Create karatsuba.py

Author: Amogh Singhal

karatsuba.py

@@ -0,0 +1,55 @@
+import random
+from math import ceil
+from math import log10
+
+
+def get_digits(n):
+    if n > 0:
+        digits = int(log10(n)) + 1
+    elif n == 0:
+        digits = 1
+    else:
+        digits = int(log10(-n)) + 2
+    return digits
+
+
+def karatsuba(x, y):
+    # the base case for recursion
+    if x < 10 and y < 10:
+        return x * y
+
+    # n is the number of digits in the highest input number
+    n = max(get_digits(x), get_digits(y))
+
+    n_2 = int(ceil(n / 2.0))
+    n = n if n % 2 == 0 else n + 1
+
+    # split the input numbers
+    a, b = divmod(x, 10 ** n_2)
+    c, d = divmod(y, 10 ** n_2)
+
+    # applying the recursive steps
+    ac = karatsuba(a, c)
+    bd = karatsuba(b, d)
+    ad_bc = karatsuba((a + b), (c + d)) - ac - bd
+
+    # performs the multiplication
+    z2 = (10 ** n) * ac
+    z1 = (10 ** n_2) * ad_bc
+    z0 = bd
+    return z2 + z1 + z0
+
+
+def test():
+    for i in range(1000):
+        x = random.randint(1, 10**5)
+        y = random.randint(1, 10**5)
+        expected = x*y
+        result = karatsuba(x, y)
+        if result != expected:
+            return print("failed")
+    return print("ok")
+
+
+if __name__ == '__main__':
+    test()