SLATEC Routines --- GAUS8 ---

*DECK GAUS8
      SUBROUTINE GAUS8 (FUN, A, B, ERR, ANS, IERR)
C***BEGIN PROLOGUE  GAUS8
C***PURPOSE  Integrate a real function of one variable over a finite
C            interval using an adaptive 8-point Legendre-Gauss
C            algorithm.  Intended primarily for high accuracy
C            integration or integration of smooth functions.
C***LIBRARY   SLATEC
C***CATEGORY  H2A1A1
C***TYPE      SINGLE PRECISION (GAUS8-S, DGAUS8-D)
C***KEYWORDS  ADAPTIVE QUADRATURE, AUTOMATIC INTEGRATOR,
C             GAUSS QUADRATURE, NUMERICAL INTEGRATION
C***AUTHOR  Jones, R. E., (SNLA)
C***DESCRIPTION
C
C     Abstract
C        GAUS8 integrates real functions of one variable over finite
C        intervals using an adaptive 8-point Legendre-Gauss algorithm.
C        GAUS8 is intended primarily for high accuracy integration
C        or integration of smooth functions.
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 the calling program.
C              FUN must be a REAL function of one REAL argument.  The
C              value of the argument to FUN is the variable of
C              integration which ranges from A to B.
C        A   - lower limit of integration
C        B   - upper limit of integration (may be less than A)
C        ERR - is a requested pseudorelative error tolerance.  Normally
C              pick a value of ABS(ERR) so that STOL .LT. ABS(ERR) .LE.
C              1.0E-3 where STOL is the single precision unit roundoff
C              R1MACH(4).  ANS will normally have no more error than
C              ABS(ERR) times the integral of the absolute value of
C              FUN(X).  Usually, smaller values for ERR yield more
C              accuracy and require more function evaluations.
C
C              A negative value for ERR causes an estimate of the
C              absolute error in ANS to be returned in ERR.  Note that
C              ERR must be a variable (not a constant) in this case.
C              Note also that the user must reset the value of ERR
C              before making any more calls that use the variable ERR.
C
C        Output--
C        ERR - will be an estimate of the absolute error in ANS if the
C              input value of ERR was negative.  (ERR is unchanged if
C              the input value of ERR was non-negative.)  The estimated
C              error is solely for information to the user and should
C              not be used as a correction to the computed integral.
C        ANS - computed value of integral
C        IERR- a status code
C            --Normal codes
C               1 ANS most likely meets requested error tolerance,
C                 or A=B.
C              -1 A and B are too nearly equal to allow normal
C                 integration.  ANS is set to zero.
C            --Abnormal code
C               2 ANS probably does not meet requested error tolerance.
C
C***REFERENCES  (NONE)
C***ROUTINES CALLED  I1MACH, R1MACH, XERMSG
C***REVISION HISTORY  (YYMMDD)
C   810223  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   900326  Removed duplicate information from DESCRIPTION section.
C           (WRB)
C***END PROLOGUE  GAUS8