// Calculate the bond angle between three atoms
Angle calculateBondAngle(const Atom& a1, const Atom& a2, const Atom& a3)
throw(Exception::IllegalPosition)
{
// two atoms can't have the same position
if (a1.getPosition() == a2.getPosition() ||
a3.getPosition() == a2.getPosition())
{
throw(Exception::IllegalPosition(__FILE__, __LINE__, a2.getPosition().x,
a2.getPosition().y, a2.getPosition().z));
}
Vector3 a12(a1.getPosition() - a2.getPosition());
Vector3 a23(a3.getPosition() - a2.getPosition());
a12.normalize();
a23.normalize();
float scalar_product = a12 * a23;
if (scalar_product > 1.0)
{
scalar_product = 1.0;
}
if (scalar_product < -1.0)
{
scalar_product = -1.0;
}
Angle a(acos(scalar_product));
return a;
}
void runtest(size_t n)
{
std::vector<char> a1(n);
std::vector<char> a11(n);
std::vector<char> a12(n);
std::vector<char> a21(n);
std::vector<char> a22(n);
memset(&a1[0], 0, n * sizeof(char));
auto func = [&] (char v, char *p1, char *p2) {
volatile char *p = &a1[0];
for (size_t i = 0;i < n;i++) {
f(&p[i], v, &p1[i], &p2[i]);
}
};
std::thread t1(func, (char)1, &a11[0], &a12[0]);
std::thread t2(func, (char)2, &a21[0], &a22[0]);
t1.join();
t2.join();
for (size_t i = 0;i < n;i++) {
assert(a1[i] == 1 || a1[i] == 2);
if (a1[i] == 1) {
check(1, 2, a11[i], a12[i], a21[i], a22[i]);
}
else {
assert(a1[i] == 2);
check(2, 1, a21[i], a22[i], a11[i], a12[i]);
}
}
}
void level_three()
{
vector<DPipe> DirectPipes(13);
vector<DoublePipe> DoublePipes(13);
vector<CrossPipe> CrossPipes(2);
DPipe a0(50,SCREEN_HEIGHT-50,100,40);
DoublePipe b0(150,SCREEN_HEIGHT-50,70,40);
DPipe a1(150,SCREEN_HEIGHT-150,100,40);
DoublePipe b1(150,SCREEN_HEIGHT-250,70,40);
DPipe a2(250,SCREEN_HEIGHT-350,100,40);
DoublePipe b2(350,SCREEN_HEIGHT-250,70,40);
DPipe a3(350,SCREEN_HEIGHT-350,100,40);
DPipe a4(350,SCREEN_HEIGHT-150,100,40);
DoublePipe b3(250,SCREEN_HEIGHT-450,70,40);
DoublePipe b4(350,SCREEN_HEIGHT-450,70,40);
CrossPipe c0(250,SCREEN_HEIGHT-250,100,40);
DPipe a5(550,SCREEN_HEIGHT-50,100,40);
DoublePipe b5(250,SCREEN_HEIGHT-150,70,40);
DoublePipe b6(450,SCREEN_HEIGHT-50,70,40);
DoublePipe b7(650,SCREEN_HEIGHT-150,70,40);
DPipe a6(550,SCREEN_HEIGHT-50,100,40);
DPipe a7(550,SCREEN_HEIGHT-150,100,40);
DoublePipe b8(750,SCREEN_HEIGHT-50,70,40);
DPipe a8(550,SCREEN_HEIGHT-250,100,40);
DoublePipe b9(750,SCREEN_HEIGHT-350,70,40);
CrossPipe c1(450,SCREEN_HEIGHT-150,100,40);
DoublePipe b10(350,SCREEN_HEIGHT-450,70,40);
DPipe a9(750,SCREEN_HEIGHT-150,100,40);
DPipe a10(750,SCREEN_HEIGHT-250,100,40);
DoublePipe b11(450,SCREEN_HEIGHT-250,70,40);
DoublePipe b12(650,SCREEN_HEIGHT-250,70,40);
DPipe a11(650,SCREEN_HEIGHT-50,100,40);
DPipe a12(850,SCREEN_HEIGHT-350,100,40);
DirectPipes[0] = a0; DoublePipes[0] = b0;
DirectPipes[1] = a1; DoublePipes[1] = b1;
DirectPipes[2] = a2; DoublePipes[2] = b2;
DirectPipes[3] = a3; DoublePipes[3] = b3;
DirectPipes[4] = a4; DoublePipes[4] = b4;
DirectPipes[5] = a5; DoublePipes[5] = b5;
DirectPipes[6] = a6; DoublePipes[6] = b6;
DirectPipes[7] = a7; DoublePipes[7] = b7;
DirectPipes[8] = a8; DoublePipes[8] = b8;
DirectPipes[9] = a9; DoublePipes[9] = b9;
DirectPipes[10] = a10; DoublePipes[10] = b10;
DirectPipes[11] = a11; DoublePipes[11] = b11;
DirectPipes[12] = a12; DoublePipes[12] = b12;
CrossPipes[0] = c0; CrossPipes[1] = c1;
Water a(20,SCREEN_HEIGHT-50,40,40);
}
// Calculate the torsion angle between four atoms
Angle calculateTorsionAngle(const Atom& a1, const Atom& a2, const Atom& a3, const Atom& a4)
throw(Exception::IllegalPosition)
{
Vector3 a12(a2.getPosition() - a1.getPosition());
Vector3 a23(a3.getPosition() - a2.getPosition());
Vector3 a34(a4.getPosition() - a3.getPosition());
Vector3 n12(a12 % a23);
Vector3 n34(a23 % a34);
if (n12 == Vector3::getZero() ||
n34 == Vector3::getZero())
{
throw(Exception::IllegalPosition(__FILE__, __LINE__, 0, 0, 0));
}
n12.normalize();
n34.normalize();
Vector3 cross_n12_n34(n12 % n34);
float direction = cross_n12_n34 * a23;
float scalar_product = n12 * n34;
if (scalar_product > 1.0)
{
scalar_product = 1.0;
}
if (scalar_product < -1.0)
{
scalar_product = -1.0;
}
Angle a(acos(scalar_product));
if (direction < 0.0)
{
a = -1.0 * (float)a;
}
return a;
}
int main(int argc,char **argv)
{
setlocale(LC_ALL,"RUSSIAN");
SDL_DisplayMode displayMode;
if (SDL_Init(SDL_INIT_EVERYTHING) != 0)
