#include <assert.h>
#include <math.h>

const double pi=3.1415926;
const double half=0.5;

double cauchyDF(double x, double a, double b)
{
   assert(b > 0);
   return half+atan((x-a)/b)/pi;
}

double inv_cauchyDF(double q, double a, double b)
{
   assert((b > 0) && (q > 0) && (q < 1));
   return a+b*tan(pi*(q-half));
}

#ifdef TEST

#include <iostream.h>

void main(void)
{
   double a, b;

   while (1) {
      cout << "\n\n\rEnter a: ";
      cin >> a;
      if (a <= 0)
	 break;
      do {
         cout << "Enter b: ";
         cin >> b;
      } while (b <= 0);

      for(double x=-8; x < 8; x += 0.1)
      {
         double y=cauchyDF(x, a, b);
         cout << "x=" << x << "\tcauchy=" << y;
         double z=inv_cauchyDF(y, a, b);
         cout << "\ti_cauchy=" << z << endl;
      }
   }
}

#endif