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				<title level="a" type="main">Multi-Level power consumption modelling in the AADL design flow for DSP, GPP, and FPGA</title>
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							<persName><forename type="first">Johann</forename><surname>Laurent</surname></persName>
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							<persName><forename type="first">Jean-Philippe</forename><surname>Diguet</surname></persName>
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<div xmlns="http://www.tei-c.org/ns/1.0"><p>This paper presents a method that permits to estimate the power consumption of components in the AADL component assembly model, once deployed onto components in the AADL target platform model. This estimation is performed at different levels in the AADL refinement process. Multi-level power models have been specifically developed for the different type of possible hardware targets: General Purpose Processors (GPP), Digital Signal Processors (DSP) and Field Programmable Gate Arrays (FPGA). Three models are presented for a complex DSP (the Texas Instrument C62), a RISC GPP (the PowerPC 405), and a FPGA from Altera (Stratix EP1S80). The accuracy of these models depends on the refinement level. The maximum error introduced ranges from 70% for the FPGA at the first refinement level (only the operating frequency is considered here) to 5% for the GPP at the third refinement level (where the component's actual source code is considered).</p></div>
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<div xmlns="http://www.tei-c.org/ns/1.0"><head n="1">Introduction</head><p>Originally coming from the avionic domain, AADL (Architecture Analysis &amp; Design Language) is now commonly used as an input modelling language for real-time embedded systems <ref type="bibr" target="#b0">[1,</ref><ref type="bibr" target="#b1">2]</ref>. It allows the early analysis of the specification, the verification of functional and non functional properties of the system, and even code generation for the targeted hardware platform <ref type="bibr" target="#b2">[3]</ref><ref type="bibr" target="#b3">[4]</ref><ref type="bibr" target="#b4">[5]</ref>. In the context of the European project SPICES (Support for Predictable Integration of mission Critical Embedded Systems) <ref type="bibr" target="#b5">[6]</ref>, our aim is to enrich the AADL component based design flow to permit energy and power consumption estimations at different levels in the refinement process. However, such early verifications are only possible if power estimations are completed in a reasonable delay. Only at this condition a fast and fruitful exploration of the design space is permitted.</p><p>Significant research efforts have been devoted to develop tools for power consumption estimation at different abstraction levels in embedded system design. A lot of those tools however work at the Register Transfer Level (RTL) (this is the case for tools like SPICE, Diesel <ref type="bibr" target="#b6">[7]</ref> and Petrol <ref type="bibr" target="#b7">[8]</ref>), at the Cycle Accurate Bit Accurate (CABA) level ( <ref type="bibr" target="#b8">[9,</ref><ref type="bibr" target="#b9">10]</ref>), and a few tools at the architectural level (Wattch <ref type="bibr" target="#b10">[11]</ref> and Simplepower <ref type="bibr" target="#b11">[12]</ref>). Such approaches cannot be used at high 2 levels because simulation times at such low abstraction levels become enormous for complete and complex systems, like multiprocessor heterogeneous platforms.</p><p>In <ref type="bibr" target="#b12">[13]</ref> and <ref type="bibr" target="#b13">[14]</ref>, the authors present a characterization methodology for generating power models within TLM for peripheral components. The pertinent activities are identified at several levels and granularities. The characterization phase of the activities is performed at the gate level and is used to deduce the power of coarse-grained activities at higher level. Again, applying such approaches for complex processors or complete systems is not doable. Instruction level or functional level approaches have been proposed <ref type="bibr" target="#b14">[15]</ref><ref type="bibr" target="#b15">[16]</ref><ref type="bibr" target="#b16">[17]</ref>. They however only work at the assembly level, and need to be improved to take into account pipelined architectures, large VLIW instruction sets, and internal data and instruction caches.