{
cout << "SDL_Init Error: " << SDL_GetError() << endl;
return 1;
}
int request = SDL_GetDesktopDisplayMode(0,&displayMode);
SDL_Window *win = SDL_CreateWindow("Trubi", 300, 300,800, 800, SDL_WINDOW_SHOWN);
if (win == nullptr)
{
cout << "SDL_CreateWindow Error: " << SDL_GetError() << endl;
return 1;
}
SDL_Renderer *ren = SDL_CreateRenderer(win, -1, SDL_RENDERER_ACCELERATED | SDL_RENDERER_PRESENTVSYNC);
if (ren == nullptr)
{
cout << "SDL_CreateRenderer Error: " << SDL_GetError() << endl;
return 1;
}
vector<DPipe> DPIPES(13);
vector<DoublePipe> DOUBPIPES(6);
DPipe background(400,400,800,800);
DPipe a0(70,300,100,40);
DPipe a1(170,300,100,40);
DPipe a2(270,300,100,40);
DPipe a3(370,400,100,40);
DPipe a4(370,500,100,40);
DPipe a5(470,600,100,40);
DPipe a6(570,600,100,40);
DPipe a7(670,500,100,40);
DPipe a8(670,400,100,40);
DPipe a9(370,200,100,40);
DPipe a10(470,100,100,40);
DPipe a11(570,100,100,40);
DPipe a12(670,200,100,40);
DPipe kletka(370,300,100,100);
DoublePipe b0(370,300,70,40);
DoublePipe b1(370,600,70,40);
DoublePipe b2(670,600,70,40);
DoublePipe b3(670,300,70,40);
DoublePipe b4(370,100,70,40);
DoublePipe b5(670,100,70,40);
DPIPES[0]=a0;
DPIPES[1]=a1;
DPIPES[2]=a2;
DPIPES[3]=a3;
DPIPES[4]=a4;
DPIPES[5]=a5;
DPIPES[6]=a6;
DPIPES[7]=a7;
DPIPES[8]=a8;
DPIPES[9]=a9;
DPIPES[10]=a10;
DPIPES[11]=a11;
DPIPES[12]=a12;
DOUBPIPES[0]=b0;
DOUBPIPES[1]=b1;
DOUBPIPES[2]=b2;
DOUBPIPES[3]=b3;
DOUBPIPES[4]=b4;
DOUBPIPES[5]=b5;
SDL_RenderClear(ren);
background.default_create(ren,"newbackground.bmp");
for(int i=0;i<DPIPES.size();++i)
{
DPIPES[i].default_create(ren,"text1.bmp");
}
for(int i=0;i<DOUBPIPES.size();++i)
{
DOUBPIPES[i].default_create1(ren,"double1.bmp","double2.bmp");
}
SDL_RenderPresent(ren);
bool quit=false;
while(!quit)
{
while(SDL_PollEvent(&event))
{
SDL_PumpEvents();
if(event.type == SDL_QUIT)
quit=true;
else if(event.type==SDL_MOUSEBUTTONDOWN && event.button.button==SDL_BUTTON_LEFT)
{
for(int i=0;i<DPIPES.size();++i)
{
if(DPIPES[i].ismouse())
{
SDL_RenderClear(ren);
background.default_create(ren,"newbackground.bmp");
nochangesDoub(ren,DOUBPIPES);
somechanges(ren,DPIPES,i);
}
}
for(int i=0;i<DOUBPIPES.size();++i)
{
if(DOUBPIPES[i].ismouse())
{
SDL_RenderClear(ren);
background.default_create(ren,"newbackground.bmp");
nochanges(ren,DPIPES);
somechangesDoub(ren,DOUBPIPES,i);
}
}
}
}
}
return 1;
}
inline void
PanelHouseholder( DistMatrix<F>& A, DistMatrix<F,MD,STAR>& t )
{
#ifndef RELEASE
CallStackEntry entry("lq::PanelHouseholder");
if( A.Grid() != t.Grid() )
LogicError("{A,t} must be distributed over the same grid");
if( t.Height() != Min(A.Height(),A.Width()) || t.Width() != 1 )
LogicError
("t must be a vector of height equal to the minimum dimension of A");
if( !t.AlignedWithDiagonal( A, 0 ) )
LogicError("t must be aligned with A's main diagonal");
#endif
const Grid& g = A.Grid();
// Matrix views
DistMatrix<F>
ATL(g), ATR(g), A00(g), a01(g), A02(g), aTopRow(g), ABottomPan(g),
ABL(g), ABR(g), a10(g), alpha11(g), a12(g),
A20(g), a21(g), A22(g);
DistMatrix<F,MD,STAR>
tT(g), t0(g),
tB(g), tau1(g),
t2(g);
// Temporary distributions
DistMatrix<F> aTopRowConj(g);
DistMatrix<F,STAR,MR > aTopRowConj_STAR_MR(g);
DistMatrix<F,MC, STAR> z_MC_STAR(g);
PartitionDownDiagonal
( A, ATL, ATR,
ABL, ABR, 0 );
PartitionDown
( t, tT,
tB, 0 );
while( ATL.Height() < A.Height() && ATL.Width() < A.Width() )
{
RepartitionDownDiagonal
( ATL, /**/ ATR, A00, /**/ a01, A02,
/*************/ /**********************/
/**/ a10, /**/ alpha11, a12,
ABL, /**/ ABR, A20, /**/ a21, A22, 1 );
RepartitionDown
( tT, t0,
/**/ /****/
tau1,
tB, t2, 1 );
View1x2( aTopRow, alpha11, a12 );
View1x2( ABottomPan, a21, A22 );
aTopRowConj_STAR_MR.AlignWith( ABottomPan );
z_MC_STAR.AlignWith( ABottomPan );
//--------------------------------------------------------------------//
// Compute the Householder reflector
const F tau = Reflector( alpha11, a12 );
tau1.Set( 0, 0, tau );
// Apply the Householder reflector
const bool myDiagonalEntry = ( g.Row() == alpha11.ColAlignment() &&
g.Col() == alpha11.RowAlignment() );
F alpha = 0;
if( myDiagonalEntry )
{
alpha = alpha11.GetLocal(0,0);
alpha11.SetLocal(0,0,1);
}
Conjugate( aTopRow, aTopRowConj );
aTopRowConj_STAR_MR = aTopRowConj;
Zeros( z_MC_STAR, ABottomPan.Height(), 1 );
LocalGemv
