A compact and accurate Gaussian variate generator

  • Authors:

  • Amirhossein Alimohammad;Saeed Fouladi Fard;Bruce F. Cockburn;Christian Schlegel

  • Affiliations:

  • Department of Electrical and Computer Engineering, University of Alberta, Edmonton, AB, Canada;Department of Electrical and Computer Engineering, University of Alberta, Edmonton, AB, Canada;Department of Electrical and Computer Engineering, University of Alberta, Edmonton, AB, Canada;Department of Electrical and Computer Engineering, University of Alberta, Edmonton, AB, Canada

  • Venue:
  • IEEE Transactions on Very Large Scale Integration (VLSI) Systems
  • Year:
  • 2008

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Abstract

A compact, fast, and accurate realization of a digital Gaussian variate generator (GVG) based on the Box-Muller algorithm is presented. The proposed GVG has a faster Gaussian sample generation rate and higher tail accuracy with a lower hard-ware cost than published designs. The GVG design can be readily configured to achieve arbitrary tail accuracy (i.e., with a proposed 16-bit datapath up to ± 15 times the standard deviation σ) with only small variations in hardware utilization, and without degrading the output sample rate. Polynomial curve fitting is utilized along with a hybrid (i.e., combination of logarithmic and uniform) segmentation and a scaling scheme to maintain accuracy. A typical instantiation of the proposed GVG occupies only 534 configurable slices, two on-chip block memories, and three dedicated multipliers of the Xilinx Virtex-II XC2V4000-6 field-programmable gate array (FPGA) and operates at 248 MHz, generating 496 million Gaussian variates (GVs) per second within a range of ±6.66σ. To accurately achieve a range of ±9.4σ, the GVG uses 852 configurable slices, three block memories, and three on-chip dedicated multipliers of the same FPGA while still operating at 248 MHz, generating 496 million GVs per second. The core area and performance of a GVG implemented in a 90-nm CMOS technology are also given. The statistical characteristics of the GVG are evaluated and confirmed using multiple standard statistical goodness-of-fit tests.