#include "triangle.h"
#include "linalg.h"
#include "mat.h"

#include <gsl/gsl_poly.h>

//#define MAX_ELEMENTS 2800000
//#define MAX_ELEMENTS 720000
#define MAX_ELEMENTS 14000
//#define DRAW_PICTURE 1

void mpq_quartic(mpq_t out, mpq_t in, int a, int b, int c, int d, int e)
{
	mpq_t tmp;
	mpq_init(tmp);

	mpq_set_si(out, a, 1);
	mpq_mul(out, out, in);
	mpq_set_si(tmp, b, 1);
	mpq_add(out, out, tmp);
	mpq_mul(out, out, in);
	mpq_set_si(tmp, c, 1);
	mpq_add(out, out, tmp);
	mpq_mul(out, out, in);
	mpq_set_si(tmp, d, 1);
	mpq_add(out, out, tmp);
	mpq_mul(out, out, in);
	mpq_set_si(tmp, e, 1);
	mpq_add(out, out, tmp);

	mpq_clear(tmp);
}

void initialize_triangle_generators(mat_workspace *ws, mat *gen, mpq_t s, mpq_t t)
{
	mpq_set_ui(*mat_ref(gen[0], 0, 0), 0, 1);
	mpq_set_ui(*mat_ref(gen[0], 0, 1), 0, 1);
	mpq_set_ui(*mat_ref(gen[0], 0, 2), 1, 1);
	mpq_set_ui(*mat_ref(gen[0], 1, 0), 1, 1);
	mpq_set_ui(*mat_ref(gen[0], 1, 1), 0, 1);
	mpq_set_ui(*mat_ref(gen[0], 1, 2), 0, 1);
	mpq_set_ui(*mat_ref(gen[0], 2, 0), 0, 1);
	mpq_set_ui(*mat_ref(gen[0], 2, 1), 1, 1);
	mpq_set_ui(*mat_ref(gen[0], 2, 2), 0, 1);

	mpq_set_ui(*mat_ref(gen[1], 0, 0), 1, 1);
	mpq_set_ui(*mat_ref(gen[1], 1, 0), 0, 1);
	mpq_set_ui(*mat_ref(gen[1], 2, 0), 0, 1);
	mpq_quartic(*mat_ref(gen[1], 0, 1), t, 0, 0, 1, -1, 2);
	mpq_quartic(*mat_ref(gen[1], 1, 1), t, 0, 0, -1, 2, -2);
	mpq_quartic(*mat_ref(gen[1], 2, 1), t, 0, 0, 1, -3, 3);
	mpq_quartic(*mat_ref(gen[1], 0, 2), t, 0, 0, 1, 0, 3);
	mpq_quartic(*mat_ref(gen[1], 1, 2), t, 0, 0, -1, 1, -1);
	mpq_quartic(*mat_ref(gen[1], 2, 2), t, 0, 0, 1, -2, 1);

	mat_pseudoinverse(ws, gen[3], gen[0]); // p^{-1}
	mat_pseudoinverse(ws, gen[4], gen[1]); // q^{-1}
	mat_multiply(ws, gen[2], gen[4], gen[3]); // r = q^{-1}p^{-1}
	mat_pseudoinverse(ws, gen[5], gen[2]);

//	mat_print(gen[0]);
//	mat_print(gen[1]);
//	mat_print(gen[2]);
//	mat_print(gen[3]);
//	mat_print(gen[4]);
//	mat_print(gen[5]);
}

char *print_word(groupelement_t *g, char *str)
{
  int i = g->length - 1;

  str[g->length] = 0;
  while(g->parent) {
    str[i--] = 'a' + g->letter;
    g = g->parent;
  }

  return str;
}

int main(int argc, char *argv[])
{
  groupelement_t *group;
  mat_workspace *ws;
  mat *matrices;
  mat tmp;
  mat gen[6];
  char buf[100], buf2[100], buf3[100];
  mpq_t s,t;
  mpq_t det, tr, trinv;

  // allocate stuff
  group = malloc(MAX_ELEMENTS*sizeof(groupelement_t));
  ws = mat_workspace_init(3);
  matrices = malloc(MAX_ELEMENTS*sizeof(mat));
  for(int i = 0; i < MAX_ELEMENTS; i++)
	  mat_init(matrices[i], 3);
  for(int i = 0; i < 6; i++)
	  mat_init(gen[i], 3);
  mat_init(tmp, 3);

  mpq_inits(s, t, det, tr, trinv, NULL);

  mpq_set_ui(s,1,1);
  double t_ = atof(argv[1]);
  mpq_set_ui(t,(int)(t_*100),100);
  mpq_canonicalize(s);
  mpq_canonicalize(t);

  // the real action
  generate_triangle_group(group, MAX_ELEMENTS, 3, 3, 4);
  initialize_triangle_generators(ws, gen, s, t);

  mat_identity(matrices[0]);
  for(int i = 1; i < MAX_ELEMENTS; i++) {
	  if(group[i].length % 2 != 0)
		  continue;
	  if(!group[i].inverse)
		  continue;

	  int parent = group[i].parent->id;
	  int grandparent = group[i].parent->parent->id;
	  int letter;

	  if(group[parent].letter == 1 && group[i].letter == 2)
		  letter = 0; // p = bc
	  else if(group[parent].letter == 2 && group[i].letter == 0)
		  letter = 1; // q = ca
	  else if(group[parent].letter == 0 && group[i].letter == 1)
		  letter = 2; // r = ab
	  if(group[parent].letter == 2 && group[i].letter == 1)
		  letter = 3; // p^{-1} = cb
	  else if(group[parent].letter == 0 && group[i].letter == 2)
		  letter = 4; // q^{-1} = ac
	  else if(group[parent].letter == 1 && group[i].letter == 0)
		  letter = 5; // r^{-1} = ba

	  mat_multiply(ws, matrices[i], matrices[grandparent], gen[letter]);
  }

  for(int i = 0; i < MAX_ELEMENTS; i++) {
	  if(group[i].length % 2 != 0)
		  continue;
	  if(!group[i].inverse)
		  continue;

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

	  double lambda1, lambda2, lambda3;
//	  int realevs = gsl_poly_solve_cubic(-mpq_get_d(tr), mpq_get_d(trinv), -1, &lambda3, &lambda2, &lambda1);
//	  if(realevs != 3)
//		  continue;
//	  if(lambda1 < 0 || lambda2 < 0 || lambda3 < 0)
//		  continue;

//	  gmp_printf("%d %d %s %Qd %Qd\n", i, group[i].length, print_word(&group[i], buf), tr, trinv);
	  printf("%d %d %s %f %f %f\n", i, group[i].length, print_word(&group[i], buf), log(mpq_get_d(tr)), log(mpq_get_d(trinv)));

  }

  // free stuff
  for(int i = 0; i < MAX_ELEMENTS; i++)
    mat_clear(matrices[i]);
  for(int i = 0; i < 6; i++)
    mat_clear(gen[i]);
  mat_clear(tmp);
  mpq_clears(s, t, det, tr, trinv, NULL);
  mat_workspace_clear(ws);

  return 0;
}