During the recent years, the market of mid/low-end portable systems such as PDAs or mobile digital phones have experimented a revolution in both selling volume and features as handheld devices incorporate Multimedia applications. This fact brings to an increase in the computational demands of the devices, while still having the limitation of power (and energy) consumption. 
Instruction memoization is a promising technique to help alleviate the problem of power consumption of expensive functional units such as the floating-point one. Unfortunately, this technique could be energy-inefficient for low-end systems due to the additional power consumption of the relatively big tables required. 
In this paper we present a novel way of understanding multimedia floating point operations based on the fuzzy computation paradigm: losses in the computation precision may exchange performance for negligible errors in the output. Exploiting the implicit characteristics of media FP computation, we propose a new technique called fuzzy memoization. Fuzzy memoization expands the capabilities of classic memoization by attaching entries with similar inputs to the same output. We present a case of study for a SH4 like processor and report good performance and power-delay improvements with feasible hardware requirements.Peer ReviewedPostprint (published version

Corbal San Adrián, Jesús

Salamí San Juan, Esther

Valero Cortés, Mateo

Álvarez Martínez, Carlos

IEEE Computer Architecture Letters

English

UPCommons. Portal del coneixement obert de la UPC

Initial Results on Fuzzy Floating PointComputation for Multimedia ProcessorsCarlosAlvarez Jesus Corbal Esther Salam Mateo ValeroComputer Architecture DepartmentUniversitat Politecnica de Catalunya UPC Barcelona SpainEmail fcalvarezjcorbalesalamimateog	acupcesAbstract During the recent years the market of midlowend portable systems such as PDAs or mobile digital phoneshave experimented a revolution in both selling volume andfeatures as handheld devices incorporate Multimedia applications This fact brings to an increase in the computationaldemands of the devices while still having the limitation ofpower and energy consumptionInstruction memoization is a promising technique to helpalleviate the problem of power consumption of expensivefunctional units such as the oatingpoint one Unfortunately this technique could be energyine	cient for lowendsystems due to the additional power consumption of the relatively big tables requiredIn this paper we present a novel way of understandingmultimedia oating point operations based on the fuzzycomputation paradigm losses in the computation precision may exchange performance for negligible errors in theoutput Exploiting the implicit characteristics of media FPcomputation we propose a new technique called fuzzy memoization Fuzzy memoization expands the capabilities ofclassic memoization by attaching entries with similar inputsto the same output We present a case of study for a SHlike processor and report good performance and powerdelayimprovements with feasible hardware requirementsKeywords  Fuzzy Computation Multimedia FloatingPoint MemoizationI IntroductionARCHITECTURAL techniques targeted at increasingperformance for lowend systems are nowadays becoming an important eld of research However the potential of the adoption of the same techniques introducedin generalpurpose processors to increase performance inDSP systems is still a matter of controversy Most authorsidentify speculation and dynamic execution as unsuitablefor portable systems due to the power and energy ineciencies of such techniques Therefore many designers ofembedded processors 	 	 	 have opted for other techniques that do not jeopardize the power and energy consumption of the system as for instance the inclusion ofsubword level SIMD instructionsThis paper deals with the problem of oatingpoint computation for multimedia processors targeted at D imagingand D applications such as the Hitachi SH 	 Trendsin multimedia applications development indicate that media codes are migrating from xedpoint to oatingpointcomputation to adapt to more complex protocol and mediadata types Floating point units are expensive in terms ofboth area and power and their high latencies are usuallyManuscript submitted  Dec  Manuscript accepted Jan  Final manuscript received  Jan dicult to hide using inorder processors 	A very promising energyecient technique to improveperformance for oatingpoint units is instruction memoization 	 It allows to skip the execution of long latencyinstructions such as multiplication and division