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



John Bryan






(P,b,n)=(0,0,0)
Loop P=0 of p=log2N=log264=6 loops indexed P=0...p-1=0...6-1=0...5.
Subblock b=0 of BP=B0=2P=20=1 subblocks, indexed b=0...B0-1=0...0.
Subblock size=NP|P=0=N0=N/BP|(N=64,P=0)=(2p/2P)|(p=6,P=0)=2p-P|(p=6,P=0)=26-0=64.
Butterfly n=0 of N'P=NP/2=2p-P-1=26-0-1=32 butterflies indexed by n=0...N'P-1=0...31.
Even base index e = 2NPb = 2(64)(0) = 0.
Odd base index o = e + 2N'P = 0 + 2(32) = 64.
Twiddle step size s = 2P+1 = 20+1 = 2.
x[e+2n] ={x[e+2n]+x[o+2n]}>>1
x[0+0] ={x[0+0]+x[64+0]}>>1
x[0] ={x[0]+x[64]}>>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[64+1]}>>1
x[1] ={x[1]+x[65]}>>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[64+2(0)] = {(x[64+2(0)]-x[0+2(0)])t[(2)(0)]-(x[0+2(0)+1]-x[64+2(0)+1])t[(2)(0)+1]}>>1
x[64+0] = {(x[64+0]-x[0+0])t[0]-(x[0+0+1]-x[64+0+1])t[0+1]}>>1
x[64] = {(x[64]-x[0])t[0]-(x[1]-x[65])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[64+2(0)+1] = {(x[64+2(0)+1]-x[0+2(0)+1])t[(2)(0)]+(x[0+2(0)]-x[64+2(0)])t[(2)(0)+1]}>>1
x[64+1] = {(x[64+1]-x[0+1])t[0]+(x[0+0]-x[64+0])t[0+1]}>>1
x[65] = {(x[65]-x[1])t[0]+(x[0]-x[64])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)=(0,0,1)
Loop P=0 of p=log2N=log264=6 loops indexed P=0...p-1=0...6-1=0...5.
Subblock b=0 of BP=B0=2P=20=1 subblocks, indexed b=0...B0-1=0...0.
Subblock size=NP|P=0=N0=N/BP|(N=64,P=0)=(2p/2P)|(p=6,P=0)=2p-P|(p=6,P=0)=26-0=64.
Butterfly n=1 of N'P=NP/2=2p-P-1=26-0-1=32 butterflies indexed by n=0...N'P-1=0...31.
Even base index e = 2NPb = 2(64)(0) = 0.
Odd base index o = e + 2N'P = 0 + 2(32) = 64.
Twiddle step size s = 2P+1 = 20+1 = 2.
x[e+2n] ={x[e+2n]+x[o+2n]}>>1
x[0+2] ={x[0+2]+x[64+2]}>>1
x[2] ={x[2]+x[66]}>>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[64+3]}>>1
x[3] ={x[3]+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[64+2(1)] = {(x[64+2(1)]-x[0+2(1)])t[(2)(1)]-(x[0+2(1)+1]-x[64+2(1)+1])t[(2)(1)+1]}>>1
x[64+2] = {(x[64+2]-x[0+2])t[2]-(x[0+2+1]-x[64+2+1])t[2+1]}>>1
x[66] = {(x[66]-x[2])t[2]-(x[3]-x[67])t[3]}>>1
= {(1000-1000)809d-(0000-0000)f374}>>1
= {(00000)809d-(00000)f374}>>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[64+2(1)+1] = {(x[64+2(1)+1]-x[0+2(1)+1])t[(2)(1)]+(x[0+2(1)]-x[64+2(1)])t[(2)(1)+1]}>>1
x[64+3] = {(x[64+3]-x[0+3])t[2]+(x[0+2]-x[64+2])t[2+1]}>>1
x[67] = {(x[67]-x[3])t[2]+(x[2]-x[66])t[3]}>>1
= {(0000-0000)809d+(1000-1000)f374}>>1
= {(00000)809d+(00000)f374}>>1
= {00000+00000}>>1
= {00000}>>1
= 0000



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(P,b,n)=(0,0,2)
Loop P=0 of p=log2N=log264=6 loops indexed P=0...p-1=0...6-1=0...5.
Subblock b=0 of BP=B0=2P=20=1 subblocks, indexed b=0...B0-1=0...0.
Subblock size=NP|P=0=N0=N/BP|(N=64,P=0)=(2p/2P)|(p=6,P=0)=2p-P|(p=6,P=0)=26-0=64.
Butterfly n=2 of N'P=NP/2=2p-P-1=26-0-1=32 butterflies indexed by n=0...N'P-1=0...31.
Even base index e = 2NPb = 2(64)(0) = 0.
Odd base index o = e + 2N'P = 0 + 2(32) = 64.
Twiddle step size s = 2P+1 = 20+1 = 2.
x[e+2n] ={x[e+2n]+x[o+2n]}>>1
x[0+4] ={x[0+4]+x[64+4]}>>1
x[4] ={x[4]+x[68]}>>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[64+5]}>>1
x[5] ={x[5]+x[69]}>>1
={0000 +0000}>>1
={00000}>>1
=0000
x[o+2n] = {(x[o+2n]-x[e+2n])t[sn]-(x[e+2n+1]-x[o+2n+1])t[sn+1]}>>1
x[64+2(2)] = {(x[64+2(2)]-x[0+2(2)])t[(2)(2)]-(x[0+2(2)+1]-x[64+2(2)+1])t[(2)(2)+1]}>>1
x[64+4] = {(x[64+4]-x[0+4])t[4]-(x[0+4+1]-x[64+4+1])t[4+1]}>>1
x[68] = {(x[68]-x[4])t[4]-(x[5]-x[69])t[5]}>>1
= {(0000-0000)8275-(0000-0000)e707}>>1
= {(00000)8275-(00000)e707}>>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[64+2(2)+1] = {(x[64+2(2)+1]-x[0+2(2)+1])t[(2)(2)]+(x[0+2(2)]-x[64+2(2)])t[(2)(2)+1]}>>1
x[64+5] = {(x[64+5]-x[0+5])t[4]+(x[0+4]-x[64+4])t[4+1]}>>1
x[69] = {(x[69]-x[5])t[4]+(x[4]-x[68])t[5]}>>1
= {(0000-0000)8275+(0000-0000)e707}>>1
= {(00000)8275+(00000)e707}>>1
= {00000+00000}>>1
= {00000}>>1
= 0000



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(P,b,n)=(0,0,3)
Loop P=0 of p=log2N=log264=6 loops indexed P=0...p-1=0...6-1=0...5.
Subblock b=0 of BP=B0=2P=20=1 subblocks, indexed b=0...B0-1=0...0.
Subblock size=NP|P=0=N0=N/BP|(N=64,P=0)=(2p/2P)|(p=6,P=0)=2p-P|(p=6,P=0)=26-0=64.
Butterfly n=3 of N'P=NP/2=2p-P-1=26-0-1=32 butterflies indexed by n=0...N'P-1=0...31.
Even base index e = 2NPb = 2(64)(0) = 0.
Odd base index o = e + 2N'P = 0 + 2(32) = 64.
Twiddle step size s = 2P+1 = 20+1 = 2.
x[e+2n] ={x[e+2n]+x[o+2n]}>>1
x[0+6] ={x[0+6]+x[64+6]}>>1
x[6] ={x[6]+x[70]}>>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[64+7]}>>1
x[7] ={x[7]+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[64+2(3)] = {(x[64+2(3)]-x[0+2(3)])t[(2)(3)]-(x[0+2(3)+1]-x[64+2(3)+1])t[(2)(3)+1]}>>1
x[64+6] = {(x[64+6]-x[0+6])t[6]-(x[0+6+1]-x[64+6+1])t[6+1]}>>1
x[70] = {(x[70]-x[6])t[6]-(x[7]-x[71])t[7]}>>1
= {(f000-f000)8582-(0000-0000)dad7}>>1
= {(00000)8582-(00000)dad7}>>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[64+2(3)+1] = {(x[64+2(3)+1]-x[0+2(3)+1])t[(2)(3)]+(x[0+2(3)]-x[64+2(3)])t[(2)(3)+1]}>>1
x[64+7] = {(x[64+7]-x[0+7])t[6]+(x[0+6]-x[64+6])t[6+1]}>>1
x[71] = {(x[71]-x[7])t[6]+(x[6]-x[70])t[7]}>>1
= {(0000-0000)8582+(f000-f000)dad7}>>1
= {(00000)8582+(00000)dad7}>>1
= {00000+00000}>>1
= {00000}>>1
= 0000



