void
test1(int denom)
{
double r1, r2;
int t1, t2;
r1 = recip(denom); /* Stored in memory */
r2 = recip(denom); /* Stored in register */
t1 = r1 == r2; /* Compares register to memory */
do_nothing(); /* Forces register save to memory */
t2 = r1 == r2; /* Compares memory to memory */
printf("test1 t1: r1 %f %c= r2 %f\n", r1, t1 ? '=' : '!', r2);
printf("test1 t2: r1 %f %c= r2 %f\n", r1, t2 ? '=' : '!', r2);
}
doubledouble erf(const doubledouble x) {
if (0.0==x.h()) return 0.0;
int i; doubledouble y,r;
// const below is evalf(1/sqrt(Pi),40)
static const doubledouble oneonrootpi="0.564189583547756286948079451560772585844";
const double cut=1.5; // switch to continued fraction here
y=fabs(x);
if (y.h()>26.0) { // erf is +or- 1 to 300 dp.
r=1;
} else if (y.h()<cut) { // use power series
doubledouble ap=0.5,s,t,x2;
s=t=2.0; x2=sqr(x);
for (i=0; i<200; i++) {
ap+=1;
t*=x2/ap;
s+=t;
if (fabs(t.h())<1e-35*fabs(s.h())) {
r=x*oneonrootpi*s/exp(x2);
break;
}
}
if (i>199)
{ cerr<<"\ndoubledouble: no convergence in erf power series, x="<<x<<endl; exit(1); }
} else { // |x|>=cut, use continued fraction, Lentz method
double an,small=1e-300;
doubledouble b,c,d,h,del,x2;
x2=sqr(x);
b=x2+0.5;
c=1.0e300;
d=recip(b);
h=d;
for (i=1; i<300; i++) {
an=i*(0.5-i);
b+=2.0;
d=an*d+b;
if (fabs(d.h())<small) d=small;
c=b+an/c;
if (fabs(c.h())<small) c=small;
d=recip(d);
del=d*c;
h*=del;
if (del.h()==1.0 && del.l()<1.0e-30) break;
if (299==i)
{ cerr<<"\ndoubledouble: no convergence in erf continued fraction, x="<<x<<endl; exit(1); }
}
r=1.0-oneonrootpi*sqrt(x2)/exp(x2)*h;
}
if (x.h()>0.0) return r; else return -r;
}
static A jttayamp(J jt,A w,B nf,A x,A h){A y;B ng=!nf;I j,n;V*v=VAV(h);
ASSERT(AR(x)<=(nf?v->lr:v->rr),EVRANK);
switch(v->id){
case CPLUS: R tpoly(over(x,one));
case CMINUS: R tpoly(nf?over(x,num[-1]):over(negate(x),one));
case CSTAR: R tpoly(over(zero,x));
case CDIV: ASSERT(ng,EVDOMAIN); R tpoly(over(zero,recip(x)));
case CJDOT: R tpoly(nf?over(x,a0j1):over(jdot1(x),one));
case CPOLY: ASSERT(nf,EVDOMAIN); R tpoly(BOX&AT(x)?poly1(x):x);
case CHGEOM: ASSERT(nf,EVDOMAIN); RE(j=i0(x)); ASSERT(0<=j,EVDOMAIN);
y=IX(j);
R tpoly(divide(hgcoeff(y,h),fact(y)));
case CBANG: ASSERT(nf,EVDOMAIN); RE(j=i0(x)); ASSERT(0<=j,EVDOMAIN);
R tpoly(divide(poly1(box(iota(x))),fact(x)));
case CEXP: if(nf)R eva(x,"(^.x)&^ % !");
RE(n=i0(x));
R 0<=n?tpoly(over(reshape(x,zero),one)):atop(ds(CDIV),amp(h,sc(-n)));
case CFIT: ASSERT(nf&&CPOLY==ID(v->f),EVDOMAIN);
y=over(x,IX(IC(x)));
R tpoly(mdiv(df2(x,y,h),atab(CEXP,y,IX(IC(x)))));
case CCIRCLE:
switch(i0(x)){
case 1: R eval("{&0 1 0 _1@(4&|) % !");
case -3: R eval("{&0 1 0 _1@(4&|) % ]");
case 2: R eval("{&1 0 _1 0@(4&|) % !");
case 5: R eval("2&| % !");
case -7: R eval("2&| % ]");
case 6: R eval("2&|@>: % !");
case -1: R eval("(2&| % ]) * ([: */ (1&+ % 2&+)@(i.@<.&.-:))\"0");
case -5: R eval("({&0 1 0 _1@(4&|) % ]) * ([: */ (1&+ % 2&+)@(i.@<.&.-:))\"0");
}}
ASSERT(0,EVDOMAIN);
}
void
test2(int denom)
{
double r1;
int t1;
r1 = recip(denom);
t1 = r1 == 1.0 / (double) denom;
printf("test2 t1: r1 %f %c= 1.0/10.0\n", r1, t1 ? '=' : '!');
}
doubledouble atan(const doubledouble& x) {
double xh=x.h();
if (0.0==xh) return doubledouble(0.0);
// Asymptotic formula for large |x|...
