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Power estimation for diverse field programmable gate array architectures Jeffrey, Goeders 2012

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Power Estimation for Diverse Field Programmable Gate Array Architectures by Jeffrey Goeders BASc, University of Toronto, 2010 A THESIS SUBMITTED IN PARTIAL FULFILLMENT OF THE REQUIREMENTS FOR THE DEGREE OF Master of Applied Science in THE FACULTY OF GRADUATE STUDIES (Electrical and Computer Engineering) The University Of British Columbia (Vancouver) October 2012 © Jeffrey Goeders, 2012 Abstract This thesis presents a new power model, which is capable of modelling the power usage of many different field-programmable gate array (FPGA) architectures. FPGA power models have been developed in the past; however, they were de- signed for a single, simple architecture, with known circuitry. This work explores a method for estimating power usage for many different user-created architec- tures. This requires a fundamentally new technique. Although the user specifies the functionality of the FPGA architecture, the physical circuitry is not specified. Central to this work is an algorithm which translates these functional descriptions into physical circuits. After this translation to circuit components, standard meth- ods can be used to estimate power dissipation. In addition to enlarged architecture support, this model also provides support for modern FPGA features such as fracturable look-up tables and hard blocks. Compared to past models, this work provides substantially more detailed static power estimations, which is increasingly relevant as CMOS is scaled to smaller technologies. The model is designed to operate with modern CMOS technologies, and is validated against SPICE using 22 nm, 45 nm and 130 nm technologies. ii of 96 Results show that for common architectures, roughly 73% of power consump- tion is due to the routing fabric, 21% from logic blocks and 3% from the clock net- work. Architectures supporting fracturable look-up tables require 3.5-14% more power, as each logic element has additional I/O pins, increasing both local and global routing resources. iii of 96 Preface The work presented in this thesis will be published in the following conference proceedings: Jeffrey Goeders and Steven Wilton. VersaPower: Power Estimation for Diverse FPGA Architectures. In International Conference on Field Programmable Tech- nology, December 2012. Accepted. (Poster Presentation) Portions of this publication are used in all chapters of this thesis. I was solely responsible for the code development of this work, as well as performing the nec- essary experiments. I am the primary author of this publication, and wrote the ma- jority of the paper. I collaborated with my supervisor, Steve Wilton, in designing this work, and he provided instruction and guidance throughout the development. He also aided in revising and editing the above paper. iv of 96 Table of Contents Abstract . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . ii Preface . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . iv Table of Contents . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . v List of Tables . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . ix List of Figures . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . x Acronyms . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . xii Acknowledgments . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . xiv 1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1 1.1 Motivation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1 1.2 Contributions of this Work . . . . . . . . . . . . . . . . . . . . . 5 1.3 Challenges . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 6 1.4 Overview of Results . . . . . . . . . . . . . . . . . . . . . . . . . 7 v of 96 1.5 Thesis Organization . . . . . . . . . . . . . . . . . . . . . . . . . 8 2 Background . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 9 2.1 FPGAs . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 9 2.1.1 Basic Architectures . . . . . . . . . . . . . . . . . . . . . 10 2.1.2 Modern Architectures . . . . . . . . . . . . . . . . . . . . 15 2.2 FPGA Computer Automated Design (CAD) . . . . . . . . . . . . 17 2.2.1 CAD Flow Steps . . . . . . . . . . . . . . . . . . . . . . 17 2.2.2 Verilog-to-Routing (VTR) . . . . . . . . . . . . . . . . . 19 2.3 Power Estimation Techniques . . . . . . . . . . . . . . . . . . . . 20 2.3.1 Abstraction Levels . . . . . . . . . . . . . . . . . . . . . 20 2.3.2 Simulation-Based Power Estimation . . . . . . . . . . . . 22 2.3.3 Probabilistic Power Estimation . . . . . . . . . . . . . . . 23 2.4 FPGA Power Estimation Tools . . . . . . . . . . . . . . . . . . . 25 2.4.1 The Poon Power Model . . . . . . . . . . . . . . . . . . . 25 2.4.2 The Jamieson Power Model . . . . . . . . . . . . . . . . 26 2.4.3 The Li Model . . . . . . . . . . . . . . . . . . . . . . . . 26 2.4.4 The Estimation Technique of this Work . . . . . . . . . . 27 3 System Design and Architecture Generation . . . . . . . . . . . . . 28 3.1 Power Model Overview . . . . . . . . . . . . . . . . . . . . . . . 28 3.2 The Architecture Generator . . . . . . . . . . . . . . . . . . . . . 32 3.2.1 Global Routing . . . . . . . . . . . . . . . . . . . . . . . 33 3.2.2 Complex Logic Blocks . . . . . . . . . . . . . . . . . . . 40 vi of 96 3.2.3 Clock Network . . . . . . . . . . . . . . . . . . . . . . . 50 3.2.4 Physical Size Estimation . . . . . . . . . . . . . . . . . . 52 3.3 Summary . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 53 4 Power Estimation . . . . . . . . . . . . . . . . . . . . . . . . . . . . 55 4.1 Low-Level Power Estimation . . . . . . . . . . . . . . . . . . . . 55 4.1.1 Switching Power . . . . . . . . . . . . . . . . . . . . . . 56 4.1.2 Short-Circuit Power . . . . . . . . . . . . . . . . . . . . . 57 4.1.3 Subthreshold Leakage Power . . . . . . . . . . . . . . . . 58 4.1.4 Gate Leakage Power . . . . . . . . . . . . . . . . . . . . 59 4.2 Activity Estimation . . . . . . . . . . . . . . . . . . . . . . . . . 60 4.2.1 Algorithm . . . . . . . . . . . . . . . . . . . . . . . . . . 61 4.2.2 Limitation: Black Boxes . . . . . . . . . . . . . . . . . . 62 4.3 Transistor Properties Generator . . . . . . . . . . . . . . . . . . . 63 4.3.1 Transistor Node Capacitances . . . . . . . . . . . . . . . 64 4.3.2 Subthreshold Leakage Current . . . . . . . . . . . . . . . 64 4.3.3 Gate Leakage Current . . . . . . . . . . . . . . . . . . . . 65 4.3.4 P/N Ratio Sizing . . . . . . . . . . . . . . . . . . . . . . 65 4.3.5 Multiplexer Voltage Drop . . . . . . . . . . . . . . . . . . 66 4.3.6 Short-Circuit Buffer Factor . . . . . . . . . . . . . . . . . 67 4.4 Summary . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 68 5 Verification and Results . . . . . . . . . . . . . . . . . . . . . . . . . 70 5.1 Verification of Power Estimation . . . . . . . . . . . . . . . . . . 70 vii of 96 5.1.1 Verification Procedure . . . . . . . . . . . . . . . . . . . 71 5.1.2 Verification Results . . . . . . . . . . . . . . . . . . . . . 72 5.2 Sources of Estimation Error . . . . . . . . . . . . . . . . . . . . . 75 5.2.1 Short-Circuit Current . . . . . . . . . . . . . . . . . . . . 75 5.2.2 Transistor Node Capacitances . . . . . . . . . . . . . . . 76 5.2.3 Gate Leakage Currents . . . . . . . . . . . . . . . . . . . 77 5.3 Experiment 1: Component Breakdown . . . . . . . . . . . . . . . 77 5.3.1 Methodology . . . . . . . . . . . . . . . . . . . . . . . . 77 5.3.2 Results . . . . . . . . . . . . . . . . . . . . . . . . . . . 78 5.3.3 Analysis . . . . . . . . . . . . . . . . . . . . . . . . . . . 78 5.4 Experiment 2: Fracturable LUTs . . . . . . . . . . . . . . . . . . 80 5.4.1 Methodology . . . . . . . . . . . . . . . . . . . . . . . . 81 5.4.2 Results . . . . . . . . . . . . . . . . . . . . . . . . . . . 81 5.4.3 Analysis . . . . . . . . . . . . . . . . . . . . . . . . . . . 83 5.5 Summary . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 84 6 Conclusions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 86 6.1 Future Work . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 87 6.2 Summary of Contributions . . . . . . . . . . . . . . . . . . . . . 89 Bibliography . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 90 viii of 96 List of Tables Table 1.1 Comparison of this work with past power models . . . . . . . . 6 Table 3.1 System modules . . . . . . . . . . . . . . . . . . . . . . . . . 30 Table 5.1 CMOS process characteristics . . . . . . . . . . . . . . . . . . 72 Table 5.2 Accuracy of high-activity power estimations . . . . . . . . . . 73 Table 5.3 Accuracy of zero-activity power estimations . . . . . . . . . . 74 Table 5.4 Power breakdown by component type . . . . . . . . . . . . . . 78 Table 5.5 Power usage, and breakdown by circuit . . . . . . . . . . . . . 79 Table 5.6 Power of fracturable LUTs . . . . . . . . . . . . . . . . . . . . 82 ix of 96 List of Figures Figure 2.1 Taxonomy of PLD devices . . . . . . . . . . . . . . . . . . . 10 Figure 2.2 2-input LUT . . . . . . . . . . . . . . . . . . . . . . . . . . . 12 Figure 2.3 Basic logic element (BLE) . . . . . . . . . . . . . . . . . . . 12 Figure 2.4 Logic block containing 4 BLEs . . . . . . . . . . . . . . . . . 13 Figure 2.5 FPGA architecture . . . . . . . . . . . . . . . . . . . . . . . 14 Figure 2.6 Heterogeneous FPGA architecture . . . . . . . . . . . . . . . 16 Figure 2.7 Fracturing of a LUT . . . . . . . . . . . . . . . . . . . . . . . 17 Figure 2.8 FPGA CAD flow . . . . . . . . . . . . . . . . . . . . . . . . 18 Figure 2.9 Circuit abstraction levels . . . . . . . . . . . . . . . . . . . . 21 Figure 3.1 Modifications to the VTR flow for power estimation . . . . . . 29 Figure 3.2 Switch box component . . . . . . . . . . . . . . . . . . . . . 35 Figure 3.3 Connection box . . . . . . . . . . . . . . . . . . . . . . . . . 36 Figure 3.4 4:1 2-level multiplexer . . . . . . . . . . . . . . . . . . . . . 37 Figure 3.5 4:1 2-level multiplexer, decomposed into single-levels . . . . . 37 Figure 3.6 Multi-stage buffer . . . . . . . . . . . . . . . . . . . . . . . . 39 x of 96 Figure 3.7 Types of local interconnect . . . . . . . . . . . . . . . . . . . 42 Figure 3.8 Local interconnect spanning distance . . . . . . . . . . . . . . 44 Figure 3.9 Wire length in a local interconnect structure . . . . . . . . . . 45 Figure 3.10 4-input LUT . . . . . . . . . . . . . . . . . . . . . . . . . . . 47 Figure 3.11 D Flip-Flop . . . . . . . . . . . . . . . . . . . . . . . . . . . 48 Figure 3.12 The clock network . . . . . . . . . . . . . . . . . . . . . . . 51 Figure 4.1 Subthreshold leakage in a multiplexer . . . . . . . . . . . . . 60 Figure 4.2 Short circuit currents in inverters . . . . . . . . . . . . . . . . 67 xi of 96 Acronyms ASIC application-specific integrated circuit. BLE basic logic element. CAD computer-aided design. CLB configurable logic block. FPGA field-programmable gate array. HDL hardware description language. ITRS International Technology Roadmap for Semiconductors. LUT look-up table. PLD programmable logic device. PTM Predictive Technology Model. RTL register-transfer level. xii of 96 SPICE Simulation Program with IC Emphasis. VLSI very-large-scale integration. VPR Versatile Place and Route. VTR Verilog-to-Routing. xiii of 96 Acknowledgments First and foremost, I would like to thank my family. My wife, Jessie, for her en- couragement to complete this degree, and her support and patience during busy times. My parents, for their examples, and their emphasis on the value of educa- tion. This work would not be possible without the guidence, instruction and exam- ple of my supervisor, Steve Wilton. He is always generous with his time, provid- ing ideas, editing papers, and answering questions. I would also like to thank my labmates for their help and suggestions: Kyle Balston, Assem Bsoul, Stuart Dueck, and Eddie Hung, as well as others who answered questions, and gave advice: Jason Luu, Guy Lemieux, Jonathan Rose, and the VTR team. I would also like to thank NSERC and Altera for funding this research. xiv of 96 Chapter 1 Introduction 1.1 Motivation Power dissipation has become a first-class concern in the development of new in- tegrated circuits. For the past 9 years, the International Technology Roadmap for Semiconductors (ITRS) has identified power consumption as one of the top three challenges facing semiconductor development [1], and in the latest report [2], it states that power management will continue to be a grand challenge in the foresee- able future. In the past, dynamic power was the primary concern, growing rapidly as circuit operating frequencies increased. However, as transistor technologies have scaled down, static power from leakage currents has become equally impor- tant. In fact, the ITRS predicts that in the long-term, static power increases will lead to a major industry crisis, threatening the survival of CMOS technologies [2]. 