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stencils.cc

/***************************************************************************
 * blitz/array/stencils.cc  Apply stencils to arrays
 *
 * $Id: stencils.cc,v 1.1 2002/09/12 07:02:06 eric Exp $
 *
 * Copyright (C) 1997-2001 Todd Veldhuizen <tveldhui@oonumerics.org>
 *
 * This program is free software; you can redistribute it and/or
 * modify it under the terms of the GNU General Public License
 * as published by the Free Software Foundation; either version 2
 * of the License, or (at your option) any later version.
 *
 * This program is distributed in the hope that it will be useful,
 * but WITHOUT ANY WARRANTY; without even the implied warranty of
 * MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE.  See the
 * GNU General Public License for more details.
 *
 * Suggestions:          blitz-dev@oonumerics.org
 * Bugs:                 blitz-bugs@oonumerics.org
 *
 * For more information, please see the Blitz++ Home Page:
 *    http://oonumerics.org/blitz/
 *
 ***************************************************************************
 * $Log: stencils.cc,v $
 * Revision 1.1  2002/09/12 07:02:06  eric
 * major rewrite of weave.
 *
 * 0.
 * The underlying library code is significantly re-factored and simpler. There used to be a xxx_spec.py and xxx_info.py file for every group of type conversion classes.  The spec file held the python code that handled the conversion and the info file had most of the C code templates that were generated.  This proved pretty confusing in practice, so the two files have mostly been merged into the spec file.
 *
 * Also, there was quite a bit of code duplication running around.  The re-factoring was able to trim the standard conversion code base (excluding blitz and accelerate stuff) by about 40%.  This should be a huge maintainability and extensibility win.
 *
 * 1.
 * With multiple months of using Numeric arrays, I've found some of weave's "magic variable" names unwieldy and want to change them.  The following are the old declarations for an array x of Float32 type:
 *
 *         PyArrayObject* x = convert_to_numpy(...);
 *         float* x_data = (float*) x->data;
 *         int*   _Nx = x->dimensions;
 *         int*   _Sx = x->strides;
 *         int    _Dx = x->nd;
 *
 * The new declaration looks like this:
 *
 *         PyArrayObject* x_array = convert_to_numpy(...);
 *         float* x = (float*) x->data;
 *         int*   Nx = x->dimensions;
 *         int*   Sx = x->strides;
 *         int    Dx = x->nd;
 *
 * This is obviously not backward compatible, and will break some code (including a lot of mine).  It also makes inline() code more readable and natural to write.
 *
 * 2.
 * I've switched from CXX to Gordon McMillan's SCXX for list, tuples, and dictionaries.  I like CXX pretty well, but its use of advanced C++ (templates, etc.) caused some portability problems.  The SCXX library is similar to CXX but doesn't use templates at all.  This, like (1) is not an
 * API compatible change and requires repairing existing code.
 *
 * I have also thought about boost python, but it also makes heavy use of templates.  Moving to SCXX gets rid of almost all template usage for the standard type converters which should help portability.  std::complex and std::string from the STL are the only templates left.  Of course blitz still uses templates in a major way so weave.blitz will continue to be hard on compilers.
 *
 * I've actually considered scrapping the C++ classes for list, tuples, and
 * dictionaries, and just fall back to the standard Python C API because the classes are waaay slower than the raw API in many cases.  They are also more convenient and less error prone in many cases, so I've decided to stick with them.  The PyObject variable will always be made available for variable "x" under the name "py_x" for more speedy operations.  You'll definitely want to use these for anything that needs to be speedy.
 *
 * 3.
 * strings are converted to std::string now.  I found this to be the most useful type in for strings in my code.  Py::String was used previously.
 *
 * 4.
 * There are a number of reference count "errors" in some of the less tested conversion codes such as instance, module, etc.  I've cleaned most of these up.  I put errors in quotes here because I'm actually not positive that objects passed into "inline" really need reference counting applied to them.  The dictionaries passed in by inline() hold references to these objects so it doesn't seem that they could ever be garbage collected inadvertently.  Variables used by ext_tools, though, definitely need the reference counting done.  I don't think this is a major cost in speed, so it probably isn't worth getting rid of the ref count code.
 *
 * 5.
 * Unicode objects are now supported.  This was necessary to support rendering Unicode strings in the freetype wrappers for Chaco.
 *
 * 6.
 * blitz++ was upgraded to the latest CVS.  It compiles about twice as fast as the old blitz and looks like it supports a large number of compilers (though only gcc 2.95.3 is tested).  Compile times now take about 9 seconds on my 850 MHz PIII laptop.
 *
 * Revision 1.3  2001/01/26 19:37:38  tveldhui
 * Incorporated 1D stencil fix from Derrick Bass.
 *
 * Revision 1.2  2001/01/25 00:25:55  tveldhui
 * Ensured that source files have cvs logs.
 *
 */

