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



John Bryan






(P,b,n)=(5,0,0)
Loop P=5 of p=log2N=log264=6 loops indexed P=0...p-1=0...6-1=0...5.
Subblock b=0 of BP=B5=2P=25=32 subblocks, indexed b=0...B5-1=0...31.
Subblock size=NP|P=5=N5=N/BP|(N=64,P=5)=(2p/2P)|(p=6,P=5)=2p-P|(p=6,P=5)=26-5=2.
Butterfly n=0 of N'P=NP/2=2p-P-1=26-5-1=1 butterflies indexed by n=0...N'P-1=0...0.
Even base index e = 2NPb = 2(2)(0) = 0.
Odd base index o = e + 2N'P = 0 + 2(1) = 2.
Twiddle step size s = 2P+1 = 25+1 = 64.
x[e+2n] ={x[e+2n]+x[o+2n]}>>1
x[0+0] ={x[0+0]+x[2+0]}>>1
x[0] ={x[0]+x[2]}>>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[2+1]}>>1
x[1] ={x[1]+x[3]}>>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[2+2(0)] = {(x[2+2(0)]-x[0+2(0)])t[(64)(0)]-(x[0+2(0)+1]-x[2+2(0)+1])t[(64)(0)+1]}>>1
x[2+0] = {(x[2+0]-x[0+0])t[0]-(x[0+0+1]-x[2+0+1])t[0+1]}>>1
x[2] = {(x[2]-x[0])t[0]-(x[1]-x[3])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[2+2(0)+1] = {(x[2+2(0)+1]-x[0+2(0)+1])t[(64)(0)]+(x[0+2(0)]-x[2+2(0)])t[(64)(0)+1]}>>1
x[2+1] = {(x[2+1]-x[0+1])t[0]+(x[0+0]-x[2+0])t[0+1]}>>1
x[3] = {(x[3]-x[1])t[0]+(x[0]-x[2])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)=(5,1,0)
Loop P=5 of p=log2N=log264=6 loops indexed P=0...p-1=0...6-1=0...5.
Subblock b=1 of BP=B5=2P=25=32 subblocks, indexed b=0...B5-1=0...31.
Subblock size=NP|P=5=N5=N/BP|(N=64,P=5)=(2p/2P)|(p=6,P=5)=2p-P|(p=6,P=5)=26-5=2.
Butterfly n=0 of N'P=NP/2=2p-P-1=26-5-1=1 butterflies indexed by n=0...N'P-1=0...0.
Even base index e = 2NPb = 2(2)(1) = 4.
Odd base index o = e + 2N'P = 4 + 2(1) = 6.
Twiddle step size s = 2P+1 = 25+1 = 64.
x[e+2n] ={x[e+2n]+x[o+2n]}>>1
x[4+0] ={x[4+0]+x[6+0]}>>1
x[4] ={x[4]+x[6]}>>1
={0000 +0000}>>1
={00000}>>1
=0000
x[e+2n+1] ={x[e+2n+1]+x[o+2n+1]}>>1
x[4+1] ={x[4+1]+x[6+1]}>>1
x[5] ={x[5]+x[7]}>>1
={0000 +e000}>>1
={fe000}>>1
=f000
x[o+2n] = {(x[o+2n]-x[e+2n])t[sn]-(x[e+2n+1]-x[o+2n+1])t[sn+1]}>>1
x[6+2(0)] = {(x[6+2(0)]-x[4+2(0)])t[(64)(0)]-(x[4+2(0)+1]-x[6+2(0)+1])t[(64)(0)+1]}>>1
x[6+0] = {(x[6+0]-x[4+0])t[0]-(x[4+0+1]-x[6+0+1])t[0+1]}>>1
x[6] = {(x[6]-x[4])t[0]-(x[5]-x[7])t[1]}>>1
= {(0000-0000)8000-(0000-e000)0000}>>1
= {(00000)8000-(02000)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[6+2(0)+1] = {(x[6+2(0)+1]-x[4+2(0)+1])t[(64)(0)]+(x[4+2(0)]-x[6+2(0)])t[(64)(0)+1]}>>1
x[6+1] = {(x[6+1]-x[4+1])t[0]+(x[4+0]-x[6+0])t[0+1]}>>1
x[7] = {(x[7]-x[5])t[0]+(x[4]-x[6])t[1]}>>1
= {(e000-0000)8000+(0000-0000)0000}>>1
= {(fe000)8000+(00000)0000}>>1
= {02000+00000}>>1
= {02000}>>1
= 1000



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(P,b,n)=(5,2,0)
Loop P=5 of p=log2N=log264=6 loops indexed P=0...p-1=0...6-1=0...5.
Subblock b=2 of BP=B5=2P=25=32 subblocks, indexed b=0...B5-1=0...31.
Subblock size=NP|P=5=N5=N/BP|(N=64,P=5)=(2p/2P)|(p=6,P=5)=2p-P|(p=6,P=5)=26-5=2.
Butterfly n=0 of N'P=NP/2=2p-P-1=26-5-1=1 butterflies indexed by n=0...N'P-1=0...0.
Even base index e = 2NPb = 2(2)(2) = 8.
Odd base index o = e + 2N'P = 8 + 2(1) = 10.
Twiddle step size s = 2P+1 = 25+1 = 64.
x[e+2n] ={x[e+2n]+x[o+2n]}>>1
x[8+0] ={x[8+0]+x[10+0]}>>1
x[8] ={x[8]+x[10]}>>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[10+1]}>>1
x[9] ={x[9]+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[10+2(0)] = {(x[10+2(0)]-x[8+2(0)])t[(64)(0)]-(x[8+2(0)+1]-x[10+2(0)+1])t[(64)(0)+1]}>>1
x[10+0] = {(x[10+0]-x[8+0])t[0]-(x[8+0+1]-x[10+0+1])t[0+1]}>>1
x[10] = {(x[10]-x[8])t[0]-(x[9]-x[11])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[10+2(0)+1] = {(x[10+2(0)+1]-x[8+2(0)+1])t[(64)(0)]+(x[8+2(0)]-x[10+2(0)])t[(64)(0)+1]}>>1
x[10+1] = {(x[10+1]-x[8+1])t[0]+(x[8+0]-x[10+0])t[0+1]}>>1
x[11] = {(x[11]-x[9])t[0]+(x[8]-x[10])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)=(5,3,0)
Loop P=5 of p=log2N=log264=6 loops indexed P=0...p-1=0...6-1=0...5.
Subblock b=3 of BP=B5=2P=25=32 subblocks, indexed b=0...B5-1=0...31.
Subblock size=NP|P=5=N5=N/BP|(N=64,P=5)=(2p/2P)|(p=6,P=5)=2p-P|(p=6,P=5)=26-5=2.
Butterfly n=0 of N'P=NP/2=2p-P-1=26-5-1=1 butterflies indexed by n=0...N'P-1=0...0.
Even base index e = 2NPb = 2(2)(3) = 12.
Odd base index o = e + 2N'P = 12 + 2(1) = 14.
Twiddle step size s = 2P+1 = 25+1 = 64.
x[e+2n] ={x[e+2n]+x[o+2n]}>>1
x[12+0] ={x[12+0]+x[14+0]}>>1
x[12] ={x[12]+x[14]}>>1
={0000 +0000}>>1
={00000}>>1
=0000
x[e+2n+1] ={x[e+2n+1]+x[o+2n+1]}>>1
x[12+1] ={x[12+1]+x[14+1]}>>1
x[13] ={x[13]+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[14+2(0)] = {(x[14+2(0)]-x[12+2(0)])t[(64)(0)]-(x[12+2(0)+1]-x[14+2(0)+1])t[(64)(0)+1]}>>1
x[14+0] = {(x[14+0]-x[12+0])t[0]-(x[12+0+1]-x[14+0+1])t[0+1]}>>1
x[14] = {(x[14]-x[12])t[0]-(x[13]-x[15])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[14+2(0)+1] = {(x[14+2(0)+1]-x[12+2(0)+1])t[(64)(0)]+(x[12+2(0)]-x[14+2(0)])t[(64)(0)+1]}>>1
x[14+1] = {(x[14+1]-x[12+1])t[0]+(x[12+0]-x[14+0])t[0+1]}>>1
x[15] = {(x[15]-x[13])t[0]+(x[12]-x[14])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)=(5,4,0)
Loop P=5 of p=log2N=log264=6 loops indexed P=0...p-1=0...6-1=0...5.
