november 11 update

build.sh

@@ -1,6 +1,8 @@
 set -eux
 
+mkdir -p verbatim/output
 rm -f verbatim/output/*.svg
+(cd verbatim; make -j8)
 
 make4ht --shell-escape index.tex "pic-m,pic-equation,svg"
 
@@ -17,15 +19,18 @@ sed -i 's|color-scheme: light dark;||g' index.css
 echo 'figcaption.caption { margin-bottom: 1.3em; margin-top: 0.3em; }' >> index.css
 echo '.cmti-10 { font-style: italic; }' >> index.css
 
+echo '[data="diagrams/complete_particle_data_flow.svg"] { margin-left: -2.5em; }' >> index.css
+echo '[href="diagrams/simplified_particle_data_flow.svg"] { width: 100%; text-align: center; display: inline-block; }' >> index.css
+
 sed -i 's/˜/~/g' index.html
 
 sed -i "s|<p class='noindent'><object class='graphics' data='diagrams/z_operations.svg' name='picture diagrams/z_operations' type='image/svg+xml'></object>|<p class='noindent' style='text-align: center;'><object class='graphics' style='width: 40em;' data='diagrams/z_operations.svg' name='picture diagrams/z_operations' type='image/svg+xml'></object>|g" index.html
 
 sed -i '/height: 2.5em;/d' index.css
 
-sed -i 's/index.css/index3.css/g' index.html
+sed -i 's/index.css/index4.css/g' index.html
 
-mv index.css index3.css
+mv index.css index4.css
 
 python replace_video.py index.html
 

diagrams/c4_32_fp.tex

@@ -0,0 +1,32 @@
+\documentclass{standalone}
+\usepackage{tikz}
+\usepackage[dvipsnames]{xcolor}
+\begin{document}
+\begin{tikzpicture}[scale=1]
+
+  \draw[ultra thick] (0,0) rectangle (32,-1.2);
+
+  \foreach \j in {1,...,3} {
+    \draw[ultra thick] (\j * 8,0) -- (\j * 8,-1.2);
+  }
+
+  \foreach \j in {0,...,3} {
+    \foreach \i in {1,...,31} {
+      \draw[very thick] (\i / 4 + \j * 8,0) -- (\i / 4 + \j * 8,-0.15);
+    }
+
+    \foreach \i in {1,...,3} {
+      \draw[ultra thick] (\i * 8 / 4 + \j * 8,0) -- (\i * 8 / 4 + \j * 8,-0.25);
+    }
+  }
+
+  \foreach \j in {0,...,3} {
+    \node[font=\huge\bfseries]  at (8 * \j + 4.0,-0.7)  {C\pgfmathparse{int(3 - \j)}\pgfmathresult};
+    \node[font=\large\bfseries]  at (8 * \j + 7.9,0.25)  {\pgfmathparse{int((3 - \j) * 32)}\pgfmathresult};
+  }
+  \node[font=\large\bfseries]  at (8 * 0 + 0.0,0.25)  {\pgfmathparse{int((4 - 0) * 32)}\pgfmathresult};
+
+
+\end{tikzpicture}
+
+\end{document}

diagrams/c4_8.tex

@@ -0,0 +1,33 @@
+\documentclass{standalone}
+\usepackage{tikz}
+\usepackage[dvipsnames]{xcolor}
+\begin{document}
+\begin{tikzpicture}[scale=1]
+
+  \draw[ultra thick] (0,0) rectangle (32,-1.2);
+
+  \foreach \j in {1,...,3} {
+    \draw[ultra thick] (\j * 8,0) -- (\j * 8,-1.2);
+  }
+
+  \foreach \j in {0,...,3} {
+    \foreach \i in {1,...,7} {
+      \draw[very thick] (\i + \j * 8,0) -- (\i + \j * 8,-0.2);
+    }
+  }
+
+  \foreach \j in {0,...,3} {
+    \node[font=\huge\bfseries]  at (8 * \j + 4.0,-0.7)  {C\pgfmathparse{int(3 - \j)}\pgfmathresult};
+    \node[font=\large\bfseries]  at (8 * \j + 7.5,0.25)  {\pgfmathparse{int((3 - \j) * 8)}\pgfmathresult};
+  }
+  \node[font=\large\bfseries]  at (8 * 0 + 0.0,0.25)  {\pgfmathparse{int((4 - 0) * 8)}\pgfmathresult};
+
+
+  %\node[font=\huge\bfseries,text=MidnightBlue ]  at ( 0 + 4.5,-1.5)  {blue };
+  %\node[font=\huge\bfseries,text=OliveGreen   ]  at ( 8 + 4.5,-1.5)  {green};
+  %\node[font=\huge\bfseries,text=BrickRed     ]  at (16 + 4.5,-1.5)  {red  };
+  %\node[font=\huge\bfseries,text=black        ]  at (24 + 4.5,-1.5)  {alpha};
+
+\end{tikzpicture}
+
+\end{document}

diagrams/simplified_particle_data_flow.dot

@@ -0,0 +1,66 @@
+digraph
+{
+        //graph [ranksep=1 nodesep=1]
+        graph [nodesep=0.5, margin=0]
+	fontname="Computer Modern,Arial,sans-serif"
+	node [fontname="Helvetica,Arial,sans-serif"]
+	edge [fontname="Helvetica,Arial,sans-serif"]
+	layout=dot
+	labelloc = "t"
+
+        node [shape=plaintext]
+
+        read [label=<<b>read buffer</b>> height=0]
+        write [label=<<b>write buffer</b>> height=0]
+        shader [label=<<b>fragment shader</b>> height=0]
+
+        particle_stateA [label=<
+<TABLE BORDER="0" CELLBORDER="1" CELLSPACING="0" CELLPADDING="4">
+  <TR>
+    <TD COLSPAN="2" ROWSPAN="2">state </TD>
+    <TD BGCOLOR="chartreuse2" PORT="src">a</TD>
+  </TR>
+  <TR>
+    <TD BGCOLOR="azure3">b</TD>
+  </TR>
+</TABLE>>]
+
+        particle_stateB [label=<
+<TABLE BORDER="0" CELLBORDER="1" CELLSPACING="0" CELLPADDING="4">
+  <TR>
+    <TD BGCOLOR="azure3">a</TD>
+    <TD COLSPAN="2" ROWSPAN="2">state</TD>
+  </TR>
+  <TR>
+    <TD BGCOLOR="chartreuse2" PORT="dst">b</TD>
+  </TR>
+</TABLE>>]
+
+        node [shape=ellipse]
+        simulation [label="arbitrary\ncomputation"]
+
+        edge [style=invis]
+	rank=same {read -> shader -> write}
+	read -> particle_stateA
+	shader -> simulation
+	write -> particle_stateB
+
+        subgraph program {
+
+	edge [weight=1000 style=dashed]
+
+	// uncomment to hide the grid
+	//edge [style=invis]
+
+        //
+        // vertex_buffer_copy * 4
+
+	edge [weight=1000 style=solid]
+
+	rank=same {
+          particle_stateA:src -> simulation:w
+          simulation:e -> particle_stateB:dst
+        }
+
+        }
+}