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(P,b,n)=(0,0,4)
Loop P=0 of p=log2N=log264=6 loops indexed P=0...p-1=0...6-1=0...5.
Subblock b=0 of BP=B0=2P=20=1 subblocks, indexed b=0...B0-1=0...0.
Subblock size=NP|P=0=N0=N/BP|(N=64,P=0)=(2p/2P)|(p=6,P=0)=2p-P|(p=6,P=0)=26-0=64.
Butterfly n=4 of N'P=NP/2=2p-P-1=26-0-1=32 butterflies indexed by n=0...N'P-1=0...31.
Even base index e = 2NPb = 2(64)(0) = 0.
Odd base index o = e + 2N'P = 0 + 2(32) = 64.
Twiddle step size s = 2P+1 = 20+1 = 2.
x[e+2n] ={x[e+2n]+x[o+2n]}>>1
x[0+8] ={x[0+8]+x[64+8]}>>1
x[8] ={x[8]+x[72]}>>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[64+9]}>>1
x[9] ={x[9]+x[73]}>>1
={0000 +0000}>>1
={00000}>>1
=0000
x[o+2n] = {(x[o+2n]-x[e+2n])t[sn]-(x[e+2n+1]-x[o+2n+1])t[sn+1]}>>1
x[64+2(4)] = {(x[64+2(4)]-x[0+2(4)])t[(2)(4)]-(x[0+2(4)+1]-x[64+2(4)+1])t[(2)(4)+1]}>>1
x[64+8] = {(x[64+8]-x[0+8])t[8]-(x[0+8+1]-x[64+8+1])t[8+1]}>>1
x[72] = {(x[72]-x[8])t[8]-(x[9]-x[73])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[64+2(4)+1] = {(x[64+2(4)+1]-x[0+2(4)+1])t[(2)(4)]+(x[0+2(4)]-x[64+2(4)])t[(2)(4)+1]}>>1
x[64+9] = {(x[64+9]-x[0+9])t[8]+(x[0+8]-x[64+8])t[8+1]}>>1
x[73] = {(x[73]-x[9])t[8]+(x[8]-x[72])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)=(0,0,5)
Loop P=0 of p=log2N=log264=6 loops indexed P=0...p-1=0...6-1=0...5.
Subblock b=0 of BP=B0=2P=20=1 subblocks, indexed b=0...B0-1=0...0.
Subblock size=NP|P=0=N0=N/BP|(N=64,P=0)=(2p/2P)|(p=6,P=0)=2p-P|(p=6,P=0)=26-0=64.
Butterfly n=5 of N'P=NP/2=2p-P-1=26-0-1=32 butterflies indexed by n=0...N'P-1=0...31.
Even base index e = 2NPb = 2(64)(0) = 0.
Odd base index o = e + 2N'P = 0 + 2(32) = 64.
Twiddle step size s = 2P+1 = 20+1 = 2.
x[e+2n] ={x[e+2n]+x[o+2n]}>>1
x[0+10] ={x[0+10]+x[64+10]}>>1
x[10] ={x[10]+x[74]}>>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[64+11]}>>1
x[11] ={x[11]+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[64+2(5)] = {(x[64+2(5)]-x[0+2(5)])t[(2)(5)]-(x[0+2(5)+1]-x[64+2(5)+1])t[(2)(5)+1]}>>1
x[64+10] = {(x[64+10]-x[0+10])t[10]-(x[0+10+1]-x[64+10+1])t[10+1]}>>1
x[74] = {(x[74]-x[10])t[10]-(x[11]-x[75])t[11]}>>1
= {(1000-1000)8f1d-(0000-0000)c3a9}>>1
= {(00000)8f1d-(00000)c3a9}>>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[64+2(5)+1] = {(x[64+2(5)+1]-x[0+2(5)+1])t[(2)(5)]+(x[0+2(5)]-x[64+2(5)])t[(2)(5)+1]}>>1
x[64+11] = {(x[64+11]-x[0+11])t[10]+(x[0+10]-x[64+10])t[10+1]}>>1
x[75] = {(x[75]-x[11])t[10]+(x[10]-x[74])t[11]}>>1
= {(0000-0000)8f1d+(1000-1000)c3a9}>>1
= {(00000)8f1d+(00000)c3a9}>>1
= {00000+00000}>>1
= {00000}>>1
= 0000



Return to Table of Contents




(P,b,n)=(0,0,6)
Loop P=0 of p=log2N=log264=6 loops indexed P=0...p-1=0...6-1=0...5.
Subblock b=0 of BP=B0=2P=20=1 subblocks, indexed b=0...B0-1=0...0.
Subblock size=NP|P=0=N0=N/BP|(N=64,P=0)=(2p/2P)|(p=6,P=0)=2p-P|(p=6,P=0)=26-0=64.
Butterfly n=6 of N'P=NP/2=2p-P-1=26-0-1=32 butterflies indexed by n=0...N'P-1=0...31.
Even base index e = 2NPb = 2(64)(0) = 0.
Odd base index o = e + 2N'P = 0 + 2(32) = 64.
Twiddle step size s = 2P+1 = 20+1 = 2.
x[e+2n] ={x[e+2n]+x[o+2n]}>>1
x[0+12] ={x[0+12]+x[64+12]}>>1
x[12] ={x[12]+x[76]}>>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[64+13]}>>1
x[13] ={x[13]+x[77]}>>1
={0000 +0000}>>1
={00000}>>1
=0000
x[o+2n] = {(x[o+2n]-x[e+2n])t[sn]-(x[e+2n+1]-x[o+2n+1])t[sn+1]}>>1
x[64+2(6)] = {(x[64+2(6)]-x[0+2(6)])t[(2)(6)]-(x[0+2(6)+1]-x[64+2(6)+1])t[(2)(6)+1]}>>1
x[64+12] = {(x[64+12]-x[0+12])t[12]-(x[0+12+1]-x[64+12+1])t[12+1]}>>1
x[76] = {(x[76]-x[12])t[12]-(x[13]-x[77])t[13]}>>1
= {(0000-0000)9592-(0000-0000)b8e3}>>1
= {(00000)9592-(00000)b8e3}>>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[64+2(6)+1] = {(x[64+2(6)+1]-x[0+2(6)+1])t[(2)(6)]+(x[0+2(6)]-x[64+2(6)])t[(2)(6)+1]}>>1
x[64+13] = {(x[64+13]-x[0+13])t[12]+(x[0+12]-x[64+12])t[12+1]}>>1
x[77] = {(x[77]-x[13])t[12]+(x[12]-x[76])t[13]}>>1
= {(0000-0000)9592+(0000-0000)b8e3}>>1
= {(00000)9592+(00000)b8e3}>>1
= {00000+00000}>>1
= {00000}>>1
= 0000



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(P,b,n)=(0,0,7)
Loop P=0 of p=log2N=log264=6 loops indexed P=0...p-1=0...6-1=0...5.
Subblock b=0 of BP=B0=2P=20=1 subblocks, indexed b=0...B0-1=0...0.
Subblock size=NP|P=0=N0=N/BP|(N=64,P=0)=(2p/2P)|(p=6,P=0)=2p-P|(p=6,P=0)=26-0=64.
Butterfly n=7 of N'P=NP/2=2p-P-1=26-0-1=32 butterflies indexed by n=0...N'P-1=0...31.
Even base index e = 2NPb = 2(64)(0) = 0.
Odd base index o = e + 2N'P = 0 + 2(32) = 64.
Twiddle step size s = 2P+1 = 20+1 = 2.
x[e+2n] ={x[e+2n]+x[o+2n]}>>1
x[0+14] ={x[0+14]+x[64+14]}>>1
x[14] ={x[14]+x[78]}>>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[64+15]}>>1
x[15] ={x[15]+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[64+2(7)] = {(x[64+2(7)]-x[0+2(7)])t[(2)(7)]-(x[0+2(7)+1]-x[64+2(7)+1])t[(2)(7)+1]}>>1
x[64+14] = {(x[64+14]-x[0+14])t[14]-(x[0+14+1]-x[64+14+1])t[14+1]}>>1
x[78] = {(x[78]-x[14])t[14]-(x[15]-x[79])t[15]}>>1
= {(f000-f000)9d0d-(0000-0000)aecc}>>1
= {(00000)9d0d-(00000)aecc}>>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[64+2(7)+1] = {(x[64+2(7)+1]-x[0+2(7)+1])t[(2)(7)]+(x[0+2(7)]-x[64+2(7)])t[(2)(7)+1]}>>1
x[64+15] = {(x[64+15]-x[0+15])t[14]+(x[0+14]-x[64+14])t[14+1]}>>1
x[79] = {(x[79]-x[15])t[14]+(x[14]-x[78])t[15]}>>1
= {(0000-0000)9d0d+(f000-f000)aecc}>>1
= {(00000)9d0d+(00000)aecc}>>1
= {00000+00000}>>1
= {00000}>>1
= 0000



