// Prime-power factorization
void pp_factorize(vector<long>& factors, long N)
{
Vec< Pair<long, long> > pf;
factorize(pf,N); // prime factors, N = \prod_i pf[i].first^{pf[i].second}
factors.resize(pf.length());
for (long i=0; i<pf.length(); i++)
factors[i] = power_long(pf[i].a, pf[i].b); // p_i^e_i
}
void assert_vec_p(const Vec<T> &ref, const Vec<T> &act, int line)
{
static const double tol = 1e-3;
ASSERT_EQ(ref.length(), ref.length()) << line;
for (int n = 0; n < ref.length(); ++n) {
ASSERT_NEAR(ref(n), act(n), tol) << line;
}
}
double computeAverageDouble(Vec<double> &result){
RR average = 0;
for (int i = 1; i <= result.length() ; i++){
average += result(i);
}
return to_double(average/result.length());
}
void setHyperColumn(const Vec<T>& v, const CubeSlice<T>& s, long pos)
{
long m = s.getProd(1);
long n = s.getDim(0);
assert(pos >= 0 && pos < m);
if (v.length() < n) n = v.length();
for (long i = 0; i < n; i++)
s[pos + i*m] = v[i];
}
void
DEMParticleCreator::addExtraTranslations(const Vec& shift,
REAL boundaryMargin,
Vec inPlaneDiag,
REAL widthX, REAL widthY, REAL widthZ,
const Face& face,
const IntersectionStatus status,
std::vector<Vec>& translations)
{
if (status.second.first == Face::Location::VERTEX) {
int vertIndex = status.second.second;
//std::cout << "is vertex " << vertIndex << "\n";
if (vertIndex == 0) {
for (int ii = 1; ii < 4; ++ii) {
Vec inPlane = face.vertex[ii] - face.vertex[vertIndex];
auto length = inPlane.length();
inPlane.normalizeInPlace();
if (ii == 2) {
inPlane *= length;
inPlane += (inPlaneDiag*boundaryMargin);
} else {
inPlane *= (length + boundaryMargin);
}
Vec outOfPlane = inPlane + shift;
translations.push_back(inPlane);
translations.push_back(outOfPlane);
}
} else if (vertIndex == 1 || vertIndex == 3) {
Vec normal = Vec(1,1,1) - inPlaneDiag;
Vec vec1 = normal * Vec(widthX + boundaryMargin,
widthY + boundaryMargin, widthZ + boundaryMargin);
Vec vec2 = face.vertex[2] - face.vertex[vertIndex];
auto length = vec2.length();
vec2.normalizeInPlace();
vec2 *= (length + boundaryMargin);
//std::cout << "vec1 = " << vec1 << " vec2 = " << vec2 << "\n";
translations.push_back(vec1 + vec2);
}
}
else if (status.second.first == Face::Location::EDGE) {
int edgeIndex = status.second.second;
//std::cout << "is edge " << edgeIndex << "\n";
if (edgeIndex == 0 || edgeIndex == 3) {
int oppIndex = (edgeIndex+3) % 4;
Vec inPlane = face.vertex[oppIndex] - face.vertex[edgeIndex];
auto length = inPlane.length() + boundaryMargin;
inPlane.normalizeInPlace();
inPlane *= length;
Vec outOfPlane = inPlane + shift;
translations.push_back(inPlane);
translations.push_back(outOfPlane);
}
}
}
QString TetraGPSEncoder::generate(TGPSReal lat, TGPSReal lon, TGPSReal precMeters){
const Vec coord(cos(lat)*cos(lon), cos(lat)*sin(lon), sin(lat));
qDebug()<<"COORD:"<<coord<<coord.length()<<coord.latlon();
QVector<Tri> faces;
const TGPSReal ma=(M_PI*2.0)/3.0;
const Vec north( +0.0, +1.0, +0.0);
const Vec prime( +0.0, +sin(-ma), +cos(-ma));