</p><p>We introduced the Functional Level Power Analysis (FLPA) methodology which we have applied to the building of high-level power models for different hardware components, from simple RISC processors to complex superscalar VLIW DSP <ref type="bibr" target="#b17">[18,</ref><ref type="bibr" target="#b18">19]</ref>, and for different FPGA circuits <ref type="bibr" target="#b19">[20]</ref>. In this paper we show how this modelling approach fits into the AADL design flow and how our power models, being interoperable, are used at different refinement levels. Section 2 presents the AADL component based design flow and the deployment of the Platform Independent Models (PIM) to obtain the Platform Specific Model (PSM) of the target. Section 3 presents the methodology for power estimations and the global power analysis of a complete system described with AADL. Section 4 presents the building of power models and define the three refinement levels where they can be used. The power models of the DSP TI C62, the GPP Pow-erPC 405, and the FPGA Altera Stratix EP1S80 are presented as examples. The accuracy of our power estimations is finally evaluated.</p></div>
<div xmlns="http://www.tei-c.org/ns/1.0"><head n="2">AADL design flow</head><p>Figure <ref type="figure" target="#fig_0">1</ref> presents the component based AADL design flow. The AADL component assembly model contains all the components and connections instances of the application, and references the implementation models of the components instances from the AADL models library. The AADL target platform model describes the hardware of the physical target platform. This platform is composed of at least one processor, one memory, and one bus entity to home processes and threads execution. The AADL deployment plan model describes the AADL-PSM composition process. It defines all the binding properties that are necessary to deploy the processes and services model of the component-based application on the target platform. All those models are combined to obtain the AADL-PSM model of the complete component-based system. The final implementation of the system is obtained afterward through model transformations and code generation.</p><p>The Open Source AADL Environment Tool (OSATE) <ref type="bibr" target="#b20">[21]</ref> permits the specification of a complete system using AADL. It also permits to check some of its functional and non-functional properties. Those verifications rely on the use  <ref type="bibr" target="#b21">[22]</ref>. According to the deployment plan model, OSATE scheduling analysis plug-in uses information embedded in the software components description to propose a binding for the system <ref type="bibr" target="#b22">[23]</ref>. Figure <ref type="figure" target="#fig_1">2</ref> shows the typical binding of an application on a multiprocessor architecture.</p><p>In this example, process main_process and its data block data_b are bound to the memory sysRAM. Threads control_thread, ethernet_driver_thread and post_thread are bound to the first general purpose processor GPP1. Thread pre_thread is bound to GPP2. Thread hw_thread1 is, like hw_thread2 a hardware thread. It will be implemented in the reconfigurable FPGA circuit FPGA1.</p><p>One connection between pre_thread and post_thread has been declared using in and out data ports in the threads. This connection is bound to bus sys_bus since it connects two threads bound to two different components in the platform. Intra-component connections, like between threads control_thread and ethernet_driver_thread, do not need to be bound to specific buses. They will however consume hardware resources while being used.</p><p>In addition to communication buses, dedicated supply buses can also been declared. A power analysis command in the OSATE resources analysis plug-in permits to check if the power capacity of a supply bus is not exceeded. To do that, a power capacity property (SEI::PowerCapacity) is declared for a bus, and a power budget is declared for every component that requires an access to this bus (property SEI::PowerBudget). The plug-in adds all the power budgets for a bus and compares the result with its power capacity. This mechanism, even if it is interesting, is extremely limited: power budgets for every component are only a guess from the user, and are only used to compute the power consumption of buses in a very simplistic way. In this paper, we propose a method to greatly enhance power analysis in the AADL flow, and to do it in an efficient way not only for buses, but for every consuming component in the system. Moreover, we propose to base power analysis on realistic power estimates, by using an accurate power estimation tool and precise power consumption models for every component in the targeted hardware platform.</p></div>