Subblock b=4 of BP=B5=2P=25=32 subblocks, indexed b=0...B5-1=0...31.
Subblock size=NP|P=5=N5=N/BP|(N=64,P=5)=(2p/2P)|(p=6,P=5)=2p-P|(p=6,P=5)=26-5=2.
Butterfly n=0 of N'P=NP/2=2p-P-1=26-5-1=1 butterflies indexed by n=0...N'P-1=0...0.
Even base index e = 2NPb = 2(2)(4) = 16.
Odd base index o = e + 2N'P = 16 + 2(1) = 18.
Twiddle step size s = 2P+1 = 25+1 = 64.
x[e+2n] ={x[e+2n]+x[o+2n]}>>1
x[16+0] ={x[16+0]+x[18+0]}>>1
x[16] ={x[16]+x[18]}>>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[18+1]}>>1
x[17] ={x[17]+x[19]}>>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[18+2(0)] = {(x[18+2(0)]-x[16+2(0)])t[(64)(0)]-(x[16+2(0)+1]-x[18+2(0)+1])t[(64)(0)+1]}>>1
x[18+0] = {(x[18+0]-x[16+0])t[0]-(x[16+0+1]-x[18+0+1])t[0+1]}>>1
x[18] = {(x[18]-x[16])t[0]-(x[17]-x[19])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[18+2(0)+1] = {(x[18+2(0)+1]-x[16+2(0)+1])t[(64)(0)]+(x[16+2(0)]-x[18+2(0)])t[(64)(0)+1]}>>1
x[18+1] = {(x[18+1]-x[16+1])t[0]+(x[16+0]-x[18+0])t[0+1]}>>1
x[19] = {(x[19]-x[17])t[0]+(x[16]-x[18])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)=(5,5,0)
Loop P=5 of p=log2N=log264=6 loops indexed P=0...p-1=0...6-1=0...5.
Subblock b=5 of BP=B5=2P=25=32 subblocks, indexed b=0...B5-1=0...31.
Subblock size=NP|P=5=N5=N/BP|(N=64,P=5)=(2p/2P)|(p=6,P=5)=2p-P|(p=6,P=5)=26-5=2.
Butterfly n=0 of N'P=NP/2=2p-P-1=26-5-1=1 butterflies indexed by n=0...N'P-1=0...0.
Even base index e = 2NPb = 2(2)(5) = 20.
Odd base index o = e + 2N'P = 20 + 2(1) = 22.
Twiddle step size s = 2P+1 = 25+1 = 64.
x[e+2n] ={x[e+2n]+x[o+2n]}>>1
x[20+0] ={x[20+0]+x[22+0]}>>1
x[20] ={x[20]+x[22]}>>1
={0000 +0000}>>1
={00000}>>1
=0000
x[e+2n+1] ={x[e+2n+1]+x[o+2n+1]}>>1
x[20+1] ={x[20+1]+x[22+1]}>>1
x[21] ={x[21]+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[22+2(0)] = {(x[22+2(0)]-x[20+2(0)])t[(64)(0)]-(x[20+2(0)+1]-x[22+2(0)+1])t[(64)(0)+1]}>>1
x[22+0] = {(x[22+0]-x[20+0])t[0]-(x[20+0+1]-x[22+0+1])t[0+1]}>>1
x[22] = {(x[22]-x[20])t[0]-(x[21]-x[23])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[22+2(0)+1] = {(x[22+2(0)+1]-x[20+2(0)+1])t[(64)(0)]+(x[20+2(0)]-x[22+2(0)])t[(64)(0)+1]}>>1
x[22+1] = {(x[22+1]-x[20+1])t[0]+(x[20+0]-x[22+0])t[0+1]}>>1
x[23] = {(x[23]-x[21])t[0]+(x[20]-x[22])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)=(5,6,0)
Loop P=5 of p=log2N=log264=6 loops indexed P=0...p-1=0...6-1=0...5.
Subblock b=6 of BP=B5=2P=25=32 subblocks, indexed b=0...B5-1=0...31.
Subblock size=NP|P=5=N5=N/BP|(N=64,P=5)=(2p/2P)|(p=6,P=5)=2p-P|(p=6,P=5)=26-5=2.
Butterfly n=0 of N'P=NP/2=2p-P-1=26-5-1=1 butterflies indexed by n=0...N'P-1=0...0.
Even base index e = 2NPb = 2(2)(6) = 24.
Odd base index o = e + 2N'P = 24 + 2(1) = 26.
Twiddle step size s = 2P+1 = 25+1 = 64.
x[e+2n] ={x[e+2n]+x[o+2n]}>>1
x[24+0] ={x[24+0]+x[26+0]}>>1
x[24] ={x[24]+x[26]}>>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[26+1]}>>1
x[25] ={x[25]+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[26+2(0)] = {(x[26+2(0)]-x[24+2(0)])t[(64)(0)]-(x[24+2(0)+1]-x[26+2(0)+1])t[(64)(0)+1]}>>1
x[26+0] = {(x[26+0]-x[24+0])t[0]-(x[24+0+1]-x[26+0+1])t[0+1]}>>1
x[26] = {(x[26]-x[24])t[0]-(x[25]-x[27])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[26+2(0)+1] = {(x[26+2(0)+1]-x[24+2(0)+1])t[(64)(0)]+(x[24+2(0)]-x[26+2(0)])t[(64)(0)+1]}>>1
x[26+1] = {(x[26+1]-x[24+1])t[0]+(x[24+0]-x[26+0])t[0+1]}>>1
x[27] = {(x[27]-x[25])t[0]+(x[24]-x[26])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)=(5,7,0)
Loop P=5 of p=log2N=log264=6 loops indexed P=0...p-1=0...6-1=0...5.
Subblock b=7 of BP=B5=2P=25=32 subblocks, indexed b=0...B5-1=0...31.
Subblock size=NP|P=5=N5=N/BP|(N=64,P=5)=(2p/2P)|(p=6,P=5)=2p-P|(p=6,P=5)=26-5=2.
Butterfly n=0 of N'P=NP/2=2p-P-1=26-5-1=1 butterflies indexed by n=0...N'P-1=0...0.
Even base index e = 2NPb = 2(2)(7) = 28.
Odd base index o = e + 2N'P = 28 + 2(1) = 30.
Twiddle step size s = 2P+1 = 25+1 = 64.
x[e+2n] ={x[e+2n]+x[o+2n]}>>1
x[28+0] ={x[28+0]+x[30+0]}>>1
x[28] ={x[28]+x[30]}>>1
={0000 +0000}>>1
={00000}>>1
=0000
x[e+2n+1] ={x[e+2n+1]+x[o+2n+1]}>>1
x[28+1] ={x[28+1]+x[30+1]}>>1
x[29] ={x[29]+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[30+2(0)] = {(x[30+2(0)]-x[28+2(0)])t[(64)(0)]-(x[28+2(0)+1]-x[30+2(0)+1])t[(64)(0)+1]}>>1
x[30+0] = {(x[30+0]-x[28+0])t[0]-(x[28+0+1]-x[30+0+1])t[0+1]}>>1
x[30] = {(x[30]-x[28])t[0]-(x[29]-x[31])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[30+2(0)+1] = {(x[30+2(0)+1]-x[28+2(0)+1])t[(64)(0)]+(x[28+2(0)]-x[30+2(0)])t[(64)(0)+1]}>>1
x[30+1] = {(x[30+1]-x[28+1])t[0]+(x[28+0]-x[30+0])t[0+1]}>>1
x[31] = {(x[31]-x[29])t[0]+(x[28]-x[30])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)=(5,8,0)
Loop P=5 of p=log2N=log264=6 loops indexed P=0...p-1=0...6-1=0...5.
