30:Ta46,html`

${Plot.plot({ width: 300, height: 300, title: "Float Multiply", x: { ticks: 10, tickFormat: "+f" }, y: { ticks: 10, tickFormat: "+f" }, color: { scheme: "magma" }, marks: [ Plot.raster({ fill: (x, y) => x * y, x1: form.beta, y1: form.beta, x2: form.alpha, y2: form.alpha, pixelSize: 4 }), Plot.ruleX([0], { strokeOpacity: 0.2 }), Plot.ruleY([0], { strokeOpacity: 0.2 }), Plot.frame() ] })} ${Plot.plot({ width: 300, height: 300, title: "Dequantized Multiply", caption: "quant.dequantize(quant.quantize(x)) * quant.dequantize(quant.quantize(y))", x: { ticks: 10, tickFormat: "+f" }, y: { ticks: 10, tickFormat: "+f" }, color: { scheme: "magma" }, marks: [ Plot.raster({ fill: (x, y) => quant.dequantize(quant.quantize(x)) * quant.dequantize(quant.quantize(y)), x1: form.beta, y1: form.beta, x2: form.alpha, y2: form.alpha, pixelSize: 4 }), Plot.ruleX([0], { strokeOpacity: 0.2 }), Plot.ruleY([0], { strokeOpacity: 0.2 }), Plot.frame() ] })} ${Plot.plot({ width: 300, height: 300, title: "Diff", color: { legend: true // label: "Diff" }, caption: "xy - quant.dequantize(quant.quantize(x)) * quant.dequantize(quant.quantize(y))", x: { ticks: 10, tickFormat: "+f" }, y: { ticks: 10, tickFormat: "+f" }, color: { scheme: "magma", legend: true }, marks: [ Plot.raster({ fill: (x, y) => x * y - quant.dequantize(quant.quantize(x)) * quant.dequantize(quant.quantize(y)), x1: form.beta, y1: form.beta, x2: form.alpha, y2: form.alpha, pixelSize: 4 }), Plot.ruleX([0], { strokeOpacity: 0.2 }), Plot.ruleY([0], { strokeOpacity: 0.2 }), Plot.frame() ] })} ${Plot.plot({ width: 300, height: 300, title: "Diff + RandNorm", color: { legend: true // label: "Diff" }, caption: "xy - quant.dequantize(quant.quantize(x)) * quant.dequantize(quant.quantize(y)) + e", x: { ticks: 10, tickFormat: "+f" }, y: { ticks: 10, tickFormat: "+f" }, color: { scheme: "magma", legend: true }, marks: [ Plot.raster({ fill: (x, y) => x * y - (quant.dequantize(quant.quantize(x)) * quant.dequantize(quant.quantize(y)) + randNorm()), x1: form.beta, y1: form.beta, x2: form.alpha, y2: form.alpha, pixelSize: 4 }), Plot.ruleX([0], { strokeOpacity: 0.2 }), Plot.ruleY([0], { strokeOpacity: 0.2 }), Plot.frame() ] })}

` 31:[] 2e:{"title":"Quantization","cells":[{"id":4,"value":"# Quantization","pinned":false,"hidden":false,"mode":"md"},{"id":7,"value":"html`

\n${Plot.plot({\n width: 300,\n height: 300,\n style: \"overflow: visible;\",\n y: { grid: true },\n marks: [\n Plot.ruleY([0], { strokeWidth: 0.5 }),\n Plot.ruleX([0], { strokeWidth: 0.5 }),\n // Plot.lineY(data, { y: \"q\", x: \"x\", stroke: \"red\", tip: \"xy\" }),\n Plot.lineY(data, { y: \"dq\", x: \"x\", stroke: \"blue\", tip: \"xy\" })\n // Plot.lineY(data, { y: \"x\", x: \"x\", stroke: \"black\" })\n ]\n})}\n${Plot.plot({\n width: 300,\n height: 300,\n style: \"overflow: visible;\",\n title: \"Diff\",\n y: { grid: true },\n marks: [\n Plot.axisY({ anchor: \"left\", label: \"Quantization Error\" }),\n Plot.ruleY([0], { strokeWidth: 0.5 }),\n Plot.ruleX([0], { strokeWidth: 0.5 }),\n // Plot.lineY(data, { y: \"q\", x: \"x\", stroke: \"red\", tip: \"xy\" }),\n Plot.lineY(data, {\n y: (d) => d[\"x\"] - d[\"dq\"],\n x: \"x\",\n stroke: \"blue\",\n tip: \"xy\"\n })\n // Plot.lineY(data, { y: \"x\", x: \"x\", stroke: \"black\" })\n ]\n})}\n\n

`\n","pinned":false,"hidden":false,"mode":"ojs"},{"id":109,"value":"html`

\n${form.b}\n

`","pinned":false,"hidden":false,"mode":"ojs"},{"id":5,"value":"viewof form = Inputs.form(\n {\n b: Inputs.range([1, 32], { step: 1, label: \"Bits\" }),\n alpha: Inputs.range([0, 1000], { step: 1, label: \"alpha\" }),\n beta: Inputs.range([-1000, 0], { step: 1, label: \"beta\" }),\n N: Inputs.range([0, 100], { step: 1, label: \"N\" }),\n dx: Inputs.range([0, 10], { label: \"dx\" })\n },\n {\n template: (\n inputs\n ) => htl.html`

