SLATEC Routines --- QK51 ---

*DECK QK51
      SUBROUTINE QK51 (F, A, B, RESULT, ABSERR, RESABS, RESASC)
C***BEGIN PROLOGUE  QK51
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***LIBRARY   SLATEC (QUADPACK)
C***CATEGORY  H2A1A2
C***TYPE      SINGLE PRECISION (QK51-S, DQK51-D)
C***KEYWORDS  51-POINT GAUSS-KRONROD RULES, QUADPACK, QUADRATURE
C***AUTHOR  Piessens, Robert
C             Applied Mathematics and Programming Division
C             K. U. Leuven
C           de Doncker, Elise
C             Applied Mathematics and Programming Division
C             K. U. Leuven
C***DESCRIPTION
C
C           Integration rules
C           Standard fortran subroutine
C           Real version
C
C           PARAMETERS
C            ON ENTRY
C              F      - Real
C                       Function subroutine 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 51-point
C                       Kronrod rule (RESK) obtained by optimal addition
C                       of abscissae to the 25-point Gauss rule (RESG).
C
C              ABSERR - Real
C                       Estimate of the modulus of the absolute error,
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
C***REFERENCES  (NONE)
C***ROUTINES CALLED  R1MACH
C***REVISION HISTORY  (YYMMDD)
C   800101  DATE WRITTEN
C   890531  Changed all specific intrinsics to generic.  (WRB)
C   890531  REVISION DATE from Version 3.2
C   891214  Prologue converted to Version 4.0 format.  (BAB)
C***END PROLOGUE  QK51