xref: /aosp_15_r20/external/eigen/test/half_float.cpp (revision bf2c37156dfe67e5dfebd6d394bad8b2ab5804d4) 
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/Default/Half.h>
13 
14 #define VERIFY_HALF_BITS_EQUAL(h, bits) \
15   VERIFY_IS_EQUAL((numext::bit_cast<numext::uint16_t>(h)), (static_cast<numext::uint16_t>(bits)))
16 
17 // Make sure it's possible to forward declare Eigen::half
18 namespace Eigen {
19 struct half;
20 }
21 
22 using Eigen::half;
23 
test_conversion()24 void test_conversion()
25 {
26   using Eigen::half_impl::__half_raw;
27 
28   // Round-trip bit-cast with uint16.
29   VERIFY_IS_EQUAL(
30     numext::bit_cast<half>(numext::bit_cast<numext::uint16_t>(half(1.0f))),
31     half(1.0f));
32   VERIFY_IS_EQUAL(
33     numext::bit_cast<half>(numext::bit_cast<numext::uint16_t>(half(0.5f))),
34     half(0.5f));
35   VERIFY_IS_EQUAL(
36     numext::bit_cast<half>(numext::bit_cast<numext::uint16_t>(half(-0.33333f))),
37     half(-0.33333f));
38    VERIFY_IS_EQUAL(
39     numext::bit_cast<half>(numext::bit_cast<numext::uint16_t>(half(0.0f))),
40     half(0.0f));
41 
42   // Conversion from float.
43   VERIFY_HALF_BITS_EQUAL(half(1.0f), 0x3c00);
44   VERIFY_HALF_BITS_EQUAL(half(0.5f), 0x3800);
45   VERIFY_HALF_BITS_EQUAL(half(0.33333f), 0x3555);
46   VERIFY_HALF_BITS_EQUAL(half(0.0f), 0x0000);
47   VERIFY_HALF_BITS_EQUAL(half(-0.0f), 0x8000);
48   VERIFY_HALF_BITS_EQUAL(half(65504.0f), 0x7bff);
49   VERIFY_HALF_BITS_EQUAL(half(65536.0f), 0x7c00);  // Becomes infinity.
50 
51   // Denormals.
52   VERIFY_HALF_BITS_EQUAL(half(-5.96046e-08f), 0x8001);
53   VERIFY_HALF_BITS_EQUAL(half(5.96046e-08f), 0x0001);
54   VERIFY_HALF_BITS_EQUAL(half(1.19209e-07f), 0x0002);
55 
56   // Verify round-to-nearest-even behavior.
57   float val1 = float(half(__half_raw(0x3c00)));
58   float val2 = float(half(__half_raw(0x3c01)));
59   float val3 = float(half(__half_raw(0x3c02)));
60   VERIFY_HALF_BITS_EQUAL(half(0.5f * (val1 + val2)), 0x3c00);
61   VERIFY_HALF_BITS_EQUAL(half(0.5f * (val2 + val3)), 0x3c02);
62 
63   // Conversion from int.
64   VERIFY_HALF_BITS_EQUAL(half(-1), 0xbc00);
65   VERIFY_HALF_BITS_EQUAL(half(0), 0x0000);
66   VERIFY_HALF_BITS_EQUAL(half(1), 0x3c00);
67   VERIFY_HALF_BITS_EQUAL(half(2), 0x4000);
68   VERIFY_HALF_BITS_EQUAL(half(3), 0x4200);
69 
70   // Conversion from bool.
71   VERIFY_HALF_BITS_EQUAL(half(false), 0x0000);
72   VERIFY_HALF_BITS_EQUAL(half(true), 0x3c00);
73 
74   // Conversion to float.
75   VERIFY_IS_EQUAL(float(half(__half_raw(0x0000))), 0.0f);
76   VERIFY_IS_EQUAL(float(half(__half_raw(0x3c00))), 1.0f);
77 
78   // Denormals.
79   VERIFY_IS_APPROX(float(half(__half_raw(0x8001))), -5.96046e-08f);
80   VERIFY_IS_APPROX(float(half(__half_raw(0x0001))), 5.96046e-08f);
81   VERIFY_IS_APPROX(float(half(__half_raw(0x0002))), 1.19209e-07f);
82 
83   // NaNs and infinities.