#ifndef BZ_ARRAYSTENCILS_CC
#define BZ_ARRAYSTENCILS_CC

#ifndef BZ_ARRAYSTENCILS_H
 #error <blitz/array/stencil.cc> must be included via <blitz/array/stencils.h>
#endif

BZ_NAMESPACE(blitz)

// NEEDS_WORK:
// o Need to allow scalar arguments as well as arrays
// o Unit stride optimization
// o Tiling
// o Pass coordinate vector to stencil, so that where-like constructs
//   can depend on location
// o Maybe allow expression templates to be passed as
//   array parameters?

/*
 * There are a lot of kludges in this code to work around the fact that
 * you can't have default template parameters with function templates.
 * Ideally, one would implement applyStencil(..) as:
 *
 * template<class T_stencil, class T_numtype1, class T_array2,
 *    class T_array3, class T_array4, class T_array5, class T_array6,
 *    class T_array7, class T_array8, class T_array9, class T_array10,
 *    class T_array11>
 * void applyStencil(const T_stencil& stencil, Array<T_numtype1,3>& A,
 *    T_array2& B = _dummyArray, T_array3& C = _dummyArray, ......)
 *
 * and allow for up to (say) 11 arrays to be passed.  But this doesn't
 * appear to be legal C++.  Instead, 11 versions of applyStencil are
 * provided, each one with a different number of array parameters,
 * and these stubs fill in the _dummyArray parameters and invoke
 * applyStencil_imp().
 */

template<int N_rank, class T_numtype1, class T_array2,
    class T_array3, class T_array4, class T_array5, class T_array6,
    class T_array7, class T_array8, class T_array9, class T_array10,
    class T_array11>
void checkShapes(const Array<T_numtype1,N_rank>& A,
    const T_array2& B, const T_array3& C, const T_array4& D, 
    const T_array5& E, const T_array6& F, const T_array7& G, 
    const T_array8& H, const T_array9& I, const T_array10& J, 
    const T_array11& K)
{
    BZPRECONDITION(areShapesConformable(A.shape(),B.shape())
        && areShapesConformable(A.shape(),C.shape())
        && areShapesConformable(A.shape(),D.shape())
        && areShapesConformable(A.shape(),E.shape())
        && areShapesConformable(A.shape(),F.shape())
        && areShapesConformable(A.shape(),G.shape())
        && areShapesConformable(A.shape(),H.shape())
        && areShapesConformable(A.shape(),I.shape())
        && areShapesConformable(A.shape(),J.shape())
        && areShapesConformable(A.shape(),K.shape()));
}

template<class T_extent, int N_rank, 
    class T_stencil, class T_numtype1, class T_array2,
    class T_array3, class T_array4, class T_array5, class T_array6,
    class T_array7, class T_array8, class T_array9, class T_array10,
    class T_array11>
void calcStencilExtent(T_extent& At, const T_stencil& stencil, 
    const Array<T_numtype1,N_rank>& A,
    const T_array2& B, const T_array3& C, const T_array4& D, const T_array5& E, 
    const T_array6& F, const T_array7& G, const T_array8& H, const T_array9& I, 
    const T_array10& J, const T_array11& K)
{
    // Interrogate the stencil to find out its extent
    _bz_typename stencilExtent_traits<T_array2>::T_stencilExtent Bt;
    _bz_typename stencilExtent_traits<T_array3>::T_stencilExtent Ct;
    _bz_typename stencilExtent_traits<T_array4>::T_stencilExtent Dt;
    _bz_typename stencilExtent_traits<T_array5>::T_stencilExtent Et;
    _bz_typename stencilExtent_traits<T_array6>::T_stencilExtent Ft;
    _bz_typename stencilExtent_traits<T_array7>::T_stencilExtent Gt;
    _bz_typename stencilExtent_traits<T_array8>::T_stencilExtent Ht;
    _bz_typename stencilExtent_traits<T_array9>::T_stencilExtent It;
    _bz_typename stencilExtent_traits<T_array10>::T_stencilExtent Jt;
    _bz_typename stencilExtent_traits<T_array11>::T_stencilExtent Kt;

