A pipeline polish string computer*

Transcription

1 A pipeline polish sring compuer* by GERARD G. BAILLE and JEAN P. SCHOELLKOPF Co--,np'ueT ATcli-iecure Group Grenoble "Universiy, France ABSTRACT This paper describes a new compuer organizaion which allows he pipeline execuion of a polish-sring code. The cenral characerisic of he proposed organizaion is a FI-FO queue, ha holds values jus accessed by an Access Saion, unil hey are used as operands by an Execuion Saion for an arihmeic or logical operaion. Operands are aken ou of he queue by means of wo poiners whose modificaions are managed by a Conrol Saion. This new compuer organizaion is capable of high performance, since access o variables and execuion of operaions are performed in parallel wih conrol funcions required by he inpu program. A soluion o access conflics is proposed, using a conen addressable memory ha holds he names of he variables whose modificaion is deferred. This archiecure is currenly in applicaion for he design of a high-level PASCAL compuer. INTRODUCTION Design of high performance compuers can be achieved using he echnique ha is called "pipeline" design, characerized by he fac ha concurren operaions are suppored by he machine. 0 A high-level insrucion can be iniiaed wihin a module, and in he same ime he oher modules are execuing some operaion relaed o a preceding insrucion. The IBM 360/9 and he CDC 6600 are wo examples of pipeline execuion. Efficiency of pipeline compuers depends srongly on he way ha hey are programmed. Many aemps were made o solve his problem and several echniques are proposed for generaing opimized code in erms of pipeline execuion. 3-5 These echniques imply an imporan amoun of preprocessing, which does no always jusify he complexiy of pipeline execuion. The soluion proposed in his paper is based on a naural decomposiion of he work o be execued in a * The research repored on his projec is sponsored by he French Comiy for Compuer Science Research under conrac SESORI No pipeline manner. The firs aspec of a naural decomposiion is relaed o he kind of language proposed o he machine. Tomasulo 9 gives an efficien algorihm for exploiing a pipeline archiecure, bu is applicaion is limied o a low level language. On he oher hand polish-sring code appears as bes suied for he execuion of high level language. 6 Sones' proposes a pipeline archiecure for a pushdown sack compuer, bu he suggess o ranslae he inpu polish-sring code ino hree address insrucion code. This paper shows, in a firs secion, how polishsring code can be direcly execued by a pipeline compuer. The second aspec of a naural decomposiion, as shown by Abrams, 8 is relaed o he decomposiion of inpu sring code execuion ino hree naural processes ha are conrol, access o operands and execuion of operaors. I would be ineresing o have he hree above processes concurrenly running in a pipeline manner: he execuion of an insrucion would be iniiaed wihin he conrol saion, and in he same ime preceding insrucions would be currenly in process eiher wihin he access saion or wihin he execuion saion. Such a pipeline organizaion is made possible using a FI-FO queue insead of a push-down sack as a work area for expression evaluaion. Operands are accessed from he queue by means of wo poiners whose modificaions are conrolled by he conrol saion which generaes exra-orders. The generaion algorihm is presened and he rae of exra-orders is evaluaed in he firs secion. The second secion of his paper gives he general archiecure of he pipeline polish sring compuer. Concurrency beween access o operands and evaluaion of expression o be assigned o variable leads o he well-known problem of reading he value of a variable whose modificaion is no ye performed. This problem, ha is called "dependency" problem, is solved a execuion ime using a conen-addressable memory which holds he name (no he address as in classical pipeline compuers) of he variables whose modificaion is deferred. A brief summary is given a he end of his paper, which shows he possible applicaions of he proposed pipeline archiecure. 73

