test/half_float.cpp - mirror - Git at Google


            
            // 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 "main.h"


            #include <Eigen/src/Core/arch/Default/Half.h>


            // Make sure it's possible to forward declare Eigen::half

            
            namespace Eigen {

            
            struct half;

            
            }


            using Eigen::half;


            void test_conversion()

            
            {

            
              using Eigen::half_impl::__half_raw;


              // Conversion from float.

            
              VERIFY_IS_EQUAL(half(1.0f).x, 0x3c00);

            
              VERIFY_IS_EQUAL(half(0.5f).x, 0x3800);

            
              VERIFY_IS_EQUAL(half(0.33333f).x, 0x3555);

            
              VERIFY_IS_EQUAL(half(0.0f).x, 0x0000);

            
              VERIFY_IS_EQUAL(half(-0.0f).x, 0x8000);

            
              VERIFY_IS_EQUAL(half(65504.0f).x, 0x7bff);

            
              VERIFY_IS_EQUAL(half(65536.0f).x, 0x7c00);  // Becomes infinity.


              // Denormals.

            
              VERIFY_IS_EQUAL(half(-5.96046e-08f).x, 0x8001);

            
              VERIFY_IS_EQUAL(half(5.96046e-08f).x, 0x0001);

            
              VERIFY_IS_EQUAL(half(1.19209e-07f).x, 0x0002);


              // Verify round-to-nearest-even behavior.

            
              float val1 = float(half(__half_raw(0x3c00)));

            
              float val2 = float(half(__half_raw(0x3c01)));

            
              float val3 = float(half(__half_raw(0x3c02)));

            
              VERIFY_IS_EQUAL(half(0.5f * (val1 + val2)).x, 0x3c00);

            
              VERIFY_IS_EQUAL(half(0.5f * (val2 + val3)).x, 0x3c02);


              // Conversion from int.

            
              VERIFY_IS_EQUAL(half(-1).x, 0xbc00);

            
              VERIFY_IS_EQUAL(half(0).x, 0x0000);

            
              VERIFY_IS_EQUAL(half(1).x, 0x3c00);

            
              VERIFY_IS_EQUAL(half(2).x, 0x4000);

            
              VERIFY_IS_EQUAL(half(3).x, 0x4200);


              // Conversion from bool.

            
              VERIFY_IS_EQUAL(half(false).x, 0x0000);

            
              VERIFY_IS_EQUAL(half(true).x, 0x3c00);


              // Conversion to float.

            
              VERIFY_IS_EQUAL(float(half(__half_raw(0x0000))), 0.0f);

            
              VERIFY_IS_EQUAL(float(half(__half_raw(0x3c00))), 1.0f);


              // Denormals.

            
              VERIFY_IS_APPROX(float(half(__half_raw(0x8001))), -5.96046e-08f);

            
              VERIFY_IS_APPROX(float(half(__half_raw(0x0001))), 5.96046e-08f);

            
              VERIFY_IS_APPROX(float(half(__half_raw(0x0002))), 1.19209e-07f);


              // NaNs and infinities.

            
              VERIFY(!(numext::isinf)(float(half(65504.0f))));  // Largest finite number.

            
              VERIFY(!(numext::isnan)(float(half(0.0f))));

            
              VERIFY((numext::isinf)(float(half(__half_raw(0xfc00)))));

            
              VERIFY((numext::isnan)(float(half(__half_raw(0xfc01)))));

            
              VERIFY((numext::isinf)(float(half(__half_raw(0x7c00)))));

            
              VERIFY((numext::isnan)(float(half(__half_raw(0x7c01)))));


            #if !EIGEN_COMP_MSVC

            
              // Visual Studio errors out on divisions by 0

            
              VERIFY((numext::isnan)(float(half(0.0 / 0.0))));

            
              VERIFY((numext::isinf)(float(half(1.0 / 0.0))));

            
              VERIFY((numext::isinf)(float(half(-1.0 / 0.0))));

            
            #endif


              // Exactly same checks as above, just directly on the half representation.