diagrams/simplified_particle_data_flow.svg

@@ -0,0 +1,332 @@
+<?xml version="1.0" encoding="UTF-8" standalone="no"?>
+<!-- Generated by graphviz version 12.2.1 (20241206.2353)
+ -->
+
+<!-- Pages: 1 -->
+
+<svg
+   width="378.63464pt"
+   height="91.165062pt"
+   viewBox="0 0 379.01428 91.344521"
+   version="1.1"
+   id="svg15"
+   sodipodi:docname="simplified_particle_data_flow.svg"
+   inkscape:version="1.4 (e7c3feb100, 2024-10-09)"
+   xmlns:inkscape="http://www.inkscape.org/namespaces/inkscape"
+   xmlns:sodipodi="http://sodipodi.sourceforge.net/DTD/sodipodi-0.dtd"
+   xmlns="http://www.w3.org/2000/svg"
+   xmlns:svg="http://www.w3.org/2000/svg">
+  <defs
+     id="defs15" />
+  <sodipodi:namedview
+     id="namedview15"
+     pagecolor="#ffffff"
+     bordercolor="#666666"
+     borderopacity="1.0"
+     inkscape:showpageshadow="2"
+     inkscape:pageopacity="0.0"
+     inkscape:pagecheckerboard="0"
+     inkscape:deskcolor="#d1d1d1"
+     inkscape:document-units="pt"
+     inkscape:zoom="2.469657"
+     inkscape:cx="252.26175"
+     inkscape:cy="36.847222"
+     inkscape:window-width="2048"
+     inkscape:window-height="1124"
+     inkscape:window-x="0"
+     inkscape:window-y="0"
+     inkscape:window-maximized="1"
+     inkscape:current-layer="node1-2" />
+  <g
+     id="graph0"
+     class="graph"
+     transform="translate(3.816959,87.344522)">
+    <g
+       id="node2"
+       class="node"
+       transform="translate(0,32.254074)">
+      <title
+         id="title7">write</title>
+      <text
+         text-anchor="start"
+         x="289.12"
+         y="-102.95"
+         font-family="Helvetica, Arial, sans-serif"
+         font-weight="bold"
+         font-size="14px"
+         id="text8">write buffer</text>
+    </g>
+    <polygon
+       fill="#ffffff"
+       stroke="none"
+       points="375.38,4 -4,4 -4,-123.25 375.38,-123.25 "
+       id="polygon1"
+       transform="matrix(1,0,0,0.71783514,0,1.1286594)" />
+    <!-- read -->
+    <g
+       id="node1"
+       class="node"
+       transform="translate(-3.0428371,27.081251)">
+      <title
+         id="title1">read</title>
+      <text
+         text-anchor="start"
+         x="48.986347"
+         y="-102.95"
+         font-family="Helvetica, Arial, sans-serif"
+         font-weight="bold"
+         font-size="14px"
+         id="text1"
+         style="line-height:0"><tspan
+           style="line-height:1.25;text-align:center;text-anchor:middle"
+           sodipodi:role="line"
+           id="tspan23"
+           x="48.986347"
+           y="-102.95">read buffer</tspan><tspan
+           sodipodi:role="line"
+           x="48.986347"
+           y="-90.287735"
+           id="tspan17"
+           style="font-size:10.0197px;line-height:1;text-align:center;text-anchor:middle">(texture sample)</tspan></text>
+      <text
+         xml:space="preserve"
+         style="font-size:10.0197px;line-height:1.25;font-family:Monospace;-inkscape-font-specification:Monospace;text-align:center;text-anchor:middle;stroke-width:0.751476"
+         x="44.38129"
+         y="-87.754082"
+         id="text18"><tspan
+           sodipodi:role="line"
+           id="tspan18"
+           style="stroke-width:0.751476"
+           x="47.387688"
+           y="-87.754082"> </tspan></text>
+    </g>
+    <!-- shader -->
+    <g
+       id="node3"
+       class="node"
+       transform="translate(0,32.254074)">
+      <title
+         id="title2">shader</title>
+      <text
+         text-anchor="start"
+         x="131"
+         y="-102.95"
+         font-family="Helvetica, Arial, sans-serif"
+         font-weight="bold"
+         font-size="14px"
+         id="text2">fragment shader</text>
+    </g>
+    <!-- read&#45;&gt;shader -->
+    <!-- particle_stateA -->
+    <g
+       id="node4"
+       class="node">
+      <title
+         id="title3">particle_stateA</title>
+      <polygon
+         fill="none"
+         stroke="#000000"
+         points="59,-55.5 59,-4 16,-4 16,-55.5 "
+         id="polygon3" />
+      <text
+         text-anchor="start"
+         x="21"
+         y="-24.32"
+         font-family="Helvetica, Arial, sans-serif"
+         font-size="14px"
+         id="text3">state</text>
+      <polygon
+         fill="#76ee00"
+         stroke="none"
+         points="76.5,-55.5 76.5,-29.75 59,-29.75 59,-55.5 "
+         id="polygon4" />
+      <polygon
+         fill="none"
+         stroke="#000000"
+         points="76.5,-55.5 76.5,-29.75 59,-29.75 59,-55.5 "
+         id="polygon5" />
+      <text
+         text-anchor="start"
+         x="64"
+         y="-37.200001"
+         font-family="Helvetica, Arial, sans-serif"
+         font-size="14px"
+         id="text5">a</text>
+      <polygon
+         fill="#c1cdcd"
+         stroke="none"
+         points="76.5,-29.75 76.5,-4 59,-4 59,-29.75 "
+         id="polygon6" />
+      <polygon
+         fill="none"
+         stroke="#000000"
+         points="76.5,-29.75 76.5,-4 59,-4 59,-29.75 "
+         id="polygon7" />
+      <text
+         text-anchor="start"
+         x="64"
+         y="-11.45"
+         font-family="Helvetica, Arial, sans-serif"
+         font-size="14px"
+         id="text7">b</text>
+    </g>
+    <!-- read&#45;&gt;particle_stateA -->
+    <!-- write -->
+    <!-- particle_stateB -->
+    <g
+       id="node5"
+       class="node">
+      <title
+         id="title8">particle_stateB</title>
+      <polygon
+         fill="#c1cdcd"
+         stroke="none"
+         points="309.38,-55.5 309.38,-29.75 291.88,-29.75 291.88,-55.5 "
+         id="polygon8" />
+      <polygon
+         fill="none"
+         stroke="#000000"
+         points="309.38,-55.5 309.38,-29.75 291.88,-29.75 291.88,-55.5 "
+         id="polygon9" />
+      <text
+         text-anchor="start"
+         x="296.88"
+         y="-37.200001"
+         font-family="Helvetica, Arial, sans-serif"
+         font-size="14px"
+         id="text9">a</text>
+      <polygon
+         fill="none"
+         stroke="#000000"
+         points="348.62,-55.5 348.62,-4 309.38,-4 309.38,-55.5 "
+         id="polygon10" />
+      <text
+         text-anchor="start"
+         x="314.38"
+         y="-24.32"
+         font-family="Helvetica, Arial, sans-serif"
+         font-size="14px"
+         id="text10">state</text>
+      <polygon
+         fill="#76ee00"
+         stroke="none"
+         points="309.38,-29.75 309.38,-4 291.88,-4 291.88,-29.75 "
+         id="polygon11" />
+      <polygon
+         fill="none"
+         stroke="#000000"
+         points="309.38,-29.75 309.38,-4 291.88,-4 291.88,-29.75 "
+         id="polygon12" />
+      <text
+         text-anchor="start"
+         x="296.88"
+         y="-11.45"
+         font-family="Helvetica, Arial, sans-serif"
+         font-size="14px"
+         id="text12">b</text>
+    </g>
+    <!-- write&#45;&gt;particle_stateB -->
+    <!-- shader&#45;&gt;write -->
+    <!-- simulation -->
+    <g
+       id="node6"
+       class="node">
+      <title
+         id="title12">simulation</title>
+      <ellipse
+         fill="none"
+         stroke="#000000"
+         cx="184.25"
+         cy="-29.75"
+         rx="63.82"
+         ry="27.93"
+         id="ellipse12" />
+      <text
+         text-anchor="middle"
+         x="184.25"
+         y="-32.200001"
+         font-family="Helvetica, Arial, sans-serif"
+         font-size="14px"
+         id="text13">arbitrary</text>
+      <text
+         text-anchor="middle"
+         x="184.25"
+         y="-16.450001"
+         font-family="Helvetica, Arial, sans-serif"
+         font-size="14px"
+         id="text14">computation</text>
+    </g>
+    <!-- shader&#45;&gt;simulation -->
+    <!-- particle_stateA&#45;&gt;simulation -->
+    <g
+       id="edge6"
+       class="edge">
+      <title
+         id="title14">particle_stateA:src-&gt;simulation:w</title>
+      <path
+         fill="none"
+         stroke="#000000"
+         d="m 77.5,-42.62 c 15.41,0 20.75,7.7 31.59,11.19"
+         id="path14" />
+      <polygon
+         fill="#000000"
+         stroke="#000000"
+         points="108.53,-27.98 109.56,-34.9 118.94,-29.97 "
+         id="polygon14" />
+    </g>
+    <!-- simulation&#45;&gt;particle_stateB -->
+    <g
+       id="edge7"
+       class="edge">
+      <title
+         id="title15">simulation:e-&gt;particle_stateB:dst</title>
+      <path
+         fill="none"
+         stroke="#000000"
+         d="m 248.07,-29.75 c 15.36,0 20.68,7.7 31.5,11.19"
+         id="path15" />
+      <polygon
+         fill="#000000"
+         stroke="#000000"
+         points="278.97,-15.11 280,-22.03 289.38,-17.1 "
+         id="polygon15" />
+    </g>
+    <g
+       id="node1-2"
+       class="node"
+       transform="translate(273.90725,26.773649)">
+      <title
+         id="title1-9">read</title>
+      <text
+         text-anchor="start"
+         x="48.986347"
+         y="-102.95"
+         font-family="Helvetica, Arial, sans-serif"
+         font-weight="bold"
+         font-size="14px"
+         id="text1-1"
+         style="line-height:0"><tspan
+           style="line-height:1.25;text-align:center;text-anchor:middle"
+           sodipodi:role="line"
+           id="tspan23-2"
+           x="48.986347"
+           y="-102.95">write buffer</tspan><tspan
+           sodipodi:role="line"
+           x="48.986351"
+           y="-90.287735"
+           id="tspan17-7"
+           style="font-size:10.0197px;line-height:1;text-align:center;text-anchor:middle">(render target)</tspan></text>
+      <text
+         xml:space="preserve"
+         style="font-size:10.0197px;line-height:1.25;font-family:Monospace;-inkscape-font-specification:Monospace;text-align:center;text-anchor:middle;stroke-width:0.751476"
+         x="44.38129"
+         y="-87.754082"
+         id="text18-0"><tspan
+           sodipodi:role="line"
+           id="tspan18-9"
+           style="stroke-width:0.751476"
+           x="47.387688"
+           y="-87.754082"> </tspan></text>
+    </g>
+  </g>
+</svg>

