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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/.
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# include <sstream>
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# include "main.h"
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# include <Eigen/src/Core/arch/GPU/Half.h>
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// Make sure it's possible to forward declare Eigen::half
namespace Eigen {
struct half ;
}
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using Eigen : : half ;
void test_conversion ( )
{
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using Eigen : : half_impl : : __half_raw ;
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// 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-08 f ) . x , 0x8001 ) ;
VERIFY_IS_EQUAL ( half ( 5.96046e-08 f ) . x , 0x0001 ) ;
VERIFY_IS_EQUAL ( half ( 1.19209e-07 f ) . x , 0x0002 ) ;
// Verify round-to-nearest-even behavior.
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float val1 = float ( half ( __half_raw ( 0x3c00 ) ) ) ;
float val2 = float ( half ( __half_raw ( 0x3c01 ) ) ) ;
float val3 = float ( half ( __half_raw ( 0x3c02 ) ) ) ;
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VERIFY_IS_EQUAL ( half ( 0.5f * ( val1 + val2 ) ) . x , 0x3c00 ) ;
VERIFY_IS_EQUAL ( half ( 0.5f * ( val2 + val3 ) ) . x , 0x3c02 ) ;
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// 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.
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VERIFY_IS_EQUAL ( float ( half ( __half_raw ( 0x0000 ) ) ) , 0.0f ) ;
VERIFY_IS_EQUAL ( float ( half ( __half_raw ( 0x3c00 ) ) ) , 1.0f ) ;
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// Denormals.
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VERIFY_IS_APPROX ( float ( half ( __half_raw ( 0x8001 ) ) ) , - 5.96046e-08 f ) ;
VERIFY_IS_APPROX ( float ( half ( __half_raw ( 0x0001 ) ) ) , 5.96046e-08 f ) ;
VERIFY_IS_APPROX ( float ( half ( __half_raw ( 0x0002 ) ) ) , 1.19209e-07 f ) ;
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// NaNs and infinities.
VERIFY ( ! ( numext : : isinf ) ( float ( half ( 65504.0f ) ) ) ) ; // Largest finite number.
VERIFY ( ! ( numext : : isnan ) ( float ( half ( 0.0f ) ) ) ) ;
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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 ) ) ) ) ) ;
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# if !EIGEN_COMP_MSVC
// Visual Studio errors out on divisions by 0
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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 ) ) ) ) ;
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# endif
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// Exactly same checks as above, just directly on the half representation.
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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 ) ) ) ) ;
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# if !EIGEN_COMP_MSVC
// Visual Studio errors out on divisions by 0
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VERIFY ( ( numext : : isnan ) ( half ( 0.0 / 0.0 ) ) ) ;
VERIFY ( ( numext : : isinf ) ( half ( 1.0 / 0.0 ) ) ) ;
VERIFY ( ( numext : : isinf ) ( half ( - 1.0 / 0.0 ) ) ) ;
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# endif
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}
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void test_numtraits ( )
{
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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 ) ) ;
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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 ) ) ;
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}
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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.
