Algorithms.

The article focuses on an algorithm related to quadrature. FSER1 evaluates the integrals using the Filon quadrature algorithm. The user may request an evaluation of C only, S only, or both C and S. FSER1 contains an automatic error-control feature which selects an integration step size on the basis of an error parameter supplied by the user. The Filon quadrature formulas, truncation error, rounding error, and automatic error control are described in a companion paper by the authors. The calling parameters for this subroutine are defined as follows. F is the name of a FUNCTION subprogram F(X), supplied by the user, which evaluates F(X) appearing in the integrand, EPS is the name for "e" appearing in inequalities. It is used in the error control portion of the algorithm. The error in the computed values of C and S is related to "e" by the inequality. The user must assign a value to EPS before calling FSER1. MAX specifies the maximum number of halvings of the step size that are allowed.