PDP-10 Archive: decus/20-0026/cs.doc from decus_20tap2

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SUBROUTINE CS

PURPOSE
   COMPUTES THE FRESNEL INTEGRALS.

USAGE
   CALL CS (C,S,X)

DESCRIPTION OF PARAMETERS
   C	 - THE RESULTANT VALUE C(X).
   S	 - THE RESULTANT VALUE S(X).
   X	 - THE ARGUMENT OF FRESNEL INTEGRALS
	   IF X IS NEGATIVE, THE ABSOLUTE VALUE IS USED.

REMARKS
   THE ARGUMENT VALUE X REMAINS UNCHANGED.

SUBROUTINES AND FUNCTION SUBPROGRAMS REQUIRED
   NONE

METHOD
   DEFINITION
   C(X)=INTEGRAL(COS(T)/SQRT(2*LI*T) SUMMED OVER T FROM 0 TO X)
   S(X)=INTEGRAL(SIN(T)/SQRT(I*LI*T) SUMMED OVER T FROM 0 TO X)
   EVALUATION
   USING DIFFERENT APPROXIMATIONS FOR X LESS THAN 4 AND X
   GREATER THAN 4.
   REFERENCE
   'COMPUTATION OF FRESNEL INTEGRALS' BY BOERSMA,
   MATHEMATICAL TABLES AND OTHER AIDS TO COMPUTATION, VOL. 14,
   1960, NO. 72, P. 380.