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(P,b,n)=(0,0,8)
Loop P=0 of p=log2N=log264=6 loops indexed P=0...p-1=0...6-1=0...5.
Subblock b=0 of BP=B0=2P=20=1 subblocks, indexed b=0...B0-1=0...0.
Subblock size=NP|P=0=N0=N/BP|(N=64,P=0)=(2p/2P)|(p=6,P=0)=2p-P|(p=6,P=0)=26-0=64.
Butterfly n=8 of N'P=NP/2=2p-P-1=26-0-1=32 butterflies indexed by n=0...N'P-1=0...31.
Even base index e = 2NPb = 2(64)(0) = 0.
Odd base index o = e + 2N'P = 0 + 2(32) = 64.
Twiddle step size s = 2P+1 = 20+1 = 2.
x[e+2n] ={x[e+2n]+x[o+2n]}>>1
x[0+16] ={x[0+16]+x[64+16]}>>1
x[16] ={x[16]+x[80]}>>1
={0000 +0000}>>1
={00000}>>1
=0000
x[e+2n+1] ={x[e+2n+1]+x[o+2n+1]}>>1
x[0+17] ={x[0+17]+x[64+17]}>>1
x[17] ={x[17]+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[64+2(8)] = {(x[64+2(8)]-x[0+2(8)])t[(2)(8)]-(x[0+2(8)+1]-x[64+2(8)+1])t[(2)(8)+1]}>>1
x[64+16] = {(x[64+16]-x[0+16])t[16]-(x[0+16+1]-x[64+16+1])t[16+1]}>>1
x[80] = {(x[80]-x[16])t[16]-(x[17]-x[81])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[64+2(8)+1] = {(x[64+2(8)+1]-x[0+2(8)+1])t[(2)(8)]+(x[0+2(8)]-x[64+2(8)])t[(2)(8)+1]}>>1
x[64+17] = {(x[64+17]-x[0+17])t[16]+(x[0+16]-x[64+16])t[16+1]}>>1
x[81] = {(x[81]-x[17])t[16]+(x[16]-x[80])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)=(0,0,9)
Loop P=0 of p=log2N=log264=6 loops indexed P=0...p-1=0...6-1=0...5.
Subblock b=0 of BP=B0=2P=20=1 subblocks, indexed b=0...B0-1=0...0.
Subblock size=NP|P=0=N0=N/BP|(N=64,P=0)=(2p/2P)|(p=6,P=0)=2p-P|(p=6,P=0)=26-0=64.
Butterfly n=9 of N'P=NP/2=2p-P-1=26-0-1=32 butterflies indexed by n=0...N'P-1=0...31.
Even base index e = 2NPb = 2(64)(0) = 0.
Odd base index o = e + 2N'P = 0 + 2(32) = 64.
Twiddle step size s = 2P+1 = 20+1 = 2.
x[e+2n] ={x[e+2n]+x[o+2n]}>>1
x[0+18] ={x[0+18]+x[64+18]}>>1
x[18] ={x[18]+x[82]}>>1
={1000 +1000}>>1
={02000}>>1
=1000
x[e+2n+1] ={x[e+2n+1]+x[o+2n+1]}>>1
x[0+19] ={x[0+19]+x[64+19]}>>1
x[19] ={x[19]+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[64+2(9)] = {(x[64+2(9)]-x[0+2(9)])t[(2)(9)]-(x[0+2(9)+1]-x[64+2(9)+1])t[(2)(9)+1]}>>1
x[64+18] = {(x[64+18]-x[0+18])t[18]-(x[0+18+1]-x[64+18+1])t[18+1]}>>1
x[82] = {(x[82]-x[18])t[18]-(x[19]-x[83])t[19]}>>1
= {(1000-1000)aecc-(0000-0000)9d0d}>>1
= {(00000)aecc-(00000)9d0d}>>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[64+2(9)+1] = {(x[64+2(9)+1]-x[0+2(9)+1])t[(2)(9)]+(x[0+2(9)]-x[64+2(9)])t[(2)(9)+1]}>>1
x[64+19] = {(x[64+19]-x[0+19])t[18]+(x[0+18]-x[64+18])t[18+1]}>>1
x[83] = {(x[83]-x[19])t[18]+(x[18]-x[82])t[19]}>>1
= {(0000-0000)aecc+(1000-1000)9d0d}>>1
= {(00000)aecc+(00000)9d0d}>>1
= {00000+00000}>>1
= {00000}>>1
= 0000



Return to Table of Contents




(P,b,n)=(0,0,10)
Loop P=0 of p=log2N=log264=6 loops indexed P=0...p-1=0...6-1=0...5.
Subblock b=0 of BP=B0=2P=20=1 subblocks, indexed b=0...B0-1=0...0.
Subblock size=NP|P=0=N0=N/BP|(N=64,P=0)=(2p/2P)|(p=6,P=0)=2p-P|(p=6,P=0)=26-0=64.
Butterfly n=10 of N'P=NP/2=2p-P-1=26-0-1=32 butterflies indexed by n=0...N'P-1=0...31.
Even base index e = 2NPb = 2(64)(0) = 0.
Odd base index o = e + 2N'P = 0 + 2(32) = 64.
Twiddle step size s = 2P+1 = 20+1 = 2.
x[e+2n] ={x[e+2n]+x[o+2n]}>>1
x[0+20] ={x[0+20]+x[64+20]}>>1
x[20] ={x[20]+x[84]}>>1
={0000 +0000}>>1
={00000}>>1
=0000
x[e+2n+1] ={x[e+2n+1]+x[o+2n+1]}>>1
x[0+21] ={x[0+21]+x[64+21]}>>1
x[21] ={x[21]+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[64+2(10)] = {(x[64+2(10)]-x[0+2(10)])t[(2)(10)]-(x[0+2(10)+1]-x[64+2(10)+1])t[(2)(10)+1]}>>1
x[64+20] = {(x[64+20]-x[0+20])t[20]-(x[0+20+1]-x[64+20+1])t[20+1]}>>1
x[84] = {(x[84]-x[20])t[20]-(x[21]-x[85])t[21]}>>1
= {(0000-0000)b8e3-(0000-0000)9592}>>1
= {(00000)b8e3-(00000)9592}>>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[64+2(10)+1] = {(x[64+2(10)+1]-x[0+2(10)+1])t[(2)(10)]+(x[0+2(10)]-x[64+2(10)])t[(2)(10)+1]}>>1
x[64+21] = {(x[64+21]-x[0+21])t[20]+(x[0+20]-x[64+20])t[20+1]}>>1
x[85] = {(x[85]-x[21])t[20]+(x[20]-x[84])t[21]}>>1
= {(0000-0000)b8e3+(0000-0000)9592}>>1
= {(00000)b8e3+(00000)9592}>>1
= {00000+00000}>>1
= {00000}>>1
= 0000



Return to Table of Contents




(P,b,n)=(0,0,11)
Loop P=0 of p=log2N=log264=6 loops indexed P=0...p-1=0...6-1=0...5.
Subblock b=0 of BP=B0=2P=20=1 subblocks, indexed b=0...B0-1=0...0.
Subblock size=NP|P=0=N0=N/BP|(N=64,P=0)=(2p/2P)|(p=6,P=0)=2p-P|(p=6,P=0)=26-0=64.
Butterfly n=11 of N'P=NP/2=2p-P-1=26-0-1=32 butterflies indexed by n=0...N'P-1=0...31.
Even base index e = 2NPb = 2(64)(0) = 0.
Odd base index o = e + 2N'P = 0 + 2(32) = 64.
Twiddle step size s = 2P+1 = 20+1 = 2.
x[e+2n] ={x[e+2n]+x[o+2n]}>>1
x[0+22] ={x[0+22]+x[64+22]}>>1
x[22] ={x[22]+x[86]}>>1
={f000 +f000}>>1
={fe000}>>1
=f000
x[e+2n+1] ={x[e+2n+1]+x[o+2n+1]}>>1
x[0+23] ={x[0+23]+x[64+23]}>>1
x[23] ={x[23]+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[64+2(11)] = {(x[64+2(11)]-x[0+2(11)])t[(2)(11)]-(x[0+2(11)+1]-x[64+2(11)+1])t[(2)(11)+1]}>>1
x[64+22] = {(x[64+22]-x[0+22])t[22]-(x[0+22+1]-x[64+22+1])t[22+1]}>>1
x[86] = {(x[86]-x[22])t[22]-(x[23]-x[87])t[23]}>>1
= {(f000-f000)c3a9-(0000-0000)8f1d}>>1
= {(00000)c3a9-(00000)8f1d}>>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[64+2(11)+1] = {(x[64+2(11)+1]-x[0+2(11)+1])t[(2)(11)]+(x[0+2(11)]-x[64+2(11)])t[(2)(11)+1]}>>1
x[64+23] = {(x[64+23]-x[0+23])t[22]+(x[0+22]-x[64+22])t[22+1]}>>1
x[87] = {(x[87]-x[23])t[22]+(x[22]-x[86])t[23]}>>1
= {(0000-0000)c3a9+(f000-f000)8f1d}>>1
= {(00000)c3a9+(00000)8f1d}>>1
= {00000+00000}>>1
= {00000}>>1
= 0000



