Using Bitboards for Move Generation in Shogi

Transcription

1 Usn Btors or Mov Gnrton n So Rjr Grmrn Dprtmnt o Inormts, Ymt Unvrsty Jonn --, Yonzw-s, - Jpn E-ml: rm@yz.ymt-u..jp Astrt In ts ppr t wll xpln ow to us tors or mov nrton n so. In ss, tors v n us n most stron prorms us o t sy rprsntton o ss or y snl -t ntr. For so, lss nt rprsntton s to us us so or s squrs nst o. A rprsntton wt n rry o tr ntrs s propos, wr ntr rprsnts squrs o t or. Ts rprsntton s tn us or mov nrton n smlr wy to t mtos us n ss, or xmpl y usn rott tors or nrtn t movs o t sln ps rook, sop n ln. A omprson o mov nrton sp twn t mto usn tors n y usn t mor ommon mto o ttk tls sow tt y usn tors t mov nrton sp o t prorm Spr ws mprov y.%. Kywors: Btors, mov nrton, omputr so. Introuton Btors r nry rprsntton o knowl or ll squrs on t or or rtn m. T prsn o rtn normton or squr s rprsnt y sttn t t or ts squr on t or to, wl t sn s rprsnt y. Btors v n us xtnsvly n ss prorms us t sz o t or ( = squrs) mks t possl to t on tor nto snl -t ntr. Ts mks t rprsntton o tors vry nt (no unus mmory) n rprsntn nw knowl y omnn t normton rom rnt tors vry st, us lol oprtons lk AND, OR, NOT n XOR n us. So s rnt or sz ( = squrs), so t onvnnt snl ntr rprsntton or on tor nnot us. Dspt ts, t tor rprsntton ors mny wys to ntly rprsnt normton us n t sr n vluton prt o m prorm. Ts my outw t svnt o lss tn optml or rprsntton. Untl rntly, most so prorms us ttk tls (ll kk n Jpns) to rprsnt mportnt sr n vluton knowl. My prorm Spr lso ttk tls, ut tr rn susson on Hros Ymst s ulltn or [] out tors n Auust I to urtr nvstt t us o tors n so. Ymst s onluson ws tt tors my not mk mu rn, ut wn t prorm Bonnz, on o t w so prorms usn t tor rprsntton won t Worl Computr So Cmponsps lst My, t sm lr to m tt tors n so srv mor ttnton. Ymst s xplnton ws vry mportnt to unrstn t rn twn usn tors n ss n so n srvs mor promnnt pl tn n ur ply nto t rvs o t BBS. Howvr, vn wt t ornl ppr y Rort Hytt (utor o t stron ss prorm Crty) [] n t torou srpton on Wkp [] on tors, t tks som tm to rsp t ull. Furtrmor, tr r som tls o t rprsntton s vn y Ymst tt n mprov. Also, tr t mplmntton ws ns, ntl tsts sm to sow snnt mprovmnt n prormn, vn tou Ymst rport only n nrs n sp o out % or tsum so solvr. Fnlly, y usn tors, Spr m mu mor trnsprnt prorm n tr sm plnty o posslts to us tors n rnt prts o t prorm n t utur. Tror, I tnk tt tryn t tor rprsntton s mportnt or vry so prorm, ltou t wll pn on t strutur o t nvul prorm wtr or not snnt nrs n prormn n v. By wrtn ts ppr, I op I wll mk t sr or otr

