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#include "externals.h"
*###[ ffdel2:
subroutine ffdel2(del2,piDpj,ns,i1,i2,i3,lerr,ier)
*************************************************************************
* calculate in a numerically stable way *
* del2(piDpj(i1,i1),piDpj(i2,i2),piDpj(i3,i3)) = *
* = piDpj(i1,i1)*piDpj(i2,i2) - piDpj(i1,i2)^2 *
* = piDpj(i1,i1)*piDpj(i3,i3) - piDpj(i1,i3)^2 *
* = piDpj(i2,i2)*piDpj(i3,i3) - piDpj(i2,i3)^2 *
* ier is the usual error flag. *
*************************************************************************
implicit none
*
* arguments:
*
integer ns,i1,i2,i3,lerr,ier
DOUBLE PRECISION del2,piDpj(ns,ns)
*
* local variables
*
DOUBLE PRECISION s1,s2
*
* common blocks
*
#include "ff.h"
*
* calculations
*
idsub = idsub + 1
if ( abs(piDpj(i1,i2)) .lt. abs(piDpj(i1,i3)) .and.
+ abs(piDpj(i1,i2)) .lt. abs(piDpj(i2,i3)) ) then
s1 = piDpj(i1,i1)*piDpj(i2,i2)
s2 = piDpj(i1,i2)**2
elseif ( abs(piDpj(i1,i3)) .lt. abs(piDpj(i2,i3)) ) then
s1 = piDpj(i1,i1)*piDpj(i3,i3)
s2 = piDpj(i1,i3)**2
else
s1 = piDpj(i2,i2)*piDpj(i3,i3)
s2 = piDpj(i2,i3)**2
endif
del2 = s1 - s2
if ( abs(del2) .lt. xloss*s2 ) then
if ( lerr .eq. 0 ) then
* we know we have another chance
if ( del2.ne.0 ) then
ier = ier + int(log10(xloss*abs(s2/del2)))
else
ier = ier + int(log10(xloss*abs(s2)/xclogm))
endif
endif
endif
*###] ffdel2:
end
*###[ ffdl2p:
subroutine ffdl2p(delps1,xpi,dpipj,piDpj,
+ ip1,ip2,ip3,is1,is2,is3,ns)
***#[*comment:***********************************************************
* *
* calculate in a numerically stable way *
* delta_{ip1,is2}^{ip1,ip2} *
* ier is the usual error flag. *
* *
***#]*comment:***********************************************************
* #[ declarations:
implicit none
*
* arguments:
*
integer ns,ip1,ip2,ip3,is1,is2,is3
DOUBLE PRECISION delps1,xpi(ns),dpipj(ns,ns),piDpj(ns,ns)
*
* local variables
*
DOUBLE PRECISION s1,s2,s3,xmax,som
*
* common blocks
*
#include "ff.h"
* #] declarations:
* #[ stupid tree:
* 1
s1 = xpi(ip1)*piDpj(ip2,is2)
s2 = piDpj(ip1,ip2)*piDpj(ip1,is2)
delps1 = s1 - s2
if ( abs(delps1) .ge. xloss*abs(s1) ) goto 100
som = delps1
xmax = abs(s1)
* 2
s1 = piDpj(ip1,ip2)*piDpj(ip3,is2)
s2 = piDpj(ip1,ip3)*piDpj(ip2,is2)
delps1 = s1 - s2
if ( abs(delps1) .ge. xloss*abs(s1) ) goto 100
if ( abs(s1) .lt. xmax ) then
som = delps1
xmax = abs(s1)
endif
* 3
s1 = piDpj(ip1,ip3)*piDpj(ip1,is2)
s2 = xpi(ip1)*piDpj(ip3,is2)
delps1 = s1 - s2
if ( abs(delps1) .ge. xloss*abs(s1) ) goto 100
if ( abs(s1) .lt. xmax ) then
som = delps1
xmax = abs(s1)
endif
* 4
s1 = xpi(ip1)*piDpj(ip2,is1)
s2 = piDpj(ip1,is1)*piDpj(ip1,ip2)
delps1 = s1 - s2