2 74 Naional Compuer Conference, 976 PIPELINE EXECUTION OF POLISH STRING CODE This secion firs explains he choice of a FI-FO queue as a work area for evaluaion of polish sring. A model is inroduced for polish sring expressions which allows he definiion of wo poiners for operand access. The operaor se is reduced o monadic and diadic operaors. The managemen of he wo poiners is conrolled by special exra-orders generaed by a Conrol saion. The generaion algorihm is presened and discussed. The cenral characerisics of he pipeline execuion is ha he inpu polish sream is analyzed by a processor which generaes wo parallel insrucion sreams owards wo concurren processors specialized he one for access o operands, he oher for execuion of operaions. Polish sring evaluaion A polish sring can be seen as a sequence of groups, each group being a sequence of operands followed by a sequence of operaors. An operand is eiher an immediae value or he inernal name of a variable (for example, lexical level and offse) which allows he calculaion of he variable address in main memory. example: [A,B,C,D,+,*,] [E,F,+,] [G,*,+,- ] group group group 3 The evaluaion of such a polish sring requires he use of a working sorage classically organized as a push-down sack. All he operands of a given group are pushed, one afer he oher, ino he sack, in he same order as in he inpu sring, nex operaors are sequenially execued, poping he wo opmos elemens from he sack, and pushing he resul ono he sack. When all he operaors of he curren group are execued, he operands of he nex group are pushed ono he sack, and he above process is performed again. Therefore, wo processes appear when evaluaing a polish sring: -an ACCESS process which sores he operands ino he working sorage (eiher from he sring when immediae access, or from main memory in he oher case) -an EXECUTION process which execues he operaors, aking is operands ou of he working sorage and soring inermediae resuls ino i. Using a push-down sack as working sorage implies he sequenialiy of he wo above processes. The aim of his paper is o propose an evaluaion mehod which allows parallel execuion beween ACCESS and EXECUTION process: parallelism is made possible using a FI-FO queue insead of a PUSH-DOWN sack. Organizaion The above wo processes are execued by wo independen processors. Le PAC be he processor which sores he operands ino he FI-FO queue, and POP be he processor which execues he operaors, aking is operands ou of he queue. Hence, when POP is execuing an operaor, PAC can ACcess o a new operand and sore i ino he queue. example: sequenial execuion ABC D + * E F + G * + _ (using a STACK) I I I I I I I I I I I I I parallel execuion (using a QUEUE) ABC D E F G (PAC) J I I I I I I I + *+* + - (POP) I I I i I I I Such an organizaion requires a hird processor which is called PAN, whose work is he ANalysis of he inpu polish sring in order o generae insrucions for boh processors (PAC and POP). The archiecure is given by Figure. THE EVALUATION PROCESS USING A FIFO QUEUE Variables whose names appear in he inpu polish sring are sored ino he FIFO queue by he Access Processor. The sequence of he access insrucions is he same as he sequence of he variable names in he inpu sring. So, we can define he relaive locaion of any variable in he queue, depending on is relaive locaion in he inpu sring. Le S= (VII,..., VIDI, 0... Olm,..., V/... VpDI', PCP insrucion queue ~ [ ri~o ()QElIE I~ UAI!I ::::::r:ory FiguTe polish sring

