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https://github.com/AtHeartEngineer/upgrading-ethereum-book.git
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Add chart generators
This commit is contained in:
Ben Edgington
538
src/charts/charts.html
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538
src/charts/charts.html
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@@ -0,0 +1,538 @@
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<html lang="en-GB">
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<head>
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<meta charset="utf-8">
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<title>Charts</title>
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<script src="./roughviz.min.js">
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<!-- This library can be built from https://github.com/benjaminion/roughViz -->
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</script>
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<style>
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div.svg {border: solid black 1px; margin: 1ex 0;}
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div.all {width: 1200px; margin: 10ex auto;}
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</style>
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</head>
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<body>
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<div class="all">
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<script>
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// set some defaults
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opts = {
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width: 1200,
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height: 600,
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roughness: 1,
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bowing: 0,
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simplification: 0.2,
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axisRoughness: 1,
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axisStrokeWidth: 1.0,
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axisFontSize: 20,
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labelFontSize: 30,
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legend: false,
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interactive: false,
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};
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// Make a right-click download link forthe SVG data
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function makeLink(chart, id) {
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const svg = chart.svg;
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const serializer = new XMLSerializer();
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var source = serializer.serializeToString(svg.node());
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source = '<?xml version="1.0" standalone="no"?>\r\n<svg xmlns="http://www.w3.org/2000/svg" viewBox="0 0 1200 600">' + source + '</svg>';
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//convert svg source to URI data scheme.
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const url = "data:image/svg+xml;charset=utf-8,"+encodeURIComponent(source);
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//set url value to a element's href attribute.
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const div = document.getElementById(id);
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if (div !== null) {
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const anchor = document.createElement('a');
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anchor.appendChild(document.createTextNode('Download'));
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anchor.href = url;
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anchor.download = id + '.svg'
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div.appendChild(anchor);
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}
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}
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</script>
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<!-- Issuance Curve ------------------------------------------------ -->
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<div class="svg" id="issuance_curve"></div>
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<script>
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{
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const nPoints = 12;
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const xVals = [];
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const yVals = [];
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const epochsPerYear = 365.25 * 225;
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const xFunc = i => (1 + i) * 50;
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const yFunc = x => epochsPerYear * 32 * x * 64 / Math.floor(Math.sqrt(1000000000 * 32 * x));
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for (let i = 0; i < nPoints; i++) {
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xVals[i] = xFunc(i);
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yVals[i] = yFunc(1000 * xVals[i]) / 1000;
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}
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const chart = new roughViz.Line({
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element: '#issuance_curve',
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width: opts.width,
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height: opts.height,
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data: {
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y: yVals,
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},
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x: xVals,
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xLabel: "Number of active validators (thousands)",
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yLabel: "Annual issuance (thousand ETH)",
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xLabelDelta: 0,