    stencil.apply(At, Bt, Ct, Dt, Et, Ft, Gt, Ht, It, Jt, Kt);
    At.combine(Bt);
    At.combine(Ct);
    At.combine(Dt);
    At.combine(Et);
    At.combine(Ft);
    At.combine(Gt);
    At.combine(Ht);
    At.combine(It);
    At.combine(Jt);
    At.combine(Kt);
}

template<int N_rank, class T_stencil, class T_numtype1, class T_array2>
RectDomain<N_rank> interiorDomain(const T_stencil& stencil,
    const Array<T_numtype1,N_rank>& A,
    const T_array2& B)
{
    RectDomain<N_rank> domain = A.domain();

    // Interrogate the stencil to find out its extent
    stencilExtent<3, T_numtype1> At;
    calcStencilExtent(At, stencil, A, B, _dummyArray, _dummyArray, 
        _dummyArray, _dummyArray, _dummyArray, _dummyArray, _dummyArray, 
        _dummyArray, _dummyArray);

    // Shrink the domain according to the stencil size
    TinyVector<int,N_rank> lbound, ubound;
    lbound = domain.lbound() - At.min();
    ubound = domain.ubound() - At.max();
    return RectDomain<N_rank>(lbound,ubound);
}

template<int hasExtents>
struct _getStencilExtent {
template<int N_rank,
    class T_stencil, class T_numtype1, class T_array2,
    class T_array3, class T_array4, class T_array5, class T_array6,
    class T_array7, class T_array8, class T_array9, class T_array10,
    class T_array11>
static void getStencilExtent(TinyVector<int,N_rank>& minb,
    TinyVector<int,N_rank>& maxb,
    const T_stencil& stencil, Array<T_numtype1,N_rank>& A,
    T_array2& B, T_array3& C, T_array4& D, T_array5& E, T_array6& F,
    T_array7& G, T_array8& H, T_array9& I, T_array10& J, T_array11& K)
{
    // Interrogate the stencil to find out its extent
    stencilExtent<N_rank, T_numtype1> At;
    calcStencilExtent(At, stencil, A, B, C, D, E, F, G, H, I, J, K);
    minb = At.min();
    maxb = At.max();
}
};

template<>
struct _getStencilExtent<1> {
template<int N_rank,
    class T_stencil, class T_numtype1, class T_array2,
    class T_array3, class T_array4, class T_array5, class T_array6,
    class T_array7, class T_array8, class T_array9, class T_array10,
    class T_array11>
static inline void getStencilExtent(TinyVector<int,N_rank>& minb,
    TinyVector<int,N_rank>& maxb,
    const T_stencil& stencil, Array<T_numtype1,N_rank>& A,
    T_array2& B, T_array3& C, T_array4& D, T_array5& E, T_array6& F,
    T_array7& G, T_array8& H, T_array9& I, T_array10& J, T_array11& K)
{
    stencil.getExtent(minb, maxb);
}
};

template<int N_rank,
    class T_stencil, class T_numtype1, class T_array2,
    class T_array3, class T_array4, class T_array5, class T_array6,
    class T_array7, class T_array8, class T_array9, class T_array10,
    class T_array11>
inline void getStencilExtent(TinyVector<int,N_rank>& minb,
    TinyVector<int,N_rank>& maxb,
    const T_stencil& stencil, Array<T_numtype1,N_rank>& A,
    T_array2& B, T_array3& C, T_array4& D, T_array5& E, T_array6& F,
    T_array7& G, T_array8& H, T_array9& I, T_array10& J, T_array11& K)
{
    _getStencilExtent<T_stencil::hasExtent>::getStencilExtent(
        minb, maxb, stencil, A, B, C, D, E, F, G, H, I, J, K);
}

/*
 * This version applies a stencil to a set of 3D arrays.  Up to 11 arrays
 * may be used.  Any unused arrays are turned into dummyArray objects.
 * Operations on dummyArray objects are translated into no-ops.
 */
template<class T_stencil, class T_numtype1, class T_array2,
    class T_array3, class T_array4, class T_array5, class T_array6,
    class T_array7, class T_array8, class T_array9, class T_array10,
    class T_array11>
void applyStencil_imp(const T_stencil& stencil, Array<T_numtype1,3>& A,
    T_array2& B, T_array3& C, T_array4& D, T_array5& E, T_array6& F,
    T_array7& G, T_array8& H, T_array9& I, T_array10& J, T_array11& K)
{
    checkShapes(A,B,C,D,E,F,G,H,I,J,K);
 
