static int
mprimef(unsigned int *n, unsigned int *q, int k)
{
int i, j;
unsigned int *t, *x, *y;
// generate x
t = mcopy(n);
while (1) {
for (i = 0; i < MLENGTH(t); i++)
t[i] = rand();
x = mmod(t, n);
if (!MZERO(x) && !MEQUAL(x, 1))
break;
mfree(x);
}
mfree(t);
// exponentiate
y = mmodpow(x, q, n);
// done?
if (MEQUAL(y, 1)) {
mfree(x);
mfree(y);
return 1;
}
j = 0;
while (1) {
// y = n - 1?
t = msub(n, y);
if (MEQUAL(t, 1)) {
mfree(t);
mfree(x);
mfree(y);
return 1;
}
mfree(t);
if (++j == k) {
mfree(x);
mfree(y);
return 0;
}
// y = (y ^ 2) mod n
t = mmul(y, y);
mfree(y);
y = mmod(t, n);
mfree(t);
// y = 1?
if (MEQUAL(y, 1)) {
mfree(x);
mfree(y);
return 0;
}
}
}
void
yybesselj(void)
{
double d;
int n;
N = pop();
X = pop();
push(N);
n = pop_integer();
// numerical result
if (isdouble(X) && n != (int) 0x80000000) {
//d = jn(n, X->u.d);
push_double(d);
return;
}
// bessej(0,0) = 1
if (iszero(X) && iszero(N)) {
push_integer(1);
return;
}
// besselj(0,n) = 0
if (iszero(X) && n != (int) 0x80000000) {
push_integer(0);
return;
}
// half arguments
if (N->k == NUM && MEQUAL(N->u.q.b, 2)) {
// n = 1/2
if (MEQUAL(N->u.q.a, 1)) {
push_integer(2);
push_symbol(PI);
divide();
push(X);
divide();
push_rational(1, 2);
power();
push(X);
sine();
multiply();
return;
}
// n = -1/2
if (MEQUAL(N->u.q.a, -1)) {
push_integer(2);
push_symbol(PI);
divide();
push(X);
divide();
push_rational(1, 2);
power();
push(X);
cosine();
multiply();
return;
}
// besselj(x,n) = (2/x) (n-sgn(n)) besselj(x,n-sgn(n)) - besselj(x,n-2*sgn(n))
push_integer(MSIGN(N->u.q.a));
SGN = pop();
push_integer(2);
push(X);
divide();
push(N);
push(SGN);
subtract();
multiply();
push(X);
push(N);
push(SGN);
subtract();
besselj();
multiply();
push(X);
push(N);
push_integer(2);
push(SGN);
multiply();
subtract();
besselj();
subtract();
return;
}
push(symbol(BESSELJ));
push(X);
push(N);
list(3);
}
