bfloat16_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 #include <memory>
10 #include <math.h>
11 
12 #include "main.h"
13 
14 #include <Eigen/src/Core/arch/Default/BFloat16.h>
15 
16 #define VERIFY_BFLOAT16_BITS_EQUAL(h, bits) \
17  VERIFY_IS_EQUAL((numext::bit_cast<numext::uint16_t>(h)), (static_cast<numext::uint16_t>(bits)))
18 
19 // Make sure it's possible to forward declare Eigen::bfloat16
20 namespace Eigen {
21 struct bfloat16;
22 }
23 
24 using Eigen::bfloat16;
25 
26 float BinaryToFloat(uint32_t sign, uint32_t exponent, uint32_t high_mantissa,
27  uint32_t low_mantissa) {
28  float dest;
29  uint32_t src = (sign << 31) + (exponent << 23) + (high_mantissa << 16) + low_mantissa;
30  memcpy(static_cast<void*>(&dest),
31  static_cast<const void*>(&src), sizeof(dest));
32  return dest;
33 }
34 
35 template<typename T>
36  void test_roundtrip() {
37  // Representable T round trip via bfloat16
38  VERIFY_IS_EQUAL((internal::cast<bfloat16,T>(internal::cast<T,bfloat16>(-std::numeric_limits<T>::infinity()))), -std::numeric_limits<T>::infinity());
39  VERIFY_IS_EQUAL((internal::cast<bfloat16,T>(internal::cast<T,bfloat16>(std::numeric_limits<T>::infinity()))), std::numeric_limits<T>::infinity());
40  VERIFY_IS_EQUAL((internal::cast<bfloat16,T>(internal::cast<T,bfloat16>(T(-1.0)))), T(-1.0));
41  VERIFY_IS_EQUAL((internal::cast<bfloat16,T>(internal::cast<T,bfloat16>(T(-0.5)))), T(-0.5));
42  VERIFY_IS_EQUAL((internal::cast<bfloat16,T>(internal::cast<T,bfloat16>(T(-0.0)))), T(-0.0));
43  VERIFY_IS_EQUAL((internal::cast<bfloat16,T>(internal::cast<T,bfloat16>(T(1.0)))), T(1.0));
44  VERIFY_IS_EQUAL((internal::cast<bfloat16,T>(internal::cast<T,bfloat16>(T(0.5)))), T(0.5));
45  VERIFY_IS_EQUAL((internal::cast<bfloat16,T>(internal::cast<T,bfloat16>(T(0.0)))), T(0.0));
46 }
47 
48 void test_conversion()
49 {
50  using Eigen::bfloat16_impl::__bfloat16_raw;
51 
52  // Round-trip casts
53  VERIFY_IS_EQUAL(
54  numext::bit_cast<bfloat16>(numext::bit_cast<numext::uint16_t>(bfloat16(1.0f))),
55  bfloat16(1.0f));
56  VERIFY_IS_EQUAL(
57  numext::bit_cast<bfloat16>(numext::bit_cast<numext::uint16_t>(bfloat16(0.5f))),
58  bfloat16(0.5f));
59  VERIFY_IS_EQUAL(
60  numext::bit_cast<bfloat16>(numext::bit_cast<numext::uint16_t>(bfloat16(-0.33333f))),
61  bfloat16(-0.33333f));
62  VERIFY_IS_EQUAL(
63  numext::bit_cast<bfloat16>(numext::bit_cast<numext::uint16_t>(bfloat16(0.0f))),
64  bfloat16(0.0f));
65 
66  // Conversion from float.
67  VERIFY_BFLOAT16_BITS_EQUAL(bfloat16(1.0f), 0x3f80);
68  VERIFY_BFLOAT16_BITS_EQUAL(bfloat16(0.5f), 0x3f00);
69  VERIFY_BFLOAT16_BITS_EQUAL(bfloat16(0.33333f), 0x3eab);
70  VERIFY_BFLOAT16_BITS_EQUAL(bfloat16(3.38e38f), 0x7f7e);
71  VERIFY_BFLOAT16_BITS_EQUAL(bfloat16(3.40e38f), 0x7f80); // Becomes infinity.
72 
73  // Verify round-to-nearest-even behavior.
