Add pi computation numba example

Author: gjbex

source-code/numba/computing_pi.ipynb

@@ -0,0 +1,176 @@
+{
+ "cells": [
+  {
+   "cell_type": "markdown",
+   "id": "dad1f0e2-bc13-4d67-b40e-e5f8946e7e6f",
+   "metadata": {},
+   "source": [
+    "# Requirements"
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": 1,
+   "id": "694413b5-380c-4239-8bce-09b90df7fe79",
+   "metadata": {},
+   "outputs": [],
+   "source": [
+    "from numba import njit\n",
+    "import numpy as np\n",
+    "import random"
+   ]
+  },
+  {
+   "cell_type": "markdown",
+   "id": "aee5369d-7b69-4fb4-8567-52bd8e92571b",
+   "metadata": {},
+   "source": [
+    "# Random $\\pi$"
+   ]
+  },
+  {
+   "cell_type": "markdown",
+   "id": "70202ae4-ad82-4c91-aea0-a3aeccfb7bdc",
+   "metadata": {},
+   "source": [
+    "Compute $\\pi$ by generating random points in a square and counting how many there are in the circle inscribed in the square."
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": 5,
+   "id": "b5f095c0-58f6-4098-829c-6e696ae2a2bd",
+   "metadata": {},
+   "outputs": [],
+   "source": [
+    "def compute_pi(nr_tries):\n",
+    "    hits = 0\n",
+    "    for _ in range(nr_tries):\n",
+    "        x = random.random()\n",
+    "        y = random.random()\n",
+    "        if x**2 + y**2 < 1.0:\n",
+    "            hits += 1\n",
+    "    return 4.0*hits/nr_tries"
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": 6,
+   "id": "805f4c9f-5d19-486a-988e-bf103683c37c",
+   "metadata": {},
+   "outputs": [],
+   "source": [
+    "@njit\n",
+    "def compute_pi_jit(nr_tries):\n",
+    "    hits = 0\n",
+    "    for _ in range(nr_tries):\n",
+    "        x = random.random()\n",
+    "        y = random.random()\n",
+    "        if x**2 + y**2 < 1.0:\n",
+    "            hits += 1\n",
+    "    return 4.0*hits/nr_tries"
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": 32,
+   "id": "f7a7bb7e-6ad1-4b6d-bb5b-d99ebedf7991",
+   "metadata": {},
+   "outputs": [],
+   "source": [
+    "@njit(['float64(int64)'])\n",
+    "def compute_pi_jit_sign(nr_tries):\n",
+    "    hits = 0\n",
+    "    for _ in range(nr_tries):\n",
+    "        x = random.random()\n",
+    "        y = random.random()\n",
+    "        if x**2 + y**2 < 1.0:\n",
+    "            hits += 1\n",
+    "    return 4.0*hits/nr_tries"
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": 9,
+   "id": "13f3c23d-674e-43b2-b503-a83c20cf5075",
+   "metadata": {},
+   "outputs": [
+    {
+     "name": "stdout",
+     "output_type": "stream",
+     "text": [
+      "27.1 ms ± 277 µs per loop (mean ± std. dev. of 7 runs, 10 loops each)\n"
+     ]
+    }
+   ],
+   "source": [
+    "%timeit compute_pi(100_000)"
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": 10,
+   "id": "de965fa5-b3e3-4548-8d41-661baf6abe65",
+   "metadata": {},
+   "outputs": [
+    {
+     "name": "stdout",
+     "output_type": "stream",
+     "text": [
+      "687 µs ± 9.53 µs per loop (mean ± std. dev. of 7 runs, 1000 loops each)\n"
+     ]
+    }
+   ],
+   "source": [
+    "%timeit compute_pi_jit(100_000)"
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": 34,
+   "id": "f240d35d-2fdb-45db-9e59-d392887c9a16",
+   "metadata": {},
+   "outputs": [
+    {
+     "name": "stdout",
+     "output_type": "stream",
+     "text": [
+      "685 µs ± 8.96 µs per loop (mean ± std. dev. of 7 runs, 1000 loops each)\n"
+     ]
+    }
+   ],
+   "source": [
+    "%timeit compute_pi_jit_sign(np.int64(100_000))"
+   ]
+  },
+  {
+   "cell_type": "markdown",
+   "id": "da96c2f7-afc2-4122-ad80-62d7c57272e9",
+   "metadata": {},
+   "source": [
+    "Using numba's just-in-time compiler significantly speeds up the computations."
+   ]
+  }
+ ],
+ "metadata": {
+  "kernelspec": {
+   "display_name": "Python 3 (ipykernel)",
+   "language": "python",
+   "name": "python3"
+  },
+  "language_info": {
+   "codemirror_mode": {
+    "name": "ipython",
+    "version": 3
+   },
+   "file_extension": ".py",
+   "mimetype": "text/x-python",
+   "name": "python",
+   "nbconvert_exporter": "python",
+   "pygments_lexer": "ipython3",
+   "version": "3.9.7"
+  }
+ },
+ "nbformat": 4,
+ "nbformat_minor": 5
+}