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yLabelDelta: -40,
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roughness: opts.roughness,
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bowing: opts.bowing,
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simplification: opts.simplification,
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colors: ["black"],
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strokeWidth: 1.5,
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interpolation: ["curve"],
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circle: true,
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circleRadius: 6,
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circleRoughness: 1,
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axisStrokeWidth: opts.axisStrokeWidth,
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axisRoughness: opts.axisRoughness,
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axisFontSize: opts.axisFontSize,
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labelFontSize: opts.labelFontSize,
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margin: {top: 30, right: 20, bottom: 80, left: 100},
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legend: opts.legend,
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interactive: opts.interactive,
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});
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makeLink(chart, 'issuance_curve');
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}
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</script>
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<!-- Issuance Curve ------------------------------------------------ -->
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<div class="svg" id="rewards_curve"></div>
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<script>
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{
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const nPoints = 12;
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const xVals = [];
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const yVals = [];
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const epochsPerYear = 365.25 * 225;
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const xFunc = i => (1 + i) * 50;
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const yFunc = x => epochsPerYear * 64 / Math.floor(Math.sqrt(1000000000 * 32 * x));
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for (let i = 0; i < nPoints; i++) {
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xVals[i] = xFunc(i);
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yVals[i] = yFunc(1000 * xVals[i]) * 100;
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}
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const chart = new roughViz.Line({
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element: '#rewards_curve',
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width: opts.width,
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height: opts.height,
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data: {
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y: yVals,
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},
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x: xVals,
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xLabel: "Number of active validators (thousands)",
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yLabel: "Annual return on 32 ETH stake (%)",
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xLabelDelta: 0,
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yLabelDelta: -40,
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roughness: opts.roughness,
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bowing: opts.bowing,
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simplification: opts.simplification,
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colors: ["black"],
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strokeWidth: 1.5,
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interpolation: ["curve"],
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circle: true,
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circleRadius: 6,
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circleRoughness: 1,
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axisStrokeWidth: opts.axisStrokeWidth,
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axisRoughness: opts.axisRoughness,
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axisFontSize: opts.axisFontSize,
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labelFontSize: opts.labelFontSize,
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margin: {top: 30, right: 20, bottom: 80, left: 100},
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legend: opts.legend,
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interactive: opts.interactive,
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});
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makeLink(chart, 'rewards_curve');
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}
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</script>
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<!-- Reward Variance ----------------------------------------------- -->
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<div class="svg" id="reward_variance"></div>
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<script>
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{
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const chart = new roughViz.Bar({
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element: '#reward_variance',
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width: opts.width,
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height: opts.height,
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data: {
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labels: [1.4, 1.425, 1.45, 1.475, 1.5, 1.525, 1.55, 1.575, 1.6, 1.625, 1.65, 1.675, 1.7, 1.725, 1.75, 1.775, 1.8, 1.825, 1.85, 1.875, 1.9, 1.925, 1.95, 1.975],
