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#include "externals.h"
*###[ ffxxyz:
subroutine ffxxyz(y,z,dyz,d2yzz,dy2z,ivert,sdel2p,sdel2s,etalam,
+ etami,delps,xpi,dpipj,piDpj,isoort,ldel2s,ns,ier)
***#[*comment:***********************************************************
* *
* calculate in a numerically stable way *
* *
* z(1,2) = (-p(ip1).p(is2) +/- sdel2s)/xpi(ip1) *
* y(1,2) = (-p(ip1).p(is2) +/- sdisc)/xpi(ip1) *
* disc = del2s + etaslam*xpi(ip1) *
* *
* y(3,4) = 1-y(1,2) *
* z(3,4) = 1-z(1,2) *
* dyz(i,j) = y(i) - z(j) *
* d2yzz = y(2) - z(1) - z(2) *
* dy2z(j) = y(2) - 2*z(j) *
* *
* Input: ivert (integer) defines the vertex *
* sdel2p (real) sqrt(lam(p1,p2,p3))/2 *
* sdel2s (real) sqrt(lam(p,ma,mb))/2 *
* etalam (real) det(si.sj)/det(pi.pj) *
* etami(6) (real) si.si - etalam *
* xpi(ns) (real) standard *
* piDpj(ns,ns) (real) standard *
* ns (integer) dim of xpi,piDpj *
* *
* Output: y(4),z(4),dyz(4,4) (real) see above *
* *
* Calls: fferr,ffroot *
* *
***#]*comment:***********************************************************
* #[ declarations:
implicit none
*
* arguments:
*
integer ivert,ns,ier,isoort(2)
logical ldel2s
DOUBLE PRECISION y(4),z(4),dyz(2,2),d2yzz,dy2z(4),
+ sdel2p,sdel2s,etalam,etami(6),delps,xpi(ns),
+ dpipj(ns,ns),piDpj(ns,ns)
*
* local variables:
*
integer i,j,n,ip1,ip2,ip3,is1,is2,is3,iwarn,ier1
DOUBLE PRECISION disc,hulp,s,smax,som(51),xmax
DOUBLE PRECISION t1,t2,t4,t5,t8,t3,t7,t9,t12,t14,t21,t23,t24,
+ t28,t6,t35,t44,t42,t36,t55,t41,t19,t59,t25,t69,t82,t75,t84,t92,
+ t31,t98,t74,t101,t89,t106,t112,t113,t13,t117,t126,t127,t129,
+ t130,t133,t128,t132,t134,t137,t139,t146,t148,t149,t153,t131,
+ t160,t171,t169,t161,t182,t168,t144,t186,t150,t208,t201,t210,
+ t219,t156,t225,t200,t228,t215,t233,t239,t240,t138,t244
*
* common blocks:
*
#include "ff.h"
* #] declarations:
* #[ set up pointers:
if ( ldel2s .and. ivert .ne. 1 ) goto 100
is1 = ivert
is2 = ivert+1
if ( is2 .eq. 4 ) is2 = 1
is3 = ivert-1
if ( is3 .eq. 0 ) is3 = 3
ip1 = is1 + 3
ip2 = is2 + 3
ip3 = is3 + 3
* #] set up pointers:
* #[ xk = 0:
if ( xpi(ip1) .eq. 0 ) then
isoort(2) = 0
if ( piDpj(is1,ip1) .eq. 0 ) then
isoort(1) = 0
return
endif
isoort(1) = 1
y(1) = etami(is2) / piDpj(is1,ip1) /2
y(2) = y(1)
y(3) = - etami(is1) / piDpj(is1,ip1) /2
y(4) = y(3)
z(1) = xpi(is2) / piDpj(is1,ip1) /2
z(2) = z(1)
z(3) = - xpi(is1) / piDpj(is1,ip1) /2
z(4) = z(3)
dyz(1,1) = - etalam / piDpj(is1,ip1) /2
dyz(1,2) = dyz(1,1)