    // Determine stencil extent
    TinyVector<int,3> minb, maxb;
    getStencilExtent(minb, maxb, stencil, A, B, C, D, E, F, G, H, I, J, K);

    // Now determine the subdomain over which the stencil
    // can be applied without worrying about overrunning the
    // boundaries of the array
    int stencil_lbound0 = minb(0);
    int stencil_lbound1 = minb(1);
    int stencil_lbound2 = minb(2);

    int stencil_ubound0 = maxb(0);
    int stencil_ubound1 = maxb(1);
    int stencil_ubound2 = maxb(2);

    int lbound0 = minmax::max(A.lbound(0), A.lbound(0) - stencil_lbound0);
    int lbound1 = minmax::max(A.lbound(1), A.lbound(1) - stencil_lbound1);
    int lbound2 = minmax::max(A.lbound(2), A.lbound(2) - stencil_lbound2);

    int ubound0 = minmax::min(A.ubound(0), A.ubound(0) - stencil_ubound0);
    int ubound1 = minmax::min(A.ubound(1), A.ubound(1) - stencil_ubound1);
    int ubound2 = minmax::min(A.ubound(2), A.ubound(2) - stencil_ubound2);

#if 0
    cout << "Stencil bounds are:" << endl
     << lbound0 << '\t' << ubound0 << endl
     << lbound1 << '\t' << ubound1 << endl
     << lbound2 << '\t' << ubound2 << endl;
#endif

    // Now do the actual loop
    FastArrayIterator<T_numtype1,3> Aiter(A);
    _bz_typename T_array2::T_iterator Biter(B);
    _bz_typename T_array3::T_iterator Citer(C);
    _bz_typename T_array4::T_iterator Diter(D);
    _bz_typename T_array5::T_iterator Eiter(E);
    _bz_typename T_array6::T_iterator Fiter(F);
    _bz_typename T_array7::T_iterator Giter(G);
    _bz_typename T_array8::T_iterator Hiter(H);
    _bz_typename T_array9::T_iterator Iiter(I);
    _bz_typename T_array10::T_iterator Jiter(J);
    _bz_typename T_array11::T_iterator Kiter(K);

    // Load the strides for the innermost loop
    Aiter.loadStride(2);
    Biter.loadStride(2);
    Citer.loadStride(2);
    Diter.loadStride(2);
    Eiter.loadStride(2);
    Fiter.loadStride(2);
    Giter.loadStride(2);
    Hiter.loadStride(2);
    Iiter.loadStride(2);
    Jiter.loadStride(2);
    Kiter.loadStride(2);

    for (int i=lbound0; i <= ubound0; ++i)
    {
      for (int j=lbound1; j <= ubound1; ++j)
      {
        Aiter.moveTo(i,j,lbound2);
        Biter.moveTo(i,j,lbound2);
        Citer.moveTo(i,j,lbound2);
        Diter.moveTo(i,j,lbound2);
        Eiter.moveTo(i,j,lbound2);
        Fiter.moveTo(i,j,lbound2);
        Giter.moveTo(i,j,lbound2);
        Hiter.moveTo(i,j,lbound2);
        Iiter.moveTo(i,j,lbound2);
        Jiter.moveTo(i,j,lbound2);
        Kiter.moveTo(i,j,lbound2);

        for (int k=lbound2; k <= ubound2; ++k)
        {
            stencil.apply(Aiter, Biter, Citer, Diter, Eiter, Fiter, Giter,
                Hiter, Iiter, Jiter, Kiter);

            Aiter.advance();
            Biter.advance();
            Citer.advance();
            Diter.advance();
            Eiter.advance();
            Fiter.advance();
            Giter.advance();
            Hiter.advance();
            Iiter.advance();
            Jiter.advance();
            Kiter.advance();
        }
      }
    }
}

