Multiplication by Integer constants
Software—Practice & Experience
Maximally fast and arbitrarily fast implementation of linear computations
ICCAD '92 1992 IEEE/ACM international conference proceedings on Computer-aided design
DAC '93 Proceedings of the 30th international Design Automation Conference
DAC '94 Proceedings of the 31st annual Design Automation Conference
Fast Prototyping of Datapath-Intensive Architectures
IEEE Design & Test
Algebraic Methods for Optimizing Constant Multiplications in Linear Systems
Journal of VLSI Signal Processing Systems
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Most behavioral synthesis tools perform limited architectural transformations to optimize hardware and power. Previously, researchers have proposed decomposition of multiplications into shifts and adds to achieve average savings of 2.5 times in hardware. In this paper, we propose a new program called OPTIMUS and related algorithms, that combine an architectural transformation procedure called number-splitting with shift-and-add decomposition to obtain up to an additional 2 fold savings, giving a factor of up to 5 savings in overall hardware. The number-splitting transformation changes the circuit interconnections and the descriptions of constant multipliers. The scheme is based on numerical matrix transformation algorithms that allow a given matrix to be expressed as the product of several matrices while maintaining numerical accuracy.