            
              VERIFY(!(numext::isinf)(half(__half_raw(0x7bff))));

            
              VERIFY(!(numext::isnan)(half(__half_raw(0x0000))));

            
              VERIFY((numext::isinf)(half(__half_raw(0xfc00))));

            
              VERIFY((numext::isnan)(half(__half_raw(0xfc01))));

            
              VERIFY((numext::isinf)(half(__half_raw(0x7c00))));

            
              VERIFY((numext::isnan)(half(__half_raw(0x7c01))));


            #if !EIGEN_COMP_MSVC

            
              // Visual Studio errors out on divisions by 0

            
              VERIFY((numext::isnan)(half(0.0 / 0.0)));

            
              VERIFY((numext::isinf)(half(1.0 / 0.0)));

            
              VERIFY((numext::isinf)(half(-1.0 / 0.0)));

            
            #endif

            
            }


            void test_numtraits()

            
            {

            
              std::cout << "epsilon       = " << NumTraits<half>::epsilon() << "  (0x" << std::hex << NumTraits<half>::epsilon().x << ")" << std::endl;

            
              std::cout << "highest       = " << NumTraits<half>::highest() << "  (0x" << std::hex << NumTraits<half>::highest().x << ")" << std::endl;

            
              std::cout << "lowest        = " << NumTraits<half>::lowest() << "  (0x" << std::hex << NumTraits<half>::lowest().x << ")" << std::endl;

            
              std::cout << "min           = " << (std::numeric_limits<half>::min)() << "  (0x" << std::hex << half((std::numeric_limits<half>::min)()).x << ")" << std::endl;

            
              std::cout << "denorm min    = " << (std::numeric_limits<half>::denorm_min)() << "  (0x" << std::hex << half((std::numeric_limits<half>::denorm_min)()).x << ")" << std::endl;

            
              std::cout << "infinity      = " << NumTraits<half>::infinity() << "  (0x" << std::hex << NumTraits<half>::infinity().x << ")" << std::endl;

            
              std::cout << "quiet nan     = " << NumTraits<half>::quiet_NaN() << "  (0x" << std::hex << NumTraits<half>::quiet_NaN().x << ")" << std::endl;

            
              std::cout << "signaling nan = " << std::numeric_limits<half>::signaling_NaN() << "  (0x" << std::hex << std::numeric_limits<half>::signaling_NaN().x << ")" << std::endl;


              VERIFY(NumTraits<half>::IsSigned);


              VERIFY_IS_EQUAL( std::numeric_limits<half>::infinity().x, half(std::numeric_limits<float>::infinity()).x );

            
              VERIFY_IS_EQUAL( std::numeric_limits<half>::quiet_NaN().x, half(std::numeric_limits<float>::quiet_NaN()).x );

            
              VERIFY_IS_EQUAL( std::numeric_limits<half>::signaling_NaN().x, half(std::numeric_limits<float>::signaling_NaN()).x );

            
              VERIFY( (std::numeric_limits<half>::min)() > half(0.f) );

            
              VERIFY( (std::numeric_limits<half>::denorm_min)() > half(0.f) );

            
              VERIFY( (std::numeric_limits<half>::min)()/half(2) > half(0.f) );

            
              VERIFY_IS_EQUAL( (std::numeric_limits<half>::denorm_min)()/half(2), half(0.f) );

            
            }


            void test_arithmetic()

            
            {

            
              VERIFY_IS_EQUAL(float(half(2) + half(2)), 4);

            
              VERIFY_IS_EQUAL(float(half(2) + half(-2)), 0);

            
              VERIFY_IS_APPROX(float(half(0.33333f) + half(0.66667f)), 1.0f);

            
              VERIFY_IS_EQUAL(float(half(2.0f) * half(-5.5f)), -11.0f);

            
              VERIFY_IS_APPROX(float(half(1.0f) / half(3.0f)), 0.33333f);

            
              VERIFY_IS_EQUAL(float(-half(4096.0f)), -4096.0f);

            
              VERIFY_IS_EQUAL(float(-half(-4096.0f)), 4096.0f);

            
            }


            void test_comparison()

            
            {

            
              VERIFY(half(1.0f) > half(0.5f));

