ALL the CTFS of Crypto2025 finally

crypto-asimmetric/inferious_prime/ContinuedFractions.py

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+#!/usr/bin/env python3
+
+'''
+Created on Dec 14, 2011
+
+@author: pablocelayes
+
+'''
+# Types
+CFListT = list[int]  # CF coefficients
+CVListT = list[tuple[int, int]]  # Convergents at each coefficient level
+
+def rational_to_contfrac(x: int, y: int) -> tuple[CFListT, CVListT]:
+    """
+    Converts a rational x/y fraction into
+    a list of partial coefficients [a0, ..., an], and
+    a list of convergents at each coefficient level [(n0, d0), (n1, d1), ...]
+
+    The algorithm of computing the convergents from left to right is available
+    in Section 9.1 of https://r-knott.surrey.ac.uk/Fibonacci/cfINTRO.html#CFtofract
+
+    Args:
+        x (int): numerator of the given rational number
+        y (int): denominator of the given rational number
+
+    Returns:
+        tuple[CFListT, CVListT]: a tuple of coefficients and convergents at each
+        coefficient level
+    """
+    a = x // y
+    cflist = [a]
+    cvlist = [(a, 1)]
+    ppn, ppd = 1, 0  # pre-pre numerator and denominator of convergent
+    pn, pd = a, 1  # pre numerator and denominator of convergent
+    while a * y != x:
+        x, y = y, x - a * y
+        a = x // y
+        cflist.append(a)
+        cn, cd = a * pn + ppn, a * pd + ppd
+        cvlist.append((cn, cd))
+        ppn, ppd = pn, pd
+        pn, pd = cn, cd
+    return cflist, cvlist