We present an evaluation of 32-bit POSIT arithmetic through its implementation as accelerators on FPGAs and GPUs. POSIT, a floating-point number format, adaptively changes the size of its fractional part. We developed hardware designs for FPGAs and software for GPUs to accelerate linear algebra operations using Posit(32,2) arithmetic. Our FPGA- and GPU-based accelerators in Posit(32,2) arithmetic significantly accelerated the Cholesky and LU decomposition algorithms for dense matrices. In terms of numerical accuracy, Posit(32,2) arithmetic is approximately 0.5 - 1.0 digits more accurate than the standard 32-bit format, especially when the norm of the elements of the input matrix is close to 1. Evaluating power consumption, we observed that the power efficiency of the accelerators ranged between 0.043 - 0.076 Gflops/watts for the LU decomposition in Posit(32,2) arithmetic. The power efficiency of the latest GPUs as accelerators of Posit(32,2) arithmetic is better than that of the evaluated FPGA chip.

翻译：我们通过将32位POSIT算术实现为FPGA和GPU上的加速器进行评估。POSIT是一种浮点数格式，能够自适应地调整其小数部分的位宽。我们开发了FPGA硬件设计及GPU软件方案，利用Posit(32,2)算术加速线性代数运算。基于FPGA和GPU的Posit(32,2)算术加速器显著提升了稠密矩阵的Cholesky与LU分解算法效率。在数值精度方面，Posit(32,2)算术比标准32位格式大约精确0.5至1.0个十进制位数，尤其当输入矩阵元素的范数接近1时优势更为明显。通过功耗评估，我们观察到在Posit(32,2)算术的LU分解中，加速器的能效范围为0.043至0.076 Gflops/瓦特。作为Posit(32,2)算术加速器，最新GPU的能效优于所评估的FPGA芯片。