C
C     ..................................................................
C
C        SUBROUTINE DQH8
C
C        PURPOSE
C           TO COMPUTE INTEGRAL(EXP(-X*X)*FCT(X), SUMMED OVER X FROM
C                               -INFINITY TO +INFINITY).
C
C        USAGE
C           CALL DQH8 (FCT,Y)
C           PARAMETER FCT REQUIRES AN EXTERNAL STATEMENT
C
C        DESCRIPTION OF PARAMETERS
C           FCT    - THE NAME OF AN EXTERNAL DOUBLE PRECISION FUNCTION
C                    SUBPROGRAM USED.
C           Y      - THE RESULTING DOUBLE PRECISION INTEGRAL VALUE.
C
C        REMARKS
C           NONE
C
C        SUBROUTINES AND FUNCTION SUBPROGRAMS REQUIRED
C           THE EXTERNAL DOUBLE PRECISION FUNCTION SUBPROGRAM FCT(X)
C           MUST BE FURNISHED BY THE USER.
C
C        METHOD
C           EVALUATION IS DONE BY MEANS OF 8-POINT GAUSSIAN-HERMITE
C           QUADRATURE FORMULA, WHICH INTEGRATES EXACTLY WHENEVER
C           FCT(X) IS A POLYNOMIAL UP TO DEGREE 15.
C           FOR REFERENCE, SEE
C           SHAO/CHEN/FRANK, TABLES OF ZEROS AND GAUSSIAN WEIGHTS OF
C           CERTAIN ASSOCIATED LAGUERRE POLYNOMIALS AND THE RELATED
C           GENERALIZED HERMITE POLYNOMIALS, IBM TECHNICAL REPORT
C           TR00.1100 (MARCH 1964), PP.213-214.
C
C     ..................................................................
C
      SUBROUTINE DQH8(FCT,Y)
C
C
      DOUBLE PRECISION X,Y,Z,FCT
C
      X=.29306374202572440D1
      Z=-X
      Y=.19960407221136762D-3*(FCT(X)+FCT(Z))
      X=.19816567566958429D1
      Z=-X
      Y=Y+.17077983007413475D-1*(FCT(X)+FCT(Z))
      X=.11571937124467802D1
      Z=-X
      Y=Y+.20780232581489188D0*(FCT(X)+FCT(Z))
      X=.38118699020732212D0
      Z=-X
      Y=Y+.66114701255824129D0*(FCT(X)+FCT(Z))
      RETURN
      END