// This file is part of Eigen, a lightweight C++ template library // for linear algebra. // // This Source Code Form is subject to the terms of the Mozilla // Public License v. 2.0. If a copy of the MPL was not distributed // with this file, You can obtain one at http://mozilla.org/MPL/2.0/. #include <sstream> #include <memory> #include <math.h> #include "main.h" #include <Eigen/src/Core/arch/Default/BFloat16.h> #define VERIFY_BFLOAT16_BITS_EQUAL(h, bits) \ VERIFY_IS_EQUAL((numext::bit_cast<numext::uint16_t>(h)), (static_cast<numext::uint16_t>(bits))) // Make sure it's possible to forward declare Eigen::bfloat16 namespace Eigen { struct bfloat16; } using Eigen::bfloat16; float BinaryToFloat(uint32_t sign, uint32_t exponent, uint32_t high_mantissa, uint32_t low_mantissa) { float dest; uint32_t src = (sign << 31) + (exponent << 23) + (high_mantissa << 16) + low_mantissa; memcpy(static_cast<void*>(&dest), static_cast<const void*>(&src), sizeof(dest)); return dest; } template<typename T> void test_roundtrip() { // Representable T round trip via bfloat16 VERIFY_IS_EQUAL((internal::cast<bfloat16,T>(internal::cast<T,bfloat16>(-std::numeric_limits<T>::infinity()))), -std::numeric_limits<T>::infinity()); VERIFY_IS_EQUAL((internal::cast<bfloat16,T>(internal::cast<T,bfloat16>(std::numeric_limits<T>::infinity()))), std::numeric_limits<T>::infinity()); VERIFY_IS_EQUAL((internal::cast<bfloat16,T>(internal::cast<T,bfloat16>(T(-1.0)))), T(-1.0)); VERIFY_IS_EQUAL((internal::cast<bfloat16,T>(internal::cast<T,bfloat16>(T(-0.5)))), T(-0.5)); VERIFY_IS_EQUAL((internal::cast<bfloat16,T>(internal::cast<T,bfloat16>(T(-0.0)))), T(-0.0)); VERIFY_IS_EQUAL((internal::cast<bfloat16,T>(internal::cast<T,bfloat16>(T(1.0)))), T(1.0)); VERIFY_IS_EQUAL((internal::cast<bfloat16,T>(internal::cast<T,bfloat16>(T(0.5)))), T(0.5)); VERIFY_IS_EQUAL((internal::cast<bfloat16,T>(internal::cast<T,bfloat16>(T(0.0)))), T(0.0)); } void test_conversion() { using Eigen::bfloat16_impl::__bfloat16_raw; // Round-trip casts VERIFY_IS_EQUAL( numext::bit_cast<bfloat16>(numext::bit_cast<numext::uint16_t>(bfloat16(1.0f))), bfloat16(1.0f)); VERIFY_IS_EQUAL( numext::bit_cast<bfloat16>(numext::bit_cast<numext::uint16_t>(bfloat16(0.5f))), bfloat16(0.5f)); VERIFY_IS_EQUAL( numext::bit_cast<bfloat16>(numext::bit_cast<numext::uint16_t>(bfloat16(-0.33333f))), bfloat16(-0.33333f)); VERIFY_IS_EQUAL( numext::bit_cast<bfloat16>(numext::bit_cast<numext::uint16_t>(bfloat16(0.0f))), bfloat16(0.0f)); // Conversion from float. VERIFY_BFLOAT16_BITS_EQUAL(bfloat16(1.0f), 0x3f80); VERIFY_BFLOAT16_BITS_EQUAL(bfloat16(0.5f), 0x3f00); VERIFY_BFLOAT16_BITS_EQUAL(bfloat16(0.33333f), 0x3eab); VERIFY_BFLOAT16_BITS_EQUAL(bfloat16(3.38e38f), 0x7f7e); VERIFY_BFLOAT16_BITS_EQUAL(bfloat16(3.40e38f), 0x7f80); // Becomes infinity. // Verify round-to-nearest-even