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c
c-----------------------------------------------------------------------
c subroutine: r8tr
c radix 8 iteration subroutine
c-----------------------------------------------------------------------
c
subroutine r8tr(int, nn, br0, br1, br2, br3, br4, br5, br6, br7,
* bi0, bi1, bi2, bi3, bi4, bi5, bi6, bi7)
dimension l(15), br0(2), br1(2), br2(2), br3(2), br4(2), br5(2),
* br6(2), br7(2), bi0(2), bi1(2), bi2(2), bi3(2), bi4(2),
* bi5(2), bi6(2), bi7(2)
common /con/ pii, p7, p7two, c22, s22, pi2
equivalence (l15,l(1)), (l14,l(2)), (l13,l(3)), (l12,l(4)),
* (l11,l(5)), (l10,l(6)), (l9,l(7)), (l8,l(8)), (l7,l(9)),
* (l6,l(10)), (l5,l(11)), (l4,l(12)), (l3,l(13)), (l2,l(14)),
* (l1,l(15))
c
c set up counters such that jthet steps through the arguments
c of w, jr steps through starting locations for the real part of the
c intermediate results and ji steps through starting locations
c of the imaginary part of the intermediate results.
c
l(1) = nn/8
do 40 k=2,15
if (l(k-1)-2) 10, 20, 30
10 l(k-1) = 2
20 l(k) = 2
go to 40
30 l(k) = l(k-1)/2
40 continue
piovn = pii/float(nn)
ji = 3
jl = 2
jr = 2
do 120 j1=2,l1,2
do 120 j2=j1,l2,l1
do 120 j3=j2,l3,l2
do 120 j4=j3,l4,l3
do 120 j5=j4,l5,l4
do 120 j6=j5,l6,l5
do 120 j7=j6,l7,l6
do 120 j8=j7,l8,l7
do 120 j9=j8,l9,l8
do 120 j10=j9,l10,l9
do 120 j11=j10,l11,l10
do 120 j12=j11,l12,l11
do 120 j13=j12,l13,l12
do 120 j14=j13,l14,l13
do 120 jthet=j14,l15,l14
th2 = jthet - 2
if (th2) 50, 50, 90
50 do 60 k=1,int
t0 = br0(k) + br4(k)
t1 = br1(k) + br5(k)
t2 = br2(k) + br6(k)
t3 = br3(k) + br7(k)
t4 = br0(k) - br4(k)
t5 = br1(k) - br5(k)
t6 = br2(k) - br6(k)
t7 = br3(k) - br7(k)
br2(k) = t0 - t2
br3(k) = t1 - t3
t0 = t0 + t2
t1 = t1 + t3
br0(k) = t0 + t1
br1(k) = t0 - t1
pr = p7*(t5-t7)
pi = p7*(t5+t7)
br4(k) = t4 + pr
br7(k) = t6 + pi
br6(k) = t4 - pr
br5(k) = pi - t6
60 continue
if (nn-8) 120, 120, 70
70 k0 = int*8 + 1
kl = k0 + int - 1
do 80 k=k0,kl
pr = p7*(bi2(k)-bi6(k))
pi = p7*(bi2(k)+bi6(k))
tr0 = bi0(k) + pr
ti0 = bi4(k) + pi
tr2 = bi0(k) - pr
ti2 = bi4(k) - pi
pr = p7*(bi3(k)-bi7(k))
pi = p7*(bi3(k)+bi7(k))
tr1 = bi1(k) + pr
ti1 = bi5(k) + pi
tr3 = bi1(k) - pr
ti3 = bi5(k) - pi
pr = tr1*c22 - ti1*s22
pi = ti1*c22 + tr1*s22
bi0(k) = tr0 + pr
bi6(k) = tr0 - pr
bi7(k) = ti0 + pi
bi1(k) = pi - ti0
pr = -tr3*s22 - ti3*c22
pi = tr3*c22 - ti3*s22
bi2(k) = tr2 + pr
bi4(k) = tr2 - pr
bi5(k) = ti2 + pi
bi3(k) = pi - ti2
80 continue
go to 120
90 arg = th2*piovn
c1 = cos(arg)
s1 = sin(arg)
c2 = c1**2 - s1**2
s2 = c1*s1 + c1*s1
c3 = c1*c2 - s1*s2
s3 = c2*s1 + s2*c1
c4 = c2**2 - s2**2
s4 = c2*s2 + c2*s2
c5 = c2*c3 - s2*s3
s5 = c3*s2 + s3*c2
c6 = c3**2 - s3**2
s6 = c3*s3 + c3*s3
c7 = c3*c4 - s3*s4
s7 = c4*s3 + s4*c3
int8 = int*8
j0 = jr*int8 + 1
k0 = ji*int8 + 1
jlast = j0 + int - 1
do 100 j=j0,jlast
k = k0 + j - j0
tr1 = br1(j)*c1 - bi1(k)*s1
ti1 = br1(j)*s1 + bi1(k)*c1
tr2 = br2(j)*c2 - bi2(k)*s2
ti2 = br2(j)*s2 + bi2(k)*c2
tr3 = br3(j)*c3 - bi3(k)*s3
ti3 = br3(j)*s3 + bi3(k)*c3
tr4 = br4(j)*c4 - bi4(k)*s4
ti4 = br4(j)*s4 + bi4(k)*c4
tr5 = br5(j)*c5 - bi5(k)*s5
ti5 = br5(j)*s5 + bi5(k)*c5
tr6 = br6(j)*c6 - bi6(k)*s6
ti6 = br6(j)*s6 + bi6(k)*c6
tr7 = br7(j)*c7 - bi7(k)*s7
ti7 = br7(j)*s7 + bi7(k)*c7
c
t0 = br0(j) + tr4
t1 = bi0(k) + ti4
tr4 = br0(j) - tr4
ti4 = bi0(k) - ti4
t2 = tr1 + tr5
t3 = ti1 + ti5
tr5 = tr1 - tr5
ti5 = ti1 - ti5
t4 = tr2 + tr6
t5 = ti2 + ti6
tr6 = tr2 - tr6
ti6 = ti2 - ti6
t6 = tr3 + tr7
t7 = ti3 + ti7
tr7 = tr3 - tr7
ti7 = ti3 - ti7
c
tr0 = t0 + t4
ti0 = t1 + t5
tr2 = t0 - t4
ti2 = t1 - t5
tr1 = t2 + t6
ti1 = t3 + t7
tr3 = t2 - t6
ti3 = t3 - t7
t0 = tr4 - ti6
t1 = ti4 + tr6
t4 = tr4 + ti6
t5 = ti4 - tr6
t2 = tr5 - ti7
t3 = ti5 + tr7
t6 = tr5 + ti7
t7 = ti5 - tr7
br0(j) = tr0 + tr1
bi7(k) = ti0 + ti1
bi6(k) = tr0 - tr1
br1(j) = ti1 - ti0
br2(j) = tr2 - ti3
bi5(k) = ti2 + tr3
bi4(k) = tr2 + ti3
br3(j) = tr3 - ti2
pr = p7*(t2-t3)
pi = p7*(t2+t3)
br4(j) = t0 + pr
bi3(k) = t1 + pi
bi2(k) = t0 - pr
br5(j) = pi - t1
pr = -p7*(t6+t7)
pi = p7*(t6-t7)
br6(j) = t4 + pr
bi1(k) = t5 + pi
bi0(k) = t4 - pr
br7(j) = pi - t5
100 continue
jr = jr + 2
ji = ji - 2
if (ji-jl) 110, 110, 120
110 ji = 2*jr - 1
jl = jr
120 continue
return
end
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