June 2018 Update

Task/Multiplicative-order/Kotlin/multiplicative-order.kotlin

@@ -0,0 +1,94 @@
+// version 1.2.10
+
+import java.math.BigInteger
+
+val bigOne   = BigInteger.ONE
+val bigTwo   = 2.toBigInteger()
+val bigThree = 3.toBigInteger()
+val bigTen   = BigInteger.TEN
+
+class PExp(val prime: BigInteger, val exp: Long)
+
+fun moTest(a: BigInteger, n: BigInteger) {
+    if (!n.isProbablePrime(20)) {
+        println("Not computed. Modulus must be prime for this algorithm.")
+        return
+    }
+    if (a.bitLength() < 100) print("ord($a)") else print("ord([big])")
+    if (n.bitLength() < 100) print(" mod $n ") else print(" mod [big] ")
+    val mob = moBachShallit58(a, n, factor(n - bigOne))
+    println("= $mob")
+}
+
+fun moBachShallit58(a: BigInteger, n: BigInteger, pf: List<PExp>): BigInteger {
+    val n1 = n - bigOne
+    var mo = bigOne
+    for (pe in pf) {
+        val y = n1 / pe.prime.pow(pe.exp.toInt())
+        var o = 0L
+        var x = a.modPow(y, n.abs())
+        while (x > bigOne) {
+            x = x.modPow(pe.prime, n.abs())
+            o++
+        }
+        var o1 = o.toBigInteger()
+        o1 = pe.prime.pow(o1.toInt())
+        o1 /= mo.gcd(o1)
+        mo *= o1
+    }
+    return mo
+}
+
+fun factor(n: BigInteger): List<PExp> {
+    val pf = mutableListOf<PExp>()
+    var nn = n
+    var e = 0L
+    while (!nn.testBit(e.toInt())) e++
+    if (e > 0L) {
+        nn = nn shr e.toInt()
+        pf.add(PExp(bigTwo, e))
+    }
+    var s = bigSqrt(nn)
+    var d = bigThree
+    while (nn > bigOne) {
+        if (d > s) d = nn
+        e = 0L
+        while (true) {
+            val (q, r) = nn.divideAndRemainder(d)
+            if (r.bitLength() > 0) break
+            nn = q
+            e++
+        }
+        if (e > 0L) {
+            pf.add(PExp(d, e))
+            s = bigSqrt(nn)
+        }
+        d += bigTwo
+    }
+    return pf
+}
+
+fun bigSqrt(n: BigInteger): BigInteger {
+    var b = n
+    while (true) {
+        val a = b
+        b = (n / a + a) shr 1
+        if (b >= a) return a
+    }
+}
+
+fun main(args: Array<String>) {
+    moTest(37.toBigInteger(), 3343.toBigInteger())
+
+    var b = bigTen.pow(100) + bigOne
+    moTest(b, 7919.toBigInteger())
+
+    b = bigTen.pow(1000) + bigOne
+    moTest(b, BigInteger("15485863"))
+
+    b = bigTen.pow(10000) - bigOne
+    moTest(b, BigInteger("22801763489"))
+
+    moTest(BigInteger("1511678068"), BigInteger("7379191741"))
+    moTest(BigInteger("3047753288"), BigInteger("2257683301"))
+}