Subblock b=8 of BP=B5=2P=25=32 subblocks, indexed b=0...B5-1=0...31.
Subblock size=NP|P=5=N5=N/BP|(N=64,P=5)=(2p/2P)|(p=6,P=5)=2p-P|(p=6,P=5)=26-5=2.
Butterfly n=0 of N'P=NP/2=2p-P-1=26-5-1=1 butterflies indexed by n=0...N'P-1=0...0.
Even base index e = 2NPb = 2(2)(8) = 32.
Odd base index o = e + 2N'P = 32 + 2(1) = 34.
Twiddle step size s = 2P+1 = 25+1 = 64.
x[e+2n] ={x[e+2n]+x[o+2n]}>>1
x[32+0] ={x[32+0]+x[34+0]}>>1
x[32] ={x[32]+x[34]}>>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[34+1]}>>1
x[33] ={x[33]+x[35]}>>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[34+2(0)] = {(x[34+2(0)]-x[32+2(0)])t[(64)(0)]-(x[32+2(0)+1]-x[34+2(0)+1])t[(64)(0)+1]}>>1
x[34+0] = {(x[34+0]-x[32+0])t[0]-(x[32+0+1]-x[34+0+1])t[0+1]}>>1
x[34] = {(x[34]-x[32])t[0]-(x[33]-x[35])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[34+2(0)+1] = {(x[34+2(0)+1]-x[32+2(0)+1])t[(64)(0)]+(x[32+2(0)]-x[34+2(0)])t[(64)(0)+1]}>>1
x[34+1] = {(x[34+1]-x[32+1])t[0]+(x[32+0]-x[34+0])t[0+1]}>>1
x[35] = {(x[35]-x[33])t[0]+(x[32]-x[34])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)=(5,9,0)
Loop P=5 of p=log2N=log264=6 loops indexed P=0...p-1=0...6-1=0...5.
Subblock b=9 of BP=B5=2P=25=32 subblocks, indexed b=0...B5-1=0...31.
Subblock size=NP|P=5=N5=N/BP|(N=64,P=5)=(2p/2P)|(p=6,P=5)=2p-P|(p=6,P=5)=26-5=2.
Butterfly n=0 of N'P=NP/2=2p-P-1=26-5-1=1 butterflies indexed by n=0...N'P-1=0...0.
Even base index e = 2NPb = 2(2)(9) = 36.
Odd base index o = e + 2N'P = 36 + 2(1) = 38.
Twiddle step size s = 2P+1 = 25+1 = 64.
x[e+2n] ={x[e+2n]+x[o+2n]}>>1
x[36+0] ={x[36+0]+x[38+0]}>>1
x[36] ={x[36]+x[38]}>>1
={0000 +0000}>>1
={00000}>>1
=0000
x[e+2n+1] ={x[e+2n+1]+x[o+2n+1]}>>1
x[36+1] ={x[36+1]+x[38+1]}>>1
x[37] ={x[37]+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[38+2(0)] = {(x[38+2(0)]-x[36+2(0)])t[(64)(0)]-(x[36+2(0)+1]-x[38+2(0)+1])t[(64)(0)+1]}>>1
x[38+0] = {(x[38+0]-x[36+0])t[0]-(x[36+0+1]-x[38+0+1])t[0+1]}>>1
x[38] = {(x[38]-x[36])t[0]-(x[37]-x[39])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[38+2(0)+1] = {(x[38+2(0)+1]-x[36+2(0)+1])t[(64)(0)]+(x[36+2(0)]-x[38+2(0)])t[(64)(0)+1]}>>1
x[38+1] = {(x[38+1]-x[36+1])t[0]+(x[36+0]-x[38+0])t[0+1]}>>1
x[39] = {(x[39]-x[37])t[0]+(x[36]-x[38])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)=(5,10,0)
Loop P=5 of p=log2N=log264=6 loops indexed P=0...p-1=0...6-1=0...5.
Subblock b=10 of BP=B5=2P=25=32 subblocks, indexed b=0...B5-1=0...31.
Subblock size=NP|P=5=N5=N/BP|(N=64,P=5)=(2p/2P)|(p=6,P=5)=2p-P|(p=6,P=5)=26-5=2.
Butterfly n=0 of N'P=NP/2=2p-P-1=26-5-1=1 butterflies indexed by n=0...N'P-1=0...0.
Even base index e = 2NPb = 2(2)(10) = 40.
Odd base index o = e + 2N'P = 40 + 2(1) = 42.
Twiddle step size s = 2P+1 = 25+1 = 64.
x[e+2n] ={x[e+2n]+x[o+2n]}>>1
x[40+0] ={x[40+0]+x[42+0]}>>1
x[40] ={x[40]+x[42]}>>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[42+1]}>>1
x[41] ={x[41]+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[42+2(0)] = {(x[42+2(0)]-x[40+2(0)])t[(64)(0)]-(x[40+2(0)+1]-x[42+2(0)+1])t[(64)(0)+1]}>>1
x[42+0] = {(x[42+0]-x[40+0])t[0]-(x[40+0+1]-x[42+0+1])t[0+1]}>>1
x[42] = {(x[42]-x[40])t[0]-(x[41]-x[43])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[42+2(0)+1] = {(x[42+2(0)+1]-x[40+2(0)+1])t[(64)(0)]+(x[40+2(0)]-x[42+2(0)])t[(64)(0)+1]}>>1
x[42+1] = {(x[42+1]-x[40+1])t[0]+(x[40+0]-x[42+0])t[0+1]}>>1
x[43] = {(x[43]-x[41])t[0]+(x[40]-x[42])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)=(5,11,0)
Loop P=5 of p=log2N=log264=6 loops indexed P=0...p-1=0...6-1=0...5.
Subblock b=11 of BP=B5=2P=25=32 subblocks, indexed b=0...B5-1=0...31.
Subblock size=NP|P=5=N5=N/BP|(N=64,P=5)=(2p/2P)|(p=6,P=5)=2p-P|(p=6,P=5)=26-5=2.
Butterfly n=0 of N'P=NP/2=2p-P-1=26-5-1=1 butterflies indexed by n=0...N'P-1=0...0.
Even base index e = 2NPb = 2(2)(11) = 44.
Odd base index o = e + 2N'P = 44 + 2(1) = 46.
Twiddle step size s = 2P+1 = 25+1 = 64.
x[e+2n] ={x[e+2n]+x[o+2n]}>>1
x[44+0] ={x[44+0]+x[46+0]}>>1
x[44] ={x[44]+x[46]}>>1
={0000 +0000}>>1
={00000}>>1
=0000
x[e+2n+1] ={x[e+2n+1]+x[o+2n+1]}>>1
x[44+1] ={x[44+1]+x[46+1]}>>1
x[45] ={x[45]+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[46+2(0)] = {(x[46+2(0)]-x[44+2(0)])t[(64)(0)]-(x[44+2(0)+1]-x[46+2(0)+1])t[(64)(0)+1]}>>1
x[46+0] = {(x[46+0]-x[44+0])t[0]-(x[44+0+1]-x[46+0+1])t[0+1]}>>1
x[46] = {(x[46]-x[44])t[0]-(x[45]-x[47])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[46+2(0)+1] = {(x[46+2(0)+1]-x[44+2(0)+1])t[(64)(0)]+(x[44+2(0)]-x[46+2(0)])t[(64)(0)+1]}>>1
x[46+1] = {(x[46+1]-x[44+1])t[0]+(x[44+0]-x[46+0])t[0+1]}>>1
x[47] = {(x[47]-x[45])t[0]+(x[44]-x[46])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)=(5,12,0)
Loop P=5 of p=log2N=log264=6 loops indexed P=0...p-1=0...6-1=0...5.