84   VERIFY(!(numext::isinf)(float(half(65504.0f))));  // Largest finite number.
85   VERIFY(!(numext::isnan)(float(half(0.0f))));
86   VERIFY((numext::isinf)(float(half(__half_raw(0xfc00)))));
87   VERIFY((numext::isnan)(float(half(__half_raw(0xfc01)))));
88   VERIFY((numext::isinf)(float(half(__half_raw(0x7c00)))));
89   VERIFY((numext::isnan)(float(half(__half_raw(0x7c01)))));
90 
91 #if !EIGEN_COMP_MSVC
92   // Visual Studio errors out on divisions by 0
93   VERIFY((numext::isnan)(float(half(0.0 / 0.0))));
94   VERIFY((numext::isinf)(float(half(1.0 / 0.0))));
95   VERIFY((numext::isinf)(float(half(-1.0 / 0.0))));
96 #endif
97 
98   // Exactly same checks as above, just directly on the half representation.
99   VERIFY(!(numext::isinf)(half(__half_raw(0x7bff))));
100   VERIFY(!(numext::isnan)(half(__half_raw(0x0000))));
101   VERIFY((numext::isinf)(half(__half_raw(0xfc00))));
102   VERIFY((numext::isnan)(half(__half_raw(0xfc01))));
103   VERIFY((numext::isinf)(half(__half_raw(0x7c00))));
104   VERIFY((numext::isnan)(half(__half_raw(0x7c01))));
105 
106 #if !EIGEN_COMP_MSVC
107   // Visual Studio errors out on divisions by 0
108   VERIFY((numext::isnan)(half(0.0 / 0.0)));
109   VERIFY((numext::isinf)(half(1.0 / 0.0)));
110   VERIFY((numext::isinf)(half(-1.0 / 0.0)));
111 #endif
112 
113   // Conversion to bool
114   VERIFY(!static_cast<bool>(half(0.0)));
115   VERIFY(!static_cast<bool>(half(-0.0)));
116   VERIFY(static_cast<bool>(half(__half_raw(0x7bff))));
117   VERIFY(static_cast<bool>(half(-0.33333)));
118   VERIFY(static_cast<bool>(half(1.0)));
119   VERIFY(static_cast<bool>(half(-1.0)));
120   VERIFY(static_cast<bool>(half(-5.96046e-08f)));
121 }
122 
test_numtraits()123 void test_numtraits()
124 {
125   std::cout << "epsilon       = " << NumTraits<half>::epsilon() << "  (0x" << std::hex << numext::bit_cast<numext::uint16_t>(NumTraits<half>::epsilon()) << ")" << std::endl;
126   std::cout << "highest       = " << NumTraits<half>::highest() << "  (0x" << std::hex << numext::bit_cast<numext::uint16_t>(NumTraits<half>::highest()) << ")" << std::endl;
127   std::cout << "lowest        = " << NumTraits<half>::lowest() << "  (0x" << std::hex << numext::bit_cast<numext::uint16_t>(NumTraits<half>::lowest()) << ")" << std::endl;
128   std::cout << "min           = " << (std::numeric_limits<half>::min)() << "  (0x" << std::hex << numext::bit_cast<numext::uint16_t>(half((std::numeric_limits<half>::min)())) << ")" << std::endl;
129   std::cout << "denorm min    = " << (std::numeric_limits<half>::denorm_min)() << "  (0x" << std::hex << numext::bit_cast<numext::uint16_t>(half((std::numeric_limits<half>::denorm_min)())) << ")" << std::endl;
130   std::cout << "infinity      = " << NumTraits<half>::infinity() << "  (0x" << std::hex << numext::bit_cast<numext::uint16_t>(NumTraits<half>::infinity()) << ")" << std::endl;
131   std::cout << "quiet nan     = " << NumTraits<half>::quiet_NaN() << "  (0x" << std::hex << numext::bit_cast<numext::uint16_t>(NumTraits<half>::quiet_NaN()) << ")" << std::endl;
132   std::cout << "signaling nan = " << std::numeric_limits<half>::signaling_NaN() << "  (0x" << std::hex << numext::bit_cast<numext::uint16_t>(std::numeric_limits<half>::signaling_NaN()) << ")" << std::endl;
133 
134   VERIFY(NumTraits<half>::IsSigned);
135 
136   VERIFY_IS_EQUAL(
137     numext::bit_cast<numext::uint16_t>(std::numeric_limits<half>::infinity()),
138     numext::bit_cast<numext::uint16_t>(half(std::numeric_limits<float>::infinity())) );
139   // There is no guarantee that casting a 32-bit NaN to 16-bit has a precise
140   // bit pattern.  We test that it is in fact a NaN, then test the signaling
141   // bit (msb of significand is 1 for quiet, 0 for signaling).
