Data update

Task/Square-form-factorization/Python/square-form-factorization.py

@@ -0,0 +1,110 @@
+from math import sqrt, gcd
+
+M = [1, 3, 5, 7, 11]
+UINT64_MAX = 18446744073709551615
+
+def isqrt(n: int):
+    return int(sqrt(n))
+
+def squfof(n: int):
+    if n % 2 == 0:
+        return 2
+
+    h = int(sqrt(n) + 0.5)
+
+    if h ** 2 == n:
+        return h
+
+    for m in M:
+        if m > 1 and n % m == 0:
+            return m
+
+        if n > UINT64_MAX / m:
+            break
+
+        mn = m * n
+        r = isqrt(mn)
+
+        if r ** 2 > mn:
+            r -= 1
+
+        rn = r
+
+        b = r
+        a = 1
+        h = ((rn + b) // a) * a - b
+        c = (mn - h * h) // a
+
+        for i in range(2, 4 * isqrt(2 * r)):
+            a, c = c, a
+            q = (rn + b) // a
+            t = b
+            b = q * a - b
+            c += q * (t - b)
+
+            if i % 2 == 0:
+                r = int(sqrt(c) + 0.5)
+
+                if r ** 2 == c:
+                    q = (rn - b) // r
+                    v = q * r + b
+                    w = (mn - v * v) // r
+
+                    u = r
+
+                    while True:
+                        w, u = u, w
+                        r = v
+                        q = (rn + v) // u
+                        v = q * u - v
+
+                        if v == r:
+                            break
+
+                        w += q * (r - v)
+
+                    h = gcd(n, u)
+
+                    if h != 1:
+                        return h
+
+    return 1
+
+data = [
+    2501,
+    12851,
+    13289,
+    75301,
+    120787,
+    967009,
+    997417,
+    7091569,
+    13290059,
+    42854447,
+    223553581,
+    2027651281,
+    11111111111,
+    100895598169,
+    1002742628021,
+    60012462237239,
+    287129523414791,
+    9007199254740931,
+    11111111111111111,
+    314159265358979323,
+    384307168202281507,
+    419244183493398773,
+    658812288346769681,
+    922337203685477563,
+    1000000000000000127,
+    1152921505680588799,
+    1537228672809128917,
+    4611686018427387877
+]
+
+print("N                      f          N/f")
+print("======================================")
+
+for n in data:
+    f = squfof(n)
+    res = 'fail' if f == 1 else f'{f:<10} {n // f}'
+    print(f'{n:<22} {res}')