src/System/Half.hpp

// Copyright 2016 The SwiftShader Authors. All Rights Reserved.
//
// Licensed under the Apache License, Version 2.0 (the "License");
// you may not use this file except in compliance with the License.
// You may obtain a copy of the License at
//
//    http://www.apache.org/licenses/LICENSE-2.0
//
// Unless required by applicable law or agreed to in writing, software
// distributed under the License is distributed on an "AS IS" BASIS,
// WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied.
// See the License for the specific language governing permissions and
// limitations under the License.

#ifndef sw_Half_hpp
#define sw_Half_hpp

#include "Math.hpp"

#include <algorithm>
#include <cmath>

namespace sw
{
	class half
	{
	public:
		half() = default;
		explicit half(float f);

		operator float() const;

		half &operator=(half h);
		half &operator=(float f);

	private:
		unsigned short fp16i;
	};

	inline half shortAsHalf(short s)
	{
		union
		{
			half h;
			short s;
		} hs;

		hs.s = s;

		return hs.h;
	}

	class RGB9E5
	{
		unsigned int R : 9;
		unsigned int G : 9;
		unsigned int B : 9;
		unsigned int E : 5;

	public:
		RGB9E5(float rgb[3]) : RGB9E5(rgb[0], rgb[1], rgb[2])
		{
		}

		RGB9E5(float r, float g, float b)
		{
			// Vulkan 1.1.117 section 15.2.1 RGB to Shared Exponent Conversion

			// B is the exponent bias (15)
			constexpr int g_sharedexp_bias = 15;

			// N is the number of mantissa bits per component (9)
			constexpr int g_sharedexp_mantissabits = 9;

			// Emax is the maximum allowed biased exponent value (31)
			constexpr int g_sharedexp_maxexponent = 31;

			constexpr float g_sharedexp_max =
				((static_cast<float>(1 << g_sharedexp_mantissabits) - 1) /
					static_cast<float>(1 << g_sharedexp_mantissabits)) *
				static_cast<float>(1 << (g_sharedexp_maxexponent - g_sharedexp_bias));

			// Clamp components to valid range. NaN becomes 0.
			const float red_c =   std::min(!(r > 0) ? 0 : r, g_sharedexp_max);
			const float green_c = std::min(!(g > 0) ? 0 : g, g_sharedexp_max);
			const float blue_c =  std::min(!(b > 0) ? 0 : b, g_sharedexp_max);

			// We're reducing the mantissa to 9 bits, so we must round up if the next
			// bit is 1. In other words add 0.5 to the new mantissa's position and
			// allow overflow into the exponent so we can scale correctly.
			constexpr int half = 1 << (23 - g_sharedexp_mantissabits);
			const float red_r = bit_cast<float>(bit_cast<int>(red_c) + half);
			const float green_r = bit_cast<float>(bit_cast<int>(green_c) + half);
			const float blue_r = bit_cast<float>(bit_cast<int>(blue_c) + half);

			// The largest component determines the shared exponent. It can't be lower
			// than 0 (after bias subtraction) so also limit to the mimimum representable.
			constexpr float min_s = 0.5f / (1 << g_sharedexp_bias);
			float max_s = std::max(std::max(red_r, green_r), std::max(blue_r, min_s));

			// Obtain the reciprocal of the shared exponent by inverting the bits,
			// and scale by the new mantissa's size. Note that the IEEE-754 single-precision
			// format has an implicit leading 1, but this shared component format does not.
			float scale = bit_cast<float>((bit_cast<int>(max_s) & 0x7F800000) ^ 0x7F800000) * (1 << (g_sharedexp_mantissabits - 2));

			R = static_cast<unsigned int>(round(red_c * scale));
			G = static_cast<unsigned int>(round(green_c * scale));
			B = static_cast<unsigned int>(round(blue_c * scale));
			E = (bit_cast<unsigned int>(max_s) >> 23) - 127 + 15 + 1;
		}

		operator unsigned int() const
		{
			return *reinterpret_cast<const unsigned int*>(this);
		}

		void toRGB16F(half rgb[3]) const
		{
			constexpr int offset = 24;   // Exponent bias (15) + number of mantissa bits per component (9) = 24

			const float factor = (1u << E) * (1.0f / (1 << offset));
			rgb[0] = half(R * factor);
			rgb[1] = half(G * factor);
			rgb[2] = half(B * factor);
		}
	};

	class R11G11B10F
	{
		unsigned int R : 11;
		unsigned int G : 11;
		unsigned int B : 10;

		static inline half float11ToFloat16(unsigned short fp11)
		{
			return shortAsHalf(fp11 << 4);   // Sign bit 0
		}

		static inline half float10ToFloat16(unsigned short fp10)
		{
			return shortAsHalf(fp10 << 5);   // Sign bit 0
		}

		inline unsigned short float32ToFloat11(float fp32)
		{
			const unsigned int float32MantissaMask = 0x7FFFFF;
			const unsigned int float32ExponentMask = 0x7F800000;
			const unsigned int float32SignMask = 0x80000000;
			const unsigned int float32ValueMask = ~float32SignMask;
			const unsigned int float32ExponentFirstBit = 23;
			const unsigned int float32ExponentBias = 127;