behavior. float val1 = static_cast<float>(bfloat16(__bfloat16_raw(0x3c00))); float val2 = static_cast<float>(bfloat16(__bfloat16_raw(0x3c01))); float val3 = static_cast<float>(bfloat16(__bfloat16_raw(0x3c02))); VERIFY_BFLOAT16_BITS_EQUAL(bfloat16(0.5f * (val1 + val2)), 0x3c00); VERIFY_BFLOAT16_BITS_EQUAL(bfloat16(0.5f * (val2 + val3)), 0x3c02); // Conversion from int. VERIFY_BFLOAT16_BITS_EQUAL(bfloat16(-1), 0xbf80); VERIFY_BFLOAT16_BITS_EQUAL(bfloat16(0), 0x0000); VERIFY_BFLOAT16_BITS_EQUAL(bfloat16(1), 0x3f80); VERIFY_BFLOAT16_BITS_EQUAL(bfloat16(2), 0x4000); VERIFY_BFLOAT16_BITS_EQUAL(bfloat16(3), 0x4040); VERIFY_BFLOAT16_BITS_EQUAL(bfloat16(12), 0x4140); // Conversion from bool. VERIFY_BFLOAT16_BITS_EQUAL(bfloat16(false), 0x0000); VERIFY_BFLOAT16_BITS_EQUAL(bfloat16(true), 0x3f80); // Conversion to bool VERIFY_IS_EQUAL(static_cast<bool>(bfloat16(3)), true); VERIFY_IS_EQUAL(static_cast<bool>(bfloat16(0.33333f)), true); VERIFY_IS_EQUAL(bfloat16(-0.0), false); VERIFY_IS_EQUAL(static_cast<bool>(bfloat16(0.0)), false); // Explicit conversion to float. VERIFY_IS_EQUAL(static_cast<float>(bfloat16(__bfloat16_raw(0x0000))), 0.0f); VERIFY_IS_EQUAL(static_cast<float>(bfloat16(__bfloat16_raw(0x3f80))), 1.0f); // Implicit conversion to float VERIFY_IS_EQUAL(bfloat16(__bfloat16_raw(0x0000)), 0.0f); VERIFY_IS_EQUAL(bfloat16(__bfloat16_raw(0x3f80)), 1.0f); // Zero representations VERIFY_IS_EQUAL(bfloat16(0.0f), bfloat16(0.0f)); VERIFY_IS_EQUAL(bfloat16(-0.0f), bfloat16(0.0f)); VERIFY_IS_EQUAL(bfloat16(-0.0f), bfloat16(-0.0f)); VERIFY_BFLOAT16_BITS_EQUAL(bfloat16(0.0f), 0x0000); VERIFY_BFLOAT16_BITS_EQUAL(bfloat16(-0.0f), 0x8000); // Default is zero VERIFY_IS_EQUAL(static_cast<float>(bfloat16()), 0.0f); // Representable floats round trip via bfloat16 test_roundtrip<float>(); test_roundtrip<double>(); test_roundtrip<std::complex<float> >(); test_roundtrip<std::complex<double> >(); // Conversion Array<float,1,100> a; for (int i = 0; i < 100; i++) a(i) = i + 1.25; Array<bfloat16,1,100> b = a.cast<bfloat16>(); Array<float,1,100> c = b.cast<float>(); for (int i = 0; i < 100; ++i) { VERIFY_LE(numext::abs(c(i) - a(i)), a(i) / 128); } // Epsilon VERIFY_LE(1.0f, static_cast<float>((std::numeric_limits<bfloat16>::epsilon)() + bfloat16(1.0f))); VERIFY_IS_EQUAL(1.0f, static_cast<float>((std::numeric_limits<bfloat16>::epsilon)() / bfloat16(2.0f) + bfloat16(1.0f))); // Negate VERIFY_IS_EQUAL(static_cast<float>(-bfloat16(3.0f)), -3.0f); VERIFY_IS_EQUAL(static_cast<float>(-bfloat16(-4.5f)), 4.5f); #if !EIGEN_COMP_MSVC // Visual Studio errors out on divisions by 0 VERIFY((numext::isnan)(static_cast<float>(bfloat16(0.0 / 0.0)))); VERIFY((numext::isinf)(static_cast<float>(bfloat16(1.0 / 0.0)))); VERIFY((numext::isinf)(static_cast<float>(bfloat16(-1.0 / 0.0)))); // Visual Studio errors out on divisions by 0 VERIFY((numext::isnan)(bfloat16(0.0 / 0.0))); VERIFY((numext::isinf)(bfloat16(1.0 / 0.0))); VERIFY((numext::isinf)(bfloat16(-1.0 / 0.0))); #endif // NaNs and infinities. VERIFY(!