Research On Floating-point Word Length Matching For Embedded System High-performance Computing

Embedded systems have been widely used in various fields of life.The performance,power consumption,real-time performance and other requirements of embedded devices are different from the general environment,resulting in the need for efficient and reliable implementation of algorithm programs.Algorithm in its mathematical form may have beautiful formula,but in the actual operation process,due to the restrictions of floatingpoint number of storage number,the results may not be accurate,resulting in a lack of credibility of the results.The floating-point stability of an algorithm is often overlooked,and this error can be magnified with the size of the calculation,and even accumulate to the point where the stability and credibility of the calculation exceed the minimum,resulting in unacceptable results.This paper studies the effect of floating-point numbers on the performance and stability of algorithms in embedded computers.The main work is as follows:1.Reduce the precision of some floating-point Numbers in the algorithm to speed up the algorithm,namely,mixed precision technology.Preconditioning conjugate gradient iteration method is studied in CUDA GPU platform environment.By reducing polynomial preconditioner precision of the conjugate gradient iteration method,the speed of solving linear equations is accelerated.The technique of different matrix solving speed up to about 1.67 times and the average speed up is about 1.32 times faster.2 Light path computing is studied in detail of the 2 order,3 order and 4 order equation solving algorithm.Numerical stability is required according to the existing environment,we using the theory of numerical stability,optimize its application process.The three kinds of algorithm accuracy rate were 99.9935%,58.2868% and 67.4891%,improved respectively up to 100%,100% and 99.9976%,which makes the stability of the algorithm satisfies the requirement of engineering application.3.Developed an automatic analysis tool for floating-point computing stability based on LLVM.Users do not need to modifying the source code with this tool which inserting the corresponding floating-point stability analysis code in the middle process of compilation.The real significant digits of each position of the algorithm can be detected automatically,which accelerates the numerical stability analysis process of the existing algorithm.At present,the tool will reduce the program speed by about 1000 times after processing,which is still in the optimization process.