64-point radix-2 fixed-point DIF FFT IV-KAT Tables (continued)



John Bryan






(P,b,n)=(3,0,0)
Loop P=3 of p=log2N=log264=6 loops indexed P=0...p-1=0...6-1=0...5.
Subblock b=0 of BP=B3=2P=23=8 subblocks, indexed b=0...B3-1=0...7.
Subblock size=NP|P=3=N3=N/BP|(N=64,P=3)=(2p/2P)|(p=6,P=3)=2p-P|(p=6,P=3)=26-3=8.
Butterfly n=0 of N'P=NP/2=2p-P-1=26-3-1=4 butterflies indexed by n=0...N'P-1=0...3.
Even base index e = 2NPb = 2(8)(0) = 0.
Odd base index o = e + 2N'P = 0 + 2(4) = 8.
Twiddle step size s = 2P+1 = 23+1 = 16.
x[e+2n] ={x[e+2n]+x[o+2n]}>>1
x[0+0] ={x[0+0]+x[8+0]}>>1
x[0] ={x[0]+x[8]}>>1
={0000 +0000}>>1
={00000}>>1
=0000
x[e+2n+1] ={x[e+2n+1]+x[o+2n+1]}>>1
x[0+1] ={x[0+1]+x[8+1]}>>1
x[1] ={x[1]+x[9]}>>1
={0000 +0000}>>1
={00000}>>1
=0000
x[o+2n] = {(x[o+2n]-x[e+2n])t[sn]-(x[e+2n+1]-x[o+2n+1])t[sn+1]}>>1
x[8+2(0)] = {(x[8+2(0)]-x[0+2(0)])t[(16)(0)]-(x[0+2(0)+1]-x[8+2(0)+1])t[(16)(0)+1]}>>1
x[8+0] = {(x[8+0]-x[0+0])t[0]-(x[0+0+1]-x[8+0+1])t[0+1]}>>1
x[8] = {(x[8]-x[0])t[0]-(x[1]-x[9])t[1]}>>1
= {(0000-0000)8000-(0000-0000)0000}>>1
= {(00000)8000-(00000)0000}>>1
= {00000 - 00000}>>1
= {00000}>>1
= 0000
x[o+2n+1] = {(x[o+2n+1]-x[e+2n+1])t[sn]+(x[e+2n]-x[o+2n])t[sn+1]}>>1
x[8+2(0)+1] = {(x[8+2(0)+1]-x[0+2(0)+1])t[(16)(0)]+(x[0+2(0)]-x[8+2(0)])t[(16)(0)+1]}>>1
x[8+1] = {(x[8+1]-x[0+1])t[0]+(x[0+0]-x[8+0])t[0+1]}>>1
x[9] = {(x[9]-x[1])t[0]+(x[0]-x[8])t[1]}>>1
= {(0000-0000)8000+(0000-0000)0000}>>1
= {(00000)8000+(00000)0000}>>1
= {00000+00000}>>1
= {00000}>>1
= 0000



Return to Table of Contents




(P,b,n)=(3,0,1)
Loop P=3 of p=log2N=log264=6 loops indexed P=0...p-1=0...6-1=0...5.
Subblock b=0 of BP=B3=2P=23=8 subblocks, indexed b=0...B3-1=0...7.
Subblock size=NP|P=3=N3=N/BP|(N=64,P=3)=(2p/2P)|(p=6,P=3)=2p-P|(p=6,P=3)=26-3=8.
Butterfly n=1 of N'P=NP/2=2p-P-1=26-3-1=4 butterflies indexed by n=0...N'P-1=0...3.
Even base index e = 2NPb = 2(8)(0) = 0.
Odd base index o = e + 2N'P = 0 + 2(4) = 8.
Twiddle step size s = 2P+1 = 23+1 = 16.
x[e+2n] ={x[e+2n]+x[o+2n]}>>1
x[0+2] ={x[0+2]+x[8+2]}>>1
x[2] ={x[2]+x[10]}>>1
={1000 +1000}>>1
={02000}>>1
=1000
x[e+2n+1] ={x[e+2n+1]+x[o+2n+1]}>>1
x[0+3] ={x[0+3]+x[8+3]}>>1
x[3] ={x[3]+x[11]}>>1
={0000 +0000}>>1
={00000}>>1
=0000
x[o+2n] = {(x[o+2n]-x[e+2n])t[sn]-(x[e+2n+1]-x[o+2n+1])t[sn+1]}>>1
x[8+2(1)] = {(x[8+2(1)]-x[0+2(1)])t[(16)(1)]-(x[0+2(1)+1]-x[8+2(1)+1])t[(16)(1)+1]}>>1
x[8+2] = {(x[8+2]-x[0+2])t[16]-(x[0+2+1]-x[8+2+1])t[16+1]}>>1
x[10] = {(x[10]-x[2])t[16]-(x[3]-x[11])t[17]}>>1
= {(1000-1000)a57d-(0000-0000)a57d}>>1
= {(00000)a57d-(00000)a57d}>>1
= {00000 - 00000}>>1
= {00000}>>1
= 0000
x[o+2n+1] = {(x[o+2n+1]-x[e+2n+1])t[sn]+(x[e+2n]-x[o+2n])t[sn+1]}>>1
x[8+2(1)+1] = {(x[8+2(1)+1]-x[0+2(1)+1])t[(16)(1)]+(x[0+2(1)]-x[8+2(1)])t[(16)(1)+1]}>>1
x[8+3] = {(x[8+3]-x[0+3])t[16]+(x[0+2]-x[8+2])t[16+1]}>>1
x[11] = {(x[11]-x[3])t[16]+(x[2]-x[10])t[17]}>>1
= {(0000-0000)a57d+(1000-1000)a57d}>>1
= {(00000)a57d+(00000)a57d}>>1
= {00000+00000}>>1
= {00000}>>1
= 0000



Return to Table of Contents




(P,b,n)=(3,0,2)
Loop P=3 of p=log2N=log264=6 loops indexed P=0...p-1=0...6-1=0...5.
Subblock b=0 of BP=B3=2P=23=8 subblocks, indexed b=0...B3-1=0...7.
Subblock size=NP|P=3=N3=N/BP|(N=64,P=3)=(2p/2P)|(p=6,P=3)=2p-P|(p=6,P=3)=26-3=8.
Butterfly n=2 of N'P=NP/2=2p-P-1=26-3-1=4 butterflies indexed by n=0...N'P-1=0...3.
Even base index e = 2NPb = 2(8)(0) = 0.
Odd base index o = e + 2N'P = 0 + 2(4) = 8.
Twiddle step size s = 2P+1 = 23+1 = 16.
x[e+2n] ={x[e+2n]+x[o+2n]}>>1
x[0+4] ={x[0+4]+x[8+4]}>>1
x[4] ={x[4]+x[12]}>>1
={0000 +0000}>>1
={00000}>>1
=0000
x[e+2n+1] ={x[e+2n+1]+x[o+2n+1]}>>1
x[0+5] ={x[0+5]+x[8+5]}>>1
x[5] ={x[5]+x[13]}>>1
={0000 +0000}>>1
={00000}>>1
=0000
x[o+2n] = {(x[o+2n]-x[e+2n])t[sn]-(x[e+2n+1]-x[o+2n+1])t[sn+1]}>>1
x[8+2(2)] = {(x[8+2(2)]-x[0+2(2)])t[(16)(2)]-(x[0+2(2)+1]-x[8+2(2)+1])t[(16)(2)+1]}>>1
x[8+4] = {(x[8+4]-x[0+4])t[32]-(x[0+4+1]-x[8+4+1])t[32+1]}>>1
x[12] = {(x[12]-x[4])t[32]-(x[5]-x[13])t[33]}>>1
= {(0000-0000)ffff-(0000-0000)8000}>>1
= {(00000)ffff-(00000)8000}>>1
= {00000 - 00000}>>1
= {00000}>>1
= 0000
x[o+2n+1] = {(x[o+2n+1]-x[e+2n+1])t[sn]+(x[e+2n]-x[o+2n])t[sn+1]}>>1
x[8+2(2)+1] = {(x[8+2(2)+1]-x[0+2(2)+1])t[(16)(2)]+(x[0+2(2)]-x[8+2(2)])t[(16)(2)+1]}>>1
x[8+5] = {(x[8+5]-x[0+5])t[32]+(x[0+4]-x[8+4])t[32+1]}>>1
x[13] = {(x[13]-x[5])t[32]+(x[4]-x[12])t[33]}>>1
= {(0000-0000)ffff+(0000-0000)8000}>>1
= {(00000)ffff+(00000)8000}>>1
= {00000+00000}>>1
= {00000}>>1
= 0000



Return to Table of Contents




(P,b,n)=(3,0,3)
Loop P=3 of p=log2N=log264=6 loops indexed P=0...p-1=0...6-1=0...5.
Subblock b=0 of BP=B3=2P=23=8 subblocks, indexed b=0...B3-1=0...7.
Subblock size=NP|P=3=N3=N/BP|(N=64,P=3)=(2p/2P)|(p=6,P=3)=2p-P|(p=6,P=3)=26-3=8.
Butterfly n=3 of N'P=NP/2=2p-P-1=26-3-1=4 butterflies indexed by n=0...N'P-1=0...3.
Even base index e = 2NPb = 2(8)(0) = 0.
Odd base index o = e + 2N'P = 0 + 2(4) = 8.
Twiddle step size s = 2P+1 = 23+1 = 16.
x[e+2n] ={x[e+2n]+x[o+2n]}>>1
x[0+6] ={x[0+6]+x[8+6]}>>1
x[6] ={x[6]+x[14]}>>1
={f000 +f000}>>1
={fe000}>>1
=f000
x[e+2n+1] ={x[e+2n+1]+x[o+2n+1]}>>1
x[0+7] ={x[0+7]+x[8+7]}>>1
x[7] ={x[7]+x[15]}>>1
={0000 +0000}>>1
={00000}>>1
=0000
x[o+2n] = {(x[o+2n]-x[e+2n])t[sn]-(x[e+2n+1]-x[o+2n+1])t[sn+1]}>>1
x[8+2(3)] = {(x[8+2(3)]-x[0+2(3)])t[(16)(3)]-(x[0+2(3)+1]-x[8+2(3)+1])t[(16)(3)+1]}>>1
x[8+6] = {(x[8+6]-x[0+6])t[48]-(x[0+6+1]-x[8+6+1])t[48+1]}>>1
x[14] = {(x[14]-x[6])t[48]-(x[7]-x[15])t[49]}>>1
= {(f000-f000)5a82-(0000-0000)a57d}>>1
= {(00000)5a82-(00000)a57d}>>1
= {00000 - 00000}>>1
= {00000}>>1
= 0000
x[o+2n+1] = {(x[o+2n+1]-x[e+2n+1])t[sn]+(x[e+2n]-x[o+2n])t[sn+1]}>>1
x[8+2(3)+1] = {(x[8+2(3)+1]-x[0+2(3)+1])t[(16)(3)]+(x[0+2(3)]-x[8+2(3)])t[(16)(3)+1]}>>1
x[8+7] = {(x[8+7]-x[0+7])t[48]+(x[0+6]-x[8+6])t[48+1]}>>1
x[15] = {(x[15]-x[7])t[48]+(x[6]-x[14])t[49]}>>1
= {(0000-0000)5a82+(f000-f000)a57d}>>1
= {(00000)5a82+(00000)a57d}>>1
= {00000+00000}>>1
= {00000}>>1
= 0000