			const unsigned short float11Max = 0x7BF;
			const unsigned short float11MantissaMask = 0x3F;
			const unsigned short float11ExponentMask = 0x7C0;
			const unsigned short float11BitMask = 0x7FF;
			const unsigned int float11ExponentBias = 14;

			const unsigned int float32Maxfloat11 = 0x477E0000;
			const unsigned int float32Minfloat11 = 0x38800000;

			const unsigned int float32Bits = *reinterpret_cast<unsigned int*>(&fp32);
			const bool float32Sign = (float32Bits & float32SignMask) == float32SignMask;

			unsigned int float32Val = float32Bits & float32ValueMask;

			if((float32Val & float32ExponentMask) == float32ExponentMask)
			{
				// INF or NAN
				if((float32Val & float32MantissaMask) != 0)
				{
					return float11ExponentMask |
						(((float32Val >> 17) | (float32Val >> 11) | (float32Val >> 6) | (float32Val)) &
							float11MantissaMask);
				}
				else if(float32Sign)
				{
					// -INF is clamped to 0 since float11 is positive only
					return 0;
				}
				else
				{
					return float11ExponentMask;
				}
			}
			else if(float32Sign)
			{
				// float11 is positive only, so clamp to zero
				return 0;
			}
			else if(float32Val > float32Maxfloat11)
			{
				// The number is too large to be represented as a float11, set to max
				return float11Max;
			}
			else
			{
				if(float32Val < float32Minfloat11)
				{
					// The number is too small to be represented as a normalized float11
					// Convert it to a denormalized value.
					const unsigned int shift = (float32ExponentBias - float11ExponentBias) -
						(float32Val >> float32ExponentFirstBit);
					float32Val =
						((1 << float32ExponentFirstBit) | (float32Val & float32MantissaMask)) >> shift;
				}
				else
				{
					// Rebias the exponent to represent the value as a normalized float11
					float32Val += 0xC8000000;
				}

				return ((float32Val + 0xFFFF + ((float32Val >> 17) & 1)) >> 17) & float11BitMask;
			}
		}

		inline unsigned short float32ToFloat10(float fp32)
		{
			const unsigned int float32MantissaMask = 0x7FFFFF;
			const unsigned int float32ExponentMask = 0x7F800000;
			const unsigned int float32SignMask = 0x80000000;
			const unsigned int float32ValueMask = ~float32SignMask;
			const unsigned int float32ExponentFirstBit = 23;
			const unsigned int float32ExponentBias = 127;

			const unsigned short float10Max = 0x3DF;
			const unsigned short float10MantissaMask = 0x1F;
			const unsigned short float10ExponentMask = 0x3E0;
			const unsigned short float10BitMask = 0x3FF;
			const unsigned int float10ExponentBias = 14;

			const unsigned int float32Maxfloat10 = 0x477C0000;
			const unsigned int float32Minfloat10 = 0x38800000;

			const unsigned int float32Bits = *reinterpret_cast<unsigned int*>(&fp32);
			const bool float32Sign = (float32Bits & float32SignMask) == float32SignMask;

			unsigned int float32Val = float32Bits & float32ValueMask;

			if((float32Val & float32ExponentMask) == float32ExponentMask)
			{
				// INF or NAN
				if((float32Val & float32MantissaMask) != 0)
				{
					return float10ExponentMask |
						(((float32Val >> 18) | (float32Val >> 13) | (float32Val >> 3) | (float32Val)) &
							float10MantissaMask);
				}
				else if(float32Sign)
				{
					// -INF is clamped to 0 since float11 is positive only
					return 0;
				}
				else
				{
					return float10ExponentMask;
				}
			}
			else if(float32Sign)
			{
				// float10 is positive only, so clamp to zero
				return 0;
			}
			else if(float32Val > float32Maxfloat10)
			{
				// The number is too large to be represented as a float11, set to max
				return float10Max;
			}
			else
			{
				if(float32Val < float32Minfloat10)
				{
					// The number is too small to be represented as a normalized float11
					// Convert it to a denormalized value.
					const unsigned int shift = (float32ExponentBias - float10ExponentBias) -
						(float32Val >> float32ExponentFirstBit);
					float32Val =
						((1 << float32ExponentFirstBit) | (float32Val & float32MantissaMask)) >> shift;
				}
				else
				{
					// Rebias the exponent to represent the value as a normalized float11
					float32Val += 0xC8000000;
				}

				return ((float32Val + 0x1FFFF + ((float32Val >> 18) & 1)) >> 18) & float10BitMask;
			}
		}

	public:
		R11G11B10F(float rgb[3])
		{
			R = float32ToFloat11(rgb[0]);
			G = float32ToFloat11(rgb[1]);
			B = float32ToFloat10(rgb[2]);
		}

		operator unsigned int() const
		{
			return *reinterpret_cast<const unsigned int*>(this);
		}

		void toRGB16F(half rgb[3]) const
		{
			rgb[0] = float11ToFloat16(R);
			rgb[1] = float11ToFloat16(G);
			rgb[2] = float10ToFloat16(B);
		}
	};
}

#endif   // sw_Half_hpp