Initial data commit

Task/Square-form-factorization/Julia/square-form-factorization.julia

@@ -0,0 +1,56 @@
+function square_form_factor(n::T)::T where T <: Integer
+    multiplier = T.([1, 3, 5, 7, 11, 3*5, 3*7, 3*11, 5*7, 5*11, 7*11, 3*5*7, 3*5*11, 3*7*11, 5*7*11, 3*5*7*11])
+    s = T(round(sqrt(n)))
+    s * s == n && return s
+    for k in multiplier
+        T != BigInt && n > typemax(T) ÷ k && break
+        d = k * n
+        p0 = pprev = p = isqrt(d)
+        qprev = one(T)
+        Q = d - p0 * p0
+        l = T(floor(2 * sqrt(2 * s)))
+        B, i = 3 * l, 2
+        while i < B
+            b = (p0 + p) ÷ Q
+            p = b * Q - p
+            q = Q
+            Q = qprev + b * (pprev - p)
+            r = T(round(sqrt(Q)))
+            iseven(i) && r * r == Q && break
+            qprev, pprev = q, p
+            i += 1
+        end
+        i >= B && continue
+        b = (p0 - p) ÷ r
+        pprev = p = b * r + p
+        qprev = r
+        Q = (d - pprev * pprev) ÷ qprev
+        i = 0
+        while true
+            b = (p0 + p) ÷ Q
+            pprev = p
+            p = b * Q - p
+            q = Q
+            Q = qprev + b * (pprev - p)
+            qprev = q
+            i += 1
+            p == pprev && break
+        end
+        r = gcd(n, qprev)
+        r != 1 && r != n && return r
+    end
+    return zero(T)
+end
+
+println("Integer              Factor   Quotient\n", "-"^45)
+@time for n in Int128.([
+    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(rpad(n, 22))
+    factr = square_form_factor(n)
+    print(rpad(factr, 10))
+    println(factr == 0 ? "fail" : n ÷ factr)
+end