            
              VERIFY(half(0.5f) < half(1.0f));

            
              VERIFY(!(half(1.0f) < half(0.5f)));

            
              VERIFY(!(half(0.5f) > half(1.0f)));


              VERIFY(!(half(4.0f) > half(4.0f)));

            
              VERIFY(!(half(4.0f) < half(4.0f)));


              VERIFY(!(half(0.0f) < half(-0.0f)));

            
              VERIFY(!(half(-0.0f) < half(0.0f)));

            
              VERIFY(!(half(0.0f) > half(-0.0f)));

            
              VERIFY(!(half(-0.0f) > half(0.0f)));


              VERIFY(half(0.2f) > half(-1.0f));

            
              VERIFY(half(-1.0f) < half(0.2f));

            
              VERIFY(half(-16.0f) < half(-15.0f));


              VERIFY(half(1.0f) == half(1.0f));

            
              VERIFY(half(1.0f) != half(2.0f));


              // Comparisons with NaNs and infinities.

            
            #if !EIGEN_COMP_MSVC

            
              // Visual Studio errors out on divisions by 0

            
              VERIFY(!(half(0.0 / 0.0) == half(0.0 / 0.0)));

            
              VERIFY(half(0.0 / 0.0) != half(0.0 / 0.0));


              VERIFY(!(half(1.0) == half(0.0 / 0.0)));

            
              VERIFY(!(half(1.0) < half(0.0 / 0.0)));

            
              VERIFY(!(half(1.0) > half(0.0 / 0.0)));

            
              VERIFY(half(1.0) != half(0.0 / 0.0));


              VERIFY(half(1.0) < half(1.0 / 0.0));

            
              VERIFY(half(1.0) > half(-1.0 / 0.0));

            
            #endif

            
            }


            void test_basic_functions()

            
            {

            
              VERIFY_IS_EQUAL(float(numext::abs(half(3.5f))), 3.5f);

            
              VERIFY_IS_EQUAL(float(abs(half(3.5f))), 3.5f);

            
              VERIFY_IS_EQUAL(float(numext::abs(half(-3.5f))), 3.5f);

            
              VERIFY_IS_EQUAL(float(abs(half(-3.5f))), 3.5f);


              VERIFY_IS_EQUAL(float(numext::floor(half(3.5f))), 3.0f);

            
              VERIFY_IS_EQUAL(float(floor(half(3.5f))), 3.0f);

            
              VERIFY_IS_EQUAL(float(numext::floor(half(-3.5f))), -4.0f);

            
              VERIFY_IS_EQUAL(float(floor(half(-3.5f))), -4.0f);


              VERIFY_IS_EQUAL(float(numext::ceil(half(3.5f))), 4.0f);

            
              VERIFY_IS_EQUAL(float(ceil(half(3.5f))), 4.0f);

            
              VERIFY_IS_EQUAL(float(numext::ceil(half(-3.5f))), -3.0f);

            
              VERIFY_IS_EQUAL(float(ceil(half(-3.5f))), -3.0f);


              VERIFY_IS_APPROX(float(numext::sqrt(half(0.0f))), 0.0f);

            
              VERIFY_IS_APPROX(float(sqrt(half(0.0f))), 0.0f);

            
              VERIFY_IS_APPROX(float(numext::sqrt(half(4.0f))), 2.0f);

            
              VERIFY_IS_APPROX(float(sqrt(half(4.0f))), 2.0f);


              VERIFY_IS_APPROX(float(numext::pow(half(0.0f), half(1.0f))), 0.0f);

            
              VERIFY_IS_APPROX(float(pow(half(0.0f), half(1.0f))), 0.0f);

            
              VERIFY_IS_APPROX(float(numext::pow(half(2.0f), half(2.0f))), 4.0f);

            
              VERIFY_IS_APPROX(float(pow(half(2.0f), half(2.0f))), 4.0f);


              VERIFY_IS_EQUAL(float(numext::exp(half(0.0f))), 1.0f);

            
              VERIFY_IS_EQUAL(float(exp(half(0.0f))), 1.0f);

            
              VERIFY_IS_APPROX(float(numext::exp(half(EIGEN_PI))), 20.f + float(EIGEN_PI));