dyz(2,1) = dyz(1,1)
dyz(2,2) = dyz(1,1)
ier1 = ier
do 10 i=1,3,2
dy2z(i) = y(i) - 2*z(i)
smax = abs(y(i))
dy2z(i+1) = dy2z(i)
10 continue
ier = ier1
return
endif
* #] xk = 0:
* #[ get y(1,2),z(1,2):
if ( sdel2s .eq. 0 ) then
isoort(1) = 2
isoort(2) = 2
z(1) = piDpj(ip1,is2)/xpi(ip1)
z(2) = z(1)
else
isoort(1) = 1
isoort(2) = 1
call ffroot(z(1),z(2),xpi(ip1),piDpj(ip1,is2),xpi(is2),
+ sdel2s,ier)
endif
disc = delps/sdel2p
call ffroot(y(1),y(2),xpi(ip1),piDpj(ip1,is2),etami(is2),disc,
+ ier)
* #] get y(1,2),z(1,2):
* #[ get y(3,4),z(3,4):
if ( isoort(1) .eq. 2 ) then
z(3) = -piDpj(ip1,is1)/xpi(ip1)
z(4) = z(3)
else
z(3) = 1-z(1)
z(4) = 1-z(2)
if ( abs(z(3)) .lt. xloss .or. abs(z(4)) .lt. xloss )
+ call ffroot(z(4),z(3),xpi(ip1),-piDpj(ip1,is1),
+ xpi(is1),sdel2s,ier)
endif
y(3) = 1-y(1)
y(4) = 1-y(2)
if ( abs(y(3)) .lt. xloss .or. abs(y(4)) .lt. xloss ) then
call ffroot(y(4),y(3),xpi(ip1),-piDpj(ip1,is1),
+ etami(is1),disc,ier)
endif
* #] get y(3,4),z(3,4):
* #[ get dyz:
* Note that dyz(i,j) only exists for i,j=1,2!
if ( isoort(1) .eq. 2 ) then
dyz(2,1) = disc/xpi(ip1)
dyz(2,2) = dyz(2,1)
elseif ( disc .gt. 0 .eqv. sdel2s .gt. 0 ) then
dyz(2,1) = ( disc + sdel2s )/xpi(ip1)
dyz(2,2) = etalam/(xpi(ip1)*dyz(2,1))
else
dyz(2,2) = ( disc - sdel2s )/xpi(ip1)
dyz(2,1) = etalam/(xpi(ip1)*dyz(2,2))
endif
dyz(1,1) = -dyz(2,2)
dyz(1,2) = -dyz(2,1)
d2yzz = 2*disc/xpi(ip1)
*
* these are very rarely needed, but ...
*
iwarn = 0
ier1 = ier
do 20 i=1,4
j = 2*((i+1)/2)
dy2z(i) = y(j) - 2*z(i)
smax = abs(y(j))
if ( abs(dy2z(i)) .lt. xloss*smax ) then
if ( i/2 .eq. 1 ) then
s = -y(j-1) - 2*sdel2s/xpi(ip1)
else
s = -y(j-1) + 2*sdel2s/xpi(ip1)
endif
if ( abs(y(j-1)) .lt. smax ) then
dy2z(i) = s
smax = abs(y(j-1))
endif
if ( abs(dy2z(i)) .lt. xloss*smax ) then
if ( iwarn .ne. 0 ) then
else
iwarn = i
xmax = smax
endif
endif
endif
20 continue
if ( iwarn .ne. 0 ) then
*
* we should import the differences, but later...
*
if ( abs(dpipj(is3,ip1)) .lt. xloss*xpi(is3)
+ .and. abs(dpipj(is1,is2)) .lt. xloss*abs(xpi(ip1))) then
*
* give it another try - multiply roots (see dy2z.frm)
*
if ( iwarn.lt.3 ) then
*prod1=
* som(1)=+160*xpi(ip1)*xpi(ip2)*xpi(is2)*piDpj(ip1,ip2)**2*
* + dpipj(is2,is1)**2
* som(2)=-40*xpi(ip1)*xpi(ip2)*piDpj(ip1,ip2)*piDpj(ip2,
* + is2)*dpipj(is2,is1)**3
* som(3)=-32*xpi(ip1)*xpi(ip2)*piDpj(ip1,ip2)**2*dpipj(is2,
* + is1)**3
* som(4)=+9*xpi(ip1)*xpi(ip2)**2*dpipj(is2,is1)**4