1 of 96 The ITRS classifies devices into three types: 1) high-performance, 2) cost- performance, and 3) portable, or battery-powered. Power is a major design factor in all of these categories. In high-performance, such as desktop processors, the power must not exceed the rate at which heat can be removed from the device. In cost-performance, the goal is to reduce the energy cost per computation; for example, in server farms [3]. In portable applications, an area of rapid growth, power is minimized in order to extend battery life. In addition, the ITRS cites the need to reduce global energy usage as a motivating factor in reducing power consumption of electronic devices [1]. This work focuses on power consumption of one type of integrated circuit, field-programmable gate arrays (FPGAs). FPGAs are a type of user programmable computer chip. They contain many programmable logic blocks that can be used to implement circuits with hundreds of thousands of logic gates. These logic blocks are surrounded by a vast network of configurable routing segments. Together, the logic and routing allow FPGAs to implement almost any type of digital circuit. This flexibility has made FPGAs a popular choice in many different circuit applications, including both high-performance [4] and cost-performance [5, 6] scenarios. However, the flexibility comes at a cost; the generic logic and routing in an FPGA have a large overhead, requiring a larger circuit and more power than an application-specific integrated circuit (ASIC). One study found that FPGAs require over 10 times the power of an equivalent ASIC [7]. The power usage of an FPGA depends on two main factors: 1) the FPGA architecture, which includes how the FPGA is designed and which CMOS tech- 2 of 96 nology is used, and 2) the user circuit, including how the circuit is mapped to the FPGA resources. This mapping of the user circuit to the FPGA is performed by computer-aided design (CAD) tools. Recent years have seen numerous tech- niques for creating power-efficient FPGA architectures [8, 9], power-aware CAD algorithms [10, 11], and low-power applications [12]. As the capacities of FPGAs continue to grow, the importance of power efficient operation will only increase. In order to evaluate new FPGA architectures, or new CAD algorithms, re- searchers need a customizable CAD flow that supports experimental architectures. Furthermore, if researchers want to investigate how these architectures and algo- rithms affect power dissipation, an accurate power model, typically integrated into the CAD tools [13, 14], is required. Although vendor tools can quickly estimate the power dissipation of an application on an existing FPGA, they cannot be used to estimate the power of novel architectures or new low-level mapping algorithms. Versatile Place and Route (VPR) [15], an academic, open source, FPGA CAD tool has become the most popular tool used in the academic community to test experimental FPGA architectures and CAD algorithms. When VPR was first re- leased in 1997, it supported only basic FPGA architectures. Over time, new FPGA architectures and algorithms have been developed by industry and academia, and many have been integrated into VPR. Throughout these years, there have been power models that have been devel- oped, which integrate with VPR. These include the Poon model [13], the Jamieson model [14], and the Li model [16]. These models use probabilistic power estima- tion [17], as opposed to simulation, with a switch-level abstraction of the FPGA 3 of 96 circuit. This allows for fast power estimations that are sufficiently accurate to evaluate architectural trade-offs. These models were integrated with VPR 4.3 and VPR 5.0, which supported only simple FPGA architectures with a handful of con- figuration parameters. Recently, a new version of VPR has been developed, VPR 6.0. This new version of VPR is a significant advance over its predecessors; among other im- provements, it includes an overhaul of the types of FPGA architectures than can be supported. The tool now supports an architecture description language that users can leverage to test custom FPGA architectures, with support for complex logic blocks. Users can define a hierarchy of block types, which can be used to describe traditional FPGA architectures, as well as more modern features, such as fracturable look-up tables (LUTs). In addition, user-defined heterogeneous hard- blocks, such as memories and multipliers, are now supported. One demonstration of functionality included the evaluation of a floating point unit within an FPGA architecture [18]. This new tool opens the door for research into many more types of FPGA architectures. However, its powerful architecture language requires a much more flexible power model than any previously developed. The past power models, while flexible enough to support different lookup-table sizes, cluster sizes, and interconnect topologies, are not able to estimate the power dissipation for most architectures that will be studied using the new CAD flow. This new CAD flow is the door to the investigation of much more exotic architectures than ever before, 4 of 96 yet without an accompanying flexible power model, this potential will not be fully realized. Another issue with past power models is that they are outdated in the assump- tions they make regarding CMOS technology. The power estimations made in those models were targeted to technologies ranging in the hundreds of nanome- tres. However, today’s technologies range in the tens of nanometres, and many of the modelling techniques used in the past models are not accurate at this level. 1.2 Contributions of this Work Although FPGA power models have been created in the past, they were designed for a single, simple architecture, with known circuitry. This work explores a method for estimating power usage for many different user-created architectures. This requires a fundamentally new technique. Although the user specifies the functionality of the architecture, the actual circuitry is not specified. These func- tional descriptions of FPGA architectures must be translated into physical circuits. After this translation to circuit components, power estimation can be performed. We have implemented, verified, and used this new approach to FPGA power modelling as follows: 1. We have devloped a power model, integrated into the VPR 6.0 CAD flow, which is capable of providing power estimations for all architectures sup- ported by the tool. In addition, we have added detailed static power esti- mation, and support for fracturable LUTs, hard blocks, and modern CMOS 5 of 96 Feature Poon/ Jamieson Models Li Model This Work Architectures Supported Traditional Traditional User-designed CMOS Technologies 180 nm 100 nm 22-130 nm Fracturable LUTs No No Yes Hard Blocks No No Yes Static Power Worst-case Worst-case Detailed Autosizing of buffers and interconnect No No Yes Transistor Properties User-provided User-provided Automatic Table 1.1: Comparison of this work with past power models. processes. Table 1.1 provides a comparison of this model to past FPGA power models. 2. The power estimations of the model are verified against SPICE simulations. Dynamic power estimates are within 20% and static power estimates are within 5%. 3. The model is used to investigate power characteristics of different FPGA architectures. This includes a breakdown of power beween FPGA compo- nents, and a study of the power characteristics of fracturable LUTs. 1.3 Challenges In undertaking these research goals, there are two major challenges that exist. First, the new model must be flexible enough to process any architecture that 6 of 96 can be described using VPR 6.0’s architecture description language. Providing such flexibility, while maintaining accuracy and ease-of-use is a significant chal- lenge. The limited coverage of previous models meant that it was reasonable to ig- nore some FPGA components that did not contribute greatly to the overall power, such as local interconnect buffers, local wire capacitance, and internal multiplexer nodes. However, to accurately cover the much enlarged design space, all of these components must be accurately modelled. Secondly, in past models, the most detailed estimations were performed for the dynamic switching power, where switch-level estimation was performed on every transistor. However, other contributers to power were estimated in less de- tail. Subthreshold leakage was calculated using a simple worst-case estimate, and short-circuit power was simplified to be 10% of dynamic power. However, when modelling transistors into the tens of nanometres, these secondary power compo- nents begin to play a greater role in the overall power dissipation. More detailed estimation methods are necessary to obtain acceptable levels of accuracy. 1.4 Overview of Results This thesis includes a new power model, designed to work with architectures in versions 6.0 (and higher) of the VPR tool suite. The model is validated against 22 nm, 45 nm and 130 nm technologies. When compared to SPICE circuit simula- tions, the estimates of our model were within 20% for dynamic power estimations and within 5% for static power estimations. 7 of 96 Once verified, we use the model to study the power characteristics of different architectures. In the first of two experiments we test the power breakdown be- tween major FPGA components for the three different technologies. Results show that for a 45 nm 6-LUT, 10 LUTs per CLB architecture, 73% of power usage is due to the routing fabric, 21% due to logic blocks and 3% due to the clock network (single clock). In the second experiment we study the effect of fracturable LUTs on overall power usage. Of particular interest is the fact that modifying the archi- tecture to support fracturable LUTs increases power consumption by 3.5-14%. 1.5 Thesis Organization The thesis is organized as follows: Chapter 2 provides background information on FPGAs, CAD tools, power estimation techniques, and power models. Chapter 3 provides an overview of our power model and details the architecture genera- tor. The architecture generator creates the entire FPGA circuitry from the user- supplied architecture description. Chapter 4 details the low-level power mod- elling, which describes how power estimation is performed once the FPGA cir- cuitry is known. Chapter 5 provides verification of the model, as well as experi- ments that test the power characteristics of different FPGA architectures. Chapter 6 concludes the document. 8 of 96 Chapter 2 Background This chapter provides background information on FPGAs, their architecture, and their associated CAD tools. It also outlines different power estimation techniques, including descriptions of the estimation methods used by past power models. 2.1 FPGAs Programmable logic devices (PLDs) are electronic components that are programmed by the user to implement a digital circuit. Unlike fixed logic devices, which are manufactured for a specific function, PLDs are standard, off-the-shelf parts, that can be used for a wide range of functions. PLDs offer many advantages over fixed logic, such as shorter design times, lower non-recurring costs, and in some devices the ability to be reprogrammed [19]. Figure 2.1 shows a taxonomy of PLDs. This work focuses on power estimation for one type of PLD, SRAM-based field-programmable gate arrays (FPGAs). 9 of 96 Programmable Logic Simple PLDs High-Capacity PLDs FLASH FPGAs CPLDs EPROM EEPROM SRAM SRAM FLASH EPROM EEPROM FLASH < 600 Gates > 600 Gates Antifuse Figure 2.1: Taxonomy of PLD devices, from [20]. Field-programmable gate arrays (FPGAs) are the largest devices in the PLD family, containing thousands to millions of logic gates [20]. FPGAs consist of many fined-grained logic elements, surrounded by a very large segmented routing network. This design makes FPGAs highly flexible, and capable of implement- ing virtually any digital circuit. Most FPGA architectures are programmed by configuring a set of SRAM bits, which control the logic and routing of the chip [21]. This allows the FPGA to be reprogrammed as needed. The size, flexibility, and reprogrammability has led to the use of FPGAs in many applications, such as ASIC prototyping, image processing, internet infrastructure, medical devices, automotive, and others. 2.1.1 Basic Architectures The first FPGAs were introduced by Xilinx Inc. in 1985. Early FPGA architec- tures contained three main components: 1) logic blocks, 2) routing, and 3) I/O blocks [22]. Logic blocks are responsible for performing the actual computation, 10 of 96 such as arithmetic or logical functions. Routing allows for data to be moved be- tween logic blocks, and I/O blocks allow for data to be moved on and off the FPGA chip [21]. The following sections describe the logic blocks and routing in greater detail. Logic Blocks The basic functional unit within the FPGA is the look-up table (LUT). A k-input LUT has 2k configuration bits, which are used to store the values of a k-input truth table. The inputs to the LUT control a multiplexer which chooses between the stored values (Figure 2.2). A k-input LUT can implement any k-input logic function, since any logic function can be represented in truth table form [21]. Typically, LUTs are paired with a flip-flop, which saves state, and allows for im- plementation of sequential circuits. The LUT and flip-flop, together with a multi- plexer to select between the two outputs, are referred to as a basic logic element (BLE) (Figure 2.3). Multiple BLEs are combined to form a logic block, also known as a config- urable logic block (CLB). FPGA architectures differ in the number of BLEs per CLB. For example, the Altera Stratix V architecture uses 10 BLEs per block [23], and the Xilinx Virtex 7 architecture uses 8 BLEs per block [24]. The logic block also contains routing structures that connect the input and output pins of the logic block to the BLEs, as well as connecting the BLEs to each other. These connec- tions are referred to as local interconnect, and are often implemented as a single 11 of 96 00 1 1 in 0 in 1 out Figure 2.2: 2-input LUT, implementing the XOR function. FF LUT Figure 2.3: Basic logic element (BLE). crossbar [25]. Figure 2.4 shows a logic block that contains 4 BLEs, with a local interconnect crossbar. Routing Most FPGAs employ an island style architecture, where the logic blocks are ar- ranged in a grid, and are surrounded by many horizontal and vertical routing seg- ments. Modern FPGAs usually use unidirectional routing segments, while older FPGAs used bidirectional routing [26, 27]. The routing segments are connected to each other through a switch box, and the logic blocks connect to the routing channels through connection boxes [28]. Figure 2.5 provides an illustration of a 12 of 96 BLE BLE BLE BLE C ro ss b ar Logic Block Figure 2.4: Logic block containing 4 BLEs. simple, hypothetical FPGA architecture. Commercial FPGAs vary in their im- plementation details, and sometimes the connection boxes and switch boxes are combined into a single structure. Switch boxes are located at the intersection of vertical and horizontal routing segments. They contain programmable switches that allow each wire segment to connect to multiple other wire segments, in order to route signals throughout the FPGA. The topology of these connections depends on the FPGA architec- ture [29, 30]. In addition, the architecture may be designed to contain longer wire segments that bypass some switch boxes [26]. Figure 2.5 shows an architecture than contains a combination of length-1 and length-2 wire segments. 13 of 96 Logic Block Switch Box CB CB Logic Block CB CB Logic Block Switch Box CB Logic Block Switch Box CB CB Switch Box Logic Block Switch Box CB Logic Block Switch Box CB CB Logic Block Switch Box CB CB Logic Block Switch Box CB CB Logic Block Switch Box CB CB CB CB Figure 2.5: Island-style FPGA architecture, containing logic blocks, switch boxes and connection boxes. This architecture contains both length-1 and length-2 routing segments. 