142   const numext::uint16_t HALF_QUIET_BIT = 0x0200;
143   VERIFY(
144     (numext::isnan)(std::numeric_limits<half>::quiet_NaN())
145     && (numext::isnan)(half(std::numeric_limits<float>::quiet_NaN()))
146     && ((numext::bit_cast<numext::uint16_t>(std::numeric_limits<half>::quiet_NaN()) & HALF_QUIET_BIT) > 0)
147     && ((numext::bit_cast<numext::uint16_t>(half(std::numeric_limits<float>::quiet_NaN())) & HALF_QUIET_BIT) > 0) );
148   // After a cast to half, a signaling NaN may become non-signaling
149   // (e.g. in the case of casting float to native __fp16). Thus, we check that
150   // both are NaN, and that only the `numeric_limits` version is signaling.
151   VERIFY(
152     (numext::isnan)(std::numeric_limits<half>::signaling_NaN())
153     && (numext::isnan)(half(std::numeric_limits<float>::signaling_NaN()))
154     && ((numext::bit_cast<numext::uint16_t>(std::numeric_limits<half>::signaling_NaN()) & HALF_QUIET_BIT) == 0) );
155 
156   VERIFY( (std::numeric_limits<half>::min)() > half(0.f) );
157   VERIFY( (std::numeric_limits<half>::denorm_min)() > half(0.f) );
158   VERIFY( (std::numeric_limits<half>::min)()/half(2) > half(0.f) );
159   VERIFY_IS_EQUAL( (std::numeric_limits<half>::denorm_min)()/half(2), half(0.f) );
160 }
161 
test_arithmetic()162 void test_arithmetic()
163 {
164   VERIFY_IS_EQUAL(float(half(2) + half(2)), 4);
165   VERIFY_IS_EQUAL(float(half(2) + half(-2)), 0);
166   VERIFY_IS_APPROX(float(half(0.33333f) + half(0.66667f)), 1.0f);
167   VERIFY_IS_EQUAL(float(half(2.0f) * half(-5.5f)), -11.0f);
168   VERIFY_IS_APPROX(float(half(1.0f) / half(3.0f)), 0.33333f);
169   VERIFY_IS_EQUAL(float(-half(4096.0f)), -4096.0f);
170   VERIFY_IS_EQUAL(float(-half(-4096.0f)), 4096.0f);
171 
172   half x(3);
173   half y = ++x;
174   VERIFY_IS_EQUAL(x, half(4));
175   VERIFY_IS_EQUAL(y, half(4));
176   y = --x;
177   VERIFY_IS_EQUAL(x, half(3));
178   VERIFY_IS_EQUAL(y, half(3));
179   y = x++;
180   VERIFY_IS_EQUAL(x, half(4));
181   VERIFY_IS_EQUAL(y, half(3));
182   y = x--;
183   VERIFY_IS_EQUAL(x, half(3));
184   VERIFY_IS_EQUAL(y, half(4));
185 }
186 
test_comparison()187 void test_comparison()
188 {
189   VERIFY(half(1.0f) > half(0.5f));
190   VERIFY(half(0.5f) < half(1.0f));
191   VERIFY(!(half(1.0f) < half(0.5f)));
192   VERIFY(!(half(0.5f) > half(1.0f)));
193 
194   VERIFY(!(half(4.0f) > half(4.0f)));
195   VERIFY(!(half(4.0f) < half(4.0f)));
196 
197   VERIFY(!(half(0.0f) < half(-0.0f)));
198   VERIFY(!(half(-0.0f) < half(0.0f)));
199   VERIFY(!(half(0.0f) > half(-0.0f)));
200   VERIFY(!(half(-0.0f) > half(0.0f)));
201 
202   VERIFY(half(0.2f) > half(-1.0f));
203   VERIFY(half(-1.0f) < half(0.2f));
204   VERIFY(half(-16.0f) < half(-15.0f));
205 
206   VERIFY(half(1.0f) == half(1.0f));
207   VERIFY(half(1.0f) != half(2.0f));
208 
209   // Comparisons with NaNs and infinities.