const Vec meridian2(prime.x()*cos(+ma) - prime.z()*sin(+ma), prime.y(), prime.z()*cos(+ma) + prime.x()*sin(+ma));
const Vec meridian3(prime.x()*cos(-ma) - prime.z()*sin(-ma), prime.y(), prime.z()*cos(-ma) + prime.x()*sin(-ma));
qDebug()<<"north= "<<north<<north.length();
qDebug()<<"prime= "<<prime<<prime.length();
qDebug()<<"meridian2="<<meridian2<<meridian2.length();
qDebug()<<"meridian3="<<meridian3<<meridian3.length();
faces.push_back(Tri(north,prime,meridian2, 1));
faces.push_back(Tri(north,prime,meridian3, 2));
faces.push_back(Tri(north,meridian2,meridian3, 3));
faces.push_back(Tri(prime,meridian2,meridian3, 4));
TGPSReal score=1000.0;
QStringList ret;
int sub=0;
Tri best,second;
while((score*planetRadiusMeters)>precMeters && sub++<9){
//qDebug()<<"----ROUND "<<sub<< score;
TGPSReal eps=1000.0;
for(auto tri:faces) {
TGPSReal delta=(tri.center-coord).length();
//qDebug()<<"DELTA: "<<delta<<tri.center<<tri.center.length();
if(delta<eps){
if(delta<score){
score=delta;
}
eps=delta;
best=tri;
qDebug()<<"NEW BEST: "<<best<<"!";
}
}
QString name=best.name();
//if("0"==name){ break; }
ret<<name;
faces=best.subdivide();
if(best!=second){
second=best;
}
else{
break;
}
}
TGPSReal d=(coord-best.center).length()/best.reach();
qDebug()<<"BEST: "<<best<<" with "<< d<<" normalized distance from center and " << (score*planetRadiusMeters)<<" meters after "<<sub<<" iterations";
return ret.join(".");
}
// Get multiple layers of a Benes permutation network. Returns in out[i][j]
// the shift amount to move item j in the i'th layer. Also isID[i]=true if
// the i'th layer is the identity (i.e., contains only 0 shift amounts).
void ColPerm::getBenesShiftAmounts(Vec<Permut>& out, Vec<bool>& isID,
const Vec<long>& benesLvls) const
{
// Go over the columns one by one. For each column extract the columns
// permutation, prepare a Benes network for it, and then for every layer
// compute the shift amounts for this columns.
long n = getDim(dim); // the permutations are over [0,n-1]
// Allocate space
out.SetLength(benesLvls.length());
isID.SetLength(benesLvls.length());
for (long k=0; k<benesLvls.length(); k++) {
out[k].SetLength(getSize());
isID[k] = true;
}
Vec<long> col;
col.SetLength(n);
for (long slice_index = 0; slice_index < numSlices(dim); slice_index++) {
ConstCubeSlice<long> slice(*this, slice_index, dim);
for (long col_index = 0; col_index < slice.numCols(); col_index++) {
getHyperColumn(col, slice, col_index);
GeneralBenesNetwork net(col); // build a Benes network for this column
// Sanity checks: width of network == n,
// and sum of benesLvls entries == # of levels
assert(net.getSize()==n);
{long sum=0;
for (long k=0; k<benesLvls.length(); k++) sum+=benesLvls[k];
assert(net.getNumLevels()==sum);
}
// Compute the layers of the collapased network for this column
for (long lvl=0,k=0; k<benesLvls.length(); lvl += benesLvls[k], k++) {
// Returns in col the shift amounts for this layer in the network,
// restricted to this column. Also returns true if the returned
// permutation is the idendity, false otherwise.
