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



John Bryan






(P,b,n)=(1,0,0)
Loop P=1 of p=log2N=log264=6 loops indexed P=0...p-1=0...6-1=0...5.
Subblock b=0 of BP=B1=2P=21=2 subblocks, indexed b=0...B1-1=0...1.
Subblock size=NP|P=1=N1=N/BP|(N=64,P=1)=(2p/2P)|(p=6,P=1)=2p-P|(p=6,P=1)=26-1=32.
Butterfly n=0 of N'P=NP/2=2p-P-1=26-1-1=16 butterflies indexed by n=0...N'P-1=0...15.
Even base index e = 2NPb = 2(32)(0) = 0.
Odd base index o = e + 2N'P = 0 + 2(16) = 32.
Twiddle step size s = 2P+1 = 21+1 = 4.
x[e+2n] ={x[e+2n]+x[o+2n]}>>1
x[0+0] ={x[0+0]+x[32+0]}>>1
x[0] ={x[0]+x[32]}>>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[32+1]}>>1
x[1] ={x[1]+x[33]}>>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[32+2(0)] = {(x[32+2(0)]-x[0+2(0)])t[(4)(0)]-(x[0+2(0)+1]-x[32+2(0)+1])t[(4)(0)+1]}>>1
x[32+0] = {(x[32+0]-x[0+0])t[0]-(x[0+0+1]-x[32+0+1])t[0+1]}>>1
x[32] = {(x[32]-x[0])t[0]-(x[1]-x[33])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[32+2(0)+1] = {(x[32+2(0)+1]-x[0+2(0)+1])t[(4)(0)]+(x[0+2(0)]-x[32+2(0)])t[(4)(0)+1]}>>1
x[32+1] = {(x[32+1]-x[0+1])t[0]+(x[0+0]-x[32+0])t[0+1]}>>1
x[33] = {(x[33]-x[1])t[0]+(x[0]-x[32])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)=(1,0,1)
Loop P=1 of p=log2N=log264=6 loops indexed P=0...p-1=0...6-1=0...5.
Subblock b=0 of BP=B1=2P=21=2 subblocks, indexed b=0...B1-1=0...1.
Subblock size=NP|P=1=N1=N/BP|(N=64,P=1)=(2p/2P)|(p=6,P=1)=2p-P|(p=6,P=1)=26-1=32.
Butterfly n=1 of N'P=NP/2=2p-P-1=26-1-1=16 butterflies indexed by n=0...N'P-1=0...15.
Even base index e = 2NPb = 2(32)(0) = 0.
Odd base index o = e + 2N'P = 0 + 2(16) = 32.
Twiddle step size s = 2P+1 = 21+1 = 4.
x[e+2n] ={x[e+2n]+x[o+2n]}>>1
x[0+2] ={x[0+2]+x[32+2]}>>1
x[2] ={x[2]+x[34]}>>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[32+3]}>>1
x[3] ={x[3]+x[35]}>>1
={0000 +0000}>>1
={00000}>>1
=0000
x[o+2n] = {(x[o+2n]-x[e+2n])t[sn]-(x[e+2n+1]-x[o+2n+1])t[sn+1]}>>1
x[32+2(1)] = {(x[32+2(1)]-x[0+2(1)])t[(4)(1)]-(x[0+2(1)+1]-x[32+2(1)+1])t[(4)(1)+1]}>>1
x[32+2] = {(x[32+2]-x[0+2])t[4]-(x[0+2+1]-x[32+2+1])t[4+1]}>>1
x[34] = {(x[34]-x[2])t[4]-(x[3]-x[35])t[5]}>>1
= {(1000-1000)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[32+2(1)+1] = {(x[32+2(1)+1]-x[0+2(1)+1])t[(4)(1)]+(x[0+2(1)]-x[32+2(1)])t[(4)(1)+1]}>>1
x[32+3] = {(x[32+3]-x[0+3])t[4]+(x[0+2]-x[32+2])t[4+1]}>>1
x[35] = {(x[35]-x[3])t[4]+(x[2]-x[34])t[5]}>>1
= {(0000-0000)8275+(1000-1000)e707}>>1
= {(00000)8275+(00000)e707}>>1
= {00000+00000}>>1
= {00000}>>1
= 0000



Return to Table of Contents




(P,b,n)=(1,0,2)
Loop P=1 of p=log2N=log264=6 loops indexed P=0...p-1=0...6-1=0...5.
Subblock b=0 of BP=B1=2P=21=2 subblocks, indexed b=0...B1-1=0...1.
Subblock size=NP|P=1=N1=N/BP|(N=64,P=1)=(2p/2P)|(p=6,P=1)=2p-P|(p=6,P=1)=26-1=32.
Butterfly n=2 of N'P=NP/2=2p-P-1=26-1-1=16 butterflies indexed by n=0...N'P-1=0...15.
Even base index e = 2NPb = 2(32)(0) = 0.
Odd base index o = e + 2N'P = 0 + 2(16) = 32.
Twiddle step size s = 2P+1 = 21+1 = 4.
x[e+2n] ={x[e+2n]+x[o+2n]}>>1
x[0+4] ={x[0+4]+x[32+4]}>>1
x[4] ={x[4]+x[36]}>>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[32+5]}>>1
x[5] ={x[5]+x[37]}>>1
={0000 +0000}>>1
={00000}>>1
=0000
x[o+2n] = {(x[o+2n]-x[e+2n])t[sn]-(x[e+2n+1]-x[o+2n+1])t[sn+1]}>>1
x[32+2(2)] = {(x[32+2(2)]-x[0+2(2)])t[(4)(2)]-(x[0+2(2)+1]-x[32+2(2)+1])t[(4)(2)+1]}>>1
x[32+4] = {(x[32+4]-x[0+4])t[8]-(x[0+4+1]-x[32+4+1])t[8+1]}>>1
x[36] = {(x[36]-x[4])t[8]-(x[5]-x[37])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[32+2(2)+1] = {(x[32+2(2)+1]-x[0+2(2)+1])t[(4)(2)]+(x[0+2(2)]-x[32+2(2)])t[(4)(2)+1]}>>1
x[32+5] = {(x[32+5]-x[0+5])t[8]+(x[0+4]-x[32+4])t[8+1]}>>1
x[37] = {(x[37]-x[5])t[8]+(x[4]-x[36])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)=(1,0,3)
Loop P=1 of p=log2N=log264=6 loops indexed P=0...p-1=0...6-1=0...5.
Subblock b=0 of BP=B1=2P=21=2 subblocks, indexed b=0...B1-1=0...1.
Subblock size=NP|P=1=N1=N/BP|(N=64,P=1)=(2p/2P)|(p=6,P=1)=2p-P|(p=6,P=1)=26-1=32.
Butterfly n=3 of N'P=NP/2=2p-P-1=26-1-1=16 butterflies indexed by n=0...N'P-1=0...15.
Even base index e = 2NPb = 2(32)(0) = 0.
Odd base index o = e + 2N'P = 0 + 2(16) = 32.
Twiddle step size s = 2P+1 = 21+1 = 4.
x[e+2n] ={x[e+2n]+x[o+2n]}>>1
x[0+6] ={x[0+6]+x[32+6]}>>1
x[6] ={x[6]+x[38]}>>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[32+7]}>>1
x[7] ={x[7]+x[39]}>>1
={0000 +0000}>>1
={00000}>>1
=0000
x[o+2n] = {(x[o+2n]-x[e+2n])t[sn]-(x[e+2n+1]-x[o+2n+1])t[sn+1]}>>1
x[32+2(3)] = {(x[32+2(3)]-x[0+2(3)])t[(4)(3)]-(x[0+2(3)+1]-x[32+2(3)+1])t[(4)(3)+1]}>>1
x[32+6] = {(x[32+6]-x[0+6])t[12]-(x[0+6+1]-x[32+6+1])t[12+1]}>>1
x[38] = {(x[38]-x[6])t[12]-(x[7]-x[39])t[13]}>>1
= {(f000-f000)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[32+2(3)+1] = {(x[32+2(3)+1]-x[0+2(3)+1])t[(4)(3)]+(x[0+2(3)]-x[32+2(3)])t[(4)(3)+1]}>>1
x[32+7] = {(x[32+7]-x[0+7])t[12]+(x[0+6]-x[32+6])t[12+1]}>>1
x[39] = {(x[39]-x[7])t[12]+(x[6]-x[38])t[13]}>>1
= {(0000-0000)9592+(f000-f000)b8e3}>>1
= {(00000)9592+(00000)b8e3}>>1
= {00000+00000}>>1
= {00000}>>1
= 0000