3 A Pipeline Polish Sring Compuer 75 0, Oflm p ) be he inpu sring, where Vij is a variable name, and Oi j is an operaor name. If he relaive locaion of he firs variable VII is equal o, hen he locaion of any variable Vij is given by he formula: i (Vij) = Ln+j, wih no=o r=o How can we access o he operaris locaed in he queue The evaluaion of polish sring is a sequence of monadic or diadic operaors execuion. In a firs approach, le us consider ha all he operaors are diadic ones. We mus associae o each operaor is wo operands, whose locaions are parly defined by he nex wo rules: RULE : if Oil is a diadic operaor, hen is second operand is variable vin i, and is firs operand is eiher variable V/\-l if ni>, or he resul of he immediaely preceding operaor Oi- mi-l if ni =. RULE : for j = o ni, he second operand of operaor Oi j is he resul of he preceding operaor Oi j - We see ha he variables are no referred o as operands in he same order as in he inpu sring: for each group Gi= (V/;,,., V i, Oil,.. '; Oimi) he firs accessed variables are V{i and v i n i - as operands for operaor 0/, he las accessed variable V/. Hence, i is idle o pull he operands ou of he queue in a FIFO mode, since i should be necessary o sore hem again ino anoher memory, organized as a Pushdown sack. So, we propose o use he queue as a working sorage from which operands are accessed by means of wo poiners, and ino which inermediae resuls are sored during he evaluaion process. Definiion of wo poiners Le us define PI and P as wo poiners which hold respecively he address of he firs and second operand of any diadic operaor during he evaluaion process. As an example, le S= (VII, V/, V 3, 0\ 0, V \ V, O \ 0 ) be he inpu sring. The variables are sored ino he queue in he following manner:.-.. -R I v 3 vi firs-in v V las-in II ITJJI 'J I ' Push-dm-!Il sack Ii' ;;:::- GJ FOP!"I-FO Figure -Classical organizaion The inpu polish sring defines he sequence of operaions as follows: Figure 3 We mus generae orders for iniializing P on variable VIS, PIon variable V before execuing operaor 0/, whose resul is immediaely used as second operand for he nex operaor 0/, whereas poiner Pl mus be decremened by one in order o give he address of variable VII as firs operand for operaor 0 The nex diagram shows he successive saes of he queue and he successive values of poiners PI and P. Iniializaion of poiners Boh poiners PI and P mus be iniialized afer execuion of he las operaor of group Gi- (Oi- m i - ) and before execuion of he firs operaor of he nex group Gi(O/). We know ha poiner P gives he address of he locaion which holds he resuls of operaor r (Oi-l m i - ) : his address is equal o (Vi_ n i-l). We mus assign o P he address of he second operand of operaor 0/, which is variable vim i (from rule ), whose address is equal o i i-i (V{i) = L nr= L nr+ni r=o r=o = (V i - ) +ni So we mus incremen he previous value of P by nl Moreover, poiner PI mus hold he address of he firs operand of operaor 0/, which is eiher variable V i - if ni>, or he resul of operaor Oi-l mi-l if ni =.

4 76 Naional Compuer Conference, 976 iniial sae afer 0 afer 0 P I v~ I v! PI VI v PI VI v I v 3 P r(oi) P vi v V v r(o~) I v v p The inel'mediae saes of he queue Each ime a diadic operaor is execued, he locaion which holds he firs operand will be no more accessed: we say ha a "hole" is creaed or he he locaion becomes "empy". So, during evaluaion process, he sae of he queue is defined as a sequence of empy locaions followed by full locaions which hold eiher no ye accessed variables or inermediae resuls. We associae o he sae of he queue, afer execuion of any operaor Oi j a finie sequence {(d, ), (d, ), " (dk, k)}, where each di is he lengh of a full locaion sequence, and each i is he lengh of an empy locaion sequence before 0 vi v r(o~) I v P v p FIRST-IN d I~I.. I p P LAST-IN afer 0 afer o~ final sae ~_v_~ _'----_--'- -L ----L- ~ PI Figure 4 In boh cases: Pl=l(vi_ni- ) = (Vini) -=P- ifni>l, Pl= (vi_ni-) = (Vini) -ni=p- if nj=l So, we define an EXTRA-ORDER, generaed beween he execuion of Oi-l mi-l and he execuion of Oil, called UP (ni), which is inerpreed as: p The successive values of poiners PI and P can be defined relaed o he sae of he queue: P mus hold he address of he resul r (Oi j ), and PI mus poin o he full locaion downsream of he locaion poined by P. Each ime an operaor is execued, a new hole is creaed, herefore he las elemen of he sequence {(djj )} mus be modified: k is incremened by and dk is decremened by. During execuion, poiner PI will be decremened by one. However, dk may become zero, in which case poiner PI mus be decremened again by a value equal o k-, in order o poin o he firs full locaion downsream of P. In he same ime, he queue sae is updaed, by suppressing he las elemen k... k-l before o~ ~ p... p + n. ; pi... p - l. n. > l. I m.,r(oi~~ ) I p,... Vi + n. l. m i I r(oi_l ) v~ ". l. I ni'- I n. V.l. before UP(n i ) Vi l. n _ n. i V. V.l. afer UP (n. ) l. l. l. PI p af'er o~ C k!~. -!...,/ /.-- / p\ J, pi, P p~ Figure 5 Figure 6

5 A Pipeline Polish Sring Compuer 77 Conclusion-An exra-order called DO\VN mus be generaed by he PAN processor, when he queue sae is updaed: is execuion is defined by: Pl~Pl-n, where n is equal o k-, when he order is generaed. Modificaion of he queue sae before execuion of a new group Beween execuion of operaor Oi_l m - (he las operaor of group Gi- ) and execuion of operaor 0/ (he firs operaor of group G i ), an exra-order UP mus be generaed. This movemen of poiners corresponds o a modificaion of he queue sae: a new elemen (dk+, k+d is creaed, iniialized as follows: he new group Gi is defined as a sequence of ni operands, hence dk"'l~ni' and zero hole has been creaed, hence k+l~o. Conclusion-An exra-order called UP mus be generaed by PAN processor in order o updae he queue sae before he firs operaor of a new group. Is execuion is defined by: P~P+n ; Pl~P- where n is equal o dk=nh when he order is generaed. GENERATION OF EXTRA-ORDERS FOR THE MANAGEMENT OF THE POINTERS The proposed evaluaion process using a FIFO queue requires he generaion of exra orders for he managemen of he poiners. As shown above, hree kinds of orders mus be sen o he execuion processor: or -he firs kind consiss in all he monadic or diadic operaors, whose execuion is defined by: Q(P)~Q(Pl) <Op>Q(P) Q (P) ~<Op>Q (P) (diadic operaor) (monadic operaor) The arihmeic or logical diadic operaion is followed by a modificaion of poiner PI : '\ Pl~Pl-l k ~r(o~i-l) I n i BEFORE V. ;:::;; /%:.-. Vi : Pi, p -he second kind is he UP (n) exra-order which is execued when a new group is enered. I is defined as: P~P+n; Pl~P-. -he las kind is he DOWN (n) exra-order, which consiss in he updaing of poiner PI; i is defined as: Pl~Pl-n Evaluaion of he number of exra-orders o be generaed The number of exra-orders (nup+ndown) o be generaed only depends on he inpu sring. Le S= (V/,..., V/'\ all,..., Olm\..., V p \ Vl'n p, 0/,..., O"ml') be he inpu sring. Such a sring conains p N = :L.nr variable names, hence N access insrucions r-l for he access processor PAC, and p M = :,m r operaors, hence M insrucions for he exr-l ecuion processor POP. If all operaors are diadic ones, hen M=N -, bu in general we have M~N-l. Hence he iniial number of orders is equal o M+N~N-l. Each ime a new group is enered, one mus jump over is sequence of variables, ha is o say ha he number of exra UP orders o be generaed is equal o he number p of groups in he inpu sring. The evaluaion of he number of exra DOWN orders is a bi more difficul o do. Le ki be he number of exra DOWN orders generaed during he execuion of group Gi. The maximum value of ki is equal o i-i, since he queue has a maximum number of holes equal o i-l. Furhermore, each execued DOWN order decreases he number of furher possible DOWN orders by, since one hole is suppressed. i-i Hence we have O:S;k(~;: (i-i) - :,k j, for all i. j= When adding he above formula for all i, we ge: ~_../-.. ~,.~, r~. US~Kj:S;~ ~J-l} -L~Kj+. AFTER d k _ l, I _ k l ~= 0 ~'"i- r0~~ m. I v: i /":</': /' '0.-) v. ////Ir'i-l. Figure 7 - Pl? which becomes: Hence we have he number of exra Down orders given by O:S; kj:s; p (p; ) J= (p-l) (p-) p-l.