bool id = collapseBenesLevels(col, net, lvl, benesLvls[k]);
isID[k] = isID[k] && id;
CubeSlice<long> oslice(out[k], getSig());
CubeSlice<long> osubslice(oslice, slice_index, dim);
setHyperColumn(col, osubslice, col_index);
} // next collapsed layer
} // next column
} // next slice
}
void vecRed(Vec<ZZ>& out, const Vec<ZZ>& in, long q, bool abs)
{
out.SetLength(in.length()); // allocate space if needed
for (long i=0; i<in.length(); i++) {
long c = in[i]%q;
if (abs) { if (c<0) c+=q; }
else if (q==2) { if (in[i]<0) c = -c; }
else {
if (c >= q/2) c -= q;
else if (c < -(q/2)) c += q;
}
out[i] = c;
}
}
// powVec[d] = m_d = p_d^{e_d}
// computes multiEvalPoints[d] as a vector of length phi(m_d)
// containing base^{(m/m_d) j} for j in Z_{m_d}^*
void computeMultiEvalPoints(Vec< Vec<zz_p> >& multiEvalPoints,
const zz_p& base,
long m,
const Vec<long>& powVec,
const Vec<long>& phiVec)
{
long k = powVec.length();
multiEvalPoints.SetLength(k);
for (long d = 0; d < k; d++) {
long m_d = powVec[d];
long phi_d = phiVec[d];
long count = 0;
zz_p pow = conv<zz_p>(1);
zz_p mult = power(base, m/m_d);
multiEvalPoints[d].SetLength(phi_d);
for (long j = 0; j < m_d; j++) {
if (GCD(j, m_d) == 1) {
multiEvalPoints[d][count] = pow;
count++;
}
pow = pow * mult;
}
}
}
// factors[d] = (p_d, e_d)
// computes powVec[d] = p_d^{e_d}
void computePowVec(Vec<long>& powVec,
const Vec< Pair<long, long> >& factors)
{
long k = factors.length();
powVec.SetLength(k);
for (long d = 0; d < k; d++)
powVec[d] = computePow(factors[d]);
}
// returns \prod_d vec[d]
long computeProd(const Vec<long>& vec)
{
long prod = 1;
long k = vec.length();
for (long d = 0; d < k; d++)
prod = prod * vec[d];
return prod;
}
void computePowVec(Vec<long>& powVec,
const Vec< Pair<long, long> >& factors)
{
long k = factors.length();
powVec.SetLength(k);
for (long i = 0; i < k; i++)
powVec[i] = computePow(factors[i]);
}
// computeProd(vec) returns the product of the entries of vec
long computeProd(const Vec<long>& vec)
{
long prod = 1;
long k = vec.length();
for (long i = 0; i < k; i++)
prod = prod * vec[i];
return prod;
}
// powVec[d] = p_d^{e_d}, m = \prod_d p_d^{e_d}
// computes divVec[d] = m/p_d^{e_d}
void computeDivVec(Vec<long>& divVec, long m,
const Vec<long>& powVec)
{
long k = powVec.length();
divVec.SetLength(k);
for (long d = 0; d < k; d++)
divVec[d] = m/powVec[d];
}
// vec[d] = (a_d , b_d)
// returns \prod_d a_d^{b_d}
long computeProd(const Vec< Pair<long, long> >& vec)
{
long prod = 1;
long k = vec.length();
for (long d = 0; d < k; d++) {
prod = prod * computePow(vec[d]);
}
return prod;
}
void computeDivVec(Vec<long>& divVec, long m,
const Vec<long>& powVec)
{
long k = powVec.length();
divVec.SetLength(k);
for (long i = 0; i < k; i++)
divVec[i] = m/powVec[i];
}
void readContextBinary(istream& str, FHEcontext& context)
{
assert(readEyeCatcher(str, BINIO_EYE_CONTEXT_BEGIN)==0);
// Get the standard deviation
context.stdev = read_raw_xdouble(str);
long sizeOfS = read_raw_int(str);
IndexSet s;
for(long tmp, i=0; i<sizeOfS; i++){
tmp = read_raw_int(str);
s.insert(tmp);
}
context.moduli.clear();
context.specialPrimes.clear();
context.ctxtPrimes.clear();
long nPrimes = read_raw_int(str);
for (long p,i=0; i<nPrimes; i++) {
p = read_raw_int(str);
context.moduli.push_back(Cmodulus(context.zMStar,p,0));
if (s.contains(i))
context.specialPrimes.insert(i); // special prime