Return to Table of Contents




(P,b,n)=(1,0,4)
Loop P=1 of p=log2N=log264=6 loops indexed P=0...p-1=0...6-1=0...5.
Subblock b=0 of BP=B1=2P=21=2 subblocks, indexed b=0...B1-1=0...1.
Subblock size=NP|P=1=N1=N/BP|(N=64,P=1)=(2p/2P)|(p=6,P=1)=2p-P|(p=6,P=1)=26-1=32.
Butterfly n=4 of N'P=NP/2=2p-P-1=26-1-1=16 butterflies indexed by n=0...N'P-1=0...15.
Even base index e = 2NPb = 2(32)(0) = 0.
Odd base index o = e + 2N'P = 0 + 2(16) = 32.
Twiddle step size s = 2P+1 = 21+1 = 4.
x[e+2n] ={x[e+2n]+x[o+2n]}>>1
x[0+8] ={x[0+8]+x[32+8]}>>1
x[8] ={x[8]+x[40]}>>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[32+9]}>>1
x[9] ={x[9]+x[41]}>>1
={0000 +0000}>>1
={00000}>>1
=0000
x[o+2n] = {(x[o+2n]-x[e+2n])t[sn]-(x[e+2n+1]-x[o+2n+1])t[sn+1]}>>1
x[32+2(4)] = {(x[32+2(4)]-x[0+2(4)])t[(4)(4)]-(x[0+2(4)+1]-x[32+2(4)+1])t[(4)(4)+1]}>>1
x[32+8] = {(x[32+8]-x[0+8])t[16]-(x[0+8+1]-x[32+8+1])t[16+1]}>>1
x[40] = {(x[40]-x[8])t[16]-(x[9]-x[41])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[32+2(4)+1] = {(x[32+2(4)+1]-x[0+2(4)+1])t[(4)(4)]+(x[0+2(4)]-x[32+2(4)])t[(4)(4)+1]}>>1
x[32+9] = {(x[32+9]-x[0+9])t[16]+(x[0+8]-x[32+8])t[16+1]}>>1
x[41] = {(x[41]-x[9])t[16]+(x[8]-x[40])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)=(1,0,5)
Loop P=1 of p=log2N=log264=6 loops indexed P=0...p-1=0...6-1=0...5.
Subblock b=0 of BP=B1=2P=21=2 subblocks, indexed b=0...B1-1=0...1.
Subblock size=NP|P=1=N1=N/BP|(N=64,P=1)=(2p/2P)|(p=6,P=1)=2p-P|(p=6,P=1)=26-1=32.
Butterfly n=5 of N'P=NP/2=2p-P-1=26-1-1=16 butterflies indexed by n=0...N'P-1=0...15.
Even base index e = 2NPb = 2(32)(0) = 0.
Odd base index o = e + 2N'P = 0 + 2(16) = 32.
Twiddle step size s = 2P+1 = 21+1 = 4.
x[e+2n] ={x[e+2n]+x[o+2n]}>>1
x[0+10] ={x[0+10]+x[32+10]}>>1
x[10] ={x[10]+x[42]}>>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[32+11]}>>1
x[11] ={x[11]+x[43]}>>1
={0000 +0000}>>1
={00000}>>1
=0000
x[o+2n] = {(x[o+2n]-x[e+2n])t[sn]-(x[e+2n+1]-x[o+2n+1])t[sn+1]}>>1
x[32+2(5)] = {(x[32+2(5)]-x[0+2(5)])t[(4)(5)]-(x[0+2(5)+1]-x[32+2(5)+1])t[(4)(5)+1]}>>1
x[32+10] = {(x[32+10]-x[0+10])t[20]-(x[0+10+1]-x[32+10+1])t[20+1]}>>1
x[42] = {(x[42]-x[10])t[20]-(x[11]-x[43])t[21]}>>1
= {(1000-1000)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[32+2(5)+1] = {(x[32+2(5)+1]-x[0+2(5)+1])t[(4)(5)]+(x[0+2(5)]-x[32+2(5)])t[(4)(5)+1]}>>1
x[32+11] = {(x[32+11]-x[0+11])t[20]+(x[0+10]-x[32+10])t[20+1]}>>1
x[43] = {(x[43]-x[11])t[20]+(x[10]-x[42])t[21]}>>1
= {(0000-0000)b8e3+(1000-1000)9592}>>1
= {(00000)b8e3+(00000)9592}>>1
= {00000+00000}>>1
= {00000}>>1
= 0000



Return to Table of Contents




(P,b,n)=(1,0,6)
Loop P=1 of p=log2N=log264=6 loops indexed P=0...p-1=0...6-1=0...5.
Subblock b=0 of BP=B1=2P=21=2 subblocks, indexed b=0...B1-1=0...1.
Subblock size=NP|P=1=N1=N/BP|(N=64,P=1)=(2p/2P)|(p=6,P=1)=2p-P|(p=6,P=1)=26-1=32.
Butterfly n=6 of N'P=NP/2=2p-P-1=26-1-1=16 butterflies indexed by n=0...N'P-1=0...15.
Even base index e = 2NPb = 2(32)(0) = 0.
Odd base index o = e + 2N'P = 0 + 2(16) = 32.
Twiddle step size s = 2P+1 = 21+1 = 4.
x[e+2n] ={x[e+2n]+x[o+2n]}>>1
x[0+12] ={x[0+12]+x[32+12]}>>1
x[12] ={x[12]+x[44]}>>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[32+13]}>>1
x[13] ={x[13]+x[45]}>>1
={0000 +0000}>>1
={00000}>>1
=0000
x[o+2n] = {(x[o+2n]-x[e+2n])t[sn]-(x[e+2n+1]-x[o+2n+1])t[sn+1]}>>1
x[32+2(6)] = {(x[32+2(6)]-x[0+2(6)])t[(4)(6)]-(x[0+2(6)+1]-x[32+2(6)+1])t[(4)(6)+1]}>>1
x[32+12] = {(x[32+12]-x[0+12])t[24]-(x[0+12+1]-x[32+12+1])t[24+1]}>>1
x[44] = {(x[44]-x[12])t[24]-(x[13]-x[45])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[32+2(6)+1] = {(x[32+2(6)+1]-x[0+2(6)+1])t[(4)(6)]+(x[0+2(6)]-x[32+2(6)])t[(4)(6)+1]}>>1
x[32+13] = {(x[32+13]-x[0+13])t[24]+(x[0+12]-x[32+12])t[24+1]}>>1
x[45] = {(x[45]-x[13])t[24]+(x[12]-x[44])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)=(1,0,7)
Loop P=1 of p=log2N=log264=6 loops indexed P=0...p-1=0...6-1=0...5.
Subblock b=0 of BP=B1=2P=21=2 subblocks, indexed b=0...B1-1=0...1.
Subblock size=NP|P=1=N1=N/BP|(N=64,P=1)=(2p/2P)|(p=6,P=1)=2p-P|(p=6,P=1)=26-1=32.
Butterfly n=7 of N'P=NP/2=2p-P-1=26-1-1=16 butterflies indexed by n=0...N'P-1=0...15.
Even base index e = 2NPb = 2(32)(0) = 0.
Odd base index o = e + 2N'P = 0 + 2(16) = 32.
Twiddle step size s = 2P+1 = 21+1 = 4.
x[e+2n] ={x[e+2n]+x[o+2n]}>>1
x[0+14] ={x[0+14]+x[32+14]}>>1
x[14] ={x[14]+x[46]}>>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[32+15]}>>1
x[15] ={x[15]+x[47]}>>1
={0000 +0000}>>1
={00000}>>1
=0000
x[o+2n] = {(x[o+2n]-x[e+2n])t[sn]-(x[e+2n+1]-x[o+2n+1])t[sn+1]}>>1
x[32+2(7)] = {(x[32+2(7)]-x[0+2(7)])t[(4)(7)]-(x[0+2(7)+1]-x[32+2(7)+1])t[(4)(7)+1]}>>1
x[32+14] = {(x[32+14]-x[0+14])t[28]-(x[0+14+1]-x[32+14+1])t[28+1]}>>1
x[46] = {(x[46]-x[14])t[28]-(x[15]-x[47])t[29]}>>1
= {(f000-f000)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[32+2(7)+1] = {(x[32+2(7)+1]-x[0+2(7)+1])t[(4)(7)]+(x[0+2(7)]-x[32+2(7)])t[(4)(7)+1]}>>1
x[32+15] = {(x[32+15]-x[0+15])t[28]+(x[0+14]-x[32+14])t[28+1]}>>1
x[47] = {(x[47]-x[15])t[28]+(x[14]-x[46])t[29]}>>1
= {(0000-0000)e707+(f000-f000)8275}>>1
= {(00000)e707+(00000)8275}>>1
= {00000+00000}>>1
= {00000}>>1
= 0000



