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



John Bryan






(P,b,n)=(4,0,0)
Loop P=4 of p=log2N=log264=6 loops indexed P=0...p-1=0...6-1=0...5.
Subblock b=0 of BP=B4=2P=24=16 subblocks, indexed b=0...B4-1=0...15.
Subblock size=NP|P=4=N4=N/BP|(N=64,P=4)=(2p/2P)|(p=6,P=4)=2p-P|(p=6,P=4)=26-4=4.
Butterfly n=0 of N'P=NP/2=2p-P-1=26-4-1=2 butterflies indexed by n=0...N'P-1=0...1.
Even base index e = 2NPb = 2(4)(0) = 0.
Odd base index o = e + 2N'P = 0 + 2(2) = 4.
Twiddle step size s = 2P+1 = 24+1 = 32.
x[e+2n] ={x[e+2n]+x[o+2n]}>>1
x[0+0] ={x[0+0]+x[4+0]}>>1
x[0] ={x[0]+x[4]}>>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[4+1]}>>1
x[1] ={x[1]+x[5]}>>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[4+2(0)] = {(x[4+2(0)]-x[0+2(0)])t[(32)(0)]-(x[0+2(0)+1]-x[4+2(0)+1])t[(32)(0)+1]}>>1
x[4+0] = {(x[4+0]-x[0+0])t[0]-(x[0+0+1]-x[4+0+1])t[0+1]}>>1
x[4] = {(x[4]-x[0])t[0]-(x[1]-x[5])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[4+2(0)+1] = {(x[4+2(0)+1]-x[0+2(0)+1])t[(32)(0)]+(x[0+2(0)]-x[4+2(0)])t[(32)(0)+1]}>>1
x[4+1] = {(x[4+1]-x[0+1])t[0]+(x[0+0]-x[4+0])t[0+1]}>>1
x[5] = {(x[5]-x[1])t[0]+(x[0]-x[4])t[1]}>>1
= {(0000-0000)8000+(0000-0000)0000}>>1
= {(00000)8000+(00000)0000}>>1
= {00000+00000}>>1
= {00000}>>1
= 0000



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(P,b,n)=(4,0,1)
Loop P=4 of p=log2N=log264=6 loops indexed P=0...p-1=0...6-1=0...5.
Subblock b=0 of BP=B4=2P=24=16 subblocks, indexed b=0...B4-1=0...15.
Subblock size=NP|P=4=N4=N/BP|(N=64,P=4)=(2p/2P)|(p=6,P=4)=2p-P|(p=6,P=4)=26-4=4.
Butterfly n=1 of N'P=NP/2=2p-P-1=26-4-1=2 butterflies indexed by n=0...N'P-1=0...1.
Even base index e = 2NPb = 2(4)(0) = 0.
Odd base index o = e + 2N'P = 0 + 2(2) = 4.
Twiddle step size s = 2P+1 = 24+1 = 32.
x[e+2n] ={x[e+2n]+x[o+2n]}>>1
x[0+2] ={x[0+2]+x[4+2]}>>1
x[2] ={x[2]+x[6]}>>1
={1000 +f000}>>1
={00000}>>1
=0000
x[e+2n+1] ={x[e+2n+1]+x[o+2n+1]}>>1
x[0+3] ={x[0+3]+x[4+3]}>>1
x[3] ={x[3]+x[7]}>>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[4+2(1)] = {(x[4+2(1)]-x[0+2(1)])t[(32)(1)]-(x[0+2(1)+1]-x[4+2(1)+1])t[(32)(1)+1]}>>1
x[4+2] = {(x[4+2]-x[0+2])t[32]-(x[0+2+1]-x[4+2+1])t[32+1]}>>1
x[6] = {(x[6]-x[2])t[32]-(x[3]-x[7])t[33]}>>1
= {(f000-1000)ffff-(0000-0000)8000}>>1
= {(fe000)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[4+2(1)+1] = {(x[4+2(1)+1]-x[0+2(1)+1])t[(32)(1)]+(x[0+2(1)]-x[4+2(1)])t[(32)(1)+1]}>>1
x[4+3] = {(x[4+3]-x[0+3])t[32]+(x[0+2]-x[4+2])t[32+1]}>>1
x[7] = {(x[7]-x[3])t[32]+(x[2]-x[6])t[33]}>>1
= {(0000-0000)ffff+(1000-f000)8000}>>1
= {(00000)ffff+(02000)8000}>>1
= {00000+fc000}>>1
= {fc000}>>1
= e000



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(P,b,n)=(4,1,0)
Loop P=4 of p=log2N=log264=6 loops indexed P=0...p-1=0...6-1=0...5.
Subblock b=1 of BP=B4=2P=24=16 subblocks, indexed b=0...B4-1=0...15.
Subblock size=NP|P=4=N4=N/BP|(N=64,P=4)=(2p/2P)|(p=6,P=4)=2p-P|(p=6,P=4)=26-4=4.
Butterfly n=0 of N'P=NP/2=2p-P-1=26-4-1=2 butterflies indexed by n=0...N'P-1=0...1.
Even base index e = 2NPb = 2(4)(1) = 8.
Odd base index o = e + 2N'P = 8 + 2(2) = 12.
Twiddle step size s = 2P+1 = 24+1 = 32.
x[e+2n] ={x[e+2n]+x[o+2n]}>>1
x[8+0] ={x[8+0]+x[12+0]}>>1
x[8] ={x[8]+x[12]}>>1
={0000 +0000}>>1
={00000}>>1
=0000
x[e+2n+1] ={x[e+2n+1]+x[o+2n+1]}>>1
x[8+1] ={x[8+1]+x[12+1]}>>1
x[9] ={x[9]+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[12+2(0)] = {(x[12+2(0)]-x[8+2(0)])t[(32)(0)]-(x[8+2(0)+1]-x[12+2(0)+1])t[(32)(0)+1]}>>1
x[12+0] = {(x[12+0]-x[8+0])t[0]-(x[8+0+1]-x[12+0+1])t[0+1]}>>1
x[12] = {(x[12]-x[8])t[0]-(x[9]-x[13])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[12+2(0)+1] = {(x[12+2(0)+1]-x[8+2(0)+1])t[(32)(0)]+(x[8+2(0)]-x[12+2(0)])t[(32)(0)+1]}>>1
x[12+1] = {(x[12+1]-x[8+1])t[0]+(x[8+0]-x[12+0])t[0+1]}>>1
x[13] = {(x[13]-x[9])t[0]+(x[8]-x[12])t[1]}>>1
= {(0000-0000)8000+(0000-0000)0000}>>1
= {(00000)8000+(00000)0000}>>1
= {00000+00000}>>1
= {00000}>>1
= 0000



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(P,b,n)=(4,1,1)
Loop P=4 of p=log2N=log264=6 loops indexed P=0...p-1=0...6-1=0...5.
Subblock b=1 of BP=B4=2P=24=16 subblocks, indexed b=0...B4-1=0...15.
Subblock size=NP|P=4=N4=N/BP|(N=64,P=4)=(2p/2P)|(p=6,P=4)=2p-P|(p=6,P=4)=26-4=4.
Butterfly n=1 of N'P=NP/2=2p-P-1=26-4-1=2 butterflies indexed by n=0...N'P-1=0...1.
Even base index e = 2NPb = 2(4)(1) = 8.
Odd base index o = e + 2N'P = 8 + 2(2) = 12.
