Associative Law And Floating-Point Addition Accuracy

For a set of data accumulation is often used in all kinds of program computingfunction, such as average calculation, vector calculation, matrix calculation, neuralnetwork, the aerodynamic calculation and fluid mechanics. Floating point calculationaccuracy problem has always been the hot spot of the study. Floating-pointaccumulation as a common floating point arithmetic, the importance of accuracy ofthe arithmetic for a variety of computing is obvious. Second, Today, large amounts ofdata are in need to operate in parallel computer, such as matrix operation, the dotproduct,etc. but we know that the original accumulation order will surely charge afterthe data parallelism. namely binding sequence must change, leading to the calculationresults will be different, the error will be different accordingly, for a given data set,the species of binding will increase sharply with the size of the data sets. this articlediscussed the influence of different binding order of floating point numbers on theerror of accumulative sum in the process of single precision floating-pointaccumulation through experimental methods on account of data sets of characteristics,and aimed to explore the law of causing calculation error by the binding sequence,provided a basis for a selection of binding method for computing paradigm andcalculating structure as multi-core calculation, GPU computation and multi-processorcalculation. and facilitated the advantage of parallel computing. On the other hand,the study not only is meaningful to improve the floating-point calculation precision,also has important significance to application developers, designer of the compiler,designers of the system the structure.