1 | // |
---|
2 | // Lol Engine |
---|
3 | // |
---|
4 | // Copyright: (c) 2010-2011 Sam Hocevar <sam@hocevar.net> |
---|
5 | // This program is free software; you can redistribute it and/or |
---|
6 | // modify it under the terms of the Do What The Fuck You Want To |
---|
7 | // Public License, Version 2, as published by Sam Hocevar. See |
---|
8 | // http://sam.zoy.org/projects/COPYING.WTFPL for more details. |
---|
9 | // |
---|
10 | |
---|
11 | #if defined HAVE_CONFIG_H |
---|
12 | # include "config.h" |
---|
13 | #endif |
---|
14 | |
---|
15 | #include "core.h" |
---|
16 | |
---|
17 | using namespace std; |
---|
18 | |
---|
19 | namespace lol |
---|
20 | { |
---|
21 | |
---|
22 | /* These macros implement a finite iterator useful to build lookup |
---|
23 | * tables. For instance, S64(0) will call S1(x) for all values of x |
---|
24 | * between 0 and 63. |
---|
25 | * Due to the exponential behaviour of the calls, the stress on the |
---|
26 | * compiler may be important. */ |
---|
27 | #define S4(x) S1((x)), S1((x)+1), S1((x)+2), S1((x)+3) |
---|
28 | #define S16(x) S4((x)), S4((x)+4), S4((x)+8), S4((x)+12) |
---|
29 | #define S64(x) S16((x)), S16((x)+16), S16((x)+32), S16((x)+48) |
---|
30 | #define S256(x) S64((x)), S64((x)+64), S64((x)+128), S64((x)+192) |
---|
31 | #define S1024(x) S256((x)), S256((x)+256), S256((x)+512), S256((x)+768) |
---|
32 | |
---|
33 | /* Lookup table-based algorithm from “Fast Half Float Conversions” |
---|
34 | * by Jeroen van der Zijp, November 2008. No rounding is performed, |
---|
35 | * and some NaN values may be incorrectly converted to Inf. */ |
---|
36 | static inline uint16_t float_to_half_nobranch(uint32_t x) |
---|
37 | { |
---|
38 | static uint16_t const basetable[512] = |
---|
39 | { |
---|
40 | #define S1(i) (((i) < 103) ? 0x0000: \ |
---|
41 | ((i) < 113) ? 0x0400 >> (113 - (i)) : \ |
---|
42 | ((i) < 143) ? ((i) - 112) << 10 : 0x7c00) |
---|
43 | S256(0), |
---|
44 | #undef S1 |
---|
45 | #define S1(i) (0x8000 | (((i) < 103) ? 0x0000 : \ |
---|
46 | ((i) < 113) ? 0x0400 >> (113 - (i)): \ |
---|
47 | ((i) < 143) ? ((i) - 112) << 10 : 0x7c00)) |
---|
48 | S256(0), |
---|
49 | #undef S1 |
---|
50 | }; |
---|
51 | |
---|
52 | static uint8_t const shifttable[512] = |
---|
53 | { |
---|
54 | #define S1(i) (((i) < 103) ? 24 : \ |
---|
55 | ((i) < 113) ? 126 - (i) : \ |
---|
56 | ((i) < 143 || (i) == 255) ? 13 : 24) |
---|
57 | S256(0), S256(0), |
---|
58 | #undef S1 |
---|
59 | }; |
---|
60 | |
---|
61 | uint16_t bits = basetable[(x >> 23) & 0x1ff]; |
---|
62 | bits |= (x & 0x007fffff) >> shifttable[(x >> 23) & 0x1ff]; |
---|
63 | return bits; |
---|
64 | } |
---|
65 | |
---|
66 | /* This method is faster than the OpenEXR implementation (very often |
---|
67 | * used, eg. in Ogre), with the additional benefit of rounding, inspired |
---|
68 | * by James Tursa’s half-precision code. */ |
---|
69 | static inline uint16_t float_to_half_branch(uint32_t x) |
---|
70 | { |
---|
71 | uint16_t bits = (x >> 16) & 0x8000; /* Get the sign */ |
---|
72 | uint16_t m = (x >> 12) & 0x07ff; /* Keep one extra bit for rounding */ |
---|
73 | unsigned int e = (x >> 23) & 0xff; /* Using int is faster here */ |
---|
74 | |
---|
75 | /* If zero, or denormal, or exponent underflows too much for a denormal, |
---|
76 | * return signed zero. */ |
---|
77 | if (e < 103) |
---|
78 | return bits; |
---|
79 | |
---|
80 | /* If NaN, return NaN. If Inf or exponent overflow, return Inf. */ |
---|
81 | if (e > 142) |
---|
82 | { |
---|
83 | bits |= 0x7c00u; |
---|
84 | /* If exponent was 0xff and one mantissa bit was set, it means NaN, |
---|
85 | * not Inf, so make sure we set one mantissa bit too. */ |
---|
86 | bits |= e == 255 && (x & 0x007fffffu); |
---|
87 | return bits; |
---|
88 | } |
---|
89 | |
---|
90 | /* If exponent underflows but not too much, return a denormal */ |
---|
91 | if (e < 113) |
---|
92 | { |
---|
93 | m |= 0x0800u; |
---|
94 | /* Extra rounding may overflow and set mantissa to 0 and exponent |
---|
95 | * to 1, which is OK. */ |
---|
96 | bits |= (m >> (114 - e)) + ((m >> (113 - e)) & 1); |
---|
97 | return bits; |
---|
98 | } |
---|
99 | |
---|
100 | bits |= ((e - 112) << 10) | (m >> 1); |
---|
