.. module:: math

****
Math
****


This module implements various mathematical functions. 

Except when explicitly noted otherwise, all return values are floats. The underlying implementations works on double precision floats that are converted back to single precision if the VM does not support double precision.

No exceptions are raised: in case of error, the return value can be infinite or NaN. Such cases can be checked with the provided functions.

The following constants are defined:

    * :samp:`pi` 3.14159265
    * :samp:`e`  2.71828182

    
.. function:: tan(x)

   Return the tangent of *x* radians.
    
.. function:: cos(x)

   Return the cosine of *x* radians.
    
.. function:: sin(x)

   Return the sine of *x* radians.
    
.. function:: 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 :func:`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``.
    
.. function:: atan(x)

   Return the arc tangent of *x*, in radians.
    
.. function:: acos(x)

   Return the arc cosine of *x*, in radians.

    
.. function:: asin(x)

   Return the arc sine of *x*, in radians.

    
.. function:: degress(rad)

   Converts *rad* from radians to degrees.
    
    
.. function:: radians(degree)

   Converts *degree* from degrees to radians.
    
    
.. function:: exp(x)

   Return ``e**x``.
    
.. function:: log(x[, base])

   With one argument or with *base* non positive, 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)``.

    
.. function:: pow(x, y)

   Return ``x`` raised to the power ``y``.  

   Unlike the built-in ``**`` operator, :func:`math.pow` converts both
   its arguments to type :class:`float`.  Use ``**`` or the built-in
   :func:`pow` function for computing exact integer powers.
    
.. function:: sqrt(x)

   Return the square root of *x*.
    
.. function:: isnan(x)

   Return ``True`` if *x* is a NaN (not a number), and ``False`` otherwise.

    
.. function:: isinf(x)

   Return ``True`` if *x* is a positive or negative infinity, and
   ``False`` otherwise.
    
.. function:: floor(x)

   Return the floor of *x*, the largest integer less than or equal to *x*.
    
.. function:: ceil(x)

   Return the ceiling of *x*, the smallest integer greater than or equal to *x*.