Return to Table of Contents




(P,b,n)=(1,0,8)
Loop P=1 of p=log2N=log264=6 loops indexed P=0...p-1=0...6-1=0...5.
Subblock b=0 of BP=B1=2P=21=2 subblocks, indexed b=0...B1-1=0...1.
Subblock size=NP|P=1=N1=N/BP|(N=64,P=1)=(2p/2P)|(p=6,P=1)=2p-P|(p=6,P=1)=26-1=32.
Butterfly n=8 of N'P=NP/2=2p-P-1=26-1-1=16 butterflies indexed by n=0...N'P-1=0...15.
Even base index e = 2NPb = 2(32)(0) = 0.
Odd base index o = e + 2N'P = 0 + 2(16) = 32.
Twiddle step size s = 2P+1 = 21+1 = 4.
x[e+2n] ={x[e+2n]+x[o+2n]}>>1
x[0+16] ={x[0+16]+x[32+16]}>>1
x[16] ={x[16]+x[48]}>>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[32+17]}>>1
x[17] ={x[17]+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[32+2(8)] = {(x[32+2(8)]-x[0+2(8)])t[(4)(8)]-(x[0+2(8)+1]-x[32+2(8)+1])t[(4)(8)+1]}>>1
x[32+16] = {(x[32+16]-x[0+16])t[32]-(x[0+16+1]-x[32+16+1])t[32+1]}>>1
x[48] = {(x[48]-x[16])t[32]-(x[17]-x[49])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[32+2(8)+1] = {(x[32+2(8)+1]-x[0+2(8)+1])t[(4)(8)]+(x[0+2(8)]-x[32+2(8)])t[(4)(8)+1]}>>1
x[32+17] = {(x[32+17]-x[0+17])t[32]+(x[0+16]-x[32+16])t[32+1]}>>1
x[49] = {(x[49]-x[17])t[32]+(x[16]-x[48])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)=(1,0,9)
Loop P=1 of p=log2N=log264=6 loops indexed P=0...p-1=0...6-1=0...5.
Subblock b=0 of BP=B1=2P=21=2 subblocks, indexed b=0...B1-1=0...1.
Subblock size=NP|P=1=N1=N/BP|(N=64,P=1)=(2p/2P)|(p=6,P=1)=2p-P|(p=6,P=1)=26-1=32.
Butterfly n=9 of N'P=NP/2=2p-P-1=26-1-1=16 butterflies indexed by n=0...N'P-1=0...15.
Even base index e = 2NPb = 2(32)(0) = 0.
Odd base index o = e + 2N'P = 0 + 2(16) = 32.
Twiddle step size s = 2P+1 = 21+1 = 4.
x[e+2n] ={x[e+2n]+x[o+2n]}>>1
x[0+18] ={x[0+18]+x[32+18]}>>1
x[18] ={x[18]+x[50]}>>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[32+19]}>>1
x[19] ={x[19]+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[32+2(9)] = {(x[32+2(9)]-x[0+2(9)])t[(4)(9)]-(x[0+2(9)+1]-x[32+2(9)+1])t[(4)(9)+1]}>>1
x[32+18] = {(x[32+18]-x[0+18])t[36]-(x[0+18+1]-x[32+18+1])t[36+1]}>>1
x[50] = {(x[50]-x[18])t[36]-(x[19]-x[51])t[37]}>>1
= {(1000-1000)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[32+2(9)+1] = {(x[32+2(9)+1]-x[0+2(9)+1])t[(4)(9)]+(x[0+2(9)]-x[32+2(9)])t[(4)(9)+1]}>>1
x[32+19] = {(x[32+19]-x[0+19])t[36]+(x[0+18]-x[32+18])t[36+1]}>>1
x[51] = {(x[51]-x[19])t[36]+(x[18]-x[50])t[37]}>>1
= {(0000-0000)18f8+(1000-1000)8275}>>1
= {(00000)18f8+(00000)8275}>>1
= {00000+00000}>>1
= {00000}>>1
= 0000



Return to Table of Contents




(P,b,n)=(1,0,10)
Loop P=1 of p=log2N=log264=6 loops indexed P=0...p-1=0...6-1=0...5.
Subblock b=0 of BP=B1=2P=21=2 subblocks, indexed b=0...B1-1=0...1.
Subblock size=NP|P=1=N1=N/BP|(N=64,P=1)=(2p/2P)|(p=6,P=1)=2p-P|(p=6,P=1)=26-1=32.
Butterfly n=10 of N'P=NP/2=2p-P-1=26-1-1=16 butterflies indexed by n=0...N'P-1=0...15.
Even base index e = 2NPb = 2(32)(0) = 0.
Odd base index o = e + 2N'P = 0 + 2(16) = 32.
Twiddle step size s = 2P+1 = 21+1 = 4.
x[e+2n] ={x[e+2n]+x[o+2n]}>>1
x[0+20] ={x[0+20]+x[32+20]}>>1
x[20] ={x[20]+x[52]}>>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[32+21]}>>1
x[21] ={x[21]+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[32+2(10)] = {(x[32+2(10)]-x[0+2(10)])t[(4)(10)]-(x[0+2(10)+1]-x[32+2(10)+1])t[(4)(10)+1]}>>1
x[32+20] = {(x[32+20]-x[0+20])t[40]-(x[0+20+1]-x[32+20+1])t[40+1]}>>1
x[52] = {(x[52]-x[20])t[40]-(x[21]-x[53])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[32+2(10)+1] = {(x[32+2(10)+1]-x[0+2(10)+1])t[(4)(10)]+(x[0+2(10)]-x[32+2(10)])t[(4)(10)+1]}>>1
x[32+21] = {(x[32+21]-x[0+21])t[40]+(x[0+20]-x[32+20])t[40+1]}>>1
x[53] = {(x[53]-x[21])t[40]+(x[20]-x[52])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)=(1,0,11)
Loop P=1 of p=log2N=log264=6 loops indexed P=0...p-1=0...6-1=0...5.
Subblock b=0 of BP=B1=2P=21=2 subblocks, indexed b=0...B1-1=0...1.
Subblock size=NP|P=1=N1=N/BP|(N=64,P=1)=(2p/2P)|(p=6,P=1)=2p-P|(p=6,P=1)=26-1=32.
Butterfly n=11 of N'P=NP/2=2p-P-1=26-1-1=16 butterflies indexed by n=0...N'P-1=0...15.
Even base index e = 2NPb = 2(32)(0) = 0.
Odd base index o = e + 2N'P = 0 + 2(16) = 32.
Twiddle step size s = 2P+1 = 21+1 = 4.
x[e+2n] ={x[e+2n]+x[o+2n]}>>1
x[0+22] ={x[0+22]+x[32+22]}>>1
x[22] ={x[22]+x[54]}>>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[32+23]}>>1
x[23] ={x[23]+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[32+2(11)] = {(x[32+2(11)]-x[0+2(11)])t[(4)(11)]-(x[0+2(11)+1]-x[32+2(11)+1])t[(4)(11)+1]}>>1
x[32+22] = {(x[32+22]-x[0+22])t[44]-(x[0+22+1]-x[32+22+1])t[44+1]}>>1
x[54] = {(x[54]-x[22])t[44]-(x[23]-x[55])t[45]}>>1
= {(f000-f000)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[32+2(11)+1] = {(x[32+2(11)+1]-x[0+2(11)+1])t[(4)(11)]+(x[0+2(11)]-x[32+2(11)])t[(4)(11)+1]}>>1
x[32+23] = {(x[32+23]-x[0+23])t[44]+(x[0+22]-x[32+22])t[44+1]}>>1
x[55] = {(x[55]-x[23])t[44]+(x[22]-x[54])t[45]}>>1
= {(0000-0000)471c+(f000-f000)9592}>>1
= {(00000)471c+(00000)9592}>>1
= {00000+00000}>>1
= {00000}>>1
= 0000