210 #if !EIGEN_COMP_MSVC
211   // Visual Studio errors out on divisions by 0
212   VERIFY(!(half(0.0 / 0.0) == half(0.0 / 0.0)));
213   VERIFY(half(0.0 / 0.0) != half(0.0 / 0.0));
214 
215   VERIFY(!(half(1.0) == half(0.0 / 0.0)));
216   VERIFY(!(half(1.0) < half(0.0 / 0.0)));
217   VERIFY(!(half(1.0) > half(0.0 / 0.0)));
218   VERIFY(half(1.0) != half(0.0 / 0.0));
219 
220   VERIFY(half(1.0) < half(1.0 / 0.0));
221   VERIFY(half(1.0) > half(-1.0 / 0.0));
222 #endif
223 }
224 
test_basic_functions()225 void test_basic_functions()
226 {
227   VERIFY_IS_EQUAL(float(numext::abs(half(3.5f))), 3.5f);
228   VERIFY_IS_EQUAL(float(abs(half(3.5f))), 3.5f);
229   VERIFY_IS_EQUAL(float(numext::abs(half(-3.5f))), 3.5f);
230   VERIFY_IS_EQUAL(float(abs(half(-3.5f))), 3.5f);
231 
232   VERIFY_IS_EQUAL(float(numext::floor(half(3.5f))), 3.0f);
233   VERIFY_IS_EQUAL(float(floor(half(3.5f))), 3.0f);
234   VERIFY_IS_EQUAL(float(numext::floor(half(-3.5f))), -4.0f);
235   VERIFY_IS_EQUAL(float(floor(half(-3.5f))), -4.0f);
236 
237   VERIFY_IS_EQUAL(float(numext::ceil(half(3.5f))), 4.0f);
238   VERIFY_IS_EQUAL(float(ceil(half(3.5f))), 4.0f);
239   VERIFY_IS_EQUAL(float(numext::ceil(half(-3.5f))), -3.0f);
240   VERIFY_IS_EQUAL(float(ceil(half(-3.5f))), -3.0f);
241 
242   VERIFY_IS_APPROX(float(numext::sqrt(half(0.0f))), 0.0f);
243   VERIFY_IS_APPROX(float(sqrt(half(0.0f))), 0.0f);
244   VERIFY_IS_APPROX(float(numext::sqrt(half(4.0f))), 2.0f);
245   VERIFY_IS_APPROX(float(sqrt(half(4.0f))), 2.0f);
246 
247   VERIFY_IS_APPROX(float(numext::pow(half(0.0f), half(1.0f))), 0.0f);
248   VERIFY_IS_APPROX(float(pow(half(0.0f), half(1.0f))), 0.0f);
249   VERIFY_IS_APPROX(float(numext::pow(half(2.0f), half(2.0f))), 4.0f);
250   VERIFY_IS_APPROX(float(pow(half(2.0f), half(2.0f))), 4.0f);
251 
252   VERIFY_IS_EQUAL(float(numext::exp(half(0.0f))), 1.0f);
253   VERIFY_IS_EQUAL(float(exp(half(0.0f))), 1.0f);
254   VERIFY_IS_APPROX(float(numext::exp(half(EIGEN_PI))), 20.f + float(EIGEN_PI));
255   VERIFY_IS_APPROX(float(exp(half(EIGEN_PI))), 20.f + float(EIGEN_PI));
256 
257   VERIFY_IS_EQUAL(float(numext::expm1(half(0.0f))), 0.0f);
258   VERIFY_IS_EQUAL(float(expm1(half(0.0f))), 0.0f);
259   VERIFY_IS_APPROX(float(numext::expm1(half(2.0f))), 6.3890561f);
260   VERIFY_IS_APPROX(float(expm1(half(2.0f))), 6.3890561f);
261 
262   VERIFY_IS_EQUAL(float(numext::log(half(1.0f))), 0.0f);
263   VERIFY_IS_EQUAL(float(log(half(1.0f))), 0.0f);
264   VERIFY_IS_APPROX(float(numext::log(half(10.0f))), 2.30273f);
265   VERIFY_IS_APPROX(float(log(half(10.0f))), 2.30273f);
266 
267   VERIFY_IS_EQUAL(float(numext::log1p(half(0.0f))), 0.0f);
268   VERIFY_IS_EQUAL(float(log1p(half(0.0f))), 0.0f);
269   VERIFY_IS_APPROX(float(numext::log1p(half(10.0f))), 2.3978953f);
270   VERIFY_IS_APPROX(float(log1p(half(10.0f))), 2.3978953f);
271 
272   VERIFY_IS_APPROX(numext::fmod(half(5.3f), half(2.0f)), half(1.3f));
273   VERIFY_IS_APPROX(fmod(half(5.3f), half(2.0f)), half(1.3f));
274   VERIFY_IS_APPROX(numext::fmod(half(-18.5f), half(-4.2f)), half(-1.7f));
275   VERIFY_IS_APPROX(fmod(half(-18.5f), half(-4.2f)), half(-1.7f));
276 }
277 
test_trigonometric_functions()278 void test_trigonometric_functions()
