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Fixed-point multiplication: a probabilistic bit-pattern view

Fixed-point multiplication: a probabilistic bit-pattern view
Fixed-point multiplication: a probabilistic bit-pattern view
The truncation error of fixed-point multiplication is commonly modelled as white noise with a uniform distribution. This paper shows the inaccuracy of this assumption by using a bitwise approach. A probabilistic bit-pattern analysis of the fixed-point multiplication is presented from which an accurate probability model for the truncation error is derived. Using this PDF model, exact values for the mean and variance of the truncation error in the output of the fixed-point multiplication are formulated for the first time. The proposed PDF model, mean and variance values are compact and usable in word-length optimization algorithms.
Fixed-point multiplication, Quantization noise, Quantization error, Quantization error model
0026-2714
790-796
Ahmadi, Arash
c88cc469-b208-4dad-9541-af5e555e0748
Zwolinski, Mark
adfcb8e7-877f-4bd7-9b55-7553b6cb3ea0
Ahmadi, Arash
c88cc469-b208-4dad-9541-af5e555e0748
Zwolinski, Mark
adfcb8e7-877f-4bd7-9b55-7553b6cb3ea0

Ahmadi, Arash and Zwolinski, Mark (2011) Fixed-point multiplication: a probabilistic bit-pattern view. Microelectronics Reliability, 51 (4), 790-796.

Record type: Article

Abstract

The truncation error of fixed-point multiplication is commonly modelled as white noise with a uniform distribution. This paper shows the inaccuracy of this assumption by using a bitwise approach. A probabilistic bit-pattern analysis of the fixed-point multiplication is presented from which an accurate probability model for the truncation error is derived. Using this PDF model, exact values for the mean and variance of the truncation error in the output of the fixed-point multiplication are formulated for the first time. The proposed PDF model, mean and variance values are compact and usable in word-length optimization algorithms.

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More information

e-pub ahead of print date: 18 December 2010
Published date: April 2011
Keywords: Fixed-point multiplication, Quantization noise, Quantization error, Quantization error model
Organisations: EEE

Identifiers

Local EPrints ID: 271707
URI: https://eprints.soton.ac.uk/id/eprint/271707
ISSN: 0026-2714
PURE UUID: 00ea7e16-41f9-4cca-802c-38e5d7105df8
ORCID for Mark Zwolinski: ORCID iD orcid.org/0000-0002-2230-625X

Catalogue record

Date deposited: 23 Nov 2010 11:31
Last modified: 06 Jun 2018 13:14

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Contributors

Author: Arash Ahmadi
Author: Mark Zwolinski ORCID iD

University divisions

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