14 of 96 Connection boxes provide the connection between the routing segments and the logic blocks pins. Each logic block pin connects to some of the neighbour- ing routing channels, as illustrated in Figure 2.5. Real-world architectures may contain routing channels that are hundreds of segments wide, so it is not feasible for each pin to connect to all of the channels [27]. The pattern of connections is determined by the FPGA vendor. Each connection is programmable, and can be either enabled or disabled when configuring the FPGA. 2.1.2 Modern Architectures Modern FPGA are much more complex than described above. They have evolved from a homogeneous architecture, as described previously, to heterogeneous ar- chitectures that contain many different types of blocks, and blocks with complex features. Heterogeneous FPGAs In heterogeneous architectures, some logic blocks are replaced by memories and multipliers, to more efficiently implement certain functions (Figure 2.6) [27]. There may be multiple types of logic blocks throughout the FPGA; for exam- ple, some blocks may contain larger or smaller LUTs [31]. Additional hard cores may also be built into the FPGA to accelerate some functions, such as ethernet in- terfaces or SerDes functions [23]. Some FPGAs also contain built-in processors. As an example, the Altera Cyclone 5 SoC FPGAs contain an ARM Cortex-A9 core [32]. 15 of 96 Logic Block M e m o ry Logic Block Logic Block Logic Block Logic Block Logic Block M e m o ry M u lt ip lie r M u lt ip lie r M u lt ip lie r Logic Block Logic Block Logic Block Logic Block Logic Block Logic Block Logic Block Logic Block Logic Block Logic Block Logic Block Logic Block M e m o ry M e m o ry Logic Block M e m o ry Logic Block Logic Block Logic Block Logic Block Logic Block M e m o ry M u lt ip lie r M u lt ip lie r Logic Block Logic Block Logic Block Logic Block Ethernet Figure 2.6: Heterogeneous FPGA architecture (routing not shown). Complex Logic Blocks Modern logic blocks contain additional features, such as carry-chain logic and fracturable logic. Carry-chain logic provides support for accelerating arithmetic and logical operations [33]. Fracturable logic allows LUT hardware to be split so that LUTs can implement two smaller logic functions, instead of a single large function. This is accomplished by allowing the truth table to be shared between two logic functions, splitting the multiplexer, and providing an extra out- put. Figure 2.7 illustrates the modifications to enable fracturable LUTs. This work provides power estimations of FPGA architectures containing fracturable LUTs; however, carry-chains are not yet supported. 16 of 96 0 in 0 in 1 out 1 1 0 1 0 0 1 in 2 0 in 0 in 1 out1 0 0 1 0 1 1 1 Fractured out2 Figure 2.7: Fracturing of a LUT. On the left is a 3-input LUT, implementing a 3-input XOR function. On the right, the same hardware is used to implement two 2-input functions. Out1 implements the AND function, and out2 implements the OR function. 2.2 FPGA Computer Automated Design (CAD) Modern FPGAs contain millions of configuration bits, making it impractical for designers to manually implement their circuits. Instead, computer-aided design (CAD) tools are used, which perform the steps required to translate a hardware description language (HDL) circuit to a set of configuration bits used to program the FPGA [34]. 2.2.1 CAD Flow Steps Figure 2.8 illustrates the steps of the FPGA CAD flow, and the following briefly describes each step. 17 of 96 Circuit (HDL) Logic Synthesis Logic Optimization Technology Mapping Packing Placement Routing FPGA Programming File ODIN II ABC VPR 6.0 Figure 2.8: FPGA CAD flow [34], with associated tools [18]. • Logic Synthesis converts a circuit specified in register-transfer level (RTL) format, such as Verilog or VHDL, to a gate-level representation [35]. • Logic Optimization, often called technology-independent optimization, re- moves redundant logic and simplifies logic where possible [36]. • Technology Mapping converts the logic functions to fit within the LUTs. For example, if the FPGA architecture uses 4-input LUTs, all logic functions must be transformed into functions with four or less inputs. • Packing groups the LUTs together into logic blocks. 18 of 96 • Placement decides where each logic block should be placed on the FPGA. • Routing determines the configuration of the routing switches to provide con- nections between the necessary logic blocks pins. Upon completion of this flow, the CAD tools will have determined the config- uration bits for the LUTs, the local interconnect switches, and the global intercon- nect switches. These configuration bits are combined into a file called a bitstream, which is used to program the FPGA. 2.2.2 Verilog-to-Routing (VTR) FPGA power models are typically integrated into CAD tools because the power estimation is dependent on placement and routing information [13, 14, 16]. In addition, integration of CAD and power estimation allows for the development of power-aware CAD algorithms, such as in [10]. The power model presented in this work is integrated with Verilog-to-Routing (VTR), a recently developed, academic, open-source FPGA CAD suite [18]. VTR is a collection of tools that are used to perform the full CAD flow. ODIN II [37] is used for logic synthesis, and converts a Verilog circuit to a gate-level sum-of- products representation. Next, ABC [38] performs logic optimization using logic balancing and refactoring algorithms [39], followed by technology mapping us- ing the WireMap algorithm [40]. Finally, VPR 6.0 performs packing, placement and routing. Packing uses the AAPack algorithm [41], placement uses a simu- lated annealing algorithm [15, 42], and routing is performed using the Pathfinder 19 of 96 algorithm [43]. Together, these tools allow researchers to test experimental FPGA architectures that are not supported by commercial tools. Past FPGA CAD tools, such as VPR 4.3 [15] and VPR 5.0 [44], supported basic homogeneous FPGA architectures with some user-supplied parameters to configure the architecture. The architecture space supported by VTR is dramat- ically larger. It supports heterogeneous architectures, hard blocks and complex logic blocks. The architecture is specified through a new architecture description language, which users can leverage to provide a much more detailed specifica- tion of the FPGA architecture. In the past users were restricted to the traditional paradigm for logic block design; however, this new language allows users to fully customize logic blocks. The language supports a hierarchical model, where logic blocks are comprised of entities. Each entity can instantiate child entities, with custom interconnect between parent and children. This allows for exotic FPGA architectures with arbitrary complexity. 2.3 Power Estimation Techniques Power estimation techniques for very-large-scale integration (VLSI) circuits can be classified in two ways: 1) the level of abstraction, and 2) the method of estima- tion, either simulation or probabilistic [17, 45, 46]. 2.3.1 Abstraction Levels Figure 2.9 provides the different circuit abstraction levels at which power esti- mation can be performed [45]. More detailed circuit abstractions allow for more 20 of 96 Algorithm System Hardware Behaviour Register Transfer (RTL) Logic/Gate Switch Circuit/Transistor Es ti m at io n  A cc u ra cy C o m p u ti n g R es o u rc es Worst BestMost Least Abstraction Levels Figure 2.9: Circuit abstraction levels used for power estimation, and impacts on accuracy and resources. accurate power estimations, but at the cost of increased computation. Likewise, higher abstractions allow for quicker estimations, but with reduced accuracy. Gen- erally, power estimation tools operate at the gate-level or lower, as it is difficult to obtain sufficient accuracy at higher levels [46]. The most commonly used abstraction levels are gate-level, switch-level, and circuit-level. Circuit-level estimation requires detailed transistor models in order to determine nonlinear voltages and currents. Switch-level simplifies the circuit to a collection of nodes and transistors, where each node is modelled as a capac- itance to ground, and each transistor is modelled as an on/off switch with finite 21 of 96 resistance. Gate-level further abstracts the design, grouping transistors into logic cells, such as NAND, NOR, etc [47]. It is possible to model FPGA hadware at the lowest abstraction levels. The GILES project [48] provides a tool for generating complete transistor layouts based on VPR architectures. Although this level of detail allows for the most ac- curate power estimations, it is rarely used for large circuits due to computational requirements. For large circuits, such as FPGAs, it is more feasible to perform power estimation at the switch-level or gate-level. 2.3.2 Simulation-Based Power Estimation Power estimation through simulation is performed by providing a set of inputs to the circuit, simulating the circuit for a predetermined number of clock cycles, and measuring the power. Although simulation can provide accurate power estima- tions, it suffers from being computationally intensive and being highly dependent on circuit inputs, known as strong input-pattern dependence. Simulation Program with IC Emphasis (SPICE) is the de facto tool for circuit- level simulation and power analysis, and provides very accurate estimations. How- ever, the level of detail of SPICE leads to long run times as circuits increase in size, making SPICE unsuitable for very large circuits, such as FPGAs [46]. Other approaches have performed simulation at higher abstraction levels, such as switch- level or gate-level, to reduce the amount of computation [49–51]. However, even if computation can be reduced, the issue remains that the power dissipation is highly dependent on the inputs provided to the circuit; inputs that 22 of 96 are more active will cause the circuit to consume more power. In order to provide accurate estimation, realistic input vectors are required. It may be difficult to gen- erate realistic input vectors, especially if the circuit is still under design [17]. One solution to this problem is to use a statistical approach, which employs a Monte Carlo simulation with randomly generated input vectors [52, 53]. This technique involves repeatedly generating random input vectors, performing gate-level sim- ulation, and measuring the power, until the result reaches a certain accuracy and confidence level. The statistical Monte Carlo method provides acceptably accurate estimates, without substantial computation; however, the estimate is only of the total power. It does not provide visibility to the gate level, or even groups of gates [17]. This internal visibility is a desired property as it allows designers to determine the power requirements of different architectural components. In [54], the Monte Carlo method was modified to add internal visibility, but the increase to run time was significant. 2.3.3 Probabilistic Power Estimation The other method of power estimation is the probabilistic approach. The ma- jor advantage over simulation is that it does not require actual input vectors, only statistical properties of the inputs, and thus is characterized as being weakly input- pattern dependent. The behaviour of the inputs is characterized using the follow- ing two properties [17]: 23 of 96 1. The Signal Probability, P1, is the long-term probability that a signal is logic- high. For example, a clock signal with a 50% duty cycle will have P1(clk) = 0.5. 2. The Transition Density (or switching activity), AS, is the average number of times the signal will switch during each clock cycle. For example, a clock has AS(clk) = 2. Once the user provides the signal probability and transition density for the inputs, activity estimation tools such as [13, 37, 55–57] can be used to determine these properties for the internal nets. These tools use simulation, static analysis, or a combination of both to determine these properties. Once these properties are known for all nets, power estimation can be performed. For example, switching power is directly proportional to the transition density, and leakage currents are dependent on the signal probabilities [58]. Although the probabilistic method is faster than simulation, and less input dependent, it is generally less accurate [45]. The signal properties used by the probabilistic method assume certain statistical behaviour, which may not be true of the actual input signals. The first assumption is that all signals are independent, referred to as spatial independence [17]. In reality, signals may be correlated; for example, two signals may never be logic high at the same time. Another assumption is that signal values are independent from one clock cycle to the next, referred to as temporal independence [17]. These behaviours cannot be captured in the signal probability or transition density metrics. 24 of 96 Although the probabilistic approach is less accurate than simulation, it re- quires much less computation resources, making it possible to use more detailed abstraction levels [45]. This allows for finer-grained power details, with less run time. 2.4 FPGA Power Estimation Tools There have been three major power models developed for use with academic FPGA CAD tools. They are outlined in the following sections, including a de- scription of the approach used in this work. 2.4.1 The Poon Power Model The Poon power model [13] was developed by Kara Poon at the University of British Columbia in 1999. The tool was designed to work in conjunction with the popular academic CAD tool VPR 4.3. It supports a traditional homogeneous architecture with bidirectional routing, as described in Section 2.1.1. It includes architecture parameter support for LUT suze, LUTs per logic block, and intercon- nect topology. The model uses a probabilistic approach to power estimation and switch-level circuit abstraction. This work also includes ACE-1.0 [13], a tool that provides activity estimations of signals. The Poon power model calculates switching power of all transistors in the FPGA, based on the switching density of the signals. Short-circuit power is as- sumed to be 10% of dynamic power. Subthreshold leakage is calculated using the equation in [59]. A worst-case is assumed for subthreshold leakage where half of 25 of 96 all CMOS transistors, and all pass-transistors, are assumed to be leaking. Other types of static power, such as gate leakage, are ignored. 2.4.2 The Jamieson Power Model The Jamieson model [14] was developed by Peter Jamieson in 2009. This is a modified version of the Poon model, designed to work in conjunction with VPR 5.0. The main difference is that it supports more modern routing topologies, the most significant being unidirectional routing. Also, this model uses ODIN II [37] to perform activity estimation, instead of ACE-1.0. The model uses the same techniques as the Poon model to calculate the dynamic and static power dissipa- tion, and supports the same architectural parameters. 