source/src/geom/morton.hpp

/*
 * Copyright (C) 2021  Christopher J. Howard
 *
 * This file is part of Antkeeper source code.
 *
 * Antkeeper source code is free software: you can redistribute it and/or modify
 * it under the terms of the GNU General Public License as published by
 * the Free Software Foundation, either version 3 of the License, or
 * (at your option) any later version.
 *
 * Antkeeper source code is distributed in the hope that it will be useful,
 * but WITHOUT ANY WARRANTY; without even the implied warranty of
 * MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE.  See the
 * GNU General Public License for more details.
 *
 * You should have received a copy of the GNU General Public License
 * along with Antkeeper source code.  If not, see <http://www.gnu.org/licenses/>.
 */

#ifndef ANTKEEPER_GEOM_MORTON_HPP
#define ANTKEEPER_GEOM_MORTON_HPP

#include <array>
#include <cstdlib>

namespace geom {

/// Morton location code encoding and decoding functions.
namespace morton {

/**
 * Encodes 2D coordinates as a Morton location code.
 *
 * @param[in] x X-coordinate to encode.
 * @param[in] y Y-coordinate to encode.
 * @return Morton location code.
 */
template <typename T>
T encode(T x, T y);

/**
 * Encodes 3D coordinates as a Morton location code.
 *
 * @param[in] x X-coordinate to encode.
 * @param[in] y Y-coordinate to encode.
 * @param[in] z Z-coordinate to encode.
 * @return Morton location code.
 */
template <typename T>
T encode(T x, T y, T z);

/**
 * Decodes 2D coordinates from a Morton location code.
 *
 * @param[in] code Morton location code to decode.
 * @param[out] x Decoded x-coordinate.
 * @param[out] y Decoded y-coordinate.
 */
template <typename T>
void decode(T code, T& x, T& y);

/**
 * Decodes 3D coordinates from a Morton location code.
 *
 * @param[in] code Morton location code to decode.
 * @param[out] x Decoded x-coordinate.
 * @param[out] y Decoded y-coordinate.
 * @param[out] z Decoded z-coordinate.
 */
template <typename T>
void decode(T code, T& x, T& y, T& z);

template <typename T>
T encode(T x, T y)
{
	auto expand = [](T x) -> T
	{
		x &= (1 << (sizeof(T) << 2)) - 1;
		
		if constexpr(sizeof(T) >= 8)
			x = (x ^ (x << 16)) & T(0x0000ffff0000ffff);
		if constexpr(sizeof(T) >= 4)
			x = (x ^ (x <<  8)) & T(0x00ff00ff00ff00ff);
		if constexpr(sizeof(T) >= 2)
			x = (x ^ (x <<  4)) & T(0x0f0f0f0f0f0f0f0f);
		
		x = (x ^ (x << 2)) & T(0x3333333333333333);
		x = (x ^ (x << 1)) & T(0x5555555555555555);
		
		return x;
	};
	
	return expand(x) | (expand(y) << 1);
}

template <typename T>
T encode(T x, T y, T z)
{
	auto expand = [](T x) -> T
	{
		if constexpr(sizeof(T) == 1)
		{
			x &=               0x3;
			x = (x | x << 2) & 0x9;
		}
		else if constexpr(sizeof(T) == 2)
		{
			x &=               0x001f;
			x = (x | x << 8) & 0x100f;
			x = (x | x << 4) & 0x10c3;
			x = (x | x << 2) & 0x1249;
		}
		else if constexpr(sizeof(T) == 4)
		{
			x &=                0x00003ff;
			x = (x | x << 16) & 0x30000ff;
			x = (x | x <<  8) & 0x300f00f;
			x = (x | x <<  4) & 0x30c30c3;
			x = (x | x <<  2) & 0x9249249;
		}
		else if constexpr(sizeof(T) == 8)
		{
			x &=                0x00000000001fffff;
			x = (x | x << 32) & 0x001f00000000ffff;
			x = (x | x << 16) & 0x001f0000ff0000ff;
			x = (x | x <<  8) & 0x100f00f00f00f00f;
			x = (x | x <<  4) & 0x10c30c30c30c30c3;
			x = (x | x <<  2) & 0x1249249249249249;
		}

		return x;
	};
	
	return expand(x) | (expand(y) << 1) | (expand(z) << 2);
}

template <typename T>
void decode(T code, T& x, T& y)
{
	auto compress = [](T x) -> T
	{
		x &= T(0x5555555555555555);
		
		x = (x ^ (x >> 1)) & T(0x3333333333333333);
		x = (x ^ (x >> 2)) & T(0x0f0f0f0f0f0f0f0f);
		
		if constexpr(sizeof(T) >= 2)
			x = (x ^ (x >>  4)) & T(0x00ff00ff00ff00ff);
		if constexpr(sizeof(T) >= 4)
			x = (x ^ (x >>  8)) & T(0x0000ffff0000ffff);
		if constexpr(sizeof(T) >= 8)
			x = (x ^ (x >> 16)) & T(0x00000000ffffffff);
		
		return x;
	};
	
	x = compress(code);
	y = compress(code >> 1);
}

template <typename T>
void decode(T code, T& x, T& y, T& z)
{
	auto compress = [](T x) -> T
	{
		if constexpr(sizeof(T) == 1)
		{
			x &=               0x9;
			x = (x ^ x >> 2) & 0x3;
		}
		else if constexpr(sizeof(T) == 2)
		{
			x &=               0x1249;
			x = (x ^ x >> 2) & 0x10c3;
			x = (x ^ x >> 4) & 0x100f;
			x = (x ^ x >> 8) & 0x001f;
		}
		else if constexpr(sizeof(T) == 4)
		{
			x &=                0x9249249;
			x = (x ^ x >>  2) & 0x30c30c3;
			x = (x ^ x >>  4) & 0x300f00f;
			x = (x ^ x >>  8) & 0x30000ff;
			x = (x ^ x >> 16) & 0x00003ff;
		}
		else if constexpr(sizeof(T) == 8)
		{
			x &=                0x1249249249249249;
			x = (x ^ x >>  2) & 0x10c30c30c30c30c3;
			x = (x ^ x >>  4) & 0x100f00f00f00f00f;
			x = (x ^ x >>  8) & 0x001f0000ff0000ff;
			x = (x ^ x >> 16) & 0x001f00000000ffff;
			x = (x ^ x >> 32) & 0x00000000001fffff;
		}
		
		return x;
	};
	
	x = compress(code);
	y = compress(code >> 1);
	z = compress(code >> 2);
}

} // namespace morton
} // namespace geom

#endif // ANTKEEPER_GEOM_MORTON_HPP