Continued Fraction

continued_fraction.py

from fractions import Fraction as F
from math import floor, pi


def to_cf(value):
    head = floor(value)
    value = F(value - head)
    parts = [head]
    while value:
        value = F(1, value)
        part = int(value)
        parts.append(part)
        value -= part
    return tuple(parts)


def from_cf(parts):
    iterator = reversed(parts)
    value = F(next(iterator))
    for part in iterator:
        value = part + F(1, value)
    return value


PICF = (
    3, 7, 15, 1, 292, 1, 1, 1, 2, 1, 3, 1, 14, 2, 1, 1, 2, 2, 2, 2, 1, 84, 2,
    1, 1, 15, 3, 13, 1, 4, 2, 6, 6, 99, 1, 2, 2, 6, 3, 5, 1, 1, 6, 8, 1, 7, 1,
    2, 3, 7, 1, 2, 1, 1, 12, 1, 1, 1, 3, 1, 1, 8, 1, 1, 2, 1, 6, 1, 1, 5, 2, 2,
    3, 1, 2, 4, 4, 16, 1, 161, 45, 1, 22, 1, 2, 2, 1, 4, 1, 2, 24, 1, 2, 1, 3,
    1, 2, 1, 1, 10, 2, 5, 4, 1, 2, 2, 8, 1, 5, 2, 2, 26, 1, 4, 1, 1, 8, 2, 42,
    2, 1, 7, 3, 3, 1, 1, 7, 2, 4, 9, 7, 2, 3, 1, 57, 1, 18, 1, 9, 19, 1, 2, 18,
    1, 3, 7, 30, 1, 1, 1, 3, 3, 3, 1, 2, 8, 1, 1, 2, 1, 15, 1, 2, 13, 1, 2, 1,
    4, 1, 12, 1, 1, 3, 3, 28, 1, 10, 3, 2, 20, 1, 1, 1, 1, 4, 1, 1, 1, 5, 3, 2,
    1, 6, 1, 4, 1, 120, 2, 1, 1, 3, 1, 23, 1, 15, 1, 3, 7, 1, 16, 1, 2, 1, 21,
    2, 1, 1, 2, 9, 1, 6, 4, 127, 14, 5, 1, 3, 13, 7, 9, 1, 1, 1, 1, 1, 5, 4, 1,
    1, 3, 1, 1, 29, 3, 1, 1, 2, 2, 1, 3, 1, 1, 1, 3, 1, 1, 10, 3, 1, 3, 1, 2,
    1, 12, 1, 4, 1, 1, 1, 1, 7, 1, 1, 2, 1, 11, 3, 1, 7, 1, 4, 1, 48, 16, 1, 4,
    5, 2, 1, 1, 4, 3, 1, 2, 3, 1, 2, 2, 1, 2, 5, 20, 1, 1, 5, 4, 1, 436, 8, 1,
    2, 2, 1, 1, 1, 1, 1, 5, 1, 2, 1, 3, 6, 11, 4, 3, 1, 1, 1, 2, 5, 4, 6, 9, 1,
    5, 1, 5, 15, 1, 11, 24, 4, 4, 5, 2, 1, 4, 1, 6, 1, 1, 1, 4, 3, 2, 2, 1, 1,
    2, 1, 58, 5, 1, 2, 1, 2, 1, 1, 2, 2, 7, 1, 15, 1, 4, 8, 1, 1, 4, 2, 1, 1,
    1, 3, 1, 1, 1, 2, 1, 1, 1, 1, 1, 9, 1, 4, 3, 15, 1, 2, 1, 13, 1, 1, 1, 3,
    24, 1, 2, 4, 10, 5, 12, 3, 3, 21, 1, 2, 1, 34, 1, 1, 1, 4, 15, 1, 4, 44, 1,
    4, 20776, 1, 1, 1, 1, 1, 1, 1, 23, 1, 7, 2, 1, 94, 55, 1, 1, 2, 1, 1, 3, 1,
    1, 32, 5, 1, 14, 1, 1, 1, 1, 1, 3, 50, 2, 16, 5, 1, 2, 1, 4, 6, 3, 1, 3, 3,
)

if __name__ == '__main__':
    print(PICF[:20])
    print(to_cf(pi))
    print(from_cf(PICF))