# Half order causal derivative.
#
subroutine halfdif(  conj, n, x,    y)
integer n2, i,       conj, n
real	omega,                x(n), y(n)
complex cz,                              cv(4096)
n2=1; while(n2<n) n2=2*n2;         if( n2 > 4096) call erexit('halfdif memory')
do i= 1, n2 {		  cv(i) = 0.}
do i= 1, n
	if( conj == 0)	{ cv(i) = x(i)}
	else		{ cv(i) = y(i)}
call ftu( +1., n2, cv)
			do i= 1, n2 {
				omega = (i-1.) * 2.*3.14159265 / n2
				cz = csqrt( 1. - cexp( cmplx( 0., omega)))
				if( conj != 0)   cz = conjg( cz)
				cv(i) = cv(i) * cz
				}
call ftu( -1., n2, cv)
do i= 1, n
	if( conj == 0)	{ y(i) = cv(i)}
	else		{ x(i) = cv(i)}
return; end