<div xmlns="http://www.tei-c.org/ns/1.0"><head n="3">High-level power consumption estimations</head><p>In order to complete power consumption analysis for the whole system, we need first to compute the power budget for every software component in the AADL component assembly model. This is the power estimation phase (1) represented with plain edges on figure 3 in the case of the binding of a thread to a processor. Next, the power budgets of software components are combined to get the power budgets for hardware components. This is the power analysis phase (2) represented with thick dotted edges on the figure. Using timing information, the energy analysis will be performed afterwards (thin dotted edges).</p><p>The challenge for our power estimation tool is to provide a realistic power budget for every component in the application. This tool gathers several information in the system's AADL specification at different places, here from the process and thread descriptions, and from the processor specification. It also uses binding information that may come from a preliminary scheduling analysis. The tool uses the power model of the targeted hardware component (here a processor) to compute the power budget for the (software) component. In fact, it determines the input parameters of the model from the set of information it has gathered. This process is repeated, not only for threads bound to processors, but also for any possible binding of software components onto hardware components, and that means: (i-) threads onto processors or FPGA, (ii-) processes and data onto memories, and (iii-) inter-components connections onto buses. </p><p>A process and a thread in the component assembly model Once the power budgets have been computed for every component in the application, the power analysis is performed. The power analysis tool retrieves all the component power budgets, together with additional information from the specification, and computes the power budget for every hardware component in the system. Then it computes the power estimation for the whole system. The result of the scheduling analysis (which gives the load of processors) is also taken into account at this level. Indeed, whenever a processor is idle, its power consumption is at the minimum level. Scheduling analysis is performed using basic information on the threads properties defined as properties for each thread implementation in the AADL component assembly model: dispatch protocol (periodic, aperiodic, sporadic, background), period, deadline, execution time ... This paper will concentrate on the power estimation phase, no further details will be given on the power analysis. Energy analysis will be finally performed using information from the timing analysis tools currently being developed by some of our partners in the SPICES project.</p></div>
<div xmlns="http://www.tei-c.org/ns/1.0"><head n="4">Multi-level power models</head><p>Our Power Estimation Tool, PET, is an evolution of the former SoftExplorer, initially dedicated to power and energy consumption estimation for processors (from simple RISC General Purpose Processors to very complex VLIW Digital Signal Processors) <ref type="bibr" target="#b23">[24]</ref>. This tool comes with a library of power models for every hardware component on the platform.</p></div>
<div xmlns="http://www.tei-c.org/ns/1.0"><head>MoDELS'08 ACES-MB Workshop Proceedings</head><p>Toulouse, France, September 29, 2008 Our objective is to allow power estimation at different levels in the flow. This involves the use of multi-level power models, which are models that can be used with more or less information, depending on the refinement level. In fact, while the specification is being refined, more information is available and power estimations get more precise.</p><p>Let's consider a case study platform including one GPP (the PowerPC 405), one DSP (the Texas Instrument C62), and one FPGA circuit (the Xillinx Virtex 400E). The description of those components' power models can be found respectively in <ref type="bibr" target="#b24">[25]</ref>, <ref type="bibr" target="#b17">[18]</ref>, and <ref type="bibr" target="#b19">[20]</ref>. Power models are built following our Functional Level Power Analysis methodology <ref type="bibr" target="#b18">[19]</ref>. The component's architecture is firstly analysed and relevant parameters regarding its power consumption are identified. Then physical measurements are performed to assess the evolution of the power consumption with the models' input parameters (using little benchmarking programs called "scenario"), and finally power consumption laws are established.</p></div>