by tryingto reuse previously invoked instances of the same operationwith the same source operands via a lookup table LUTThe major drawback of the technique is that large tablesare usually required for leveraging signicant reuse ratesand so the energy consumption of such tables may osetpotential savingsIn this paper we present a novel way of applying thefuzzy computation paradigm to oatingpoint instructionmemoization With fuzzy computation more eective reusecan be obtained by exploiting the fact that imprecision incalculation can exchange redundancy for negligible errorsin the output of multimedia applications 	 We present aninitial evaluation of the performance and power benets ofthis fuzzy memoization technique in a SHlike processorInitial results show a great potential for high energy andpower savings Given the properties of the fuzzy computation we discuss the tradeos between performance andquality of the media outputsII Rationale for fuzzy floatingpointmemoizationA Tolerance in media applicationsOur focus is on improving the hit rate of memoizationtables by exploiting an intrinsic characteristic of multimedia algorithms tolerance By tolerance we understand therobustness of media data types such as image pixels oraudio samples to losses in the precision of computationPrecision of operations can be traded for a higher valuelocality in oating point instructionsIn sharp contrast with any other kind of applicationsmultimedia programs exhibit tolerance to losses in the accuracy of their outputs Any given output of a D videoimage or audio application may present dierences that arenot visually or audibly perceptible In other words output errors may be ltered by the human senses in sucha way that no dierence in the subjective quality of theresult is observedFuzzy computation is a novel way of performing certaincomputations that takes advantage of this precise property Precision in computation is exchanged for time andpower savings If we look closely at typical compressionIEEE Computer Architecture  Letters Vol. 1, 2002Posted to IEEE & CSDL on 1/27/2006DOI 10.1109/L-CA.2002.6      1556-6056/02/$20.00 © 2002        Published by the IEEE Computer SocietyAccuracySizeSpeedBinarySystemsCompressionProtocolsFuzzyComputationFig  Basis for the Fuzzy Computation Paradigmalgorithms such as JPEG MPEG or MP we observethat these applications in fact exchange quality for output compression ratios Fuzzy computation extends thistradeo with a third dimension speed as gure  illustratesTwo reasons explain why fuzzy computation works We have high redundancy in the data representationFloating point data represents a much broader range ofnumbers than what is really required for the capacity ofhuman senses Fuzzy computation takes advantage of thefact that most of the error introduced is overridden by thenal conversion of data to bounded integer representations In media processing the nal destination are the human senses and human senses have not unlimited capabilities For example the human eye can distinguish millionsof dierent colors but only some thousands at the sametime Moreover the information received by human sensesis processed by the brain which has a natural tendency toadjust the perception For instance we detect very welledges in the images but detect poorly dierent color graduations in a at surface which is a property typically exploited by fuzzy computationB Why oating point fuzzy memoizationThe oatingpoint units are not a very critical factor ofperformance and power consumption for aggressive processors Floatingpoint latency is hidden thanks to outoforder execution and the energy consumption is not a verysignicant part of the whole processor Nevertheless inlowend systems execution is typically inorder and therefore the inclusion of oatingpoint units has a time andpower consumption impact that is worth being addressedwith special techniques such as memoizationIn this paper we want to apply the concept of fuzzy computation to oatingpoint instruction memoization TheHitachi SH 	 is a way RISC processor specially targeted at homevideogame systems and handheld devicesThe oatingpoint unit is the most critical part of the design in terms of power and area Our objective is to evaluate the eect of tolerance over execution time power andoutput quality when applied to a basic memoization unittargeted at oatingpoint multiplication and divisionLUTFPALUMUXhit/missop 1op 2ResultFig  Hardware conguration of a sequential LUTIII Fuzzy memoization implementationIn classical memoization two instances of the same operation are only reused when the two pairs