diagrams/simplified_particle_data_flow_split.svg

@@ -0,0 +1,563 @@
+<?xml version="1.0" encoding="UTF-8" standalone="no"?>
+<!-- Generated by graphviz version 12.2.1 (20241206.2353)
+ -->
+
+<!-- Pages: 1 -->
+
+<svg
+   width="414.87pt"
+   height="152.91658pt"
+   viewBox="0 0 414.87 152.8295"
+   version="1.1"
+   id="svg42"
+   sodipodi:docname="simplified_particle_data_flow_split.svg"
+   inkscape:version="1.4 (e7c3feb100, 2024-10-09)"
+   xmlns:inkscape="http://www.inkscape.org/namespaces/inkscape"
+   xmlns:sodipodi="http://sodipodi.sourceforge.net/DTD/sodipodi-0.dtd"
+   xmlns="http://www.w3.org/2000/svg"
+   xmlns:svg="http://www.w3.org/2000/svg">
+  <defs
+     id="defs42" />
+  <sodipodi:namedview
+     id="namedview42"
+     pagecolor="#ffffff"
+     bordercolor="#666666"
+     borderopacity="1.0"
+     inkscape:showpageshadow="2"
+     inkscape:pageopacity="0.0"
+     inkscape:pagecheckerboard="0"
+     inkscape:deskcolor="#d1d1d1"
+     inkscape:document-units="pt"
+     inkscape:zoom="1.6025057"
+     inkscape:cx="201.55935"
+     inkscape:cy="141.65316"
+     inkscape:window-width="2048"
+     inkscape:window-height="1124"
+     inkscape:window-x="0"
+     inkscape:window-y="0"
+     inkscape:window-maximized="1"
+     inkscape:current-layer="graph0" />
+  <g
+     id="graph0"
+     class="graph"
+     transform="translate(-17.109999,401.93205)">
+    <polygon
+       fill="#ffffff"
+       stroke="none"
+       points="473,-434.75 473,4 -4,4 -4,-434.75 "
+       id="polygon1"
+       transform="matrix(0.86974843,0,0,0.34852783,20.588993,-250.45698)" />
+    <text
+       text-anchor="start"
+       x="147.09796"
+       y="-315.17871"
+       font-family="Helvetica, Arial, sans-serif"
+       font-size="14px"
+       id="text18-9-3"
+       style="font-size:10px;line-height:0;fill:#ff21e0;fill-opacity:1"><tspan
+         sodipodi:role="line"
+         x="147.09796"
+         y="-315.17871"
+         style="font-size:8px;line-height:1;text-align:center;text-anchor:middle;fill:#ff21e0;fill-opacity:1"
+         id="tspan8">multiple</tspan><tspan
+         sodipodi:role="line"
+         x="147.09796"
+         y="-307.17871"
+         style="font-size:8px;line-height:1;text-align:center;text-anchor:middle;fill:#ff21e0;fill-opacity:1"
+         id="tspan9">texture</tspan><tspan
+         sodipodi:role="line"
+         x="147.09796"
+         y="-299.17871"
+         style="font-size:8px;line-height:1;text-align:center;text-anchor:middle;fill:#ff21e0;fill-opacity:1"
+         id="tspan7">samples</tspan></text>
+    <text
+       text-anchor="start"
+       x="304.98917"
+       y="-321.75287"
+       font-family="Helvetica, Arial, sans-serif"
+       font-size="14px"
+       id="text18-9-3-5"
+       style="font-size:10px;line-height:0"><tspan
+         sodipodi:role="line"
+         id="tspan44-6-3"
+         x="304.98917"
+         y="-321.75287"
+         style="line-height:1.25;text-align:center;text-anchor:middle" /><tspan
+         sodipodi:role="line"
+         x="304.98917"
+         y="-312.05438"
+         style="font-size:8px;line-height:1;text-align:center;text-anchor:middle;fill:#ff00db;fill-opacity:1"
+         id="tspan2-6">multiple</tspan><tspan
+         sodipodi:role="line"
+         x="304.98917"
+         y="-304.05438"
+         style="font-size:8px;line-height:1;text-align:center;text-anchor:middle;fill:#ff00db;fill-opacity:1"
+         id="tspan3">render</tspan><tspan
+         sodipodi:role="line"
+         x="304.98917"
+         y="-296.05438"
+         style="font-size:8px;line-height:1;text-align:center;text-anchor:middle;fill:#ff00db;fill-opacity:1"
+         id="tspan4">targets</tspan></text>
+    <!-- read -->
+    <g
+       id="node1"
+       class="node"
+       transform="translate(-1.8720682,29.953092)">
+      <title
+         id="title1">read</title>
+      <text
+         text-anchor="start"
+         x="71.853073"
+         y="-419.13019"
+         font-family="Helvetica, Arial, sans-serif"
+         font-weight="bold"
+         font-size="14px"
+         id="text1"
+         style="line-height:0"><tspan
+           style="line-height:1.25;text-align:center;text-anchor:middle"
+           sodipodi:role="line"
+           id="tspan1"
+           x="71.853073"
+           y="-419.13019">read buffer</tspan><tspan
+           sodipodi:role="line"
+           x="71.853073"
+           y="-405.23322"
+           id="tspan52"
+           style="font-size:10px;line-height:1.25;text-align:center;text-anchor:middle">(texture samples)</tspan></text>
+    </g>
+    <!-- shader -->
+    <g
+       id="node3"
+       class="node"
+       transform="translate(-1.8720682,29.953092)">
+      <title
+         id="title2">shader</title>
+      <text
+         text-anchor="start"
+         x="177.18303"
+         y="-410.23785"
+         font-family="Helvetica, Arial, sans-serif"
+         font-weight="bold"
+         font-size="14px"
+         id="text2">fragment shader</text>
+    </g>
+    <!-- read&#45;&gt;shader -->
+    <!-- particle_stateA -->
+    <polygon
+       fill="none"
+       stroke="#000000"
+       points="107.36,-367 107.36,-315.5 17.11,-315.5 17.11,-367 "
+       id="polygon3" />
+    <text
+       text-anchor="start"
+       x="61.174942"
+       y="-344.71234"
+       font-family="Helvetica, Arial, sans-serif"
+       font-size="14px"
+       id="text3"><tspan
+         sodipodi:role="line"
+         id="tspan42"
+         x="61.174942"
+         y="-344.71234"
+         style="text-align:center;text-anchor:middle">particle state</tspan><tspan
+         sodipodi:role="line"
+         id="tspan43"
+         x="61.174942"
+         y="-327.21234"
+         style="font-size:10px;text-align:center;text-anchor:middle">(position, age)</tspan></text>
+    <polygon
+       fill="#76ee00"
+       stroke="none"
+       points="124.86,-367 124.86,-341.25 107.36,-341.25 107.36,-367 "
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+       fill="none"
+       stroke="#000000"
+       points="124.86,-367 124.86,-341.25 107.36,-341.25 107.36,-367 "
+       id="polygon5" />
+    <text
+       text-anchor="start"
+       x="112.36"
+       y="-348.70001"
+       font-family="Helvetica, Arial, sans-serif"
+       font-size="14px"
+       id="text5">a</text>
+    <polygon
+       fill="#c1cdcd"
+       stroke="none"
+       points="124.86,-341.25 124.86,-315.5 107.36,-315.5 107.36,-341.25 "
+       id="polygon6" />
+    <polygon
+       fill="none"
+       stroke="#000000"
+       points="124.86,-341.25 124.86,-315.5 107.36,-315.5 107.36,-341.25 "
+       id="polygon7" />
+    <text
+       text-anchor="start"
+       x="112.36"
+       y="-322.95001"
+       font-family="Helvetica, Arial, sans-serif"
+       font-size="14px"
+       id="text7">b</text>
+    <!-- read&#45;&gt;particle_stateA -->
+    <!-- write -->
+    <g
+       id="node2"
+       class="node"
+       transform="translate(-1.8720687,25.272921)">
+      <title
+         id="title7">write</title>
+      <text
+         text-anchor="start"
+         x="389.26624"
+         y="-414.45001"
+         font-family="Helvetica, Arial, sans-serif"
+         font-weight="bold"
+         font-size="14px"
+         id="text8"
+         style="line-height:0"><tspan
+           style="line-height:1.25;text-align:center;text-anchor:middle"
+           sodipodi:role="line"
+           id="tspan2"
+           x="389.26624"
+           y="-414.45001">write buffer</tspan><tspan
+           sodipodi:role="line"
+           x="389.26624"
+           y="-400.55304"
+           id="tspan55"
+           style="font-size:10px;line-height:1.25;text-align:center;text-anchor:middle">(render targets)</tspan></text>
+    </g>
+    <!-- particle_stateB -->
+    <polygon
+       fill="#c1cdcd"
+       stroke="none"
+       points="345.48,-367 345.48,-341.25 327.98,-341.25 327.98,-367 "
+       id="polygon8" />
+    <polygon
+       fill="none"
+       stroke="#000000"
+       points="345.48,-367 345.48,-341.25 327.98,-341.25 327.98,-367 "
+       id="polygon9" />
+    <text
+       text-anchor="start"
+       x="332.98001"
+       y="-348.70001"
+       font-family="Helvetica, Arial, sans-serif"
+       font-size="14px"
+       id="text9">a</text>
+    <polygon
+       fill="none"
+       stroke="#000000"
+       points="431.98,-367 431.98,-315.5 345.48,-315.5 345.48,-367 "
+       id="polygon10" />
+    <text
+       text-anchor="start"
+       x="389.54495"
+       y="-344.71234"
+       font-family="Helvetica, Arial, sans-serif"
+       font-size="14px"
+       id="text10"><tspan
+         sodipodi:role="line"
+         id="tspan48"
+         x="389.54495"
+         y="-344.71234"
+         style="text-align:center;text-anchor:middle">particle state</tspan><tspan
+         sodipodi:role="line"
+         id="tspan49"
+         x="389.54495"
+         y="-327.21234"
+         style="font-size:10px;text-align:center;text-anchor:middle">(position, age)</tspan></text>
+    <polygon
+       fill="#76ee00"
+       stroke="none"
+       points="345.48,-341.25 345.48,-315.5 327.98,-315.5 327.98,-341.25 "