Return to Table of Contents




(P,b,n)=(0,0,12)
Loop P=0 of p=log2N=log264=6 loops indexed P=0...p-1=0...6-1=0...5.
Subblock b=0 of BP=B0=2P=20=1 subblocks, indexed b=0...B0-1=0...0.
Subblock size=NP|P=0=N0=N/BP|(N=64,P=0)=(2p/2P)|(p=6,P=0)=2p-P|(p=6,P=0)=26-0=64.
Butterfly n=12 of N'P=NP/2=2p-P-1=26-0-1=32 butterflies indexed by n=0...N'P-1=0...31.
Even base index e = 2NPb = 2(64)(0) = 0.
Odd base index o = e + 2N'P = 0 + 2(32) = 64.
Twiddle step size s = 2P+1 = 20+1 = 2.
x[e+2n] ={x[e+2n]+x[o+2n]}>>1
x[0+24] ={x[0+24]+x[64+24]}>>1
x[24] ={x[24]+x[88]}>>1
={0000 +0000}>>1
={00000}>>1
=0000
x[e+2n+1] ={x[e+2n+1]+x[o+2n+1]}>>1
x[0+25] ={x[0+25]+x[64+25]}>>1
x[25] ={x[25]+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[64+2(12)] = {(x[64+2(12)]-x[0+2(12)])t[(2)(12)]-(x[0+2(12)+1]-x[64+2(12)+1])t[(2)(12)+1]}>>1
x[64+24] = {(x[64+24]-x[0+24])t[24]-(x[0+24+1]-x[64+24+1])t[24+1]}>>1
x[88] = {(x[88]-x[24])t[24]-(x[25]-x[89])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[64+2(12)+1] = {(x[64+2(12)+1]-x[0+2(12)+1])t[(2)(12)]+(x[0+2(12)]-x[64+2(12)])t[(2)(12)+1]}>>1
x[64+25] = {(x[64+25]-x[0+25])t[24]+(x[0+24]-x[64+24])t[24+1]}>>1
x[89] = {(x[89]-x[25])t[24]+(x[24]-x[88])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)=(0,0,13)
Loop P=0 of p=log2N=log264=6 loops indexed P=0...p-1=0...6-1=0...5.
Subblock b=0 of BP=B0=2P=20=1 subblocks, indexed b=0...B0-1=0...0.
Subblock size=NP|P=0=N0=N/BP|(N=64,P=0)=(2p/2P)|(p=6,P=0)=2p-P|(p=6,P=0)=26-0=64.
Butterfly n=13 of N'P=NP/2=2p-P-1=26-0-1=32 butterflies indexed by n=0...N'P-1=0...31.
Even base index e = 2NPb = 2(64)(0) = 0.
Odd base index o = e + 2N'P = 0 + 2(32) = 64.
Twiddle step size s = 2P+1 = 20+1 = 2.
x[e+2n] ={x[e+2n]+x[o+2n]}>>1
x[0+26] ={x[0+26]+x[64+26]}>>1
x[26] ={x[26]+x[90]}>>1
={1000 +1000}>>1
={02000}>>1
=1000
x[e+2n+1] ={x[e+2n+1]+x[o+2n+1]}>>1
x[0+27] ={x[0+27]+x[64+27]}>>1
x[27] ={x[27]+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[64+2(13)] = {(x[64+2(13)]-x[0+2(13)])t[(2)(13)]-(x[0+2(13)+1]-x[64+2(13)+1])t[(2)(13)+1]}>>1
x[64+26] = {(x[64+26]-x[0+26])t[26]-(x[0+26+1]-x[64+26+1])t[26+1]}>>1
x[90] = {(x[90]-x[26])t[26]-(x[27]-x[91])t[27]}>>1
= {(1000-1000)dad7-(0000-0000)8582}>>1
= {(00000)dad7-(00000)8582}>>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[64+2(13)+1] = {(x[64+2(13)+1]-x[0+2(13)+1])t[(2)(13)]+(x[0+2(13)]-x[64+2(13)])t[(2)(13)+1]}>>1
x[64+27] = {(x[64+27]-x[0+27])t[26]+(x[0+26]-x[64+26])t[26+1]}>>1
x[91] = {(x[91]-x[27])t[26]+(x[26]-x[90])t[27]}>>1
= {(0000-0000)dad7+(1000-1000)8582}>>1
= {(00000)dad7+(00000)8582}>>1
= {00000+00000}>>1
= {00000}>>1
= 0000



Return to Table of Contents




(P,b,n)=(0,0,14)
Loop P=0 of p=log2N=log264=6 loops indexed P=0...p-1=0...6-1=0...5.
Subblock b=0 of BP=B0=2P=20=1 subblocks, indexed b=0...B0-1=0...0.
Subblock size=NP|P=0=N0=N/BP|(N=64,P=0)=(2p/2P)|(p=6,P=0)=2p-P|(p=6,P=0)=26-0=64.
Butterfly n=14 of N'P=NP/2=2p-P-1=26-0-1=32 butterflies indexed by n=0...N'P-1=0...31.
Even base index e = 2NPb = 2(64)(0) = 0.
Odd base index o = e + 2N'P = 0 + 2(32) = 64.
Twiddle step size s = 2P+1 = 20+1 = 2.
x[e+2n] ={x[e+2n]+x[o+2n]}>>1
x[0+28] ={x[0+28]+x[64+28]}>>1
x[28] ={x[28]+x[92]}>>1
={0000 +0000}>>1
={00000}>>1
=0000
x[e+2n+1] ={x[e+2n+1]+x[o+2n+1]}>>1
x[0+29] ={x[0+29]+x[64+29]}>>1
x[29] ={x[29]+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[64+2(14)] = {(x[64+2(14)]-x[0+2(14)])t[(2)(14)]-(x[0+2(14)+1]-x[64+2(14)+1])t[(2)(14)+1]}>>1
x[64+28] = {(x[64+28]-x[0+28])t[28]-(x[0+28+1]-x[64+28+1])t[28+1]}>>1
x[92] = {(x[92]-x[28])t[28]-(x[29]-x[93])t[29]}>>1
= {(0000-0000)e707-(0000-0000)8275}>>1
= {(00000)e707-(00000)8275}>>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[64+2(14)+1] = {(x[64+2(14)+1]-x[0+2(14)+1])t[(2)(14)]+(x[0+2(14)]-x[64+2(14)])t[(2)(14)+1]}>>1
x[64+29] = {(x[64+29]-x[0+29])t[28]+(x[0+28]-x[64+28])t[28+1]}>>1
x[93] = {(x[93]-x[29])t[28]+(x[28]-x[92])t[29]}>>1
= {(0000-0000)e707+(0000-0000)8275}>>1
= {(00000)e707+(00000)8275}>>1
= {00000+00000}>>1
= {00000}>>1
= 0000



Return to Table of Contents




(P,b,n)=(0,0,15)
Loop P=0 of p=log2N=log264=6 loops indexed P=0...p-1=0...6-1=0...5.
Subblock b=0 of BP=B0=2P=20=1 subblocks, indexed b=0...B0-1=0...0.
Subblock size=NP|P=0=N0=N/BP|(N=64,P=0)=(2p/2P)|(p=6,P=0)=2p-P|(p=6,P=0)=26-0=64.
Butterfly n=15 of N'P=NP/2=2p-P-1=26-0-1=32 butterflies indexed by n=0...N'P-1=0...31.
Even base index e = 2NPb = 2(64)(0) = 0.
Odd base index o = e + 2N'P = 0 + 2(32) = 64.
Twiddle step size s = 2P+1 = 20+1 = 2.
x[e+2n] ={x[e+2n]+x[o+2n]}>>1
x[0+30] ={x[0+30]+x[64+30]}>>1
x[30] ={x[30]+x[94]}>>1
={f000 +f000}>>1
={fe000}>>1
=f000
x[e+2n+1] ={x[e+2n+1]+x[o+2n+1]}>>1
x[0+31] ={x[0+31]+x[64+31]}>>1
x[31] ={x[31]+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[64+2(15)] = {(x[64+2(15)]-x[0+2(15)])t[(2)(15)]-(x[0+2(15)+1]-x[64+2(15)+1])t[(2)(15)+1]}>>1
x[64+30] = {(x[64+30]-x[0+30])t[30]-(x[0+30+1]-x[64+30+1])t[30+1]}>>1
x[94] = {(x[94]-x[30])t[30]-(x[31]-x[95])t[31]}>>1
= {(f000-f000)f374-(0000-0000)809d}>>1
= {(00000)f374-(00000)809d}>>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[64+2(15)+1] = {(x[64+2(15)+1]-x[0+2(15)+1])t[(2)(15)]+(x[0+2(15)]-x[64+2(15)])t[(2)(15)+1]}>>1
x[64+31] = {(x[64+31]-x[0+31])t[30]+(x[0+30]-x[64+30])t[30+1]}>>1
x[95] = {(x[95]-x[31])t[30]+(x[30]-x[94])t[31]}>>1
= {(0000-0000)f374+(f000-f000)809d}>>1
= {(00000)f374+(00000)809d}>>1
= {00000+00000}>>1
= {00000}>>1
= 0000



