1// This file is part of Eigen, a lightweight C++ template library
2// for linear algebra.
3//
4// This Source Code Form is subject to the terms of the Mozilla
5// Public License v. 2.0. If a copy of the MPL was not distributed
6// with this file, You can obtain one at http://mozilla.org/MPL/2.0/.
7
8#include <sstream>
9
10#include "main.h"
11
12#include <Eigen/src/Core/arch/CUDA/Half.h>
13
14// Make sure it's possible to forward declare Eigen::half
15namespace Eigen {
16struct half;
17}
18
19using Eigen::half;
20
21void test_conversion()
22{
23  using Eigen::half_impl::__half;
24
25  // Conversion from float.
26  VERIFY_IS_EQUAL(half(1.0f).x, 0x3c00);
27  VERIFY_IS_EQUAL(half(0.5f).x, 0x3800);
28  VERIFY_IS_EQUAL(half(0.33333f).x, 0x3555);
29  VERIFY_IS_EQUAL(half(0.0f).x, 0x0000);
30  VERIFY_IS_EQUAL(half(-0.0f).x, 0x8000);
31  VERIFY_IS_EQUAL(half(65504.0f).x, 0x7bff);
32  VERIFY_IS_EQUAL(half(65536.0f).x, 0x7c00);  // Becomes infinity.
33
34  // Denormals.
35  VERIFY_IS_EQUAL(half(-5.96046e-08f).x, 0x8001);
36  VERIFY_IS_EQUAL(half(5.96046e-08f).x, 0x0001);
37  VERIFY_IS_EQUAL(half(1.19209e-07f).x, 0x0002);
38
39  // Verify round-to-nearest-even behavior.
40  float val1 = float(half(__half(0x3c00)));
41  float val2 = float(half(__half(0x3c01)));
42  float val3 = float(half(__half(0x3c02)));
43  VERIFY_IS_EQUAL(half(0.5f * (val1 + val2)).x, 0x3c00);
44  VERIFY_IS_EQUAL(half(0.5f * (val2 + val3)).x, 0x3c02);
45
46  // Conversion from int.
47  VERIFY_IS_EQUAL(half(-1).x, 0xbc00);
48  VERIFY_IS_EQUAL(half(0).x, 0x0000);
49  VERIFY_IS_EQUAL(half(1).x, 0x3c00);
50  VERIFY_IS_EQUAL(half(2).x, 0x4000);
51  VERIFY_IS_EQUAL(half(3).x, 0x4200);
52
53  // Conversion from bool.
54  VERIFY_IS_EQUAL(half(false).x, 0x0000);
55  VERIFY_IS_EQUAL(half(true).x, 0x3c00);
56
57  // Conversion to float.
58  VERIFY_IS_EQUAL(float(half(__half(0x0000))), 0.0f);
59  VERIFY_IS_EQUAL(float(half(__half(0x3c00))), 1.0f);
60
61  // Denormals.
62  VERIFY_IS_APPROX(float(half(__half(0x8001))), -5.96046e-08f);
63  VERIFY_IS_APPROX(float(half(__half(0x0001))), 5.96046e-08f);
64  VERIFY_IS_APPROX(float(half(__half(0x0002))), 1.19209e-07f);
65
66  // NaNs and infinities.
67  VERIFY(!(numext::isinf)(float(half(65504.0f))));  // Largest finite number.
68  VERIFY(!(numext::isnan)(float(half(0.0f))));
69  VERIFY((numext::isinf)(float(half(__half(0xfc00)))));
70  VERIFY((numext::isnan)(float(half(__half(0xfc01)))));
71  VERIFY((numext::isinf)(float(half(__half(0x7c00)))));
72  VERIFY((numext::isnan)(float(half(__half(0x7c01)))));
73
74#if !EIGEN_COMP_MSVC
75  // Visual Studio errors out on divisions by 0
76  VERIFY((numext::isnan)(float(half(0.0 / 0.0))));
77  VERIFY((numext::isinf)(float(half(1.0 / 0.0))));
78  VERIFY((numext::isinf)(float(half(-1.0 / 0.0))));
79#endif
80
81  // Exactly same checks as above, just directly on the half representation.