            
              VERIFY_IS_APPROX(float(exp(half(EIGEN_PI))), 20.f + float(EIGEN_PI));


              VERIFY_IS_EQUAL(float(numext::expm1(half(0.0f))), 0.0f);

            
              VERIFY_IS_EQUAL(float(expm1(half(0.0f))), 0.0f);

            
              VERIFY_IS_APPROX(float(numext::expm1(half(2.0f))), 6.3890561f);

            
              VERIFY_IS_APPROX(float(expm1(half(2.0f))), 6.3890561f);


              VERIFY_IS_EQUAL(float(numext::log(half(1.0f))), 0.0f);

            
              VERIFY_IS_EQUAL(float(log(half(1.0f))), 0.0f);

            
              VERIFY_IS_APPROX(float(numext::log(half(10.0f))), 2.30273f);

            
              VERIFY_IS_APPROX(float(log(half(10.0f))), 2.30273f);


              VERIFY_IS_EQUAL(float(numext::log1p(half(0.0f))), 0.0f);

            
              VERIFY_IS_EQUAL(float(log1p(half(0.0f))), 0.0f);

            
              VERIFY_IS_APPROX(float(numext::log1p(half(10.0f))), 2.3978953f);

            
              VERIFY_IS_APPROX(float(log1p(half(10.0f))), 2.3978953f);

            
            }


            void test_trigonometric_functions()

            
            {

            
              VERIFY_IS_APPROX(numext::cos(half(0.0f)), half(cosf(0.0f)));

            
              VERIFY_IS_APPROX(cos(half(0.0f)), half(cosf(0.0f)));

            
              VERIFY_IS_APPROX(numext::cos(half(EIGEN_PI)), half(cosf(EIGEN_PI)));

            
              //VERIFY_IS_APPROX(numext::cos(half(EIGEN_PI/2)), half(cosf(EIGEN_PI/2)));

            
              //VERIFY_IS_APPROX(numext::cos(half(3*EIGEN_PI/2)), half(cosf(3*EIGEN_PI/2)));

            
              VERIFY_IS_APPROX(numext::cos(half(3.5f)), half(cosf(3.5f)));


              VERIFY_IS_APPROX(numext::sin(half(0.0f)), half(sinf(0.0f)));

            
              VERIFY_IS_APPROX(sin(half(0.0f)), half(sinf(0.0f)));

            
              //  VERIFY_IS_APPROX(numext::sin(half(EIGEN_PI)), half(sinf(EIGEN_PI)));

            
              VERIFY_IS_APPROX(numext::sin(half(EIGEN_PI/2)), half(sinf(EIGEN_PI/2)));

            
              VERIFY_IS_APPROX(numext::sin(half(3*EIGEN_PI/2)), half(sinf(3*EIGEN_PI/2)));

            
              VERIFY_IS_APPROX(numext::sin(half(3.5f)), half(sinf(3.5f)));


              VERIFY_IS_APPROX(numext::tan(half(0.0f)), half(tanf(0.0f)));

            
              VERIFY_IS_APPROX(tan(half(0.0f)), half(tanf(0.0f)));

            
              //  VERIFY_IS_APPROX(numext::tan(half(EIGEN_PI)), half(tanf(EIGEN_PI)));

            
              //  VERIFY_IS_APPROX(numext::tan(half(EIGEN_PI/2)), half(tanf(EIGEN_PI/2)));

            
              //VERIFY_IS_APPROX(numext::tan(half(3*EIGEN_PI/2)), half(tanf(3*EIGEN_PI/2)));

            
              VERIFY_IS_APPROX(numext::tan(half(3.5f)), half(tanf(3.5f)));

            
            }


            void test_array()

            
            {

            
              typedef Array<half,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, half(2)*a1 );

            
              VERIFY( (a1.abs() >= half(0)).all() );

            
              VERIFY_IS_APPROX( (a1*a1).sqrt(), a1.abs() );


              VERIFY( ((a1.min)(a2) <= (a1.max)(a2)).all() );

            
              a1(i) = half(-10.);