<div xmlns="http://www.tei-c.org/ns/1.0"><head n="4.1">A complex Digital Signal Processor</head><p>The TI C62 processor has a complex architecture. It has a VLIW instructions set, a deep pipeline (up to 15 stages), fixed point operators, and parallelism capabilities (up to 8 operations in parallel). Its internal program memory can be used like a cache in several modes, and an External Memory Interface (EMIF) is used to load and store data and program from the external memory <ref type="bibr" target="#b25">[26]</ref>. In the case of the C62, the 6 following parameters are considered. The clock frequency (F) and the memory mode (MM) are what we call architectural parameters. They are directly related to the target platform and the hardware component, and can be changed according to the users will. The influence of F is obvious. The C62 maximum frequency is 200MHz (it is for our version of the chip); the designer can tweak this parameter to adjust consumption and performances.</p><p>The remaining parameters are called algorithmic parameters; they directly depend on the application code itself. The parallelism rate α assesses the flow between the processor's instruction fetch stages and its internal program memory controller inside its IMU (Instruction Management Unit). The activity of the processing units is represented by the processing rate β. This parameter links the the IMU and the PU (Processing Unit). The activity rate between the IMU and the MMU (Memory Management Unit) is expressed by the program cache miss rate γ. The pipeline stall rate (PSR) counts the number of pipeline stalls during execution. It depends on the mapping of data in memory and on the memory mode.</p><p>The memory mode MM illustrates the way the internal program memory is used. Four modes are available. All the instructions are in the internal memory in the mapped mode (M M M ). They are in the external memory in the bypass mode (M M B ). In the cache mode, the internal memory is used like a direct mapped cache (M M C ), as well as in the freeze mode where no writing in the cache is allowed (M M F ). Internal logic components used to fetch instructions (for instance tag comparison in cache mode) actually depends on the memory mode, and so the power consumption.</p><p>A precise description of the C62 power model and its building may be found in <ref type="bibr" target="#b17">[18]</ref>. The variation of the power consumption with the input parameters, more precisely the fact that the estimation is not equally sensitive to every parameter, allows to use the model in three different situations.</p><p>In the first situation, only the operating frequency is known. The tool returns the average value of the power consumption, which comes from the minimum and maximum values obtained when all the others parameters are being made to vary. The designer can also ask for the maximum value if a higher bound is needed for the power consumption.</p><p>In the second situation, we suppose that the architectural parameters (here F and MM) are known. We also assume that the code is not known and that the designer is able to give some realistic values for every algorithmic parameter. If not, default values are proposed, from the values that we have observed running different representative applications on this DSP (see table <ref type="table" target="#tab_1">1</ref>).</p><p>In the third situation, the source code is known. It is then parsed by our power estimation tools: the value of every algorithmic parameter is computed and the power consumption is estimated, using the power model and the values enter by the user for the frequency and memory mode. The error introduced by our tool obviously differs in these three situations. To calculate the maximum error, estimations are performed with given values for the parameters known in the situation, and with all the possible values of the remaining unknown parameters. The maximum error comes then from the difference between the average and the maximum estimations. This is repeated MoDELS'08 ACES-MB Workshop Proceedings Toulouse, France, September 29, 2008 for every valid set of known input parameters. The final maximum error is the maximum of the maximum errors. Table <ref type="table" target="#tab_2">2</ref> gives the maximum error in the three situations above, which correspond to three levels of the specification refinement. Note that the maximal errors computed at level 2 are really pessimistic since we assume here that the designer is completely (100%) wrong on his evaluation of all the input parameters. If his evaluation of those parameters is only 50%, or 25% wrong, then the error introduced by our tool is reduced as well. </p></div>
<div xmlns="http://www.tei-c.org/ns/1.0"><head n="4.2">A more simple General Purpose Processor</head><p>The PowerPC 405 is a light version of the IBM PowerPC, embedded in the Xilinx VirtexII Pro FPGA. It includes one prefetch instruction unit that allows to reduce the number of pipeline stalls due to instruction misses, two caches (16KB each) (one for the data and the other for instructions). These two caches can be involved separately and use LRU policy. They are two ways associative with 32 bytes line size. And three TLB translating addresses from logical to physical (2 shadow TLB -one for the instructions and one for data -are used and coupled with an unified one).