src/System/Half.hpp - SwiftShader - Git at Google

 // 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=(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(const 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
 {
 public:
 	R11G11B10F(const 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);
 	}

 	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
 	}

 	static 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 float32MinNormfloat11 = 0x38800000;
 		const unsigned int float32MinDenormfloat11 = 0x35000080;

 		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 < float32MinDenormfloat11)
 		{
 			// The number is too small to be represented as a denormalized float11, set to 0
 			return 0;
 		}
 		else
 		{
 			if(float32Val < float32MinNormfloat11)
 			{
 				// 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;
 		}
 	}

 	static 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 float32MinNormfloat10 = 0x38800000;
 		const unsigned int float32MinDenormfloat10 = 0x35800040;

 		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 float10 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 float10, set to max
 			return float10Max;
 		}
 		else if(float32Val < float32MinDenormfloat10)
 		{
 			// The number is too small to be represented as a denormalized float10, set to 0
 			return 0;
 		}
 		else
 		{
 			if(float32Val < float32MinNormfloat10)
 			{
 				// The number is too small to be represented as a normalized float10
 				// 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 float10
 				float32Val += 0xC8000000;
 			}

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

 private:
 	unsigned int R : 11;
 	unsigned int G : 11;
 	unsigned int B : 10;
 };

 }  // namespace sw

 #endif  // sw_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=(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(const 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
	{
	public:
	R11G11B10F(const 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);
	}

	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
	}

	static 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 float32MinNormfloat11 = 0x38800000;
	const unsigned int float32MinDenormfloat11 = 0x35000080;

	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 < float32MinDenormfloat11)
	{
	// The number is too small to be represented as a denormalized float11, set to 0
	return 0;
	}
	else
	{
	if(float32Val < float32MinNormfloat11)
	{
	// 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;
	}
	}

	static 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 float32MinNormfloat10 = 0x38800000;
	const unsigned int float32MinDenormfloat10 = 0x35800040;

	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 float10 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 float10, set to max
	return float10Max;
	}
	else if(float32Val < float32MinDenormfloat10)
	{
	// The number is too small to be represented as a denormalized float10, set to 0
	return 0;
	}
	else
	{
	if(float32Val < float32MinNormfloat10)
	{
	// The number is too small to be represented as a normalized float10
	// 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 float10
	float32Val += 0xC8000000;
	}

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

	private:
	unsigned int R : 11;
	unsigned int G : 11;
	unsigned int B : 10;
	};

	} // namespace sw

	#endif // sw_Half_hpp