anchor.diff:         ! These expressions are the V_{L,R} in Colella (1990) at the 
          ! bottom of page 191.  They are also in Saltzman (1994) as
          ! V_ref on page 161.
  -       r_xp = r + 0.5_dp_t*(1.0_dp_t - dtdx*max(eval(3), 0.0_dp_t))*ldr
  -       r_xm = r - 0.5_dp_t*(1.0_dp_t + dtdx*min(eval(1), 0.0_dp_t))*ldr
  -
  -       u_xp = ux + 0.5_dp_t*(1.0_dp_t - dtdx*max(eval(3), 0.0_dp_t))*ldu
  -       u_xm = ux - 0.5_dp_t*(1.0_dp_t + dtdx*min(eval(1), 0.0_dp_t))*ldu
  -
  -       p_xp = p + 0.5_dp_t*(1.0_dp_t - dtdx*max(eval(3), 0.0_dp_t))*ldp
  -       p_xm = p - 0.5_dp_t*(1.0_dp_t + dtdx*min(eval(1), 0.0_dp_t))*ldp
  +       r_xp = r + HALF*(ONE - dtdx*max(eval(3), ZERO))*ldr
  +       r_xm = r - HALF*(ONE + dtdx*min(eval(1), ZERO))*ldr
  +
  +       u_xp = ux + HALF*(ONE - dtdx*max(eval(3), ZERO))*ldu
  +       u_xm = ux - HALF*(ONE + dtdx*min(eval(1), ZERO))*ldu
  +
  +       p_xp = p + HALF*(ONE - dtdx*max(eval(3), ZERO))*ldp
  +       p_xm = p - HALF*(ONE + dtdx*min(eval(1), ZERO))*ldp
   
          !                                                   ^
          ! Now compute the interface states.   These are the V expressions
  
positive.code: 
  
         ! velocity
         sum_xm = 0.0_dp_t
         sum_xp = 0.0_dp_t
         do n = 1, nwaves
            sum_xm = sum_xm + beta_xm(n)*rvec(n,2)
            sum_xp = sum_xp + beta_xp(n)*rvec(n,2)
  
negative.code:        ! total energy
         call eos(eos_input_p, Q_l%data(i,iqpres), e, Q_l%data(i,iqdens))
         U_l%data(i,iuener) = Q_l%data(i,iqdens)*e + &
              HALF*Q_l%data(i,iqdens)*Q_l%data(i,iqxvel)**2
  
         call eos(eos_input_p, Q_r%data(i,iqpres), e, Q_r%data(i,iqdens))
         U_r%data(i,iuener) = Q_r%data(i,iqdens)*e + &
              HALF*Q_r%data(i,iqdens)*Q_r%data(i,iqxvel)**2
  
      enddo
      
  