# Guaranteed DGEMM Accuracy While Using Reduced Precision Tensor Cores Through Extensions of the Ozaki Scheme

arXiv: https://arxiv.org/abs/2511.13778 · HTML: https://mlsanity.com/paper/2511.13778/

## Key facts

- Cited by 4 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 16 Nov 2025.

## Built on by (most cited first, 4 of 4)

- [Double-Precision Matrix Multiplication Emulation via Ozaki-II Scheme with FP8 Quantization](https://mlsanity.com/paper/2603.10634/) (2026)
- [FP8 is All You Need (Part 1): Debunking Hardware FP64 as the HPC Holy Grail (Sep 3rd version)](https://mlsanity.com/paper/2606.06510/) (2026)
- [FP8 is All You Need (Part 2): Full-FP64 3-D FFT on FP8-Generation Tensor CoresThe Integer-Epilogue Wall and the Minimal Hardware That Would Remove It](https://mlsanity.com/paper/2606.23698/) (2026)
- [The Missing Fourth Term for the Emulation Tensor Memory Equilibrium (TME) Model: The Residue Deconstruction Cost](https://mlsanity.com/paper/2610.10924/) (2026)

## Abstract (arXiv)

The rapid growth of artificial intelligence (AI) has made low-precision formats such as FP16, FP8, and, most recently, block-scaled FP4 the primary focus of modern GPUs, where Tensor Cores now deliver orders-of-magnitude higher throughput than traditional FP64 pipelines. This hardware shift has sparked a new line of algorithm research: using low-precision units to emulate double-precision accuracy through schemes such as Ozaki decompositions. We advance this direction with Automatic Dynamic Precision (ADP), a fully GPU-resident framework that makes emulated FP64 matrix multiplication both efficient and reliable. At its core is the Exponent Span Capacity (ESC), a hardware-agnostic estimator that conservatively determines the decomposition parameter (also known as slices) required to achieve FP64-level accuracy. Built on ESC, ADP integrates exception handling, run time heuristics, and seamless fallback to native FP64, ensuring correctness without host-device synchronization or user intervention. Additionally, we further improve Ozaki-style decompositions with an unsigned integer slicing scheme, which increases representational efficiency and reduces computational waste. Validated against recently proposed BLAS grading tests, ADP consistently preserves FP64 fidelity on challenging inputs while incurring less than 10% run time overhead. In a 55-bit mantissa setting, our approach achieves up to 2.3x and 13.2x speedups over native FP64 GEMM on NVIDIA Blackwell GB200 and the RTX Pro 6000 Blackwell Server Edition, respectively. Our results demonstrate that low-precision accelerators can serve as a practical, production-ready foundation for high-fidelity and high-performance scientific computing workloads.