hut2.f

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    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)
        common/cflag/ iflag,iq

    u(1)=spin10
    u(2)=spin20
        iflag = 0
        iq = 0

        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)
*       IF (iflag.GT.0) go to 10
*       enddo

        iter = 0
    6   call rk4c(dtau,u)
        iter = iter + 1
        IF (iflag.EQ.0.AND.iter.LT.nsteps) go to 6

        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,c30,c40,c5,semi
        common/radii/  r1,r2
        common/cflag/ iflag,iq
        SAVE ic,id
        DATA ic,id /0,0/

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

    c3=c30*r1**6
    c4=c40*r2**6

*       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
      IF (iq.EQ.0) THEN
      oa0 = oa
      iq = 1
      END IF
    
*       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)

*     quit on relative change exceeding 2 % (sja 05/09).
        IF (abs(oa - oa0).GT.0.02*oa0) iflag = 1

*       ic = ic + 1
*       ic = ic + 1
*       IF (ic.LT.10) THEN
*           WRITE (6,1)  ic, spin1, spin2, udot, c5
*   1       FORMAT (' HUT DERIV    # s1 s2 udot C5 ',i5,1p,6e9.1)
*       END IF

    end