Efficient algorithm and architecture for implementation of multiplier circuits in modern EPGAs

High speed multiplication in Field Programmable Gate Arrays is often performed either using logic cells or with built-in DSP blocks. The latter provides the highest performance for arithmetic operations while being also optimized in terms of power and area utilization. Scalability of input operands is limited to that of a single DSP block and the current CAD tools provide little help when the designer needs to build larger arithmetic blocks. The present thesis proposes an effective approach to the problem of building large integer multipliers out of smaller ones by giving two algorithms to the system designer, for a given FPGA technology. Large word length is required in applications such as cryptography and video processing. The first proposed algorithm partitions large input multipliers into an architecture-aware design. The second algorithm then places the generated design in an optimal layout minimizing interconnect delay. The thesis concludes with simulation and hardware generated data to support the proposed algorithms

Uso eficiente de aritmética redundante en FPGAs

Hasta hace pocos años, la utilización de aritmética redundante en FPGAs había sido descartada por dos razones principalmente. En primer lugar, por el buen rendimiento que ofrecían los sumadores de acarreo propagado, gracias a la lógica de de acarreo que poseían de fábrica y al pequeño tamaño de los operandos en las aplicaciones típicas para FPGAs. En segundo lugar, el excesivo consumo de área que las herramientas de síntesis obtenían cuando mapeaban unidades que trabajan en carrysave. En este trabajo, se muestra que es posible la utilización de aritmética redundante carry-save en FPGAs de manera eficiente, consiguiendo un aumento en la velocidad de operación con un consumo de recursos razonable. Se ha introducido un nuevo formato redundante doble carry-save y se ha demostrado que la manera óptima para la realización de multiplicadores de elevado ancho de palabra es la combinación de multiplicadores empotrados con sumadores carry-save.Till a few years ago, redundant arithmetic had been discarded to be use in FPGA mainly for two reasons. First, the efficient results obtained using carry-propagate adders thanks to the carry-logic embedded in FPGAs and the small sizes of operands in typical FPGA applications. Second, the high number of resources that the synthesis tools utilizes to implement carry-save circuits. In this work, it is demonstrated that carry-save arithmetic can be efficiently used in FPGA, obtaining an important speed improvement with a reasonable area cost. A new redundant format, double carry-save, has been introduced, and the optimal implementation of large size multipliers has been shown based on embedded multipliers and carry-save adders