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 #ifdef EIGEN_HAS_CUDA_FP16
15 #error "EIGEN_HAS_CUDA_FP16 should not be defined in this CPU unit test"
16 #endif
17
18 // Make sure it's possible to forward declare Eigen::half
19 namespace Eigen {
20 struct half;
21 }
22
23 using Eigen::half;
24
test_conversion()25 void test_conversion()
26 {
27 using Eigen::half_impl::__half_raw;
28
29 // Conversion from float.
30 VERIFY_IS_EQUAL(half(1.0f).x, 0x3c00);
31 VERIFY_IS_EQUAL(half(0.5f).x, 0x3800);
32 VERIFY_IS_EQUAL(half(0.33333f).x, 0x3555);
33 VERIFY_IS_EQUAL(half(0.0f).x, 0x0000);
34 VERIFY_IS_EQUAL(half(-0.0f).x, 0x8000);
35 VERIFY_IS_EQUAL(half(65504.0f).x, 0x7bff);
36 VERIFY_IS_EQUAL(half(65536.0f).x, 0x7c00); // Becomes infinity.
37
38 // Denormals.
39 VERIFY_IS_EQUAL(half(-5.96046e-08f).x, 0x8001);
40 VERIFY_IS_EQUAL(half(5.96046e-08f).x, 0x0001);
41 VERIFY_IS_EQUAL(half(1.19209e-07f).x, 0x0002);
42
43 // Verify round-to-nearest-even behavior.
44 float val1 = float(half(__half_raw(0x3c00)));
45 float val2 = float(half(__half_raw(0x3c01)));
46 float val3 = float(half(__half_raw(0x3c02)));
47 VERIFY_IS_EQUAL(half(0.5f * (val1 + val2)).x, 0x3c00);
48 VERIFY_IS_EQUAL(half(0.5f * (val2 + val3)).x, 0x3c02);
49
50 // Conversion from int.
51 VERIFY_IS_EQUAL(half(-1).x, 0xbc00);
52 VERIFY_IS_EQUAL(half(0).x, 0x0000);
53 VERIFY_IS_EQUAL(half(1).x, 0x3c00);
54 VERIFY_IS_EQUAL(half(2).x, 0x4000);
55 VERIFY_IS_EQUAL(half(3).x, 0x4200);
56
57 // Conversion from bool.
58 VERIFY_IS_EQUAL(half(false).x, 0x0000);
59 VERIFY_IS_EQUAL(half(true).x, 0x3c00);
60
61 // Conversion to float.
62 VERIFY_IS_EQUAL(float(half(__half_raw(0x0000))), 0.0f);
63 VERIFY_IS_EQUAL(float(half(__half_raw(0x3c00))), 1.0f);
64
65 // Denormals.
66 VERIFY_IS_APPROX(float(half(__half_raw(0x8001))), -5.96046e-08f);
67 VERIFY_IS_APPROX(float(half(__half_raw(0x0001))), 5.96046e-08f);
68 VERIFY_IS_APPROX(float(half(__half_raw(0x0002))), 1.19209e-07f);
69
70 // NaNs and infinities.
71 VERIFY(!(numext::isinf)(float(half(65504.0f)))); // Largest finite number.
72 VERIFY(!(numext::isnan)(float(half(0.0f))));
73 VERIFY((numext::isinf)(float(half(__half_raw(0xfc00)))));
74 VERIFY((numext::isnan)(float(half(__half_raw(0xfc01)))));
75 VERIFY((numext::isinf)(float(half(__half_raw(0x7c00)))));
76 VERIFY((numext::isnan)(float(half(__half_raw(0x7c01)))));
77
78 #if !EIGEN_COMP_MSVC
79 // Visual Studio errors out on divisions by 0
80 VERIFY((numext::isnan)(float(half(0.0 / 0.0))));
81 VERIFY((numext::isinf)(float(half(1.0 / 0.0))));
82 VERIFY((numext::isinf)(float(half(-1.0 / 0.0))));
83 #endif
84
85 // Exactly same checks as above, just directly on the half representation.