of input operandsare identical Applying the concept of tolerance we canconsider that two instances of the same operation can bereused not only when their pairs of input operands areequal but also when they are close enough As an example if two multiplications have as input values    and     the result of the two will be that is the result of the rst multiplicationThis implementation of fuzzy computation has the mainadvantage of being very simple because tolerance is performed by just cutting o the N less signicant bits ofevery operand before being used to access the table Inaddition the table is smaller than in classical memoizationbecause it does not need to keep the   N bits droppedWe use this number of bits dropped N to dene the levelof tolerance Look up table works as in classical memoization so if there is a hit in the table the result  bits isforwarded If there is a miss the pair of input operands ispassed to the oatingpoint unit to do the complete operation and update the reuse tableAs we are focusing on the low power domain the tablehas been implemented sequentially with the oatingpointunit Therefore a miss in the table will increase the operation latency by one but a hit will make the FPALU tonot consume any power gure  As table size is criticalonly the two most demanding operations multiplicationand division were memoized in a single shared table Inaddition trivial operations 	 were treated apart so theydo not pollute the reuse tableA Downsides and limits of fuzzy computing for FPThe main drawback of fuzzy computation is as it hasbeen already said the introduction of an error in the output data Although there are a lot of computation environments that cannot aord such kind of losses the specialcharacteristics of media applications make this error notonly aordable but negligible Media outputs are targetedto human senses so their quality is subjective and cannotbe easily measured Great errors that spread out over allthe signal like an increment in the luminosity in entireIEEE Computer Architecture  Letters Vol. 1, 2002Original Image N   bits Good Quality N   bits Regular Quality N   bits Bad Quality N   bitsFig  Dierent outputs of the algorithm when dierent tolerance levels are usedTABLE IPower Breakdowns of the modelHardware Structure Percentage of total PowerCaches  Registers  Instruction Queues  Integer Execution Unit  Floating Point Unit  Total Clock Power image are hardly perceived however concentrated littleerrors like a red dot in a white wall are easily perceivedThis behavior makes it dicult to set an objective errormeasure The most common measure used in the signalprocessing environment is the Signal Noise Ratio The SNRis dened asSNR  logPSlogPNwherePSrowXcolXxPNrowXcolXx yand x is a pixel of the original image and y is the samepixel of the image with tolerance The SNR is used to makean objective measurement of the quality of the output dataB Implementation DetailsTo measure the eectiveness of our method we havehacked the SimpleScalar 	 and Wattch 	 simulators toincorporate the Fuzzy LUT at the IEEE double precisionmultiplication unit Our model was parameterized so thatdierent tolerance levels dierent values ofN can be usedThe measures has been applied to the Epic compression algorithm 	The Simplescalar and Wattch tool sets have been congured to model a SH like processor The Wattch powerresults were scaled down to emulate the ones of a SHTABLE IIConfiguration of model processorProcessor CoreIssue In orderPhysical Registers Fetch width per cycle Decode width per cycle Issue width per cycle Commit width per cycle FP units Integer units Branch prediction Not TakenFloating Point Latencies 	issue latenciesAddition  	Multiplication  	Division  	Memory HierarchyL Dcache Size  KL Dcache Assoc wayL Icache Size  KL Icache Assoc wayDTLB Size 	full assoc ITLB Size 	full assoc L Cache noneProcess SpecicationsFeature Size umVdd  VMHz  micron technology at  MHz and  Voltage supply The power consumed by the LUTs has been measuredusing Cacti models and taking into account LUT delayedupdate in a miss due to operation latencies Table I showsthe power breakdowns of the SH like processor modeledand table II shows its hardware characteristics The totalpower obtained for the model is a little bit more than W at full power which is something more than the powerdeclared for an SH Nevertheless we are only interestedin percentage of reduction so the total power is not significantC Final ResultsFigure  presents the total power consumption and overall execution time savings obtained with a  KB LUT table for dierent tolerance levels