            
              VERIFY_IS_EQUAL( a1.minCoeff(), half(-10.) );

            
              a1(i) = half(10.);

            
              VERIFY_IS_EQUAL( a1.maxCoeff(), half(10.) );


              std::stringstream ss;

            
              ss << a1;

            
            }


            void test_product()

            
            {

            
              typedef Matrix<half,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<half>());

            
            }


            EIGEN_DECLARE_TEST(half_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());

            
              }

            
            }
	// 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 "main.h"

	#include <Eigen/src/Core/arch/Default/Half.h>

	// Make sure it's possible to forward declare Eigen::half
	namespace Eigen {
	struct half;
	}

	using Eigen::half;

	void test_conversion()
	{
	using Eigen::half_impl::__half_raw;

	// Conversion from float.
	VERIFY_IS_EQUAL(half(1.0f).x, 0x3c00);
	VERIFY_IS_EQUAL(half(0.5f).x, 0x3800);
	VERIFY_IS_EQUAL(half(0.33333f).x, 0x3555);
	VERIFY_IS_EQUAL(half(0.0f).x, 0x0000);
	VERIFY_IS_EQUAL(half(-0.0f).x, 0x8000);
	VERIFY_IS_EQUAL(half(65504.0f).x, 0x7bff);
	VERIFY_IS_EQUAL(half(65536.0f).x, 0x7c00); // Becomes infinity.

	// Denormals.
	VERIFY_IS_EQUAL(half(-5.96046e-08f).x, 0x8001);
	VERIFY_IS_EQUAL(half(5.96046e-08f).x, 0x0001);
	VERIFY_IS_EQUAL(half(1.19209e-07f).x, 0x0002);

	// Verify round-to-nearest-even behavior.
	float val1 = float(half(__half_raw(0x3c00)));
	float val2 = float(half(__half_raw(0x3c01)));
	float val3 = float(half(__half_raw(0x3c02)));
	VERIFY_IS_EQUAL(half(0.5f * (val1 + val2)).x, 0x3c00);
	VERIFY_IS_EQUAL(half(0.5f * (val2 + val3)).x, 0x3c02);

	// Conversion from int.
	VERIFY_IS_EQUAL(half(-1).x, 0xbc00);
	VERIFY_IS_EQUAL(half(0).x, 0x0000);
	VERIFY_IS_EQUAL(half(1).x, 0x3c00);
	VERIFY_IS_EQUAL(half(2).x, 0x4000);
	VERIFY_IS_EQUAL(half(3).x, 0x4200);

	// Conversion from bool.
	VERIFY_IS_EQUAL(half(false).x, 0x0000);
	VERIFY_IS_EQUAL(half(true).x, 0x3c00);

	// Conversion to float.
	VERIFY_IS_EQUAL(float(half(__half_raw(0x0000))), 0.0f);
	VERIFY_IS_EQUAL(float(half(__half_raw(0x3c00))), 1.0f);

	// Denormals.
	VERIFY_IS_APPROX(float(half(__half_raw(0x8001))), -5.96046e-08f);
	VERIFY_IS_APPROX(float(half(__half_raw(0x0001))), 5.96046e-08f);
	VERIFY_IS_APPROX(float(half(__half_raw(0x0002))), 1.19209e-07f);

	// NaNs and infinities.
	VERIFY(!(numext::isinf)(float(half(65504.0f)))); // Largest finite number.
	VERIFY(!(numext::isnan)(float(half(0.0f))));
	VERIFY((numext::isinf)(float(half(__half_raw(0xfc00)))));
	VERIFY((numext::isnan)(float(half(__half_raw(0xfc01)))));
	VERIFY((numext::isinf)(float(half(__half_raw(0x7c00)))));
	VERIFY((numext::isnan)(float(half(__half_raw(0x7c01)))));

	#if !EIGEN_COMP_MSVC
	// Visual Studio errors out on divisions by 0
	VERIFY((numext::isnan)(float(half(0.0 / 0.0))));
	VERIFY((numext::isinf)(float(half(1.0 / 0.0))));
	VERIFY((numext::isinf)(float(half(-1.0 / 0.0))));
	#endif