( NORMAL, F(1), ABottomPan, aTopRowConj_STAR_MR, F(0), z_MC_STAR );
z_MC_STAR.SumOverRow();
Ger
( -Conj(tau),
z_MC_STAR.LockedMatrix(),
aTopRowConj_STAR_MR.LockedMatrix(),
ABottomPan.Matrix() );
if( myDiagonalEntry )
alpha11.SetLocal(0,0,alpha);
//--------------------------------------------------------------------//
SlidePartitionDown
( tT, t0,
tau1,
/**/ /****/
tB, t2 );
SlidePartitionDownDiagonal
( ATL, /**/ ATR, A00, a01, /**/ A02,
/**/ a10, alpha11, /**/ a12,
/*************/ /**********************/
ABL, /**/ ABR, A20, a21, /**/ A22 );
}
}
void Foam::threePhaseInterfaceProperties::correctContactAngle
(
surfaceVectorField::GeometricBoundaryField& nHatb
) const
{
const volScalarField::GeometricBoundaryField& alpha1 =
mixture_.alpha1().boundaryField();
const volScalarField::GeometricBoundaryField& alpha2 =
mixture_.alpha2().boundaryField();
const volScalarField::GeometricBoundaryField& alpha3 =
mixture_.alpha3().boundaryField();
const volVectorField::GeometricBoundaryField& U =
mixture_.U().boundaryField();
const fvMesh& mesh = mixture_.U().mesh();
const fvBoundaryMesh& boundary = mesh.boundary();
forAll(boundary, patchi)
{
if (isA<alphaContactAngleFvPatchScalarField>(alpha1[patchi]))
{
const alphaContactAngleFvPatchScalarField& a2cap =
refCast<const alphaContactAngleFvPatchScalarField>
(alpha2[patchi]);
const alphaContactAngleFvPatchScalarField& a3cap =
refCast<const alphaContactAngleFvPatchScalarField>
(alpha3[patchi]);
scalarField twoPhaseAlpha2(max(a2cap, scalar(0)));
scalarField twoPhaseAlpha3(max(a3cap, scalar(0)));
scalarField sumTwoPhaseAlpha
(
twoPhaseAlpha2 + twoPhaseAlpha3 + SMALL
);
twoPhaseAlpha2 /= sumTwoPhaseAlpha;
twoPhaseAlpha3 /= sumTwoPhaseAlpha;
fvsPatchVectorField& nHatp = nHatb[patchi];
scalarField theta
(
convertToRad
* (
twoPhaseAlpha2*(180 - a2cap.theta(U[patchi], nHatp))
+ twoPhaseAlpha3*(180 - a3cap.theta(U[patchi], nHatp))
)
);
vectorField nf(boundary[patchi].nf());
// Reset nHatPatch to correspond to the contact angle
scalarField a12(nHatp & nf);
scalarField b1(cos(theta));
scalarField b2(nHatp.size());
forAll(b2, facei)
{
b2[facei] = cos(acos(a12[facei]) - theta[facei]);
}
scalarField det(1.0 - a12*a12);
scalarField a((b1 - a12*b2)/det);
scalarField b((b2 - a12*b1)/det);
nHatp = a*nf + b*nHatp;
nHatp /= (mag(nHatp) + deltaN_.value());
}
}
inline void UnblockedBidiagU
( DistMatrix<Complex<R> >& A,
DistMatrix<Complex<R>,MD,STAR>& tP,
DistMatrix<Complex<R>,MD,STAR>& tQ )
{
#ifndef RELEASE
PushCallStack("BidiagU");
#endif
const int tPHeight = std::max(A.Width()-1,0);
const int tQHeight = A.Width();
#ifndef RELEASE
if( A.Grid() != tP.Grid() || tP.Grid() != tQ.Grid() )
throw std::logic_error("Process grids do not match");
if( A.Height() < A.Width() )
throw std::logic_error("A must be at least as tall as it is wide");
if( tP.Viewing() && (tP.Height() != tPHeight || tP.Width() != 1) )
throw std::logic_error("tP is the wrong height");
if( tQ.Viewing() && (tQ.Height() != tQHeight || tQ.Width() != 1) )
throw std::logic_error("tQ is the wrong height");
#endif
typedef Complex<R> C;
const Grid& g = A.Grid();
if( !tP.Viewing() )
tP.ResizeTo( tPHeight, 1 );
if( !tQ.Viewing() )
tQ.ResizeTo( tQHeight, 1 );
// Matrix views
DistMatrix<C>
ATL(g), ATR(g), A00(g), a01(g), A02(g), alpha12L(g), a12R(g),
ABL(g), ABR(g), a10(g), alpha11(g), a12(g), aB1(g), AB2(g),
A20(g), a21(g), A22(g);
// Temporary matrices
DistMatrix<C,STAR,MR > a12_STAR_MR(g);
DistMatrix<C,MC, STAR> aB1_MC_STAR(g);
DistMatrix<C,MR, STAR> x12Adj_MR_STAR(g);
DistMatrix<C,MC, STAR> w21_MC_STAR(g);
PushBlocksizeStack( 1 );
PartitionDownDiagonal
( A, ATL, ATR,
ABL, ABR, 0 );
while( ATL.Width() < A.Width() )
{
RepartitionDownDiagonal
( ATL, /**/ ATR, A00, /**/ a01, A02,
/*************/ /**********************/
/**/ a10, /**/ alpha11, a12,
ABL, /**/ ABR, A20, /**/ a21, A22 );
View2x1
( aB1, alpha11,
a21 );
View2x1
( AB2, a12,
A22 );
aB1_MC_STAR.AlignWith( aB1 );
a12_STAR_MR.AlignWith( a12 );
x12Adj_MR_STAR.AlignWith( AB2 );
w21_MC_STAR.AlignWith( A22 );
Zeros( a12.Width(), 1, x12Adj_MR_STAR );
Zeros( a21.Height(), 1, w21_MC_STAR );
const bool thisIsMyRow = ( g.Row() == alpha11.ColAlignment() );
const bool thisIsMyCol = ( g.Col() == alpha11.RowAlignment() );
const bool nextIsMyCol = ( g.Col() == a12.RowAlignment() );
