Improving Memory Energy Using Access Pattern Classification

Transcription

1 Iproving Meory Energy Using Access Pattern Cassification Mahut Kandeir Microsystes Design Lab Pennsyvania State University University Par, PA Ugur Sezer ECE Departent University of Wisconsin Madison, WI Victor Deauz Microsystes Design Lab Pennsyvania State University University Par, PA ABSTRACT In this paper, we propose a data-driven strategy to optiize the eory energy consuption in a baned eory syste. Our copier-based strategy odies the origina execution order of oop iterations in array-doinated appications to increase the ength of the tie period(s) in which eory bans are ide (i.e., not accessed by any oop iteration). To achieve this, it rst cassies oop iterations according to their ban access patterns and then, with the hep of a poyhedra too, tries to bring the iterations with siiar ban access patterns cose together. Increasing the ide periods of eory bans brings two aor benets; rst, it aows us to pace ore eory bans into ow-power operating odes, and second, it enabes us to use a ore aggressive (i.e., ore energy saving) operating ode for a given ban. Our strategy has been evauated using seven array-doinated appications on both a cacheess syste and a syste with cache eory. Our resuts indicate that the strategy is very successfu in reducing the eory syste energy, and iproves the eory energy by as uch as 34% on the average. 1. Introduction and Motivation Energy consuption is an iportant consideration in ebedded syste design as reducing it heps axiize battery ife and reduce heat dissipation [9]. The increasing roe of energy consuption deands that the energy constraints shoud be taen into account eary in the syste design process, aong with other etrics such as perforance and for factor. Meory coponents of an ebedded syste are nown to consue a arge percentage of the overa syste energy [2, 6]. This is particuary true for systes designed to run iage and video processing appications in which arge uti-diensiona arrays of signas are anipuated using nested oops. These data-intensive appications ight put a great pressure on the eory subsyste and ae the eory perforance the priary factor shaping the runtie energy behavior of the syste. For a given eory syste, size (capacity) has a arge ipact on the energy consuption. Typicay, arge eory coponents (e.g., bans) consue ore energy per access than sa eory coponents, ainy due to onger bitines and wordines. Consequenty, epoying severa sa eory bans instead of a singe arge eory ban ight reduce the per access energy cost. Moreover, unused eory bans can be turned o to further increase energy savings. Turning o a eory ban in this context eans pacing it into a ow-power This wor is supported by the NSF Career Award operating ode (an energy-saving ode) in which the ban consues uch ess energy than it woud have if it reained in the fuy-active ode. Whie such a strategy can, in genera, iprove the eory energy consuption, it is possibe to obtain even arger savings by re-ordering data eeents and/or oop iteration accesses to tae better advantage of the uti-ban nature of the eory subsyste. This paper presents a copier-based strategy that odi- es the origina execution order of oop iterations in arraydoinated appications to increase the ength of the tie period(s) in which eory bans are ide (i.e., not accessed by any oop iteration). Such an optiization can bring two ain benets. First, as a resut of onger ide period, we can put a ban into a ow-power operating ode (whie, in the origina case, it ay not be possibe to do so). Second, even in the origina case it was possibe to use a ow-power ode, after the transforation we ight be abe to use a ore aggressive (i.e., ore energy-saving) operating ode, and thus obtain arger savings. Maor contributions of this paper can be suarized as foows: We present a data-centric access pattern cassication technique using which an optiizing copier can cassify oop iterations based on their eory ban access patterns. We discuss a transforation technique that odies the origina oop accesses to ipeent the cassication deterined by the copier. The transforation technique operates with both fuy-parae oops and oops with data dependences. Our experienta resuts indicate that our approach isvery successfu in optiizing the eory syste energy, and reduces the eory energy by asuch as 34% on the average. We proceed with a brief review of uti-ban eory syste and ow-power operating odes. Next, in Section 3, we present a oop iteration cassication strategy based on ban access patterns. We discuss an access pattern optiization strategy in Section 4. Preiinary experienta resuts are given in Section 5. Finay, we suarize the ain points of this wor in Section Energy Consuption in Meory Bans We can thin of a eory syste as a group of bans each of which can be controed individuay and be put in a owpower operating ode (energy-saving ode) when it is not in active use. Typicay, a nuber of ow-power operating odes

