浮点运算错误计算原因

%The mode of significant digits and representation errors.As we all know, there are often miscalculations in floating-point arithmetic. And generally agreed that representationerrors are major causes. The paper points out that, in fact, there is another reason: the mode of fixed-precision computation, inwhich all intermediate calculations are kept the same number of significant digits, so the combined results are unstable. Furthermore, we find out the relationship between the significant digits of argument and that of univariate function value, and the concept of "Error Number" and its calculation method are proposed, which can be used to obtain the number of contaminateddigits of the function value. Finally, based on the above theory, combined the qualitative and quantitative methods, through the analysisof the calculation process, the paper reveals the reasons for the erroneous computation of some well-known cases.