ff.h

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*       $Id: ff.h,v 1.1 1995/12/12 10:03:48 gj Exp $
*       -------------------------------------------------------------
*       INCLUDE FILE FOR THE FF ROUTINES.  
*                                       Geert Jan van Oldenborgh.
*       -------------------------------------------------------------
*       please do not change, and recompile _everything_ when you do.
*       -------------------------------------------------------------
*
*       this parameter determines how far the scalar npoint functions
*       will look back to find the same parameters (when lmem is true)
*
        integer memory
        parameter (memory = 12)
*
*               if .TRUE. then                        default (ffinit)
*       l4also: in C0 (and higher), also consider the algorithm with 16
*               dilogs                                .TRUE.
*       ldc3c4: in D0 (and higher), also consider possible cancellations
*               between the C0s                      .TRUE.
*       lmem:   before computing the C0 and higher, first check whether
*               it has already been done recently     .FALSE.
*       ldot:   leave the dotproducts and some determinants in common
*                                                     .FALSE.
*       onshel: (in ffz?0 only): use onshell momenta  .TRUE.
*       lsmug:  internal use
*       lnasty: internal use
*
        logical l4also,ldc3c4,lmem,ldot,onshel,lsmug,lnasty
*
*       nwidth: number of widths within which the complex mass is used
*       nschem: scheme to handle the complex mass (see ffinit.f)
*       idot:   internal flags to signal that some of the dotproducts 
*               are input: 0: none; 1: external pi.pj, 2: external + 
*               kinematical determinant, 3: all dotproducts + kindet.
*
        integer nwidth,nschem,idot
*
*       xloss:  factor that the final result of a subtraction can be
*               smaller than the terms without warning (default 1/8)
*       precx:  precision of real numbers, determined at runtime by
*               ffinit (IEEE: 4.e-16)
*       precc:  same for complex numbers
*       xalogm: smallest real number of which a log can be taken,
*               determined at runtime by ffinit (IEEE: 2.e-308)
*       xclogm: same for complex.
*       xalog2: xalogm**2
*       xclog2: xclogm**2
*       reqprc: not used
*       pi:     pi
*       pi6:    pi**2/6
*       pi12:   pi**2/12
*       xlg2:   log(2)
*       bf:     factors in the expansion of dilog (~Bernouilli numbers)
*       xninv:  1/n
*       xn2inv: 1/n**2
*       xinfac: 1/n!
*       fpij2:  vi.vj for 2point function 1-2: si, 3-3:  pi
*       fpij3:  vi.vj for 3point function 1-3: si, 4-6:  pi
*       fpij4:  vi.vj for 4point function 1-4: si, 5-10: pi
*       fpij5:  vi.vj for 5point function 1-5: si, 6-15: pi
*       fpij6:  vi.vj for 6point function 1-6: si, 7-21: pi
*       fdel2:  del2 = delta_(p1,p2)^(p1,p2) = p1^2.p2^2 - p1.p2^2 in C0
*       fdel3:  del3 = delta_(p1,p2,p3)^(p1,p2,p3) in D0
*       fdel4s: del4s = delta_(s1,s2,s3,s4)^(s1,s2,s3,s4) in D0
*       fdel4:  del4 = delta_(p1,p2,p3,p4)^(p1,p2,p3,p4) in E0
*       fdl3i:  del3i = delta_(pj,pk,pl)^(pj,pk,pl) in E0, D0 without si
*       fdl4si: dl4si = del4s in E0, D0 without si
*       fdl3ij: same in F0 without si and sj.
*       fd4sij: dl4si = del4s in E0, D0 without si
*       fdl4i:  delta4 in F0 without si.