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values: [0, 9.012097147132001e-05, 0.0007900030693065276, 0.0034625936780776404, 0.010117724758439453, 0.022222501861968585, 0.03930741130795962, 0.05869508559787125, 0.07667608389578497, 0.09011582615639349, 0.097360246574628, 0.0982297322584306, 0.0935787996300737, 0.08483788991116106, 0.07363622456242747, 0.06149378860071459, 0.04961300241343375, 0.03880057869052064, 0.029494711073457386, 0.021843117625188306, 0.015791505923118995, 0.011164359278243946, 0.007730431979276688, 0],
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},
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xLabel: "Annual reward (ETH, 300k validators)",
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yLabel: "Proportion of validators",
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xLabelDelta: 0,
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yLabelDelta: -40,
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roughness: opts.roughness,
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bowing: opts.bowing,
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simplification: opts.simplification,
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color: 'black',
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fillStyle: 'hachure',
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fillWeight: 0.2,
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strokeWidth: 1.5,
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padding: 0.01,
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axisStrokeWidth: opts.axisStrokeWidth,
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axisRoughness: opts.axisRoughness,
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axisFontSize: opts.axisFontSize,
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labelFontSize: opts.labelFontSize,
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margin: {top: 30, right: 20, bottom: 90, left: 100},
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legend: opts.legend,
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interactive: opts.interactive,
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});
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makeLink(chart, 'reward_variance');
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}
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</script>
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<!-- Reward Timeliness against exponential ------------------------- -->
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<div class="svg" id="reward_timeliness"></div>
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<script>
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{
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const nPoints = 40;
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const xVals = [];
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const y1Vals = [];
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const y2Vals = [];
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const y1Func = i => {
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if (i == 0) return 0.844;
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if (i <= 4) return 0.625;
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if (i <= 31) return 0.188;
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return -0.625;
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}
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const y2Func = i => -0.6 + 1.44 * Math.exp(-0.1 * i);
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for (let i = 0; i < nPoints; i++) {
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xVals[i] = (1 + i);
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y1Vals[i] = y1Func(i);
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y2Vals[i] = y2Func(i);
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}
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xVals[0] = "";
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const chart = new roughViz.Line({
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element: '#reward_timeliness',
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width: opts.width,
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height: opts.height,
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data: {
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y1: y1Vals,
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y2: y2Vals,
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},
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x: xVals,
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xLabel: "Slots delay",
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yLabel: "Net attestation reward weight",
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xLabelDelta: -190,
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yLabelDelta: -40,
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roughness: 0.7,
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bowing: opts.bowing,
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simplification: opts.simplification,
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colors: ["black"],
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interpolation: ["straight", "curve"],
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dash: [[0], [8, 6]],
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strokeWidth: 1.5,
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circle: false,
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axisStrokeWidth: opts.axisStrokeWidth,
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axisRoughness: opts.axisRoughness,
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axisFontSize: opts.axisFontSize,
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labelFontSize: opts.labelFontSize,
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margin: {top: 30, right: 20, bottom: 30, left: 100},
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legend: opts.legend,
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interactive: opts.interactive,
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});
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makeLink(chart, 'reward_timeliness');
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}
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</script>