For those cases in whichsome error is introduced the SNR of the output image isalso included Two dierent areas can be distinguishedIn the rst one up to  bits of tolerance the toleranceintroduced has nearly no eect in the output image Thisarea is where fuzzy computing takes benet of the redunIEEE Computer Architecture  Letters Vol. 1, 20020 38 39 40 41 42 43 44 45 46 47 Tolerance (N)0102030% SavingsSNRpowertime61.1 dB56.3 dB51.6 dB48.1 dB44.2 dB39.8 dB35.5 dB31.8 dBFig  Total power  overall execution time savings with  KBLUT0 38 39 40 41 42 43 44 45 46 47 Tolerance (N)05101520% Savings in energy1 KB LUT10 KB LUT20 KB LUTFig  Energy savings of dierent size tablesdancy in the representation of the image If we take outthe redundancy we can make the LUT table thinner because we do not need to store the redundant bits howeverthe hit rate does not increase because bits taken o are notsignicant and so dierent input values remain dierentIn the second area is where we are in fact tolerating as thesame result is assigned to dierent but close enough inputvalues In this case both power and time are saved at thecost of introducing some error but as gure  shows errorsare negligible until tolerance levels of  bits Furthermorewhen using low quality output devices such as handheldscreens  or even  tolerated bits could be acceptableOn the other hand it can be seen that classical memoization N   only gets little savings in power but spendsmore time than the original conguration This behavioris due to the low hit rate achieved and the sequential conguration so a miss in the LUT means one more cycle peroperation In order to avoid this additional cycle the LUTcould be placed in parallel with the FPALU However inthat case power savings would decreaseIn gure  we show the energy savings for dierent tablesizes This table shows that with very cheap tables lessthan  KB  energy savings can be achieved while withmore aggressive but still feasible tables  KB savings canraise up to a IV SummaryIn this paper we have evaluated the impact of the memoization technique for oating point operations in multimedia for the lowend domain We have shown that althoughmemoization could save some energy the size of the tablesrequired to achieve these results makes this technique notworth in a low power environmentWe have presented and developed the novel idea of fuzzycomputation that could be used in multimedia algorithmsto increase the hit rate of memoization tables by doingfuzzy memoization This new technique has been implemented and evaluated in a lowend model processor and ithas been shown that reuse is signicantly improved Withrealistic table sizes considerable power and time savingsare achieved up to a  in energy and a  in theenergydelay productWe believe that fuzzy computation opens a newparadigm for multimedia applications that will deserve future work Currently we are evaluating other congurations such as memoizing additions or memoizing completeFP functions which we call Fuzzy Block Reuse Also morebenchmarks should be includedAcknowledgmentsThis work has been supported by Direccio General deRecerca de la Generalitat under grant FI bythe Ministry of Education of Spain under contract CICYTTICC and by the CEPBAReferences TI TMSCXX family Tech RephttpwwwticomscdocsproductsdsptmschtmlTexas Instruments  Philips Semiconductors Trimedia tm vol httpwwwussemiconductorscomtrimedia  Analog Devices Introducing tigersharc Whitepaper volhttpwwwanalogcomnewadshtmlSHARC F Arakawa O Nishii K Uchiyama and N Nakagawa Shrisc multimedia processor MarchApril  Stuart Franklin Oberman Design issues in high performanceoating point arithmetic units PhD thesis Stanford University November  D Citron D Feitelson and L Rudolph Accelerating multimedia processing by implementing memoing in multiplicationand division units ASPLOS VIII  Carlos Alvarez Jesus Corbal Esther Salami and Mateo ValeroOn the potential of tolerance reuse for multimedia applications International Conference on Supercomputing ICSSorrento Italy  Stephen E Richardson Exploiting trivial and redundant computation th IEEE Symposium on Computer Arithmetic Doug Burger and Todd M Austin The simplescalar toolset version  WisconsinMadison CS Dep technical Report	  David Brooks Vivek Tiwari and Margaret Martonosi WattchA framework for architecturallevel power analysis and optimizations International Symposium on Computer ArchitectureISCA Vancouver  C Lee M Potkonjak and WH MagioneSmith MediabenchA tool for evaluating and synthesizing multimedia and communication systems MICRO  IEEE Computer Architecture  Letters Vol. 1, 2002

