Sync

Task/Miller-Rabin-primality-test/C/miller-rabin-primality-test-4.c

@@ -0,0 +1,72 @@
+// calcul a^n%mod
+size_t power(size_t a, size_t n, size_t mod)
+{
+    size_t power = a;
+    size_t result = 1;
+
+    while (n)
+    {
+        if (n & 1)
+            result = (result * power) % mod;
+        power = (power * power) % mod;
+        n >>= 1;
+    }
+    return result;
+}
+
+// n−1 = 2^s * d with d odd by factoring powers of 2 from n−1
+bool witness(size_t n, size_t s, size_t d, size_t a)
+{
+    size_t x = power(a, d, n);
+    size_t y;
+
+    while (s) {
+        y = (x * x) % n;
+        if (y == 1 && x != 1 && x != n-1)
+            return false;
+        x = y;
+        --s;
+    }
+    if (y != 1)
+        return false;
+    return true;
+}
+
+/*
+ * if n < 1,373,653, it is enough to test a = 2 and 3;
+ * if n < 9,080,191, it is enough to test a = 31 and 73;
+ * if n < 4,759,123,141, it is enough to test a = 2, 7, and 61;
+ * if n < 1,122,004,669,633, it is enough to test a = 2, 13, 23, and 1662803;
+ * if n < 2,152,302,898,747, it is enough to test a = 2, 3, 5, 7, and 11;
+ * if n < 3,474,749,660,383, it is enough to test a = 2, 3, 5, 7, 11, and 13;
+ * if n < 341,550,071,728,321, it is enough to test a = 2, 3, 5, 7, 11, 13, and 17.
+ */
+
+bool is_prime_mr(size_t n)
+{
+    if (((!(n & 1)) && n != 2 ) || (n < 2) || (n % 3 == 0 && n != 3))
+        return false;
+    if (n <= 3)
+        return true;
+
+    size_t d = n / 2;
+    size_t s = 1;
+    while (!(d & 1)) {
+        d /= 2;
+        ++s;
+    }
+
+    if (n < 1373653)
+        return witness(n, s, d, 2) && witness(n, s, d, 3);
+    if (n < 9080191)
+        return witness(n, s, d, 31) && witness(n, s, d, 73);
+    if (n < 4759123141)
+        return witness(n, s, d, 2) && witness(n, s, d, 7) && witness(n, s, d, 61);
+    if (n < 1122004669633)
+        return witness(n, s, d, 2) && witness(n, s, d, 13) && witness(n, s, d, 23) && witness(n, s, d, 1662803);
+    if (n < 2152302898747)
+        return witness(n, s, d, 2) && witness(n, s, d, 3) && witness(n, s, d, 5) && witness(n, s, d, 7) && witness(n, s, d, 11);
+    if (n < 3474749660383)
+        return witness(n, s, d, 2) && witness(n, s, d, 3) && witness(n, s, d, 5) && witness(n, s, d, 7) && witness(n, s, d, 11) && witness(n, s, d, 13);
+    return witness(n, s, d, 2) && witness(n, s, d, 3) && witness(n, s, d, 5) && witness(n, s, d, 7) && witness(n, s, d, 11) && witness(n, s, d, 13) && witness(n, s, d, 17);
+}