Twiddle step size s = 2P+1 = 24+1 = 32.
x[e+2n] ={x[e+2n]+x[o+2n]}>>1
x[8+2] ={x[8+2]+x[12+2]}>>1
x[10] ={x[10]+x[14]}>>1
={0000 +0000}>>1
={00000}>>1
=0000
x[e+2n+1] ={x[e+2n+1]+x[o+2n+1]}>>1
x[8+3] ={x[8+3]+x[12+3]}>>1
x[11] ={x[11]+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[12+2(1)] = {(x[12+2(1)]-x[8+2(1)])t[(32)(1)]-(x[8+2(1)+1]-x[12+2(1)+1])t[(32)(1)+1]}>>1
x[12+2] = {(x[12+2]-x[8+2])t[32]-(x[8+2+1]-x[12+2+1])t[32+1]}>>1
x[14] = {(x[14]-x[10])t[32]-(x[11]-x[15])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[12+2(1)+1] = {(x[12+2(1)+1]-x[8+2(1)+1])t[(32)(1)]+(x[8+2(1)]-x[12+2(1)])t[(32)(1)+1]}>>1
x[12+3] = {(x[12+3]-x[8+3])t[32]+(x[8+2]-x[12+2])t[32+1]}>>1
x[15] = {(x[15]-x[11])t[32]+(x[10]-x[14])t[33]}>>1
= {(0000-0000)ffff+(0000-0000)8000}>>1
= {(00000)ffff+(00000)8000}>>1
= {00000+00000}>>1
= {00000}>>1
= 0000



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(P,b,n)=(4,2,0)
Loop P=4 of p=log2N=log264=6 loops indexed P=0...p-1=0...6-1=0...5.
Subblock b=2 of BP=B4=2P=24=16 subblocks, indexed b=0...B4-1=0...15.
Subblock size=NP|P=4=N4=N/BP|(N=64,P=4)=(2p/2P)|(p=6,P=4)=2p-P|(p=6,P=4)=26-4=4.
Butterfly n=0 of N'P=NP/2=2p-P-1=26-4-1=2 butterflies indexed by n=0...N'P-1=0...1.
Even base index e = 2NPb = 2(4)(2) = 16.
Odd base index o = e + 2N'P = 16 + 2(2) = 20.
Twiddle step size s = 2P+1 = 24+1 = 32.
x[e+2n] ={x[e+2n]+x[o+2n]}>>1
x[16+0] ={x[16+0]+x[20+0]}>>1
x[16] ={x[16]+x[20]}>>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[20+1]}>>1
x[17] ={x[17]+x[21]}>>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[20+2(0)] = {(x[20+2(0)]-x[16+2(0)])t[(32)(0)]-(x[16+2(0)+1]-x[20+2(0)+1])t[(32)(0)+1]}>>1
x[20+0] = {(x[20+0]-x[16+0])t[0]-(x[16+0+1]-x[20+0+1])t[0+1]}>>1
x[20] = {(x[20]-x[16])t[0]-(x[17]-x[21])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[20+2(0)+1] = {(x[20+2(0)+1]-x[16+2(0)+1])t[(32)(0)]+(x[16+2(0)]-x[20+2(0)])t[(32)(0)+1]}>>1
x[20+1] = {(x[20+1]-x[16+1])t[0]+(x[16+0]-x[20+0])t[0+1]}>>1
x[21] = {(x[21]-x[17])t[0]+(x[16]-x[20])t[1]}>>1
= {(0000-0000)8000+(0000-0000)0000}>>1
= {(00000)8000+(00000)0000}>>1
= {00000+00000}>>1
= {00000}>>1
= 0000



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(P,b,n)=(4,2,1)
Loop P=4 of p=log2N=log264=6 loops indexed P=0...p-1=0...6-1=0...5.
Subblock b=2 of BP=B4=2P=24=16 subblocks, indexed b=0...B4-1=0...15.
Subblock size=NP|P=4=N4=N/BP|(N=64,P=4)=(2p/2P)|(p=6,P=4)=2p-P|(p=6,P=4)=26-4=4.
Butterfly n=1 of N'P=NP/2=2p-P-1=26-4-1=2 butterflies indexed by n=0...N'P-1=0...1.
Even base index e = 2NPb = 2(4)(2) = 16.
Odd base index o = e + 2N'P = 16 + 2(2) = 20.
Twiddle step size s = 2P+1 = 24+1 = 32.
x[e+2n] ={x[e+2n]+x[o+2n]}>>1
x[16+2] ={x[16+2]+x[20+2]}>>1
x[18] ={x[18]+x[22]}>>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[20+3]}>>1
x[19] ={x[19]+x[23]}>>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[20+2(1)] = {(x[20+2(1)]-x[16+2(1)])t[(32)(1)]-(x[16+2(1)+1]-x[20+2(1)+1])t[(32)(1)+1]}>>1
x[20+2] = {(x[20+2]-x[16+2])t[32]-(x[16+2+1]-x[20+2+1])t[32+1]}>>1
x[22] = {(x[22]-x[18])t[32]-(x[19]-x[23])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[20+2(1)+1] = {(x[20+2(1)+1]-x[16+2(1)+1])t[(32)(1)]+(x[16+2(1)]-x[20+2(1)])t[(32)(1)+1]}>>1
x[20+3] = {(x[20+3]-x[16+3])t[32]+(x[16+2]-x[20+2])t[32+1]}>>1
x[23] = {(x[23]-x[19])t[32]+(x[18]-x[22])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)=(4,3,0)
Loop P=4 of p=log2N=log264=6 loops indexed P=0...p-1=0...6-1=0...5.
Subblock b=3 of BP=B4=2P=24=16 subblocks, indexed b=0...B4-1=0...15.
Subblock size=NP|P=4=N4=N/BP|(N=64,P=4)=(2p/2P)|(p=6,P=4)=2p-P|(p=6,P=4)=26-4=4.
Butterfly n=0 of N'P=NP/2=2p-P-1=26-4-1=2 butterflies indexed by n=0...N'P-1=0...1.
Even base index e = 2NPb = 2(4)(3) = 24.
Odd base index o = e + 2N'P = 24 + 2(2) = 28.
Twiddle step size s = 2P+1 = 24+1 = 32.
x[e+2n] ={x[e+2n]+x[o+2n]}>>1
x[24+0] ={x[24+0]+x[28+0]}>>1
x[24] ={x[24]+x[28]}>>1
={0000 +0000}>>1
={00000}>>1
=0000
x[e+2n+1] ={x[e+2n+1]+x[o+2n+1]}>>1
x[24+1] ={x[24+1]+x[28+1]}>>1
x[25] ={x[25]+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[28+2(0)] = {(x[28+2(0)]-x[24+2(0)])t[(32)(0)]-(x[24+2(0)+1]-x[28+2(0)+1])t[(32)(0)+1]}>>1
x[28+0] = {(x[28+0]-x[24+0])t[0]-(x[24+0+1]-x[28+0+1])t[0+1]}>>1
x[28] = {(x[28]-x[24])t[0]-(x[25]-x[29])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[28+2(0)+1] = {(x[28+2(0)+1]-x[24+2(0)+1])t[(32)(0)]+(x[24+2(0)]-x[28+2(0)])t[(32)(0)+1]}>>1
x[28+1] = {(x[28+1]-x[24+1])t[0]+(x[24+0]-x[28+0])t[0+1]}>>1
x[29] = {(x[29]-x[25])t[0]+(x[24]-x[28])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)=(4,3,1)
Loop P=4 of p=log2N=log264=6 loops indexed P=0...p-1=0...6-1=0...5.
Subblock b=3 of BP=B4=2P=24=16 subblocks, indexed b=0...B4-1=0...15.
Subblock size=NP|P=4=N4=N/BP|(N=64,P=4)=(2p/2P)|(p=6,P=4)=2p-P|(p=6,P=4)=26-4=4.
Butterfly n=1 of N'P=NP/2=2p-P-1=26-4-1=2 butterflies indexed by n=0...N'P-1=0...1.
Even base index e = 2NPb = 2(4)(3) = 24.
Odd base index o = e + 2N'P = 24 + 2(2) = 28.