Initial results on fuzzy floating point computation for multimedia processors

UPCommons (Universitat Politècnica de Catalunya)

Initial Results on Fuzzy Floating PointComputation for Multimedia ProcessorsCarlos Alvarez Jesus Corbal Esther Salam Mateo ValeroComputer Architecture DepartmentUniversitat Politecnica de Catalunya UPC Barcelona SpainEmail fcalvarezjcorbalesalamimateog	acupcesAbstract During the recent years the market of midlowend portable systems such as PDAs or mobile digital phoneshave experimented a revolution in both selling volume andfeatures as handheld devices incorporate Multimedia applications This fact brings to an increase in the computationaldemands of the devices while still having the limitation ofpower and energy consumptionInstruction memoization is a promising technique to helpalleviate the problem of power consumption of expensivefunctional units such as the oatingpoint one Unfortunately this technique could be energyine	cient for lowendsystems due to the additional power consumption of the relatively big tables requiredIn this paper we present a novel way of understandingmultimedia oating point operations based on the fuzzycomputation paradigm losses in the computation precision may exchange performance for negligible errors in theoutput Exploiting the implicit characteristics of media FPcomputation we propose a new technique called fuzzy memoization Fuzzy memoization expands the capabilities ofclassic memoization by attaching entries with similar inputsto the same output We present a case of study for a SHlike processor and report good performance and powerdelayimprovements with feasible hardware requirementsKeywords  Fuzzy Computation Multimedia FloatingPoint MemoizationI IntroductionARCHITECTURAL techniques targeted at increasingperformance for lowend systems are nowadays becoming an important eld of research However the potential of the adoption of the same techniques introducedin generalpurpose processors to increase performance inDSP systems is still a matter of controversy Most authorsidentify speculation and dynamic execution as unsuitablefor portable systems due to the power and energy ineciencies of such techniques Therefore many designers ofembedded processors 	 	 	 have opted for other techniques that do not jeopardize the power and energy consumption of the system as for instance the inclusion ofsubword level SIMD instructionsThis paper deals with the problem of oatingpoint computation for multimedia processors targeted at D imagingand D applications such as the Hitachi SH 	 Trendsin multimedia applications development indicate that media codes are migrating from xedpoint to oatingpointcomputation to adapt to more complex protocol and mediadata types Floating point units are expensive in terms ofboth area and power and their high latencies are usuallyManuscript submitted  Dec  Manuscript accepted Jan  Final manuscript received  Jan dicult to hide using inorder processors 	A very promising energyecient technique to improveperformance for oatingpoint units is instruction memoization 	 It allows to skip the execution of long latencyinstructions such as multiplication and division by tryingto reuse previously invoked instances of the same operationwith the same source operands via a lookup table LUTThe major drawback of the technique is that large tablesare usually required for leveraging signicant reuse ratesand so the energy consumption of such tables may osetpotential savingsIn this paper we present a novel way of applying thefuzzy computation paradigm to oatingpoint instructionmemoization With fuzzy computation more eective reusecan be obtained by exploiting the fact that imprecision incalculation can exchange redundancy for negligible errorsin the output of multimedia applications 	 We present aninitial evaluation of the performance and power benets ofthis fuzzy memoization technique in a SHlike processorInitial results show a great potential for high energy andpower savings Given the properties of the fuzzy computation we discuss the tradeos between performance andquality of the media outputsII Rationale for fuzzy floatingpointmemoizationA Tolerance in media applicationsOur focus is on improving the hit rate of memoizationtables by exploiting an intrinsic characteristic of multimedia algorithms tolerance By tolerance we understand therobustness of media data types such as image pixels oraudio samples to losses in the precision of computationPrecision of operations can be traded for a higher valuelocality in oating point instructionsIn sharp contrast with any other kind of applicationsmultimedia