1
2
3
4
5
6
7
8
9
10
11
12
13
14
15
16
17
18
19
20
21
22
23
24
25
26
27
28
29
30
31
32
33
34
35
36
37
38
39
40
41
42
43
44
45
46
47
48
49
50
51
52
53
54
55
56
57
58
59
60
61
62
63
64
65
66
67
68
69
70
71
72
73
74
75
76
77
78
79
80
81
82
83
84
85
86
87
88
89
90
91
92
93
94
95
96
97
98
99
100
101
102
103
104
105
106
107
108
109
110
111
112
113
114
115
116
117
118
119
120
121
122
123
124
125
126
127
128
129
130
131
132
133
134
135
136
137
138
139
140
141
142
143
144
145
146
147
148
149
150
151
152
153
154
155
156
157
158
159
160
161
162
163
164
165
166
167
168
169
170
171
172
173
174
175
176
177
178
179
180
181
182
183
184
185
186
187
188
189
190
191
192
193
194
195
196
197
198
199
200
201
202
203
204
205
206
207
208
209
210
211
212
213
214
215
216
217
218
219
220
221
222
223
224
225
226
227
228
229
230
231
232
233
234
235
236
237
238
239
240
241
242
243
244
|
/// @ref core
/// @file glm/detail/type_half.inl
namespace glm{
namespace detail
{
GLM_FUNC_QUALIFIER float overflow()
{
volatile float f = 1e10;
for(int i = 0; i < 10; ++i)
f *= f; // this will overflow before the for loop terminates
return f;
}
union uif32
{
GLM_FUNC_QUALIFIER uif32() :
i(0)
{}
GLM_FUNC_QUALIFIER uif32(float f_) :
f(f_)
{}
GLM_FUNC_QUALIFIER uif32(uint32 i_) :
i(i_)
{}
float f;
uint32 i;
};
GLM_FUNC_QUALIFIER float toFloat32(hdata value)
{
int s = (value >> 15) & 0x00000001;
int e = (value >> 10) & 0x0000001f;
int m = value & 0x000003ff;
if(e == 0)
{
if(m == 0)
{
//
// Plus or minus zero
//
detail::uif32 result;
result.i = (unsigned int)(s << 31);
return result.f;
}
else
{
//
// Denormalized number -- renormalize it
//
while(!(m & 0x00000400))
{
m <<= 1;
e -= 1;
}
e += 1;
m &= ~0x00000400;
}
}
else if(e == 31)
{
if(m == 0)
{
//
// Positive or negative infinity
//
uif32 result;
result.i = (unsigned int)((s << 31) | 0x7f800000);
return result.f;
}
else
{
//
// Nan -- preserve sign and significand bits
//
uif32 result;
result.i = (unsigned int)((s << 31) | 0x7f800000 | (m << 13));
return result.f;
}
}
//
// Normalized number
//
e = e + (127 - 15);
m = m << 13;
//
// Assemble s, e and m.
//
uif32 Result;
Result.i = (unsigned int)((s << 31) | (e << 23) | m);
return Result.f;
}
GLM_FUNC_QUALIFIER hdata toFloat16(float const & f)
{
uif32 Entry;
Entry.f = f;
int i = (int)Entry.i;
//
// Our floating point number, f, is represented by the bit
// pattern in integer i. Disassemble that bit pattern into
// the sign, s, the exponent, e, and the significand, m.
// Shift s into the position where it will go in in the
// resulting half number.
// Adjust e, accounting for the different exponent bias
// of float and half (127 versus 15).
//
int s = (i >> 16) & 0x00008000;
int e = ((i >> 23) & 0x000000ff) - (127 - 15);
int m = i & 0x007fffff;
//
// Now reassemble s, e and m into a half:
//
if(e <= 0)
{
if(e < -10)
{
//
// E is less than -10. The absolute value of f is
// less than half_MIN (f may be a small normalized
// float, a denormalized float or a zero).
//
// We convert f to a half zero.
//
return hdata(s);
}
//
// E is between -10 and 0. F is a normalized float,
// whose magnitude is less than __half_NRM_MIN.
//
// We convert f to a denormalized half.
//
m = (m | 0x00800000) >> (1 - e);
//
// Round to nearest, round "0.5" up.
//
// Rounding may cause the significand to overflow and make
// our number normalized. Because of the way a half's bits
// are laid out, we don't have to treat this case separately;
// the code below will handle it correctly.
//
if(m & 0x00001000)
m += 0x00002000;
//
// Assemble the half from s, e (zero) and m.
//
return hdata(s | (m >> 13));
}
else if(e == 0xff - (127 - 15))
{
if(m == 0)
{
//
// F is an infinity; convert f to a half
// infinity with the same sign as f.
//
return hdata(s | 0x7c00);
}
else
{
//
// F is a NAN; we produce a half NAN that preserves
// the sign bit and the 10 leftmost bits of the
// significand of f, with one exception: If the 10
// leftmost bits are all zero, the NAN would turn
// into an infinity, so we have to set at least one
// bit in the significand.
//
m >>= 13;
return hdata(s | 0x7c00 | m | (m == 0));
}
}
else
{
//
// E is greater than zero. F is a normalized float.
// We try to convert f to a normalized half.
//
//
// Round to nearest, round "0.5" up
//
if(m & 0x00001000)
{
m += 0x00002000;
if(m & 0x00800000)
{
m = 0; // overflow in significand,
e += 1; // adjust exponent
}
}
//
// Handle exponent overflow
//
if (e > 30)
{
overflow(); // Cause a hardware floating point overflow;
return hdata(s | 0x7c00);
// if this returns, the half becomes an
} // infinity with the same sign as f.
//
// Assemble the half from s, e and m.
//
return hdata(s | (e << 10) | (m >> 13));
}
}
}//namespace detail
}//namespace glm
|
