constexpr functions to encode and decode IEEE754 binary64 doubles.

ieee754.cpp

#include <iostream>
#include <vector>
#include <cstdint>

constexpr double decode_double(std::uint64_t encoded) {
	bool s = encoded >> 63;
	std::int16_t e = encoded >> 52 & 0x7FF;
	std::int64_t m = encoded & (1ULL << 52) - 1;
	if (e == 2047) return m ? s ? 0/0.0 : -(0/0.0) : s ? -1/0.0 : 1/0.0;
	double x = m | (e ? 1ULL << 52 : 0);
	e -= 1024 + 51 - (e == 0);
	while (e > 0) { x *= 2; --e; }
	while (e < 0) { x /= 2; ++e; }
	return s ? -x : x;
}

constexpr std::uint64_t encode_double(double x) {
	bool s = !(x == 0 ? 1/x >= 0 : x >= 0);
	if (s) x = -x;
	int e = 1024 + 51;
	while (!(x <= (1ULL << 53)) && e < 2047) { x /= 2; ++e; }
	while (x < (1ULL << 52) && e > 1) { x *= 2; --e; }
	std::uint64_t m = e < 2047 ? x : std::uint64_t(!(x == x)) << 51;
	if (e == 1 && !(m >> 52 & 1)) e = 0;
	m = m & (1ULL << 52) - 1;
	return std::uint64_t(s) << 63 | std::uint64_t(e) << 52 | m;
}

int main() {
	std::vector<double> testcases{
		1, -123e-100, 1234e100, 0.7e-308, -1.3e-308, 1.1e308,
		1/0.0, -1/0.0, 0/0.0
	};
	for (double d : testcases) {
		std::cout << std::hex << reinterpret_cast<std::uint64_t const &>(d) << ' ' << d << std::endl;
		auto e = encode_double(d);
		std::cout << std::hex << e << ' ' << decode_double(e) << std::endl;
		std::cout << std::endl;
	}
}