74  float val1 = static_cast<float>(bfloat16(__bfloat16_raw(0x3c00)));
75  float val2 = static_cast<float>(bfloat16(__bfloat16_raw(0x3c01)));
76  float val3 = static_cast<float>(bfloat16(__bfloat16_raw(0x3c02)));
77  VERIFY_BFLOAT16_BITS_EQUAL(bfloat16(0.5f * (val1 + val2)), 0x3c00);
78  VERIFY_BFLOAT16_BITS_EQUAL(bfloat16(0.5f * (val2 + val3)), 0x3c02);
79 
80  // Conversion from int.
81  VERIFY_BFLOAT16_BITS_EQUAL(bfloat16(-1), 0xbf80);
82  VERIFY_BFLOAT16_BITS_EQUAL(bfloat16(0), 0x0000);
83  VERIFY_BFLOAT16_BITS_EQUAL(bfloat16(1), 0x3f80);
84  VERIFY_BFLOAT16_BITS_EQUAL(bfloat16(2), 0x4000);
85  VERIFY_BFLOAT16_BITS_EQUAL(bfloat16(3), 0x4040);
86  VERIFY_BFLOAT16_BITS_EQUAL(bfloat16(12), 0x4140);
87 
88  // Conversion from bool.
89  VERIFY_BFLOAT16_BITS_EQUAL(bfloat16(false), 0x0000);
90  VERIFY_BFLOAT16_BITS_EQUAL(bfloat16(true), 0x3f80);
91 
92  // Conversion to bool
93  VERIFY_IS_EQUAL(static_cast<bool>(bfloat16(3)), true);
94  VERIFY_IS_EQUAL(static_cast<bool>(bfloat16(0.33333f)), true);
95  VERIFY_IS_EQUAL(bfloat16(-0.0), false);
96  VERIFY_IS_EQUAL(static_cast<bool>(bfloat16(0.0)), false);
97 
98  // Explicit conversion to float.
99  VERIFY_IS_EQUAL(static_cast<float>(bfloat16(__bfloat16_raw(0x0000))), 0.0f);
100  VERIFY_IS_EQUAL(static_cast<float>(bfloat16(__bfloat16_raw(0x3f80))), 1.0f);
101 
102  // Implicit conversion to float
103  VERIFY_IS_EQUAL(bfloat16(__bfloat16_raw(0x0000)), 0.0f);
104  VERIFY_IS_EQUAL(bfloat16(__bfloat16_raw(0x3f80)), 1.0f);
105 
106  // Zero representations
107  VERIFY_IS_EQUAL(bfloat16(0.0f), bfloat16(0.0f));
108  VERIFY_IS_EQUAL(bfloat16(-0.0f), bfloat16(0.0f));
109  VERIFY_IS_EQUAL(bfloat16(-0.0f), bfloat16(-0.0f));
110  VERIFY_BFLOAT16_BITS_EQUAL(bfloat16(0.0f), 0x0000);
111  VERIFY_BFLOAT16_BITS_EQUAL(bfloat16(-0.0f), 0x8000);
112 
113  // Default is zero
114  VERIFY_IS_EQUAL(static_cast<float>(bfloat16()), 0.0f);
115 
116  // Representable floats round trip via bfloat16
117  test_roundtrip<float>();
118  test_roundtrip<double>();
119  test_roundtrip<std::complex<float> >();
120  test_roundtrip<std::complex<double> >();
121 
122  // Conversion
123  Array<float,1,100> a;
124  for (int i = 0; i < 100; i++) a(i) = i + 1.25;
125  Array<bfloat16,1,100> b = a.cast<bfloat16>();
126  Array<float,1,100> c = b.cast<float>();
127  for (int i = 0; i < 100; ++i) {
128  VERIFY_LE(numext::abs(c(i) - a(i)), a(i) / 128);
129  }
130 
131  // Epsilon
132  VERIFY_LE(1.0f, static_cast<float>((std::numeric_limits<bfloat16>::epsilon)() + bfloat16(1.0f)));
133  VERIFY_IS_EQUAL(1.0f, static_cast<float>((std::numeric_limits<bfloat16>::epsilon)() / bfloat16(2.0f) + bfloat16(1.0f)));
134 
135  // Negate
136  VERIFY_IS_EQUAL(static_cast<float>(-bfloat16(3.0f)), -3.0f);
137  VERIFY_IS_EQUAL(static_cast<float>(-bfloat16(-4.5f)), 4.5f);
138 
139 
140 #if !EIGEN_COMP_MSVC
141  // Visual Studio errors out on divisions by 0
142  VERIFY((numext::isnan)(static_cast<float>(bfloat16(0.0 / 0.0))));
143  VERIFY((numext::isinf)(static_cast<float>(bfloat16(1.0 / 0.0))));
144  VERIFY((numext::isinf)(static_cast<float>(bfloat16(-1.0 / 0.0))));
145 
146  // Visual Studio errors out on divisions by 0
147  VERIFY((numext::isnan)(bfloat16(0.0 / 0.0)));
148  VERIFY((numext::isinf)(bfloat16(1.0 / 0.0)));
149  VERIFY((numext::isinf)(bfloat16(-1.0 / 0.0)));
150 #endif
151 
152  // NaNs and infinities.
