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gjbexgjbex
committedMar 25, 2022
Add notebook comparing classic and lazy prime number generation
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‎source-code/prime_time.ipynb

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{
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"cells": [
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{
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"cell_type": "markdown",
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"id": "fc3b2761-8665-477a-8bfc-58bdf2ac4f7a",
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"metadata": {},
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"source": [
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"# Requirements"
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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": "47182c93-a8f7-4772-9a9c-e58a433d02ba",
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"metadata": {},
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"outputs": [],
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"source": [
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"import itertools\n",
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"import math"
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]
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},
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{
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"cell_type": "markdown",
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"id": "4e0adefe-f566-4a81-a0df-0b5d0c7604cf",
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"metadata": {},
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"source": [
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"# Precomputed sieve"
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]
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},
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{
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"cell_type": "markdown",
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"id": "0f0a2be6-515a-4d25-a5c8-67b9dfefe69a",
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"metadata": {},
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"source": [
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"The sieve of Eratosthenes is computed and stored in a list. The overall implementation is a generator for convenience."
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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": "b6c3ba8e-e5c5-4a3a-b059-02fa0283776a",
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"metadata": {},
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"outputs": [],
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"source": [
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"def prime_numbers_precomputed(max_n):\n",
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" sieve = [True]*(max_n + 1)\n",
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" sieve[0], sieve[1] = False, False\n",
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" for n in range(2, math.isqrt(max_n) + 1):\n",
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" if sieve[n]:\n",
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" for non_prime in range(2*n, max_n + 1, n):\n",
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" sieve[non_prime] = False\n",
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" yield from (n for n, is_prime in enumerate(sieve) if is_prime)"
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]
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},
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{
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"cell_type": "markdown",
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"id": "3ad4ec7f-303b-4980-8405-db68f8e86339",
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"metadata": {},
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"source": [
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"Generate prime numbers upto 50."
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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": "a1ee6b85-5af0-4f4a-9a70-e1f08d177349",
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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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"2\n",
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"3\n",
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"5\n",
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"7\n",
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"11\n",
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"13\n",
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"17\n",
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"19\n",
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"23\n",
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"29\n",
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"31\n",
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"37\n",
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"41\n",
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"43\n",
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"47\n"
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]
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}
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],
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"source": [
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"for prime in prime_numbers_precomputed(50):\n",
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" print(prime)"
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]
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},
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{
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"cell_type": "markdown",
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"id": "6eef26fa-d00d-4fab-a8d7-08ffc52590bd",
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"metadata": {},
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"source": [
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"# Sieve using generators"
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]
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},
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{
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"cell_type": "markdown",
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"id": "54049286-713e-48fa-a1fb-44078942d348",
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"metadata": {},
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"source": [
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"Implementation using generators, entirely lazy."
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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": 5,
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"id": "ab70534d-688f-46f4-8b30-44bf1e34ab5b",
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"metadata": {},
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"outputs": [],
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"source": [
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"def prime_numbers():\n",
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" def prime_number_sieve(numbers):\n",
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" prime = next(numbers)\n",
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" yield prime\n",
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" yield from (n for n in numbers if n % prime != 0)\n",
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" yield 2\n",
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" yield from prime_number_sieve(itertools.count(3, 2))"
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]
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},
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{
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"cell_type": "markdown",
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"id": "b54d4fd3-4e5a-4556-9bac-85da2ceb9e19",
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"metadata": {},
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"source": [
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"Again, generating the prime numbers up to 50."
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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": 7,
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"id": "d67bb1fe-8e55-45b0-aace-36ab4397acb0",
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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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"2\n",
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"3\n",
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"5\n",
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"7\n",
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"11\n",
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"13\n",
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"17\n",
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"19\n",
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"23\n",
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"25\n",
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"29\n",
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"31\n",
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"35\n",
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"37\n",
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"41\n",
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"43\n",
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"47\n",
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"49\n"
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]
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}
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],
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"source": [
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"for prime in prime_numbers():\n",
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" if prime <= 50:\n",
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" print(prime)\n",
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" else:\n",
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" break"
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]
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},
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{
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"cell_type": "markdown",
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"id": "edf1943a-31b2-4a4e-bf96-47ea2875b567",
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"metadata": {},
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"source": [
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"# Comparing performance"
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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": 10,
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"id": "83d6696e-b31c-4dbc-9b0c-702c9aedc4a9",
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"metadata": {},
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"outputs": [],
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"source": [
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"max_n = 1_000_000"
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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": 11,
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"id": "bbea5e94-d82a-4be9-b4f4-152a8136c608",
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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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"80.4 ms ± 2.83 ms per loop (mean ± std. dev. of 7 runs, 10 loops each)\n"
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]
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}
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],
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"source": [
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"%%timeit\n",
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"numbers = []\n",
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"for prime in prime_numbers_precomputed(max_n):\n",
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" if prime <= max_n:\n",
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" numbers.append(prime)\n",
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" else:\n",
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" break"
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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": 12,
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"id": "351d9f27-6d04-4d70-b8e3-451d223f64a4",
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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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"46.9 ms ± 1.48 ms per loop (mean ± std. dev. of 7 runs, 10 loops each)\n"
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]
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}
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],
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"source": [
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"%%timeit\n",
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"numbers = []\n",
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"for prime in prime_numbers():\n",
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" if prime <= max_n:\n",
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" numbers.append(prime)\n",
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" else:\n",
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" break"
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]
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},
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{
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"cell_type": "markdown",
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"id": "1111d621-2f13-456c-ba62-a493df7fdc64",
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"metadata": {},
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"source": [
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"Interestingly, the lazy implementation is faster by a substantial factor, perhaps this could be improved by using a different data representation for the precomputed sieve."
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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": "3.9.7"
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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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