Return to Table of Contents




(P,b,n)=(1,0,12)
Loop P=1 of p=log2N=log264=6 loops indexed P=0...p-1=0...6-1=0...5.
Subblock b=0 of BP=B1=2P=21=2 subblocks, indexed b=0...B1-1=0...1.
Subblock size=NP|P=1=N1=N/BP|(N=64,P=1)=(2p/2P)|(p=6,P=1)=2p-P|(p=6,P=1)=26-1=32.
Butterfly n=12 of N'P=NP/2=2p-P-1=26-1-1=16 butterflies indexed by n=0...N'P-1=0...15.
Even base index e = 2NPb = 2(32)(0) = 0.
Odd base index o = e + 2N'P = 0 + 2(16) = 32.
Twiddle step size s = 2P+1 = 21+1 = 4.
x[e+2n] ={x[e+2n]+x[o+2n]}>>1
x[0+24] ={x[0+24]+x[32+24]}>>1
x[24] ={x[24]+x[56]}>>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[32+25]}>>1
x[25] ={x[25]+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[32+2(12)] = {(x[32+2(12)]-x[0+2(12)])t[(4)(12)]-(x[0+2(12)+1]-x[32+2(12)+1])t[(4)(12)+1]}>>1
x[32+24] = {(x[32+24]-x[0+24])t[48]-(x[0+24+1]-x[32+24+1])t[48+1]}>>1
x[56] = {(x[56]-x[24])t[48]-(x[25]-x[57])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[32+2(12)+1] = {(x[32+2(12)+1]-x[0+2(12)+1])t[(4)(12)]+(x[0+2(12)]-x[32+2(12)])t[(4)(12)+1]}>>1
x[32+25] = {(x[32+25]-x[0+25])t[48]+(x[0+24]-x[32+24])t[48+1]}>>1
x[57] = {(x[57]-x[25])t[48]+(x[24]-x[56])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)=(1,0,13)
Loop P=1 of p=log2N=log264=6 loops indexed P=0...p-1=0...6-1=0...5.
Subblock b=0 of BP=B1=2P=21=2 subblocks, indexed b=0...B1-1=0...1.
Subblock size=NP|P=1=N1=N/BP|(N=64,P=1)=(2p/2P)|(p=6,P=1)=2p-P|(p=6,P=1)=26-1=32.
Butterfly n=13 of N'P=NP/2=2p-P-1=26-1-1=16 butterflies indexed by n=0...N'P-1=0...15.
Even base index e = 2NPb = 2(32)(0) = 0.
Odd base index o = e + 2N'P = 0 + 2(16) = 32.
Twiddle step size s = 2P+1 = 21+1 = 4.
x[e+2n] ={x[e+2n]+x[o+2n]}>>1
x[0+26] ={x[0+26]+x[32+26]}>>1
x[26] ={x[26]+x[58]}>>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[32+27]}>>1
x[27] ={x[27]+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[32+2(13)] = {(x[32+2(13)]-x[0+2(13)])t[(4)(13)]-(x[0+2(13)+1]-x[32+2(13)+1])t[(4)(13)+1]}>>1
x[32+26] = {(x[32+26]-x[0+26])t[52]-(x[0+26+1]-x[32+26+1])t[52+1]}>>1
x[58] = {(x[58]-x[26])t[52]-(x[27]-x[59])t[53]}>>1
= {(1000-1000)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[32+2(13)+1] = {(x[32+2(13)+1]-x[0+2(13)+1])t[(4)(13)]+(x[0+2(13)]-x[32+2(13)])t[(4)(13)+1]}>>1
x[32+27] = {(x[32+27]-x[0+27])t[52]+(x[0+26]-x[32+26])t[52+1]}>>1
x[59] = {(x[59]-x[27])t[52]+(x[26]-x[58])t[53]}>>1
= {(0000-0000)6a6d+(1000-1000)b8e3}>>1
= {(00000)6a6d+(00000)b8e3}>>1
= {00000+00000}>>1
= {00000}>>1
= 0000



Return to Table of Contents




(P,b,n)=(1,0,14)
Loop P=1 of p=log2N=log264=6 loops indexed P=0...p-1=0...6-1=0...5.
Subblock b=0 of BP=B1=2P=21=2 subblocks, indexed b=0...B1-1=0...1.
Subblock size=NP|P=1=N1=N/BP|(N=64,P=1)=(2p/2P)|(p=6,P=1)=2p-P|(p=6,P=1)=26-1=32.
Butterfly n=14 of N'P=NP/2=2p-P-1=26-1-1=16 butterflies indexed by n=0...N'P-1=0...15.
Even base index e = 2NPb = 2(32)(0) = 0.
Odd base index o = e + 2N'P = 0 + 2(16) = 32.
Twiddle step size s = 2P+1 = 21+1 = 4.
x[e+2n] ={x[e+2n]+x[o+2n]}>>1
x[0+28] ={x[0+28]+x[32+28]}>>1
x[28] ={x[28]+x[60]}>>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[32+29]}>>1
x[29] ={x[29]+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[32+2(14)] = {(x[32+2(14)]-x[0+2(14)])t[(4)(14)]-(x[0+2(14)+1]-x[32+2(14)+1])t[(4)(14)+1]}>>1
x[32+28] = {(x[32+28]-x[0+28])t[56]-(x[0+28+1]-x[32+28+1])t[56+1]}>>1
x[60] = {(x[60]-x[28])t[56]-(x[29]-x[61])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[32+2(14)+1] = {(x[32+2(14)+1]-x[0+2(14)+1])t[(4)(14)]+(x[0+2(14)]-x[32+2(14)])t[(4)(14)+1]}>>1
x[32+29] = {(x[32+29]-x[0+29])t[56]+(x[0+28]-x[32+28])t[56+1]}>>1
x[61] = {(x[61]-x[29])t[56]+(x[28]-x[60])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)=(1,0,15)
Loop P=1 of p=log2N=log264=6 loops indexed P=0...p-1=0...6-1=0...5.
Subblock b=0 of BP=B1=2P=21=2 subblocks, indexed b=0...B1-1=0...1.
Subblock size=NP|P=1=N1=N/BP|(N=64,P=1)=(2p/2P)|(p=6,P=1)=2p-P|(p=6,P=1)=26-1=32.
Butterfly n=15 of N'P=NP/2=2p-P-1=26-1-1=16 butterflies indexed by n=0...N'P-1=0...15.
Even base index e = 2NPb = 2(32)(0) = 0.
Odd base index o = e + 2N'P = 0 + 2(16) = 32.
Twiddle step size s = 2P+1 = 21+1 = 4.
x[e+2n] ={x[e+2n]+x[o+2n]}>>1
x[0+30] ={x[0+30]+x[32+30]}>>1
x[30] ={x[30]+x[62]}>>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[32+31]}>>1
x[31] ={x[31]+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[32+2(15)] = {(x[32+2(15)]-x[0+2(15)])t[(4)(15)]-(x[0+2(15)+1]-x[32+2(15)+1])t[(4)(15)+1]}>>1
x[32+30] = {(x[32+30]-x[0+30])t[60]-(x[0+30+1]-x[32+30+1])t[60+1]}>>1
x[62] = {(x[62]-x[30])t[60]-(x[31]-x[63])t[61]}>>1
= {(f000-f000)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[32+2(15)+1] = {(x[32+2(15)+1]-x[0+2(15)+1])t[(4)(15)]+(x[0+2(15)]-x[32+2(15)])t[(4)(15)+1]}>>1
x[32+31] = {(x[32+31]-x[0+31])t[60]+(x[0+30]-x[32+30])t[60+1]}>>1
x[63] = {(x[63]-x[31])t[60]+(x[30]-x[62])t[61]}>>1
= {(0000-0000)7d8a+(f000-f000)e707}>>1
= {(00000)7d8a+(00000)e707}>>1
= {00000+00000}>>1
= {00000}>>1
= 0000