(numext::isinf)(static_cast<float>(bfloat16(3.38e38f)))); // Largest finite number. VERIFY(!(numext::isnan)(static_cast<float>(bfloat16(0.0f)))); VERIFY((numext::isinf)(static_cast<float>(bfloat16(__bfloat16_raw(0xff80))))); VERIFY((numext::isnan)(static_cast<float>(bfloat16(__bfloat16_raw(0xffc0))))); VERIFY((numext::isinf)(static_cast<float>(bfloat16(__bfloat16_raw(0x7f80))))); VERIFY((numext::isnan)(static_cast<float>(bfloat16(__bfloat16_raw(0x7fc0))))); // Exactly same checks as above, just directly on the bfloat16 representation. VERIFY(!(numext::isinf)(bfloat16(__bfloat16_raw(0x7bff)))); VERIFY(!(numext::isnan)(bfloat16(__bfloat16_raw(0x0000)))); VERIFY((numext::isinf)(bfloat16(__bfloat16_raw(0xff80)))); VERIFY((numext::isnan)(bfloat16(__bfloat16_raw(0xffc0)))); VERIFY((numext::isinf)(bfloat16(__bfloat16_raw(0x7f80)))); VERIFY((numext::isnan)(bfloat16(__bfloat16_raw(0x7fc0)))); VERIFY_BFLOAT16_BITS_EQUAL(bfloat16(BinaryToFloat(0x0, 0xff, 0x40, 0x0)), 0x7fc0); VERIFY_BFLOAT16_BITS_EQUAL(bfloat16(BinaryToFloat(0x1, 0xff, 0x40, 0x0)), 0xffc0); } void test_numtraits() { std::cout << "epsilon = " << NumTraits<bfloat16>::epsilon() << " (0x" << std::hex << numext::bit_cast<numext::uint16_t>(NumTraits<bfloat16>::epsilon()) << ")" << std::endl; std::cout << "highest = " << NumTraits<bfloat16>::highest() << " (0x" << std::hex << numext::bit_cast<numext::uint16_t>(NumTraits<bfloat16>::highest()) << ")" << std::endl; std::cout << "lowest = " << NumTraits<bfloat16>::lowest() << " (0x" << std::hex << numext::bit_cast<numext::uint16_t>(NumTraits<bfloat16>::lowest()) << ")" << std::endl; std::cout << "min = " << (std::numeric_limits<bfloat16>::min)() << " (0x" << std::hex << numext::bit_cast<numext::uint16_t>((std::numeric_limits<bfloat16>::min)()) << ")" << std::endl; 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; std::cout << "infinity = " << NumTraits<bfloat16>::infinity() << " (0x" << std::hex << numext::bit_cast<numext::uint16_t>(NumTraits<bfloat16>::infinity()) << ")" << std::endl; std::cout << "quiet nan = " << NumTraits<bfloat16>::quiet_NaN() << " (0x" << std::hex << numext::bit_cast<numext::uint16_t>(NumTraits<bfloat16>::quiet_NaN()) << ")" << std::endl; 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; VERIFY(NumTraits<bfloat16>::IsSigned); VERIFY_IS_EQUAL( numext::bit_cast<numext::uint16_t>(std::numeric_limits<bfloat16>::infinity()), numext::bit_cast<numext::uint16_t>(bfloat16(std::numeric_limits<float>::infinity())) ); // There is no guarantee that casting a 32-bit NaN to bfloat16 has a precise // bit pattern. We test that it is in fact a NaN, then test the signaling // bit (msb of significand is 1 for quiet, 0 for signaling). const numext::uint16_t BFLOAT16_QUIET_BIT = 0x0040; VERIFY( (numext::isnan)(std::numeric_limits<bfloat16>::quiet_NaN()) && (numext::isnan)(bfloat16(std::numeric_limits<float>::quiet_NaN())) && ((numext::bit_cast<numext::uint16_t>(std::numeric_limits<bfloat16>::quiet_NaN()) & BFLOAT16_QUIET_BIT) > 0) && ((numext::bit_cast<numext::uint16_t>(bfloat16(std::numeric_limits<float>::quiet_NaN())) & BFLOAT16_QUIET_BIT) > 0) ); // After a cast to bfloat16, a signaling NaN may become non-signaling. Thus, // we check that both are NaN, and that only the `numeric_limits` version is // signaling. VERIFY( (numext::isnan)(std::numeric_limits<bfloat16>::signaling_NaN()) && (numext::isnan)(bfloat16(std::numeric_limits<float>::signaling_NaN())) && ((numext::bit_cast<numext::uint16_t>(std::numeric_limits<bfloat16>::signaling_NaN()) & BFLOAT16_QUIET_BIT) == 0) ); VERIFY( (std::numeric_limits<bfloat16>::min)() > bfloat16(0.f) ); VERIFY( (std::numeric_limits<bfloat16>::denorm_min)() > bfloat16(0.f) ); VERIFY_IS_EQUAL( (std::numeric_limits<bfloat16>::denorm_min)()/bfloat16(2), bfloat16(0.f) ); } void test_arithmetic() { VERIFY_IS_EQUAL(static_cast<float>(bfloat16(2) + bfloat16(2)), 4.f); VERIFY_IS_EQUAL(static_cast<float>(bfloat16(2) + bfloat16(-2)), 0.f); VERIFY_IS_APPROX(static_cast<float>(bfloat16(0.33333f) + bfloat16(0.66667f)), 1.0f); VERIFY_IS_EQUAL(static_cast<float>(bfloat16(2.0f) * bfloat16(-5.5f)), -11.0f); VERIFY_IS_APPROX(static_cast<float>(bfloat16(1.0f) / bfloat16(3.0f)), 0.3339f); VERIFY_IS_EQUAL(static_cast<float>(-bfloat16(4096.0f)), -4096.0f); VERIFY_IS_EQUAL(static_cast<float>(-bfloat16(-4096.0f)), 4096.0f); } void test_comparison() { VERIFY(bfloat16(1.0f) > bfloat16(0.5f)); VERIFY(bfloat16(0.5f) < bfloat16(1.0f)); VERIFY(!(bfloat16(1.0f) < bfloat16(0.5f))); VERIFY(!(bfloat16(0.5f) > bfloat16(1.0f))); VERIFY(!(bfloat16(4.0f) > bfloat16(4.0f))); VERIFY(!(bfloat16(4.0f) < bfloat16(4.0f))); VERIFY(!(bfloat16(0.0f) < bfloat16(-0.0f))); VERIFY(!(bfloat16(-0.0f) < bfloat16(0.0f))); VERIFY(!(bfloat16(0.0f) > bfloat16(-0.0f))); VERIFY(!(bfloat16(-0.0f) > bfloat16(0.0f))); VERIFY(bfloat16(0.2f) > bfloat16(-1.0f)); VERIFY(bfloat16(-1.0f) < bfloat16(0.2f)); VERIFY(bfloat16(-16.0f) < bfloat16(-15.0f)); VERIFY(bfloat16(1.0f) == bfloat16(1.0f)); VERIFY(bfloat16(1.0f) != bfloat16(2.0f)); // Comparisons with NaNs and infinities. #if !EIGEN_COMP_MSVC // Visual Studio errors out on divisions by 0 VERIFY(!(bfloat16(0.0 / 0.0) == bfloat16(0.0 / 0.0))); VERIFY(bfloat16(0.0 / 0.0) != bfloat16(0.0 / 0.0)); VERIFY(!(bfloat16(1.0) == bfloat16(0.0 / 0.0))); VERIFY(!(bfloat16(1.0) < bfloat16(0.0 / 0.0))); VERIFY(!