Return to Table of Contents




(P,b,n)=(3,1,0)
Loop P=3 of p=log2N=log264=6 loops indexed P=0...p-1=0...6-1=0...5.
Subblock b=1 of BP=B3=2P=23=8 subblocks, indexed b=0...B3-1=0...7.
Subblock size=NP|P=3=N3=N/BP|(N=64,P=3)=(2p/2P)|(p=6,P=3)=2p-P|(p=6,P=3)=26-3=8.
Butterfly n=0 of N'P=NP/2=2p-P-1=26-3-1=4 butterflies indexed by n=0...N'P-1=0...3.
Even base index e = 2NPb = 2(8)(1) = 16.
Odd base index o = e + 2N'P = 16 + 2(4) = 24.
Twiddle step size s = 2P+1 = 23+1 = 16.
x[e+2n] ={x[e+2n]+x[o+2n]}>>1
x[16+0] ={x[16+0]+x[24+0]}>>1
x[16] ={x[16]+x[24]}>>1
={0000 +0000}>>1
={00000}>>1
=0000
x[e+2n+1] ={x[e+2n+1]+x[o+2n+1]}>>1
x[16+1] ={x[16+1]+x[24+1]}>>1
x[17] ={x[17]+x[25]}>>1
={0000 +0000}>>1
={00000}>>1
=0000
x[o+2n] = {(x[o+2n]-x[e+2n])t[sn]-(x[e+2n+1]-x[o+2n+1])t[sn+1]}>>1
x[24+2(0)] = {(x[24+2(0)]-x[16+2(0)])t[(16)(0)]-(x[16+2(0)+1]-x[24+2(0)+1])t[(16)(0)+1]}>>1
x[24+0] = {(x[24+0]-x[16+0])t[0]-(x[16+0+1]-x[24+0+1])t[0+1]}>>1
x[24] = {(x[24]-x[16])t[0]-(x[17]-x[25])t[1]}>>1
= {(0000-0000)8000-(0000-0000)0000}>>1
= {(00000)8000-(00000)0000}>>1
= {00000 - 00000}>>1
= {00000}>>1
= 0000
x[o+2n+1] = {(x[o+2n+1]-x[e+2n+1])t[sn]+(x[e+2n]-x[o+2n])t[sn+1]}>>1
x[24+2(0)+1] = {(x[24+2(0)+1]-x[16+2(0)+1])t[(16)(0)]+(x[16+2(0)]-x[24+2(0)])t[(16)(0)+1]}>>1
x[24+1] = {(x[24+1]-x[16+1])t[0]+(x[16+0]-x[24+0])t[0+1]}>>1
x[25] = {(x[25]-x[17])t[0]+(x[16]-x[24])t[1]}>>1
= {(0000-0000)8000+(0000-0000)0000}>>1
= {(00000)8000+(00000)0000}>>1
= {00000+00000}>>1
= {00000}>>1
= 0000



Return to Table of Contents




(P,b,n)=(3,1,1)
Loop P=3 of p=log2N=log264=6 loops indexed P=0...p-1=0...6-1=0...5.
Subblock b=1 of BP=B3=2P=23=8 subblocks, indexed b=0...B3-1=0...7.
Subblock size=NP|P=3=N3=N/BP|(N=64,P=3)=(2p/2P)|(p=6,P=3)=2p-P|(p=6,P=3)=26-3=8.
Butterfly n=1 of N'P=NP/2=2p-P-1=26-3-1=4 butterflies indexed by n=0...N'P-1=0...3.
Even base index e = 2NPb = 2(8)(1) = 16.
Odd base index o = e + 2N'P = 16 + 2(4) = 24.
Twiddle step size s = 2P+1 = 23+1 = 16.
x[e+2n] ={x[e+2n]+x[o+2n]}>>1
x[16+2] ={x[16+2]+x[24+2]}>>1
x[18] ={x[18]+x[26]}>>1
={0000 +0000}>>1
={00000}>>1
=0000
x[e+2n+1] ={x[e+2n+1]+x[o+2n+1]}>>1
x[16+3] ={x[16+3]+x[24+3]}>>1
x[19] ={x[19]+x[27]}>>1
={0000 +0000}>>1
={00000}>>1
=0000
x[o+2n] = {(x[o+2n]-x[e+2n])t[sn]-(x[e+2n+1]-x[o+2n+1])t[sn+1]}>>1
x[24+2(1)] = {(x[24+2(1)]-x[16+2(1)])t[(16)(1)]-(x[16+2(1)+1]-x[24+2(1)+1])t[(16)(1)+1]}>>1
x[24+2] = {(x[24+2]-x[16+2])t[16]-(x[16+2+1]-x[24+2+1])t[16+1]}>>1
x[26] = {(x[26]-x[18])t[16]-(x[19]-x[27])t[17]}>>1
= {(0000-0000)a57d-(0000-0000)a57d}>>1
= {(00000)a57d-(00000)a57d}>>1
= {00000 - 00000}>>1
= {00000}>>1
= 0000
x[o+2n+1] = {(x[o+2n+1]-x[e+2n+1])t[sn]+(x[e+2n]-x[o+2n])t[sn+1]}>>1
x[24+2(1)+1] = {(x[24+2(1)+1]-x[16+2(1)+1])t[(16)(1)]+(x[16+2(1)]-x[24+2(1)])t[(16)(1)+1]}>>1
x[24+3] = {(x[24+3]-x[16+3])t[16]+(x[16+2]-x[24+2])t[16+1]}>>1
x[27] = {(x[27]-x[19])t[16]+(x[18]-x[26])t[17]}>>1
= {(0000-0000)a57d+(0000-0000)a57d}>>1
= {(00000)a57d+(00000)a57d}>>1
= {00000+00000}>>1
= {00000}>>1
= 0000



Return to Table of Contents




(P,b,n)=(3,1,2)
Loop P=3 of p=log2N=log264=6 loops indexed P=0...p-1=0...6-1=0...5.
Subblock b=1 of BP=B3=2P=23=8 subblocks, indexed b=0...B3-1=0...7.
Subblock size=NP|P=3=N3=N/BP|(N=64,P=3)=(2p/2P)|(p=6,P=3)=2p-P|(p=6,P=3)=26-3=8.
Butterfly n=2 of N'P=NP/2=2p-P-1=26-3-1=4 butterflies indexed by n=0...N'P-1=0...3.
Even base index e = 2NPb = 2(8)(1) = 16.
Odd base index o = e + 2N'P = 16 + 2(4) = 24.
Twiddle step size s = 2P+1 = 23+1 = 16.
x[e+2n] ={x[e+2n]+x[o+2n]}>>1
x[16+4] ={x[16+4]+x[24+4]}>>1
x[20] ={x[20]+x[28]}>>1
={0000 +0000}>>1
={00000}>>1
=0000
x[e+2n+1] ={x[e+2n+1]+x[o+2n+1]}>>1
x[16+5] ={x[16+5]+x[24+5]}>>1
x[21] ={x[21]+x[29]}>>1
={0000 +0000}>>1
={00000}>>1
=0000
x[o+2n] = {(x[o+2n]-x[e+2n])t[sn]-(x[e+2n+1]-x[o+2n+1])t[sn+1]}>>1
x[24+2(2)] = {(x[24+2(2)]-x[16+2(2)])t[(16)(2)]-(x[16+2(2)+1]-x[24+2(2)+1])t[(16)(2)+1]}>>1
x[24+4] = {(x[24+4]-x[16+4])t[32]-(x[16+4+1]-x[24+4+1])t[32+1]}>>1
x[28] = {(x[28]-x[20])t[32]-(x[21]-x[29])t[33]}>>1
= {(0000-0000)ffff-(0000-0000)8000}>>1
= {(00000)ffff-(00000)8000}>>1
= {00000 - 00000}>>1
= {00000}>>1
= 0000
x[o+2n+1] = {(x[o+2n+1]-x[e+2n+1])t[sn]+(x[e+2n]-x[o+2n])t[sn+1]}>>1
x[24+2(2)+1] = {(x[24+2(2)+1]-x[16+2(2)+1])t[(16)(2)]+(x[16+2(2)]-x[24+2(2)])t[(16)(2)+1]}>>1
x[24+5] = {(x[24+5]-x[16+5])t[32]+(x[16+4]-x[24+4])t[32+1]}>>1
x[29] = {(x[29]-x[21])t[32]+(x[20]-x[28])t[33]}>>1
= {(0000-0000)ffff+(0000-0000)8000}>>1
= {(00000)ffff+(00000)8000}>>1
= {00000+00000}>>1
= {00000}>>1
= 0000



Return to Table of Contents




(P,b,n)=(3,1,3)
Loop P=3 of p=log2N=log264=6 loops indexed P=0...p-1=0...6-1=0...5.
Subblock b=1 of BP=B3=2P=23=8 subblocks, indexed b=0...B3-1=0...7.
Subblock size=NP|P=3=N3=N/BP|(N=64,P=3)=(2p/2P)|(p=6,P=3)=2p-P|(p=6,P=3)=26-3=8.
Butterfly n=3 of N'P=NP/2=2p-P-1=26-3-1=4 butterflies indexed by n=0...N'P-1=0...3.
Even base index e = 2NPb = 2(8)(1) = 16.
Odd base index o = e + 2N'P = 16 + 2(4) = 24.
Twiddle step size s = 2P+1 = 23+1 = 16.
x[e+2n] ={x[e+2n]+x[o+2n]}>>1
x[16+6] ={x[16+6]+x[24+6]}>>1
x[22] ={x[22]+x[30]}>>1
={0000 +0000}>>1
={00000}>>1
=0000
x[e+2n+1] ={x[e+2n+1]+x[o+2n+1]}>>1
x[16+7] ={x[16+7]+x[24+7]}>>1
x[23] ={x[23]+x[31]}>>1
={0000 +0000}>>1
={00000}>>1
=0000
x[o+2n] = {(x[o+2n]-x[e+2n])t[sn]-(x[e+2n+1]-x[o+2n+1])t[sn+1]}>>1
x[24+2(3)] = {(x[24+2(3)]-x[16+2(3)])t[(16)(3)]-(x[16+2(3)+1]-x[24+2(3)+1])t[(16)(3)+1]}>>1
x[24+6] = {(x[24+6]-x[16+6])t[48]-(x[16+6+1]-x[24+6+1])t[48+1]}>>1
x[30] = {(x[30]-x[22])t[48]-(x[23]-x[31])t[49]}>>1
= {(0000-0000)5a82-(0000-0000)a57d}>>1
= {(00000)5a82-(00000)a57d}>>1
= {00000 - 00000}>>1
= {00000}>>1
= 0000
x[o+2n+1] = {(x[o+2n+1]-x[e+2n+1])t[sn]+(x[e+2n]-x[o+2n])t[sn+1]}>>1
x[24+2(3)+1] = {(x[24+2(3)+1]-x[16+2(3)+1])t[(16)(3)]+(x[16+2(3)]-x[24+2(3)])t[(16)(3)+1]}>>1
x[24+7] = {(x[24+7]-x[16+7])t[48]+(x[16+6]-x[24+6])t[48+1]}>>1
x[31] = {(x[31]-x[23])t[48]+(x[22]-x[30])t[49]}>>1
= {(0000-0000)5a82+(0000-0000)a57d}>>1
= {(00000)5a82+(00000)a57d}>>1
= {00000+00000}>>1
= {00000}>>1
= 0000