*       fodel2: same offshell (in case of complex or z-functions)
*       fodel3: -''-
*       cfdl4s: -''-
*       fodel4: -''-
*       fodl3i: -''-
*       fod3ij: -''-
*       fodl4i: -''-
*       fidel3: ier of del3 (is not included in D0)
*       fidel4: ier of del4 (is not included in E0)
*       fidl3i: ier of dl3i (is not included in E0)
*       fid3ij: ier of dl3ij (is not included in F0)
*       fidl4i: ier of dl4i (is not included in F0)
*
        RealType xloss,precx,precc,xalogm,xclogm,xalog2,xclog2,
     &          reqprc,pi,pi6,pi12,xlg2,sqrt2,bf(20),
     &          xninv(30),xn2inv(30),xinfac(30),
     &          fpij2(3,3),fpij3(6,6),fpij4(10,10),fpij5(15,15),
     &          fpij6(21,21),fdel2,fdel3,fdel4s,fdel4,fdl3i(5),
     &          fdl4si(5),fdl3ij(6,6),fd4sij(6,6),fdl4i(6),fodel2,
     &          fodel3,fodel4,fodl3i(5),fod3ij(6,6),fodl4i(6)
        integer fidel3,fidel4,fidl3i(5),fid3ij(6,6),fidl4i(6)
*
*       cI:     imaginary unit
*       c[zero1]:0,1 complex
*       c2ipi:  2*i*pi
*       cipi2:  i*pi**2
*       cfp..:  complex version of fp..., only defined in ff[cz]*
*       cmipj:  (internal only) mi^2 - pj^2 in C0
*       c2sisj: (internal only) 2*si.sj in D0
*       cfdl4s: del4s in complex case (D0)
*       ca1:    (internal only) complex A1
*       csdl2p: (internal only) complex transformed sqrt(del2)
*
        ComplexType cI,czero,chalf,cone,c2ipi,cipi2,
     &          cfpij2(3,3),cfpij3(6,6),cfpij4(10,10),cfpij5(15,15),
     &          cfpij6(21,21),cmipj(3,3),c2sisj(4,4),cfdl4s,ca1
*
*       nevent: number in integration loop (to be updated by user)
*       ner:    can be used to signal numerical problems (see ffrcvr)
*       id:     identifier of scalar function (to be set by user)
*       idsub:  internal identifier to pinpoint errors
*       inx:    in D0: p(inx(i,j)) = isgn(i,j)*(s(i)-s(j))
*       inx5:   in E0: p(inx5(i,j)) = isgn5(i,j)*(s(i)-s(j))
*       inx6:   in F0: p(inx6(i,j)) = isgn6(i,j)*(s(i)-s(j))
*       isgn:   see inx
*       isgn5:  see inx5
*       isgn6:  see inx6
*       iold:   rotation matrix for 4point function
*       isgrot: signs to iold
*       isgn34: +1 or -1: which root to choose in the transformation (D0)
*       isgnal: +1 or -1: which root to choose in the alpha-trick (C0)
*       irota3: save the number of positions the C0 configuration has been 
*               rotated over
*       irota4: same for the D0
*       irota5: same for the E0
*       irota6: same for the F0
*
        integer nevent,ner,id,idsub,inx(4,4),isgn(4,4),inx5(5,5),
     &          isgn5(5,5),inx6(6,6),isgn6(6,6),isgn34,isgnal,iold(13,
     &          12),isgrot(10,12),irota3,irota4,irota5,irota6
        integer idum93(2)
*
        RealType acc, eps
        ComplexType cIeps
*
*       parameters
*
        parameter(
     &          cI = (0D0, 1D0),
     &          czero = (0D0,0D0),
     &          chalf = (.5D0,0D0),
     &          cone = (1D0,0D0),
     &          c2ipi = (0D0,6.28318530717958647692528676655896D0),
     &          cipi2 = (0D0,9.869604401089358618834490999876D0),
     &          pi  = 3.14159265358979323846264338327948D0,
     &          pi6 = 1.644934066848226436472415166646D0,
     &          pi12 = .822467033424113218236207583323D0,
     &          xlg2 = .6931471805599453094172321214581D0,
     &          sqrt2 = 1.4142135623730950488016887242096981D0,
     &          acc = 1D-13,
     &          eps = 1D-22,
     &          cIeps = (0D0,1D-50) )
*
*       common
*
        common /ffsign/isgn34,isgnal
        common /ffprec/ xloss,precx,precc,xalogm,xclogm,xalog2,xclog2,
     &          reqprc
        common /ffflag/ l4also,ldc3c4,lmem,ldot,
     &          nevent,ner,id,idsub,nwidth,nschem,onshel,idot
        common /ffcnst/ bf,xninv,xn2inv,xinfac,inx,isgn,iold,isgrot,
     &          inx5,isgn5,inx6,isgn6
        common /ffrota/ irota3,irota4,irota5,irota6
        common /ffdot/ fpij2,fpij3,fpij4,fpij5,fpij6
        common /ffdel/ fdel2,fdel3,fdel4s,fdel4,fdl3i,fdl4si,fdl3ij,
     &          fd4sij,fdl4i
        common /ffidel/ fidel3,fidel4,fidl3i,fid3ij,fidl4i
        common /ffcdot/ cfpij2,cfpij3,cfpij4,cfpij5,cfpij6
        common /ffcdel/ fodel2,fodel3,cfdl4s,fodel4,fodl3i,fod3ij,fodl4i
        common /ffsmug/ lsmug,lnasty,idum93,cmipj,c2sisj,ca1
*
*       regularization parameters
*
        ComplexType mudimc
        RealType delta,lambda,minmass
        common /ltregul/ mudimc,delta,lambda,minmass
 
        RealType mudim
        equivalence (mudimc, mudim)
*
*       nan is used for undefined values and is supposed to
*       "poison" a result, much as the IEEE NaN, which is just
*       too unportable in Fortran
*
        ComplexType nan
        parameter (nan = (1D123, 1D123))