/*
 * This version applies a stencil to a set of 2D arrays.  Up to 11 arrays
 * may be used.  Any unused arrays are turned into dummyArray objects.
 * Operations on dummyArray objects are translated into no-ops.
 */
template<class T_stencil, class T_numtype1, class T_array2,
    class T_array3, class T_array4, class T_array5, class T_array6,
    class T_array7, class T_array8, class T_array9, class T_array10,
    class T_array11>
void applyStencil_imp(const T_stencil& stencil, Array<T_numtype1,2>& A,
    T_array2& B, T_array3& C, T_array4& D, T_array5& E, T_array6& F, 
    T_array7& G, T_array8& H, T_array9& I, T_array10& J, T_array11& K)
{
    checkShapes(A,B,C,D,E,F,G,H,I,J,K);

    // Determine stencil extent
    TinyVector<int,2> minb, maxb;
    getStencilExtent(minb, maxb, stencil, A, B, C, D, E, F, G, H, I, J, K);

    // Now determine the subdomain over which the stencil
    // can be applied without worrying about overrunning the
    // boundaries of the array
    int stencil_lbound0 = minb(0);
    int stencil_lbound1 = minb(1);

    int stencil_ubound0 = maxb(0);
    int stencil_ubound1 = maxb(1);

    int lbound0 = minmax::max(A.lbound(0), A.lbound(0) - stencil_lbound0);
    int lbound1 = minmax::max(A.lbound(1), A.lbound(1) - stencil_lbound1);

    int ubound0 = minmax::min(A.ubound(0), A.ubound(0) - stencil_ubound0);
    int ubound1 = minmax::min(A.ubound(1), A.ubound(1) - stencil_ubound1);

#if 0
    cout << "Stencil bounds are:" << endl
     << lbound0 << '\t' << ubound0 << endl
     << lbound1 << '\t' << ubound1 << endl;
#endif 

    // Now do the actual loop
    FastArrayIterator<T_numtype1,2> Aiter(A);
    _bz_typename T_array2::T_iterator Biter(B);
    _bz_typename T_array3::T_iterator Citer(C);
    _bz_typename T_array4::T_iterator Diter(D);
    _bz_typename T_array5::T_iterator Eiter(E);
    _bz_typename T_array6::T_iterator Fiter(F);
    _bz_typename T_array7::T_iterator Giter(G);
    _bz_typename T_array8::T_iterator Hiter(H);
    _bz_typename T_array9::T_iterator Iiter(I);
    _bz_typename T_array10::T_iterator Jiter(J);
    _bz_typename T_array11::T_iterator Kiter(K);

    // Load the strides for the innermost loop
    Aiter.loadStride(1);
    Biter.loadStride(1);
    Citer.loadStride(1);
    Diter.loadStride(1);
    Eiter.loadStride(1);
    Fiter.loadStride(1);
    Giter.loadStride(1);
    Hiter.loadStride(1);
    Iiter.loadStride(1);
    Jiter.loadStride(1);
    Kiter.loadStride(1);

    for (int i=lbound0; i <= ubound0; ++i)
    {
        Aiter.moveTo(i,lbound1);
        Biter.moveTo(i,lbound1);
        Citer.moveTo(i,lbound1);
        Diter.moveTo(i,lbound1);
        Eiter.moveTo(i,lbound1);
        Fiter.moveTo(i,lbound1);
        Giter.moveTo(i,lbound1);
        Hiter.moveTo(i,lbound1);
        Iiter.moveTo(i,lbound1);
        Jiter.moveTo(i,lbound1);
        Kiter.moveTo(i,lbound1);

        for (int k=lbound1; k <= ubound1; ++k)
        {
            stencil.apply(Aiter, Biter, Citer, Diter, Eiter, Fiter, Giter,
                Hiter, Iiter, Jiter, Kiter);

            Aiter.advance();
            Biter.advance();
            Citer.advance();
            Diter.advance();
            Eiter.advance();
            Fiter.advance();
            Giter.advance();
            Hiter.advance();
            Iiter.advance();
            Jiter.advance();
            Kiter.advance();
        }
    }
}

/*
 * This version applies a stencil to a set of 1D arrays.  Up to 11 arrays
 * may be used.  Any unused arrays are turned into dummyArray objects.
 * Operations on dummyArray objects are translated into no-ops.
 */
template<class T_stencil, class T_numtype1, class T_array2,
    class T_array3, class T_array4, class T_array5, class T_array6,
    class T_array7, class T_array8, class T_array9, class T_array10,
    class T_array11>
void applyStencil_imp(const T_stencil& stencil, Array<T_numtype1,1>& A,
    T_array2& B, T_array3& C, T_array4& D, T_array5& E, T_array6& F, 
    T_array7& G, T_array8& H, T_array9& I, T_array10& J, T_array11& K)
{
    checkShapes(A,B,C,D,E,F,G,H,I,J,K);

