Design and Implementation of Numerical Linear Algebra Algorithms on Fixed Point DSPs

Abstract

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.Gene Frantz is responsible for finding new opportunities and creating new businesses utilizing TI's digital signal processing technology. Frantz has been with Texas Instruments for over thirty years, most of it in digital signal processing. He is a recognized leader in DSP technology both within TI and throughout the industry. Frantz is a Fellow of the Institution of Electric and Electronics Engineers. He holds 40 patents in the area of memories, speech, consumer products and DSP. He has written more than 50 papers and articles and continually presents at universities and conferences worldwide. Frantz is also among industry experts widely quoted in the media due to his tremendous knowledge and visionary view of DSP solutions.

Comparative Evaluation of Symmetric SVD Algorithms for Real-Time Face and Eye Tracking

“…To convert floating-point algorithms into fixed-point,it is necessary to first estimate the range of the required floating-point variables followed by choice of Q-format. Then the floating-point variables and floating-point arithmetic equations are converted to fixed-point format [22], [24]. The fixed-point algorithm is then tested for error and the algorithm is optimized for our purpose.…”

Algorithmic and software techniques for embedded vision on programmable processors

“…For high-end vision applications requiring high clock rates fixed-point representation can still be an optimum choice. Hence, there is still considerable interest in making floating-point implementations of algorithms amenable to fixed-point arithmetic as shown in Nikolić et al [27], Kim et al [18] and Coors et al [5].…”

“…In these cases, algorithmic alternatives need to be employed. Some semi-automatic tools for conversion are suggested by Nikolić et al [27], Kim et al [18] and Coors et al [5].…”

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“…Some published approaches for floating-point to fixedpoint conversion use an analytic approach for range and error estimation [10,15], while others use a statistical approach [2,8].…”

“…In cases when the overhead of the floating-point emulation is too great and performance improvements are needed, algorithms that require intensive real-time signal processing must be converted to a fixedpoint implementation. Therefore, there is considerable interest in making floating-point implementations of driver assist algorithms amenable to fixed-point implementation [2,3].…”