* som(5)=-128*xpi(ip1)*xpi(is2)*piDpj(ip1,ip2)**3*piDpj(ip2,
* + is2)*dpipj(is2,is1)
* som(6)=-128*xpi(ip1)*xpi(is2)*piDpj(ip1,ip2)**4*dpipj(is2,
* + is1)
* som(7)=+256*xpi(ip1)*xpi(is2)**2*piDpj(ip1,ip2)**4
* som(8)=-16*xpi(ip1)*piDpj(ip1,ip2)**2*piDpj(ip2,is2)**2*
* + dpipj(is2,is1)**2
* som(9)=+96*xpi(ip1)*piDpj(ip1,ip2)**3*piDpj(ip2,is2)*dpipj(is2,
* + is1)**2
* som(10)=+128*xpi(ip1)**2*xpi(ip2)*xpi(is2)*piDpj(ip1,ip2)*piDpj(
* + ip2,is2)*dpipj(is2,is1)
* som(11)=+320*xpi(ip1)**2*xpi(ip2)*xpi(is2)*piDpj(ip1,ip2)**2*
* + dpipj(is2,is1)
* som(12)=-512*xpi(ip1)**2*xpi(ip2)*xpi(is2)**2*piDpj(ip1,ip2)**2
* som(13)=-120*xpi(ip1)**2*xpi(ip2)*piDpj(ip1,ip2)*piDpj(ip2,
* + is2)*dpipj(is2,is1)**2
* som(14)=-48*xpi(ip1)**2*xpi(ip2)*piDpj(ip1,ip2)**2*dpipj(is2,
* + is1)**2
* som(15)=+40*xpi(ip1)**2*xpi(ip2)*piDpj(ip2,is2)**2*dpipj(is2,
* + is1)**2
* som(16)=-96*xpi(ip1)**2*xpi(ip2)**2*xpi(is2)*dpipj(is2,is1)**2
* som(17)=+36*xpi(ip1)**2*xpi(ip2)**2*dpipj(is2,is1)**3
* som(18)=+128*xpi(ip1)**2*xpi(is2)*piDpj(ip1,ip2)**2*piDpj(ip2,
* + is2)**2
* som(19)=-128*xpi(ip1)**2*xpi(is2)*piDpj(ip1,ip2)**3*piDpj(ip2,
* + is2)
* som(20)=-64*xpi(ip1)**2*xpi(is2)*piDpj(ip1,ip2)**4
* som(21)=-32*xpi(ip1)**2*piDpj(ip1,ip2)*piDpj(ip2,is2)**3*
* + dpipj(is2,is1)
* som(22)=-32*xpi(ip1)**2*piDpj(ip1,ip2)**2*piDpj(ip2,is2)**2*
* + dpipj(is2,is1)
* som(23)=+96*xpi(ip1)**2*piDpj(ip1,ip2)**3*piDpj(ip2,is2)*
* + dpipj(is2,is1)
* som(24)=+128*xpi(ip1)**3*xpi(ip2)*xpi(is2)*piDpj(ip1,ip2)*piDpj(
* + ip2,is2)
* som(25)=+160*xpi(ip1)**3*xpi(ip2)*xpi(is2)*piDpj(ip1,ip2)**2
* som(26)=-128*xpi(ip1)**3*xpi(ip2)*xpi(is2)*piDpj(ip2,is2)**2
* som(27)=+32*xpi(ip1)**3*xpi(ip2)*piDpj(ip1,ip2)*piDpj(ip2,
* + is1)*piDpj(ip2,is2)
* som(28)=-120*xpi(ip1)**3*xpi(ip2)*piDpj(ip1,ip2)*piDpj(ip2,
* + is2)*dpipj(is2,is1)
* som(29)=-32*xpi(ip1)**3*xpi(ip2)*piDpj(ip1,ip2)**2*dpipj(is2,
* + is1)
* som(30)=-16*xpi(ip1)**3*xpi(ip2)*piDpj(ip2,is1)*piDpj(ip2,
* + is2)**2
* som(31)=+80*xpi(ip1)**3*xpi(ip2)*piDpj(ip2,is2)**2*dpipj(is2,
* + is1)
* som(32)=-192*xpi(ip1)**3*xpi(ip2)**2*xpi(is2)*dpipj(is2,is1)
* som(33)=+256*xpi(ip1)**3*xpi(ip2)**2*xpi(is2)**2
* som(34)=+54*xpi(ip1)**3*xpi(ip2)**2*dpipj(is2,is1)**2
* som(35)=-16*xpi(ip1)**3*xpi(ip3)*piDpj(ip1,ip2)*piDpj(ip2,
* + is1)*piDpj(ip2,is2)
* som(36)=+8*xpi(ip1)**3*xpi(ip3)*piDpj(ip2,is1)*piDpj(ip2,is2)**2
* som(37)=+16*xpi(ip1)**3*xpi(is2)*piDpj(ip1,ip2)*piDpj(ip2,
* + is1)*piDpj(ip2,is2)
