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Kokkos_Complex.hpp
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/*
//@HEADER
// ************************************************************************
//
// Kokkos v. 2.0
// Copyright (2014) Sandia Corporation
//
// Under the terms of Contract DE-AC04-94AL85000 with Sandia Corporation,
// the U.S. Government retains certain rights in this software.
//
// Redistribution and use in source and binary forms, with or without
// modification, are permitted provided that the following conditions are
// met:
//
// 1. Redistributions of source code must retain the above copyright
// notice, this list of conditions and the following disclaimer.
//
// 2. Redistributions in binary form must reproduce the above copyright
// notice, this list of conditions and the following disclaimer in the
// documentation and/or other materials provided with the distribution.
//
// 3. Neither the name of the Corporation nor the names of the
// contributors may be used to endorse or promote products derived from
// this software without specific prior written permission.
//
// THIS SOFTWARE IS PROVIDED BY SANDIA CORPORATION "AS IS" AND ANY
// EXPRESS OR IMPLIED WARRANTIES, INCLUDING, BUT NOT LIMITED TO, THE
// IMPLIED WARRANTIES OF MERCHANTABILITY AND FITNESS FOR A PARTICULAR
// PURPOSE ARE DISCLAIMED. IN NO EVENT SHALL SANDIA CORPORATION OR THE
// CONTRIBUTORS BE LIABLE FOR ANY DIRECT, INDIRECT, INCIDENTAL, SPECIAL,
// EXEMPLARY, OR CONSEQUENTIAL DAMAGES (INCLUDING, BUT NOT LIMITED TO,
// PROCUREMENT OF SUBSTITUTE GOODS OR SERVICES; LOSS OF USE, DATA, OR
// PROFITS; OR BUSINESS INTERRUPTION) HOWEVER CAUSED AND ON ANY THEORY OF
// LIABILITY, WHETHER IN CONTRACT, STRICT LIABILITY, OR TORT (INCLUDING
// NEGLIGENCE OR OTHERWISE) ARISING IN ANY WAY OUT OF THE USE OF THIS
// SOFTWARE, EVEN IF ADVISED OF THE POSSIBILITY OF SUCH DAMAGE.
//
// Questions? Contact H. Carter Edwards (hcedwar@sandia.gov)
//
// ************************************************************************
//@HEADER
*/
#ifndef KOKKOS_COMPLEX_HPP
#define KOKKOS_COMPLEX_HPP
#include <Kokkos_Atomic.hpp>
#include <complex>
#include <iostream>
namespace
Kokkos
{
/// \class complex
/// \brief Partial reimplementation of std::complex that works as the
/// result of a Kokkos::parallel_reduce.
/// \tparam RealType The type of the real and imaginary parts of the
/// complex number. As with std::complex, this is only defined for
/// \c float, \c double, and <tt>long double</tt>. The latter is
/// currently forbidden in CUDA device kernels.
template
<
class
RealType
>
class
complex
{
private
:
RealType
re_
,
im_
;
public
:
//! The type of the real or imaginary parts of this complex number.
typedef
RealType
value_type
;
//! Default constructor (initializes both real and imaginary parts to zero).
KOKKOS_INLINE_FUNCTION
complex
()
:
re_
(
0.0
),
im_
(
0.0
)
{}
//! Copy constructor.
KOKKOS_INLINE_FUNCTION
complex
(
const
complex
<
RealType
>&
src
)
:
re_
(
src
.
re_
),
im_
(
src
.
im_
)
{}
//! Copy constructor from volatile.
KOKKOS_INLINE_FUNCTION
complex
(
const
volatile
complex
<
RealType
>&
src
)
:
re_
(
src
.
re_
),
im_
(
src
.
im_
)
{}
/// \brief Conversion constructor from std::complex.
///
/// This constructor cannot be called in a CUDA device function,
/// because std::complex's methods and nonmember functions are not
/// marked as CUDA device functions.
template
<
class
InputRealType
>
complex
(
const
std
::
complex
<
InputRealType
>&
src
)
:
re_
(
std
::
real
(
src
)),
im_
(
std
::
imag
(
src
))
{}
/// \brief Conversion operator to std::complex.