82  VERIFY(!(numext::isinf)(half(__half(0x7bff))));
83  VERIFY(!(numext::isnan)(half(__half(0x0000))));
84  VERIFY((numext::isinf)(half(__half(0xfc00))));
85  VERIFY((numext::isnan)(half(__half(0xfc01))));
86  VERIFY((numext::isinf)(half(__half(0x7c00))));
87  VERIFY((numext::isnan)(half(__half(0x7c01))));
88
89#if !EIGEN_COMP_MSVC
90  // Visual Studio errors out on divisions by 0
91  VERIFY((numext::isnan)(half(0.0 / 0.0)));
92  VERIFY((numext::isinf)(half(1.0 / 0.0)));
93  VERIFY((numext::isinf)(half(-1.0 / 0.0)));
94#endif
95}
96
97void test_numtraits()
98{
99  std::cout << "epsilon       = " << NumTraits<half>::epsilon() << "  (0x" << std::hex << NumTraits<half>::epsilon().x << ")" << std::endl;
100  std::cout << "highest       = " << NumTraits<half>::highest() << "  (0x" << std::hex << NumTraits<half>::highest().x << ")" << std::endl;
101  std::cout << "lowest        = " << NumTraits<half>::lowest() << "  (0x" << std::hex << NumTraits<half>::lowest().x << ")" << std::endl;
102  std::cout << "min           = " << (std::numeric_limits<half>::min)() << "  (0x" << std::hex << half((std::numeric_limits<half>::min)()).x << ")" << std::endl;
103  std::cout << "denorm min    = " << (std::numeric_limits<half>::denorm_min)() << "  (0x" << std::hex << half((std::numeric_limits<half>::denorm_min)()).x << ")" << std::endl;
104  std::cout << "infinity      = " << NumTraits<half>::infinity() << "  (0x" << std::hex << NumTraits<half>::infinity().x << ")" << std::endl;
105  std::cout << "quiet nan     = " << NumTraits<half>::quiet_NaN() << "  (0x" << std::hex << NumTraits<half>::quiet_NaN().x << ")" << std::endl;
106  std::cout << "signaling nan = " << std::numeric_limits<half>::signaling_NaN() << "  (0x" << std::hex << std::numeric_limits<half>::signaling_NaN().x << ")" << std::endl;
107
108  VERIFY(NumTraits<half>::IsSigned);
109
110  VERIFY_IS_EQUAL( std::numeric_limits<half>::infinity().x, half(std::numeric_limits<float>::infinity()).x );
111  VERIFY_IS_EQUAL( std::numeric_limits<half>::quiet_NaN().x, half(std::numeric_limits<float>::quiet_NaN()).x );
112  VERIFY_IS_EQUAL( std::numeric_limits<half>::signaling_NaN().x, half(std::numeric_limits<float>::signaling_NaN()).x );
113  VERIFY( (std::numeric_limits<half>::min)() > half(0.f) );
114  VERIFY( (std::numeric_limits<half>::denorm_min)() > half(0.f) );
115  VERIFY( (std::numeric_limits<half>::min)()/half(2) > half(0.f) );
116  VERIFY_IS_EQUAL( (std::numeric_limits<half>::denorm_min)()/half(2), half(0.f) );
117}
118
119void test_arithmetic()
120{
121  VERIFY_IS_EQUAL(float(half(2) + half(2)), 4);
122  VERIFY_IS_EQUAL(float(half(2) + half(-2)), 0);
123  VERIFY_IS_APPROX(float(half(0.33333f) + half(0.66667f)), 1.0f);
124  VERIFY_IS_EQUAL(float(half(2.0f) * half(-5.5f)), -11.0f);
125  VERIFY_IS_APPROX(float(half(1.0f) / half(3.0f)), 0.33333f);
126  VERIFY_IS_EQUAL(float(-half(4096.0f)), -4096.0f);
127  VERIFY_IS_EQUAL(float(-half(-4096.0f)), 4096.0f);
128}
129
130void test_comparison()
131{
132  VERIFY(half(1.0f) > half(0.5f));
133  VERIFY(half(0.5f) < half(1.0f));
134  VERIFY(!(half(1.0f) < half(0.5f)));
135  VERIFY(!(half(0.5f) > half(1.0f)));
136
137  VERIFY(!(half(4.0f) > half(4.0f)));
138  VERIFY(!(half(4.0f) < half(4.0f)));
139
140  VERIFY(!(half(0.0f) < half(-0.0f)));
141  VERIFY(!(half(-0.0f) < half(0.0f)));
142  VERIFY(!(half(0.0f) > half(-0.0f)));
143  VERIFY(!(half(-0.0f) > half(0.0f)));
144
145  VERIFY(half(0.2f) > half(-1.0f));
146  VERIFY(half(-1.0f) < half(0.2f));
147  VERIFY(half(-16.0f) < half(-15.0f));
148
149  VERIFY(half(1.0f) == half(1.0f));
150  VERIFY(half(1.0f) != half(2.0f));
151
152  // Comparisons with NaNs and infinities.