Return to Table of Contents




(P,b,n)=(0,0,16)
Loop P=0 of p=log2N=log264=6 loops indexed P=0...p-1=0...6-1=0...5.
Subblock b=0 of BP=B0=2P=20=1 subblocks, indexed b=0...B0-1=0...0.
Subblock size=NP|P=0=N0=N/BP|(N=64,P=0)=(2p/2P)|(p=6,P=0)=2p-P|(p=6,P=0)=26-0=64.
Butterfly n=16 of N'P=NP/2=2p-P-1=26-0-1=32 butterflies indexed by n=0...N'P-1=0...31.
Even base index e = 2NPb = 2(64)(0) = 0.
Odd base index o = e + 2N'P = 0 + 2(32) = 64.
Twiddle step size s = 2P+1 = 20+1 = 2.
x[e+2n] ={x[e+2n]+x[o+2n]}>>1
x[0+32] ={x[0+32]+x[64+32]}>>1
x[32] ={x[32]+x[96]}>>1
={0000 +0000}>>1
={00000}>>1
=0000
x[e+2n+1] ={x[e+2n+1]+x[o+2n+1]}>>1
x[0+33] ={x[0+33]+x[64+33]}>>1
x[33] ={x[33]+x[97]}>>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[64+2(16)] = {(x[64+2(16)]-x[0+2(16)])t[(2)(16)]-(x[0+2(16)+1]-x[64+2(16)+1])t[(2)(16)+1]}>>1
x[64+32] = {(x[64+32]-x[0+32])t[32]-(x[0+32+1]-x[64+32+1])t[32+1]}>>1
x[96] = {(x[96]-x[32])t[32]-(x[33]-x[97])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[64+2(16)+1] = {(x[64+2(16)+1]-x[0+2(16)+1])t[(2)(16)]+(x[0+2(16)]-x[64+2(16)])t[(2)(16)+1]}>>1
x[64+33] = {(x[64+33]-x[0+33])t[32]+(x[0+32]-x[64+32])t[32+1]}>>1
x[97] = {(x[97]-x[33])t[32]+(x[32]-x[96])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)=(0,0,17)
Loop P=0 of p=log2N=log264=6 loops indexed P=0...p-1=0...6-1=0...5.
Subblock b=0 of BP=B0=2P=20=1 subblocks, indexed b=0...B0-1=0...0.
Subblock size=NP|P=0=N0=N/BP|(N=64,P=0)=(2p/2P)|(p=6,P=0)=2p-P|(p=6,P=0)=26-0=64.
Butterfly n=17 of N'P=NP/2=2p-P-1=26-0-1=32 butterflies indexed by n=0...N'P-1=0...31.
Even base index e = 2NPb = 2(64)(0) = 0.
Odd base index o = e + 2N'P = 0 + 2(32) = 64.
Twiddle step size s = 2P+1 = 20+1 = 2.
x[e+2n] ={x[e+2n]+x[o+2n]}>>1
x[0+34] ={x[0+34]+x[64+34]}>>1
x[34] ={x[34]+x[98]}>>1
={1000 +1000}>>1
={02000}>>1
=1000
x[e+2n+1] ={x[e+2n+1]+x[o+2n+1]}>>1
x[0+35] ={x[0+35]+x[64+35]}>>1
x[35] ={x[35]+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[64+2(17)] = {(x[64+2(17)]-x[0+2(17)])t[(2)(17)]-(x[0+2(17)+1]-x[64+2(17)+1])t[(2)(17)+1]}>>1
x[64+34] = {(x[64+34]-x[0+34])t[34]-(x[0+34+1]-x[64+34+1])t[34+1]}>>1
x[98] = {(x[98]-x[34])t[34]-(x[35]-x[99])t[35]}>>1
= {(1000-1000)0c8b-(0000-0000)809d}>>1
= {(00000)0c8b-(00000)809d}>>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[64+2(17)+1] = {(x[64+2(17)+1]-x[0+2(17)+1])t[(2)(17)]+(x[0+2(17)]-x[64+2(17)])t[(2)(17)+1]}>>1
x[64+35] = {(x[64+35]-x[0+35])t[34]+(x[0+34]-x[64+34])t[34+1]}>>1
x[99] = {(x[99]-x[35])t[34]+(x[34]-x[98])t[35]}>>1
= {(0000-0000)0c8b+(1000-1000)809d}>>1
= {(00000)0c8b+(00000)809d}>>1
= {00000+00000}>>1
= {00000}>>1
= 0000



Return to Table of Contents




(P,b,n)=(0,0,18)
Loop P=0 of p=log2N=log264=6 loops indexed P=0...p-1=0...6-1=0...5.
Subblock b=0 of BP=B0=2P=20=1 subblocks, indexed b=0...B0-1=0...0.
Subblock size=NP|P=0=N0=N/BP|(N=64,P=0)=(2p/2P)|(p=6,P=0)=2p-P|(p=6,P=0)=26-0=64.
Butterfly n=18 of N'P=NP/2=2p-P-1=26-0-1=32 butterflies indexed by n=0...N'P-1=0...31.
Even base index e = 2NPb = 2(64)(0) = 0.
Odd base index o = e + 2N'P = 0 + 2(32) = 64.
Twiddle step size s = 2P+1 = 20+1 = 2.
x[e+2n] ={x[e+2n]+x[o+2n]}>>1
x[0+36] ={x[0+36]+x[64+36]}>>1
x[36] ={x[36]+x[100]}>>1
={0000 +0000}>>1
={00000}>>1
=0000
x[e+2n+1] ={x[e+2n+1]+x[o+2n+1]}>>1
x[0+37] ={x[0+37]+x[64+37]}>>1
x[37] ={x[37]+x[101]}>>1
={0000 +0000}>>1
={00000}>>1
=0000
x[o+2n] = {(x[o+2n]-x[e+2n])t[sn]-(x[e+2n+1]-x[o+2n+1])t[sn+1]}>>1
x[64+2(18)] = {(x[64+2(18)]-x[0+2(18)])t[(2)(18)]-(x[0+2(18)+1]-x[64+2(18)+1])t[(2)(18)+1]}>>1
x[64+36] = {(x[64+36]-x[0+36])t[36]-(x[0+36+1]-x[64+36+1])t[36+1]}>>1
x[100] = {(x[100]-x[36])t[36]-(x[37]-x[101])t[37]}>>1
= {(0000-0000)18f8-(0000-0000)8275}>>1
= {(00000)18f8-(00000)8275}>>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[64+2(18)+1] = {(x[64+2(18)+1]-x[0+2(18)+1])t[(2)(18)]+(x[0+2(18)]-x[64+2(18)])t[(2)(18)+1]}>>1
x[64+37] = {(x[64+37]-x[0+37])t[36]+(x[0+36]-x[64+36])t[36+1]}>>1
x[101] = {(x[101]-x[37])t[36]+(x[36]-x[100])t[37]}>>1
= {(0000-0000)18f8+(0000-0000)8275}>>1
= {(00000)18f8+(00000)8275}>>1
= {00000+00000}>>1
= {00000}>>1
= 0000



Return to Table of Contents




(P,b,n)=(0,0,19)
Loop P=0 of p=log2N=log264=6 loops indexed P=0...p-1=0...6-1=0...5.
Subblock b=0 of BP=B0=2P=20=1 subblocks, indexed b=0...B0-1=0...0.
Subblock size=NP|P=0=N0=N/BP|(N=64,P=0)=(2p/2P)|(p=6,P=0)=2p-P|(p=6,P=0)=26-0=64.
Butterfly n=19 of N'P=NP/2=2p-P-1=26-0-1=32 butterflies indexed by n=0...N'P-1=0...31.
Even base index e = 2NPb = 2(64)(0) = 0.
Odd base index o = e + 2N'P = 0 + 2(32) = 64.
Twiddle step size s = 2P+1 = 20+1 = 2.
x[e+2n] ={x[e+2n]+x[o+2n]}>>1
x[0+38] ={x[0+38]+x[64+38]}>>1
x[38] ={x[38]+x[102]}>>1
={f000 +f000}>>1
={fe000}>>1
=f000
x[e+2n+1] ={x[e+2n+1]+x[o+2n+1]}>>1
x[0+39] ={x[0+39]+x[64+39]}>>1
x[39] ={x[39]+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[64+2(19)] = {(x[64+2(19)]-x[0+2(19)])t[(2)(19)]-(x[0+2(19)+1]-x[64+2(19)+1])t[(2)(19)+1]}>>1
x[64+38] = {(x[64+38]-x[0+38])t[38]-(x[0+38+1]-x[64+38+1])t[38+1]}>>1
x[102] = {(x[102]-x[38])t[38]-(x[39]-x[103])t[39]}>>1
= {(f000-f000)2528-(0000-0000)8582}>>1
= {(00000)2528-(00000)8582}>>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[64+2(19)+1] = {(x[64+2(19)+1]-x[0+2(19)+1])t[(2)(19)]+(x[0+2(19)]-x[64+2(19)])t[(2)(19)+1]}>>1
x[64+39] = {(x[64+39]-x[0+39])t[38]+(x[0+38]-x[64+38])t[38+1]}>>1
x[103] = {(x[103]-x[39])t[38]+(x[38]-x[102])t[39]}>>1
= {(0000-0000)2528+(f000-f000)8582}>>1
= {(00000)2528+(00000)8582}>>1
= {00000+00000}>>1
= {00000}>>1
= 0000



