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3.4 Numeric Types -- `int`, `float`, `long`, `complex`

There are four distinct numeric types: plain integers, long integers, floating point numbers, and complex numbers. In addition, Booleans are a subtype of plain integers. Plain integers (also just called integers) are implemented using `long` in C, which gives them at least 32 bits of precision (`sys.maxint` is always set to the maximum plain integer value for the current platform, the minimum value is `-sys.maxint - 1`). Long integers have unlimited precision. Floating point numbers are implemented using `double` in C. All bets on their precision are off unless you happen to know the machine you are working with.

Complex numbers have a real and imaginary part, which are each implemented using `double` in C. To extract these parts from a complex number z, use `z.real` and `z.imag`.

Numbers are created by numeric literals or as the result of built-in functions and operators. Unadorned integer literals (including hex and octal numbers) yield plain integers unless the value they denote is too large to be represented as a plain integer, in which case they yield a long integer. Integer literals with an "`L`" or "`l`" suffix yield long integers ("`L`" is preferred because "`1l`" looks too much like eleven!). Numeric literals containing a decimal point or an exponent sign yield floating point numbers. Appending "`j`" or "`J`" to a numeric literal yields a complex number with a zero real part. A complex numeric literal is the sum of a real and an imaginary part.

Python fully supports mixed arithmetic: when a binary arithmetic operator has operands of different numeric types, the operand with the ``narrower'' type is widened to that of the other, where plain integer is narrower than long integer is narrower than floating point is narrower than complex. Comparisons between numbers of mixed type use the same rule.3.2 The constructors `int()`, `long()`, `float()`, and `complex()` can be used to produce numbers of a specific type.

All numeric types (except complex) support the following operations, sorted by ascending priority (operations in the same box have the same priority; all numeric operations have a higher priority than comparison operations):

Operation | Result | Notes
--- | --- | ---
`x + y` | sum of x and y |
`x - y` | difference of x and y |
`x * y` | product of x and y |
`x / y` | quotient of x and y | (1)
`x // y` | (floored) quotient of x and y | (5)
`x % y` | remainder of `x / y` | (4)
`-x` | x negated |
`+x` | x unchanged |
`abs(x)` | absolute value or magnitude of x |
`int(x)` | x converted to integer | (2)
`long(x)` | x converted to long integer | (2)
`float(x)` | x converted to floating point |
`complex(re,im)` | a complex number with real part re, imaginary part im. im defaults to zero. |
`c.conjugate()` | conjugate of the complex number c |
`divmod(x, y)` | the pair `(x // y, x % y)` | (3)(4)
`pow(x, y)` | x to the power y |
`x ** y` | x to the power y |

Notes:

(1)
  For (plain or long) integer division, the result is an integer. The result is always rounded towards minus infinity: 1/2 is 0, (-1)/2 is -1, 1/(-2) is -1, and (-1)/(-2) is 0. Note that the result is a long integer if either operand is a long integer, regardless of the numeric value.

(2)
  Conversion from floating point to (long or plain) integer may round or truncate as in C; see functions `floor()` and `ceil()` in the `math` module for well-defined conversions.

(3)
  See section 2.1, ``Built-in Functions,'' for a full description.

(4)
  Complex floor division operator, modulo operator, and `divmod()`.

  Deprecated since release 2.3. Instead convert to float using `abs()` if appropriate.

(5)
  Also referred to as integer division. The resultant value is a whole integer, though the result's type is not necessarily int.

#### Footnotes

... rule.3.2
  As a consequence, the list `[1, 2]` is considered equal to `[1.0, 2.0]`, and similarly for tuples.