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‎_quarto.yml

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html:
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theme:
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light: cosmo
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dark: darkly
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dark: darkly # https://github.com/quarto-dev/quarto-cli/issues/6741
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css: styles.css

‎blog+gist.qmd

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---
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title: "All blogs and gists."
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listing:
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contents: "posts/**/*.qmd"
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contents: ["posts/**/*.qmd", "posts/**/*.ipynb"]
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sort: "date desc"
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fields: [date, title, reading-time]
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type: table

‎gist.qmd

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title: "Gist collection."
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listing:
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contents: "posts/**/*gist.qmd"
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contents: ["posts/**/*gist.qmd", "posts/**/*gist.ipynb"]
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sort: "date desc"
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fields: [date, title, reading-time]
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type: table

‎index.qmd

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---
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title: "Blogs"
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listing:
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contents: posts/**/*[!gist].qmd
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contents: ["posts/**/*[!gist].qmd", "posts/**/*[!gist].ipynb"]
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sort: "date desc"
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type: default
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categories: true

‎posts/2024-09-26-Float64/index-gist.ipynb

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{
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"cells": [
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{
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"cell_type": "raw",
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"id": "6ef206bd",
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"metadata": {
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"vscode": {
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"languageId": "raw"
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}
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},
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"source": [
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"---\n",
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"title: \"`exp(x)` overflow/underflow in Numpy (float64)\"\n",
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"date: \"2024-09-26\"\n",
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"date-modified: last-modified\n",
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"categories: [Numpy, Python]\n",
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"format:\n",
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" html: default\n",
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"execute: \n",
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" enabled: true\n",
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"---"
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]
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},
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{
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"cell_type": "code",
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"execution_count": 1,
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"id": "65950641",
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"metadata": {},
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"outputs": [
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{
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"name": "stdout",
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"output_type": "stream",
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"text": [
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"Numpy float info: Machine parameters for float64\n",
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"---------------------------------------------------------------\n",
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"precision = 15 resolution = 1.0000000000000001e-15\n",
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"machep = -52 eps = 2.2204460492503131e-16\n",
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"negep = -53 epsneg = 1.1102230246251565e-16\n",
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"minexp = -1022 tiny = 2.2250738585072014e-308\n",
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"maxexp = 1024 max = 1.7976931348623157e+308\n",
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"nexp = 11 min = -max\n",
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"smallest_normal = 2.2250738585072014e-308 smallest_subnormal = 4.9406564584124654e-324\n",
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"---------------------------------------------------------------\n",
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"\n"
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]
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}
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],
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"source": [
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"# | code-fold: true\n",
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"import numpy as np\n",
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"\n",
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"np.seterr(all=\"ignore\")\n",
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"print(\"Numpy float info:\", np.finfo(float))"
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]
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},
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{
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"cell_type": "code",
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"execution_count": 2,
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"id": "a2453c9d",
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"metadata": {},
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"outputs": [],
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"source": [
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"# | code-fold: true\n",
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"\n",
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"# Binary search: find the minimal integer x such that np.exp(x) is not zero\n",
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"def find_minimal_exp_x():\n",
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" left = -10000\n",
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" right = 0\n",
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" while right - left > 1:\n",
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" mid = (left + right) // 2\n",
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" if np.exp(mid) == 0:\n",
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" left = mid\n",
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" else:\n",
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" right = mid\n",
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" return right\n",
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"\n",
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"\n",
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"min_int = find_minimal_exp_x()\n",
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"\n",
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"\n",
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"# Binary search: find the maximal integer x such that np.exp(x) is not infinity\n",
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"def find_maximal_exp_x():\n",
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" left = 0\n",
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" right = 10000\n",
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" while right - left > 1:\n",
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" mid = (left + right) // 2\n",
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" if np.exp(mid) != np.inf:\n",
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" left = mid\n",
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" else:\n",
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" right = mid\n",
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" return right\n",
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"\n",
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"\n",
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"max_int = find_maximal_exp_x()"
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]
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},
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{
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"cell_type": "code",
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"execution_count": 3,
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"id": "728c922f",
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"metadata": {},
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"outputs": [
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{
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"name": "stdout",
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"output_type": "stream",
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"text": [
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"np.exp(-746) = 0.0\n",
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"np.exp(-745) = 5e-324\n"
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]
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}
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],
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"source": [
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"print(f\"np.exp({min_int - 1}) = {np.exp(min_int - 1)}\")\n",
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"print(f\"np.exp({min_int}) = {np.exp(min_int)}\")"
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]
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},
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{
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"cell_type": "code",
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"execution_count": 4,
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"id": "0b9d06a5",
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"metadata": {},
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"outputs": [
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{
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"name": "stdout",
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"output_type": "stream",
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"text": [
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"np.exp(709) = 8.218407461554972e+307\n",
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"np.exp(710) = inf\n"
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]
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}
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],
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"source": [
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"print(f\"np.exp({max_int - 1}) = {np.exp(max_int - 1)}\")\n",
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"print(f\"np.exp({max_int}) = {np.exp(max_int)}\")"
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]
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}
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],
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"metadata": {
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"kernelspec": {
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"display_name": "Python 3 (ipykernel)",
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"language": "python",
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"name": "python3"
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},
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"language_info": {
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"codemirror_mode": {
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"name": "ipython",
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"version": 3
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},
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"file_extension": ".py",
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"mimetype": "text/x-python",
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"name": "python",
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"nbconvert_exporter": "python",
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"pygments_lexer": "ipython3",
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"version": "3.9.13"
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}
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},
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"nbformat": 4,
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"nbformat_minor": 5
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}

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