High-Precision Anchored Accumulators for Reproducible Floating-Point Summation
David Lutz, Christopher Neal Hinds · 2017
This paper introduces a new datatype that allows reproducible accumulation of floating-point (FP) numbers in a programmer-selectable range. The new datatype has a larger significand and a smaller range than existing FP formats and has much better arithmetic and computational properties. In particular, it is associative, parallelizable, reproducible and correct. For the modest ranges that will accommodate most problems, it is also much faster: 3 to 12 times faster on a single 256-bit SIMD implementation. The paper also describes a new instruction and associated datapath that support the proposed datatype, and discusses how a recently published software algorithm for reproducible FP summation could be implemented using the proposed approach.