/**
* Return transformer contribution from the branch to the calling
* bus
* @param bus: pointer to the bus making the call
* @return: contribution to Y matrix from branch
*/
gridpack::ComplexType
gridpack::ymatrix::YMBranch::getTransformer(gridpack::ymatrix::YMBus *bus)
{
int i;
gridpack::ComplexType ret(0.0,0.0);
for (i=0; i<p_elems; i++) {
gridpack::ComplexType tmp(p_resistance[i],p_reactance[i]);
gridpack::ComplexType tmpB(0.0,0.5*p_charging[i]);
if (p_xform[i] && p_branch_status[i]) {
tmp = -1.0/tmp;
tmp = tmp - tmpB;
gridpack::ComplexType a(cos(p_phase_shift[i]),sin(p_phase_shift[i]));
a = p_tap_ratio[i]*a;
if ((!p_switched[i] && bus == getBus1().get()) ||
(p_switched[i] && bus == getBus2().get())) {
tmp = tmp/(conj(a)*a);
} else {
// tmp is unchanged
}
} else {
tmp = gridpack::ComplexType(0.0,0.0);
}
ret += tmp;
}
return ret;
}
int checkStringOffset(Glib::ustring str, int toffset)
{
//-- Empty string
if (str.empty() || StringOps(str).trim().empty())
return -1 ;
//-- Before text
if (toffset <= 0)
return 0 ;
//-- After text
else if (toffset >= (str.length()-1) )
return 1 ;
else
{
const Glib::ustring& tmpBefore = str.substr(0, toffset) ;
const Glib::ustring& tmpAfter = str.substr(toffset, str.length()-1) ;
StringOps tmpB(tmpBefore) ;
StringOps tmpAft(tmpAfter) ;
//-- Before is only spaces, it's before text :)
if (tmpB.trim(" \n").empty())
return 0 ;
//-- After is only spaces, it's after text :)
else if (tmpAft.trim(" \n").empty())
return 1 ;
//-- Otherwise it's middle :)
else
return 2 ;
}
}
void Dispatch::distr(const std::vector< ::Cannon::Matrix> & mA, const std::vector< ::Cannon::Matrix> &mB, int time){
assert(nproc == mA.size());
for( int i= 0; i < nproc; i++){
Cannon::Matrix tmpA(mA[i]),tmpB(mB[i]);
processor[i]->begin_injectFirst(tmpA,time);
processor[i]->begin_injectSecond(tmpB,time);
}
}
void btSliderConstraint::getInfo2NonVirtual(btConstraintInfo2* info, const btTransform& transA,const btTransform& transB, const btVector3& linVelA,const btVector3& linVelB, btScalar rbAinvMass,btScalar rbBinvMass )
{
const btTransform& trA = getCalculatedTransformA();
const btTransform& trB = getCalculatedTransformB();
btAssert(!m_useSolveConstraintObsolete);
int i, s = info->rowskip;
btScalar signFact = m_useLinearReferenceFrameA ? btScalar(1.0f) : btScalar(-1.0f);
// difference between frames in WCS
btVector3 ofs = trB.getOrigin() - trA.getOrigin();
// now get weight factors depending on masses
btScalar miA = rbAinvMass;
btScalar miB = rbBinvMass;
bool hasStaticBody = (miA < SIMD_EPSILON) || (miB < SIMD_EPSILON);
btScalar miS = miA + miB;
btScalar factA, factB;
if(miS > btScalar(0.f))
{
factA = miB / miS;
}
else
{
factA = btScalar(0.5f);
}
factB = btScalar(1.0f) - factA;
btVector3 ax1, p, q;
btVector3 ax1A = trA.getBasis().getColumn(0);
btVector3 ax1B = trB.getBasis().getColumn(0);
if(m_useOffsetForConstraintFrame)
{
// get the desired direction of slider axis
// as weighted sum of X-orthos of frameA and frameB in WCS
ax1 = ax1A * factA + ax1B * factB;
ax1.normalize();
// construct two orthos to slider axis
btPlaneSpace1 (ax1, p, q);
}
else
{ // old way - use frameA
ax1 = trA.getBasis().getColumn(0);
// get 2 orthos to slider axis (Y, Z)
p = trA.getBasis().getColumn(1);
q = trA.getBasis().getColumn(2);
}
// make rotations around these orthos equal
// the slider axis should be the only unconstrained
// rotational axis, the angular velocity of the two bodies perpendicular to
// the slider axis should be equal. thus the constraint equations are
// p*w1 - p*w2 = 0
// q*w1 - q*w2 = 0
// where p and q are unit vectors normal to the slider axis, and w1 and w2
// are the angular velocity vectors of the two bodies.
