Open-Source Coprocessor for Integer Multiple Precision Arithmetic

Abstract

This paper presents an open-source digital circuit of the coprocessor for an integer multiple-precision arithmetic (MPA). The purpose of this coprocessor is to support a central processing unit (CPU) by offloading computations requiring integer precision higher than 32/64 bits. The coprocessor is developed using the very high speed integrated circuit hardware description language (VHDL) as an intellectual property (IP) core. Therefore, it can be implemented within field programmable gate arrays (FPGAs) at various scales, e.g., within a system on chip (SoC), combining CPU cores and FPGA within a single chip as well as FPGA acceleration cards. The coprocessor handles integer numbers with precisions in the range 64 bits–32 kbits, with the limb size set to 64 bits. In our solution, the sign-magnitude representation is used to increase the efficiency of the multiplication operation as well as to provide compatibility with existing software libraries for MPA. The coprocessor is benchmarked in factorial ( n ! ), exponentiation ( n n ) and discrete Green’s function (DGF) computations on Xilinx Zynq-7000 SoC on TySOM-1 board from Aldec. In all benchmarks, the coprocessor demonstrates better runtimes than a CPU core (ARM Cortex A9) executing the same computations using a software MPA library. For sufficiently large input parameters, our coprocessor is up to three times faster when implemented in FPGA on SoC, rising to a factor of ten in DGF computations. The open-source coprocessor code is licensed under the Mozilla Public License.

Efficient GPU Implementation of Multiple-Precision Addition based on Residue Arithmetic

“…A higher level of arithmetic precision is also supported in a number of programming languages, e.g., Python (the built-in int type), Ruby (the built-in Bignum type), Perl (Math::BigInt), Java (the BigInteger class), Haskell (the Integer datatype), and C# (BigInteger). Another actual approach is to develop hardware accelerators that support integer and floating-point computations with multiple precision [13], [14], [15].…”

“…Previous research in [8], [9], [13], and [15] use the traditional way of representing multiple-precision numbers, according to which a number is represented as an array of weighted digits in some base, and the digits themselves are machineprecision numbers [16]. The need for carry propagation under this number representation is one of the main bottleneck of efficient multiple-precision algorithms.…”