2 so prormmrs to mplmnt tors y xplnn ow tors r us n ss n ow ts rprsntton ws n to us tors n so. In Ston, t rns twn t tor rprsntton us n ss prorms n tor rprsntton or so wll xpln, s wll s ow tors n us to o mov nrton n so prorm. In Ston, mov nrton sp usn tors s ompr wt mov nrton sp usn ttk tls. T onluson s tt tors lso v potntl n so, ut tt t pns on t strutur o t vluton unton ty wll v snnt prormn mprovmnt or not (Ston ). [] [] [] Btors n Css n So As xpln n Ston, tors r us to ntly rprsnt knowl out m poston. T ss prorm Crty uss tors or rprsntn mny rnt typs o knowl. For xmpl, wr o t lk n wt ps r n wr ty n mov to. Tr r lso tors us or vluton, ut r I wll xpln ow tors n us n so to o mov nrton. Wn ts s us o tors s unrstoo, t wll not ult to us tors n otr prts o t prorm lk n t vluton unton.. Bs Btors T most mportnt rn twn usn tors n ss n usn tors n so s tt t ssor s squrs, w mns tt t normton out poston ts nto snl t ntr. In so, ts normton s to v ts, w wll not t nto snl ntr. Lk Ymst [], I us tr ntrs or rprsntn t ts o t or. Ymst n strutur o tr ntrs, ut s Hok pont out [], t s ttr to n n rry o lnt (wy ts s ttr wll om lr ltr): typ strut { unsn nt []; BITBOARD; Bus o t rnt or szs o ss n so, or tor tr wll ts tt r osolt ( ts ts = ts). As wll xpln ltr, splly or p ttks lot o pr-lult tors r nssry. Runnn so prorms on smll omputrs (or xmpl Fur : Corrsponn twn soor squrs n tor ntr ts. n l vs) mt prolm wn usn tors. E o t tr ntrs rprsnts on tr o t or. In my rprsntton, t rst ts o t rst ntr rprsnt squrs to,.. t wt promoton zon. T rst ts o t son ntr rprsnt t squrs to, t nutrl zon n t ml. Fnlly, t rst ts o t tr ntr rprsnt t squrs to,.. t lk promoton zon (s Fur ). Ts rprsntton s rnt rom t ntl mplmntton sr y Ymst, w t rst two ntrs rprsnt squrs to n us t ts o t tr ntr or squrs to. Usn ts o ntr s n mprovmnt w ws n pont out y Hok []. T rson or ts mprovmnt wll om lr tr t xplnton o t ttk tors low. To mnpult tors n ss, strtorwr lol oprtons n us. Howvr, wn tor onssts o tr rnt ntrs, ts s no lonr possl. Lol oprtons lk tkn t AND o two tors v to n s ollows: vo AnBB(BITBOARD *to, BITBOARD *rom, BITBOARD *rom) { to->[] = rom->[] & rom->[]; to->[] = rom->[] & rom->[]; to->[] = rom->[] & rom->[]; In my mplmntton, I us smlr oprtons or OR, XOR n NOT. Furtrmor, I us t s oprtons ClrBB (sttn ll ts to ), StBB (sttn ll ts to ) n CopyBB (opyn tor).

3 []: []: []: My urrnt mplmntton s tors or t oup squrs (Oup), t lk ps (SntPs), t wt ps (GotPs) n or o t lk n wt ps sprtly. For xmpl, t tor SntGol s s or t squrs wt lk ols n or t strtn poston ts tor looks s ollows: []: []: []: Fur : So strtn poston. Ts tors or poston normton must upt tm t poston ns,.. tm tr plyr mks mov.. Attk Btors [] [] [] Wt t tor t strutur n t lol mnpulton o t ts n t tor n pl, t s now possl to n t squrs ttk y squr ntly usn tors. Ts wll nl mov nrton usn tors nst o ttk tls. Tr s rn twn nn t ttkn squrs o sln ps (rook, sop, ln) n t otr ps. For non-sln ps, t rprsntton o ttkn squrs wt tors s smpl, ut or sln ps, t lulton s mor omplx... Non-sln p ttks Fur : Bt sttns or t strtn poston. Wt t s tor t strutur n lk ts, t s now possl to rprsnt t knowl n n m prorm usn tors. For xmpl, usul normton s to know w squrs r oup. For t strtn poston o so (Fur ), t tor Oup s s or t squrs wt lk or wt p n s or squrs wtout ps (Fur ). In t BITBOARD t strutur ts woul : []: []: []: In t sm wy tor SntPs n us tt s s or t squrs wt lk ps n s or t otr squrs. For t strtn poston o Fur, ts tor woul look lk ts: Clultn t squrs non-sln p ttks s strtorwr. For xmpl, to know wr ol n mov to, t s sunt to pr-lult t ol ttks or lk or wt ol on o t squrs ( totl o tors). For xmpl, t ttk tor or lk ol on looks lk Fur. Wn t squrs tt ol on ttk r n, ts tor n ss y nxn t tor rry wt t numr o t squr... Horzontl ttks T smpl pr-lulton mto os not work or t sln ps rook, sop n ln us wr ts ps n mov to pns on ow ty r lok y tr own ps or y t ps o t opponnt. For xmpl, n t strtn poston o so, t rook on nnot mov orwr us tr s pwn on. Howvr, t pwn on movs to t rook n mov to.

