Procrastination Is All You Need: Exponent Indexed Accumulators for Floating Point, Posits and Logarithmic Numbers
<|reference_start|>Procrastination Is All You Need: Exponent Indexed Accumulators for Floating Point, Posits and Logarithmic Numbers: This paper discusses a simple and effective method for the summation of long sequences of floating point numbers. The method comprises two phases: an accumulation phase where the mantissas of the floating point numbers are added to accumulators indexed by the exponents and a reconstruction phase where the actual summation result is finalised. Various architectural details are given for both FPGAs and ASICs including fusing the operation with a multiplier, creating efficient MACs. Some results are presented for FPGAs, including a tensor core capable of multiplying and accumulating two 4x4 matrices of bfloat16 values every clock cycle using ~6,400 LUTs + 64 DSP48 in AMD FPGAs at 700+ MHz. The method is then extended to posits and logarithmic numbers.<|reference_end|>
@article{liguori2024procrastination,
    title={Procrastination Is All You Need: Exponent Indexed Accumulators for
  Floating Point, Posits and Logarithmic Numbers},
    author={Vincenzo Liguori},
    journal={arXiv preprint arXiv:2406.05866},
    year={2024},
    archivePrefix={arXiv},
    eprint={2406.05866},
    primaryClass={cs.CV cs.AI cs.AR}
}