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<!-- Hysteresis ---------------------------------------------------- -->
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<div class="svg" id="hysteresis"></div>
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<script>
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{
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const xVals = [0];
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const y1Vals = [32.0, 32.2, 32.4, 32.6, 32.8, 33.0, 33.2, 33.4, 33.2, 33.0, 32.8, 32.6, 32.4, 32.2, 32.0, 31.8, 31.6, 31.8, 32.0, 32.2, 32.0, 31.8, 32.0, 32.2, 32.0, 31.8, 32.0, 32.2, 32.4, 32.2, 32.0, 31.8, 32.0, 32.2, 32.4, 32.6];
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const y2Vals = [32.0];
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const nPoints = y1Vals.length;
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const y2Func = (eb, y) => {
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if (y > eb + 1.25) return eb == 32 ? 32 : eb + 1;
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if (y < eb - 0.25) return eb - 1;
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return eb;
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}
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for (let i = 1; i < nPoints; i++) {
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xVals[i] = i;
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y2Vals[i] = y2Func(y2Vals[i - 1], y1Vals[i]);
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}
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const chart = new roughViz.Line({
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element: '#hysteresis',
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width: opts.width,
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height: opts.height,
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x: xVals,
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data: {
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y1: y1Vals,
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y2: y2Vals,
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},
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yDomain: [30, 34],
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yLabel: "Balance / Effective Balance (ETH)",
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yLabelDelta: -40,
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xAxis: false,
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roughness: 0.7,
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bowing: opts.bowing,
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simplification: opts.simplification,
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colors: ["black"],
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interpolation: ["straight"],
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dash: [[0], [10, 10]],
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strokeWidth: 1.5,
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circle: false,
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axisStrokeWidth: opts.axisStrokeWidth,
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axisRoughness: opts.axisRoughness,
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axisFontSize: opts.axisFontSize,
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labelFontSize: opts.labelFontSize,
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yLines: [
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{y: 31.75, dash: [2, 6]},
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{y: 32.25, dash: [2, 6]},
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],
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margin: {top: 30, right: 20, bottom: 30, left: 100},
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legend: opts.legend,
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interactive: opts.interactive,
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});
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makeLink(chart, 'hysteresis');
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}
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</script>
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<!-- Leak Scores and Balances -------------------------------------- -->
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<div class="svg" id="inactivity_scores"></div>
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<div class="svg" id="inactivity_balances">
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<script>
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{
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const nEpochs = 150;
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const xInterval = 5;
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const xVals = [];
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const y1Score = []; // Always online
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const y2Score = []; // 90% online
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const y3Score = []; // 70% online
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const y4Score = []; // Offline
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const y5Score = []; // Temporarily offline
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const y1Balance = []; // Always online
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const y2Balance = []; // 90% online
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const y3Balance = []; // 70% online
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const y4Balance = []; // Offline
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const y5Balance = []; // Temporarily offline
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const leakEnd = 100;
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const offlineStart = 50;
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const offlineEnd = 75;
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const scoreUpdate = (score, inLeak, isOnline) => {
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return Math.max(0, score + (isOnline ? -1 : 4) + (inLeak ? 0 : -16));
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}