programs exhibit tolerance to losses in the accuracy of their outputs Any given output of a D videoimage or audio application may present dierences that arenot visually or audibly perceptible In other words output errors may be ltered by the human senses in sucha way that no dierence in the subjective quality of theresult is observedFuzzy computation is a novel way of performing certaincomputations that takes advantage of this precise property Precision in computation is exchanged for time andpower savings If we look closely at typical compressionIEEE Computer Architecture  Letters Vol. 1, 2002Posted to IEEE & CSDL on 1/27/2006DOI 10.1109/L-CA.2002.6      1556-6056/02/$20.00 © 2002        Published by the IEEE Computer SocietyAccuracySizeSpeedBinarySystemsCompressionProtocolsFuzzyComputationFig  Basis for the Fuzzy Computation Paradigmalgorithms such as JPEG MPEG or MP we observethat these applications in fact exchange quality for output compression ratios Fuzzy computation extends thistradeo with a third dimension speed as gure  illustratesTwo reasons explain why fuzzy computation works We have high redundancy in the data representationFloating point data represents a much broader range ofnumbers than what is really required for the capacity ofhuman senses Fuzzy computation takes advantage of thefact that most of the error introduced is overridden by thenal conversion of data to bounded integer representations In media processing the nal destination are the human senses and human senses have not unlimited capabilities For example the human eye can distinguish millionsof dierent colors but only some thousands at the sametime Moreover the information received by human sensesis processed by the brain which has a natural tendency toadjust the perception For instance we detect very welledges in the images but detect poorly dierent color graduations in a at surface which is a property typically exploited by fuzzy computationB Why oating point fuzzy memoizationThe oatingpoint units are not a very critical factor ofperformance and power consumption for aggressive processors Floatingpoint latency is hidden thanks to outoforder execution and the energy consumption is not a verysignicant part of the whole processor Nevertheless inlowend systems execution is typically inorder and therefore the inclusion of oatingpoint units has a time andpower consumption impact that is worth being addressedwith special techniques such as memoizationIn this paper we want to apply the concept of fuzzy computation to oatingpoint instruction memoization TheHitachi SH 	 is a way RISC processor specially targeted at homevideogame systems and handheld devicesThe oatingpoint unit is the most critical part of the design in terms of power and area Our objective is to evaluate the eect of tolerance over execution time power andoutput quality when applied to a basic memoization unittargeted at oatingpoint multiplication and divisionLUTFPALUMUXhit/missop 1op 2ResultFig  Hardware conguration of a sequential LUTIII Fuzzy memoization implementationIn classical memoization two instances of the same operation are only reused when the two pairs of input operandsare identical Applying the concept of tolerance we canconsider that two instances of the same operation can bereused not only when their pairs of input operands areequal but also when they are close enough As an example if two multiplications have as input values    and     the result of the two will be that is the result of the rst multiplicationThis implementation of fuzzy computation has the mainadvantage of being very simple because tolerance is performed by just cutting o the N less signicant bits ofevery operand before being used to access the table Inaddition the table is smaller than in classical memoizationbecause it does not need to keep the   N bits droppedWe use this number of bits dropped N to dene the levelof tolerance Look up table works as in classical memoization so if there is a hit in the table the result  bits isforwarded If there is a miss the pair of input operands ispassed to the oatingpoint unit to do the complete operation and update the reuse tableAs we are focusing on the low power domain the tablehas been implemented sequentially with the oatingpointunit Therefore a miss in the table will increase the operation latency by one but a hit will make the FPALU tonot consume any power gure  As table size is criticalonly the two most demanding operations multiplicationand division were memoized in a single shared table Inaddition trivial operations 	 were treated apart so theydo not pollute the reuse tableA