division_free_masks.tex

Paper II: Refinement Towers, Weighted Transfer, and Integral Separation of Operator Packets

division_free_masks.tex

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1 \begin{tikzpicture}[x=1cm,y=1cm,>=Latex,font=\sffamily\small,line cap=round]
2 \node[anchor=east] at (-0.20000,3.70000) {$x$};
3 \draw[fill=black!22,draw=black!45,line width=.35pt,] (0.00000,3.40000) rectangle ++(0.75000,0.60000);
4 \node[] at (0.37500,3.70000) {$1$};
5 \draw[fill=black!22,draw=black!45,line width=.35pt,] (0.75000,3.40000) rectangle ++(0.75000,0.60000);
6 \node[] at (1.12500,3.70000) {$1$};
7 \draw[fill=black!0,draw=black!45,line width=.35pt,] (1.50000,3.40000) rectangle ++(0.75000,0.60000);
8 \node[] at (1.87500,3.70000) {$0$};
9 \draw[fill=black!22,draw=black!45,line width=.35pt,] (2.25000,3.40000) rectangle ++(0.75000,0.60000);
10 \node[] at (2.62500,3.70000) {$1$};
11 \draw[fill=black!22,draw=black!45,line width=.35pt,] (3.00000,3.40000) rectangle ++(0.75000,0.60000);
12 \node[] at (3.37500,3.70000) {$1$};
13 \draw[fill=black!0,draw=black!45,line width=.35pt,] (3.75000,3.40000) rectangle ++(0.75000,0.60000);
14 \node[] at (4.12500,3.70000) {$0$};
15 \draw[fill=black!22,draw=black!45,line width=.35pt,] (4.50000,3.40000) rectangle ++(0.75000,0.60000);
16 \node[] at (4.87500,3.70000) {$1$};
17 \draw[fill=black!22,draw=black!45,line width=.35pt,] (5.25000,3.40000) rectangle ++(0.75000,0.60000);
18 \node[] at (5.62500,3.70000) {$1$};
19 \node[anchor=east] at (-0.20000,2.85000) {$P_{2,0}x$};
20 \draw[fill=black!22,draw=black!45,line width=.35pt,] (0.00000,2.55000) rectangle ++(0.75000,0.60000);
21 \node[] at (0.37500,2.85000) {$1$};
22 \draw[fill=black!0,draw=black!45,line width=.35pt,] (0.75000,2.55000) rectangle ++(0.75000,0.60000);
23 \node[] at (1.12500,2.85000) {$0$};
24 \draw[fill=black!0,draw=black!45,line width=.35pt,] (1.50000,2.55000) rectangle ++(0.75000,0.60000);
25 \node[] at (1.87500,2.85000) {$0$};
26 \draw[fill=black!0,draw=black!45,line width=.35pt,] (2.25000,2.55000) rectangle ++(0.75000,0.60000);
27 \node[] at (2.62500,2.85000) {$0$};
28 \draw[fill=black!22,draw=black!45,line width=.35pt,] (3.00000,2.55000) rectangle ++(0.75000,0.60000);
29 \node[] at (3.37500,2.85000) {$1$};
30 \draw[fill=black!0,draw=black!45,line width=.35pt,] (3.75000,2.55000) rectangle ++(0.75000,0.60000);
31 \node[] at (4.12500,2.85000) {$0$};
32 \draw[fill=black!22,draw=black!45,line width=.35pt,] (4.50000,2.55000) rectangle ++(0.75000,0.60000);
33 \node[] at (4.87500,2.85000) {$1$};
34 \draw[fill=black!0,draw=black!45,line width=.35pt,] (5.25000,2.55000) rectangle ++(0.75000,0.60000);
35 \node[] at (5.62500,2.85000) {$0$};
36 \node[anchor=east] at (-0.20000,2.00000) {$P_{2,1}x$};
37 \draw[fill=black!0,draw=black!45,line width=.35pt,] (0.00000,1.70000) rectangle ++(0.75000,0.60000);
38 \node[] at (0.37500,2.00000) {$0$};
39 \draw[fill=black!22,draw=black!45,line width=.35pt,] (0.75000,1.70000) rectangle ++(0.75000,0.60000);