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# if !EIGEN_COMP_MSVC
// Visual Studio errors out on divisions by 0
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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 ) ) ;
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# endif
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}
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void test_basic_functions ( )
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{
VERIFY_IS_EQUAL ( float ( numext : : abs ( half ( 3.5f ) ) ) , 3.5f ) ;
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VERIFY_IS_EQUAL ( float ( abs ( half ( 3.5f ) ) ) , 3.5f ) ;
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VERIFY_IS_EQUAL ( float ( numext : : abs ( half ( - 3.5f ) ) ) , 3.5f ) ;
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VERIFY_IS_EQUAL ( float ( abs ( half ( - 3.5f ) ) ) , 3.5f ) ;
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VERIFY_IS_EQUAL ( float ( numext : : floor ( half ( 3.5f ) ) ) , 3.0f ) ;
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VERIFY_IS_EQUAL ( float ( floor ( half ( 3.5f ) ) ) , 3.0f ) ;
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VERIFY_IS_EQUAL ( float ( numext : : floor ( half ( - 3.5f ) ) ) , - 4.0f ) ;
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VERIFY_IS_EQUAL ( float ( floor ( half ( - 3.5f ) ) ) , - 4.0f ) ;
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VERIFY_IS_EQUAL ( float ( numext : : ceil ( half ( 3.5f ) ) ) , 4.0f ) ;
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VERIFY_IS_EQUAL ( float ( ceil ( half ( 3.5f ) ) ) , 4.0f ) ;
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VERIFY_IS_EQUAL ( float ( numext : : ceil ( half ( - 3.5f ) ) ) , - 3.0f ) ;
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VERIFY_IS_EQUAL ( float ( ceil ( half ( - 3.5f ) ) ) , - 3.0f ) ;
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VERIFY_IS_APPROX ( float ( numext : : sqrt ( half ( 0.0f ) ) ) , 0.0f ) ;
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VERIFY_IS_APPROX ( float ( sqrt ( half ( 0.0f ) ) ) , 0.0f ) ;
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VERIFY_IS_APPROX ( float ( numext : : sqrt ( half ( 4.0f ) ) ) , 2.0f ) ;
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VERIFY_IS_APPROX ( float ( sqrt ( half ( 4.0f ) ) ) , 2.0f ) ;
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VERIFY_IS_APPROX ( float ( numext : : pow ( half ( 0.0f ) , half ( 1.0f ) ) ) , 0.0f ) ;
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VERIFY_IS_APPROX ( float ( pow ( half ( 0.0f ) , half ( 1.0f ) ) ) , 0.0f ) ;
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VERIFY_IS_APPROX ( float ( numext : : pow ( half ( 2.0f ) , half ( 2.0f ) ) ) , 4.0f ) ;
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VERIFY_IS_APPROX ( float ( pow ( half ( 2.0f ) , half ( 2.0f ) ) ) , 4.0f ) ;
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VERIFY_IS_EQUAL ( float ( numext : : exp ( half ( 0.0f ) ) ) , 1.0f ) ;
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VERIFY_IS_EQUAL ( float ( exp ( half ( 0.0f ) ) ) , 1.0f ) ;
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VERIFY_IS_APPROX ( float ( numext : : exp ( half ( EIGEN_PI ) ) ) , 20.f + float ( EIGEN_PI ) ) ;
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VERIFY_IS_APPROX ( float ( exp ( half ( EIGEN_PI ) ) ) , 20.f + float ( EIGEN_PI ) ) ;
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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 ) ;
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VERIFY_IS_EQUAL ( float ( numext : : log ( half ( 1.0f ) ) ) , 0.0f ) ;
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VERIFY_IS_EQUAL ( float ( log ( half ( 1.0f ) ) ) , 0.0f ) ;
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VERIFY_IS_APPROX ( float ( numext : : log ( half ( 10.0f ) ) ) , 2.30273f ) ;
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VERIFY_IS_APPROX ( float ( log ( half ( 10.0f ) ) ) , 2.30273f ) ;
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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 ) ;
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}
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void test_trigonometric_functions ( )
{
VERIFY_IS_APPROX ( numext : : cos ( half ( 0.0f ) ) , half ( cosf ( 0.0f ) ) ) ;
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VERIFY_IS_APPROX ( cos ( half ( 0.0f ) ) , half ( cosf ( 0.0f ) ) ) ;
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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 ) ) ) ;
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VERIFY_IS_APPROX ( sin ( half ( 0.0f ) ) , half ( sinf ( 0.0f ) ) ) ;
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// 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 ) ) ) ;
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VERIFY_IS_APPROX ( tan ( half ( 0.0f ) ) , half ( tanf ( 0.0f ) ) ) ;
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// 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 ) ) ) ;
}
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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 ;
}
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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 > ( ) ) ;
}
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EIGEN_DECLARE_TEST ( half_float )
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{
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CALL_SUBTEST ( test_numtraits ( ) ) ;
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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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}