Return to Table of Contents




(P,b,n)=(3,2,0)
Loop P=3 of p=log2N=log264=6 loops indexed P=0...p-1=0...6-1=0...5.
Subblock b=2 of BP=B3=2P=23=8 subblocks, indexed b=0...B3-1=0...7.
Subblock size=NP|P=3=N3=N/BP|(N=64,P=3)=(2p/2P)|(p=6,P=3)=2p-P|(p=6,P=3)=26-3=8.
Butterfly n=0 of N'P=NP/2=2p-P-1=26-3-1=4 butterflies indexed by n=0...N'P-1=0...3.
Even base index e = 2NPb = 2(8)(2) = 32.
Odd base index o = e + 2N'P = 32 + 2(4) = 40.
Twiddle step size s = 2P+1 = 23+1 = 16.
x[e+2n] ={x[e+2n]+x[o+2n]}>>1
x[32+0] ={x[32+0]+x[40+0]}>>1
x[32] ={x[32]+x[40]}>>1
={0000 +0000}>>1
={00000}>>1
=0000
x[e+2n+1] ={x[e+2n+1]+x[o+2n+1]}>>1
x[32+1] ={x[32+1]+x[40+1]}>>1
x[33] ={x[33]+x[41]}>>1
={0000 +0000}>>1
={00000}>>1
=0000
x[o+2n] = {(x[o+2n]-x[e+2n])t[sn]-(x[e+2n+1]-x[o+2n+1])t[sn+1]}>>1
x[40+2(0)] = {(x[40+2(0)]-x[32+2(0)])t[(16)(0)]-(x[32+2(0)+1]-x[40+2(0)+1])t[(16)(0)+1]}>>1
x[40+0] = {(x[40+0]-x[32+0])t[0]-(x[32+0+1]-x[40+0+1])t[0+1]}>>1
x[40] = {(x[40]-x[32])t[0]-(x[33]-x[41])t[1]}>>1
= {(0000-0000)8000-(0000-0000)0000}>>1
= {(00000)8000-(00000)0000}>>1
= {00000 - 00000}>>1
= {00000}>>1
= 0000
x[o+2n+1] = {(x[o+2n+1]-x[e+2n+1])t[sn]+(x[e+2n]-x[o+2n])t[sn+1]}>>1
x[40+2(0)+1] = {(x[40+2(0)+1]-x[32+2(0)+1])t[(16)(0)]+(x[32+2(0)]-x[40+2(0)])t[(16)(0)+1]}>>1
x[40+1] = {(x[40+1]-x[32+1])t[0]+(x[32+0]-x[40+0])t[0+1]}>>1
x[41] = {(x[41]-x[33])t[0]+(x[32]-x[40])t[1]}>>1
= {(0000-0000)8000+(0000-0000)0000}>>1
= {(00000)8000+(00000)0000}>>1
= {00000+00000}>>1
= {00000}>>1
= 0000



Return to Table of Contents




(P,b,n)=(3,2,1)
Loop P=3 of p=log2N=log264=6 loops indexed P=0...p-1=0...6-1=0...5.
Subblock b=2 of BP=B3=2P=23=8 subblocks, indexed b=0...B3-1=0...7.
Subblock size=NP|P=3=N3=N/BP|(N=64,P=3)=(2p/2P)|(p=6,P=3)=2p-P|(p=6,P=3)=26-3=8.
Butterfly n=1 of N'P=NP/2=2p-P-1=26-3-1=4 butterflies indexed by n=0...N'P-1=0...3.
Even base index e = 2NPb = 2(8)(2) = 32.
Odd base index o = e + 2N'P = 32 + 2(4) = 40.
Twiddle step size s = 2P+1 = 23+1 = 16.
x[e+2n] ={x[e+2n]+x[o+2n]}>>1
x[32+2] ={x[32+2]+x[40+2]}>>1
x[34] ={x[34]+x[42]}>>1
={0000 +0000}>>1
={00000}>>1
=0000
x[e+2n+1] ={x[e+2n+1]+x[o+2n+1]}>>1
x[32+3] ={x[32+3]+x[40+3]}>>1
x[35] ={x[35]+x[43]}>>1
={0000 +0000}>>1
={00000}>>1
=0000
x[o+2n] = {(x[o+2n]-x[e+2n])t[sn]-(x[e+2n+1]-x[o+2n+1])t[sn+1]}>>1
x[40+2(1)] = {(x[40+2(1)]-x[32+2(1)])t[(16)(1)]-(x[32+2(1)+1]-x[40+2(1)+1])t[(16)(1)+1]}>>1
x[40+2] = {(x[40+2]-x[32+2])t[16]-(x[32+2+1]-x[40+2+1])t[16+1]}>>1
x[42] = {(x[42]-x[34])t[16]-(x[35]-x[43])t[17]}>>1
= {(0000-0000)a57d-(0000-0000)a57d}>>1
= {(00000)a57d-(00000)a57d}>>1
= {00000 - 00000}>>1
= {00000}>>1
= 0000
x[o+2n+1] = {(x[o+2n+1]-x[e+2n+1])t[sn]+(x[e+2n]-x[o+2n])t[sn+1]}>>1
x[40+2(1)+1] = {(x[40+2(1)+1]-x[32+2(1)+1])t[(16)(1)]+(x[32+2(1)]-x[40+2(1)])t[(16)(1)+1]}>>1
x[40+3] = {(x[40+3]-x[32+3])t[16]+(x[32+2]-x[40+2])t[16+1]}>>1
x[43] = {(x[43]-x[35])t[16]+(x[34]-x[42])t[17]}>>1
= {(0000-0000)a57d+(0000-0000)a57d}>>1
= {(00000)a57d+(00000)a57d}>>1
= {00000+00000}>>1
= {00000}>>1
= 0000



Return to Table of Contents




(P,b,n)=(3,2,2)
Loop P=3 of p=log2N=log264=6 loops indexed P=0...p-1=0...6-1=0...5.
Subblock b=2 of BP=B3=2P=23=8 subblocks, indexed b=0...B3-1=0...7.
Subblock size=NP|P=3=N3=N/BP|(N=64,P=3)=(2p/2P)|(p=6,P=3)=2p-P|(p=6,P=3)=26-3=8.
Butterfly n=2 of N'P=NP/2=2p-P-1=26-3-1=4 butterflies indexed by n=0...N'P-1=0...3.
Even base index e = 2NPb = 2(8)(2) = 32.
Odd base index o = e + 2N'P = 32 + 2(4) = 40.
Twiddle step size s = 2P+1 = 23+1 = 16.
x[e+2n] ={x[e+2n]+x[o+2n]}>>1
x[32+4] ={x[32+4]+x[40+4]}>>1
x[36] ={x[36]+x[44]}>>1
={0000 +0000}>>1
={00000}>>1
=0000
x[e+2n+1] ={x[e+2n+1]+x[o+2n+1]}>>1
x[32+5] ={x[32+5]+x[40+5]}>>1
x[37] ={x[37]+x[45]}>>1
={0000 +0000}>>1
={00000}>>1
=0000
x[o+2n] = {(x[o+2n]-x[e+2n])t[sn]-(x[e+2n+1]-x[o+2n+1])t[sn+1]}>>1
x[40+2(2)] = {(x[40+2(2)]-x[32+2(2)])t[(16)(2)]-(x[32+2(2)+1]-x[40+2(2)+1])t[(16)(2)+1]}>>1
x[40+4] = {(x[40+4]-x[32+4])t[32]-(x[32+4+1]-x[40+4+1])t[32+1]}>>1
x[44] = {(x[44]-x[36])t[32]-(x[37]-x[45])t[33]}>>1
= {(0000-0000)ffff-(0000-0000)8000}>>1
= {(00000)ffff-(00000)8000}>>1
= {00000 - 00000}>>1
= {00000}>>1
= 0000
x[o+2n+1] = {(x[o+2n+1]-x[e+2n+1])t[sn]+(x[e+2n]-x[o+2n])t[sn+1]}>>1
x[40+2(2)+1] = {(x[40+2(2)+1]-x[32+2(2)+1])t[(16)(2)]+(x[32+2(2)]-x[40+2(2)])t[(16)(2)+1]}>>1
x[40+5] = {(x[40+5]-x[32+5])t[32]+(x[32+4]-x[40+4])t[32+1]}>>1
x[45] = {(x[45]-x[37])t[32]+(x[36]-x[44])t[33]}>>1
= {(0000-0000)ffff+(0000-0000)8000}>>1
= {(00000)ffff+(00000)8000}>>1
= {00000+00000}>>1
= {00000}>>1
= 0000



Return to Table of Contents




(P,b,n)=(3,2,3)
Loop P=3 of p=log2N=log264=6 loops indexed P=0...p-1=0...6-1=0...5.
Subblock b=2 of BP=B3=2P=23=8 subblocks, indexed b=0...B3-1=0...7.
Subblock size=NP|P=3=N3=N/BP|(N=64,P=3)=(2p/2P)|(p=6,P=3)=2p-P|(p=6,P=3)=26-3=8.
Butterfly n=3 of N'P=NP/2=2p-P-1=26-3-1=4 butterflies indexed by n=0...N'P-1=0...3.
Even base index e = 2NPb = 2(8)(2) = 32.
Odd base index o = e + 2N'P = 32 + 2(4) = 40.
Twiddle step size s = 2P+1 = 23+1 = 16.
x[e+2n] ={x[e+2n]+x[o+2n]}>>1
x[32+6] ={x[32+6]+x[40+6]}>>1
x[38] ={x[38]+x[46]}>>1
={0000 +0000}>>1
={00000}>>1
=0000
x[e+2n+1] ={x[e+2n+1]+x[o+2n+1]}>>1
x[32+7] ={x[32+7]+x[40+7]}>>1
x[39] ={x[39]+x[47]}>>1
={0000 +0000}>>1
={00000}>>1
=0000
x[o+2n] = {(x[o+2n]-x[e+2n])t[sn]-(x[e+2n+1]-x[o+2n+1])t[sn+1]}>>1
x[40+2(3)] = {(x[40+2(3)]-x[32+2(3)])t[(16)(3)]-(x[32+2(3)+1]-x[40+2(3)+1])t[(16)(3)+1]}>>1
x[40+6] = {(x[40+6]-x[32+6])t[48]-(x[32+6+1]-x[40+6+1])t[48+1]}>>1
x[46] = {(x[46]-x[38])t[48]-(x[39]-x[47])t[49]}>>1
= {(0000-0000)5a82-(0000-0000)a57d}>>1
= {(00000)5a82-(00000)a57d}>>1
= {00000 - 00000}>>1
= {00000}>>1
= 0000
x[o+2n+1] = {(x[o+2n+1]-x[e+2n+1])t[sn]+(x[e+2n]-x[o+2n])t[sn+1]}>>1
x[40+2(3)+1] = {(x[40+2(3)+1]-x[32+2(3)+1])t[(16)(3)]+(x[32+2(3)]-x[40+2(3)])t[(16)(3)+1]}>>1
x[40+7] = {(x[40+7]-x[32+7])t[48]+(x[32+6]-x[40+6])t[48+1]}>>1
x[47] = {(x[47]-x[39])t[48]+(x[38]-x[46])t[49]}>>1
= {(0000-0000)5a82+(0000-0000)a57d}>>1
= {(00000)5a82+(00000)a57d}>>1
= {00000+00000}>>1
= {00000}>>1
= 0000



