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() << 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 107void 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 118void 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 156void 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 199void 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 223void 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 243void 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