An FPGA Implementation of the Ewald Direct Space and LennardJones Compute Engines

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An FPGA Implementation of theEwald Direct Space
and Lennard-JonesCompute Engines

• By David Chui
• Supervisor Professor P. Chow

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Overview

• Introduction and Motivation
• Background and Previous Work
• Hardware Compute Engines
• Results and Performance
• Conclusions and Future Work

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• 1. Introduction and Motivation

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What is Molecular Dynamics (MD) simulation?

• Biomolecular simulations
• Structure and behavior of biological systems
• Uses classical mechanics to model a molecular
  system
• Newtonian equations of motion (F ma)
• Compute forces and integrate acceleration through
  time to move atoms
• A large scale MD system takes years to simulate

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Why is this an interesting computational problem?
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Motivation

• Special-purpose computers for MD simulation have
  become an interesting application
• FPGA technology
• Reconfigurable
• Low cost for system prototype
• Short turn around time and development cycle
• Latest technology
• Design portability

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Objectives

• Implement the compute engines on FPGA
• Calculate the non-bonded interactions in an MD
  simulation (Lennard-Jones and Ewald Direct Space)
• Explore the hardware resources
• Study the trade-off between hardware resources
  and computational precision
• Analyze the hardware pipeline performance
• Become the components of a larger project in the
  future

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• 2. Background and Previous Work

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Lennard-Jones Potential

• Attraction due to instantaneous dipole of
  molecules
• Pair-wise non-bonded interactions O(N2)
• Short range force
• Use cut-off radius to reduce computations
• Reduced complexity close to O(N)

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Lennard-Jones Potential of Argon gas
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Electrostatic Potential

• Attraction and repulsion due to electrostatic
  charge of particles (long range force)
• Reformulate using Ewald Summation
• Decompose to Direct Space and Reciprocal Space
• Direct Space computation similar to Lennard-Jones
• Direct Space complexity close to O(N)

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Ewald Summation - Direct Space
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Previous Hardware Developments
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Recent work - FPGA based MD simulator

• Transmogrifier-3 FPGA system
• University of Toronto (2003)
• Estimated speedup of over 20 times over software
  with better hardware resources
• Fixed-point arithmetic, function table lookup,
  and interpolation
• Xilinx Virtex-II Pro XC2VP70 FPGA
• Boston University (2005)
• Achieved a speedup of over 88 times over software
• Fixed-point arithmetic, function table lookup,
  and interpolation

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MD Simulation software - NAMD

• Parallel runtime system (Charm/Converse)
• Highly scalable
• Largest system simulated has over 300,000 atoms
  on 1000 processors
• Spatial decomposition
• Double precision floating point

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NAMD - Spatial Decomposition
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• 3. Hardware Compute Engines

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Purpose and Design Approach

• Implement the functionality of the software
  compute object
• Calculate the non-bonded interactions given the
  particle information
• Fixed-point arithmetic, function table lookup,
  and interpolation
• Pipelined architecture

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Compute Engine Block Diagram
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Function Lookup Table

• The function to be looked up is a function of
  r2 (the separation distance between a pair of
  atoms)
• Block floating point lookup
• Partition function based on different precision

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Function Lookup Table
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Hardware Testing Configuration
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• 4. Results and Performance

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Simulation Overview

• Software model
• Different coordinate precisions and lookup table
  sizes
• Obtain the error compared to computation using
  double precision

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Total Energy Fluctuation
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Average Total Energy
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Operating Frequency
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Latency and Throughput
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Hardware Improvement

• Operating frequency
• Place-and-route constraints
• More pipeline stages
• Throughput
• More hardware resources
• Avoid sharing of multipliers

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Compared with previous work

• Pipelined adders and multipliers
• Block floating point memory lookup
• Support different types of atoms

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• 5. Conclusions and Future Work

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Hardware Precision

• A combination of fixed-point arithmetic, function
  table lookup, and interpolation can achieve high
  precision
• Similar result in RMS energy fluctuation and
  average energy
• Coordinate precision of 7.41
• Table lookup size of 1K
• Block floating memory
• Data precision maximized
• Different types of functions

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Hardware Performance

• Compute engines operating frequency
• Ewald Direct Space 82.2 MHz
• Lennard-Jones 80.0 MHz
• Achieving 100 MHz is feasible with newer FPGAs

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Future Work

• Study different types of MD systems
• Simulate computation error with different table
  lookup sizes and interpolation orders
• Hardware usage storing data in block RAMs
  instead of external ZBT memory