info->m_J1angularAxis[0] = p[0];
info->m_J1angularAxis[1] = p[1];
info->m_J1angularAxis[2] = p[2];
info->m_J1angularAxis[s+0] = q[0];
info->m_J1angularAxis[s+1] = q[1];
info->m_J1angularAxis[s+2] = q[2];
info->m_J2angularAxis[0] = -p[0];
info->m_J2angularAxis[1] = -p[1];
info->m_J2angularAxis[2] = -p[2];
info->m_J2angularAxis[s+0] = -q[0];
info->m_J2angularAxis[s+1] = -q[1];
info->m_J2angularAxis[s+2] = -q[2];
// compute the right hand side of the constraint equation. set relative
// body velocities along p and q to bring the slider back into alignment.
// if ax1A,ax1B are the unit length slider axes as computed from bodyA and
// bodyB, we need to rotate both bodies along the axis u = (ax1 x ax2).
// if "theta" is the angle between ax1 and ax2, we need an angular velocity
// along u to cover angle erp*theta in one step :
// |angular_velocity| = angle/time = erp*theta / stepsize
// = (erp*fps) * theta
// angular_velocity = |angular_velocity| * (ax1 x ax2) / |ax1 x ax2|
// = (erp*fps) * theta * (ax1 x ax2) / sin(theta)
// ...as ax1 and ax2 are unit length. if theta is smallish,
// theta ~= sin(theta), so
// angular_velocity = (erp*fps) * (ax1 x ax2)
// ax1 x ax2 is in the plane space of ax1, so we project the angular
// velocity to p and q to find the right hand side.
// btScalar k = info->fps * info->erp * getSoftnessOrthoAng();
btScalar currERP = (m_flags & BT_SLIDER_FLAGS_ERP_ORTANG) ? m_softnessOrthoAng : m_softnessOrthoAng * info->erp;
btScalar k = info->fps * currERP;
btVector3 u = ax1A.cross(ax1B);
info->m_constraintError[0] = k * u.dot(p);
info->m_constraintError[s] = k * u.dot(q);
if(m_flags & BT_SLIDER_FLAGS_CFM_ORTANG)
{
info->cfm[0] = m_cfmOrthoAng;
info->cfm[s] = m_cfmOrthoAng;
}
int nrow = 1; // last filled row
int srow;
btScalar limit_err;
int limit;
int powered;
// next two rows.
// we want: velA + wA x relA == velB + wB x relB ... but this would
// result in three equations, so we project along two orthos to the slider axis
btTransform bodyA_trans = transA;
btTransform bodyB_trans = transB;
nrow++;
int s2 = nrow * s;
nrow++;
int s3 = nrow * s;
btVector3 tmpA(0,0,0), tmpB(0,0,0), relA(0,0,0), relB(0,0,0), c(0,0,0);
if(m_useOffsetForConstraintFrame)
{
// get vector from bodyB to frameB in WCS
relB = trB.getOrigin() - bodyB_trans.getOrigin();
// get its projection to slider axis
btVector3 projB = ax1 * relB.dot(ax1);
// get vector directed from bodyB to slider axis (and orthogonal to it)
btVector3 orthoB = relB - projB;
// same for bodyA
relA = trA.getOrigin() - bodyA_trans.getOrigin();
btVector3 projA = ax1 * relA.dot(ax1);
btVector3 orthoA = relA - projA;
// get desired offset between frames A and B along slider axis
btScalar sliderOffs = m_linPos - m_depth[0];
// desired vector from projection of center of bodyA to projection of center of bodyB to slider axis
btVector3 totalDist = projA + ax1 * sliderOffs - projB;
// get offset vectors relA and relB
relA = orthoA + totalDist * factA;
relB = orthoB - totalDist * factB;
// now choose average ortho to slider axis