101 | /* Extra rounding. An overflow will set mantissa to 0 and increment |
---|
102 | * the exponent, which is OK. */ |
---|
103 | bits += m & 1; |
---|
104 | return bits; |
---|
105 | } |
---|
106 | |
---|
107 | static int const shifttable[32] = |
---|
108 | { |
---|
109 | 23, 14, 22, 0, 0, 0, 21, 0, 0, 0, 0, 0, 0, 0, 20, 0, |
---|
110 | 15, 0, 0, 0, 0, 0, 0, 16, 0, 0, 0, 17, 0, 18, 19, 0, |
---|
111 | }; |
---|
112 | static uint32_t const shiftmagic = 0x07c4acddu; |
---|
113 | |
---|
114 | /* Lookup table-based algorithm from “Fast Half Float Conversions” |
---|
115 | * by Jeroen van der Zijp, November 2008. Tables are generated using |
---|
116 | * the C++ preprocessor, thanks to a branchless implementation also |
---|
117 | * used in half_to_float_branch(). This code is actually almost always |
---|
118 | * slower than the branching one. */ |
---|
119 | static inline uint32_t half_to_float_nobranch(uint16_t x) |
---|
120 | { |
---|
121 | #define M3(i) ((i) | ((i) >> 1)) |
---|
122 | #define M7(i) (M3(i) | (M3(i) >> 2)) |
---|
123 | #define MF(i) (M7(i) | (M7(i) >> 4)) |
---|
124 | #define MFF(i) (MF(i) | (MF(i) >> 8)) |
---|
125 | #define E(i) shifttable[(unsigned int)(MFF(i) * shiftmagic) >> 27] |
---|
126 | |
---|
127 | static uint32_t const mantissatable[2048] = |
---|
128 | { |
---|
129 | #define S1(i) (((i) == 0) ? 0 : ((125 - E(i)) << 23) + ((i) << E(i))) |
---|
130 | S1024(0), |
---|
131 | #undef S1 |
---|
132 | #define S1(i) (0x38000000u + ((i) << 13)) |
---|
133 | S1024(0), |
---|
134 | #undef S1 |
---|
135 | }; |
---|
136 | |
---|
137 | static uint32_t const exponenttable[64] = |
---|
138 | { |
---|
139 | #define S1(i) (((i) == 0) ? 0 : \ |
---|
140 | ((i) < 31) ? ((i) << 23) : \ |
---|
141 | ((i) == 31) ? 0x47800000u : \ |
---|
142 | ((i) == 32) ? 0x80000000u : \ |
---|
143 | ((i) < 63) ? (0x80000000u + (((i) - 32) << 23)) : 0xc7800000) |
---|
144 | S64(0), |
---|
145 | #undef S1 |
---|
146 | }; |
---|
147 | |
---|
148 | static int const offsettable[64] = |
---|
149 | { |
---|
150 | #define S1(i) (((i) == 0 || (i) == 32) ? 0 : 1024) |
---|
151 | S64(0), |
---|
152 | #undef S1 |
---|
153 | }; |
---|
154 | |
---|
155 | return mantissatable[offsettable[x >> 10] + (x & 0x3ff)] |
---|
156 | + exponenttable[x >> 10]; |
---|
157 | } |
---|
158 | |
---|
159 | /* This algorithm is similar to the OpenEXR implementation, except it |
---|
160 | * uses branchless code in the denormal path. */ |
---|
161 | static inline uint32_t half_to_float_branch(uint16_t x) |
---|
162 | { |
---|
163 | uint32_t s = (x & 0x8000u) << 16; |
---|
164 | |
---|
165 | if ((x & 0x7fffu) == 0) |
---|
166 | return (uint32_t)x << 16; |
---|
167 | |
---|
168 | uint32_t e = x & 0x7c00u; |
---|
169 | uint32_t m = x & 0x03ffu; |
---|
170 | |
---|
171 | if (e == 0) |
---|
172 | { |
---|
173 | uint32_t v = m | (m >> 1); |
---|
174 | v |= v >> 2; |
---|
175 | v |= v >> 4; |
---|
176 | v |= v >> 8; |
---|
177 | |
---|
178 | e = shifttable[(v * shiftmagic) >> 27]; |
---|
179 | |
---|
180 | /* We don't have to remove the 10th mantissa bit because it gets |
---|
181 | * added to our underestimated exponent. */ |
---|
182 | return s | (((125 - e) << 23) + (m << e)); |
---|
183 | } |
---|
184 | |
---|
185 | if (e == 0x7c00u) |
---|
186 | { |
---|
187 | /* The amd64 pipeline likes the if() better than a ternary operator |
---|
188 | * or any other trick I could find. --sam */ |
---|
189 | if (m == 0) |
---|
190 | return s | 0x7f800000u; |
---|
191 | return s | 0x7fc00000u; |
---|
192 | } |
---|
193 | |
---|
194 | return s | (((e >> 10) + 112) << 23) | (m << 13); |
---|
195 | } |
---|
196 | |
---|
197 | half half::makefast(float f) |
---|
198 | { |
---|
199 | union { float f; uint32_t x; } u = { f }; |
---|
200 | return makebits(float_to_half_nobranch(u.x)); |
---|
201 | } |
---|
202 | |
---|
203 | half half::makeslow(float f) |
---|
204 | { |
---|
205 | union { float f; uint32_t x; } u = { f }; |
---|
206 | return makebits(float_to_half_branch(u.x)); |
---|
207 | } |
---|
208 | |
---|
209 | half::operator float() const |
---|
210 | { |
---|
211 | union { float f; uint32_t x; } u; |
---|
212 | u.x = half_to_float_branch(bits); |
---|
213 | return u.f; |
---|
214 | } |
---|
215 | |
---|
216 | } /* namespace lol */ |
---|
217 | |
---|