2.4.3 The Li Model The Li model [16] was developed by Fei Li, et. al. in 2005, and was designed to work in conjunction with VPR 4.3. Like the other models, it supports a traditional architecture with basic parameters. Like the others, this model uses a probabilistic approach to power estimation. Switch-level abstraction is used for the routing and clock network. To reduce computation, a higher level abstraction is used for logic blocks, where macro-modelling is used to estimate power dissipation of LUTs. Like the other models, this model uses the signal activity to calculate switching power. Short-circuit power estimation is more detailed, and is calculated by using SPICE to simulate buffers of various sizes. A similar simulation approach is used for subthreshold leakage estimation. 26 of 96 2.4.4 The Estimation Technique of this Work This power model presented in this work also uses a probabilistic approach. This was chosen as it allows for fine-grained estimation without the heavy computation requirements of simulation. Although not as accurate as simulation, it is sufficient to evaluate trade-offs during architecture design [46]. The majority of this work uses switch-level abstraction, although in some cases more detailed modelling is used. Since VTR supports arbitrary user-designed logic blocks it is not feasible to use higher abstraction levels, as was done in the Li model. The major difference between this model and past models is the type of ar- chitectures supported. Past models only supported a traditional homogeneous ar- chitecture, with limited parameters. This model supports many new features such as heterogeneous architectures, hard blocks—such as memories and multipliers— and complex logic blocks that contain fracturable LUTs. Furthermore, while the past tools supported only a few architecture parameters, the architecture engine in VTR allows for custom designed blocks with arbitrary complexity. This architec- ture flexibility makes this model fundamentally different than past power models. The following chapters explain this new power model. 27 of 96 Chapter 3 System Design and Architecture Generation This chapter begins by providing an overview of the new power model, and an explanation of how the model is integrated into the VTR CAD flow. The remain- der of the chapter details the architecture generator. This module is the largest piece of the power model. It generates the entire FPGA circuitry based on the user-described architecture. 3.1 Power Model Overview The power model is integrated into VTR, an academic experimental FPGA CAD flow [18]. This flow was designed to allow researchers to investigate novel FPGA architectures and the associated CAD algorithms. New FPGA architectures (such as new logic block or routing structures) can be described using an architecture 28 of 96 Low-Level Power Estimator Architecture Description File Activity Estimator VPR 6.0 (Packing, Placement & Routing) Architecture Generator ODIN (Logic Synthesis) Verilog HDL ABC (Logic Optimization) Logic Netlist (BLIF) Logic Netlist (BLIF) Netlist Activity FPGA Circuitry (Multiplexers, Inverters, and Wires) Packing, Placement, and Routing SPICE CMOS Technology File Transistor Properties Generator Power Estimate Transistor Properties Figure 3.1: Modifications to the VTR flow for power estimation. 29 of 96 description language, and the CAD tools will automatically adapt to the new ar- chitecture. The original VTR flow contains detailed area and delay models which can be used to evaluate the efficiency of benchmark circuits implemented on the proposed architectures. Since the code is open-source, designers can also modify the CAD tools themselves to investigate the effectiveness of new CAD techniques, applied to novel or existing FPGA architectures. The current VTR flow uses ODIN II [37] for Verilog synthesis, ABC [38] for logic optimization and VPR 6.0 for packing, placement and routing. Our power model adds multiple components which are integrated into the VTR flow as shown in Figure 3.1. Table 3.1 provides a listing of the model components, their purpose, and the relevant sections in this thesis. Module Function Section Architecture Generator Generates FPGA circuitry Section 3.2 Low-Level Power Estimator Estimates dynamic and static power Section 4.1 Activity Estimator Estimates behaviour of the user circuit Section 4.2 Transistor Properties Generator Extracts transistor properties from SPICE simulation Section 4.3 Table 3.1: System modules. The first step in estimating power usage is to determine the actual FPGA cir- cuitry. This is a difficult task, since VTR’s architecture description language al- lows the user to create arbitrary architectures, with no limit on complexity. This task is performed by the architecture generator, which reads the architecture de- 30 of 96 scription file provided by the user, and generates the circuitry of the entire FPGA. This circuitry is a collection of inverters, simple multiplexers and wires, and in- cludes details of the transistor sizes and wire lengths. All major components such as flip-flops, LUTs, switch boxes, etc. are decomposed into these basic circuit elements. The FPGA power usage is also dependent on the behaviour of the user-provided circuit. The activity estimator analyzes the user circuit to determine its behaviour, which includes the transition density (AS) and the signal probability (P1) for each net. The power usage also depends on how the user circuit is implemented in the FPGA circuitry. These details are contained in the packing, placement and routing information that is output by VPR. Power estimation is also heavily dependent on the chosen CMOS technol- ogy. The transistor properties generator uses SPICE simulation to automatically extract the necessary transistor properties, which includes transistor sizes and ca- pacitances, leakage currents, and other characteristics. Once the information on the FPGA circuitry, the user circuit, and the transistor properties are obtained, the actual power estimation can be performed. The low- level power estimator uses standard equations to calculate the dynamic and static power of each inverter, multiplexer and wire in the FPGA circuitry. It details how much each component type, such as switch boxes, flip-flops and crossbars, contribute to the overall power. Our implementation combines VPR 6.0, the low-level power estimator, and the architecture generator into a single executable. However, in this document 31 of 96 they are described as separate entities to clearly outline their roles in the overall power estimation. The remainder of this chapter will describe the architecture generator module. The other modules will be detailed in the following chapter. 3.2 The Architecture Generator Complete power estimation requires transistor-level details of the entire FPGA circuitry in order to make power estimations. This includes the size and connec- tions of every transistor, as well as wire length of all interconnect. Since there are millions of transistors in a typical experimental architecture, it is infeasible for the user to provide this information directly. The architecture generator an- alyzes the architecture description file supplied by the user, and determines the entire FPGA circuitry. All of the FPGA components (switch boxes, connection boxes, LUTs, flip-flops, etc.) are decomposed into inverters, simple multiplexers, and wires. The size of each transistor, and the length of each wire, is calculated automatically. Generating this information is challenging. The architecture language pro- vided in VPR 6.0 is extremely flexible, allowing the user to specify a wide vari- ety of architectures. CLBs can be arbitrarily complex, consisting of a hierarchal collection of interconnect and logic elements (including facturable LUTs). The global interconnect can consist of segments of different lengths connected using different patterns. Transistor sizes, which have a first-order affect on power, de- 32 of 96 pend on the physical length and fanout of segments, which depends on, among other things, the number of transistors in various components of the architecture. VPR 6.0 contains an architecture generation engine which estimates many of these low-level quantities based on the user-described architecture. However, the existing engine is limited to generating parameters needed for timing analysis and area estimation. Power estimation requires a much more complete set of quanti- ties; buffers cannot be abstracted as delay elements, and accurate buffer sizes are needed, even for those buffers not on the critical path. This work provides a sig- nificantly enhanced architecture generation engine that provides the information needed to make accurate dynamic and static power estimates. It is important to note that previous models in [13, 14] also contain an archi- tecture generation engine; however, the limited architectural space supported by earlier versions of VPR means that the generator was far less flexible. Thus, these previous generators are not suitable for our purpose. Section 3.2.1 describes the methods used to decompose the global routing into inverters, multiplexers and wires. Section 3.2.2 describes this decomposition for the logic blocks, and Section 3.2.3 for the clock network. Transistor sizes for these components depend on the physical dimensions of different entities in the FPGA. Section 3.2.4 details the algorithm we use to approximate these dimensions. 3.2.1 Global Routing A significant portion of the transistors in an FPGA are used to implement the flexi- ble global routing network. This network consists of switch boxes and connection 33 of 96 boxes, as described in Section 2.1. The switch boxes and connection boxes are comprised of buffers and multiplexers, the sizes and topologies of which depend on architectural parameters supplied by the user. Switch Boxes Switch boxes, which lie at the intersection of horizontal and vertical channels in an FPGA, are responsible for driving the global routing wires. There may be tens to hundreds of global wires incident to each switch box. Each global wire is driven by a multiplexer followed by a buffer [26]. The buffer drives a wire, which spans one or more grid tiles of the FPGA. At the end of the wire, is a fan-out to other switch boxes or connection boxes [60]. This is illustrated in Figure 3.2, and is referred to in this thesis as a switch box component, as many of these comprise a single switch box. The power usage of a switch box component is comprised of the power dissipation in the multiplexer (See Section, the buffer (See Section, and the wire. The size of the multiplexer is determined by the number of fan-ins of the routing channel. These fan-ins can come from other global wires, or from outputs of logic blocks. The buffer size is a function of the capacitance it drives, which is composed of the wire capacitance and the input capacitance of the fan-out. The wire capacitance is a function of the wire length, which is determined using the methods in Section 3.2.4. 34 of 96 1111 To Connection Box Figure 3.2: Switch box component, comprised of a multiplexer connected to a buffer, driving a wire. The wire fans out to connection boxes and other switch boxes. Connection Boxes Connection boxes provide the interface between the routing channels and the logic blocks. They are comprised of buffers and multiplexers. There is one multiplexer for each input pin of the logic block. A buffer connects each routing track to the multiplexers, and is needed as the track may drive many pins. Figure 3.3 provides an illustration of a simple connection box. In a real FPGA architecture, there would be many more routing tracks, and many more CLB input pins. This potentially causes large buffers and multiplexers. The buffers are sized according to the capacitance they drive, which is deter- mined by the number of multiplexers they connect to. Each routing track connects to a fraction of the CLB inputs, represented by Fcin in the architecture description file. Likewise, the number of inputs to each multiplexer is equal to Fcin multiplied by the number of routing tracks. 35 of 96 sin1 in0 out outin 1 0 0 out in0 in1 inN S N stages 1/2 Si/N 0 1 a b c d 1 0 out(b) e f a b c d out 1 1 0 1 1 0 1 0 Q D clk 1111 Vdd Vdd Vdd Vdd-Vth 1 0 0 out 1 1 0 1 0 0 1 0 0 1 0 0 1 0 1 1 0 0 0 1 0 1 1 0 1111 0 1 0 1 1 0 a b c d out(b) e f A B C CLB Routing Tracks Buffers Multiplexers Figure 3.3: Sample of a connection box. Multiplexers The multiplexers in the switch boxes and connection boxes are built using NMOS pass transistor logic, using minimum sized transistors [60]. By default, two lev- els are used for any multiplexer with four or more inputs; however, the user can override the number of levels or the transistor sizes by modifying the architecture description file. Figure 3.4 shows a 4:1 two-level multiplexer. Multi-level multiplexers are decomposed into a collection of single-level mul- tiplexers. Figure 3.5 provides an illustration of this decomposition. It is conceiv- 36 of 96 01 0 1 1 0 a b c d out(b) e f Figure 3.4: 4:1 2-level multiplexer. A B C Figure 3.5: 4:1 2-level multiplexer, decomposed into single-levels. 37 of 96 able that some architectures may contain very large multiplexers, which could have many internal nodes, each having a large capacitance due to the number of connected transistors. Consider the multiplexer in Figure 3.4. Input b is selected, and any toggles on node b will also toggle nodes e and out. This was the extent of modelling of past power models [13, 14]. However, toggles on input d will still cause internal node f to toggle, consuming power. In Figure 3.5, although only multiplexers A and C belong to the activated path, multiplexer B will still consume power. For this reason, the architecture generator will include all three multiplexers in the generated FPGA circuitry. Buffers Buffers in the connection boxes and switch boxes are built using multiple stages of cascaded inverters, as illustrated in Figure 3.6. The first stage of the buffer is a sense stage with size (W/L)P = 1, and (W/L)N = 2 . The sense stage is needed as the input to the buffer may receive a weak-1 due to pass transistor logic [60, 61]. The NMOS transistors in the remaining N stages of the buffer are sized according to Equation 3.1. (W/L)N = S(i/N) (3.1) S is the size of the final stage of the buffer, N is the total number of stages, ex- cluding the sense stage, and i is the index of the stage being sized, such that i ∈ [1,N]. The PMOS transistors are sized larger, according to the P/N ratio (See Section 4.3.4). 