40 \node[] at (1.12500,2.00000) {$1$};
41 \draw[fill=black!0,draw=black!45,line width=.35pt,] (1.50000,1.70000) rectangle ++(0.75000,0.60000);
42 \node[] at (1.87500,2.00000) {$0$};
43 \draw[fill=black!22,draw=black!45,line width=.35pt,] (2.25000,1.70000) rectangle ++(0.75000,0.60000);
44 \node[] at (2.62500,2.00000) {$1$};
45 \draw[fill=black!0,draw=black!45,line width=.35pt,] (3.00000,1.70000) rectangle ++(0.75000,0.60000);
46 \node[] at (3.37500,2.00000) {$0$};
47 \draw[fill=black!0,draw=black!45,line width=.35pt,] (3.75000,1.70000) rectangle ++(0.75000,0.60000);
48 \node[] at (4.12500,2.00000) {$0$};
49 \draw[fill=black!0,draw=black!45,line width=.35pt,] (4.50000,1.70000) rectangle ++(0.75000,0.60000);
50 \node[] at (4.87500,2.00000) {$0$};
51 \draw[fill=black!22,draw=black!45,line width=.35pt,] (5.25000,1.70000) rectangle ++(0.75000,0.60000);
52 \node[] at (5.62500,2.00000) {$1$};
53 \node[anchor=east] at (-0.20000,1.15000) {$(P_{2,0}+P_{2,1})x$};
54 \draw[fill=black!22,draw=black!45,line width=.35pt,] (0.00000,0.85000) rectangle ++(0.75000,0.60000);
55 \node[] at (0.37500,1.15000) {$1$};
56 \draw[fill=black!22,draw=black!45,line width=.35pt,] (0.75000,0.85000) rectangle ++(0.75000,0.60000);
57 \node[] at (1.12500,1.15000) {$1$};
58 \draw[fill=black!0,draw=black!45,line width=.35pt,] (1.50000,0.85000) rectangle ++(0.75000,0.60000);
59 \node[] at (1.87500,1.15000) {$0$};
60 \draw[fill=black!22,draw=black!45,line width=.35pt,] (2.25000,0.85000) rectangle ++(0.75000,0.60000);
61 \node[] at (2.62500,1.15000) {$1$};
62 \draw[fill=black!22,draw=black!45,line width=.35pt,] (3.00000,0.85000) rectangle ++(0.75000,0.60000);
63 \node[] at (3.37500,1.15000) {$1$};
64 \draw[fill=black!0,draw=black!45,line width=.35pt,] (3.75000,0.85000) rectangle ++(0.75000,0.60000);
65 \node[] at (4.12500,1.15000) {$0$};
66 \draw[fill=black!22,draw=black!45,line width=.35pt,] (4.50000,0.85000) rectangle ++(0.75000,0.60000);
67 \node[] at (4.87500,1.15000) {$1$};
68 \draw[fill=black!22,draw=black!45,line width=.35pt,] (5.25000,0.85000) rectangle ++(0.75000,0.60000);
69 \node[] at (5.62500,1.15000) {$1$};
70 \node[font=\sffamily\scriptsize] at (0.37500,4.38000) {$0$};
71 \node[font=\sffamily\scriptsize] at (1.12500,4.38000) {$1$};
72 \node[font=\sffamily\scriptsize] at (1.87500,4.38000) {$2$};
73 \node[font=\sffamily\scriptsize] at (2.62500,4.38000) {$3$};
74 \node[font=\sffamily\scriptsize] at (3.37500,4.38000) {$4$};
75 \node[font=\sffamily\scriptsize] at (4.12500,4.38000) {$5$};
76 \node[font=\sffamily\scriptsize] at (4.87500,4.38000) {$6$};
77 \node[font=\sffamily\scriptsize] at (5.62500,4.38000) {$7$};
78 \node[] at (8.20000,3.65000) {$\text{Coefficient address }n$};
79 \node[] at (8.20000,2.25000) {$\text{No division by }2$};
80 \node[] at (8.20000,0.55000) {$\text{All arithmetic in }\mathbb F_2$};
81 \end{tikzpicture}

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