Return to Table of Contents




(P,b,n)=(3,3,0)
Loop P=3 of p=log2N=log264=6 loops indexed P=0...p-1=0...6-1=0...5.
Subblock b=3 of BP=B3=2P=23=8 subblocks, indexed b=0...B3-1=0...7.
Subblock size=NP|P=3=N3=N/BP|(N=64,P=3)=(2p/2P)|(p=6,P=3)=2p-P|(p=6,P=3)=26-3=8.
Butterfly n=0 of N'P=NP/2=2p-P-1=26-3-1=4 butterflies indexed by n=0...N'P-1=0...3.
Even base index e = 2NPb = 2(8)(3) = 48.
Odd base index o = e + 2N'P = 48 + 2(4) = 56.
Twiddle step size s = 2P+1 = 23+1 = 16.
x[e+2n] ={x[e+2n]+x[o+2n]}>>1
x[48+0] ={x[48+0]+x[56+0]}>>1
x[48] ={x[48]+x[56]}>>1
={0000 +0000}>>1
={00000}>>1
=0000
x[e+2n+1] ={x[e+2n+1]+x[o+2n+1]}>>1
x[48+1] ={x[48+1]+x[56+1]}>>1
x[49] ={x[49]+x[57]}>>1
={0000 +0000}>>1
={00000}>>1
=0000
x[o+2n] = {(x[o+2n]-x[e+2n])t[sn]-(x[e+2n+1]-x[o+2n+1])t[sn+1]}>>1
x[56+2(0)] = {(x[56+2(0)]-x[48+2(0)])t[(16)(0)]-(x[48+2(0)+1]-x[56+2(0)+1])t[(16)(0)+1]}>>1
x[56+0] = {(x[56+0]-x[48+0])t[0]-(x[48+0+1]-x[56+0+1])t[0+1]}>>1
x[56] = {(x[56]-x[48])t[0]-(x[49]-x[57])t[1]}>>1
= {(0000-0000)8000-(0000-0000)0000}>>1
= {(00000)8000-(00000)0000}>>1
= {00000 - 00000}>>1
= {00000}>>1
= 0000
x[o+2n+1] = {(x[o+2n+1]-x[e+2n+1])t[sn]+(x[e+2n]-x[o+2n])t[sn+1]}>>1
x[56+2(0)+1] = {(x[56+2(0)+1]-x[48+2(0)+1])t[(16)(0)]+(x[48+2(0)]-x[56+2(0)])t[(16)(0)+1]}>>1
x[56+1] = {(x[56+1]-x[48+1])t[0]+(x[48+0]-x[56+0])t[0+1]}>>1
x[57] = {(x[57]-x[49])t[0]+(x[48]-x[56])t[1]}>>1
= {(0000-0000)8000+(0000-0000)0000}>>1
= {(00000)8000+(00000)0000}>>1
= {00000+00000}>>1
= {00000}>>1
= 0000



Return to Table of Contents




(P,b,n)=(3,3,1)
Loop P=3 of p=log2N=log264=6 loops indexed P=0...p-1=0...6-1=0...5.
Subblock b=3 of BP=B3=2P=23=8 subblocks, indexed b=0...B3-1=0...7.
Subblock size=NP|P=3=N3=N/BP|(N=64,P=3)=(2p/2P)|(p=6,P=3)=2p-P|(p=6,P=3)=26-3=8.
Butterfly n=1 of N'P=NP/2=2p-P-1=26-3-1=4 butterflies indexed by n=0...N'P-1=0...3.
Even base index e = 2NPb = 2(8)(3) = 48.
Odd base index o = e + 2N'P = 48 + 2(4) = 56.
Twiddle step size s = 2P+1 = 23+1 = 16.
x[e+2n] ={x[e+2n]+x[o+2n]}>>1
x[48+2] ={x[48+2]+x[56+2]}>>1
x[50] ={x[50]+x[58]}>>1
={0000 +0000}>>1
={00000}>>1
=0000
x[e+2n+1] ={x[e+2n+1]+x[o+2n+1]}>>1
x[48+3] ={x[48+3]+x[56+3]}>>1
x[51] ={x[51]+x[59]}>>1
={0000 +0000}>>1
={00000}>>1
=0000
x[o+2n] = {(x[o+2n]-x[e+2n])t[sn]-(x[e+2n+1]-x[o+2n+1])t[sn+1]}>>1
x[56+2(1)] = {(x[56+2(1)]-x[48+2(1)])t[(16)(1)]-(x[48+2(1)+1]-x[56+2(1)+1])t[(16)(1)+1]}>>1
x[56+2] = {(x[56+2]-x[48+2])t[16]-(x[48+2+1]-x[56+2+1])t[16+1]}>>1
x[58] = {(x[58]-x[50])t[16]-(x[51]-x[59])t[17]}>>1
= {(0000-0000)a57d-(0000-0000)a57d}>>1
= {(00000)a57d-(00000)a57d}>>1
= {00000 - 00000}>>1
= {00000}>>1
= 0000
x[o+2n+1] = {(x[o+2n+1]-x[e+2n+1])t[sn]+(x[e+2n]-x[o+2n])t[sn+1]}>>1
x[56+2(1)+1] = {(x[56+2(1)+1]-x[48+2(1)+1])t[(16)(1)]+(x[48+2(1)]-x[56+2(1)])t[(16)(1)+1]}>>1
x[56+3] = {(x[56+3]-x[48+3])t[16]+(x[48+2]-x[56+2])t[16+1]}>>1
x[59] = {(x[59]-x[51])t[16]+(x[50]-x[58])t[17]}>>1
= {(0000-0000)a57d+(0000-0000)a57d}>>1
= {(00000)a57d+(00000)a57d}>>1
= {00000+00000}>>1
= {00000}>>1
= 0000



Return to Table of Contents




(P,b,n)=(3,3,2)
Loop P=3 of p=log2N=log264=6 loops indexed P=0...p-1=0...6-1=0...5.
Subblock b=3 of BP=B3=2P=23=8 subblocks, indexed b=0...B3-1=0...7.
Subblock size=NP|P=3=N3=N/BP|(N=64,P=3)=(2p/2P)|(p=6,P=3)=2p-P|(p=6,P=3)=26-3=8.
Butterfly n=2 of N'P=NP/2=2p-P-1=26-3-1=4 butterflies indexed by n=0...N'P-1=0...3.
Even base index e = 2NPb = 2(8)(3) = 48.
Odd base index o = e + 2N'P = 48 + 2(4) = 56.
Twiddle step size s = 2P+1 = 23+1 = 16.
x[e+2n] ={x[e+2n]+x[o+2n]}>>1
x[48+4] ={x[48+4]+x[56+4]}>>1
x[52] ={x[52]+x[60]}>>1
={0000 +0000}>>1
={00000}>>1
=0000
x[e+2n+1] ={x[e+2n+1]+x[o+2n+1]}>>1
x[48+5] ={x[48+5]+x[56+5]}>>1
x[53] ={x[53]+x[61]}>>1
={0000 +0000}>>1
={00000}>>1
=0000
x[o+2n] = {(x[o+2n]-x[e+2n])t[sn]-(x[e+2n+1]-x[o+2n+1])t[sn+1]}>>1
x[56+2(2)] = {(x[56+2(2)]-x[48+2(2)])t[(16)(2)]-(x[48+2(2)+1]-x[56+2(2)+1])t[(16)(2)+1]}>>1
x[56+4] = {(x[56+4]-x[48+4])t[32]-(x[48+4+1]-x[56+4+1])t[32+1]}>>1
x[60] = {(x[60]-x[52])t[32]-(x[53]-x[61])t[33]}>>1
= {(0000-0000)ffff-(0000-0000)8000}>>1
= {(00000)ffff-(00000)8000}>>1
= {00000 - 00000}>>1
= {00000}>>1
= 0000
x[o+2n+1] = {(x[o+2n+1]-x[e+2n+1])t[sn]+(x[e+2n]-x[o+2n])t[sn+1]}>>1
x[56+2(2)+1] = {(x[56+2(2)+1]-x[48+2(2)+1])t[(16)(2)]+(x[48+2(2)]-x[56+2(2)])t[(16)(2)+1]}>>1
x[56+5] = {(x[56+5]-x[48+5])t[32]+(x[48+4]-x[56+4])t[32+1]}>>1
x[61] = {(x[61]-x[53])t[32]+(x[52]-x[60])t[33]}>>1
= {(0000-0000)ffff+(0000-0000)8000}>>1
= {(00000)ffff+(00000)8000}>>1
= {00000+00000}>>1
= {00000}>>1
= 0000



Return to Table of Contents




(P,b,n)=(3,3,3)
Loop P=3 of p=log2N=log264=6 loops indexed P=0...p-1=0...6-1=0...5.
Subblock b=3 of BP=B3=2P=23=8 subblocks, indexed b=0...B3-1=0...7.
Subblock size=NP|P=3=N3=N/BP|(N=64,P=3)=(2p/2P)|(p=6,P=3)=2p-P|(p=6,P=3)=26-3=8.
Butterfly n=3 of N'P=NP/2=2p-P-1=26-3-1=4 butterflies indexed by n=0...N'P-1=0...3.
Even base index e = 2NPb = 2(8)(3) = 48.
Odd base index o = e + 2N'P = 48 + 2(4) = 56.
Twiddle step size s = 2P+1 = 23+1 = 16.
x[e+2n] ={x[e+2n]+x[o+2n]}>>1
x[48+6] ={x[48+6]+x[56+6]}>>1
x[54] ={x[54]+x[62]}>>1
={0000 +0000}>>1
={00000}>>1
=0000
x[e+2n+1] ={x[e+2n+1]+x[o+2n+1]}>>1
x[48+7] ={x[48+7]+x[56+7]}>>1
x[55] ={x[55]+x[63]}>>1
={0000 +0000}>>1
={00000}>>1
=0000
x[o+2n] = {(x[o+2n]-x[e+2n])t[sn]-(x[e+2n+1]-x[o+2n+1])t[sn+1]}>>1
x[56+2(3)] = {(x[56+2(3)]-x[48+2(3)])t[(16)(3)]-(x[48+2(3)+1]-x[56+2(3)+1])t[(16)(3)+1]}>>1
x[56+6] = {(x[56+6]-x[48+6])t[48]-(x[48+6+1]-x[56+6+1])t[48+1]}>>1
x[62] = {(x[62]-x[54])t[48]-(x[55]-x[63])t[49]}>>1
= {(0000-0000)5a82-(0000-0000)a57d}>>1
= {(00000)5a82-(00000)a57d}>>1
= {00000 - 00000}>>1
= {00000}>>1
= 0000
x[o+2n+1] = {(x[o+2n+1]-x[e+2n+1])t[sn]+(x[e+2n]-x[o+2n])t[sn+1]}>>1
x[56+2(3)+1] = {(x[56+2(3)+1]-x[48+2(3)+1])t[(16)(3)]+(x[48+2(3)]-x[56+2(3)])t[(16)(3)+1]}>>1
x[56+7] = {(x[56+7]-x[48+7])t[48]+(x[48+6]-x[56+6])t[48+1]}>>1
x[63] = {(x[63]-x[55])t[48]+(x[54]-x[62])t[49]}>>1
= {(0000-0000)5a82+(0000-0000)a57d}>>1
= {(00000)5a82+(00000)a57d}>>1
= {00000+00000}>>1
= {00000}>>1
= 0000