Twiddle step size s = 2P+1 = 24+1 = 32.
x[e+2n] ={x[e+2n]+x[o+2n]}>>1
x[24+2] ={x[24+2]+x[28+2]}>>1
x[26] ={x[26]+x[30]}>>1
={0000 +0000}>>1
={00000}>>1
=0000
x[e+2n+1] ={x[e+2n+1]+x[o+2n+1]}>>1
x[24+3] ={x[24+3]+x[28+3]}>>1
x[27] ={x[27]+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[28+2(1)] = {(x[28+2(1)]-x[24+2(1)])t[(32)(1)]-(x[24+2(1)+1]-x[28+2(1)+1])t[(32)(1)+1]}>>1
x[28+2] = {(x[28+2]-x[24+2])t[32]-(x[24+2+1]-x[28+2+1])t[32+1]}>>1
x[30] = {(x[30]-x[26])t[32]-(x[27]-x[31])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[28+2(1)+1] = {(x[28+2(1)+1]-x[24+2(1)+1])t[(32)(1)]+(x[24+2(1)]-x[28+2(1)])t[(32)(1)+1]}>>1
x[28+3] = {(x[28+3]-x[24+3])t[32]+(x[24+2]-x[28+2])t[32+1]}>>1
x[31] = {(x[31]-x[27])t[32]+(x[26]-x[30])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)=(4,4,0)
Loop P=4 of p=log2N=log264=6 loops indexed P=0...p-1=0...6-1=0...5.
Subblock b=4 of BP=B4=2P=24=16 subblocks, indexed b=0...B4-1=0...15.
Subblock size=NP|P=4=N4=N/BP|(N=64,P=4)=(2p/2P)|(p=6,P=4)=2p-P|(p=6,P=4)=26-4=4.
Butterfly n=0 of N'P=NP/2=2p-P-1=26-4-1=2 butterflies indexed by n=0...N'P-1=0...1.
Even base index e = 2NPb = 2(4)(4) = 32.
Odd base index o = e + 2N'P = 32 + 2(2) = 36.
Twiddle step size s = 2P+1 = 24+1 = 32.
x[e+2n] ={x[e+2n]+x[o+2n]}>>1
x[32+0] ={x[32+0]+x[36+0]}>>1
x[32] ={x[32]+x[36]}>>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[36+1]}>>1
x[33] ={x[33]+x[37]}>>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[36+2(0)] = {(x[36+2(0)]-x[32+2(0)])t[(32)(0)]-(x[32+2(0)+1]-x[36+2(0)+1])t[(32)(0)+1]}>>1
x[36+0] = {(x[36+0]-x[32+0])t[0]-(x[32+0+1]-x[36+0+1])t[0+1]}>>1
x[36] = {(x[36]-x[32])t[0]-(x[33]-x[37])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[36+2(0)+1] = {(x[36+2(0)+1]-x[32+2(0)+1])t[(32)(0)]+(x[32+2(0)]-x[36+2(0)])t[(32)(0)+1]}>>1
x[36+1] = {(x[36+1]-x[32+1])t[0]+(x[32+0]-x[36+0])t[0+1]}>>1
x[37] = {(x[37]-x[33])t[0]+(x[32]-x[36])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)=(4,4,1)
Loop P=4 of p=log2N=log264=6 loops indexed P=0...p-1=0...6-1=0...5.
Subblock b=4 of BP=B4=2P=24=16 subblocks, indexed b=0...B4-1=0...15.
Subblock size=NP|P=4=N4=N/BP|(N=64,P=4)=(2p/2P)|(p=6,P=4)=2p-P|(p=6,P=4)=26-4=4.
Butterfly n=1 of N'P=NP/2=2p-P-1=26-4-1=2 butterflies indexed by n=0...N'P-1=0...1.
Even base index e = 2NPb = 2(4)(4) = 32.
Odd base index o = e + 2N'P = 32 + 2(2) = 36.
Twiddle step size s = 2P+1 = 24+1 = 32.
x[e+2n] ={x[e+2n]+x[o+2n]}>>1
x[32+2] ={x[32+2]+x[36+2]}>>1
x[34] ={x[34]+x[38]}>>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[36+3]}>>1
x[35] ={x[35]+x[39]}>>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[36+2(1)] = {(x[36+2(1)]-x[32+2(1)])t[(32)(1)]-(x[32+2(1)+1]-x[36+2(1)+1])t[(32)(1)+1]}>>1
x[36+2] = {(x[36+2]-x[32+2])t[32]-(x[32+2+1]-x[36+2+1])t[32+1]}>>1
x[38] = {(x[38]-x[34])t[32]-(x[35]-x[39])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[36+2(1)+1] = {(x[36+2(1)+1]-x[32+2(1)+1])t[(32)(1)]+(x[32+2(1)]-x[36+2(1)])t[(32)(1)+1]}>>1
x[36+3] = {(x[36+3]-x[32+3])t[32]+(x[32+2]-x[36+2])t[32+1]}>>1
x[39] = {(x[39]-x[35])t[32]+(x[34]-x[38])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)=(4,5,0)
Loop P=4 of p=log2N=log264=6 loops indexed P=0...p-1=0...6-1=0...5.
Subblock b=5 of BP=B4=2P=24=16 subblocks, indexed b=0...B4-1=0...15.
Subblock size=NP|P=4=N4=N/BP|(N=64,P=4)=(2p/2P)|(p=6,P=4)=2p-P|(p=6,P=4)=26-4=4.
Butterfly n=0 of N'P=NP/2=2p-P-1=26-4-1=2 butterflies indexed by n=0...N'P-1=0...1.
Even base index e = 2NPb = 2(4)(5) = 40.
Odd base index o = e + 2N'P = 40 + 2(2) = 44.
Twiddle step size s = 2P+1 = 24+1 = 32.
x[e+2n] ={x[e+2n]+x[o+2n]}>>1
x[40+0] ={x[40+0]+x[44+0]}>>1
x[40] ={x[40]+x[44]}>>1
={0000 +0000}>>1
={00000}>>1
=0000
x[e+2n+1] ={x[e+2n+1]+x[o+2n+1]}>>1
x[40+1] ={x[40+1]+x[44+1]}>>1
x[41] ={x[41]+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[44+2(0)] = {(x[44+2(0)]-x[40+2(0)])t[(32)(0)]-(x[40+2(0)+1]-x[44+2(0)+1])t[(32)(0)+1]}>>1
x[44+0] = {(x[44+0]-x[40+0])t[0]-(x[40+0+1]-x[44+0+1])t[0+1]}>>1
x[44] = {(x[44]-x[40])t[0]-(x[41]-x[45])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[44+2(0)+1] = {(x[44+2(0)+1]-x[40+2(0)+1])t[(32)(0)]+(x[40+2(0)]-x[44+2(0)])t[(32)(0)+1]}>>1
x[44+1] = {(x[44+1]-x[40+1])t[0]+(x[40+0]-x[44+0])t[0+1]}>>1
x[45] = {(x[45]-x[41])t[0]+(x[40]-x[44])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)=(4,5,1)
Loop P=4 of p=log2N=log264=6 loops indexed P=0...p-1=0...6-1=0...5.
Subblock b=5 of BP=B4=2P=24=16 subblocks, indexed b=0...B4-1=0...15.
Subblock size=NP|P=4=N4=N/BP|(N=64,P=4)=(2p/2P)|(p=6,P=4)=2p-P|(p=6,P=4)=26-4=4.
Butterfly n=1 of N'P=NP/2=2p-P-1=26-4-1=2 butterflies indexed by n=0...N'P-1=0...1.
Even base index e = 2NPb = 2(4)(5) = 40.
Odd base index o = e + 2N'P = 40 + 2(2) = 44.