6 78 Naional Compuer Conference, 976 However, if he number N of variables is less han p (N S p), han he maximum number of diadic operaors is less han p-. As he p operaors all, 0..., Opl canno imply he generaion of a DOWN order, we have only p-i operaors which can do so. Hence he maximum number of exra DOWN orders is equal eiher o N -p- ifp+sn Sp, or o p- if N~p. Now i is easy o see ha he minimum rae of exraorders is given by: P MINRATES N- and he maximum is given by: Example: N- MAXRATES N - ifp+snsp, p- MAXRATES N - if N~p S= (A, B, C, *, +, D, -) In his case, here are p = groups, and N = 4 variables. Hence N~p MINRATES~ MAXRATEs~ memory a execuion ime. Hence, he bes soluion consiss in he analysis of he polish sring a execuion ime, since he compile ime soluion would slow down he global performance of he machine. The generaion is made by he analysis processor PAN, which can be considered as he conrol processor, and execue all he conrol funcion of he compuer. Algorihm for he generaion of exra-orders a execuion ime Generaion of orders is performed by he analysis processor PAN. Given he inpu polish sring, his processor mus generae orders owards boh processors PAC and POP, using he heoric sae of he queue, represened by he sequence {( d i i )} defined earlier. The sequence {(d ij j )} can be managed using a push-down conrol sack. Le TS and STS be he wo opmos elemens of he sack, which respecively hold he couples (d k, k ) and (d k -, k - ). These wo variables TS and STS are srucured as wo fields called D and T, so dk is equivalen o TS.D, k o TS.T ec. The generaion algorihm is illusraed in Figure 9, where he symbol (Fd represens he name of he funcion o be execued when he nex symbol in he inpu sring defines he sae ransiions. The nex symbol ype is represened eiher by [variable] or by [operaor]. Trade off beween compile ime and execuion ime for he generaion of he exra-orders The generaion of he inpu sring is performed by he compiler, which could easily generae exra-orders. However, he compiler becomes machine dependen in such a case, and he size of generaed code is increased, as he number of insrucion feches from main [variable] 4 50 fo.neraor] 0!J o:>erclncs in 5 Cjrours 0 5 N = number of oper3.nds Figure 8 Figure 9

7 A Pipeline Polish Sring Compuer 79 Funcion F iniializes he queue sae, by pushing he couple (-,0) ono he conrol sack. Funcion F generaes an Access Order owards he Access Processor, nex couns he number of variables in he curren group, by incremening he op of sack (TS.D~TS.D + ) Funcion F3 is execued when he firs operaor of he curren group is encounered. I occurs on he +_~~N~+~~~.c_~_ ~T ni +~ "\ T+_.c. _~+~~_!_ +l,..~ ~~_~_ I.LC:UICll.lVU LLV Vi - I.V vi' Ll.;::).LUl\JI.IVl.i. ;::).C ~CllCLaion of an UP exra-order, wih a parameer n equal o he number of variables in he curren group, which has been evaluaed by funcion F (he parameer is equal o ni since F has been execued ni imes). Funcion F4 generaes an Operaion order owards he execuion processor POP. If he operaor is a diadic one, hen he queue sae is updaed, modifying he op of sack elemen: TS.D~ TS.D - since here is one less operand in he las group, and TS. T ~TS.T+ since here is one more empy locaion in he las group. If TS.D becomes zero, an exra-order DOWN is generaed, wih a parameer n equal o he second op of sack elemen STS: one generaes DOWN (STS.T). Nex he queue sae is modified: STS.T--;-STS.T+TS.T since he lengh of he hole mus be incremened and PULL (TS) since he opmos elemen is deleed (STS becomes he op of sack). Funcion F5 is execued on he ransiion from Oi mi o Vi+ \ Le. when he firs variable of a new group is encounered. This funcion iniializes a new elemen on he sack, only if he previous op of sack represens a real group. if TS.D>O hen PUSH(l,O) else (TS.D~l, TS.T~O). Funcion F6 is execued on he occurrence of he endsymbol, which is any separaor symbol beween wo expressions (e.g. an Assign Symbol). I only verifies he correcness of he conrol sack sae, which mus be he empy