+       id="polygon11" />
+    <polygon
+       fill="none"
+       stroke="#000000"
+       points="345.48,-341.25 345.48,-315.5 327.98,-315.5 327.98,-341.25 "
+       id="polygon12" />
+    <text
+       text-anchor="start"
+       x="332.98001"
+       y="-322.95001"
+       font-family="Helvetica, Arial, sans-serif"
+       font-size="14px"
+       id="text12">b</text>
+    <!-- write&#45;&gt;particle_stateB -->
+    <!-- shader&#45;&gt;write -->
+    <!-- simulationA -->
+    <!-- shader&#45;&gt;simulationA -->
+    <!-- clear_input -->
+    <g
+       id="node4"
+       class="node">
+      <title
+         id="title13">clear_input</title>
+    </g>
+    <!-- clear_plane -->
+    <g
+       id="node5"
+       class="node">
+      <title
+         id="title14">clear_plane</title>
+    </g>
+    <!-- clear_input&#45;&gt;clear_plane -->
+    <!-- clear -->
+    <!-- clear_input&#45;&gt;clear -->
+    <!-- vertex_bufferB -->
+    <!-- clear_plane&#45;&gt;vertex_bufferB -->
+    <!-- plane -->
+    <!-- clear_plane&#45;&gt;plane -->
+    <!-- particle_stateC -->
+    <polygon
+       fill="none"
+       stroke="#000000"
+       points="107.36,-220 17.11,-220 17.11,-271.5 107.36,-271.5 "
+       id="polygon18"
+       transform="translate(0,-29.953092)" />
+    <text
+       text-anchor="start"
+       x="61.174942"
+       y="-279.16544"
+       font-family="Helvetica, Arial, sans-serif"
+       font-size="14px"
+       id="text18"><tspan
+         sodipodi:role="line"
+         id="tspan44"
+         x="61.174942"
+         y="-279.16544"
+         style="text-align:center;text-anchor:middle">particle state</tspan><tspan
+         sodipodi:role="line"
+         id="tspan45"
+         x="61.174942"
+         y="-261.66544"
+         style="font-size:10px;text-align:center;text-anchor:middle">(velocity, random)</tspan></text>
+    <polygon
+       fill="#c1cdcd"
+       stroke="none"
+       points="124.86,-245.75 107.36,-245.75 107.36,-271.5 124.86,-271.5 "
+       id="polygon19"
+       style="fill:#76ee00;fill-opacity:1"
+       transform="translate(0,-29.953092)" />
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+       fill="none"
+       stroke="#000000"
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+       transform="translate(0,-29.953092)" />
+    <text
+       text-anchor="start"
+       x="112.36"
+       y="-283.15308"
+       font-family="Helvetica, Arial, sans-serif"
+       font-size="14px"
+       id="text20">a</text>
+    <polygon
+       fill="#76ee00"
+       stroke="none"
+       points="124.86,-220 107.36,-220 107.36,-245.75 124.86,-245.75 "
+       id="polygon21"
+       style="fill:#c1cdcd;fill-opacity:1"
+       transform="translate(0,-29.953092)" />
+    <polygon
+       fill="none"
+       stroke="#000000"
+       points="124.86,-220 107.36,-220 107.36,-245.75 124.86,-245.75 "
+       id="polygon22"
+       transform="translate(0,-29.953092)" />
+    <text
+       text-anchor="start"
+       x="112.36"
+       y="-257.40308"
+       font-family="Helvetica, Arial, sans-serif"
+       font-size="14px"
+       id="text22">b</text>
+    <!-- particle_stateA&#45;&gt;particle_stateC -->
+    <!-- particle_stateA&#45;&gt;simulationA -->
+    <!-- particle_stateB&#45;&gt;particle_stateC -->
+    <!-- particle_stateD -->
+    <polygon
+       fill="#c1cdcd"
+       stroke="none"
+       points="345.48,-245.75 327.98,-245.75 327.98,-271.5 345.48,-271.5 "
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+       transform="translate(0,-29.953092)" />
+    <polygon
+       fill="none"
+       stroke="#000000"
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+       transform="translate(0,-29.953092)" />
+    <text
+       text-anchor="start"
+       x="332.98001"
+       y="-283.15308"
+       font-family="Helvetica, Arial, sans-serif"
+       font-size="14px"
+       id="text26">a</text>
+    <polygon
+       fill="none"
+       stroke="#000000"
+       points="431.98,-220 345.48,-220 345.48,-271.5 431.98,-271.5 "
+       id="polygon27"
+       transform="translate(0,-29.953092)" />
+    <text
+       text-anchor="start"
+       x="389.54495"
+       y="-279.16544"
+       font-family="Helvetica, Arial, sans-serif"
+       font-size="14px"
+       id="text27"><tspan
+         sodipodi:role="line"
+         id="tspan46"
+         x="389.54495"
+         y="-279.16544"
+         style="text-align:center;text-anchor:middle">particle state</tspan><tspan
+         sodipodi:role="line"
+         id="tspan47"
+         x="389.54495"
+         y="-261.66544"
+         style="font-size:10px;text-align:center;text-anchor:middle">(velocity, random)</tspan></text>
+    <polygon
+       fill="#76ee00"
+       stroke="none"
+       points="345.48,-220 327.98,-220 327.98,-245.75 345.48,-245.75 "
+       id="polygon28"
+       transform="translate(0,-29.953092)" />
+    <polygon
+       fill="none"
+       stroke="#000000"
+       points="345.48,-220 327.98,-220 327.98,-245.75 345.48,-245.75 "
+       id="polygon29"
+       transform="translate(0,-29.953092)" />
+    <text
+       text-anchor="start"
+       x="332.98001"
+       y="-257.40308"
+       font-family="Helvetica, Arial, sans-serif"
+       font-size="14px"
+       id="text29">b</text>
+    <!-- particle_stateB&#45;&gt;particle_stateD -->
+    <!-- particle_stateC&#45;&gt;clear_input -->
+    <!-- simulationB -->
+    <g
+       id="node18"
+       class="node"
+       transform="translate(-0.46801706,-62.246269)">
+      <title
+         id="title29">simulationB</title>
+      <ellipse
+         fill="none"
+         stroke="#000000"
+         cx="225.98"
+         cy="-245.75"
+         rx="57.549999"
+         ry="33.444565"
+         id="ellipse29" />
+      <text
+         text-anchor="middle"
+         x="226.44801"
+         y="-249.21233"
+         font-family="Helvetica, Arial, sans-serif"
+         font-size="14px"
+         id="text30"><tspan
+           sodipodi:role="line"
+           id="tspan59"
+           x="226.44801"
+           y="-249.21233">particle</tspan><tspan
+           sodipodi:role="line"
+           x="226.44801"
+           y="-231.71233"
+           id="tspan60">simulation</tspan></text>
+    </g>
+    <!-- particle_stateC&#45;&gt;simulationB -->
+    <g
+       id="edge11"
+       class="edge">
+      <title
+         id="title30">particle_stateC:src-&gt;simulationB:w</title>
+      <path
+         fill="none"
+         stroke="#000000"
+         d="m 124.86,-288.57809 c 15.28,0 30.65,4.73266 41.4,1.24266"
+         id="path30"
+         sodipodi:nodetypes="cc" />
+      <polygon
+         fill="#000000"
+         stroke="#000000"
+         points="156.52,-247.51 166.93,-245.53 157.56,-240.58 "
+         id="polygon30"
+         transform="translate(9.2200015,-43.290434)" />
+    </g>
+    <!-- colorbufferA -->
+    <!-- particle_stateD&#45;&gt;colorbufferA -->
+    <!-- particle_stateD&#45;&gt;vertex_bufferB -->
+    <!-- colorbufferB -->
+    <!-- colorbufferA&#45;&gt;colorbufferB -->
+    <!-- colorbufferC -->
+    <!-- colorbufferB&#45;&gt;colorbufferC -->
+    <!-- particle -->
+    <!-- vertex_bufferB&#45;&gt;particle -->
+    <!-- clear&#45;&gt;colorbufferA -->
+    <!-- plane&#45;&gt;colorbufferB -->
+    <!-- particle&#45;&gt;colorbufferC -->
+    <!-- simulationA&#45;&gt;particle_stateB -->
+    <g
+       id="edge10"
+       class="edge">
+      <title
+         id="title40">simulationA:e-&gt;particle_stateB:dst</title>
+      <path
+         fill="none"
+         stroke="#000000"
+         d="m 279.77796,-319.13241 c 15.74,0 24.86204,-14.25759 36.06204,-10.81759"
+         id="path40"
+         sodipodi:nodetypes="cc" />
+      <polygon
+         fill="#000000"
+         stroke="#000000"
+         points="315.09,-326.53 316.07,-333.46 325.48,-328.59 "
+         id="polygon40" />
+    </g>
+    <!-- simulationA&#45;&gt;simulationB -->
+    <!-- simulationB&#45;&gt;particle_stateD -->
+    <g
+       id="edge12"
+       class="edge">
+      <title
+         id="title42">simulationB:e-&gt;particle_stateD:dst</title>
+      <path
+         fill="none"
+         stroke="#000000"
+         d="m 277.22486,-293.32 c 15.74,0 27.78307,27.05096 38.98307,30.49096"
+         id="path42"
+         sodipodi:nodetypes="cc" />
+      <polygon
+         fill="#000000"
+         stroke="#000000"
+         points="315.09,-231.03 316.07,-237.96 325.48,-233.09 "
+         id="polygon42"
+         transform="translate(0.6279318,-28.33404)" />
+    </g>
+    <g
+       id="edge9-9"
+       class="edge"
+       transform="translate(-1,-0.005)">
+      <title
+         id="title22">particle_stateA:src-&gt;simulationA:w</title>
+      <path
+         fill="none"
+         stroke="#000000"
+         d="m 125.86,-354.12 c 15.28,0 30.34764,18.67423 41.09764,22.16423"
+         id="path22"
+         sodipodi:nodetypes="cc" />
+      <polygon
+         fill="#000000"
+         stroke="#000000"
+         points="166.93,-341.47 156.52,-339.49 157.56,-346.42 "
+         id="polygon23-3"
+         transform="rotate(34.394355,144.22934,-321.43324)" />
+    </g>
+  </g>
+</svg>