</p><p>Measurements show that among the most important factors in the PowerPC 405 consumption are its frequency and the frequency of the bus to which it is connected. The processor can be clocked at 100, 150, 200 or 300 MHz, and, depending on the processor frequency, the bus (OCM or PLB) frequency can take different values between 25 to 100 MHz. Another important parameter to consider is the configuration of the memory hierarchy associated to the processor's core, and that means, which caches are used (data and / or instruction) and where is located the primary memory (internal / external). Once again, the component's power model can be used at three refinement levels.</p><p>At the first refinement level, our model gives a rough estimate of the power consumption for the software component, only from the knowledge of the processor and some basic information on its operating conditions. The only information 9 we need is the processor frequency and the frequency of the internal bus (OCM or PLB) to which the processor is connected inside the FPGA. They are two architectural parameters of the PowerPC 405. They will be defined as a property of the AADL processor implementation of the PowerPC 405 in the AADL specification. The maximum error we get here is 27%.</p><p>At the second refinement level, we have to add some information about the memories used. We have to indicate which caches will be used in the PowerPC 405 (data cache, instructions cache, or both), and if its primary memory is internal (using the FPGA BRAM memory bank) or external (using a SDRAM accessed through the FPGA I/O). Indeed, while building the power model for the PowerPC 405, we have observed that it draws quite different power and energy in those various situations <ref type="bibr" target="#b24">[25]</ref>. Table <ref type="table" target="#tab_3">3</ref> show the maximal errors we obtain here for every valid set of known input parameters, the others being unknown. The maximum error we obtain is 15,3% and the average error is 6,6%. The first line indicates 0% because in this configuration, there are not remaining unknown parameters that can change the power consumption of the processor. At the lowest refinement level, the actual code of the software component is parsed. In the case of the PowerPC 405, what is important is not exactly what instruction is executed, but rather the type of instruction being executed. We have indeed exhibited that the power consumption changes noticeably from memory access instructions (load or store in memory), to calculation instructions (multiplication or addition). As we have seen before, the place where the data is stored in memory is also important, so the data mapping is also parsed here. The average error we get at this level is 2%. The maximum error is 5%. Logically, 10 that corresponds to the max and average errors for the set of consumption laws for the component.</p></div>
<div xmlns="http://www.tei-c.org/ns/1.0"><head n="4.3">Field Programmable Gate Arrays</head><p>FPGA (Field Programmable Gate Arrays) are now very common in electronic systems. They are often used in addition to GPP (General Purpose Processors) and / or DSP (Digital Signal Processors) to tackle data intensive dedicated parts of an application. They act as hardware accelerators where and when the application is very demanding regarding the performances, that typically for signal or image processing algorithms. In this case again power estimation can be performed at different refinement levels.</p><p>At the highest levels, the code of the application is not known yet. The designer needs however to quickly evaluate the application against power, energy and / or thermal constraints. A fast estimation is necessary here, and a much larger error is acceptable. The parameters we can use from the high-level specifications are the frequency F and the occupation ratio β of the targeted FPGA implementation, that we consider as architectural parameters, and the activity rate α. The experienced designer is indeed able to provide, even at this very high-level, a realistic guess of those parameters' value. As explained before, to obtain the model, i.e. the mathematical equation linking its output to the parameters, we performed a set of different measurements on the targeted FPGA. For different values of the occupation ratio, and for different values of the frequency, we made the activity rate varying and measured the power consumption.</p><p>At our first refinement level, only the frequency is known. Our power estimation tool uses the model to estimate, at the given frequency, the power consumption with α = β = 0,1 and with α = β = 0,9. Then it returns the average value between those minimal and maximal values. The maximal errors we obtain for F = 10MHz and F = 90MHz (upper bound for the Altera Stratix EP1S80) are given table <ref type="table" target="#tab_4">4</ref>.