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
245
246
247
248
249
250
251
252
253
254
255
256
257
258
259
260
261
262
263
264
265
266
267
268
269
270
271
272
273
274
275
276
277
278
279
280
281
282
283
284
|
/// Copyright (C) 1993 by Sun Microsystems, Inc. All rights reserved.
///
/// Developed at SunPro, a Sun Microsystems, Inc. business.
/// Permission to use, copy, modify, and distribute this
/// software is freely granted, provided that this notice
/// is preserved.
#include "../detail/type_float.hpp"
#include "../ext/scalar_constants.hpp"
#include <cmath>
#include <cfloat>
#if(GLM_COMPILER & GLM_COMPILER_VC)
# pragma warning(push)
# pragma warning(disable : 4127)
#endif
typedef union
{
float value;
/* FIXME: Assumes 32 bit int. */
unsigned int word;
} ieee_float_shape_type;
typedef union
{
double value;
struct
{
int lsw;
int msw;
} parts;
} ieee_double_shape_type;
#define GLM_EXTRACT_WORDS(ix0,ix1,d) \
do { \
ieee_double_shape_type ew_u; \
ew_u.value = (d); \
(ix0) = ew_u.parts.msw; \
(ix1) = ew_u.parts.lsw; \
} while (0)
#define GLM_GET_FLOAT_WORD(i,d) \
do { \
ieee_float_shape_type gf_u; \
gf_u.value = (d); \
(i) = gf_u.word; \
} while (0)
#define GLM_SET_FLOAT_WORD(d,i) \
do { \
ieee_float_shape_type sf_u; \
sf_u.word = (i); \
(d) = sf_u.value; \
} while (0)
#define GLM_INSERT_WORDS(d,ix0,ix1) \
do { \
ieee_double_shape_type iw_u; \
iw_u.parts.msw = (ix0); \
iw_u.parts.lsw = (ix1); \
(d) = iw_u.value; \
} while (0)
namespace glm{
namespace detail
{
GLM_FUNC_QUALIFIER float nextafterf(float x, float y)
{
volatile float t;
int hx, hy, ix, iy;
GLM_GET_FLOAT_WORD(hx, x);
GLM_GET_FLOAT_WORD(hy, y);
ix = hx & 0x7fffffff; // |x|
iy = hy & 0x7fffffff; // |y|
if((ix > 0x7f800000) || // x is nan
(iy > 0x7f800000)) // y is nan
return x + y;
if(abs(y - x) <= epsilon<float>())
return y; // x=y, return y
if(ix == 0)
{ // x == 0
GLM_SET_FLOAT_WORD(x, (hy & 0x80000000) | 1);// return +-minsubnormal
t = x * x;
if(abs(t - x) <= epsilon<float>())
return t;
else
return x; // raise underflow flag
}
if(hx >= 0)
{ // x > 0
if(hx > hy) // x > y, x -= ulp
hx -= 1;
else // x < y, x += ulp
hx += 1;
}
else
{ // x < 0
if(hy >= 0 || hx > hy) // x < y, x -= ulp
hx -= 1;
else // x > y, x += ulp
hx += 1;
}
hy = hx & 0x7f800000;
if(hy >= 0x7f800000)
return x + x; // overflow
if(hy < 0x00800000) // underflow
{
t = x * x;
if(abs(t - x) > epsilon<float>())
{ // raise underflow flag
GLM_SET_FLOAT_WORD(y, hx);
return y;
}
}
GLM_SET_FLOAT_WORD(x, hx);
return x;
}
GLM_FUNC_QUALIFIER double nextafter(double x, double y)
{
volatile double t;
int hx, hy, ix, iy;
unsigned int lx, ly;
GLM_EXTRACT_WORDS(hx, lx, x);
GLM_EXTRACT_WORDS(hy, ly, y);
ix = hx & 0x7fffffff; // |x|
iy = hy & 0x7fffffff; // |y|
if(((ix >= 0x7ff00000) && ((ix - 0x7ff00000) | lx) != 0) || // x is nan
((iy >= 0x7ff00000) && ((iy - 0x7ff00000) | ly) != 0)) // y is nan
return x + y;
if(abs(y - x) <= epsilon<double>())
return y; // x=y, return y
if((ix | lx) == 0)
{ // x == 0
GLM_INSERT_WORDS(x, hy & 0x80000000, 1); // return +-minsubnormal
t = x * x;
if(abs(t - x) <= epsilon<double>())
return t;
else
return x; // raise underflow flag
}
if(hx >= 0) { // x > 0
if(hx > hy || ((hx == hy) && (lx > ly))) { // x > y, x -= ulp
if(lx == 0) hx -= 1;
