The tiny code to show some of the floating point errors.

math_error.cpp

#include <iostream>
#include <string>
#include <cinttypes> // for uint32_t 
#include <cfenv>
#include <cmath>



std::string float_to_binary(float f) {
	union {float f; uint32_t i;} u;
	std::string str;
	u.f = f;
	for (int i = 0; i < 32; i++) {
		if (u.i % 2) str.push_back('1');
		else str.push_back('0');
		u.i >>= 1;
	}
	return str;

}

void print_this(std::string s, float f) {
	std::cout << s << " = " << float_to_binary(f) << std::endl;	
}


void very_many_errors() {
	float a;
	// double a; // precision errors will be fixed with change to double;
	int i;

	a = 0.1;
	print_this("0.1", a);
	a = 0.0;
	print_this("0.0", a);
	std::feclearexcept(FE_ALL_EXCEPT);
	a += 0.1;
	print_this("0.1", a);
	if(std::fetestexcept(FE_INEXACT))
		std::cout << "FE_INEXACT" << std::endl;

	a -= 0.1;
	print_this("0.0", a);

	if(std::fetestexcept(FE_INEXACT))
		std::cout << "FE_INEXACT" << std::endl;

	if (a == 0.0) {
		// The system to come to this part of the decision
		std::cout << "If 0.0" << std::endl;
	} else {
		std::cout << "Hang on why here" << std::endl;
	}

}





// Floating point roundoff error. This should not terminate but there is rounding error
int should_not_terminate() {
	double a = 0.2;
	int i;

	a += 0.1;
	a -= 0.3;

	for (i = 0; a < 1.0; i++)
		a += a;
	std::cout << "i=" << i << " ; " << "a=" << a << std::endl;
	return 0;
}






int main() {
	should_not_terminate();
	very_many_errors();
	return 0;
}