Downsides and limits of fuzzy computing for FPThe main drawback of fuzzy computation is as it hasbeen already said the introduction of an error in the output data Although there are a lot of computation environments that cannot aord such kind of losses the specialcharacteristics of media applications make this error notonly aordable but negligible Media outputs are targetedto human senses so their quality is subjective and cannotbe easily measured Great errors that spread out over allthe signal like an increment in the luminosity in entireIEEE Computer Architecture  Letters Vol. 1, 2002Original Image N   bits Good Quality N   bits Regular Quality N   bits Bad Quality N   bitsFig  Dierent outputs of the algorithm when dierent tolerance levels are usedTABLE IPower Breakdowns of the modelHardware Structure Percentage of total PowerCaches  Registers  Instruction Queues  Integer Execution Unit  Floating Point Unit  Total Clock Power image are hardly perceived however concentrated littleerrors like a red dot in a white wall are easily perceivedThis behavior makes it dicult to set an objective errormeasure The most common measure used in the signalprocessing environment is the Signal Noise Ratio The SNRis dened asSNR  logPSlogPNwherePS rowXcolXx PN rowXcolXx y and x is a pixel of the original image and y is the samepixel of the image with tolerance The SNR is used to makean objective measurement of the quality of the output dataB Implementation DetailsTo measure the eectiveness of our method we havehacked the SimpleScalar 	 and Wattch 	 simulators toincorporate the Fuzzy LUT at the IEEE double precisionmultiplication unit Our model was parameterized so thatdierent tolerance levels dierent values ofN can be usedThe measures has been applied to the Epic compression algorithm 	The Simplescalar and Wattch tool sets have been congured to model a SH like processor The Wattch powerresults were scaled down to emulate the ones of a SHTABLE IIConfiguration of model processorProcessor CoreIssue In orderPhysical Registers Fetch width per cycle Decode width per cycle Issue width per cycle Commit width per cycle FP units Integer units Branch prediction Not TakenFloating Point Latencies 	issue latenciesAddition  	Multiplication  	Division  	Memory HierarchyL Dcache Size  KL Dcache Assoc wayL Icache Size  KL Icache Assoc wayDTLB Size 	full assoc ITLB Size 	full assoc L Cache noneProcess SpecicationsFeature Size umVdd  VMHz  micron technology at  MHz and  Voltage supply The power consumed by the LUTs has been measuredusing Cacti models and taking into account LUT delayedupdate in a miss due to operation latencies Table I showsthe power breakdowns of the SH like processor modeledand table II shows its hardware characteristics The totalpower obtained for the model is a little bit more than W at full power which is something more than the powerdeclared for an SH Nevertheless we are only interestedin percentage of reduction so the total power is not significantC Final ResultsFigure  presents the total power consumption and overall execution time savings obtained with a  KB LUT table for dierent tolerance levels For those cases in whichsome error is introduced the SNR of the output image isalso included Two dierent areas can be distinguishedIn the rst one up to  bits of tolerance the toleranceintroduced has nearly no eect in the output image Thisarea is where fuzzy computing takes benet of the redunIEEE Computer Architecture  Letters Vol. 1, 20020 38 39 40 41 42 43 44 45 46 47 Tolerance (N)0102030% SavingsSNRpowertime61.1 dB56.3 dB51.6 dB48.1 dB44.2 dB39.8 dB35.5 dB31.8 dBFig  Total power  overall execution time savings with  KBLUT0 38 39 40 41 42 43 44 45 46 47 Tolerance (N)05101520% Savings in energy1 KB LUT10 KB LUT20 KB LUTFig  Energy savings of dierent size tablesdancy in the representation of the image If we take outthe redundancy we can make the LUT table thinner because we do not need to store the redundant bits howeverthe hit rate does not increase because bits taken o are notsignicant and so dierent input values remain dierentIn the second area is where we are in fact tolerating as thesame result is assigned to dierent but close enough inputvalues In this case both power and time are saved at thecost of introducing some error but as gure  shows errorsare negligible until tolerance levels of  bits Furthermorewhen using low quality output devices such as handheldscreens  or even  tolerated bits could be acceptableOn the other hand it can be seen that classical memoization N   only gets little savings in power but spendsmore time than the original conguration This