circles.ipynb

{
 "cells": [
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# How fast can we generate points on a circle?"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": [
    "{-# LANGUAGE NoMonomorphismRestriction #-}\n",
    "{-# LANGUAGE FlexibleContexts          #-}\n",
    "{-# LANGUAGE TypeFamilies              #-}\n",
    ":opt no-lint\n",
    "\n",
    "import FMorph\n",
    "import Diagrams.Prelude"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 65,
   "metadata": {},
   "outputs": [],
   "source": [
    "drawCircle = draw . (scalePts 100) "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 66,
   "metadata": {},
   "outputs": [],
   "source": [
    "-- naive:\n",
    "acircle1 n = map (\\t ->\n",
    "                    (cos (t * tau), sin (t * tau)))\n",
    "                $ linspace n\n",
    "\n",
    "-- using circle symmetries:\n",
    "-- 1/8 as many iterationss, give or take\n",
    "acircle2 n = concatMap (\\t ->\n",
    "                    let x = cos (t * pi / 4) \n",
    "                        y = sin (t * pi / 4)\n",
    "                    in [(x, y), (y, x), \n",
    "                        (-x, y), (y, -x),\n",
    "                        (x, -y), (-y, x),\n",
    "                        (-x, -y), (-y, -x)])\n",
    "                $ linspace n\n",
    "\n",
    "-- getting rid of one costly 'sin'\n",
    "acircle3 n = concatMap (\\t ->\n",
    "                    let x = cos (t * pi / 4) \n",
    "                        y = sqrt (1 - x ** 2) -- still costly\n",
    "                    in [(x, y), (y, x), \n",
    "                        (-x, y), (y, -x),\n",
    "                        (x, -y), (-y, x),\n",
    "                        (-x, -y), (-y, -x)])\n",
    "                $ linspace n\n",
    "                \n",
    "-- to be continued..\n",
    "acircle4 n = undefined"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 67,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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"
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "diagram $ ( (drawCircle (acircle1 50)) |||\n",
    "            (drawCircle (acircle2 50)) |||\n",
    "            (drawCircle (acircle3 50)) )"
   ]
  }
 ],
 "metadata": {
  "kernelspec": {
   "display_name": "Haskell",
   "language": "haskell",
   "name": "haskell"
  },
  "language_info": {
   "codemirror_mode": "ihaskell",
   "file_extension": ".hs",
   "name": "haskell",
   "version": "8.2.2"
  }
 },
 "nbformat": 4,
 "nbformat_minor": 2
}