///
/// This operator cannot be called in a CUDA device function,
/// because std::complex's methods and nonmember functions are not
/// marked as CUDA device functions.
operator
std
::
complex
<
RealType
>
()
const
{
return
std
::
complex
<
RealType
>
(
re_
,
im_
);
}
/// \brief Constructor that takes just the real part, and sets the
/// imaginary part to zero.
template
<
class
InputRealType
>
KOKKOS_INLINE_FUNCTION
complex
(
const
InputRealType
&
val
)
:
re_
(
val
),
im_
(
0.0
)
{}
//! Constructor that takes the real and imaginary parts.
template
<
class
RealType1
,
class
RealType2
>
KOKKOS_INLINE_FUNCTION
complex
(
const
RealType1
&
re
,
const
RealType2
&
im
)
:
re_
(
re
),
im_
(
im
)
{}
//! Assignment operator.
template
<
class
InputRealType
>
KOKKOS_INLINE_FUNCTION
complex
<
RealType
>&
operator
=
(
const
complex
<
InputRealType
>&
src
)
{
re_
=
src
.
re_
;
im_
=
src
.
im_
;
return
*
this
;
}
//! Assignment operator.
template
<
class
InputRealType
>
KOKKOS_INLINE_FUNCTION
volatile
complex
<
RealType
>&
operator
=
(
const
complex
<
InputRealType
>&
src
)
volatile
{
re_
=
src
.
re_
;
im_
=
src
.
im_
;
return
*
this
;
}
//! Assignment operator.
template
<
class
InputRealType
>
KOKKOS_INLINE_FUNCTION
volatile
complex
<
RealType
>&
operator
=
(
const
volatile
complex
<
InputRealType
>&
src
)
volatile
{
re_
=
src
.
re_
;
im_
=
src
.
im_
;
return
*
this
;
}
//! Assignment operator.
template
<
class
InputRealType
>
KOKKOS_INLINE_FUNCTION
complex
<
RealType
>&
operator
=
(
const
volatile
complex
<
InputRealType
>&
src
)
{
re_
=
src
.
re_
;
im_
=
src
.
im_
;
return
*
this
;
}
//! Assignment operator (from a real number).
template
<
class
InputRealType
>
KOKKOS_INLINE_FUNCTION
complex
<
RealType
>&
operator
=
(
const
InputRealType
&
val
)
{
re_
=
val
;
im_
=
static_cast
<
RealType
>
(
0.0
);
return
*
this
;
}
//! Assignment operator (from a real number).
template
<
class
InputRealType
>
KOKKOS_INLINE_FUNCTION
void
operator
=
(
const
InputRealType
&
val
)
volatile
{
re_
=
val
;
im_
=
static_cast
<
RealType
>
(
0.0
);
}
/// \brief Assignment operator from std::complex.
///
/// This constructor cannot be called in a CUDA device function,
/// because std::complex's methods and nonmember functions are not
/// marked as CUDA device functions.
template
<
class
InputRealType
>
complex
<
RealType
>&
operator
=
(
const
std
::
complex
<
InputRealType
>&
src
)
{
re_
=
std
::
real
(
src
);
im_
=
std
::
imag
(
src
);
return
*
this
;
}
//! The imaginary part of this complex number.
KOKKOS_INLINE_FUNCTION
RealType
&
imag
()
{
return
im_
;
}
//! The real part of this complex number.
KOKKOS_INLINE_FUNCTION
RealType
&
real
()
{
return
re_
;
}
//! The imaginary part of this complex number.
KOKKOS_INLINE_FUNCTION
const
RealType
imag
()
const
{
return
im_
;
}
//! The real part of this complex number.
KOKKOS_INLINE_FUNCTION
const
RealType
real
()
const
{
return
re_
;
}
//! The imaginary part of this complex number (volatile overload).
KOKKOS_INLINE_FUNCTION
volatile
RealType
&
imag
()
volatile
{
return
im_
;
}
//! The real part of this complex number (volatile overload).
KOKKOS_INLINE_FUNCTION
volatile
RealType
&
real
()
volatile
{
return
re_
;
}
//! The imaginary part of this complex number (volatile overload).
KOKKOS_INLINE_FUNCTION
const
RealType
imag
()
const
volatile
{
return
im_
;
}
//! The real part of this complex number (volatile overload).