//--------------------------------------------------------------------//
// Find tauQ, u, and epsilonQ such that
// I - conj(tauQ) | 1 | | 1, u^H | | alpha11 | = | epsilonQ |
// | u | | a21 | | 0 |
const C tauQ = Reflector( alpha11, a21 );
tQ.Set(A00.Height(),0,tauQ );
C epsilonQ=0;
if( thisIsMyCol && thisIsMyRow )
epsilonQ = alpha11.GetLocal(0,0);
// Set aB1 = | 1 | and form x12^H := (aB1^H AB2)^H = AB2^H aB1
// | u |
alpha11.Set(0,0,C(1));
aB1_MC_STAR = aB1;
internal::LocalGemv
( ADJOINT, C(1), AB2, aB1_MC_STAR, C(0), x12Adj_MR_STAR );
x12Adj_MR_STAR.SumOverCol();
// Update AB2 := AB2 - conj(tauQ) aB1 x12
// = AB2 - conj(tauQ) aB1 aB1^H AB2
// = (I - conj(tauQ) aB1 aB1^H) AB2
internal::LocalGer( -Conj(tauQ), aB1_MC_STAR, x12Adj_MR_STAR, AB2 );
// Put epsilonQ back instead of the temporary value, 1
if( thisIsMyCol && thisIsMyRow )
alpha11.SetLocal(0,0,epsilonQ);
if( A22.Width() != 0 )
{
// Due to the deficiencies in the BLAS ?gemv routines, this section
// is easier if we temporarily conjugate a12
Conjugate( a12 );
// Expose the subvector we seek to zero, a12R
PartitionRight( a12, alpha12L, a12R );
// Find tauP, v, and epsilonP such that
// I - conj(tauP) | 1 | | 1, v^H | | alpha12L | = | epsilonP |
// | v | | a12R^T | | 0 |
const C tauP = Reflector( alpha12L, a12R );
tP.Set(A00.Height(),0,tauP);
C epsilonP=0;
if( nextIsMyCol && thisIsMyRow )
epsilonP = alpha12L.GetLocal(0,0);
// Set a12^T = | 1 | and form w21 := A22 a12^T = A22 | 1 |
// | v | | v |
alpha12L.Set(0,0,C(1));
a12_STAR_MR = a12;
internal::LocalGemv
( NORMAL, C(1), A22, a12_STAR_MR, C(0), w21_MC_STAR );
w21_MC_STAR.SumOverRow();
// A22 := A22 - tauP w21 conj(a12)
// = A22 - tauP A22 a12^T conj(a12)
// = A22 (I - tauP a12^T conj(a12))
// = A22 conj(I - conj(tauP) a12^H a12)
// which compensates for the fact that the reflector was generated
// on the conjugated a12.
internal::LocalGer( -tauP, w21_MC_STAR, a12_STAR_MR, A22 );
// Put epsilonP back instead of the temporary value, 1
if( nextIsMyCol && thisIsMyRow )
alpha12L.SetLocal(0,0,epsilonP);
// Undue the temporary conjugation
Conjugate( a12 );
}
//--------------------------------------------------------------------//
aB1_MC_STAR.FreeAlignments();
a12_STAR_MR.FreeAlignments();
x12Adj_MR_STAR.FreeAlignments();
w21_MC_STAR.FreeAlignments();
SlidePartitionDownDiagonal
( ATL, /**/ ATR, A00, a01, /**/ A02,
/**/ a10, alpha11, /**/ a12,
/*************/ /**********************/
ABL, /**/ ABR, A20, a21, /**/ A22 );
}
PopBlocksizeStack();
#ifndef RELEASE
PopCallStack();
#endif
}
inline void UnblockedBidiagU( DistMatrix<R>& A )
{
#ifndef RELEASE
PushCallStack("bidiag::UnblockedBidiagU");
if( A.Height() < A.Width() )
throw std::logic_error("A must be at least as tall as it is wide");
#endif
const Grid& g = A.Grid();
// Matrix views
DistMatrix<R>
ATL(g), ATR(g), A00(g), a01(g), A02(g), alpha12L(g), a12R(g),
ABL(g), ABR(g), a10(g), alpha11(g), a12(g), aB1(g), AB2(g),
A20(g), a21(g), A22(g);
// Temporary matrices
DistMatrix<R,STAR,MR > a12_STAR_MR(g);
DistMatrix<R,MC, STAR> aB1_MC_STAR(g);
DistMatrix<R,MR, STAR> x12Trans_MR_STAR(g);
DistMatrix<R,MC, STAR> w21_MC_STAR(g);
PushBlocksizeStack( 1 );
PartitionDownDiagonal
( A, ATL, ATR,
ABL, ABR, 0 );
while( ATL.Width() < A.Width() )
{
RepartitionDownDiagonal
( ATL, /**/ ATR, A00, /**/ a01, A02,
/*************/ /**********************/
/**/ a10, /**/ alpha11, a12,
ABL, /**/ ABR, A20, /**/ a21, A22 );
View2x1
( aB1, alpha11,
a21 );
View2x1
( AB2, a12,
A22 );
aB1_MC_STAR.AlignWith( aB1 );
a12_STAR_MR.AlignWith( a12 );
x12Trans_MR_STAR.AlignWith( AB2 );
w21_MC_STAR.AlignWith( A22 );
Zeros( a12.Width(), 1, x12Trans_MR_STAR );
Zeros( a21.Height(), 1, w21_MC_STAR );
const bool thisIsMyRow = ( g.Row() == alpha11.ColAlignment() );
const bool thisIsMyCol = ( g.Col() == alpha11.RowAlignment() );
const bool nextIsMyCol = ( g.Col() == a12.RowAlignment() );
//--------------------------------------------------------------------//
// Find tauQ, u, and epsilonQ such that
// I - tauQ | 1 | | 1, u^T | | alpha11 | = | epsilonQ |
// | u | | a21 | = | 0 |
const R tauQ = Reflector( alpha11, a21 );
R epsilonQ=0;
if( thisIsMyCol && thisIsMyRow )
epsilonQ = alpha11.GetLocal(0,0);
// Set aB1 = | 1 | and form x12^T := (aB1^T AB2)^T = AB2^T aB1
// | u |
alpha11.Set(0,0,R(1));
aB1_MC_STAR = aB1;
internal::LocalGemv