153#if !EIGEN_COMP_MSVC
154  // Visual Studio errors out on divisions by 0
155  VERIFY(!(half(0.0 / 0.0) == half(0.0 / 0.0)));
156  VERIFY(half(0.0 / 0.0) != half(0.0 / 0.0));
157
158  VERIFY(!(half(1.0) == half(0.0 / 0.0)));
159  VERIFY(!(half(1.0) < half(0.0 / 0.0)));
160  VERIFY(!(half(1.0) > half(0.0 / 0.0)));
161  VERIFY(half(1.0) != half(0.0 / 0.0));
162
163  VERIFY(half(1.0) < half(1.0 / 0.0));
164  VERIFY(half(1.0) > half(-1.0 / 0.0));
165#endif
166}
167
168void test_basic_functions()
169{
170  VERIFY_IS_EQUAL(float(numext::abs(half(3.5f))), 3.5f);
171  VERIFY_IS_EQUAL(float(abs(half(3.5f))), 3.5f);
172  VERIFY_IS_EQUAL(float(numext::abs(half(-3.5f))), 3.5f);
173  VERIFY_IS_EQUAL(float(abs(half(-3.5f))), 3.5f);
174
175  VERIFY_IS_EQUAL(float(numext::floor(half(3.5f))), 3.0f);
176  VERIFY_IS_EQUAL(float(floor(half(3.5f))), 3.0f);
177  VERIFY_IS_EQUAL(float(numext::floor(half(-3.5f))), -4.0f);
178  VERIFY_IS_EQUAL(float(floor(half(-3.5f))), -4.0f);
179
180  VERIFY_IS_EQUAL(float(numext::ceil(half(3.5f))), 4.0f);
181  VERIFY_IS_EQUAL(float(ceil(half(3.5f))), 4.0f);
182  VERIFY_IS_EQUAL(float(numext::ceil(half(-3.5f))), -3.0f);
183  VERIFY_IS_EQUAL(float(ceil(half(-3.5f))), -3.0f);
184
185  VERIFY_IS_APPROX(float(numext::sqrt(half(0.0f))), 0.0f);
186  VERIFY_IS_APPROX(float(sqrt(half(0.0f))), 0.0f);
187  VERIFY_IS_APPROX(float(numext::sqrt(half(4.0f))), 2.0f);
188  VERIFY_IS_APPROX(float(sqrt(half(4.0f))), 2.0f);
189
190  VERIFY_IS_APPROX(float(numext::pow(half(0.0f), half(1.0f))), 0.0f);
191  VERIFY_IS_APPROX(float(pow(half(0.0f), half(1.0f))), 0.0f);
192  VERIFY_IS_APPROX(float(numext::pow(half(2.0f), half(2.0f))), 4.0f);
193  VERIFY_IS_APPROX(float(pow(half(2.0f), half(2.0f))), 4.0f);
194
195  VERIFY_IS_EQUAL(float(numext::exp(half(0.0f))), 1.0f);
196  VERIFY_IS_EQUAL(float(exp(half(0.0f))), 1.0f);
197  VERIFY_IS_APPROX(float(numext::exp(half(EIGEN_PI))), 20.f + float(EIGEN_PI));
198  VERIFY_IS_APPROX(float(exp(half(EIGEN_PI))), 20.f + float(EIGEN_PI));
199
200  VERIFY_IS_EQUAL(float(numext::log(half(1.0f))), 0.0f);
201  VERIFY_IS_EQUAL(float(log(half(1.0f))), 0.0f);
202  VERIFY_IS_APPROX(float(numext::log(half(10.0f))), 2.30273f);
203  VERIFY_IS_APPROX(float(log(half(10.0f))), 2.30273f);
204
205  VERIFY_IS_EQUAL(float(numext::log1p(half(0.0f))), 0.0f);
206  VERIFY_IS_EQUAL(float(log1p(half(0.0f))), 0.0f);
207  VERIFY_IS_APPROX(float(numext::log1p(half(10.0f))), 2.3978953f);