diagrams/texture_grid.tex

@@ -0,0 +1,46 @@
+\documentclass{standalone}
+\usepackage{tikz}
+\usepackage{fix-cm}
+\usepackage[dvipsnames]{xcolor}
+ \usetikzlibrary {arrows.meta}
+
+\newcommand*{\Width}{1}%
+\newcommand*{\Height}{1}%
+\newcommand*{\XOffset}{2}%
+
+\begin{document}
+\begin{tikzpicture}[scale=1]
+
+  \draw[thick,step=1.0] (0,0) grid (\Width + 1,-\Height - 1);
+
+  \foreach \y in {0,...,\Height} {
+    \foreach \x in {0,...,\Width} {
+      \node[font=\large] at (\x + 0.5,-\y - 0.3) {
+        p\pgfmathparse{int(\y * (\Height + 1) + \x)}\pgfmathresult
+      };
+      \node[font=\fontsize{8}{8}\selectfont] at (\x + 0.5,-\y - 0.75) {(x,y,z)};
+    }
+  }
+
+  %\draw[thick,step=1.0] (\Width + \XOffset,0) grid ((\XOffset + \Width) * 4 + 1,-\Height - 1);
+  \draw[thick,step=1.0] (\Width + \XOffset,0) grid (\XOffset + 2 * 4 + 1,-\Height - 1);
+
+  \foreach \y in {0,...,\Height} {
+    \foreach \x in {0,...,\Width} {
+      \foreach \i in {0,...,3} {
+        \node[font=\large] at (\Width + \XOffset + \x * 4 + \i + 0.5,-\y - 0.3) {
+          p\pgfmathparse{int(\y * (\Height + 1) + \x)}\pgfmathresult
+        };
+        \node[font=\fontsize{8}{8}\selectfont] at (\Width + \XOffset + \x * 4 + \i + 0.5,-\y - 0.75) {(x,y,z)};
+      }
+    }
+  }
+
+  \draw[-{Stealth[BrickRed]}, ultra thick, BrickRed] (2.1,-1) -- (2.9,-1);
+
+  \node[font=\large\bfseries ]  at ( 1,0.5)  {particle state};
+  \node[font=\large\bfseries ]  at ( 7,0.5)  {vertex coordinates};
+
+\end{tikzpicture}
+
+\end{document}

index.tex

@@ -1357,4 +1357,331 @@ extremely
 \href{https://git.musl-libc.org/cgit/musl/tree/src/math/powf.c?id=cb5c057c87240a9534f8e0d9b7ff2560082f6218}{computationally expensive}
 otherwise.
 
