math — Mathematical functions
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.
Numbertheoretic and representation functions:

math.ceil(x)
 Return the ceiling of x as a float, the smallest integer value greater than or
equal to x.

math.copysign(x, y)
Return x with the sign of y. copysign copies 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 of x.

math.factorial(x)
Return x factorial. Raises ValueError if x is not integral or
is negative.
New in version 2.6.

math.floor(x)
Return the floor of x as a float, the largest integer value less than or equal
to x.
Changed in version 2.6: Added __floor__() delegation.

math.fmod(x, y)
 Return fmod(x, y), as defined by the platform C library. Note that the
Python expression x % y may 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*y for some integer n such that the result has
the same sign as x and magnitude less than abs(y). Python’s x % y
returns a result with the sign of y instead, and may not be exactly computable
for float arguments. For example, fmod(1e100, 1e100) is 1e100, but
the result of Python’s 1e100 % 1e100 is 1e1001e100, 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 % y is preferred when working with integers.

math.frexp(x)
 Return the mantissa and exponent of x as the pair (m, e). m is a float
and e is an integer such that x == m * 2**e exactly. 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.

math.fsum(iterable)
Return an accurate floating point sum of values in the iterable. Avoids
loss of precision by tracking multiple intermediate partial sums. The
algorithm’s accuracy depends on IEEE754 arithmetic guarantees and the
typical case where the rounding mode is halfeven.
Note
The accuracy of fsum() may be impaired on builds that use
extended precision addition and then doubleround the results.
New in version 2.6.

math.isinf(x)
Checks if the float x is positive or negative infinite.
New in version 2.6.

math.isnan(x)
Checks if the float x is a NaN (not a number). NaNs are part of the
IEEE 754 standards. Operation like but not limited to inf * 0,
inf / inf or any operation involving a NaN, e.g. nan * 1, return
a NaN.
New in version 2.6.

math.ldexp(x, i)
 Return x * (2**i). This is essentially the inverse of function
frexp().

math.modf(x)
 Return the fractional and integer parts of x. Both results carry the sign of
x, and both are floats.

math.trunc(x)
Return the Real value x truncated to an Integral (usually
a long integer). Delegates to x.__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
floatingpoint 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:

math.exp(x)
 Return e**x.

math.log(x[, base])
Return the logarithm of x to the given base. If the base is not specified,
return the natural logarithm of x (that is, the logarithm to base e).
Changed in version 2.3: base argument added.

math.log1p(x)
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.

math.log10(x)
 Return the base10 logarithm of x.

math.pow(x, y)
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.

math.sqrt(x)
 Return the square root of x.
Trigonometric functions:

math.acos(x)
 Return the arc cosine of x, in radians.

math.asin(x)
 Return the arc sine of x, in radians.

math.atan(x)
 Return the arc tangent of x, in radians.

math.atan2(y, x)
 Return atan(y / x), in radians. The result is between pi and 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, atan(1) and atan2(1, 1) are both pi/4, but atan2(1,
1) is 3*pi/4.

math.cos(x)
 Return the cosine of x radians.

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 of x radians.

math.tan(x)
 Return the tangent of x radians.
Angular conversion:

math.degrees(x)
 Converts angle x from radians to degrees.

math.radians(x)
 Converts angle x from degrees to radians.
Hyperbolic functions:

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 of x.

math.sinh(x)
 Return the hyperbolic sine of x.

math.tanh(x)
 Return the hyperbolic tangent of x.
The module also defines two mathematical constants:

math.pi
 The mathematical constant pi.

math.e
 The mathematical constant e.
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 mathfunction
errorreporting 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 crossplatform or crossrelease 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 NaNs 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.