if ( abs(delps1) .ge. xloss*abs(s1) ) goto 100
if ( abs(s1) .lt. xmax ) then
som = delps1
xmax = abs(s1)
endif
* 5
s1 = piDpj(ip1,is2)*piDpj(ip2,is1)
s2 = piDpj(ip1,is1)*piDpj(ip2,is2)
delps1 = s1 - s2
if ( abs(delps1) .ge. xloss*abs(s1) ) goto 100
if ( abs(s1) .lt. xmax ) then
som = delps1
xmax = abs(s1)
endif
* 6
s1 = piDpj(ip1,ip2)*piDpj(ip3,is1)
s2 = piDpj(ip1,ip3)*piDpj(ip2,is1)
delps1 = s1 - s2
if ( abs(delps1) .ge. xloss*abs(s1) ) goto 100
if ( abs(s1) .lt. xmax ) then
som = delps1
xmax = abs(s1)
endif
* 7
s1 = piDpj(ip2,is2)*piDpj(ip3,is1)
s2 = piDpj(ip2,is1)*piDpj(ip3,is2)
delps1 = s1 - s2
if ( abs(delps1) .ge. xloss*abs(s1) ) goto 100
if ( abs(s1) .lt. xmax ) then
som = delps1
xmax = abs(s1)
endif
* 8
s1 = piDpj(ip1,ip3)*piDpj(ip1,is1)
s2 = xpi(ip1)*piDpj(ip3,is1)
delps1 = s1 - s2
if ( abs(delps1) .ge. xloss*abs(s1) ) goto 100
if ( abs(s1) .lt. xmax ) then
som = delps1
xmax = abs(s1)
endif
* 9
s1 = piDpj(ip1,is1)*piDpj(ip3,is2)
s2 = piDpj(ip1,is2)*piDpj(ip3,is1)
delps1 = s1 - s2
if ( abs(delps1) .ge. xloss*abs(s1) ) goto 100
if ( abs(s1) .lt. xmax ) then
som = delps1
xmax = abs(s1)
endif
*10 22-nov-1993 yet another one
if ( dpipj(1,1).eq.0 ) then
s1 = +xpi(ip1)*dpipj(is3,is2)/2
s2 = -piDpj(ip1,ip2)*dpipj(is2,is1)/2
s3 = +xpi(ip1)*piDpj(ip2,ip3)/2
delps1 = s1+s2+s3
if ( abs(delps1) .ge. xloss*max(abs(s1),abs(s2)) ) goto 100
if ( max(abs(s1),abs(s2)) .lt. xmax ) then
som = delps1
xmax = abs(s1)
endif
endif
* NO possibility
delps1 = som
100 continue
* #] stupid tree:
*###] ffdl2p:
end
*###[ ffdl2s:
subroutine ffdl2s(delps1,piDpj,in,jn,jin,isji,
+ kn,ln,lkn,islk,ns)
***#[*comment:***********************************************************
* *
* calculate in a numerically stable way *
* *
* \delta_{si,sj}^{sk,sl} *
* *
* with p(ji) = isji*(sj-si) *
* p(lk) = islk*(sl-sk) *
* *
***#]*comment:***********************************************************
* #[ declarations:
implicit none
*
* arguments:
*
integer in,jn,jin,isji,kn,ln,lkn,islk,ns
DOUBLE PRECISION delps1,piDpj(ns,ns)
*
* local variables
*
integer ii,jj,i,j,ji,k,l,lk,ihlp
DOUBLE PRECISION s1,s2,som,smax
*
* common blocks
*
#include "ff.h"
* #] declarations:
* #[ stupid tree:
idsub = idsub + 1
som = 0
smax = 0
i = in
j = jn
ji = jin
k = kn
l = ln
lk = lkn
do 20 ii=1,3
do 10 jj=1,3
s1 = piDpj(i,k)*piDpj(j,l)
s2 = piDpj(i,l)*piDpj(j,k)
delps1 = s1 - s2
if ( ii .gt. 1 ) delps1 = isji*delps1
if ( jj .gt. 1 ) delps1 = islk*delps1
if ( ii .eq. 3 .neqv. jj .eq. 3 ) delps1 = -delps1
if ( abs(delps1) .ge. xloss*abs(s1) ) goto 30
*
* Save the most accurate estimate so far:
if ( ii .eq. 1 .and. jj .eq. 1 .or. abs(s1) .lt. smax
