Introuzon M. Fvll Ennrn Dprtmnt n Frrr Introuzon Smulzon rut tl Smulzon n rut tl Prolm pplzon Alortm smulzon usto Srl Prlllo (ult prlll, tst prlll) Duttvo Conorrnt L smulzon rut tl puó vvnr vrs lvll: so lttro loo Nl so l olluo lvll so lttro sono utlzzt slusvmnt pr l vlzon nls moll usto Al lvllo loo l smulzon puó vvnr sunt lvll swt t RTL vorl Introuzon 2 Introuzon 3
Utlzzo ll smulzon usto pr l stm ll ltá Dt un ruto un squnz vttor tst un nsm moll usto Dtrmn: l oprtur usto (rzon ust mollt rvlt om rror tst pplt) l nsm ust non rvlt Applzon: stm ll qultá l olluo (t lvl) mlormnto ll squnz olluo l protto stsso uto omputzonl ll tst nrton L smulzon usto onsnt stmr l ltá rut tl Vnono ostrut op ust l ruto sono un qul struzon proltá ust stss Il ruto vn smulto on un squnz vttor nrsso rpprsnttv l norml ro lvoro Vn vlutt l proltá rror sull ust Il trt é to ust possono mnstrs urnt l norml unzonmnto l ruto (stuk-t, ust trnstor) Elvto ntrss nustrl (stnr n mpo ronuto, utomolsto) Introuzon 4 Introuzon 5 l lvllo loo Smulzon pr vrs moll usto Mollo l ruto mx lvl: t swt pr prt ustom l ruto moll vorl on ust su nrss ust Mollo snl {, } pr rt omntor, {,, X} pr rt squnzl {,, X, Z} pr rt on omponnt lt mpnz moll on onsrzon nlo (trnsstor stuk-on rn) Mollo ll tmporzzzon zro ly pr rt omntor unt ly o yl urt pr rt snron propton ly pr rt snron Stuk-t on ult ollpsn Trnsstor stuk-on opn Brn Trnston ults, t ly ults pt ly ults Fult roppn: un usto rvlto non vn ultrormnt smulto Fult smpln: s smul solo un mpon ust Introuzon 6 Introuzon 7
Alortm smulzon usto Alortmo srl L vrmo nl so pú smpl, ovvro pr ust tpo stuk-t Alortmo srl Alortmo prlllo Alortmo uttvo Alortmo onorrnt Complsstá omputzonl O(N F T) ov N é l numro t, F é l numro ust T é l numro tst In un rt omntor s puó ssumr F T sno proporzonl N O(N 3 ) S smul l ruto orrtto s mmorzzno l rspost Pr on usto nll nsm onsrto l lortmo mo l ntlst nttno un usto smul l rt ust onrontno l rspost on qull orrtt s rsono r l usto om rvlto pss l sussvo (ult roppn) Vnt: smpltá mplmntzon n qulss tpo smultor ppll vrs moll usto rott oupzon mmor (squnzl) Introuzon 8 Introuzon 9 Alortmo srl prlll (n ust) Lo svnto prnpl é to l tto vnono rptut vrs oprzon nutlmnt Tmp non omptl on rut rn mnson Com ltrntv é stt utlzzt l possltá smulr vrs rut ust n mnr onorrnt tst vtors ult-r rut rut wt ult rut wt ult 2 rut wt ult F tt 2 tt F tt Srutt l prlllsmo ll oprzon ll ALU rsptto t un prol CPU (w = 64 t) o GPU (> 64t) Smulzon ust n prlllo un prol pr on snl l prmo t un prol rpprsnt un snl n ssnz ust rmnnt w t rpprsntno qul snl n prsnz w ust vrs sun psso s smulno l mn prm ust w mn ust s puó ttur l ult roppn solo quno tutt ust l ruppo orrnt sono stt smult sp-up w non puó tnr onto rtr propzon Smulzon tst n prlllo (solo rt omntor) Introuzon Introuzon
prlll (n tst) tst = ALU tt ult-r. stuk-t- stuk-t- stuk-t- Lmtt rut omntor S smul l ruto n ssnz ust pr w vttor tst Pr sun usto s smul l ruto pr l stss vttor tst Csun t un prol ssot un snl rpprsnt l vlor tl snl pr un rto vttor nrsso Introuzon 2 Introuzon 3 Smulzon uttv tst =,,, ult-r stuk-t- tt y tst 3 Pr on vttor vn smulto l ruto ult-r A sun ln j l ruto vn ssot l lst ust ttv su j Dopo l smulzon ult-r sun vttor, l lst ust ll ust t sono lolt utlzzno smpl oprzon sul nsm prtr vlor snl (nl ruto orrtto) l lst ust l nrss t L lst ust PO ornsono t sull ult tton Lmtzon: rol sul nsm non utlzzl pr t non Booln l usr pr rtr Introuzon 4 Introuzon 5
Smulzon uttv Clolo ll lst ust pr un t tpo AND put lst L L L \ L L \ L L L Clolo ll lst ust pr un t EXOR put lst - - L L \ L L L k not l lst ust l snl k, mntr k / not l usto k stuk-t-/ snl ult lst L = { } L = { } L = {, } L = {, } L = L L { } \ L L = = {,,, } L = L { } = {,, } L = (L \ L ) { } = = {,,, } Introuzon 6 Introuzon 7 Alortmo onorrnt Consstnt on l smulzon vnt-rvn on qulss mollo rtro omponnt t vorl Pss:. smulzon vnt-rvn l ruto ult-r 2. pr sun usto vnono po smult qull prt rut ust rsono qullo prvo ust Pr sun t s tn un lst on lo stto l t (nrss ust) n ssnz ust on l stt l t n rut ust s tl stto t é vrso qullo ult-r Tutt l vnt rut ust uul qull ult-r sono smult mpltmnt Pú vlo l ltr mto, m us tropp mmor Introuzon 8 Introuzon 9