4 [] [] [] Fur : Attk tor or ol on. Tror, t possl movmnt o sln p pns on t poston o t lokn ps. T soluton to ts prolm, s pont out y Hytt [] (mon otrs) s to pr-lult tors or ll t lokn posslts. Lt s look t t most smpl s rst, w s t orzontl movmnt o t rook. I rook s pl on (lk or xmpl n Fur ), lult n ttk tor or t ss n w tr s p on,,,,,,, or not. For rnk tr s totl o = tors. T orzontl ttk pttrns or o t possl squrs s t n s ollows: BITBOARD RnkAttks[][]; For t xmpl poston n t top prt o Fur, t lok pttrn on t rnk o t rook s =. In ts s t squrs tt t rook ttks orzontlly r or t top tr rnks (.. []), or t tr rnks n t ml (.. []) n = or t ottom tr rnks (.. []). Tror, t t strt o t prorm, ts pr-lult vlu n or rook on (squr s rprsnt y n s rprsnt y ): RnkAttks[][].[] = ; RnkAttks[][].[] = ; RnkAttks[][].[] = ; Smlr, or t lok pttrn = n t ottom prt o Fur, t squrs tt t rook ttks orzontlly r lso =, t sm s or. Ts normton n tn to t pr-lult tor: Fur : Attk pttrns or lk rook on. RnkAttks[][].[] = ; RnkAttks[][].[] = ; RnkAttks[][].[] = ; In ts s, or t ttks t os not mttr tr s ln on or not or tr s pwn on or not. For t pwn on, t lok pttrns s to, us n n tul poston, t s not known orn t ol on wll tr or not. Howvr, or t ln on, t t tt t orzontl ttk os not n s snnt: or vry lok pttrn, t orzontl ttk vlu s t sm wt or wtout p on t squrs ( n n t xmpl). Ts osrvton m y Hytt s mportnt, us t rry RnkAttks lry tks up unk o mmory: yts = yts. I t squrs o not n t ttk, tn t squrs n xlu rom t lokn pttrn tors, lvn = tors or o t squrs o t or. T sz o t rry RnkAttks s now ru to yts = yts. Ts s stll not smll (splly ompr to ss, wr ts tor rry s tr tms smllr), ut os not rqur spl rwr rqurmnts, vn numr o ts rrys r n to ovr vrtl ttks n onl ttks, s wll xpln low. Wt ts pr-lult tors, t s now sy to t t orzontl ttks or rook on squr: vo ClRnkAtt(BITBOARD *, nt rom) { // Gt t lok pttrn rom // t poston tor nt ps = GtRnkBts(&Oup, rom); // Strp t ts or t squrs ps = (ps & CLEARMASK) >> ; // Gt t orzontl ttks rom t // pr-lult tors CopyBB(, &RnkAttks[rom][ps]);

5 nt GtRnkBts(BITBOARD *, nt sq) { // Tk t rnk ts rom tor // ntr,, or rturn (->[sq_to nx[sq]] >> rnk_st_no[sq]) & ALLONES_; nt sq_to nx[] = {,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,, ; nt rnk_st_no[] = {,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,, ; It s now lr wy vn n rry o tr ntrs s ttr rprsntton tn tr rnt ntrs lk n Ymst s ornl mplmntton. By usn t rrysq to nx to ss t tor ntr tt s n, no -sttmnts r rqur. Furtrmor, t s lso lr wy vn t tr ntrs rprsntn t wt promoton zon, t ml o t or n t lk promoton zon s ttr rprsntton. In t urrnt mplmntton, rnk on t or only s ts n on o t tr tor ntrs, wl n Ymst s ornl mplmntton rnk on t or oul v ts n mor tn on ntr, nn xtr oprtons to t t normton or snl rnk... Vrtl ttks Clultn t ttks lon rook l (n ln l) s lttl mor omplt tn t ttks lon rnk. T prolm s tt or orzontl ttks, t ts r n onsutv postons, so mskn n stn n us to xtrt ts ts rom toup tor (ts s on n t unton GtRnkBts ov). For ttks lon l, t ts r postons prt, so mny mor oprtons r rqur to xtrt t lok pttrn. Fur : Norml squr lloton on t lt n r rotton squr lloton on t rt. T soluton to ts prolm s to us rott tors. By rottn t or rs, t ts tt wr postons prt, r now nxt to otr (s Fur ). T r rotton to mk t ts or vrtlly onnt squrs jnt n t tor rprsntton ns t ttk lulton. Now t rry FlAttks s n n w vry rott lok pttrn s trnslt to vrtl ttk. T possl lok pttrns r t sm s n t s o orzontl ttks, ut nst o orzontl ttks, t rry s to v t vrtl ttks. An xmpl or rook on s vn n Fur. Squr s, t lok pttrn s = ( squrs strpp o ts tm) n t tor or t ttk or ts lok pttrn s t t n t o t rst ntr, t t n o t son ntr n t t o t tr ntr: FlAttks[][].[] = ; FlAttks[][].[] = ; FlAttks[][].[] = ; Furtrmor, nw tor Oup rot s n to rprsnt t oup squrs n s o rotton. T normton n ts tor must upt t vry mov, vn smll ovr. T l ttk o now s strtorwr: vo ClFlAtt(BITBOARD *, nt rom) { // Gt t lok pttrn, rottn // t sour squr rs nt ps = GtRnkBts(&Oup_rot, nt_rot[rom]); // Strp t ts or t squrs ps = (ps & CLEARMASK) >> ; // Gt t vrtl ttks CopyBB(, &FlAttks[rom][ps]);