2 exist, and seection of a specic ode (for a given duration of ideness) invoves a tradeo between perforance and energy consuption. More specicay, each operating ode can be characterized using two paraeters: per cyce energy consuption and re-activation (re-synchronization) cost, the atter of which is the tie (in cyces) it taes to bring the ban bac to the active (fuy-operationa ode). Typicay, the ore aggressive the operating ode (in saving energy), the higher the re-activation cost. Therefore, the ow-power ode to be used shoud be chosen with care. An iportant paraeter in choosing the ost suitabe ode is the estiated duration of ideness. If the ideness duration is too short, it ay not be a good idea to pace a ban into an aggressive energy-saving ode. It is iportant to note that any array-doinated codes fro iage and video processing appications aow accurate estiation of ban ideness, thans to frequent occurrence of nested oop structures and copie-tie deterinabe appings of array eeents to eory bans. In Active (nora operation) ode, the eory ban is ready to iediatey service a eory request without any deay. In the ow-power odes (Standby, Nap, and PowerDown), energy consuption can be reduced by shutting-o increasingy arger parts of the ban. The aor parts of a eory ban are the coc generation circuitry, row address/contro decode circuitry, coun address/contro decode circuitry, contro registers and power ode contro circuitry, together with the eory (DRAM) core consisting of the precharge ogic, eory ces, and sense apiers. The operating odes used in this study are very siiar to those proposed in the Direct Rabus architecture for obie PCs [1]. Whie in a ow-power operating ode, a eory request (read or write) causes the ban to transition to the Active ode to service the request. Note that at a given tie dierent eory bans can be in dierent ow-power operating odes. One of the obectives of the ow-power operating ode anageent is seecting the ost suitabe operating ode for a given duration of ideness. The copier needs to detect ide periods for each ban and transition each ide ban into aow- power ode. A naive way ofdoing this is to seect an operating ode arbitrariy and eep the ban in this ode unti it needs to be accessed. Obviousy, such astrategy pays the re-activation (re-synchronization) cost which wewant toavoid. Instead, we use a ban pre-activation strategy that eiinates the potentia perforance penaty associated with epoying ow-power operating odes. Given that we have a enu of ow-power odes to transition into, the copier can evauate a possibe choices (ow-power odes) based on the operating ode energy, corresponding re-activation costs, and the ength of the ide period to seect the best choice. A discussion of copier-directed operating ode seection can be found in [3]. Note that axiizing the duration in which a eory ban is ide is benecia (fro an energy ange) as the ban in question can be paced into a ore energy-saving (ost aggressive) operating ode. This can be achieved using sart array ayout strategies that pace array eeents with siiar ife-patterns into the sae bans, or by re-ordering the coputation to isoate the data accessed (within a tie frae) into a sa nuber of bans. This paper taes the atter approach and presents an autoatic (copier-based) technique that rst cassies the iterations of a given oop according to their ban access characteristics, and then expoits this cassication to restructure the execution order of oop iterations. 