Twiddle step size s = 2P+1 = 24+1 = 32.
x[e+2n] ={x[e+2n]+x[o+2n]}>>1
x[40+2] ={x[40+2]+x[44+2]}>>1
x[42] ={x[42]+x[46]}>>1
={0000 +0000}>>1
={00000}>>1
=0000
x[e+2n+1] ={x[e+2n+1]+x[o+2n+1]}>>1
x[40+3] ={x[40+3]+x[44+3]}>>1
x[43] ={x[43]+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[44+2(1)] = {(x[44+2(1)]-x[40+2(1)])t[(32)(1)]-(x[40+2(1)+1]-x[44+2(1)+1])t[(32)(1)+1]}>>1
x[44+2] = {(x[44+2]-x[40+2])t[32]-(x[40+2+1]-x[44+2+1])t[32+1]}>>1
x[46] = {(x[46]-x[42])t[32]-(x[43]-x[47])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[44+2(1)+1] = {(x[44+2(1)+1]-x[40+2(1)+1])t[(32)(1)]+(x[40+2(1)]-x[44+2(1)])t[(32)(1)+1]}>>1
x[44+3] = {(x[44+3]-x[40+3])t[32]+(x[40+2]-x[44+2])t[32+1]}>>1
x[47] = {(x[47]-x[43])t[32]+(x[42]-x[46])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)=(4,6,0)
Loop P=4 of p=log2N=log264=6 loops indexed P=0...p-1=0...6-1=0...5.
Subblock b=6 of BP=B4=2P=24=16 subblocks, indexed b=0...B4-1=0...15.
Subblock size=NP|P=4=N4=N/BP|(N=64,P=4)=(2p/2P)|(p=6,P=4)=2p-P|(p=6,P=4)=26-4=4.
Butterfly n=0 of N'P=NP/2=2p-P-1=26-4-1=2 butterflies indexed by n=0...N'P-1=0...1.
Even base index e = 2NPb = 2(4)(6) = 48.
Odd base index o = e + 2N'P = 48 + 2(2) = 52.
Twiddle step size s = 2P+1 = 24+1 = 32.
x[e+2n] ={x[e+2n]+x[o+2n]}>>1
x[48+0] ={x[48+0]+x[52+0]}>>1
x[48] ={x[48]+x[52]}>>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[52+1]}>>1
x[49] ={x[49]+x[53]}>>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[52+2(0)] = {(x[52+2(0)]-x[48+2(0)])t[(32)(0)]-(x[48+2(0)+1]-x[52+2(0)+1])t[(32)(0)+1]}>>1
x[52+0] = {(x[52+0]-x[48+0])t[0]-(x[48+0+1]-x[52+0+1])t[0+1]}>>1
x[52] = {(x[52]-x[48])t[0]-(x[49]-x[53])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[52+2(0)+1] = {(x[52+2(0)+1]-x[48+2(0)+1])t[(32)(0)]+(x[48+2(0)]-x[52+2(0)])t[(32)(0)+1]}>>1
x[52+1] = {(x[52+1]-x[48+1])t[0]+(x[48+0]-x[52+0])t[0+1]}>>1
x[53] = {(x[53]-x[49])t[0]+(x[48]-x[52])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)=(4,6,1)
Loop P=4 of p=log2N=log264=6 loops indexed P=0...p-1=0...6-1=0...5.
Subblock b=6 of BP=B4=2P=24=16 subblocks, indexed b=0...B4-1=0...15.
Subblock size=NP|P=4=N4=N/BP|(N=64,P=4)=(2p/2P)|(p=6,P=4)=2p-P|(p=6,P=4)=26-4=4.
Butterfly n=1 of N'P=NP/2=2p-P-1=26-4-1=2 butterflies indexed by n=0...N'P-1=0...1.
Even base index e = 2NPb = 2(4)(6) = 48.
Odd base index o = e + 2N'P = 48 + 2(2) = 52.
Twiddle step size s = 2P+1 = 24+1 = 32.
x[e+2n] ={x[e+2n]+x[o+2n]}>>1
x[48+2] ={x[48+2]+x[52+2]}>>1
x[50] ={x[50]+x[54]}>>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[52+3]}>>1
x[51] ={x[51]+x[55]}>>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[52+2(1)] = {(x[52+2(1)]-x[48+2(1)])t[(32)(1)]-(x[48+2(1)+1]-x[52+2(1)+1])t[(32)(1)+1]}>>1
x[52+2] = {(x[52+2]-x[48+2])t[32]-(x[48+2+1]-x[52+2+1])t[32+1]}>>1
x[54] = {(x[54]-x[50])t[32]-(x[51]-x[55])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[52+2(1)+1] = {(x[52+2(1)+1]-x[48+2(1)+1])t[(32)(1)]+(x[48+2(1)]-x[52+2(1)])t[(32)(1)+1]}>>1
x[52+3] = {(x[52+3]-x[48+3])t[32]+(x[48+2]-x[52+2])t[32+1]}>>1
x[55] = {(x[55]-x[51])t[32]+(x[50]-x[54])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)=(4,7,0)
Loop P=4 of p=log2N=log264=6 loops indexed P=0...p-1=0...6-1=0...5.
Subblock b=7 of BP=B4=2P=24=16 subblocks, indexed b=0...B4-1=0...15.
Subblock size=NP|P=4=N4=N/BP|(N=64,P=4)=(2p/2P)|(p=6,P=4)=2p-P|(p=6,P=4)=26-4=4.
Butterfly n=0 of N'P=NP/2=2p-P-1=26-4-1=2 butterflies indexed by n=0...N'P-1=0...1.
Even base index e = 2NPb = 2(4)(7) = 56.
Odd base index o = e + 2N'P = 56 + 2(2) = 60.
Twiddle step size s = 2P+1 = 24+1 = 32.
x[e+2n] ={x[e+2n]+x[o+2n]}>>1
x[56+0] ={x[56+0]+x[60+0]}>>1
x[56] ={x[56]+x[60]}>>1
={0000 +0000}>>1
={00000}>>1
=0000
x[e+2n+1] ={x[e+2n+1]+x[o+2n+1]}>>1
x[56+1] ={x[56+1]+x[60+1]}>>1
x[57] ={x[57]+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[60+2(0)] = {(x[60+2(0)]-x[56+2(0)])t[(32)(0)]-(x[56+2(0)+1]-x[60+2(0)+1])t[(32)(0)+1]}>>1
x[60+0] = {(x[60+0]-x[56+0])t[0]-(x[56+0+1]-x[60+0+1])t[0+1]}>>1
x[60] = {(x[60]-x[56])t[0]-(x[57]-x[61])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[60+2(0)+1] = {(x[60+2(0)+1]-x[56+2(0)+1])t[(32)(0)]+(x[56+2(0)]-x[60+2(0)])t[(32)(0)+1]}>>1
x[60+1] = {(x[60+1]-x[56+1])t[0]+(x[56+0]-x[60+0])t[0+1]}>>1
x[61] = {(x[61]-x[57])t[0]+(x[56]-x[60])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)=(4,7,1)
Loop P=4 of p=log2N=log264=6 loops indexed P=0...p-1=0...6-1=0...5.
Subblock b=7 of BP=B4=2P=24=16 subblocks, indexed b=0...B4-1=0...15.
Subblock size=NP|P=4=N4=N/BP|(N=64,P=4)=(2p/2P)|(p=6,P=4)=2p-P|(p=6,P=4)=26-4=4.
Butterfly n=1 of N'P=NP/2=2p-P-1=26-4-1=2 butterflies indexed by n=0...N'P-1=0...1.
Even base index e = 2NPb = 2(4)(7) = 56.
Odd base index o = e + 2N'P = 56 + 2(2) = 60.