* som(38)=-8*xpi(ip1)**3*xpi(is2)*piDpj(ip2,is1)*piDpj(ip2,is2)**2
* som(39)=-16*xpi(ip1)**3*piDpj(ip1,ip2)*piDpj(ip2,is1)*piDpj(ip2,
* + is2)*dpipj(is3,ip1)
* som(40)=+8*xpi(ip1)**3*piDpj(ip2,is1)*piDpj(ip2,is2)**2*
* + dpipj(is3,ip1)
* som(41)=-40*xpi(ip1)**4*xpi(ip2)*piDpj(ip1,ip2)*piDpj(ip2,is2)
* som(42)=-8*xpi(ip1)**4*xpi(ip2)*piDpj(ip1,ip2)**2
* som(43)=+40*xpi(ip1)**4*xpi(ip2)*piDpj(ip2,is2)**2
* som(44)=-96*xpi(ip1)**4*xpi(ip2)**2*xpi(is2)
* som(45)=+36*xpi(ip1)**4*xpi(ip2)**2*dpipj(is2,is1)
* som(46)=+9*xpi(ip1)**5*xpi(ip2)**2
* som(47)=-8*xpi(ip2)*piDpj(ip1,ip2)**2*dpipj(is2,is1)**4
* som(48)=-64*xpi(is2)*piDpj(ip1,ip2)**4*dpipj(is2,is1)**2
* som(49)=+32*piDpj(ip1,ip2)**3*piDpj(ip2,is2)*dpipj(is2,is1)**3
* print '(7g20.12)',(som(i),i=1,49)
*
* optimized by Maple (see ffxxyz.map)
*
t1 = xpi(ip1)
t2 = xpi(ip2)
t3 = t1*t2
t4 = xpi(is2)
t5 = piDpj(ip1,ip2)
t6 = t5**2
t7 = t4*t6
t8 = dpipj(is2,is1)
t9 = t8**2
som(1) = 160*t3*t7*t9
t12 = piDpj(ip2,is2)
t13 = t5*t12
t14 = t9*t8
som(2) = -40*t3*t13*t14
som(3) = -32*t3*t6*t14
t19 = t2**2
t21 = t9**2
som(4) = 9*t1*t19*t21
t23 = t1*t4
t24 = t6*t5
t25 = t24*t12
som(5) = -128*t23*t25*t8
t28 = t6**2
som(6) = -128*t23*t28*t8
t31 = t4**2
som(7) = 256*t1*t31*t28
t35 = t12**2
t36 = t35*t9
som(8) = -16*t1*t6*t36
som(9) = 96*t1*t24*t12*t9
t41 = t1**2
t42 = t41*t2
t44 = t13*t8
som(10) = 128*t42*t4*t44
som(11) = 320*t42*t7*t8
som(12) = -512*t42*t31*t6
som(13) = -120*t42*t13*t9
som(14) = -48*t42*t6*t9
som(15) = 40*t42*t36
t55 = t41*t19
som(16) = -96*t55*t4*t9
som(17) = 36*t55*t14
t59 = t41*t4
som(18) = 128*t59*t6*t35
som(19) = -128*t59*t25
som(20) = -64*t59*t28
som(21) = -32*t41*t5*t35*t12*t8
t69 = t35*t8
som(22) = -32*t41*t6*t69
som(23) = 96*t41*t24*t12*t8
t74 = t41*t1
t75 = t74*t2
som(24) = 128*t75*t4*t5*t12
som(25) = 160*t75*t7
som(26) = -128*t75*t4*t35
t82 = piDpj(ip2,is1)
t84 = t5*t82*t12
som(27) = 32*t75*t84
som(28) = -120*t75*t44
som(29) = -32*t75*t6*t8
t89 = t82*t35
som(30) = -16*t75*t89
som(31) = 80*t75*t69
t92 = t74*t19
som(32) = -192*t92*t4*t8
som(33) = 256*t92*t31
som(34) = 54*t92*t9
t98 = t74*xpi(ip3)
som(35) = -16*t98*t84
som(36) = 8*t98*t89
t101 = t74*t4
som(37) = 16*t101*t84
som(38) = -8*t101*t89
t106 = dpipj(is3,ip1)
som(39) = -16*t74*t5*t82*t12*t106
som(40) = 8*t74*t82*t35*t106
t112 = t41**2
t113 = t112*t2
som(41) = -40*t113*t13
som(42) = -8*t113*t6
som(43) = 40*t113*t35
t117 = t112*t19
som(44) = -96*t117*t4
som(45) = 36*t117*t8
som(46) = 9*t112*t1*t19
