Error Analysis For Floating-point Arithmetic Program

It is well-known that computer can be applied to solve many engineering problems. However, due to the limit of memory space, the result obtained from numerical computation is approximate not exact because of the fixed precision. Based on floating-point representation, not all real numbers can be represented by computer exactly, which means that the initial values input in the computer may be approximate. In the process of the computation, numerical arithmetic would cause the error.C language is a basic programming language of the computer. It has a wide range of applications in science and engineering. Given a C source code involved with computation, how to measure the error of this C program plays an important role in computer science.This paper is devoted to error analysis to the C program about basic operations in elementary functions and matrix computation. At first, we introduce some definitions and notations about floating-point numbers, floating-point arithmetic, rounding modes, interval arithmetic. We next diagnose the algorithms, such as polynomial evaluation, matrix multiplication, implemented in C language, and then present some theoretical results of error bounds about those functions in C language. Based on Boost libraries, one toolkit is implemented by use of the interval computation.