Comment by childintime | Hacker News Reader

Comment by childintime | Hacker News Reader

Chatgpt, please write a function in python for the nth digit of pi.

    Sure, here is a function in Python that calculates the nth digit of Pi using the Chudnovsky algorithm:

    from decimal import *

    def nth_digit_of_pi(n):
        getcontext().prec = n + 1
        C = 426880 * math.sqrt(10005)
        M = 1
        L = 13591409
        X = 1
        K = 6
        S = L
        for i in range(1, n):
            M = (K ** 3 - 16 * K) * M // i ** 3 
            L += 545140134
            X *= -262537412640768000
            S += Decimal(M * L) / X
            K += 12
        return +str(S / C)[n]

Seems off, but I learned something: https://www.wikiwand.com/en/Chudnovsky_algorithm

Interesting! If you correct the obvious errors, then it appears to calculate 1/pi:

    >>> from decimal import Decimal
    >>> import math
    >>> 
    >>> def nth_digit_of_pi(n):
    ...     getcontext().prec = n + 1
    ...     C = Decimal(426880 * math.sqrt(10005))
    ...     M = 1
    ...     L = 13591409
    ...     X = 1
    ...     K = 6
    ...     S = L
    ...     for i in range(1, n):
    ...         M = (K ** 3 - 16 * K) * M // i ** 3 
    ...         L += 545140134
    ...         X *= -262537412640768000
    ...         S += Decimal(M * L) / X
    ...         K += 12
    ...     return str(S / C)[n]
    ... 
    >>> "".join([ nth_digit_of_pi(i) for i in range(50) ])
    '0.318309886183790698041462054251035408427213165074'

since this is Python, `nth_digit_of_pi(-1)` should give us the last number of Pi.

But it's not a list

  Traceback (most recent call last):
    File "<stdin>", line 1, in <module>
  AttributeError: 'manojlds' object has no attribute 'humour'. Did you mean: 'joke'?

Genius.

Here is an article with an actual implementation https://www.craig-wood.com/nick/articles/pi-chudnovsky/

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