Initial data commit

Task/Square-form-factorization/Go/square-form-factorization.go

@@ -0,0 +1,127 @@
+package main
+
+import (
+    "fmt"
+    "math"
+)
+
+func isqrt(x uint64) uint64 {
+    x0 := x >> 1
+    x1 := (x0 + x/x0) >> 1
+    for x1 < x0 {
+        x0 = x1
+        x1 = (x0 + x/x0) >> 1
+    }
+    return x0
+}
+
+func gcd(x, y uint64) uint64 {
+    for y != 0 {
+        x, y = y, x%y
+    }
+    return x
+}
+
+var multiplier = []uint64{
+    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,
+}
+
+func squfof(N uint64) uint64 {
+    s := uint64(math.Sqrt(float64(N)) + 0.5)
+    if s*s == N {
+        return s
+    }
+    for k := 0; k < len(multiplier) && N <= math.MaxUint64/multiplier[k]; k++ {
+        D := multiplier[k] * N
+        P := isqrt(D)
+        Pprev := P
+        Po := Pprev
+        Qprev := uint64(1)
+        Q := D - Po*Po
+        L := uint32(isqrt(8 * s))
+        B := 3 * L
+        i := uint32(2)
+        var b, q, r uint64
+        for ; i < B; i++ {
+            b = uint64((Po + P) / Q)
+            P = b*Q - P
+            q = Q
+            Q = Qprev + b*(Pprev-P)
+            r = uint64(math.Sqrt(float64(Q)) + 0.5)
+            if (i&1) == 0 && r*r == Q {
+                break
+            }
+            Qprev = q
+            Pprev = P
+        }
+        if i >= B {
+            continue
+        }
+        b = uint64((Po - P) / r)
+        P = b*r + P
+        Pprev = P
+        Qprev = r
+        Q = (D - Pprev*Pprev) / Qprev
+        i = 0
+        for {
+            b = uint64((Po + P) / Q)
+            Pprev = P
+            P = b*Q - P
+            q = Q
+            Q = Qprev + b*(Pprev-P)
+            Qprev = q
+            i++
+            if P == Pprev {
+                break
+            }
+        }
+        r = gcd(N, Qprev)
+        if r != 1 && r != N {
+            return r
+        }
+    }
+    return 0
+}
+
+func main() {
+    examples := []uint64{
+        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,
+    }
+    fmt.Println("Integer              Factor     Quotient")
+    fmt.Println("------------------------------------------")
+    for _, N := range examples {
+        fact := squfof(N)
+        quot := "fail"
+        if fact > 0 {
+            quot = fmt.Sprintf("%d", N/fact)
+        }
+        fmt.Printf("%-20d %-10d %s\n", N, fact, quot)
+    }
+}