som(47) = -8*t2*t6*t21
som(48) = -64*t4*t28*t9
som(49) = 32*t25*t14
* print '(7g20.12)',(som(i),i=1,49)
n=49
else
*prod3=
* som(1)=+160*xpi(ip1)*xpi(ip2)*xpi(is2)*piDpj(ip1,ip2)**2*
* + dpipj(is2,is1)**2
* som(2)=-40*xpi(ip1)*xpi(ip2)*piDpj(ip1,ip2)*piDpj(ip2,
* + is2)*dpipj(is2,is1)**3
* som(3)=-88*xpi(ip1)*xpi(ip2)*piDpj(ip1,ip2)**2*dpipj(is2,
* + is1)**3
* som(4)=+9*xpi(ip1)*xpi(ip2)**2*dpipj(is2,is1)**4
* som(5)=-128*xpi(ip1)*xpi(is2)*piDpj(ip1,ip2)**3*piDpj(ip2,
* + is2)*dpipj(is2,is1)
* som(6)=-256*xpi(ip1)*xpi(is2)*piDpj(ip1,ip2)**4*dpipj(is2,is1)
* som(7)=+256*xpi(ip1)*xpi(is2)**2*piDpj(ip1,ip2)**4
* som(8)=-16*xpi(ip1)*piDpj(ip1,ip2)**2*piDpj(ip2,is2)**2*dpipj(
* + is2,is1)**2
* som(9)=+64*xpi(ip1)*piDpj(ip1,ip2)**3*piDpj(ip2,is2)*dpipj(is2,
* + is1)**2
* som(10)=+80*xpi(ip1)*piDpj(ip1,ip2)**4*dpipj(is2,is1)**2
* som(11)=+128*xpi(ip1)**2*xpi(ip2)*xpi(is2)*piDpj(ip1,ip2)*piDpj(
* + ip2,is2)*dpipj(is2,is1)
* som(12)=+576*xpi(ip1)**2*xpi(ip2)*xpi(is2)*piDpj(ip1,ip2)**2*
* + dpipj(is2,is1)
* som(13)=-512*xpi(ip1)**2*xpi(ip2)*xpi(is2)**2*piDpj(ip1,ip2)**2
* som(14)=-88*xpi(ip1)**2*xpi(ip2)*piDpj(ip1,ip2)*piDpj(ip2,
* + is2)*dpipj(is2,is1)**2
* som(15)=-192*xpi(ip1)**2*xpi(ip2)*piDpj(ip1,ip2)**2*dpipj(is2,
* + is1)**2
* som(16)=+40*xpi(ip1)**2*xpi(ip2)*piDpj(ip2,is2)**2*dpipj(is2,
* + is1)**2
* som(17)=-96*xpi(ip1)**2*xpi(ip2)**2*xpi(is2)*dpipj(is2,is1)**2
* som(18)=+60*xpi(ip1)**2*xpi(ip2)**2*dpipj(is2,is1)**3
* som(19)=+128*xpi(ip1)**2*xpi(is2)*piDpj(ip1,ip2)**2*piDpj(ip2,
* + is2)**2
* som(20)=-128*xpi(ip1)**2*xpi(is2)*piDpj(ip1,ip2)**3*piDpj(ip2,
* + is2)
* som(21)=-64*xpi(ip1)**2*xpi(is2)*piDpj(ip1,ip2)**4
* som(22)=-32*xpi(ip1)**2*piDpj(ip1,ip2)*piDpj(ip2,is2)**3*
* + dpipj(is2,is1)
* som(23)=+64*xpi(ip1)**2*piDpj(ip1,ip2)**3*piDpj(ip2,is2)*
* + dpipj(is2,is1)
* som(24)=+32*xpi(ip1)**2*piDpj(ip1,ip2)**4*dpipj(is2,is1)
* som(25)=+128*xpi(ip1)**3*xpi(ip2)*xpi(is2)*piDpj(ip1,ip2)*piDpj(
* + ip2,is2)
* som(26)=+160*xpi(ip1)**3*xpi(ip2)*xpi(is2)*piDpj(ip1,ip2)**2
* som(27)=-128*xpi(ip1)**3*xpi(ip2)*xpi(is2)*piDpj(ip2,is2)**2
* som(28)=+32*xpi(ip1)**3*xpi(ip2)*piDpj(ip1,ip2)*piDpj(ip2,
* + is1)*piDpj(ip2,is2)
* som(29)=-88*xpi(ip1)**3*xpi(ip2)*piDpj(ip1,ip2)*piDpj(ip2,
* + is2)*dpipj(is2,is1)
* som(30)=-88*xpi(ip1)**3*xpi(ip2)*piDpj(ip1,ip2)**2*dpipj(is2,
* + is1)
* som(31)=-16*xpi(ip1)**3*xpi(ip2)*piDpj(ip2,is1)*piDpj(ip2,
* + is2)**2
* som(32)=+48*xpi(ip1)**3*xpi(ip2)*piDpj(ip2,is2)**2*dpipj(is2,