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const balanceUpdate = (balance, score) => {
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const inactivity_penalty_quotient = 50331648; // 3 * 2**24 (Altair)
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const inactivity_score_bias = 4;
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// Assume effective balance does not fall below 32 (i.e. balance remains above 31.75)
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return balance - 32 * score / (inactivity_score_bias * inactivity_penalty_quotient);
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}
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var y1s = y2s = y3s = y4s = y5s = 0;
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var y1b = y2b = y3b = y4b = y5b = 32;
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for (let i = 0; i < nEpochs; i++) {
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var inLeak = (i < leakEnd);
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if (i % xInterval === 0) {
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var idx = i / xInterval;
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xVals[idx] = i;
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y1Score[idx] = y1s;
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y2Score[idx] = y2s;
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y3Score[idx] = y3s;
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y4Score[idx] = y4s;
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y5Score[idx] = y5s;
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y1Balance[idx] = y1b;
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y2Balance[idx] = y2b;
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y3Balance[idx] = y3b;
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y4Balance[idx] = y4b;
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y5Balance[idx] = y5b;
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}
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y1s = scoreUpdate(y1s, inLeak, true);
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y2s = scoreUpdate(y2s, inLeak, i % 10 < 9);
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y3s = scoreUpdate(y3s, inLeak, i % 10 < 7);
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y4s = scoreUpdate(y4s, inLeak, false);
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y5s = scoreUpdate(y5s, inLeak, (i < offlineStart) || (i >= offlineEnd));
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y1b = balanceUpdate(y1b, y1s);
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y2b = balanceUpdate(y2b, y2s);
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y3b = balanceUpdate(y3b, y3s);
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y4b = balanceUpdate(y4b, y4s);
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y5b = balanceUpdate(y5b, y5s);
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}
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xVals[leakEnd / xInterval] = "End";
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xVals[offlineStart / xInterval] = "A";
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xVals[offlineEnd / xInterval] = "B";
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const dashPattern = [[2, 6], [6, 6], [10, 6], [0], [10, 6, 4, 6]];
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const margin = {top: 30, right: 20, bottom: 80, left: 120};
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const xLines = [
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{x: leakEnd, dash: [4, 8]},
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{x: offlineStart, dash: [2, 10]},
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{x: offlineEnd, dash: [2, 10]},
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];
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const chart_1 = new roughViz.Line({
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element: '#inactivity_scores',
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width: opts.width,
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height: opts.height,
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data: {
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y1: y1Score,
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y2: y2Score,
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y3: y3Score,
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y4: y4Score,
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y5: y5Score,
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},
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x: xVals,
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xLabel: "Epochs since leak start",
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yLabel: "Inactivity score",
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xLabelDelta: 0,
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yLabelDelta: -40,
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yDomain: [-40, 420],
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circle: false,
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roughness: 0.3,
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bowing: opts.bowing,
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simplification: opts.simplification,
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colors: ["black"],
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strokeWidth: 1.5,
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interpolation: ["straight"],
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dash: dashPattern,
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axisStrokeWidth: opts.axisStrokeWidth,
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axisRoughness: opts.axisRoughness,
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axisFontSize: opts.axisFontSize,
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labelFontSize: opts.labelFontSize,
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notes: [
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{x: 200, y: 270, text: "Always offline"},
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{x: 454, y: 350, text: "Temporarily"},
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{x: 430, y: 375, text: "offline"},
