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
BinaryToFloat(uint32_t sign,uint32_t exponent,uint32_t high_mantissa,uint32_t low_mantissa)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>
test_roundtrip()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
test_conversion()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
test_numtraits()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
test_arithmetic()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
test_comparison()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
test_basic_functions()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
test_trigonometric_functions()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
test_array()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
test_product()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
EIGEN_DECLARE_TEST(bfloat16_float)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 }
379