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
15 namespace Eigen {
16 struct half;
17 }
18
19 using Eigen::half;
20
test_conversion()21 void 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
test_numtraits()97 void test_numtraits()
98 {
99 std::cout << "epsilon = " << NumTraits<half>::epsilon() << std::endl;
100 std::cout << "highest = " << NumTraits<half>::highest() << std::endl;
101 std::cout << "lowest = " << NumTraits<half>::lowest() << std::endl;
102 std::cout << "inifinty = " << NumTraits<half>::infinity() << std::endl;
103 std::cout << "nan = " << NumTraits<half>::quiet_NaN() << std::endl;
104
105 }
106
test_arithmetic()107 void test_arithmetic()
108 {
109 VERIFY_IS_EQUAL(float(half(2) + half(2)), 4);
110 VERIFY_IS_EQUAL(float(half(2) + half(-2)), 0);
111 VERIFY_IS_APPROX(float(half(0.33333f) + half(0.66667f)), 1.0f);
112 VERIFY_IS_EQUAL(float(half(2.0f) * half(-5.5f)), -11.0f);
113 VERIFY_IS_APPROX(float(half(1.0f) / half(3.0f)), 0.33333f);
114 VERIFY_IS_EQUAL(float(-half(4096.0f)), -4096.0f);
115 VERIFY_IS_EQUAL(float(-half(-4096.0f)), 4096.0f);
116 }
117
test_comparison()118 void test_comparison()
119 {
120 VERIFY(half(1.0f) > half(0.5f));
121 VERIFY(half(0.5f) < half(1.0f));
122 VERIFY(!(half(1.0f) < half(0.5f)));
123 VERIFY(!(half(0.5f) > half(1.0f)));
124
125 VERIFY(!(half(4.0f) > half(4.0f)));
126 VERIFY(!(half(4.0f) < half(4.0f)));
127
128 VERIFY(!(half(0.0f) < half(-0.0f)));
129 VERIFY(!(half(-0.0f) < half(0.0f)));
130 VERIFY(!(half(0.0f) > half(-0.0f)));
131 VERIFY(!(half(-0.0f) > half(0.0f)));
132
133 VERIFY(half(0.2f) > half(-1.0f));
134 VERIFY(half(-1.0f) < half(0.2f));
135 VERIFY(half(-16.0f) < half(-15.0f));
136
137 VERIFY(half(1.0f) == half(1.0f));
138 VERIFY(half(1.0f) != half(2.0f));
139
140 // Comparisons with NaNs and infinities.
141 #if !EIGEN_COMP_MSVC
142 // Visual Studio errors out on divisions by 0
143 VERIFY(!(half(0.0 / 0.0) == half(0.0 / 0.0)));
144 VERIFY(half(0.0 / 0.0) != half(0.0 / 0.0));
145
146 VERIFY(!(half(1.0) == half(0.0 / 0.0)));
147 VERIFY(!(half(1.0) < half(0.0 / 0.0)));
148 VERIFY(!(half(1.0) > half(0.0 / 0.0)));
149 VERIFY(half(1.0) != half(0.0 / 0.0));
150
151 VERIFY(half(1.0) < half(1.0 / 0.0));
152 VERIFY(half(1.0) > half(-1.0 / 0.0));
153 #endif
154 }
155
test_basic_functions()156 void test_basic_functions()
157 {
158 VERIFY_IS_EQUAL(float(numext::abs(half(3.5f))), 3.5f);
159 VERIFY_IS_EQUAL(float(abs(half(3.5f))), 3.5f);
160 VERIFY_IS_EQUAL(float(numext::abs(half(-3.5f))), 3.5f);
161 VERIFY_IS_EQUAL(float(abs(half(-3.5f))), 3.5f);
162
163 VERIFY_IS_EQUAL(float(numext::floor(half(3.5f))), 3.0f);
164 VERIFY_IS_EQUAL(float(floor(half(3.5f))), 3.0f);
165 VERIFY_IS_EQUAL(float(numext::floor(half(-3.5f))), -4.0f);
166 VERIFY_IS_EQUAL(float(floor(half(-3.5f))), -4.0f);
167
168 VERIFY_IS_EQUAL(float(numext::ceil(half(3.5f))), 4.0f);
169 VERIFY_IS_EQUAL(float(ceil(half(3.5f))), 4.0f);
170 VERIFY_IS_EQUAL(float(numext::ceil(half(-3.5f))), -3.0f);
171 VERIFY_IS_EQUAL(float(ceil(half(-3.5f))), -3.0f);
172
173 VERIFY_IS_APPROX(float(numext::sqrt(half(0.0f))), 0.0f);
174 VERIFY_IS_APPROX(float(sqrt(half(0.0f))), 0.0f);
175 VERIFY_IS_APPROX(float(numext::sqrt(half(4.0f))), 2.0f);
176 VERIFY_IS_APPROX(float(sqrt(half(4.0f))), 2.0f);
177
178 VERIFY_IS_APPROX(float(numext::pow(half(0.0f), half(1.0f))), 0.0f);