208  VERIFY_IS_APPROX(float(log1p(half(10.0f))), 2.3978953f);
209}
210
211void test_trigonometric_functions()
212{
213  VERIFY_IS_APPROX(numext::cos(half(0.0f)), half(cosf(0.0f)));
214  VERIFY_IS_APPROX(cos(half(0.0f)), half(cosf(0.0f)));
215  VERIFY_IS_APPROX(numext::cos(half(EIGEN_PI)), half(cosf(EIGEN_PI)));
216  //VERIFY_IS_APPROX(numext::cos(half(EIGEN_PI/2)), half(cosf(EIGEN_PI/2)));
217  //VERIFY_IS_APPROX(numext::cos(half(3*EIGEN_PI/2)), half(cosf(3*EIGEN_PI/2)));
218  VERIFY_IS_APPROX(numext::cos(half(3.5f)), half(cosf(3.5f)));
219
220  VERIFY_IS_APPROX(numext::sin(half(0.0f)), half(sinf(0.0f)));
221  VERIFY_IS_APPROX(sin(half(0.0f)), half(sinf(0.0f)));
222  //  VERIFY_IS_APPROX(numext::sin(half(EIGEN_PI)), half(sinf(EIGEN_PI)));
223  VERIFY_IS_APPROX(numext::sin(half(EIGEN_PI/2)), half(sinf(EIGEN_PI/2)));
224  VERIFY_IS_APPROX(numext::sin(half(3*EIGEN_PI/2)), half(sinf(3*EIGEN_PI/2)));
225  VERIFY_IS_APPROX(numext::sin(half(3.5f)), half(sinf(3.5f)));
226
227  VERIFY_IS_APPROX(numext::tan(half(0.0f)), half(tanf(0.0f)));
228  VERIFY_IS_APPROX(tan(half(0.0f)), half(tanf(0.0f)));
229  //  VERIFY_IS_APPROX(numext::tan(half(EIGEN_PI)), half(tanf(EIGEN_PI)));
230  //  VERIFY_IS_APPROX(numext::tan(half(EIGEN_PI/2)), half(tanf(EIGEN_PI/2)));
231  //VERIFY_IS_APPROX(numext::tan(half(3*EIGEN_PI/2)), half(tanf(3*EIGEN_PI/2)));
232  VERIFY_IS_APPROX(numext::tan(half(3.5f)), half(tanf(3.5f)));
233}
234
235void test_array()
236{
237  typedef Array<half,1,Dynamic> ArrayXh;
238  Index size = internal::random<Index>(1,10);
239  Index i = internal::random<Index>(0,size-1);
240  ArrayXh a1 = ArrayXh::Random(size), a2 = ArrayXh::Random(size);
241  VERIFY_IS_APPROX( a1+a1, half(2)*a1 );
242  VERIFY( (a1.abs() >= half(0)).all() );
243  VERIFY_IS_APPROX( (a1*a1).sqrt(), a1.abs() );
244
245  VERIFY( ((a1.min)(a2) <= (a1.max)(a2)).all() );
246  a1(i) = half(-10.);
247  VERIFY_IS_EQUAL( a1.minCoeff(), half(-10.) );
248  a1(i) = half(10.);
249  VERIFY_IS_EQUAL( a1.maxCoeff(), half(10.) );
250
251  std::stringstream ss;
252  ss << a1;
253}
254
255void test_half_float()
256{
257  CALL_SUBTEST(test_conversion());
258  CALL_SUBTEST(test_numtraits());
259  CALL_SUBTEST(test_arithmetic());
260  CALL_SUBTEST(test_comparison());
261  CALL_SUBTEST(test_basic_functions());
262  CALL_SUBTEST(test_trigonometric_functions());
263  CALL_SUBTEST(test_array());
264}
265