#include "coxeter.h"
#include "enumerate.h"
#include "generators.h"
#include "mat.h"
#include "qext.h"

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

#define LOOP(i,n) for(int i = 0; i < (n); i++)

/*
  Elements up to length 0: 1
  Elements up to length 1: 4
  Elements up to length 2: 10
  Elements up to length 3: 22
  Elements up to length 4: 46
  Elements up to length 5: 91
  Elements up to length 6: 175
  Elements up to length 7: 334
  Elements up to length 8: 634
  Elements up to length 9: 1198
  Elements up to length 10: 2260
  Elements up to length 11: 4261
  Elements up to length 12: 8029
  Elements up to length 13: 15124
  Elements up to length 14: 28486
  Elements up to length 15: 53650
  Elements up to length 16: 101038
  Elements up to length 17: 190279
  Elements up to length 18: 358339
  Elements up to length 19: 674830
  Elements up to length 20: 1270846
  Elements up to length 21: 2393266
  Elements up to length 22: 4507012
  Elements up to length 23: 8487625
*/

static double gaussian_sqrt5_real(NUMBER x)
{
	double result = 0.0;

	mpq_t tmp;
	mpq_init(tmp);

	// a_0 + sqrt(5)a_1 + 4a_2 + 2sqrt(5)a_3
	mpq_set_si(tmp, 4, 1);
	mpq_mul(tmp, tmp, x->a[2]);
	mpq_add(tmp, tmp, x->a[0]);
	result = mpq_get_d(tmp);
	mpq_set_si(tmp, 2, 1);
	mpq_mul(tmp, tmp, x->a[3]);
	mpq_add(tmp, tmp, x->a[1]);
	result += mpq_get_d(tmp)*sqrt(5);

	mpq_clear(tmp);

	return result;
}

static double gaussian_sqrt5_imag(NUMBER x)
{
	double result = 0.0;

	mpq_t tmp;
	mpq_init(tmp);

	// a_1 + 2sqrt(5)a_2 + 14a_3
	mpq_set_si(tmp, 14, 1);
	mpq_mul(tmp, tmp, x->a[3]);
	mpq_add(tmp, tmp, x->a[1]);
	result = mpq_get_d(tmp);
	mpq_set_si(tmp, 2, 1);
	mpq_mul(tmp, tmp, x->a[2]);
	result += mpq_get_d(tmp)*sqrt(5);

	mpq_clear(tmp);

	return result;
}

int main(int argc, char *argv[])
{
	char buf[100];
	int n = atoi(argv[1]);

	mpq_t qreal, qimag;
	mpq_inits(qreal, qimag, NULL);
	mpq_set_si(qreal, 50, 10);
	mpq_set_si(qimag, 1, 10);
	mpq_canonicalize(qreal);
	mpq_canonicalize(qimag);

	/*
	int length = 0;
	LOOP(i, n) {
		if(group->elements[i].length > length) {
			printf("Elements up to length %d: %d\n", length, i);
			length = group->elements[i].length;
		}
	}
	return 0;
	*/

	/*
	LOOP(i, n) {
		groupelement_t *cur = &group->elements[i];
		groupelement_t *other;

		cur->conjugacy_class = cur; // start with itself and reduce if possible

		LOOP(j, 3) {
			if(cur->left[j] && cur->left[j]->right[j]) {
				other = cur->left[j]->right[j];
				if(other->id < cur->id)
					cur->conjugacy_class = other->conjugacy_class;
			}
			if(cur->right[j] && cur->right[j]->left[j]) {
				other = cur->right[j]->left[j];
				if(other->id < cur->id)
					cur->conjugacy_class = other->conjugacy_class;
			}
		}
	}
	*/

	group_t *group = coxeter_init_triangle(5, 5, 5, n);

	mat gen[3];
	LOOP(i, 3) mat_init(gen[i], 3, QT_GAUSS_SQRT5);
	generators_triangle_reflection_group_555_complex(gen, 2, 2, 2, qreal, qimag);

	struct tracedata *traces;
	int nuniq = enumerate_coxeter_group_traces(group, gen, &traces);

	LOOP(i, nuniq) {
		printf("%d %f %f %f %f\n",
		       traces[i].id,
		       gaussian_sqrt5_real(traces[i].tr),
		       gaussian_sqrt5_imag(traces[i].tr),
		       gaussian_sqrt5_real(traces[i].trinv),
		       gaussian_sqrt5_imag(traces[i].trinv));
	}

	enumerate_tracedata_clear(traces, nuniq);
	LOOP(i, 3) mat_clear(gen[i]);
	coxeter_clear(group);
	mpq_clears(qreal, qimag, NULL);

	return 0;
}