6 Fur : Exmpl o or poston (lt), ts rprsntton wt r rotton (ml) n t tor rprsntn t ttks o t rook on (rt). // Trnslt squr to r rotton nt nt_rot[] = {,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,, ; Ts soluton ws vn y Hytt [] or ss n t n us n so s wll. In ss t s only us or rook ttks, ut n so t n us or ot rooks n lns... Donl ttks It s now lr ow to n t ttkn squrs or rooks n lns, ut tr s stll t prolm o t sop. Bsops ttk lon onls n t ts or onls r not jnt. A rotton o rs wll not lp, ut Hytt pont out tt t sm rotton trk n us or sops, ut now rottons o rs lokws n rs nt-lokws must us. In Fur, t rottons o t ornl squrs ( s, s ) r vn. In ts ur t n sn tt or r lokws rotton, ll onls on up rom lt to rt r now jnt (orzontl) squrs. For xmpl, t squrs r t onl tt strts rom n ns t. In ontrst, or r nt-lokws rotton, t onls on own rom lt to rt r jnt. For xmpl, t squrs r t onl tt strts rom n ns t. Fur : Rottn t ornl or squrs rs lokws rotton (lt) n rs ntlokws rotton (rt). To put onls n jnt ts o n ttk tor, t ts o t tor r ssn s n Fur. T prour or lultn t squrs ttk y sop s now smlr to t prour or rook n ln. For possl lok pttrn o ps on onl, t ttks r pr-lult. Furtrmor, t tors Oup r n Oup l ontn t oup squrs or r lokws rotton n rs nt-lokws rotton rsptvly. Ts two tors must upt or vry mov. Tr s on xtr prolm n t s o onl ttks. In Fur t n sn tt tr r onls ovrlown nto t nxt ntr o t tor. For lokws rotton, squr s prt o t onl ( to ) n squr s prt o t onl ( to ). Smlrly, or nt-lokws rotton, t squr s prt o t onl ( to ) n squr s prt o t onl

7 Fur : Bt ssnmnt or rs lokws rotton (lt) n rs nt-lokws rotton (rt). ( to ). Squr ( n t nt-lokws vrson) s not prolm, us ts s n squr t t top o t onl n wll strpp nywy. Tror, ts ovrlow nto t nxt ntr o t tor (rom [] to []) n nor. Squr ( n t nt-lokws vrson) s lso n squr, so ts ontnts n nor. Howvr, us ts tm t squr s t t ottom o t onl (.. t most snnt t) tr s t prolm o ttn t rmnn ts o t onl to t t lok normton. A snl lt st s n wl or ll t otr onls rt st s n. Tror, ts two onls r spl s n onton s to to t unton tt ts t lok normton rom t rott ors Oup l n Oup r. T pr-lult ttk tors r stor n t ollown tor rrys: BITBOARD DAtt_r[][]; BITBOARD DAtt_l[][]; T lulton prour s now s ollows: vo DAttRL(BITBOARD *, nt rom) { nt ps = GtDBts(&Oup_r, nt_r[rom]); ps = (ps & CLEARMASK) >> ; CopyBB(, &DAtt_r[rom][ps]); vo DAttLR(BITBOARD *, nt rom) { // Smlr, wt lt r rotton nt GtDBts(BITBOARD *, nt sq) { // Spl s o - n - (sq >= && sq <= ) rturn (->[] & ALLONES_) << ; // Otr ss rturn (->[sq_to [sq]] >> _st_no[sq]) & _msk[sq]; nt sq_to [] = {,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,, ; nt _st_no[] = {,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,, ; nt _msk[] = {,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,, ; T msk trnslton s n us unlk rnks n ls, onls o not v x lnt. Tror, mskn s n to kp only t normton tt s t prs lnt o t onl on w t prtulr squr s lot. T nt r nnt l rrys v n omtt. Ts rrys v t poston o squr tr r lokws n nt-lokws rotton.. Otr Btors T tors xpln ov r nou to nrt lmost ll o t movs n so. For xmpl, t movs or lk sop n oun y rst mkn tor wt s on t squrs wr t sop rom squr sq n mov to: BITBOARD,, movs; DAttRL(&, sq); DAttLR(&, sq); OrBB(&movs, &, &); AnBB(&movs, &movs, &GotPs);

