Paper VIII: Packet Operator Algorithms, Exact Compilation, and GPU Realization

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1 \begin{tikzpicture}[x=1cm,y=1cm,>=Stealth,line cap=round,line join=round]
2 \path[use as bounding box] (0,-.6) rectangle (14,4.8);
3 \node[font=\small,align=center,font=\small] at (2.04,4.3) {$A$ before elimination};
4 \path[draw=black!30,fill=black!8] (0.75,2.74) rectangle (1.61,3.6);
5 \node[font=\small,align=center,font=\small] at (1.18,3.17) {$2$};
6 \path[draw=black!30,fill=white] (1.61,2.74) rectangle (2.47,3.6);
7 \node[font=\small,align=center,font=\small] at (2.04,3.17) {$0$};
8 \path[draw=black!30,fill=black!8] (2.47,2.74) rectangle (3.33,3.6);
9 \node[font=\small,align=center,font=\small] at (2.9,3.17) {$1$};
10 \path[draw=black!30,fill=white] (0.75,1.88) rectangle (1.61,2.74);
11 \node[font=\small,align=center,font=\small] at (1.18,2.31) {$0$};
12 \path[draw=black!30,fill=black!8] (1.61,1.88) rectangle (2.47,2.74);
13 \node[font=\small,align=center,font=\small] at (2.04,2.31) {$2$};
14 \path[draw=black!30,fill=black!8] (2.47,1.88) rectangle (3.33,2.74);
15 \node[font=\small,align=center,font=\small] at (2.9,2.31) {$1$};
16 \path[draw=black!30,fill=black!8] (0.75,1.02) rectangle (1.61,1.88);
17 \node[font=\small,align=center,font=\small] at (1.18,1.45) {$1$};
18 \path[draw=black!30,fill=black!8] (1.61,1.02) rectangle (2.47,1.88);
19 \node[font=\small,align=center,font=\small] at (2.04,1.45) {$1$};
20 \path[draw=black!30,fill=black!8] (2.47,1.02) rectangle (3.33,1.88);
21 \node[font=\small,align=center,font=\small] at (2.9,1.45) {$2$};
22 \node[font=\small,align=center,font=\small] at (6.6,4.3) {$S=A_{RR}-A_{RH}A_{HH}^{-1}A_{HR}$};
23 \path[draw=black!30,fill=black!8] (5.65,2.65) rectangle (6.6,3.6);
24 \node[font=\small,align=center,font=\small] at (6.125,3.125) {$\frac{3}{2}$};
25 \path[draw=black!30,fill=black!8] (6.6,2.65) rectangle (7.55,3.6);
26 \node[font=\small,align=center,font=\small] at (7.075,3.125) {$- \frac{1}{2}$};
27 \path[draw=black!30,fill=black!8] (5.65,1.7) rectangle (6.6,2.65);
28 \node[font=\small,align=center,font=\small] at (6.125,2.175) {$- \frac{1}{2}$};
29 \path[draw=black!30,fill=black!8] (6.6,1.7) rectangle (7.55,2.65);
30 \node[font=\small,align=center,font=\small] at (7.075,2.175) {$\frac{3}{2}$};
31 \node[font=\small,align=center,font=\small] at (11.2,4.3) {cancelling variant};
32 \path[draw=black!30,fill=black!8] (10.25,2.65) rectangle (11.2,3.6);
33 \node[font=\small,align=center,font=\small] at (10.725,3.125) {$\frac{3}{2}$};
34 \path[draw=black!30,fill=white] (11.2,2.65) rectangle (12.15,3.6);
35 \node[font=\small,align=center,font=\small] at (11.675,3.125) {$0$};
36 \path[draw=black!30,fill=white] (10.25,1.7) rectangle (11.2,2.65);
37 \node[font=\small,align=center,font=\small] at (10.725,2.175) {$0$};
38 \path[draw=black!30,fill=black!8] (11.2,1.7) rectangle (12.15,2.65);
39 \node[font=\small,align=center,font=\small] at (11.675,2.175) {$\frac{3}{2}$};
40 \node[font=\small,align=center,font=\scriptsize] at (7,0.7) {A hidden route creates $-1/2$; adding $+1/2$ in the original block cancels it.};
41 \end{tikzpicture}

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