+\section{Progress: 11 Nov 2025}
+
+From 1 Nov 2025 to 11 Nov 2025, I achieved the following:
+
+\begin{itemize}
+\item I briefly experimented with \href{https://git.idk.st/bilbo/r500/src/commit/fdff78f1ad/drm/matrix_cubesphere_cubemap.cpp#L1081-L1088}{cubemap} \href{https://git.idk.st/bilbo/r500/src/commit/fdff78f1ad/drm/matrix_cubesphere_cubemap.cpp#L503}{textures}
+\item I experimented with point primitives and texture coordinate ``stuffing''
+\item I made a demo that generates and uses \href{https://git.idk.st/bilbo/r500/src/commit/fdff78f1ad/src/matrix_cubesphere_tiled.cpp}{macrotiled/microtiled textures}
+\item I created a particle system demo where the \href{https://git.idk.st/bilbo/r500/src/commit/fdff78f1ad/src/particle_physics.fs.asm}{particle simulation is computed in a fragment shader}
+\item I implemented \href{https://git.idk.st/bilbo/r500/commit/9e281cba583ec4a06e02470310c31cdad6962f64}{support for \texttt{\#include} directives} in my vertex and fragment shader assemblers
+\item I used the new \texttt{\#include} feature to more concisely express an \href{https://git.idk.st/bilbo/r500/commit/fdff78f1ad/main/drm/shadertoy_palette_fractal.fs.asm#L26-L29}{unrolled loop}
+\end{itemize}
+
+\subsection{Rewriting GLSL ``shadertoy'' shaders as R500 assembly}
+
+I felt \href{https://www.shadertoy.com/view/mtyGWy}{``Shader Art Coding Introduction''}
+would be fun to reimplement as R500 fragment shader assembly: it produces
+an interesting visual effect, despite not being particularly complicated.
+
+In general when writing assembly programs, I use a few techniques to improve my
+productivity and accuracy, prior to writing any actual assembly:
+
+\subsubsection{Expand/rewrite the GLSL code}
+
+In particular, my goal in this step is to make each line of GLSL roughly equal
+to one fragment shader instruction. I started by rewriting all of the function
+calls the \href{https://www.shadertoy.com/view/mtyGWy}{original} code made as:
+
+\begin{figure}
+  \href{verbatim/palette_fractal_functions.fs.glsl}{\includegraphics{verbatim/output/palette_fractal_functions.fs.glsl.pdf}}
+\end{figure}
+
+Defining replacements for GLSL's built-in functions is not a good practice for
+writing GLSL code in general. However, the goal in this specific situation is to
+give myself line-by-line hints on the R500 fragment shader assembly that I'll
+eventually need to write.
+
+I then rewrote the \texttt{main} function in a similar ``one line of GLSL per
+R500 instruction'' style as:
+
+\begin{figure}
+  \href{verbatim/palette_fractal_main.fs.glsl}{\includegraphics{verbatim/output/palette_fractal_main.fs.glsl.pdf}}
+\end{figure}
+
+I also decided the multiplication by 0.125, where it normally would have
+required a separate multiply-add instruction, was a perfect excuse to
+\href{https://git.idk.st/bilbo/r500/commit/90b486e744c14bb23283218108799186162afaad}{implement assembler support}
+for the ``OMOD'' R500 fragment shader feature/syntax that I previously
+\href{https://git.idk.st/bilbo/r500/commit/8e6e6e9750a33759b51ed73d3e238ebe77ee3f61}{implemented in my fragment shader disassembler}.
+
+\subsubsection{Assign all temporary variables to registers}
+
+Still prior to writing any fragment shader assembly, I then decided where I
+would store each GLSL variable in fragment shader temporary/constant memory:
+
+\begin{figure}
+  \href{verbatim/palette_fractal_memory.fs.asm}{\includegraphics{verbatim/output/palette_fractal_memory.fs.asm.pdf}}
+\end{figure}
+
+I intentionally stored scalar values in the alpha component of each
+vector. Given my current fragment shader assembler syntax, this allows for
+slightly more improved human-readability. For example, doing a scalar
+multiply-add with the alpha unit looks like this:
+
+\begin{figure}
+  \href{verbatim/palette_fractal_alpha_mad.fs.asm}{\includegraphics{verbatim/output/palette_fractal_alpha_mad.fs.asm.pdf}}
+\end{figure}
+
+If the \texttt{l} variable were instead stored in the green component, the code
+would be slightly uglier, as in:
+
+\begin{figure}
+  \href{verbatim/palette_fractal_rgb_mad.fs.asm}{\includegraphics{verbatim/output/palette_fractal_rgb_mad.fs.asm.pdf}}
+\end{figure}
+
+\subsubsection{Translate the GLSL to R500 fragment shader assembly, line-by-line}
+
+Because the GLSL code was transformed to very closely match the fragment shader
+assembly, this also makes it easy to test the fragment shader output when only a
+fraction of the complete program is translated (e.g: by commenting out chunks of
+the GLSL code to match the current state of the in-progress fragment shader
+assembly translation).
+
+The visual appearance of a half-translated varient of this fragment shader is
+not intuitive, so this technique greatly improves debuggability. I made at least
+at least two mistakes while translating that were not difficult to debug at a
+per-instruction level by comparing the equivalent GLSL code's visuals.
+
+\subsubsection{Translate a fixed-length GLSL loop}
+
+Though the R500 does support it, my fragment shader assembler does not currently
+implement support for loops (or any other type of flow control).
+
+R500 fragment shader flow control is also relatively expensive compared to
+``loop unrolling'', particularly in this case where the loop body is only 32
+instructions, and there are only 4 total iterations of the loop body.
+
+For this reason, I decided I wanted a concise and generalized way to ``repeat''
+chunks of source code in my fragment shader assembler, without actually
+duplicating the text.
+
+To do this, I
+\href{https://git.idk.st/bilbo/r500/commit/9e281cba583ec4a06e02470310c31cdad6962f64}{implemented}
+an ``\texttt{\#include}'' feature in my fragment shader assembler. This is
+conceptually similar to how \texttt{\#include} works in the C programming
+language, though my implementation simply feeds tokens from the included file
+directly from the (nested) lexer to the parser, rather than the much more
+complex procedure used by the C preprocessor.
+
+With this new feature, the translation of the GLSL loop is very simple:
+
+\begin{figure}
+  \href{verbatim/palette_fractal_loop.fs.asm}{\includegraphics{verbatim/output/palette_fractal_loop.fs.asm.pdf}}
+\end{figure}
+
+The full implementation is committed as
+\href{https://git.idk.st/bilbo/r500/src/commit/fdff78f1ad/drm/shadertoy_palette_fractal.fs.asm}{shadertoy\_palette\_fractal.fs.asm} and
+\href{https://git.idk.st/bilbo/r500/src/commit/fdff78f1ad/drm/shadertoy_palette_fractal_loop_inner.fs.asm}{shadertoy\_palette\_fractal\_loop\_inner.fs.asm}.
+
+\subsubsection{Demo videos}
+
+\begin{figure}
+  \includegraphics{videos/shadertoy_fractal.png}
+  \caption*{R500 DVI capture, \texttt{shadertoy\_palette\_fractal.fs.asm}\\(variant)}
+\end{figure}
+
+\begin{figure}
+  \includegraphics{videos/shadertoy_fractal2.png}
+  \caption*{R500 DVI capture, \texttt{shadertoy\_palette\_fractal.fs.asm}}
+\end{figure}
+
+\subsection{Fragment shader particle simulation}
+
+\subsubsection{Using fragment shaders to render non-pixel data}
+
+ATI documentation \href{doc/R2VB_programming.pdf}{mentioned} the existence of a
+``Render to Vertex Buffer'' feature.
+
+The general idea/revelation is:
+
+\begin{itemize}
+\item fragment shader output does not need to be ``pixel data''--it can
+  arbitrarily be assigned any desired meaning
+\item by alternating between a pair of buffers, fragment shader output can be
+  used as the input for the next invocation of the same fragment shader
+\end{itemize}
+
+The state manipulated by the pixel shader is double-buffered, where each
+iteration of the fragment shader uses alternating ``read'' and ``write''
+buffers, as in:
+
+\begin{figure}
+  \href{diagrams/simplified_particle_data_flow.svg}{\includegraphics{diagrams/simplified_particle_data_flow.svg}}
+\end{figure}
+
+On the subsequent iteration of the same computation, state ``b'' would be read
+and state ``a'' would be written.
+
+For all prior fragment shader demos, I used the 32-bit \texttt{C4\_8} surface
+format:
+
+\begin{figure}
+  \href{diagrams/c4_8.pdf}{\includegraphics{diagrams/c4_8.pdf}}
+\end{figure}
+
+Where 8-bit unsigned integer representations of blue, green, red, and alpha
+could be stored in C0, C1, C2, and C3 respectively (or any other arbitrary
+color component ordering).
+
+R500 also supports a 128-bit \texttt{C4\_32\_FP} surface format:
+
+\begin{figure}
+  \href{diagrams/c4_32_fp.pdf}{\includegraphics{diagrams/c4_32_fp.pdf}}
+\end{figure}
+
+Where each component contains a 32-bit floating point value. Compared to 8-bit
+integers, this increase in precision makes the format more useful for
+generalized computation.
+
+R500 conveniently also has an equivalent 128-bit per texel, 32-bit floating
+point per component, 4-component texture format.
+
+\subsubsection{Particle simulation data model}
+
+I decided a minimal but still ``mildly interesting'' particle system would need
+at least the following state:
+
+\begin{figure}
+  \href{verbatim/particle_system_data_model.c}{\includegraphics{verbatim/output/particle_system_data_model.c.pdf}}
+\end{figure}
+
+\texttt{age} is used to both ``reset'' the particle after some time (allowing
+the simulation to repeat indefinitely) and to give the particles non-uniform
+reset timing. \texttt{random} is used to further make the behavior of each
+particle less uniform. At the start of the particle simulation, all values are
+randomly initialized.
+
+This data model requires 8 components in total, which is more than the 4
+components provided by both the pixel shader output surface format as well as
+the texture sampler texel format. However:
+
+\begin{itemize}
+\item R500 fragment shaders can have up to 4 independent render targets
+\item R500 fragment shaders can sample from up to 16 independent textures
+\end{itemize}
+
+Following this model, it makes sense to break up the data structure like this:
+
+\begin{figure}
+  \href{verbatim/particle_system_data_model_split.c}{\includegraphics{verbatim/output/particle_system_data_model_split.c.pdf}}
+\end{figure}
+
+Where each fragment samples from two separate texture buffers, and has two
+separate render targets as output:
+
+\begin{figure}
+  \href{diagrams/simplified_particle_data_flow_split.svg}{\includegraphics{diagrams/simplified_particle_data_flow_split.svg}}
+\end{figure}
+
+\subsubsection{Drawing particles}
+
+I decided to draw particles using the R500's ``quad list'' primitive. In a
+non-fragment-shader-computed version of my particle simulation demo, I sent the
+particle position as a vertex shader constant, as in:
+
+\begin{figure}
+  \href{verbatim/particle_system_cpu.cpp}{\includegraphics{verbatim/output/particle_system_cpu.cpp.pdf}}
+\end{figure}
+
+The vertex shader is then able to calculate the quad vertex positions using a
+vertex shader program that is equivalent to this GLSL code:
+
+\begin{figure}
+  \href{verbatim/particle_system_position.glsl}{\includegraphics{verbatim/output/particle_system_position.glsl.pdf}}
+\end{figure}
+
+This works reasonably well for small particle system demos where particle
+position is calculated on the CPU. However, the goal is to compute (much larger)
+particle system positions via the pixel shader, and it would be highly preferred
+that the particle system state never leaves R500 VRAM. In the latter case, the
+``combine quad position coordinates with particle position coordinates via
+vertex shader constants'' approach does not work for several reasons:
+
+\begin{itemize}
+  \item R500 constant memory has 256 vectors; I'd like to make particle systems
+    with at least 100,000 particles.
+  \item The R500 pixel shader is not able to write to vertex shader constant
+    memory, it can only write to texture memory.
+  \item The \texttt{radeon} Linux kernel module generates a segmentation fault
+    in kernel space when given an indirect buffer larger than ~2MB (a Linux
+    kernel bug, not a R500 hardware limitation). Including the overhead of
+    multiple \texttt{3D\_DRAW\_IMMD} commands and vertex constant transfers,
+    100,000 particles is easily larger than 2MB of indirect buffer.
+\end{itemize}
+
+The only remaining option is to store particle position coordinates as a vertex
+buffer. However, because I am drawing quads, despite the R500 vertex fetcher's
+generous flexibility, the particle state buffer can't be used directly by the
+vertex shader because it only operates on individual vertices.
+
+For example, if a particle is at position \texttt{(4.0, 5.0, 6.0)}, the data
+that needs to be sent to the vertex shader should be:
+
+\begin{figure}
+  \href{verbatim/particle_position_vertex_shader_example.c}{\includegraphics{verbatim/output/particle_position_vertex_shader_example.c.pdf}}
+\end{figure}
+
+Or, \textit{expressed as a texture}, the desired transformation is:
+
+\begin{figure}
+  \href{diagrams/texture_grid.pdf}{\includegraphics{diagrams/texture_grid.pdf}}
+\end{figure}
+
+While the R500 pixel shader unit can't itself perform this transformation
+directly, the transformation can indeed be achieved by ``scaling'' the particle
+state via the R500 setup engine and fragment interpolators using point texture
+sampling.
+
+Doing this via point texture sampling is absolutely critical, because a linear
+interpolation between the state of two adjacent-in-memory particles is a
+completely meaningless operation in this context.
+
+This is implemented in
+\href{https://git.idk.st/bilbo/r500/src/branch/main/src/particle_oriented_animated_quad_vbuf_pixel_shader.cpp#L583}{\texttt{\_copy\_to\_vertexbuffer}}
+as simply ``rendering'' the particle positions into a viewport that is 4x wider
+than the width of the original particle state texture.
+
+\subsubsection{The complete rendering pipeline}
+
+All buffers in the following diagram are entirely stored in R500 texture memory,
+and are never transferred to x86 RAM.
+
+\begin{figure}
+  \href{diagrams/complete_particle_data_flow.svg}{\includegraphics{diagrams/complete_particle_data_flow.svg}}
+\end{figure}
+
+The full rendering pipeline implementation is committed as
+\href{https://git.idk.st/bilbo/r500/src/commit/fdff78f1ad/src/particle_oriented_animated_quad_vbuf_pixel_shader.cpp}{particle\_oriented\_animated\_quad\_vbuf\_pixel\_shader.cpp}.
+
+The full particle simulation pixel shader implementation is committed as
+\href{https://git.idk.st/bilbo/r500/src/commit/fdff78f1ad/src/particle_physics.fs.asm}{particle\_physics.fs.asm}.
+
+\subsubsection{Demo video}
+
+Speed comparison of my test system's Pentium 4 CPU and R500 pixel shader
+simulating the same particle system (131,072 particles):
+
+\begin{figure}
+  \includegraphics{videos/cpu_particle_simulation.png}
+  \caption*{R500 DVI capture, \texttt{particle\_oriented\_animated\_quad\_vbuf.cpp}\\(CPU -generated particle system)}
+\end{figure}
+
+\begin{figure}
+  \includegraphics{videos/pixel_shader_particle_simulation.png}
+  \caption*{R500 DVI capture, \texttt{particle\_oriented\_animated\_quad\_vbuf\_pixel\_shader.cpp}\\(pixel shader -generated particle system)}
+\end{figure}
+
+A more colorful variant of the same particle system demo (65,536 particles):
+
+\begin{figure}
+  \includegraphics{videos/pixel_shader_particle_simulation_color.png}
+  \caption*{R500 DVI capture, \texttt{particle\_oriented\_animated\_quad\_vbuf\_pixel\_shader.cpp}\\(pixel shader -generated particle system)}
+\end{figure}
+
+It is exciting for me to realize that this ``perform generalized computations
+via R500 pixel shaders'' technique has myriad other possible applications.
+
 \end{document}

