Automating Transformations fromFloating Point to Fixed Point.ppt
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1、Automating Transformations from Floating Point to Fixed Point for Implementing Digital Signal Processing Algorithms,Prof. Brian L. Evans Embedded Signal Processing Laboratory Dept. of Electrical and Computer Engineering The University of Texas at Austin,July 4, 2006,Based on work by PhD student Kyun
2、gtae Han (now at Intel Research Labs),2,Outline,Introduction Background Optimize fixed-point wordlengths Reduce power consumption in arithmetic Automate transformations of systems Conclusion,3,Implementing Digital Signal Processing Algorithms,Introduction,Code Conversion,Wordlength Optimization,Floa
3、ting-Point Program,Fixed Point (Uniform Wordlength),Fixed Point (Optimized Wordlength),Floating- Point Processor,Fixed- Point Processor,Fixed- Point ASIC,$,$,$,Price,Power*,Hardware,Digital Signal Processing Algorithms,* Power consumption,H,L,H,L,ASIC: Application Specific Integrated Circuit,4,Trans
4、formations to Fixed Point,Advantages Lower hardware complexity Lower power consumption Faster speed in processing Disadvantages Introduces distortion due to quantization error Search for optimum wordlengths by trial & error is time-consuming Research goals Automate transformations to fixed point Con
5、trol distortion vs. complexity tradeoffs,Code Conversion,Wordlength Optimization,Floating-Point Program,Fixed Point (Optimized Wordlength),Transformation,Introduction,5,Outline,Introduction Background Optimize fixed-point wordlengths Reduce power consumption in arithmetic Automate transformations of
6、 systems Conclusion,6,Fixed-Point Data Format,Integer wordlength (IWL) Number of bits assigned to integer representation Includes sign bit Fractional wordlength (FWL) Number of bits assigned to fraction Wordlength: WL = IWL + FWL,SystemC format www.systemc.org, = 3.14159(10) Floating Point3.140625(1
7、0) = 011.001001(2) WL=9; IWL=3; FWL=6 3.141479492(10) = 011.00100100001110(2) WL=16; IWL=3; FWL=13,Background,7,Feasible region,Distortion vs. Complexity Tradeoffs,Different wordlengths have different application distortion and implementation complexity tradeoffs,Background,Minimize implementation c
8、ostMinimize application distortion,Implementation complexity c(w),Application distortion d(w),Optimal tradeoff curve,Vector of wordlengths:,8,Wordlength Optimization,Background,Multiple objective optimization,Single objective optimization,Proposed work fixes integer wordlengths and searches for frac
9、tional wordlengths,9,Genetic Algorithm,Evolutionary algorithm Inspired by Holland 1975 Mimic processes of plant and animal evolution Find optimum of a complex function,Greg Rohling, Ph.D Defense, Georgia Tech, 2004,Background,10,Pareto Optimality,Pareto optimality: “best that could be achieved witho
10、ut disadvantaging at least one group” Schick, 1970 Pareto optimal set is set of nondominated solutions E is dominated by C as all objectives for C are less than corresponding objectives for E Solutions A, B, C, D are nondominated (not dominated by any solution) Pareto front is boundary (tradeoff cur
11、ve) that connects Pareto optimal set solutions,Objective 2,Objective 1,Pareto Front,F,E,G,H,I,D,C,B,A,Background,11,Outline,Introduction Background Optimize fixed-point wordlengths Reduce power consumption in arithmetic Automate transformations of systems Conclusion,12,Search for Optimum Wordlength,
12、Exhaustive search impractical for many variables Gradient-based search (single objective) Utilizes gradient information to determine next candidates Complexity measure (CM) Sung & Kum, 1995 Distortion measure (DM) Han et al., 2001 Complexity-and-distortion measure (CDM) Han & Evans, 2004 Guided rand
13、om search Genetic algorithm for single objective Leban & Tasic, 2000 Multiple objective genetic algorithm Han, Olson & Evans, 2006,Optimize Fixed-Point Wordlengths,Next,Next,13,Complexity-and-Distortion Measure,Weighted combination of measuresSingle objective function Gradient-based search Initializ
14、ation Iterative greedy search based on complexity and distortion gradient information,Optimize Fixed-Point Wordlengths,14,Case Study I: Filter Design,Infinite impulse response (IIR) filter Complexity measure: Area model of field-programmable gate array (FPGA) Constantinides, Cheung & Luk 2003 Distor
15、tion measure: Root mean square (RMS) error Seven fixed-point variables (indicated by slashes),Optimize Fixed-Point Wordlengths,15,Case Study I: Gradient-Based Search,CDM could lead to lower complexity and lower number of simulations compared to DM and CM,* Maximum distortion measured by root mean sq
16、uare (RMS) error is 0.1 * 167 = 268,435,456 (8.5 years, if 1 second per 1 simulation),Optimize Fixed-Point Wordlengths,16,Case Study I: Genetic Algorithm,100th Generation,250th Generation,500th Generation,Search Pareto optimal set (nondominated) Handles multiple objectives: Error and Area,* Populati
17、on for one generation: 90,Pareto Front,LUT: Lookup table,9,000 simulations,22,500 simulations,45,000 simulations,Optimize Fixed-Point Wordlengths,17,Case Study I: Comparison,Gradient-based search (GS) results vs. GA results,GS methods can get stuck in a local minimumGS methods reduce running time (C
18、DM: 145 simulations),* Required RMSmax for gradient-based search are Dmax 0.12, 0.1, 0.08,500th Generation (45000 simulations),50th Generation (4500 simulations),Optimize Fixed-Point Wordlengths,18,Case Study II: Communication System,Simple binary phase shift keying (BPSK) system Complexity measure:
19、 Area model of field-programmable gate array (FPGA) Constantinides, Cheung, and Luk 2003 Distortion measure: Bit error rate (BER) Four fixed-point variables (indicated by slashes),Integration & Dump,Optimize Fixed-Point Wordlengths,Decision,AWGN,Source Data (1 or -1),Carrier,BER,19,Case Study II: Gr
20、adient-Based Search,CDM could lead to lower complexity and lower number of simulations compared to DM and CM,* Maximum distortion measured by bit error rate (BER) error is 0.1,Optimize Fixed-Point Wordlengths,20,Case Study II: Genetic Algorithm,Search Pareto optimal set Handles multiple objectives,5
21、0th Generation,100th Generation,200th Generation,* Population for one generation: 90,Pareto Front,LUT: Lookup table,4,500 simulations,9,000 simulations,18,000 simulations,Optimize Fixed-Point Wordlengths,Error (Bit Error Rate),Error (Bit Error Rate),Error (Bit Error Rate),For Comparison,Preliminary
22、results,21,Comparison of Proposed Methods,Optimize Fixed-Point Wordlengths,22,Outline,Introduction Background Optimize fixed-point wordlengths Reduce power consumption in arithmetic Automate transformations of systems Conclusion,23,Lower Power Consumption in DSP,Minimize power dissipation due to lim
23、ited battery power and cooling system Multipliers often a major source of dynamic power consumption in typical DSP applications Multi-precision multiplier select smaller multipliers (8, 16 or 24 bits) to reduce power consumption Wordlength reduction to select any word size Han, Evans & Swartzlander
24、2004 In general, what reductions in power are possible in software when hardware has fixed wordlengths?,Reduce Power Consumption in Arithmetic,Next,24,Wordlength Reduction in Multiplication,Input data wordlength reduction Smaller bits enough to represent, e.g. x 9 Truncation Signed right shift Move
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