KOKKOS_INLINE_FUNCTION
const
RealType
real
()
const
volatile
{
return
re_
;
}
KOKKOS_INLINE_FUNCTION
complex
<
RealType
>&
operator
+=
(
const
complex
<
RealType
>&
src
)
{
re_
+=
src
.
re_
;
im_
+=
src
.
im_
;
return
*
this
;
}
KOKKOS_INLINE_FUNCTION
void
operator
+=
(
const
volatile
complex
<
RealType
>&
src
)
volatile
{
re_
+=
src
.
re_
;
im_
+=
src
.
im_
;
}
KOKKOS_INLINE_FUNCTION
complex
<
RealType
>&
operator
+=
(
const
RealType
&
src
)
{
re_
+=
src
;
return
*
this
;
}
KOKKOS_INLINE_FUNCTION
void
operator
+=
(
const
volatile
RealType
&
src
)
volatile
{
re_
+=
src
;
}
KOKKOS_INLINE_FUNCTION
complex
<
RealType
>&
operator
-=
(
const
complex
<
RealType
>&
src
)
{
re_
-=
src
.
re_
;
im_
-=
src
.
im_
;
return
*
this
;
}
KOKKOS_INLINE_FUNCTION
complex
<
RealType
>&
operator
-=
(
const
RealType
&
src
)
{
re_
-=
src
;
return
*
this
;
}
KOKKOS_INLINE_FUNCTION
complex
<
RealType
>&
operator
*=
(
const
complex
<
RealType
>&
src
)
{
const
RealType
realPart
=
re_
*
src
.
re_
-
im_
*
src
.
im_
;
const
RealType
imagPart
=
re_
*
src
.
im_
+
im_
*
src
.
re_
;
re_
=
realPart
;
im_
=
imagPart
;
return
*
this
;
}
KOKKOS_INLINE_FUNCTION
void
operator
*=
(
const
volatile
complex
<
RealType
>&
src
)
volatile
{
const
RealType
realPart
=
re_
*
src
.
re_
-
im_
*
src
.
im_
;
const
RealType
imagPart
=
re_
*
src
.
im_
+
im_
*
src
.
re_
;
re_
=
realPart
;
im_
=
imagPart
;
}
KOKKOS_INLINE_FUNCTION
complex
<
RealType
>&
operator
*=
(
const
RealType
&
src
)
{
re_
*=
src
;
im_
*=
src
;
return
*
this
;
}
KOKKOS_INLINE_FUNCTION
void
operator
*=
(
const
volatile
RealType
&
src
)
volatile
{
re_
*=
src
;
im_
*=
src
;
}
KOKKOS_INLINE_FUNCTION
complex
<
RealType
>&
operator
/=
(
const
complex
<
RealType
>&
y
)
{
// Scale (by the "1-norm" of y) to avoid unwarranted overflow.
// If the real part is +/-Inf and the imaginary part is -/+Inf,
// this won't change the result.
const
RealType
s
=
::
fabs
(
y
.
real
())
+
::
fabs
(
y
.
imag
());
// If s is 0, then y is zero, so x/y == real(x)/0 + i*imag(x)/0.
// In that case, the relation x/y == (x/s) / (y/s) doesn't hold,
// because y/s is NaN.
if
(
s
==
0.0
)
{
this
->
re_
/=
s
;
this
->
im_
/=
s
;
}
else
{
const
complex
<
RealType
>
x_scaled
(
this
->
re_
/
s
,
this
->
im_
/
s
);
const
complex
<
RealType
>
y_conj_scaled
(
y
.
re_
/
s
,
-
(
y
.
im_
)
/
s
);
const
RealType
y_scaled_abs
=
y_conj_scaled
.
re_
*
y_conj_scaled
.
re_
+
y_conj_scaled
.
im_
*
y_conj_scaled
.
im_
;
// abs(y) == abs(conj(y))
*
this
=
x_scaled
*
y_conj_scaled
;
*
this
/=
y_scaled_abs
;
}
return
*
this
;
}
KOKKOS_INLINE_FUNCTION
complex
<
RealType
>&
operator
/=
(
const
RealType
&
src
)
{
re_
/=
src
;
im_
/=
src
;
return
*
this
;
}
};
//! Binary + operator for complex.
template
<
class
RealType
>
KOKKOS_INLINE_FUNCTION
complex
<
RealType
>
operator
+
(
const
complex
<
RealType
>&
x
,
const
complex
<
RealType
>&
y
)
{
return
complex
<
RealType
>
(
x
.
real
()
+
y
.
real
(),
x
.
imag
()
+
y
.
imag
());
}
//! Unary + operator for complex.
template
<
class
RealType
>
KOKKOS_INLINE_FUNCTION
complex
<
RealType
>
operator
+
(
const
complex
<
RealType
>&
x
)
{
return
x
;
}
//! Binary - operator for complex.
template
<
class
RealType
>
KOKKOS_INLINE_FUNCTION
complex
<
RealType
>
operator
-
(
const
complex
<
RealType
>&
x
,
const
complex
<
RealType
>&
y
)
{
return
complex
<
RealType
>
(
x
.
