akaratsuba.py

Created by bilouclic

Created on December 15, 2024

596 Bytes

def taille(x: int) -> int:
''' renvoie le nombre de chiffres de l’entier x lorsqu’il est écrit en base 2. '''
return len(bin(x)) - 2

def karatsuba(x: int, y: int, k: int) -> int:
''' calcule le produit de x et de y par la méthode de Karatsuba. '''
if k > 2:
a, b = x >> k, x % (1 << k)
c, d = y >> k, y % (1 << k)
k2 = k >> 1
p1 = karatsuba(a, c, k2)
p2 = karatsuba(b, d, k2)
p3 = karatsuba(a - b, c - d, k2)
return (p1 << (2 * k)) + ((p1 + p2 - p3) << k) + p2
else: return x * y

def mult(x: int, y: int) -> int:
n = max(taille(x), taille(y))
return karatsuba(x, y, n // 2)

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