mirror of
https://github.com/TheAlgorithms/Python.git
synced 2024-11-24 13:31:07 +00:00
f0dfc4f46d
* Add Chudnovskys algorithm for calculating many digits of pi * Update return value type hint * Initialize partial sum to be of type Decimal * Update chudnovsky_algorithm.py Co-authored-by: Christian Clauss <cclauss@me.com>
62 lines
2.0 KiB
Python
62 lines
2.0 KiB
Python
from decimal import Decimal, getcontext
|
||
from math import ceil, factorial
|
||
|
||
|
||
def pi(precision: int) -> str:
|
||
"""
|
||
The Chudnovsky algorithm is a fast method for calculating the digits of PI,
|
||
based on Ramanujan’s PI formulae.
|
||
|
||
https://en.wikipedia.org/wiki/Chudnovsky_algorithm
|
||
|
||
PI = constant_term / ((multinomial_term * linear_term) / exponential_term)
|
||
where constant_term = 426880 * sqrt(10005)
|
||
|
||
The linear_term and the exponential_term can be defined iteratively as follows:
|
||
L_k+1 = L_k + 545140134 where L_0 = 13591409
|
||
X_k+1 = X_k * -262537412640768000 where X_0 = 1
|
||
|
||
The multinomial_term is defined as follows:
|
||
6k! / ((3k)! * (k!) ^ 3)
|
||
where k is the k_th iteration.
|
||
|
||
This algorithm correctly calculates around 14 digits of PI per iteration
|
||
|
||
>>> pi(10)
|
||
'3.14159265'
|
||
>>> pi(100)
|
||
'3.14159265358979323846264338327950288419716939937510582097494459230781640628620899862803482534211706'
|
||
>>> pi('hello')
|
||
Traceback (most recent call last):
|
||
...
|
||
TypeError: Undefined for non-integers
|
||
>>> pi(-1)
|
||
Traceback (most recent call last):
|
||
...
|
||
ValueError: Undefined for non-natural numbers
|
||
"""
|
||
|
||
if not isinstance(precision, int):
|
||
raise TypeError("Undefined for non-integers")
|
||
elif precision < 1:
|
||
raise ValueError("Undefined for non-natural numbers")
|
||
|
||
getcontext().prec = precision
|
||
num_iterations = ceil(precision / 14)
|
||
constant_term = 426880 * Decimal(10005).sqrt()
|
||
multinomial_term = 1
|
||
exponential_term = 1
|
||
linear_term = 13591409
|
||
partial_sum = Decimal(linear_term)
|
||
for k in range(1, num_iterations):
|
||
multinomial_term = factorial(6 * k) // (factorial(3 * k) * factorial(k) ** 3)
|
||
linear_term += 545140134
|
||
exponential_term *= -262537412640768000
|
||
partial_sum += Decimal(multinomial_term * linear_term) / exponential_term
|
||
return str(constant_term / partial_sum)[:-1]
|
||
|
||
|
||
if __name__ == "__main__":
|
||
n = 50
|
||
print(f"The first {n} digits of pi is: {pi(n)}")
|