86 VERIFY(!(numext::isinf)(half(__half_raw(0x7bff))));
87 VERIFY(!(numext::isnan)(half(__half_raw(0x0000))));
88 VERIFY((numext::isinf)(half(__half_raw(0xfc00))));
89 VERIFY((numext::isnan)(half(__half_raw(0xfc01))));
90 VERIFY((numext::isinf)(half(__half_raw(0x7c00))));
91 VERIFY((numext::isnan)(half(__half_raw(0x7c01))));
92
93 #if !EIGEN_COMP_MSVC
94 // Visual Studio errors out on divisions by 0
95 VERIFY((numext::isnan)(half(0.0 / 0.0)));
96 VERIFY((numext::isinf)(half(1.0 / 0.0)));
97 VERIFY((numext::isinf)(half(-1.0 / 0.0)));
98 #endif
99 }
100
test_numtraits()101 void test_numtraits()
102 {
103 std::cout << "epsilon = " << NumTraits<half>::epsilon() << " (0x" << std::hex << NumTraits<half>::epsilon().x << ")" << std::endl;
104 std::cout << "highest = " << NumTraits<half>::highest() << " (0x" << std::hex << NumTraits<half>::highest().x << ")" << std::endl;
105 std::cout << "lowest = " << NumTraits<half>::lowest() << " (0x" << std::hex << NumTraits<half>::lowest().x << ")" << std::endl;
106 std::cout << "min = " << (std::numeric_limits<half>::min)() << " (0x" << std::hex << half((std::numeric_limits<half>::min)()).x << ")" << std::endl;
107 std::cout << "denorm min = " << (std::numeric_limits<half>::denorm_min)() << " (0x" << std::hex << half((std::numeric_limits<half>::denorm_min)()).x << ")" << std::endl;
108 std::cout << "infinity = " << NumTraits<half>::infinity() << " (0x" << std::hex << NumTraits<half>::infinity().x << ")" << std::endl;
109 std::cout << "quiet nan = " << NumTraits<half>::quiet_NaN() << " (0x" << std::hex << NumTraits<half>::quiet_NaN().x << ")" << std::endl;
110 std::cout << "signaling nan = " << std::numeric_limits<half>::signaling_NaN() << " (0x" << std::hex << std::numeric_limits<half>::signaling_NaN().x << ")" << std::endl;
111
112 VERIFY(NumTraits<half>::IsSigned);
113
114 VERIFY_IS_EQUAL( std::numeric_limits<half>::infinity().x, half(std::numeric_limits<float>::infinity()).x );
115 VERIFY_IS_EQUAL( std::numeric_limits<half>::quiet_NaN().x, half(std::numeric_limits<float>::quiet_NaN()).x );
116 VERIFY_IS_EQUAL( std::numeric_limits<half>::signaling_NaN().x, half(std::numeric_limits<float>::signaling_NaN()).x );
117 VERIFY( (std::numeric_limits<half>::min)() > half(0.f) );
118 VERIFY( (std::numeric_limits<half>::denorm_min)() > half(0.f) );
119 VERIFY( (std::numeric_limits<half>::min)()/half(2) > half(0.f) );
120 VERIFY_IS_EQUAL( (std::numeric_limits<half>::denorm_min)()/half(2), half(0.f) );
121 }
122
test_arithmetic()123 void test_arithmetic()
124 {
125 VERIFY_IS_EQUAL(float(half(2) + half(2)), 4);
126 VERIFY_IS_EQUAL(float(half(2) + half(-2)), 0);
127 VERIFY_IS_APPROX(float(half(0.33333f) + half(0.66667f)), 1.0f);
128 VERIFY_IS_EQUAL(float(half(2.0f) * half(-5.5f)), -11.0f);
129 VERIFY_IS_APPROX(float(half(1.0f) / half(3.0f)), 0.33333f);
130 VERIFY_IS_EQUAL(float(-half(4096.0f)), -4096.0f);
131 VERIFY_IS_EQUAL(float(-half(-4096.0f)), 4096.0f);
132 }
133
test_comparison()134 void test_comparison()
135 {
136 VERIFY(half(1.0f) > half(0.5f));
137 VERIFY(half(0.5f) < half(1.0f));
138 VERIFY(!(half(1.0f) < half(0.5f)));
139 VERIFY(!(half(0.5f) > half(1.0f)));
140
141 VERIFY(!(half(4.0f) > half(4.0f)));
142 VERIFY(!(half(4.0f) < half(4.0f)));
143
144 VERIFY(!(half(0.0f) < half(-0.0f)));
145 VERIFY(!(half(-0.0f) < half(0.0f)));
146 VERIFY(!(half(0.0f) > half(-0.0f)));
147 VERIFY(!(half(-0.0f) > half(0.0f)));
148
149 VERIFY(half(0.2f) > half(-1.0f));
150 VERIFY(half(-1.0f) < half(0.2f));
151 VERIFY(half(-16.0f) < half(-15.0f));
152
153 VERIFY(half(1.0f) == half(1.0f));
154 VERIFY(half(1.0f) != half(2.0f));
155
156 // Comparisons with NaNs and infinities.
