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



John Bryan






(P,b,n)=(2,0,0)
Loop P=2 of p=log2N=log264=6 loops indexed P=0...p-1=0...6-1=0...5.
Subblock b=0 of BP=B2=2P=22=4 subblocks, indexed b=0...B2-1=0...3.
Subblock size=NP|P=2=N2=N/BP|(N=64,P=2)=(2p/2P)|(p=6,P=2)=2p-P|(p=6,P=2)=26-2=16.
Butterfly n=0 of N'P=NP/2=2p-P-1=26-2-1=8 butterflies indexed by n=0...N'P-1=0...7.
Even base index e = 2NPb = 2(16)(0) = 0.
Odd base index o = e + 2N'P = 0 + 2(8) = 16.
Twiddle step size s = 2P+1 = 22+1 = 8.
x[e+2n] ={x[e+2n]+x[o+2n]}>>1
x[0+0] ={x[0+0]+x[16+0]}>>1
x[0] ={x[0]+x[16]}>>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[16+1]}>>1
x[1] ={x[1]+x[17]}>>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[16+2(0)] = {(x[16+2(0)]-x[0+2(0)])t[(8)(0)]-(x[0+2(0)+1]-x[16+2(0)+1])t[(8)(0)+1]}>>1
x[16+0] = {(x[16+0]-x[0+0])t[0]-(x[0+0+1]-x[16+0+1])t[0+1]}>>1
x[16] = {(x[16]-x[0])t[0]-(x[1]-x[17])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[16+2(0)+1] = {(x[16+2(0)+1]-x[0+2(0)+1])t[(8)(0)]+(x[0+2(0)]-x[16+2(0)])t[(8)(0)+1]}>>1
x[16+1] = {(x[16+1]-x[0+1])t[0]+(x[0+0]-x[16+0])t[0+1]}>>1
x[17] = {(x[17]-x[1])t[0]+(x[0]-x[16])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)=(2,0,1)
Loop P=2 of p=log2N=log264=6 loops indexed P=0...p-1=0...6-1=0...5.
Subblock b=0 of BP=B2=2P=22=4 subblocks, indexed b=0...B2-1=0...3.
Subblock size=NP|P=2=N2=N/BP|(N=64,P=2)=(2p/2P)|(p=6,P=2)=2p-P|(p=6,P=2)=26-2=16.
Butterfly n=1 of N'P=NP/2=2p-P-1=26-2-1=8 butterflies indexed by n=0...N'P-1=0...7.
Even base index e = 2NPb = 2(16)(0) = 0.
Odd base index o = e + 2N'P = 0 + 2(8) = 16.
Twiddle step size s = 2P+1 = 22+1 = 8.
x[e+2n] ={x[e+2n]+x[o+2n]}>>1
x[0+2] ={x[0+2]+x[16+2]}>>1
x[2] ={x[2]+x[18]}>>1
={1000 +1000}>>1
={02000}>>1
=1000
x[e+2n+1] ={x[e+2n+1]+x[o+2n+1]}>>1
x[0+3] ={x[0+3]+x[16+3]}>>1
x[3] ={x[3]+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[16+2(1)] = {(x[16+2(1)]-x[0+2(1)])t[(8)(1)]-(x[0+2(1)+1]-x[16+2(1)+1])t[(8)(1)+1]}>>1
x[16+2] = {(x[16+2]-x[0+2])t[8]-(x[0+2+1]-x[16+2+1])t[8+1]}>>1
x[18] = {(x[18]-x[2])t[8]-(x[3]-x[19])t[9]}>>1
= {(1000-1000)89be-(0000-0000)cf04}>>1
= {(00000)89be-(00000)cf04}>>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[16+2(1)+1] = {(x[16+2(1)+1]-x[0+2(1)+1])t[(8)(1)]+(x[0+2(1)]-x[16+2(1)])t[(8)(1)+1]}>>1
x[16+3] = {(x[16+3]-x[0+3])t[8]+(x[0+2]-x[16+2])t[8+1]}>>1
x[19] = {(x[19]-x[3])t[8]+(x[2]-x[18])t[9]}>>1
= {(0000-0000)89be+(1000-1000)cf04}>>1
= {(00000)89be+(00000)cf04}>>1
= {00000+00000}>>1
= {00000}>>1
= 0000



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(P,b,n)=(2,0,2)
Loop P=2 of p=log2N=log264=6 loops indexed P=0...p-1=0...6-1=0...5.
Subblock b=0 of BP=B2=2P=22=4 subblocks, indexed b=0...B2-1=0...3.
Subblock size=NP|P=2=N2=N/BP|(N=64,P=2)=(2p/2P)|(p=6,P=2)=2p-P|(p=6,P=2)=26-2=16.
Butterfly n=2 of N'P=NP/2=2p-P-1=26-2-1=8 butterflies indexed by n=0...N'P-1=0...7.
Even base index e = 2NPb = 2(16)(0) = 0.
Odd base index o = e + 2N'P = 0 + 2(8) = 16.
Twiddle step size s = 2P+1 = 22+1 = 8.
x[e+2n] ={x[e+2n]+x[o+2n]}>>1
x[0+4] ={x[0+4]+x[16+4]}>>1
x[4] ={x[4]+x[20]}>>1
={0000 +0000}>>1
={00000}>>1
=0000
x[e+2n+1] ={x[e+2n+1]+x[o+2n+1]}>>1
x[0+5] ={x[0+5]+x[16+5]}>>1
x[5] ={x[5]+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[16+2(2)] = {(x[16+2(2)]-x[0+2(2)])t[(8)(2)]-(x[0+2(2)+1]-x[16+2(2)+1])t[(8)(2)+1]}>>1
x[16+4] = {(x[16+4]-x[0+4])t[16]-(x[0+4+1]-x[16+4+1])t[16+1]}>>1
x[20] = {(x[20]-x[4])t[16]-(x[5]-x[21])t[17]}>>1
= {(0000-0000)a57d-(0000-0000)a57d}>>1
= {(00000)a57d-(00000)a57d}>>1
= {00000 - 00000}>>1
= {00000}>>1
= 0000
x[o+2n+1] = {(x[o+2n+1]-x[e+2n+1])t[sn]+(x[e+2n]-x[o+2n])t[sn+1]}>>1
x[16+2(2)+1] = {(x[16+2(2)+1]-x[0+2(2)+1])t[(8)(2)]+(x[0+2(2)]-x[16+2(2)])t[(8)(2)+1]}>>1
x[16+5] = {(x[16+5]-x[0+5])t[16]+(x[0+4]-x[16+4])t[16+1]}>>1
x[21] = {(x[21]-x[5])t[16]+(x[4]-x[20])t[17]}>>1
= {(0000-0000)a57d+(0000-0000)a57d}>>1
= {(00000)a57d+(00000)a57d}>>1
= {00000+00000}>>1
= {00000}>>1
= 0000



Return to Table of Contents




(P,b,n)=(2,0,3)
Loop P=2 of p=log2N=log264=6 loops indexed P=0...p-1=0...6-1=0...5.
Subblock b=0 of BP=B2=2P=22=4 subblocks, indexed b=0...B2-1=0...3.
Subblock size=NP|P=2=N2=N/BP|(N=64,P=2)=(2p/2P)|(p=6,P=2)=2p-P|(p=6,P=2)=26-2=16.
Butterfly n=3 of N'P=NP/2=2p-P-1=26-2-1=8 butterflies indexed by n=0...N'P-1=0...7.
Even base index e = 2NPb = 2(16)(0) = 0.
Odd base index o = e + 2N'P = 0 + 2(8) = 16.
Twiddle step size s = 2P+1 = 22+1 = 8.
x[e+2n] ={x[e+2n]+x[o+2n]}>>1
x[0+6] ={x[0+6]+x[16+6]}>>1
x[6] ={x[6]+x[22]}>>1
={f000 +f000}>>1
={fe000}>>1
=f000
x[e+2n+1] ={x[e+2n+1]+x[o+2n+1]}>>1
x[0+7] ={x[0+7]+x[16+7]}>>1
x[7] ={x[7]+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[16+2(3)] = {(x[16+2(3)]-x[0+2(3)])t[(8)(3)]-(x[0+2(3)+1]-x[16+2(3)+1])t[(8)(3)+1]}>>1
x[16+6] = {(x[16+6]-x[0+6])t[24]-(x[0+6+1]-x[16+6+1])t[24+1]}>>1
x[22] = {(x[22]-x[6])t[24]-(x[7]-x[23])t[25]}>>1
= {(f000-f000)cf04-(0000-0000)89be}>>1
= {(00000)cf04-(00000)89be}>>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[16+2(3)+1] = {(x[16+2(3)+1]-x[0+2(3)+1])t[(8)(3)]+(x[0+2(3)]-x[16+2(3)])t[(8)(3)+1]}>>1
x[16+7] = {(x[16+7]-x[0+7])t[24]+(x[0+6]-x[16+6])t[24+1]}>>1
x[23] = {(x[23]-x[7])t[24]+(x[6]-x[22])t[25]}>>1
= {(0000-0000)cf04+(f000-f000)89be}>>1
= {(00000)cf04+(00000)89be}>>1
= {00000+00000}>>1
= {00000}>>1
= 0000