(bfloat16(1.0) > bfloat16(0.0 / 0.0))); VERIFY(bfloat16(1.0) != bfloat16(0.0 / 0.0)); VERIFY(bfloat16(1.0) < bfloat16(1.0 / 0.0)); VERIFY(bfloat16(1.0) > bfloat16(-1.0 / 0.0)); #endif } void test_basic_functions() { VERIFY_IS_EQUAL(static_cast<float>(numext::abs(bfloat16(3.5f))), 3.5f); VERIFY_IS_EQUAL(static_cast<float>(abs(bfloat16(3.5f))), 3.5f); VERIFY_IS_EQUAL(static_cast<float>(numext::abs(bfloat16(-3.5f))), 3.5f); VERIFY_IS_EQUAL(static_cast<float>(abs(bfloat16(-3.5f))), 3.5f); VERIFY_IS_EQUAL(static_cast<float>(numext::floor(bfloat16(3.5f))), 3.0f); VERIFY_IS_EQUAL(static_cast<float>(floor(bfloat16(3.5f))), 3.0f); VERIFY_IS_EQUAL(static_cast<float>(numext::floor(bfloat16(-3.5f))), -4.0f); VERIFY_IS_EQUAL(static_cast<float>(floor(bfloat16(-3.5f))), -4.0f); VERIFY_IS_EQUAL(static_cast<float>(numext::ceil(bfloat16(3.5f))), 4.0f); VERIFY_IS_EQUAL(static_cast<float>(ceil(bfloat16(3.5f))), 4.0f); VERIFY_IS_EQUAL(static_cast<float>(numext::ceil(bfloat16(-3.5f))), -3.0f); VERIFY_IS_EQUAL(static_cast<float>(ceil(bfloat16(-3.5f))), -3.0f); VERIFY_IS_APPROX(static_cast<float>(numext::sqrt(bfloat16(0.0f))), 0.0f); VERIFY_IS_APPROX(static_cast<float>(sqrt(bfloat16(0.0f))), 0.0f); VERIFY_IS_APPROX(static_cast<float>(numext::sqrt(bfloat16(4.0f))), 2.0f); VERIFY_IS_APPROX(static_cast<float>(sqrt(bfloat16(4.0f))), 2.0f); VERIFY_IS_APPROX(static_cast<float>(numext::pow(bfloat16(0.0f), bfloat16(1.0f))), 0.0f); VERIFY_IS_APPROX(static_cast<float>(pow(bfloat16(0.0f), bfloat16(1.0f))), 0.0f); VERIFY_IS_APPROX(static_cast<float>(numext::pow(bfloat16(2.0f), bfloat16(2.0f))), 4.0f); VERIFY_IS_APPROX(static_cast<float>(pow(bfloat16(2.0f), bfloat16(2.0f))), 4.0f); VERIFY_IS_EQUAL(static_cast<float>(numext::exp(bfloat16(0.0f))), 1.0f); VERIFY_IS_EQUAL(static_cast<float>(exp(bfloat16(0.0f))), 1.0f); VERIFY_IS_APPROX(static_cast<float>(numext::exp(bfloat16(EIGEN_PI))), 20.f + static_cast<float>(EIGEN_PI)); VERIFY_IS_APPROX(static_cast<float>(exp(bfloat16(EIGEN_PI))), 20.f + static_cast<float>(EIGEN_PI)); VERIFY_IS_EQUAL(static_cast<float>(numext::expm1(bfloat16(0.0f))), 0.0f); VERIFY_IS_EQUAL(static_cast<float>(expm1(bfloat16(0.0f))), 0.0f); VERIFY_IS_APPROX(static_cast<float>(numext::expm1(bfloat16(2.0f))), 6.375f); VERIFY_IS_APPROX(static_cast<float>(expm1(bfloat16(2.0f))), 6.375f); VERIFY_IS_EQUAL(static_cast<float>(numext::log(bfloat16(1.0f))), 0.0f); VERIFY_IS_EQUAL(static_cast<float>(log(bfloat16(1.0f))), 0.0f); VERIFY_IS_APPROX(static_cast<float>(numext::log(bfloat16(10.0f))), 2.296875f); VERIFY_IS_APPROX(static_cast<float>(log(bfloat16(10.0f))), 2.296875f); VERIFY_IS_EQUAL(static_cast<float>(numext::log1p(bfloat16(0.0f))), 0.0f); VERIFY_IS_EQUAL(static_cast<float>(log1p(bfloat16(0.0f))), 0.0f); VERIFY_IS_APPROX(static_cast<float>(numext::log1p(bfloat16(10.0f))), 2.390625f); VERIFY_IS_APPROX(static_cast<float>(log1p(bfloat16(10.0f))), 2.390625f); } void