This module is always available. It provides access to the mathematical functions defined by the C standard.
These functions cannot be used with complex numbers; use the functions of the same name from the cmath module if you require support for complex numbers. The distinction between functions which support complex numbers and those which don't is made since most users do not want to learn quite as much mathematics as required to understand complex numbers. Receiving an exception instead of a complex result allows earlier detection of the unexpected complex number used as a parameter, so that the programmer can determine how and why it was generated in the first place.
The following functions are provided by this module. Except when explicitly noted otherwise, all return values are floats.
Number-theoretic and representation functions:
fmod(x, y), as defined by the platform C library. Note that the Python expression
x % ymay not return the same result. The intent of the C standard is that
fmod(x, y)be exactly (mathematically; to infinite precision) equal to
x - n*yfor some integer n such that the result has the same sign as x and magnitude less than
x % yreturns a result with the sign of y instead, and may not be exactly computable for float arguments. For example,
-1e-100, but the result of Python's
-1e-100 % 1e100is
1e100-1e-100, which cannot be represented exactly as a float, and rounds to the surprising
1e100. For this reason, function fmod() is generally preferred when working with floats, while Python's
x % yis preferred when working with integers.
(m, e). m is a float and e is an integer such that
x == m * 2**eexactly. If x is zero, returns
(0.0, 0), otherwise
0.5 <= abs(m) < 1. This is used to "pick apart" the internal representation of a float in a portable way.
x * (2**i). This is essentially the inverse of function frexp().
Note that frexp() and modf() have a different call/return pattern than their C equivalents: they take a single argument and return a pair of values, rather than returning their second return value through an `output parameter' (there is no such thing in Python).
For the ceil(), floor(), and modf()
functions, note that all floating-point numbers of sufficiently
large magnitude are exact integers. Python floats typically carry no more
than 53 bits of precision (the same as the platform C double type), in
which case any float x with
abs(x) >= 2**52
necessarily has no fractional bits.
Power and logarithmic functions:
atan(y / x), in radians. The result is between
pi. The vector in the plane from the origin to point
(x, y)makes this angle with the positive X axis. The point of atan2() is that the signs of both inputs are known to it, so it can compute the correct quadrant for the angle. For example,
atan2(1, 1)are both
sqrt(x*x + y*y). This is the length of the vector from the origin to point
The module also defines two mathematical constants:
-Infor raises ValueError or OverflowError isn't defined, and in cases where
math.log(0L)may raise ValueError instead.