Subblock b=12 of BP=B5=2P=25=32 subblocks, indexed b=0...B5-1=0...31.
Subblock size=NP|P=5=N5=N/BP|(N=64,P=5)=(2p/2P)|(p=6,P=5)=2p-P|(p=6,P=5)=26-5=2.
Butterfly n=0 of N'P=NP/2=2p-P-1=26-5-1=1 butterflies indexed by n=0...N'P-1=0...0.
Even base index e = 2NPb = 2(2)(12) = 48.
Odd base index o = e + 2N'P = 48 + 2(1) = 50.
Twiddle step size s = 2P+1 = 25+1 = 64.
x[e+2n] ={x[e+2n]+x[o+2n]}>>1
x[48+0] ={x[48+0]+x[50+0]}>>1
x[48] ={x[48]+x[50]}>>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[50+1]}>>1
x[49] ={x[49]+x[51]}>>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[50+2(0)] = {(x[50+2(0)]-x[48+2(0)])t[(64)(0)]-(x[48+2(0)+1]-x[50+2(0)+1])t[(64)(0)+1]}>>1
x[50+0] = {(x[50+0]-x[48+0])t[0]-(x[48+0+1]-x[50+0+1])t[0+1]}>>1
x[50] = {(x[50]-x[48])t[0]-(x[49]-x[51])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[50+2(0)+1] = {(x[50+2(0)+1]-x[48+2(0)+1])t[(64)(0)]+(x[48+2(0)]-x[50+2(0)])t[(64)(0)+1]}>>1
x[50+1] = {(x[50+1]-x[48+1])t[0]+(x[48+0]-x[50+0])t[0+1]}>>1
x[51] = {(x[51]-x[49])t[0]+(x[48]-x[50])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)=(5,13,0)
Loop P=5 of p=log2N=log264=6 loops indexed P=0...p-1=0...6-1=0...5.
Subblock b=13 of BP=B5=2P=25=32 subblocks, indexed b=0...B5-1=0...31.
Subblock size=NP|P=5=N5=N/BP|(N=64,P=5)=(2p/2P)|(p=6,P=5)=2p-P|(p=6,P=5)=26-5=2.
Butterfly n=0 of N'P=NP/2=2p-P-1=26-5-1=1 butterflies indexed by n=0...N'P-1=0...0.
Even base index e = 2NPb = 2(2)(13) = 52.
Odd base index o = e + 2N'P = 52 + 2(1) = 54.
Twiddle step size s = 2P+1 = 25+1 = 64.
x[e+2n] ={x[e+2n]+x[o+2n]}>>1
x[52+0] ={x[52+0]+x[54+0]}>>1
x[52] ={x[52]+x[54]}>>1
={0000 +0000}>>1
={00000}>>1
=0000
x[e+2n+1] ={x[e+2n+1]+x[o+2n+1]}>>1
x[52+1] ={x[52+1]+x[54+1]}>>1
x[53] ={x[53]+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[54+2(0)] = {(x[54+2(0)]-x[52+2(0)])t[(64)(0)]-(x[52+2(0)+1]-x[54+2(0)+1])t[(64)(0)+1]}>>1
x[54+0] = {(x[54+0]-x[52+0])t[0]-(x[52+0+1]-x[54+0+1])t[0+1]}>>1
x[54] = {(x[54]-x[52])t[0]-(x[53]-x[55])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[54+2(0)+1] = {(x[54+2(0)+1]-x[52+2(0)+1])t[(64)(0)]+(x[52+2(0)]-x[54+2(0)])t[(64)(0)+1]}>>1
x[54+1] = {(x[54+1]-x[52+1])t[0]+(x[52+0]-x[54+0])t[0+1]}>>1
x[55] = {(x[55]-x[53])t[0]+(x[52]-x[54])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)=(5,14,0)
Loop P=5 of p=log2N=log264=6 loops indexed P=0...p-1=0...6-1=0...5.
Subblock b=14 of BP=B5=2P=25=32 subblocks, indexed b=0...B5-1=0...31.
Subblock size=NP|P=5=N5=N/BP|(N=64,P=5)=(2p/2P)|(p=6,P=5)=2p-P|(p=6,P=5)=26-5=2.
Butterfly n=0 of N'P=NP/2=2p-P-1=26-5-1=1 butterflies indexed by n=0...N'P-1=0...0.
Even base index e = 2NPb = 2(2)(14) = 56.
Odd base index o = e + 2N'P = 56 + 2(1) = 58.
Twiddle step size s = 2P+1 = 25+1 = 64.
x[e+2n] ={x[e+2n]+x[o+2n]}>>1
x[56+0] ={x[56+0]+x[58+0]}>>1
x[56] ={x[56]+x[58]}>>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[58+1]}>>1
x[57] ={x[57]+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[58+2(0)] = {(x[58+2(0)]-x[56+2(0)])t[(64)(0)]-(x[56+2(0)+1]-x[58+2(0)+1])t[(64)(0)+1]}>>1
x[58+0] = {(x[58+0]-x[56+0])t[0]-(x[56+0+1]-x[58+0+1])t[0+1]}>>1
x[58] = {(x[58]-x[56])t[0]-(x[57]-x[59])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[58+2(0)+1] = {(x[58+2(0)+1]-x[56+2(0)+1])t[(64)(0)]+(x[56+2(0)]-x[58+2(0)])t[(64)(0)+1]}>>1
x[58+1] = {(x[58+1]-x[56+1])t[0]+(x[56+0]-x[58+0])t[0+1]}>>1
x[59] = {(x[59]-x[57])t[0]+(x[56]-x[58])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)=(5,15,0)
Loop P=5 of p=log2N=log264=6 loops indexed P=0...p-1=0...6-1=0...5.
Subblock b=15 of BP=B5=2P=25=32 subblocks, indexed b=0...B5-1=0...31.
Subblock size=NP|P=5=N5=N/BP|(N=64,P=5)=(2p/2P)|(p=6,P=5)=2p-P|(p=6,P=5)=26-5=2.
Butterfly n=0 of N'P=NP/2=2p-P-1=26-5-1=1 butterflies indexed by n=0...N'P-1=0...0.
Even base index e = 2NPb = 2(2)(15) = 60.
Odd base index o = e + 2N'P = 60 + 2(1) = 62.
Twiddle step size s = 2P+1 = 25+1 = 64.
x[e+2n] ={x[e+2n]+x[o+2n]}>>1
x[60+0] ={x[60+0]+x[62+0]}>>1
x[60] ={x[60]+x[62]}>>1
={0000 +0000}>>1
={00000}>>1
=0000
x[e+2n+1] ={x[e+2n+1]+x[o+2n+1]}>>1
x[60+1] ={x[60+1]+x[62+1]}>>1
x[61] ={x[61]+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[62+2(0)] = {(x[62+2(0)]-x[60+2(0)])t[(64)(0)]-(x[60+2(0)+1]-x[62+2(0)+1])t[(64)(0)+1]}>>1
x[62+0] = {(x[62+0]-x[60+0])t[0]-(x[60+0+1]-x[62+0+1])t[0+1]}>>1
x[62] = {(x[62]-x[60])t[0]-(x[61]-x[63])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[62+2(0)+1] = {(x[62+2(0)+1]-x[60+2(0)+1])t[(64)(0)]+(x[60+2(0)]-x[62+2(0)])t[(64)(0)+1]}>>1
x[62+1] = {(x[62+1]-x[60+1])t[0]+(x[60+0]-x[62+0])t[0+1]}>>1
x[63] = {(x[63]-x[61])t[0]+(x[60]-x[62])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)=(5,16,0)
Loop P=5 of p=log2N=log264=6 loops indexed P=0...p-1=0...6-1=0...5.