153  VERIFY(!(numext::isinf)(static_cast<float>(bfloat16(3.38e38f)))); // Largest finite number.
154  VERIFY(!(numext::isnan)(static_cast<float>(bfloat16(0.0f))));
155  VERIFY((numext::isinf)(static_cast<float>(bfloat16(__bfloat16_raw(0xff80)))));
156  VERIFY((numext::isnan)(static_cast<float>(bfloat16(__bfloat16_raw(0xffc0)))));
157  VERIFY((numext::isinf)(static_cast<float>(bfloat16(__bfloat16_raw(0x7f80)))));
158  VERIFY((numext::isnan)(static_cast<float>(bfloat16(__bfloat16_raw(0x7fc0)))));
159 
160  // Exactly same checks as above, just directly on the bfloat16 representation.
161  VERIFY(!(numext::isinf)(bfloat16(__bfloat16_raw(0x7bff))));
162  VERIFY(!(numext::isnan)(bfloat16(__bfloat16_raw(0x0000))));
163  VERIFY((numext::isinf)(bfloat16(__bfloat16_raw(0xff80))));
164  VERIFY((numext::isnan)(bfloat16(__bfloat16_raw(0xffc0))));
165  VERIFY((numext::isinf)(bfloat16(__bfloat16_raw(0x7f80))));
166  VERIFY((numext::isnan)(bfloat16(__bfloat16_raw(0x7fc0))));
167 
168  VERIFY_BFLOAT16_BITS_EQUAL(bfloat16(BinaryToFloat(0x0, 0xff, 0x40, 0x0)), 0x7fc0);
169  VERIFY_BFLOAT16_BITS_EQUAL(bfloat16(BinaryToFloat(0x1, 0xff, 0x40, 0x0)), 0xffc0);
170 }
171 
172 void test_numtraits()
173 {
174  std::cout << "epsilon = " << NumTraits<bfloat16>::epsilon() << " (0x" << std::hex << numext::bit_cast<numext::uint16_t>(NumTraits<bfloat16>::epsilon()) << ")" << std::endl;
175  std::cout << "highest = " << NumTraits<bfloat16>::highest() << " (0x" << std::hex << numext::bit_cast<numext::uint16_t>(NumTraits<bfloat16>::highest()) << ")" << std::endl;
176  std::cout << "lowest = " << NumTraits<bfloat16>::lowest() << " (0x" << std::hex << numext::bit_cast<numext::uint16_t>(NumTraits<bfloat16>::lowest()) << ")" << std::endl;
177  std::cout << "min = " << (std::numeric_limits<bfloat16>::min)() << " (0x" << std::hex << numext::bit_cast<numext::uint16_t>((std::numeric_limits<bfloat16>::min)()) << ")" << std::endl;
178  std::cout << "denorm min = " << (std::numeric_limits<bfloat16>::denorm_min)() << " (0x" << std::hex << numext::bit_cast<numext::uint16_t>((std::numeric_limits<bfloat16>::denorm_min)()) << ")" << std::endl;
179  std::cout << "infinity = " << NumTraits<bfloat16>::infinity() << " (0x" << std::hex << numext::bit_cast<numext::uint16_t>(NumTraits<bfloat16>::infinity()) << ")" << std::endl;
180  std::cout << "quiet nan = " << NumTraits<bfloat16>::quiet_NaN() << " (0x" << std::hex << numext::bit_cast<numext::uint16_t>(NumTraits<bfloat16>::quiet_NaN()) << ")" << std::endl;