p = orthoB * factA + orthoA * factB;
btScalar len2 = p.length2();
if(len2 > SIMD_EPSILON)
{
p /= btSqrt(len2);
}
else
{
p = trA.getBasis().getColumn(1);
}
// make one more ortho
q = ax1.cross(p);
// fill two rows
tmpA = relA.cross(p);
tmpB = relB.cross(p);
for (i=0; i<3; i++) info->m_J1angularAxis[s2+i] = tmpA[i];
for (i=0; i<3; i++) info->m_J2angularAxis[s2+i] = -tmpB[i];
tmpA = relA.cross(q);
tmpB = relB.cross(q);
if(hasStaticBody && getSolveAngLimit())
{ // to make constraint between static and dynamic objects more rigid
// remove wA (or wB) from equation if angular limit is hit
tmpB *= factB;
tmpA *= factA;
}
for (i=0; i<3; i++) info->m_J1angularAxis[s3+i] = tmpA[i];
for (i=0; i<3; i++) info->m_J2angularAxis[s3+i] = -tmpB[i];
for (i=0; i<3; i++) info->m_J1linearAxis[s2+i] = p[i];
for (i=0; i<3; i++) info->m_J1linearAxis[s3+i] = q[i];
for (i=0; i<3; i++) info->m_J2linearAxis[s2+i] = -p[i];
for (i=0; i<3; i++) info->m_J2linearAxis[s3+i] = -q[i];
}
else
{ // old way - maybe incorrect if bodies are not on the slider axis
// see discussion "Bug in slider constraint" http://bulletphysics.org/Bullet/phpBB3/viewtopic.php?f=9&t=4024&start=0
c = bodyB_trans.getOrigin() - bodyA_trans.getOrigin();
btVector3 tmp = c.cross(p);
for (i=0; i<3; i++) info->m_J1angularAxis[s2+i] = factA*tmp[i];
for (i=0; i<3; i++) info->m_J2angularAxis[s2+i] = factB*tmp[i];
tmp = c.cross(q);
for (i=0; i<3; i++) info->m_J1angularAxis[s3+i] = factA*tmp[i];
for (i=0; i<3; i++) info->m_J2angularAxis[s3+i] = factB*tmp[i];
for (i=0; i<3; i++) info->m_J1linearAxis[s2+i] = p[i];
for (i=0; i<3; i++) info->m_J1linearAxis[s3+i] = q[i];
for (i=0; i<3; i++) info->m_J2linearAxis[s2+i] = -p[i];
for (i=0; i<3; i++) info->m_J2linearAxis[s3+i] = -q[i];
}
// compute two elements of right hand side
// k = info->fps * info->erp * getSoftnessOrthoLin();
currERP = (m_flags & BT_SLIDER_FLAGS_ERP_ORTLIN) ? m_softnessOrthoLin : m_softnessOrthoLin * info->erp;
k = info->fps * currERP;
btScalar rhs = k * p.dot(ofs);
info->m_constraintError[s2] = rhs;
rhs = k * q.dot(ofs);
info->m_constraintError[s3] = rhs;
if(m_flags & BT_SLIDER_FLAGS_CFM_ORTLIN)
{
info->cfm[s2] = m_cfmOrthoLin;
info->cfm[s3] = m_cfmOrthoLin;
}
// check linear limits
limit_err = btScalar(0.0);
limit = 0;
if(getSolveLinLimit())
{
limit_err = getLinDepth() * signFact;
limit = (limit_err > btScalar(0.0)) ? 2 : 1;
}
powered = 0;
if(getPoweredLinMotor())
{
powered = 1;
}
// if the slider has joint limits or motor, add in the extra row
if (limit || powered)
{
nrow++;
srow = nrow * info->rowskip;
info->m_J1linearAxis[srow+0] = ax1[0];
info->m_J1linearAxis[srow+1] = ax1[1];
info->m_J1linearAxis[srow+2] = ax1[2];
info->m_J2linearAxis[srow+0] = -ax1[0];
info->m_J2linearAxis[srow+1] = -ax1[1];
info->m_J2linearAxis[srow+2] = -ax1[2];
// linear torque decoupling step:
//
// we have to be careful that the linear constraint forces (+/- ax1) applied to the two bodies
// do not create a torque couple. in other words, the points that the
// constraint force is applied at must lie along the same ax1 axis.
