#include <math.h>
#include <stdio.h>
double const pi = 3.1415926535897932385;
static double pyr(double x, double t){
  if(t<0) return pyr(x, -t);
  if(x<0) return pyr(-x, t);
  if(t>pi) return -pyr(x, t-pi);
  if(x>pi) return -pyr(x-pi, t);
  if(x>pi/2) return -pyr(pi-x, t);
  if(t>pi/2) return -pyr(x, pi-t);
  return x+t<pi/2?1:0;}
static double fs(double x, double t, int n){
  double s = 0;
  while (n--) if(n&1) s += (n&2?-1:1)*cos(n*x)*cos(n*t)/n;
  return 4./pi*s;}
static void rp(double x, double t){
  printf("%11.7f %11.7f %10.4f %16.11f\n", x, t, pyr(x,t), fs(x,t,100000));}
int main(){
  rp(0,0); rp(pi/2+.001,0); rp(pi/2-.001, 0); rp(1,0); rp(.1, .2);
  rp(2, pi/2); rp(.2, 1.45); rp(2, 1.7);
  rp(-1,4); rp(-3,-5);
  rp(pi/2-1, .99);   rp(pi/2-1, 1.01);
  rp(pi-2, 7-2*pi); rp(2, 7-2*pi); rp(2,7); rp(2.,-7);
  return 0;}

/*
  0.0000000   0.0000000     1.0000    0.99999363380
  1.5717963   0.0000000    -1.0000   -0.99454362020
  1.5697963   0.0000000     1.0000    0.99454362020
  1.0000000   0.0000000     1.0000    1.00001177513
  0.1000000   0.2000000     1.0000    1.00000503326
  2.0000000   1.5707963    -0.0000   -0.00000000000
  0.2000000   1.4500000     0.0000   -0.00003005031
  2.0000000   1.7000000     0.0000    0.00000020096
 -1.0000000   4.0000000    -0.0000    0.00000784572
 -3.0000000  -5.0000000    -1.0000   -0.99997138300
  0.5707963   0.9900000     1.0000    0.99981897444
  0.5707963   1.0100000     0.0000    0.00017709610
  1.1415927   0.7168147     0.0000   -0.00000772829
  2.0000000   0.7168147    -0.0000    0.00000772829
  2.0000000   7.0000000    -0.0000    0.00000772829
  2.0000000  -7.0000000    -0.0000    0.00000772829
*/