( TRANSPOSE, R(1), AB2, aB1_MC_STAR, R(0), x12Trans_MR_STAR );
x12Trans_MR_STAR.SumOverCol();
// Update AB2 := AB2 - tauQ aB1 x12
// = AB2 - tauQ aB1 aB1^T AB2
// = (I - tauQ aB1 aB1^T) AB2
internal::LocalGer( -tauQ, aB1_MC_STAR, x12Trans_MR_STAR, AB2 );
// Put epsilonQ back instead of the temporary value, 1
if( thisIsMyCol && thisIsMyRow )
alpha11.SetLocal(0,0,epsilonQ);
if( A22.Width() != 0 )
{
// Expose the subvector we seek to zero, a12R
PartitionRight( a12, alpha12L, a12R );
// Find tauP, v, and epsilonP such that
// I - tauP | 1 | | 1, v^T | | alpha12L | = | epsilonP |
// | v | | a12R^T | = | 0 |
const R tauP = Reflector( alpha12L, a12R );
R epsilonP=0;
if( nextIsMyCol && thisIsMyRow )
epsilonP = alpha12L.GetLocal(0,0);
// Set a12^T = | 1 | and form w21 := A22 a12^T = A22 | 1 |
// | v | | v |
alpha12L.Set(0,0,R(1));
a12_STAR_MR = a12;
internal::LocalGemv
( NORMAL, R(1), A22, a12_STAR_MR, R(0), w21_MC_STAR );
w21_MC_STAR.SumOverRow();
// A22 := A22 - tauP w21 a12
// = A22 - tauP A22 a12^T a12
// = A22 (I - tauP a12^T a12)
internal::LocalGer( -tauP, w21_MC_STAR, a12_STAR_MR, A22 );
// Put epsilonP back instead of the temporary value, 1
if( nextIsMyCol && thisIsMyRow )
alpha12L.SetLocal(0,0,epsilonP);
}
//--------------------------------------------------------------------//
aB1_MC_STAR.FreeAlignments();
a12_STAR_MR.FreeAlignments();
x12Trans_MR_STAR.FreeAlignments();
w21_MC_STAR.FreeAlignments();
SlidePartitionDownDiagonal
( ATL, /**/ ATR, A00, a01, /**/ A02,
/**/ a10, alpha11, /**/ a12,
/*************/ /**********************/
ABL, /**/ ABR, A20, a21, /**/ A22 );
}
PopBlocksizeStack();
#ifndef RELEASE
PopCallStack();
#endif
}
inline void
PanelLU
( DistMatrix<F, STAR,STAR>& A,
DistMatrix<F, MC, STAR>& B,
DistMatrix<int,STAR,STAR>& p,
int pivotOffset )
{
#ifndef RELEASE
PushCallStack("internal::PanelLU");
if( A.Grid() != p.Grid() || p.Grid() != B.Grid() )
throw std::logic_error
("Matrices must be distributed over the same grid");
if( A.Width() != B.Width() )
throw std::logic_error("A and B must be the same width");
if( A.Height() != p.Height() || p.Width() != 1 )
throw std::logic_error("p must be a vector that conforms with A");
#endif
const Grid& g = A.Grid();
const int r = g.Height();
const int colShift = B.ColShift();
const int colAlignment = B.ColAlignment();
// Matrix views
DistMatrix<F,STAR,STAR>
ATL(g), ATR(g), A00(g), a01(g), A02(g),
ABL(g), ABR(g), a10(g), alpha11(g), a12(g),
A20(g), a21(g), A22(g);
DistMatrix<F,MC,STAR>
BL(g), BR(g),
B0(g), b1(g), B2(g);
const int width = A.Width();
const int numBytes = (width+1)*sizeof(F)+sizeof(int);
std::vector<byte> sendData(numBytes);
std::vector<byte> recvData(numBytes);
// Extract pointers to send and recv data
// TODO: Think of how to make this safer with respect to alignment issues
F* sendBufFloat = (F*)&sendData[0];
F* recvBufFloat = (F*)&recvData[0];
int* sendBufInt = (int*)&sendData[(width+1)*sizeof(F)];
int* recvBufInt = (int*)&recvData[(width+1)*sizeof(F)];
// Start the algorithm
PushBlocksizeStack( 1 );
PartitionDownDiagonal
( A, ATL, ATR,
ABL, ABR, 0 );
PartitionRight( B, BL, BR, 0 );
while( ATL.Height() < A.Height() )
{
RepartitionDownDiagonal
( ATL, /**/ ATR, A00, /**/ a01, A02,
/*************/ /**********************/
/**/ a10, /**/ alpha11, a12,
ABL, /**/ ABR, A20, /**/ a21, A22 );
RepartitionRight
( BL, /**/ BR,
B0, /**/ b1, B2 );
//--------------------------------------------------------------------//
const int currentRow = a01.Height();
// Store the index/value of the pivot candidate in A
F pivot = alpha11.GetLocal(0,0);
int pivotRow = currentRow;
for( int i=0; i<a21.Height(); ++i )
{
F value = a21.GetLocal(i,0);
if( FastAbs(value) > FastAbs(pivot) )
{
pivot = value;
pivotRow = currentRow + i + 1;
}
}
// Update the pivot candidate to include local data from B
for( int i=0; i<B.LocalHeight(); ++i )
{
F value = b1.GetLocal(i,0);
if( FastAbs(value) > FastAbs(pivot) )
{
pivot = value;
pivotRow = A.Height() + colShift + i*r;
}
}
// Fill the send buffer with:
// [ pivotValue | pivot row data | pivotRow ]
if( pivotRow < A.Height() )
{
sendBufFloat[0] = A.GetLocal(pivotRow,a10.Width());
const int ALDim = A.LocalLDim();
const F* ABuffer = A.LocalBuffer(pivotRow,0);
for( int j=0; j<width; ++j )
sendBufFloat[j+1] = ABuffer[j*ALDim];
}
else
{
