src.pydasa.structs.tools.math
=============================

.. py:module:: src.pydasa.structs.tools.math

.. autoapi-nested-parse::

   Module math.py
   ===========================================

   Module with math functions for finding prime numbers and calculating factorials. in *PyDASA*.

   Module with math functions for handling data in the for Separate Chaining Hash Table.

   *IMPORTANT:* based on the implementations proposed by the following authors/books:

       #. Algorithms, 4th Edition, Robert Sedgewick and Kevin Wayne.
       #. Data Structure and Algorithms in Python, M.T. Goodrich, R. Tamassia, M.H. Goldwasser.

   *NOTE:* code contributed by Sanjit_Prasad in https://www.geeksforgeeks.org/prime-numbers/



Functions
---------

.. autoapisummary::

   src.pydasa.structs.tools.math.is_prime
   src.pydasa.structs.tools.math.next_prime
   src.pydasa.structs.tools.math.previous_prime
   src.pydasa.structs.tools.math.gfactorial


Module Contents
---------------

.. py:function:: is_prime(n)

   *is_prime()* checks if a number is prime or not. Original code from Sanjit_Prasad.

   :param n: number to check if it is prime.
   :type n: int

   :returns: True if the number is prime, False otherwise.
   :rtype: bool


.. py:function:: next_prime(n)

   *next_prime()* returns the next prime number greater than n.

   :param n: number to check if it is prime.
   :type n: int

   :returns: the next prime number greater than n.
   :rtype: int


.. py:function:: previous_prime(n)

   *previous_prime()* returns the previous prime number less than n.

   :param n: number to check if it is prime.
   :type n: int

   :returns: the previous prime number less than n.
   :rtype: int


.. py:function:: gfactorial(x, prec = None)

   *gfactorial()* calculates the factorial of a number, including support for floats less than 1.0.

       - For integers n ≥ 0: Returns n! (n factorial).
       - For floats x: Returns Γ(x+1) (gamma function).

   :param x: The number to compute the factorial for.
   :type x: Union[int, float]
   :param prec: precision, or the number of decimal places to round the result to. Defaults to None.
   :type prec: Optional[int], optional

   :raises ValueError: If x is a negative integer.

   :returns: The factorial of x. Returns an integer for integer inputs ≥ 0, and a float for float inputs or integers < 0.
   :rtype: Union[int, float]

   .. rubric:: Examples

   >>> gfactorial(5)
   120
   >>> gfactorial(0)
   1
   >>> gfactorial(0.5)  # Equivalent to Γ(1.5) = 0.5 * Γ(0.5) = 0.5 * √Pi
   0.8862269254527579
   >>> gfactorial(-0.5)  # Equivalent to Γ(0.5) = √Pi
   1.7724538509055159