	// Exactly same checks as above, just directly on the half representation.
	VERIFY(!(numext::isinf)(half(__half_raw(0x7bff))));
	VERIFY(!(numext::isnan)(half(__half_raw(0x0000))));
	VERIFY((numext::isinf)(half(__half_raw(0xfc00))));
	VERIFY((numext::isnan)(half(__half_raw(0xfc01))));
	VERIFY((numext::isinf)(half(__half_raw(0x7c00))));
	VERIFY((numext::isnan)(half(__half_raw(0x7c01))));

	#if !EIGEN_COMP_MSVC
	// Visual Studio errors out on divisions by 0
	VERIFY((numext::isnan)(half(0.0 / 0.0)));
	VERIFY((numext::isinf)(half(1.0 / 0.0)));
	VERIFY((numext::isinf)(half(-1.0 / 0.0)));
	#endif
	}

	void test_numtraits()
	{
	std::cout << "epsilon = " << NumTraits<half>::epsilon() << " (0x" << std::hex << NumTraits<half>::epsilon().x << ")" << std::endl;
	std::cout << "highest = " << NumTraits<half>::highest() << " (0x" << std::hex << NumTraits<half>::highest().x << ")" << std::endl;
	std::cout << "lowest = " << NumTraits<half>::lowest() << " (0x" << std::hex << NumTraits<half>::lowest().x << ")" << std::endl;
	std::cout << "min = " << (std::numeric_limits<half>::min)() << " (0x" << std::hex << half((std::numeric_limits<half>::min)()).x << ")" << std::endl;
	std::cout << "denorm min = " << (std::numeric_limits<half>::denorm_min)() << " (0x" << std::hex << half((std::numeric_limits<half>::denorm_min)()).x << ")" << std::endl;
	std::cout << "infinity = " << NumTraits<half>::infinity() << " (0x" << std::hex << NumTraits<half>::infinity().x << ")" << std::endl;
	std::cout << "quiet nan = " << NumTraits<half>::quiet_NaN() << " (0x" << std::hex << NumTraits<half>::quiet_NaN().x << ")" << std::endl;
	std::cout << "signaling nan = " << std::numeric_limits<half>::signaling_NaN() << " (0x" << std::hex << std::numeric_limits<half>::signaling_NaN().x << ")" << std::endl;

	VERIFY(NumTraits<half>::IsSigned);

	VERIFY_IS_EQUAL( std::numeric_limits<half>::infinity().x, half(std::numeric_limits<float>::infinity()).x );
	VERIFY_IS_EQUAL( std::numeric_limits<half>::quiet_NaN().x, half(std::numeric_limits<float>::quiet_NaN()).x );
	VERIFY_IS_EQUAL( std::numeric_limits<half>::signaling_NaN().x, half(std::numeric_limits<float>::signaling_NaN()).x );
	VERIFY( (std::numeric_limits<half>::min)() > half(0.f) );
	VERIFY( (std::numeric_limits<half>::denorm_min)() > half(0.f) );
	VERIFY( (std::numeric_limits<half>::min)()/half(2) > half(0.f) );
	VERIFY_IS_EQUAL( (std::numeric_limits<half>::denorm_min)()/half(2), half(0.f) );
	}

	void test_arithmetic()
	{
	VERIFY_IS_EQUAL(float(half(2) + half(2)), 4);
	VERIFY_IS_EQUAL(float(half(2) + half(-2)), 0);
	VERIFY_IS_APPROX(float(half(0.33333f) + half(0.66667f)), 1.0f);
	VERIFY_IS_EQUAL(float(half(2.0f) * half(-5.5f)), -11.0f);
	VERIFY_IS_APPROX(float(half(1.0f) / half(3.0f)), 0.33333f);
	VERIFY_IS_EQUAL(float(-half(4096.0f)), -4096.0f);
	VERIFY_IS_EQUAL(float(-half(-4096.0f)), 4096.0f);
	}

	void test_comparison()
	{
	VERIFY(half(1.0f) > half(0.5f));
	VERIFY(half(0.5f) < half(1.0f));
	VERIFY(!(half(1.0f) < half(0.5f)));
	VERIFY(!(half(0.5f) > half(1.0f)));

