Small Multiplier-based Multiplication and Division Operators for Virtex-II Devices
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(2) INSTITUT NATIONAL DE RECHERCHE EN INFORMATIQUE ET EN AUTOMATIQUE. Small Multiplier-based Multiplication and Division Operators for Virtex-II Devices Jean-Luc Beuchat, Arnaud Tisserand. No 4494 July 2002. ISSN 0249-6399. ISRN INRIA/RR--4494--FR+ENG. ` THEME 2. apport de recherche.
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(81) /n g%$ . m bits n = 17. .... Y1 X1. .... Y0. ... ... .... 17. . ... = n. . ... . ... −n m. ... .. pa. rti a. lp. ro d. uc. ts. ... PP0 ... PP1 ... PP2 ... PP3 ... .... n = 17. PP1 PP0. X0. ... ... .... n = 17. ... .... ... ... .... PP3 PP2. MULT18x18. (a) Proposed multiplier. (b) Adding the partial products (tree structure) 0 0 0 0 0 0 0 0 0 0. ... ... ... ... .... 0 0 0 PP3 0 0 PP2 0 PP1 PP0. (c) Adding the partial products. ¡>l{q:vm~d É vmo{sl{mo{lnrutCslnpSk 14 l{sa t wl{kmq:ond É LP ºA`-uª^Ouª zmonpr«§ Ct k m = 19 41ad_~d-sadwl{kmq:ond É P8º`-uª^OuªetC~raml{sd3r_svm~d
(82) lnwwc©tCo{ond_~u§®`%ad-sO4¢pC 4%t3y ced_sapAlnw lnwtCmMpSl{kQsl{kmq sapSvmq:ael{sHw tC~d3wËt-wc©tCo{omcgvmo{sl{mo{lnd_~u²l{s lnwHwonp*4Ëd_~%tCk sad tSml{slnpSk tCo®onpSq:lnr lnwLsR41lnr3dzml{q:qd_~-sa tCksadl{Alnmd]ÐtCkA r3pSk|Qvd_~
(83) tCmm~ptSra³§ ¡>l{k tCo{o{y²³sad tC~raml{sd3r_svm~dmd3wr_~l{zMd3 l{k tC~tCq:~tCma 2 § 2 lnw=teqpAp s~tSmd] pC¯YzMd_Os 4Ëd3d_kwAl @ud tCk d_~lnpA 41ad_k lnw(r_onp:wd=sp 17 § m (k½l{ksd_~d3wsl{kmq©MpSl{kQs1lnw1sa tCs(sad=m~pSp:wd3 wl{kmq:ond É P8ºA`-uª^MuªetC~raml{sd3r_svm~dglnw(wsl{o{o ,d >©r_lnd_ks0£¤pS~ ² 41amlnra;lnw©sad c©tCkQslnwwVtYwAl @ud l{k M M M wstCktC~ B ptCsl{kmqSÒpSl{ks C m = 23 kvmcgzMd_~w°twvm~d_y©pSk B ptCsl{kmqSÒpSl{ks(rutCk0zdL£pSvmk©l{ k BÝGf F\´]§ d8a t3d8l{cmond_ced_kQsd3¼Os 4Ëp d_~wlnpSkwxpC£sad®f 2 ×f 2 vmkwl{q:kd3cgvmo{sl{mo{lnd_~$l{kQpSo{d3
(84) l{ksa`d B ptCsl{kmqSÒMpSl{kQs$cgvmo{sl{mo{lnrutCslnpSk 41l{saYOs 4Ëp ml{d_o{l{kd©wstCqd3w
(85) tCksad É P8º`-uª^Ouª ; m~l{cl{sl{d:§K`%ad©l{Alnmd]ÐtCkA r3pSk|Qvd_~ tCmm~ptSra l{cmo{lnd3w wo{lnr3d3wu²A£pSvm~ É PLºA`-uª^Muª ; zmonpr«Aw»²tCk½a tSwLtMd_~lnp d3|v tCo³sY p D kw»§ 9Lvm~
(86) tCo{qpS~l{samc 50kd3d3mw 182 wo{lnr3d3w»²>twl{kmq:ond É PLºA`-uª^Ouª ; zmonpAr« tCk¨lnwgτ t0o{l{ssondzml{s won5p 4Ëd_~° τ = 8 kwV´]§ d=mo¬tCk¼spewsvy B ptCsl{kmqSÒMpSl{kQs=tC~l{samced_slnrgpSk ¡}Ëi=8wu§ º³d_sgvw