181  std::cout << "signaling nan = " << std::numeric_limits<bfloat16>::signaling_NaN() << " (0x" << std::hex << numext::bit_cast<numext::uint16_t>(std::numeric_limits<bfloat16>::signaling_NaN()) << ")" << std::endl;
182 
183  VERIFY(NumTraits<bfloat16>::IsSigned);
184 
185  VERIFY_IS_EQUAL(
186  numext::bit_cast<numext::uint16_t>(std::numeric_limits<bfloat16>::infinity()),
187  numext::bit_cast<numext::uint16_t>(bfloat16(std::numeric_limits<float>::infinity())) );
188  // There is no guarantee that casting a 32-bit NaN to bfloat16 has a precise
189  // bit pattern. We test that it is in fact a NaN, then test the signaling
190  // bit (msb of significand is 1 for quiet, 0 for signaling).
191  const numext::uint16_t BFLOAT16_QUIET_BIT = 0x0040;
192  VERIFY(
193  (numext::isnan)(std::numeric_limits<bfloat16>::quiet_NaN())
194  && (numext::isnan)(bfloat16(std::numeric_limits<float>::quiet_NaN()))
195  && ((numext::bit_cast<numext::uint16_t>(std::numeric_limits<bfloat16>::quiet_NaN()) & BFLOAT16_QUIET_BIT) > 0)
196  && ((numext::bit_cast<numext::uint16_t>(bfloat16(std::numeric_limits<float>::quiet_NaN())) & BFLOAT16_QUIET_BIT) > 0) );
197  // After a cast to bfloat16, a signaling NaN may become non-signaling. Thus,
198  // we check that both are NaN, and that only the `numeric_limits` version is
199  // signaling.
200  VERIFY(
201  (numext::isnan)(std::numeric_limits<bfloat16>::signaling_NaN())
202  && (numext::isnan)(bfloat16(std::numeric_limits<float>::signaling_NaN()))
203  && ((numext::bit_cast<numext::uint16_t>(std::numeric_limits<bfloat16>::signaling_NaN()) & BFLOAT16_QUIET_BIT) == 0) );
204 
205  VERIFY( (std::numeric_limits<bfloat16>::min)() > bfloat16(0.f) );
206  VERIFY( (std::numeric_limits<bfloat16>::denorm_min)() > bfloat16(0.f) );
207  VERIFY_IS_EQUAL( (std::numeric_limits<bfloat16>::denorm_min)()/bfloat16(2), bfloat16(0.f) );
208 }
209 
210 void test_arithmetic()
211 {
212  VERIFY_IS_EQUAL(static_cast<float>(bfloat16(2) + bfloat16(2)), 4);
213  VERIFY_IS_EQUAL(static_cast<float>(bfloat16(2) + bfloat16(-2)), 0);
214  VERIFY_IS_APPROX(static_cast<float>(bfloat16(0.33333f) + bfloat16(0.66667f)), 1.0f);
215  VERIFY_IS_EQUAL(static_cast<float>(bfloat16(2.0f) * bfloat16(-5.5f)), -11.0f);
216  VERIFY_IS_APPROX(static_cast<float>(bfloat16(1.0f) / bfloat16(3.0f)), 0.3339f);
217  VERIFY_IS_EQUAL(static_cast<float>(-bfloat16(4096.0f)), -4096.0f);
218  VERIFY_IS_EQUAL(static_cast<float>(-bfloat16(-4096.0f)), 4096.0f);
219 }
220 
221 void test_comparison()
222 {
223  VERIFY(bfloat16(1.0f) > bfloat16(0.5f));