Return to Table of Contents




(P,b,n)=(3,4,0)
Loop P=3 of p=log2N=log264=6 loops indexed P=0...p-1=0...6-1=0...5.
Subblock b=4 of BP=B3=2P=23=8 subblocks, indexed b=0...B3-1=0...7.
Subblock size=NP|P=3=N3=N/BP|(N=64,P=3)=(2p/2P)|(p=6,P=3)=2p-P|(p=6,P=3)=26-3=8.
Butterfly n=0 of N'P=NP/2=2p-P-1=26-3-1=4 butterflies indexed by n=0...N'P-1=0...3.
Even base index e = 2NPb = 2(8)(4) = 64.
Odd base index o = e + 2N'P = 64 + 2(4) = 72.
Twiddle step size s = 2P+1 = 23+1 = 16.
x[e+2n] ={x[e+2n]+x[o+2n]}>>1
x[64+0] ={x[64+0]+x[72+0]}>>1
x[64] ={x[64]+x[72]}>>1
={0000 +0000}>>1
={00000}>>1
=0000
x[e+2n+1] ={x[e+2n+1]+x[o+2n+1]}>>1
x[64+1] ={x[64+1]+x[72+1]}>>1
x[65] ={x[65]+x[73]}>>1
={0000 +0000}>>1
={00000}>>1
=0000
x[o+2n] = {(x[o+2n]-x[e+2n])t[sn]-(x[e+2n+1]-x[o+2n+1])t[sn+1]}>>1
x[72+2(0)] = {(x[72+2(0)]-x[64+2(0)])t[(16)(0)]-(x[64+2(0)+1]-x[72+2(0)+1])t[(16)(0)+1]}>>1
x[72+0] = {(x[72+0]-x[64+0])t[0]-(x[64+0+1]-x[72+0+1])t[0+1]}>>1
x[72] = {(x[72]-x[64])t[0]-(x[65]-x[73])t[1]}>>1
= {(0000-0000)8000-(0000-0000)0000}>>1
= {(00000)8000-(00000)0000}>>1
= {00000 - 00000}>>1
= {00000}>>1
= 0000
x[o+2n+1] = {(x[o+2n+1]-x[e+2n+1])t[sn]+(x[e+2n]-x[o+2n])t[sn+1]}>>1
x[72+2(0)+1] = {(x[72+2(0)+1]-x[64+2(0)+1])t[(16)(0)]+(x[64+2(0)]-x[72+2(0)])t[(16)(0)+1]}>>1
x[72+1] = {(x[72+1]-x[64+1])t[0]+(x[64+0]-x[72+0])t[0+1]}>>1
x[73] = {(x[73]-x[65])t[0]+(x[64]-x[72])t[1]}>>1
= {(0000-0000)8000+(0000-0000)0000}>>1
= {(00000)8000+(00000)0000}>>1
= {00000+00000}>>1
= {00000}>>1
= 0000



Return to Table of Contents




(P,b,n)=(3,4,1)
Loop P=3 of p=log2N=log264=6 loops indexed P=0...p-1=0...6-1=0...5.
Subblock b=4 of BP=B3=2P=23=8 subblocks, indexed b=0...B3-1=0...7.
Subblock size=NP|P=3=N3=N/BP|(N=64,P=3)=(2p/2P)|(p=6,P=3)=2p-P|(p=6,P=3)=26-3=8.
Butterfly n=1 of N'P=NP/2=2p-P-1=26-3-1=4 butterflies indexed by n=0...N'P-1=0...3.
Even base index e = 2NPb = 2(8)(4) = 64.
Odd base index o = e + 2N'P = 64 + 2(4) = 72.
Twiddle step size s = 2P+1 = 23+1 = 16.
x[e+2n] ={x[e+2n]+x[o+2n]}>>1
x[64+2] ={x[64+2]+x[72+2]}>>1
x[66] ={x[66]+x[74]}>>1
={0000 +0000}>>1
={00000}>>1
=0000
x[e+2n+1] ={x[e+2n+1]+x[o+2n+1]}>>1
x[64+3] ={x[64+3]+x[72+3]}>>1
x[67] ={x[67]+x[75]}>>1
={0000 +0000}>>1
={00000}>>1
=0000
x[o+2n] = {(x[o+2n]-x[e+2n])t[sn]-(x[e+2n+1]-x[o+2n+1])t[sn+1]}>>1
x[72+2(1)] = {(x[72+2(1)]-x[64+2(1)])t[(16)(1)]-(x[64+2(1)+1]-x[72+2(1)+1])t[(16)(1)+1]}>>1
x[72+2] = {(x[72+2]-x[64+2])t[16]-(x[64+2+1]-x[72+2+1])t[16+1]}>>1
x[74] = {(x[74]-x[66])t[16]-(x[67]-x[75])t[17]}>>1
= {(0000-0000)a57d-(0000-0000)a57d}>>1
= {(00000)a57d-(00000)a57d}>>1
= {00000 - 00000}>>1
= {00000}>>1
= 0000
x[o+2n+1] = {(x[o+2n+1]-x[e+2n+1])t[sn]+(x[e+2n]-x[o+2n])t[sn+1]}>>1
x[72+2(1)+1] = {(x[72+2(1)+1]-x[64+2(1)+1])t[(16)(1)]+(x[64+2(1)]-x[72+2(1)])t[(16)(1)+1]}>>1
x[72+3] = {(x[72+3]-x[64+3])t[16]+(x[64+2]-x[72+2])t[16+1]}>>1
x[75] = {(x[75]-x[67])t[16]+(x[66]-x[74])t[17]}>>1
= {(0000-0000)a57d+(0000-0000)a57d}>>1
= {(00000)a57d+(00000)a57d}>>1
= {00000+00000}>>1
= {00000}>>1
= 0000



Return to Table of Contents




(P,b,n)=(3,4,2)
Loop P=3 of p=log2N=log264=6 loops indexed P=0...p-1=0...6-1=0...5.
Subblock b=4 of BP=B3=2P=23=8 subblocks, indexed b=0...B3-1=0...7.
Subblock size=NP|P=3=N3=N/BP|(N=64,P=3)=(2p/2P)|(p=6,P=3)=2p-P|(p=6,P=3)=26-3=8.
Butterfly n=2 of N'P=NP/2=2p-P-1=26-3-1=4 butterflies indexed by n=0...N'P-1=0...3.
Even base index e = 2NPb = 2(8)(4) = 64.
Odd base index o = e + 2N'P = 64 + 2(4) = 72.
Twiddle step size s = 2P+1 = 23+1 = 16.
x[e+2n] ={x[e+2n]+x[o+2n]}>>1
x[64+4] ={x[64+4]+x[72+4]}>>1
x[68] ={x[68]+x[76]}>>1
={0000 +0000}>>1
={00000}>>1
=0000
x[e+2n+1] ={x[e+2n+1]+x[o+2n+1]}>>1
x[64+5] ={x[64+5]+x[72+5]}>>1
x[69] ={x[69]+x[77]}>>1
={0000 +0000}>>1
={00000}>>1
=0000
x[o+2n] = {(x[o+2n]-x[e+2n])t[sn]-(x[e+2n+1]-x[o+2n+1])t[sn+1]}>>1
x[72+2(2)] = {(x[72+2(2)]-x[64+2(2)])t[(16)(2)]-(x[64+2(2)+1]-x[72+2(2)+1])t[(16)(2)+1]}>>1
x[72+4] = {(x[72+4]-x[64+4])t[32]-(x[64+4+1]-x[72+4+1])t[32+1]}>>1
x[76] = {(x[76]-x[68])t[32]-(x[69]-x[77])t[33]}>>1
= {(0000-0000)ffff-(0000-0000)8000}>>1
= {(00000)ffff-(00000)8000}>>1
= {00000 - 00000}>>1
= {00000}>>1
= 0000
x[o+2n+1] = {(x[o+2n+1]-x[e+2n+1])t[sn]+(x[e+2n]-x[o+2n])t[sn+1]}>>1
x[72+2(2)+1] = {(x[72+2(2)+1]-x[64+2(2)+1])t[(16)(2)]+(x[64+2(2)]-x[72+2(2)])t[(16)(2)+1]}>>1
x[72+5] = {(x[72+5]-x[64+5])t[32]+(x[64+4]-x[72+4])t[32+1]}>>1
x[77] = {(x[77]-x[69])t[32]+(x[68]-x[76])t[33]}>>1
= {(0000-0000)ffff+(0000-0000)8000}>>1
= {(00000)ffff+(00000)8000}>>1
= {00000+00000}>>1
= {00000}>>1
= 0000



Return to Table of Contents




(P,b,n)=(3,4,3)
Loop P=3 of p=log2N=log264=6 loops indexed P=0...p-1=0...6-1=0...5.
Subblock b=4 of BP=B3=2P=23=8 subblocks, indexed b=0...B3-1=0...7.
Subblock size=NP|P=3=N3=N/BP|(N=64,P=3)=(2p/2P)|(p=6,P=3)=2p-P|(p=6,P=3)=26-3=8.
Butterfly n=3 of N'P=NP/2=2p-P-1=26-3-1=4 butterflies indexed by n=0...N'P-1=0...3.
Even base index e = 2NPb = 2(8)(4) = 64.
Odd base index o = e + 2N'P = 64 + 2(4) = 72.
Twiddle step size s = 2P+1 = 23+1 = 16.
x[e+2n] ={x[e+2n]+x[o+2n]}>>1
x[64+6] ={x[64+6]+x[72+6]}>>1
x[70] ={x[70]+x[78]}>>1
={0000 +0000}>>1
={00000}>>1
=0000
x[e+2n+1] ={x[e+2n+1]+x[o+2n+1]}>>1
x[64+7] ={x[64+7]+x[72+7]}>>1
x[71] ={x[71]+x[79]}>>1
={0000 +0000}>>1
={00000}>>1
=0000
x[o+2n] = {(x[o+2n]-x[e+2n])t[sn]-(x[e+2n+1]-x[o+2n+1])t[sn+1]}>>1
x[72+2(3)] = {(x[72+2(3)]-x[64+2(3)])t[(16)(3)]-(x[64+2(3)+1]-x[72+2(3)+1])t[(16)(3)+1]}>>1
x[72+6] = {(x[72+6]-x[64+6])t[48]-(x[64+6+1]-x[72+6+1])t[48+1]}>>1
x[78] = {(x[78]-x[70])t[48]-(x[71]-x[79])t[49]}>>1
= {(0000-0000)5a82-(0000-0000)a57d}>>1
= {(00000)5a82-(00000)a57d}>>1
= {00000 - 00000}>>1
= {00000}>>1
= 0000
x[o+2n+1] = {(x[o+2n+1]-x[e+2n+1])t[sn]+(x[e+2n]-x[o+2n])t[sn+1]}>>1
x[72+2(3)+1] = {(x[72+2(3)+1]-x[64+2(3)+1])t[(16)(3)]+(x[64+2(3)]-x[72+2(3)])t[(16)(3)+1]}>>1
x[72+7] = {(x[72+7]-x[64+7])t[48]+(x[64+6]-x[72+6])t[48+1]}>>1
x[79] = {(x[79]-x[71])t[48]+(x[70]-x[78])t[49]}>>1
= {(0000-0000)5a82+(0000-0000)a57d}>>1
= {(00000)5a82+(00000)a57d}>>1
= {00000+00000}>>1
= {00000}>>1
= 0000



Return to Table of Contents




(P,b,n)=(3,5,0)
Loop P=3 of p=log2N=log264=6 loops indexed P=0...p-1=0...6-1=0...5.
Subblock b=5 of BP=B3=2P=23=8 subblocks, indexed b=0...B3-1=0...7.
Subblock size=NP|P=3=N3=N/BP|(N=64,P=3)=(2p/2P)|(p=6,P=3)=2p-P|(p=6,P=3)=26-3=8.
Butterfly n=0 of N'P=NP/2=2p-P-1=26-3-1=4 butterflies indexed by n=0...N'P-1=0...3.
Even base index e = 2NPb = 2(8)(5) = 80.
Odd base index o = e + 2N'P = 80 + 2(4) = 88.
Twiddle step size s = 2P+1 = 23+1 = 16.
x[e+2n] ={x[e+2n]+x[o+2n]}>>1
x[80+0] ={x[80+0]+x[88+0]}>>1
x[80] ={x[80]+x[88]}>>1
={0000 +0000}>>1
={00000}>>1
=0000
x[e+2n+1] ={x[e+2n+1]+x[o+2n+1]}>>1
x[80+1] ={x[80+1]+x[88+1]}>>1
x[81] ={x[81]+x[89]}>>1
={0000 +0000}>>1
={00000}>>1
=0000
x[o+2n] = {(x[o+2n]-x[e+2n])t[sn]-(x[e+2n+1]-x[o+2n+1])t[sn+1]}>>1
x[88+2(0)] = {(x[88+2(0)]-x[80+2(0)])t[(16)(0)]-(x[80+2(0)+1]-x[88+2(0)+1])t[(16)(0)+1]}>>1
x[88+0] = {(x[88+0]-x[80+0])t[0]-(x[80+0+1]-x[88+0+1])t[0+1]}>>1
x[88] = {(x[88]-x[80])t[0]-(x[81]-x[89])t[1]}>>1
= {(0000-0000)8000-(0000-0000)0000}>>1
= {(00000)8000-(00000)0000}>>1
= {00000 - 00000}>>1
= {00000}>>1
= 0000
x[o+2n+1] = {(x[o+2n+1]-x[e+2n+1])t[sn]+(x[e+2n]-x[o+2n])t[sn+1]}>>1
x[88+2(0)+1] = {(x[88+2(0)+1]-x[80+2(0)+1])t[(16)(0)]+(x[80+2(0)]-x[88+2(0)])t[(16)(0)+1]}>>1
x[88+1] = {(x[88+1]-x[80+1])t[0]+(x[80+0]-x[88+0])t[0+1]}>>1
x[89] = {(x[89]-x[81])t[0]+(x[80]-x[88])t[1]}>>1
= {(0000-0000)8000+(0000-0000)0000}>>1
= {(00000)8000+(00000)0000}>>1
= {00000+00000}>>1
= {00000}>>1
= 0000



