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1 // Copyright 2016 The SwiftShader Authors. All Rights Reserved.
2 //
3 // Licensed under the Apache License, Version 2.0 (the "License");
4 // you may not use this file except in compliance with the License.
5 // You may obtain a copy of the License at
6 //
7 //    http://www.apache.org/licenses/LICENSE-2.0
8 //
9 // Unless required by applicable law or agreed to in writing, software
10 // distributed under the License is distributed on an "AS IS" BASIS,
11 // WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied.
12 // See the License for the specific language governing permissions and
13 // limitations under the License.
14 
15 #ifndef sw_Half_hpp
16 #define sw_Half_hpp
17 
18 #include "Math.hpp"
19 
20 #include <algorithm>
21 #include <cmath>
22 
23 namespace sw {
24 
25 class half
26 {
27 public:
28 	half() = default;
29 	explicit half(float f);
30 
31 	operator float() const;
32 
33 	half &operator=(float f);
34 
35 private:
36 	unsigned short fp16i;
37 };
38 
shortAsHalf(short s)39 inline half shortAsHalf(short s)
40 {
41 	union
42 	{
43 		half h;
44 		short s;
45 	} hs;
46 
47 	hs.s = s;
48 
49 	return hs.h;
50 }
51 
52 class RGB9E5
53 {
54 	unsigned int R : 9;
55 	unsigned int G : 9;
56 	unsigned int B : 9;
57 	unsigned int E : 5;
58 
59 public:
RGB9E5(const float rgb[3])60 	RGB9E5(const float rgb[3])
61 	    : RGB9E5(rgb[0], rgb[1], rgb[2])
62 	{
63 	}
64 
RGB9E5(float r,float g,float b)65 	RGB9E5(float r, float g, float b)
66 	{
67 		// Vulkan 1.1.117 section 15.2.1 RGB to Shared Exponent Conversion
68 
69 		// B is the exponent bias (15)
70 		constexpr int g_sharedexp_bias = 15;
71 
72 		// N is the number of mantissa bits per component (9)
73 		constexpr int g_sharedexp_mantissabits = 9;
74 
75 		// Emax is the maximum allowed biased exponent value (31)
76 		constexpr int g_sharedexp_maxexponent = 31;
77 
78 		constexpr float g_sharedexp_max =
79 		    ((static_cast<float>(1 << g_sharedexp_mantissabits) - 1) /
80 		     static_cast<float>(1 << g_sharedexp_mantissabits)) *
81 		    static_cast<float>(1 << (g_sharedexp_maxexponent - g_sharedexp_bias));
82 
83 		// Clamp components to valid range. NaN becomes 0.
84 		const float red_c = std::min(!(r > 0) ? 0 : r, g_sharedexp_max);
85 		const float green_c = std::min(!(g > 0) ? 0 : g, g_sharedexp_max);
86 		const float blue_c = std::min(!(b > 0) ? 0 : b, g_sharedexp_max);
87 
88 		// We're reducing the mantissa to 9 bits, so we must round up if the next
89 		// bit is 1. In other words add 0.5 to the new mantissa's position and
90 		// allow overflow into the exponent so we can scale correctly.
91 		constexpr int half = 1 << (23 - g_sharedexp_mantissabits);
92 		const float red_r = bit_cast<float>(bit_cast<int>(red_c) + half);
93 		const float green_r = bit_cast<float>(bit_cast<int>(green_c) + half);
94 		const float blue_r = bit_cast<float>(bit_cast<int>(blue_c) + half);
95 
96 		// The largest component determines the shared exponent. It can't be lower
97 		// than 0 (after bias subtraction) so also limit to the mimimum representable.
98 		constexpr float min_s = 0.5f / (1 << g_sharedexp_bias);
99 		float max_s = std::max(std::max(red_r, green_r), std::max(blue_r, min_s));
100 
101 		// Obtain the reciprocal of the shared exponent by inverting the bits,
102 		// and scale by the new mantissa's size. Note that the IEEE-754 single-precision
103 		// format has an implicit leading 1, but this shared component format does not.
