merge

Merge branch 'master' of https://github.com/pjungeblut/ChaosKITs

2 files changed, 37 insertions, 7 deletions

diff --git a/math/miller_rabin.cpp b/math/miller_rabin.cpp
new file mode 100644
index 0000000..ad8c163
--- /dev/null
+++ b/math/miller_rabin.cpp
@@ -0,0 +1,20 @@
+//theoretical: n < 318,665,857,834,031,151,167,461 ( > 10^23)
+//but: n ~<= 10^18 (because of MAX(ll))
+//O(logn)
+bool isPrime(ll n) {
+	if(n == 2) return true;
+	if(n < 2 || n % 2 == 0) return false;
+	ll d=n-1,j=0;
+	while(d % 2 == 0) d >>= 1, j++;
+	for(int a = 2; a <= min((ll)37, n-1); a++) {
+		ll v = pow_mod(a, d, n);
+		if(v == 1 || v == n-1) continue;
+		for(int i = 1;  i <= j; i++) {
+			v = mult_mod(v, v, n);
+			if(v == n-1 || v <= 1) break;
+		}
+		
+		if(v != n-1) return false;
+	}
+	return true;
+}
diff --git a/math/modExp.cpp b/math/modExp.cpp
index f738268..863ff4e 100644
--- a/math/modExp.cpp
+++ b/math/modExp.cpp
@@ -1,7 +1,17 @@
-ll modPow(ll b, ll e, ll p) {
-	if (e == 0) return 1;
-	if (e == 1) return b;
-	ll half = modPow(b, e / 2, p), res = (half * half) % p;
-	if (e & 1) res *= b; res %= p;
-	return res;
-}
\ No newline at end of file
+//0<=a,b <=n and n <= MAX(ll)/2
+ll mult_mod(ll a, ll b, ll n) {
+	if(a == 0 || b == 0) return 0;
+	if(b == 1) return a % n;
+	
+	if(b % 2 == 1) return (a + mult_mod(a, b-1, n)) % n;
+	else return mult_mod((a + a) % n, b / 2, n);
+}
+
+//0<=a,b<=n and n <= MAX(ll)/2
+ll pow_mod(ll a, ll b, ll n) {
+	if(b == 0) return 1;
+	if(b == 1) return a % n;
+	
+	if(b % 2 == 1) return mult_mod(pow_mod(a, b-1, n), a, n);
+	else return pow_mod(mult_mod(a, a, n), b / 2, n);
+}