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c { dg-do compile }

C To: egcs-bugs@cygnus.com

C Subject: -fPIC problem showing up with fortran on x86

C From: Dave Love <d.love@dl.ac.uk>

C Date: 19 Dec 1997 19:31:41 +0000

C 

C 

C This illustrates a long-standing problem noted at the end of the g77

C `Actual Bugs' info node and thought to be in the back end.  Although

C the report is against gcc 2.7 I can reproduce it (specifically on

C redhat 4.2) with the 971216 egcs snapshot.

C 

C g77 version 0.5.21

C  gcc -v -fnull-version -o /tmp/gfa00415 -xf77-cpp-input /tmp/gfa00415.f -xnone

C -lf2c -lm

C

C ------------

      subroutine dqage(f,a,b,epsabs,epsrel,limit,result,abserr,

     *   neval,ier,alist,blist,rlist,elist,iord,last)

C     --------------------------------------------------

C

C     Modified Feb 1989 by Barry W. Brown to eliminate key

C     as argument (use key=1) and to eliminate all Fortran

C     output.

C

C     Purpose: to make this routine usable from within S.

C

C     --------------------------------------------------

c***begin prologue  dqage

c***date written   800101   (yymmdd)

c***revision date  830518   (yymmdd)

c***category no.  h2a1a1

c***keywords  automatic integrator, general-purpose,

c             integrand examinator, globally adaptive,

c             gauss-kronrod

c***author  piessens,robert,appl. math. & progr. div. - k.u.leuven

c           de doncker,elise,appl. math. & progr. div. - k.u.leuven

c***purpose  the routine calculates an approximation result to a given

c            definite integral   i = integral of f over (a,b),

c            hopefully satisfying following claim for accuracy

c            abs(i-reslt).le.max(epsabs,epsrel*abs(i)).

c***description

c

c        computation of a definite integral

c        standard fortran subroutine

c        double precision version

c

c        parameters

c         on entry

c            f      - double precision

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 driver program.

c

c            a      - double precision

c                     lower limit of integration

c

c            b      - double precision

c                     upper limit of integration

c

c            epsabs - double precision

c                     absolute accuracy requested

c            epsrel - double precision

c                     relative accuracy requested

c                     if  epsabs.le.0

c                     and epsrel.lt.max(50*rel.mach.acc.,0.5d-28),

c                     the routine will end with ier = 6.

c

c            key    - integer

c                     key for choice of local integration rule

c                     a gauss-kronrod pair is used with

c                          7 - 15 points if key.lt.2,

c                         10 - 21 points if key = 2,

c                         15 - 31 points if key = 3,

c                         20 - 41 points if key = 4,

c                         25 - 51 points if key = 5,

c                         30 - 61 points if key.gt.5.

c

c            limit  - integer

c                     gives an upperbound on the number of subintervals

c                     in the partition of (a,b), limit.ge.1.

c

c         on return

c            result - double precision

c                     approximation to the integral

c

c            abserr - double precision

c                     estimate of the modulus of the absolute error,

c                     which should equal or exceed abs(i-result)

c

c            neval  - integer

c                     number of integrand evaluations

c

c            ier    - integer

c                     ier = 0 normal and reliable termination of the

c                             routine. it is assumed that the requested

c                             accuracy has been achieved.

c                     ier.gt.0 abnormal termination of the routine

c                             the estimates for result and error are

c                             less reliable. it is assumed that the

c                             requested accuracy has not been achieved.

c            error messages

c                     ier = 1 maximum number of subdivisions allowed

c                             has been achieved. one can allow more

c                             subdivisions by increasing the value

c                             of limit.

c                             however, if this yields no improvement it

c                             is rather advised to analyze the integrand

c                             in order to determine the integration

c                             difficulties. if the position of a local

c                             difficulty can be determined(e.g.

