Design and Implementation of Numerical Linear Algebra Algorithms on Fixed Point DSPs
- PDF / 1,488,760 Bytes
- 22 Pages / 600.03 x 792 pts Page_size
- 53 Downloads / 148 Views
Research Article Design and Implementation of Numerical Linear Algebra Algorithms on Fixed Point DSPs Zoran Nikoli´c,1 Ha Thai Nguyen,2 and Gene Frantz3 1 DSP
Emerging End Equipment, Texas Instruments Inc., 12203 SW Freeway, MS722, Stafford, TX 77477, USA Science Laboratory, Department of Electrical and Computer Engineering, University of Illinois at Urbana-Champaign, 1308 West Main Street, Urbana, IL 61801, USA 3 Application Specific Products, Texas Instruments Inc., 12203 SW Freeway, MS701, Stafford, TX 77477, USA 2 Coordinated
Received 29 September 2006; Revised 19 January 2007; Accepted 11 April 2007 Recommended by Nicola Mastronardi Numerical linear algebra algorithms use the inherent elegance of matrix formulations and are usually implemented using C/C++ floating point representation. The system implementation is faced with practical constraints because these algorithms usually need to run in real time on fixed point digital signal processors (DSPs) to reduce total hardware costs. Converting the simulation model to fixed point arithmetic and then porting it to a target DSP device is a difficult and time-consuming process. In this paper, we analyze the conversion process. We transformed selected linear algebra algorithms from floating point to fixed point arithmetic, and compared real-time requirements and performance between the fixed point DSP and floating point DSP algorithm implementations. We also introduce an advanced code optimization and an implementation by DSP-specific, fixed point C code generation. By using the techniques described in the paper, speed can be increased by a factor of up to 10 compared to floating point emulation on fixed point hardware. Copyright © 2007 Zoran Nikoli´c et al. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.
1.
INTRODUCTION
Numerical analysis motivated the development of the earliest computers. During the last few decades linear algebra has played an important role in advances being made in the area of digital signal processing, systems, and control [1]. Numerical algebra tools—such as eigenvalue and singular value decomposition, least squares, updating and downdating—are an essential part of signal processing [2], data fitting, Kalman filters [3], and vision and motion analysis. Computational and implementational aspects of numerical linear algebraic algorithms have strongly influenced the ways in which communications, computer vision, and signal processing problems are being solved. These algorithms depend on high data throughput and high speed computations for real-time performance. DSPs are divided into two broad categories: fixed point and floating point [4]. Numerical algebra algorithms often rely on floating point arithmetic and long word lengths for high precision, whereas digital hardware implementations of these algorithms need fixed point representation to reduce total hardware costs. In gener
Data Loading...