8 Vrson Tm (s) Attk tls Btors Tl : Rsults o ply mnmx srs n postons. Tn, loop trou t ts vs t possl stnton squrs (or promot sop, ts stnton squrs r ADD- wt tor tt s s or ll kn movs on sq). Wt rmns s to t p n promot or not. For ts, tors n us tt v s or t squrs ns t lk or wt promoton zon. T promoton zon s rprsnt y snl ntr, so kn squr s n t promoton zon n on y kn only [] or []. In t sm wy, tors n us to k ln, knt or pwn must promot (ln n knt on t top two rnks n pwn on t top rnk). Exprmntl Rsults In so prorms, tors v not n s wly us s n ss, w s to xpt us o t rn n or sz. It s mor ommon to v ttk tls (kk tls n Jpns) tt kp trk o wr p n mov to, uptn ts normton wn t or poston ns. Only tr t m lr tt t urrnt Computr So Worl Cmpon Bonnz s usn tors, t susson out ts us n so s r-opn. Ymst ompr t us o tors wt t us o ttk tls n s prorm YSS n only oun n nrs n sp o out % [] wn tors r us n tsum so solvr. Hr rnt tst s n prorm. To mk ln omprson twn tors n ttk tls, t prormn o mnmx prorm n w t movs wr nrt y ttk tls us n t prorm Spr ws ompr wt prorm n w t movs wr nrt y usn tors. Tror, t nrt trs n ot ss wr xtly t sm sz. T vluton unton only lult t mtrl ln. In ts wy, ply mnmx sr ws onut or rnt postons tkn rom two prossonl ms. Ts xprmnt ws run on.ghz Pntum mn unr WnowsXP. T rsults r summrz n Tl. From ts tl t n sn tt t mov nrton usn tors s.% str tn t mov nrton wt ttk tls. Conlusons n Futur Work In ts ppr t ws xpln ow tors n us to o mov nrton n so. Evn tou t mplmntton o tors n so s lss nt tn n ss us o t rnt or sz (t squrs o ss or t n xtly on ntr), t s n sown tt t sp o mov nrton n so n mprov snntly tors r us nst o ttk tls. Usn tors nst o t ttk tls n Spr m t mov nrton lmost tw s st. Tror, t sms lkly tt tors r oo ltrntv or ttk tls. Ts n s, mov nrton s not t only prt o so prorm wr ttk tls r us. For xmpl, ttk tls r lso us n t vluton unton, splly wn lultn p molty n t nr on squrs roun t kn. It s possl tt t xtr lultons us n tors mk t vluton slowr, tus rsn t ovrll prormn o t prorm. Tr s rn twn t vluton untons o rnt prorms, so t tvnss o t tor rprsntton mt v to tst or vry prorm. Howvr, tr r otr rsons or usn tors. Frst, otr prts o t prorm my lso nt rom usn tors. For xmpl, t stt xn vlutor us n qusn sr n mplmnt qut ntly usn tors. Son (n prps most ppln), mns om vll tt llow t rssn, t so or wll t n t tor rprsntton wll om twn two n tr tms str ovrnt wtout mu tonl ort. Su n mprovmnt nnot xpt n t s o ttk tls. Rrns [] K. Hok. ttp://.tup.om/yss/s. Mss post on Auust t. [] R. Hytt. ttp:// [] Wkp. ttp://n.wkp.or/wk/btor. [] H. Ymst. ttp://.tup.om/yss/s. Mss post on Auust t.