2.1.4 Numeric Types

There are four numeric types: plain integers, long integers, floating point numbers, and complex numbers. Plain integers (also just called integers) are implemented using long in C, which gives them at least 32 bits of precision. 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 both 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. 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.

Python fully supports mixed arithmetic: when a binary arithmetic operator has operands of different numeric types, the operand with the ``smaller'' type is converted to that of the other, where plain integer is smaller than long integer is smaller than floating point is smaller than complex. Comparisons between numbers of mixed type use the same rule.^2.3 The functions int(), long(), float(), and complex() can be used to coerce numbers to a specific type.

All numeric types 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 remainder of x / y
-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)
pow(x, y) x to the power y
x ** y x to the power y

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`	remainder of `x / y`
`-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)
`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 mathmodule for well-defined conversions.
(3): See section 2.3, ``Built-in Functions,'' for a full description.

Footnotes

... rule.^2.3: As a consequence, the list [1, 2] is considered equal to [1.0, 2.0], and similar for tuples.

Subsections

2.1.4.1 Bit-string Operations on Integer Types

See About this document... for information on suggesting changes.

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