38 of 96 sin1 in0 out outin 1 0 0 out in0 in1 inN S N stages 1/2 Si/N 0 1 a b c d 1 0 out(b) e f a b c d out 1 1 0 1 1 0 1 0 Q D clk 1111 Vdd Vdd Vdd Vdd-Vth 1 0 0 out 1 1 0 1 0 0 1 0 0 1 0 0 1 0 1 1 0 0 0 1 0 1 1 0 1111 0 1 0 1 1 0 a b c d out(b) e f A B C CLB Routing Tracks Buffers Multiplexers Figure 3.6: Multi-stage buffer, used in connection boxes and switch boxes. The size of the final buffer stage, S, is found using Equation 3.2, which is based on the logical effort model [58]. Sbu f = 1 4 ∗CLoad CINV (3.2) In this equation, CLoad is the total load capacitance driven by the buffer, and CINV is the input capacitance of a minimum sized inverter. The number of stages is chosen using N = logSlog4 , where N is rounded to the nearest integer [58]. This creates a buffer where the size from one stage to the next grows by a factor close to 4. This factor is commonly chosen when designing high-performance circuits, as it minimizes the delay. For power efficient circuits a larger factor may be used, resulting in slower, but smaller buffers [58]. The user may specify an alternative value for this factor in the architecture description file. 39 of 96 3.2.2 Complex Logic Blocks VPR 6.0 supports user-defined logic blocks, which allow for a much larger range of architecture features than was possible in previous academic FPGA flows. This flexibility is obtained through a hierarchical description of the entities within each CLB. Each entity can: • Instantiate multiple child entities, including children of different types. • Define arbitrary interconnect between itself and children, or between mul- tiple children. • Operate in multiple modes. For example, a 6-LUT could operate as a single 6-LUT, or as two 5-LUTs. Our model includes an algorithm which handles all of these features; any CLB that can be described using the new architcture language can be handled by our tool. Algorithm 1 provides pseudo code for the hierarchical power modelling al- gorithm. The algorithm employs a recursive function, which calculates the power usage for an entity. If the entity has children, the algorithm accounts for the power usage of the circuitry connecting the parent to children, as well as interconnect be- tween children. The function is then called recursively for the child entities. If the entity does not have children it must be a primitive, such as a flip-flop, a LUT, or some other hard-block. For these types, the primitive handler function is called, which will determine the type of entity, and call the appropriate function. Each component of this algorithm will be further described below. 40 of 96 Algorithm 1 Calculate power dissipation of a CLB recursively: calc entity power(entity): 1: if entity has children then 2: // This is a parent mode, determine mode of operation 3: mode⇐ entity.mode 4: // Add interconnect power 5: for each interc in mode do 6: power⇐ power+ calc interc power(interc) 7: end for 8: for each child in mode do 9: power⇐ power+ calc entity power(child) 10: end for 11: else 12: // This is a leaf node such as a LUT or Flip-Flop 13: // Call the primitive handler 14: power⇐ power+ calc primitive power(entity) 15: end if 16: return power Intra-CLB Interconnect: For each entity within a CLB, the architecture description file must specify the type of interconnect between itself and its children. This interconnect may be one of three types: direct, many-to-one, or complete. Figure 3.7 provides a diagram of a traditional logic block, and includes an example of each type of interconnect. The architecture generator must decompose each interconnect into multiplex- ers with known transistor sizes, and wires with known length. The wire length depends on the physical spanning distance between parent and child entities, rep- resented as Linterc. This distance is approximated using Equation 3.3. Figure 3.8 illustrates the derivation of this equation. 41 of 96 8 :9  C ro ss b ar  ( C o m p le te ) 6-LUT FF BLE 2:1 (Many-to-One) Clock (Direct) 5-LUT 5-LUT CLB Figure 3.7: Types of local interconnect. 42 of 96 Linterc = 0.5∗ ( √ AreaParent− √ AreaChildren) (3.3) An m-input, n-output interconnect structure contains (m+n) input/output wires, where the length of each wire is approximated as 1/2 ·Linterc. This approximation is illustrated in Figure 3.9. This approach provides a very rough approximation, and assumes a square topology with even spacing between the parent and child entities. In reality, this is unlikely, and interconnect may span much more, or much less than this value. Un- fortunately, it is difficult to provide a more accurate estimation without knowing the transistor layout of the device, which is too complex to estimate automatically, and too burdensome to require from the user. In addition, this model only con- siders the wirelength of interconnect structures between parent and child entities. The wirelength within a primitive, such as a LUT or flip-flop, is ignored. The following describes modelling techniques specific to each interconnect type: Direct Interconnect This is a pure wire connection and requires no multiplexers. The connection contains a single source input, which drives one or more sinks. In Figure 3.7, the clock wires provide an example of this type of connection. Many-to-One Interconnect This type is implemented as a single multiplexer. An example of this pattern is a multiplexer that chooses whether the BLE output is 43 of 96 Parent Entity Children Linterc Figure 3.8: Local interconnect spanning distance, Linterc, between parent and child entities in a CLB. driven by the LUT output or the flip-flop output, as shown in Figure 3.7. These potentially large multiplexers are decomposed into single-level multiplexers, in the same manner as the global routing multiplexers (see Section The architecture description file also supports the declaration of bus-based multiplexers, which can be used for coarse-grained architectures. An m-input many-to-one interconnect of n-wide buses is modelled as n instances of an m- input multiplexer. Complete Interconnect This type describes a fully populated m-input, n-output crossbar. These crossbars are modelled as n number of m-to-1 multiplexers. Each multiplexer is modelled as previously described. Figure 3.7 provides an example 44 of 96 𝐿𝑖𝑛𝑡𝑒𝑟𝑐 5 :4  C ro ss b ar  ( C o m p le te ) Parent Entity Children Figure 3.9: Wire length in a local interconnect structure. Shown here is a 5-input, 4-output complete interconnect, which results in 9 wires of length 1/2 ·Linterc. of an 8-to-9 crossbar connecting the inputs and outputs of the CLB to the inputs of the BLEs. Look-up Tables (LUTs) LUTs are assumed to be implemented as a network of two-input multiplexers, with level restorers used between every other stage [60]. Figure 3.10 provides an illustration of a 4-input LUT. Calculating the power dissipation of this structure requires the switching activity of internal nodes of the multiplexer. The activity estimator, which will be described in Section 4.2, determines the activity of each 45 of 96 net, but not the activity within the LUTs themselves. These internal activities are calculated as follows. The initial level of multiplexers is fed by SRAM bits, making P1 (the long-term probability that a node is high) equal to the value of the SRAM cell. P1 values are cascaded through the LUT levels using Equation 3.4 for each 2-input mulitplexer, where s is the select signal. P1(out) = (1−P1(s))∗P1(in0)+P1(s)∗P1(in1) (3.4) AS(out) = (1−P1(s)) ·AS(in0)+P1(s) ·AS(in1) +AS(s) ·P(in0 6= in1) (3.5) AS values (the expected switching activity of each node) are calculated at the output of each 2-input multiplexer using Equation 3.5, which is comprised of three terms. The first two terms represent the case when the selected input toggles, caus- ing the output to toggle. The third term, AS(s) ·P(in0 6= in1), represents toggles on the output due to the selector toggling, which occurs only when the two inputs are of different logic value. The probability of the two inputs being different is calculated using Algorithm 2. D Flip-Flop A D Flip-Flop, contains a master and slave loop, each with two inverters and a two input multiplexer. Figure 3.11 provides an illustration. The inverters are assumed to be minimum sized, and the multiplexers are composed of two minimum size 46 of 96 Algorithm 2 Method of calculating the probability that the two inputs of a stage-n multiplexer in a LUT have different logic values. Ptotal = 0 for all {in1, in2, ...inn−1} | ini ∈ {0,1} do // Check if SRAM values are diffent if SRAM(in1, in2, ...,0) 6= SRAM(in1, in2, ...1) then Pbranch = 1 // Sum probability of each branch for i = 1→ (n−1) do Pbranch = Pbranch ·P(inputi == ini) end for Ptotal+= Pbranch end if end for s in1 in0 out outin 1 0 0 out in0 in1 inN S n 1/2 Si/n 0 1 a b c d 1 0 out(b) e f a b c d out 1 1 0 1 Figure 3.10: 4-input LUT. transmission gates [58]. Like LUTs, the internal node activity must be calculated. The behaviour of the master loop is assumed to be P1 = P1(D) and AS = (1− 47 of 96 10 1 0 Q D clk Figure 3.11: D Flip-Flop. AS(clk)) ∗ AS(D). The slave loop behaviour is assumed to be P1 = P1(Q) and AS = AS(Q). Undefined Hard Blocks (Black Boxes) Our model does not estimate power of I/O pads, memories, multipliers, and other hard blocks designed by users. I/O pads have intentionally been excluded due to their complexity. If the user wishes to model memories, multipliers or other custom hard blocks, he/she must provide parameters for the block. This can be done in one of three ways: 1. Provide the absolute dynamic and static power of the block in the architec- ture file. This is the simplest, but least accurate approach, as power esti- mates are independent of the behaviour of input pins. 2. Provide the equivalent internal capacitance of the block in the architecture file. The power model will average the switching activity (AS) across all 48 of 96 input pins to calculate dynamic power. Static power must still be specified as an absolute in the architecture file. 3. Provide a coded function that can be called by the primitive handler. The primitive handler will provide the signal probability (P1) and switching ac- tivity (AS) of the input pins. The user provided function should use this information to make more detailed power estimations, such as is done for LUTs and flip-flops. Static Power of Unused Blocks One step of Algorithm 1 is to determine the mode of operation for each entity in the CLB. For example, it is necessary to know whether the fracturable LUT is operating in fractured or non-fractured mode. However, if an entity is unused, it is not clear which mode it is operating in. This is needed to calculate static power of the unused entity. To handle this scenario, the power model allows the user to specify the default mode of operation in the architecture file. For example, the user can specify that when unused, LUTs should be modelled as the non-fractured type. Limitations There are several limitations in the way that the architecture description file spec- ifies modes of operation. The file is designed to describe the functional behaviour of entities, and not the actual hardware. For example, functionally a 6-LUT can operate as two 5-LUTs. However, the actual hardware of the 6-LUT is not iden- 49 of 96 tical to the hardware of two distinct 5-LUTs. Unfortunately, there is no visibility within VTR to distinguish between a normal 5-LUT and a 5-LUT that is actually half of a 6-LUT. Thus when LUTs are fractured they are treated as multiple or- dinary LUTs. This results in the input buffers to the LUTs being counted twice. Our testing shows that this discrepancy should be limited to a 1-2% overestimate in the overall power usage. 3.2.3 Clock Network The clock network modelled is a four quadrant spine and rib design, as illustrated in Figure 3.12. The design is similar to the topology used in a Xilinx Virtex II Pro [62]. At this time VPR only supports a single clock; however, the power model contains infrastructure to model multiple clocks, provided that each clock is composed of the same topology as illustrated in the figure. Some FPGA multi- clock networks are more complicated, with different clocks connecting to different regions of the chip [62], but we do not model these more complex networks. The model assumes that the entire spine and rib clock network will contain buffers separated in distance by the length of a grid tile. As in Section, the buffer is multi-stage with the final stage sized according to Equation 3.2. In this case, the load capacitance is assumed to be the next clock buffer, plus the capacitance of the wire connecting to it. 50 of 96 Figure 3.12: The clock network. Squares represent CLBs, and the wires represent the clock network. 51 of 96 3.2.4 Physical Size Estimation One benefit of this power model is that all of the components are automatically sized. This includes routing buffers, clock buffers, and buffers within a CLB. The size of these buffers depends on the capacitance of the wire that is driven by the buffer. For this reason, the power model must be aware of the physical size of grid tiles in the FPGA, as well as the size of entities within CLBs, such as LUTs, flip- flops and multiplexers. The power model employs a transistor counting algorithm to determine the physical size of the various parts of the FPGA. This algorithm works with the architecture description file, so any user defined architecture is supported. Algorithm 3 provides the method used to calculate the FPGA grid tile size, as well as the sizes of all CLB entities. Similar to the power estimation algorithm, a recursive function traverses the CLB entity hierarchy, counting transistors at each level. For entities that support multiple modes, the mode that requires the largest transistor area is assumed. If the user introduces custom hard-blocks in the design, they must also provide a function that returns the number of transistors in the block. In our estimations we assumed the area of an SRAM cell to be equivalent to the layout area of 6 minimum-sized transistors [58]. The architecture description file contains a parameter that allows the user to override this value. 52 of 96 Algorithm 3 FPGA physical size estimation. calc FPGA tile length: transistor cnt = cnt entity transistors(CLB) transistor cnt = transistor cnt+2∗ cnt connection box transistors() transistor cnt = transistor cnt+ cnt switch box transistors() return √ (transistor cnt ∗ transistor unit area) cnt entity transistors(entity): max transistor cnt⇐ 0 if entity has children then // Find the mode that requires the most transistors for each mode in entity.modes do transistor cnt⇐ 0 for each interc in mode do transistor cnt⇐ transistor cnt+ cnt interc transistors(interc) end for for each child in mode do transistor cnt⇐ transistor cnt+ cnt entity transistors(child) end for max transistor cnt = max of (max transistor cnt, transistor cnt) end for else // This is a leaf node such as a LUT or Flip-Flop // Call the leaf handler max transistor cnt⇐ max transistor cnt+ cnt lea f transistors(entity) end if // Store area of this entity for later use entity.area⇐ max transistor cnt ∗ transistor unit area return max transistor cnt 3.3 Summary This chapter provided an overview of the components in our power model, and the roles they play in power estimation. The chapter also detailed the architecture generator, which is responsible for translating arbitrary FPGA architectures into 53 of 96 basic circuit components. This includes generating circuit information for the global routing fabric, the CLBs, and the clock network. All transistors and wire lengths in these circuits are automatically sized. The architecture generator is able to process any user described architecture, regardless of complexity, and produce a collection of inverters, single-level mul- tiplexers and wires. Once the FPGA circuitry has been reduced to these simple components, the other parts of the model are capable of estimating the dynamic and static power of each component. This power estimation is outlined in the next chapter. 