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14.1 decimal

The Python float data type is represented using a double-precision binary floating-point encoding (usually as defined by the IEEE 754 standard). A subtle consequence of this encoding is that decimal values such as 0.1 can’t be represented exactly. Instead, the closest value is 0.10000000000000001.

The decimal module provides an implementation of the IBM General Decimal Arithmetic Standard, which allows for the exact representation of decimals. It also gives precise control over mathematical precision, significant digits, and rounding behavior.

The decimal module defines two basic data types: a Decimal type that represents a decimal number and a Context type that represents various parameters concerning computation such as precision and round-off error-handling.

>>> from decimal import *
>>> getcontext().prec = 6
>>> Decimal(1) / Decimal(7)
Decimal('0.142857')
>>> getcontext().prec = 28
>>> Decimal(1) / Decimal(7)
Decimal('0.1428571428571428571428571429')

Normally, new Context objects aren’t created directly. Instead, the function getcontext() or localcontext() is used to return the currently active Context object.

The decimal context is unique to each thread. Changes to the context only affect that thread and not others.

14.2 fractions

The fractions module defines a class Fraction that represents a rational number. An instance f of Fraction supports all of the usual mathematical operations.

>>> from fractions import Fraction
>>> Fraction(16, -10)
Fraction(-8, 5)
>>> Fraction(123)
Fraction(123, 1)

14.3 math

The math module defines the following standard mathematical functions. These functions operate on integers and floats but don't work with complex numbers (a seperate module cmath can).

  • acos(x)
  • ceil(x)
  • exp(x)
  • isinf(x)

14.4 numbers

The numbers module defines a series of abstract base classes that serve to organize various kinds of numbers.

  • Number, A class that serves as the top of the numeric hierarchy.
  • Complex, A class, inherits from Number, that represents the complex numbers, with real and imag attributes.
  • Real, Inherits from Complex.
  • Rational, Inherits from Real.
  • Integral, Inherits from Rational. “The classes in this module are not meant to be instantiated. Instead, they can be used to perform various kinds of type checks on values”

The classes in this module are not meant to be instantiated. Instead, they can be used to perform various kinds of type checks on values.

14.5 random

The random module provides a variety of functions for generating pseudo-random numbers as well as functions for randomly generating values according to various distributions on the real numbers.

Note, The functions in this module are not thread-safe.

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