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(P,b,n)=(2,0,4)
Loop P=2 of p=log2N=log264=6 loops indexed P=0...p-1=0...6-1=0...5.
Subblock b=0 of BP=B2=2P=22=4 subblocks, indexed b=0...B2-1=0...3.
Subblock size=NP|P=2=N2=N/BP|(N=64,P=2)=(2p/2P)|(p=6,P=2)=2p-P|(p=6,P=2)=26-2=16.
Butterfly n=4 of N'P=NP/2=2p-P-1=26-2-1=8 butterflies indexed by n=0...N'P-1=0...7.
Even base index e = 2NPb = 2(16)(0) = 0.
Odd base index o = e + 2N'P = 0 + 2(8) = 16.
Twiddle step size s = 2P+1 = 22+1 = 8.
x[e+2n] ={x[e+2n]+x[o+2n]}>>1
x[0+8] ={x[0+8]+x[16+8]}>>1
x[8] ={x[8]+x[24]}>>1
={0000 +0000}>>1
={00000}>>1
=0000
x[e+2n+1] ={x[e+2n+1]+x[o+2n+1]}>>1
x[0+9] ={x[0+9]+x[16+9]}>>1
x[9] ={x[9]+x[25]}>>1
={0000 +0000}>>1
={00000}>>1
=0000
x[o+2n] = {(x[o+2n]-x[e+2n])t[sn]-(x[e+2n+1]-x[o+2n+1])t[sn+1]}>>1
x[16+2(4)] = {(x[16+2(4)]-x[0+2(4)])t[(8)(4)]-(x[0+2(4)+1]-x[16+2(4)+1])t[(8)(4)+1]}>>1
x[16+8] = {(x[16+8]-x[0+8])t[32]-(x[0+8+1]-x[16+8+1])t[32+1]}>>1
x[24] = {(x[24]-x[8])t[32]-(x[9]-x[25])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[16+2(4)+1] = {(x[16+2(4)+1]-x[0+2(4)+1])t[(8)(4)]+(x[0+2(4)]-x[16+2(4)])t[(8)(4)+1]}>>1
x[16+9] = {(x[16+9]-x[0+9])t[32]+(x[0+8]-x[16+8])t[32+1]}>>1
x[25] = {(x[25]-x[9])t[32]+(x[8]-x[24])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)=(2,0,5)
Loop P=2 of p=log2N=log264=6 loops indexed P=0...p-1=0...6-1=0...5.
Subblock b=0 of BP=B2=2P=22=4 subblocks, indexed b=0...B2-1=0...3.
Subblock size=NP|P=2=N2=N/BP|(N=64,P=2)=(2p/2P)|(p=6,P=2)=2p-P|(p=6,P=2)=26-2=16.
Butterfly n=5 of N'P=NP/2=2p-P-1=26-2-1=8 butterflies indexed by n=0...N'P-1=0...7.
Even base index e = 2NPb = 2(16)(0) = 0.
Odd base index o = e + 2N'P = 0 + 2(8) = 16.
Twiddle step size s = 2P+1 = 22+1 = 8.
x[e+2n] ={x[e+2n]+x[o+2n]}>>1
x[0+10] ={x[0+10]+x[16+10]}>>1
x[10] ={x[10]+x[26]}>>1
={1000 +1000}>>1
={02000}>>1
=1000
x[e+2n+1] ={x[e+2n+1]+x[o+2n+1]}>>1
x[0+11] ={x[0+11]+x[16+11]}>>1
x[11] ={x[11]+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[16+2(5)] = {(x[16+2(5)]-x[0+2(5)])t[(8)(5)]-(x[0+2(5)+1]-x[16+2(5)+1])t[(8)(5)+1]}>>1
x[16+10] = {(x[16+10]-x[0+10])t[40]-(x[0+10+1]-x[16+10+1])t[40+1]}>>1
x[26] = {(x[26]-x[10])t[40]-(x[11]-x[27])t[41]}>>1
= {(1000-1000)30fb-(0000-0000)89be}>>1
= {(00000)30fb-(00000)89be}>>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[16+2(5)+1] = {(x[16+2(5)+1]-x[0+2(5)+1])t[(8)(5)]+(x[0+2(5)]-x[16+2(5)])t[(8)(5)+1]}>>1
x[16+11] = {(x[16+11]-x[0+11])t[40]+(x[0+10]-x[16+10])t[40+1]}>>1
x[27] = {(x[27]-x[11])t[40]+(x[10]-x[26])t[41]}>>1
= {(0000-0000)30fb+(1000-1000)89be}>>1
= {(00000)30fb+(00000)89be}>>1
= {00000+00000}>>1
= {00000}>>1
= 0000



Return to Table of Contents




(P,b,n)=(2,0,6)
Loop P=2 of p=log2N=log264=6 loops indexed P=0...p-1=0...6-1=0...5.
Subblock b=0 of BP=B2=2P=22=4 subblocks, indexed b=0...B2-1=0...3.
Subblock size=NP|P=2=N2=N/BP|(N=64,P=2)=(2p/2P)|(p=6,P=2)=2p-P|(p=6,P=2)=26-2=16.
Butterfly n=6 of N'P=NP/2=2p-P-1=26-2-1=8 butterflies indexed by n=0...N'P-1=0...7.
Even base index e = 2NPb = 2(16)(0) = 0.
Odd base index o = e + 2N'P = 0 + 2(8) = 16.
Twiddle step size s = 2P+1 = 22+1 = 8.
x[e+2n] ={x[e+2n]+x[o+2n]}>>1
x[0+12] ={x[0+12]+x[16+12]}>>1
x[12] ={x[12]+x[28]}>>1
={0000 +0000}>>1
={00000}>>1
=0000
x[e+2n+1] ={x[e+2n+1]+x[o+2n+1]}>>1
x[0+13] ={x[0+13]+x[16+13]}>>1
x[13] ={x[13]+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[16+2(6)] = {(x[16+2(6)]-x[0+2(6)])t[(8)(6)]-(x[0+2(6)+1]-x[16+2(6)+1])t[(8)(6)+1]}>>1
x[16+12] = {(x[16+12]-x[0+12])t[48]-(x[0+12+1]-x[16+12+1])t[48+1]}>>1
x[28] = {(x[28]-x[12])t[48]-(x[13]-x[29])t[49]}>>1
= {(0000-0000)5a82-(0000-0000)a57d}>>1
= {(00000)5a82-(00000)a57d}>>1
= {00000 - 00000}>>1
= {00000}>>1
= 0000
x[o+2n+1] = {(x[o+2n+1]-x[e+2n+1])t[sn]+(x[e+2n]-x[o+2n])t[sn+1]}>>1
x[16+2(6)+1] = {(x[16+2(6)+1]-x[0+2(6)+1])t[(8)(6)]+(x[0+2(6)]-x[16+2(6)])t[(8)(6)+1]}>>1
x[16+13] = {(x[16+13]-x[0+13])t[48]+(x[0+12]-x[16+12])t[48+1]}>>1
x[29] = {(x[29]-x[13])t[48]+(x[12]-x[28])t[49]}>>1
= {(0000-0000)5a82+(0000-0000)a57d}>>1
= {(00000)5a82+(00000)a57d}>>1
= {00000+00000}>>1
= {00000}>>1
= 0000



Return to Table of Contents




(P,b,n)=(2,0,7)
Loop P=2 of p=log2N=log264=6 loops indexed P=0...p-1=0...6-1=0...5.
Subblock b=0 of BP=B2=2P=22=4 subblocks, indexed b=0...B2-1=0...3.
Subblock size=NP|P=2=N2=N/BP|(N=64,P=2)=(2p/2P)|(p=6,P=2)=2p-P|(p=6,P=2)=26-2=16.
Butterfly n=7 of N'P=NP/2=2p-P-1=26-2-1=8 butterflies indexed by n=0...N'P-1=0...7.
Even base index e = 2NPb = 2(16)(0) = 0.
Odd base index o = e + 2N'P = 0 + 2(8) = 16.
Twiddle step size s = 2P+1 = 22+1 = 8.
x[e+2n] ={x[e+2n]+x[o+2n]}>>1
x[0+14] ={x[0+14]+x[16+14]}>>1
x[14] ={x[14]+x[30]}>>1
={f000 +f000}>>1
={fe000}>>1
=f000
x[e+2n+1] ={x[e+2n+1]+x[o+2n+1]}>>1
x[0+15] ={x[0+15]+x[16+15]}>>1
x[15] ={x[15]+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[16+2(7)] = {(x[16+2(7)]-x[0+2(7)])t[(8)(7)]-(x[0+2(7)+1]-x[16+2(7)+1])t[(8)(7)+1]}>>1
x[16+14] = {(x[16+14]-x[0+14])t[56]-(x[0+14+1]-x[16+14+1])t[56+1]}>>1
x[30] = {(x[30]-x[14])t[56]-(x[15]-x[31])t[57]}>>1
= {(f000-f000)7641-(0000-0000)cf04}>>1
= {(00000)7641-(00000)cf04}>>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[16+2(7)+1] = {(x[16+2(7)+1]-x[0+2(7)+1])t[(8)(7)]+(x[0+2(7)]-x[16+2(7)])t[(8)(7)+1]}>>1
x[16+15] = {(x[16+15]-x[0+15])t[56]+(x[0+14]-x[16+14])t[56+1]}>>1
x[31] = {(x[31]-x[15])t[56]+(x[14]-x[30])t[57]}>>1
= {(0000-0000)7641+(f000-f000)cf04}>>1
= {(00000)7641+(00000)cf04}>>1
= {00000+00000}>>1
= {00000}>>1
= 0000