3. Data-Centric Access Pattern Cassification In this section, we present our coputation ode and discuss the reationship between oop iterations and eory ban accesses. We assue that the copier is in fu contro of physica address anageent and there exists no virtua eory support. Consequenty, it is possibe to cacuate at copietie the physica eory ocation accessed for a given array reference and oop iteration. Each execution of oop body is represented using an iteration vector I =[i1;i 2; :::; i n] T, where n is the nuber of oops. The oop bounds can be described using a syste of ane inequaities of the for H I h, where H is a n atrix and h a -diensiona vector. Both H and h have constant entries and together they dene a poyhedron (iteration space) which contains a oop iterations [11]. The storage for of an array can aso be viewed as a (rectiinear) poyhedron. Each array eeent can be identied by its index J =[1; 2; :::; ] T ; where is the diensionaity of the array. Then, the poyhedron (index space) which denes the possibe indices for a given array can be written as S J s, where S and s area2 atrix and a 2-diensiona vector, respectivey. The subscript expressions of a given reference to an - diensiona array dene an ane access function (F ) fro iteration space to index space; that is, F ( I)=L I +. In this foruation, L is an n atrix (caed access or reference atrix [11]) and is a -diensiona constant vector (caed oset vector). Assuing a row-aor storage for for uti-diensiona arrays, the address of the array eeent U[ 1; 2; :::; ] can be coputed as addr(u[ 1; 2; :::; ]) = B u + 1(S 2S 3:::S )+ 2(S 3:::S )+::: +,1S + under the assuptions that the ower bound for a index positions (subscript positions) is 1 and that S p is the extent (the nuber of eeents) in the p th diension and that B u is the base address for array U. Without oss of generaity, et us assue the existence of K eory bans of equa sizes (size). Under this assuption, a ban apping function (BMF) G aps a given address into a eory ban and can be written as G(addr(U[ 1; 2; :::; ])) = addr(u[ 1; 2; :::; ])=size (where the sybo = denotes integer division). Consequenty, given an array eeent U[F ( I)] (accessed by iteration vector I), G(addr(U[F ( I)])) gives the ban that it is apped to. An iteration vector I is said to access ban i (1 i K) if at east one of the array eeents it touches is apped into ban i. In atheatica ters, we say ban(i; I)istrue if and ony if there exists at east one array U and an access function F ( I) in the nest such that G(addr(U[F ( I)])) = i; otherwise, we say that ban(i; I)isfase. Note that we can cassify the iterations of a given nested oop according to the (subset of the) bans they access (i.e., their ban access patterns). As an exape, et us focus on a scenario where a nested oop (possiby iperfecty nested) accesses arrays stored in a eory syste that consists of two bans. We can divide the iterations in this nest into three groups: fig 1 2 = f I ban(1; I)=true and ban(2; I)=faseg; fig12 = f I ban(1; I)=fase and ban(2; I)=trueg;

3 and, fig 12 = f I ban(1; I)=true and ban(2; I)=trueg: Inforay, the rst group (fig 1 2) corresponds to the iterations that access ony the rst ban whist the second group (fig12) corresponds to iterations that access ony the second ban. The third group (fig 12), on the other hand, consists of the iterations that access both the bans. Note that the origina iteration space, fig a,isfig 1 2 [fig12 [fig 12 (assuing that each oop iteration accesses at east one ban). A subscript notation such as 12 indicates that the iterations in the cass subscripted using this access ony the rst ban. Other subscript notations can be interpreted in a siiar fashion. In genera, assuing K eory bans, a given iteration space fig a can be divided into 2 K, 1 disoint groups (caed casses in the rest of this paper): fig 1 23::: K, fig123::: K,..., fig123:::k, fig 12 3::: K, fig 1 23::: K,..., fig 123::: K,..., fig 123:::K. This grouping is caed access pattern cassication (for a given, possiby iperfecty-nested, oop nest) and fors the basis of our optiization ethod presented in the next section. 4. Access Pattern Optiization In this section, we show how to optiize the eory accesses based on the cassication given above. The ain idea is to reorder the oop iterations such that a the iterations that beong to the sae cass are executed one after another (successivey). 