Function scalar_ring_kernel 

pub fn scalar_ring_kernel(
    _cr: ClockReset,
    i: ScalarRingIn,
    q: Q,
) -> (ScalarRingOut, D)

State transition for ScalarRing.

Each cycle every stage advances its context by one register: stage K reads sK and its intermediates and writes s(K+1), and stage 8 writes back to s1. The finisher runs alongside on its own registers.