\n${Object.values(inputs).map(\n (d) => htl.html`

${d}

`\n)}\n

`\n }\n)","pinned":false,"hidden":false,"mode":"ojs"},{"id":181,"value":"form","pinned":true,"hidden":false,"mode":"ojs"},{"id":73,"value":"$30","pinned":false,"hidden":false,"mode":"ojs"},{"id":196,"value":"Plot.plot({\n round: true,\n color: { legend: true },\n title: \"xy Dist\",\n // y: { type: \"log\" },\n // x: { type: \"symlog\" },\n marks: [\n Plot.lineY(\n mulSamples,\n Plot.binX(\n { y: \"count\", filter: null },\n { x: \"xy\", thresholds: 100, stroke: \"blue\", cumulative: false }\n )\n // { }\n ),\n Plot.lineY(\n mulSamples,\n Plot.binX(\n { y: \"count\", filter: null },\n { x: \"dqxy\", thresholds: 100, stroke: \"red\", cumulative: false }\n )\n // { }\n ),\n Plot.ruleY([0])\n // Plot.ruleX([form.alpha]),\n // Plot.ruleX([form.beta])\n ]\n})","pinned":false,"hidden":false,"mode":"ojs"},{"id":223,"value":"Plot.plot({\n round: true,\n color: { legend: true },\n title: \"xy error Dist\",\n // y: { type: \"log\" },\n // x: { type: \"symlog\" },\n marks: [\n Plot.lineY(\n mulSamples,\n Plot.binX(\n { y: \"count\", filter: null },\n { x: \"de\", thresholds: 100, stroke: \"blue\", cumulative: false }\n )\n ),\n Plot.ruleY([0])\n // Plot.ruleX([form.alpha]),\n // Plot.ruleX([form.beta])\n ]\n})","pinned":true,"hidden":false,"mode":"ojs"},{"id":147,"value":"Plot.plot({\n round: true,\n color: { legend: true },\n marks: [\n Plot.lineY(\n samples,\n Plot.binX(\n { y: \"count\", filter: null },\n { x: \"x\", thresholds: 20, stroke: \"blue\", cumulative: true }\n )\n // { }\n ),\n Plot.lineY(\n samples,\n Plot.binX(\n { y: \"count\", filter: null },\n { x: \"dq\", thresholds: 20, stroke: \"red\", cumulative: true }\n )\n // { }\n ),\n Plot.ruleY([0]),\n Plot.ruleX([form.alpha]),\n Plot.ruleX([form.beta])\n ]\n})","pinned":false,"hidden":false,"mode":"ojs"},{"id":193,"value":"mulSamples = data\n .flatMap((x) =>\n data.map((y) => Object.assign({ xy: x.x * y.x, dqxy: x.dq * y.dq }))\n )\n .map((d) => Object.assign(d, { de: d.xy - d.dqxy }))","pinned":false,"hidden":false,"mode":"ojs"},{"id":187,"value":"randNorm = d3.randomNormal(0, quant.s)","pinned":true,"hidden":false,"mode":"ojs"},{"id":149,"value":"sampleRandGen = d3.randomNormal(0, (form.alpha - form.beta) / 2)","pinned":true,"hidden":false,"mode":"ojs"},{"id":152,"value":"samples = new Array(form.N)\n .fill(0)\n .map((d) => sampleRandGen())\n .map((d) =>\n Object.assign({\n x: d,\n q: quant.quantize(d),\n dq: quant.dequantize(quant.quantize(d))\n })\n )","pinned":false,"hidden":false,"mode":"ojs"},{"id":6,"value":"x = d3.ticks(form.beta, form.alpha, form.N)\n// x = d3.range(form.beta, form.alpha, form.dx)","pinned":true,"hidden":false,"mode":"ojs"},{"id":20,"value":"class IntQuant {\n constructor(b, alpha, beta) {\n this.b = b;\n this.alpha = alpha;\n this.beta = beta;\n this.int_low = -Math.pow(2, b - 1);\n this.int_high = Math.pow(2, b - 1) - 1;\n this.s = (this.int_high - this.int_low) / (this.alpha - this.beta);\n this.z = Math.round(this.beta * this.s) - this.int_low;\n }\n\n quantize(x) {\n const q = x * this.s - this.z;\n return Math.min(Math.max(Math.round(q), this.int_low), this.int_high);\n // return Math.round(q);\n }\n\n dequantize(q) {\n const x = (q + this.z) / this.s;\n return x;\n }\n}","pinned":true,"hidden":false,"mode":"ojs"},{"id":24,"value":"quant = new IntQuant(form.b, form.alpha, form.beta)\n// quant = new IntQuant(2, 4, -4)","pinned":true,"hidden":false,"mode":"ojs"},{"id":29,"value":"quant.quantize(-1)","pinned":true,"hidden":false,"mode":"ojs"},{"id":22,"value":"data = x\n .map((d) => {\n return { x: d, q: quant.quantize(d) };\n })\n .map((d) => Object.assign(d, { dq: quant.dequantize(d.q) }))","pinned":true,"hidden":false,"mode":"ojs"}],"files":"$W31","stdlib":"1","titling":"auto"}