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.

math.ceil(x)

Return the ceiling ofxas a float, the smallest integer value greater than or equal tox.

math.copysign(x, y)

Return

xwith the sign ofy.copysigncopies the sign bit of an IEEE 754 float,copysign(1, -0.0)returns-1.0.New in version 2.6.

math.fabs(x)

Return the absolute value ofx.

math.factorial(x)

Return

xfactorial. RaisesValueErrorifxis not integral or is negative.New in version 2.6.

math.floor(x)

Return the floor of

xas a float, the largest integer value less than or equal tox.Changed in version 2.6: Added

__floor__()delegation.

math.fmod(x, y)

Returnfmod(x, y), as defined by the platform C library. Note that the Python expressionx % ymay not return the same result. The intent of the C standard is thatfmod(x, y)be exactly (mathematically; to infinite precision) equal tox - n*yfor some integernsuch that the result has the same sign asxand magnitude less thanabs(y). Python’sx % yreturns a result with the sign ofyinstead, and may not be exactly computable for float arguments. For example,fmod(-1e-100, 1e100)is-1e-100, but the result of Python’s-1e-100 % 1e100is1e100-1e-100, which cannot be represented exactly as a float, and rounds to the surprising1e100. For this reason, functionfmod()is generally preferred when working with floats, while Python’sx % yis preferred when working with integers.

math.frexp(x)

Return the mantissa and exponent ofxas the pair(m, e).mis a float andeis an integer such thatx == m * 2**eexactly. Ifxis zero, returns(0.0, 0), otherwise0.5 <= abs(m) < 1. This is used to “pick apart” the internal representation of a float in a portable way.

math.fsum(iterable)

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]) 1.0The 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.

math.isinf(x)

Checks if the float

xis positive or negative infinite.New in version 2.6.

math.isnan(x)

Checks if the float

xis a NaN (not a number). NaNs are part of the IEEE 754 standards. Operation like but not limited toinf * 0,inf / infor any operation involving a NaN, e.g.nan * 1, return a NaN.New in version 2.6.

math.ldexp(x, i)

Returnx * (2**i). This is essentially the inverse of functionfrexp().

math.modf(x)

Return the fractional and integer parts ofx. Both results carry the sign ofxand are floats.

math.trunc(x)

Return the

Realvaluextruncated to anIntegral(usually a long integer). Delegates tox.__trunc__().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.

math.exp(x)

Returne**x.

math.log(x[, base])

Return the logarithm of

xto the givenbase. If thebaseis not specified, return the natural logarithm ofx(that is, the logarithm to basee).Changed in version 2.3:

baseargument added.

math.log1p(x)

Return the natural logarithm of

1+x(basee). The result is calculated in a way which is accurate forxnear zero.New in version 2.6.

math.log10(x)

Return the base-10 logarithm ofx.

math.pow(x, y)

Return

xraised to the powery. Exceptional cases follow Annex ‘F’ of the C99 standard as far as possible. In particular,pow(1.0, x)andpow(x, 0.0)always return1.0, even whenxis a zero or a NaN. If bothxandyare finite,xis negative, andyis not an integer thenpow(x, y)is undefined, and raisesValueError.Changed in version 2.6: The outcome of

1**nanandnan**0was undefined.

math.sqrt(x)

Return the square root ofx.

math.acos(x)

Return the arc cosine ofx, in radians.

math.asin(x)

Return the arc sine ofx, in radians.

math.atan(x)

Return the arc tangent ofx, in radians.

math.atan2(y, x)

Returnatan(y / x), in radians. The result is between-piandpi. The vector in the plane from the origin to point(x, y)makes this angle with the positive X axis. The point ofatan2()is that the signs of both inputs are known to it, so it can compute the correct quadrant for the angle. For example,atan(1) andatan2(1, 1)are bothpi/4, butatan2(-1, -1)is-3*pi/4.

math.cos(x)

Return the cosine ofxradians.

math.hypot(x, y)

Return the Euclidean norm,sqrt(x*x + y*y). This is the length of the vector from the origin to point(x, y).

math.sin(x)

Return the sine ofxradians.

math.tan(x)

Return the tangent ofxradians.

math.degrees(x)

Converts anglexfrom radians to degrees.

math.radians(x)

Converts anglexfrom degrees to radians.

math.acosh(x)

Return the inverse hyperbolic cosine of

x.New in version 2.6.

math.asinh(x)

Return the inverse hyperbolic sine of

x.New in version 2.6.

math.atanh(x)

Return the inverse hyperbolic tangent of

x.New in version 2.6.

math.cosh(x)

Return the hyperbolic cosine ofx.

math.sinh(x)

Return the hyperbolic sine ofx.

math.tanh(x)

Return the hyperbolic tangent ofx.

math.pi

The mathematical constantpi.

math.e

The mathematical constante.

- Note: The
`math`module consists mostly of thin wrappers around the platform C math library functions. Behavior in exceptional cases is loosely specified by the C standards, and Python inherits much of its math-function error-reporting behavior from the platform C implementation. As a result, the specific exceptions raised in error cases (and even whether some arguments are considered to be exceptional at all) are not defined in any useful cross-platform or cross-release way. For example, whether

`math.log(0)`returns`-Inf`or raises`ValueError`or`OverflowError`isn’t defined, and in cases where`math.log(0)`raises`OverflowError`,`math.log(0L)`may raise`ValueError`instead.All functions return a quiet*NaN*if at least one of the args is*NaN*. Signaling*NaN*s raise an exception. The exception type still depends on the platform and libm implementation. It’s usually ``ValueError`` for *EDOM*and`OverflowError`for errno*ERANGE*.Changed in version 2.6: In earlier versions of Python the outcome of an operation with NaN as input depended on platform and libm implementation.

See also:

- Module
cmath- Complex number versions of many of these functions.