Implementation And Comparison Of High Efficiency And High Accuracy Floating Point Summation Methods

Since the advent of electronic computers,the method and accuracy of the summation of floating point numbers has been one of the fundamental issues concerned by computer and computational mathematics.Due to the storage and operation of data on the computer,there may be some problems such as rounding,effective bit cancellation,large numbers“eating”small numbers,etc.,so there may be error accumulation,or even upper(lower)overflow phenomenon when summing large floating point numbers,which makes the summing result completely distorted.Therefore,the efficient and reliable floating point sum algorithm is computational mathematics and computer science,this paper also pays attention to the problem of high-efficiency and high-precision floating point summation.After introducing some general summation methods,this paper firstly reviews some high precision summation algorithms in literature,including compensation,double compensation,Sum K,Acc Sum and FastAccSum algorithms.The theoretical error bounds of each algorithm are given,and the advantages and disadvantages of each algorithm are compared.Secondly,under the same computation scale,the serial implementation of various algorithms are carried out,and using MATLAB to compare their running time and achievable accuracy,and found that the double compensation algorithm and FastAccSum algorithm are more efficient and accurate.Thirdly,this paper uses MPI+C language to achieve some of the existing parallel summation method,and the parallel implementation of double compensation algorithm and FastAccSum algorithm is innovatively carried out,and these algorithms are carried out parallel numerical experiments on a domestic Dawning parallel computer,and various parallel algorithms are compared in terms of the number of processors,problem size and data ill-condition degree.The comparative results of the parallel summation algorithms with high efficiency and high precision are obtained.Finally,from the results of numerical experiments,we find that whether serial or parallel implementation,FastAccSum algorithm has a very good performance in terms of calculation time and accuracy,so we recommend using Fast Accsum algorithm perform the floating point sum.