void test_trigonometric_functions()
{
VERIFY_IS_APPROX(numext::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(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(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_conversion()
{
// 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(0x3c00)));
float val2 = float(half(__half(0x3c01)));
float val3 = float(half(__half(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(0x0000))), 0.0f);
VERIFY_IS_EQUAL(float(half(__half(0x3c00))), 1.0f);
// Denormals.
VERIFY_IS_APPROX(float(half(__half(0x8001))), -5.96046e-08f);
VERIFY_IS_APPROX(float(half(__half(0x0001))), 5.96046e-08f);
VERIFY_IS_APPROX(float(half(__half(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(0xfc00)))));
VERIFY((numext::isnan)(float(half(__half(0xfc01)))));
VERIFY((numext::isinf)(float(half(__half(0x7c00)))));
VERIFY((numext::isnan)(float(half(__half(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(0x7bff))));
VERIFY(!(numext::isnan)(half(__half(0x0000))));
VERIFY((numext::isinf)(half(__half(0xfc00))));
VERIFY((numext::isnan)(half(__half(0xfc01))));
VERIFY((numext::isinf)(half(__half(0x7c00))));
VERIFY((numext::isnan)(half(__half(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_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(numext::abs(half(-3.5f))), 3.5f);
VERIFY_IS_EQUAL(float(numext::floor(half(3.5f))), 3.0f);
VERIFY_IS_EQUAL(float(numext::floor(half(-3.5f))), -4.0f);
VERIFY_IS_EQUAL(float(numext::ceil(half(3.5f))), 4.0f);
VERIFY_IS_EQUAL(float(numext::ceil(half(-3.5f))), -3.0f);
VERIFY_IS_APPROX(float(numext::sqrt(half(0.0f))), 0.0f);
VERIFY_IS_APPROX(float(numext::sqrt(half(4.0f))), 2.0f);
VERIFY_IS_APPROX(float(numext::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_EQUAL(float(numext::exp(half(0.0f))), 1.0f);
VERIFY_IS_APPROX(float(numext::exp(half(EIGEN_PI))), 20.f + float(EIGEN_PI));
VERIFY_IS_EQUAL(float(numext::log(half(1.0f))), 0.0f);
VERIFY_IS_APPROX(float(numext::log(half(10.0f))), 2.30273f);
}
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);
}
