374 lines
10 KiB
C
374 lines
10 KiB
C
#include "coxeter.h"
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#include "linalg.h"
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#include "mat.h"
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#include "enumerate_triangle_group.h"
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#include <time.h>
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#define SWAP(t,x,y) do { t _tmp = (x); (x) = (y); (y) = _tmp; } while (0);
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#define DEBUG(msg, ...) fprintf(stderr, "[%10.3f] " msg, runtime(), ##__VA_ARGS__);
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//#define DEBUG(msg, ...)
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struct result {
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int id;
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int count;
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mpq_t tr;
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mpq_t trinv;
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double x;
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double y;
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};
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static int compare_result(const void *a_, const void *b_)
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{
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int d = 0;
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struct result **a = (struct result **)a_;
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struct result **b = (struct result **)b_;
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d = mpq_cmp((*a)->tr,(*b)->tr);
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if(d == 0) {
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d = mpq_cmp((*a)->trinv, (*b)->trinv);
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}
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return d;
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}
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static int compare_result_by_id(const void *a_, const void *b_)
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{
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int d = 0;
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struct result **a = (struct result **)a_;
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struct result **b = (struct result **)b_;
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return (*a)->id - (*b)->id;
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}
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static int compare_result_by_tr_trinv_id(const void *a_, const void *b_)
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{
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int d = 0;
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struct result **a = (struct result **)a_;
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struct result **b = (struct result **)b_;
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d = mpq_cmp((*a)->tr,(*b)->tr);
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if(d == 0) {
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d = mpq_cmp((*a)->trinv, (*b)->trinv);
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if(d == 0) {
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d = (*b)->id - (*a)->id;
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}
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}
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return d;
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}
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static int compare_result_by_slope(const void *a_, const void *b_)
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{
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int d = 0;
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struct result **a = (struct result **)a_;
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struct result **b = (struct result **)b_;
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double slopea = (*a)->x / (*a)->y;
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double slopeb = (*b)->x / (*b)->y;
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return slopea > slopeb ? -1 : slopea < slopeb ? 1 : 0;
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}
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struct timespec starttime;
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static void start_timer()
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{
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clock_gettime(CLOCK_MONOTONIC, &starttime);
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}
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static double runtime()
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{
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struct timespec curtime;
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double diff;
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clock_gettime(CLOCK_MONOTONIC, &curtime);
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return (curtime.tv_sec - starttime.tv_sec) + (curtime.tv_nsec - starttime.tv_nsec) / 1e9;
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}
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int compute_invariants(group_t *group, mat *matrices, struct result **invariants, int *n, int unique)
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{
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mpq_t tmp;
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mps_context *solver;
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mps_monomial_poly *poly;
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int index;
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int ntraces = *n, nuniq;
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int retval;
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double evs[3];
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int max_slope_id;
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double max_slope;
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char buf[100];
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// DEBUG("Compute traces\n");
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for(int i = 0; i < ntraces; i++) {
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int id = invariants[i]->id;
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int invid = group->elements[id].inverse->id;
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mat_trace(invariants[i]->tr, matrices[id]);
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mat_trace(invariants[i]->trinv, matrices[invid]);
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}
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if(!unique)
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nuniq = ntraces;
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else {
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// DEBUG("Get unique traces\n");
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qsort(invariants, ntraces, sizeof(struct result*), compare_result);
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nuniq = 0;
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for(int i = 0; i < ntraces; i++) {
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if(i == 0 || compare_result(&invariants[i], &invariants[nuniq-1]) != 0) {
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invariants[nuniq] = invariants[i];
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invariants[nuniq]->count = 1;
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nuniq++;
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} else {
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invariants[nuniq-1]->count++;
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int oldlength = group->elements[invariants[nuniq-1]->id].length;
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int newlength = group->elements[invariants[i]->id].length;
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if(newlength < oldlength)
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invariants[nuniq-1]->id = invariants[i]->id;
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}
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}
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}
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DEBUG("Solve characteristic polynomials\n");
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solver = mps_context_new();
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poly = mps_monomial_poly_new(solver, 3);
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mps_context_set_output_prec(solver, 20); // relative precision
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mps_context_set_output_goal(solver, MPS_OUTPUT_GOAL_APPROXIMATE);
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max_slope = 0;
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for(int i = 0; i < nuniq; i++) {
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retval = solve_characteristic_polynomial(solver, poly, invariants[i]->tr, invariants[i]->trinv, evs);
