Create miller_robin.cpp

miller robin 素性测试

Author: tmp-coder

template/miller_robin.cpp

@@ -0,0 +1,41 @@
+namespace Prime{
+    #define random(a,b) (rand() % ((b) -(a)) +(a))
+    LL power_mod(LL x,LL n,LL mod){
+        LL ret =1;
+        while(n){
+            if(n & 1) ret = x * ret % mod;
+            x = x * x % mod;
+            n >>=1;
+        }
+        return ret;
+    }
+    LL mulmod(LL x,LL y,LL n){ // x ,y <= 10^9
+        return x * y % n;
+    }
+    bool witness(LL a,LL n,LL u,LL t){
+        LL x0 = power_mod(a,u,n),x1;
+        for(int i=1 ;i<=t ; ++i){
+            x1 = mulmod(x0,x0,n);
+            if(x1==1 && x0!=1 && x0!=n-1)
+                return false;
+            x0 = x1;
+        }
+        if(x1 !=1)return false;
+        return true;
+    }
+
+    bool miller_rabin(LL n, int times = 20){
+        if(n < 3) return n==2;
+        if(!(n&1))return false;
+        LL u = n-1,t =0;
+        while (u%2==0) {
+            t++;u>>=1;
+        }
+        while (times--) {
+            LL a = random(1,n-1);
+            //if(a == 0)std::cout << a << " "<<n<< " "<<u<<" " << t<<'\n';
+            if(!witness(a,n,u,t))return false;
+        }
+        return true;
+    }
+};