Return to Table of Contents




(P,b,n)=(2,1,0)
Loop P=2 of p=log2N=log264=6 loops indexed P=0...p-1=0...6-1=0...5.
Subblock b=1 of BP=B2=2P=22=4 subblocks, indexed b=0...B2-1=0...3.
Subblock size=NP|P=2=N2=N/BP|(N=64,P=2)=(2p/2P)|(p=6,P=2)=2p-P|(p=6,P=2)=26-2=16.
Butterfly n=0 of N'P=NP/2=2p-P-1=26-2-1=8 butterflies indexed by n=0...N'P-1=0...7.
Even base index e = 2NPb = 2(16)(1) = 32.
Odd base index o = e + 2N'P = 32 + 2(8) = 48.
Twiddle step size s = 2P+1 = 22+1 = 8.
x[e+2n] ={x[e+2n]+x[o+2n]}>>1
x[32+0] ={x[32+0]+x[48+0]}>>1
x[32] ={x[32]+x[48]}>>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[48+1]}>>1
x[33] ={x[33]+x[49]}>>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[48+2(0)] = {(x[48+2(0)]-x[32+2(0)])t[(8)(0)]-(x[32+2(0)+1]-x[48+2(0)+1])t[(8)(0)+1]}>>1
x[48+0] = {(x[48+0]-x[32+0])t[0]-(x[32+0+1]-x[48+0+1])t[0+1]}>>1
x[48] = {(x[48]-x[32])t[0]-(x[33]-x[49])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[48+2(0)+1] = {(x[48+2(0)+1]-x[32+2(0)+1])t[(8)(0)]+(x[32+2(0)]-x[48+2(0)])t[(8)(0)+1]}>>1
x[48+1] = {(x[48+1]-x[32+1])t[0]+(x[32+0]-x[48+0])t[0+1]}>>1
x[49] = {(x[49]-x[33])t[0]+(x[32]-x[48])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)=(2,1,1)
Loop P=2 of p=log2N=log264=6 loops indexed P=0...p-1=0...6-1=0...5.
Subblock b=1 of BP=B2=2P=22=4 subblocks, indexed b=0...B2-1=0...3.
Subblock size=NP|P=2=N2=N/BP|(N=64,P=2)=(2p/2P)|(p=6,P=2)=2p-P|(p=6,P=2)=26-2=16.
Butterfly n=1 of N'P=NP/2=2p-P-1=26-2-1=8 butterflies indexed by n=0...N'P-1=0...7.
Even base index e = 2NPb = 2(16)(1) = 32.
Odd base index o = e + 2N'P = 32 + 2(8) = 48.
Twiddle step size s = 2P+1 = 22+1 = 8.
x[e+2n] ={x[e+2n]+x[o+2n]}>>1
x[32+2] ={x[32+2]+x[48+2]}>>1
x[34] ={x[34]+x[50]}>>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[48+3]}>>1
x[35] ={x[35]+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[48+2(1)] = {(x[48+2(1)]-x[32+2(1)])t[(8)(1)]-(x[32+2(1)+1]-x[48+2(1)+1])t[(8)(1)+1]}>>1
x[48+2] = {(x[48+2]-x[32+2])t[8]-(x[32+2+1]-x[48+2+1])t[8+1]}>>1
x[50] = {(x[50]-x[34])t[8]-(x[35]-x[51])t[9]}>>1
= {(0000-0000)89be-(0000-0000)cf04}>>1
= {(00000)89be-(00000)cf04}>>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[48+2(1)+1] = {(x[48+2(1)+1]-x[32+2(1)+1])t[(8)(1)]+(x[32+2(1)]-x[48+2(1)])t[(8)(1)+1]}>>1
x[48+3] = {(x[48+3]-x[32+3])t[8]+(x[32+2]-x[48+2])t[8+1]}>>1
x[51] = {(x[51]-x[35])t[8]+(x[34]-x[50])t[9]}>>1
= {(0000-0000)89be+(0000-0000)cf04}>>1
= {(00000)89be+(00000)cf04}>>1
= {00000+00000}>>1
= {00000}>>1
= 0000



Return to Table of Contents




(P,b,n)=(2,1,2)
Loop P=2 of p=log2N=log264=6 loops indexed P=0...p-1=0...6-1=0...5.
Subblock b=1 of BP=B2=2P=22=4 subblocks, indexed b=0...B2-1=0...3.
Subblock size=NP|P=2=N2=N/BP|(N=64,P=2)=(2p/2P)|(p=6,P=2)=2p-P|(p=6,P=2)=26-2=16.
Butterfly n=2 of N'P=NP/2=2p-P-1=26-2-1=8 butterflies indexed by n=0...N'P-1=0...7.
Even base index e = 2NPb = 2(16)(1) = 32.
Odd base index o = e + 2N'P = 32 + 2(8) = 48.
Twiddle step size s = 2P+1 = 22+1 = 8.
x[e+2n] ={x[e+2n]+x[o+2n]}>>1
x[32+4] ={x[32+4]+x[48+4]}>>1
x[36] ={x[36]+x[52]}>>1
={0000 +0000}>>1
={00000}>>1
=0000
x[e+2n+1] ={x[e+2n+1]+x[o+2n+1]}>>1
x[32+5] ={x[32+5]+x[48+5]}>>1
x[37] ={x[37]+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[48+2(2)] = {(x[48+2(2)]-x[32+2(2)])t[(8)(2)]-(x[32+2(2)+1]-x[48+2(2)+1])t[(8)(2)+1]}>>1
x[48+4] = {(x[48+4]-x[32+4])t[16]-(x[32+4+1]-x[48+4+1])t[16+1]}>>1
x[52] = {(x[52]-x[36])t[16]-(x[37]-x[53])t[17]}>>1
= {(0000-0000)a57d-(0000-0000)a57d}>>1
= {(00000)a57d-(00000)a57d}>>1
= {00000 - 00000}>>1
= {00000}>>1
= 0000
x[o+2n+1] = {(x[o+2n+1]-x[e+2n+1])t[sn]+(x[e+2n]-x[o+2n])t[sn+1]}>>1
x[48+2(2)+1] = {(x[48+2(2)+1]-x[32+2(2)+1])t[(8)(2)]+(x[32+2(2)]-x[48+2(2)])t[(8)(2)+1]}>>1
x[48+5] = {(x[48+5]-x[32+5])t[16]+(x[32+4]-x[48+4])t[16+1]}>>1
x[53] = {(x[53]-x[37])t[16]+(x[36]-x[52])t[17]}>>1
= {(0000-0000)a57d+(0000-0000)a57d}>>1
= {(00000)a57d+(00000)a57d}>>1
= {00000+00000}>>1
= {00000}>>1
= 0000



Return to Table of Contents




(P,b,n)=(2,1,3)
Loop P=2 of p=log2N=log264=6 loops indexed P=0...p-1=0...6-1=0...5.
Subblock b=1 of BP=B2=2P=22=4 subblocks, indexed b=0...B2-1=0...3.
Subblock size=NP|P=2=N2=N/BP|(N=64,P=2)=(2p/2P)|(p=6,P=2)=2p-P|(p=6,P=2)=26-2=16.
Butterfly n=3 of N'P=NP/2=2p-P-1=26-2-1=8 butterflies indexed by n=0...N'P-1=0...7.
Even base index e = 2NPb = 2(16)(1) = 32.
Odd base index o = e + 2N'P = 32 + 2(8) = 48.
Twiddle step size s = 2P+1 = 22+1 = 8.
x[e+2n] ={x[e+2n]+x[o+2n]}>>1
x[32+6] ={x[32+6]+x[48+6]}>>1
x[38] ={x[38]+x[54]}>>1
={0000 +0000}>>1
={00000}>>1
=0000
x[e+2n+1] ={x[e+2n+1]+x[o+2n+1]}>>1
x[32+7] ={x[32+7]+x[48+7]}>>1
x[39] ={x[39]+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[48+2(3)] = {(x[48+2(3)]-x[32+2(3)])t[(8)(3)]-(x[32+2(3)+1]-x[48+2(3)+1])t[(8)(3)+1]}>>1
x[48+6] = {(x[48+6]-x[32+6])t[24]-(x[32+6+1]-x[48+6+1])t[24+1]}>>1
x[54] = {(x[54]-x[38])t[24]-(x[39]-x[55])t[25]}>>1
= {(0000-0000)cf04-(0000-0000)89be}>>1
= {(00000)cf04-(00000)89be}>>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[48+2(3)+1] = {(x[48+2(3)+1]-x[32+2(3)+1])t[(8)(3)]+(x[32+2(3)]-x[48+2(3)])t[(8)(3)+1]}>>1
x[48+7] = {(x[48+7]-x[32+7])t[24]+(x[32+6]-x[48+6])t[24+1]}>>1
x[55] = {(x[55]-x[39])t[24]+(x[38]-x[54])t[25]}>>1
= {(0000-0000)cf04+(0000-0000)89be}>>1
= {(00000)cf04+(00000)89be}>>1
= {00000+00000}>>1
= {00000}>>1
= 0000