Subblock b=16 of BP=B5=2P=25=32 subblocks, indexed b=0...B5-1=0...31.
Subblock size=NP|P=5=N5=N/BP|(N=64,P=5)=(2p/2P)|(p=6,P=5)=2p-P|(p=6,P=5)=26-5=2.
Butterfly n=0 of N'P=NP/2=2p-P-1=26-5-1=1 butterflies indexed by n=0...N'P-1=0...0.
Even base index e = 2NPb = 2(2)(16) = 64.
Odd base index o = e + 2N'P = 64 + 2(1) = 66.
Twiddle step size s = 2P+1 = 25+1 = 64.
x[e+2n] ={x[e+2n]+x[o+2n]}>>1
x[64+0] ={x[64+0]+x[66+0]}>>1
x[64] ={x[64]+x[66]}>>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[66+1]}>>1
x[65] ={x[65]+x[67]}>>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[66+2(0)] = {(x[66+2(0)]-x[64+2(0)])t[(64)(0)]-(x[64+2(0)+1]-x[66+2(0)+1])t[(64)(0)+1]}>>1
x[66+0] = {(x[66+0]-x[64+0])t[0]-(x[64+0+1]-x[66+0+1])t[0+1]}>>1
x[66] = {(x[66]-x[64])t[0]-(x[65]-x[67])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[66+2(0)+1] = {(x[66+2(0)+1]-x[64+2(0)+1])t[(64)(0)]+(x[64+2(0)]-x[66+2(0)])t[(64)(0)+1]}>>1
x[66+1] = {(x[66+1]-x[64+1])t[0]+(x[64+0]-x[66+0])t[0+1]}>>1
x[67] = {(x[67]-x[65])t[0]+(x[64]-x[66])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)=(5,17,0)
Loop P=5 of p=log2N=log264=6 loops indexed P=0...p-1=0...6-1=0...5.
Subblock b=17 of BP=B5=2P=25=32 subblocks, indexed b=0...B5-1=0...31.
Subblock size=NP|P=5=N5=N/BP|(N=64,P=5)=(2p/2P)|(p=6,P=5)=2p-P|(p=6,P=5)=26-5=2.
Butterfly n=0 of N'P=NP/2=2p-P-1=26-5-1=1 butterflies indexed by n=0...N'P-1=0...0.
Even base index e = 2NPb = 2(2)(17) = 68.
Odd base index o = e + 2N'P = 68 + 2(1) = 70.
Twiddle step size s = 2P+1 = 25+1 = 64.
x[e+2n] ={x[e+2n]+x[o+2n]}>>1
x[68+0] ={x[68+0]+x[70+0]}>>1
x[68] ={x[68]+x[70]}>>1
={0000 +0000}>>1
={00000}>>1
=0000
x[e+2n+1] ={x[e+2n+1]+x[o+2n+1]}>>1
x[68+1] ={x[68+1]+x[70+1]}>>1
x[69] ={x[69]+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[70+2(0)] = {(x[70+2(0)]-x[68+2(0)])t[(64)(0)]-(x[68+2(0)+1]-x[70+2(0)+1])t[(64)(0)+1]}>>1
x[70+0] = {(x[70+0]-x[68+0])t[0]-(x[68+0+1]-x[70+0+1])t[0+1]}>>1
x[70] = {(x[70]-x[68])t[0]-(x[69]-x[71])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[70+2(0)+1] = {(x[70+2(0)+1]-x[68+2(0)+1])t[(64)(0)]+(x[68+2(0)]-x[70+2(0)])t[(64)(0)+1]}>>1
x[70+1] = {(x[70+1]-x[68+1])t[0]+(x[68+0]-x[70+0])t[0+1]}>>1
x[71] = {(x[71]-x[69])t[0]+(x[68]-x[70])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)=(5,18,0)
Loop P=5 of p=log2N=log264=6 loops indexed P=0...p-1=0...6-1=0...5.
Subblock b=18 of BP=B5=2P=25=32 subblocks, indexed b=0...B5-1=0...31.
Subblock size=NP|P=5=N5=N/BP|(N=64,P=5)=(2p/2P)|(p=6,P=5)=2p-P|(p=6,P=5)=26-5=2.
Butterfly n=0 of N'P=NP/2=2p-P-1=26-5-1=1 butterflies indexed by n=0...N'P-1=0...0.
Even base index e = 2NPb = 2(2)(18) = 72.
Odd base index o = e + 2N'P = 72 + 2(1) = 74.
Twiddle step size s = 2P+1 = 25+1 = 64.
x[e+2n] ={x[e+2n]+x[o+2n]}>>1
x[72+0] ={x[72+0]+x[74+0]}>>1
x[72] ={x[72]+x[74]}>>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[74+1]}>>1
x[73] ={x[73]+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[74+2(0)] = {(x[74+2(0)]-x[72+2(0)])t[(64)(0)]-(x[72+2(0)+1]-x[74+2(0)+1])t[(64)(0)+1]}>>1
x[74+0] = {(x[74+0]-x[72+0])t[0]-(x[72+0+1]-x[74+0+1])t[0+1]}>>1
x[74] = {(x[74]-x[72])t[0]-(x[73]-x[75])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[74+2(0)+1] = {(x[74+2(0)+1]-x[72+2(0)+1])t[(64)(0)]+(x[72+2(0)]-x[74+2(0)])t[(64)(0)+1]}>>1
x[74+1] = {(x[74+1]-x[72+1])t[0]+(x[72+0]-x[74+0])t[0+1]}>>1
x[75] = {(x[75]-x[73])t[0]+(x[72]-x[74])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)=(5,19,0)
Loop P=5 of p=log2N=log264=6 loops indexed P=0...p-1=0...6-1=0...5.
Subblock b=19 of BP=B5=2P=25=32 subblocks, indexed b=0...B5-1=0...31.
Subblock size=NP|P=5=N5=N/BP|(N=64,P=5)=(2p/2P)|(p=6,P=5)=2p-P|(p=6,P=5)=26-5=2.
Butterfly n=0 of N'P=NP/2=2p-P-1=26-5-1=1 butterflies indexed by n=0...N'P-1=0...0.
Even base index e = 2NPb = 2(2)(19) = 76.
Odd base index o = e + 2N'P = 76 + 2(1) = 78.
Twiddle step size s = 2P+1 = 25+1 = 64.
x[e+2n] ={x[e+2n]+x[o+2n]}>>1
x[76+0] ={x[76+0]+x[78+0]}>>1
x[76] ={x[76]+x[78]}>>1
={0000 +0000}>>1
={00000}>>1
=0000
x[e+2n+1] ={x[e+2n+1]+x[o+2n+1]}>>1
x[76+1] ={x[76+1]+x[78+1]}>>1
x[77] ={x[77]+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[78+2(0)] = {(x[78+2(0)]-x[76+2(0)])t[(64)(0)]-(x[76+2(0)+1]-x[78+2(0)+1])t[(64)(0)+1]}>>1
x[78+0] = {(x[78+0]-x[76+0])t[0]-(x[76+0+1]-x[78+0+1])t[0+1]}>>1
x[78] = {(x[78]-x[76])t[0]-(x[77]-x[79])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[78+2(0)+1] = {(x[78+2(0)+1]-x[76+2(0)+1])t[(64)(0)]+(x[76+2(0)]-x[78+2(0)])t[(64)(0)+1]}>>1
x[78+1] = {(x[78+1]-x[76+1])t[0]+(x[76+0]-x[78+0])t[0+1]}>>1
x[79] = {(x[79]-x[77])t[0]+(x[76]-x[78])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)=(5,20,0)
Loop P=5 of p=log2N=log264=6 loops indexed P=0...p-1=0...6-1=0...5.
