Computer Arithmetic Algorithms
Computer Arithmetic Algorithms
Accuracy and Stability of Numerical Algorithms
Accuracy and Stability of Numerical Algorithms
Short Vector Code Generation for the Discrete Fourier Transform
IPDPS '03 Proceedings of the 17th International Symposium on Parallel and Distributed Processing
Automated fixed-point data-type optimization tool for signal processing and communication systems
Proceedings of the 41st annual Design Automation Conference
An algorithm for converting floating-point computations to fixed-point in MATLAB based FPGA design
Proceedings of the 41st annual Design Automation Conference
Fast, Accurate Static Analysis for Fixed-Point Finite-Precision Effects in DSP Designs
Proceedings of the 2003 IEEE/ACM international conference on Computer-aided design
Spiral: A Generator for Platform-Adapted Libraries of Signal Processing Algorithms
International Journal of High Performance Computing Applications
Fast multiplierless approximations of the DCT with the liftingscheme
IEEE Transactions on Signal Processing
Algorithm selection: a quantitative optimization-intensive approach
IEEE Transactions on Computer-Aided Design of Integrated Circuits and Systems
Multiplierless multiple constant multiplication
ACM Transactions on Algorithms (TALG)
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Linear DSP kernels such as transforms and filters are comprised exclusively of additions and multiplications by constants. These multiplications may be realized as networks of additions and wired shifts in hardware. The cost of such a "multiplierless" implementation is determined by the number of additions, which in turn depends on the value and precision of these constants. For a given transform or filter, the set of constants and their required precision is affected by algorithmic and implementation choices and hence provides a degree of freedom for optimization. In This work we present an automated method to generate, for a given linear transform, a minimum addition multiplierless implementation that satisfies a given quality constraint. The method combines automatic algorithm selection to improve numerical robustness and automatic search methods to minimize constant precisions in a chosen algorithm. We present experiments that show the trade-offs between cost and quality, including custom optimizations of the transforms used in JPEG image and MP3 audio decoders.