Return to Table of Contents




(P,b,n)=(2,1,4)
Loop P=2 of p=log2N=log264=6 loops indexed P=0...p-1=0...6-1=0...5.
Subblock b=1 of BP=B2=2P=22=4 subblocks, indexed b=0...B2-1=0...3.
Subblock size=NP|P=2=N2=N/BP|(N=64,P=2)=(2p/2P)|(p=6,P=2)=2p-P|(p=6,P=2)=26-2=16.
Butterfly n=4 of N'P=NP/2=2p-P-1=26-2-1=8 butterflies indexed by n=0...N'P-1=0...7.
Even base index e = 2NPb = 2(16)(1) = 32.
Odd base index o = e + 2N'P = 32 + 2(8) = 48.
Twiddle step size s = 2P+1 = 22+1 = 8.
x[e+2n] ={x[e+2n]+x[o+2n]}>>1
x[32+8] ={x[32+8]+x[48+8]}>>1
x[40] ={x[40]+x[56]}>>1
={0000 +0000}>>1
={00000}>>1
=0000
x[e+2n+1] ={x[e+2n+1]+x[o+2n+1]}>>1
x[32+9] ={x[32+9]+x[48+9]}>>1
x[41] ={x[41]+x[57]}>>1
={0000 +0000}>>1
={00000}>>1
=0000
x[o+2n] = {(x[o+2n]-x[e+2n])t[sn]-(x[e+2n+1]-x[o+2n+1])t[sn+1]}>>1
x[48+2(4)] = {(x[48+2(4)]-x[32+2(4)])t[(8)(4)]-(x[32+2(4)+1]-x[48+2(4)+1])t[(8)(4)+1]}>>1
x[48+8] = {(x[48+8]-x[32+8])t[32]-(x[32+8+1]-x[48+8+1])t[32+1]}>>1
x[56] = {(x[56]-x[40])t[32]-(x[41]-x[57])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[48+2(4)+1] = {(x[48+2(4)+1]-x[32+2(4)+1])t[(8)(4)]+(x[32+2(4)]-x[48+2(4)])t[(8)(4)+1]}>>1
x[48+9] = {(x[48+9]-x[32+9])t[32]+(x[32+8]-x[48+8])t[32+1]}>>1
x[57] = {(x[57]-x[41])t[32]+(x[40]-x[56])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)=(2,1,5)
Loop P=2 of p=log2N=log264=6 loops indexed P=0...p-1=0...6-1=0...5.
Subblock b=1 of BP=B2=2P=22=4 subblocks, indexed b=0...B2-1=0...3.
Subblock size=NP|P=2=N2=N/BP|(N=64,P=2)=(2p/2P)|(p=6,P=2)=2p-P|(p=6,P=2)=26-2=16.
Butterfly n=5 of N'P=NP/2=2p-P-1=26-2-1=8 butterflies indexed by n=0...N'P-1=0...7.
Even base index e = 2NPb = 2(16)(1) = 32.
Odd base index o = e + 2N'P = 32 + 2(8) = 48.
Twiddle step size s = 2P+1 = 22+1 = 8.
x[e+2n] ={x[e+2n]+x[o+2n]}>>1
x[32+10] ={x[32+10]+x[48+10]}>>1
x[42] ={x[42]+x[58]}>>1
={0000 +0000}>>1
={00000}>>1
=0000
x[e+2n+1] ={x[e+2n+1]+x[o+2n+1]}>>1
x[32+11] ={x[32+11]+x[48+11]}>>1
x[43] ={x[43]+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[48+2(5)] = {(x[48+2(5)]-x[32+2(5)])t[(8)(5)]-(x[32+2(5)+1]-x[48+2(5)+1])t[(8)(5)+1]}>>1
x[48+10] = {(x[48+10]-x[32+10])t[40]-(x[32+10+1]-x[48+10+1])t[40+1]}>>1
x[58] = {(x[58]-x[42])t[40]-(x[43]-x[59])t[41]}>>1
= {(0000-0000)30fb-(0000-0000)89be}>>1
= {(00000)30fb-(00000)89be}>>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[48+2(5)+1] = {(x[48+2(5)+1]-x[32+2(5)+1])t[(8)(5)]+(x[32+2(5)]-x[48+2(5)])t[(8)(5)+1]}>>1
x[48+11] = {(x[48+11]-x[32+11])t[40]+(x[32+10]-x[48+10])t[40+1]}>>1
x[59] = {(x[59]-x[43])t[40]+(x[42]-x[58])t[41]}>>1
= {(0000-0000)30fb+(0000-0000)89be}>>1
= {(00000)30fb+(00000)89be}>>1
= {00000+00000}>>1
= {00000}>>1
= 0000



Return to Table of Contents




(P,b,n)=(2,1,6)
Loop P=2 of p=log2N=log264=6 loops indexed P=0...p-1=0...6-1=0...5.
Subblock b=1 of BP=B2=2P=22=4 subblocks, indexed b=0...B2-1=0...3.
Subblock size=NP|P=2=N2=N/BP|(N=64,P=2)=(2p/2P)|(p=6,P=2)=2p-P|(p=6,P=2)=26-2=16.
Butterfly n=6 of N'P=NP/2=2p-P-1=26-2-1=8 butterflies indexed by n=0...N'P-1=0...7.
Even base index e = 2NPb = 2(16)(1) = 32.
Odd base index o = e + 2N'P = 32 + 2(8) = 48.
Twiddle step size s = 2P+1 = 22+1 = 8.
x[e+2n] ={x[e+2n]+x[o+2n]}>>1
x[32+12] ={x[32+12]+x[48+12]}>>1
x[44] ={x[44]+x[60]}>>1
={0000 +0000}>>1
={00000}>>1
=0000
x[e+2n+1] ={x[e+2n+1]+x[o+2n+1]}>>1
x[32+13] ={x[32+13]+x[48+13]}>>1
x[45] ={x[45]+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[48+2(6)] = {(x[48+2(6)]-x[32+2(6)])t[(8)(6)]-(x[32+2(6)+1]-x[48+2(6)+1])t[(8)(6)+1]}>>1
x[48+12] = {(x[48+12]-x[32+12])t[48]-(x[32+12+1]-x[48+12+1])t[48+1]}>>1
x[60] = {(x[60]-x[44])t[48]-(x[45]-x[61])t[49]}>>1
= {(0000-0000)5a82-(0000-0000)a57d}>>1
= {(00000)5a82-(00000)a57d}>>1
= {00000 - 00000}>>1
= {00000}>>1
= 0000
x[o+2n+1] = {(x[o+2n+1]-x[e+2n+1])t[sn]+(x[e+2n]-x[o+2n])t[sn+1]}>>1
x[48+2(6)+1] = {(x[48+2(6)+1]-x[32+2(6)+1])t[(8)(6)]+(x[32+2(6)]-x[48+2(6)])t[(8)(6)+1]}>>1
x[48+13] = {(x[48+13]-x[32+13])t[48]+(x[32+12]-x[48+12])t[48+1]}>>1
x[61] = {(x[61]-x[45])t[48]+(x[44]-x[60])t[49]}>>1
= {(0000-0000)5a82+(0000-0000)a57d}>>1
= {(00000)5a82+(00000)a57d}>>1
= {00000+00000}>>1
= {00000}>>1
= 0000



Return to Table of Contents




(P,b,n)=(2,1,7)
Loop P=2 of p=log2N=log264=6 loops indexed P=0...p-1=0...6-1=0...5.
Subblock b=1 of BP=B2=2P=22=4 subblocks, indexed b=0...B2-1=0...3.
Subblock size=NP|P=2=N2=N/BP|(N=64,P=2)=(2p/2P)|(p=6,P=2)=2p-P|(p=6,P=2)=26-2=16.
Butterfly n=7 of N'P=NP/2=2p-P-1=26-2-1=8 butterflies indexed by n=0...N'P-1=0...7.
Even base index e = 2NPb = 2(16)(1) = 32.
Odd base index o = e + 2N'P = 32 + 2(8) = 48.
Twiddle step size s = 2P+1 = 22+1 = 8.
x[e+2n] ={x[e+2n]+x[o+2n]}>>1
x[32+14] ={x[32+14]+x[48+14]}>>1
x[46] ={x[46]+x[62]}>>1
={0000 +0000}>>1
={00000}>>1
=0000
x[e+2n+1] ={x[e+2n+1]+x[o+2n+1]}>>1
x[32+15] ={x[32+15]+x[48+15]}>>1
x[47] ={x[47]+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[48+2(7)] = {(x[48+2(7)]-x[32+2(7)])t[(8)(7)]-(x[32+2(7)+1]-x[48+2(7)+1])t[(8)(7)+1]}>>1
x[48+14] = {(x[48+14]-x[32+14])t[56]-(x[32+14+1]-x[48+14+1])t[56+1]}>>1
x[62] = {(x[62]-x[46])t[56]-(x[47]-x[63])t[57]}>>1
= {(0000-0000)7641-(0000-0000)cf04}>>1
= {(00000)7641-(00000)cf04}>>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[48+2(7)+1] = {(x[48+2(7)+1]-x[32+2(7)+1])t[(8)(7)]+(x[32+2(7)]-x[48+2(7)])t[(8)(7)+1]}>>1
x[48+15] = {(x[48+15]-x[32+15])t[56]+(x[32+14]-x[48+14])t[56+1]}>>1
x[63] = {(x[63]-x[47])t[56]+(x[46]-x[62])t[57]}>>1
= {(0000-0000)7641+(0000-0000)cf04}>>1
= {(00000)7641+(00000)cf04}>>1
= {00000+00000}>>1
= {00000}>>1
= 0000