4.1 Optiizing Dependence-Free Accesses Let us rst assue that the nested oop we want to optiize is fuy-parae (i.e., does not have any oop-carried data dependence). In this case, the iterations can be executed in any order. Consider, for exape, the foowing abstract nested oop assuing two bans: for each I 2fIga U 1, U 2,..., and U r in this oop are dierent arrays, and F u is the access function (access atrix pus oset vector) for U (it is straightforward to extend the idea to the case where there exist utipe references to the sae array). Let fig 1 2, fig12, and fig 12 be the casses dened as above. Then, we can transfor this oop nest into: for each I 2fIg1 2 for each I 2fIg 12 for each I 2fIg12 Each nested oop in this code executes the iterations fro a singe cass and such a division of the iteration space (into casses) is caed cassication. Note that it is not necessary that these three nested oops shoud be executed in this order. In fact, as copared to the origina code above, any execution order of these new nests (as ong as the iterations in a cass are executed successivey) wi usuay bring an iproveent. To see this ipact in a concrete exape, consider the foowing C- ie code that consists of a two-diensiona iperfecty-nested oop nest: for(t =1;t T ; t ++) f for(i =1;i 10; i ++) 1+ = W [30, i], 1; for( =1; 10; ++) 2+ = (U[]+V [])=2; for( =1; 10; ++) 3+ = V [ + 10] + 1; for( =1; 10; ++) 4+ = W []+V [16]; for( =1; 10; ++) 5+ = V [15, ]+1;... g assuing the foowing array apping (to a eory syste of two bans each hoding, for iustrative purposes, 45 array eeents): Ban 1:fU[a]1 a 30g + fv [a]1 a 15g; Ban 2:fV [a]16 a 30g + fw [a]1 a 30g: We aso assue here that the scaar variabes 1 through 5 are stored in registers. Figure 1(a) shows the ban access pattern for this code. We ceary identify ve dierent regions corresponding to ve inner oops and see that four opportunities exist for putting a eory ban into ow-power ode: one in the rst region (for ban 1), one in the second region (for ban 2), one in the fourth region (for ban 1), and one in the ast region (for ban 2). Let us now consider the foowing equivaent code where iterations of the nested oop are cassied according to their ban access patterns: for(t =1;t T ; t ++) f fig12 : for(i =1;i 10; i ++) 1+ = W [30, i], 1; for( =1; 10; ++) 4+ = W []+V [16] fig 12 : for( =1; 10; ++) 3+ = V [ + 10] + 1; fig 1 2 : for( =1; 10; ++) 2+ = (U[]+V [])=2; for( =1; 10; ++) 5+ = V [15, ]+1;... g The new ban access pattern is iustrated in Figure 1(b). We can abe this access pattern as [fig12; fig 12; fig 1 2]. Figures 1(c-d), on the other hand, depict two aternate (optiized) ban access patterns corresponding to [fig12; fig 1 2; fig 12] and [fig 1 2; fig12;fig 12], respectivey. It shoud be noted that iteration re-ordering custers the ide regions in both the bans. Note aso that these three optiized access patterns (shown in Figures 1(b), (c), and (d)) are ony representative and that there are other access patterns (for this exape) which custer the ide regions. Note that whie our approach to custering array accesses is siiar to the data-centric tiing technique proposed by Koduua et a. [8], there are three iportant dierences. First, our approach deas with physica addresses rather than virtua

4 i (a) Ban 1 Ban 2 Ban 1 Ban 2 i (c) C1 C2 C3 C4 C5 C6 C7 (a) C1 C3 C2 C4 C5 C6 C7 (b) i Ban 1 Ban 2 (b) i (d) Ban 1 Ban 2 Figure 1: Dierent access patterns to a eory syste of two bans. A `' indicates that the corresponding region is in use. addresses which aes expected runtie benets ore reaizabe. Second, instead of custering the accesses to array bocs, we custer accesses to eory bans. Third, our strategy custers oop iterations for ow power and is not concerned whether the iterations executed together (within a boc) wi have cache ocaity. 4.2 Optiizing Accesses with Dependences So far, we have assued that once the casses are deterined, they can be executed in any order. This assuption hods true as ong as there are no data dependences between iterations beonging to dierent casses. In this section, we address the probe when the oop nest to be optiized exhibits oop-carried dependences. A cass fig is said to be dependent on another cass fi 0 g if there exists two iterations, I 2fIg and I 0 2fI 0 g, such that there is a dependence fro I0 to I. We express this reationship saying dep(fi 0 g!fig) istrue (or, fig is cass-dependent on fi 0 g). Otherwise, we say that dep(fi 0 g! fig) is fase. Then, given a cassication, we can dene the cass-eve dependence graph, CLDG(V; E), as a directed-graph where each node v 2 V denotes a cass and each edge e 2 E indicates a data dependence fro one cass to another. That is, there is a directed edge fro fi 0 g to fig i dep(fi 0 g!fig) hods true. Note that cass dependences prevent the copier fro executing the casses in any order; instead, these dependences shoud be satised when seecting an execution order for casses. Let us assue that fig 1, fig 2, fig 3,..., fig 2 K,2, fig 2 K,1 is the cassication that we woud ie to optiize. As a rst step, we re-nuber each cass using a K-bit binary nuber as foows. Each ban is assigned a bit position (in the binary nuber) starting