Using Accurate Arithmetics to Improve Numerical Reproducibility and Stability in Parallel Applications


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Table of contents

sing Accurate Arithmetics to Improve Numerical Reproducibility and Stability in Parallel Applications

Importance of Reproducibility for Coupled Atmosphere-Ocean Systems

Scenario Experiment (CO2)

Nonreproducibility Comes From ...

Factors Affect Execution Orders

Different Summation Orders

Computations Sensitive to Rounding Errors

Existing Approach (fix execution order)

New Approach

Accurate Summation Methods

Fixed-Point Arithmetic

Multi-Precision Arithmetic

Self-Compensated Summation

Sum and Error

Sensitivity Regarding to Summation Order Seven Different Orders of the Array Tested

Sensitivity Regarding to Summation Order Results of the Summation in Seven Sorting Orders

Double-Double Precision Arithmetic (Bailey)

DDPDD

Distributed Systems Adding Double1 and Double2 Separately

MPI_SUMDD

MPI_SUMDD

Slide 24

Key Implementation

(sum, error) = (double, double)

Practical Implementations

Conclusion

Multi-Processor Handshaking

Multi-Processor Handshaking (cnt'd)

Multi-Processor Handshaking (cnt'd)

Author: Yun (Helen) He and Chris H.Q. Ding

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