void new_tri(xint in[])
{
int i;
xint t[3], p;
xint x = in[0], y = in[1], z = in[2];
recur: p = x + y + z;
if (p > max_peri) return;
prim ++;
total += max_peri / p;
t[0] = x - 2 * y + 2 * z;
t[1] = 2 * x - y + 2 * z;
t[2] = t[1] - y + z;
new_tri(t);
t[0] += 4 * y;
t[1] += 2 * y;
t[2] += 4 * y;
new_tri(t);
z = t[2] - 4 * x;
y = t[1] - 4 * x;
x = t[0] - 2 * x;
goto recur;
}
int main()
{
xint seed[3] = {3, 4, 5};
for (max_peri = 10; max_peri <= 100000000; max_peri *= 10) {
total = prim = 0;
new_tri(seed);
printf( "Up to "FMT": "FMT" triples, "FMT" primitives.\n",
max_peri, total, prim);
}
return 0;
}
void new_tri(xint in[])
{
int i;
xint t[3], p = in[0] + in[1] + in[2];
if (p > max_peri) return;
prim ++;
/* for every primitive triangle, its multiples would be right-angled too;
* count them up to the max perimeter */
total += max_peri / p;
/* recursively produce next tier by multiplying the matrices */
for (i = 0; i < 3; i++) {
t[0] = U[i][0] * in[0] + U[i][1] * in[1] + U[i][2] * in[2];
t[1] = U[i][3] * in[0] + U[i][4] * in[1] + U[i][5] * in[2];
t[2] = U[i][6] * in[0] + U[i][7] * in[1] + U[i][8] * in[2];
new_tri(t);
}
}
