Stochastic Bit-Width Approximation Using Extreme Value Theory for Customizable Processors

Abstract

Application-specific logic can be generated with a balance and mix of functional units tailored to match an application’s computational requirements. The area and power consumption of application-specific functional units, registers and memory blocks is heavily dependent on the bit-widths of operands used in computations. The actual bit-width required to store the values assigned to a variable during execution of a program will not in general match the built-in C data types with fixed sizes of 8, 16, 32 and 64 bits. Thus, precious area is wasted if the built-in data type sizes are used to declare the size of operands. A novel stochastic bit-width approximation technique is introduced to estimate the required bit-width of integer variables using Extreme Value Theory. Results are presented to demonstrate reductions in bit-widths, area and power consumption when the probability of overflow/underflow occurring is varied from 0.1 to infinitesimal levels. Our experimental results show that the stochastic bit-width approximation results in overall 32% reduction in area and overall 21% reduction in the design power consumption on a FPGA chip for nine embedded benchmarks.