Twiddle step size s = 2P+1 = 24+1 = 32.
x[e+2n] ={x[e+2n]+x[o+2n]}>>1
x[56+2] ={x[56+2]+x[60+2]}>>1
x[58] ={x[58]+x[62]}>>1
={0000 +0000}>>1
={00000}>>1
=0000
x[e+2n+1] ={x[e+2n+1]+x[o+2n+1]}>>1
x[56+3] ={x[56+3]+x[60+3]}>>1
x[59] ={x[59]+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[60+2(1)] = {(x[60+2(1)]-x[56+2(1)])t[(32)(1)]-(x[56+2(1)+1]-x[60+2(1)+1])t[(32)(1)+1]}>>1
x[60+2] = {(x[60+2]-x[56+2])t[32]-(x[56+2+1]-x[60+2+1])t[32+1]}>>1
x[62] = {(x[62]-x[58])t[32]-(x[59]-x[63])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[60+2(1)+1] = {(x[60+2(1)+1]-x[56+2(1)+1])t[(32)(1)]+(x[56+2(1)]-x[60+2(1)])t[(32)(1)+1]}>>1
x[60+3] = {(x[60+3]-x[56+3])t[32]+(x[56+2]-x[60+2])t[32+1]}>>1
x[63] = {(x[63]-x[59])t[32]+(x[58]-x[62])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)=(4,8,0)
Loop P=4 of p=log2N=log264=6 loops indexed P=0...p-1=0...6-1=0...5.
Subblock b=8 of BP=B4=2P=24=16 subblocks, indexed b=0...B4-1=0...15.
Subblock size=NP|P=4=N4=N/BP|(N=64,P=4)=(2p/2P)|(p=6,P=4)=2p-P|(p=6,P=4)=26-4=4.
Butterfly n=0 of N'P=NP/2=2p-P-1=26-4-1=2 butterflies indexed by n=0...N'P-1=0...1.
Even base index e = 2NPb = 2(4)(8) = 64.
Odd base index o = e + 2N'P = 64 + 2(2) = 68.
Twiddle step size s = 2P+1 = 24+1 = 32.
x[e+2n] ={x[e+2n]+x[o+2n]}>>1
x[64+0] ={x[64+0]+x[68+0]}>>1
x[64] ={x[64]+x[68]}>>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[68+1]}>>1
x[65] ={x[65]+x[69]}>>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[68+2(0)] = {(x[68+2(0)]-x[64+2(0)])t[(32)(0)]-(x[64+2(0)+1]-x[68+2(0)+1])t[(32)(0)+1]}>>1
x[68+0] = {(x[68+0]-x[64+0])t[0]-(x[64+0+1]-x[68+0+1])t[0+1]}>>1
x[68] = {(x[68]-x[64])t[0]-(x[65]-x[69])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[68+2(0)+1] = {(x[68+2(0)+1]-x[64+2(0)+1])t[(32)(0)]+(x[64+2(0)]-x[68+2(0)])t[(32)(0)+1]}>>1
x[68+1] = {(x[68+1]-x[64+1])t[0]+(x[64+0]-x[68+0])t[0+1]}>>1
x[69] = {(x[69]-x[65])t[0]+(x[64]-x[68])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)=(4,8,1)
Loop P=4 of p=log2N=log264=6 loops indexed P=0...p-1=0...6-1=0...5.
Subblock b=8 of BP=B4=2P=24=16 subblocks, indexed b=0...B4-1=0...15.
Subblock size=NP|P=4=N4=N/BP|(N=64,P=4)=(2p/2P)|(p=6,P=4)=2p-P|(p=6,P=4)=26-4=4.
Butterfly n=1 of N'P=NP/2=2p-P-1=26-4-1=2 butterflies indexed by n=0...N'P-1=0...1.
Even base index e = 2NPb = 2(4)(8) = 64.
Odd base index o = e + 2N'P = 64 + 2(2) = 68.
Twiddle step size s = 2P+1 = 24+1 = 32.
x[e+2n] ={x[e+2n]+x[o+2n]}>>1
x[64+2] ={x[64+2]+x[68+2]}>>1
x[66] ={x[66]+x[70]}>>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[68+3]}>>1
x[67] ={x[67]+x[71]}>>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[68+2(1)] = {(x[68+2(1)]-x[64+2(1)])t[(32)(1)]-(x[64+2(1)+1]-x[68+2(1)+1])t[(32)(1)+1]}>>1
x[68+2] = {(x[68+2]-x[64+2])t[32]-(x[64+2+1]-x[68+2+1])t[32+1]}>>1
x[70] = {(x[70]-x[66])t[32]-(x[67]-x[71])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[68+2(1)+1] = {(x[68+2(1)+1]-x[64+2(1)+1])t[(32)(1)]+(x[64+2(1)]-x[68+2(1)])t[(32)(1)+1]}>>1
x[68+3] = {(x[68+3]-x[64+3])t[32]+(x[64+2]-x[68+2])t[32+1]}>>1
x[71] = {(x[71]-x[67])t[32]+(x[66]-x[70])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)=(4,9,0)
Loop P=4 of p=log2N=log264=6 loops indexed P=0...p-1=0...6-1=0...5.
Subblock b=9 of BP=B4=2P=24=16 subblocks, indexed b=0...B4-1=0...15.
Subblock size=NP|P=4=N4=N/BP|(N=64,P=4)=(2p/2P)|(p=6,P=4)=2p-P|(p=6,P=4)=26-4=4.
Butterfly n=0 of N'P=NP/2=2p-P-1=26-4-1=2 butterflies indexed by n=0...N'P-1=0...1.
Even base index e = 2NPb = 2(4)(9) = 72.
Odd base index o = e + 2N'P = 72 + 2(2) = 76.
Twiddle step size s = 2P+1 = 24+1 = 32.
x[e+2n] ={x[e+2n]+x[o+2n]}>>1
x[72+0] ={x[72+0]+x[76+0]}>>1
x[72] ={x[72]+x[76]}>>1
={0000 +0000}>>1
={00000}>>1
=0000
x[e+2n+1] ={x[e+2n+1]+x[o+2n+1]}>>1
x[72+1] ={x[72+1]+x[76+1]}>>1
x[73] ={x[73]+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[76+2(0)] = {(x[76+2(0)]-x[72+2(0)])t[(32)(0)]-(x[72+2(0)+1]-x[76+2(0)+1])t[(32)(0)+1]}>>1
x[76+0] = {(x[76+0]-x[72+0])t[0]-(x[72+0+1]-x[76+0+1])t[0+1]}>>1
x[76] = {(x[76]-x[72])t[0]-(x[73]-x[77])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[76+2(0)+1] = {(x[76+2(0)+1]-x[72+2(0)+1])t[(32)(0)]+(x[72+2(0)]-x[76+2(0)])t[(32)(0)+1]}>>1
x[76+1] = {(x[76+1]-x[72+1])t[0]+(x[72+0]-x[76+0])t[0+1]}>>1
x[77] = {(x[77]-x[73])t[0]+(x[72]-x[76])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)=(4,9,1)
Loop P=4 of p=log2N=log264=6 loops indexed P=0...p-1=0...6-1=0...5.
Subblock b=9 of BP=B4=2P=24=16 subblocks, indexed b=0...B4-1=0...15.
Subblock size=NP|P=4=N4=N/BP|(N=64,P=4)=(2p/2P)|(p=6,P=4)=2p-P|(p=6,P=4)=26-4=4.
Butterfly n=1 of N'P=NP/2=2p-P-1=26-4-1=2 butterflies indexed by n=0...N'P-1=0...1.
Even base index e = 2NPb = 2(4)(9) = 72.
Odd base index o = e + 2N'P = 72 + 2(2) = 76.
Twiddle step size s = 2P+1 = 24+1 = 32.
x[e+2n] ={x[e+2n]+x[o+2n]}>>1
x[72+2] ={x[72+2]+x[76+2]}>>1
x[74] ={x[74]+x[78]}>>1
={0000 +0000}>>1
={00000}>>1
=0000
x[e+2n+1] ={x[e+2n+1]+x[o+2n+1]}>>1
x[72+3] ={x[72+3]+x[76+3]}>>1
x[75] ={x[75]+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[76+2(1)] = {(x[76+2(1)]-x[72+2(1)])t[(32)(1)]-(x[72+2(1)+1]-x[76+2(1)+1])t[(32)(1)+1]}>>1
x[76+2] = {(x[76+2]-x[72+2])t[32]-(x[72+2+1]-x[76+2+1])t[32+1]}>>1
x[78] = {(x[78]-x[74])t[32]-(x[75]-x[79])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[76+2(1)+1] = {(x[76+2(1)+1]-x[72+2(1)+1])t[(32)(1)]+(x[72+2(1)]-x[76+2(1)])t[(32)(1)+1]}>>1
x[76+3] = {(x[76+3]-x[72+3])t[32]+(x[72+2]-x[76+2])t[32+1]}>>1
x[79] = {(x[79]-x[75])t[32]+(x[74]-x[78])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)=(4,10,0)
Loop P=4 of p=log2N=log264=6 loops indexed P=0...p-1=0...6-1=0...5.