279 {
280   VERIFY_IS_APPROX(numext::cos(half(0.0f)), half(cosf(0.0f)));
281   VERIFY_IS_APPROX(cos(half(0.0f)), half(cosf(0.0f)));
282   VERIFY_IS_APPROX(numext::cos(half(EIGEN_PI)), half(cosf(EIGEN_PI)));
283   // VERIFY_IS_APPROX(numext::cos(half(EIGEN_PI/2)), half(cosf(EIGEN_PI/2)));
284   // VERIFY_IS_APPROX(numext::cos(half(3*EIGEN_PI/2)), half(cosf(3*EIGEN_PI/2)));
285   VERIFY_IS_APPROX(numext::cos(half(3.5f)), half(cosf(3.5f)));
286 
287   VERIFY_IS_APPROX(numext::sin(half(0.0f)), half(sinf(0.0f)));
288   VERIFY_IS_APPROX(sin(half(0.0f)), half(sinf(0.0f)));
289   //  VERIFY_IS_APPROX(numext::sin(half(EIGEN_PI)), half(sinf(EIGEN_PI)));
290   VERIFY_IS_APPROX(numext::sin(half(EIGEN_PI/2)), half(sinf(EIGEN_PI/2)));
291   VERIFY_IS_APPROX(numext::sin(half(3*EIGEN_PI/2)), half(sinf(3*EIGEN_PI/2)));
292   VERIFY_IS_APPROX(numext::sin(half(3.5f)), half(sinf(3.5f)));
293 
294   VERIFY_IS_APPROX(numext::tan(half(0.0f)), half(tanf(0.0f)));
295   VERIFY_IS_APPROX(tan(half(0.0f)), half(tanf(0.0f)));
296   //  VERIFY_IS_APPROX(numext::tan(half(EIGEN_PI)), half(tanf(EIGEN_PI)));
297   //  VERIFY_IS_APPROX(numext::tan(half(EIGEN_PI/2)), half(tanf(EIGEN_PI/2)));
298   //VERIFY_IS_APPROX(numext::tan(half(3*EIGEN_PI/2)), half(tanf(3*EIGEN_PI/2)));
299   VERIFY_IS_APPROX(numext::tan(half(3.5f)), half(tanf(3.5f)));
300 }
301 
test_array()302 void test_array()
303 {
304   typedef Array<half,1,Dynamic> ArrayXh;
305   Index size = internal::random<Index>(1,10);
306   Index i = internal::random<Index>(0,size-1);
307   ArrayXh a1 = ArrayXh::Random(size), a2 = ArrayXh::Random(size);
308   VERIFY_IS_APPROX( a1+a1, half(2)*a1 );
309   VERIFY( (a1.abs() >= half(0)).all() );
310   VERIFY_IS_APPROX( (a1*a1).sqrt(), a1.abs() );
311 
312   VERIFY( ((a1.min)(a2) <= (a1.max)(a2)).all() );
313   a1(i) = half(-10.);
314   VERIFY_IS_EQUAL( a1.minCoeff(), half(-10.) );
315   a1(i) = half(10.);
316   VERIFY_IS_EQUAL( a1.maxCoeff(), half(10.) );
317 
318   std::stringstream ss;
319   ss << a1;
320 }
321 
test_product()322 void test_product()
323 {
324   typedef Matrix<half,Dynamic,Dynamic> MatrixXh;
325   Index rows  = internal::random<Index>(1,EIGEN_TEST_MAX_SIZE);
326   Index cols  = internal::random<Index>(1,EIGEN_TEST_MAX_SIZE);
327   Index depth = internal::random<Index>(1,EIGEN_TEST_MAX_SIZE);
328   MatrixXh Ah = MatrixXh::Random(rows,depth);
329   MatrixXh Bh = MatrixXh::Random(depth,cols);
330   MatrixXh Ch = MatrixXh::Random(rows,cols);
331   MatrixXf Af = Ah.cast<float>();
332   MatrixXf Bf = Bh.cast<float>();
333   MatrixXf Cf = Ch.cast<float>();
334   VERIFY_IS_APPROX(Ch.noalias()+=Ah*Bh, (Cf.noalias()+=Af*Bf).cast<half>());
335 }
336 
EIGEN_DECLARE_TEST(half_float)337 EIGEN_DECLARE_TEST(half_float)
338 {
339   CALL_SUBTEST(test_numtraits());
340   for(int i = 0; i < g_repeat; i++) {
341     CALL_SUBTEST(test_conversion());
342     CALL_SUBTEST(test_arithmetic());
343     CALL_SUBTEST(test_comparison());
344     CALL_SUBTEST(test_basic_functions());
345     CALL_SUBTEST(test_trigonometric_functions());
346     CALL_SUBTEST(test_array());
347     CALL_SUBTEST(test_product());
348   }
349 }
350