104 		float scale = bit_cast<float>((bit_cast<int>(max_s) & 0x7F800000) ^ 0x7F800000) * (1 << (g_sharedexp_mantissabits - 2));
105 
106 		R = static_cast<unsigned int>(round(red_c * scale));
107 		G = static_cast<unsigned int>(round(green_c * scale));
108 		B = static_cast<unsigned int>(round(blue_c * scale));
109 		E = (bit_cast<unsigned int>(max_s) >> 23) - 127 + 15 + 1;
110 	}
111 
operator unsigned int() const112 	operator unsigned int() const
113 	{
114 		return *reinterpret_cast<const unsigned int *>(this);
115 	}
116 
toRGB16F(half rgb[3]) const117 	void toRGB16F(half rgb[3]) const
118 	{
119 		constexpr int offset = 24;  // Exponent bias (15) + number of mantissa bits per component (9) = 24
120 
121 		const float factor = (1u << E) * (1.0f / (1 << offset));
122 		rgb[0] = half(R * factor);
123 		rgb[1] = half(G * factor);
124 		rgb[2] = half(B * factor);
125 	}
126 };
127 
128 class R11G11B10F
129 {
130 public:
R11G11B10F(const float rgb[3])131 	R11G11B10F(const float rgb[3])
132 	{
133 		R = float32ToFloat11(rgb[0]);
134 		G = float32ToFloat11(rgb[1]);
135 		B = float32ToFloat10(rgb[2]);
136 	}
137 
operator unsigned int() const138 	operator unsigned int() const
139 	{
140 		return *reinterpret_cast<const unsigned int *>(this);
141 	}
142 
toRGB16F(half rgb[3]) const143 	void toRGB16F(half rgb[3]) const
144 	{
145 		rgb[0] = float11ToFloat16(R);
146 		rgb[1] = float11ToFloat16(G);
147 		rgb[2] = float10ToFloat16(B);
148 	}
149 
float11ToFloat16(unsigned short fp11)150 	static inline half float11ToFloat16(unsigned short fp11)
151 	{
152 		return shortAsHalf(fp11 << 4);  // Sign bit 0
153 	}
154 
float10ToFloat16(unsigned short fp10)155 	static inline half float10ToFloat16(unsigned short fp10)
156 	{
157 		return shortAsHalf(fp10 << 5);  // Sign bit 0
158 	}
159 
float32ToFloat11(float fp32)160 	static inline unsigned short float32ToFloat11(float fp32)
161 	{
162 		const unsigned int float32MantissaMask = 0x7FFFFF;
163 		const unsigned int float32ExponentMask = 0x7F800000;
164 		const unsigned int float32SignMask = 0x80000000;
165 		const unsigned int float32ValueMask = ~float32SignMask;
166 		const unsigned int float32ExponentFirstBit = 23;
167 		const unsigned int float32ExponentBias = 127;
168 
169 		const unsigned short float11Max = 0x7BF;
170 		const unsigned short float11MantissaMask = 0x3F;
171 		const unsigned short float11ExponentMask = 0x7C0;
172 		const unsigned short float11BitMask = 0x7FF;
173 		const unsigned int float11ExponentBias = 14;
174 
175 		const unsigned int float32Maxfloat11 = 0x477E0000;
176 		const unsigned int float32MinNormfloat11 = 0x38800000;
177 		const unsigned int float32MinDenormfloat11 = 0x35000080;
178 
179 		const unsigned int float32Bits = *reinterpret_cast<unsigned int *>(&fp32);
180 		const bool float32Sign = (float32Bits & float32SignMask) == float32SignMask;
181 
182 		unsigned int float32Val = float32Bits & float32ValueMask;
183 
184 		if((float32Val & float32ExponentMask) == float32ExponentMask)
185 		{
186 			// INF or NAN
187 			if((float32Val & float32MantissaMask) != 0)
188 			{
189 				return float11ExponentMask |
190 				       (((float32Val >> 17) | (float32Val >> 11) | (float32Val >> 6) | (float32Val)) &
191 				        float11MantissaMask);
192 			}
193 			else if(float32Sign)
194 			{
195 				// -INF is clamped to 0 since float11 is positive only
196 				return 0;
197 			}
198 			else
199 			{
200 				return float11ExponentMask;
201 			}
202 		}
203 		else if(float32Sign)
204 		{
205 			// float11 is positive only, so clamp to zero
206 			return 0;
207 		}
208 		else if(float32Val > float32Maxfloat11)
209 		{
210 			// The number is too large to be represented as a float11, set to max
211 			return float11Max;
212 		}
213 		else if(float32Val < float32MinDenormfloat11)
214 		{
215 			// The number is too small to be represented as a denormalized float11, set to 0
216 			return 0;
217 		}
218 		else
219 		{
220 			if(float32Val < float32MinNormfloat11)
221 			{
222 				// The number is too small to be represented as a normalized float11
223 				// Convert it to a denormalized value.