behavioris due to the low hit rate achieved and the sequential conguration so a miss in the LUT means one more cycle peroperation In order to avoid this additional cycle the LUTcould be placed in parallel with the FPALU However inthat case power savings would decreaseIn gure  we show the energy savings for dierent tablesizes This table shows that with very cheap tables lessthan  KB  energy savings can be achieved while withmore aggressive but still feasible tables  KB savings canraise up to a IV SummaryIn this paper we have evaluated the impact of the memoization technique for oating point operations in multimedia for the lowend domain We have shown that althoughmemoization could save some energy the size of the tablesrequired to achieve these results makes this technique notworth in a low power environmentWe have presented and developed the novel idea of fuzzycomputation that could be used in multimedia algorithmsto increase the hit rate of memoization tables by doingfuzzy memoization This new technique has been implemented and evaluated in a lowend model processor and ithas been shown that reuse is signicantly improved Withrealistic table sizes considerable power and time savingsare achieved up to a  in energy and a  in theenergydelay productWe believe that fuzzy computation opens a newparadigm for multimedia applications that will deserve future work Currently we are evaluating other congurations such as memoizing additions or memoizing completeFP functions which we call Fuzzy Block Reuse Also morebenchmarks should be includedAcknowledgmentsThis work has been supported by Direccio General deRecerca de la Generalitat under grant FI bythe Ministry of Education of Spain under contract CICYTTICC and by the CEPBAReferences TI TMSCXX family Tech RephttpwwwticomscdocsproductsdsptmschtmlTexas Instruments  Philips Semiconductors Trimedia tm vol httpwwwussemiconductorscomtrimedia  Analog Devices Introducing tigersharc Whitepaper volhttpwwwanalogcomnewadshtmlSHARC F Arakawa O Nishii K Uchiyama and N Nakagawa Shrisc multimedia processor MarchApril  Stuart Franklin Oberman Design issues in high performanceoating point arithmetic units PhD thesis Stanford University November  D Citron D Feitelson and L Rudolph Accelerating multimedia processing by implementing memoing in multiplicationand division units ASPLOS VIII  Carlos Alvarez Jesus Corbal Esther Salami and Mateo ValeroOn the potential of tolerance reuse for multimedia applications International Conference on Supercomputing ICSSorrento Italy  Stephen E Richardson Exploiting trivial and redundant computation th IEEE Symposium on Computer Arithmetic Doug Burger and Todd M Austin The simplescalar toolset version  WisconsinMadison CS Dep technical Report	  David Brooks Vivek Tiwari and Margaret Martonosi WattchA framework for architecturallevel power analysis and optimizations International Symposium on Computer ArchitectureISCA Vancouver  C Lee M Potkonjak and WH MagioneSmith MediabenchA tool for evaluating and synthesizing multimedia and communication systems MICRO  IEEE Computer Architecture  Letters Vol. 1, 2002

During the recent years, the market of mid/low-end portable systems such as PDAs or mobile digital phones have experimented a revolution in both selling volume and features as handheld devices incorporate Multimedia applications. This fact brings to an increase in the computational demands of the devices, while still having the limitation of power (and energy) consumption. 

Instruction memoization is a promising technique to help alleviate the problem of power consumption of expensive functional units such as the floating-point one. Unfortunately, this technique could be energy-inefficient for low-end systems due to the additional power consumption of the relatively big tables required. 

In this paper we present a novel way of understanding multimedia floating point operations based on the fuzzy computation paradigm: losses in the computation precision may exchange performance for negligible errors in the output. Exploiting the implicit characteristics of media FP computation, we propose a new technique called fuzzy memoization. Fuzzy memoization expands the capabilities of classic memoization by attaching entries with similar inputs to the same output. We present a case of study for a SH4 like processor and report good performance and power-delay improvements with feasible hardware requirements.Peer Reviewe

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Initial results on fuzzy floating point computation for multimedia processors

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