Return to Table of Contents




(P,b,n)=(1,1,0)
Loop P=1 of p=log2N=log264=6 loops indexed P=0...p-1=0...6-1=0...5.
Subblock b=1 of BP=B1=2P=21=2 subblocks, indexed b=0...B1-1=0...1.
Subblock size=NP|P=1=N1=N/BP|(N=64,P=1)=(2p/2P)|(p=6,P=1)=2p-P|(p=6,P=1)=26-1=32.
Butterfly n=0 of N'P=NP/2=2p-P-1=26-1-1=16 butterflies indexed by n=0...N'P-1=0...15.
Even base index e = 2NPb = 2(32)(1) = 64.
Odd base index o = e + 2N'P = 64 + 2(16) = 96.
Twiddle step size s = 2P+1 = 21+1 = 4.
x[e+2n] ={x[e+2n]+x[o+2n]}>>1
x[64+0] ={x[64+0]+x[96+0]}>>1
x[64] ={x[64]+x[96]}>>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[96+1]}>>1
x[65] ={x[65]+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[96+2(0)] = {(x[96+2(0)]-x[64+2(0)])t[(4)(0)]-(x[64+2(0)+1]-x[96+2(0)+1])t[(4)(0)+1]}>>1
x[96+0] = {(x[96+0]-x[64+0])t[0]-(x[64+0+1]-x[96+0+1])t[0+1]}>>1
x[96] = {(x[96]-x[64])t[0]-(x[65]-x[97])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[96+2(0)+1] = {(x[96+2(0)+1]-x[64+2(0)+1])t[(4)(0)]+(x[64+2(0)]-x[96+2(0)])t[(4)(0)+1]}>>1
x[96+1] = {(x[96+1]-x[64+1])t[0]+(x[64+0]-x[96+0])t[0+1]}>>1
x[97] = {(x[97]-x[65])t[0]+(x[64]-x[96])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)=(1,1,1)
Loop P=1 of p=log2N=log264=6 loops indexed P=0...p-1=0...6-1=0...5.
Subblock b=1 of BP=B1=2P=21=2 subblocks, indexed b=0...B1-1=0...1.
Subblock size=NP|P=1=N1=N/BP|(N=64,P=1)=(2p/2P)|(p=6,P=1)=2p-P|(p=6,P=1)=26-1=32.
Butterfly n=1 of N'P=NP/2=2p-P-1=26-1-1=16 butterflies indexed by n=0...N'P-1=0...15.
Even base index e = 2NPb = 2(32)(1) = 64.
Odd base index o = e + 2N'P = 64 + 2(16) = 96.
Twiddle step size s = 2P+1 = 21+1 = 4.
x[e+2n] ={x[e+2n]+x[o+2n]}>>1
x[64+2] ={x[64+2]+x[96+2]}>>1
x[66] ={x[66]+x[98]}>>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[96+3]}>>1
x[67] ={x[67]+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[96+2(1)] = {(x[96+2(1)]-x[64+2(1)])t[(4)(1)]-(x[64+2(1)+1]-x[96+2(1)+1])t[(4)(1)+1]}>>1
x[96+2] = {(x[96+2]-x[64+2])t[4]-(x[64+2+1]-x[96+2+1])t[4+1]}>>1
x[98] = {(x[98]-x[66])t[4]-(x[67]-x[99])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[96+2(1)+1] = {(x[96+2(1)+1]-x[64+2(1)+1])t[(4)(1)]+(x[64+2(1)]-x[96+2(1)])t[(4)(1)+1]}>>1
x[96+3] = {(x[96+3]-x[64+3])t[4]+(x[64+2]-x[96+2])t[4+1]}>>1
x[99] = {(x[99]-x[67])t[4]+(x[66]-x[98])t[5]}>>1
= {(0000-0000)8275+(0000-0000)e707}>>1
= {(00000)8275+(00000)e707}>>1
= {00000+00000}>>1
= {00000}>>1
= 0000



Return to Table of Contents




(P,b,n)=(1,1,2)
Loop P=1 of p=log2N=log264=6 loops indexed P=0...p-1=0...6-1=0...5.
Subblock b=1 of BP=B1=2P=21=2 subblocks, indexed b=0...B1-1=0...1.
Subblock size=NP|P=1=N1=N/BP|(N=64,P=1)=(2p/2P)|(p=6,P=1)=2p-P|(p=6,P=1)=26-1=32.
Butterfly n=2 of N'P=NP/2=2p-P-1=26-1-1=16 butterflies indexed by n=0...N'P-1=0...15.
Even base index e = 2NPb = 2(32)(1) = 64.
Odd base index o = e + 2N'P = 64 + 2(16) = 96.
Twiddle step size s = 2P+1 = 21+1 = 4.
x[e+2n] ={x[e+2n]+x[o+2n]}>>1
x[64+4] ={x[64+4]+x[96+4]}>>1
x[68] ={x[68]+x[100]}>>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[96+5]}>>1
x[69] ={x[69]+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[96+2(2)] = {(x[96+2(2)]-x[64+2(2)])t[(4)(2)]-(x[64+2(2)+1]-x[96+2(2)+1])t[(4)(2)+1]}>>1
x[96+4] = {(x[96+4]-x[64+4])t[8]-(x[64+4+1]-x[96+4+1])t[8+1]}>>1
x[100] = {(x[100]-x[68])t[8]-(x[69]-x[101])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[96+2(2)+1] = {(x[96+2(2)+1]-x[64+2(2)+1])t[(4)(2)]+(x[64+2(2)]-x[96+2(2)])t[(4)(2)+1]}>>1
x[96+5] = {(x[96+5]-x[64+5])t[8]+(x[64+4]-x[96+4])t[8+1]}>>1
x[101] = {(x[101]-x[69])t[8]+(x[68]-x[100])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)=(1,1,3)
Loop P=1 of p=log2N=log264=6 loops indexed P=0...p-1=0...6-1=0...5.
Subblock b=1 of BP=B1=2P=21=2 subblocks, indexed b=0...B1-1=0...1.
Subblock size=NP|P=1=N1=N/BP|(N=64,P=1)=(2p/2P)|(p=6,P=1)=2p-P|(p=6,P=1)=26-1=32.
Butterfly n=3 of N'P=NP/2=2p-P-1=26-1-1=16 butterflies indexed by n=0...N'P-1=0...15.
Even base index e = 2NPb = 2(32)(1) = 64.
Odd base index o = e + 2N'P = 64 + 2(16) = 96.
Twiddle step size s = 2P+1 = 21+1 = 4.
x[e+2n] ={x[e+2n]+x[o+2n]}>>1
x[64+6] ={x[64+6]+x[96+6]}>>1
x[70] ={x[70]+x[102]}>>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[96+7]}>>1
x[71] ={x[71]+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[96+2(3)] = {(x[96+2(3)]-x[64+2(3)])t[(4)(3)]-(x[64+2(3)+1]-x[96+2(3)+1])t[(4)(3)+1]}>>1
x[96+6] = {(x[96+6]-x[64+6])t[12]-(x[64+6+1]-x[96+6+1])t[12+1]}>>1
x[102] = {(x[102]-x[70])t[12]-(x[71]-x[103])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[96+2(3)+1] = {(x[96+2(3)+1]-x[64+2(3)+1])t[(4)(3)]+(x[64+2(3)]-x[96+2(3)])t[(4)(3)+1]}>>1
x[96+7] = {(x[96+7]-x[64+7])t[12]+(x[64+6]-x[96+6])t[12+1]}>>1
x[103] = {(x[103]-x[71])t[12]+(x[70]-x[102])t[13]}>>1
= {(0000-0000)9592+(0000-0000)b8e3}>>1
= {(00000)9592+(00000)b8e3}>>1
= {00000+00000}>>1
= {00000}>>1
= 0000



