Function external_initial_permute_state 

pub fn external_initial_permute_state<R: PrimeCharacteristicRing, CT: Copy, MdsPerm4: MdsPermutation<R, 4>, const WIDTH: usize>(
    state: &mut [R; WIDTH],
    initial_external_constants: &[[CT; WIDTH]],
    add_rc_and_sbox: fn(&mut R, CT),
    mat4: &MdsPerm4,
)

Applies the initial external rounds of the Poseidon2 permutation.

Apply the external linear layer and run a sequence of standard external rounds consisting of

1. Adding round constants to each element of the state.
2. Apply the S-box to each element of the state.
3. Applying an external linear layer (based on a 4x4 MDS matrix).

Parameters

• state: The state array at the start of the permutation.
• initial_external_constants: Per-round constants which are added to each state element.
• add_rc_and_sbox: A function that adds the round constant and applies the S-box to a given element.
• mat4: The 4x4 MDS matrix used in the external linear layer.