Essential Books

Computing large integer roots

suggest change

Even though Python natively supports big integers, taking the nth root of very large numbers can fail in Python. 

x = 2 ** 100
cube = x ** 3
root = cube ** (1.0 / 3)
OverflowError: long int too large to convert to float

When dealing with such large integers, you will need to use a custom function to compute the nth root of a number. 

def nth_root(x, n):
    # Start with some reasonable bounds around the nth root.
    upper_bound = 1
    while upper_bound ** n <= x:
        upper_bound *= 2
    lower_bound = upper_bound // 2
    # Keep searching for a better result as long as the bounds make sense.
    while lower_bound < upper_bound:
        mid = (lower_bound + upper_bound) // 2
        mid_nth = mid ** n
        if lower_bound < mid and mid_nth < x:
            lower_bound = mid
        elif upper_bound > mid and mid_nth > x:
            upper_bound = mid
        else:
            # Found perfect nth root.
            return mid
    return mid + 1

x = 2 ** 100
cube = x ** 3
root = nth_root(cube, 3)
x == root
# True
Found a mistake? Have a question or improvement idea? Let me know.

Feedback about page:

Feedback:
Optional: your email if you want me to get back to you:

Exponentation:
* Exponentiation
* Exponentiation using builtins and pow
* Square root math.sqrt and cmath.sqrt
* Modular exponentiation pow with 3 arguments
* Exponentiation using the math module math.pow
* Exponential function math.exp and cmath.exp
* Exponential function minus 1 math.expm1
* Magic methods and exponentiation builtin math and cmath
* Roots nth-root with fractional exponents
* Computing large integer roots
Table Of Contents
0 Getting Started
1 List comprehension
2 Filter
3 List
4 Functions
5 Decorators
6 Math module
7 Loops
8 Random module
9 Comparisons
10 Importing modules
11 Sorting Minimum and Maximium
12 Operator module
13 Variable Scope and Binding
14 Basic Input and Output
15 Files, Folders, I/O
16 JSON Module
17 String Methods
18 Metaclasses
19 Indexing and Slicing
20 Generators
21 Simple Mathematical Operators
22 Reduce
23 Map Function
24 Exponentation
25 Searching
26 Dictionary
27 Classes
28 Counting
29 Manipulating XML
30 Date and Time
31 Set
32 Collections module
33 Parallel computation
34 Multithreading
35 Writing C extensions
36 Unit Testing
37 Regular Expressions
38 Bitwise Operators
39 Incompatibilities moving from Python 2 to Python 3
40 Virtual environments
41 Copying data
42 Tuple
43 Context Managers with Statement
44 Hidden Features
45 Enum
46 String Formatting
47 Conditionals
48 Complex math
49 Unicode and bytes
50 The __name__ special variable
51 Check if path exists
52 Networking
53 Asyncio Module
54 Print Function
55 os.path module
56 Creating Python packages
57 Parsing Command Line Arguments
58 HTML Parsing
59 Subprocess Library
60 setup.py
61 List slicing
62 Sockets
63 Itertools Module
64 Recursion
65 Boolean Operators
66 dis module
67 Type Hints
68 pip PyPI Package Manager
69 locale module
70 Exceptions
71 Web scraping
72 deque module
73 Distributing self-contained applications
74 Property Objects
75 Overloading
76 Debugging
77 Reading and Writing CSV
78 Dynamic code execution with exec and eval
79 PyInstaller - Distributing Python Code
80 Iterables and Iterators
81 Data Visualization
82 The interpreter command line console
83 args and kwargs
84 functools module
85 Garbage Collection
86 Indentation
87 Security and Cryptograhy
88 Pickle data serialization
89 urllib
90 Binary Data
91 Python and Excel
92 Idioms
93 Method Overriding
94 Difference between a module and a package
95 Data Serialization
96 Python Concurrency
97 RabbitMQ using AMQPStorm
98 PostgreSQL
99 Descriptor
100 Common Pitfalls
101 Multiprocessing
102 Creating temporary files with tempfile
103 Working with ZIP files
104 Stack
105 Profiling
106 User-Defined Methods
107 Working around Global Interpreter Lock
108 Deployment using conda
109 Logging
110 Processes and Threads
111 os module
112 Comments and documentation
113 Database Access
114 Python HTTP Server
115 Alternatives to switch statement from other languages
116 List destructuring
117 Accessing Python source code and bytecode
118 Mixins
119 Attribute Access
120 ArcPy
121 Python Anti-Patterns
122 Plugin and Extension Classes
123 Websockets
124 Immutable data types
125 String representations of class
126 Arrays
127 Operator Precedence
128 Polymorphism
129 Alternative Python implementations
130 List Comprehensions
131 Web Server Gateway Intrerface WSGI
132 2to3 tool
133 Abstract Syntax Tree
134 Abstract Base Classes
135 Unicode
136 ssh in Python
137 Serial Communication with pyserial
138 Neo4j
139 Performance optimization
140 Curses
141 Templates
142 pass statement
143 Testing with py.test
144 Date Formatting
145 heapq
146 tkinter
147 CLI subcommands
148 Defining functions with list arguments
149 SQLite3 module
150 Persistence with pickle
151 Connecting to SQL Server
152 Design Patterns
153 Multidimensional arrays
154 Audio
155 pyglet
156 queue module
157 ijson
158 webbrowser module
159 base64 module
160 Flask
161 Groupby
162 Sockets and Message Encryption / Decryption
163 pygame
164 Input Subset and Output External Data Files using Pandas
165 hashlib
166 Gzip
167 ctypes
168 Creating a Windows Service
169 Mutable vs. Immutable
170 configparser
171 Common Exceptions
172 Optical Character Recognition OCR
173 Python Data Types
174 Partial functions
175 Generating graphs
176 Unzipping Files
177 Functional Programming
178 Python Virtual Environment - virtualenv
179 sys module
180 virtual environment with virtualenvwrapper
181 virtualenvwrapper on Windows
182 Python Requests Post
183 Plotting with Matplotlib
184 Python Lex-Yacc
185 pyaudio
186 shelve
187 pip and PyPI Package Manager
188 Writing to CSV from String or List
189 Raise Custom Errors Exceptions
190 Using loops within functions
191 Contributors