else
context.ctxtPrimes.insert(i); // ciphertext prime
}
long nDigits = read_raw_int(str);
context.digits.resize(nDigits);
for(long i=0; i<(long)context.digits.size(); i++){
sizeOfS = read_raw_int(str);
for(long tmp, n=0; n<sizeOfS; n++){
tmp = read_raw_int(str);
context.digits[i].insert(tmp);
}
}
// Read in the partition of m into co-prime factors (if bootstrappable)
Vec<long> mv;
read_ntl_vec_long(str, mv);
long t = read_raw_int(str);
bool consFlag = read_raw_int(str);
if (mv.length()>0) {
context.makeBootstrappable(mv, t, consFlag);
}
assert(readEyeCatcher(str, BINIO_EYE_CONTEXT_END)==0);
}
void setHyperColumn(const Vec<T>& v, const CubeSlice<T>& s, long pos, const T& val)
{
long m = s.getProd(1);
long n = s.getDim(0);
long n1 = n;
assert(pos >= 0 && pos < m);
if (v.length() < n) n1 = v.length();
const T* vp = &v[0];
T* sp = &s[0];
for (long i = 0; i < n1; i++)
sp[pos + i*m] = vp[i];
for (long i = n1; i < n; i++)
sp[pos + i*m] = val;
}
// NOTE: the signature for this is in lzz_p.h
void conv(vec_zz_p& x, const Vec<long>& a)
{
long i, n;
n = a.length();
x.SetLength(n);
VectorConv(n, x.elts(), a.elts());
}
bool SubdivScene::repositionSelectedVertex(int x, int y) {
if (!selectedVertex)
return false;
printf("Repositioning vertex, (%i, %i)...\n", x,y);
//In the plane perpendicular to camera->look, and through which the vertex passes,
//move vertex from where it is to where the mouse is
//Use current vertex position to calculate the center of the screen
Vec camPos = camera->getPos();
Vec vPos = selectedVertex->getData().p;
Vec diff = vPos - camPos;
Vec look = camera->getLook().normalize();
float cosAngle = sqrt(diff.normalize().dot(look));
float lookLength = diff.length()*cosAngle;
Vec centreDiff = look*lookLength;
Vec diffInPlane = vPos - (camPos + centreDiff);
printf(" diffInPlane is"); diffInPlane.print();
printf(" Cam pos is"); camPos.print();
float anglex = (x - Globals::getWidth()/2)*Globals::getFovx() * Globals::PI/180/Globals::getWidth();
float angley = (y - Globals::getHeight()/2)*Globals::getFovy() * Globals::PI/180/Globals::getHeight();
float hLength = tan(anglex)*centreDiff.length();
float vLength = tan(angley)*centreDiff.length();
printf(" anglex is %f and angley is %f, fovx is %f\n", anglex, angley, Globals::getFovx());
printf(" hLength is %f and vLength is %f, hrat is %i\n", hLength, vLength, x - Globals::getWidth()/2);
//calculate the shifts in the horiz and vertical directions
Vec right = camera->getLook().cross(camera->getUp()).normalize()*hLength;
Vec up = camera->getUp().normalize()*vLength;
printf(" Right is"); right.print();
printf(" up is"); up.print();
Vec newPos = vPos + right + up - diffInPlane;
selectedVertex->getData().p = newPos;
printf(" Old position was (%f, %f, %f)\n", vPos.x, vPos.y, vPos.z);
printf(" New position is (%f, %f, %f)\n", newPos.x, newPos.y, newPos.z);
redrawRequired = true;
}
void mapPowerfulToPoly(ZZX& poly,
const Vec<long>& pow,
const Vec<long>& divVec,
long m,
const ZZX& phimX)
{
long k = pow.length();
assert(divVec.length() == k);
long j = 0;
for (long i = 0; i < k; i++)
j += pow[i] * divVec[i];
j %= m;
ZZX f = ZZX(j, 1);
poly = f % phimX;
}
// powVec[d] = p_d^{e_d}
// cycVec[d] = Phi_{p_d^{e_d}}(X) mod p
void computeCycVec(Vec<zz_pX>& cycVec, const Vec<long>& powVec)
{
long k = powVec.length();
cycVec.SetLength(k);
for (long d = 0; d < k; d++) {