54 of 96 Chapter 4 Power Estimation This chapter describes the remaining components of our model: The low-level power estimator, the activity estimator, and the transistor properties generator. The architecture generator translates the entire FPGA circuitry into a collec- tion of inverters, multiplexers and wires, after which the low-level power estima- tor provides power estimates of these components. These estimates, described in Section 4.1, depend on the signal behaviour and transistor properties. Signal behaviours are determined by the activity estimator, as described in Section 4.2. Transistor properties are generated by running SPICE simulations and extracting the necessary values, as described in Section 4.3. 4.1 Low-Level Power Estimation The power dissipated in the inverters, multiplexers and wires is comprised of both dynamic and static power. Dynamic power includes both switching power and 55 of 96 short-circuit power. Static power consists of subthreshold and gate leakage. Other sources of power are not significant and are ignored [58]. 4.1.1 Switching Power Switching power is the result of charging and dissipating energy stored in the ca- pacitance of transistor nodes and wires, and is proportional to the frequency with which the nodes toggle. The switching power dissipated by every wire, as well as the source, drain, and gate of every transistor is estimated using Equation 4.1 [63]. Pdyn = αCVswingVDD f (4.1) The parameters of the above equation are: • α: The expected switching activity of the node. α = 1 represents a node that toggles once, or switches twice, per clock cycle. • C: The node or wire capacitance. • VDD: The supply voltage. • Vswing: The swing voltage, which is the voltage range of the node or wire. • f : The operating frequency of the circuit. In our implementation, transistor node capacitances are provided by the transistor properties generator, which will be described in Section 4.3.1. Wire capacitances are calculated by multiplying the wire length provided by the architecture genera- tor with the unit-length wire capacitances provided in the architecture description file. The activity factor, α , is calculated as α = AS/2, where AS is the transi- 56 of 96 tion density from the activity estimator, which will be described in Section 4.2. The operating frequency, f , is provided by VPR 6.0. Typically, the swing volt- age, Vswing, is equal to the supply voltage. However, in pass-transistor logic, there may be voltage drop since NMOS transistors transmit a weak logic-1 [61]. This voltage drop is estimated using techniques described in Section 4.3.5. 4.1.2 Short-Circuit Power Short-circuit current occurs in CMOS logic during an input transition, as both the pull-up and pull-down networks are simultaneously enabled for a short period of time [58]. In the components handled by this model, short-circuit power occurs only in inverters. It is highly dependent on the speed of the input transition; slower input transitions lead to longer periods of short-circuit current. In cases where the inverter is driven by a pass-transistor multiplexer, the input voltage must be pulled up to VDD, creating a slow input transition, and increased short-circuit power [64]. If the input multiplexer is large, the input capacitance will be larger, further slow- ing the input transition. The model estimates the short-circuit power of all buffers as a factor of the switching power. This factor is extracted from SPICE, as described in Section 4.3.6. This factor depends on the size of the buffer, the type of logic driving the buffer, and the capacitance at the input. 57 of 96 4.1.3 Subthreshold Leakage Power Subthreshold leakage current occurs in transistors that are operating in the cut-off region, but have a non-zero source-drain voltage (Vds). The amount of leakage is highly dependent on Vds [58]. Subthreshold leakage occurs in both inverters and multiplexers. Inverters In an inverter, the subthreshold leakage power, Pst , of the two transistors is: Pst, PMOS =VDD ·P1 · Ist((W/L)P) (4.2) Pst, NMOS =VDD · (1−P1) · Ist((W/L)N) (4.3) Ist is the subthreshold leakage current of the transistor when Vds = VDD, which is a function of the transistor size. It is determined automatically through SPICE, as described in Section 4.3.2. Multiplexers For muliplexers, past power models [13, 14] used a simple worst-case analysis, where all transistors were assumed to be leaking. We use a different approach, analyzing the leakage behaviour of each transistor. In an m-input, single-level multiplexer, there will always be one input that is selected. The voltage drop (Vds) across the selected transistor is small, and the subthreshold leakage can be ig- nored. However, the other m− 1 transistors in the multiplexer may experience a more significant voltage drop and exhibit significant leakage [65]. The subthresh- 58 of 96 old leakage power of each of these transistors is: Pst =Vdd ·P[V (i) 6=V (o)] · Ist(Vds) (4.4) P[V (i) 6=V (o)] is the probability that the logic-value of the input is different than the logic value of the output, and is determined using the signal probabilities (P1 values). Figure 4.1 provides an example of a three-input multiplexer, and illus- trates how the leaking transistors depend on the values of the inputs. Ist is the subthreshold current of a minimum-sized NMOS transistor, for a given voltage drop, Vds. As mentioned earlier, the voltage drop across the multiplexer is a func- tion of the size of the multiplexer, and the values of the inputs. SPICE simulations are used to determine the leakage current for various Vds values, as described later in Section 4.3.2. 4.1.4 Gate Leakage Power Gate leakage occurs when currents tunnel through the transistor gate to the source- drain channel. We found that gate leakage was only significant for large inverters. The gate leakage power (Pg) of the two transistors in the inverter is calculated as: Pg, PMOS =VDD · (1−P1) · Ig(W/LP) (4.5) Pg, NMOS =VDD ·P1 · Ig(W/LN) (4.6) 59 of 96 10 0 0 1 1 1 (a) Output→Input 1 0 0 0 0 0 1 (b) Input→Output Figure 4.1: Subthreshold leakage in a multiplexer, which can occur between input and output in either direction. Leaking transistor shown with an arrow. In these equations, Ig is the gate leakage current of the transistor, and is a func- tion of the transistor size. It is extracted from SPICE, as described later in Sec- tion 4.3.3. 4.2 Activity Estimation The dynamic and static power estimates described in the previous section are de- pendent on the behaviour of the user-supplied circuit. For each net in the circuit, the activity estimator determines: • The Transition Density, or switching activity, AS. • The Signal Probability, P1. 60 of 96 These values were described in greater detail in Section 2.3.3 4.2.1 Algorithm Previous power models have used ACE-1.0 [13] and ACE-2.0 [55] to generate these values. ACE-1.0 is fast, but is inaccurate for large and/or sequential circuits. ACE-2.0 provides an improved algorithm that better handles sequential circuits. Unfortunately, ACE-2.0 is built on the Berkeley SIS tool [66], which is obsolete. SIS has been superseded by the Berkeley ABC circuit tool [38], which is more robust, has better performance, and supports much larger circuits. As part of this work, we have implemented the algorithms from ACE-2.0, us- ing the ABC libraries. Our implementation consists of two phases: simulation and static analysis. Although ACE-2.0 used three phases, the second phase was an optimization, designed to improve run-time when estimating activity of large circuits. Because of the improved performance of ABC, the second phase is no longer necessary. The following describe the two phases of the activity estima- tor, which correspond to the first and third stages of ACE-2.0. These phases are described in greater detail in [55]. Stage 1: Simulation In the first stage, the circuit is simulated for 5000 cycles. The user has the option of providing a vector of inputs, or they may specify P1 and AS for each of the input nodes. If neither is provided, the inputs are assumed to have the behaviour P1 = 0.5 and AS = 0.2. These are the same values used by ACE-1.0 and ACE- 61 of 96 2.0. The overall power of the circuit is highly dependent on activity of the inputs. Inputs with larger activity will directly increase the estimated dynamic power of the circuit. During circuit simulation, the logic values of each register are monitored. This is used to calculate P1 and AS for each register in the circuit. The simulation phase is necessary as the static analysis method is not accurate when there are sequential loops present [55]. Stage 2: Static Analysis The second stage is a static analysis of the behaviour of the combinational logic nodes between the registers. It determines the probability of changes on the inputs, and whether these changes will cause a change on the output. The algorithm also provides an estimation of circuit glitching, using a low-pass filter approach as described in [67]. 4.2.2 Limitation: Black Boxes ACE-2.0 was created to be used with older versions of VPR, which did not sup- port heterogeneous FPGA architectures. The latest version of VPR allows for the specification of hard-blocks, such as memories, multipliers, or other user-defined functions. In the BLIF format, these functions are represented as black boxes, with no definition of their behaviour. A major limitation of the activity estimator is that it does not consider the contents of the black boxes. It uses ABC to read the BLIF file, which removes 62 of 96 black boxes from the circuit. The outputs of the black box become primary inputs to the circuit, and the black box inputs become primary outputs of the circuit. The activity estimation then proceeds as usual. The outputs of the black box will be assigned activity values, just as if they were an input to the circuit. This results in activity information that does not reflect the functionality of the black box. It is possible to work around this limitation by providing realistic activity values for the black box outputs, just as can be done with primary inputs. 4.3 Transistor Properties Generator Static and dynamic power calculations rely heavily upon the CMOS technology being used. In past power models [13, 14] users were responsible for providing many properties of the CMOS technology, such as capacitances, short-circuit be- haviour, and other transistor parameters. The models used these parameters with equations to approximate transistor capacitances and leakage currents. There are two main disadvantages to this method. First, this technique does not scale well to modern CMOS technologies. The equations used to estimate leakage currents in older CMOS technologies are not accurate across modern technologies. Secondly, this method places a burden on the user to determine all of these parameters prior to using the power model. Our model takes a different approach; it provides a script that performs multi- ple SPICE simulations, extracts relevant transistor characteristics, and writes them to a file. The user is only required to provide a transistor technology file, the op- erating voltage, and the operating temperature. The entire process takes about 5 63 of 96 minutes to execute. This process needs to be performed only once, and the file can be reused for subsequent executions of the power model. A new file needs to be created only when changing CMOS technologies, operating voltage, or tem- perature. When performing SPICE simulations, the script uses the default parameters included in the technology file. In addition, parameters are provided for the source/drain areas and perimters (AS, PS, AD, PD). The width of the source and drain regions is assumed to be equal to the width of the transistor. The length of these regions is assumed to be 2.5 times the length of the transistor. The following explains how the script determines relevant transistor charac- teristics for the CMOS technology. 4.3.1 Transistor Node Capacitances Transistor nodal capacitances are determined for both PMOS and NMOS minimum- length transistors. The transistor sizes begin at the minimum width, and increase by 5% until reaching 2000 times the minimum width, resulting in data for over 150 different transistor sizes. For each size, a SPICE simulation is performed on a single transistor. The desired node (source, drain, or gate) is kept logic-high and the voltages to the other two nodes are varied. The capacitance of the desired node is measured and averaged across the simulation. 4.3.2 Subthreshold Leakage Current Subthreshold leakage currents are required for two different scenarios: 64 of 96 1. For inverters, where transistor size varies, but Vds is always equal to VDD. 2. For multiplexers, where transistor size is always minimal, but Vds varies. For the first case, where transistor size varies, the process is similar to that de- scribed above. Over 150 different transistor sizes are simulated in SPICE, and the subthreshold leakage current is measured. For PMOS transistors the source and gate are set to VDD, and the drain is set to ground. The voltages are reversed for NMOS transistors. For the second case, where Vds varies, a minimum-sized NMOS transistor is simulated. The gate is set to ground, the drain-source voltage is incremented from 1/2VDD to VDD, and the subthreshold current is measured. 4.3.3 Gate Leakage Current To determine gate leakages, a similar process was followed. SPICE simulation was performed for over 150 PMOS and NMOS transistor sizes. For PMOS tran- sistors, the gate was set to ground, the source and drain were set to VDD, and the current through the gate was measured. For NMOS transistors, the node voltages were reversed. 4.3.4 P/N Ratio Sizing In order to properly model transistor sizes, the P/N ratio must be determined. The P/N ratio is the ratio of the width of the PMOS transistor to the width of the NMOS transistor in an inverter, and depends on the CMOS process. SPICE simulation is performed on a single inverter with a square input wave. The NMOS transistor is 65 of 96 sized such that W/L = 1, and the PMOS transistor is swept in size from W/L = 1 to W/L= 5, by increments of 0.05. The P/N ratio is chosen to minimize the difference in rise and fall delays, which is common design practise [58]. 