half_float.cpp
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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 
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 
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 
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 
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 
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 
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 
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 
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 }
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autogenerated on Sat May 8 2021 02:42:10