xref: /aosp_15_r20/external/eigen/test/bfloat16_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 #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