// a torque couple will result in limited slider-jointed free
// bodies from gaining angular momentum.
if(m_useOffsetForConstraintFrame)
{
// this is needed only when bodyA and bodyB are both dynamic.
if(!hasStaticBody)
{
tmpA = relA.cross(ax1);
tmpB = relB.cross(ax1);
info->m_J1angularAxis[srow+0] = tmpA[0];
info->m_J1angularAxis[srow+1] = tmpA[1];
info->m_J1angularAxis[srow+2] = tmpA[2];
info->m_J2angularAxis[srow+0] = -tmpB[0];
info->m_J2angularAxis[srow+1] = -tmpB[1];
info->m_J2angularAxis[srow+2] = -tmpB[2];
}
}
else
{ // The old way. May be incorrect if bodies are not on the slider axis
btVector3 ltd; // Linear Torque Decoupling vector (a torque)
ltd = c.cross(ax1);
info->m_J1angularAxis[srow+0] = factA*ltd[0];
info->m_J1angularAxis[srow+1] = factA*ltd[1];
info->m_J1angularAxis[srow+2] = factA*ltd[2];
info->m_J2angularAxis[srow+0] = factB*ltd[0];
info->m_J2angularAxis[srow+1] = factB*ltd[1];
info->m_J2angularAxis[srow+2] = factB*ltd[2];
}
// right-hand part
btScalar lostop = getLowerLinLimit();
btScalar histop = getUpperLinLimit();
if(limit && (lostop == histop))
{ // the joint motor is ineffective
powered = 0;
}
info->m_constraintError[srow] = 0.;
info->m_lowerLimit[srow] = 0.;
info->m_upperLimit[srow] = 0.;
currERP = (m_flags & BT_SLIDER_FLAGS_ERP_LIMLIN) ? m_softnessLimLin : info->erp;
if(powered)
{
if(m_flags & BT_SLIDER_FLAGS_CFM_DIRLIN)
{
info->cfm[srow] = m_cfmDirLin;
}
btScalar tag_vel = getTargetLinMotorVelocity();
btScalar mot_fact = getMotorFactor(m_linPos, m_lowerLinLimit, m_upperLinLimit, tag_vel, info->fps * currERP);
info->m_constraintError[srow] -= signFact * mot_fact * getTargetLinMotorVelocity();
info->m_lowerLimit[srow] += -getMaxLinMotorForce() * info->fps;
info->m_upperLimit[srow] += getMaxLinMotorForce() * info->fps;
}
if(limit)
{
k = info->fps * currERP;
info->m_constraintError[srow] += k * limit_err;
if(m_flags & BT_SLIDER_FLAGS_CFM_LIMLIN)
{
info->cfm[srow] = m_cfmLimLin;
}
if(lostop == histop)
{ // limited low and high simultaneously
info->m_lowerLimit[srow] = -SIMD_INFINITY;
info->m_upperLimit[srow] = SIMD_INFINITY;
}
else if(limit == 1)
{ // low limit
info->m_lowerLimit[srow] = -SIMD_INFINITY;
info->m_upperLimit[srow] = 0;
}
else
{ // high limit
info->m_lowerLimit[srow] = 0;
info->m_upperLimit[srow] = SIMD_INFINITY;
}
// bounce (we'll use slider parameter abs(1.0 - m_dampingLimLin) for that)
btScalar bounce = btFabs(btScalar(1.0) - getDampingLimLin());
if(bounce > btScalar(0.0))
{
btScalar vel = linVelA.dot(ax1);
vel -= linVelB.dot(ax1);
vel *= signFact;
// only apply bounce if the velocity is incoming, and if the
// resulting c[] exceeds what we already have.