+ ) then
som = delps1
smax = abs(s1)
endif
*
* rotate the jj's
if ( lk .eq. 0 ) goto 20
ihlp = k
k = l
l = lk
lk = ihlp
10 continue
*
* and the ii's
if ( ji .eq. 0 ) goto 25
ihlp = i
i = j
j = ji
ji = ihlp
20 continue
25 continue
delps1 = som
30 continue
* #] stupid tree:
*###] ffdl2s:
end
*###[ ffdl2t:
subroutine ffdl2t(delps,piDpj,in,jn,kn,ln,lkn,islk,iss,ns)
***#[*comment:***********************************************************
* *
* calculate in a numerically stable way *
* *
* \delta_{si,sj}^{sk,sl} *
* *
* with p(lk) = islk*(iss*sl - sk) (islk,iss = +/-1) *
* and NO relationship between s1,s2 assumed (so 1/2 the *
* possibilities of ffdl2s). *
* *
***#]*comment:***********************************************************
* #[ declarations:
implicit none
*
* arguments:
*
integer in,jn,kn,ln,lkn,islk,iss,ns
DOUBLE PRECISION delps,piDpj(ns,ns)
*
* local variables
*
DOUBLE PRECISION s1,s2,som,smax
*
* common blocks
*
#include "ff.h"
* #] declarations:
* #[ calculations:
if ( in .eq. jn ) then
delps = 0
return
endif
s1 = piDpj(kn,in)*piDpj(ln,jn)
s2 = piDpj(ln,in)*piDpj(kn,jn)
delps = s1 - s2
if ( abs(delps) .ge. xloss*abs(s1) ) goto 20
som = delps
smax = abs(s1)
s1 = piDpj(kn,in)*piDpj(lkn,jn)
s2 = piDpj(lkn,in)*piDpj(kn,jn)
delps = iss*islk*(s1 - s2)
if ( abs(delps) .ge. xloss*abs(s1) ) goto 20
if ( abs(s1) .lt. smax ) then
som = delps
smax = abs(s1)
endif
s1 = piDpj(lkn,in)*piDpj(ln,jn)
s2 = piDpj(ln,in)*piDpj(lkn,jn)
delps = islk*(- s1 + s2)
if ( abs(delps) .ge. xloss*abs(s1) ) goto 20
if ( abs(s1) .lt. smax ) then
som = delps
smax = abs(s1)
endif
*
* give up
*
delps = som
20 continue
* #] calculations:
*###] ffdl2t:
end
*###[ ffdl3m:
subroutine ffdl3m(del3mi,ldel,del3,del2,xpi,dpipj,piDpj,ns,ip1n,
+ ip2n,ip3n,is,itime)
***#[*comment:***********************************************************
* *
* Calculate xpi(i)*del2 - del3(piDpj) *
* *
* / si mu \2 (This appears to be one of the harder *
* = | d | determinants to calculate accurately. *
* \ p1 p2 / Note that we allow a loss of xloss^2) *
* *
* Input: ldel iff .true. del2 and del3 exist *
* del3 \delta^{s(1),p1,p2}_{s(1),p1,p2} *
* del2 \delta^{p1,p2}_{p1,p2} *
* xpi(ns) standard *
* dpipj(ns,ns) standard *
* piDpj(ns,ns) standard *
* ipi pi = xpi(abs(ipi)) [p3=-p1 +/-p2] *
* is si = xpi(is,is+1,..,is+itime-1) *
* itime number of functions to calculate *
* *
* Output: del3mi(3) (\delta^{s_i \mu}_{p_1 p_2})^2 *
* *
***#]*comment:***********************************************************
* #[ declarations:
implicit none
*
* arguments:
*
integer ns,ip1n,ip2n,ip3n,is,itime
logical ldel
