Calculates the flux over a Cat

flux.c

// Calculates the flux of f(x,y) = x^2/2 + y^2/2 over a cat. CAN I HAZ SUM FLUXZ?
#include "flux.h"

double M(double x, double y){
	return x; // X component of our gradient field.
}
double N(double x, double y){
	return y; // Y component of our gradient field.
}

int main(){
	
	B _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ R R _ _ _ _ _ _ _ _ _ _ P
	_ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _  R R R  _ _ _ _ _ _ _ _ _ P
	_ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _  R R  _ _ _ _ _ _ _ _ _ P
	_ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ R R _ _ _ _ _ _ _ _ _ P
	_ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _  R R  _ _ _ _ _ _ _ _ P
	_ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _  R R R  _ _ _ _ _ _ _ P
	_ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _  R R R  _ _ _ _ _ _ _ P
	_ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _  R R R  _ _ _ _ _ _ _ P
	_  R R _ R R  _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _  R R R  _ _ _ _ _ _ _ P
	_  R R R R R R R R R  _ _ _ _ _ _ _ _ _ _ _ _ _ _  R R R  _ _ _ _ _ _ _ P
	_ R R R R R R R R R R R R R  _ _ _ _ R R R R R R R R R R  _ _ _ _ _ _ _ P
	_ R R R R R R R R R R R R R R R R R R R R R R R R R R R _ _ _ _ _ _ _ _ P
	 R R R R R R R R R R R R R R R R R R R R R R R R R R R R  _ _ _ _ _ _ _ P
	 R R R R R R R R R R R R R R R R R R R R R R R R R R R R R  _ _ _ _ _ _ P
	R R R R R R R R R R R R R R R R R R R R R R R R R R R R R R _ _ _ _ _ _ P
	R R R R R R R R R R R R R R R R R R R R R R R R R R R R R R _ _ _ _ _ _ P
	_ R R  _ _ _ _ R R R R R R R R R R R R R R R R R R R R R R R R  _ _ _ _ P
	_ _ _ _ _ _ _ _  R R R R R R R R R R R R R R R R R R R R R R R  _ _ _ _ P
	_ _ _ _ _ _ _ _ R R R R R R R R R R R R R R R R R R R R R R R R R R _ _ P
	_ _ _ _ _ _  R R R R R R R R R R R R R R R R R R R R R R R R R R R R R  P
	_ _ _ _ _ _ R R R R R R R R R R R R R R R R R R R R R R R R R R R R R _ P
	_ _ _ _ _  R R R R  _ R R R  _ _ _ _ _ _ _  R R R R R  _ R R R R R R R  P
	_ _ _ _ _ R R R  _ _ R R R  _ _ _ _ _ _ _  R R R R R R  _ _ _ _  R R R  P
	_ _ _ _ _ R R  _ _ R R R R  _ _ _ _ _ _ R R R R R R  _ _ _ _ _  R R R _ P
	_ _ _ _ _ _ _ _ _ R R R R  _ _ _ _ _ _  R R R R  _ _ _ _ _ _ _ R R R R  P
	_ _ _ _ _ _ _ _ _ R R R  _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ R R R R  E

}

flux.h

#ifndef FLUX_H_
#define FLUX_H_

double M(double x, double y);
double N(double x, double y);

double Flux		(double x, double y, double d){return   M(x+d, y) - M(x, y) + N(x, y+d) - N(x, y);}
double Circulation(double x, double y, double d){return - N(x+d, y) + N(x, y) + M(x, y+d) - M(x, y);}

int X = 0, Y = 0, len = 0, max = 0;
int* list;

#define B list?free(list):0;list = (int*)malloc(sizeof(int));_
#define _ X++;
#define R X++;list[len]=hash(X,Y);list=(int*)realloc(list, (1+ ++len) * sizeof(int));list[len]=0;
#define P max=X>max?X:max;X=0;Y++;
#define E P X=max;printFlux();

unsigned int hash(unsigned int x, unsigned int y){
   return ((x << 19) | (y << 7));
}

int find(int* list, int target){
	while (*list && *list != target) list++;
	return *list;
}

double AreaIntegrator(int X, int Y, double d){
	float integral = 0.0;
	int x, y;
	for (x = 0; x < X; x++){
		float slice = 0.0;
		for (y = 0; y < Y; y++)
			if (find(list, hash(x,y)))
				slice += Flux(x, y, d);
		integral += slice*d;
	}
	return integral;
}

void printFlux(){
	printf("%f",AreaIntegrator(X,Y,0.05));
}

#endif /* FLUX_H_ */

Hey you might want to change B to

#define B list ? free(list) : 0; list = (int*)malloc(sizeof(int));_

Thanks, I haven't considered that before

Wait, it looks like you're integrating over a half circle there (what remains if you remove the spaces. Is that as intended?
*Sorry, that was in reference to the previous circle glyph. Don't forget the _ between the ears.

@cwgreene: It's actually suppose to be an approximation of a circle with four extra blocks (near the equator) to make it look prettier:

            R R R R            
       R R R R R R R R R       
    R R R R R R R R R R R R    
  R R R R R R R R R R R R R R  
 R R R R R R R R R R R R R R R 
 R R R R R R R R R R R R R R R 
R R R R R R R R R R R R R R R R R
R R R R R R R R R R R R R R R R R
R R R R R R R R R R R R R R R R R
R R R R R R R R R R R R R R R R R
 R R R R R R R R R R R R R R R 
 R R R R R R R R R R R R R R R 
  R R R R R R R R R R R R R R  
    R R R R R R R R R R R R    
        R R R R R R R R        
            R R R R            

also, thanks for pointing that out