SUBROUTINE QK31(F,A,B,RESULT,ABSERR,RESABS,RESASC)
C***BEGIN PROLOGUE  QK31
C***DATE WRITTEN   800101   (YYMMDD)
C***REVISION DATE  830518   (YYMMDD)
C***CATEGORY NO.  H2A1A2
C***KEYWORDS  31-POINT GAUSS-KRONROD RULES
C***AUTHOR  PIESSENS, ROBERT, APPLIED MATH. AND PROGR. DIV. -
C             K. U. LEUVEN
C           DE DONCKER, ELISE, APPLIED MATH. AND PROGR. DIV. -
C             K. U. LEUVEN
C***PURPOSE  To compute I = Integral of F over (A,B) with error
C                           estimate
C                       J = Integral of ABS(F) over (A,B)
C***DESCRIPTION
C
C           Integration rules
C           Standard fortran subroutine
C           Real version
C
C           PARAMETERS
C            ON ENTRY
C              F      - Real
C                       Function subprogram defining the integrand
C                       FUNCTION F(X). The actual name for F needs to be
C                       Declared E X T E R N A L in the calling program.
C
C              A      - Real
C                       Lower limit of integration
C
C              B      - Real
C                       Upper limit of integration
C
C            ON RETURN
C              RESULT - Real
C                       Approximation to the integral I
C                       RESULT is computed by applying the 31-POINT
C                       GAUSS-KRONROD RULE (RESK), obtained by optimal
C                       addition of abscissae to the 15-POINT GAUSS
C                       RULE (RESG).
C
C              ABSERR - Real
C                       Estimate of the modulus of the modulus,
C                       which should not exceed ABS(I-RESULT)
C
C              RESABS - Real
C                       Approximation to the integral J
C
C              RESASC - Real
C                       Approximation to the integral of ABS(F-I/(B-A))
C                       over (A,B)
C***REFERENCES  (NONE)
C***ROUTINES CALLED  R1MACH
C***END PROLOGUE  QK31