Subblock b=10 of BP=B4=2P=24=16 subblocks, indexed b=0...B4-1=0...15.
Subblock size=NP|P=4=N4=N/BP|(N=64,P=4)=(2p/2P)|(p=6,P=4)=2p-P|(p=6,P=4)=26-4=4.
Butterfly n=0 of N'P=NP/2=2p-P-1=26-4-1=2 butterflies indexed by n=0...N'P-1=0...1.
Even base index e = 2NPb = 2(4)(10) = 80.
Odd base index o = e + 2N'P = 80 + 2(2) = 84.
Twiddle step size s = 2P+1 = 24+1 = 32.
x[e+2n] ={x[e+2n]+x[o+2n]}>>1
x[80+0] ={x[80+0]+x[84+0]}>>1
x[80] ={x[80]+x[84]}>>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[84+1]}>>1
x[81] ={x[81]+x[85]}>>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[84+2(0)] = {(x[84+2(0)]-x[80+2(0)])t[(32)(0)]-(x[80+2(0)+1]-x[84+2(0)+1])t[(32)(0)+1]}>>1
x[84+0] = {(x[84+0]-x[80+0])t[0]-(x[80+0+1]-x[84+0+1])t[0+1]}>>1
x[84] = {(x[84]-x[80])t[0]-(x[81]-x[85])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[84+2(0)+1] = {(x[84+2(0)+1]-x[80+2(0)+1])t[(32)(0)]+(x[80+2(0)]-x[84+2(0)])t[(32)(0)+1]}>>1
x[84+1] = {(x[84+1]-x[80+1])t[0]+(x[80+0]-x[84+0])t[0+1]}>>1
x[85] = {(x[85]-x[81])t[0]+(x[80]-x[84])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)=(4,10,1)
Loop P=4 of p=log2N=log264=6 loops indexed P=0...p-1=0...6-1=0...5.
Subblock b=10 of BP=B4=2P=24=16 subblocks, indexed b=0...B4-1=0...15.
Subblock size=NP|P=4=N4=N/BP|(N=64,P=4)=(2p/2P)|(p=6,P=4)=2p-P|(p=6,P=4)=26-4=4.
Butterfly n=1 of N'P=NP/2=2p-P-1=26-4-1=2 butterflies indexed by n=0...N'P-1=0...1.
Even base index e = 2NPb = 2(4)(10) = 80.
Odd base index o = e + 2N'P = 80 + 2(2) = 84.
Twiddle step size s = 2P+1 = 24+1 = 32.
x[e+2n] ={x[e+2n]+x[o+2n]}>>1
x[80+2] ={x[80+2]+x[84+2]}>>1
x[82] ={x[82]+x[86]}>>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[84+3]}>>1
x[83] ={x[83]+x[87]}>>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[84+2(1)] = {(x[84+2(1)]-x[80+2(1)])t[(32)(1)]-(x[80+2(1)+1]-x[84+2(1)+1])t[(32)(1)+1]}>>1
x[84+2] = {(x[84+2]-x[80+2])t[32]-(x[80+2+1]-x[84+2+1])t[32+1]}>>1
x[86] = {(x[86]-x[82])t[32]-(x[83]-x[87])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[84+2(1)+1] = {(x[84+2(1)+1]-x[80+2(1)+1])t[(32)(1)]+(x[80+2(1)]-x[84+2(1)])t[(32)(1)+1]}>>1
x[84+3] = {(x[84+3]-x[80+3])t[32]+(x[80+2]-x[84+2])t[32+1]}>>1
x[87] = {(x[87]-x[83])t[32]+(x[82]-x[86])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)=(4,11,0)
Loop P=4 of p=log2N=log264=6 loops indexed P=0...p-1=0...6-1=0...5.
Subblock b=11 of BP=B4=2P=24=16 subblocks, indexed b=0...B4-1=0...15.
Subblock size=NP|P=4=N4=N/BP|(N=64,P=4)=(2p/2P)|(p=6,P=4)=2p-P|(p=6,P=4)=26-4=4.
Butterfly n=0 of N'P=NP/2=2p-P-1=26-4-1=2 butterflies indexed by n=0...N'P-1=0...1.
Even base index e = 2NPb = 2(4)(11) = 88.
Odd base index o = e + 2N'P = 88 + 2(2) = 92.
Twiddle step size s = 2P+1 = 24+1 = 32.
x[e+2n] ={x[e+2n]+x[o+2n]}>>1
x[88+0] ={x[88+0]+x[92+0]}>>1
x[88] ={x[88]+x[92]}>>1
={0000 +0000}>>1
={00000}>>1
=0000
x[e+2n+1] ={x[e+2n+1]+x[o+2n+1]}>>1
x[88+1] ={x[88+1]+x[92+1]}>>1
x[89] ={x[89]+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[92+2(0)] = {(x[92+2(0)]-x[88+2(0)])t[(32)(0)]-(x[88+2(0)+1]-x[92+2(0)+1])t[(32)(0)+1]}>>1
x[92+0] = {(x[92+0]-x[88+0])t[0]-(x[88+0+1]-x[92+0+1])t[0+1]}>>1
x[92] = {(x[92]-x[88])t[0]-(x[89]-x[93])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[92+2(0)+1] = {(x[92+2(0)+1]-x[88+2(0)+1])t[(32)(0)]+(x[88+2(0)]-x[92+2(0)])t[(32)(0)+1]}>>1
x[92+1] = {(x[92+1]-x[88+1])t[0]+(x[88+0]-x[92+0])t[0+1]}>>1
x[93] = {(x[93]-x[89])t[0]+(x[88]-x[92])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)=(4,11,1)
Loop P=4 of p=log2N=log264=6 loops indexed P=0...p-1=0...6-1=0...5.
Subblock b=11 of BP=B4=2P=24=16 subblocks, indexed b=0...B4-1=0...15.
Subblock size=NP|P=4=N4=N/BP|(N=64,P=4)=(2p/2P)|(p=6,P=4)=2p-P|(p=6,P=4)=26-4=4.
Butterfly n=1 of N'P=NP/2=2p-P-1=26-4-1=2 butterflies indexed by n=0...N'P-1=0...1.
Even base index e = 2NPb = 2(4)(11) = 88.
Odd base index o = e + 2N'P = 88 + 2(2) = 92.
Twiddle step size s = 2P+1 = 24+1 = 32.
x[e+2n] ={x[e+2n]+x[o+2n]}>>1
x[88+2] ={x[88+2]+x[92+2]}>>1
x[90] ={x[90]+x[94]}>>1
={0000 +0000}>>1
={00000}>>1
=0000
x[e+2n+1] ={x[e+2n+1]+x[o+2n+1]}>>1
x[88+3] ={x[88+3]+x[92+3]}>>1
x[91] ={x[91]+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[92+2(1)] = {(x[92+2(1)]-x[88+2(1)])t[(32)(1)]-(x[88+2(1)+1]-x[92+2(1)+1])t[(32)(1)+1]}>>1
x[92+2] = {(x[92+2]-x[88+2])t[32]-(x[88+2+1]-x[92+2+1])t[32+1]}>>1
x[94] = {(x[94]-x[90])t[32]-(x[91]-x[95])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[92+2(1)+1] = {(x[92+2(1)+1]-x[88+2(1)+1])t[(32)(1)]+(x[88+2(1)]-x[92+2(1)])t[(32)(1)+1]}>>1
x[92+3] = {(x[92+3]-x[88+3])t[32]+(x[88+2]-x[92+2])t[32+1]}>>1
x[95] = {(x[95]-x[91])t[32]+(x[90]-x[94])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)=(4,12,0)
Loop P=4 of p=log2N=log264=6 loops indexed P=0...p-1=0...6-1=0...5.