Subblock b=20 of BP=B5=2P=25=32 subblocks, indexed b=0...B5-1=0...31.
Subblock size=NP|P=5=N5=N/BP|(N=64,P=5)=(2p/2P)|(p=6,P=5)=2p-P|(p=6,P=5)=26-5=2.
Butterfly n=0 of N'P=NP/2=2p-P-1=26-5-1=1 butterflies indexed by n=0...N'P-1=0...0.
Even base index e = 2NPb = 2(2)(20) = 80.
Odd base index o = e + 2N'P = 80 + 2(1) = 82.
Twiddle step size s = 2P+1 = 25+1 = 64.
x[e+2n] ={x[e+2n]+x[o+2n]}>>1
x[80+0] ={x[80+0]+x[82+0]}>>1
x[80] ={x[80]+x[82]}>>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[82+1]}>>1
x[81] ={x[81]+x[83]}>>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[82+2(0)] = {(x[82+2(0)]-x[80+2(0)])t[(64)(0)]-(x[80+2(0)+1]-x[82+2(0)+1])t[(64)(0)+1]}>>1
x[82+0] = {(x[82+0]-x[80+0])t[0]-(x[80+0+1]-x[82+0+1])t[0+1]}>>1
x[82] = {(x[82]-x[80])t[0]-(x[81]-x[83])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[82+2(0)+1] = {(x[82+2(0)+1]-x[80+2(0)+1])t[(64)(0)]+(x[80+2(0)]-x[82+2(0)])t[(64)(0)+1]}>>1
x[82+1] = {(x[82+1]-x[80+1])t[0]+(x[80+0]-x[82+0])t[0+1]}>>1
x[83] = {(x[83]-x[81])t[0]+(x[80]-x[82])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)=(5,21,0)
Loop P=5 of p=log2N=log264=6 loops indexed P=0...p-1=0...6-1=0...5.
Subblock b=21 of BP=B5=2P=25=32 subblocks, indexed b=0...B5-1=0...31.
Subblock size=NP|P=5=N5=N/BP|(N=64,P=5)=(2p/2P)|(p=6,P=5)=2p-P|(p=6,P=5)=26-5=2.
Butterfly n=0 of N'P=NP/2=2p-P-1=26-5-1=1 butterflies indexed by n=0...N'P-1=0...0.
Even base index e = 2NPb = 2(2)(21) = 84.
Odd base index o = e + 2N'P = 84 + 2(1) = 86.
Twiddle step size s = 2P+1 = 25+1 = 64.
x[e+2n] ={x[e+2n]+x[o+2n]}>>1
x[84+0] ={x[84+0]+x[86+0]}>>1
x[84] ={x[84]+x[86]}>>1
={0000 +0000}>>1
={00000}>>1
=0000
x[e+2n+1] ={x[e+2n+1]+x[o+2n+1]}>>1
x[84+1] ={x[84+1]+x[86+1]}>>1
x[85] ={x[85]+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[86+2(0)] = {(x[86+2(0)]-x[84+2(0)])t[(64)(0)]-(x[84+2(0)+1]-x[86+2(0)+1])t[(64)(0)+1]}>>1
x[86+0] = {(x[86+0]-x[84+0])t[0]-(x[84+0+1]-x[86+0+1])t[0+1]}>>1
x[86] = {(x[86]-x[84])t[0]-(x[85]-x[87])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[86+2(0)+1] = {(x[86+2(0)+1]-x[84+2(0)+1])t[(64)(0)]+(x[84+2(0)]-x[86+2(0)])t[(64)(0)+1]}>>1
x[86+1] = {(x[86+1]-x[84+1])t[0]+(x[84+0]-x[86+0])t[0+1]}>>1
x[87] = {(x[87]-x[85])t[0]+(x[84]-x[86])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)=(5,22,0)
Loop P=5 of p=log2N=log264=6 loops indexed P=0...p-1=0...6-1=0...5.
Subblock b=22 of BP=B5=2P=25=32 subblocks, indexed b=0...B5-1=0...31.
Subblock size=NP|P=5=N5=N/BP|(N=64,P=5)=(2p/2P)|(p=6,P=5)=2p-P|(p=6,P=5)=26-5=2.
Butterfly n=0 of N'P=NP/2=2p-P-1=26-5-1=1 butterflies indexed by n=0...N'P-1=0...0.
Even base index e = 2NPb = 2(2)(22) = 88.
Odd base index o = e + 2N'P = 88 + 2(1) = 90.
Twiddle step size s = 2P+1 = 25+1 = 64.
x[e+2n] ={x[e+2n]+x[o+2n]}>>1
x[88+0] ={x[88+0]+x[90+0]}>>1
x[88] ={x[88]+x[90]}>>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[90+1]}>>1
x[89] ={x[89]+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[90+2(0)] = {(x[90+2(0)]-x[88+2(0)])t[(64)(0)]-(x[88+2(0)+1]-x[90+2(0)+1])t[(64)(0)+1]}>>1
x[90+0] = {(x[90+0]-x[88+0])t[0]-(x[88+0+1]-x[90+0+1])t[0+1]}>>1
x[90] = {(x[90]-x[88])t[0]-(x[89]-x[91])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[90+2(0)+1] = {(x[90+2(0)+1]-x[88+2(0)+1])t[(64)(0)]+(x[88+2(0)]-x[90+2(0)])t[(64)(0)+1]}>>1
x[90+1] = {(x[90+1]-x[88+1])t[0]+(x[88+0]-x[90+0])t[0+1]}>>1
x[91] = {(x[91]-x[89])t[0]+(x[88]-x[90])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)=(5,23,0)
Loop P=5 of p=log2N=log264=6 loops indexed P=0...p-1=0...6-1=0...5.
Subblock b=23 of BP=B5=2P=25=32 subblocks, indexed b=0...B5-1=0...31.
Subblock size=NP|P=5=N5=N/BP|(N=64,P=5)=(2p/2P)|(p=6,P=5)=2p-P|(p=6,P=5)=26-5=2.
Butterfly n=0 of N'P=NP/2=2p-P-1=26-5-1=1 butterflies indexed by n=0...N'P-1=0...0.
Even base index e = 2NPb = 2(2)(23) = 92.
Odd base index o = e + 2N'P = 92 + 2(1) = 94.
Twiddle step size s = 2P+1 = 25+1 = 64.
x[e+2n] ={x[e+2n]+x[o+2n]}>>1
x[92+0] ={x[92+0]+x[94+0]}>>1
x[92] ={x[92]+x[94]}>>1
={0000 +0000}>>1
={00000}>>1
=0000
x[e+2n+1] ={x[e+2n+1]+x[o+2n+1]}>>1
x[92+1] ={x[92+1]+x[94+1]}>>1
x[93] ={x[93]+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[94+2(0)] = {(x[94+2(0)]-x[92+2(0)])t[(64)(0)]-(x[92+2(0)+1]-x[94+2(0)+1])t[(64)(0)+1]}>>1
x[94+0] = {(x[94+0]-x[92+0])t[0]-(x[92+0+1]-x[94+0+1])t[0+1]}>>1
x[94] = {(x[94]-x[92])t[0]-(x[93]-x[95])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[94+2(0)+1] = {(x[94+2(0)+1]-x[92+2(0)+1])t[(64)(0)]+(x[92+2(0)]-x[94+2(0)])t[(64)(0)+1]}>>1
x[94+1] = {(x[94+1]-x[92+1])t[0]+(x[92+0]-x[94+0])t[0+1]}>>1
x[95] = {(x[95]-x[93])t[0]+(x[92]-x[94])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)=(5,24,0)
Loop P=5 of p=log2N=log264=6 loops indexed P=0...p-1=0...6-1=0...5.
