Fast FPGA Placement Based on Quantum Model

Transcription

1 Fast FPGA Placement Based on Quantum Model Lingli Wang School of Microelectronics Fudan University, Shanghai, China 1

2 Outline Background & Motivation VPR placement Quantum Model Fast FPGA Placement Algorithm Experimental Results Conclusions 2

3 What is FPGA? Field-Programmable Gate Array General-Purpose Programmable Hardware C/C++ MatLab scripts Verilog, VHDL Compilers: Visual Studio, GCC, MathLab/Simulink etc FPGA Compilers: ISE, Quartus CPU Memory DSP FPGA

4 FPGA Architecture FPGA bit stream

5 FPGA Compilation Flow RTL input Logic Synthesis Placement Routing Timing/Power Analysis Bit Stream File

6 Motivation How to reduce the compilation time? Placement LUT4 # Equivalent LE# Virtex-2 Virtex-4 Virtex-5 Virtex Stratix(.13um) Stratix-II(90nm) Stratix-III(65nm) Stratix-IV(40nm)

7 Outline Background & Motivation VPR placement Quantum Model Fast FPGA Placement Algorithm Experimental Results Conclusions 7

8 VPR Placement Versatile Place and Route Developed by University of Toronto Best in the academic research

9 VPR Placement Algorithm Based on Simulated Annealing

10 Outline Background & Motivation VPR placement Quantum Model Fast FPGA Placement Algorithm Experimental Results Conclusions 10

11 Qubit: Quantum Bit z 0 cos 0 2 e i After the measurement: 0 or 1 sin 1 2 n-qubits can represent 2 n states simultaneously! (linear combinations ) -- Superstate x θ φ 1 Bloch Sphere y

12 Quantum gates Not: X ' Rotation: G cos sin sin cos i i cos i sini sini i cos i i CNOT: a b a a b U CN

13 Quantum model for FPGA placement Quantum encoding For an FPGA device with N CLB logic blocks and N IO IO blocks: 0 N N 2 n CLB The number of qubits n: n ceil{log [ N N ]} 2 CLB For example: With 400 CLB blocks and 80 IOs, n is 9, i.e. 2 9 = 512 > : CLB locations : IO locations IO IO

14 Outline Background & Motivation VPR placement Quantum Model Fast FPGA Placement Algorithm Experimental Results Conclusions 14

15 FPGA Placement Flow t : iteration number Qt ( ) : quantum representation of placement Pt ( ) : placement location after measurement G : rotation gate operation t 0; Initialize Q( t); Measure Q( t) to obtain P( t); Calculate the placement cost of Save P( t) as the best solution; while(! stop_condition ) begin t t1; P( t); measure Q( t 1) to obtain P( t); Calculate the placement cost of P( t); Update Q( t 1) with Q( t) using G; Save the best solution; end 1 1 i for all qubits VPR function VPR function 15

16 How to measure a qubit? Qubit: 0 1 Generate a random number, r : r 2 0 r Messure Index Real location:

17 How to avoid location confliction? CLB block IO block 17

18 Rotation Gate Operation G cos sin sin cos i i cos i sini sini i cos i i where s(, ) i i i 18

19 Quantum Model Efficiency 19

20 Quantum + VPR Flow RTL input Quantum model VPR placement Global Placement Local Placement Logic Synthesis Placement Routing Timing/Power analysis Bit Stream

21 Outline Background & Motivation VPR placement Quantum Model Fast FPGA Placement Algorithm Experimental Results Conclusions 21

22 Experimental Results:before routing Quantum+VPR VPR Comparison =0.01 Average over 5 runs Iteration number for Quantum: 1000 Benchmark Cost Time Cost Time ( 10-8 s) (ms) ( 10-8 s) (ms) Placement Cost Speed-up ratio alu X apex X apex X clma X diffeq X elliptic X ex5p X ex X frisc X pdc X s X s X s X seq X spla X Average: X

23 Experimental Results: after routing Benchmark Quantum+VPR VPR ( 10-9 s) (10-9 s) Critical-Path Delay alu apex apex clma diffeq elliptic ex5p ex frisc pdc s s s seq spla Average: 1.01

24 Outline Background & Motivation VPR placement Quantum Model Fast FPGA Placement Algorithm Experimental Results Conclusions 24

25 Conclusions Quantum model is proposed for FPGA placement. FPGA placement can be more than 3 times faster if the quantum model is adopted. About 1% of the timing performance is sacrificed. Many future works It is only a start point. 25

26 Acknowledgement This research is sponsored by Shanghai Municipal Pu-Jiang Research Foundation,2008 National Science Foundation of China,

27 Thank you! Q & A 27

28 Unit Hadamard I I H H Pauli-X Rotation-X X X R x cos i sin 2 2 i sin cos 2 2 Rx(θ) Pauli-Y Rotation-Y Y 0 i i 0 Y R y cos sin 2 2 sin cos 2 2 Ry(θ) Pauli-Z Rotation-Z Z Z R z i /2 i /2 e 0 e 0 Rz(θ) S Phase i S T 8 gate i /4 e T 28