Error Analysis on Floating-Point Arithmetic in C Programming Language Library Functions

Verification and interval arithmetic are the fundamental methods that we deal with in error analysis. Verification strategy is used in most error analysis on solution sets of linear and nonlinear systems. On the other hand, interval arithmetic seems to be the best method for analyzing errors in floating point arithmetic by now. This paper devotes to analyze errors of floating-point arithmetic in C programming language library functions based on interval arithmetic. The authors gives algorithm descriptions of trigonometric, radical and exponential functions as well as algorithm analysis, and gives an upper bound of theoretical errors by comparing floating-point arithmetic's result with that of interval arithmetic.