Return to Table of Contents




(P,b,n)=(2,2,0)
Loop P=2 of p=log2N=log264=6 loops indexed P=0...p-1=0...6-1=0...5.
Subblock b=2 of BP=B2=2P=22=4 subblocks, indexed b=0...B2-1=0...3.
Subblock size=NP|P=2=N2=N/BP|(N=64,P=2)=(2p/2P)|(p=6,P=2)=2p-P|(p=6,P=2)=26-2=16.
Butterfly n=0 of N'P=NP/2=2p-P-1=26-2-1=8 butterflies indexed by n=0...N'P-1=0...7.
Even base index e = 2NPb = 2(16)(2) = 64.
Odd base index o = e + 2N'P = 64 + 2(8) = 80.
Twiddle step size s = 2P+1 = 22+1 = 8.
x[e+2n] ={x[e+2n]+x[o+2n]}>>1
x[64+0] ={x[64+0]+x[80+0]}>>1
x[64] ={x[64]+x[80]}>>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[80+1]}>>1
x[65] ={x[65]+x[81]}>>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[80+2(0)] = {(x[80+2(0)]-x[64+2(0)])t[(8)(0)]-(x[64+2(0)+1]-x[80+2(0)+1])t[(8)(0)+1]}>>1
x[80+0] = {(x[80+0]-x[64+0])t[0]-(x[64+0+1]-x[80+0+1])t[0+1]}>>1
x[80] = {(x[80]-x[64])t[0]-(x[65]-x[81])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[80+2(0)+1] = {(x[80+2(0)+1]-x[64+2(0)+1])t[(8)(0)]+(x[64+2(0)]-x[80+2(0)])t[(8)(0)+1]}>>1
x[80+1] = {(x[80+1]-x[64+1])t[0]+(x[64+0]-x[80+0])t[0+1]}>>1
x[81] = {(x[81]-x[65])t[0]+(x[64]-x[80])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)=(2,2,1)
Loop P=2 of p=log2N=log264=6 loops indexed P=0...p-1=0...6-1=0...5.
Subblock b=2 of BP=B2=2P=22=4 subblocks, indexed b=0...B2-1=0...3.
Subblock size=NP|P=2=N2=N/BP|(N=64,P=2)=(2p/2P)|(p=6,P=2)=2p-P|(p=6,P=2)=26-2=16.
Butterfly n=1 of N'P=NP/2=2p-P-1=26-2-1=8 butterflies indexed by n=0...N'P-1=0...7.
Even base index e = 2NPb = 2(16)(2) = 64.
Odd base index o = e + 2N'P = 64 + 2(8) = 80.
Twiddle step size s = 2P+1 = 22+1 = 8.
x[e+2n] ={x[e+2n]+x[o+2n]}>>1
x[64+2] ={x[64+2]+x[80+2]}>>1
x[66] ={x[66]+x[82]}>>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[80+3]}>>1
x[67] ={x[67]+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[80+2(1)] = {(x[80+2(1)]-x[64+2(1)])t[(8)(1)]-(x[64+2(1)+1]-x[80+2(1)+1])t[(8)(1)+1]}>>1
x[80+2] = {(x[80+2]-x[64+2])t[8]-(x[64+2+1]-x[80+2+1])t[8+1]}>>1
x[82] = {(x[82]-x[66])t[8]-(x[67]-x[83])t[9]}>>1
= {(0000-0000)89be-(0000-0000)cf04}>>1
= {(00000)89be-(00000)cf04}>>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[80+2(1)+1] = {(x[80+2(1)+1]-x[64+2(1)+1])t[(8)(1)]+(x[64+2(1)]-x[80+2(1)])t[(8)(1)+1]}>>1
x[80+3] = {(x[80+3]-x[64+3])t[8]+(x[64+2]-x[80+2])t[8+1]}>>1
x[83] = {(x[83]-x[67])t[8]+(x[66]-x[82])t[9]}>>1
= {(0000-0000)89be+(0000-0000)cf04}>>1
= {(00000)89be+(00000)cf04}>>1
= {00000+00000}>>1
= {00000}>>1
= 0000



Return to Table of Contents




(P,b,n)=(2,2,2)
Loop P=2 of p=log2N=log264=6 loops indexed P=0...p-1=0...6-1=0...5.
Subblock b=2 of BP=B2=2P=22=4 subblocks, indexed b=0...B2-1=0...3.
Subblock size=NP|P=2=N2=N/BP|(N=64,P=2)=(2p/2P)|(p=6,P=2)=2p-P|(p=6,P=2)=26-2=16.
Butterfly n=2 of N'P=NP/2=2p-P-1=26-2-1=8 butterflies indexed by n=0...N'P-1=0...7.
Even base index e = 2NPb = 2(16)(2) = 64.
Odd base index o = e + 2N'P = 64 + 2(8) = 80.
Twiddle step size s = 2P+1 = 22+1 = 8.
x[e+2n] ={x[e+2n]+x[o+2n]}>>1
x[64+4] ={x[64+4]+x[80+4]}>>1
x[68] ={x[68]+x[84]}>>1
={0000 +0000}>>1
={00000}>>1
=0000
x[e+2n+1] ={x[e+2n+1]+x[o+2n+1]}>>1
x[64+5] ={x[64+5]+x[80+5]}>>1
x[69] ={x[69]+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[80+2(2)] = {(x[80+2(2)]-x[64+2(2)])t[(8)(2)]-(x[64+2(2)+1]-x[80+2(2)+1])t[(8)(2)+1]}>>1
x[80+4] = {(x[80+4]-x[64+4])t[16]-(x[64+4+1]-x[80+4+1])t[16+1]}>>1
x[84] = {(x[84]-x[68])t[16]-(x[69]-x[85])t[17]}>>1
= {(0000-0000)a57d-(0000-0000)a57d}>>1
= {(00000)a57d-(00000)a57d}>>1
= {00000 - 00000}>>1
= {00000}>>1
= 0000
x[o+2n+1] = {(x[o+2n+1]-x[e+2n+1])t[sn]+(x[e+2n]-x[o+2n])t[sn+1]}>>1
x[80+2(2)+1] = {(x[80+2(2)+1]-x[64+2(2)+1])t[(8)(2)]+(x[64+2(2)]-x[80+2(2)])t[(8)(2)+1]}>>1
x[80+5] = {(x[80+5]-x[64+5])t[16]+(x[64+4]-x[80+4])t[16+1]}>>1
x[85] = {(x[85]-x[69])t[16]+(x[68]-x[84])t[17]}>>1
= {(0000-0000)a57d+(0000-0000)a57d}>>1
= {(00000)a57d+(00000)a57d}>>1
= {00000+00000}>>1
= {00000}>>1
= 0000



Return to Table of Contents




(P,b,n)=(2,2,3)
Loop P=2 of p=log2N=log264=6 loops indexed P=0...p-1=0...6-1=0...5.
Subblock b=2 of BP=B2=2P=22=4 subblocks, indexed b=0...B2-1=0...3.
Subblock size=NP|P=2=N2=N/BP|(N=64,P=2)=(2p/2P)|(p=6,P=2)=2p-P|(p=6,P=2)=26-2=16.
Butterfly n=3 of N'P=NP/2=2p-P-1=26-2-1=8 butterflies indexed by n=0...N'P-1=0...7.
Even base index e = 2NPb = 2(16)(2) = 64.
Odd base index o = e + 2N'P = 64 + 2(8) = 80.
Twiddle step size s = 2P+1 = 22+1 = 8.
x[e+2n] ={x[e+2n]+x[o+2n]}>>1
x[64+6] ={x[64+6]+x[80+6]}>>1
x[70] ={x[70]+x[86]}>>1
={0000 +0000}>>1
={00000}>>1
=0000
x[e+2n+1] ={x[e+2n+1]+x[o+2n+1]}>>1
x[64+7] ={x[64+7]+x[80+7]}>>1
x[71] ={x[71]+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[80+2(3)] = {(x[80+2(3)]-x[64+2(3)])t[(8)(3)]-(x[64+2(3)+1]-x[80+2(3)+1])t[(8)(3)+1]}>>1
x[80+6] = {(x[80+6]-x[64+6])t[24]-(x[64+6+1]-x[80+6+1])t[24+1]}>>1
x[86] = {(x[86]-x[70])t[24]-(x[71]-x[87])t[25]}>>1
= {(0000-0000)cf04-(0000-0000)89be}>>1
= {(00000)cf04-(00000)89be}>>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[80+2(3)+1] = {(x[80+2(3)+1]-x[64+2(3)+1])t[(8)(3)]+(x[64+2(3)]-x[80+2(3)])t[(8)(3)+1]}>>1
x[80+7] = {(x[80+7]-x[64+7])t[24]+(x[64+6]-x[80+6])t[24+1]}>>1
x[87] = {(x[87]-x[71])t[24]+(x[70]-x[86])t[25]}>>1
= {(0000-0000)cf04+(0000-0000)89be}>>1
= {(00000)cf04+(00000)89be}>>1
= {00000+00000}>>1
= {00000}>>1
= 0000