const int localRow = ((pivotRow-A.Height())-colShift)/r;
sendBufFloat[0] = b1.GetLocal(localRow,0);
const int BLDim = B.LocalLDim();
const F* BBuffer = B.LocalBuffer(localRow,0);
for( int j=0; j<width; ++j )
sendBufFloat[j+1] = BBuffer[j*BLDim];
}
*sendBufInt = pivotRow;
// Communicate to establish the pivot information
mpi::AllReduce
( &sendData[0], &recvData[0], numBytes, PivotOp<F>(), g.ColComm() );
// Update the pivot vector
pivotRow = *recvBufInt;
p.SetLocal(currentRow,0,pivotRow+pivotOffset);
// Copy the current row into the pivot row
if( pivotRow < A.Height() )
{
const int ALDim = A.LocalLDim();
F* ASetBuffer = A.LocalBuffer(pivotRow,0);
const F* AGetBuffer = A.LocalBuffer(currentRow,0);
for( int j=0; j<width; ++j )
ASetBuffer[j*ALDim] = AGetBuffer[j*ALDim];
}
else
{
const int ownerRank = (colAlignment+(pivotRow-A.Height())) % r;
if( g.Row() == ownerRank )
{
const int localRow = ((pivotRow-A.Height())-colShift) / r;
const int ALDim = A.LocalLDim();
const int BLDim = B.LocalLDim();
F* BBuffer = B.LocalBuffer(localRow,0);
const F* ABuffer = A.LocalBuffer(currentRow,0);
for( int j=0; j<width; ++j )
BBuffer[j*BLDim] = ABuffer[j*ALDim];
}
}
// Copy the pivot row into the current row
{
F* ABuffer = A.LocalBuffer(currentRow,0);
const int ALDim = A.LocalLDim();
for( int j=0; j<width; ++j )
ABuffer[j*ALDim] = recvBufFloat[j+1];
}
// Now we can perform the update of the current panel
const F alpha = alpha11.GetLocal(0,0);
if( alpha == F(0) )
throw SingularMatrixException();
const F alpha11Inv = F(1) / alpha;
Scale( alpha11Inv, a21.LocalMatrix() );
Scale( alpha11Inv, b1.LocalMatrix() );
Geru( F(-1), a21.LocalMatrix(), a12.LocalMatrix(), A22.LocalMatrix() );
Geru( F(-1), b1.LocalMatrix(), a12.LocalMatrix(), B2.LocalMatrix() );
//--------------------------------------------------------------------//
SlidePartitionDownDiagonal
( ATL, /**/ ATR, A00, a01, /**/ A02,
/**/ a10, alpha11, /**/ a12,
/*************/ /**********************/
ABL, /**/ ABR, A20, a21, /**/ A22 );
SlidePartitionRight
( BL, /**/ BR,
B0, b1, /**/ B2 );
}
PopBlocksizeStack();
#ifndef RELEASE
PopCallStack();
#endif
}
void level_two()
{
vector<DPipe> DPIPES(44);
vector<DoublePipe> DOUBPIPES(18);
vector<CrossPipe> CROSSPIPES(3);
DPipe background(600,400,1200,800);
DPipe a0(50,750,100,40);
DPipe a1(150,650,100,40);
DPipe a2(150,550,100,40);
DPipe a3(650,450,100,40);
DPipe a4(550,550,100,40);
DPipe a5(450,350,100,40);
DPipe a6(550,250,100,40);
DPipe a7(650,250,100,40);
DPipe a8(750,350,100,40);
DPipe a9(750,450,100,40);
DPipe a10(750,550,100,40);
DPipe a11(650,650,100,40);
DPipe a12(550,650,100,40);
DPipe a13(450,650,100,40);
DPipe a14(350,550,100,40);
DPipe a15(350,350,100,40);
DPipe a16(350,250,100,40);
DPipe a17(450,150,100,40);
DPipe a18(550,150,100,40);
DPipe a19(650,150,100,40);
DPipe a20(750,150,100,40);
DPipe a21(850,250,100,40);
DPipe a22(850,350,100,40);
DPipe a23(850,450,100,40);
DPipe a24(850,550,100,40);
DPipe a25(850,650,100,40);
DPipe a26(750,750,100,40);
DPipe a27(650,750,100,40);
DPipe a28(550,750,100,40);
DPipe a29(450,750,100,40);
DPipe a30(350,750,100,40);
DPipe a31(250,650,100,40);
DPipe a32(250,550,100,40);
DPipe a33(250,350,100,40);
DPipe a34(250,250,100,40);
DPipe a35(250,150,100,40);
DPipe a36(350,50,100,40);
DPipe a37(450,50,100,40);
DPipe a38(550,50,100,40);
DPipe a39(650,50,100,40);
DPipe a40(750,50,100,40);
DPipe a41(850,50,100,40);
DPipe a42(950,150,100,40);
DPipe a43(950,250,100,40);
DoublePipe b0(150,750,70,40);
DoublePipe b1(150,450,70,40);
DoublePipe b2(550,450,70,40);
DoublePipe b3(550,350,70,40);
DoublePipe b4(650,350,70,40);
DoublePipe b5(650,550,70,40);
DoublePipe b6(450,550,70,40);
DoublePipe b7(450,250,70,40);
DoublePipe b8(750,250,70,40);
DoublePipe b9(750,650,70,40);
DoublePipe b10(350,650,70,40);
DoublePipe b11(350,150,70,40);
DoublePipe b12(850,150,70,40);
DoublePipe b13(850,750,70,40);
DoublePipe b14(250,750,70,40);
DoublePipe b15(250,50,70,40);
DoublePipe b16(950,50,70,40);
DoublePipe b17(950,350,70,40);
CrossPipe c0(250,450,100,40);
CrossPipe c1(350,450,100,40);
CrossPipe c2(450,450,100,40);
DPIPES[0]=a0;
DPIPES[1]=a1;
DPIPES[2]=a2;
DPIPES[3]=a3;
DPIPES[4]=a4;
DPIPES[5]=a5;
DPIPES[6]=a6;
DPIPES[7]=a7;
DPIPES[8]=a8;
DPIPES[9]=a9;
DPIPES[10]=a10;
DPIPES[11]=a11;
DPIPES[12]=a12;
DPIPES[13]=a13;