224 				const unsigned int shift = (float32ExponentBias - float11ExponentBias) -
225 				                           (float32Val >> float32ExponentFirstBit);
226 				float32Val =
227 				    ((1 << float32ExponentFirstBit) | (float32Val & float32MantissaMask)) >> shift;
228 			}
229 			else
230 			{
231 				// Rebias the exponent to represent the value as a normalized float11
232 				float32Val += 0xC8000000;
233 			}
234 
235 			return ((float32Val + 0xFFFF + ((float32Val >> 17) & 1)) >> 17) & float11BitMask;
236 		}
237 	}
238 
float32ToFloat10(float fp32)239 	static inline unsigned short float32ToFloat10(float fp32)
240 	{
241 		const unsigned int float32MantissaMask = 0x7FFFFF;
242 		const unsigned int float32ExponentMask = 0x7F800000;
243 		const unsigned int float32SignMask = 0x80000000;
244 		const unsigned int float32ValueMask = ~float32SignMask;
245 		const unsigned int float32ExponentFirstBit = 23;
246 		const unsigned int float32ExponentBias = 127;
247 
248 		const unsigned short float10Max = 0x3DF;
249 		const unsigned short float10MantissaMask = 0x1F;
250 		const unsigned short float10ExponentMask = 0x3E0;
251 		const unsigned short float10BitMask = 0x3FF;
252 		const unsigned int float10ExponentBias = 14;
253 
254 		const unsigned int float32Maxfloat10 = 0x477C0000;
255 		const unsigned int float32MinNormfloat10 = 0x38800000;
256 		const unsigned int float32MinDenormfloat10 = 0x35800040;
257 
258 		const unsigned int float32Bits = *reinterpret_cast<unsigned int *>(&fp32);
259 		const bool float32Sign = (float32Bits & float32SignMask) == float32SignMask;
260 
261 		unsigned int float32Val = float32Bits & float32ValueMask;
262 
263 		if((float32Val & float32ExponentMask) == float32ExponentMask)
264 		{
265 			// INF or NAN
266 			if((float32Val & float32MantissaMask) != 0)
267 			{
268 				return float10ExponentMask |
269 				       (((float32Val >> 18) | (float32Val >> 13) | (float32Val >> 3) | (float32Val)) &
270 				        float10MantissaMask);
271 			}
272 			else if(float32Sign)
273 			{
274 				// -INF is clamped to 0 since float10 is positive only
275 				return 0;
276 			}
277 			else
278 			{
279 				return float10ExponentMask;
280 			}
281 		}
282 		else if(float32Sign)
283 		{
284 			// float10 is positive only, so clamp to zero
285 			return 0;
286 		}
287 		else if(float32Val > float32Maxfloat10)
288 		{
289 			// The number is too large to be represented as a float10, set to max
290 			return float10Max;
291 		}
292 		else if(float32Val < float32MinDenormfloat10)
293 		{
294 			// The number is too small to be represented as a denormalized float10, set to 0
295 			return 0;
296 		}
297 		else
298 		{
299 			if(float32Val < float32MinNormfloat10)
300 			{
301 				// The number is too small to be represented as a normalized float10
302 				// Convert it to a denormalized value.
303 				const unsigned int shift = (float32ExponentBias - float10ExponentBias) -
304 				                           (float32Val >> float32ExponentFirstBit);
305 				float32Val =
306 				    ((1 << float32ExponentFirstBit) | (float32Val & float32MantissaMask)) >> shift;
307 			}
308 			else
309 			{
310 				// Rebias the exponent to represent the value as a normalized float10
311 				float32Val += 0xC8000000;
312 			}
313 
314 			return ((float32Val + 0x1FFFF + ((float32Val >> 18) & 1)) >> 18) & float10BitMask;
315 		}
316 	}
317 
318 private:
319 	unsigned int R : 11;
320 	unsigned int G : 11;
321 	unsigned int B : 10;
322 };
323 
324 }  // namespace sw
325 
326 #endif  // sw_Half_hpp
327