#include "coxeter.h"
#include "linalg.h"
#include "mat.h"
#include "enumerate_triangle_group.h"

#define SWAP(t,x,y) do { t _tmp = (x); (x) = (y); (y) = _tmp; } while (0);
//#define DEBUG(msg, ...) fprintf(stderr, msg, ##__VA_ARGS__)
#define DEBUG(msg, ...)

struct result {
	int id;
	int count;
	mpq_t tr;
	mpq_t trinv;
	double x;
	double y;
};

static int compare_result(const void *a_, const void *b_)
{
	int d = 0;

	struct result **a = (struct result **)a_;
	struct result **b = (struct result **)b_;

	d = mpq_cmp((*a)->tr,(*b)->tr);
	if(d == 0) {
		d = mpq_cmp((*a)->trinv, (*b)->trinv);
	}

	return d;
}

static int compare_result_with_id(const void *a_, const void *b_)
{
	int d = 0;

	struct result **a = (struct result **)a_;
	struct result **b = (struct result **)b_;

	d = mpq_cmp((*a)->tr,(*b)->tr);
	if(d == 0) {
		d = mpq_cmp((*a)->trinv, (*b)->trinv);
		if(d == 0) {
			d = (*b)->id - (*a)->id;
		}
	}

	return d;
}

static int compare_result_by_slope(const void *a_, const void *b_)
{
	int d = 0;

	struct result **a = (struct result **)a_;
	struct result **b = (struct result **)b_;

	double slopea = (*a)->x / (*a)->y;
	double slopeb = (*b)->x / (*b)->y;

	return slopea > slopeb ? -1 : slopea < slopeb ? 1 : 0;
}

int main(int argc, char *argv[])
{
	mpq_t s, q, t, tmp;
	double sapprox, tapprox, qapprox, tqfactor;
	mat *matrices;
	group_t *group;
	int index;
	mps_context *solver;
	int acc = 100;
	int n, nuniq, nmax;
	int retval;
	double evs[3];
	double max_slope;
	char buf[100];
	char buf2[100];

	struct result *invariants;
	struct result **distinct_invariants;

	if(argc < 4) {
		fprintf(stderr, "Usage: %s <N> <s> <q>\n", argv[0]);
		exit(1);
	}

	nmax = atoi(argv[1]);

	DEBUG("Allocate\n");

	mpq_inits(s, q, t, tmp, NULL);
	matrices = malloc(nmax*sizeof(mat));
	for(int i = 0; i < nmax; i++)
		mat_init(matrices[i], 3);
	invariants = malloc(nmax*sizeof(struct result));
	distinct_invariants = malloc(nmax*sizeof(struct result));
	for(int i = 0; i < nmax; i++) {
		mpq_init(invariants[i].tr);
		mpq_init(invariants[i].trinv);
		distinct_invariants[i] = &invariants[i];
	}

	solver = mps_context_new();
	mps_context_set_output_prec(solver, 20); // relative precision
	mps_context_set_output_goal(solver, MPS_OUTPUT_GOAL_APPROXIMATE);

	DEBUG("Approximate parameters\n");

	// get approximate s and q values
	sapprox = atof(argv[2]);
	qapprox = atof(argv[3]);
//	tapprox = atof(argv[3]);
//	tqfactor = pow((sapprox*sapprox-sapprox+1)*(sapprox*sapprox-sapprox+1)*(sapprox*sapprox+1), 1/6.0);
//	qapprox = tapprox/tqfactor;

	for(int i = 0; ; i++) {
		continued_fraction_approximation(tmp, sapprox, i);
		if(fabs(mpq_get_d(t)-sapprox) < 1e-10
		   || (mpz_cmpabs_ui(mpq_numref(tmp),acc) > 0 && mpz_cmpabs_ui(mpq_denref(tmp),acc) > 0))
			break;
		mpq_set(s, tmp);
	}
	mpq_canonicalize(s);

	for(int i = 0; ; i++) {
		continued_fraction_approximation(tmp, qapprox, i);
		if(fabs(mpq_get_d(t)-qapprox) < 1e-10
		   || (mpz_cmpabs_ui(mpq_numref(tmp),acc) > 0 && mpz_cmpabs_ui(mpq_denref(tmp),acc) > 0))
			break;
		mpq_set(q, tmp);
	}
	mpq_canonicalize(q);

	tqfactor = pow((mpq_get_d(s)*mpq_get_d(s)-mpq_get_d(s)+1)*(mpq_get_d(s)*mpq_get_d(s)-mpq_get_d(s)+1)*(mpq_get_d(s)*mpq_get_d(s)+1), 1/6.0);

	// group
	// order of the triangle reflection generators: a, b, c
	// order of the rotation orders: bc, ac, ab
	DEBUG("Generate group\n");
	group = coxeter_init_triangle(4, 3, 3, nmax);

