# NVIDIA cuBLAS introduces Ozaki-II and 2M algorithms for faster FP64 simulations

> **Key takeaway:** New algorithms in CUDA Toolkit 13.4.2 use integer Tensor Cores to emulate double-precision math, significantly accelerating scientific workloads without losing accuracy.

**Published:** 2026-11-13T22:14:10+00:00 
**Source:** NVIDIA Technical & Open Source Blog 
**Category:** bigtech-foss 
**Canonical URL:** https://fosswire.org/news/nvidia-cublas-introduces-ozaki-ii-and-2m-algorithms-for-fast.html 

## Summary
NVIDIA has updated its cuBLAS library within CUDA Toolkit 13.4.2 to include new algorithms designed to accelerate high-precision scientific simulations. By utilizing the Automatic Dynamic Precision (ADP) framework, the library can now map 64-bit floating-point (FP64) operations onto faster integer Tensor Cores. This approach allows for massive speedups in dense general matrix multiplications (GEMM) while maintaining full double-precision accuracy.

The update specifically targets DGEMM (real 64-bit) and ZGEMM (complex 64-bit) operations, which are critical for fields like molecular chemistry and materials science. The release introduces the Ozaki-II algorithm for real numbers and the 2M method for complex numbers. These improvements are validated on high-end hardware including NVIDIA GB200 and VR NVL72 systems, showing significant end-to-end performance gains in real-world applications like CCSD and BerkeleyGW.

## Technical breakdown of Ozaki-II and 2M algorithms
- **Ozaki-II Algorithm:** Unlike the previous Ozaki-I method which used 8-bit slices and grew quadratically, Ozaki-II employs the Chinese Remainder Theorem (CRT) to reduce the number of required integer multiplications to a linear relationship with the number of moduli.
- **2M Method:** This algorithm optimizes complex matrix multiplication (ZGEMM) by reducing the computational requirement from four real multiplications down to two.
- **Automatic Dynamic Precision (ADP):** The framework automatically handles the conversion of FP64 numbers into integer pieces for Tensor Core processing and reassembles them, offering users manual control via the `cublasSetEmulationStrategy` API.
- **Hardware Acceleration:** The new algorithms are further optimized for NVIDIA Rubin GPUs, which introduce the TI16 numeric format and the `tcgen05.mma` instruction to boost emulation performance.

## Why it matters
This development provides a significant performance boost for High-Performance Computing (HPC) researchers and software engineers working on scientific modeling without requiring manual code rewrites. By enabling high-precision results on integer-optimized hardware, NVIDIA is narrowing the performance gap between specialized FP64 units and high-throughput Tensor Cores.