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retval = 0;evs[0] = 2;evs[1] = 1;evs[2] = 0.5; // fake solving the polynomial for memory leak test
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if(retval == 1) {
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fprintf(stderr, "Error! Could not solve polynomial.\n");
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continue;
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} else if(retval == 2) {
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continue;
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}
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if(fabs(evs[0]) < fabs(evs[1]))
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SWAP(double, evs[0], evs[1]);
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if(fabs(evs[1]) < fabs(evs[2]))
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SWAP(double, evs[1], evs[2]);
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if(fabs(evs[0]) < fabs(evs[1]))
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SWAP(double, evs[0], evs[1]);
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double x = log(fabs(evs[0]));
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double y = -log(fabs(evs[2]));
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invariants[i]->x = x;
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invariants[i]->y = y;
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if(y/x > max_slope + 1e-12 && (x > 0.1 || y > 0.1)) {
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max_slope_id = invariants[i]->id;
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max_slope = y/x;
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} else if(y/x > max_slope - 1e-12 && (x > 0.1 || y > 0.1)) {
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// DEBUG("%s didn't quite make it\n",
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// print_word(&group->elements[invariants[i]->id], buf));
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}
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}
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mps_context_free(solver);
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qsort(invariants, nuniq, sizeof(struct result*), compare_result_by_id);
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*n = nuniq;
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return max_slope_id;
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}
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long check_memory_usage(mat *matrices, int n)
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{
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mpq_t x;
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long total;
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for(int i = 0; i < n; i++)
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{
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LOOP(j,3) LOOP(k,3) {
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total += mpq_numref(M(matrices[i], j, k))->_mp_size;
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total += mpq_denref(M(matrices[i], j, k))->_mp_size;
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}
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}
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return total;
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}
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int main(int argc, char *argv[])
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{
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mpq_t s, q, t, tmp;
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int p1, p2, p3;
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int sstart, send, sdenom, qstart, qend, qdenom;
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mat *matrices;
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group_t *group;
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int nmax, n;
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int max_slope_id;
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char buf[100];
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char buf2[100];
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struct result *invariants;
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struct result **distinct_invariants;
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start_timer();
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mpq_inits(s, q, t, tmp, NULL);
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if(argc < 11) {
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fprintf(stderr, "Usage: %s <N> <p1> <p2> <p3> <s start> <s end> <s denom> <q start> <q end> <q denom>\n", argv[0]);
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exit(1);
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}
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nmax = atoi(argv[1]);
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p1 = atoi(argv[2]);
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p2 = atoi(argv[3]);
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p3 = atoi(argv[4]);
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sstart = atoi(argv[5]);
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send = atoi(argv[6]);
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sdenom = atoi(argv[7]);
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qstart = atoi(argv[8]);
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qend = atoi(argv[9]);
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qdenom = atoi(argv[10]);
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DEBUG("Allocate\n");
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matrices = malloc(nmax*sizeof(mat));
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for(int i = 0; i < nmax; i++)
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mat_init(matrices[i], 3);
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invariants = malloc(nmax*sizeof(struct result));
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distinct_invariants = malloc(nmax*sizeof(struct result));
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for(int i = 0; i < nmax; i++) {
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mpq_init(invariants[i].tr);
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mpq_init(invariants[i].trinv);
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}
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// order of the triangle reflection generators: a, b, c
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// order of the rotation orders: bc, ac, ab
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DEBUG("Generate group\n");
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group = coxeter_init_triangle(p1, p2, p3, nmax);
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// first run; compute all matrices
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for(int i = 0; i < group->size; i++)
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group->elements[i].need_to_compute = 1;
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// use very generic values for the pilot run unless sstart=send and qstart=qend
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if(sstart == send && qstart == qend) {
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mpq_set_ui(s, sstart, sdenom);
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mpq_set_ui(q, qstart, qdenom);
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DEBUG("Single run for s = %d/%d, q = %d/%d\n", sstart, sdenom, qstart, qdenom);
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} else {
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mpq_set_ui(s, 4, 100);
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mpq_set_ui(q, 7, 100);
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DEBUG("Initial run for s = %d/%d, q = %d/%d\n", 4, 100, 7, 100);
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}
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DEBUG("Compute matrices\n");
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enumerate(group, matrices, p1, p2, p3, s, q);
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// prepare array of ids
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n = 0;
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for(int i = 0; i < group->size; i++)
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{
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if(group->elements[i].length % 2 != 0 || !group->elements[i].inverse)
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continue;
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invariants[i].id = i;
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distinct_invariants[n++] = &invariants[i];
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}
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DEBUG("Compute invariants\n");
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max_slope_id = compute_invariants(group, matrices, distinct_invariants, &n, 1);
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// prepare for next time; don't need to change ids in distinct_invariants!