4.3.5 Multiplexer Voltage Drop In pass-transistor multiplexers, when the output is logic-high, the output voltage will always be less than VDD. This is because NMOS transistors transmit a weak logic-1 [58]. Our testing showed that the output voltage depends on both the size of the multiplexer, and the logic value of the non-selected inputs. Adding more transistors to the multiplexer, or having more inputs that are grounded, cause the output voltage to drop. This is because both scenarios decrease the equivalent resistance between the output and ground. In addition, since multiplexers may be stacked in series, the input voltage to a multiplexer may be less than VDD, further decreasing the output voltage. To determine the expected voltage drop across a multiplexer we simulated many different multiplexers, varying both the size and the input voltage. For a given size and input voltage, we simulate the multiplexer with all non-selected inputs set to ground, and then with all inputs set to the input voltage. The results are extracted and stored in a table. This allows the model to predict the output voltage of a multiplexer based upon 1) the size, 2) the input voltage, and 3) the expected logic-value of the inputs. Although this may seem excessively detailed, it is necessary to make accurate static power estimates. Subthreshold currents are 66 of 96 ISW+ISC ISC ISC ISW+ISC Figure 4.2: Short circuit currents in inverters during input transitions. The left-hand side shows an inverter experiencing a rising edge. The out- put capacitance discharges through ground (ISW ), and the short-circuit current (ISC) enters from the supply and exits through ground. On the right-hand side, a falling edge input is shown, where the output capac- itance in charged. highly dependent on Vds; even small changes to the multiplexer voltage drop can cause large changes in static power dissipation. 4.3.6 Short-Circuit Buffer Factor As described in Section 4.1.2, CMOS buffers experience short-circuit currents during a switching of the input. The short-circuit currents are increased when the buffer is driven by a pass-transistor multiplexer, as it takes time for the input to be pulled up to VDD. If the input multiplexer is large, the pull-up takes longer due to the increased capacitance. 67 of 96 To determine the effect of short-circuit power we used SPICE to automatically simulate buffers of various sizes, driven by either CMOS logic, or pass-transistor logic with various multiplexer sizes. We measured the currents from the supply, and to ground, during rising and falling edges. When the input to an inverter ex- periences a falling edge, the output experiences a rising edge, and the capacitance at the output is charged. The current from the supply includes both the current to charge the output, as well as the short-circuit current. The current to ground is only the short circuit current. A similar, but reverse scenario occurs on the rising edge of an input. Figure 4.2 illustrates the full behaviour. Using this technique we can isolate the short-circuit current, and represent it as a factor of the switching power. 4.4 Summary This chapter detailed the low-level power estimator, activity estimator, and tran- sistor properties generator. Together, these modules are able to estimate the static and dynamic power of every inverter, multiplexer and wire that make up the FPGA circuitry. The activity estimator determines the behaviour of the user circuit, which di- rectly influences the power estimates. The transistor properties generator uses SPICE simulations to extract characteristics of the CMOS process, such as tran- sistor capacitances and leakage currents, which are essential in making accurate transistor-level power estimates. The low-level power estimator combines all of this information, and calculates the static and dynamic power of the entire FPGA. 68 of 96 This chapter, together with the previous chapter, contain all of the implementa- tion details of our model. The following chapter explains how the tool is verified, as well as experimental results. 69 of 96 Chapter 5 Verification and Results This chapter includes an evaluation of the accuracy of the power model estima- tions, compared to those obtained from SPICE simulations, as well as experiments performed using the model to estimate the impact of various FPGA architecture parameters on power. The first experiment (Section 5.3) provides a breakdown of power usage between major FPGA components for three CMOS processes. The second experiment (Section 5.4) studies the effect of fracturable LUTs on overall power usage. 5.1 Verification of Power Estimation In order to verify that our model produces accurate power estimations, we com- pared the power estimates from our model to results from SPICE simulations for many different FPGA components. 70 of 96 5.1.1 Verification Procedure SPICE circuits were created for various sizes of inverters and multiplexers, which are the basic blocks of the FPGA circuitry. To test the interaction between these basic components we also designed some larger components, which include multi- stage buffers, LUTs, flip-flops and switch box components. The circuits were simulated in HSPICE [68] for one clock cycle, with a 5 ns period. For each component, we tested both high-activity and zero-activity sce- narios. In the high-activity test, each input was toggled once during the clock cycle, such that P1 = 0.5 (signal probability) and AS = 2 (activity factor). The high-activity scenario verifies the accuracy of the dynamic power estimations, as these large activity values will cause the dynamic power to dominate the overall power usage. The second experiment simulates a zero-activity circuit. In this case, the inputs are held at logic-high and are unchanged for the duration of the simulation, thus P1 = 1 and AS = 0 for each input. This scenario tests the accuracy of the static power estimations, as there is no dynamic power when the inputs do not toggle. The energy usage is estimated in SPICE by integrating the supply current over the simulation time, and the result is compared to the estimate provided by our power model. This comparison was performed for three different CMOS pro- cesses: 22 nm, 45 nm, and 130 nm. The CMOS technology files were obtained from the Berkeley Predictive Technology Model (PTM) [69], which are predic- tions of real-world technologies. Table 5.1 lists characteristics of these CMOS processes. 71 of 96 Process VDD P/N Ratio NMOS PMOS Cg (aF) Cs/d (aF) Ist (nA) Cg Cs/d Ist 22 nm 0.8 1.70 15 57 4.8 8 80 4.3 45 nm 1.0 1.75 53 118 2.3 28 182 0.5 130 nm 1.3 2.50 255 351 10.2 131 602 6.2 Table 5.1: CMOS process characteristics. All transistor values are shown for a minimum-sized transistor. Ist is the subthreshold leakage current when Vds =VDD. Parameters were extracted at 85◦ C. 5.1.2 Verification Results Table 5.2 and Table 5.3 contain the results of the high-activity and zero-activity tests, respectively. Each table lists the energy usage obtained through SPICE sim- ulations, and the error percentages of our model. The results show that for all component types, the high-activity estimation is within 20% of SPICE results, which demonstrates the accuracy of the dynamic power estimations. In the case of the zero-activity scenario, the estimations are even more accurate, falling within 5% of the SPICE results. This demonstrates the high accuracy of the static power estimations. In general, our model provides good estimates of both dynamic and static power usage for all component types. However, it should be noted that the to- tal estimated FPGA power will still be significantly lower than if the power were measured for a physical FPGA. This is because the model does not incorporate all components of the FPGA, such as the I/O pads, the clock generator, and other spe- cialized circuitry. Unlike power estimation algorithms integrated into commercial CAD tools, the purpose of our model is not to provide absolute FPGA power es- 72 of 96 Component Type Size 22 nm 45 nm 130 nm Act. (fJ) % Est. Error Act. (fJ) % Est. Error Act. (fJ) % Est. Error Inverter 1 0.16 -6 0.5 -7 4 -16 8 1.06 -14 2.9 -12 26 -21 16 2.08 -14 5.7 -13 52 -21 32 4.15 -14 11.2 -13 102 -21 64 8.25 -14 22.3 -13 205 -22 Multiplexer 4 0.40 +1 1.4 -7 8 -16 8 0.74 +1 2.8 -6 14 -16 12 1.01 +3 3.4 -6 19 -14 16 1.34 +3 4.6 -8 25 -14 20 1.61 +3 5.4 -6 30 -13 Multi-Stage Buffer 16 2.89 +3 8.0 +6 95 -15 25 4.37 -1 12.5 +1 156 -17 64 11.34 -3 31.9 -4 396 -21 LUT 2 1.59 +15 3.89 +17 28 0 4 6.70 +18 17.12 +14 115 -7 6 25.82 +20 67.56 +13 437 -10 D Flip-Flop - 1.15 -8 3.7 -9 26 -10 Switch Box Component (Mux./Buffer) 4/9 3.73 +4 8.8 +4 77 -14 8/9 4.32 -2 9.5 0 84 -15 12/16 6.80 -9 15.0 -8 143 -19 16/16 7.44 -12 15.6 -4 150 -19 20/25 10.79 -15 22.9 -13 229 -20 25/25 11.65 -18 23.8 -11 234 -19 Table 5.2: High-Activity energy estimation, versus SPICE simulation. Act. shows actual energy (femtojoules), obtained through SPICE simulation, for a single cycle (5 ns). % Est. Error shows the percentage difference between our model estimation and the actual energy, where positive percentages indicate overestimates. All inputs toggle twice during the cycle. 73 of 96 Component Type Size 22 nm 45 nm 130 nm Act. (fJ) % Est. Error Act. (fJ) % Est. Error Act. (fJ) % Est. Error Inverter 1 0.03 0% 0.01 0% 0.11 0% 8 0.33 0% 0.05 0% 0.92 0% 16 0.66 0% 0.11 0% 1.84 0% 32 1.33 0% 0.21 0% 3.69 0% 64 2.68 0% 0.42 0% 7.38 0% Multiplexer 4 0.01 +6% 0.01 +4% 0.08 +3% 8 0.02 +7% 0.02 +4% 0.15 +3% 12 0.02 +5% 0.02 +3% 0.19 +2% 16 0.03 +7% 0.03 +4% 0.22 +3% 20 0.03 +6% 0.03 +4% 0.26 +2% Multi-Stage Buffer 16 0.78 +1% 0.17 +2% 2.17 +3% 25 1.18 +1% 0.24 +1% 3.28 +2% 64 2.51 0% 1.16 0% 6.83 +1% LUT 2 0.35 0% 0.12 +1% 1.16 +1% 4 0.92 -1% 0.39 -4% 3.22 -2% 6 2.26 0% 1.19 -1% 8.35 -2% D Flip-Flop - 0.10 0% 0.04 -2% 0.37 -2% Switch Box Component (Mux./Buffer) 4/9 0.48 0% 0.12 -1% 1.41 -1% 8/9 0.50 0% 0.14 -1% 1.52 -1% 12/16 0.83 0% 0.21 -1% 2.44 -1% 16/16 0.85 0% 0.22 -1% 2.51 -1% 20/25 1.26 0% 0.30 -1% 3.66 -1% 25/25 1.28 0% 0.31 -1% 3.73 -1% Table 5.3: Zero-Activity energy estimation, versus SPICE simulation. Act. shows actual energy (femtojoules), obtained through SPICE simulation, for a single cycle (5 ns). % Est. Error shows the percentage difference between our model estimation and the actual energy, where positive percentages indicate overestimates. Inputs do not toggle. 74 of 96 timates. Instead, the purpose is to quantify relative improvements or degradation in power efficiency as architectural or CAD parameters are changed. The results show that the power model is scalable between small and large components, as well as between small and large transistor technologies. The scalability of the power model across different technologies and components makes it useful for evaluating trade-offs during FPGA architecture and CAD design. Although our model is sufficiently accurate for architectural evaluations, some error still exists between estimates of our model, and the result from SPICE sim- ulations. The following section provides explanations for these differences. 5.2 Sources of Estimation Error The following outlines sources of error in our power model estimations, specifi- cally in comparison to SPICE results for identical components. 5.2.1 Short-Circuit Current The largest source of error is short-circuit currents, which are complex and diffi- cult to estimate. All CMOS circuity experiences some short-circuit current; how- ever, it is particularly significant when the CMOS logic is driven by pass-transistor logic. This pattern occurs in both switch boxes and LUTs. For example, switch box components (Figure 3.2) contain a multiplexer, made up of pass-transistor logic, that drives the input of a multi-stage buffer. The pass-transistor logic can- not produce a strong logic-1, so a weak PMOS transistor is added in a feedback configuration, which pulls the input to VDD. However, this pull-up takes time, 75 of 96 resulting in a slow rising edge to the input and substantially larger short-circuit currents than if the buffer were driven by CMOS logic. This behaviour can be seen in Table 5.2, which shows that the power usage of a switch box component is much larger than just the sum of the multiplexer and buffer that compose it. For example, at 22 nm, a 12-input multiplexer re- quires 1.0 fJ of energy per cycle, and a size-16 buffer requires 2.9 fJ. However, when combined, resulting in the buffer being driven by pass-transistor logic, they require 6.8 fJ of energy, an increase of 74%. We do perform some estimation of this short circuit current, as explained in Section 4.1.2. This has allowed us to reduce the error from 50% to within 20%. More extensive short-circuit modelling would be required to improve accuracy further. 5.2.2 Transistor Node Capacitances Another source of error is our method of estimating transistor node capacitances. In our power model they are extracted from SPICE simulation, as explained in Section 4.3.1. Our model uses a single value that represents the average transistor capacitance. In reality, transistor node capacitances are a function of the state of the transistor, and vary based on the voltages present at the other nodes of the transistor. We do not model this level of complexity, and this simplification is likely responsible for some of the error in dynamic power estimations. 76 of 96 5.2.3 Gate Leakage Currents Our model estimates gate leakage currents only for CMOS inverters, as described in Section 4.1.4. We ignore gate leakage in multiplexers because 1) multiplexers are built using small transistors, so the gate leakage is minimal, and 2) variations in internal node voltages of multiplexers make accurate gate leakage difficult. This simplification accounts for the error in static power estimations of multiplexers, which is at most 7%. 5.3 Experiment 1: Component Breakdown With the accuracy of the model verified, we now use it to study power characteris- tics of different architectures. The first experiment provides a breakdown of power usage between the major FPGA components, for different CMOS technologies. 5.3.1 Methodology We executed the full VTR flow, and measured the power for the entire suite of VTR benchmarks. The architecture file used resembles the architecture of an Altera Stratix IV FPGA [70]. The architecture consists of 6-input LUTs arranged in CLBs, where each CLB contains 10 LUTs and has 33 inputs. The CLBs are connected using length-4 segments. The timing information is taken from the iFAR FPGA architecture repository [71], and interconnect capacitances are taken from the 2007 ITRS interconnect roadmap [72]. The transistor technologies used are 22 nm, 45 nm, and 130 nm PTM [69] models, as described in the previous section. Table 5.1 lists characteristics of these processes. 