eemmg-lib/ff/ff.h

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*   $Id: ff.h,v 1.1 2016/09/30 06:57:58 pingrg 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)
*   lwrite: give debug output                     .FALSE.
*   ltest:  test consistency internally (slow)    .TRUE.
*   l4also: in C0 (and higher), also consider the algorithm with 16
*           dilogs                                .TRUE.
*   ldc3c4: in D0 (and higher), also consider possible cancellations
*           between the C0's                      .TRUE.
*   lmem:   before computing the C0 and higher, first check whether
*           it has already been done recently     .FALSE.
*   lwarn:  give warning messages (concerning numerical stability)
*                                                 .TRUE.
*   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 lwrite,ltest,l4also,ldc3c4,lmem,lwarn,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
*   x[0124]:0,1,2,4
*   x05:    1/2
*   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)
*
    DOUBLE PRECISION xloss,precx,precc,xalogm,xclogm,xalog2,xclog2,
     +      reqprc,x0,x05,x1,x2,x4,pi,pi6,pi12,xlg2,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)
*
*   c[0124]:0,1,2,4 complex
*   c05:    1/2 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)
*
    DOUBLE COMPLEX c0,c05,c1,c2,c4,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)
*
*   parameters
*
    parameter(x0 = 0.d0,x1 = 1.d0,x05 = .5d0,x2 = 2.d0,x4 = 4.d0,
     +      c0 = (0.D0,0.D0),c05 = (.5D0,0.D0),c1 = (1.D0,0.D0),
     +      c2 = (2.D0,0.D0),c4 = (4.D0,0.D0))
    parameter(
     +      c2ipi = (0.D+0,6.28318530717958647692528676655896D+0),
     +      cipi2 = (0.D+0,9.869604401089358618834490999876D+0),
     +      pi  = 3.14159265358979323846264338327948D+0,
     +      pi6 = 1.644934066848226436472415166646D+0,
     +      pi12 = .822467033424113218236207583323D+0,
     +      xlg2 = .6931471805599453094172321214581D+0)
*
*   common
*
    common /ffsign/isgn34,isgnal
    common /ffprec/ xloss,precx,precc,xalogm,xclogm,xalog2,xclog2,
     +      reqprc
    common /ffflag/ lwrite,ltest,l4also,ldc3c4,lmem,lwarn,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