Return to Table of Contents




(P,b,n)=(0,0,20)
Loop P=0 of p=log2N=log264=6 loops indexed P=0...p-1=0...6-1=0...5.
Subblock b=0 of BP=B0=2P=20=1 subblocks, indexed b=0...B0-1=0...0.
Subblock size=NP|P=0=N0=N/BP|(N=64,P=0)=(2p/2P)|(p=6,P=0)=2p-P|(p=6,P=0)=26-0=64.
Butterfly n=20 of N'P=NP/2=2p-P-1=26-0-1=32 butterflies indexed by n=0...N'P-1=0...31.
Even base index e = 2NPb = 2(64)(0) = 0.
Odd base index o = e + 2N'P = 0 + 2(32) = 64.
Twiddle step size s = 2P+1 = 20+1 = 2.
x[e+2n] ={x[e+2n]+x[o+2n]}>>1
x[0+40] ={x[0+40]+x[64+40]}>>1
x[40] ={x[40]+x[104]}>>1
={0000 +0000}>>1
={00000}>>1
=0000
x[e+2n+1] ={x[e+2n+1]+x[o+2n+1]}>>1
x[0+41] ={x[0+41]+x[64+41]}>>1
x[41] ={x[41]+x[105]}>>1
={0000 +0000}>>1
={00000}>>1
=0000
x[o+2n] = {(x[o+2n]-x[e+2n])t[sn]-(x[e+2n+1]-x[o+2n+1])t[sn+1]}>>1
x[64+2(20)] = {(x[64+2(20)]-x[0+2(20)])t[(2)(20)]-(x[0+2(20)+1]-x[64+2(20)+1])t[(2)(20)+1]}>>1
x[64+40] = {(x[64+40]-x[0+40])t[40]-(x[0+40+1]-x[64+40+1])t[40+1]}>>1
x[104] = {(x[104]-x[40])t[40]-(x[41]-x[105])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[64+2(20)+1] = {(x[64+2(20)+1]-x[0+2(20)+1])t[(2)(20)]+(x[0+2(20)]-x[64+2(20)])t[(2)(20)+1]}>>1
x[64+41] = {(x[64+41]-x[0+41])t[40]+(x[0+40]-x[64+40])t[40+1]}>>1
x[105] = {(x[105]-x[41])t[40]+(x[40]-x[104])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)=(0,0,21)
Loop P=0 of p=log2N=log264=6 loops indexed P=0...p-1=0...6-1=0...5.
Subblock b=0 of BP=B0=2P=20=1 subblocks, indexed b=0...B0-1=0...0.
Subblock size=NP|P=0=N0=N/BP|(N=64,P=0)=(2p/2P)|(p=6,P=0)=2p-P|(p=6,P=0)=26-0=64.
Butterfly n=21 of N'P=NP/2=2p-P-1=26-0-1=32 butterflies indexed by n=0...N'P-1=0...31.
Even base index e = 2NPb = 2(64)(0) = 0.
Odd base index o = e + 2N'P = 0 + 2(32) = 64.
Twiddle step size s = 2P+1 = 20+1 = 2.
x[e+2n] ={x[e+2n]+x[o+2n]}>>1
x[0+42] ={x[0+42]+x[64+42]}>>1
x[42] ={x[42]+x[106]}>>1
={1000 +1000}>>1
={02000}>>1
=1000
x[e+2n+1] ={x[e+2n+1]+x[o+2n+1]}>>1
x[0+43] ={x[0+43]+x[64+43]}>>1
x[43] ={x[43]+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[64+2(21)] = {(x[64+2(21)]-x[0+2(21)])t[(2)(21)]-(x[0+2(21)+1]-x[64+2(21)+1])t[(2)(21)+1]}>>1
x[64+42] = {(x[64+42]-x[0+42])t[42]-(x[0+42+1]-x[64+42+1])t[42+1]}>>1
x[106] = {(x[106]-x[42])t[42]-(x[43]-x[107])t[43]}>>1
= {(1000-1000)3c56-(0000-0000)8f1d}>>1
= {(00000)3c56-(00000)8f1d}>>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[64+2(21)+1] = {(x[64+2(21)+1]-x[0+2(21)+1])t[(2)(21)]+(x[0+2(21)]-x[64+2(21)])t[(2)(21)+1]}>>1
x[64+43] = {(x[64+43]-x[0+43])t[42]+(x[0+42]-x[64+42])t[42+1]}>>1
x[107] = {(x[107]-x[43])t[42]+(x[42]-x[106])t[43]}>>1
= {(0000-0000)3c56+(1000-1000)8f1d}>>1
= {(00000)3c56+(00000)8f1d}>>1
= {00000+00000}>>1
= {00000}>>1
= 0000



Return to Table of Contents




(P,b,n)=(0,0,22)
Loop P=0 of p=log2N=log264=6 loops indexed P=0...p-1=0...6-1=0...5.
Subblock b=0 of BP=B0=2P=20=1 subblocks, indexed b=0...B0-1=0...0.
Subblock size=NP|P=0=N0=N/BP|(N=64,P=0)=(2p/2P)|(p=6,P=0)=2p-P|(p=6,P=0)=26-0=64.
Butterfly n=22 of N'P=NP/2=2p-P-1=26-0-1=32 butterflies indexed by n=0...N'P-1=0...31.
Even base index e = 2NPb = 2(64)(0) = 0.
Odd base index o = e + 2N'P = 0 + 2(32) = 64.
Twiddle step size s = 2P+1 = 20+1 = 2.
x[e+2n] ={x[e+2n]+x[o+2n]}>>1
x[0+44] ={x[0+44]+x[64+44]}>>1
x[44] ={x[44]+x[108]}>>1
={0000 +0000}>>1
={00000}>>1
=0000
x[e+2n+1] ={x[e+2n+1]+x[o+2n+1]}>>1
x[0+45] ={x[0+45]+x[64+45]}>>1
x[45] ={x[45]+x[109]}>>1
={0000 +0000}>>1
={00000}>>1
=0000
x[o+2n] = {(x[o+2n]-x[e+2n])t[sn]-(x[e+2n+1]-x[o+2n+1])t[sn+1]}>>1
x[64+2(22)] = {(x[64+2(22)]-x[0+2(22)])t[(2)(22)]-(x[0+2(22)+1]-x[64+2(22)+1])t[(2)(22)+1]}>>1
x[64+44] = {(x[64+44]-x[0+44])t[44]-(x[0+44+1]-x[64+44+1])t[44+1]}>>1
x[108] = {(x[108]-x[44])t[44]-(x[45]-x[109])t[45]}>>1
= {(0000-0000)471c-(0000-0000)9592}>>1
= {(00000)471c-(00000)9592}>>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[64+2(22)+1] = {(x[64+2(22)+1]-x[0+2(22)+1])t[(2)(22)]+(x[0+2(22)]-x[64+2(22)])t[(2)(22)+1]}>>1
x[64+45] = {(x[64+45]-x[0+45])t[44]+(x[0+44]-x[64+44])t[44+1]}>>1
x[109] = {(x[109]-x[45])t[44]+(x[44]-x[108])t[45]}>>1
= {(0000-0000)471c+(0000-0000)9592}>>1
= {(00000)471c+(00000)9592}>>1
= {00000+00000}>>1
= {00000}>>1
= 0000



Return to Table of Contents




(P,b,n)=(0,0,23)
Loop P=0 of p=log2N=log264=6 loops indexed P=0...p-1=0...6-1=0...5.
Subblock b=0 of BP=B0=2P=20=1 subblocks, indexed b=0...B0-1=0...0.
Subblock size=NP|P=0=N0=N/BP|(N=64,P=0)=(2p/2P)|(p=6,P=0)=2p-P|(p=6,P=0)=26-0=64.
Butterfly n=23 of N'P=NP/2=2p-P-1=26-0-1=32 butterflies indexed by n=0...N'P-1=0...31.
Even base index e = 2NPb = 2(64)(0) = 0.
Odd base index o = e + 2N'P = 0 + 2(32) = 64.
Twiddle step size s = 2P+1 = 20+1 = 2.
x[e+2n] ={x[e+2n]+x[o+2n]}>>1
x[0+46] ={x[0+46]+x[64+46]}>>1
x[46] ={x[46]+x[110]}>>1
={f000 +f000}>>1
={fe000}>>1
=f000
x[e+2n+1] ={x[e+2n+1]+x[o+2n+1]}>>1
x[0+47] ={x[0+47]+x[64+47]}>>1
x[47] ={x[47]+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[64+2(23)] = {(x[64+2(23)]-x[0+2(23)])t[(2)(23)]-(x[0+2(23)+1]-x[64+2(23)+1])t[(2)(23)+1]}>>1
x[64+46] = {(x[64+46]-x[0+46])t[46]-(x[0+46+1]-x[64+46+1])t[46+1]}>>1
x[110] = {(x[110]-x[46])t[46]-(x[47]-x[111])t[47]}>>1
= {(f000-f000)5133-(0000-0000)9d0d}>>1
= {(00000)5133-(00000)9d0d}>>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[64+2(23)+1] = {(x[64+2(23)+1]-x[0+2(23)+1])t[(2)(23)]+(x[0+2(23)]-x[64+2(23)])t[(2)(23)+1]}>>1
x[64+47] = {(x[64+47]-x[0+47])t[46]+(x[0+46]-x[64+46])t[46+1]}>>1
x[111] = {(x[111]-x[47])t[46]+(x[46]-x[110])t[47]}>>1
= {(0000-0000)5133+(f000-f000)9d0d}>>1
= {(00000)5133+(00000)9d0d}>>1
= {00000+00000}>>1
= {00000}>>1
= 0000



