This paper introduces a novel mixed precision methodology applicable to any Monte Carlo (MC) simulation. It involves the use of data-paths with reduced precision, and the resulting errors are corrected by auxiliary sampling. An analytical model is developed for a reconfigurable accelerator system with a field-programmable gate array (FPGA) and a general purpose processor (GPP). Optimisation based on mixed integer geometric programming is employed for determining the optimal reduced precision and optimal resource allocation among the MC data-paths and correction datapaths. Experiments show that the proposed mixed precision methodology requires up to 11 % additional evaluations while less than 4 % of all the evaluations are computed in the reference precision; the resulting designs are up to 7.1 times faster and 3.1 times more energy efficient than baseline double precision FPGA designs, and up to 163 times faster and 170 times more energy efficient than quad-core software designs optimised with the Intel compiler and Math Kernel Library. Our methodology also produces designs for pricing Asian options which are 4.6 times faster and 5.5 times more energy efficient than NVIDIA Tesla C2070 GPU implementations.

Customisable data formats provide an opportunity for exploring trade-offs in accuracy and performance of reconfigurable systems. This paper introduces a novel methodology for mixed-precision comparison, which improves comparison performance by using reduced-precision data paths while maintaining accuracy by using high-precision data paths. Our methodology adopts reduced-precision data-paths for preliminary comparison, and high-precision data-paths when the accuracy for preliminary comparison is insufficient. We develop an analytical model for performance estimation of the proposed mixed-precision methodology. Optimisation based on integer linear programming is employed for determining the optimal precision and resource allocation for each of the data paths. The effectiveness of our approach is evaluated using a common collision detection problem. Performance gains of 4 to 7.3 times are obtained over baseline fixed-precision designs for the same FPGAs. With the help of the proposed mixed-precision methodology, our FPGA designs are 15.4 to 16.7 times faster than software running on multi-core CPUs with the same technology.

We present Constant Power Reconfigurable Computing, a general and device-independent framework based on a closed-loop control system used to keep the power consumption constant for any reconfigurable computing design targeting FPGA implementation. We develop an on-chip power consumer, an on-chip power monitor and a proportional-integral-derivative controller with circuit primitives available in most commercial FPGAs. We demonstrate the effectiveness of the proposed methodology on a square-and-multiply exponentiation circuit implemented on a Spartan-6 LX45 FPGA board. By reducing the peak autocorrelation values by a factor of 2.7 on average, the proposed Constant Power Reconfigurable Computing approach decreases the information leaked by the power consumption of this system with only 26% area overhead and 28% power overhead.

Modular multiplication of long integers is an important building block for cryptographic algorithms. Although several FPGA accelerators have been proposed for large modular multiplication, previous systems have been based on O(N2) algorithms. In this paper, we present a Montgomery multiplier that incorporates the more efficient Karatsuba algorithm which is O(N(log 3/log 2)). This system is parameterizable to different bitwidths and makes excellent use of both embedded multipliers and fine-grained logic. The design has significantly lower LUT-delay product and multiplier-delay product compared with previous designs. Initial testing on a Virtex-6 FPGA showed that it is 60-190 times faster than an optimized multi-threaded software implementation running on an Intel Xeon 2.5 GHz CPU. The proposed multiplier system is also estimated to be 95-189 times more energy efficient than the software-based implementation. This high performance and energy efficiency makes it suitable for server-side applications running in a datacenter environment.

In this paper, the authors have developed an adaptive precision technique for genetic algorithms (GA) (Mitchell, 1996), which is similar in spirit to the mixed precision techniques, but instead, a global precision is used at any time. The global precision is increased adaptively, greatly simplifying the partitioning and switching decision problems.