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// 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>
#define VERIFY_HALF_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::half
namespace Eigen {
struct half;
}
using Eigen::half;
void test_conversion()
{
using Eigen::half_impl::__half_raw;
// Round-trip bit-cast with uint16.
VERIFY_IS_EQUAL(
numext::bit_cast<half>(numext::bit_cast<numext::uint16_t>(half(1.0f))),
half(1.0f));
VERIFY_IS_EQUAL(
numext::bit_cast<half>(numext::bit_cast<numext::uint16_t>(half(0.5f))),
half(0.5f));
VERIFY_IS_EQUAL(
numext::bit_cast<half>(numext::bit_cast<numext::uint16_t>(half(-0.33333f))),
half(-0.33333f));
VERIFY_IS_EQUAL(
numext::bit_cast<half>(numext::bit_cast<numext::uint16_t>(half(0.0f))),
half(0.0f));
// Conversion from float.
VERIFY_HALF_BITS_EQUAL(half(1.0f), 0x3c00);
VERIFY_HALF_BITS_EQUAL(half(0.5f), 0x3800);
VERIFY_HALF_BITS_EQUAL(half(0.33333f), 0x3555);
VERIFY_HALF_BITS_EQUAL(half(0.0f), 0x0000);
VERIFY_HALF_BITS_EQUAL(half(-0.0f), 0x8000);
VERIFY_HALF_BITS_EQUAL(half(65504.0f), 0x7bff);
VERIFY_HALF_BITS_EQUAL(half(65536.0f), 0x7c00); // Becomes infinity.
// Denormals.
VERIFY_HALF_BITS_EQUAL(half(-5.96046e-08f), 0x8001);
VERIFY_HALF_BITS_EQUAL(half(5.96046e-08f), 0x0001);
VERIFY_HALF_BITS_EQUAL(half(1.19209e-07f), 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_HALF_BITS_EQUAL(half(0.5f * (val1 + val2)), 0x3c00);
VERIFY_HALF_BITS_EQUAL(half(0.5f * (val2 + val3)), 0x3c02);
// Conversion from int.
VERIFY_HALF_BITS_EQUAL(half(-1), 0xbc00);
VERIFY_HALF_BITS_EQUAL(half(0), 0x0000);
VERIFY_HALF_BITS_EQUAL(half(1), 0x3c00);
VERIFY_HALF_BITS_EQUAL(half(2), 0x4000);
VERIFY_HALF_BITS_EQUAL(half(3), 0x4200);
// Conversion from bool.
VERIFY_HALF_BITS_EQUAL(half(false), 0x0000);
VERIFY_HALF_BITS_EQUAL(half(true), 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
// Conversion to bool
VERIFY(!static_cast<bool>(half(0.0)));
VERIFY(!static_cast<bool>(half(-0.0)));
VERIFY(static_cast<bool>(half(__half_raw(0x7bff))));
VERIFY(static_cast<bool>(half(-0.33333)));
VERIFY(static_cast<bool>(half(1.0)));
VERIFY(static_cast<bool>(half(-1.0)));
VERIFY(static_cast<bool>(half(-5.96046e-08f)));
}
void test_numtraits()
{
std::cout << "epsilon = " << NumTraits<half>::epsilon() << " (0x" << std::hex << numext::bit_cast<numext::uint16_t>(NumTraits<half>::epsilon()) << ")" << std::endl;
std::cout << "highest = " << NumTraits<half>::highest() << " (0x" << std::hex << numext::bit_cast<numext::uint16_t>(NumTraits<half>::highest()) << ")" << std::endl;
std::cout << "lowest = " << NumTraits<half>::lowest() << " (0x" << std::hex << numext::bit_cast<numext::uint16_t>(NumTraits<half>::lowest()) << ")" << std::endl;
std::cout << "min = " << (std::numeric_limits<half>::min)() << " (0x" << std::hex << numext::bit_cast<numext::uint16_t>(half((std::numeric_limits<half>::min)())) << ")" << std::endl;
std::cout << "denorm min = " << (std::numeric_limits<half>::denorm_min)() << " (0x" << std::hex << numext::bit_cast<numext::uint16_t>(half((std::numeric_limits<half>::denorm_min)())) << ")" << std::endl;
std::cout << "infinity = " << NumTraits<half>::infinity() << " (0x" << std::hex << numext::bit_cast<numext::uint16_t>(NumTraits<half>::infinity()) << ")" << std::endl;
std::cout << "quiet nan = " << NumTraits<half>::quiet_NaN() << " (0x" << std::hex << numext::bit_cast<numext::uint16_t>(NumTraits<half>::quiet_NaN()) << ")" << std::endl;
std::cout << "signaling nan = " << std::numeric_limits<half>::signaling_NaN() << " (0x" << std::hex << numext::bit_cast<numext::uint16_t>(std::numeric_limits<half>::signaling_NaN()) << ")" << std::endl;
VERIFY(NumTraits<half>::IsSigned);
VERIFY_IS_EQUAL(
numext::bit_cast<numext::uint16_t>(std::numeric_limits<half>::infinity()),
numext::bit_cast<numext::uint16_t>(half(std::numeric_limits<float>::infinity())) );
// There is no guarantee that casting a 32-bit NaN to 16-bit 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 HALF_QUIET_BIT = 0x0200;
VERIFY(
(numext::isnan)(std::numeric_limits<half>::quiet_NaN())
&& (numext::isnan)(half(std::numeric_limits<float>::quiet_NaN()))
&& ((numext::bit_cast<numext::uint16_t>(std::numeric_limits<half>::quiet_NaN()) & HALF_QUIET_BIT) > 0)
&& ((numext::bit_cast<numext::uint16_t>(half(std::numeric_limits<float>::quiet_NaN())) & HALF_QUIET_BIT) > 0) );
// After a cast to half, a signaling NaN may become non-signaling
// (e.g. in the case of casting float to native __fp16). Thus, we check that
// both are NaN, and that only the `numeric_limits` version is signaling.
VERIFY(
(numext::isnan)(std::numeric_limits<half>::signaling_NaN())
&& (numext::isnan)(half(std::numeric_limits<float>::signaling_NaN()))
&& ((numext::bit_cast<numext::uint16_t>(std::numeric_limits<half>::signaling_NaN()) & HALF_QUIET_BIT) == 0) );
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);
half x(3);
half y = ++x;
VERIFY_IS_EQUAL(x, half(4));
VERIFY_IS_EQUAL(y, half(4));
y = --x;
VERIFY_IS_EQUAL(x, half(3));
VERIFY_IS_EQUAL(y, half(3));
y = x++;
VERIFY_IS_EQUAL(x, half(4));
VERIFY_IS_EQUAL(y, half(3));
y = x--;
VERIFY_IS_EQUAL(x, half(3));
VERIFY_IS_EQUAL(y, half(4));
}
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);
VERIFY_IS_APPROX(numext::fmod(half(5.3f), half(2.0f)), half(1.3f));
VERIFY_IS_APPROX(fmod(half(5.3f), half(2.0f)), half(1.3f));
VERIFY_IS_APPROX(numext::fmod(half(-18.5f), half(-4.2f)), half(-1.7f));
VERIFY_IS_APPROX(fmod(half(-18.5f), half(-4.2f)), half(-1.7f));
}
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());
}
}
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