From 87b9f4bc529aab4e8f3bb05638c7d49c8e5a4d50 Mon Sep 17 00:00:00 2001
From: npav5057 <npav5057@gmail.com>
Date: Mon, 2 Oct 2023 11:48:29 +0530
Subject: [PATCH] Added Primality test cpp files

---
 C++/ISPRIME.cpp     | 35 ++++++++++++++++++++++++
 C++/MillerRabin.cpp | 65 +++++++++++++++++++++++++++++++++++++++++++++
 2 files changed, 100 insertions(+)
 create mode 100644 C++/ISPRIME.cpp
 create mode 100644 C++/MillerRabin.cpp

diff --git a/C++/ISPRIME.cpp b/C++/ISPRIME.cpp
new file mode 100644
index 0000000..c11c936
--- /dev/null
+++ b/C++/ISPRIME.cpp
@@ -0,0 +1,35 @@
+/*
+
+    Simple algorthiam to check Primality of a 32 bit int
+    Time complaxity : O(sqrt(n/3))
+*/
+
+#include <iostream>
+#include <cassert>
+
+using namespace std;
+bool isPrime(int num)
+{
+	if(num < 4) return n>1;
+	
+	if(!(num&1)  or num%3==0 ) return false;
+
+	for(int i=5;i*i<=num;i+=6) 
+		if(num%i==0 or num%(i+2)==0) 
+			return false;
+
+	return true;
+}
+
+int main()
+{
+	int num;
+	cout<<"Enter number to check:";
+	cin>>num;
+	assert(num>0);
+	if(isPrime(num))
+		cout<< num <<" is Prime Number\n";
+	else 
+		cout<< num <<" is not a Prime Number\n";
+
+}
\ No newline at end of file
diff --git a/C++/MillerRabin.cpp b/C++/MillerRabin.cpp
new file mode 100644
index 0000000..0096443
--- /dev/null
+++ b/C++/MillerRabin.cpp
@@ -0,0 +1,65 @@
+/*
+
+ Miller Ranbin test Deterministic method for checking a prime number;
+ Time Complexity : O(12*log(n));
+ Its Implementation 
+
+*/
+
+#include<bits/stdc++.h>
+using namespace std;
+using u64 = uint64_t;
+using u128 = __uint128_t;
+
+u64 bin_exp(u64 base, u64 e, u64 mod) {
+    u64 result = 1;
+    base %= mod;
+    while (e) {
+        if (e & 1)
+            result = (u128)result * base % mod;
+        base = (u128)base * base % mod;
+        e >>= 1;
+    }
+    return result;
+}
+
+bool check_composite(u64 n, u64 a, u64 d, int s) {
+    u64 x = bin_exp(a, d, n);
+    if (x == 1 || x == n - 1)
+        return false;
+    for (int r = 1; r < s; r++) {
+        x = (u128)x * x % n;
+        if (x == n - 1)
+            return false;
+    }
+    return true;
+};
+
+bool MillerRabin(u64 n) { 
+    if (n < 4)
+    	return n > 1;
+
+    int r = 0; u64 d = n - 1;
+    while ((d & 1) == 0) {
+        d >>= 1,r++;
+    }
+
+    for (int a : {2, 3, 5, 7, 11, 13, 17, 19, 23, 29, 31, 37}) {
+        if (n == a)
+            return true;
+        if (check_composite(n, a, d, r))
+            return false;
+    }
+    return true;
+}
+int main()
+{
+	u64 num;
+	cout<<"Enter number to check:";
+	cin>>num;
+	assert(num>0);
+	if(MillerRabin(num))
+		cout<< num <<" is Prime Number\n";
+	else 
+		cout<< num <<" is not a Prime Number\n";
+}
\ No newline at end of file