Return to Table of Contents




(P,b,n)=(0,0,24)
Loop P=0 of p=log2N=log264=6 loops indexed P=0...p-1=0...6-1=0...5.
Subblock b=0 of BP=B0=2P=20=1 subblocks, indexed b=0...B0-1=0...0.
Subblock size=NP|P=0=N0=N/BP|(N=64,P=0)=(2p/2P)|(p=6,P=0)=2p-P|(p=6,P=0)=26-0=64.
Butterfly n=24 of N'P=NP/2=2p-P-1=26-0-1=32 butterflies indexed by n=0...N'P-1=0...31.
Even base index e = 2NPb = 2(64)(0) = 0.
Odd base index o = e + 2N'P = 0 + 2(32) = 64.
Twiddle step size s = 2P+1 = 20+1 = 2.
x[e+2n] ={x[e+2n]+x[o+2n]}>>1
x[0+48] ={x[0+48]+x[64+48]}>>1
x[48] ={x[48]+x[112]}>>1
={0000 +0000}>>1
={00000}>>1
=0000
x[e+2n+1] ={x[e+2n+1]+x[o+2n+1]}>>1
x[0+49] ={x[0+49]+x[64+49]}>>1
x[49] ={x[49]+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[64+2(24)] = {(x[64+2(24)]-x[0+2(24)])t[(2)(24)]-(x[0+2(24)+1]-x[64+2(24)+1])t[(2)(24)+1]}>>1
x[64+48] = {(x[64+48]-x[0+48])t[48]-(x[0+48+1]-x[64+48+1])t[48+1]}>>1
x[112] = {(x[112]-x[48])t[48]-(x[49]-x[113])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[64+2(24)+1] = {(x[64+2(24)+1]-x[0+2(24)+1])t[(2)(24)]+(x[0+2(24)]-x[64+2(24)])t[(2)(24)+1]}>>1
x[64+49] = {(x[64+49]-x[0+49])t[48]+(x[0+48]-x[64+48])t[48+1]}>>1
x[113] = {(x[113]-x[49])t[48]+(x[48]-x[112])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)=(0,0,25)
Loop P=0 of p=log2N=log264=6 loops indexed P=0...p-1=0...6-1=0...5.
Subblock b=0 of BP=B0=2P=20=1 subblocks, indexed b=0...B0-1=0...0.
Subblock size=NP|P=0=N0=N/BP|(N=64,P=0)=(2p/2P)|(p=6,P=0)=2p-P|(p=6,P=0)=26-0=64.
Butterfly n=25 of N'P=NP/2=2p-P-1=26-0-1=32 butterflies indexed by n=0...N'P-1=0...31.
Even base index e = 2NPb = 2(64)(0) = 0.
Odd base index o = e + 2N'P = 0 + 2(32) = 64.
Twiddle step size s = 2P+1 = 20+1 = 2.
x[e+2n] ={x[e+2n]+x[o+2n]}>>1
x[0+50] ={x[0+50]+x[64+50]}>>1
x[50] ={x[50]+x[114]}>>1
={1000 +1000}>>1
={02000}>>1
=1000
x[e+2n+1] ={x[e+2n+1]+x[o+2n+1]}>>1
x[0+51] ={x[0+51]+x[64+51]}>>1
x[51] ={x[51]+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[64+2(25)] = {(x[64+2(25)]-x[0+2(25)])t[(2)(25)]-(x[0+2(25)+1]-x[64+2(25)+1])t[(2)(25)+1]}>>1
x[64+50] = {(x[64+50]-x[0+50])t[50]-(x[0+50+1]-x[64+50+1])t[50+1]}>>1
x[114] = {(x[114]-x[50])t[50]-(x[51]-x[115])t[51]}>>1
= {(1000-1000)62f2-(0000-0000)aecc}>>1
= {(00000)62f2-(00000)aecc}>>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[64+2(25)+1] = {(x[64+2(25)+1]-x[0+2(25)+1])t[(2)(25)]+(x[0+2(25)]-x[64+2(25)])t[(2)(25)+1]}>>1
x[64+51] = {(x[64+51]-x[0+51])t[50]+(x[0+50]-x[64+50])t[50+1]}>>1
x[115] = {(x[115]-x[51])t[50]+(x[50]-x[114])t[51]}>>1
= {(0000-0000)62f2+(1000-1000)aecc}>>1
= {(00000)62f2+(00000)aecc}>>1
= {00000+00000}>>1
= {00000}>>1
= 0000



Return to Table of Contents




(P,b,n)=(0,0,26)
Loop P=0 of p=log2N=log264=6 loops indexed P=0...p-1=0...6-1=0...5.
Subblock b=0 of BP=B0=2P=20=1 subblocks, indexed b=0...B0-1=0...0.
Subblock size=NP|P=0=N0=N/BP|(N=64,P=0)=(2p/2P)|(p=6,P=0)=2p-P|(p=6,P=0)=26-0=64.
Butterfly n=26 of N'P=NP/2=2p-P-1=26-0-1=32 butterflies indexed by n=0...N'P-1=0...31.
Even base index e = 2NPb = 2(64)(0) = 0.
Odd base index o = e + 2N'P = 0 + 2(32) = 64.
Twiddle step size s = 2P+1 = 20+1 = 2.
x[e+2n] ={x[e+2n]+x[o+2n]}>>1
x[0+52] ={x[0+52]+x[64+52]}>>1
x[52] ={x[52]+x[116]}>>1
={0000 +0000}>>1
={00000}>>1
=0000
x[e+2n+1] ={x[e+2n+1]+x[o+2n+1]}>>1
x[0+53] ={x[0+53]+x[64+53]}>>1
x[53] ={x[53]+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[64+2(26)] = {(x[64+2(26)]-x[0+2(26)])t[(2)(26)]-(x[0+2(26)+1]-x[64+2(26)+1])t[(2)(26)+1]}>>1
x[64+52] = {(x[64+52]-x[0+52])t[52]-(x[0+52+1]-x[64+52+1])t[52+1]}>>1
x[116] = {(x[116]-x[52])t[52]-(x[53]-x[117])t[53]}>>1
= {(0000-0000)6a6d-(0000-0000)b8e3}>>1
= {(00000)6a6d-(00000)b8e3}>>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[64+2(26)+1] = {(x[64+2(26)+1]-x[0+2(26)+1])t[(2)(26)]+(x[0+2(26)]-x[64+2(26)])t[(2)(26)+1]}>>1
x[64+53] = {(x[64+53]-x[0+53])t[52]+(x[0+52]-x[64+52])t[52+1]}>>1
x[117] = {(x[117]-x[53])t[52]+(x[52]-x[116])t[53]}>>1
= {(0000-0000)6a6d+(0000-0000)b8e3}>>1
= {(00000)6a6d+(00000)b8e3}>>1
= {00000+00000}>>1
= {00000}>>1
= 0000



Return to Table of Contents




(P,b,n)=(0,0,27)
Loop P=0 of p=log2N=log264=6 loops indexed P=0...p-1=0...6-1=0...5.
Subblock b=0 of BP=B0=2P=20=1 subblocks, indexed b=0...B0-1=0...0.
Subblock size=NP|P=0=N0=N/BP|(N=64,P=0)=(2p/2P)|(p=6,P=0)=2p-P|(p=6,P=0)=26-0=64.
Butterfly n=27 of N'P=NP/2=2p-P-1=26-0-1=32 butterflies indexed by n=0...N'P-1=0...31.
Even base index e = 2NPb = 2(64)(0) = 0.
Odd base index o = e + 2N'P = 0 + 2(32) = 64.
Twiddle step size s = 2P+1 = 20+1 = 2.
x[e+2n] ={x[e+2n]+x[o+2n]}>>1
x[0+54] ={x[0+54]+x[64+54]}>>1
x[54] ={x[54]+x[118]}>>1
={f000 +f000}>>1
={fe000}>>1
=f000
x[e+2n+1] ={x[e+2n+1]+x[o+2n+1]}>>1
x[0+55] ={x[0+55]+x[64+55]}>>1
x[55] ={x[55]+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[64+2(27)] = {(x[64+2(27)]-x[0+2(27)])t[(2)(27)]-(x[0+2(27)+1]-x[64+2(27)+1])t[(2)(27)+1]}>>1
x[64+54] = {(x[64+54]-x[0+54])t[54]-(x[0+54+1]-x[64+54+1])t[54+1]}>>1
x[118] = {(x[118]-x[54])t[54]-(x[55]-x[119])t[55]}>>1
= {(f000-f000)70e2-(0000-0000)c3a9}>>1
= {(00000)70e2-(00000)c3a9}>>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[64+2(27)+1] = {(x[64+2(27)+1]-x[0+2(27)+1])t[(2)(27)]+(x[0+2(27)]-x[64+2(27)])t[(2)(27)+1]}>>1
x[64+55] = {(x[64+55]-x[0+55])t[54]+(x[0+54]-x[64+54])t[54+1]}>>1
x[119] = {(x[119]-x[55])t[54]+(x[54]-x[118])t[55]}>>1
= {(0000-0000)70e2+(f000-f000)c3a9}>>1
= {(00000)70e2+(00000)c3a9}>>1
= {00000+00000}>>1
= {00000}>>1
= 0000