	VERIFY(!(half(4.0f) > half(4.0f)));
	VERIFY(!(half(4.0f) < half(4.0f)));

	VERIFY(!(half(0.0f) < half(-0.0f)));
	VERIFY(!(half(-0.0f) < half(0.0f)));
	VERIFY(!(half(0.0f) > half(-0.0f)));
	VERIFY(!(half(-0.0f) > half(0.0f)));

	VERIFY(half(0.2f) > half(-1.0f));
	VERIFY(half(-1.0f) < half(0.2f));
	VERIFY(half(-16.0f) < half(-15.0f));

	VERIFY(half(1.0f) == half(1.0f));
	VERIFY(half(1.0f) != half(2.0f));

	// Comparisons with NaNs and infinities.
	#if !EIGEN_COMP_MSVC
	// Visual Studio errors out on divisions by 0
	VERIFY(!(half(0.0 / 0.0) == half(0.0 / 0.0)));
	VERIFY(half(0.0 / 0.0) != half(0.0 / 0.0));

	VERIFY(!(half(1.0) == half(0.0 / 0.0)));
	VERIFY(!(half(1.0) < half(0.0 / 0.0)));
	VERIFY(!(half(1.0) > half(0.0 / 0.0)));
	VERIFY(half(1.0) != half(0.0 / 0.0));

	VERIFY(half(1.0) < half(1.0 / 0.0));
	VERIFY(half(1.0) > half(-1.0 / 0.0));
	#endif
	}

	void test_basic_functions()
	{
	VERIFY_IS_EQUAL(float(numext::abs(half(3.5f))), 3.5f);
	VERIFY_IS_EQUAL(float(abs(half(3.5f))), 3.5f);
	VERIFY_IS_EQUAL(float(numext::abs(half(-3.5f))), 3.5f);
	VERIFY_IS_EQUAL(float(abs(half(-3.5f))), 3.5f);

	VERIFY_IS_EQUAL(float(numext::floor(half(3.5f))), 3.0f);
	VERIFY_IS_EQUAL(float(floor(half(3.5f))), 3.0f);
	VERIFY_IS_EQUAL(float(numext::floor(half(-3.5f))), -4.0f);
	VERIFY_IS_EQUAL(float(floor(half(-3.5f))), -4.0f);

	VERIFY_IS_EQUAL(float(numext::ceil(half(3.5f))), 4.0f);
	VERIFY_IS_EQUAL(float(ceil(half(3.5f))), 4.0f);
	VERIFY_IS_EQUAL(float(numext::ceil(half(-3.5f))), -3.0f);
	VERIFY_IS_EQUAL(float(ceil(half(-3.5f))), -3.0f);

	VERIFY_IS_APPROX(float(numext::sqrt(half(0.0f))), 0.0f);
	VERIFY_IS_APPROX(float(sqrt(half(0.0f))), 0.0f);
	VERIFY_IS_APPROX(float(numext::sqrt(half(4.0f))), 2.0f);
	VERIFY_IS_APPROX(float(sqrt(half(4.0f))), 2.0f);

	VERIFY_IS_APPROX(float(numext::pow(half(0.0f), half(1.0f))), 0.0f);
	VERIFY_IS_APPROX(float(pow(half(0.0f), half(1.0f))), 0.0f);
	VERIFY_IS_APPROX(float(numext::pow(half(2.0f), half(2.0f))), 4.0f);
	VERIFY_IS_APPROX(float(pow(half(2.0f), half(2.0f))), 4.0f);

	VERIFY_IS_EQUAL(float(numext::exp(half(0.0f))), 1.0f);
	VERIFY_IS_EQUAL(float(exp(half(0.0f))), 1.0f);
	VERIFY_IS_APPROX(float(numext::exp(half(EIGEN_PI))), 20.f + float(EIGEN_PI));
	VERIFY_IS_APPROX(float(exp(half(EIGEN_PI))), 20.f + float(EIGEN_PI));

