I'm trying to implement the Miller-Rabin primality test in C99, but I'm coming across some problems getting it to work. I crafted a small test-set to verify whether or not the implementation works, here's how I'm checking for primes
int main() {
int foo[11] = {0, 1, 2, 3, 4, 7, 28, 73, 125, 991, 1000};
for (int i = 0; i < 11; i++) {
printf("%s; ", isprime(foo[i], 5000) ? "Yes" : "No");
}
return 0;
}
From the numbers listed, the expected output would be
No; No; Yes; Yes; No; Yes; No; Yes; No; Yes; No;
However, as implemented , the output I get is the following:
No; No; Yes; Yes; No; Yes; No; No; No; No; No;
Here's how I wrote the algorithm
int randint (int low, int up){
return rand() % (++up - low)+low;
}
int modpow(int a, int b, int m) {
int c = 1;
while (b) {
if (b & 1) {
c *= a;
}
b >>= 1;
a *= a;
}
return c % m;
}
bool witness(int a, int s, int d, int n) {
int x = modpow(a,d,n);
if(x == 1) return true;
for(int i = 0; i< s-1; i++){
if(x == n-1) return true;
x = modpow(x,2,n);
}
return (x == n- 1);
}
bool isprime(int x, int j) {
if (x == 2) {
return true;
}
if (!(x & 1) || x <= 1) {
return false;
}
int a = 0;
int s = 0;
int d = x - 1;
while (!d&1){
d >>=1;
s+=1;
}
for(int i = 0; i < j; i++){
a = randint(2, x-1);
if(!witness(a,s,d,x)){
return false;
}
}
return true;
}
What am I doing wrong? Why is the test failing for "large" primes, but working for very small ones? How may I fix this?
With Visual Studio 2015 Community edition I found two problems. First the line:
while (!d&1){
needs to be:
while (!(d&1)){
Secondly, as mentioned in the comments your modpow function is overflowing. Try:
int modpow(int a, int d, int m) {
int c = a;
for (int i = 1; i < d; i++)
c = (c*a) % m;
return c % m;
}