Python Programming/Numbers

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Python 2.x supports 4 built-in numeric types - int, long, float and complex. Of these, the long type has been dropped in Python 3.x - the int type is now of unlimited length by default. You don’t have to specify what type of variable you want; Python does that automatically.

  • Int: The basic integer type in python, equivalent to the hardware 'c long' for the platform you are using in Python 2.x, unlimited in length in Python 3.x.
  • Long: Integer type with unlimited length. In python 2.2 and later, Ints are automatically turned into long ints when they overflow. Dropped since Python 3.0, use int type instead.
  • Float: This is a binary floating point number. Longs and Ints are automatically converted to floats when a float is used in an expression, and with the true-division / operator. In CPython, floats are usually implemented using the C languages double, which often yields 52 bits of significand, 11 bits of exponent, and 1 sign bit, but this is machine dependent.
  • Complex: This is a complex number consisting of two floats. Complex literals are written as a + bj where a and b are floating-point numbers denoting the real and imaginary parts respectively.

In general, the number types are automatically 'up cast' in this order:

Int → Long → Float → Complex. The farther to the right you go, the higher the precedence.

>>> x = 5
>>> type(x)
<type 'int'>
>>> x = 187687654564658970978909869576453
>>> type(x)
<type 'long'>
>>> x = 1.34763
>>> type(x)
<type 'float'>
>>> x = 5 + 2j
>>> type(x)
<type 'complex'>

The result of divisions is somewhat confusing. In Python 2.x, using the / operator on two integers will return another integer, using floor division. For example, 5/2 will give you 2. You have to specify one of the operands as a float to get true division, e.g. 5/2. or 5./2 (the dot specifies you want to work with float) will yield 2.5. Starting with Python 2.2 this behavior can be changed to true division by the future division statement from __future__ import division. In Python 3.x, the result of using the / operator is always true division (you can ask for floor division explicitly by using the // operator since Python 2.2).

This illustrates the behavior of the / operator in Python 2.2+:

>>> 5/2
>>> 5/2.
>>> 5./2
>>> from __future__ import division
>>> 5/2
>>> 5//2

For operations on numbers, see chapters Basic Math and Math.

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