Return to Table of Contents




(P,b,n)=(3,5,1)
Loop P=3 of p=log2N=log264=6 loops indexed P=0...p-1=0...6-1=0...5.
Subblock b=5 of BP=B3=2P=23=8 subblocks, indexed b=0...B3-1=0...7.
Subblock size=NP|P=3=N3=N/BP|(N=64,P=3)=(2p/2P)|(p=6,P=3)=2p-P|(p=6,P=3)=26-3=8.
Butterfly n=1 of N'P=NP/2=2p-P-1=26-3-1=4 butterflies indexed by n=0...N'P-1=0...3.
Even base index e = 2NPb = 2(8)(5) = 80.
Odd base index o = e + 2N'P = 80 + 2(4) = 88.
Twiddle step size s = 2P+1 = 23+1 = 16.
x[e+2n] ={x[e+2n]+x[o+2n]}>>1
x[80+2] ={x[80+2]+x[88+2]}>>1
x[82] ={x[82]+x[90]}>>1
={0000 +0000}>>1
={00000}>>1
=0000
x[e+2n+1] ={x[e+2n+1]+x[o+2n+1]}>>1
x[80+3] ={x[80+3]+x[88+3]}>>1
x[83] ={x[83]+x[91]}>>1
={0000 +0000}>>1
={00000}>>1
=0000
x[o+2n] = {(x[o+2n]-x[e+2n])t[sn]-(x[e+2n+1]-x[o+2n+1])t[sn+1]}>>1
x[88+2(1)] = {(x[88+2(1)]-x[80+2(1)])t[(16)(1)]-(x[80+2(1)+1]-x[88+2(1)+1])t[(16)(1)+1]}>>1
x[88+2] = {(x[88+2]-x[80+2])t[16]-(x[80+2+1]-x[88+2+1])t[16+1]}>>1
x[90] = {(x[90]-x[82])t[16]-(x[83]-x[91])t[17]}>>1
= {(0000-0000)a57d-(0000-0000)a57d}>>1
= {(00000)a57d-(00000)a57d}>>1
= {00000 - 00000}>>1
= {00000}>>1
= 0000
x[o+2n+1] = {(x[o+2n+1]-x[e+2n+1])t[sn]+(x[e+2n]-x[o+2n])t[sn+1]}>>1
x[88+2(1)+1] = {(x[88+2(1)+1]-x[80+2(1)+1])t[(16)(1)]+(x[80+2(1)]-x[88+2(1)])t[(16)(1)+1]}>>1
x[88+3] = {(x[88+3]-x[80+3])t[16]+(x[80+2]-x[88+2])t[16+1]}>>1
x[91] = {(x[91]-x[83])t[16]+(x[82]-x[90])t[17]}>>1
= {(0000-0000)a57d+(0000-0000)a57d}>>1
= {(00000)a57d+(00000)a57d}>>1
= {00000+00000}>>1
= {00000}>>1
= 0000



Return to Table of Contents




(P,b,n)=(3,5,2)
Loop P=3 of p=log2N=log264=6 loops indexed P=0...p-1=0...6-1=0...5.
Subblock b=5 of BP=B3=2P=23=8 subblocks, indexed b=0...B3-1=0...7.
Subblock size=NP|P=3=N3=N/BP|(N=64,P=3)=(2p/2P)|(p=6,P=3)=2p-P|(p=6,P=3)=26-3=8.
Butterfly n=2 of N'P=NP/2=2p-P-1=26-3-1=4 butterflies indexed by n=0...N'P-1=0...3.
Even base index e = 2NPb = 2(8)(5) = 80.
Odd base index o = e + 2N'P = 80 + 2(4) = 88.
Twiddle step size s = 2P+1 = 23+1 = 16.
x[e+2n] ={x[e+2n]+x[o+2n]}>>1
x[80+4] ={x[80+4]+x[88+4]}>>1
x[84] ={x[84]+x[92]}>>1
={0000 +0000}>>1
={00000}>>1
=0000
x[e+2n+1] ={x[e+2n+1]+x[o+2n+1]}>>1
x[80+5] ={x[80+5]+x[88+5]}>>1
x[85] ={x[85]+x[93]}>>1
={0000 +0000}>>1
={00000}>>1
=0000
x[o+2n] = {(x[o+2n]-x[e+2n])t[sn]-(x[e+2n+1]-x[o+2n+1])t[sn+1]}>>1
x[88+2(2)] = {(x[88+2(2)]-x[80+2(2)])t[(16)(2)]-(x[80+2(2)+1]-x[88+2(2)+1])t[(16)(2)+1]}>>1
x[88+4] = {(x[88+4]-x[80+4])t[32]-(x[80+4+1]-x[88+4+1])t[32+1]}>>1
x[92] = {(x[92]-x[84])t[32]-(x[85]-x[93])t[33]}>>1
= {(0000-0000)ffff-(0000-0000)8000}>>1
= {(00000)ffff-(00000)8000}>>1
= {00000 - 00000}>>1
= {00000}>>1
= 0000
x[o+2n+1] = {(x[o+2n+1]-x[e+2n+1])t[sn]+(x[e+2n]-x[o+2n])t[sn+1]}>>1
x[88+2(2)+1] = {(x[88+2(2)+1]-x[80+2(2)+1])t[(16)(2)]+(x[80+2(2)]-x[88+2(2)])t[(16)(2)+1]}>>1
x[88+5] = {(x[88+5]-x[80+5])t[32]+(x[80+4]-x[88+4])t[32+1]}>>1
x[93] = {(x[93]-x[85])t[32]+(x[84]-x[92])t[33]}>>1
= {(0000-0000)ffff+(0000-0000)8000}>>1
= {(00000)ffff+(00000)8000}>>1
= {00000+00000}>>1
= {00000}>>1
= 0000



Return to Table of Contents




(P,b,n)=(3,5,3)
Loop P=3 of p=log2N=log264=6 loops indexed P=0...p-1=0...6-1=0...5.
Subblock b=5 of BP=B3=2P=23=8 subblocks, indexed b=0...B3-1=0...7.
Subblock size=NP|P=3=N3=N/BP|(N=64,P=3)=(2p/2P)|(p=6,P=3)=2p-P|(p=6,P=3)=26-3=8.
Butterfly n=3 of N'P=NP/2=2p-P-1=26-3-1=4 butterflies indexed by n=0...N'P-1=0...3.
Even base index e = 2NPb = 2(8)(5) = 80.
Odd base index o = e + 2N'P = 80 + 2(4) = 88.
Twiddle step size s = 2P+1 = 23+1 = 16.
x[e+2n] ={x[e+2n]+x[o+2n]}>>1
x[80+6] ={x[80+6]+x[88+6]}>>1
x[86] ={x[86]+x[94]}>>1
={0000 +0000}>>1
={00000}>>1
=0000
x[e+2n+1] ={x[e+2n+1]+x[o+2n+1]}>>1
x[80+7] ={x[80+7]+x[88+7]}>>1
x[87] ={x[87]+x[95]}>>1
={0000 +0000}>>1
={00000}>>1
=0000
x[o+2n] = {(x[o+2n]-x[e+2n])t[sn]-(x[e+2n+1]-x[o+2n+1])t[sn+1]}>>1
x[88+2(3)] = {(x[88+2(3)]-x[80+2(3)])t[(16)(3)]-(x[80+2(3)+1]-x[88+2(3)+1])t[(16)(3)+1]}>>1
x[88+6] = {(x[88+6]-x[80+6])t[48]-(x[80+6+1]-x[88+6+1])t[48+1]}>>1
x[94] = {(x[94]-x[86])t[48]-(x[87]-x[95])t[49]}>>1
= {(0000-0000)5a82-(0000-0000)a57d}>>1
= {(00000)5a82-(00000)a57d}>>1
= {00000 - 00000}>>1
= {00000}>>1
= 0000
x[o+2n+1] = {(x[o+2n+1]-x[e+2n+1])t[sn]+(x[e+2n]-x[o+2n])t[sn+1]}>>1
x[88+2(3)+1] = {(x[88+2(3)+1]-x[80+2(3)+1])t[(16)(3)]+(x[80+2(3)]-x[88+2(3)])t[(16)(3)+1]}>>1
x[88+7] = {(x[88+7]-x[80+7])t[48]+(x[80+6]-x[88+6])t[48+1]}>>1
x[95] = {(x[95]-x[87])t[48]+(x[86]-x[94])t[49]}>>1
= {(0000-0000)5a82+(0000-0000)a57d}>>1
= {(00000)5a82+(00000)a57d}>>1
= {00000+00000}>>1
= {00000}>>1
= 0000



Return to Table of Contents




(P,b,n)=(3,6,0)
Loop P=3 of p=log2N=log264=6 loops indexed P=0...p-1=0...6-1=0...5.
Subblock b=6 of BP=B3=2P=23=8 subblocks, indexed b=0...B3-1=0...7.
Subblock size=NP|P=3=N3=N/BP|(N=64,P=3)=(2p/2P)|(p=6,P=3)=2p-P|(p=6,P=3)=26-3=8.
Butterfly n=0 of N'P=NP/2=2p-P-1=26-3-1=4 butterflies indexed by n=0...N'P-1=0...3.
Even base index e = 2NPb = 2(8)(6) = 96.
Odd base index o = e + 2N'P = 96 + 2(4) = 104.
Twiddle step size s = 2P+1 = 23+1 = 16.
x[e+2n] ={x[e+2n]+x[o+2n]}>>1
x[96+0] ={x[96+0]+x[104+0]}>>1
x[96] ={x[96]+x[104]}>>1
={0000 +0000}>>1
={00000}>>1
=0000
x[e+2n+1] ={x[e+2n+1]+x[o+2n+1]}>>1
x[96+1] ={x[96+1]+x[104+1]}>>1
x[97] ={x[97]+x[105]}>>1
={0000 +0000}>>1
={00000}>>1
=0000
x[o+2n] = {(x[o+2n]-x[e+2n])t[sn]-(x[e+2n+1]-x[o+2n+1])t[sn+1]}>>1
x[104+2(0)] = {(x[104+2(0)]-x[96+2(0)])t[(16)(0)]-(x[96+2(0)+1]-x[104+2(0)+1])t[(16)(0)+1]}>>1
x[104+0] = {(x[104+0]-x[96+0])t[0]-(x[96+0+1]-x[104+0+1])t[0+1]}>>1
x[104] = {(x[104]-x[96])t[0]-(x[97]-x[105])t[1]}>>1
= {(0000-0000)8000-(0000-0000)0000}>>1
= {(00000)8000-(00000)0000}>>1
= {00000 - 00000}>>1
= {00000}>>1
= 0000
x[o+2n+1] = {(x[o+2n+1]-x[e+2n+1])t[sn]+(x[e+2n]-x[o+2n])t[sn+1]}>>1
x[104+2(0)+1] = {(x[104+2(0)+1]-x[96+2(0)+1])t[(16)(0)]+(x[96+2(0)]-x[104+2(0)])t[(16)(0)+1]}>>1
x[104+1] = {(x[104+1]-x[96+1])t[0]+(x[96+0]-x[104+0])t[0+1]}>>1
x[105] = {(x[105]-x[97])t[0]+(x[96]-x[104])t[1]}>>1
= {(0000-0000)8000+(0000-0000)0000}>>1
= {(00000)8000+(00000)0000}>>1
= {00000+00000}>>1
= {00000}>>1
= 0000