Return to Table of Contents




(P,b,n)=(1,1,4)
Loop P=1 of p=log2N=log264=6 loops indexed P=0...p-1=0...6-1=0...5.
Subblock b=1 of BP=B1=2P=21=2 subblocks, indexed b=0...B1-1=0...1.
Subblock size=NP|P=1=N1=N/BP|(N=64,P=1)=(2p/2P)|(p=6,P=1)=2p-P|(p=6,P=1)=26-1=32.
Butterfly n=4 of N'P=NP/2=2p-P-1=26-1-1=16 butterflies indexed by n=0...N'P-1=0...15.
Even base index e = 2NPb = 2(32)(1) = 64.
Odd base index o = e + 2N'P = 64 + 2(16) = 96.
Twiddle step size s = 2P+1 = 21+1 = 4.
x[e+2n] ={x[e+2n]+x[o+2n]}>>1
x[64+8] ={x[64+8]+x[96+8]}>>1
x[72] ={x[72]+x[104]}>>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[96+9]}>>1
x[73] ={x[73]+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[96+2(4)] = {(x[96+2(4)]-x[64+2(4)])t[(4)(4)]-(x[64+2(4)+1]-x[96+2(4)+1])t[(4)(4)+1]}>>1
x[96+8] = {(x[96+8]-x[64+8])t[16]-(x[64+8+1]-x[96+8+1])t[16+1]}>>1
x[104] = {(x[104]-x[72])t[16]-(x[73]-x[105])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[96+2(4)+1] = {(x[96+2(4)+1]-x[64+2(4)+1])t[(4)(4)]+(x[64+2(4)]-x[96+2(4)])t[(4)(4)+1]}>>1
x[96+9] = {(x[96+9]-x[64+9])t[16]+(x[64+8]-x[96+8])t[16+1]}>>1
x[105] = {(x[105]-x[73])t[16]+(x[72]-x[104])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)=(1,1,5)
Loop P=1 of p=log2N=log264=6 loops indexed P=0...p-1=0...6-1=0...5.
Subblock b=1 of BP=B1=2P=21=2 subblocks, indexed b=0...B1-1=0...1.
Subblock size=NP|P=1=N1=N/BP|(N=64,P=1)=(2p/2P)|(p=6,P=1)=2p-P|(p=6,P=1)=26-1=32.
Butterfly n=5 of N'P=NP/2=2p-P-1=26-1-1=16 butterflies indexed by n=0...N'P-1=0...15.
Even base index e = 2NPb = 2(32)(1) = 64.
Odd base index o = e + 2N'P = 64 + 2(16) = 96.
Twiddle step size s = 2P+1 = 21+1 = 4.
x[e+2n] ={x[e+2n]+x[o+2n]}>>1
x[64+10] ={x[64+10]+x[96+10]}>>1
x[74] ={x[74]+x[106]}>>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[96+11]}>>1
x[75] ={x[75]+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[96+2(5)] = {(x[96+2(5)]-x[64+2(5)])t[(4)(5)]-(x[64+2(5)+1]-x[96+2(5)+1])t[(4)(5)+1]}>>1
x[96+10] = {(x[96+10]-x[64+10])t[20]-(x[64+10+1]-x[96+10+1])t[20+1]}>>1
x[106] = {(x[106]-x[74])t[20]-(x[75]-x[107])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[96+2(5)+1] = {(x[96+2(5)+1]-x[64+2(5)+1])t[(4)(5)]+(x[64+2(5)]-x[96+2(5)])t[(4)(5)+1]}>>1
x[96+11] = {(x[96+11]-x[64+11])t[20]+(x[64+10]-x[96+10])t[20+1]}>>1
x[107] = {(x[107]-x[75])t[20]+(x[74]-x[106])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)=(1,1,6)
Loop P=1 of p=log2N=log264=6 loops indexed P=0...p-1=0...6-1=0...5.
Subblock b=1 of BP=B1=2P=21=2 subblocks, indexed b=0...B1-1=0...1.
Subblock size=NP|P=1=N1=N/BP|(N=64,P=1)=(2p/2P)|(p=6,P=1)=2p-P|(p=6,P=1)=26-1=32.
Butterfly n=6 of N'P=NP/2=2p-P-1=26-1-1=16 butterflies indexed by n=0...N'P-1=0...15.
Even base index e = 2NPb = 2(32)(1) = 64.
Odd base index o = e + 2N'P = 64 + 2(16) = 96.
Twiddle step size s = 2P+1 = 21+1 = 4.
x[e+2n] ={x[e+2n]+x[o+2n]}>>1
x[64+12] ={x[64+12]+x[96+12]}>>1
x[76] ={x[76]+x[108]}>>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[96+13]}>>1
x[77] ={x[77]+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[96+2(6)] = {(x[96+2(6)]-x[64+2(6)])t[(4)(6)]-(x[64+2(6)+1]-x[96+2(6)+1])t[(4)(6)+1]}>>1
x[96+12] = {(x[96+12]-x[64+12])t[24]-(x[64+12+1]-x[96+12+1])t[24+1]}>>1
x[108] = {(x[108]-x[76])t[24]-(x[77]-x[109])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[96+2(6)+1] = {(x[96+2(6)+1]-x[64+2(6)+1])t[(4)(6)]+(x[64+2(6)]-x[96+2(6)])t[(4)(6)+1]}>>1
x[96+13] = {(x[96+13]-x[64+13])t[24]+(x[64+12]-x[96+12])t[24+1]}>>1
x[109] = {(x[109]-x[77])t[24]+(x[76]-x[108])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)=(1,1,7)
Loop P=1 of p=log2N=log264=6 loops indexed P=0...p-1=0...6-1=0...5.
Subblock b=1 of BP=B1=2P=21=2 subblocks, indexed b=0...B1-1=0...1.
Subblock size=NP|P=1=N1=N/BP|(N=64,P=1)=(2p/2P)|(p=6,P=1)=2p-P|(p=6,P=1)=26-1=32.
Butterfly n=7 of N'P=NP/2=2p-P-1=26-1-1=16 butterflies indexed by n=0...N'P-1=0...15.
Even base index e = 2NPb = 2(32)(1) = 64.
Odd base index o = e + 2N'P = 64 + 2(16) = 96.
Twiddle step size s = 2P+1 = 21+1 = 4.
x[e+2n] ={x[e+2n]+x[o+2n]}>>1
x[64+14] ={x[64+14]+x[96+14]}>>1
x[78] ={x[78]+x[110]}>>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[96+15]}>>1
x[79] ={x[79]+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[96+2(7)] = {(x[96+2(7)]-x[64+2(7)])t[(4)(7)]-(x[64+2(7)+1]-x[96+2(7)+1])t[(4)(7)+1]}>>1
x[96+14] = {(x[96+14]-x[64+14])t[28]-(x[64+14+1]-x[96+14+1])t[28+1]}>>1
x[110] = {(x[110]-x[78])t[28]-(x[79]-x[111])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[96+2(7)+1] = {(x[96+2(7)+1]-x[64+2(7)+1])t[(4)(7)]+(x[64+2(7)]-x[96+2(7)])t[(4)(7)+1]}>>1
x[96+15] = {(x[96+15]-x[64+15])t[28]+(x[64+14]-x[96+14])t[28+1]}>>1
x[111] = {(x[111]-x[79])t[28]+(x[78]-x[110])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)=(1,1,8)
Loop P=1 of p=log2N=log264=6 loops indexed P=0...p-1=0...6-1=0...5.
Subblock b=1 of BP=B1=2P=21=2 subblocks, indexed b=0...B1-1=0...1.
