#include <stdio.h>
#include <stdlib.h>
#include <stdint.h>

/* should be 64-bit integers if going over 1 billion */
typedef unsigned long xint;
#define FMT "%lu"

xint total, prim, max_peri;
xint U[][9] =  {{ 1, -2, 2,  2, -1, 2,  2, -2, 3},
        { 1,  2, 2,  2,  1, 2,  2,  2, 3},
        {-1,  2, 2, -2,  1, 2, -2,  2, 3}};

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);
    }
}

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;
}