computeEpsilon.cpp

struct FloatBits
{
	u32 mantissa : 23;
	u32 exponent : 8;
	u32 sign : 1;
};

template <typename ResultT, typename InputT>
inline ResultT bitCast(InputT v)
{
	static_assert(sizeof(ResultT) == sizeof(InputT), "Size of source and destination must match.");
	ResultT result;
	memcpy(&result, &v, sizeof(v));
	return result;
}

inline float computeEpsilon(float f, u32 epsilonMantissa /*e.g. 16*/)
{
	FloatBits inputBits = bitCast<FloatBits>(f);

	FloatBits epsilonBits1;
	epsilonBits1.sign = 0;
	epsilonBits1.exponent = inputBits.exponent;
	epsilonBits1.mantissa = 0;

	FloatBits epsilonBits2;
	epsilonBits2.sign = 0;
	epsilonBits2.exponent = inputBits.exponent;
	epsilonBits2.mantissa = epsilonMantissa;

	float e1 = bitCast<float>(epsilonBits1);
	float e2 = bitCast<float>(epsilonBits2);

	float result = e2 - e1;

	return result;
}

inline float computeEpsilonPow2(float f, u32 exponentDiff /*e.g. 19*/)
{
	FloatBits inputBits = bitCast<FloatBits>(f);

	FloatBits epsilonBits;
	epsilonBits.sign = 0;
	epsilonBits.exponent = inputBits.exponent - std::min(inputBits.exponent, exponentDiff);
	epsilonBits.mantissa = 0;

	float result = bitCast<float>(epsilonBits);

	return result;
}