Return to Table of Contents




(P,b,n)=(2,2,4)
Loop P=2 of p=log2N=log264=6 loops indexed P=0...p-1=0...6-1=0...5.
Subblock b=2 of BP=B2=2P=22=4 subblocks, indexed b=0...B2-1=0...3.
Subblock size=NP|P=2=N2=N/BP|(N=64,P=2)=(2p/2P)|(p=6,P=2)=2p-P|(p=6,P=2)=26-2=16.
Butterfly n=4 of N'P=NP/2=2p-P-1=26-2-1=8 butterflies indexed by n=0...N'P-1=0...7.
Even base index e = 2NPb = 2(16)(2) = 64.
Odd base index o = e + 2N'P = 64 + 2(8) = 80.
Twiddle step size s = 2P+1 = 22+1 = 8.
x[e+2n] ={x[e+2n]+x[o+2n]}>>1
x[64+8] ={x[64+8]+x[80+8]}>>1
x[72] ={x[72]+x[88]}>>1
={0000 +0000}>>1
={00000}>>1
=0000
x[e+2n+1] ={x[e+2n+1]+x[o+2n+1]}>>1
x[64+9] ={x[64+9]+x[80+9]}>>1
x[73] ={x[73]+x[89]}>>1
={0000 +0000}>>1
={00000}>>1
=0000
x[o+2n] = {(x[o+2n]-x[e+2n])t[sn]-(x[e+2n+1]-x[o+2n+1])t[sn+1]}>>1
x[80+2(4)] = {(x[80+2(4)]-x[64+2(4)])t[(8)(4)]-(x[64+2(4)+1]-x[80+2(4)+1])t[(8)(4)+1]}>>1
x[80+8] = {(x[80+8]-x[64+8])t[32]-(x[64+8+1]-x[80+8+1])t[32+1]}>>1
x[88] = {(x[88]-x[72])t[32]-(x[73]-x[89])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[80+2(4)+1] = {(x[80+2(4)+1]-x[64+2(4)+1])t[(8)(4)]+(x[64+2(4)]-x[80+2(4)])t[(8)(4)+1]}>>1
x[80+9] = {(x[80+9]-x[64+9])t[32]+(x[64+8]-x[80+8])t[32+1]}>>1
x[89] = {(x[89]-x[73])t[32]+(x[72]-x[88])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)=(2,2,5)
Loop P=2 of p=log2N=log264=6 loops indexed P=0...p-1=0...6-1=0...5.
Subblock b=2 of BP=B2=2P=22=4 subblocks, indexed b=0...B2-1=0...3.
Subblock size=NP|P=2=N2=N/BP|(N=64,P=2)=(2p/2P)|(p=6,P=2)=2p-P|(p=6,P=2)=26-2=16.
Butterfly n=5 of N'P=NP/2=2p-P-1=26-2-1=8 butterflies indexed by n=0...N'P-1=0...7.
Even base index e = 2NPb = 2(16)(2) = 64.
Odd base index o = e + 2N'P = 64 + 2(8) = 80.
Twiddle step size s = 2P+1 = 22+1 = 8.
x[e+2n] ={x[e+2n]+x[o+2n]}>>1
x[64+10] ={x[64+10]+x[80+10]}>>1
x[74] ={x[74]+x[90]}>>1
={0000 +0000}>>1
={00000}>>1
=0000
x[e+2n+1] ={x[e+2n+1]+x[o+2n+1]}>>1
x[64+11] ={x[64+11]+x[80+11]}>>1
x[75] ={x[75]+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[80+2(5)] = {(x[80+2(5)]-x[64+2(5)])t[(8)(5)]-(x[64+2(5)+1]-x[80+2(5)+1])t[(8)(5)+1]}>>1
x[80+10] = {(x[80+10]-x[64+10])t[40]-(x[64+10+1]-x[80+10+1])t[40+1]}>>1
x[90] = {(x[90]-x[74])t[40]-(x[75]-x[91])t[41]}>>1
= {(0000-0000)30fb-(0000-0000)89be}>>1
= {(00000)30fb-(00000)89be}>>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[80+2(5)+1] = {(x[80+2(5)+1]-x[64+2(5)+1])t[(8)(5)]+(x[64+2(5)]-x[80+2(5)])t[(8)(5)+1]}>>1
x[80+11] = {(x[80+11]-x[64+11])t[40]+(x[64+10]-x[80+10])t[40+1]}>>1
x[91] = {(x[91]-x[75])t[40]+(x[74]-x[90])t[41]}>>1
= {(0000-0000)30fb+(0000-0000)89be}>>1
= {(00000)30fb+(00000)89be}>>1
= {00000+00000}>>1
= {00000}>>1
= 0000



Return to Table of Contents




(P,b,n)=(2,2,6)
Loop P=2 of p=log2N=log264=6 loops indexed P=0...p-1=0...6-1=0...5.
Subblock b=2 of BP=B2=2P=22=4 subblocks, indexed b=0...B2-1=0...3.
Subblock size=NP|P=2=N2=N/BP|(N=64,P=2)=(2p/2P)|(p=6,P=2)=2p-P|(p=6,P=2)=26-2=16.
Butterfly n=6 of N'P=NP/2=2p-P-1=26-2-1=8 butterflies indexed by n=0...N'P-1=0...7.
Even base index e = 2NPb = 2(16)(2) = 64.
Odd base index o = e + 2N'P = 64 + 2(8) = 80.
Twiddle step size s = 2P+1 = 22+1 = 8.
x[e+2n] ={x[e+2n]+x[o+2n]}>>1
x[64+12] ={x[64+12]+x[80+12]}>>1
x[76] ={x[76]+x[92]}>>1
={0000 +0000}>>1
={00000}>>1
=0000
x[e+2n+1] ={x[e+2n+1]+x[o+2n+1]}>>1
x[64+13] ={x[64+13]+x[80+13]}>>1
x[77] ={x[77]+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[80+2(6)] = {(x[80+2(6)]-x[64+2(6)])t[(8)(6)]-(x[64+2(6)+1]-x[80+2(6)+1])t[(8)(6)+1]}>>1
x[80+12] = {(x[80+12]-x[64+12])t[48]-(x[64+12+1]-x[80+12+1])t[48+1]}>>1
x[92] = {(x[92]-x[76])t[48]-(x[77]-x[93])t[49]}>>1
= {(0000-0000)5a82-(0000-0000)a57d}>>1
= {(00000)5a82-(00000)a57d}>>1
= {00000 - 00000}>>1
= {00000}>>1
= 0000
x[o+2n+1] = {(x[o+2n+1]-x[e+2n+1])t[sn]+(x[e+2n]-x[o+2n])t[sn+1]}>>1
x[80+2(6)+1] = {(x[80+2(6)+1]-x[64+2(6)+1])t[(8)(6)]+(x[64+2(6)]-x[80+2(6)])t[(8)(6)+1]}>>1
x[80+13] = {(x[80+13]-x[64+13])t[48]+(x[64+12]-x[80+12])t[48+1]}>>1
x[93] = {(x[93]-x[77])t[48]+(x[76]-x[92])t[49]}>>1
= {(0000-0000)5a82+(0000-0000)a57d}>>1
= {(00000)5a82+(00000)a57d}>>1
= {00000+00000}>>1
= {00000}>>1
= 0000



Return to Table of Contents




(P,b,n)=(2,2,7)
Loop P=2 of p=log2N=log264=6 loops indexed P=0...p-1=0...6-1=0...5.
Subblock b=2 of BP=B2=2P=22=4 subblocks, indexed b=0...B2-1=0...3.
Subblock size=NP|P=2=N2=N/BP|(N=64,P=2)=(2p/2P)|(p=6,P=2)=2p-P|(p=6,P=2)=26-2=16.
Butterfly n=7 of N'P=NP/2=2p-P-1=26-2-1=8 butterflies indexed by n=0...N'P-1=0...7.
Even base index e = 2NPb = 2(16)(2) = 64.
Odd base index o = e + 2N'P = 64 + 2(8) = 80.
Twiddle step size s = 2P+1 = 22+1 = 8.
x[e+2n] ={x[e+2n]+x[o+2n]}>>1
x[64+14] ={x[64+14]+x[80+14]}>>1
x[78] ={x[78]+x[94]}>>1
={0000 +0000}>>1
={00000}>>1
=0000
x[e+2n+1] ={x[e+2n+1]+x[o+2n+1]}>>1
x[64+15] ={x[64+15]+x[80+15]}>>1
x[79] ={x[79]+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[80+2(7)] = {(x[80+2(7)]-x[64+2(7)])t[(8)(7)]-(x[64+2(7)+1]-x[80+2(7)+1])t[(8)(7)+1]}>>1
x[80+14] = {(x[80+14]-x[64+14])t[56]-(x[64+14+1]-x[80+14+1])t[56+1]}>>1
x[94] = {(x[94]-x[78])t[56]-(x[79]-x[95])t[57]}>>1
= {(0000-0000)7641-(0000-0000)cf04}>>1
= {(00000)7641-(00000)cf04}>>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[80+2(7)+1] = {(x[80+2(7)+1]-x[64+2(7)+1])t[(8)(7)]+(x[64+2(7)]-x[80+2(7)])t[(8)(7)+1]}>>1
x[80+15] = {(x[80+15]-x[64+15])t[56]+(x[64+14]-x[80+14])t[56+1]}>>1
x[95] = {(x[95]-x[79])t[56]+(x[78]-x[94])t[57]}>>1
= {(0000-0000)7641+(0000-0000)cf04}>>1
= {(00000)7641+(00000)cf04}>>1
= {00000+00000}>>1
= {00000}>>1
= 0000