Return to Table of Contents




(P,b,n)=(3,6,1)
Loop P=3 of p=log2N=log264=6 loops indexed P=0...p-1=0...6-1=0...5.
Subblock b=6 of BP=B3=2P=23=8 subblocks, indexed b=0...B3-1=0...7.
Subblock size=NP|P=3=N3=N/BP|(N=64,P=3)=(2p/2P)|(p=6,P=3)=2p-P|(p=6,P=3)=26-3=8.
Butterfly n=1 of N'P=NP/2=2p-P-1=26-3-1=4 butterflies indexed by n=0...N'P-1=0...3.
Even base index e = 2NPb = 2(8)(6) = 96.
Odd base index o = e + 2N'P = 96 + 2(4) = 104.
Twiddle step size s = 2P+1 = 23+1 = 16.
x[e+2n] ={x[e+2n]+x[o+2n]}>>1
x[96+2] ={x[96+2]+x[104+2]}>>1
x[98] ={x[98]+x[106]}>>1
={0000 +0000}>>1
={00000}>>1
=0000
x[e+2n+1] ={x[e+2n+1]+x[o+2n+1]}>>1
x[96+3] ={x[96+3]+x[104+3]}>>1
x[99] ={x[99]+x[107]}>>1
={0000 +0000}>>1
={00000}>>1
=0000
x[o+2n] = {(x[o+2n]-x[e+2n])t[sn]-(x[e+2n+1]-x[o+2n+1])t[sn+1]}>>1
x[104+2(1)] = {(x[104+2(1)]-x[96+2(1)])t[(16)(1)]-(x[96+2(1)+1]-x[104+2(1)+1])t[(16)(1)+1]}>>1
x[104+2] = {(x[104+2]-x[96+2])t[16]-(x[96+2+1]-x[104+2+1])t[16+1]}>>1
x[106] = {(x[106]-x[98])t[16]-(x[99]-x[107])t[17]}>>1
= {(0000-0000)a57d-(0000-0000)a57d}>>1
= {(00000)a57d-(00000)a57d}>>1
= {00000 - 00000}>>1
= {00000}>>1
= 0000
x[o+2n+1] = {(x[o+2n+1]-x[e+2n+1])t[sn]+(x[e+2n]-x[o+2n])t[sn+1]}>>1
x[104+2(1)+1] = {(x[104+2(1)+1]-x[96+2(1)+1])t[(16)(1)]+(x[96+2(1)]-x[104+2(1)])t[(16)(1)+1]}>>1
x[104+3] = {(x[104+3]-x[96+3])t[16]+(x[96+2]-x[104+2])t[16+1]}>>1
x[107] = {(x[107]-x[99])t[16]+(x[98]-x[106])t[17]}>>1
= {(0000-0000)a57d+(0000-0000)a57d}>>1
= {(00000)a57d+(00000)a57d}>>1
= {00000+00000}>>1
= {00000}>>1
= 0000



Return to Table of Contents




(P,b,n)=(3,6,2)
Loop P=3 of p=log2N=log264=6 loops indexed P=0...p-1=0...6-1=0...5.
Subblock b=6 of BP=B3=2P=23=8 subblocks, indexed b=0...B3-1=0...7.
Subblock size=NP|P=3=N3=N/BP|(N=64,P=3)=(2p/2P)|(p=6,P=3)=2p-P|(p=6,P=3)=26-3=8.
Butterfly n=2 of N'P=NP/2=2p-P-1=26-3-1=4 butterflies indexed by n=0...N'P-1=0...3.
Even base index e = 2NPb = 2(8)(6) = 96.
Odd base index o = e + 2N'P = 96 + 2(4) = 104.
Twiddle step size s = 2P+1 = 23+1 = 16.
x[e+2n] ={x[e+2n]+x[o+2n]}>>1
x[96+4] ={x[96+4]+x[104+4]}>>1
x[100] ={x[100]+x[108]}>>1
={0000 +0000}>>1
={00000}>>1
=0000
x[e+2n+1] ={x[e+2n+1]+x[o+2n+1]}>>1
x[96+5] ={x[96+5]+x[104+5]}>>1
x[101] ={x[101]+x[109]}>>1
={0000 +0000}>>1
={00000}>>1
=0000
x[o+2n] = {(x[o+2n]-x[e+2n])t[sn]-(x[e+2n+1]-x[o+2n+1])t[sn+1]}>>1
x[104+2(2)] = {(x[104+2(2)]-x[96+2(2)])t[(16)(2)]-(x[96+2(2)+1]-x[104+2(2)+1])t[(16)(2)+1]}>>1
x[104+4] = {(x[104+4]-x[96+4])t[32]-(x[96+4+1]-x[104+4+1])t[32+1]}>>1
x[108] = {(x[108]-x[100])t[32]-(x[101]-x[109])t[33]}>>1
= {(0000-0000)ffff-(0000-0000)8000}>>1
= {(00000)ffff-(00000)8000}>>1
= {00000 - 00000}>>1
= {00000}>>1
= 0000
x[o+2n+1] = {(x[o+2n+1]-x[e+2n+1])t[sn]+(x[e+2n]-x[o+2n])t[sn+1]}>>1
x[104+2(2)+1] = {(x[104+2(2)+1]-x[96+2(2)+1])t[(16)(2)]+(x[96+2(2)]-x[104+2(2)])t[(16)(2)+1]}>>1
x[104+5] = {(x[104+5]-x[96+5])t[32]+(x[96+4]-x[104+4])t[32+1]}>>1
x[109] = {(x[109]-x[101])t[32]+(x[100]-x[108])t[33]}>>1
= {(0000-0000)ffff+(0000-0000)8000}>>1
= {(00000)ffff+(00000)8000}>>1
= {00000+00000}>>1
= {00000}>>1
= 0000



Return to Table of Contents




(P,b,n)=(3,6,3)
Loop P=3 of p=log2N=log264=6 loops indexed P=0...p-1=0...6-1=0...5.
Subblock b=6 of BP=B3=2P=23=8 subblocks, indexed b=0...B3-1=0...7.
Subblock size=NP|P=3=N3=N/BP|(N=64,P=3)=(2p/2P)|(p=6,P=3)=2p-P|(p=6,P=3)=26-3=8.
Butterfly n=3 of N'P=NP/2=2p-P-1=26-3-1=4 butterflies indexed by n=0...N'P-1=0...3.
Even base index e = 2NPb = 2(8)(6) = 96.
Odd base index o = e + 2N'P = 96 + 2(4) = 104.
Twiddle step size s = 2P+1 = 23+1 = 16.
x[e+2n] ={x[e+2n]+x[o+2n]}>>1
x[96+6] ={x[96+6]+x[104+6]}>>1
x[102] ={x[102]+x[110]}>>1
={0000 +0000}>>1
={00000}>>1
=0000
x[e+2n+1] ={x[e+2n+1]+x[o+2n+1]}>>1
x[96+7] ={x[96+7]+x[104+7]}>>1
x[103] ={x[103]+x[111]}>>1
={0000 +0000}>>1
={00000}>>1
=0000
x[o+2n] = {(x[o+2n]-x[e+2n])t[sn]-(x[e+2n+1]-x[o+2n+1])t[sn+1]}>>1
x[104+2(3)] = {(x[104+2(3)]-x[96+2(3)])t[(16)(3)]-(x[96+2(3)+1]-x[104+2(3)+1])t[(16)(3)+1]}>>1
x[104+6] = {(x[104+6]-x[96+6])t[48]-(x[96+6+1]-x[104+6+1])t[48+1]}>>1
x[110] = {(x[110]-x[102])t[48]-(x[103]-x[111])t[49]}>>1
= {(0000-0000)5a82-(0000-0000)a57d}>>1
= {(00000)5a82-(00000)a57d}>>1
= {00000 - 00000}>>1
= {00000}>>1
= 0000
x[o+2n+1] = {(x[o+2n+1]-x[e+2n+1])t[sn]+(x[e+2n]-x[o+2n])t[sn+1]}>>1
x[104+2(3)+1] = {(x[104+2(3)+1]-x[96+2(3)+1])t[(16)(3)]+(x[96+2(3)]-x[104+2(3)])t[(16)(3)+1]}>>1
x[104+7] = {(x[104+7]-x[96+7])t[48]+(x[96+6]-x[104+6])t[48+1]}>>1
x[111] = {(x[111]-x[103])t[48]+(x[102]-x[110])t[49]}>>1
= {(0000-0000)5a82+(0000-0000)a57d}>>1
= {(00000)5a82+(00000)a57d}>>1
= {00000+00000}>>1
= {00000}>>1
= 0000



Return to Table of Contents




(P,b,n)=(3,7,0)
Loop P=3 of p=log2N=log264=6 loops indexed P=0...p-1=0...6-1=0...5.
Subblock b=7 of BP=B3=2P=23=8 subblocks, indexed b=0...B3-1=0...7.
Subblock size=NP|P=3=N3=N/BP|(N=64,P=3)=(2p/2P)|(p=6,P=3)=2p-P|(p=6,P=3)=26-3=8.
Butterfly n=0 of N'P=NP/2=2p-P-1=26-3-1=4 butterflies indexed by n=0...N'P-1=0...3.
Even base index e = 2NPb = 2(8)(7) = 112.
Odd base index o = e + 2N'P = 112 + 2(4) = 120.
Twiddle step size s = 2P+1 = 23+1 = 16.
x[e+2n] ={x[e+2n]+x[o+2n]}>>1
x[112+0] ={x[112+0]+x[120+0]}>>1
x[112] ={x[112]+x[120]}>>1
={0000 +0000}>>1
={00000}>>1
=0000
x[e+2n+1] ={x[e+2n+1]+x[o+2n+1]}>>1
x[112+1] ={x[112+1]+x[120+1]}>>1
x[113] ={x[113]+x[121]}>>1
={0000 +0000}>>1
={00000}>>1
=0000
x[o+2n] = {(x[o+2n]-x[e+2n])t[sn]-(x[e+2n+1]-x[o+2n+1])t[sn+1]}>>1
x[120+2(0)] = {(x[120+2(0)]-x[112+2(0)])t[(16)(0)]-(x[112+2(0)+1]-x[120+2(0)+1])t[(16)(0)+1]}>>1
x[120+0] = {(x[120+0]-x[112+0])t[0]-(x[112+0+1]-x[120+0+1])t[0+1]}>>1
x[120] = {(x[120]-x[112])t[0]-(x[113]-x[121])t[1]}>>1
= {(0000-0000)8000-(0000-0000)0000}>>1
= {(00000)8000-(00000)0000}>>1
= {00000 - 00000}>>1
= {00000}>>1
= 0000
x[o+2n+1] = {(x[o+2n+1]-x[e+2n+1])t[sn]+(x[e+2n]-x[o+2n])t[sn+1]}>>1
x[120+2(0)+1] = {(x[120+2(0)+1]-x[112+2(0)+1])t[(16)(0)]+(x[112+2(0)]-x[120+2(0)])t[(16)(0)+1]}>>1
x[120+1] = {(x[120+1]-x[112+1])t[0]+(x[112+0]-x[120+0])t[0+1]}>>1
x[121] = {(x[121]-x[113])t[0]+(x[112]-x[120])t[1]}>>1
= {(0000-0000)8000+(0000-0000)0000}>>1
= {(00000)8000+(00000)0000}>>1
= {00000+00000}>>1
= {00000}>>1
= 0000