DPIPES[14]=a14;
DPIPES[15]=a15;
DPIPES[16]=a16;
DPIPES[17]=a17;
DPIPES[18]=a18;
DPIPES[19]=a19;
DPIPES[20]=a20;
DPIPES[21]=a21;
DPIPES[22]=a22;
DPIPES[23]=a23;
DPIPES[24]=a24;
DPIPES[25]=a25;
DPIPES[26]=a26;
DPIPES[27]=a27;
DPIPES[28]=a28;
DPIPES[29]=a29;
DPIPES[30]=a30;
DPIPES[31]=a31;
DPIPES[32]=a32;
DPIPES[33]=a33;
DPIPES[34]=a34;
DPIPES[35]=a35;
DPIPES[36]=a36;
DPIPES[37]=a37;
DPIPES[38]=a38;
DPIPES[39]=a39;
DPIPES[40]=a40;
DPIPES[41]=a41;
DPIPES[42]=a42;
DPIPES[43]=a43;
DOUBPIPES[0]=b0;
DOUBPIPES[1]=b1;
DOUBPIPES[2]=b2;
DOUBPIPES[3]=b3;
DOUBPIPES[4]=b4;
DOUBPIPES[5]=b5;
DOUBPIPES[6]=b6;
DOUBPIPES[7]=b7;
DOUBPIPES[8]=b8;
DOUBPIPES[9]=b9;
DOUBPIPES[10]=b10;
DOUBPIPES[11]=b11;
DOUBPIPES[12]=b12;
DOUBPIPES[13]=b13;
DOUBPIPES[14]=b14;
DOUBPIPES[15]=b15;
DOUBPIPES[16]=b16;
DOUBPIPES[17]=b17;
CROSSPIPES[0]=c0;
CROSSPIPES[1]=c1;
CROSSPIPES[2]=c2;
}
inline void
PanelLQ( DistMatrix<Real>& A )
{
#ifndef RELEASE
PushCallStack("internal::PanelLQ");
#endif
const Grid& g = A.Grid();
// Matrix views
DistMatrix<Real>
ATL(g), ATR(g), A00(g), a01(g), A02(g), aTopRow(g), ABottomPan(g),
ABL(g), ABR(g), a10(g), alpha11(g), a12(g),
A20(g), a21(g), A22(g);
// Temporary distributions
DistMatrix<Real,STAR,MR> aTopRow_STAR_MR(g);
DistMatrix<Real,MC,STAR> z_MC_STAR(g);
PushBlocksizeStack( 1 );
PartitionDownLeftDiagonal
( A, ATL, ATR,
ABL, ABR, 0 );
while( ATL.Height() < A.Height() && ATL.Width() < A.Width() )
{
RepartitionDownDiagonal
( ATL, /**/ ATR, A00, /**/ a01, A02,
/*************/ /**********************/
/**/ a10, /**/ alpha11, a12,
ABL, /**/ ABR, A20, /**/ a21, A22 );
aTopRow.View1x2( alpha11, a12 );
ABottomPan.View1x2( a21, A22 );
aTopRow_STAR_MR.AlignWith( ABottomPan );
z_MC_STAR.AlignWith( ABottomPan );
Zeros( ABottomPan.Height(), 1, z_MC_STAR );
//--------------------------------------------------------------------//
const Real tau = Reflector( alpha11, a12 );
const bool myDiagonalEntry = ( g.Row() == alpha11.ColAlignment() &&
g.Col() == alpha11.RowAlignment() );
Real alpha = 0;
if( myDiagonalEntry )
{
alpha = alpha11.GetLocal(0,0);
alpha11.SetLocal(0,0,1);
}
aTopRow_STAR_MR = aTopRow;
Gemv
( NORMAL,
Real(1), ABottomPan.LockedLocalMatrix(),
aTopRow_STAR_MR.LockedLocalMatrix(),
Real(0), z_MC_STAR.LocalMatrix() );
z_MC_STAR.SumOverRow();
Ger
( -tau,
z_MC_STAR.LockedLocalMatrix(),
aTopRow_STAR_MR.LockedLocalMatrix(),
ABottomPan.LocalMatrix() );
if( myDiagonalEntry )
alpha11.SetLocal(0,0,alpha);
//--------------------------------------------------------------------//
aTopRow_STAR_MR.FreeAlignments();
z_MC_STAR.FreeAlignments();
SlidePartitionDownDiagonal
( ATL, /**/ ATR, A00, a01, /**/ A02,
/**/ a10, alpha11, /**/ a12,
/*************/ /**********************/
ABL, /**/ ABR, A20, a21, /**/ A22 );
}
PopBlocksizeStack();
#ifndef RELEASE
PopCallStack();
#endif
}
inline void
PanelLQ
( DistMatrix<Complex<Real> >& A,
DistMatrix<Complex<Real>,MD,STAR>& t )
{
#ifndef RELEASE
PushCallStack("internal::PanelLQ");
if( A.Grid() != t.Grid() )
throw std::logic_error("{A,t} must be distributed over the same grid");
if( t.Height() != std::min(A.Height(),A.Width()) || t.Width() != 1 )
throw std::logic_error
("t must be a vector of height equal to the minimum dimension of A");
if( !t.AlignedWithDiagonal( A, 0 ) )
throw std::logic_error("t must be aligned with A's main diagonal");
#endif
typedef Complex<Real> C;
const Grid& g = A.Grid();
// Matrix views
DistMatrix<C>
ATL(g), ATR(g), A00(g), a01(g), A02(g), aTopRow(g), ABottomPan(g),
ABL(g), ABR(g), a10(g), alpha11(g), a12(g),
A20(g), a21(g), A22(g);
DistMatrix<C,MD,STAR>
tT(g), t0(g),
tB(g), tau1(g),
t2(g);
// Temporary distributions
DistMatrix<C> aTopRowConj(g);
DistMatrix<C,STAR,MR > aTopRowConj_STAR_MR(g);
DistMatrix<C,MC, STAR> z_MC_STAR(g);
PushBlocksizeStack( 1 );
PartitionDownLeftDiagonal
( A, ATL, ATR,
ABL, ABR, 0 );
PartitionDown
( t, tT,
tB, 0 );
while( ATL.Height() < A.Height() && ATL.Width() < A.Width() )
{
RepartitionDownDiagonal
( ATL, /**/ ATR, A00, /**/ a01, A02,
/*************/ /**********************/
/**/ a10, /**/ alpha11, a12,
ABL, /**/ ABR, A20, /**/ a21, A22 );
RepartitionDown
( tT, t0,
/**/ /****/
tau1,
tB, t2 );
aTopRow.View1x2( alpha11, a12 );
ABottomPan.View1x2( a21, A22 );
aTopRowConj_STAR_MR.AlignWith( ABottomPan );
z_MC_STAR.AlignWith( ABottomPan );
