void rotnumber(long double xi1, long double yi1, int time) {
__float128 x = xi1;
__float128 y = yi1;
__float128 xn;
__float128 yn;
__float128 xav=0.Q;
__float128 yav=0.Q;
__float128 cosval=0.Q;
__float128 dot, mo, mn, theta;
__float128 rho=0.Q;
__float128 wsum=0.Q;
for(int t=0; t< time; t++) {
wsum+=weight((__float128)t/(__float128)time);
}
for(int t=0; t < time; t++) {
xav+=x*weight((__float128)t/(__float128)time);
yav+=y*weight((__float128)t/(__float128)time);
xn = smod(x+y,2.Q*M_PIq);
yn = smod(y+1.4Q*sinq(x+y),2.Q*M_PIq);
x=xn;
y=yn;
}
xav/=wsum;
yav/=wsum;
mn = sqrtq((x-xav)*(x-xav) + (y-yav)*(y-yav));
for(int t=0; t< time; t++) {
xn = smod(x+y,2.Q*M_PIq);
yn = smod(y+1.4Q*sinq(x+y),2.Q*M_PIq);
dot = (xn-xav)*(x-xav) + (yn-yav)*(y-yav);
mo = mn;
mn = sqrtq((xn-xav)*(xn-xav) + (yn-yav)*(yn-yav));
cosval = dot/(mo*mn);
theta = acosq(cosval);
rho += theta*weight((__float128)t/(__float128)time);
x=xn;
y=yn;
}
rho/=wsum*2.Q*M_PIq;
printf("The rotation number at (xi=%Lf, yi=%Lf) is %.20Lf\n",xi1,yi1,(long double)rho);
}
void test() {
for (ll a = -20; a < 20; a++) {
for (ll b = 2; b < 40; b++) {
if (gcd(a, b) == 1) {
assert_equal(1LL, smod((a * mod_inv(a, b)), b));
} else {
assert_equal(-1LL, mod_inv(a, b));
}
}
}
}
pair<ll,ll> linear_congruence(ll a, ll b, ll n) {
ll x, y, d = egcd(smod(a,n), n, x, y);
if ((b = smod(b,n)) % d != 0) return ii(0,0);
return make_pair(smod(b / d * x, n),n/d); }
void curve_convergence(long double ax1, long double ay1, long double bx1, long double by1, long double anonlin, int numpoints, int time, int fnum, int preshift, double (*points)[2]) {
FILE *f;
const char name[] = "outputs/text_quasi_curve_t%u_np%u_ax%.2Lf_ay%.2Lf_bx%.2Lf_by%.2Lf.txt";
char fname[100];
sprintf(fname, name, time,numpoints,ax1,ay1,bx1,by1);
f= fopen(fname,"w");
int t, v;
__float128 wsum=0;
for(t=0; t<time; t++) {
wsum += weight((__float128)t/(__float128)time);
}
__float128 ax = ax1;
__float128 bx = bx1;
__float128 ay = ay1;
__float128 by = by1;
__float128 x,y, xn, yn;
__float128 first[fnum];
__float128 second[fnum];
__float128 diff[fnum];
__float128 diff_mag;
__float128 numzeros;
__float128 wvar;
__float128 nonlin=anonlin;
for(int p=0; p < numpoints; p++) {
x = ax + (bx-ax)*((__float128)p/(__float128)numpoints);
y = ay + (by-ay)*((__float128)p/(__float128)numpoints);
fprintf(f,"x: %.10Lf, y: %.10Lf, ", (long double)x, (long double)y);
for(int s=0; s < preshift; s++) {
for(t=0; t< time; t++) {
xn = smod(x+y,2.Q*M_PIq);
yn = smod(nonlin*sinq(x+y)+y,2.Q*M_PIq);
x = xn;
y = yn;
}
}
memset(first, 0, sizeof(__float128)*fnum);
for( t=0; t<time; t++) {
wvar = weight((__float128)t/(__float128)time);
for(v=0; v<fnum;v++) {
first[v] += (*fvec[v])(x,y)*wvar;
}
xn = smod(x+y,2.Q*M_PIq);
yn = smod(nonlin*sinq(x+y)+y,2.Q*M_PIq);