fro the rst ban. If a given cass accesses ban i, then the i th bit of the nuber associated with the cass is set to 1; otherwise, it is set to 0. For exape, in a four ban eory syste, if a cass accesses ony the rst and the fourth bans, it wi have `1001' as its nuber. We express this fact by writing this cass as fig The binary nuber associated with a cass (e.g., 1001 in this exape) is tered as the cass nuber. The probe of optiizing ban accesses can be dened as one of deterining a suitabe traversa order of the nodes in the CLDG. When a node is visited, a nested oop which enuerates ony the iterations in that cass is constructed and inserted in the code. A traversa order is vaid (or ega) ifit respects a the data dependences. Note that the intra-cass Figure 2: Two dierent cass-eve dependence graphs (CLDG). dependences are satised if we execute the iterations in a given cass in their origina order with respect to each other. Intercass dependences (cass-eve dependences), on the other hand, are satised by visiting a node in the CLDG ony after a the nodes that it is dependent on have been visited. Note that a given CLDG can have severa vaid traversas, and seecting the ost suitabe one is the priary factor that deterines the eory syste energy consuption (through ow-power ode seection). The foowing observation guides us in seecting a suitabe order: If fig a and fig b are the two casses that are successivey visited, the variation in ban access (activation) and ban ideness (deactivation) patterns in going fro fig a to fig b is a function of the Haing distance between a and b. For instance, if we traverse fig 1001 and fig 1010 one after another, the rst two bans preserve their states (between these traversas), whereas the reaining two bans change their states (ore specicay, the third ban is activated {corresponding to a 0 to 1 transition in the associated bit{ in going fro the rst cass to the second, and the fourth ban is deactivated {corresponding to a 1 to 0 transition). We cai that iniizing the Haing distance between the nubers of casses that are visited successivey is usefu in reducing the energy consuption. In other words, for a given eory ban, in going fro one cass to another, it is better to eep its state the sae (active or ide) as uch as possibe. This is because if the rst state is 0 and the second is aso 0, the ban wi have a ong ide period (which is good fro an energy viewpoint); and siiary, if the both states in question are 1, this eans that the active periods are custered together, so hopefuy, we wi aso have custered ide periods for the ban in question (ater when we visit the reaining casses). Note that then the probe of optiizing eory energy consuption becoes one of scheduing a group of nodes taing into account soe constraints (inter-cass dependences) to iniize (optiize) soe obective function (iniizing the Haing distance between the nubers of successivey visited casses). This probe is a constrained scheduing probe and is nown to be NP-hard [4]. Consequenty, we propose a greedy heuristic siiar to the ist scheduing agorith used in ow-eve (bacend) copiation to schedue the instructions in a basic boc. Inforay, in each step, our agorith seects a cass to schedue (visit) such that the Haing distance between the (cass) nuber of this cass and that of the ost recenty schedued one is iniu (aong a aternatives). After scheduing a cass, it deterines a casses that can be schedued in the next step, and evauates their Haing distance with respect to the schedued cass. We can evauate a given traversa order using two dierent etrics, both of which are directy reated to the ban energy consuptions. The rst etric is the su of the nuber of bit

5 C1 C2 C3 C4 C5 C6 C8 C9 C10 C7 C11 C1,C5 C2 C3 C4,C9 C6 C7 C8,C13 C10 C11 Operating Mode Energy Consuption (nj) Resynchronization Cost (cyces) Active Standby Nap PowerDown ,000 C12 C13 C14 C15 C12,C14,C15 (a) Figure 3: (a) A cycic CLDG. (b) Transfored version of (a). transitions between successive cass nubers (i.e, the cuuative Haing distance). Let a i, a represent the Haing distance between the cass nubers a i and a. Assuing a traversa order of fig a1, fig a2, fig a3,..., fig a2, the cuuative Haing distance is dened K,1 as 2 K,2 =1 a, a +1: Note that the scheduing technique discussed above tries to reduce this cuuative su. The second etric is the axiu nuber of consecutive 0s in the bit positions of each ban. Note that, in a K-ban eory syste, there ight be, at the ost, 2 (K,1) consecutive 0s. For an exape, et