    // Determine stencil extent
    TinyVector<int,1> minb, maxb;
    getStencilExtent(minb, maxb, stencil, A, B, C, D, E, F, G, H, I, J, K);

    // Now determine the subdomain over which the stencil
    // can be applied without worrying about overrunning the
    // boundaries of the array
    int stencil_lbound0 = minb(0);
    int stencil_ubound0 = maxb(0);

    int lbound0 = minmax::max(A.lbound(0), A.lbound(0) - stencil_lbound0);
    int ubound0 = minmax::min(A.ubound(0), A.ubound(0) - stencil_ubound0);

#if 0
    cout << "Stencil bounds are:" << endl
     << lbound0 << '\t' << ubound0 << endl;
#endif

    // Now do the actual loop
    FastArrayIterator<T_numtype1,1> Aiter(A);
    _bz_typename T_array2::T_iterator Biter(B);
    _bz_typename T_array3::T_iterator Citer(C);
    _bz_typename T_array4::T_iterator Diter(D);
    _bz_typename T_array5::T_iterator Eiter(E);
    _bz_typename T_array6::T_iterator Fiter(F);
    _bz_typename T_array7::T_iterator Giter(G);
    _bz_typename T_array8::T_iterator Hiter(H);
    _bz_typename T_array9::T_iterator Iiter(I);
    _bz_typename T_array10::T_iterator Jiter(J);
    _bz_typename T_array11::T_iterator Kiter(K);

    // Load the strides for the innermost loop
    Aiter.loadStride(0);
    Biter.loadStride(0);
    Citer.loadStride(0);
    Diter.loadStride(0);
    Eiter.loadStride(0);
    Fiter.loadStride(0);
    Giter.loadStride(0);
    Hiter.loadStride(0);
    Iiter.loadStride(0);
    Jiter.loadStride(0);
    Kiter.loadStride(0);

    // Patch from Derrick Bass
    Aiter.moveTo(lbound0);
    Biter.moveTo(lbound0);
    Citer.moveTo(lbound0);
    Diter.moveTo(lbound0);
    Eiter.moveTo(lbound0);
    Fiter.moveTo(lbound0);
    Giter.moveTo(lbound0);
    Hiter.moveTo(lbound0);
    Iiter.moveTo(lbound0);
    Jiter.moveTo(lbound0);
    Kiter.moveTo(lbound0);

    for (int i=lbound0; i <= ubound0; ++i)
    {
        stencil.apply(Aiter, Biter, Citer, Diter, Eiter, Fiter, Giter,
            Hiter, Iiter, Jiter, Kiter);

        Aiter.advance();
        Biter.advance();
        Citer.advance();
        Diter.advance();
        Eiter.advance();
        Fiter.advance();
        Giter.advance();
        Hiter.advance();
        Iiter.advance();
        Jiter.advance();
        Kiter.advance();
    }
}

/*
 * These 11 versions of applyStencil handle from 1 to 11 array parameters.
 * They pad their argument list with enough dummyArray objects to call
 * applyStencil_imp with 11 array parameters.
 */
template<class T_stencil, class T_numtype1, int N_rank>
inline void applyStencil(const T_stencil& stencil, Array<T_numtype1,N_rank>& A)
{
    applyStencil_imp(stencil, A, _dummyArray, _dummyArray,
        _dummyArray, _dummyArray, _dummyArray, _dummyArray,
        _dummyArray, _dummyArray, _dummyArray, _dummyArray);
}

template<class T_stencil, class T_numtype1, int N_rank, class T_array2>
inline void applyStencil(const T_stencil& stencil, Array<T_numtype1,N_rank>& A,
    T_array2& B)
{
    applyStencil_imp(stencil, A, B, _dummyArray, _dummyArray,
        _dummyArray, _dummyArray, _dummyArray, _dummyArray,
        _dummyArray, _dummyArray, _dummyArray);
}

template<class T_stencil, class T_numtype1, int N_rank, class T_array2,
    class T_array3>
inline void applyStencil(const T_stencil& stencil, Array<T_numtype1,N_rank>& A,
    T_array2& B, T_array3& C)
{
    applyStencil_imp(stencil, A, B, C, _dummyArray, _dummyArray,
        _dummyArray, _dummyArray, _dummyArray, _dummyArray, _dummyArray,
        _dummyArray);
}