* + is1)
* som(33)=-320*xpi(ip1)**3*xpi(ip2)**2*xpi(is2)*dpipj(is2,is1)
* som(34)=+256*xpi(ip1)**3*xpi(ip2)**2*xpi(is2)**2
* som(35)=+118*xpi(ip1)**3*xpi(ip2)**2*dpipj(is2,is1)**2
* som(36)=-16*xpi(ip1)**3*xpi(ip3)*piDpj(ip1,ip2)*piDpj(ip2,
* + is1)*piDpj(ip2,is2)
* som(37)=+8*xpi(ip1)**3*xpi(ip3)*piDpj(ip2,is1)*piDpj(ip2,is2)**2
* som(38)=+16*xpi(ip1)**3*xpi(is2)*piDpj(ip1,ip2)*piDpj(ip2,
* + is1)*piDpj(ip2,is2)
* som(39)=-8*xpi(ip1)**3*xpi(is2)*piDpj(ip2,is1)*piDpj(ip2,is2)**2
* som(40)=-16*xpi(ip1)**3*piDpj(ip1,ip2)*piDpj(ip2,is1)*piDpj(ip2,
* + is2)*dpipj(is3,ip1)
* som(41)=+8*xpi(ip1)**3*piDpj(ip2,is1)*piDpj(ip2,is2)**2*
* + dpipj(is3,ip1)
* som(42)=-40*xpi(ip1)**4*xpi(ip2)*piDpj(ip1,ip2)*piDpj(ip2,is2)
* som(43)=-8*xpi(ip1)**4*xpi(ip2)*piDpj(ip1,ip2)**2
* som(44)=+40*xpi(ip1)**4*xpi(ip2)*piDpj(ip2,is2)**2
* som(45)=-96*xpi(ip1)**4*xpi(ip2)**2*xpi(is2)
* som(46)=+60*xpi(ip1)**4*xpi(ip2)**2*dpipj(is2,is1)
* som(47)=+9*xpi(ip1)**5*xpi(ip2)**2
* som(48)=-8*xpi(ip2)*piDpj(ip1,ip2)**2*dpipj(is2,is1)**4
* som(49)=-64*xpi(is2)*piDpj(ip1,ip2)**4*dpipj(is2,is1)**2
* som(50)=+32*piDpj(ip1,ip2)**3*piDpj(ip2,is2)*dpipj(is2,is1)**3
* som(51)=+32*piDpj(ip1,ip2)**4*dpipj(is2,is1)**3
* print '(7g20.12)',(som(i),i=1,51)
*
* optimized by Maple (see ffxxyz.map)
*
t126 = xpi(ip1)
t127 = xpi(ip2)
t128 = t126*t127
t129 = xpi(is2)
t130 = piDpj(ip1,ip2)
t131 = t130**2
t132 = t129*t131
t133 = dpipj(is2,is1)
t134 = t133**2
som(1) = 160*t128*t132*t134
t137 = piDpj(ip2,is2)
t138 = t130*t137
t139 = t134*t133
som(2) = -40*t128*t138*t139
som(3) = -88*t128*t131*t139
t144 = t127**2
t146 = t134**2
som(4) = 9*t126*t144*t146
t148 = t126*t129
t149 = t131*t130
t150 = t149*t137
som(5) = -128*t148*t150*t133
t153 = t131**2
som(6) = -256*t148*t153*t133
t156 = t129**2
som(7) = 256*t126*t156*t153
t160 = t137**2
t161 = t160*t134
som(8) = -16*t126*t131*t161
som(9) = 64*t126*t149*t137*t134
som(10) = 80*t126*t153*t134
t168 = t126**2
t169 = t168*t127
t171 = t138*t133
som(11) = 128*t169*t129*t171
som(12) = 576*t169*t132*t133
som(13) = -512*t169*t156*t131
som(14) = -88*t169*t138*t134
som(15) = -192*t169*t131*t134
som(16) = 40*t169*t161
t182 = t168*t144
som(17) = -96*t182*t129*t134
som(18) = 60*t182*t139
t186 = t168*t129
som(19) = 128*t186*t131*t160
som(20) = -128*t186*t150
som(21) = -64*t186*t153
som(22) = -32*t168*t130*t160*t137*t133
som(23) = 64*t168*t149*t137*t133
som(24) = 32*t168*t153*t133
t200 = t168*t126