	DEBUG("Compute matrices\n");
	enumerate(group, matrices, 4, 3, 3, s, q);

	n = 0;
	DEBUG("Compute traces\n");
	for(int i = 0; i < nmax; i++) {
		if(group->elements[i].length % 2 != 0 || !group->elements[i].inverse)
			continue;

		invariants[i].id = i;
		mat_trace(invariants[i].tr, matrices[i]);
		mat_trace(invariants[i].trinv, matrices[group->elements[i].inverse->id]);

		distinct_invariants[n++] = &invariants[i];
	}

	DEBUG("Get unique traces\n");

	qsort(distinct_invariants, n, sizeof(struct result*), compare_result);

	nuniq = 0;
	for(int i = 0; i < n; i++) {
		if(i == 0 || compare_result(&distinct_invariants[i], &distinct_invariants[nuniq-1]) != 0) {
			distinct_invariants[nuniq] = distinct_invariants[i];
			distinct_invariants[nuniq]->count = 1;
			nuniq++;
		} else {
			distinct_invariants[nuniq-1]->count++;
			int oldlength = group->elements[distinct_invariants[nuniq-1]->id].length;
			int newlength = group->elements[distinct_invariants[i]->id].length;
			if(newlength < oldlength)
				distinct_invariants[nuniq-1]->id = distinct_invariants[i]->id;
		}

//		gmp_printf("%d %d %s\n", i, nuniq-1, print_word(&group->elements[i], buf));
	}

	max_slope = 0;
	int max_slope_index;

	DEBUG("Solve characteristic polynomials\n");
	for(int i = 0; i < nuniq; i++) {
		retval = solve_characteristic_polynomial(solver, distinct_invariants[i]->tr, distinct_invariants[i]->trinv, evs);
		if(retval == 1) {
			fprintf(stderr, "Error! Could not solve polynomial.\n");
			continue;
		} else if(retval == 2) {
			continue;
		}

		if(fabs(evs[0]) < fabs(evs[1]))
			SWAP(double, evs[0], evs[1]);
		if(fabs(evs[1]) < fabs(evs[2]))
			SWAP(double, evs[1], evs[2]);
		if(fabs(evs[0]) < fabs(evs[1]))
			SWAP(double, evs[0], evs[1]);

		double x = log(fabs(evs[0]));
		double y = -log(fabs(evs[2]));

		distinct_invariants[i]->x = x;
		distinct_invariants[i]->y = y;

		if(y/x > max_slope && (x > 0.1 || y > 0.1)) {
			max_slope_index = distinct_invariants[i] - invariants;
			max_slope = y/x;
		}
	}

	qsort(distinct_invariants, nuniq, sizeof(struct result*), compare_result_by_slope);

	gmp_fprintf(stdout, "\"s = %Qd = %.3f, q = %Qd, t = %.3f\"\n", s, mpq_get_d(s), q, mpq_get_d(q)*tqfactor);

//	printf("- 0 0 - - - - 0.5\n");
	int cumulative = 0;
	double slope;
	for(int i = 0; i < nuniq; i++) {
		slope = distinct_invariants[i]->y/distinct_invariants[i]->x;

		mpq_set_si(tmp, 1, 1);
		if(mpq_cmp(distinct_invariants[i]->tr, tmp) == 0 && mpq_cmp(distinct_invariants[i]->trinv, tmp) == 0) {
			continue;
		}
		mpq_set_si(tmp, 0, 1);
		if(mpq_cmp(distinct_invariants[i]->tr, tmp) == 0 && mpq_cmp(distinct_invariants[i]->trinv, tmp) == 0) {
			continue;
		}
		mpq_set_si(tmp, -1, 1);
		if(mpq_cmp(distinct_invariants[i]->tr, tmp) == 0 && mpq_cmp(distinct_invariants[i]->trinv, tmp) == 0) {
			continue;
		}
		mpq_set_si(tmp, 3, 1);
		if(mpq_cmp(distinct_invariants[i]->tr, tmp) == 0 && mpq_cmp(distinct_invariants[i]->trinv, tmp) == 0) {
			continue;
		}

		cumulative += distinct_invariants[i]->count;
		gmp_printf("%d %d %d %Qd %Qd %f %f %f %f %f %s\n",
		           distinct_invariants[i]->id, distinct_invariants[i]->count, cumulative,
		           distinct_invariants[i]->tr, distinct_invariants[i]->trinv,
		           log(fabs(mpq_get_d(distinct_invariants[i]->tr))), log(fabs(mpq_get_d(distinct_invariants[i]->trinv))),
		           distinct_invariants[i]->x, distinct_invariants[i]->y, slope,
		           print_word(&group->elements[distinct_invariants[i]->id], buf)
			);
	}
//	printf("- 0 %d - - - - 2.0\n", cumulative);

	DEBUG("Clean up\n");
	for(int i = 0; i < nmax; i++) {
		mpq_clear(invariants[i].tr);
		mpq_clear(invariants[i].trinv);
	}
	free(invariants);
	free(distinct_invariants);
	for(int i = 0; i < nmax; i++)
		mat_clear(matrices[i]);
	free(matrices);
	coxeter_clear(group);
	mpq_clears(s, q, t, tmp, NULL);
	mps_context_free(solver);
}