subroutine ftu( signi, nx, cx )
#   complex fourier transform with unitary scaling
#
#               1         nx          signi*2*pi*i*(j-1)*(k-1)/nx
#   cx(k)  =  -------- * sum cx(j) * e
#             sqrt(nx)   j=1             for k=1,2,...,nx=2**integer
#
integer	nx, i, j, k, m, istep, pad2
real	signi, scale, arg
complex	cx(nx), cmplx, cw, cdel, ct
if( nx != pad2(nx) )	call erexit('ftu: nx not a power of 2')
scale = 1. / sqrt( 1.*nx)
do i= 1, nx
	cx(i) = cx(i) * scale
j = 1;	k = 1
do i= 1, nx {
	if (i<=j) { ct = cx(j); cx(j) = cx(i); cx(i) = ct }
	m = nx/2
	while (j>m & m>1) { j = j-m; m = m/2 }		# "&" means .AND.
	j = j+m
	}
repeat {
	istep = 2*k;   cw = 1.;   arg = signi*3.14159265/k
	cdel = cmplx( cos(arg), sin(arg))
	do m= 1, k {
		do i= m, nx, istep
			{ ct=cw*cx(i+k);  cx(i+k)=cx(i)-ct;  cx(i)=cx(i)+ct }
		cw = cw * cdel
		}
	k = istep
	}  until(k>=nx)
return; end