224  VERIFY(bfloat16(0.5f) < bfloat16(1.0f));
225  VERIFY(!(bfloat16(1.0f) < bfloat16(0.5f)));
226  VERIFY(!(bfloat16(0.5f) > bfloat16(1.0f)));
227 
228  VERIFY(!(bfloat16(4.0f) > bfloat16(4.0f)));
229  VERIFY(!(bfloat16(4.0f) < bfloat16(4.0f)));
230 
231  VERIFY(!(bfloat16(0.0f) < bfloat16(-0.0f)));
232  VERIFY(!(bfloat16(-0.0f) < bfloat16(0.0f)));
233  VERIFY(!(bfloat16(0.0f) > bfloat16(-0.0f)));
234  VERIFY(!(bfloat16(-0.0f) > bfloat16(0.0f)));
235 
236  VERIFY(bfloat16(0.2f) > bfloat16(-1.0f));
237  VERIFY(bfloat16(-1.0f) < bfloat16(0.2f));
238  VERIFY(bfloat16(-16.0f) < bfloat16(-15.0f));
239 
240  VERIFY(bfloat16(1.0f) == bfloat16(1.0f));
241  VERIFY(bfloat16(1.0f) != bfloat16(2.0f));
242 
243  // Comparisons with NaNs and infinities.
244 #if !EIGEN_COMP_MSVC
245  // Visual Studio errors out on divisions by 0
246  VERIFY(!(bfloat16(0.0 / 0.0) == bfloat16(0.0 / 0.0)));
247  VERIFY(bfloat16(0.0 / 0.0) != bfloat16(0.0 / 0.0));
248 
249  VERIFY(!(bfloat16(1.0) == bfloat16(0.0 / 0.0)));
250  VERIFY(!(bfloat16(1.0) < bfloat16(0.0 / 0.0)));
251  VERIFY(!(bfloat16(1.0) > bfloat16(0.0 / 0.0)));
252  VERIFY(bfloat16(1.0) != bfloat16(0.0 / 0.0));
253 
254  VERIFY(bfloat16(1.0) < bfloat16(1.0 / 0.0));
255  VERIFY(bfloat16(1.0) > bfloat16(-1.0 / 0.0));
256 #endif
257 }
258 
259 void test_basic_functions()
260 {
261  VERIFY_IS_EQUAL(static_cast<float>(numext::abs(bfloat16(3.5f))), 3.5f);
262  VERIFY_IS_EQUAL(static_cast<float>(abs(bfloat16(3.5f))), 3.5f);
263  VERIFY_IS_EQUAL(static_cast<float>(numext::abs(bfloat16(-3.5f))), 3.5f);
264  VERIFY_IS_EQUAL(static_cast<float>(abs(bfloat16(-3.5f))), 3.5f);
265 
266  VERIFY_IS_EQUAL(static_cast<float>(numext::floor(bfloat16(3.5f))), 3.0f);
267  VERIFY_IS_EQUAL(static_cast<float>(floor(bfloat16(3.5f))), 3.0f);
268  VERIFY_IS_EQUAL(static_cast<float>(numext::floor(bfloat16(-3.5f))), -4.0f);
269  VERIFY_IS_EQUAL(static_cast<float>(floor(bfloat16(-3.5f))), -4.0f);
270 
271  VERIFY_IS_EQUAL(static_cast<float>(numext::ceil(bfloat16(3.5f))), 4.0f);
272  VERIFY_IS_EQUAL(static_cast<float>(ceil(bfloat16(3.5f))), 4.0f);
273  VERIFY_IS_EQUAL(static_cast<float>(numext::ceil(bfloat16(-3.5f))), -3.0f);
274  VERIFY_IS_EQUAL(static_cast<float>(ceil(bfloat16(-3.5f))), -3.0f);
275 
276  VERIFY_IS_APPROX(static_cast<float>(numext::sqrt(bfloat16(0.0f))), 0.0f);
277  VERIFY_IS_APPROX(static_cast<float>(sqrt(bfloat16(0.0f))), 0.0f);
278  VERIFY_IS_APPROX(static_cast<float>(numext::sqrt(bfloat16(4.0f))), 2.0f);
279  VERIFY_IS_APPROX(static_cast<float>(sqrt(bfloat16(4.0f))), 2.0f);