Return to Table of Contents




(P,b,n)=(2,3,0)
Loop P=2 of p=log2N=log264=6 loops indexed P=0...p-1=0...6-1=0...5.
Subblock b=3 of BP=B2=2P=22=4 subblocks, indexed b=0...B2-1=0...3.
Subblock size=NP|P=2=N2=N/BP|(N=64,P=2)=(2p/2P)|(p=6,P=2)=2p-P|(p=6,P=2)=26-2=16.
Butterfly n=0 of N'P=NP/2=2p-P-1=26-2-1=8 butterflies indexed by n=0...N'P-1=0...7.
Even base index e = 2NPb = 2(16)(3) = 96.
Odd base index o = e + 2N'P = 96 + 2(8) = 112.
Twiddle step size s = 2P+1 = 22+1 = 8.
x[e+2n] ={x[e+2n]+x[o+2n]}>>1
x[96+0] ={x[96+0]+x[112+0]}>>1
x[96] ={x[96]+x[112]}>>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[112+1]}>>1
x[97] ={x[97]+x[113]}>>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[112+2(0)] = {(x[112+2(0)]-x[96+2(0)])t[(8)(0)]-(x[96+2(0)+1]-x[112+2(0)+1])t[(8)(0)+1]}>>1
x[112+0] = {(x[112+0]-x[96+0])t[0]-(x[96+0+1]-x[112+0+1])t[0+1]}>>1
x[112] = {(x[112]-x[96])t[0]-(x[97]-x[113])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[112+2(0)+1] = {(x[112+2(0)+1]-x[96+2(0)+1])t[(8)(0)]+(x[96+2(0)]-x[112+2(0)])t[(8)(0)+1]}>>1
x[112+1] = {(x[112+1]-x[96+1])t[0]+(x[96+0]-x[112+0])t[0+1]}>>1
x[113] = {(x[113]-x[97])t[0]+(x[96]-x[112])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)=(2,3,1)
Loop P=2 of p=log2N=log264=6 loops indexed P=0...p-1=0...6-1=0...5.
Subblock b=3 of BP=B2=2P=22=4 subblocks, indexed b=0...B2-1=0...3.
Subblock size=NP|P=2=N2=N/BP|(N=64,P=2)=(2p/2P)|(p=6,P=2)=2p-P|(p=6,P=2)=26-2=16.
Butterfly n=1 of N'P=NP/2=2p-P-1=26-2-1=8 butterflies indexed by n=0...N'P-1=0...7.
Even base index e = 2NPb = 2(16)(3) = 96.
Odd base index o = e + 2N'P = 96 + 2(8) = 112.
Twiddle step size s = 2P+1 = 22+1 = 8.
x[e+2n] ={x[e+2n]+x[o+2n]}>>1
x[96+2] ={x[96+2]+x[112+2]}>>1
x[98] ={x[98]+x[114]}>>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[112+3]}>>1
x[99] ={x[99]+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[112+2(1)] = {(x[112+2(1)]-x[96+2(1)])t[(8)(1)]-(x[96+2(1)+1]-x[112+2(1)+1])t[(8)(1)+1]}>>1
x[112+2] = {(x[112+2]-x[96+2])t[8]-(x[96+2+1]-x[112+2+1])t[8+1]}>>1
x[114] = {(x[114]-x[98])t[8]-(x[99]-x[115])t[9]}>>1
= {(0000-0000)89be-(0000-0000)cf04}>>1
= {(00000)89be-(00000)cf04}>>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[112+2(1)+1] = {(x[112+2(1)+1]-x[96+2(1)+1])t[(8)(1)]+(x[96+2(1)]-x[112+2(1)])t[(8)(1)+1]}>>1
x[112+3] = {(x[112+3]-x[96+3])t[8]+(x[96+2]-x[112+2])t[8+1]}>>1
x[115] = {(x[115]-x[99])t[8]+(x[98]-x[114])t[9]}>>1
= {(0000-0000)89be+(0000-0000)cf04}>>1
= {(00000)89be+(00000)cf04}>>1
= {00000+00000}>>1
= {00000}>>1
= 0000



Return to Table of Contents




(P,b,n)=(2,3,2)
Loop P=2 of p=log2N=log264=6 loops indexed P=0...p-1=0...6-1=0...5.
Subblock b=3 of BP=B2=2P=22=4 subblocks, indexed b=0...B2-1=0...3.
Subblock size=NP|P=2=N2=N/BP|(N=64,P=2)=(2p/2P)|(p=6,P=2)=2p-P|(p=6,P=2)=26-2=16.
Butterfly n=2 of N'P=NP/2=2p-P-1=26-2-1=8 butterflies indexed by n=0...N'P-1=0...7.
Even base index e = 2NPb = 2(16)(3) = 96.
Odd base index o = e + 2N'P = 96 + 2(8) = 112.
Twiddle step size s = 2P+1 = 22+1 = 8.
x[e+2n] ={x[e+2n]+x[o+2n]}>>1
x[96+4] ={x[96+4]+x[112+4]}>>1
x[100] ={x[100]+x[116]}>>1
={0000 +0000}>>1
={00000}>>1
=0000
x[e+2n+1] ={x[e+2n+1]+x[o+2n+1]}>>1
x[96+5] ={x[96+5]+x[112+5]}>>1
x[101] ={x[101]+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[112+2(2)] = {(x[112+2(2)]-x[96+2(2)])t[(8)(2)]-(x[96+2(2)+1]-x[112+2(2)+1])t[(8)(2)+1]}>>1
x[112+4] = {(x[112+4]-x[96+4])t[16]-(x[96+4+1]-x[112+4+1])t[16+1]}>>1
x[116] = {(x[116]-x[100])t[16]-(x[101]-x[117])t[17]}>>1
= {(0000-0000)a57d-(0000-0000)a57d}>>1
= {(00000)a57d-(00000)a57d}>>1
= {00000 - 00000}>>1
= {00000}>>1
= 0000
x[o+2n+1] = {(x[o+2n+1]-x[e+2n+1])t[sn]+(x[e+2n]-x[o+2n])t[sn+1]}>>1
x[112+2(2)+1] = {(x[112+2(2)+1]-x[96+2(2)+1])t[(8)(2)]+(x[96+2(2)]-x[112+2(2)])t[(8)(2)+1]}>>1
x[112+5] = {(x[112+5]-x[96+5])t[16]+(x[96+4]-x[112+4])t[16+1]}>>1
x[117] = {(x[117]-x[101])t[16]+(x[100]-x[116])t[17]}>>1
= {(0000-0000)a57d+(0000-0000)a57d}>>1
= {(00000)a57d+(00000)a57d}>>1
= {00000+00000}>>1
= {00000}>>1
= 0000



Return to Table of Contents




(P,b,n)=(2,3,3)
Loop P=2 of p=log2N=log264=6 loops indexed P=0...p-1=0...6-1=0...5.
Subblock b=3 of BP=B2=2P=22=4 subblocks, indexed b=0...B2-1=0...3.
Subblock size=NP|P=2=N2=N/BP|(N=64,P=2)=(2p/2P)|(p=6,P=2)=2p-P|(p=6,P=2)=26-2=16.
Butterfly n=3 of N'P=NP/2=2p-P-1=26-2-1=8 butterflies indexed by n=0...N'P-1=0...7.
Even base index e = 2NPb = 2(16)(3) = 96.
Odd base index o = e + 2N'P = 96 + 2(8) = 112.
Twiddle step size s = 2P+1 = 22+1 = 8.
x[e+2n] ={x[e+2n]+x[o+2n]}>>1
x[96+6] ={x[96+6]+x[112+6]}>>1
x[102] ={x[102]+x[118]}>>1
={0000 +0000}>>1
={00000}>>1
=0000
x[e+2n+1] ={x[e+2n+1]+x[o+2n+1]}>>1
x[96+7] ={x[96+7]+x[112+7]}>>1
x[103] ={x[103]+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[112+2(3)] = {(x[112+2(3)]-x[96+2(3)])t[(8)(3)]-(x[96+2(3)+1]-x[112+2(3)+1])t[(8)(3)+1]}>>1
x[112+6] = {(x[112+6]-x[96+6])t[24]-(x[96+6+1]-x[112+6+1])t[24+1]}>>1
x[118] = {(x[118]-x[102])t[24]-(x[103]-x[119])t[25]}>>1
= {(0000-0000)cf04-(0000-0000)89be}>>1
= {(00000)cf04-(00000)89be}>>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[112+2(3)+1] = {(x[112+2(3)+1]-x[96+2(3)+1])t[(8)(3)]+(x[96+2(3)]-x[112+2(3)])t[(8)(3)+1]}>>1
x[112+7] = {(x[112+7]-x[96+7])t[24]+(x[96+6]-x[112+6])t[24+1]}>>1
x[119] = {(x[119]-x[103])t[24]+(x[102]-x[118])t[25]}>>1
= {(0000-0000)cf04+(0000-0000)89be}>>1
= {(00000)cf04+(00000)89be}>>1
= {00000+00000}>>1
= {00000}>>1
= 0000