t201 = t200*t127
som(25) = 128*t201*t129*t130*t137
som(26) = 160*t201*t132
som(27) = -128*t201*t129*t160
t208 = piDpj(ip2,is1)
t210 = t130*t208*t137
som(28) = 32*t201*t210
som(29) = -88*t201*t171
som(30) = -88*t201*t131*t133
t215 = t208*t160
som(31) = -16*t201*t215
som(32) = 48*t201*t160*t133
t219 = t200*t144
som(33) = -320*t219*t129*t133
som(34) = 256*t219*t156
som(35) = 118*t219*t134
t225 = t200*xpi(ip3)
som(36) = -16*t225*t210
som(37) = 8*t225*t215
t228 = t200*t129
som(38) = 16*t228*t210
som(39) = -8*t228*t215
t233 = dpipj(is3,ip1)
som(40) = -16*t200*t130*t208*t137*t233
som(41) = 8*t200*t208*t160*t233
t239 = t168**2
t240 = t239*t127
som(42) = -40*t240*t138
som(43) = -8*t240*t131
som(44) = 40*t240*t160
t244 = t239*t144
som(45) = -96*t244*t129
som(46) = 60*t244*t133
som(47) = 9*t239*t126*t144
som(48) = -8*t127*t131*t146
som(49) = -64*t129*t153*t134
som(50) = 32*t150*t139
som(51) = 32*t153*t139
* print '(7g20.12)',(som(i),i=1,51)
n=51
endif
*
s = 0
smax = 0
do 30 j=1,n
s = s + som(j)
smax = max(smax,som(j))
30 continue
if ( iwarn .lt. 3 ) then
hulp = 1/(16*xpi(ip1)**3*sdel2p**4*dy2z(3-iwarn)*
+ (y(1)-2*z(1))*(y(1)-2*z(2)))
else
hulp = 1/(16*xpi(ip1)**3*sdel2p**4*dy2z(7-iwarn)*
+ (y(3)-2*z(3))*(y(3)-2*z(4)))
endif
s = s*hulp
smax = smax*hulp
if ( smax .lt. xmax ) then
dy2z(iwarn) = s
xmax = smax
endif
else
n=0
endif
endif
ier = ier1
*
goto 200
* #] get dyz:
* #[ special case, get indices:
100 continue
if ( ivert.eq.2 ) then
is1 = 2
ip1 = 5
else
is1 = 1
ip1 = 6
endif
* #] special case, get indices:
* #[ xk = 0:
if ( xpi(ip1) .eq. 0 ) then
call fferr(88,ier)
endif
* #] xk = 0:
* #[ get ypm,zpm:
*
* special case del2s = 0, hence the roots are not the real roots
* but z_2'' = (z_2'-1)/delta, z''_3 = -z'_3/delta
*
hulp = sdel2s
disc = delps/sdel2p
if ( ivert .eq. 3 ) then
hulp = -hulp
disc = -disc
endif
if ( sdel2s .eq. 0 ) then
isoort(1) = 102
isoort(2) = 102
z(1) = piDpj(is1,3)/xpi(3)
z(2) = z(1)
else
isoort(1) = 101
isoort(2) = 101
call ffroot(z(1),z(2),xpi(3),piDpj(is1,3),xpi(is1),hulp,ier)
endif
call ffroot(y(1),y(2),xpi(3),piDpj(is1,3),etami(is1),disc,ier)
* #] get ypm,zpm:
* #[ get ypm1,zpm1:
z(3) = 1 - z(1)
z(4) = 1 - z(2)
if ( abs(z(3)).lt.xloss .or. abs(z(4)).lt.xloss ) then
if ( ivert.eq.2 ) then
call ffroot(z(4),z(3),xpi(3),piDpj(ip1,3),xpi(ip1),hulp,
+ ier)
else
call ffroot(z(4),z(3),xpi(3),-piDpj(ip1,3),xpi(ip1),hulp
+ ,ier)
endif
endif
y(3) = 1 - y(1)
y(4) = 1 - y(2)