77 of 96 5.3.2 Results Component 22nm 45nm 130nm Avg % Min % Max % Avg % Avg % Routing 83.8 61.9 87.2 72.7 68.2 Switch Box 73.2 33.7 64.6 46.4 47.7 Connection Box 8.8 7.8 30.3 17.8 12.6 Global Wires 1.0 1.2 11.6 5.6 5.9 CLBs 13.9 5.3 33.7 21.4 26.0 LUTs 9.0 2.2 14.8 7.7 10.9 Flip-Flops 1.0 0.9 6.3 2.6 4.9 MUXs / Crossbars 3.1 0.7 11.4 5.7 6.4 Local Wires 1.2 1.9 13.1 7.0 7.3 Clock 1.4 0.7 8.6 3.4 3.3 Buffers 1.2 0.6 5.8 2.4 2.2 Wires 0.2 0.1 2.9 1.0 1.1 Table 5.4: Power breakdown by component type. Table 5.4 provides the breakdown of power usage between major components for 22 nm, 45 nm and 130 nm technologies, where the results are averaged across all VTR benchmarks. Table 5.5 provides a breakdown for each benchmark cir- cuit for the 45 nm technology. As evident from the results, the total power, and breakdown between components, is highly dependent on the benchmark circuit. 5.3.3 Analysis The 45 nm results show that on average, 73% of the power consumption is due to the routing fabric, 21% from CLBs, and 3% from the clock network. The results show that routing is responsible for an increasing fraction of overall power as the 78 of 96 Benchmark Circuit 6-LUTs Power (mW) Routing % Total CLBs % Total Clock % Total bgm 30089 78.6 70 28 2 blob merge 6016 10.3 73 23 4 boundtop 2921 6.6 67 27 6 ch intrinsics 413 2.1 66 26 9 diffeq1 434 2.2 72 25 3 diffeq2 277 2 79 18 4 LU8PEEng 21954 35.9 75 24 1 mcml 99700 109.3 75 24 1 mkDelayWorker32B 5580 32.8 83 13 5 mkPktMerge 226 18.2 87 5 8 mkSMAdapter4B 1977 5.5 72 22 6 or1200 2963 7.4 73 25 3 raygentop 2134 10.2 69 27 4 sha 2212 3.3 62 34 4 stereovision0 11462 36.9 64 29 7 stereovision1 10366 58.1 73 24 3 stereovision2 29849 227.4 82 17 1 stereovision3 174 0.9 52 36 12 Table 5.5: Power usage, and breakdown by circuit (45 nm). technology is scaled down. From 130 nm to 22 nm the percentage of power due to the routing network grows from 68% to 84%. This behavior is due to the fact that the wire capacitance does not scale down at nearly the same rate as the tran- sistor node capacitances. For example, the capacitance of routing segments from 45 nm to 22 nm drops by 57% due to shorter segments and lower wire capacitance per length. However, the input capacitance of a minimum sized inverter between 45 nm and 22 nm drops by 71%, significantly more than the drop in wire capaci- 79 of 96 tance. According to Equation 3.2, the switch box driver strength will need to be 50% larger, requiring almost double the number of equivalent transistors. The percentage of power that is attributed to the clock network is very small. This is because the architecture contains only a single clock, wheras commercial architectures typically contain several clocks [23, 24]. At this point, VPR only supports single clock architectures. We expect that once VPR supports multiple clocks, and the architectures are modified to reflect this, the clock network power will increase substantially. It should be noted that this architecture was optimized for the 45 nm tech- nology. It is likely that a different architecture would be chosen for different CMOS technologies. For example, the segment lengths may be reduced at 22 nm to decrease the buffer sizes. Although this architecture may not be ideal for tech- nologies other than 45 nm, the results are useful in illustrating the trends that oc- cur between CMOS technologies. Understanding these trends is important when designing architectures for future technologies. Furthermore, both the transistor technologies and interconnect capacitances are based on predictive models, and real world technologies may be different. 5.4 Experiment 2: Fracturable LUTs The second experiment explores the effect of fracturable LUTs on total power dissipation. 80 of 96 5.4.1 Methodology The baseline architecture is the same 6-LUT design, as used in the previous exper- iment. We modified the baseline architecture to support fracturable LUTs, so that the 6-LUT can operate as two 5-LUTs. This allows two 5-input (or smaller) logic functions to be packed into each LUT. However, in order for two logic functions to be packed into a single LUT they must share some inputs. The parameter Fi indicates the number of inputs available to the LUT. For example, when Fi = 7, the two logic functions packed into the 5-LUTs must share three inputs. The experiment tests Fi values of 6, 7 and 8. In addition, we test both scaling the number of CLB inputs up with Fi, and leaving the number of inputs constant at 33. Furthermore, this architecture can be modified to include either one or two flip-flops for each LUT. If only a single flip-flop is used, the two outputs of the fractured LUT are multiplexed before connecting to the flip-flop. For this experiment we used the 45 nm technology model described in the previous section, as well as the same interconnect capacitances. 5.4.2 Results Table 5.6 lists the results of the experiment. This table includes the baseline, non- fractured architecture, as well as architectures where we varied 1) the LUT input- sharing flexibility, Fi, 2) the number of CLB inputs, and 3) whether there is one or two flip-flops per LUT. The results show the change in total power compared to the baseline architecture, as well as the change in total number of CLBs, average power per CLB, average power per LUT, and total routing power. 81 of 96 Fi CLB Inputs Total Power # CLBs Power / CLB Power / LUT Routing Power Non-fractured (Baseline) 6 33 13 mW 726 3.8 nW 0.14 nW 9 mW Fractured, One Flip-Flop per LUT 6 33 +4.6% -7.8% +12.5% +7.5% +5.6% 7 33 +9.5% -8.8% +25.6% +8.8% +9.6% 8 33 +14.3% -9.9% +38.7% +9.5% +12.4% Fractured, Two Flip-Flops per LUT 6 33 +3.5% -17.2% +23.5% +14.8% +4.5% 7 33 +6.8% -18.9% +39.3% +16.9% +5.5% 8 33 +10.9% -18.9% +52.6% +16.7% +8.2% Fractured, One Flip-Flop per LUT, CLB inputs scale with Fi 7 39 +9.7% -9.6% +29.2% +8.9% +8.8% 8 44 +14.3% -10.9% +45.4% +9.7% +11.6% Fractured, Two Flip-Flops per LUT, CLB inputs scale with Fi 7 39 +6.2% -19.2% +43.2% +16.7% +4.4% 8 44 +11.2% -19.6% +61.3% +17.5% +5.9% Table 5.6: Power of fracturable LUTs. 82 of 96 One might expect that fracturing the LUTs will cause the power usage to de- crease, since the circuit will require fewer CLBs. However, the results show the opposite; adding the fracturable LUT feature actually increases power usage. The total power usage increases by 3.5-14% depending on the type of fracturable LUT architecture. Although the number of CLBs is decreasing, both the power con- sumed per CLB and the routing power is increasing. 5.4.3 Analysis By adding the fracturable LUT feature, we can pack more logic functions into each CLB. Further modifying the architecture to increase either Fi and/or the num- ber of CLB inputs will increase the likelihood of packing logic functions together. The more logic functions that can be packed together, the fewer CLBs are required to implement the circuit, allowing for a smaller FPGA. However, each of these modifications require changes to the hardware that increase the power demand. Fracturing LUTs: By adding the fracturable LUT feature, each LUT will now have two output pins instead of one. This increases the CLB crossbar size, since all LUT outputs are fed back into the crossbar. It also doubles the number of CLB output pins, which leads to larger multiplexers in the routing switch boxes. Additionally, LUTs that contain two logic functions will consume more dynamic power than if they implemented just one of the logic functions. These behaviours are evident in the results, as adding the fracturable LUT feature increases the power per CLB, power per LUT, and global routing power. 83 of 96 Increasing Fi: Since the LUT inputs are fed by the CLB crossbar, increasing Fi will cause a linear increase in the crossbar size. The results show that although increasing Fi does reduce the number of CLBs by an additional 1 or 2%, the power per CLB increases rapidly. Increasing CLB inputs: Each of the CLB inputs is fed into the CLB crossbar. Thus, increasing the number of inputs increases the crossbar size. Additionally, the connection boxes will need to be larger to accommodate the increased number of CLB input pins. The results show that increasing the number of CLB inputs reduces the number of CLBs by an additional 1%, but at the cost of a large increase to the power per CLB. Flip-Flops per LUT: Adding a second flip-flop per LUT allows for many more logic functions to be packed together, at only the power cost of the second flip- flop. The results show that the increase in power over the baseline is a lower penalty than when only using one flop-flop. The lowest power penalty for a fracturable LUT architecture is when there are two flip-flips per LUT, Fi = 6, and 33 CLB inputs. In this case the number of CLBs is reduced by 17% over the non-fractured architecture, at a power cost of only 3.5%. 5.5 Summary This chapter outlined the verification of the power model, as well as experiments performed with the model. When comparing against SPICE simulations, the power model produces dynamic power estimates within 20%, and static power 84 of 96 estimates within 7% of SPICE simulations. The power estimates are accurate across a wide range of component sizes and CMOS technologies. This makes the power model suitable for evaluating trade-offs during architecture and CAD design. Two experiments were performed using the model. In the first experiment, the VTR benchmarks were tested for a 6-input LUT, 10 LUTs per CLB architec- ture. The results show that on average, for a 45 nm technology, 73% of the power consumption is due to the routing fabric, 21% from CLBs, and 3% from the clock network. In the second experiment we modified the architecture to add fracturable LUTs. This resulted in a 3.5-14% increase in power consumption, depending on the type of architecture. The best fracturable LUT architecture reduced the num- ber of CLBs by 17%, at only a 3.5% increase in power. 85 of 96 Chapter 6 Conclusions A new power model has been developed which can provide power estimates for modern FPGA architectures, not supported by previous power models. This in- cludes support for fracturable LUTs, hard-blocks, and user-defined logic blocks. It is designed to operate with modern CMOS technologies, ranging into the tens of nanometres. The model is integrated into VTR, the newest academic CAD flow. This allows researchers to test the power characteristics of new architectures, as well as new CAD algorithms. Chapter 2 outlined FPGA architectures, their associated CAD tools, and power estimation techniques. Like past models, this model uses a probabilistic approach to power estimation. This allows for detailed estimation, without the high compu- tation requirements of simulation. Chapters 3 and 4 provided details of the new model. A new architecture gen- erator is developed, which is capable of transforming arbitrary user-described 86 of 96 architectures into basic circuit components, comprised of inverters, multiplex- ers and wires. Once decomposed into basic components, the power estimation is performed. Estimates are made for dynamic power, consisting of switching and short-circuit power, as well as static power, which consists of subthreshold and gate leakage. These estimates depend on signal activities, determined using the ACE-2.0 [55] tool, and transistor characteristics, which are automatically ex- tracted from SPICE simulations. Chapter 5 provides verification of the model, and results of experiments. The model was verified against SPICE for a variety of circuit components, sizes and transistor technologies. Dynamic power estimations are within 20% of SPICE, and static power estimations are within 5%. This accuracy makes the model suit- able for evaluating and comparing power requirements of different FPGA archi- tectures. Once verified, we used the model to test power characteristics of com- mon architectures. Results show that for a 45 nm 6-LUT, 10 LUTs per CLB archi- tecture, 73% of power usage is due to the routing fabric, 21% due to logic blocks and 3% due to the clock network (single-clock). Results also show that fracturing LUTs increases power consumption by 3.5-14%. This is because fractured LUTs add additional pins to the logic block, increasing both local and global routing requirements. 6.1 Future Work The power model presented in this work is built on the academic CAD suite, VTR. VTR is an actively developed project, and the developers are constantly 87 of 96 working to add architectural support for more modern FPGA features. Currently in development is support for carry chains and multiple clock networks. The power model will need to be updated to support these features, as well as any others that are developed in the future. In [10], the CAD algorithms in VPR were modified to be power aware. This work could be updated to support this new model. The results would be interest- ing as some of the CAD algorithms have changed since the publication of [10]. Furthermore, VTR supports the full CAD flow, from synthesis to routing, while VPR only supported the last steps of the flow. This makes it possible to perform power optimizations at earlier stages, possibly reducing power even further. Another area of development could be spatial or temporal power estimations. Currently, the model estimates only the average power dissipation. Temporal power estimation would expand power estimates into the time domain, giving information about how power requirements change during circuit operation. It would provide the minimum and maximum power, which are especially relevant for embedded applications. Spatial power estimation would provide details about power requirements for different areas of the FPGA. It could be used to isolate areas of high power, and with modifications to the CAD algorithms, spread power dissipation evenly across the chip, increasing reliability. Most importantly, this work provides a method for other researchers to test their own ideas for architectures or CAD algorithms. 88 of 96 6.2 Summary of Contributions In summary, this work has made the following contributions: 1. A new FPGA power model, capable of performing power estimates for all FPGA architectures supported in VPR 6.0. This includes features such as fracturable LUTs and hard blocks. In addition, this model provides a more detailed estimation of static power compared to previous models. 2. The model was verified against SPICE, achieving accuracy within 20% for dynamic and 5% for static power estimates. 3. 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