Using floating-point arithmetic on FPGAs to accelerate scientific N-Body simulations

Rapid development of high performance floating-point pipelines for scientific simulation

“…The first is related to gravity calculation for astrophysical N-body simulation. A pipeline has been generated which implements equation (2) and additionally the potential and the time derivative of the force as these are required for state of the art simulation codes. The resulting pipeline consists of 21 adders, four of them for unsigned inputs, 16 multipliers and 3 square units, one divider, one square root and one multiply-by-3 element, in total 43 operators.…”

“…In [1] the authors presented a parameterized library of floatingpoint operators, which supports adders and multipliers up to single precision. In [2] a parameterized library for operands up to single precision was described, which additionally contains divider and square root units. In [3] the authors pointed out the benefits from hardware multipliers and shift registers for the design of floating-point adders, multipliers and dividers on modern FPGAs.…”

“…As the programmable logic resources of today's FPGAs allows the design of fast and highly complex computation units, FPGA based reconfigurable computing attracts more and more attention in the scientific and engineering community. Already published implementations of this kind are for example [9] were an FPGA based coprocessor for astrophysics simulations has been presented, [2] where the realization of a particle based hydrodynamics simulation with FPGAs is shown, and [7] where a force calculation pipeline for molecular dynamics is discussed.…”

A Hybrid Approach for Mapping Conjugate Gradient onto an FPGA-Augmented Reconfigurable Supercomputer

“…FPGA-based floating-point computational kernels targeting specific problem domains such as molecular dynamics have been demonstrated [10,22,16], as have generalpurpose floating-point scientific kernels such as linear algebra routines [5,26,12,4]. Underwood argues that by 2009, FPGAs will have an order of magnitude peak floating-point performance over GPPs [20].…”

Pipelined Mixed Precision Algorithms on FPGAs for Fast and Accurate PDE Solvers from Low Precision Components

“…Floating point FIR filters have been analyzed in detail [29], the Fast-Fourier-Transform has received particular attention [8,19], and Lienhart et al perform an N-body simulation [22] with custom floating point numbers. In our context vector and matrix operations are of particular interest.…”