DOUBLE PRECISION del3mi(itime),del3,del2,xpi(ns),dpipj(ns,ns),
+ piDpj(ns,ns)
*
* local variables:
*
DOUBLE PRECISION s(7),som,smax,xsom,xmax
integer i,j,k,ip1,ip2,ip3,ipn,is1,is2,isi,is3,ihlp,iqn,
+ jsgn1,jsgn2,jsgn3,jsgnn,iadj(10,10,3:4),init,nm
save iadj,init
logical lmax,ltwist
*
* common blocks:
*
#include "ff.h"
*
* data
*
data iadj /200*0/
data init /0/
* #] declarations:
* #[ initialisations:
if ( init .eq. 0 ) then
init = 1
*
* Fill the array with adjacent values: if
* x = iadj(i,j)
* k = abs(mod(k,100))
* jsgnk = sign(x)
* jsgnj = 1-2*theta(x-100) (ie -1 iff |x|>100)
* then
* pi(k) = jsgnk*( p(i) - jsgnj*pi(j) )
*
do 5 nm=3,4
do 4 i=1,nm
is1 = i
is2 = i+1
if ( is2 .gt. nm ) is2 = 1
is3 = i-1
if ( is3 .eq. 0 ) is3 = nm
ip1 = is1 + nm
iadj(is1,is2,nm) = -ip1
iadj(is2,is1,nm) = ip1
iadj(ip1,is2,nm) = -is1
iadj(is2,ip1,nm) = is1
iadj(is1,ip1,nm) = 100+is2
iadj(ip1,is1,nm) = 100+is2
if ( nm .eq. 3 ) then
iadj(ip1,is2+3,3) = -100-is3-3
iadj(is2+3,ip1,3) = -100-is3-3
endif
4 continue
5 continue
iadj(3,1,4) = -9
iadj(1,3,4) = 9
iadj(9,1,4) = -3
iadj(1,9,4) = 3
iadj(3,9,4) = 100+1
iadj(9,3,4) = 100+1
iadj(2,4,4) = -10
iadj(4,2,4) = 10
iadj(10,4,4) = -2
iadj(4,10,4) = 2
iadj(2,10,4) = 100+4
iadj(10,2,4) = 100+4
endif
if ( ns .eq. 6 ) then
nm = 3
else
nm = 4
endif
* #] initialisations:
* #[ easy tries:
do 40 i=1,itime
isi = i+is-1
lmax = .FALSE.
*
* get xpi(isi)*del2 - del3 ... if del3 and del2 are defined
*
if ( ldel ) then
s(1) = xpi(isi)*del2
som = s(1) - del3
smax = abs(s(1))
if ( abs(som) .ge. xloss**2*smax ) goto 35
xsom = som
xmax = smax
lmax = .TRUE.
endif
ip1 = ip1n
ip2 = ip2n
ip3 = ip3n
do 20 j=1,3
*
* otherwise use the simple threeterm formula
*
s(1) = xpi(ip2)*piDpj(ip1,isi)**2
s(2) = xpi(ip1)*piDpj(ip2,isi)*piDpj(ip2,isi)
s(3) = -2*piDpj(ip2,isi)*piDpj(ip2,ip1)*piDpj(ip1,isi)
som = s(1) + s(2) + s(3)
smax = max(abs(s(1)),abs(s(2)),abs(s(3)))
if ( abs(som) .ge. xloss**2*smax ) goto 35
if ( .not. lmax .or. smax .lt. xmax ) then
xsom = som
xmax = smax
lmax = .TRUE.
endif
*
* if there are cancellations between two of the terms:
* we try mixing with isi.
*
* First map cancellation to s(2)+s(3) (do not mess up
* rotations...)
*
if ( abs(s(1)+s(3)) .lt. abs(s(3))/2 ) then
ihlp = ip1
ip1 = ip2
ip2 = ihlp
som = s(1)
s(1) = s(2)
s(2) = som
ltwist = .TRUE.
else
ltwist = .FALSE.
endif
if ( abs(s(2)+s(3)) .lt. abs(s(3))/2 ) then
*
* switch to the vector pn so that si = jsgn1*p1 + jsgnn*pn
*
k = iadj(isi,ip1,nm)
if ( k .ne. 0 ) then
ipn = abs(k)
jsgnn = isign(1,k)
if ( ipn .gt. 100 ) then
ipn = ipn - 100
jsgn1 = -1
else
jsgn1 = +1
endif
if (abs(dpipj(ipn,isi)).lt.xloss*abs(piDpj(ip1,isi))
+ .and.