if(limit == 1)
{ // low limit
if(vel < 0)
{
btScalar newc = -bounce * vel;
if (newc > info->m_constraintError[srow])
{
info->m_constraintError[srow] = newc;
}
}
}
else
{ // high limit - all those computations are reversed
if(vel > 0)
{
btScalar newc = -bounce * vel;
if(newc < info->m_constraintError[srow])
{
info->m_constraintError[srow] = newc;
}
}
}
}
info->m_constraintError[srow] *= getSoftnessLimLin();
} // if(limit)
} // if linear limit
// check angular limits
limit_err = btScalar(0.0);
limit = 0;
if(getSolveAngLimit())
{
limit_err = getAngDepth();
limit = (limit_err > btScalar(0.0)) ? 1 : 2;
}
// if the slider has joint limits, add in the extra row
powered = 0;
if(getPoweredAngMotor())
{
powered = 1;
}
if(limit || powered)
{
nrow++;
srow = nrow * info->rowskip;
info->m_J1angularAxis[srow+0] = ax1[0];
info->m_J1angularAxis[srow+1] = ax1[1];
info->m_J1angularAxis[srow+2] = ax1[2];
info->m_J2angularAxis[srow+0] = -ax1[0];
info->m_J2angularAxis[srow+1] = -ax1[1];
info->m_J2angularAxis[srow+2] = -ax1[2];
btScalar lostop = getLowerAngLimit();
btScalar histop = getUpperAngLimit();
if(limit && (lostop == histop))
{ // the joint motor is ineffective
powered = 0;
}
currERP = (m_flags & BT_SLIDER_FLAGS_ERP_LIMANG) ? m_softnessLimAng : info->erp;
if(powered)
{
if(m_flags & BT_SLIDER_FLAGS_CFM_DIRANG)
{
info->cfm[srow] = m_cfmDirAng;
}
btScalar mot_fact = getMotorFactor(m_angPos, m_lowerAngLimit, m_upperAngLimit, getTargetAngMotorVelocity(), info->fps * currERP);
info->m_constraintError[srow] = mot_fact * getTargetAngMotorVelocity();
info->m_lowerLimit[srow] = -getMaxAngMotorForce() * info->fps;
info->m_upperLimit[srow] = getMaxAngMotorForce() * info->fps;
}
if(limit)
{
k = info->fps * currERP;
info->m_constraintError[srow] += k * limit_err;
if(m_flags & BT_SLIDER_FLAGS_CFM_LIMANG)
{
info->cfm[srow] = m_cfmLimAng;
}
if(lostop == histop)
{
// limited low and high simultaneously
info->m_lowerLimit[srow] = -SIMD_INFINITY;
info->m_upperLimit[srow] = SIMD_INFINITY;
}
else if(limit == 1)
{ // low limit
info->m_lowerLimit[srow] = 0;
info->m_upperLimit[srow] = SIMD_INFINITY;
}
else
{ // high limit
info->m_lowerLimit[srow] = -SIMD_INFINITY;
info->m_upperLimit[srow] = 0;
}
// bounce (we'll use slider parameter abs(1.0 - m_dampingLimAng) for that)
btScalar bounce = btFabs(btScalar(1.0) - getDampingLimAng());
if(bounce > btScalar(0.0))
{
btScalar vel = m_rbA.getAngularVelocity().dot(ax1);
vel -= m_rbB.getAngularVelocity().dot(ax1);
// only apply bounce if the velocity is incoming, and if the
// resulting c[] exceeds what we already have.