Subblock b=12 of BP=B4=2P=24=16 subblocks, indexed b=0...B4-1=0...15.
Subblock size=NP|P=4=N4=N/BP|(N=64,P=4)=(2p/2P)|(p=6,P=4)=2p-P|(p=6,P=4)=26-4=4.
Butterfly n=0 of N'P=NP/2=2p-P-1=26-4-1=2 butterflies indexed by n=0...N'P-1=0...1.
Even base index e = 2NPb = 2(4)(12) = 96.
Odd base index o = e + 2N'P = 96 + 2(2) = 100.
Twiddle step size s = 2P+1 = 24+1 = 32.
x[e+2n] ={x[e+2n]+x[o+2n]}>>1
x[96+0] ={x[96+0]+x[100+0]}>>1
x[96] ={x[96]+x[100]}>>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[100+1]}>>1
x[97] ={x[97]+x[101]}>>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[100+2(0)] = {(x[100+2(0)]-x[96+2(0)])t[(32)(0)]-(x[96+2(0)+1]-x[100+2(0)+1])t[(32)(0)+1]}>>1
x[100+0] = {(x[100+0]-x[96+0])t[0]-(x[96+0+1]-x[100+0+1])t[0+1]}>>1
x[100] = {(x[100]-x[96])t[0]-(x[97]-x[101])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[100+2(0)+1] = {(x[100+2(0)+1]-x[96+2(0)+1])t[(32)(0)]+(x[96+2(0)]-x[100+2(0)])t[(32)(0)+1]}>>1
x[100+1] = {(x[100+1]-x[96+1])t[0]+(x[96+0]-x[100+0])t[0+1]}>>1
x[101] = {(x[101]-x[97])t[0]+(x[96]-x[100])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)=(4,12,1)
Loop P=4 of p=log2N=log264=6 loops indexed P=0...p-1=0...6-1=0...5.
Subblock b=12 of BP=B4=2P=24=16 subblocks, indexed b=0...B4-1=0...15.
Subblock size=NP|P=4=N4=N/BP|(N=64,P=4)=(2p/2P)|(p=6,P=4)=2p-P|(p=6,P=4)=26-4=4.
Butterfly n=1 of N'P=NP/2=2p-P-1=26-4-1=2 butterflies indexed by n=0...N'P-1=0...1.
Even base index e = 2NPb = 2(4)(12) = 96.
Odd base index o = e + 2N'P = 96 + 2(2) = 100.
Twiddle step size s = 2P+1 = 24+1 = 32.
x[e+2n] ={x[e+2n]+x[o+2n]}>>1
x[96+2] ={x[96+2]+x[100+2]}>>1
x[98] ={x[98]+x[102]}>>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[100+3]}>>1
x[99] ={x[99]+x[103]}>>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[100+2(1)] = {(x[100+2(1)]-x[96+2(1)])t[(32)(1)]-(x[96+2(1)+1]-x[100+2(1)+1])t[(32)(1)+1]}>>1
x[100+2] = {(x[100+2]-x[96+2])t[32]-(x[96+2+1]-x[100+2+1])t[32+1]}>>1
x[102] = {(x[102]-x[98])t[32]-(x[99]-x[103])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[100+2(1)+1] = {(x[100+2(1)+1]-x[96+2(1)+1])t[(32)(1)]+(x[96+2(1)]-x[100+2(1)])t[(32)(1)+1]}>>1
x[100+3] = {(x[100+3]-x[96+3])t[32]+(x[96+2]-x[100+2])t[32+1]}>>1
x[103] = {(x[103]-x[99])t[32]+(x[98]-x[102])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)=(4,13,0)
Loop P=4 of p=log2N=log264=6 loops indexed P=0...p-1=0...6-1=0...5.
Subblock b=13 of BP=B4=2P=24=16 subblocks, indexed b=0...B4-1=0...15.
Subblock size=NP|P=4=N4=N/BP|(N=64,P=4)=(2p/2P)|(p=6,P=4)=2p-P|(p=6,P=4)=26-4=4.
Butterfly n=0 of N'P=NP/2=2p-P-1=26-4-1=2 butterflies indexed by n=0...N'P-1=0...1.
Even base index e = 2NPb = 2(4)(13) = 104.
Odd base index o = e + 2N'P = 104 + 2(2) = 108.
Twiddle step size s = 2P+1 = 24+1 = 32.
x[e+2n] ={x[e+2n]+x[o+2n]}>>1
x[104+0] ={x[104+0]+x[108+0]}>>1
x[104] ={x[104]+x[108]}>>1
={0000 +0000}>>1
={00000}>>1
=0000
x[e+2n+1] ={x[e+2n+1]+x[o+2n+1]}>>1
x[104+1] ={x[104+1]+x[108+1]}>>1
x[105] ={x[105]+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[108+2(0)] = {(x[108+2(0)]-x[104+2(0)])t[(32)(0)]-(x[104+2(0)+1]-x[108+2(0)+1])t[(32)(0)+1]}>>1
x[108+0] = {(x[108+0]-x[104+0])t[0]-(x[104+0+1]-x[108+0+1])t[0+1]}>>1
x[108] = {(x[108]-x[104])t[0]-(x[105]-x[109])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[108+2(0)+1] = {(x[108+2(0)+1]-x[104+2(0)+1])t[(32)(0)]+(x[104+2(0)]-x[108+2(0)])t[(32)(0)+1]}>>1
x[108+1] = {(x[108+1]-x[104+1])t[0]+(x[104+0]-x[108+0])t[0+1]}>>1
x[109] = {(x[109]-x[105])t[0]+(x[104]-x[108])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)=(4,13,1)
Loop P=4 of p=log2N=log264=6 loops indexed P=0...p-1=0...6-1=0...5.
Subblock b=13 of BP=B4=2P=24=16 subblocks, indexed b=0...B4-1=0...15.
Subblock size=NP|P=4=N4=N/BP|(N=64,P=4)=(2p/2P)|(p=6,P=4)=2p-P|(p=6,P=4)=26-4=4.
Butterfly n=1 of N'P=NP/2=2p-P-1=26-4-1=2 butterflies indexed by n=0...N'P-1=0...1.
Even base index e = 2NPb = 2(4)(13) = 104.
Odd base index o = e + 2N'P = 104 + 2(2) = 108.
Twiddle step size s = 2P+1 = 24+1 = 32.
x[e+2n] ={x[e+2n]+x[o+2n]}>>1
x[104+2] ={x[104+2]+x[108+2]}>>1
x[106] ={x[106]+x[110]}>>1
={0000 +0000}>>1
={00000}>>1
=0000
x[e+2n+1] ={x[e+2n+1]+x[o+2n+1]}>>1
x[104+3] ={x[104+3]+x[108+3]}>>1
x[107] ={x[107]+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[108+2(1)] = {(x[108+2(1)]-x[104+2(1)])t[(32)(1)]-(x[104+2(1)+1]-x[108+2(1)+1])t[(32)(1)+1]}>>1
x[108+2] = {(x[108+2]-x[104+2])t[32]-(x[104+2+1]-x[108+2+1])t[32+1]}>>1
x[110] = {(x[110]-x[106])t[32]-(x[107]-x[111])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[108+2(1)+1] = {(x[108+2(1)+1]-x[104+2(1)+1])t[(32)(1)]+(x[104+2(1)]-x[108+2(1)])t[(32)(1)+1]}>>1
x[108+3] = {(x[108+3]-x[104+3])t[32]+(x[104+2]-x[108+2])t[32+1]}>>1
x[111] = {(x[111]-x[107])t[32]+(x[106]-x[110])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)=(4,14,0)
Loop P=4 of p=log2N=log264=6 loops indexed P=0...p-1=0...6-1=0...5.