Return to Table of Contents




(P,b,n)=(2,3,4)
Loop P=2 of p=log2N=log264=6 loops indexed P=0...p-1=0...6-1=0...5.
Subblock b=3 of BP=B2=2P=22=4 subblocks, indexed b=0...B2-1=0...3.
Subblock size=NP|P=2=N2=N/BP|(N=64,P=2)=(2p/2P)|(p=6,P=2)=2p-P|(p=6,P=2)=26-2=16.
Butterfly n=4 of N'P=NP/2=2p-P-1=26-2-1=8 butterflies indexed by n=0...N'P-1=0...7.
Even base index e = 2NPb = 2(16)(3) = 96.
Odd base index o = e + 2N'P = 96 + 2(8) = 112.
Twiddle step size s = 2P+1 = 22+1 = 8.
x[e+2n] ={x[e+2n]+x[o+2n]}>>1
x[96+8] ={x[96+8]+x[112+8]}>>1
x[104] ={x[104]+x[120]}>>1
={0000 +0000}>>1
={00000}>>1
=0000
x[e+2n+1] ={x[e+2n+1]+x[o+2n+1]}>>1
x[96+9] ={x[96+9]+x[112+9]}>>1
x[105] ={x[105]+x[121]}>>1
={0000 +0000}>>1
={00000}>>1
=0000
x[o+2n] = {(x[o+2n]-x[e+2n])t[sn]-(x[e+2n+1]-x[o+2n+1])t[sn+1]}>>1
x[112+2(4)] = {(x[112+2(4)]-x[96+2(4)])t[(8)(4)]-(x[96+2(4)+1]-x[112+2(4)+1])t[(8)(4)+1]}>>1
x[112+8] = {(x[112+8]-x[96+8])t[32]-(x[96+8+1]-x[112+8+1])t[32+1]}>>1
x[120] = {(x[120]-x[104])t[32]-(x[105]-x[121])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[112+2(4)+1] = {(x[112+2(4)+1]-x[96+2(4)+1])t[(8)(4)]+(x[96+2(4)]-x[112+2(4)])t[(8)(4)+1]}>>1
x[112+9] = {(x[112+9]-x[96+9])t[32]+(x[96+8]-x[112+8])t[32+1]}>>1
x[121] = {(x[121]-x[105])t[32]+(x[104]-x[120])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)=(2,3,5)
Loop P=2 of p=log2N=log264=6 loops indexed P=0...p-1=0...6-1=0...5.
Subblock b=3 of BP=B2=2P=22=4 subblocks, indexed b=0...B2-1=0...3.
Subblock size=NP|P=2=N2=N/BP|(N=64,P=2)=(2p/2P)|(p=6,P=2)=2p-P|(p=6,P=2)=26-2=16.
Butterfly n=5 of N'P=NP/2=2p-P-1=26-2-1=8 butterflies indexed by n=0...N'P-1=0...7.
Even base index e = 2NPb = 2(16)(3) = 96.
Odd base index o = e + 2N'P = 96 + 2(8) = 112.
Twiddle step size s = 2P+1 = 22+1 = 8.
x[e+2n] ={x[e+2n]+x[o+2n]}>>1
x[96+10] ={x[96+10]+x[112+10]}>>1
x[106] ={x[106]+x[122]}>>1
={0000 +0000}>>1
={00000}>>1
=0000
x[e+2n+1] ={x[e+2n+1]+x[o+2n+1]}>>1
x[96+11] ={x[96+11]+x[112+11]}>>1
x[107] ={x[107]+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[112+2(5)] = {(x[112+2(5)]-x[96+2(5)])t[(8)(5)]-(x[96+2(5)+1]-x[112+2(5)+1])t[(8)(5)+1]}>>1
x[112+10] = {(x[112+10]-x[96+10])t[40]-(x[96+10+1]-x[112+10+1])t[40+1]}>>1
x[122] = {(x[122]-x[106])t[40]-(x[107]-x[123])t[41]}>>1
= {(0000-0000)30fb-(0000-0000)89be}>>1
= {(00000)30fb-(00000)89be}>>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[112+2(5)+1] = {(x[112+2(5)+1]-x[96+2(5)+1])t[(8)(5)]+(x[96+2(5)]-x[112+2(5)])t[(8)(5)+1]}>>1
x[112+11] = {(x[112+11]-x[96+11])t[40]+(x[96+10]-x[112+10])t[40+1]}>>1
x[123] = {(x[123]-x[107])t[40]+(x[106]-x[122])t[41]}>>1
= {(0000-0000)30fb+(0000-0000)89be}>>1
= {(00000)30fb+(00000)89be}>>1
= {00000+00000}>>1
= {00000}>>1
= 0000



Return to Table of Contents




(P,b,n)=(2,3,6)
Loop P=2 of p=log2N=log264=6 loops indexed P=0...p-1=0...6-1=0...5.
Subblock b=3 of BP=B2=2P=22=4 subblocks, indexed b=0...B2-1=0...3.
Subblock size=NP|P=2=N2=N/BP|(N=64,P=2)=(2p/2P)|(p=6,P=2)=2p-P|(p=6,P=2)=26-2=16.
Butterfly n=6 of N'P=NP/2=2p-P-1=26-2-1=8 butterflies indexed by n=0...N'P-1=0...7.
Even base index e = 2NPb = 2(16)(3) = 96.
Odd base index o = e + 2N'P = 96 + 2(8) = 112.
Twiddle step size s = 2P+1 = 22+1 = 8.
x[e+2n] ={x[e+2n]+x[o+2n]}>>1
x[96+12] ={x[96+12]+x[112+12]}>>1
x[108] ={x[108]+x[124]}>>1
={0000 +0000}>>1
={00000}>>1
=0000
x[e+2n+1] ={x[e+2n+1]+x[o+2n+1]}>>1
x[96+13] ={x[96+13]+x[112+13]}>>1
x[109] ={x[109]+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[112+2(6)] = {(x[112+2(6)]-x[96+2(6)])t[(8)(6)]-(x[96+2(6)+1]-x[112+2(6)+1])t[(8)(6)+1]}>>1
x[112+12] = {(x[112+12]-x[96+12])t[48]-(x[96+12+1]-x[112+12+1])t[48+1]}>>1
x[124] = {(x[124]-x[108])t[48]-(x[109]-x[125])t[49]}>>1
= {(0000-0000)5a82-(0000-0000)a57d}>>1
= {(00000)5a82-(00000)a57d}>>1
= {00000 - 00000}>>1
= {00000}>>1
= 0000
x[o+2n+1] = {(x[o+2n+1]-x[e+2n+1])t[sn]+(x[e+2n]-x[o+2n])t[sn+1]}>>1
x[112+2(6)+1] = {(x[112+2(6)+1]-x[96+2(6)+1])t[(8)(6)]+(x[96+2(6)]-x[112+2(6)])t[(8)(6)+1]}>>1
x[112+13] = {(x[112+13]-x[96+13])t[48]+(x[96+12]-x[112+12])t[48+1]}>>1
x[125] = {(x[125]-x[109])t[48]+(x[108]-x[124])t[49]}>>1
= {(0000-0000)5a82+(0000-0000)a57d}>>1
= {(00000)5a82+(00000)a57d}>>1
= {00000+00000}>>1
= {00000}>>1
= 0000



Return to Table of Contents




(P,b,n)=(2,3,7)
Loop P=2 of p=log2N=log264=6 loops indexed P=0...p-1=0...6-1=0...5.
Subblock b=3 of BP=B2=2P=22=4 subblocks, indexed b=0...B2-1=0...3.
Subblock size=NP|P=2=N2=N/BP|(N=64,P=2)=(2p/2P)|(p=6,P=2)=2p-P|(p=6,P=2)=26-2=16.
Butterfly n=7 of N'P=NP/2=2p-P-1=26-2-1=8 butterflies indexed by n=0...N'P-1=0...7.
Even base index e = 2NPb = 2(16)(3) = 96.
Odd base index o = e + 2N'P = 96 + 2(8) = 112.
Twiddle step size s = 2P+1 = 22+1 = 8.
x[e+2n] ={x[e+2n]+x[o+2n]}>>1
x[96+14] ={x[96+14]+x[112+14]}>>1
x[110] ={x[110]+x[126]}>>1
={0000 +0000}>>1
={00000}>>1
=0000
x[e+2n+1] ={x[e+2n+1]+x[o+2n+1]}>>1
x[96+15] ={x[96+15]+x[112+15]}>>1
x[111] ={x[111]+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[112+2(7)] = {(x[112+2(7)]-x[96+2(7)])t[(8)(7)]-(x[96+2(7)+1]-x[112+2(7)+1])t[(8)(7)+1]}>>1
x[112+14] = {(x[112+14]-x[96+14])t[56]-(x[96+14+1]-x[112+14+1])t[56+1]}>>1
x[126] = {(x[126]-x[110])t[56]-(x[111]-x[127])t[57]}>>1
= {(0000-0000)7641-(0000-0000)cf04}>>1
= {(00000)7641-(00000)cf04}>>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[112+2(7)+1] = {(x[112+2(7)+1]-x[96+2(7)+1])t[(8)(7)]+(x[96+2(7)]-x[112+2(7)])t[(8)(7)+1]}>>1
x[112+15] = {(x[112+15]-x[96+15])t[56]+(x[96+14]-x[112+14])t[56+1]}>>1
x[127] = {(x[127]-x[111])t[56]+(x[110]-x[126])t[57]}>>1
= {(0000-0000)7641+(0000-0000)cf04}>>1
= {(00000)7641+(00000)cf04}>>1
= {00000+00000}>>1
= {00000}>>1
= 0000



Return to Table of Contents



End of loop 2
x[0]=0000 x[1]=0000
x[2]=1000 x[3]=0000
x[4]=0000 x[5]=0000
x[6]=f000 x[7]=0000
x[8]=0000 x[9]=0000
x[10]=1000 x[11]=0000
x[12]=0000 x[13]=0000
x[14]=f000 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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