Subblock b=24 of BP=B5=2P=25=32 subblocks, indexed b=0...B5-1=0...31.
Subblock size=NP|P=5=N5=N/BP|(N=64,P=5)=(2p/2P)|(p=6,P=5)=2p-P|(p=6,P=5)=26-5=2.
Butterfly n=0 of N'P=NP/2=2p-P-1=26-5-1=1 butterflies indexed by n=0...N'P-1=0...0.
Even base index e = 2NPb = 2(2)(24) = 96.
Odd base index o = e + 2N'P = 96 + 2(1) = 98.
Twiddle step size s = 2P+1 = 25+1 = 64.
x[e+2n] ={x[e+2n]+x[o+2n]}>>1
x[96+0] ={x[96+0]+x[98+0]}>>1
x[96] ={x[96]+x[98]}>>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[98+1]}>>1
x[97] ={x[97]+x[99]}>>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[98+2(0)] = {(x[98+2(0)]-x[96+2(0)])t[(64)(0)]-(x[96+2(0)+1]-x[98+2(0)+1])t[(64)(0)+1]}>>1
x[98+0] = {(x[98+0]-x[96+0])t[0]-(x[96+0+1]-x[98+0+1])t[0+1]}>>1
x[98] = {(x[98]-x[96])t[0]-(x[97]-x[99])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[98+2(0)+1] = {(x[98+2(0)+1]-x[96+2(0)+1])t[(64)(0)]+(x[96+2(0)]-x[98+2(0)])t[(64)(0)+1]}>>1
x[98+1] = {(x[98+1]-x[96+1])t[0]+(x[96+0]-x[98+0])t[0+1]}>>1
x[99] = {(x[99]-x[97])t[0]+(x[96]-x[98])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)=(5,25,0)
Loop P=5 of p=log2N=log264=6 loops indexed P=0...p-1=0...6-1=0...5.
Subblock b=25 of BP=B5=2P=25=32 subblocks, indexed b=0...B5-1=0...31.
Subblock size=NP|P=5=N5=N/BP|(N=64,P=5)=(2p/2P)|(p=6,P=5)=2p-P|(p=6,P=5)=26-5=2.
Butterfly n=0 of N'P=NP/2=2p-P-1=26-5-1=1 butterflies indexed by n=0...N'P-1=0...0.
Even base index e = 2NPb = 2(2)(25) = 100.
Odd base index o = e + 2N'P = 100 + 2(1) = 102.
Twiddle step size s = 2P+1 = 25+1 = 64.
x[e+2n] ={x[e+2n]+x[o+2n]}>>1
x[100+0] ={x[100+0]+x[102+0]}>>1
x[100] ={x[100]+x[102]}>>1
={0000 +0000}>>1
={00000}>>1
=0000
x[e+2n+1] ={x[e+2n+1]+x[o+2n+1]}>>1
x[100+1] ={x[100+1]+x[102+1]}>>1
x[101] ={x[101]+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[102+2(0)] = {(x[102+2(0)]-x[100+2(0)])t[(64)(0)]-(x[100+2(0)+1]-x[102+2(0)+1])t[(64)(0)+1]}>>1
x[102+0] = {(x[102+0]-x[100+0])t[0]-(x[100+0+1]-x[102+0+1])t[0+1]}>>1
x[102] = {(x[102]-x[100])t[0]-(x[101]-x[103])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[102+2(0)+1] = {(x[102+2(0)+1]-x[100+2(0)+1])t[(64)(0)]+(x[100+2(0)]-x[102+2(0)])t[(64)(0)+1]}>>1
x[102+1] = {(x[102+1]-x[100+1])t[0]+(x[100+0]-x[102+0])t[0+1]}>>1
x[103] = {(x[103]-x[101])t[0]+(x[100]-x[102])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)=(5,26,0)
Loop P=5 of p=log2N=log264=6 loops indexed P=0...p-1=0...6-1=0...5.
Subblock b=26 of BP=B5=2P=25=32 subblocks, indexed b=0...B5-1=0...31.
Subblock size=NP|P=5=N5=N/BP|(N=64,P=5)=(2p/2P)|(p=6,P=5)=2p-P|(p=6,P=5)=26-5=2.
Butterfly n=0 of N'P=NP/2=2p-P-1=26-5-1=1 butterflies indexed by n=0...N'P-1=0...0.
Even base index e = 2NPb = 2(2)(26) = 104.
Odd base index o = e + 2N'P = 104 + 2(1) = 106.
Twiddle step size s = 2P+1 = 25+1 = 64.
x[e+2n] ={x[e+2n]+x[o+2n]}>>1
x[104+0] ={x[104+0]+x[106+0]}>>1
x[104] ={x[104]+x[106]}>>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[106+1]}>>1
x[105] ={x[105]+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[106+2(0)] = {(x[106+2(0)]-x[104+2(0)])t[(64)(0)]-(x[104+2(0)+1]-x[106+2(0)+1])t[(64)(0)+1]}>>1
x[106+0] = {(x[106+0]-x[104+0])t[0]-(x[104+0+1]-x[106+0+1])t[0+1]}>>1
x[106] = {(x[106]-x[104])t[0]-(x[105]-x[107])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[106+2(0)+1] = {(x[106+2(0)+1]-x[104+2(0)+1])t[(64)(0)]+(x[104+2(0)]-x[106+2(0)])t[(64)(0)+1]}>>1
x[106+1] = {(x[106+1]-x[104+1])t[0]+(x[104+0]-x[106+0])t[0+1]}>>1
x[107] = {(x[107]-x[105])t[0]+(x[104]-x[106])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)=(5,27,0)
Loop P=5 of p=log2N=log264=6 loops indexed P=0...p-1=0...6-1=0...5.
Subblock b=27 of BP=B5=2P=25=32 subblocks, indexed b=0...B5-1=0...31.
Subblock size=NP|P=5=N5=N/BP|(N=64,P=5)=(2p/2P)|(p=6,P=5)=2p-P|(p=6,P=5)=26-5=2.
Butterfly n=0 of N'P=NP/2=2p-P-1=26-5-1=1 butterflies indexed by n=0...N'P-1=0...0.
Even base index e = 2NPb = 2(2)(27) = 108.
Odd base index o = e + 2N'P = 108 + 2(1) = 110.
Twiddle step size s = 2P+1 = 25+1 = 64.
x[e+2n] ={x[e+2n]+x[o+2n]}>>1
x[108+0] ={x[108+0]+x[110+0]}>>1
x[108] ={x[108]+x[110]}>>1
={0000 +0000}>>1
={00000}>>1
=0000
x[e+2n+1] ={x[e+2n+1]+x[o+2n+1]}>>1
x[108+1] ={x[108+1]+x[110+1]}>>1
x[109] ={x[109]+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[110+2(0)] = {(x[110+2(0)]-x[108+2(0)])t[(64)(0)]-(x[108+2(0)+1]-x[110+2(0)+1])t[(64)(0)+1]}>>1
x[110+0] = {(x[110+0]-x[108+0])t[0]-(x[108+0+1]-x[110+0+1])t[0+1]}>>1
x[110] = {(x[110]-x[108])t[0]-(x[109]-x[111])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[110+2(0)+1] = {(x[110+2(0)+1]-x[108+2(0)+1])t[(64)(0)]+(x[108+2(0)]-x[110+2(0)])t[(64)(0)+1]}>>1
x[110+1] = {(x[110+1]-x[108+1])t[0]+(x[108+0]-x[110+0])t[0+1]}>>1
x[111] = {(x[111]-x[109])t[0]+(x[108]-x[110])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)=(5,28,0)
Loop P=5 of p=log2N=log264=6 loops indexed P=0...p-1=0...6-1=0...5.
