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61 lines
2.0 KiB
Python
61 lines
2.0 KiB
Python
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from decimal import Decimal, getcontext
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from math import ceil, factorial
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def pi(precision: int) -> str:
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"""
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The Chudnovsky algorithm is a fast method for calculating the digits of PI,
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based on Ramanujan’s PI formulae.
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https://en.wikipedia.org/wiki/Chudnovsky_algorithm
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PI = constant_term / ((multinomial_term * linear_term) / exponential_term)
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where constant_term = 426880 * sqrt(10005)
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The linear_term and the exponential_term can be defined iteratively as follows:
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L_k+1 = L_k + 545140134 where L_0 = 13591409
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X_k+1 = X_k * -262537412640768000 where X_0 = 1
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The multinomial_term is defined as follows:
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6k! / ((3k)! * (k!) ^ 3)
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where k is the k_th iteration.
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This algorithm correctly calculates around 14 digits of PI per iteration
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>>> pi(10)
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'3.14159265'
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>>> pi(100)
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'3.14159265358979323846264338327950288419716939937510582097494459230781640628620899862803482534211706'
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>>> pi('hello')
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Traceback (most recent call last):
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...
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TypeError: Undefined for non-integers
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>>> pi(-1)
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Traceback (most recent call last):
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...
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ValueError: Undefined for non-natural numbers
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"""
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if not isinstance(precision, int):
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raise TypeError("Undefined for non-integers")
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elif precision < 1:
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raise ValueError("Undefined for non-natural numbers")
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getcontext().prec = precision
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num_iterations = ceil(precision / 14)
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constant_term = 426880 * Decimal(10005).sqrt()
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exponential_term = 1
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linear_term = 13591409
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partial_sum = Decimal(linear_term)
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for k in range(1, num_iterations):
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multinomial_term = factorial(6 * k) // (factorial(3 * k) * factorial(k) ** 3)
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linear_term += 545140134
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exponential_term *= -262537412640768000
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partial_sum += Decimal(multinomial_term * linear_term) / exponential_term
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return str(constant_term / partial_sum)[:-1]
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if __name__ == "__main__":
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n = 50
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print(f"The first {n} digits of pi is: {pi(n)}")
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