test_trigonometric_functions() { VERIFY_IS_APPROX(numext::cos(bfloat16(0.0f)), bfloat16(cosf(0.0f))); VERIFY_IS_APPROX(cos(bfloat16(0.0f)), bfloat16(cosf(0.0f))); VERIFY_IS_APPROX(numext::cos(bfloat16(EIGEN_PI)), bfloat16(cosf(EIGEN_PI))); // VERIFY_IS_APPROX(numext::cos(bfloat16(EIGEN_PI/2)), bfloat16(cosf(EIGEN_PI/2))); // VERIFY_IS_APPROX(numext::cos(bfloat16(3*EIGEN_PI/2)), bfloat16(cosf(3*EIGEN_PI/2))); VERIFY_IS_APPROX(numext::cos(bfloat16(3.5f)), bfloat16(cosf(3.5f))); VERIFY_IS_APPROX(numext::sin(bfloat16(0.0f)), bfloat16(sinf(0.0f))); VERIFY_IS_APPROX(sin(bfloat16(0.0f)), bfloat16(sinf(0.0f))); // VERIFY_IS_APPROX(numext::sin(bfloat16(EIGEN_PI)), bfloat16(sinf(EIGEN_PI))); VERIFY_IS_APPROX(numext::sin(bfloat16(EIGEN_PI/2)), bfloat16(sinf(EIGEN_PI/2))); VERIFY_IS_APPROX(numext::sin(bfloat16(3*EIGEN_PI/2)), bfloat16(sinf(3*EIGEN_PI/2))); VERIFY_IS_APPROX(numext::sin(bfloat16(3.5f)), bfloat16(sinf(3.5f))); VERIFY_IS_APPROX(numext::tan(bfloat16(0.0f)), bfloat16(tanf(0.0f))); VERIFY_IS_APPROX(tan(bfloat16(0.0f)), bfloat16(tanf(0.0f))); // VERIFY_IS_APPROX(numext::tan(bfloat16(EIGEN_PI)), bfloat16(tanf(EIGEN_PI))); // VERIFY_IS_APPROX(numext::tan(bfloat16(EIGEN_PI/2)), bfloat16(tanf(EIGEN_PI/2))); // VERIFY_IS_APPROX(numext::tan(bfloat16(3*EIGEN_PI/2)), bfloat16(tanf(3*EIGEN_PI/2))); VERIFY_IS_APPROX(numext::tan(bfloat16(3.5f)), bfloat16(tanf(3.5f))); } void test_array() { typedef Array<bfloat16,1,Dynamic> ArrayXh; Index size = internal::random<Index>(1,10); Index i = internal::random<Index>(0,size-1); ArrayXh a1 = ArrayXh::Random(size), a2 = ArrayXh::Random(size); VERIFY_IS_APPROX( a1+a1, bfloat16(2)*a1 ); VERIFY( (a1.abs() >= bfloat16(0)).all() ); VERIFY_IS_APPROX( (a1*a1).sqrt(), a1.abs() ); VERIFY( ((a1.min)(a2) <= (a1.max)(a2)).all() ); a1(i) = bfloat16(-10.); VERIFY_IS_EQUAL( a1.minCoeff(), bfloat16(-10.) ); a1(i) = bfloat16(10.); VERIFY_IS_EQUAL( a1.maxCoeff(), bfloat16(10.) ); std::stringstream ss; ss << a1; } void test_product() { typedef Matrix<bfloat16,Dynamic,Dynamic> MatrixXh; Index rows = internal::random<Index>(1,EIGEN_TEST_MAX_SIZE); Index cols = internal::random<Index>(1,EIGEN_TEST_MAX_SIZE); Index depth = internal::random<Index>(1,EIGEN_TEST_MAX_SIZE); MatrixXh Ah = MatrixXh::Random(rows,depth); MatrixXh Bh = MatrixXh::Random(depth,cols); MatrixXh Ch = MatrixXh::Random(rows,cols); MatrixXf Af = Ah.cast<float>(); MatrixXf Bf = Bh.cast<float>(); MatrixXf Cf = Ch.cast<float>(); VERIFY_IS_APPROX(Ch.noalias()+=Ah*Bh, (Cf.noalias()+=Af*Bf).cast<bfloat16>()); } EIGEN_DECLARE_TEST(bfloat16_float) { CALL_SUBTEST(test_numtraits()); for(int i = 0; i < g_repeat; i++) { CALL_SUBTEST(test_conversion()); CALL_SUBTEST(test_arithmetic()); CALL_SUBTEST(test_comparison()); CALL_SUBTEST(test_basic_functions()); CALL_SUBTEST(test_trigonometric_functions()); CALL_SUBTEST(test_array()); CALL_SUBTEST(test_product()); } }