Subblock b=14 of BP=B4=2P=24=16 subblocks, indexed b=0...B4-1=0...15.
Subblock size=NP|P=4=N4=N/BP|(N=64,P=4)=(2p/2P)|(p=6,P=4)=2p-P|(p=6,P=4)=26-4=4.
Butterfly n=0 of N'P=NP/2=2p-P-1=26-4-1=2 butterflies indexed by n=0...N'P-1=0...1.
Even base index e = 2NPb = 2(4)(14) = 112.
Odd base index o = e + 2N'P = 112 + 2(2) = 116.
Twiddle step size s = 2P+1 = 24+1 = 32.
x[e+2n] ={x[e+2n]+x[o+2n]}>>1
x[112+0] ={x[112+0]+x[116+0]}>>1
x[112] ={x[112]+x[116]}>>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[116+1]}>>1
x[113] ={x[113]+x[117]}>>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[116+2(0)] = {(x[116+2(0)]-x[112+2(0)])t[(32)(0)]-(x[112+2(0)+1]-x[116+2(0)+1])t[(32)(0)+1]}>>1
x[116+0] = {(x[116+0]-x[112+0])t[0]-(x[112+0+1]-x[116+0+1])t[0+1]}>>1
x[116] = {(x[116]-x[112])t[0]-(x[113]-x[117])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[116+2(0)+1] = {(x[116+2(0)+1]-x[112+2(0)+1])t[(32)(0)]+(x[112+2(0)]-x[116+2(0)])t[(32)(0)+1]}>>1
x[116+1] = {(x[116+1]-x[112+1])t[0]+(x[112+0]-x[116+0])t[0+1]}>>1
x[117] = {(x[117]-x[113])t[0]+(x[112]-x[116])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)=(4,14,1)
Loop P=4 of p=log2N=log264=6 loops indexed P=0...p-1=0...6-1=0...5.
Subblock b=14 of BP=B4=2P=24=16 subblocks, indexed b=0...B4-1=0...15.
Subblock size=NP|P=4=N4=N/BP|(N=64,P=4)=(2p/2P)|(p=6,P=4)=2p-P|(p=6,P=4)=26-4=4.
Butterfly n=1 of N'P=NP/2=2p-P-1=26-4-1=2 butterflies indexed by n=0...N'P-1=0...1.
Even base index e = 2NPb = 2(4)(14) = 112.
Odd base index o = e + 2N'P = 112 + 2(2) = 116.
Twiddle step size s = 2P+1 = 24+1 = 32.
x[e+2n] ={x[e+2n]+x[o+2n]}>>1
x[112+2] ={x[112+2]+x[116+2]}>>1
x[114] ={x[114]+x[118]}>>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[116+3]}>>1
x[115] ={x[115]+x[119]}>>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[116+2(1)] = {(x[116+2(1)]-x[112+2(1)])t[(32)(1)]-(x[112+2(1)+1]-x[116+2(1)+1])t[(32)(1)+1]}>>1
x[116+2] = {(x[116+2]-x[112+2])t[32]-(x[112+2+1]-x[116+2+1])t[32+1]}>>1
x[118] = {(x[118]-x[114])t[32]-(x[115]-x[119])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[116+2(1)+1] = {(x[116+2(1)+1]-x[112+2(1)+1])t[(32)(1)]+(x[112+2(1)]-x[116+2(1)])t[(32)(1)+1]}>>1
x[116+3] = {(x[116+3]-x[112+3])t[32]+(x[112+2]-x[116+2])t[32+1]}>>1
x[119] = {(x[119]-x[115])t[32]+(x[114]-x[118])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)=(4,15,0)
Loop P=4 of p=log2N=log264=6 loops indexed P=0...p-1=0...6-1=0...5.
Subblock b=15 of BP=B4=2P=24=16 subblocks, indexed b=0...B4-1=0...15.
Subblock size=NP|P=4=N4=N/BP|(N=64,P=4)=(2p/2P)|(p=6,P=4)=2p-P|(p=6,P=4)=26-4=4.
Butterfly n=0 of N'P=NP/2=2p-P-1=26-4-1=2 butterflies indexed by n=0...N'P-1=0...1.
Even base index e = 2NPb = 2(4)(15) = 120.
Odd base index o = e + 2N'P = 120 + 2(2) = 124.
Twiddle step size s = 2P+1 = 24+1 = 32.
x[e+2n] ={x[e+2n]+x[o+2n]}>>1
x[120+0] ={x[120+0]+x[124+0]}>>1
x[120] ={x[120]+x[124]}>>1
={0000 +0000}>>1
={00000}>>1
=0000
x[e+2n+1] ={x[e+2n+1]+x[o+2n+1]}>>1
x[120+1] ={x[120+1]+x[124+1]}>>1
x[121] ={x[121]+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[124+2(0)] = {(x[124+2(0)]-x[120+2(0)])t[(32)(0)]-(x[120+2(0)+1]-x[124+2(0)+1])t[(32)(0)+1]}>>1
x[124+0] = {(x[124+0]-x[120+0])t[0]-(x[120+0+1]-x[124+0+1])t[0+1]}>>1
x[124] = {(x[124]-x[120])t[0]-(x[121]-x[125])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[124+2(0)+1] = {(x[124+2(0)+1]-x[120+2(0)+1])t[(32)(0)]+(x[120+2(0)]-x[124+2(0)])t[(32)(0)+1]}>>1
x[124+1] = {(x[124+1]-x[120+1])t[0]+(x[120+0]-x[124+0])t[0+1]}>>1
x[125] = {(x[125]-x[121])t[0]+(x[120]-x[124])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)=(4,15,1)
Loop P=4 of p=log2N=log264=6 loops indexed P=0...p-1=0...6-1=0...5.
Subblock b=15 of BP=B4=2P=24=16 subblocks, indexed b=0...B4-1=0...15.
Subblock size=NP|P=4=N4=N/BP|(N=64,P=4)=(2p/2P)|(p=6,P=4)=2p-P|(p=6,P=4)=26-4=4.
Butterfly n=1 of N'P=NP/2=2p-P-1=26-4-1=2 butterflies indexed by n=0...N'P-1=0...1.
Even base index e = 2NPb = 2(4)(15) = 120.
Odd base index o = e + 2N'P = 120 + 2(2) = 124.
Twiddle step size s = 2P+1 = 24+1 = 32.
x[e+2n] ={x[e+2n]+x[o+2n]}>>1
x[120+2] ={x[120+2]+x[124+2]}>>1
x[122] ={x[122]+x[126]}>>1
={0000 +0000}>>1
={00000}>>1
=0000
x[e+2n+1] ={x[e+2n+1]+x[o+2n+1]}>>1
x[120+3] ={x[120+3]+x[124+3]}>>1
x[123] ={x[123]+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[124+2(1)] = {(x[124+2(1)]-x[120+2(1)])t[(32)(1)]-(x[120+2(1)+1]-x[124+2(1)+1])t[(32)(1)+1]}>>1
x[124+2] = {(x[124+2]-x[120+2])t[32]-(x[120+2+1]-x[124+2+1])t[32+1]}>>1
x[126] = {(x[126]-x[122])t[32]-(x[123]-x[127])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[124+2(1)+1] = {(x[124+2(1)+1]-x[120+2(1)+1])t[(32)(1)]+(x[120+2(1)]-x[124+2(1)])t[(32)(1)+1]}>>1
x[124+3] = {(x[124+3]-x[120+3])t[32]+(x[120+2]-x[124+2])t[32+1]}>>1
x[127] = {(x[127]-x[123])t[32]+(x[122]-x[126])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



End of loop 4
x[0]=0000 x[1]=0000
x[2]=0000 x[3]=0000
x[4]=0000 x[5]=0000
x[6]=0000 x[7]=e000
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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