real
()
-
y
.
real
(),
x
.
imag
()
-
y
.
imag
());
}
//! Unary - operator for complex.
template
<
class
RealType
>
KOKKOS_INLINE_FUNCTION
complex
<
RealType
>
operator
-
(
const
complex
<
RealType
>&
x
)
{
return
complex
<
RealType
>
(
-
x
.
real
(),
-
x
.
imag
());
}
//! Binary * operator for complex.
template
<
class
RealType
>
KOKKOS_INLINE_FUNCTION
complex
<
RealType
>
operator
*
(
const
complex
<
RealType
>&
x
,
const
complex
<
RealType
>&
y
)
{
return
complex
<
RealType
>
(
x
.
real
()
*
y
.
real
()
-
x
.
imag
()
*
y
.
imag
(),
x
.
real
()
*
y
.
imag
()
+
x
.
imag
()
*
y
.
real
());
}
/// \brief Binary * operator for std::complex and complex.
///
/// This function exists because GCC 4.7.2 (and perhaps other
/// compilers) are not able to deduce that they can multiply
/// std::complex by Kokkos::complex, by first converting std::complex
/// to Kokkos::complex.
///
/// This function cannot be called in a CUDA device function, because
/// std::complex's methods and nonmember functions are not marked as
/// CUDA device functions.
template
<
class
RealType
>
complex
<
RealType
>
operator
*
(
const
std
::
complex
<
RealType
>&
x
,
const
complex
<
RealType
>&
y
)
{
return
complex
<
RealType
>
(
x
.
real
()
*
y
.
real
()
-
x
.
imag
()
*
y
.
imag
(),
x
.
real
()
*
y
.
imag
()
+
x
.
imag
()
*
y
.
real
());
}
/// \brief Binary * operator for RealType times complex.
///
/// This function exists because the compiler doesn't know that
/// RealType and complex<RealType> commute with respect to operator*.
template
<
class
RealType
>
KOKKOS_INLINE_FUNCTION
complex
<
RealType
>
operator
*
(
const
RealType
&
x
,
const
complex
<
RealType
>&
y
)
{
return
complex
<
RealType
>
(
x
*
y
.
real
(),
x
*
y
.
imag
());
}
//! Imaginary part of a complex number.
template
<
class
RealType
>
KOKKOS_INLINE_FUNCTION
RealType
imag
(
const
complex
<
RealType
>&
x
)
{
return
x
.
imag
();
}
//! Real part of a complex number.
template
<
class
RealType
>
KOKKOS_INLINE_FUNCTION
RealType
real
(
const
complex
<
RealType
>&
x
)
{
return
x
.
real
();
}
//! Absolute value (magnitude) of a complex number.
template
<
class
RealType
>
KOKKOS_INLINE_FUNCTION
RealType
abs
(
const
complex
<
RealType
>&
x
)
{
// FIXME (mfh 31 Oct 2014) Scale to avoid unwarranted overflow.
return
::
sqrt
(
real
(
x
)
*
real
(
x
)
+
imag
(
x
)
*
imag
(
x
));
}
//! Conjugate of a complex number.
template
<
class
RealType
>
KOKKOS_INLINE_FUNCTION
complex
<
RealType
>
conj
(
const
complex
<
RealType
>&
x
)
{
return
complex
<
RealType
>
(
real
(
x
),
-
imag
(
x
));
}
//! Binary operator / for complex and real numbers
template
<
class
RealType1
,
class
RealType2
>
KOKKOS_INLINE_FUNCTION
complex
<
RealType1
>
operator
/
(
const
complex
<
RealType1
>&
x
,
const
RealType2
&
y
)
{
return
complex
<
RealType1
>
(
real
(
x
)
/
y
,
imag
(
x
)
/
y
);
}
//! Binary operator / for complex.
template
<
class
RealType
>
KOKKOS_INLINE_FUNCTION
complex
<
RealType
>
operator
/
(
const
complex
<
RealType
>&
x
,
const
complex
<
RealType
>&
y
)
{
// Scale (by the "1-norm" of y) to avoid unwarranted overflow.
// If the real part is +/-Inf and the imaginary part is -/+Inf,
// this won't change the result.
const
RealType
s
=
::
fabs
(
real
(
y
))
+
::
fabs
(
imag
(
y
));
// If s is 0, then y is zero, so x/y == real(x)/0 + i*imag(x)/0.