Subblock size=NP|P=1=N1=N/BP|(N=64,P=1)=(2p/2P)|(p=6,P=1)=2p-P|(p=6,P=1)=26-1=32.
Butterfly n=8 of N'P=NP/2=2p-P-1=26-1-1=16 butterflies indexed by n=0...N'P-1=0...15.
Even base index e = 2NPb = 2(32)(1) = 64.
Odd base index o = e + 2N'P = 64 + 2(16) = 96.
Twiddle step size s = 2P+1 = 21+1 = 4.
x[e+2n] ={x[e+2n]+x[o+2n]}>>1
x[64+16] ={x[64+16]+x[96+16]}>>1
x[80] ={x[80]+x[112]}>>1
={0000 +0000}>>1
={00000}>>1
=0000
x[e+2n+1] ={x[e+2n+1]+x[o+2n+1]}>>1
x[64+17] ={x[64+17]+x[96+17]}>>1
x[81] ={x[81]+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[96+2(8)] = {(x[96+2(8)]-x[64+2(8)])t[(4)(8)]-(x[64+2(8)+1]-x[96+2(8)+1])t[(4)(8)+1]}>>1
x[96+16] = {(x[96+16]-x[64+16])t[32]-(x[64+16+1]-x[96+16+1])t[32+1]}>>1
x[112] = {(x[112]-x[80])t[32]-(x[81]-x[113])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[96+2(8)+1] = {(x[96+2(8)+1]-x[64+2(8)+1])t[(4)(8)]+(x[64+2(8)]-x[96+2(8)])t[(4)(8)+1]}>>1
x[96+17] = {(x[96+17]-x[64+17])t[32]+(x[64+16]-x[96+16])t[32+1]}>>1
x[113] = {(x[113]-x[81])t[32]+(x[80]-x[112])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)=(1,1,9)
Loop P=1 of p=log2N=log264=6 loops indexed P=0...p-1=0...6-1=0...5.
Subblock b=1 of BP=B1=2P=21=2 subblocks, indexed b=0...B1-1=0...1.
Subblock size=NP|P=1=N1=N/BP|(N=64,P=1)=(2p/2P)|(p=6,P=1)=2p-P|(p=6,P=1)=26-1=32.
Butterfly n=9 of N'P=NP/2=2p-P-1=26-1-1=16 butterflies indexed by n=0...N'P-1=0...15.
Even base index e = 2NPb = 2(32)(1) = 64.
Odd base index o = e + 2N'P = 64 + 2(16) = 96.
Twiddle step size s = 2P+1 = 21+1 = 4.
x[e+2n] ={x[e+2n]+x[o+2n]}>>1
x[64+18] ={x[64+18]+x[96+18]}>>1
x[82] ={x[82]+x[114]}>>1
={0000 +0000}>>1
={00000}>>1
=0000
x[e+2n+1] ={x[e+2n+1]+x[o+2n+1]}>>1
x[64+19] ={x[64+19]+x[96+19]}>>1
x[83] ={x[83]+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[96+2(9)] = {(x[96+2(9)]-x[64+2(9)])t[(4)(9)]-(x[64+2(9)+1]-x[96+2(9)+1])t[(4)(9)+1]}>>1
x[96+18] = {(x[96+18]-x[64+18])t[36]-(x[64+18+1]-x[96+18+1])t[36+1]}>>1
x[114] = {(x[114]-x[82])t[36]-(x[83]-x[115])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[96+2(9)+1] = {(x[96+2(9)+1]-x[64+2(9)+1])t[(4)(9)]+(x[64+2(9)]-x[96+2(9)])t[(4)(9)+1]}>>1
x[96+19] = {(x[96+19]-x[64+19])t[36]+(x[64+18]-x[96+18])t[36+1]}>>1
x[115] = {(x[115]-x[83])t[36]+(x[82]-x[114])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)=(1,1,10)
Loop P=1 of p=log2N=log264=6 loops indexed P=0...p-1=0...6-1=0...5.
Subblock b=1 of BP=B1=2P=21=2 subblocks, indexed b=0...B1-1=0...1.
Subblock size=NP|P=1=N1=N/BP|(N=64,P=1)=(2p/2P)|(p=6,P=1)=2p-P|(p=6,P=1)=26-1=32.
Butterfly n=10 of N'P=NP/2=2p-P-1=26-1-1=16 butterflies indexed by n=0...N'P-1=0...15.
Even base index e = 2NPb = 2(32)(1) = 64.
Odd base index o = e + 2N'P = 64 + 2(16) = 96.
Twiddle step size s = 2P+1 = 21+1 = 4.
x[e+2n] ={x[e+2n]+x[o+2n]}>>1
x[64+20] ={x[64+20]+x[96+20]}>>1
x[84] ={x[84]+x[116]}>>1
={0000 +0000}>>1
={00000}>>1
=0000
x[e+2n+1] ={x[e+2n+1]+x[o+2n+1]}>>1
x[64+21] ={x[64+21]+x[96+21]}>>1
x[85] ={x[85]+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[96+2(10)] = {(x[96+2(10)]-x[64+2(10)])t[(4)(10)]-(x[64+2(10)+1]-x[96+2(10)+1])t[(4)(10)+1]}>>1
x[96+20] = {(x[96+20]-x[64+20])t[40]-(x[64+20+1]-x[96+20+1])t[40+1]}>>1
x[116] = {(x[116]-x[84])t[40]-(x[85]-x[117])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[96+2(10)+1] = {(x[96+2(10)+1]-x[64+2(10)+1])t[(4)(10)]+(x[64+2(10)]-x[96+2(10)])t[(4)(10)+1]}>>1
x[96+21] = {(x[96+21]-x[64+21])t[40]+(x[64+20]-x[96+20])t[40+1]}>>1
x[117] = {(x[117]-x[85])t[40]+(x[84]-x[116])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)=(1,1,11)
Loop P=1 of p=log2N=log264=6 loops indexed P=0...p-1=0...6-1=0...5.
Subblock b=1 of BP=B1=2P=21=2 subblocks, indexed b=0...B1-1=0...1.
Subblock size=NP|P=1=N1=N/BP|(N=64,P=1)=(2p/2P)|(p=6,P=1)=2p-P|(p=6,P=1)=26-1=32.
Butterfly n=11 of N'P=NP/2=2p-P-1=26-1-1=16 butterflies indexed by n=0...N'P-1=0...15.
Even base index e = 2NPb = 2(32)(1) = 64.
Odd base index o = e + 2N'P = 64 + 2(16) = 96.
Twiddle step size s = 2P+1 = 21+1 = 4.
x[e+2n] ={x[e+2n]+x[o+2n]}>>1
x[64+22] ={x[64+22]+x[96+22]}>>1
x[86] ={x[86]+x[118]}>>1
={0000 +0000}>>1
={00000}>>1
=0000
x[e+2n+1] ={x[e+2n+1]+x[o+2n+1]}>>1
x[64+23] ={x[64+23]+x[96+23]}>>1
x[87] ={x[87]+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[96+2(11)] = {(x[96+2(11)]-x[64+2(11)])t[(4)(11)]-(x[64+2(11)+1]-x[96+2(11)+1])t[(4)(11)+1]}>>1
x[96+22] = {(x[96+22]-x[64+22])t[44]-(x[64+22+1]-x[96+22+1])t[44+1]}>>1
x[118] = {(x[118]-x[86])t[44]-(x[87]-x[119])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[96+2(11)+1] = {(x[96+2(11)+1]-x[64+2(11)+1])t[(4)(11)]+(x[64+2(11)]-x[96+2(11)])t[(4)(11)+1]}>>1
x[96+23] = {(x[96+23]-x[64+23])t[44]+(x[64+22]-x[96+22])t[44+1]}>>1
x[119] = {(x[119]-x[87])t[44]+(x[86]-x[118])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)=(1,1,12)
Loop P=1 of p=log2N=log264=6 loops indexed P=0...p-1=0...6-1=0...5.
Subblock b=1 of BP=B1=2P=21=2 subblocks, indexed b=0...B1-1=0...1.
Subblock size=NP|P=1=N1=N/BP|(N=64,P=1)=(2p/2P)|(p=6,P=1)=2p-P|(p=6,P=1)=26-1=32.
