In this paper

we propose routing algorithms for permutation-reverse and permutation-rotation operations based on Inverse Butterfly and Butterfly Networks respectively.The algorithms utilize self-routing and self-reconfigurable characteristics of the networks

and are capable of completing all reverse and rotation operations of arbitrary permutation-P.Their computational complexities are low and the hardware implementations are simple.Following this

we extend the functions of the previous permutation operations based on the networks with our proposed algorithms.And then

permutation-reverse

permutation-rotation and permutation-reverse-rotation hardware units are developed and synthesized in SMIC 65-nm process.The results show that when the reverse operations are extended in previous designs

the area of the original circuits is only increased by 6%

and the latency of original circuits is almost not affected.In addition

when the rotation and reverse-rotation operations are extended in previous designs

the area of the original circuits is increased by 18% and 21%

and the latency of them is increased by 30%

while the functions of original circuits are expanded 2 times.