c                             singularity, discontinuity within the

c                             interval) one will probably gain from

c                             splitting up the interval at this point

c                             and calling the integrator on the

c                             subranges. if possible, an appropriate

c                             special-purpose integrator should be used

c                             which is designed for handling the type of

c                             difficulty involved.

c                         = 2 the occurrence of roundoff error is

c                             detected, which prevents the requested

c                             tolerance from being achieved.

c                         = 3 extremely bad integrand behavior occurs

c                             at some points of the integration

c                             interval.

c                         = 6 the input is invalid, because

c                             (epsabs.le.0 and

c                              epsrel.lt.max(50*rel.mach.acc.,0.5d-28),

c                             result, abserr, neval, last, rlist(1) ,

c                             elist(1) and iord(1) are set to zero.

c                             alist(1) and blist(1) are set to a and b

c                             respectively.

c

c            alist   - double precision

c                      vector of dimension at least limit, the first

c                       last  elements of which are the left

c                      end points of the subintervals in the partition

c                      of the given integration range (a,b)

c

c            blist   - double precision

c                      vector of dimension at least limit, the first

c                       last  elements of which are the right

c                      end points of the subintervals in the partition

c                      of the given integration range (a,b)

c

c            rlist   - double precision

c                      vector of dimension at least limit, the first

c                       last  elements of which are the

c                      integral approximations on the subintervals

c

c            elist   - double precision

c                      vector of dimension at least limit, the first

c                       last  elements of which are the moduli of the

c                      absolute error estimates on the subintervals

c

c            iord    - integer

c                      vector of dimension at least limit, the first k

c                      elements of which are pointers to the

c                      error estimates over the subintervals,

c                      such that elist(iord(1)), ...,

c                      elist(iord(k)) form a decreasing sequence,

c                      with k = last if last.le.(limit/2+2), and

c                      k = limit+1-last otherwise

c

c            last    - integer

c                      number of subintervals actually produced in the

c                      subdivision process

c

c***references  (none)

c***routines called  d1mach,dqk15,dqk21,dqk31,

c                    dqk41,dqk51,dqk61,dqpsrt

c***end prologue  dqage

c

      double precision a,abserr,alist,area,area1,area12,area2,a1,a2,b,

     *  blist,b1,b2,dabs,defabs,defab1,defab2,dmax1,d1mach,elist,epmach,

     *  epsabs,epsrel,errbnd,errmax,error1,error2,erro12,errsum,f,

     *  resabs,result,rlist,uflow

      integer ier,iord,iroff1,iroff2,k,last,limit,maxerr,neval,

     *  nrmax

c

      dimension alist(limit),blist(limit),elist(limit),iord(limit),

     *  rlist(limit)

c

      external f

c

c            list of major variables

c            -----------------------

c

c           alist     - list of left end points of all subintervals

c                       considered up to now

c           blist     - list of right end points of all subintervals

c                       considered up to now

c           rlist(i)  - approximation to the integral over

c                      (alist(i),blist(i))

c           elist(i)  - error estimate applying to rlist(i)

c           maxerr    - pointer to the interval with largest

c                       error estimate

c           errmax    - elist(maxerr)

c           area      - sum of the integrals over the subintervals

c           errsum    - sum of the errors over the subintervals

c           errbnd    - requested accuracy max(epsabs,epsrel*

c                       abs(result))

c           *****1    - variable for the left subinterval

c           *****2    - variable for the right subinterval

c           last      - index for subdivision

c

c

c           machine dependent constants

c           ---------------------------

c

c           epmach  is the largest relative spacing.

c           uflow  is the smallest positive magnitude.

c

c***first executable statement  dqage

      epmach = d1mach(4)

      uflow = d1mach(1)

c

c           test on validity of parameters

c           ------------------------------

c

      ier = 0

      neval = 0

      last = 0

      result = 0.0d+00

      abserr = 0.0d+00

      alist(1) = a

      blist(1) = b

      rlist(1) = 0.0d+00

      elist(1) = 0.0d+00

      iord(1) = 0

      if(epsabs.le.0.0d+00.and.