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(88) zd_~=sa tCs8sad n ondutSws8wl{q:kml· rutCks=zml{swLr3pSced l{~d3r_so{y½£¤~pSc¦t É P8ºA`-uª^Muª©zmonpr«§ À¢pSkwd3|Qvd_kso{y²xsado¬tC~qd_~ lnwu²³sadewc©tCo{ond_~sad o¬tSwstSmmd_~gpC£¢¡$l{q:vm~d©fzMd3r3pSced3wu§¡pS~ tKr3pScgzml{k tCspS~l¬tCo¢r_l{~r_vml{su²OranpAp:wl{kmq n = m/2 ondutSmw=a*p 4Ëd_d_~spt©£tSwsd_~8r_l{~r_vml{su§ ;ad_k 4¢d-l{kQs~pAvr3dgtml{Md_o{l{kdwstCqd=zyK~d_mo¬tSr_l{kmqtCo{o É P8º`-uª^Ouª zmonpAr«w1zQy É PLºA`-uª^Muª ; ² pSvm~8d]AMd_~l{ced_kQsw8wa*p 4 sa tCs lnwsadgzd3ws8wpSo{vmslnpSk ¢sadgwAl @udlnwLd]tSr_so{ysad
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(91) pSk½sad-StCo{vdgpC£ n §. m = 18. ðeixð.
(92) . 550 r 500 450 r 400 r 350 300 r 250 r 200 150 r e 100 e e e e e e r e 50 r 3 3 3 3 3 3 3 03 18 20 22 24 26 28 30 32 operand size. τ [ns]. slice number.
(93)
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(95) vmo{sl{mo{lnd_~w pSk¿t ¥LÀ%fCXD::^ Demd_Alnr3d 3 Hl{lnmd]ÐtCkA r3pSk|vd_~-tCo{qpS~l{samc X tCk Y tC~d©*V»Òzml{sl{kQsd_qd_~w °\ É P8º`-uª^OuªzmonpAr«wV´ ◦ -sO4¢pC14¢t3yYced_sap ° 2 É P8º`-u0ª^Ouª½zmon0pAr«wV´ • gtCo{qpS~l{samc md3wr_~l{zd3½l{k½ tC~tCq:~tCma 2 § 2 ° É PLºA`-uª^Muªzmonpr«m´]§. slice number. 50. r. r 3 r 3 40 r 3 35 r 3 30 r r 3 3 25 3 45. 3r. 3r. 20 18 20 22 24 26 28 30 32 34 operand size. τ [ns]. 55. 19 18 17 16 3 15 14 r 13 12 11 10 e 18. r. 3 3 r. r. 3 3 3 3 3 3 r. r. r. r. e e e e. r. e. e. e e 20 22 24 26 28 30 32 34 operand size. ¡$l{q:vm~d D 1 c tSr_s=pC£HsadgrapSlnr3d pC£ n pSk sadl{Alnmd]ÐtCkA r3pSk|Qvd_~=ced_sapA. 41l{sa É PLºA`-uª^Ouª ; § • n = m/2 ◦ n = 17. 3 n = 17. `%ad¼tC~raml{sd3r_svm~d3w©md3wr_~l{zd3 l{k samlnwwd3r_slnpSk¶pSkmo{y kd3d3 o{l{cl{sd3¶ra tCkmqd3w©wptSwsp Md_~£pS~cµwl{q:kd3¶c
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(166) Unit´e de recherche INRIA Lorraine, Technopˆole de Nancy-Brabois, Campus scientifique, ` NANCY 615 rue du Jardin Botanique, BP 101, 54600 VILLERS LES Unit´e de recherche INRIA Rennes, Irisa, Campus universitaire de Beaulieu, 35042 RENNES Cedex Unit´e de recherche INRIA Rhˆone-Alpes, 655, avenue de l’Europe, 38330 MONTBONNOT ST MARTIN Unit´e de recherche INRIA Rocquencourt, Domaine de Voluceau, Rocquencourt, BP 105, 78153 LE CHESNAY Cedex Unit´e de recherche INRIA Sophia-Antipolis, 2004 route des Lucioles, BP 93, 06902 SOPHIA-ANTIPOLIS Cedex. ´ Editeur INRIA, Domaine de Voluceau, Rocquencourt, BP 105, 78153 LE CHESNAY Cedex (France) http://www.inria.fr ISSN 0249-6399.
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