ZZX PhimX = Cyclotomic(powVec[d]);
cycVec[d] = conv<zz_pX>(PhimX);
}
}
void Spring::apply() const
{
Vec delta = mB->pos - mA->pos;
float distance = delta.length();
float offset = mRestLength - distance;
if( distance > ci::EPSILON_VALUE )
{ offset /= distance; }
Vec correction = delta * offset / 2.0f * mStiffness;
mA->pos -= correction;
mB->pos += correction;
}
ZZ sum(const Vec<ZZ>& v)
{
ZZ acc;
acc = 0;
for (long i = 0; i < v.length(); i++)
acc += v[i];
return acc;
}
// Adds one to the little-endian representation of an integer in base digits,
// returns true if there was an overflow
static bool addOne(Vec<long>& rep, const Vec<long> digits)
{
for (long i=rep.length()-1; i>=0; --i) {
rep[i]++;
if (rep[i] >= digits[i])
rep[i] -= digits[i];
else
return false;
}
return true;
}
void mapPowerfulToPoly(ZZX& poly,
const Vec<long>& pow,
const Vec<long>& divVec,
long m,
const ZZX& phimX)
{
long k = pow.length();
//OLD: assert(divVec.length() == k);
helib::assertEq(divVec.length(), k, "pow and divVec have different sizes");
long j = 0;
for (long i = 0; i < k; i++)
j += pow[i] * divVec[i];
j %= m;
ZZX f = ZZX(j, 1);
poly = f % phimX;
}
// Compute one or more layers corresponding to one network of one leaf
void PermNetwork::setLayers4Leaf(long lyrIdx, const ColPerm& p,
const Vec<long>& benesLvls, long gIdx,
const SubDimension& leafData,
const Permut& map2cube)
{
#ifdef DEBUG_PRINTOUT
std::cerr << "Layer "<<lyrIdx<<", column-permutation="<< p << endl;
#endif
// Compute the shift amounts for all the layers in this network
Vec<bool> isID;
Vec<Permut> shifts;
if (benesLvls.length()==1) {// Special case for a "trivial" 1-layer network
shifts.SetLength(1);
isID.SetLength(1);
isID[0] = !p.getShiftAmounts(shifts[0]);
}
else // The general case of a multi-layer Benes network
p.getBenesShiftAmounts(shifts,isID,benesLvls);
// Copy the shift amounts to the right place in the bigger network,
// renaming the slots from a linear array to the hyper cube
for (long i=0; i<benesLvls.length(); i++) {
PermNetLayer& lyr = layers[lyrIdx+i];
lyr.genIdx = gIdx;
lyr.isID = isID[i];
lyr.e = leafData.e;
if (!lyr.isID) {
#ifdef DEBUG_PRINTOUT
std::cerr << "layer "<<lyrIdx+i<<": "<<shifts[i]<<endl;
#endif
if (leafData.good) // For good leaves, shift by -x is the same as size-x
for (long k=0; k<shifts[i].length(); k++)
if (shifts[i][k]<0) shifts[i][k] += leafData.size;
applyPermToVec(lyr.shifts, shifts[i], map2cube); // do the renaming
#ifdef DEBUG_PRINTOUT
std::cerr << " : "<<lyr.shifts<<endl;
#endif
}
// else std::cerr << "layer "<<lyrIdx+i<<"= identity\n";
}
}
// divVec[d] = m/p_d^{e_d}, powVec[d] = p^{e_d}
// computes invVec[d] = divVec[d]^{-1} mod powVec[d]
void computeInvVec(Vec<long>& invVec,
const Vec<long>& divVec, const Vec<long>& powVec)
{
long k = divVec.length();
invVec.SetLength(k);
for (long d = 0; d < k; d++) {
long t1 = divVec[d] % powVec[d];
long t2 = InvMod(t1, powVec[d]);
invVec[d] = t2;
}
}
void computeInvVec(Vec<long>& invVec,
const Vec<long>& divVec, const Vec<long>& powVec)
{
long k = divVec.length();
invVec.SetLength(k);
for (long i = 0; i < k; i++) {
long t1 = divVec[i] % powVec[i];
long t2 = InvMod(t1, powVec[i]);
invVec[i] = t2;
}
}
void Spring::apply()
{
Vec x = *p1->x - *p2->x,
v = *p1->v - *p2->v;
if (!x)
return;
unit l = x.length();
Vec f = ((ks * (l - rest)) + (kd * (v * x) / l)) * (x / l);
*p1->f += f;
*p2->f -= f;
}