This paper presents the design and implementation of high-level numerical analysis functions in CH, a superset of C language developed for the convenience of scientific and engineering computations. In CH, complex number is treated as a built-in data type, so that the syntaxes of complex arithmetic, relational operations, and built-in mathematical functions are the same as those for real numbers. The variable number of arguments is used in the built-in mathematical functions to simplify the computation of different branches of multi-valued complex functions. The computational arrays are introduced to handle the arrays in the numerical computations. Passing arrays of variable length by arrays of deferred-shape and arrays of assumed-shape to functions are discussed. These methods allow the arrays to be passed with their rank, dimensions and data types. A list of high-level numerical functions and two examples of the applications in the scientific and engineering are given in the paper.