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{x: 620, y: 390, text: "70% online"},
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{x: 620, y: 436, text: "90% online"},
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{x: 630, y: 473, text: "Always online"},
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],
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notesFontSize: 0.8 * opts.labelFontSize,
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xLines: xLines,
|
||||
|
||||
margin: margin,
|
||||
legend: opts.legend,
|
||||
interactive: opts.interactive,
|
||||
});
|
||||
|
||||
makeLink(chart_1, 'inactivity_scores');
|
||||
|
||||
const chart_2 = new roughViz.Line({
|
||||
element: '#inactivity_balances',
|
||||
width: opts.width,
|
||||
height: opts.height,
|
||||
|
||||
data: {
|
||||
y1: y1Balance,
|
||||
y2: y2Balance,
|
||||
y3: y3Balance,
|
||||
y4: y4Balance,
|
||||
y5: y5Balance,
|
||||
},
|
||||
x: xVals,
|
||||
yValueFormat: ".4f",
|
||||
xLabel: "Epochs since leak start",
|
||||
yLabel: "Balance (ETH)",
|
||||
xLabelDelta: 0,
|
||||
yLabelDelta: -60,
|
||||
|
||||
circle: false,
|
||||
roughness: 0.3,
|
||||
bowing: opts.bowing,
|
||||
simplification: opts.simplification,
|
||||
|
||||
colors: ["black"],
|
||||
strokeWidth: 1.5,
|
||||
interpolation: ["straight"],
|
||||
dash: dashPattern,
|
||||
|
||||
axisStrokeWidth: opts.axisStrokeWidth,
|
||||
axisRoughness: opts.axisRoughness,
|
||||
axisFontSize: opts.axisFontSize,
|
||||
labelFontSize: opts.labelFontSize,
|
||||
|
||||
notes: [
|
||||
{x: 170, y: 80, text: "Always offline"},
|
||||
{x: 876, y: 105, text: "Temporarily offline"},
|
||||
{x: 840, y: 62, text: "70% online"},
|
||||
{x: 1000, y: 47, text: "90% online"},
|
||||
{x: 990, y: 13, text: "Always online"},
|
||||
],
|
||||
notesFontSize: 0.8 * opts.labelFontSize,
|
||||
|
||||
xLines: xLines,
|
||||
|
||||
margin: margin,
|
||||
legend: opts.legend,
|
||||
interactive: opts.interactive,
|
||||
});
|
||||
|
||||
makeLink(chart_2, 'inactivity_balances');
|
||||
}
|
||||
</script>
|
||||
|
||||
</div>
|
||||
</body>
|
||||
99
src/charts/reward_variance.py
Normal file
99
src/charts/reward_variance.py
Normal file
@@ -0,0 +1,99 @@
|
||||
# Adapted from https://pintail.xyz/posts/modelling-the-impact-of-altair/
|
||||
|
||||
import math
|
||||
from scipy.stats import binom
|
||||
|
||||
def get_quantile(pmf, quantile):
|
||||
cumulative = 0
|
||||
for x, prob in sorted(pmf.items()):
|
||||
cumulative += prob
|
||||
if cumulative >= quantile:
|
||||
return x
|
||||
|
||||
NUM_VALIDATORS = 300000
|
||||
|
||||
SECONDS_PER_YEAR = 31557600
|
||||
SECONDS_PER_SLOT = 12
|
||||
SLOTS_PER_EPOCH = 32
|
||||
COMMITTEE_EPOCHS = 256
|
||||
COMMITTEE_VALIDATORS = 512
|
||||
|
||||
slots_per_year = SECONDS_PER_YEAR / SECONDS_PER_SLOT
|
||||
epochs_per_year = slots_per_year / SLOTS_PER_EPOCH
|
||||
committees_per_year = epochs_per_year / COMMITTEE_EPOCHS
|
||||
|
||||
GWEI_PER_ETH = int(1e9)
|
||||
gwei_per_validator = 32 * GWEI_PER_ETH
|
||||
BASE_REWARD_FACTOR = 64
|
||||
|
||||
HEAD_WEIGHT = 14
|
||||
SOURCE_WEIGHT = 14
|
||||
TARGET_WEIGHT = 26
|
||||
SYNC_WEIGHT = 2
|
||||
PROPOSER_WEIGHT = 8
|
||||
WEIGHT_DENOMINATOR = 64
|
||||
|
||||
base_reward = gwei_per_validator * BASE_REWARD_FACTOR // math.isqrt(NUM_VALIDATORS * gwei_per_validator)
|
||||
total_reward = base_reward * NUM_VALIDATORS
|
||||
|
||||
altair_proposer_reward = total_reward * PROPOSER_WEIGHT // SLOTS_PER_EPOCH // WEIGHT_DENOMINATOR
|
||||
altair_att_reward = base_reward * (HEAD_WEIGHT + SOURCE_WEIGHT + TARGET_WEIGHT) // WEIGHT_DENOMINATOR
|
||||
sync_reward = total_reward * COMMITTEE_EPOCHS * SYNC_WEIGHT // COMMITTEE_VALIDATORS // WEIGHT_DENOMINATOR
|
||||
|
||||
max_committees = 10
|
||||
max_proposals = 50
|
||||
|
||||
# distribution of committee selections per year
|
||||
n_committees = [el for el in range(max_committees + 1)]
|
||||
pmf_committees = binom.pmf(n_committees, committees_per_year, COMMITTEE_VALIDATORS / NUM_VALIDATORS)
|
||||
|
||||
# distribution of block proposal opportunities per year
|
||||
n_proposals = [el for el in range(max_proposals + 1)]
|
||||
pmf_proposals = binom.pmf(n_proposals, slots_per_year, 1 / NUM_VALIDATORS)
|
||||
|
||||
# calculate all possible reward levels (up to 50 block proposals and 10 committee selections)
|
||||
altair_pmf = {}
|
||||
attestation_rewards = epochs_per_year * altair_att_reward
|
||||
for comms in n_committees:
|
||||
for props in n_proposals:
|
||||
reward = comms * sync_reward + props * altair_proposer_reward + attestation_rewards
|
||||
prob = pmf_committees[comms] * pmf_proposals[props]
|
||||
if reward in altair_pmf:
|
||||
altair_pmf[reward] += prob
|
||||
else:
|
||||
altair_pmf[reward] = prob
|
||||
|
||||
#min_reward = attestation_rewards / GWEI_PER_ETH
|
||||
#max_reward = (max_committees * sync_reward + max_proposals * altair_proposer_reward + attestation_rewards) / GWEI_PER_ETH
|
||||
min_reward = 1.4
|
||||
max_reward = 2.0
|
||||
n_bins = 24
|
||||
bins = [min_reward + i * (max_reward - min_reward) / n_bins for i in range(n_bins)]
|
||||
altair_hist = [0] * n_bins
|
||||
|
||||
# bin the rewards to generate histogram
|
||||
for reward_gwei, prob in altair_pmf.items():
|
||||
reward = reward_gwei / GWEI_PER_ETH
|
||||
for i, edge in enumerate(bins[1:]):
|
||||
if reward < edge:
|
||||
altair_hist[i] += prob
|
||||
break
|
||||
|
||||
altair_mean = sum([p * r / GWEI_PER_ETH for r, p in altair_pmf.items()])
|
||||
altair_sigma = math.sqrt(sum([p * (r / GWEI_PER_ETH)**2 for r, p in altair_pmf.items()]) - altair_mean**2)
|
||||
altair_median = get_quantile(altair_pmf, 0.5) / GWEI_PER_ETH
|
||||
|
||||
print('\nAltair annual reward statistics (ETH)')
|
||||
print('-------------------------------------')
|
||||
print(f' median: {altair_median:.4f}')
|
||||
print(f' mean: {altair_mean:.4f}')
|
||||
print(f' standard deviation: {altair_sigma:.4f}')
|
||||
|
||||
print(sum(altair_hist)) # check histogram sums to unity
|
||||
print(altair_hist)
|
||||
print(bins)
|
||||
|
||||
c10 = get_quantile(altair_pmf, 0.10) / GWEI_PER_ETH
|
||||
c90 = get_quantile(altair_pmf, 0.90) / GWEI_PER_ETH
|
||||
print(f'10th percentile: {c10:.4f}')
|
||||
print(f'90th percentile: {c90:.4f}')
|
||||
Reference in New Issue
Block a user