verbatim.sh

@@ -1,72 +0,0 @@
-set -eux
-
-cd verbatim/
-
-mkdir -p output
-
-for i in *.asm; do
-    cat <<EOF > $i.tex
-\documentclass[varwidth=13.1cm, border={0.0cm 0.0cm 0.0cm 0.0cm}]{standalone}
-\usepackage{minted}
-\setminted[python]{breaklines, linenos, frame=lines, framesep=2mm, fontsize=\huge, numbersep=5pt}
-\standaloneenv{minted}
-\begin{document}
-
-\begin{minted}{haskell}
-EOF
-    cat $i >> $i.tex
-
-    cat <<EOF >> $i.tex
-\end{minted}
-
-\end{document}
-EOF
-
-    pdflatex -shell-escape -output-directory=output $i.tex
-    pdflatex -shell-escape -output-directory=output $i.tex
-done
-
-
-for i in *.glsl; do
-    cat <<EOF > $i.tex
-\documentclass[varwidth=13.1cm, border={0.0cm 0.0cm 0.0cm 0.0cm}]{standalone}
-\usepackage{minted}
-\setminted[python]{breaklines, linenos, frame=lines, framesep=2mm, fontsize=\huge, numbersep=5pt}
-\standaloneenv{minted}
-\begin{document}
-
-\begin{minted}{glsl}
-EOF
-    cat $i >> $i.tex
-
-    cat <<EOF >> $i.tex
-\end{minted}
-
-\end{document}
-EOF
-
-    pdflatex -shell-escape -output-directory=output $i.tex
-    pdflatex -shell-escape -output-directory=output $i.tex
-done
-
-for i in *.c; do
-    cat <<EOF > $i.tex
-\documentclass[varwidth=13.1cm, border={0.0cm 0.0cm 0.0cm 0.0cm}]{standalone}
-\usepackage{minted}
-\setminted[python]{breaklines, linenos, frame=lines, framesep=2mm, fontsize=\huge, numbersep=5pt}
-\standaloneenv{minted}
-\begin{document}
-
-\begin{minted}{c}
-EOF
-    cat $i >> $i.tex
-
-    cat <<EOF >> $i.tex
-\end{minted}
-
-\end{document}
-EOF
-
-    pdflatex -shell-escape -output-directory=output $i.tex
-    pdflatex -shell-escape -output-directory=output $i.tex
-done

verbatim/Makefile

@@ -0,0 +1,20 @@
+PDF += $(wildcard *.asm)
+PDF += $(wildcard *.glsl)
+PDF += $(wildcard *.c)
+PDF += $(wildcard *.cpp)
+
+PDF_OBJ := $(PDF:%=output/%.pdf)
+
+all: $(PDF_OBJ)
+
+output/%.asm.pdf: %.asm
+	sh verbatim.sh $< haskell
+
+output/%.glsl.pdf: %.glsl
+	sh verbatim.sh $< glsl
+
+output/%.c.pdf: %.c
+	sh verbatim.sh $< c
+
+output/%.cpp.pdf: %.cpp
+	sh verbatim.sh $< cpp

verbatim/palette_fractal_alpha_mad.fs.asm

@@ -0,0 +1,5 @@
+-- d = i * 0.4 + l;
+src0.a = const[0] , -- 0.4
+src1.a = temp[0]  , -- l
+src2.a = temp[3]  : -- i
+  temp[1].a   = MAD src2.a src0.a src1.a ;

verbatim/palette_fractal_functions.fs.asm

@@ -0,0 +1,97 @@
+--
+-- float length_(vec2 v)
+--
+
+-- float n = dot(v, v);
+src0.rgb = temp[0] : -- v
+                 DP3 src0.rg0 src0.rg0 ,
+  temp[0].a    = DP ;
+
+-- n = 1.0 / sqrt(n);
+src0.a   = temp[0] : -- n
+  temp[0].a    = RSQ |src0.a| ;
+
+-- n = 1.0 / n;
+src0.a   = temp[0] : -- n
+  temp[0].a    = RCP src0.a ;
+
+--
+-- float pow_(float x, float n)
+--
+
+-- x = log2(x);
+src0.a = temp[0] : -- x
+  temp[0].a = LN2 src0.a ;
+
+-- x = x * n;
+src0.a = temp[0] , -- x
+src1.a = temp[1] : -- n
+  temp[0].a = MAD src0.a src1.a src0.0 ;
+
+-- x = exp2(x);
+src0.a = temp[0] : -- x
+  temp[0].a = EX2 src0.a ;
+
+--
+-- float sin_(float x)
+--
+-- const[0] = { 1.0 / (pi * 2.0), 0, 0, 0 }
+--
+
+-- x = x * 0.159154936671257019043 + 0.5;
+src0.a   = temp[0]   , -- x
+src1.rgb = const[0]  , -- I_PI_2 (r)
+src2.a   = float(48) : -- 0.5
+  temp[0].a  = MAD src0.a src1.r src2.a ;
+
+-- x = fract(x);
+NOP
+src0.a   = temp[0] : -- x
+  temp[0].a  = FRC src0.a ;
+
+-- x = sin((x - 0.5) * PI_2);
+src0.a = float(48) , -- 0.5
+src1.a = temp[0]   , -- x
+srcp.a = neg       : -- (src1.a - src0.a)
+  temp[0].a = SIN srcp.a ;
+-- the R500 fragment shader SIN instruction multiplies
+-- the operand by 2 * pi
+
+--
+-- vec3 palette(float d)
+--
+-- the call to cos_ is inlined and algebraically simplified
+--
+-- const[1] = {0.25, 0.40625, 0.5625, 0}
+--
+-- v = d + (vec3(0.25, 0.40625, 0.5625) + 0.5)
+src0.a = temp[0]     , -- d
+src0.rgb = const[1]  , -- vec3(0.25, 0.40625, 0.5625)
+src1.rgb = float(48) , -- 0.5
+srcp.rgb = add       : -- (vec3(0.25, 0.40625, 0.5625) + 0.5)
+  temp[0].rgb = MAD src0.111 src0.aaa srcp.rgb ;
+
+-- v = frac(v)
+src0.rgb = temp[0] : -- v
+  temp[0].rgb = FRC src0.rgb ;
+
+-- v = v - 0.5
+src0.rgb = temp[0]   , -- v
+src1.rgb = float(48) : -- 0.5
+  temp[0].rgb = MAD src0.111 src0.rgb -src1.rgb ;
+
+-- v = cos(v)
+src0.rgb = temp[0] : -- v
+              COS src0.r ,
+  temp[0].r = SOP ;
+src0.rgb = temp[0] : -- v
+              COS src0.g ,
+  temp[0].g = SOP ;
+src0.rgb = temp[0] : -- v
+              COS src0.b ,
+  temp[0].b = SOP ;
+
+-- col = vec3(0.5, 0.5, 0.5) * v + vec3(0.5, 0.5, 0.5)
+src0.rgb = temp[0]   , -- v
+src1.rgb = float(48) : -- 0.5
+  temp[0].rgb = MAD src1.rgb src0.rgb src1.rgb;