</p><p>At the next refinement level, the two architectural parameters F and β, are known to the user. Like in the case of the former processor's models, default values are proposed for α and also β, coming from a set of representative applications. The maximal error introduced in this case ranges from 6,9% to 44,8%. To determine this error we compute the maximum and minimum estimations for the four extreme (F , β) couples, and compare them to the estimations with α default value.</p><p>At the lowest refinement level, the source code (a synthesizable hardware description of the component behaviour, may be written in VHDL or SystemC ...) is used. A High-Level Synthesis tool <ref type="bibr" target="#b26">[27]</ref> permits to estimate the amount of resources necessary to implement the application, and given the targeted circuit, to obtain its occupation ratio (β) and its activity rate (α). Those two parameters and the frequency are finally used with the model.</p></div>
<div xmlns="http://www.tei-c.org/ns/1.0"><head>MoDELS'08 ACES-MB Workshop Proceedings</head><p>Toulouse, France, September 29, 2008 </p></div>
<div xmlns="http://www.tei-c.org/ns/1.0"><head n="5">AADL Property Sets</head><p>Table <ref type="table" target="#tab_5">5</ref> and 6 show the property sets associated respectively to the TI C62 and the PowerPC 405 for power estimation at the three refinement levels defined above. Table <ref type="table" target="#tab_7">7</ref> shows the property set for the FPGA Alter Stratix EP1S80. As described section 3, the power estimation tool, when it is invoked, extracts relevant information (a set of parameters) from the AADL specification, then computes the components' power consumption, and returns the results to fill the power budget properties for the software components. The binding makes it possible to put in relation components in the AADL component assembly model with the power models of hardware components on the targeted platform.</p><p>As we have just seen, depending on the information refinement, coarse or fine precision power estimations will be performed. Given the refinement level, information to be provided to the estimation tool depends on the selected target (which component). The information is more general if the refinement level is high, it will be more dedicated to the target if the refinement level is low. The set of properties that are used by the estimation tool actually depends on the MoDELS'08 ACES-MB Workshop Proceedings Toulouse, France, September 29, 2008 19  component itself, and more precisely, on its power model. Even between two components of the same type, another set of specific properties might be necessary since another set of configuration parameters might apply. This is the case here for the two processor components TI C62 and PowerPC405. The property set of the processor comes finally as a part of its power model, and, as this, will remain separated from the general property set associated to the current AADL working project for the application being designed in the OSATE environment.</p></div>
<div xmlns="http://www.tei-c.org/ns/1.0"><head n="6">Conclusion</head><p>We have presented a method to perform power consumption estimations in the component based AADL design flow. The power consumption of components in the AADL component assembly model is estimated whatever the targeted hardware resource, in the AADL target platform model, is: a DSP (Digital Signal Processor), a GPP (General Purpose Processor), or a FPGA (Field Programmable Gate Array). A power estimation tool has been developed with a library of multilevel power models for those (hardware) components. These models can be used at different levels in the AADL specification refinement process. We have currently defined three refinement levels in the AADL flow. At the lowest level, level 3, the (software) component's actual business code is considered and an accurate estimation is performed. This code, written in C, or C++, for standard threads, can also be written in VHDL or SystemC for hardware threads. At level 2, the power consumption is only estimated from the component operating frequency, and its architectural parameters (mainly linked to its memory configuration in the case of processors). At level 1, the highest level, only the operating frequency of the component is considered. Three power models have been presented for the TIC62 GPP, the Pow-erPC405 GPP, and the Altera Stratix EP1S80 FPGA. The maximum errors introduced by these models, at the three refinement levels, are given table <ref type="table" target="#tab_8">8</ref>.</p></div>
<div xmlns="http://www.tei-c.org/ns/1.0"><head>MoDELS'08 ACES-MB Workshop Proceedings</head><p>Toulouse, France, September 29, 2008 20 In the frame of the SPICES project, we are currently working at the integration of our Power Estimation Tool and Power Analysis Tool in the AADL OSATE tool environment.</p></div><figure xmlns="http://www.tei-c.org/ns/1.0" xml:id="fig_0"><head>Fig. 1 .</head><label>1</label><figDesc>Fig. 1. AADL component based design flow</figDesc></figure>