x = xn;
y = yn;
}
memset(second,0,sizeof(__float128)*fnum);
for( t=0; t <time; t++) {
wvar = weight((__float128)t/(__float128)time);
for(v=0; v<fnum;v++) {
second[v]+= (*fvec[v])(x,y)*wvar;
}
xn = smod(x+y,2.Q*M_PIq);
yn = smod(nonlin*sinq(x+y)+y,2.Q*M_PIq);
x = xn;
y = yn;
}
diff_mag=0.Q;
for(v=0; v<fnum; v++) {
diff[v]=(second[v]-first[v])/wsum;
diff_mag+=diff[v]*diff[v];
}
diff_mag = sqrtq(diff_mag);
numzeros = (__float128)(-1.Q*log10q(diff_mag));
fprintf(f,"numzeros: %.12Lf\n",(long double)numzeros);
points[p][0] = (double)p/(__float128)numpoints;
points[p][1] = (double)numzeros;
printf("numzeros: %.20Lf\n",(long double)numzeros);
}
}
void convergence(int rows, int cols, int time, long double aleastx, long double aleasty,
long double adeltax, long double adeltay, int fnum, char (*m)[cols]) {
printf("Running Optimized Version of Quasiperiodicity\n");
unsigned int i, j, t, v;
FILE *f;
const char name[] = "outputs/text_optquasi_conv_t%u_g%u_xs%.2Lf_ys%.2Lf_xb%.2Lf_yb%.2Lf.txt";
char fname[100];
sprintf(fname, name, time,rows, aleastx, aleasty, aleastx+rows*adeltax,aleasty+cols*adeltay);
f= fopen(fname,"w");
fprintf(f,"ONLY BOX IS CERTAIN\n\n");
unsigned int** traj = (unsigned int**) malloc(sizeof(unsigned int*)*time);
int ntraj=0;
for(int o=0; o < time; o++) {
traj[o] = (unsigned int*) malloc(sizeof(unsigned int)*2);
}
__float128 wsum=0;
for(t=0; t<time; t++) {
wsum += weight((__float128)t/(__float128)time);
}
__float128 x,y, xn, yn;
__float128 first[fnum];
__float128 second[fnum];
__float128 diff[fnum];
__float128 diff_mag;
char numzeros;
__float128 wvar;
__float128 leastx = aleastx;
__float128 leasty = aleasty;
__float128 deltax = adeltax;
__float128 deltay = adeltay;
for(i=0; i < rows; i++) {
printf("i is: %u\n", i);
for(j=0; j < cols; j++) {
if(m[i][j]==-1) {
ntraj++;
x = leastx + j*deltax+0.5*deltax;
y = leasty + i*deltay+0.5*deltay;
memset(first, 0, sizeof(__float128)*fnum);
for( t=0; t<time; t++) {
wvar = weight((__float128)t/(__float128)time);
for(v=0; v<fnum;v++) {
first[v] += (*fvec[v])(x,y)*wvar;
}
xn = smod(x+y,2.Q*M_PIq);
yn = smod(1.4Q*sinq(x+y)+y,2.Q*M_PIq);
traj[t][0] = floorq((x-leastx)/deltax);
traj[t][1] = floorq((y-leasty)/deltay);
x = xn;
y = yn;
}
memset(second,0,sizeof(__float128)*fnum);
for( t=0; t <time; t++) {
wvar = weight((__float128)t/(__float128)time);
for(v=0; v<fnum;v++) {
second[v]+= (*fvec[v])(x,y)*wvar;
}
xn = smod(x+y,2.Q*M_PIq);
yn = smod(1.4Q*sinq(x+y)+y,2.Q*M_PIq);
x = xn;
y = yn;
}
diff_mag=0.Q;
for(v=0; v<fnum; v++) {
diff[v]=(second[v]-first[v])/wsum;
diff_mag+=diff[v]*diff[v];
}
diff_mag = sqrtq(diff_mag);
numzeros = (char)(-1.Q*log10q(diff_mag));
for(t=0;t<time;t++) {
m[(int)fmin(fmax(traj[t][1],0),rows-1)][(int)fmin(fmax(traj[t][0],0),cols-1)] = numzeros;
}