280 
281  VERIFY_IS_APPROX(static_cast<float>(numext::pow(bfloat16(0.0f), bfloat16(1.0f))), 0.0f);
282  VERIFY_IS_APPROX(static_cast<float>(pow(bfloat16(0.0f), bfloat16(1.0f))), 0.0f);
283  VERIFY_IS_APPROX(static_cast<float>(numext::pow(bfloat16(2.0f), bfloat16(2.0f))), 4.0f);
284  VERIFY_IS_APPROX(static_cast<float>(pow(bfloat16(2.0f), bfloat16(2.0f))), 4.0f);
285 
286  VERIFY_IS_EQUAL(static_cast<float>(numext::exp(bfloat16(0.0f))), 1.0f);
287  VERIFY_IS_EQUAL(static_cast<float>(exp(bfloat16(0.0f))), 1.0f);
288  VERIFY_IS_APPROX(static_cast<float>(numext::exp(bfloat16(EIGEN_PI))), 20.f + static_cast<float>(EIGEN_PI));
289  VERIFY_IS_APPROX(static_cast<float>(exp(bfloat16(EIGEN_PI))), 20.f + static_cast<float>(EIGEN_PI));
290 
291  VERIFY_IS_EQUAL(static_cast<float>(numext::expm1(bfloat16(0.0f))), 0.0f);
292  VERIFY_IS_EQUAL(static_cast<float>(expm1(bfloat16(0.0f))), 0.0f);
293  VERIFY_IS_APPROX(static_cast<float>(numext::expm1(bfloat16(2.0f))), 6.375f);
294  VERIFY_IS_APPROX(static_cast<float>(expm1(bfloat16(2.0f))), 6.375f);
295 
296  VERIFY_IS_EQUAL(static_cast<float>(numext::log(bfloat16(1.0f))), 0.0f);
297  VERIFY_IS_EQUAL(static_cast<float>(log(bfloat16(1.0f))), 0.0f);
298  VERIFY_IS_APPROX(static_cast<float>(numext::log(bfloat16(10.0f))), 2.296875f);
299  VERIFY_IS_APPROX(static_cast<float>(log(bfloat16(10.0f))), 2.296875f);
300 
301  VERIFY_IS_EQUAL(static_cast<float>(numext::log1p(bfloat16(0.0f))), 0.0f);
302  VERIFY_IS_EQUAL(static_cast<float>(log1p(bfloat16(0.0f))), 0.0f);
303  VERIFY_IS_APPROX(static_cast<float>(numext::log1p(bfloat16(10.0f))), 2.390625f);
304  VERIFY_IS_APPROX(static_cast<float>(log1p(bfloat16(10.0f))), 2.390625f);
305 }
306 
307 void test_trigonometric_functions()
308 {
309  VERIFY_IS_APPROX(numext::cos(bfloat16(0.0f)), bfloat16(cosf(0.0f)));
310  VERIFY_IS_APPROX(cos(bfloat16(0.0f)), bfloat16(cosf(0.0f)));
311  VERIFY_IS_APPROX(numext::cos(bfloat16(EIGEN_PI)), bfloat16(cosf(EIGEN_PI)));
312  // VERIFY_IS_APPROX(numext::cos(bfloat16(EIGEN_PI/2)), bfloat16(cosf(EIGEN_PI/2)));
313  // VERIFY_IS_APPROX(numext::cos(bfloat16(3*EIGEN_PI/2)), bfloat16(cosf(3*EIGEN_PI/2)));
314  VERIFY_IS_APPROX(numext::cos(bfloat16(3.5f)), bfloat16(cosf(3.5f)));
315 
316  VERIFY_IS_APPROX(numext::sin(bfloat16(0.0f)), bfloat16(sinf(0.0f)));
317  VERIFY_IS_APPROX(sin(bfloat16(0.0f)), bfloat16(sinf(0.0f)));
318  // VERIFY_IS_APPROX(numext::sin(bfloat16(EIGEN_PI)), bfloat16(sinf(EIGEN_PI)));
319  VERIFY_IS_APPROX(numext::sin(bfloat16(EIGEN_PI/2)), bfloat16(sinf(EIGEN_PI/2)));
