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);
}
tFloat GaussSeidel::residual(tFloat *_x)
{
// Residuo
tFloat sum, res = 0.0q;
for(tInteger i = 0; i<neqmax; i++){
sum = b[i]-ax[i]*_x[i];
for(tInteger j=0; j<neIndex[i]; j++)
sum -= A[i][j]*_x[AIndex[i][j]];
res += sum*sum;
}
return sqrtq(res);
}
/* Square root algorithm from glibc. */
__complex128
csqrtq (__complex128 z)
{
__float128 re = REALPART(z), im = IMAGPART(z);
__complex128 v;
if (im == 0)
{
if (re < 0)
{
COMPLEX_ASSIGN (v, 0, copysignq (sqrtq (-re), im));
}
else
{
COMPLEX_ASSIGN (v, fabsq (sqrtq (re)), copysignq (0, im));
}
}
else if (re == 0)
{
__float128 r = sqrtq (0.5 * fabsq (im));
COMPLEX_ASSIGN (v, r, copysignq (r, im));
}
else
{
__float128 d = hypotq (re, im);
__float128 r, s;
/* Use the identity 2 Re res Im res = Im x
to avoid cancellation error in d +/- Re x. */
if (re > 0)
r = sqrtq (0.5 * d + 0.5 * re), s = (0.5 * im) / r;
else
s = sqrtq (0.5 * d - 0.5 * re), r = fabsq ((0.5 * im) / s);
COMPLEX_ASSIGN (v, r, copysignq (s, im));
}
return v;
}
bool is_prime(long long int x) {
long long int root = sqrtq(x);
long long int i;
if(x == 2) {
return 1;
}
for(i = 3; i < root; i += 2) {
if(x % i ==0) {
return 0;
}
}
return 1;
}
inline __float128 abs( std::complex< __float128 > x )
{
return sqrtq( x.real() * x.real() + x.imag() * x.imag() );
}
inline __float128 sqrt( __float128 x )
{
return sqrtq( x );
}
inline void eval_sqrt(float128_backend& result, const float128_backend& arg)
{
result.value() = sqrtq(arg.value());
}
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]);
}
inline Quad Sqrt( const Quad& alpha ) { return sqrtq(alpha); }
__float128
hypotq (__float128 x, __float128 y)
{
__float128 a, b, t1, t2, y1, y2, w;
int64_t j, k, ha, hb;
GET_FLT128_MSW64(ha,x);
ha &= 0x7fffffffffffffffLL;
GET_FLT128_MSW64(hb,y);
hb &= 0x7fffffffffffffffLL;
if(hb > ha) {a=y;b=x;j=ha; ha=hb;hb=j;} else {a=x;b=y;}
SET_FLT128_MSW64(a,ha); /* a <- |a| */
SET_FLT128_MSW64(b,hb); /* b <- |b| */
if((ha-hb)>0x78000000000000LL) {return a+b;} /* x/y > 2**120 */
k=0;
if(ha > 0x5f3f000000000000LL) { /* a>2**8000 */
if(ha >= 0x7fff000000000000LL) { /* Inf or NaN */
uint64_t low;
w = a+b; /* for sNaN */
GET_FLT128_LSW64(low,a);
if(((ha&0xffffffffffffLL)|low)==0) w = a;
GET_FLT128_LSW64(low,b);
if(((hb^0x7fff000000000000LL)|low)==0) w = b;
return w;
}
/* scale a and b by 2**-9600 */
ha -= 0x2580000000000000LL;
hb -= 0x2580000000000000LL; k += 9600;
SET_FLT128_MSW64(a,ha);
SET_FLT128_MSW64(b,hb);
}
if(hb < 0x20bf000000000000LL) { /* b < 2**-8000 */
if(hb <= 0x0000ffffffffffffLL) { /* subnormal b or 0 */
uint64_t low;
GET_FLT128_LSW64(low,b);
if((hb|low)==0) return a;
t1=0;
SET_FLT128_MSW64(t1,0x7ffd000000000000LL); /* t1=2^16382 */
b *= t1;
a *= t1;
k -= 16382;
} else { /* scale a and b by 2^9600 */
ha += 0x2580000000000000LL; /* a *= 2^9600 */
hb += 0x2580000000000000LL; /* b *= 2^9600 */
k -= 9600;
SET_FLT128_MSW64(a,ha);
SET_FLT128_MSW64(b,hb);
}
}
/* medium size a and b */
w = a-b;
if (w>b) {
t1 = 0;
SET_FLT128_MSW64(t1,ha);
t2 = a-t1;
w = sqrtq(t1*t1-(b*(-b)-t2*(a+t1)));
} else {
a = a+a;
y1 = 0;
SET_FLT128_MSW64(y1,hb);
y2 = b - y1;
t1 = 0;
SET_FLT128_MSW64(t1,ha+0x0001000000000000LL);
t2 = a - t1;
w = sqrtq(t1*y1-(w*(-w)-(t1*y2+t2*b)));
}
if(k!=0) {
uint64_t high;
t1 = 1.0Q;
GET_FLT128_MSW64(high,t1);
SET_FLT128_MSW64(t1,high+(k<<48));
return t1*w;
} else return w;
}
