# shithub: drawterm

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```#include "os.h"
#include <mp.h>
#include <libsec.h>

/*
* Miller-Rabin probabilistic primality testing
*	Knuth (1981) Seminumerical Algorithms, p.379
*	Menezes et al () Handbook, p.39
* 0 if composite; 1 if almost surely prime, Pr(err)<1/4**nrep
*/
int
probably_prime(mpint *n, int nrep)
{
int j, k, rep, nbits, isprime;
mpint *nm1, *q, *x, *y, *r;

if(n->sign < 0)
sysfatal("negative prime candidate");

if(nrep <= 0)
nrep = 18;

k = mptoi(n);
if(k < 2)		/* 1 is not prime */
return 0;
if(k == 2 || k == 3)	/* 2, 3 is prime */
return 1;
if((n->p[0] & 1) == 0)	/* even is not prime */
return 0;

/* test against small prime numbers */
if(smallprimetest(n) < 0)
return 0;

/* fermat test, 2^n mod n == 2 if p is prime */
x = uitomp(2, nil);
y = mpnew(0);
mpexp(x, n, n, y);
k = mptoi(y);
if(k != 2){
mpfree(x);
mpfree(y);
return 0;
}

nbits = mpsignif(n);
nm1 = mpnew(nbits);
mpsub(n, mpone, nm1);	/* nm1 = n - 1 */
k = mplowbits0(nm1);
q = mpnew(0);
mpright(nm1, k, q);	/* q = (n-1)/2**k */

for(rep = 0; rep < nrep; rep++){
for(;;){
/* find x = random in [2, n-2] */
r = mprand(nbits, prng, nil);
mpmod(r, nm1, x);
mpfree(r);
if(mpcmp(x, mpone) > 0)
break;
}

/* y = x**q mod n */
mpexp(x, q, n, y);

if(mpcmp(y, mpone) == 0 || mpcmp(y, nm1) == 0)
continue;

for(j = 1;; j++){
if(j >= k) {
isprime = 0;
goto done;
}
mpmul(y, y, x);
mpmod(x, n, y);	/* y = y*y mod n */
if(mpcmp(y, nm1) == 0)
break;
if(mpcmp(y, mpone) == 0){
isprime = 0;
goto done;
}
}
}
isprime = 1;
done:
mpfree(y);
mpfree(x);
mpfree(q);
mpfree(nm1);
return isprime;
}
```