The Effects of Numerical Precision In Scientific Applications

Throughout the last decades, multiple formats have appeared as alternatives to the IEEE 754™ standard for floating-point arithmetic. The use of low-precision formats, such as bfloat16, or of new arithmetic systems, such as posit™, has an increasing interest not only in areas like machine learning or HPC, but also general-purpose numerical algorithms can benefit from those non-standard formats, reducing computation time, power consumption or memory requirements. However, dedicated hardware for new arithmetics is not always available, and simulating different numerical precisions is essential to experiment with such alternative formats not yet implemented in hardware. In this work, we examine via software emulation the effects that different arithmetic formats and numerical precisions have in a wide variety of scientific applications. The experiments reveal that, under the same bitwidth, posit arithmetic provides up to two orders of magnitude less error than floating-point format.