Subblock b=28 of BP=B5=2P=25=32 subblocks, indexed b=0...B5-1=0...31.
Subblock size=NP|P=5=N5=N/BP|(N=64,P=5)=(2p/2P)|(p=6,P=5)=2p-P|(p=6,P=5)=26-5=2.
Butterfly n=0 of N'P=NP/2=2p-P-1=26-5-1=1 butterflies indexed by n=0...N'P-1=0...0.
Even base index e = 2NPb = 2(2)(28) = 112.
Odd base index o = e + 2N'P = 112 + 2(1) = 114.
Twiddle step size s = 2P+1 = 25+1 = 64.
x[e+2n] ={x[e+2n]+x[o+2n]}>>1
x[112+0] ={x[112+0]+x[114+0]}>>1
x[112] ={x[112]+x[114]}>>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[114+1]}>>1
x[113] ={x[113]+x[115]}>>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[114+2(0)] = {(x[114+2(0)]-x[112+2(0)])t[(64)(0)]-(x[112+2(0)+1]-x[114+2(0)+1])t[(64)(0)+1]}>>1
x[114+0] = {(x[114+0]-x[112+0])t[0]-(x[112+0+1]-x[114+0+1])t[0+1]}>>1
x[114] = {(x[114]-x[112])t[0]-(x[113]-x[115])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[114+2(0)+1] = {(x[114+2(0)+1]-x[112+2(0)+1])t[(64)(0)]+(x[112+2(0)]-x[114+2(0)])t[(64)(0)+1]}>>1
x[114+1] = {(x[114+1]-x[112+1])t[0]+(x[112+0]-x[114+0])t[0+1]}>>1
x[115] = {(x[115]-x[113])t[0]+(x[112]-x[114])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)=(5,29,0)
Loop P=5 of p=log2N=log264=6 loops indexed P=0...p-1=0...6-1=0...5.
Subblock b=29 of BP=B5=2P=25=32 subblocks, indexed b=0...B5-1=0...31.
Subblock size=NP|P=5=N5=N/BP|(N=64,P=5)=(2p/2P)|(p=6,P=5)=2p-P|(p=6,P=5)=26-5=2.
Butterfly n=0 of N'P=NP/2=2p-P-1=26-5-1=1 butterflies indexed by n=0...N'P-1=0...0.
Even base index e = 2NPb = 2(2)(29) = 116.
Odd base index o = e + 2N'P = 116 + 2(1) = 118.
Twiddle step size s = 2P+1 = 25+1 = 64.
x[e+2n] ={x[e+2n]+x[o+2n]}>>1
x[116+0] ={x[116+0]+x[118+0]}>>1
x[116] ={x[116]+x[118]}>>1
={0000 +0000}>>1
={00000}>>1
=0000
x[e+2n+1] ={x[e+2n+1]+x[o+2n+1]}>>1
x[116+1] ={x[116+1]+x[118+1]}>>1
x[117] ={x[117]+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[118+2(0)] = {(x[118+2(0)]-x[116+2(0)])t[(64)(0)]-(x[116+2(0)+1]-x[118+2(0)+1])t[(64)(0)+1]}>>1
x[118+0] = {(x[118+0]-x[116+0])t[0]-(x[116+0+1]-x[118+0+1])t[0+1]}>>1
x[118] = {(x[118]-x[116])t[0]-(x[117]-x[119])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[118+2(0)+1] = {(x[118+2(0)+1]-x[116+2(0)+1])t[(64)(0)]+(x[116+2(0)]-x[118+2(0)])t[(64)(0)+1]}>>1
x[118+1] = {(x[118+1]-x[116+1])t[0]+(x[116+0]-x[118+0])t[0+1]}>>1
x[119] = {(x[119]-x[117])t[0]+(x[116]-x[118])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)=(5,30,0)
Loop P=5 of p=log2N=log264=6 loops indexed P=0...p-1=0...6-1=0...5.
Subblock b=30 of BP=B5=2P=25=32 subblocks, indexed b=0...B5-1=0...31.
Subblock size=NP|P=5=N5=N/BP|(N=64,P=5)=(2p/2P)|(p=6,P=5)=2p-P|(p=6,P=5)=26-5=2.
Butterfly n=0 of N'P=NP/2=2p-P-1=26-5-1=1 butterflies indexed by n=0...N'P-1=0...0.
Even base index e = 2NPb = 2(2)(30) = 120.
Odd base index o = e + 2N'P = 120 + 2(1) = 122.
Twiddle step size s = 2P+1 = 25+1 = 64.
x[e+2n] ={x[e+2n]+x[o+2n]}>>1
x[120+0] ={x[120+0]+x[122+0]}>>1
x[120] ={x[120]+x[122]}>>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[122+1]}>>1
x[121] ={x[121]+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[122+2(0)] = {(x[122+2(0)]-x[120+2(0)])t[(64)(0)]-(x[120+2(0)+1]-x[122+2(0)+1])t[(64)(0)+1]}>>1
x[122+0] = {(x[122+0]-x[120+0])t[0]-(x[120+0+1]-x[122+0+1])t[0+1]}>>1
x[122] = {(x[122]-x[120])t[0]-(x[121]-x[123])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[122+2(0)+1] = {(x[122+2(0)+1]-x[120+2(0)+1])t[(64)(0)]+(x[120+2(0)]-x[122+2(0)])t[(64)(0)+1]}>>1
x[122+1] = {(x[122+1]-x[120+1])t[0]+(x[120+0]-x[122+0])t[0+1]}>>1
x[123] = {(x[123]-x[121])t[0]+(x[120]-x[122])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)=(5,31,0)
Loop P=5 of p=log2N=log264=6 loops indexed P=0...p-1=0...6-1=0...5.
Subblock b=31 of BP=B5=2P=25=32 subblocks, indexed b=0...B5-1=0...31.
Subblock size=NP|P=5=N5=N/BP|(N=64,P=5)=(2p/2P)|(p=6,P=5)=2p-P|(p=6,P=5)=26-5=2.
Butterfly n=0 of N'P=NP/2=2p-P-1=26-5-1=1 butterflies indexed by n=0...N'P-1=0...0.
Even base index e = 2NPb = 2(2)(31) = 124.
Odd base index o = e + 2N'P = 124 + 2(1) = 126.
Twiddle step size s = 2P+1 = 25+1 = 64.
x[e+2n] ={x[e+2n]+x[o+2n]}>>1
x[124+0] ={x[124+0]+x[126+0]}>>1
x[124] ={x[124]+x[126]}>>1
={0000 +0000}>>1
={00000}>>1
=0000
x[e+2n+1] ={x[e+2n+1]+x[o+2n+1]}>>1
x[124+1] ={x[124+1]+x[126+1]}>>1
x[125] ={x[125]+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[126+2(0)] = {(x[126+2(0)]-x[124+2(0)])t[(64)(0)]-(x[124+2(0)+1]-x[126+2(0)+1])t[(64)(0)+1]}>>1
x[126+0] = {(x[126+0]-x[124+0])t[0]-(x[124+0+1]-x[126+0+1])t[0+1]}>>1
x[126] = {(x[126]-x[124])t[0]-(x[125]-x[127])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[126+2(0)+1] = {(x[126+2(0)+1]-x[124+2(0)+1])t[(64)(0)]+(x[124+2(0)]-x[126+2(0)])t[(64)(0)+1]}>>1
x[126+1] = {(x[126+1]-x[124+1])t[0]+(x[124+0]-x[126+0])t[0+1]}>>1
x[127] = {(x[127]-x[125])t[0]+(x[124]-x[126])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



End of loop 5
x[0]=0000 x[1]=0000
x[2]=0000 x[3]=0000
x[4]=0000 x[5]=f000
x[6]=0000 x[7]=1000
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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