//m[i][j]=(unsigned char)numzeros; (old way)
}
}
}
for(int o=0; o< time; o++) {
free(traj[o]);
}
free(traj);
for(int i=0; i<rows; i++) {
for(int j=0; j<cols; j++) {
fprintf(f, "m[%u][%u] is %d",i,j,m[i][j]);
}
}
printf("%u\n",m[8][8]);
}
void partition(int weighted, int rows, int cols, int time, long double aleastx, long double aleasty,
long double adeltax, long double adeltay, int kgrid, unsigned long (*m)[cols]) {
FILE *f;
const char name[] = "outputs/text_birkhoff_fvals_t%u_g%u_xs%.2Lf_ys%.2Lf_xb%.2Lf_yb%.2Lf_%s_2.txt";
char fname[100];
if(weighted) {
sprintf(fname, name, time,rows, aleastx, aleasty, aleastx+rows*adeltax,aleasty+cols*adeltay,"weighted");
} else {
sprintf(fname, name, time,rows, aleastx, aleasty, aleastx+rows*adeltax,aleasty+cols*adeltay,"unweighted");
}
__float128 leastx = aleastx;
__float128 leasty = aleasty;
__float128 deltax = adeltax;
__float128 deltay = adeltay;
f= fopen(fname,"w");
clock_t begin,end;
begin = clock();
int i, j, t, v;
__float128 x,y, xn, yn;
__float128 wsum=0.;
__float128* weights = (__float128*) malloc(sizeof(__float128)*time);
for(t=0; t<time; t++) {
weights[t]=weight((__float128)t/(__float128)time);
wsum += weights[t];
}
__float128 ***evecs = (__float128***) malloc(sizeof(__float128**)*rows);
for(int i=0; i < rows; i++) {
evecs[i] = (__float128 **) malloc(sizeof(__float128*)*cols);
for(int j=0; j < cols; j++) {
evecs[i][j] = calloc(sizeof(__float128),2);
}
}
for(i=0; i < rows; i++) {
for(j=0; j < cols; j++) {
if(m[i][j]==1) {
x = leastx + j*deltax + 0.5Q*deltax;
y = leasty + i*deltay + 0.5Q*deltay;
for( t=0; t <time; t++) {
for( v=0; v<2;v++) {
if(weighted) {
evecs[i][j][v]+= (*hvec[v])(x,y)*weights[t];
} else {
evecs[i][j][v]+= (*hvec[v])(x,y);
}
}
xn = smod(x+y,2.Q*M_PIq);
yn = smod(.5*sin(x+y)+y,2.Q*M_PIq);
x = xn;
y = yn;
}
for( v=0; v<2;v++) {
if(weighted) {
evecs[i][j][v]/=wsum;
} else {
evecs[i][j][v]/=(__float128)time;
}
}
}
}
}
//__float128 fdelta = 1.Q/(__float128)kgrid;
for(i=0; i < rows; i++) {
for(j=0; j < cols; j++) {
fprintf(f,"i: %u, j: %u,x: %.2f, y: %.2f, h1: %.2f, h2: %.2f, h2/h1: %.2f\n", i, j, (double)leastx+j*(double)deltax,(double)leasty+i*(double)deltay,(double)evecs[i][j][0],(double)evecs[i][j][1],(double)evecs[i][j][1]/(double)evecs[i][j][0]);
if(m[i][j]==1) {
m[i][j]=0;
//for(v=0; v<2; v++) {
printf("evecs[%u][%u][0] = %f\n",i,j,(double)evecs[i][j][0]);
printf("evecs[%u][%u][1] = %f\n",i,j,(double)evecs[i][j][1]);
m[i][j] = floor(100000.Q*evecs[i][j][1]/evecs[i][j][0]);//+= floor(evecs[i][j][v]/fdelta) * pow(kgrid,v);
//}
}
}
}
fclose(f);
end=clock();
double runtime = (double)(end-begin)/(double)CLOCKS_PER_SEC;
printf("run time: %f\n",runtime);
/*for(i=0; i <rows; i++) {
for(j=0; j<cols; j++) {
printf("%u", m[i][j]);
}
printf("\n");
}*/
}