157 #if !EIGEN_COMP_MSVC
158 // Visual Studio errors out on divisions by 0
159 VERIFY(!(half(0.0 / 0.0) == half(0.0 / 0.0)));
160 VERIFY(half(0.0 / 0.0) != half(0.0 / 0.0));
161
162 VERIFY(!(half(1.0) == half(0.0 / 0.0)));
163 VERIFY(!(half(1.0) < half(0.0 / 0.0)));
164 VERIFY(!(half(1.0) > half(0.0 / 0.0)));
165 VERIFY(half(1.0) != half(0.0 / 0.0));
166
167 VERIFY(half(1.0) < half(1.0 / 0.0));
168 VERIFY(half(1.0) > half(-1.0 / 0.0));
169 #endif
170 }
171
test_basic_functions()172 void test_basic_functions()
173 {
174 VERIFY_IS_EQUAL(float(numext::abs(half(3.5f))), 3.5f);
175 VERIFY_IS_EQUAL(float(abs(half(3.5f))), 3.5f);
176 VERIFY_IS_EQUAL(float(numext::abs(half(-3.5f))), 3.5f);
177 VERIFY_IS_EQUAL(float(abs(half(-3.5f))), 3.5f);
178
179 VERIFY_IS_EQUAL(float(numext::floor(half(3.5f))), 3.0f);
180 VERIFY_IS_EQUAL(float(floor(half(3.5f))), 3.0f);
181 VERIFY_IS_EQUAL(float(numext::floor(half(-3.5f))), -4.0f);
182 VERIFY_IS_EQUAL(float(floor(half(-3.5f))), -4.0f);
183
184 VERIFY_IS_EQUAL(float(numext::ceil(half(3.5f))), 4.0f);
185 VERIFY_IS_EQUAL(float(ceil(half(3.5f))), 4.0f);
186 VERIFY_IS_EQUAL(float(numext::ceil(half(-3.5f))), -3.0f);
187 VERIFY_IS_EQUAL(float(ceil(half(-3.5f))), -3.0f);
188
189 VERIFY_IS_APPROX(float(numext::sqrt(half(0.0f))), 0.0f);
190 VERIFY_IS_APPROX(float(sqrt(half(0.0f))), 0.0f);
191 VERIFY_IS_APPROX(float(numext::sqrt(half(4.0f))), 2.0f);
192 VERIFY_IS_APPROX(float(sqrt(half(4.0f))), 2.0f);
193
194 VERIFY_IS_APPROX(float(numext::pow(half(0.0f), half(1.0f))), 0.0f);
195 VERIFY_IS_APPROX(float(pow(half(0.0f), half(1.0f))), 0.0f);
196 VERIFY_IS_APPROX(float(numext::pow(half(2.0f), half(2.0f))), 4.0f);
197 VERIFY_IS_APPROX(float(pow(half(2.0f), half(2.0f))), 4.0f);
198
199 VERIFY_IS_EQUAL(float(numext::exp(half(0.0f))), 1.0f);
200 VERIFY_IS_EQUAL(float(exp(half(0.0f))), 1.0f);
201 VERIFY_IS_APPROX(float(numext::exp(half(EIGEN_PI))), 20.f + float(EIGEN_PI));
202 VERIFY_IS_APPROX(float(exp(half(EIGEN_PI))), 20.f + float(EIGEN_PI));
203
204 VERIFY_IS_EQUAL(float(numext::log(half(1.0f))), 0.0f);
205 VERIFY_IS_EQUAL(float(log(half(1.0f))), 0.0f);
206 VERIFY_IS_APPROX(float(numext::log(half(10.0f))), 2.30273f);
207 VERIFY_IS_APPROX(float(log(half(10.0f))), 2.30273f);
208
209 VERIFY_IS_EQUAL(float(numext::log1p(half(0.0f))), 0.0f);
210 VERIFY_IS_EQUAL(float(log1p(half(0.0f))), 0.0f);
211 VERIFY_IS_APPROX(float(numext::log1p(half(10.0f))), 2.3978953f);
