/* GSoC12: Tobenna Peter, Igwe (Edited) */
double rattodouble(Rat a)
{
/*return (double)a.num/(double)a.den*/
int num, den;
mptoi(a.num, &num, 1);
mptoi(a.den, &den, 1);
return (double)num / (double)den;
}
void mixedtorealplan(int pl, Rat *mixed, Rat *rplan)
{
int r ;
int i, len;
int *list;
mp num, den; /* numerator and denominator of sum */
mp x, y;
list = TALLOC(nstrats[pl], int);
/* for test purposes, we even compute the probability
* of the empty sequence. Otherwise, we would start like this:
* rplan[0] = ratfromi(1);
* for (r = 1 ....
*/
for (r = 0; r < nseqs[pl]; r++)
{
itomp(0, num);
itomp(1, den);
len = seqtostratlist(firstmove[pl] + r, pl, list);
for (i=0; i<len; i++)
{
itomp(mixed[list[i]].den, y);
mulint (y, num, num);
itomp(mixed[list[i]].num, x);
mulint (den, x, x);
linint (num, 1, x, 1);
mulint (y, den, den);
reduce(num, den) ;
}
/* mptoi( num, &(rplan[r].num), 1 ); */
if (mptoi( num, &(rplan[r].num), 1 ))
printf(" numerator in mixed strategy probability %3d overflown\n",
i);
/* mptoi( den, &(rplan[r].den), 1 ); */
if (mptoi( den, &(rplan[r].den), 1 ))
printf(" denominator in mixed strategy probability %3d overflown\n",
i);
}
free(list);
}
Rat ratadd (Rat a, Rat b)
{
/*
a.num = a.num * b.den + a.den * b.num;
a.den *= b.den;
return ratreduce(a);
*/
mp num, den, x, y;
itomp (a.num, num) ;
itomp (a.den, den) ;
itomp (b.num, x) ;
itomp (b.den, y) ;
mulint (y, num, num);
mulint (den, x, x);
linint (num, 1, x, 1);
mulint (y, den, den);
reduce(num, den) ;
mptoi( num, &a.num, 1 );
mptoi( den, &a.den, 1 );
return a ;
}
/*
* 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) /* 2 is prime */
return 1;
if(k < 2) /* 1 is not prime */
return 0;
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;
}
// 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 = 1;
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) // 2 is prime
return 1;
if(k < 2) // 1 is not prime
return 0;
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++){
// x = random in [2, n-2]
r = mprand(nbits, prng, nil);
mpmod(r, nm1, x);
mpfree(r);
if(mpcmp(x, mpone) <= 0)
continue;
// y = x**q mod n
mpexp(x, q, n, y);
if(mpcmp(y, mpone) == 0 || mpcmp(y, nm1) == 0)
goto done;
for(j = 1; j < k; j++){
mpmul(y, y, x);
mpmod(x, n, y); // y = y*y mod n
if(mpcmp(y, nm1) == 0)
goto done;
if(mpcmp(y, mpone) == 0){
isprime = 0;
goto done;
}
}
isprime = 0;
}
done:
mpfree(y);
mpfree(x);
mpfree(q);
mpfree(nm1);
return isprime;
}