     *  epsrel.lt.dmax1(0.5d+02*epmach,0.5d-28)) ier = 6

      if(ier.eq.6) go to 999

c

c           first approximation to the integral

c           -----------------------------------

c

      neval = 0

      call dqk15(f,a,b,result,abserr,defabs,resabs)

      last = 1

      rlist(1) = result

      elist(1) = abserr

      iord(1) = 1

c

c           test on accuracy.

c

      errbnd = dmax1(epsabs,epsrel*dabs(result))

      if(abserr.le.0.5d+02*epmach*defabs.and.abserr.gt.errbnd) ier = 2

      if(limit.eq.1) ier = 1

      if(ier.ne.0.or.(abserr.le.errbnd.and.abserr.ne.resabs)

     *  .or.abserr.eq.0.0d+00) go to 60

c

c           initialization

c           --------------

c

c

      errmax = abserr

      maxerr = 1

      area = result

      errsum = abserr

      nrmax = 1

      iroff1 = 0

      iroff2 = 0

c

c           main do-loop

c           ------------

c

      do 30 last = 2,limit

c

c           bisect the subinterval with the largest error estimate.

c

        a1 = alist(maxerr)

        b1 = 0.5d+00*(alist(maxerr)+blist(maxerr))

        a2 = b1

        b2 = blist(maxerr)

        call dqk15(f,a1,b1,area1,error1,resabs,defab1)

        call dqk15(f,a2,b2,area2,error2,resabs,defab2)

c

c           improve previous approximations to integral

c           and error and test for accuracy.

c

        neval = neval+1

        area12 = area1+area2

        erro12 = error1+error2

        errsum = errsum+erro12-errmax

        area = area+area12-rlist(maxerr)

        if(defab1.eq.error1.or.defab2.eq.error2) go to 5

        if(dabs(rlist(maxerr)-area12).le.0.1d-04*dabs(area12)

     *  .and.erro12.ge.0.99d+00*errmax) iroff1 = iroff1+1

        if(last.gt.10.and.erro12.gt.errmax) iroff2 = iroff2+1

    5   rlist(maxerr) = area1

        rlist(last) = area2

        errbnd = dmax1(epsabs,epsrel*dabs(area))

        if(errsum.le.errbnd) go to 8

c

c           test for roundoff error and eventually set error flag.

c

        if(iroff1.ge.6.or.iroff2.ge.20) ier = 2

c

c           set error flag in the case that the number of subintervals

c           equals limit.

c

        if(last.eq.limit) ier = 1

c

c           set error flag in the case of bad integrand behavior

c           at a point of the integration range.

c

        if(dmax1(dabs(a1),dabs(b2)).le.(0.1d+01+0.1d+03*

     *  epmach)*(dabs(a2)+0.1d+04*uflow)) ier = 3

c

c           append the newly-created intervals to the list.

c

    8   if(error2.gt.error1) go to 10

        alist(last) = a2

        blist(maxerr) = b1

        blist(last) = b2

        elist(maxerr) = error1

        elist(last) = error2

        go to 20

   10   alist(maxerr) = a2

        alist(last) = a1

        blist(last) = b1

        rlist(maxerr) = area2

        rlist(last) = area1

        elist(maxerr) = error2

        elist(last) = error1

c

c           call subroutine dqpsrt to maintain the descending ordering

c           in the list of error estimates and select the subinterval

c           with the largest error estimate (to be bisected next).

c

   20   call dqpsrt(limit,last,maxerr,errmax,elist,iord,nrmax)

c ***jump out of do-loop

        if(ier.ne.0.or.errsum.le.errbnd) go to 40

   30 continue

c

c           compute final result.

c           ---------------------

c

   40 result = 0.0d+00

      do 50 k=1,last

        result = result+rlist(k)

   50 continue

      abserr = errsum

   60 neval = 30*neval+15

  999 return

      end