# Procrastination Is All You Need: Exponent Indexed Accumulators for Floating Point, Posits and Logarithmic Numbers

arXiv: https://arxiv.org/abs/2406.05866 · HTML: https://mlsanity.com/paper/2406.05866/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Builds on 2 of its 7 references that are in the map.
- First posted on arXiv 9 Jun 2024.

## Builds on (most cited first, 2 of 2)

- [FP8 versus INT8 for efficient deep learning inference](https://mlsanity.com/paper/2303.17951/) (2023)
- [From a Lossless (~1.5:1) Compression Algorithm for Llama2 7B Weights to Variable Precision, Variable Range, Compressed Numeric Data Types for CNNs and LLMs](https://mlsanity.com/paper/2404.10896/) (2024)

## Abstract (arXiv)

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.