template<class T_stencil, class T_numtype1, int N_rank, class T_array2,
    class T_array3, class T_array4>
inline void applyStencil(const T_stencil& stencil, Array<T_numtype1,N_rank>& A,
    T_array2& B, T_array3& C, T_array4& D)
{
    applyStencil_imp(stencil, A, B, C, D, _dummyArray, _dummyArray,
        _dummyArray, _dummyArray, _dummyArray, _dummyArray, _dummyArray);
}

template<class T_stencil, class T_numtype1, int N_rank, class T_array2,
    class T_array3, class T_array4, class T_array5>
inline void applyStencil(const T_stencil& stencil, Array<T_numtype1,N_rank>& A,
   T_array2& B, T_array3& C, T_array4& D, T_array5& E)
{
    applyStencil_imp(stencil, A, B, C, D, E, _dummyArray,
        _dummyArray, _dummyArray, _dummyArray, _dummyArray, _dummyArray);
}

template<class T_stencil, class T_numtype1, int N_rank, class T_array2,
    class T_array3, class T_array4, class T_array5, class T_array6>
inline void applyStencil(const T_stencil& stencil, Array<T_numtype1,N_rank>& A,
   T_array2& B, T_array3& C, T_array4& D, T_array5& E, T_array6& F)
{
    applyStencil_imp(stencil, A, B, C, D, E, F,
        _dummyArray, _dummyArray, _dummyArray, _dummyArray, _dummyArray);
}

template<class T_stencil, class T_numtype1, int N_rank, class T_array2,
    class T_array3, class T_array4, class T_array5, class T_array6,
    class T_array7>
inline void applyStencil(const T_stencil& stencil, Array<T_numtype1,N_rank>& A,
   T_array2& B, T_array3& C, T_array4& D, T_array5& E, T_array6& F,
   T_array7& G)
{
    applyStencil_imp(stencil, A, B, C, D, E, F, G,
        _dummyArray, _dummyArray, _dummyArray, _dummyArray);
}

template<class T_stencil, class T_numtype1, int N_rank, class T_array2,
    class T_array3, class T_array4, class T_array5, class T_array6,
    class T_array7, class T_array8>
inline void applyStencil(const T_stencil& stencil, Array<T_numtype1,N_rank>& A,
   T_array2& B, T_array3& C, T_array4& D, T_array5& E, T_array6& F,
   T_array7& G, T_array8& H)
{
    applyStencil_imp(stencil, A, B, C, D, E, F, G, H,
        _dummyArray, _dummyArray, _dummyArray);
}

template<class T_stencil, class T_numtype1, int N_rank, class T_array2,
    class T_array3, class T_array4, class T_array5, class T_array6,
    class T_array7, class T_array8, class T_array9>
inline void applyStencil(const T_stencil& stencil, Array<T_numtype1,N_rank>& A,
   T_array2& B, T_array3& C, T_array4& D, T_array5& E, T_array6& F,
   T_array7& G, T_array8& H, T_array9& I)
{
    applyStencil_imp(stencil, A, B, C, D, E, F, G, H, I,
        _dummyArray, _dummyArray);
}

template<class T_stencil, class T_numtype1, int N_rank, class T_array2,
    class T_array3, class T_array4, class T_array5, class T_array6,
    class T_array7, class T_array8, class T_array9, class T_array10>
inline void applyStencil(const T_stencil& stencil, Array<T_numtype1,N_rank>& A,
   T_array2& B, T_array3& C, T_array4& D, T_array5& E, T_array6& F,
   T_array7& G, T_array8& H, T_array9& I, T_array10& J)
{
    applyStencil_imp(stencil, A, B, C, D, E, F, G, H, I, J,
        _dummyArray);
}

template<class T_stencil, class T_numtype1, int N_rank, class T_array2,
    class T_array3, class T_array4, class T_array5, class T_array6,
    class T_array7, class T_array8, class T_array9, class T_array10,
    class T_array11>
inline void applyStencil(const T_stencil& stencil, Array<T_numtype1,N_rank>& A,
   T_array2& B, T_array3& C, T_array4& D, T_array5& E, T_array6& F,
   T_array7& G, T_array8& H, T_array9& I, T_array10& J, T_array11& K)
{
    applyStencil_imp(stencil, A, B, C, D, E, F, G, H, I, J, K);
}

BZ_NAMESPACE_END

#endif // BZ_ARRAYSTENCIL_CC

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