Return to Table of Contents




(P,b,n)=(3,7,1)
Loop P=3 of p=log2N=log264=6 loops indexed P=0...p-1=0...6-1=0...5.
Subblock b=7 of BP=B3=2P=23=8 subblocks, indexed b=0...B3-1=0...7.
Subblock size=NP|P=3=N3=N/BP|(N=64,P=3)=(2p/2P)|(p=6,P=3)=2p-P|(p=6,P=3)=26-3=8.
Butterfly n=1 of N'P=NP/2=2p-P-1=26-3-1=4 butterflies indexed by n=0...N'P-1=0...3.
Even base index e = 2NPb = 2(8)(7) = 112.
Odd base index o = e + 2N'P = 112 + 2(4) = 120.
Twiddle step size s = 2P+1 = 23+1 = 16.
x[e+2n] ={x[e+2n]+x[o+2n]}>>1
x[112+2] ={x[112+2]+x[120+2]}>>1
x[114] ={x[114]+x[122]}>>1
={0000 +0000}>>1
={00000}>>1
=0000
x[e+2n+1] ={x[e+2n+1]+x[o+2n+1]}>>1
x[112+3] ={x[112+3]+x[120+3]}>>1
x[115] ={x[115]+x[123]}>>1
={0000 +0000}>>1
={00000}>>1
=0000
x[o+2n] = {(x[o+2n]-x[e+2n])t[sn]-(x[e+2n+1]-x[o+2n+1])t[sn+1]}>>1
x[120+2(1)] = {(x[120+2(1)]-x[112+2(1)])t[(16)(1)]-(x[112+2(1)+1]-x[120+2(1)+1])t[(16)(1)+1]}>>1
x[120+2] = {(x[120+2]-x[112+2])t[16]-(x[112+2+1]-x[120+2+1])t[16+1]}>>1
x[122] = {(x[122]-x[114])t[16]-(x[115]-x[123])t[17]}>>1
= {(0000-0000)a57d-(0000-0000)a57d}>>1
= {(00000)a57d-(00000)a57d}>>1
= {00000 - 00000}>>1
= {00000}>>1
= 0000
x[o+2n+1] = {(x[o+2n+1]-x[e+2n+1])t[sn]+(x[e+2n]-x[o+2n])t[sn+1]}>>1
x[120+2(1)+1] = {(x[120+2(1)+1]-x[112+2(1)+1])t[(16)(1)]+(x[112+2(1)]-x[120+2(1)])t[(16)(1)+1]}>>1
x[120+3] = {(x[120+3]-x[112+3])t[16]+(x[112+2]-x[120+2])t[16+1]}>>1
x[123] = {(x[123]-x[115])t[16]+(x[114]-x[122])t[17]}>>1
= {(0000-0000)a57d+(0000-0000)a57d}>>1
= {(00000)a57d+(00000)a57d}>>1
= {00000+00000}>>1
= {00000}>>1
= 0000



Return to Table of Contents




(P,b,n)=(3,7,2)
Loop P=3 of p=log2N=log264=6 loops indexed P=0...p-1=0...6-1=0...5.
Subblock b=7 of BP=B3=2P=23=8 subblocks, indexed b=0...B3-1=0...7.
Subblock size=NP|P=3=N3=N/BP|(N=64,P=3)=(2p/2P)|(p=6,P=3)=2p-P|(p=6,P=3)=26-3=8.
Butterfly n=2 of N'P=NP/2=2p-P-1=26-3-1=4 butterflies indexed by n=0...N'P-1=0...3.
Even base index e = 2NPb = 2(8)(7) = 112.
Odd base index o = e + 2N'P = 112 + 2(4) = 120.
Twiddle step size s = 2P+1 = 23+1 = 16.
x[e+2n] ={x[e+2n]+x[o+2n]}>>1
x[112+4] ={x[112+4]+x[120+4]}>>1
x[116] ={x[116]+x[124]}>>1
={0000 +0000}>>1
={00000}>>1
=0000
x[e+2n+1] ={x[e+2n+1]+x[o+2n+1]}>>1
x[112+5] ={x[112+5]+x[120+5]}>>1
x[117] ={x[117]+x[125]}>>1
={0000 +0000}>>1
={00000}>>1
=0000
x[o+2n] = {(x[o+2n]-x[e+2n])t[sn]-(x[e+2n+1]-x[o+2n+1])t[sn+1]}>>1
x[120+2(2)] = {(x[120+2(2)]-x[112+2(2)])t[(16)(2)]-(x[112+2(2)+1]-x[120+2(2)+1])t[(16)(2)+1]}>>1
x[120+4] = {(x[120+4]-x[112+4])t[32]-(x[112+4+1]-x[120+4+1])t[32+1]}>>1
x[124] = {(x[124]-x[116])t[32]-(x[117]-x[125])t[33]}>>1
= {(0000-0000)ffff-(0000-0000)8000}>>1
= {(00000)ffff-(00000)8000}>>1
= {00000 - 00000}>>1
= {00000}>>1
= 0000
x[o+2n+1] = {(x[o+2n+1]-x[e+2n+1])t[sn]+(x[e+2n]-x[o+2n])t[sn+1]}>>1
x[120+2(2)+1] = {(x[120+2(2)+1]-x[112+2(2)+1])t[(16)(2)]+(x[112+2(2)]-x[120+2(2)])t[(16)(2)+1]}>>1
x[120+5] = {(x[120+5]-x[112+5])t[32]+(x[112+4]-x[120+4])t[32+1]}>>1
x[125] = {(x[125]-x[117])t[32]+(x[116]-x[124])t[33]}>>1
= {(0000-0000)ffff+(0000-0000)8000}>>1
= {(00000)ffff+(00000)8000}>>1
= {00000+00000}>>1
= {00000}>>1
= 0000



Return to Table of Contents




(P,b,n)=(3,7,3)
Loop P=3 of p=log2N=log264=6 loops indexed P=0...p-1=0...6-1=0...5.
Subblock b=7 of BP=B3=2P=23=8 subblocks, indexed b=0...B3-1=0...7.
Subblock size=NP|P=3=N3=N/BP|(N=64,P=3)=(2p/2P)|(p=6,P=3)=2p-P|(p=6,P=3)=26-3=8.
Butterfly n=3 of N'P=NP/2=2p-P-1=26-3-1=4 butterflies indexed by n=0...N'P-1=0...3.
Even base index e = 2NPb = 2(8)(7) = 112.
Odd base index o = e + 2N'P = 112 + 2(4) = 120.
Twiddle step size s = 2P+1 = 23+1 = 16.
x[e+2n] ={x[e+2n]+x[o+2n]}>>1
x[112+6] ={x[112+6]+x[120+6]}>>1
x[118] ={x[118]+x[126]}>>1
={0000 +0000}>>1
={00000}>>1
=0000
x[e+2n+1] ={x[e+2n+1]+x[o+2n+1]}>>1
x[112+7] ={x[112+7]+x[120+7]}>>1
x[119] ={x[119]+x[127]}>>1
={0000 +0000}>>1
={00000}>>1
=0000
x[o+2n] = {(x[o+2n]-x[e+2n])t[sn]-(x[e+2n+1]-x[o+2n+1])t[sn+1]}>>1
x[120+2(3)] = {(x[120+2(3)]-x[112+2(3)])t[(16)(3)]-(x[112+2(3)+1]-x[120+2(3)+1])t[(16)(3)+1]}>>1
x[120+6] = {(x[120+6]-x[112+6])t[48]-(x[112+6+1]-x[120+6+1])t[48+1]}>>1
x[126] = {(x[126]-x[118])t[48]-(x[119]-x[127])t[49]}>>1
= {(0000-0000)5a82-(0000-0000)a57d}>>1
= {(00000)5a82-(00000)a57d}>>1
= {00000 - 00000}>>1
= {00000}>>1
= 0000
x[o+2n+1] = {(x[o+2n+1]-x[e+2n+1])t[sn]+(x[e+2n]-x[o+2n])t[sn+1]}>>1
x[120+2(3)+1] = {(x[120+2(3)+1]-x[112+2(3)+1])t[(16)(3)]+(x[112+2(3)]-x[120+2(3)])t[(16)(3)+1]}>>1
x[120+7] = {(x[120+7]-x[112+7])t[48]+(x[112+6]-x[120+6])t[48+1]}>>1
x[127] = {(x[127]-x[119])t[48]+(x[118]-x[126])t[49]}>>1
= {(0000-0000)5a82+(0000-0000)a57d}>>1
= {(00000)5a82+(00000)a57d}>>1
= {00000+00000}>>1
= {00000}>>1
= 0000



Return to Table of Contents



End of loop 3
x[0]=0000 x[1]=0000
x[2]=1000 x[3]=0000
x[4]=0000 x[5]=0000
x[6]=f000 x[7]=0000
x[8]=0000 x[9]=0000
x[10]=0000 x[11]=0000
x[12]=0000 x[13]=0000
x[14]=0000 x[15]=0000
x[16]=0000 x[17]=0000
x[18]=0000 x[19]=0000
x[20]=0000 x[21]=0000
x[22]=0000 x[23]=0000
x[24]=0000 x[25]=0000
x[26]=0000 x[27]=0000
x[28]=0000 x[29]=0000
x[30]=0000 x[31]=0000
x[32]=0000 x[33]=0000
x[34]=0000 x[35]=0000
x[36]=0000 x[37]=0000
x[38]=0000 x[39]=0000
x[40]=0000 x[41]=0000
x[42]=0000 x[43]=0000
x[44]=0000 x[45]=0000
x[46]=0000 x[47]=0000
x[48]=0000 x[49]=0000
x[50]=0000 x[51]=0000
x[52]=0000 x[53]=0000
x[54]=0000 x[55]=0000
x[56]=0000 x[57]=0000
x[58]=0000 x[59]=0000
x[60]=0000 x[61]=0000
x[62]=0000 x[63]=0000
x[64]=0000 x[65]=0000
x[66]=0000 x[67]=0000
x[68]=0000 x[69]=0000
x[70]=0000 x[71]=0000
x[72]=0000 x[73]=0000
x[74]=0000 x[75]=0000
x[76]=0000 x[77]=0000
x[78]=0000 x[79]=0000
x[80]=0000 x[81]=0000
x[82]=0000 x[83]=0000
x[84]=0000 x[85]=0000
x[86]=0000 x[87]=0000
x[88]=0000 x[89]=0000
x[90]=0000 x[91]=0000
x[92]=0000 x[93]=0000
x[94]=0000 x[95]=0000
x[96]=0000 x[97]=0000
x[98]=0000 x[99]=0000
x[100]=0000 x[101]=0000
x[102]=0000 x[103]=0000
x[104]=0000 x[105]=0000
x[106]=0000 x[107]=0000
x[108]=0000 x[109]=0000
x[110]=0000 x[111]=0000
x[112]=0000 x[113]=0000
x[114]=0000 x[115]=0000
x[116]=0000 x[117]=0000
x[118]=0000 x[119]=0000
x[120]=0000 x[121]=0000
x[122]=0000 x[123]=0000
x[124]=0000 x[125]=0000
x[126]=0000 x[127]=0000



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