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c
c-----------------------------------------------------------------------
c subroutine: fr4tr
c radix 4 iteration subroutine
c-----------------------------------------------------------------------
c
subroutine fr4tr(int, nn, b0, b1, b2, b3, b4, b5, b6, b7)
dimension l(15), b0(2), b1(2), b2(2), b3(2), b4(2), b5(2), b6(2),
* b7(2)
common /cons/ 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 jthet is a reversed binary counter, jr steps two at a time to
c locate the real parts of intermediate results, and ji locates
c the imaginary part corresponding to jr.
c
l(1) = nn/4
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
c
piovn = pii/float(nn)
ji = 3
jl = 2
jr = 2
c
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 = b0(k) + b2(k)
t1 = b1(k) + b3(k)
b2(k) = b0(k) - b2(k)
b3(k) = b1(k) - b3(k)
b0(k) = t0 + t1
b1(k) = t0 - t1
60 continue
c
if (nn-4) 120, 120, 70
70 k0 = int*4 + 1
kl = k0 + int - 1
do 80 k=k0,kl
pr = p7*(b1(k)-b3(k))
pi = p7*(b1(k)+b3(k))
b3(k) = b2(k) + pi
b1(k) = pi - b2(k)
b2(k) = b0(k) - pr
b0(k) = b0(k) + pr
80 continue
go to 120
c
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
c
int4 = int*4
j0 = jr*int4 + 1
k0 = ji*int4 + 1
jlast = j0 + int - 1
do 100 j=j0,jlast
k = k0 + j - j0
r1 = b1(j)*c1 - b5(k)*s1
r5 = b1(j)*s1 + b5(k)*c1
t2 = b2(j)*c2 - b6(k)*s2
t6 = b2(j)*s2 + b6(k)*c2
t3 = b3(j)*c3 - b7(k)*s3
t7 = b3(j)*s3 + b7(k)*c3
t0 = b0(j) + t2
t4 = b4(k) + t6
t2 = b0(j) - t2
t6 = b4(k) - t6
t1 = r1 + t3
t5 = r5 + t7
t3 = r1 - t3
t7 = r5 - t7
b0(j) = t0 + t1
b7(k) = t4 + t5
b6(k) = t0 - t1
b1(j) = t5 - t4
b2(j) = t2 - t7
b5(k) = t6 + t3
b4(k) = t2 + t7
b3(j) = t3 - t6
100 continue
c
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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