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.
Return x with the sign of y. On a platform that supports signed zeros, copysign(1.0, -0.0) returns -1.0.
New in version 2.6.
Return x factorial. Raises ValueError if x is not integral or is negative.
New in version 2.6.
Return an accurate floating point sum of values in the iterable. Avoids loss of precision by tracking multiple intermediate partial sums:
>>> sum([.1, .1, .1, .1, .1, .1, .1, .1, .1, .1])
0.99999999999999989
>>> fsum([.1, .1, .1, .1, .1, .1, .1, .1, .1, .1])
1.0
The algorithm’s accuracy depends on IEEE-754 arithmetic guarantees and the typical case where the rounding mode is half-even. On some non-Windows builds, the underlying C library uses extended precision addition and may occasionally double-round an intermediate sum causing it to be off in its least significant bit.
For further discussion and two alternative approaches, see the ASPN cookbook recipes for accurate floating point summation.
New in version 2.6.
Check if the float x is positive or negative infinity.
New in version 2.6.
Check if the float x is a NaN (not a number). For more information on NaNs, see the IEEE 754 standards.
New in version 2.6.
Return the Real value x truncated to an Integral (usually a long integer). Uses the __trunc__ method.
New in version 2.6.
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.
With one argument, return the natural logarithm of x (to base e).
With two arguments, return the logarithm of x to the given base, calculated as log(x)/log(base).
Changed in version 2.3: base argument added.
Return the natural logarithm of 1+x (base e). The result is calculated in a way which is accurate for x near zero.
New in version 2.6.
Return x raised to the power y. Exceptional cases follow Annex ‘F’ of the C99 standard as far as possible. In particular, pow(1.0, x) and pow(x, 0.0) always return 1.0, even when x is a zero or a NaN. If both x and y are finite, x is negative, and y is not an integer then pow(x, y) is undefined, and raises ValueError.
Changed in version 2.6: The outcome of 1**nan and nan**0 was undefined.
Return the inverse hyperbolic cosine of x.
New in version 2.6.
Return the inverse hyperbolic sine of x.
New in version 2.6.
Return the inverse hyperbolic tangent of x.
New in version 2.6.
CPython implementation detail: The math module consists mostly of thin wrappers around the platform C math library functions. Behavior in exceptional cases follows Annex F of the C99 standard where appropriate. The current implementation will raise ValueError for invalid operations like sqrt(-1.0) or log(0.0) (where C99 Annex F recommends signaling invalid operation or divide-by-zero), and OverflowError for results that overflow (for example, exp(1000.0)). A NaN will not be returned from any of the functions above unless one or more of the input arguments was a NaN; in that case, most functions will return a NaN, but (again following C99 Annex F) there are some exceptions to this rule, for example pow(float('nan'), 0.0) or hypot(float('nan'), float('inf')).
Note that Python makes no effort to distinguish signaling NaNs from quiet NaNs, and behavior for signaling NaNs remains unspecified. Typical behavior is to treat all NaNs as though they were quiet.
Changed in version 2.6: Behavior in special cases now aims to follow C99 Annex F. In earlier versions of Python the behavior in special cases was loosely specified.
See also