us consider the CLDG in Figure 2(a) for a three-ban syste, assuing that the cass nubers for C1, C2, C3, C4, C5, C6, and C7 are 100, 010, 011, 101, 111, 001, and 110, respectivey. An unoptiized schee can traverse the casses in the order C1, C2, C3, C4, C5, C6, and C7, eading to a cuuative Haing distance of eeven. We aso see that the axiu nuber of consecutive 0s (as a resut of this cass traversa pattern) in this case is 2, 1, and 2, for ban 1, ban 2, and ban 3, respectivey. However, if we use our approach, we obtain the traversa order of C1, C4, C5, C3, C6, C2, and C7. This new order resuts in a cuuative Haing distance of 7. Aso, it achieves the axiu possibe consecutive 0s for the rst ban (for the other bans, it achieves two consecutive 0s), a denite iproveent over the unoptiized traversa. As another exape, consider the CLDG given in Figure 2(b). Assuing the sae cass nubers used in Figure 2(a) and the sae eory ban architecture, our approach seects the order of C3, C5, C4, C6, C1, C7, and C2, achieving a cuuative Haing distance of seven (which is ony one ore fro the optia which is six) and obtaining the axiu nuber of consecutive 0s for two out of three bans. In soe cases, the CLDG ay contain cyces which prevent a ega traversa. We ca these types of graphs cycic CLDGs. In order to schedue the, we need to appy soe node transforations and eiinate the cyces. An exape cycic CLDG is iustrated in Figure 3(a) for a four-ban eory syste. We use two types of transforations to hande these graphs, naey, node erging and node spitting, detais of which are oitted due to ac of space. Figure 3(b) shows the transfored version of Figure 3(a) using node erging. 5. Experienta Resuts We used the Oega ibrary [7] to transfor the progras' access patterns into ban-ecient ones. The Oega ibrary is a poyhedra too that aows enueration of bounded poyhedrons and heps us to deterine the iteration casses and create the oops that enuerate the. (b) Figure 4: Energy consuptions and resynchronizations costs for our operating odes. During transitions fro a ow-power ode to the active ode, a fu active ode energy is assued to be spent. Benchar Input Size (MB) Base1 (J) Base2 (J) phods ,492 36,007 seq ,525 39,237 ft ,078 43,521 tocatv ,221 30,012 swi ,660 33,964 efux ,719 71,900 u ,868 60,384 Figure 5: Benchar codes used in the experients and their iportant characteristics. Figure 4 shows the energy consuptions (per access) and resynchronization costs for the operating odes used in our experients. We used seven array-doinated codes to easure the benets of our approach. The iportant characteristics of these codes are given in Figure 5. phods and seq are two dierent otion estiation codes; ft is a digita tering routine; tocatv and swi are two array-based benchars fro the Spec suite; efux is an array-based benchar fro the Perfect Cub suite; and u is an LU decoposition code. Base1 and Base2 refers to base (origina) eory syste energy consuptions (data accesses ony) for a cacheess syste and a syste with a 16KB, 2-way set-associative cache with a ine size of 32 bytes, respectivey. Note that the energy gures in the Base2 coun incude the energy expended in cache as we as ain eory. In both the cases, the defaut eory con- guration consists of eight 8MB eory bans (denoted 8 8MB). The reaining gures given in this section are percentage iproveents (reductions) over these base gures. In a experients, we epoyed a powerfu bac-end copier which perfors severa iportant optiizations such as goba register aocation and instruction scheduing. The use of node erging was necessary in ony one case (efux) to eiinate a cyce in the CLDG; we did not use node erging to reduce the oop overhead. The increase in execution ties due to our optiizations was aways ess than 1%. Aso, there was no opportunity to use node spitting. The second coun in Figure 6 (Iprv1) gives the percentage reductions over Base1 (in a cacheess syste) when our approach is used. We see that our strategy based on the iteration cass concept brings a 26.3% iproveent on the average. The third coun in the sae gure reports the energy iproveents (again, over Base1) when cassica cache ocaity optiizations are used. 1 The ocaity optiizations used incude inear oop transforations and iteration space tiing 1 Note that in this case, these ocaity optiizations shoud noray not be appied as the syste does not contain cache. Our purpose here is to see whether ocaity-oriented optiizations are as successfu as our strategy in optiizing o-chip eory energy.

