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c  ______________________
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	subroutine cslquat(qq,numsig,theta,qresult)
	real qq(4),theta,qresult(4),tmp(2)
	real pi
	integer numsig	! index of CSL boundary - must be supplied
	common/a2/quatcsl(4,50),numcsl,nsig(50)
c
       PI=3.14159265
c
c  algorithm for forming resultant quaternion
c  and determining angle based on fourth component
c
c  note change of signs to get inverse of second orientation
c
	qresult(1)=qq(1)*quatcsl(4,numsig)-qq(4)*quatcsl(1,numsig)
     &	+qq(2)*quatcsl(3,numsig)-qq(3)*quatcsl(2,numsig)
	qresult(2)=qq(2)*quatcsl(4,numsig)-qq(4)*quatcsl(2,numsig)
     &	+qq(3)*quatcsl(1,numsig)-qq(1)*quatcsl(3,numsig)
	qresult(3)=qq(3)*quatcsl(4,numsig)-qq(4)*quatcsl(3,numsig)
     &	+qq(1)*quatcsl(2,numsig)-qq(2)*quatcsl(1,numsig)
	qresult(4)=qq(4)*quatcsl(4,numsig)+qq(1)*quatcsl(1,numsig)
     &	+qq(2)*quatcsl(2,numsig)+qq(3)*quatcsl(3,numsig)
c
c	write(*,*) 'qresult ',qresult
	if(qresult(4).gt.1.0) qresult(4)=1.0
	if(qresult(4).lt.-1.0) qresult(4)=-1.0
	theta=acos(qresult(4))*360./pi
c	write(*,*) 'theta= ',theta
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	return
	end
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