subroutine hut2(spin10,spin20,spin1,spin2,nsteps,dtau)
*
*       Spin evolution of circular binary.
*       ----------------------------------

         implicit real*8 (A-H,O-Z)
	real*8 u(2),udot(2)

	u(1)=spin10
	u(2)=spin20

         call deriv3(u,udot)

*       Include step reduction for large derivatives.
         IT = 0
     1   IF (ABS(udot(1))*dtau.GT.0.01*spin10) THEN
             dtau = 0.5D0*dtau
             nsteps = 2*nsteps
             IT = IT + 1
             IF (IT.LT.5) GO TO 1
         END IF

     5   IF (ABS(udot(2))*dtau.GT.0.01*spin20) THEN
             dtau = 0.5D0*dtau
             nsteps = 2*nsteps
             IT = IT + 1
             IF (IT.LT.5) GO TO 5
         END IF

	do i=1,nsteps
	   call rk4c(dtau,u)
	enddo

	spin1=u(1)
	spin2=u(2)

	end

       subroutine rk4c(dt,u)

*	Runge-Kutta integrator.
*       -----------------------

*       Author:  Rosemary Mardling (3/98).

       parameter (n=2)
       implicit real*8 (A-H,O-Z)
       real*8 u0(n),ut(n),du(n),u(n)
       real*8 a(4),b(4)

       a(1)=dt/2.0d0
       a(2)=a(1)
       a(3)=dt
       a(4)=0.0d0

       b(1)=dt/6.0d0
       b(2)=dt/3.0d0
       b(3)=b(2)
       b(4)=b(1)

       do i=1,n
          u0(i)=u(i)
          ut(i)=0.0d0
       enddo

       do j=1,4
          call deriv3(u,du)

          do i=1,n
             u(i)=u0(i)+a(j)*du(i)
             ut(i)=ut(i)+b(j)*du(i)
          enddo
       enddo

       do i=1,n
          u(i)=u0(i)+ut(i)
       enddo

       end
	
	subroutine deriv3(u,udot)

         implicit real*8 (A-H,M,O-Z)
	real*8 u(2),udot(2)
	common/spins/angmom0,rg2(2),m21,r21,semi0,C1,C2,C3,C4,C5,semi
         SAVE IC
         DATA IC /0/

*       Assume e=0.
	spin1=u(1)
	spin2=u(2)

*       e2=e**2
*       e4=e2**2
*       e6=e4*e2
*       fac=1-e2

*       f2=1+7.5*e2+5.625*e4+0.3125*e6
*       f3=1+3.75*e2+1.875*e4+0.078125*e6
*       f4=1+1.5*e2+0.125*e4
*       f5=1+3*e2+0.375*e4


	semi=angmom0-rg2(1)*spin1-m21*r21**2*rg2(2)*spin2
*       semi=(semi*(1+m21)/m21/semi0**2)**2/fac
         semi=(semi*(1+m21)/m21/semi0**2)**2
         oa = 1.0/semi
	
*       udot(1)=(oa/fac)**6*C3*(oa**1.5*f2-fac**1.5*f5*spin1)
*       udot(2)=(oa/fac)**6*C4*(oa**1.5*f2-fac**1.5*f5*spin2)
         udot(1)=oa**6*C3*(oa**1.5-spin1) - C5*spin1
         udot(2)=oa**6*C4*(oa**1.5-spin2)

*       IC = IC + 1
*       IF (IC.LT.10) THEN
*           WRITE (6,1)  IC, spin1, spin2, udot
*   1       FORMAT (' HUT DERIV    # s1 s2 udot ',I8,1P,6E9.1)
*       END IF

	end