+ abs(piDpj(ipn,ip2)).lt.xloss*abs(piDpj(ip2,isi))
+ ) then
* same: s(1) = xpi(ip2)*piDpj(ip1,isi)**2
s(2) = jsgnn*piDpj(isi,ip2)*piDpj(ipn,ip2)*
+ xpi(ip1)
s(3) = jsgn1*piDpj(isi,ip2)*piDpj(ip1,ip2)*
+ dpipj(ipn,isi)
som = s(1) + s(2) + s(3)
smax = max(abs(s(1)),abs(s(2)),abs(s(3)))
if ( abs(som) .ge. xloss**2*smax ) goto 35
if ( smax .lt. xmax ) then
xsom = som
xmax = smax
endif
*
* there may be a cancellation between s(1) and
* s(2) left. Introduce a vector q such that
* pn = jsgnq*q + jsgn2*p2. We also need the sign
* jsgn3 in p3 = -p1 - jsgn3*p2
*
k = iadj(ipn,ip2,nm)
if ( k .ne. 0 ) then
iqn = abs(k)
if ( iqn .gt. 100 ) then
iqn = iqn - 100
jsgn2 = -1
else
jsgn2 = +1
endif
k = iadj(ip1,ip2,nm)
if ( k .eq. 0 .or. k .lt. 100 ) then
* we have p1,p2,p3 all p's
jsgn3 = +1
elseif ( k .lt. 0 ) then
* ip1,ip2 are 2*s,1*p such that p2-p1=ip3
jsgn3 = -1
else
jsgn3 = 0
endif
* we need one condition on the signs for this
* to work
if ( ip3.ne.0 .and. jsgn1*jsgn2.eq.jsgnn*
+ jsgn3 .and. abs(s(3)).lt.xloss*smax ) then
s(1) = piDpj(ip1,isi)**2*dpipj(iqn,ipn)
s(2) = -jsgn2*jsgn1*piDpj(ipn,ip2)*
+ piDpj(ip1,isi)*dpipj(ipn,isi)
* s(3) stays the same
s(4) = -jsgn2*jsgn1*piDpj(ipn,ip2)*
+ xpi(ip1)*piDpj(isi,ip3)
som = s(1) + s(2) + s(3) + s(4)
smax =max(abs(s(1)),abs(s(2)),abs(s(3)),
+ abs(s(4)))
if ( abs(som).ge.xloss**2*smax ) goto 35
if ( smax .lt. xmax ) then
xsom = som
xmax = smax
endif
endif
endif
endif
endif
k = iadj(isi,ip2,nm)
if ( k .ne. 0 ) then
ipn = abs(k)
jsgnn = isign(1,k)
if ( ipn .gt. 100 ) then
jsgn1 = -1
ipn = ipn - 100
else
jsgn1 = +1
endif
if (abs(dpipj(ipn,isi)).lt.xloss*abs(piDpj(ip2,isi))
+ .and.
+ abs(piDpj(ipn,ip1)).lt.xloss*abs(piDpj(ip1,isi))
+ ) then
s(1) = jsgnn*piDpj(isi,ip1)*piDpj(ipn,ip1)*
+ xpi(ip2)
s(2) = xpi(ip1)*piDpj(ip2,isi)**2
s(3) = jsgn1*piDpj(isi,ip1)*piDpj(ip2,ip1)*
+ dpipj(ipn,isi)
som = s(1) + s(2) + s(3)
smax = max(abs(s(1)),abs(s(2)),abs(s(3)))
print *,' (isi+ip2) with isi,ip1,ip2,ipn: ',
+ isi,ip1,ip2,ipn
if ( abs(som) .ge. xloss**2*smax ) goto 35
if ( smax .lt. xmax ) then
xsom = som
xmax = smax
endif
endif
endif
endif
*
* rotate the ipi
*
if ( ip3 .eq. 0 ) goto 30
if ( j .ne. 3 ) then
if ( .not. ltwist ) then
ihlp = ip1
ip1 = ip2
ip2 = ip3
ip3 = ihlp
else
ihlp = ip2
ip2 = ip3
ip3 = ihlp
endif
endif
20 continue
30 continue
* #] easy tries:
* #[ choose the best value:
*
* These values are the best found:
*
som = xsom
smax = xmax
35 continue
del3mi(i) = som
40 continue
* #] choose the best value:
*###] ffdl3m:
end
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