r (erformance)h(on)321 3168 y(h)n(yp)r(ercub)r(es.)50 b(In)32 b Fn(Pr)l(o)l(c)l(e)l(e)l(dings)j(of)g(the)f(1992)h(Sc)l(alable)g(High)g (Performanc)l(e)h(Computing)e(Confer-)321 3268 y(enc)l(e)p Fx(,)27 b(pages)g(190{194.)d(IEEE)i(Press,)g(1992.)150 3434 y([36])41 b(J.)24 b(Rice.)32 b(Problems)23 b(to)i(T)-7 b(est)24 b(P)n(arallel)f(and)h(V)-7 b(ector)24 b(Languages.)30 b(T)-7 b(ec)n(hnical)24 b(Rep)r(ort)g(CSDTR)h(516,)321 3533 y(Purdue)i(Univ)n(ersit) n(y)-7 b(,)26 b(W)-7 b(est)28 b(Lafa)n(y)n(ette,)f(Indiana,)g(Octob)r(er)g (1990.)1796 5428 y(47)p eop PNP restore /PNP save def 628.2618 89.4750 translate 49 bop 150 935 a Fr(App)6 b(endix)67 b(A)150 1350 y Fu(Compact)78 b(Applications)150 1599 y(Submission)f(F)-20 b(orm)150 2031 y Fx(This)36 b(app)r(endix)g(giv)n(es)e(the)i(form)f(to)h(b)r(e)g(completed)g (when)g(submitting)g(a)f(compact)h(application)f(for)150 2130 y(inclusion)e(in)h(the)f Fo(P)-7 b(ARKBENCH)30 b Fx(suite.)54 b(F)-7 b(or)32 b(an)h(electronic)g(v)n(ersion)e(of)j(this)f(form)g(send)g (email)g(to)150 2230 y Fk(walker@msr.epm.o)o(rnl)o(.g)o(ov)26 b Fx(or)32 b(obtain)g(a)g(cop)n(y)g(from)g(netlib)h(under)g(pb)n(wg)f(\(see)g (Chapter)g(1\).)52 b(The)150 2330 y(completed)28 b(form)f(should)g(b)r(e)h (emailed)g(to)f(the)h(same)f(address.)p 150 2449 3375 4 v 150 2556 a(Name)h(of)f(Program)677 b(:)p 150 2601 V 150 2708 a(Submitter's)28 b(Name)669 b(:)150 2808 y(Submitter's)28 b(Organization)406 b(:)150 2907 y(Submitter's)28 b(Address)589 b(:)150 3307 y(Submitter's)28 b(Phone)f(Num)n(b)r(er)331 b(:)150 3407 y(Submitter's)28 b(F)-7 b(ax)27 b(Num)n(b)r(er)426 b(:)150 3506 y(Submitter's)28 b(F)-7 b(ax)27 b(Email)505 b(:)p 150 3534 V 150 3646 a(Cognizan)n(t)26 b(Exp)r(ert\(s\))585 b(:)150 3746 y(CE's)27 b(Organization)654 b(:)150 3846 y(CE's)27 b(Address)837 b(:)150 4245 y(CE's)27 b(Phone)g(Num)n(b)r(er)579 b(:)150 4345 y(CE's)27 b(F)-7 b(ax)27 b(Num)n(b)r(er)674 b(:)150 4445 y(CE's)27 b(F)-7 b(ax)27 b(Email)753 b(:)p 150 4473 V 150 4580 a(Exten)n(t)34 b(and)h(timeliness)f(with)i(whic)n (h)e(CE)g(is)h(prepared)e(to)i(resp)r(ond)f(to)g(questions)g(and)h(bug)f(rep) r(orts)150 4680 y(from)27 b Fo(P)-7 b(ARKBENCH)30 b Fx(:)p 150 4888 V 150 4996 a(Ma)5 b(jor)26 b(Application)i(Field)445 b(:)150 5095 y(Minor)27 b(Application)h(Field)447 b(:)p 150 5140 V 1796 5428 a(48)p eop PNP restore PNEP %%Page: ? 26 0.6303 -612.00 PNLS /PNP save def 12.6922 89.4750 translate 50 bop 150 312 a Fx(Application)28 b("p)r(edigree")e(\(origin,)h(history)-7 b(,)26 b(ma)5 b(jor)27 b(p)r(orts)g(and)g(mo)r(di\014cations\))h(:)p 150 781 3375 4 v 150 893 a(Ma)n(y)f(this)h(co)r(de)f(b)r(e)h(freely)f 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