SLATEC Routines --- QNC79 ---

*DECK QNC79
      SUBROUTINE QNC79 (FUN, A, B, ERR, ANS, IERR, K)
C***BEGIN PROLOGUE  QNC79
C***PURPOSE  Integrate a function using a 7-point adaptive Newton-Cotes
C            quadrature rule.
C***LIBRARY   SLATEC
C***CATEGORY  H2A1A1
C***TYPE      SINGLE PRECISION (QNC79-S, DQNC79-D)
C***KEYWORDS  ADAPTIVE QUADRATURE, INTEGRATION, NEWTON-COTES
C***AUTHOR  Kahaner, D. K., (NBS)
C           Jones, R. E., (SNLA)
C***DESCRIPTION
C
C     Abstract
C       QNC79 is a general purpose program for evaluation of
C       one dimensional integrals of user defined functions.
C       QNC79 will pick its own points for evaluation of the
C       integrand and these will vary from problem to problem.
C       Thus, QNC79 is not designed to integrate over data sets.
C       Moderately smooth integrands will be integrated efficiently
C       and reliably.  For problems with strong singularities,
C       oscillations etc., the user may wish to use more sophis-
C       ticated routines such as those in QUADPACK.  One measure
C       of the reliability of QNC79 is the output parameter K,
C       giving the number of integrand evaluations that were needed.
C
C     Description of Arguments
C
C     --Input--
C       FUN  - name of external function to be integrated.  This name
C              must be in an EXTERNAL statement in your calling
C              program.  You must write a Fortran function to evaluate
C              FUN.  This should be of the form
C                    REAL FUNCTION FUN (X)
C              C
C              C     X can vary from A to B
C              C     FUN(X) should be finite for all X on interval.
C              C
C                    FUN = ...
C                    RETURN
C                    END
C       A    - lower limit of integration
C       B    - upper limit of integration (may be less than A)
C       ERR  - is a requested error tolerance.  Normally, pick a value
C              0 .LT. ERR .LT. 1.0E-3.
C
C     --Output--
C       ANS  - computed value of the integral.  Hopefully, ANS is
C              accurate to within ERR * integral of ABS(FUN(X)).
C       IERR - a status code
C            - Normal codes
C               1  ANS most likely meets requested error tolerance.
C              -1  A equals B, or A and B are too nearly equal to
C                  allow normal integration.  ANS is set to zero.
C            - Abnormal code
C               2  ANS probably does not meet requested error tolerance.
C       K    - the number of function evaluations actually used to do
C              the integration.  A value of K .GT. 1000 indicates a
C              difficult problem; other programs may be more efficient.
C              QNC79 will gracefully give up if K exceeds 2000.
C
C***REFERENCES  (NONE)
C***ROUTINES CALLED  I1MACH, R1MACH, XERMSG
C***REVISION HISTORY  (YYMMDD)
C   790601  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   900315  CALLs to XERROR changed to CALLs to XERMSG.  (THJ)
C   920218  Code and prologue polished.  (WRB)
C***END PROLOGUE  QNC79