	VERIFY_IS_EQUAL(float(numext::expm1(half(0.0f))), 0.0f);
	VERIFY_IS_EQUAL(float(expm1(half(0.0f))), 0.0f);
	VERIFY_IS_APPROX(float(numext::expm1(half(2.0f))), 6.3890561f);
	VERIFY_IS_APPROX(float(expm1(half(2.0f))), 6.3890561f);

	VERIFY_IS_EQUAL(float(numext::log(half(1.0f))), 0.0f);
	VERIFY_IS_EQUAL(float(log(half(1.0f))), 0.0f);
	VERIFY_IS_APPROX(float(numext::log(half(10.0f))), 2.30273f);
	VERIFY_IS_APPROX(float(log(half(10.0f))), 2.30273f);

	VERIFY_IS_EQUAL(float(numext::log1p(half(0.0f))), 0.0f);
	VERIFY_IS_EQUAL(float(log1p(half(0.0f))), 0.0f);
	VERIFY_IS_APPROX(float(numext::log1p(half(10.0f))), 2.3978953f);
	VERIFY_IS_APPROX(float(log1p(half(10.0f))), 2.3978953f);
	}

	void test_trigonometric_functions()
	{
	VERIFY_IS_APPROX(numext::cos(half(0.0f)), half(cosf(0.0f)));
	VERIFY_IS_APPROX(cos(half(0.0f)), half(cosf(0.0f)));
	VERIFY_IS_APPROX(numext::cos(half(EIGEN_PI)), half(cosf(EIGEN_PI)));
	//VERIFY_IS_APPROX(numext::cos(half(EIGEN_PI/2)), half(cosf(EIGEN_PI/2)));
	//VERIFY_IS_APPROX(numext::cos(half(3EIGEN_PI/2)), half(cosf(3EIGEN_PI/2)));
	VERIFY_IS_APPROX(numext::cos(half(3.5f)), half(cosf(3.5f)));

	VERIFY_IS_APPROX(numext::sin(half(0.0f)), half(sinf(0.0f)));
	VERIFY_IS_APPROX(sin(half(0.0f)), half(sinf(0.0f)));
	// VERIFY_IS_APPROX(numext::sin(half(EIGEN_PI)), half(sinf(EIGEN_PI)));
	VERIFY_IS_APPROX(numext::sin(half(EIGEN_PI/2)), half(sinf(EIGEN_PI/2)));
	VERIFY_IS_APPROX(numext::sin(half(3EIGEN_PI/2)), half(sinf(3EIGEN_PI/2)));
	VERIFY_IS_APPROX(numext::sin(half(3.5f)), half(sinf(3.5f)));

	VERIFY_IS_APPROX(numext::tan(half(0.0f)), half(tanf(0.0f)));
	VERIFY_IS_APPROX(tan(half(0.0f)), half(tanf(0.0f)));
	// VERIFY_IS_APPROX(numext::tan(half(EIGEN_PI)), half(tanf(EIGEN_PI)));
	// VERIFY_IS_APPROX(numext::tan(half(EIGEN_PI/2)), half(tanf(EIGEN_PI/2)));
	//VERIFY_IS_APPROX(numext::tan(half(3EIGEN_PI/2)), half(tanf(3EIGEN_PI/2)));
	VERIFY_IS_APPROX(numext::tan(half(3.5f)), half(tanf(3.5f)));
	}

	void test_array()
	{
	typedef Array<half,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, half(2)*a1 );
	VERIFY( (a1.abs() >= half(0)).all() );
	VERIFY_IS_APPROX( (a1*a1).sqrt(), a1.abs() );

	VERIFY( ((a1.min)(a2) <= (a1.max)(a2)).all() );
	a1(i) = half(-10.);
	VERIFY_IS_EQUAL( a1.minCoeff(), half(-10.) );
	a1(i) = half(10.);
	VERIFY_IS_EQUAL( a1.maxCoeff(), half(10.) );

	std::stringstream ss;
	ss << a1;
	}

	void test_product()
	{
	typedef Matrix<half,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()+=AhBh, (Cf.noalias()+=AfBf).cast<half>());
	}

	EIGEN_DECLARE_TEST(half_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());
	}
	}