verbatim/palette_fractal_functions.fs.glsl

@@ -0,0 +1,39 @@
+float length_(vec2 v)
+{
+  float n = dot(v, v);
+  n = 1.0 / sqrt(n);
+  n = 1.0 / n;
+  return n;
+}
+
+float pow_(float x, float n)
+{
+  x = log2(x);
+  x = x * n;
+  x = exp2(x);
+  return x;
+}
+
+float sin_(float x)
+{
+  x = x * 0.159154936671257019043 + 0.5; // 48
+  x = fract(x); // nop
+  x = sin((x - 0.5) * 6.28318548202514648438); // presubtract
+  return x;
+}
+
+float cos_(float x)
+{
+  x = x * 0.159154936671257019043 + 0.5; // 48
+  x = fract(x); // nop
+  x = cos((x - 0.5) * 6.28318548202514648438); // presubtract
+  return x;
+}
+
+vec3 palette(float d) {
+  vec3 v = d + vec3(0.25, 0.40625, 0.5625); // 40 45 49
+  v = v * 6.28318548202514648438; // (2 * pi * (1 / (2 * pi))) == 1
+  v = cos_(v);
+  v = vec3(0.5, 0.5, 0.5) * v + vec3(0.5, 0.5, 0.5); // 48
+  return v;
+}

verbatim/palette_fractal_loop.fs.asm

@@ -0,0 +1,25 @@
+-- vec4 final_color = vec4(0, 0, 0, 1);
+:
+  temp[2].a   = MAX src0.1 src0.1 ,
+  temp[2].rgb = MAX src0.000 src0.000 ;
+
+-- i = 0;
+:
+  temp[3].a   = MAX src0.0 src0.0 ;
+
+--------------------------------------------------------------------------------
+-- loop start
+--------------------------------------------------------------------------------
+#include "shadertoy_palette_fractal_loop_inner.fs.asm"
+#include "shadertoy_palette_fractal_loop_inner.fs.asm"
+#include "shadertoy_palette_fractal_loop_inner.fs.asm"
+#include "shadertoy_palette_fractal_loop_inner.fs.asm"
+--------------------------------------------------------------------------------
+-- loop end
+--------------------------------------------------------------------------------
+
+-- gl_FragColor = final_color;
+OUT TEX_SEM_WAIT
+src0.rgb = temp[2] :
+  out[0].a     = MAX src0.1 src0.1 ,
+  out[0].rgb   = MAX src0.rgb src0.rgb ;

verbatim/palette_fractal_main.fs.glsl

@@ -0,0 +1,33 @@
+void main()
+{
+  vec2 uv = uv0; // temp[1]
+
+  vec4 final_color = vec4(0, 0, 0, 1);
+
+  for (float i = 0.0; i < 4.0; i++) {
+    uv = uv * vec2(1.5, 1.5); // 60
+    uv = fract(uv);
+    uv = uv - vec2(0.5, 0.5); // 48
+
+    float l = length_(uv0);
+
+    float d = i * 0.4 + l;    // const[0].a
+    d = time * 0.4 + d;       // const[0].a
+
+    vec3 col = palette(d);
+
+    d = exp2(-l);
+
+    l = length_(uv);
+    d = l * d;
+    d = d * 8.0 + time;       // 80
+    d = 0.125 * sin_(d);      // omod
+    d = 1.0 / abs(d);
+    d = 0.01 * d;             // const[0].b
+    d = pow_(d, 1.2);         // const[0].g
+
+    final_color.xyz = col * vec3(d, d, d) + final_color.xyz;
+  }
+
+  gl_FragColor = final_color;
+}

verbatim/palette_fractal_memory.fs.asm

@@ -0,0 +1,8 @@
+-- CONST[0] = { time, 1.2, 0.01, 0.4 }
+-- CONST[1] = { PI_2, I_PI_2, 0, 0 },
+-- CONST[2] = { 0.25, 0.40625, 0.5625, 0 },
+
+-- temp[0] : { uv0.xy , _, l }
+-- temp[1] : { uv.xy  , _, d }
+-- temp[2] : final_color.xyzw
+-- temp[3] : {col.xyz , i }

verbatim/palette_fractal_rgb_mad.fs.asm

@@ -0,0 +1,5 @@
+-- d = i * 0.4 + l;
+src0.a = const[0]  , -- 0.4
+src1.rgb = temp[0] , -- l
+src2.a = temp[3]   : -- i
+  temp[1].g   = MAD src2.0a0 src0.0a0 src1.0g0 ;

verbatim/particle_position_vertex_shader_example.c

@@ -0,0 +1,7 @@
+const float vertices[] = {
+// [particle position]   [quad texture coordinate]
+   4.0, 5.0, 6.0,        0.0, 0.0, // vertex 0
+   4.0, 5.0, 6.0,        1.0, 0.0, // vertex 1
+   4.0, 5.0, 6.0,        1.0, 1.0, // vertex 2
+   4.0, 5.0, 6.0,        0.0, 1.0, // vertex 3
+};

verbatim/particle_system_cpu.cpp

@@ -0,0 +1,56 @@
+const int particles_length = 128;
+
+for (int i = 0; i < particles_length; i++) {
+  T0V(VAP_PVS_STATE_FLUSH_REG, 0x00000000);
+
+  const vec3 position = particles[i].position;
+
+  const float consts[] = {
+    // 0: local space to clip space transformation matrix
+    trans[0][0], trans[0][1], trans[0][2], trans[0][3],
+    trans[1][0], trans[1][1], trans[1][2], trans[1][3],
+    trans[2][0], trans[2][1], trans[2][2], trans[2][3],
+    trans[3][0], trans[3][1], trans[3][2], trans[3][3],
+
+    // 4: dx ("right" change of basis vector)
+    local_to_view[0][0], local_to_view[0][1], local_to_view[0][2], 0,
+
+    // 5: dy ("up" change of basis vector)
+    local_to_view[1][0], local_to_view[1][1], local_to_view[1][2], 0,
+
+    // 6: particle position, scale
+    position.x, position.y, position.z, scale
+  };
+  // transfer the constants to vertex shader constant memory
+  ib_vap_pvs_const_cntl(consts, (sizeof (consts)));
+
+  const int dwords_per_vtx = 2;
+
+  T0V(VAP_VTX_SIZE
+      , VAP_VTX_SIZE__DWORDS_PER_VTX(dwords_per_vtx)
+      );
+
+  const int vertex_count = 4;
+  const vec2 vertices[vertex_count] = {
+    {0.0, 0.0f},
+    {1.0, 0.0f},
+    {1.0, 1.0f},
+    {0.0, 1.0f},
+  };
+
+  T3(_3D_DRAW_IMMD_2, (1 + vertex_count * dwords_per_vtx) - 1);
+  TU( VAP_VF_CNTL__PRIM_TYPE(13) // quad list
+    | VAP_VF_CNTL__PRIM_WALK(3)  // embedded/immediate vertex data
+    | VAP_VF_CNTL__INDEX_SIZE(0)
+    | VAP_VF_CNTL__VTX_REUSE_DIS(0)
+    | VAP_VF_CNTL__DUAL_INDEX_MODE(0)
+    | VAP_VF_CNTL__USE_ALT_NUM_VERTS(0)
+    | VAP_VF_CNTL__NUM_VERTICES(vertex_count)
+    );
+
+  // transfer particle quad vertices
+  for (int j = 0; j < vertex_count; j++) {
+    TF(vertices[i].x);
+    TF(vertices[i].y);
+  }
+}

verbatim/particle_system_data_model.c

@@ -0,0 +1,9 @@
+struct particle_state {
+  vec3 position;
+  vec3 velocity;
+  float age;
+  float random;
+};
+
+const int particle_count = 128;
+struct particle_state particle_system[particle_count];

verbatim/particle_system_data_model_split.c

@@ -0,0 +1,12 @@
+struct position_age {
+  vec3 position;
+  float age;
+};
+struct velocity_random {
+  vec3 velocity;
+  float random;
+};
+
+const int particle_count = 128;
+struct position_age position_age[particle_count];
+struct velocity_random velocity_random[particle_count];

verbatim/particle_system_position.glsl

@@ -0,0 +1,27 @@
+#version 120
+
+uniform mat4 trans; // local space to clip space
+uniform vec3 dx; // "right" change of basis vector
+uniform vec3 dy; // "up" change of basis vector
+uniform vec3 particle_position;
+uniform float scale;
+
+
+attribute vec2 quad_texture;
+attribute float age;
+
+void main()
+{
+  // calculate unit quad position coordinates from texture coordinates
+  vec2 quad_position = quad_texture * 2 + 1;
+
+  vec3 position = particle_position;
+  position += position.xxx * dx;
+  position += position.yyy * dy;
+  position *= scale;
+
+  position = trans * position;
+
+  gl_Position = vec4(position, 1);
+  gl_TexCoord[0] = vec4(quad_texture, 0, age);
+}

verbatim/verbatim.sh

@@ -0,0 +1,24 @@
+set -eux
+cat <<EOF > $1.tex
+\documentclass[varwidth=13.1cm, border={0.0cm 0.0cm 0.0cm 0.0cm}]{standalone}
+\usepackage{minted}
+\setminted[python]{breaklines, linenos, frame=lines, framesep=2mm, fontsize=\huge, numbersep=5pt}
+\standaloneenv{minted}
+\begin{document}
+
+\begin{minted}
+EOF
+
+echo "{$2}" >> $1.tex
+
+cat $1 >> $1.tex
+
+cat <<EOF >> $1.tex
+\end{minted}
+
+\end{document}
+EOF
+
+pdflatex -shell-escape -output-directory=output $1.tex
+pdflatex -shell-escape -output-directory=output $1.tex
+pdflatex -shell-escape -output-directory=output $1.tex