320  VERIFY_IS_APPROX(numext::sin(bfloat16(3*EIGEN_PI/2)), bfloat16(sinf(3*EIGEN_PI/2)));
321  VERIFY_IS_APPROX(numext::sin(bfloat16(3.5f)), bfloat16(sinf(3.5f)));
322 
323  VERIFY_IS_APPROX(numext::tan(bfloat16(0.0f)), bfloat16(tanf(0.0f)));
324  VERIFY_IS_APPROX(tan(bfloat16(0.0f)), bfloat16(tanf(0.0f)));
325  // VERIFY_IS_APPROX(numext::tan(bfloat16(EIGEN_PI)), bfloat16(tanf(EIGEN_PI)));
326  // VERIFY_IS_APPROX(numext::tan(bfloat16(EIGEN_PI/2)), bfloat16(tanf(EIGEN_PI/2)));
327  // VERIFY_IS_APPROX(numext::tan(bfloat16(3*EIGEN_PI/2)), bfloat16(tanf(3*EIGEN_PI/2)));
328  VERIFY_IS_APPROX(numext::tan(bfloat16(3.5f)), bfloat16(tanf(3.5f)));
329 }
330 
331 void test_array()
332 {
333  typedef Array<bfloat16,1,Dynamic> ArrayXh;
334  Index size = internal::random<Index>(1,10);
335  Index i = internal::random<Index>(0,size-1);
336  ArrayXh a1 = ArrayXh::Random(size), a2 = ArrayXh::Random(size);
337  VERIFY_IS_APPROX( a1+a1, bfloat16(2)*a1 );
338  VERIFY( (a1.abs() >= bfloat16(0)).all() );
339  VERIFY_IS_APPROX( (a1*a1).sqrt(), a1.abs() );
340 
341  VERIFY( ((a1.min)(a2) <= (a1.max)(a2)).all() );
342  a1(i) = bfloat16(-10.);
343  VERIFY_IS_EQUAL( a1.minCoeff(), bfloat16(-10.) );
344  a1(i) = bfloat16(10.);
345  VERIFY_IS_EQUAL( a1.maxCoeff(), bfloat16(10.) );
346 
347  std::stringstream ss;
348  ss << a1;
349 }
350 
351 void test_product()
352 {
353  typedef Matrix<bfloat16,Dynamic,Dynamic> MatrixXh;
354  Index rows = internal::random<Index>(1,EIGEN_TEST_MAX_SIZE);
355  Index cols = internal::random<Index>(1,EIGEN_TEST_MAX_SIZE);
356  Index depth = internal::random<Index>(1,EIGEN_TEST_MAX_SIZE);
357  MatrixXh Ah = MatrixXh::Random(rows,depth);
358  MatrixXh Bh = MatrixXh::Random(depth,cols);
359  MatrixXh Ch = MatrixXh::Random(rows,cols);
360  MatrixXf Af = Ah.cast<float>();
361  MatrixXf Bf = Bh.cast<float>();
362  MatrixXf Cf = Ch.cast<float>();
363  VERIFY_IS_APPROX(Ch.noalias()+=Ah*Bh, (Cf.noalias()+=Af*Bf).cast<bfloat16>());
364 }
365 
366 EIGEN_DECLARE_TEST(bfloat16_float)
367 {
368  CALL_SUBTEST(test_numtraits());
369  for(int i = 0; i < g_repeat; i++) {
370  CALL_SUBTEST(test_conversion());
371  CALL_SUBTEST(test_arithmetic());
372  CALL_SUBTEST(test_comparison());
373  CALL_SUBTEST(test_basic_functions());
374  CALL_SUBTEST(test_trigonometric_functions());
375  CALL_SUBTEST(test_array());
376  CALL_SUBTEST(test_product());
377  }
378 }
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autogenerated on Tue Jul 4 2023 02:33:58