<figure xmlns="http://www.tei-c.org/ns/1.0" xml:id="fig_1"><head>Fig. 2 .</head><label>2</label><figDesc>Fig. 2. Binding components to the target platform</figDesc></figure>
<figure xmlns="http://www.tei-c.org/ns/1.0" xml:id="fig_2"><head>A processor in the target platform model BINDINGFig. 3 .</head><label>model3</label><figDesc>Fig. 3. Power and Energy consumption estimation in the AADL design flow</figDesc></figure>
<figure xmlns="http://www.tei-c.org/ns/1.0" xml:id="fig_3"><head>6</head><label>6</label><figDesc></figDesc></figure>
<figure xmlns="http://www.tei-c.org/ns/1.0" type="table" xml:id="tab_1"><head>Table 1 .</head><label>1</label><figDesc>Default algorithmic parameters for the C62</figDesc><table><row><cell>α</cell><cell>β</cell><cell>PSR</cell></row></table></figure>
<figure xmlns="http://www.tei-c.org/ns/1.0" type="table" xml:id="tab_2"><head>Table 2 .</head><label>2</label><figDesc>Maximum errors for the C62 power model (Power in mW)</figDesc><table><row><cell>Known parameters</cell><cell cols="4">Memory Max Min Average Max</cell></row><row><cell></cell><cell cols="4">Mode Power Power Power Error</cell></row><row><cell></cell><cell>Level 1</cell><cell></cell><cell></cell><cell></cell></row><row><cell>Frequency</cell><cell>X</cell><cell>3037 848</cell><cell>2076</cell><cell>59%</cell></row><row><cell></cell><cell>Level 2</cell><cell></cell><cell></cell><cell></cell></row><row><cell cols="3">Frequency, MM, α, β, γ, PSR Mapped 2954 848</cell><cell>1809</cell><cell>53%</cell></row><row><cell></cell><cell cols="2">Cache 2955 756</cell><cell>1778</cell><cell>57%</cell></row><row><cell></cell><cell cols="2">Freeze 3018 882</cell><cell>1801</cell><cell>51%</cell></row><row><cell></cell><cell cols="2">Bypass 3037 2014</cell><cell>2397</cell><cell>21%</cell></row><row><cell></cell><cell>Level 3</cell><cell></cell><cell></cell><cell></cell></row><row><cell cols="5">F, MM, and the source code Max Error = 8%, Average Error = 4%</cell></row><row><cell>is provided</cell><cell></cell><cell></cell><cell></cell><cell></cell></row></table></figure>
<figure xmlns="http://www.tei-c.org/ns/1.0" type="table" xml:id="tab_3"><head>Table 3 .</head><label>3</label><figDesc>Maximal Errors for the PowerPC 405 at refinement level 2 (Power in mW)</figDesc><table><row><cell></cell><cell></cell><cell></cell><cell></cell><cell cols="4">Fprocessor/F bus (MHz)</cell><cell></cell></row><row><cell></cell><cell cols="9">300/ 200/ 100/ 200/ 200/ 150/ 100/ 100/ 100/ Max</cell></row><row><cell></cell><cell>100</cell><cell>100</cell><cell>100</cell><cell>66</cell><cell>50</cell><cell>50</cell><cell>50</cell><cell>33</cell><cell>25 Error</cell></row><row><cell>2 caches BRAM</cell><cell cols="9">2595 2555 2515 2262 2134 2104 2084 1938 1869 0%</cell></row><row><cell>2 caches SDRAM MAX</cell><cell cols="9">3129 3091 3053 2760 2604 2585 2566 2400 2321</cell></row><row><cell>2 caches SDRAM MIN</cell><cell cols="9">2719 2681 2643 2350 2194 2175 2156 1990 1911</cell></row><row><cell>Error</cell><cell cols="9">7,0% 7,1% 7,2% 8,0% 8,5% 8,6% 8,7% 9,3% 9,7% 9,7%</cell></row><row><cell>BRAM MAX</cell><cell cols="9">2570 2515 2460 2241 2112 2084 2057 1920 1856</cell></row><row><cell>BRAM MIN</cell><cell cols="9">2472 2440 2408 2177 2053 2037 2021 1890 1829</cell></row><row><cell>Error</cell><cell cols="9">1,9% 1,5% 1,1% 1,4% 1,4% 1,1% 0,9% 0,8% 0,7% 1,9%</cell></row><row><cell cols="10">Icache BRAM&amp;BRAM MAX 2662 2592 2522 2305 2170 2135 2100 1957 1890</cell></row><row><cell cols="10">Icache BRAM&amp;BRAM MIN 2497 2451 2405 2193 2071 2048 2025 1897 1836</cell></row><row><cell>Error</cell><cell cols="9">3,2% 2,8% 2,4% 2,5% 2,3% 2,1% 1,8% 1,6% 1,4% 3,2%</cell></row><row><cell>Icache SDRAM MAX</cell><cell cols="9">3432 3267 3102 3155 3103 3020 2938 2882 2856</cell></row><row><cell>Icache SDRAM MIN</cell><cell cols="9">2600 2478 2356 2403 2367 2306 2239 2208 2190</cell></row><row><cell>Error</cell><cell cols="9">13,8% 13,7% 13,7% 13,5% 13,5% 13,4% 13,5% 13,2% 13,2% 13,8%</cell></row><row><cell>Dcache BRAM MAX</cell><cell cols="9">2595 2555 2515 2262 2124 2104 2084 1938 1869</cell></row><row><cell>Dcache BRAM MIN</cell><cell cols="9">2588 2544 2500 2254 2118 2096 2074 1930 1861</cell></row><row><cell>Error</cell><cell cols="9">0,1% 0,2% 0,3% 0,2% 0,1% 0,2% 0,2% 0,2% 0,2% 0,3%</cell></row><row><cell>Dcache SDRAM MAX</cell><cell cols="9">3535 3497 3459 3133 2960 2941 2922 2741 2622</cell></row><row><cell>Dcache SDRAM MIN</cell><cell cols="9">2744 2706 2668 2375 2218 2199 2180 2015 1936</cell></row><row><cell>Error</cell><cell cols="9">12,6% 12,8% 12,9% 13,8% 14,3% 14,4% 14,5% 15,3% 15,1% 15,3%</cell></row></table></figure>