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for(int i = 0; i < group->size; i++)
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group->elements[i].need_to_compute = 0;
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group->elements[0].need_to_compute = 1;
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int multiplication_count = 1;
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for(int i = 0; i < n; i++) {
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groupelement_t *cur = &group->elements[distinct_invariants[i]->id];
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while(cur->need_to_compute == 0) {
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cur->need_to_compute = 1;
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multiplication_count++;
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cur = cur->parent->parent; // also need to compute its even-length ancestors
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}
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cur = group->elements[distinct_invariants[i]->id].inverse;
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while(cur->need_to_compute == 0) {
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cur->need_to_compute = 1;
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multiplication_count++;
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cur = cur->parent->parent;
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}
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}
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DEBUG("Would have needed %d matrix multiplications for %d unique traces up to reflection length %d\n", multiplication_count, n, group->elements[group->size-1].length);
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if(sstart != send || qstart != qend) {
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for(int sloop = sstart; sloop <= send; sloop++) {
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for(int qloop = qstart; qloop <= qend; qloop++) {
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DEBUG("Loop for s = %d/%d, q = %d/%d\n", sloop, sdenom, qloop, qdenom);
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mpq_set_ui(s, sloop, sdenom);
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mpq_set_ui(q, qloop, qdenom);
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DEBUG("Compute matrices\n");
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enumerate(group, matrices, p1, p2, p3, s, q);
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DEBUG("Compute invariants\n");
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max_slope_id = compute_invariants(group, matrices, distinct_invariants, &n, 0);
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// output
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gmp_printf("%Qd %Qd %s\n", s, q,
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print_word(&group->elements[max_slope_id], buf));
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fflush(stdout);
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}
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}
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} else {
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// output
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for(int i = 0; i < n; i++) {
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double slope = distinct_invariants[i]->y/distinct_invariants[i]->x;
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// exclude tr = trinv = 2/1/0/-1/3
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mpq_set_si(tmp, 2, 1);
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if(mpq_cmp(distinct_invariants[i]->tr, tmp) == 0 &&
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mpq_cmp(distinct_invariants[i]->trinv, tmp) == 0)
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continue;
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mpq_set_si(tmp, 1, 1);
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if(mpq_cmp(distinct_invariants[i]->tr, tmp) == 0 &&
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mpq_cmp(distinct_invariants[i]->trinv, tmp) == 0)
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continue;
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mpq_set_si(tmp, 0, 1);
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if(mpq_cmp(distinct_invariants[i]->tr, tmp) == 0 &&
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mpq_cmp(distinct_invariants[i]->trinv, tmp) == 0)
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continue;
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mpq_set_si(tmp, -1, 1);
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if(mpq_cmp(distinct_invariants[i]->tr, tmp) == 0 &&
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mpq_cmp(distinct_invariants[i]->trinv, tmp) == 0)
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continue;
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mpq_set_si(tmp, 3, 1);
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if(mpq_cmp(distinct_invariants[i]->tr, tmp) == 0 &&
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mpq_cmp(distinct_invariants[i]->trinv, tmp) == 0)
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continue;
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gmp_printf("%d %d %s %f\n",
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distinct_invariants[i]->id, distinct_invariants[i]->count,
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print_word(&group->elements[distinct_invariants[i]->id], buf),
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slope
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);
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/*
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gmp_printf("%d %d %d %Qd %Qd %f %f %f %f %f %s\n",
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distinct_invariants[i]->id, distinct_invariants[i]->count, cumulative,
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distinct_invariants[i]->tr, distinct_invariants[i]->trinv,
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log(fabs(mpq_get_d(distinct_invariants[i]->tr))), log(fabs(mpq_get_d(distinct_invariants[i]->trinv))),
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distinct_invariants[i]->x, distinct_invariants[i]->y, slope,
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print_word(&group->elements[distinct_invariants[i]->id], buf)
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);
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*/
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}
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}
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DEBUG("Clean up\n");
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for(int i = 0; i < nmax; i++) {
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mpq_clear(invariants[i].tr);
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mpq_clear(invariants[i].trinv);
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}
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free(invariants);
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free(distinct_invariants);
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for(int i = 0; i < nmax; i++)
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mat_clear(matrices[i]);
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free(matrices);
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coxeter_clear(group);
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mpq_clears(s, q, t, tmp, NULL);
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}
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