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Integers
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‎Integers.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": "2fcc44e4",
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"metadata": {},
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"source": [
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"### Integers are objects - instances of the int class."
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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": "58bfe28e",
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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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"<class 'int'>\n"
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]
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}
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],
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"source": [
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"print(type(100))"
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]
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},
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{
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"cell_type": "markdown",
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"id": "d8804491",
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"metadata": {},
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"source": [
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"They are a variable length data type that can theoretically handle any integer magnitude. This will take up a variable amount of memory that depends on the particular size of the integer."
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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": "a57cbc3b",
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"metadata": {},
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"outputs": [],
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"source": [
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"import sys"
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]
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},
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{
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"cell_type": "markdown",
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"id": "da285253",
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"metadata": {},
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"source": [
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"### Creating an integer object requires an overhead of 24 bytes:"
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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": "dcbe7547",
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"metadata": {},
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"outputs": [
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{
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"data": {
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"text/plain": [
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"24"
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]
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},
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"execution_count": 3,
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"metadata": {},
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"output_type": "execute_result"
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}
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],
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"source": [
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"sys.getsizeof(0)"
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]
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},
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{
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"cell_type": "markdown",
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"id": "bc5d5dd4",
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"metadata": {},
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"source": [
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"### Here we see that to store the number 1 required 4 bytes (32 bits) on top of the 24 byte overhead."
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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": "5b299861",
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"metadata": {},
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"outputs": [
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{
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"data": {
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"text/plain": [
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"28"
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]
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},
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"execution_count": 4,
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"metadata": {},
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"output_type": "execute_result"
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}
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],
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"source": [
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"sys.getsizeof(1)"
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]
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},
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{
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"cell_type": "markdown",
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"id": "75a16990",
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"metadata": {},
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"source": [
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"Larger numbers will require more storage space."
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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": 6,
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"id": "732d72fc",
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"metadata": {},
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"outputs": [
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{
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"data": {
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"text/plain": [
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"160"
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]
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},
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"execution_count": 6,
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"metadata": {},
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"output_type": "execute_result"
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}
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],
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"source": [
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"sys.getsizeof(2**1000)"
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]
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},
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{
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"cell_type": "markdown",
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"id": "079cfe0f",
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"metadata": {},
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"source": [
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"### Larger integers will also slow down calculations."
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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": 9,
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"id": "546f4497",
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"metadata": {},
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"outputs": [],
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"source": [
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"import time"
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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": "4918c5d7",
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"metadata": {},
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"outputs": [],
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"source": [
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"def calc(a):\n",
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" for i in range(10000000):\n",
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" a * 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": "a3f02850",
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"metadata": {},
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"source": [
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"We start with a small integer value for a (10):"
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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": "5bdc40d4",
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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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"0.8892209999999636\n"
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]
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}
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],
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"source": [
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"start = time.perf_counter()\n",
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"calc(10)\n",
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"end = time.perf_counter()\n",
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"print(end - start)"
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]
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},
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{
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"cell_type": "markdown",
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"id": "cf3ba121",
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"metadata": {},
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"source": [
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"### Now we set a to something larger (2^100)):"
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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": 13,
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"id": "efd8a237",
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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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"1.5697594000000095\n"
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]
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}
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],
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"source": [
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"start = time.perf_counter()\n",
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"calc(2**100)\n",
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"end = time.perf_counter()\n",
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"print(end - start)"
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]
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},
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{
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"cell_type": "markdown",
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"id": "1eda1abc",
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"metadata": {},
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"source": [
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"### Finally we set a to some really large value (2^10,000)"
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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": 14,
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"id": "5928ae07",
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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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"8.066712399999972\n"
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]
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}
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],
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"source": [
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"start = time.perf_counter()\n",
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"calc(2**10000)\n",
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"end = time.perf_counter()\n",
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"print(end - start)"
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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": "3.9.12"
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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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