A Mixed Precision Methodology for Mathematical Optimisation

2012 ◽  
Author(s):  
Gary C.T. Chow ◽  
Wayne Luk ◽  
Philip H.W. Leong
Keyword(s):  
Mixed Precision ◽  
Mathematical Optimisation

Adaptive Precision Block-Jacobi for High Performance Preconditioning in the Ginkgo Linear Algebra Software

2021 ◽  
Vol 47 (2) ◽  
pp. 1-28
Author(s):  
Goran Flegar ◽  
Hartwig Anzt ◽  
Terry Cojean ◽  
Enrique S. Quintana-Ortí
Keyword(s):  
Linear Algebra ◽  
Graphics Processing Units ◽  
High Performance ◽  
Numerical Algorithms ◽  
Mixed Precision ◽  
Before And After ◽  
Memory Accesses ◽  
Specialized Hardware ◽  
The Individual ◽  
Graphics Processing

The use of mixed precision in numerical algorithms is a promising strategy for accelerating scientific applications. In particular, the adoption of specialized hardware and data formats for low-precision arithmetic in high-end GPUs (graphics processing units) has motivated numerous efforts aiming at carefully reducing the working precision in order to speed up the computations. For algorithms whose performance is bound by the memory bandwidth, the idea of compressing its data before (and after) memory accesses has received considerable attention. One idea is to store an approximate operator–like a preconditioner–in lower than working precision hopefully without impacting the algorithm output. We realize the first high-performance implementation of an adaptive precision block-Jacobi preconditioner which selects the precision format used to store the preconditioner data on-the-fly, taking into account the numerical properties of the individual preconditioner blocks. We implement the adaptive block-Jacobi preconditioner as production-ready functionality in the Ginkgo linear algebra library, considering not only the precision formats that are part of the IEEE standard, but also customized formats which optimize the length of the exponent and significand to the characteristics of the preconditioner blocks. Experiments run on a state-of-the-art GPU accelerator show that our implementation offers attractive runtime savings.

Rigorous floating-point mixed-precision tuning

2017 ◽  
Author(s):  
Wei-Fan Chiang ◽  
Mark Baranowski ◽  
Ian Briggs ◽  
Alexey Solovyev ◽  
Ganesh Gopalakrishnan ◽  
...  
Keyword(s):  
Floating Point ◽  
Mixed Precision

scholarly journals GRAM

2021 ◽  
Vol 18 (2) ◽  
pp. 1-24
Author(s):  
Nhut-Minh Ho ◽  
Himeshi De silva ◽  
Weng-Fai Wong
Keyword(s):  
Performance Improvement ◽  
Trade Off ◽  
Accuracy Requirement ◽  
Output Error ◽  
Fine Grain ◽  
Mixed Precision ◽  
And Performance ◽  
Effective Use

This article presents GRAM (<underline>G</underline>PU-based <underline>R</underline>untime <underline>A</underline>daption for <underline>M</underline>ixed-precision) a framework for the effective use of mixed precision arithmetic for CUDA programs. Our method provides a fine-grain tradeoff between output error and performance. It can create many variants that satisfy different accuracy requirements by assigning different groups of threads to different precision levels adaptively at runtime . To widen the range of applications that can benefit from its approximation, GRAM comes with an optional half-precision approximate math library. Using GRAM, we can trade off precision for any performance improvement of up to 540%, depending on the application and accuracy requirement.

scholarly journals Integration of various dimensions in food-based dietary guidelines via mathematical approaches Report of a DGE/FENS Workshop in Bonn, Germany, 23-24 September 2019

2020 ◽  
pp. 1-18
Author(s):  
Anne Carolin Schäfer ◽  
Annemarie Schmidt ◽  
Angela Bechthold ◽  
Heiner Boeing ◽  
Bernhard Watzl ◽  
...  
Keyword(s):  
Population Based ◽  
Dietary Guidelines ◽  
Dietary Recommendations ◽  
Mathematical Methods ◽  
Trade Offs ◽  
Simultaneous Integration ◽  
Joint Workshop ◽  
Different Dimensions ◽  
Diverse Data ◽  
Mathematical Optimisation

Abstract In the past, food-based dietary guidelines (FBDGs) were derived nearly exclusively by using systematic reviews on diet-health-relationships and translating dietary reference values for nutrient intake into foods. This approach neglects many other implications that dietary recommendations have on society, the economy and environment. In view of pressing challenges, such as climate change and the rising burden of diet-related diseases, the simultaneous integration of evidence-based findings from different dimensions into FBDGs is required. Consequently, mathematical methods and data processing are evolving as powerful tools in nutritional sciences. The possibilities and reasons for the derivation of FBDGs via mathematical approaches were the subject of a joint workshop hosted by the German Nutrition Society (DGE) and the Federation of European Nutrition Societies (FENS) in September 2019 in Bonn, Germany. European scientists were invited to discuss and exchange on the topics of mathematical optimisation for the development of FBDGs and different approaches to integrate various dimensions into FBDGs. We concluded that mathematical optimisation is a suitable tool to formulate FBDGs finding trade-offs between conflicting goals and taking several dimensions into account. We identified a lack of evidence for the extent to which constraints and weights for different dimensions are set and the challenge to compile diverse data that suit the demands of optimisation models. We also found that individualisation via mathematical optimisation is one perspective of FBDGs to increase consumer acceptance, but the application of mathematical optimisation for population-based and individual FBDGs requires more experience and evaluation for further improvements.

Synthesis of a sustainable integrated biorefinery to produce value-added chemicals from palm-based biomass via mathematical optimisation

2021 ◽  
Vol 26 ◽  
pp. 288-315 ◽  
Author(s):  
Tiong Oon Tey ◽  
Sharon Chen ◽  
Zhi Xiang Cheong ◽  
Abigail Shu Xian Choong ◽  
Lik Yin Ng ◽  
...  
Keyword(s):  
Value Added ◽  
Integrated Biorefinery ◽  
Mathematical Optimisation
Sign in / Sign up

Export Citation Format

Share Document