Quick-Div: Rethinking Integer Divider Design for FPGA-based Soft-processors

Abstract

In today’s FPGA-based soft-processors, one of the slowest instructions is integer division. Compared to the low single-digit latency of other arithmetic operations, the fixed 32-cycle latency of radix-2 division is substantially longer. Given that today’s soft-processors typically only implement radix-2 division—if they support hardware division at all—there is significant potential to improve the performance of integer dividers. In this work, we present a set of high-performance, data-dependent, variable-latency integer dividers for FPGA-based soft-processors that we call Quick-Div . We compare them to various radix-N dividers and provide a thorough analysis in terms of latency and resource usage. In addition, we analyze the frequency scaling for such divider designs when (1) treated as a stand-alone unit and (2) integrated as part of a high-performance soft-processor. Moreover, we provide additional theoretical analysis of different dividers’ behaviour and develop a new better-performing Quick-Div variant, called Quick-radix-4 . Experimental results show that our Quick-radix-4 design can achieve up to 6.8× better performance and 6.1× better performance-per-LUT over the radix-2 divider for applications such as random number generation. Even in cases where division operations constitute as little as 1% of all executed instructions, Quick-radix-4 provides a performance uplift of 16% compared to the radix-2 divider.