Return to Table of Contents




(P,b,n)=(0,0,28)
Loop P=0 of p=log2N=log264=6 loops indexed P=0...p-1=0...6-1=0...5.
Subblock b=0 of BP=B0=2P=20=1 subblocks, indexed b=0...B0-1=0...0.
Subblock size=NP|P=0=N0=N/BP|(N=64,P=0)=(2p/2P)|(p=6,P=0)=2p-P|(p=6,P=0)=26-0=64.
Butterfly n=28 of N'P=NP/2=2p-P-1=26-0-1=32 butterflies indexed by n=0...N'P-1=0...31.
Even base index e = 2NPb = 2(64)(0) = 0.
Odd base index o = e + 2N'P = 0 + 2(32) = 64.
Twiddle step size s = 2P+1 = 20+1 = 2.
x[e+2n] ={x[e+2n]+x[o+2n]}>>1
x[0+56] ={x[0+56]+x[64+56]}>>1
x[56] ={x[56]+x[120]}>>1
={0000 +0000}>>1
={00000}>>1
=0000
x[e+2n+1] ={x[e+2n+1]+x[o+2n+1]}>>1
x[0+57] ={x[0+57]+x[64+57]}>>1
x[57] ={x[57]+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[64+2(28)] = {(x[64+2(28)]-x[0+2(28)])t[(2)(28)]-(x[0+2(28)+1]-x[64+2(28)+1])t[(2)(28)+1]}>>1
x[64+56] = {(x[64+56]-x[0+56])t[56]-(x[0+56+1]-x[64+56+1])t[56+1]}>>1
x[120] = {(x[120]-x[56])t[56]-(x[57]-x[121])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[64+2(28)+1] = {(x[64+2(28)+1]-x[0+2(28)+1])t[(2)(28)]+(x[0+2(28)]-x[64+2(28)])t[(2)(28)+1]}>>1
x[64+57] = {(x[64+57]-x[0+57])t[56]+(x[0+56]-x[64+56])t[56+1]}>>1
x[121] = {(x[121]-x[57])t[56]+(x[56]-x[120])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)=(0,0,29)
Loop P=0 of p=log2N=log264=6 loops indexed P=0...p-1=0...6-1=0...5.
Subblock b=0 of BP=B0=2P=20=1 subblocks, indexed b=0...B0-1=0...0.
Subblock size=NP|P=0=N0=N/BP|(N=64,P=0)=(2p/2P)|(p=6,P=0)=2p-P|(p=6,P=0)=26-0=64.
Butterfly n=29 of N'P=NP/2=2p-P-1=26-0-1=32 butterflies indexed by n=0...N'P-1=0...31.
Even base index e = 2NPb = 2(64)(0) = 0.
Odd base index o = e + 2N'P = 0 + 2(32) = 64.
Twiddle step size s = 2P+1 = 20+1 = 2.
x[e+2n] ={x[e+2n]+x[o+2n]}>>1
x[0+58] ={x[0+58]+x[64+58]}>>1
x[58] ={x[58]+x[122]}>>1
={1000 +1000}>>1
={02000}>>1
=1000
x[e+2n+1] ={x[e+2n+1]+x[o+2n+1]}>>1
x[0+59] ={x[0+59]+x[64+59]}>>1
x[59] ={x[59]+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[64+2(29)] = {(x[64+2(29)]-x[0+2(29)])t[(2)(29)]-(x[0+2(29)+1]-x[64+2(29)+1])t[(2)(29)+1]}>>1
x[64+58] = {(x[64+58]-x[0+58])t[58]-(x[0+58+1]-x[64+58+1])t[58+1]}>>1
x[122] = {(x[122]-x[58])t[58]-(x[59]-x[123])t[59]}>>1
= {(1000-1000)7a7d-(0000-0000)dad7}>>1
= {(00000)7a7d-(00000)dad7}>>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[64+2(29)+1] = {(x[64+2(29)+1]-x[0+2(29)+1])t[(2)(29)]+(x[0+2(29)]-x[64+2(29)])t[(2)(29)+1]}>>1
x[64+59] = {(x[64+59]-x[0+59])t[58]+(x[0+58]-x[64+58])t[58+1]}>>1
x[123] = {(x[123]-x[59])t[58]+(x[58]-x[122])t[59]}>>1
= {(0000-0000)7a7d+(1000-1000)dad7}>>1
= {(00000)7a7d+(00000)dad7}>>1
= {00000+00000}>>1
= {00000}>>1
= 0000



Return to Table of Contents




(P,b,n)=(0,0,30)
Loop P=0 of p=log2N=log264=6 loops indexed P=0...p-1=0...6-1=0...5.
Subblock b=0 of BP=B0=2P=20=1 subblocks, indexed b=0...B0-1=0...0.
Subblock size=NP|P=0=N0=N/BP|(N=64,P=0)=(2p/2P)|(p=6,P=0)=2p-P|(p=6,P=0)=26-0=64.
Butterfly n=30 of N'P=NP/2=2p-P-1=26-0-1=32 butterflies indexed by n=0...N'P-1=0...31.
Even base index e = 2NPb = 2(64)(0) = 0.
Odd base index o = e + 2N'P = 0 + 2(32) = 64.
Twiddle step size s = 2P+1 = 20+1 = 2.
x[e+2n] ={x[e+2n]+x[o+2n]}>>1
x[0+60] ={x[0+60]+x[64+60]}>>1
x[60] ={x[60]+x[124]}>>1
={0000 +0000}>>1
={00000}>>1
=0000
x[e+2n+1] ={x[e+2n+1]+x[o+2n+1]}>>1
x[0+61] ={x[0+61]+x[64+61]}>>1
x[61] ={x[61]+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[64+2(30)] = {(x[64+2(30)]-x[0+2(30)])t[(2)(30)]-(x[0+2(30)+1]-x[64+2(30)+1])t[(2)(30)+1]}>>1
x[64+60] = {(x[64+60]-x[0+60])t[60]-(x[0+60+1]-x[64+60+1])t[60+1]}>>1
x[124] = {(x[124]-x[60])t[60]-(x[61]-x[125])t[61]}>>1
= {(0000-0000)7d8a-(0000-0000)e707}>>1
= {(00000)7d8a-(00000)e707}>>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[64+2(30)+1] = {(x[64+2(30)+1]-x[0+2(30)+1])t[(2)(30)]+(x[0+2(30)]-x[64+2(30)])t[(2)(30)+1]}>>1
x[64+61] = {(x[64+61]-x[0+61])t[60]+(x[0+60]-x[64+60])t[60+1]}>>1
x[125] = {(x[125]-x[61])t[60]+(x[60]-x[124])t[61]}>>1
= {(0000-0000)7d8a+(0000-0000)e707}>>1
= {(00000)7d8a+(00000)e707}>>1
= {00000+00000}>>1
= {00000}>>1
= 0000



Return to Table of Contents




(P,b,n)=(0,0,31)
Loop P=0 of p=log2N=log264=6 loops indexed P=0...p-1=0...6-1=0...5.
Subblock b=0 of BP=B0=2P=20=1 subblocks, indexed b=0...B0-1=0...0.
Subblock size=NP|P=0=N0=N/BP|(N=64,P=0)=(2p/2P)|(p=6,P=0)=2p-P|(p=6,P=0)=26-0=64.
Butterfly n=31 of N'P=NP/2=2p-P-1=26-0-1=32 butterflies indexed by n=0...N'P-1=0...31.
Even base index e = 2NPb = 2(64)(0) = 0.
Odd base index o = e + 2N'P = 0 + 2(32) = 64.
Twiddle step size s = 2P+1 = 20+1 = 2.
x[e+2n] ={x[e+2n]+x[o+2n]}>>1
x[0+62] ={x[0+62]+x[64+62]}>>1
x[62] ={x[62]+x[126]}>>1
={f000 +f000}>>1
={fe000}>>1
=f000
x[e+2n+1] ={x[e+2n+1]+x[o+2n+1]}>>1
x[0+63] ={x[0+63]+x[64+63]}>>1
x[63] ={x[63]+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[64+2(31)] = {(x[64+2(31)]-x[0+2(31)])t[(2)(31)]-(x[0+2(31)+1]-x[64+2(31)+1])t[(2)(31)+1]}>>1
x[64+62] = {(x[64+62]-x[0+62])t[62]-(x[0+62+1]-x[64+62+1])t[62+1]}>>1
x[126] = {(x[126]-x[62])t[62]-(x[63]-x[127])t[63]}>>1
= {(f000-f000)7f62-(0000-0000)f374}>>1
= {(00000)7f62-(00000)f374}>>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[64+2(31)+1] = {(x[64+2(31)+1]-x[0+2(31)+1])t[(2)(31)]+(x[0+2(31)]-x[64+2(31)])t[(2)(31)+1]}>>1
x[64+63] = {(x[64+63]-x[0+63])t[62]+(x[0+62]-x[64+62])t[62+1]}>>1
x[127] = {(x[127]-x[63])t[62]+(x[62]-x[126])t[63]}>>1
= {(0000-0000)7f62+(f000-f000)f374}>>1
= {(00000)7f62+(00000)f374}>>1
= {00000+00000}>>1
= {00000}>>1
= 0000



Return to Table of Contents



End of loop 0
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]=1000 x[19]=0000
x[20]=0000 x[21]=0000
x[22]=f000 x[23]=0000
x[24]=0000 x[25]=0000
x[26]=1000 x[27]=0000
x[28]=0000 x[29]=0000
x[30]=f000 x[31]=0000
x[32]=0000 x[33]=0000
x[34]=1000 x[35]=0000
x[36]=0000 x[37]=0000
x[38]=f000 x[39]=0000
x[40]=0000 x[41]=0000
x[42]=1000 x[43]=0000
x[44]=0000 x[45]=0000
x[46]=f000 x[47]=0000
x[48]=0000 x[49]=0000
x[50]=1000 x[51]=0000
x[52]=0000 x[53]=0000
x[54]=f000 x[55]=0000
x[56]=0000 x[57]=0000
x[58]=1000 x[59]=0000
x[60]=0000 x[61]=0000
x[62]=f000 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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