basel.py

from codetiming import Timer
from decimal import Decimal, getcontext

@Timer()
def BBPzeta2(n: int) -> Decimal:
    s = Decimal(0)
    f = Decimal(1)
    # TODO: figure out exactly how fast this converges, 
    # but I think math.log(10, 64) should be the right factor here
    for k in range(int(n*0.5536546824812272) + 1):
        sixk = Decimal(6)*Decimal(k)
        s += f*(  Decimal(16)/ (sixk + 1)**2 
                - Decimal(24)/ (sixk + 2)**2 
                - Decimal(8) / (sixk + 3)**2 
                - Decimal(6) / (sixk + 4)**2 
                + Decimal(1) / (sixk + 5)**2)
        f *= Decimal(1)/Decimal(64)
    return Decimal(3)/Decimal(16)*s