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Exponential function minus 1 math.expm1

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The math module contains the expm1()-function that can compute the expression math.e ** x - 1 for very small x with higher precision than math.exp(x) or cmath.exp(x) would allow: 

import math

print(math.e ** 1e-3 - 1)  # 0.0010005001667083846
print(math.exp(1e-3) - 1)  # 0.0010005001667083846
print(math.expm1(1e-3))    # 0.0010005001667083417
#                            ------------------^

For very small x the difference gets bigger: 

print(math.e ** 1e-15 - 1) # 1.1102230246251565e-15
print(math.exp(1e-15) - 1) # 1.1102230246251565e-15
print(math.expm1(1e-15))   # 1.0000000000000007e-15
#                              ^-------------------

The improvement is significant in scientic computing. For example the Planck’s law contains an exponential function minus 1: 

def planks_law(lambda_, T):
    from scipy.constants import h, k, c  # If no scipy installed hardcode these!
    return 2 * h * c ** 2 / (lambda_ ** 5 * math.expm1(h * c / (lambda_ * k * T)))

def planks_law_naive(lambda_, T):
    from scipy.constants import h, k, c  # If no scipy installed hardcode these!
    return 2 * h * c ** 2 / (lambda_ ** 5 * (math.e ** (h * c / (lambda_ * k * T)) - 1))

planks_law(100, 5000)        # 4.139080074896474e-19
planks_law_naive(100, 5000)  # 4.139080073488451e-19
#                                        ^---------- 

planks_law(1000, 5000)       # 4.139080128493406e-23
planks_law_naive(1000, 5000) # 4.139080233183142e-23
#                                      ^------------
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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
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40 Virtual environments
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68 pip PyPI Package Manager
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73 Distributing self-contained applications
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76 Debugging
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79 PyInstaller - Distributing Python Code
80 Iterables and Iterators
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83 args and kwargs
84 functools module
85 Garbage Collection
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88 Pickle data serialization
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91 Python and Excel
92 Idioms
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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
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107 Working around Global Interpreter Lock
108 Deployment using conda
109 Logging
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111 os module
112 Comments and documentation
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114 Python HTTP Server
115 Alternatives to switch statement from other languages
116 List destructuring
117 Accessing Python source code and bytecode
118 Mixins
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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
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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
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170 configparser
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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