6 Benchar Iprv1 Iprv2 Iprv3 Iprv4 Iprv5 phods seq ft tocatv swi efux u Figure 6: Percentage energy iproveents. Figure 7: Ipact of eory ban conguration. (bocing) [11]. We experiented with dierent tie sizes and (for each benchar) seected the one which gave the best resut. In coparing the second and third couns of Figure 6, we observe that our approach, in genera, perfors uch better than a pure ocaity-oriented approach. The fourth coun of the gure (Iprv3) gives the percentage iproveents due to our approach over Base2 (with cache). We see that the average energy iproveent is about 23.4%. Using cache ocaity optiizations instead brings an iproveent of 9.4% (see the fth coun). The ast coun (Iprv5), on the other hand, shows the percentage energy iproveents if our current strategy is sighty odied to tae cache considerations into account (and if doing so does not conict with our iteration cass based optiizations). Note that this ast strategy has not been fuy ipeented yet and obtained here through hand optiizations. The resuts show that by incorporating ocaity based techniques into our fraewor, we can achieve (on average) a 27.4% iproveent (over Base2). This ast resut otivates us to integrate our strategy with ocaity optiizations in the future. So far, we have used ony a singe eory conguration: 8 8MB. Figure 7 gives noraized energy consuptions (with respect to Base1) for two representative codes, u and tocatv, when dierent eory congurations are used (in a cacheess syste). We observe fro this gure that increasing the nuber of bans (by eeping the tota eory size constant) generay increases energy savings (as it gives ore contro to the copier in pacing arger sections of the address space into ow-power odes). In any codes, however, beyond a certain point (depending on the access pattern), a ner-granuar eory syste does not bring ore benets. This happens for exape with the u code beyond sixteen bans (see Figure 7). is to increase the duration of ide periods of eory bans, thereby saving energy using ow-power operating odes ore aggressivey. Our experienta evauation indicates that arge energy savings are possibe using this technique. 7. REFERENCES [1] 128/144-MBit Direct RDRAM Data Sheet, Rabus Inc., May [2] F. Catthoor, S. Wuytac, E. D. Greef, F. Baasa, L. Nachtergaee, and A. Vandecappee. Custo Meory Manageent Methodoogy { Exporation of Meory Organization for Ebedded Mutiedia Syste Design. Kuwer Acadeic Pubishers, [3] V. Deauz, M. Kandeir, N. Viayrishnan, A. Sivasubraania, and M. J. Irwin. DRAM energy anageent using software and hardware directed power ode contro. In Proc. the 7th Internationa Conference on High Perforance Coputer Architecture, Monterrey, Mexico, January [4] G. De Michei. Synthesis and Optiization of Digita Circuits. McGraw-Hi, Inc., [5] C. Eis. The case for higher eve power anageent. In Proceedings of HotOS, March [6] M. Kandeir, N. Viayrishnan, M. J. Irwin, and W. Ye. Inuence of copier optiizations on syste power. In Proc. the 37th Design Autoation Conference, Los Angees, Caifornia USA, June 5-9, [7] W. Key, V. Masov, W. Pugh, E. Rosser, T. Shpeisan, and David Wonnacott. The Oega Library interface guide. Technica Report CS-TR-3445, CS Dept., University of Maryand, Coege Par, MD, March [8] I. Koduua, N. Ahed, and K. Pingai. Data-centric uti-eve bocing. In Proc. SIGPLAN Conf. Prograing Language Design and Ipeentation, June [9] J. R. Lorch and A. J. Sith. Software strategies for portabe coputer energy anageent. IEEE Persona Counications, pp. 60{73, June [10] V. Tiwari, S. Mai, A. Wofe, and T. C. Lee. Instruction eve power anaysis and optiization of software, Journa of VLSI Signa Processing Systes, Vo. 13, No. 2, August [11] M. Wofe. High Perforance Copiers for Parae Coputing, Addison-Wesey Pubishing Copany, Concusions In this paper, we have presented a copier-oriented eory energy optiization technique based on a concept caed (oop) iteration cassication. The obective of this technique