Fourier Cosine Integral

TOMS427 is a FORTRAN77 library which implements ACM TOMS algorithm 427, for approximating a Fourier cosine integral of the form

        Integral ( 0 <= T < +oo ) f(t) cos ( w * t ) dt

While the text of many ACM TOMS algorithms is available online through ACM: or NETLIB:, most of the early algorithms are not available. This is one of them. I typed it in.


value = frcos ( fc, w, t, et, hl )
where FC is a function that evaluates f(t), W is the multiplier of the argument, T is the finite upper limit for the integral, ET is the requested absolute accuracy, and HL is a limit on step size convergence, such that convergence in any subinterval is not recognized unless the subinterval is smaller than HL.


TOMS427 is available in a FORTRAN77 version.


  1. Peter Linz,
    Algorithm 427: Fourier Cosine Integral,
    Communications of the ACM,
    Volume 15, Number 5, May 1972, pages 358-360.

Source Code:

Examples and Tests:

List of Routines:

You can go up one level to the FORTRAN77 source codes.

Last revised on 08 December 2005.