Leveraging Posits for the Conjugate Gradient Linear Solver on an Application-Level RISC-V Core

Sammanfattning: Emerging floating-point arithmetics provide a way to optimize the execution of computationally-intensive algorithms. This is the case with scientific computational kernels such as the Conjugate Gradient (CG) linear solver. Exploring new arithmetics is of paramount importance to maximize the accuracy and timing performance of these algorithms. In this thesis, I have studied the use of the novel posit arithmetic in hardware to improve the accuracy of the CG method. In particular, on PERCIVAL, an application-level RISC-V core with support for posits and quire. The open RISC-V architecture supplies a flexible platform for the exploration of new computer architecture studies. Previous works have tackled the use of posits in the high-performance computing and machine learning fields, amongst others. However, until recently, the lack of hardware support has been a significant barrier to their scalability. The key results from this thesis show that posits are a promising alternative when solving 1D and 2D Poisson equations using the CG linear solver. Notably, this novel arithmetic can execute as fast as IEEE 754 floating-point numbers on specialized hardware, and provide up to 2 orders of magnitude higher accuracy. This accuracy improvement spans both the error of the output values of the algorithms and the value of the final residual in the CG iterative method. Furthermore, the use of the quire accumulator register in the computation of dot-products in posit arithmetic significantly boosts the accuracy of the outputs. Since 32-bit posits perform practically as fast as 32-bit floats, and thus faster than 64-bit floats, they present an intermediate solution between single- and double-precision arithmetic. This paves the way for the deployment of high-efficiency solutions that make intensive use of floating-point operations.