<figure xmlns="http://www.tei-c.org/ns/1.0" type="table" xml:id="tab_4"><head>Table 4 .</head><label>4</label><figDesc>Maximum errors for the Altera Stratix EP1S80 (Power in mW)</figDesc><table><row><cell>Known parameters</cell><cell cols="3">Max Min Average</cell><cell>Max</cell></row><row><cell></cell><cell cols="3">Power Power Power</cell><cell>Error</cell></row><row><cell></cell><cell></cell><cell>Level 1</cell><cell></cell><cell></cell></row><row><cell cols="2">Frequency (F=10MHz) 789</cell><cell>307</cell><cell>548</cell><cell>44%</cell></row><row><cell cols="3">Frequency (F=90MHz) 4824 835</cell><cell>2830</cell><cell>70%</cell></row><row><cell></cell><cell></cell><cell>Level 2</cell><cell></cell><cell></cell></row><row><cell>Frequency, α, β</cell><cell></cell><cell></cell><cell></cell><cell></cell></row><row><cell>F=10MHz, β=0,1</cell><cell>353</cell><cell>307</cell><cell>324</cell><cell>8,8%</cell></row><row><cell>F=10MHz, β=0,9</cell><cell>789</cell><cell>544</cell><cell>667</cell><cell>24,1%</cell></row><row><cell>F=90MHz, β=0,1</cell><cell>931</cell><cell>835</cell><cell>883</cell><cell>6,9%</cell></row><row><cell>F=90MHz, β=0,9</cell><cell cols="2">4824 2435</cell><cell>3630</cell><cell>44,8%</cell></row><row><cell></cell><cell></cell><cell>Level 3</cell><cell></cell><cell></cell></row><row><cell cols="5">F and the source code Max Error = 4,2%, Average Error = 1,3%</cell></row><row><cell>is provided</cell><cell></cell><cell></cell><cell></cell><cell></cell></row></table></figure>
<figure xmlns="http://www.tei-c.org/ns/1.0" type="table" xml:id="tab_5"><head>Table 5 .</head><label>5</label><figDesc>Property set for the TI C62</figDesc><table><row><cell>TI C62 property set</cell></row><row><cell>Processor_Frequency : aadlreal applies to (processor);</cell></row><row><cell>Processor_Memory_Mode : TIC62::Processor_Memory_Mode_Type applies to (processor);</cell></row><row><cell>Processor_Parallelism_Rate : aadlreal applies to (processor);</cell></row><row><cell>Processor_Processing_Rate : aadlreal applies to (processor);</cell></row><row><cell>Processor_Cache_Miss_Rate : aadlreal applies to (processor);</cell></row><row><cell>Processor_Pipeline_Stall_Rate : aadlreal applies to (processor);</cell></row><row><cell>Processor_Memory_Mode_Type : type enumeration (CACHE,FREEZE,BYPASS,MAPPED);</cell></row><row><cell>Processor_Parallelism_Rate_Default : constant aadlreal =&gt; 0,7549;</cell></row><row><cell>Processor_Processing_Rate_Default : constant aadlreal =&gt; 0,5298;</cell></row><row><cell>Processor_Cache_Miss_Rate_Default : constant aadlreal =&gt; 0,25;</cell></row><row><cell>Processor_Pipeline_Stall_Rate_Default : constant aadlreal =&gt; 0,2919;</cell></row></table></figure>
<figure xmlns="http://www.tei-c.org/ns/1.0" type="table" xml:id="tab_6"><head>Table 6 .</head><label>6</label><figDesc>Property set for the PowerPC 405</figDesc><table><row><cell>PowerPC 405 property set</cell></row><row><cell>Processor_Frequency : aadlreal applies to (processor);</cell></row><row><cell>Processor_Bus_Frequency : aadlreal applies to (processor);</cell></row><row><cell>Processor_Primary_Memory : PPC405::Primary_Memory_Type applies to (processor);</cell></row><row><cell>Processor_Data_Cache : aadlboolean applies to (processor);</cell></row><row><cell>Processor_Instructions_Cache : aadlboolean applies to (processor);</cell></row><row><cell>Primary_Memory_Type : type enumeration (BRAM,SDRAM);</cell></row></table></figure>
<figure xmlns="http://www.tei-c.org/ns/1.0" type="table" xml:id="tab_7"><head>Table 7 .</head><label>7</label><figDesc>Property set for the Altera Stratix EP1S80</figDesc><table><row><cell>FPGA Altera Stratix EP1S80 property set</cell></row><row><cell>FPGA_Frequency : aadlreal applies to (fpga);</cell></row><row><cell>FPGA_Activity_Rate : TIC62::Processor_Memory_Mode_Type applies to (fpga);</cell></row><row><cell>FPGA_Occupation_Ratio : aadlreal applies to (fpga);</cell></row><row><cell>FPGA_Activity_Rate_Default : constant aadlreal =&gt; 0,4;</cell></row><row><cell>FPGA_Occupation_Ratio_Default : constant aadlreal =&gt; 0,5;</cell></row></table></figure>
<figure xmlns="http://www.tei-c.org/ns/1.0" type="table" xml:id="tab_8"><head>Table 8 .</head><label>8</label><figDesc>Maximal errors summary</figDesc><table><row><cell>Component</cell><cell cols="3">Max Error Level 1 Max Error Level 2 Max Error Level 3</cell></row><row><cell>TI C62</cell><cell>59%</cell><cell>57%</cell><cell>8%</cell></row><row><cell>PowerPC 405</cell><cell>27%</cell><cell>15,3%</cell><cell>5%</cell></row><row><cell>Altera Stratix EP1S80</cell><cell>70%</cell><cell>44,8%</cell><cell>4,2%</cell></row></table></figure>
			<note xmlns="http://www.tei-c.org/ns/1.0" place="foot" xml:id="foot_0">MoDELS'08 ACES-MB Workshop ProceedingsToulouse, France, September 29, 2008</note>
			<note xmlns="http://www.tei-c.org/ns/1.0" place="foot" xml:id="foot_1">Toulouse, France, September 29, 2008</note>
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