212 VERIFY_IS_APPROX(float(log1p(half(10.0f))), 2.3978953f);
213 }
214
test_trigonometric_functions()215 void test_trigonometric_functions()
216 {
217 VERIFY_IS_APPROX(numext::cos(half(0.0f)), half(cosf(0.0f)));
218 VERIFY_IS_APPROX(cos(half(0.0f)), half(cosf(0.0f)));
219 VERIFY_IS_APPROX(numext::cos(half(EIGEN_PI)), half(cosf(EIGEN_PI)));
220 //VERIFY_IS_APPROX(numext::cos(half(EIGEN_PI/2)), half(cosf(EIGEN_PI/2)));
221 //VERIFY_IS_APPROX(numext::cos(half(3*EIGEN_PI/2)), half(cosf(3*EIGEN_PI/2)));
222 VERIFY_IS_APPROX(numext::cos(half(3.5f)), half(cosf(3.5f)));
223
224 VERIFY_IS_APPROX(numext::sin(half(0.0f)), half(sinf(0.0f)));
225 VERIFY_IS_APPROX(sin(half(0.0f)), half(sinf(0.0f)));
226 // VERIFY_IS_APPROX(numext::sin(half(EIGEN_PI)), half(sinf(EIGEN_PI)));
227 VERIFY_IS_APPROX(numext::sin(half(EIGEN_PI/2)), half(sinf(EIGEN_PI/2)));
228 VERIFY_IS_APPROX(numext::sin(half(3*EIGEN_PI/2)), half(sinf(3*EIGEN_PI/2)));
229 VERIFY_IS_APPROX(numext::sin(half(3.5f)), half(sinf(3.5f)));
230
231 VERIFY_IS_APPROX(numext::tan(half(0.0f)), half(tanf(0.0f)));
232 VERIFY_IS_APPROX(tan(half(0.0f)), half(tanf(0.0f)));
233 // VERIFY_IS_APPROX(numext::tan(half(EIGEN_PI)), half(tanf(EIGEN_PI)));
234 // VERIFY_IS_APPROX(numext::tan(half(EIGEN_PI/2)), half(tanf(EIGEN_PI/2)));
235 //VERIFY_IS_APPROX(numext::tan(half(3*EIGEN_PI/2)), half(tanf(3*EIGEN_PI/2)));
236 VERIFY_IS_APPROX(numext::tan(half(3.5f)), half(tanf(3.5f)));
237 }
238
test_array()239 void test_array()
240 {
241 typedef Array<half,1,Dynamic> ArrayXh;
242 Index size = internal::random<Index>(1,10);
243 Index i = internal::random<Index>(0,size-1);
244 ArrayXh a1 = ArrayXh::Random(size), a2 = ArrayXh::Random(size);
245 VERIFY_IS_APPROX( a1+a1, half(2)*a1 );
246 VERIFY( (a1.abs() >= half(0)).all() );
247 VERIFY_IS_APPROX( (a1*a1).sqrt(), a1.abs() );
248
249 VERIFY( ((a1.min)(a2) <= (a1.max)(a2)).all() );
250 a1(i) = half(-10.);
251 VERIFY_IS_EQUAL( a1.minCoeff(), half(-10.) );
252 a1(i) = half(10.);
253 VERIFY_IS_EQUAL( a1.maxCoeff(), half(10.) );
254
255 std::stringstream ss;
256 ss << a1;
257 }
258
test_half_float()259 void test_half_float()
260 {
261 CALL_SUBTEST(test_conversion());
262 CALL_SUBTEST(test_numtraits());
263 CALL_SUBTEST(test_arithmetic());
264 CALL_SUBTEST(test_comparison());
265 CALL_SUBTEST(test_basic_functions());
266 CALL_SUBTEST(test_trigonometric_functions());
267 CALL_SUBTEST(test_array());
268 }
269