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

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SUBROUTINE EXPI

PURPOSE
   COMPUTES THE EXPONENTIAL INTEGRAL -EI(-X)

USAGE
   CALL EXPI(X,RES)

DESCRIPTION OF PARAMETERS
   X	 - ARGUMENT OF EXPONENTIAL INTEGRAL
   RES	 - RESULT VALUE
   AUX	 - RESULTANT AUXILIARY VALUE

REMARKS
   X GT 170 (X LT -174) MAY CAUSE UNDERFLOW (OVERFLOW)
   WITH THE EXPONENTIAL FUNCTION
   FOR X = 0 THE RESULT VALUE IS SET TO -1.E75

SUBROUTINES AND FUNCTION SUBPROGRAMS REQUIRED
   NONE

METHOD
   DEFINITION
   RES=INTEGRAL(EXP(-T)/T, SUMMED OVER T FROM X TO INFINITY).
   EVALUATION
   THREE DIFFERENT RATIONAL APPROXIMATIONS ARE USED IN THE
   RANGES 1 LE X, X LE -9 AND -9 LT X LE -3 RESPECTIVELY,
   A POLYNOMIAL APPROXIMATION IS USED IN -3 LT X LT 1.