sae. ARCHITECTURE OF A HIGH-LEVEL PIPELINE COMPUTER The firs secion of his paper has shown ha pipeline execuion of polish sring code is made possible using a FI-FO queue. In his secion, an archiecure is presened for a high-level pipeline compuer whose code is in polish sring forma. The dependency problem is firs sudied and a soluion is given. THE DEPENDENCY PROBLEM insrucion queues, or is in he process of execuion by processor POP, when he access o variable X insrucion eners he access processor PAC. The access processor mus be able o deec he fac ha boh insrucions refer o he same variable X, and ha he second insrucion migh have o be deferred unil he compleion of he firs insrucion, since a reference o he locaion of X in main memory would no give he rue value of variable X, bu is old value. The soluion consiss in he definiion of a conen addressable memory, organized in a FI-FO mode, which holds he name of he variables whose modificaion is deferred, and he name of he variables which have been jus modified. In he firs case (deferred modificaion), any reference o he variable is processed as an indirec reference by creaing a link beween he assignmen and all he deferred references. In he second case a reference o main memory is eliminaed, since he curren value of he variable is available in he conen-addressable memory afer he compleion of he las assignmen. Using he above mechanism, he access insrucion (VALUE X) can be deferred unil he compleion of he assignmen. All he deferred references are linked ogeher, eliminaing a number of memory references equal o he number of linked locaions. THE CONDITIONAL BRANCH PROBLEM Boh PAC and POP processors may be considered as SLAVES of he PAN processor in he following sense: hen only execue he inernal insrucions ha hey receive from he PAN processor. Moreover, every in- ~rk am A +- <expl> \ B C D E F G conen addressableb +- <exp> v V v V C +- <exp3> D... <exp4> \ @ E +- <exp5> L L L L coren U U (J U F +- <exp6>( E ) e E E E JI I ~ Assign E I when here <exp5> \. I Assign F when here G"'" <exp7>( E F. H... <ex!>b>( F ) ~ I \ <ex!'7> "" ~ ~ I II '.ssiqn G "Then here PAC poiner Suppose, for example, ha he high level insrucion "X~<exp>" has been prepared in boh PAC and POP e:-:pression : execuion process Figure 0

8 730 Naional Compuer Conference, 976 srucion belonging o he inpu sring is feched by he P AN processor. So, his processor can be considered as he MASTER of he conrol, and i is involved in all conrol funcions in he compuer during execuion of a single high-level program. When a condiional branch occurs, he PAN processor is no able o fech he nex insrucion, since he condiional expression is currenly in he process of evaluaion. However, he PAN processor may choose one insrucion among all he possible nex insrucions (generally wo). The probabiliy of a bad choice srongly depends on he conex of he condiional branch: i is much lower for a LOOP saemen han for an IF saemen. When a choice is made, we say ha he PAN processor eners a Condiional Sae, characerized by he fac ha is aciviy is limied o a preparaion work. Especially, if a condiional branch occurs during his condiional sae, no choice is made, he processor waiing for he resoluion of he firs condiional branch. When he value of he condiional expression is available, wo cases may occur: eiher he choice was good, in which case he process goes on wihou any modificaion, or he choice was bad, in which case all he prepared work mus be disabled. This is simply achieved by wriing as "empy" he inpu insrucion queues of boh PAC and POP processors which hold bad insrucions and updaing boh evaluaion and dependency queues by deleing he sequence of "bad" operands or "bad" deferred variables (hey are "bad" because hey belong o he bad choice). HOW TO SAVE THE EVALUATION CONTEXT The evaluaion conex (inermediae sae of he evaluaion queue) mus be saved when a "funcion call" occurs wihin an expression. Funcion calls are inroduced in he inpu polish code in he following manner: any operand