179 VERIFY_IS_APPROX(float(pow(half(0.0f), half(1.0f))), 0.0f);
180 VERIFY_IS_APPROX(float(numext::pow(half(2.0f), half(2.0f))), 4.0f);
181 VERIFY_IS_APPROX(float(pow(half(2.0f), half(2.0f))), 4.0f);
182
183 VERIFY_IS_EQUAL(float(numext::exp(half(0.0f))), 1.0f);
184 VERIFY_IS_EQUAL(float(exp(half(0.0f))), 1.0f);
185 VERIFY_IS_APPROX(float(numext::exp(half(EIGEN_PI))), 20.f + float(EIGEN_PI));
186 VERIFY_IS_APPROX(float(exp(half(EIGEN_PI))), 20.f + float(EIGEN_PI));
187
188 VERIFY_IS_EQUAL(float(numext::log(half(1.0f))), 0.0f);
189 VERIFY_IS_EQUAL(float(log(half(1.0f))), 0.0f);
190 VERIFY_IS_APPROX(float(numext::log(half(10.0f))), 2.30273f);
191 VERIFY_IS_APPROX(float(log(half(10.0f))), 2.30273f);
192
193 VERIFY_IS_EQUAL(float(numext::log1p(half(0.0f))), 0.0f);
194 VERIFY_IS_EQUAL(float(log1p(half(0.0f))), 0.0f);
195 VERIFY_IS_APPROX(float(numext::log1p(half(10.0f))), 2.3978953f);
196 VERIFY_IS_APPROX(float(log1p(half(10.0f))), 2.3978953f);
197 }
198
test_trigonometric_functions()199 void test_trigonometric_functions()
200 {
201 VERIFY_IS_APPROX(numext::cos(half(0.0f)), half(cosf(0.0f)));
202 VERIFY_IS_APPROX(cos(half(0.0f)), half(cosf(0.0f)));
203 VERIFY_IS_APPROX(numext::cos(half(EIGEN_PI)), half(cosf(EIGEN_PI)));
204 //VERIFY_IS_APPROX(numext::cos(half(EIGEN_PI/2)), half(cosf(EIGEN_PI/2)));
205 //VERIFY_IS_APPROX(numext::cos(half(3*EIGEN_PI/2)), half(cosf(3*EIGEN_PI/2)));
206 VERIFY_IS_APPROX(numext::cos(half(3.5f)), half(cosf(3.5f)));
207
208 VERIFY_IS_APPROX(numext::sin(half(0.0f)), half(sinf(0.0f)));
209 VERIFY_IS_APPROX(sin(half(0.0f)), half(sinf(0.0f)));
210 // VERIFY_IS_APPROX(numext::sin(half(EIGEN_PI)), half(sinf(EIGEN_PI)));
211 VERIFY_IS_APPROX(numext::sin(half(EIGEN_PI/2)), half(sinf(EIGEN_PI/2)));
212 VERIFY_IS_APPROX(numext::sin(half(3*EIGEN_PI/2)), half(sinf(3*EIGEN_PI/2)));
213 VERIFY_IS_APPROX(numext::sin(half(3.5f)), half(sinf(3.5f)));
214
215 VERIFY_IS_APPROX(numext::tan(half(0.0f)), half(tanf(0.0f)));
216 VERIFY_IS_APPROX(tan(half(0.0f)), half(tanf(0.0f)));
217 // VERIFY_IS_APPROX(numext::tan(half(EIGEN_PI)), half(tanf(EIGEN_PI)));
218 // VERIFY_IS_APPROX(numext::tan(half(EIGEN_PI/2)), half(tanf(EIGEN_PI/2)));
219 //VERIFY_IS_APPROX(numext::tan(half(3*EIGEN_PI/2)), half(tanf(3*EIGEN_PI/2)));
220 VERIFY_IS_APPROX(numext::tan(half(3.5f)), half(tanf(3.5f)));
221 }
222
test_array()223 void test_array()
224 {
225 typedef Array<half,1,Dynamic> ArrayXh;
226 Index size = internal::random<Index>(1,10);
227 Index i = internal::random<Index>(0,size-1);
228 ArrayXh a1 = ArrayXh::Random(size), a2 = ArrayXh::Random(size);
229 VERIFY_IS_APPROX( a1+a1, half(2)*a1 );
230 VERIFY( (a1.abs() >= half(0)).all() );
231 VERIFY_IS_APPROX( (a1*a1).sqrt(), a1.abs() );
232
233 VERIFY( ((a1.min)(a2) <= (a1.max)(a2)).all() );
234 a1(i) = half(-10.);
235 VERIFY_IS_EQUAL( a1.minCoeff(), half(-10.) );
236 a1(i) = half(10.);
237 VERIFY_IS_EQUAL( a1.maxCoeff(), half(10.) );
238
239 std::stringstream ss;
240 ss << a1;
241 }
242
test_half_float()243 void test_half_float()
244 {
245 CALL_SUBTEST(test_conversion());
246 CALL_SUBTEST(test_numtraits());
247 CALL_SUBTEST(test_arithmetic());
248 CALL_SUBTEST(test_comparison());
249 CALL_SUBTEST(test_basic_functions());
250 CALL_SUBTEST(test_trigonometric_functions());
251 CALL_SUBTEST(test_array());
252 }
253