Butterfly n=12 of N'P=NP/2=2p-P-1=26-1-1=16 butterflies indexed by n=0...N'P-1=0...15.
Even base index e = 2NPb = 2(32)(1) = 64.
Odd base index o = e + 2N'P = 64 + 2(16) = 96.
Twiddle step size s = 2P+1 = 21+1 = 4.
x[e+2n] ={x[e+2n]+x[o+2n]}>>1
x[64+24] ={x[64+24]+x[96+24]}>>1
x[88] ={x[88]+x[120]}>>1
={0000 +0000}>>1
={00000}>>1
=0000
x[e+2n+1] ={x[e+2n+1]+x[o+2n+1]}>>1
x[64+25] ={x[64+25]+x[96+25]}>>1
x[89] ={x[89]+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[96+2(12)] = {(x[96+2(12)]-x[64+2(12)])t[(4)(12)]-(x[64+2(12)+1]-x[96+2(12)+1])t[(4)(12)+1]}>>1
x[96+24] = {(x[96+24]-x[64+24])t[48]-(x[64+24+1]-x[96+24+1])t[48+1]}>>1
x[120] = {(x[120]-x[88])t[48]-(x[89]-x[121])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[96+2(12)+1] = {(x[96+2(12)+1]-x[64+2(12)+1])t[(4)(12)]+(x[64+2(12)]-x[96+2(12)])t[(4)(12)+1]}>>1
x[96+25] = {(x[96+25]-x[64+25])t[48]+(x[64+24]-x[96+24])t[48+1]}>>1
x[121] = {(x[121]-x[89])t[48]+(x[88]-x[120])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)=(1,1,13)
Loop P=1 of p=log2N=log264=6 loops indexed P=0...p-1=0...6-1=0...5.
Subblock b=1 of BP=B1=2P=21=2 subblocks, indexed b=0...B1-1=0...1.
Subblock size=NP|P=1=N1=N/BP|(N=64,P=1)=(2p/2P)|(p=6,P=1)=2p-P|(p=6,P=1)=26-1=32.
Butterfly n=13 of N'P=NP/2=2p-P-1=26-1-1=16 butterflies indexed by n=0...N'P-1=0...15.
Even base index e = 2NPb = 2(32)(1) = 64.
Odd base index o = e + 2N'P = 64 + 2(16) = 96.
Twiddle step size s = 2P+1 = 21+1 = 4.
x[e+2n] ={x[e+2n]+x[o+2n]}>>1
x[64+26] ={x[64+26]+x[96+26]}>>1
x[90] ={x[90]+x[122]}>>1
={0000 +0000}>>1
={00000}>>1
=0000
x[e+2n+1] ={x[e+2n+1]+x[o+2n+1]}>>1
x[64+27] ={x[64+27]+x[96+27]}>>1
x[91] ={x[91]+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[96+2(13)] = {(x[96+2(13)]-x[64+2(13)])t[(4)(13)]-(x[64+2(13)+1]-x[96+2(13)+1])t[(4)(13)+1]}>>1
x[96+26] = {(x[96+26]-x[64+26])t[52]-(x[64+26+1]-x[96+26+1])t[52+1]}>>1
x[122] = {(x[122]-x[90])t[52]-(x[91]-x[123])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[96+2(13)+1] = {(x[96+2(13)+1]-x[64+2(13)+1])t[(4)(13)]+(x[64+2(13)]-x[96+2(13)])t[(4)(13)+1]}>>1
x[96+27] = {(x[96+27]-x[64+27])t[52]+(x[64+26]-x[96+26])t[52+1]}>>1
x[123] = {(x[123]-x[91])t[52]+(x[90]-x[122])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)=(1,1,14)
Loop P=1 of p=log2N=log264=6 loops indexed P=0...p-1=0...6-1=0...5.
Subblock b=1 of BP=B1=2P=21=2 subblocks, indexed b=0...B1-1=0...1.
Subblock size=NP|P=1=N1=N/BP|(N=64,P=1)=(2p/2P)|(p=6,P=1)=2p-P|(p=6,P=1)=26-1=32.
Butterfly n=14 of N'P=NP/2=2p-P-1=26-1-1=16 butterflies indexed by n=0...N'P-1=0...15.
Even base index e = 2NPb = 2(32)(1) = 64.
Odd base index o = e + 2N'P = 64 + 2(16) = 96.
Twiddle step size s = 2P+1 = 21+1 = 4.
x[e+2n] ={x[e+2n]+x[o+2n]}>>1
x[64+28] ={x[64+28]+x[96+28]}>>1
x[92] ={x[92]+x[124]}>>1
={0000 +0000}>>1
={00000}>>1
=0000
x[e+2n+1] ={x[e+2n+1]+x[o+2n+1]}>>1
x[64+29] ={x[64+29]+x[96+29]}>>1
x[93] ={x[93]+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[96+2(14)] = {(x[96+2(14)]-x[64+2(14)])t[(4)(14)]-(x[64+2(14)+1]-x[96+2(14)+1])t[(4)(14)+1]}>>1
x[96+28] = {(x[96+28]-x[64+28])t[56]-(x[64+28+1]-x[96+28+1])t[56+1]}>>1
x[124] = {(x[124]-x[92])t[56]-(x[93]-x[125])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[96+2(14)+1] = {(x[96+2(14)+1]-x[64+2(14)+1])t[(4)(14)]+(x[64+2(14)]-x[96+2(14)])t[(4)(14)+1]}>>1
x[96+29] = {(x[96+29]-x[64+29])t[56]+(x[64+28]-x[96+28])t[56+1]}>>1
x[125] = {(x[125]-x[93])t[56]+(x[92]-x[124])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)=(1,1,15)
Loop P=1 of p=log2N=log264=6 loops indexed P=0...p-1=0...6-1=0...5.
Subblock b=1 of BP=B1=2P=21=2 subblocks, indexed b=0...B1-1=0...1.
Subblock size=NP|P=1=N1=N/BP|(N=64,P=1)=(2p/2P)|(p=6,P=1)=2p-P|(p=6,P=1)=26-1=32.
Butterfly n=15 of N'P=NP/2=2p-P-1=26-1-1=16 butterflies indexed by n=0...N'P-1=0...15.
Even base index e = 2NPb = 2(32)(1) = 64.
Odd base index o = e + 2N'P = 64 + 2(16) = 96.
Twiddle step size s = 2P+1 = 21+1 = 4.
x[e+2n] ={x[e+2n]+x[o+2n]}>>1
x[64+30] ={x[64+30]+x[96+30]}>>1
x[94] ={x[94]+x[126]}>>1
={0000 +0000}>>1
={00000}>>1
=0000
x[e+2n+1] ={x[e+2n+1]+x[o+2n+1]}>>1
x[64+31] ={x[64+31]+x[96+31]}>>1
x[95] ={x[95]+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[96+2(15)] = {(x[96+2(15)]-x[64+2(15)])t[(4)(15)]-(x[64+2(15)+1]-x[96+2(15)+1])t[(4)(15)+1]}>>1
x[96+30] = {(x[96+30]-x[64+30])t[60]-(x[64+30+1]-x[96+30+1])t[60+1]}>>1
x[126] = {(x[126]-x[94])t[60]-(x[95]-x[127])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[96+2(15)+1] = {(x[96+2(15)+1]-x[64+2(15)+1])t[(4)(15)]+(x[64+2(15)]-x[96+2(15)])t[(4)(15)+1]}>>1
x[96+31] = {(x[96+31]-x[64+31])t[60]+(x[64+30]-x[96+30])t[60+1]}>>1
x[127] = {(x[127]-x[95])t[60]+(x[94]-x[126])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



End of loop 1
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]=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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