if(limit == 1)
{ // low limit
if(vel < 0)
{
btScalar newc = -bounce * vel;
if(newc > info->m_constraintError[srow])
{
info->m_constraintError[srow] = newc;
}
}
}
else
{ // high limit - all those computations are reversed
if(vel > 0)
{
btScalar newc = -bounce * vel;
if(newc < info->m_constraintError[srow])
{
info->m_constraintError[srow] = newc;
}
}
}
}
info->m_constraintError[srow] *= getSoftnessLimAng();
} // if(limit)
} // if angular limit or powered
}
void SurfaceTensionBoundaryCondition :: computeTangentFromElement(FloatMatrix &answer, Element *e, int side, TimeStep *tStep)
{
FEInterpolation *fei = e->giveInterpolation();
if ( !fei ) {
OOFEM_ERROR("No interpolation available for element.");
}
std :: unique_ptr< IntegrationRule > iRule( fei->giveBoundaryIntegrationRule(fei->giveInterpolationOrder()-1, side) );
int nsd = e->giveDomain()->giveNumberOfSpatialDimensions();
int nodes = e->giveNumberOfNodes();
if ( side == -1 ) {
side = 1;
}
answer.clear();
if ( nsd == 2 ) {
FEInterpolation2d *fei2d = static_cast< FEInterpolation2d * >(fei);
///@todo More of this grunt work should be moved to the interpolation classes
FloatMatrix xy(2, nodes);
Node *node;
for ( int i = 1; i <= nodes; i++ ) {
node = e->giveNode(i);
xy.at(1, i) = node->giveCoordinate(1);
xy.at(2, i) = node->giveCoordinate(2);
}
FloatArray tmpA(2 *nodes);
FloatArray es; // Tangent vector to curve
FloatArray dNds;
FloatMatrix B(2, 2 *nodes);
B.zero();
if ( e->giveDomain()->isAxisymmetric() ) {
FloatArray N;
FloatArray gcoords;
FloatArray tmpB(2 *nodes);
for ( GaussPoint *gp: *iRule ) {
fei2d->edgeEvaldNds( dNds, side, gp->giveNaturalCoordinates(), FEIElementGeometryWrapper(e) );
fei->boundaryEvalN( N, side, gp->giveNaturalCoordinates(), FEIElementGeometryWrapper(e) );
double J = fei->boundaryGiveTransformationJacobian( side, gp->giveNaturalCoordinates(), FEIElementGeometryWrapper(e) );
fei->boundaryLocal2Global( gcoords, side, gp->giveNaturalCoordinates(), FEIElementGeometryWrapper(e) );
double r = gcoords(0); // First coordinate is the radial coord.
es.beProductOf(xy, dNds);
// Construct the different matrices in the integrand;
for ( int i = 0; i < nodes; i++ ) {
tmpA(i * 2 + 0) = dNds(i) * es(0);
tmpA(i * 2 + 1) = dNds(i) * es(1);
tmpB(i * 2 + 0) = N(i);
tmpB(i * 2 + 1) = 0;
B(i * 2, 0) = B(i * 2 + 1, 1) = dNds(i);
}
double dV = 2 *M_PI *gamma *J *gp->giveWeight();
answer.plusDyadUnsym(tmpA, tmpB, dV);
answer.plusDyadUnsym(tmpB, tmpA, dV);
answer.plusProductSymmUpper(B, B, r * dV);
answer.plusDyadUnsym(tmpA, tmpA, -r * dV);
}
} else {
for ( GaussPoint *gp: *iRule ) {
double t = e->giveCrossSection()->give(CS_Thickness, gp); ///@todo The thickness is not often relevant or used in FM.
fei2d->edgeEvaldNds( dNds, side, gp->giveNaturalCoordinates(), FEIElementGeometryWrapper(e) );
double J = fei->boundaryGiveTransformationJacobian( side, gp->giveNaturalCoordinates(), FEIElementGeometryWrapper(e) );
es.beProductOf(xy, dNds);
// Construct the different matrices in the integrand;
for ( int i = 0; i < nodes; i++ ) {
tmpA(i * 2 + 0) = dNds(i) * es(0);
tmpA(i * 2 + 1) = dNds(i) * es(1);
B(i * 2, 0) = B(i * 2 + 1, 1) = dNds(i);
}
double dV = t * gamma * J * gp->giveWeight();
answer.plusProductSymmUpper(B, B, dV);
answer.plusDyadSymmUpper(tmpA, -dV);
}
}
answer.symmetrized();
} else if ( nsd == 3 ) {
FEInterpolation3d *fei3d = static_cast< FEInterpolation3d * >(fei);
OOFEM_ERROR("3D tangents not implemented yet.");
//FloatMatrix tmp(3 *nodes, 3 *nodes);
FloatMatrix dNdx;
FloatArray n;
for ( GaussPoint *gp: *iRule ) {
fei3d->surfaceEvaldNdx( dNdx, side, gp->giveNaturalCoordinates(), FEIElementGeometryWrapper(e) );
/*double J = */ fei->boundaryEvalNormal( n, side, gp->giveNaturalCoordinates(), FEIElementGeometryWrapper(e) );
//double dV = gamma * J * gp->giveWeight();
for ( int i = 0; i < nodes; i++ ) {
//tmp(3*i+0) = dNdx(i,0) - (dNdx(i,0)*n(0)* + dNdx(i,1)*n(1) + dNdx(i,2)*n(2))*n(0);
//tmp(3*i+1) = dNdx(i,1) - (dNdx(i,0)*n(0)* + dNdx(i,1)*n(1) + dNdx(i,2)*n(2))*n(1);
//tmp(3*i+2) = dNdx(i,2) - (dNdx(i,0)*n(0)* + dNdx(i,1)*n(1) + dNdx(i,2)*n(2))*n(2);
}
//answer.plusProductSymmUpper(A,B, dV);
///@todo Derive expressions for this.
