Matrix Multiplication in Multiword Arithmetic: Error Analysis and Application to GPU Tensor Cores

DOI10.1137/21M1465032WikidataQ128147866 ScholiaQ128147866MaRDI QIDQ5886842

Mantas Mikaitis, Nicholas J. Higham, Massimiliano Fasi, Florent Lopez, Theo A. Mary

Publication date: 11 April 2023

Published in: SIAM Journal on Scientific Computing (Search for Journal in Brave)

zbMATH Keywords

numerical linear algebrafloating-point arithmeticmatrix multiplicationGPUsrounding error analysismixed precisionreduced precisionrounding modesblocked summation\texttt{FABsum}multiword arithmetic

Mathematics Subject Classification ID

Roundoff error (65G50) Mathematical problems of computer architecture (68M07) Numerical algorithms for specific classes of architectures (65Y10) Numerical algorithms for computer arithmetic, etc. (65Y04)

Related Items

Mixed precision algorithms in numerical linear algebra

Uses Software

• mctoolbox
• CUBLAS
• CUTLASS
• CPFloat

Cites Work

• Performance and energy consumption of accurate and mixed-precision linear algebra kernels on GPUs
• Mixed Precision Block Fused Multiply-Add: Error Analysis and Application to GPU Tensor Cores
• Handbook of Floating-Point Arithmetic
• Accuracy and Stability of Numerical Algorithms
• A Class of Fast and Accurate Summation Algorithms
• Sharper Probabilistic Backward Error Analysis for Basic Linear Algebra Kernels with Random Data
• Mixed-precision iterative refinement using tensor cores on GPUs to accelerate solution of linear systems
• Squeezing a Matrix into Half Precision, with an Application to Solving Linear Systems
• A New Approach to Probabilistic Rounding Error Analysis
• Stochastic Rounding and Its Probabilistic Backward Error Analysis
• Mixed precision algorithms in numerical linear algebra