// In that case, the relation x/y == (x/s) / (y/s) doesn't hold,
// because y/s is NaN.
if
(
s
==
0.0
)
{
return
complex
<
RealType
>
(
real
(
x
)
/
s
,
imag
(
x
)
/
s
);
}
else
{
const
complex
<
RealType
>
x_scaled
(
real
(
x
)
/
s
,
imag
(
x
)
/
s
);
const
complex
<
RealType
>
y_conj_scaled
(
real
(
y
)
/
s
,
-
imag
(
y
)
/
s
);
const
RealType
y_scaled_abs
=
real
(
y_conj_scaled
)
*
real
(
y_conj_scaled
)
+
imag
(
y_conj_scaled
)
*
imag
(
y_conj_scaled
);
// abs(y) == abs(conj(y))
complex
<
RealType
>
result
=
x_scaled
*
y_conj_scaled
;
result
/=
y_scaled_abs
;
return
result
;
}
}
//! Equality operator for two complex numbers.
template
<
class
RealType
>
KOKKOS_INLINE_FUNCTION
bool
operator
==
(
const
complex
<
RealType
>&
x
,
const
complex
<
RealType
>&
y
)
{
return
real
(
x
)
==
real
(
y
)
&&
imag
(
x
)
==
imag
(
y
);
}
//! Equality operator for std::complex and Kokkos::complex.
template
<
class
RealType
>
KOKKOS_INLINE_FUNCTION
bool
operator
==
(
const
std
::
complex
<
RealType
>&
x
,
const
complex
<
RealType
>&
y
)
{
return
std
::
real
(
x
)
==
real
(
y
)
&&
std
::
imag
(
x
)
==
imag
(
y
);
}
//! Equality operator for complex and real number.
template
<
class
RealType1
,
class
RealType2
>
KOKKOS_INLINE_FUNCTION
bool
operator
==
(
const
complex
<
RealType1
>&
x
,
const
RealType2
&
y
)
{
return
real
(
x
)
==
y
&&
imag
(
x
)
==
static_cast
<
RealType1
>
(
0.0
);
}
//! Equality operator for real and complex number.
template
<
class
RealType
>
KOKKOS_INLINE_FUNCTION
bool
operator
==
(
const
RealType
&
x
,
const
complex
<
RealType
>&
y
)
{
return
y
==
x
;
}
//! Inequality operator for two complex numbers.
template
<
class
RealType
>
KOKKOS_INLINE_FUNCTION
bool
operator
!=
(
const
complex
<
RealType
>&
x
,
const
complex
<
RealType
>&
y
)
{
return
real
(
x
)
!=
real
(
y
)
||
imag
(
x
)
!=
imag
(
y
);
}
//! Inequality operator for std::complex and Kokkos::complex.
template
<
class
RealType
>
KOKKOS_INLINE_FUNCTION
bool
operator
!=
(
const
std
::
complex
<
RealType
>&
x
,
const
complex
<
RealType
>&
y
)
{
return
std
::
real
(
x
)
!=
real
(
y
)
||
std
::
imag
(
x
)
!=
imag
(
y
);
}
//! Inequality operator for complex and real number.
template
<
class
RealType1
,
class
RealType2
>
KOKKOS_INLINE_FUNCTION
bool
operator
!=
(
const
complex
<
RealType1
>&
x
,
const
RealType2
&
y
)
{
return
real
(
x
)
!=
y
||
imag
(
x
)
!=
static_cast
<
RealType1
>
(
0.0
);
}
//! Inequality operator for real and complex number.
template
<
class
RealType
>
KOKKOS_INLINE_FUNCTION
bool
operator
!=
(
const
RealType
&
x
,
const
complex
<
RealType
>&
y
)
{
return
y
!=
x
;
}
template
<
class
RealType
>
std
::
ostream
&
operator
<<
(
std
::
ostream
&
os
,
const
complex
<
RealType
>&
x
)
{
const
std
::
complex
<
RealType
>
x_std
(
Kokkos
::
real
(
x
),
Kokkos
::
imag
(
x
));
os
<<
x_std
;
return
os
;
}
template
<
class
RealType
>
std
::
ostream
&
operator
>>
(
std
::
ostream
&
os
,
complex
<
RealType
>&
x
)
{
std
::
complex
<
RealType
>
x_std
;
os
>>
x_std
;
x
=
x_std
;
// only assigns on success of above
return
os
;
}
}
// namespace Kokkos
#endif
// KOKKOS_COMPLEX_HPP
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