Zeros( ABottomPan.Height(), 1, z_MC_STAR );
//--------------------------------------------------------------------//
const C tau = Reflector( alpha11, a12 );
tau1.Set( 0, 0, tau );
const bool myDiagonalEntry = ( g.Row() == alpha11.ColAlignment() &&
g.Col() == alpha11.RowAlignment() );
C alpha = 0;
if( myDiagonalEntry )
{
alpha = alpha11.GetLocal(0,0);
alpha11.SetLocal(0,0,1);
}
Conjugate( aTopRow, aTopRowConj );
aTopRowConj_STAR_MR = aTopRowConj;
Gemv
( NORMAL,
C(1), ABottomPan.LockedLocalMatrix(),
aTopRowConj_STAR_MR.LockedLocalMatrix(),
C(0), z_MC_STAR.LocalMatrix() );
z_MC_STAR.SumOverRow();
Ger
( -Conj(tau),
z_MC_STAR.LockedLocalMatrix(),
aTopRowConj_STAR_MR.LockedLocalMatrix(),
ABottomPan.LocalMatrix() );
if( myDiagonalEntry )
alpha11.SetLocal(0,0,alpha);
//--------------------------------------------------------------------//
aTopRowConj_STAR_MR.FreeAlignments();
z_MC_STAR.FreeAlignments();
SlidePartitionDown
( tT, t0,
tau1,
/**/ /****/
tB, t2 );
SlidePartitionDownDiagonal
( ATL, /**/ ATR, A00, a01, /**/ A02,
/**/ a10, alpha11, /**/ a12,
/*************/ /**********************/
ABL, /**/ ABR, A20, a21, /**/ A22 );
}
PopBlocksizeStack();
#ifndef RELEASE
PopCallStack();
#endif
}
int main()
{
tQ4 a4( 1.1 );
tQ4 b4( 1 );
tQ12 a12( 3.3 );
tQ12 b12( 3 );
tQ18 a18;
double ad;
double bd;
tQ8 a8( -2.3 );
tQ8 b8( 2 );
tQ8 c8( Q8CONST( -2,3 ) );
tQ8 d8( a8 );
tQ8 e8( a4 );
// tQ8 f8( a12 ); // Warning: left shift count is negative
tQ8 g8( a12.roundedTo< tQ8 >() );
tQ8 h8( a12.roundedTo< 8 >() );
// a8 = a4.roundedTo( h8 ); //Warning: left/right shift is negative
a8 = 1;
a8 = -2;
a8 = 3;
a8 = Q8CONST( 3,001 );
a8 = tQ8( 3.001 );
a8 = tQ8::truncated( 3.001 );
a8 = tQ8::rounded( 3.001 );
a8.setTruncated( 3.2 );
a8.setRounded( 3.3 );
a8 = tQ8( 123, 8 );
a8 = tQ8::create( 123 << 8 );
a8 = a4;
a8 = a8;
// a8 = a12; // Warning: left shift count is negative
a8 = a12.roundedTo< tQ8 >();
a8 = a12.roundedTo( a8 );
a8.setRounded( a12 );
a8 = -a4;
a8 = -a8;
a8 += 3;
a8 += 4u;
a8 += 5l;
a8 += 6lu;
a8 += tQ8( 3.2 );
a8 += truncatedTo( a8, 3.3 );
a8 += roundedTo( a8, 3.4 );
a8 += a4;
// a8 += a12; // Warning: left shift count is negative
a8 += a12.roundedTo< tQ8 >();
a8 += a12.roundedTo( a8 );
a8 = a8 + 2;
a8 = 3 + a8;
a8 = a8 + a4;
// a8 = a4 + a8; // Warning: left shift count is negative
a8 -= 3;
a8 -= 4u;
a8 -= 5l;
a8 -= 6lu;
a8 -= roundedTo< tQ8::cQBits >( 3.2 );
a8 -= roundedTo( a8, 3.3 );
a8 -= a4;
// a8 -= a12; // Warning: left shift count is negative
a8 -= a12.roundedTo< tQ8 >();
a8 -= a12.roundedTo( a8 );
a8 = a8 - 2;
a8 = 3 - a8;
a8 = a8 - a4;
// a8 = a4 - a8; // Warning: left shift count is negative
a8 *= 3;
a8 *= 4u;
a8 *= 5l;
a8 *= 6lu;
// a8 *= 3.2; // Warning: converting to int from double
a8 *= a4;
a8 *= a12;
a8 = a8 * 2;
a8 = 3 * a8;
a12 = a8 * a4;
a12 = a4 * a8;
a8 /= 3;
a8 /= 4u;
a8 /= 5l;
a8 /= 6lu;
// a8 /= 3.2; // Warning: converting to int from double
a8 /= a4; // Note: possible overflow due to pre-shifting "(a8 << 4) / a4"
// a8 /= a12; // Warning: left shift count is negative
a8 = a8.increasedBy( a12 ) / a12;
a8 = a8 / 2;
// a8 = 3 / a8; // Error: no match for 'operator/'
a8 = tQ16( 3 ) / a8;
a12 = a8 / a4;
a12 = a4 / a8;
a8 == 3;
a8 == 4u;
a8 == 5l;
a8 == 6lu;
a8 == tQ8( 3.2 );
a8 == truncatedTo( a8, 3.3 );
a8 == roundedTo( a8, 3.4 );
a8 == a4;
// a8 == a12; // Warning: left shift count is negative
a8 == a12.roundedTo< tQ8 >();
a8 == a12.roundedTo( a8 );
3 == a8;
int(4u) == a8;
int(5l) == a8;
int(6lu) == a8;
a8 < 3;
a8 < 4u;
a8 < 5l;
a8 < 6lu;
a8 < tQ8( 3.2 );
a8 < a4;
// a8 < a12; // Warning: left shift count is negative
3 < a8;
int(4u) < a8;
int(5l) < a8;
int(6lu) < a8;
a8 > 3;
a8 > 4u;
a8 > 5l;
a8 > 6lu;
a8 > tQ8( 3.2 );
a8 > a4;
// a8 > a12; // Warning: left shift count is negative
3 > a8;
int(4u) > a8;
int(5l) > a8;
int(6lu) > a8;
!a8;
int intPart = a8.intPart();
int fracPart = a8.fracPart();
int fracPlaces = a8.fracPlaces( 3 );
unsigned abs = a8.absolute();
ad = a8.toDouble();
a8 = ad;
// a8.set( ad ); // Warning: conversion from int to double, possible loss of data
a8.setRounded( ad );
a8 = truncatedTo( a8, ad );
a8 = truncatedTo<8>( ad );
a8 = truncatedTo<tQ8>( ad );
// tBigQ36 aB36( 123567890 ); // Error: ambiguous
tBigQ36 aB36( 123567890ll );
tBigQ36 bB36( a8 );
aB36 = tBigQ18( a18 ) * a18;
}