lx -= 1;
}
else { // x < y, x += ulp
lx += 1;
if(lx == 0) hx += 1;
}
}
else { // x < 0
if(hy >= 0 || hx > hy || ((hx == hy) && (lx > ly))){// x < y, x -= ulp
if(lx == 0) hx -= 1;
lx -= 1;
}
else { // x > y, x += ulp
lx += 1;
if(lx == 0) hx += 1;
}
}
hy = hx & 0x7ff00000;
if(hy >= 0x7ff00000)
return x + x; // overflow
if(hy < 0x00100000)
{ // underflow
t = x * x;
if(abs(t - x) > epsilon<double>())
{ // raise underflow flag
GLM_INSERT_WORDS(y, hx, lx);
return y;
}
}
GLM_INSERT_WORDS(x, hx, lx);
return x;
}
}//namespace detail
}//namespace glm
#if(GLM_COMPILER & GLM_COMPILER_VC)
# pragma warning(pop)
#endif
namespace glm
{
template<>
GLM_FUNC_QUALIFIER float nextFloat(float x)
{
# if GLM_HAS_CXX11_STL
return std::nextafter(x, std::numeric_limits<float>::max());
# elif((GLM_COMPILER & GLM_COMPILER_VC) || ((GLM_COMPILER & GLM_COMPILER_INTEL) && (GLM_PLATFORM & GLM_PLATFORM_WINDOWS)))
return detail::nextafterf(x, FLT_MAX);
# elif(GLM_PLATFORM & GLM_PLATFORM_ANDROID)
return __builtin_nextafterf(x, FLT_MAX);
# else
return nextafterf(x, FLT_MAX);
# endif
}
template<>
GLM_FUNC_QUALIFIER double nextFloat(double x)
{
# if GLM_HAS_CXX11_STL
return std::nextafter(x, std::numeric_limits<double>::max());
# elif((GLM_COMPILER & GLM_COMPILER_VC) || ((GLM_COMPILER & GLM_COMPILER_INTEL) && (GLM_PLATFORM & GLM_PLATFORM_WINDOWS)))
return detail::nextafter(x, std::numeric_limits<double>::max());
# elif(GLM_PLATFORM & GLM_PLATFORM_ANDROID)
return __builtin_nextafter(x, DBL_MAX);
# else
return nextafter(x, DBL_MAX);
# endif
}
template<typename T>
GLM_FUNC_QUALIFIER T nextFloat(T x, int ULPs)
{
GLM_STATIC_ASSERT(std::numeric_limits<T>::is_iec559, "'next_float' only accept floating-point input");
assert(ULPs >= 0);
T temp = x;
for(int i = 0; i < ULPs; ++i)
temp = nextFloat(temp);
return temp;
}
GLM_FUNC_QUALIFIER float prevFloat(float x)
{
# if GLM_HAS_CXX11_STL
return std::nextafter(x, std::numeric_limits<float>::min());
# elif((GLM_COMPILER & GLM_COMPILER_VC) || ((GLM_COMPILER & GLM_COMPILER_INTEL) && (GLM_PLATFORM & GLM_PLATFORM_WINDOWS)))
return detail::nextafterf(x, FLT_MIN);
# elif(GLM_PLATFORM & GLM_PLATFORM_ANDROID)
return __builtin_nextafterf(x, FLT_MIN);
# else
return nextafterf(x, FLT_MIN);
# endif
}
GLM_FUNC_QUALIFIER double prevFloat(double x)
{
# if GLM_HAS_CXX11_STL
return std::nextafter(x, std::numeric_limits<double>::min());
# elif((GLM_COMPILER & GLM_COMPILER_VC) || ((GLM_COMPILER & GLM_COMPILER_INTEL) && (GLM_PLATFORM & GLM_PLATFORM_WINDOWS)))
return _nextafter(x, DBL_MIN);
# elif(GLM_PLATFORM & GLM_PLATFORM_ANDROID)
return __builtin_nextafter(x, DBL_MIN);
# else
return nextafter(x, DBL_MIN);
# endif
}
template<typename T>
GLM_FUNC_QUALIFIER T prevFloat(T x, int ULPs)
{
GLM_STATIC_ASSERT(std::numeric_limits<T>::is_iec559, "'prev_float' only accept floating-point input");
assert(ULPs >= 0);
T temp = x;
for(int i = 0; i < ULPs; ++i)
temp = prevFloat(temp);
return temp;
}
GLM_FUNC_QUALIFIER int floatDistance(float x, float y)
{
detail::float_t<float> const a(x);
detail::float_t<float> const b(y);
return abs(a.i - b.i);
}
GLM_FUNC_QUALIFIER int64 floatDistance(double x, double y)
{
detail::float_t<double> const a(x);
detail::float_t<double> const b(y);
return abs(a.i - b.i);
}
}//namespace glm
|
