cfrac.dg

import '/math'

from_root = n ->
  a0 = int $ math.floor $ math.sqrt n
  r = (a0, list!)
  a, b, c = 1, 2 * a0, a0 ** 2 - n
  delta = math.sqrt $ 4 * n
  flag = True
  while flag =>
    if not c =>
      res = tuple' r !! 0
      c, flag = 2, False
    d = int $ (b + delta) / (2 * c)
    a, b, c = c, -b + 2 * c * d, a - b * d + c * d ** 2
    (r !! 1).append $ abs d
    if abs a == 1 =>
      res = r
      flag = False
  res

print $ from_root 2
print $ from_root 4
print $ from_root 97

cfrac.py

import math
 
 
def from_root(n):
    '''
    Construct a continued fraction from a square root. The argument
    `n` should be an integer representing the radicand of the root:
 
        >>> from_root(2)
        (1, [2])
        >>> from_root(4)
        (2,)
        >>> from_root(97)
        (9, [1, 5, 1, 1, 1, 1, 1, 1, 5, 1, 18])
    '''
 
    a0 = int(math.floor(math.sqrt(n)))
    r = (a0, [])
    a, b, c = 1, 2 * a0, a0 ** 2 - n
    delta = math.sqrt(4*n)
 
    while True:
        try:
            d = int((b + delta) / (2 * c))
        except ZeroDivisionError: # a perfect square
            return (r[0],)
        a, b, c = c, -b + 2*c*d, a - b*d + c*d ** 2
        r[1].append(abs(d))
        if abs(a) == 1:
            break
    return r