test/half_float.cpp

// 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/CUDA/Half.h>

#ifdef EIGEN_HAS_CUDA_FP16
#error "EIGEN_HAS_CUDA_FP16 should not be defined in this CPU unit test"
#endif

// 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::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_half_float()
{
  CALL_SUBTEST(test_conversion());
  CALL_SUBTEST(test_numtraits());
  CALL_SUBTEST(test_arithmetic());
  CALL_SUBTEST(test_comparison());
  CALL_SUBTEST(test_basic_functions());
  CALL_SUBTEST(test_trigonometric_functions());
  CALL_SUBTEST(test_array());
}