}
} else {
OOFEM_WARNING("Only 2D or 3D is possible!");
}
}
/*
* DIVISION WITH REMAINDER
* Please read the comments before the definition of
* `BigUnsigned::divideWithRemainder' in `BigUnsigned.cc' for lots of
* information you should know before reading this function.
*
* Following Knuth, I decree that x / y is to be
* 0 if y==0 and floor(real-number x / y) if y!=0.
* Then x % y shall be x - y*(integer x / y).
*
* Note that x = y * (x / y) + (x % y) always holds.
* In addition, (x % y) is from 0 to y - 1 if y > 0,
* and from -(|y| - 1) to 0 if y < 0. (x % y) = x if y = 0.
*
* Examples: (q = a / b, r = a % b)
* a b q r
* === === === ===
* 4 3 1 1
* -4 3 -2 2
* 4 -3 -2 -2
* -4 -3 1 -1
*/
void BigInteger::divideWithRemainder(const BigInteger &b, BigInteger &q) {
// Defend against aliased calls;
// same idea as in BigUnsigned::divideWithRemainder .
if (this == &q)
throw "BigInteger::divideWithRemainder: Cannot write quotient and remainder into the same variable";
if (this == &b || &q == &b) {
BigInteger tmpB(b);
divideWithRemainder(tmpB, q);
return;
}
// Division by zero gives quotient 0 and remainder *this
if (b.sign == zero) {
q.mag = 0;
q.sign = zero;
return;
}
// 0 / b gives quotient 0 and remainder 0
if (sign == zero) {
q.mag = 0;
q.sign = zero;
return;
}
// Here *this != 0, b != 0.
// Do the operands have the same sign?
if (sign == b.sign) {
// Yes: easy case. Quotient is zero or positive.
q.sign = positive;
} else {
// No: harder case. Quotient is negative.
q.sign = negative;
// Decrease the magnitude of the dividend by one.
mag--;
/*
* We tinker with the dividend before and with the
* quotient and remainder after so that the result
* comes out right. To see why it works, consider the following
* list of examples, where A is the magnitude-decreased
* a, Q and R are the results of BigUnsigned division
* with remainder on A and |b|, and q and r are the
* final results we want:
*
* a A b Q R q r
* -3 -2 3 0 2 -1 0
* -4 -3 3 1 0 -2 2
* -5 -4 3 1 1 -2 1
* -6 -5 3 1 2 -2 0
*
* It appears that we need a total of 3 corrections:
* Decrease the magnitude of a to get A. Increase the
* magnitude of Q to get q (and make it negative).
* Find r = (b - 1) - R and give it the desired sign.
*/
}
// Divide the magnitudes.
mag.divideWithRemainder(b.mag, q.mag);
if (sign != b.sign) {
// More for the harder case (as described):
// Increase the magnitude of the quotient by one.
q.mag++;
// Modify the remainder.
mag.subtract(b.mag, mag);
mag--;
}
// Sign of the remainder is always the sign of the divisor b.
sign = b.sign;
// Set signs to zero as necessary. (Thanks David Allen!)
if (mag.isZero())
sign = zero;
if (q.mag.isZero())
q.sign = zero;
// WHEW!!!
}
