Mixing precisions for performance has been an ongoing trend as the modern hardware accelerators started including new, and mostly lower-precision, data formats. The advantage of using them is a great potential of performance gain and energy savings. The disadvantage are the numerical issues not present in the standard-mandated floating-point formats. Split integer emulation of FP64 takes this to an extreme with the computation performed only by fixed-point tensor core units. We present the new issues the emulation faces for practical cases involving dense linear solver. We show extensive numerical tests indicating the effect of extended numerical range of matrix entries. We also scaled the input sizes to study the performance and numerical profiles on the NVIDIA Hopper GPUs.

翻译：混合精度计算因其性能优势已成为持续发展趋势，现代硬件加速器开始集成新型（主要为低精度）数据格式。使用这些格式的优势在于性能提升与节能的巨大潜力，其劣势则在于标准规定的浮点格式中不存在的数值问题。FP64的拆分整数模拟将这一趋势推向极致，其计算完全由定点张量核心单元执行。本文针对涉及稠密线性求解器的实际应用场景，揭示了该模拟方法面临的新问题。我们通过大量数值测试展示了矩阵元素扩展数值范围的影响效应，并扩展输入规模以研究NVIDIA Hopper GPU上的性能与数值特性曲线。