Simulating Low Precision Floating-Point Arithmetic

DOI10.1137/19M1251308OpenAlexW2937715180MaRDI QIDQ5241264

Nicholas J. Higham, Srikara Pranesh

Publication date: 30 October 2019

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

Full work available at URL: https://doi.org/10.1137/19m1251308

zbMATH Keywords

simulationMatlabfloating-point arithmeticrounding error analysisIEEE arithmeticmixed precisiondirected roundinghalf precisionstochastic roundingfp16subnormal numbersbfloat16bit flipslow precisionround to Nearest

Mathematics Subject Classification ID

Numerical algorithms for computer arithmetic, etc. (65Y04)

Related Items

Mixed precision algorithms in numerical linear algebra, Perturbed Runge-Kutta methods for mixed precision applications, Mixed-precision explicit stabilized Runge-Kutta methods for single- and multi-scale differential equations, A Note on Inexact Inner Products in GMRES, Floating-point arithmetic, Precision-aware deterministic and probabilistic error bounds for floating point summation, On stochastic roundoff errors in gradient descent with low-precision computation, A Class of Fast and Accurate Summation Algorithms, Sharper Probabilistic Backward Error Analysis for Basic Linear Algebra Kernels with Random Data, Random Matrices Generating Large Growth in LU Factorization with Pivoting, A New Approach to Probabilistic Rounding Error Analysis, Numerical algorithms for high-performance computational science, Rounding Error Analysis of Mixed Precision Block Householder QR Algorithms, Three-Precision GMRES-Based Iterative Refinement for Least Squares Problems, Stochastic Rounding and Its Probabilistic Backward Error Analysis, Exploiting Lower Precision Arithmetic in Solving Symmetric Positive Definite Linear Systems and Least Squares Problems

Uses Software

• Matlab
• MPFR
• INTLAB
• mctoolbox
• SLEEF
• advanpix
• Julia
• GitHub
• rpe
• CodeNet
• BFloat16s
• half

Cites Work

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• Elementary Functions
• MPFR
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• Accelerating the Solution of Linear Systems by Iterative Refinement in Three Precisions
• A New Preconditioner that Exploits Low-Rank Approximations to Factorization Error
• The Accuracy of Solutions to Triangular Systems
• Accuracy and Stability of Numerical Algorithms
• Innocuous Double Rounding of Basic Arithmetic Operations
• Squeezing a Matrix into Half Precision, with an Application to Solving Linear Systems
• Accelerating Numerical Dense Linear Algebra Calculations with GPUs
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