can be eiher a variable name or a funcion call. The synax of a funcion call is (FCALL <name>, <parameer-lis>, ENTER). When FCALL is decoded by he analysis processor PAN, a special order is sen o he PAC insrucion queue ha calls for he address of a save area. This area is allocaed on he op of a push-down sack, since several funcion calls can be nesed. Nex, processor PAN, which knows he curren sae of he evaluaion queue, generaes a sequence of DOWN and SAVE orders owards he POP insrucion queue. Hence he curren sae of he evaluaion queue can be saved before he funcion is enered, all previous resuls being compaced ino he save area. When he funcion is reurned, processor PAC is capable o resore he iniial sae, pushing he funcion resul jus afer he resored values, and he evaluaion process goes on. THE GLOBAL ARCHITECTURE OF THE COMPUTER The pipeline compuer archiecure is shown by Figure. Each of he hree processors can run concurrenly. Their synchronizaion is daa-driven. Processor PAN feches high-level polish form insrucion sream from Main Memory, and execues all he conrol insrucions (IF, LOOP, GOTO,... ). I analyzes inpu expressions and generaes wo inernal insrucion sreams owards boh PAC (access insrucions) and POP (execuion of operaion). Two synchronous exchanges occur: he firs one is concerned wih he ransmission of he enry address when a procedure is enered. The second one is he compleion of a condiional expression which can disable he choice made by processor PAN on he occurrence of a condiional branch. SUMMARY The pipeline archiecure described in his paper is poenially capable of high performance. Is inpu code is in a polish sring forma ha can be direcly ranslaed from a block srucured high-level language. The pipeline execuion is based on a naural decomposiion ino conrol, access o operands and execuion of operaions, execued by hree concurren processors. PROr.RAM STORAGE Figure ll-archiecul'e of he pipeline compuer

9 A Pipeline Polish Sring Compuer 73 This compuer archiecure is currenljt in applicaion for he design of a PASCAL compuer. Each of he hree processors is in design using high speed macrologic componens in Low Power Schoky Technology., ACKNOWLEDGMENTS The auhors would like o hank Dr. F. Anceau for his consan encouragemen and helpful discussions and all members of he Compuer Archiecure Group of he Universiy of Grenoble for heir consrucive criicism. Special hanks go o Mrs. H. Diaz for preparing he paper. REFERENCES. Anderson, D. W., F. J. Sparacio and R. lvi. Tomasulo, "Sysemj360 :Model 9: Machine Philosophy and Insrucion Handling," IBMJR&D,, No., January 967, pp Thornon, J. E., "Parallel Operaion in he Conrol Daa 6600," AFIPS FJCC Con!. Proc. 6, Par II, Washingon, D.C., Sparan Books, 964, pp ~ elsoll; H. L.; Progmm, Opimizing Techniques for he CDC 6600 Cenral Processor, UCRL-489, Universiy of California, Lawrence Rad. Lab. 965, also KASA N Squire, J. S., "A Translaion Algorihm for a Muliple Processor Compuer," Proc. 8h ACM Na. Con!., Denver, Colorado, Baer, J. L. and D. P. Bove, "Compilaion of Arihmeic Expressions for Parallel Compuaions," IFIPS Congress 68, Augus 968, pp. B4-B0. 6. BURROUGHS B5500 Informaion Processing Sysems Re! ence Manual, Burroughs Corp., Deroi, Michigan, Sone, H. S., "A Pipeline Push-down Sack Compuer," Parallel Processor Sysems, Technologies and Applicaions, Chaper, pp Abrams, An APL Machine, Sanford Universiy, No. CS 7058, Tomasulo, R. :M., "An Efficien Algorihm for Exploiing :viuliple Arihmeic Unis," IBM Journal, January Flynn, M. J., "Very High Speed Compuing Sysems," Proceedings of he IEEE, Vol. 54, No., December Baille, G. G. and J. P. Schoellkopf, "Evaluaion of a Polish Form Expression on a FI-FO Queue," 975 SAGAMORE Compuer Conference on Parallel Processing, Augus 9-, 975, p Anceau, F., G. G. Baille and J. P. Schoellkopf, "Concepion Descendane des :Machines Informaiques, Applicaion i Une :Machine PASCAL," Rappor Conra IRIA-SESORI No , Ocober 0, 975.

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