if ( abs(y(3)) .lt. xloss .or. abs(y(4)) .lt. xloss ) then
if ( ivert .eq. 2 ) then
call ffroot(y(4),y(3),xpi(3),piDpj(ip1,3),etami(ip1),
+ disc,ier)
else
call ffroot(y(4),y(3),xpi(3),-piDpj(ip1,3),etami(ip1),
+ disc,ier)
endif
endif
* #] get ypm1,zpm1:
* #[ get dypzp, dypzm:
if ( isoort(1) .eq. 2 ) then
dyz(2,1) = disc/xpi(3)
dyz(2,2) = dyz(2,1)
elseif ( disc .gt. 0 .eqv. sdel2s .gt. 0 ) then
dyz(2,1) = ( disc + hulp )/xpi(3)
dyz(2,2) = etalam/(xpi(3)*dyz(2,1))
else
dyz(2,2) = ( disc - hulp )/xpi(3)
dyz(2,1) = etalam/(xpi(3)*dyz(2,2))
endif
dyz(1,1) = -dyz(2,2)
dyz(1,2) = -dyz(2,1)
d2yzz = 2*disc/xpi(3)
*
* these are very rarely needed, but ...
*
do 220 i=1,4
j = 2*((i+1)/2)
dy2z(i) = y(j) - 2*z(i)
smax = abs(y(j))
220 continue
* #] get dypzp, dypzm:
200 continue
*###] ffxxyz:
end
*###[ ffdwz:
subroutine ffdwz(dwz,z,i1,j1,l,alpha,alph1,xpi,dpipj,piDpj,
+ sdel2i,ns,ier)
***#[*comment:***********************************************************
* *
* Recalculate dwz(i1,j1) = w(i1) - z(j1) *
* *
***#]*comment:***********************************************************
* #[ declarations:
implicit none
*
* arguments:
*
integer i1,j1,l,ns,ier
DOUBLE PRECISION dwz(2,2),z(4)
DOUBLE PRECISION alpha,alph1,xpi(ns),dpipj(ns,ns),piDpj(ns,ns),
+ sdel2i(3)
*
* local variables:
*
DOUBLE PRECISION s(8),sum,fac,xmax
integer i
*
* common blocks:
*
#include "ff.h"
* #] declarations:
* #[ calculations:
if ( l .eq. 1 ) then
ier = ier + 100
elseif ( l .eq. 3 ) then
if ( (i1.eq.2 .and. j1.eq.1) .or. (i1.eq.1 .and. j1.eq.2) )
+ then
fac = 1D0/(sdel2i(2) + sdel2i(3))
s(1) = dpipj(6,5)*z(j1)
s(2) = -alph1*xpi(5)*z(j1+2)
if ( max(abs(dpipj(2,1)),abs(dpipj(5,6))) .lt.
+ max(abs(dpipj(2,6)),abs(dpipj(5,1))) ) then
s(3) = .5D0*dpipj(2,1)
s(4) = .5D0*dpipj(5,6)
else
s(3) = .5D0*dpipj(2,6)
s(4) = .5D0*dpipj(5,1)
endif
s(5) = piDpj(4,3)*piDpj(5,3)*fac
s(6) = -piDpj(4,3)*piDpj(6,3)*fac
s(7) = xpi(3)*dpipj(5,6)*fac
if ( i1 .eq. 1 ) then
sum = s(1)+s(2)+s(3)+s(4) - (s(5)+s(6)+s(7))
else
sum = s(1)+s(2)+s(3)+s(4) + s(5)+s(6)+s(7)
endif
xmax = abs(s(1))
do 10 i=2,7
xmax = max(xmax,abs(s(i)))
10 continue
if ( abs(sum) .lt. xloss*xmax ) then
* this result is not used if it is not accurate (see
* ffxc0p)
ier = ier + 1
xmax = xmax/abs(alpha*xpi(5))
dwz(i1,j1) = sum/(alpha*xpi(5))
else
dwz(i1,j1) = sum/(alpha*xpi(5))
endif
else
ier = ier + 100
endif
endif
* #] calculations:
*###] ffdwz:
end
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