TOMS723
Fresnel Integrals

TOMS723 is a FORTRAN77 library which computes the Fresnel sine and cosine integrals, by W van Snyder.

        C(x) = integral ( 0 < t < x ) cos ( t^2 ) dt
        S(x) = integral ( 0 < t < x ) sin ( t^2 ) dt
      

An alternate definition, used in Abramowitz and Stegun and the NIST Mathematical Handbook, is:

        C*(x) = integral ( 0 < t < x ) cos ( pi/2 * t^2 ) dt
        S*(x) = integral ( 0 < t < x ) sin ( pi/2 * t^2 ) dt
      

Languages:

TOMS723 is available in a FORTRAN77 version.

Related Data and Programs:

Reference:

1. W van Snyder,
   Algorithm 723: Fresnel Integrals,
   ACM Transactions on Mathematical Software,
   Volume 19, Number 4, December 1993, pages 452-456.

Source Code:

• toms723.f, the source code.

Examples and Tests:

• toms723_prb.f, a sample calling program.
• toms723_prb_output.txt, the output file.

List of Routines:

• AMACH provides machine constants.
• I1MACH provides integer machine constants.
• R1MACH provides single precision machine constants.
• D1MACH provides double precision machine constants.
• AMTEST ???
• AMSUB1 returns the value of TEST1 - 1.
• DCOSPX evaluates cos(pi*x).
• DCSPXX carefully evaluates cos(pi*x*x/2).
• DERM1 ???
• DERV1 ???
• DFRENC evaluates the Fresnel cosine integral.
• DFRENF evaluates the auxilliary f function.
• DFRENG evaluates the auxilliary g function.
• DFRENS evaluates the Fresnel sine integral.
• DFREN1 computes a Fresnel integral or auxilliary function.
• DSINPX evaluates sin(pi*x).
• DSNPXX carefully evaluates sin(pi*x*x/2).
• ERFIN is the final function called when an error is encountered.
• ERMSG prints an error message.
• ERMSET ???
• ERLSET ???
• ERLGET ???

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