if (fabs(xh)>1.0e6)
{ doubledouble r=recip(x), r2=sqr(r); return doubledouble::Pion2-r+r2*r*(1.0-"0.6"*r2)/3; }
doubledouble s,c,a=atan(xh); // a=double approx to result
sincos(a,s,c);
return a+c*(c*x-s); // Newton step
}
// doubledouble^int
doubledouble powint(const doubledouble& u, const int c) {
if (c<0) return recip(powint(u,-c));
switch (c) {
case 0: return u.h()==0.0?doubledouble(pow(0.0,0.0)):doubledouble(1.0); // let math.h handle 0^0.
case 1: return u;
case 2: return sqr(u);
case 3: return sqr(u)*u;
default: { // binary method
int n=c, m; doubledouble y=1.0, z=u; if (n<0) n=-n;
while (1) {
m=n; n/=2;
if (n+n!=m) { // if m odd
y*=z; if (0==n) return y;
}
z=sqr(z);
}
}
}
}
Line getPerpendic(Line line, Point at) {
Line newLine;
// if vertical newLine => horizontal
if (line.a == 0){ // y=0; x=c
newLine.a = 1;
newLine.b = 0;
newLine.c = at.y();
}else{
if (line.b == 0) { // x=0; y=c
newLine.a = 0;
newLine.b = 1;
newLine.c = at.x();
}else{
newLine.a = 1.0;
newLine.b = -1*recip(-1*line.b); // Find the reciprocal of line
newLine.c = at.y() + newLine.b*at.x(); // Calculate the equation through the point 'at'
}
}
return newLine;
}
int main() {
Lattice lat(Cartesian(0,.5,.5), Cartesian(.5,0,.5), Cartesian(.5,.5,0));
Cartesian middle(0.5,0.5,0.5);
Relative middlerel = lat.toRelative(middle);
Reciprocal recip(0.2,0,0);
int resolution = 20;
Grid foo(lat, resolution, resolution, resolution),
bar(lat, resolution, resolution, resolution);
foo.Set(gaussian);
foo.epsSlice("demo.eps", Cartesian(1,0,0), Cartesian(0,1,0),
Cartesian(-.5,-.5,.5), 150);
foo.epsNativeSlice("native.eps", Cartesian(1,0,0), Cartesian(0,1,0),
Cartesian(-.5,-.5,.5));
//std::cout << "and here is the foo" << (foo + 2*bar + foo.cwise()*bar);
std::cout << "middle and middlerel are:\n"
<< middle << std::endl << middlerel << std::endl
<< lat.toCartesian(middlerel) << std::endl;
std::cout << "middle dot recip: " << recip * middle << std::endl;
return 0;
}
/**
* Exact polynomial division of a, b \in Z_p[x_0, \ldots, x_n]
* It doesn't check whether the inputs are proper polynomials, so be careful
* of what you pass in.
*
* @param a first multivariate polynomial (dividend)
* @param b second multivariate polynomial (divisor)
* @param q quotient (returned)
* @param var variables X iterator to first element of vector of symbols
*
* @return "true" when exact division succeeds (the quotient is returned in
* q), "false" otherwise.
* @note @a p = 0 means the base ring is Z
*/
bool divide_in_z_p(const ex &a, const ex &b, ex &q, const exvector& vars, const long p)
{
static const ex _ex1(1);
if (b.is_zero())
throw(std::overflow_error("divide_in_z: division by zero"));
if (b.is_equal(_ex1)) {
q = a;
return true;
}
if (is_exactly_a<numeric>(a)) {
if (is_exactly_a<numeric>(b)) {
// p == 0 means division in Z
if (p == 0) {
const numeric tmp = ex_to<numeric>(a/b);
if (tmp.is_integer()) {
q = tmp;
return true;
} else
return false;
} else {
q = (a*recip(ex_to<numeric>(b), p)).smod(numeric(p));
return true;
}
} else
return false;
}
if (a.is_equal(b)) {
q = _ex1;
return true;
}
// Main symbol
const ex &x = vars.back();
// Compare degrees
int adeg = a.degree(x), bdeg = b.degree(x);
if (bdeg > adeg)
return false;
// Polynomial long division (recursive)
ex r = a.expand();
if (r.is_zero())
return true;
int rdeg = adeg;
ex eb = b.expand();
ex blcoeff = eb.coeff(x, bdeg);
exvector v;
v.reserve(std::max(rdeg - bdeg + 1, 0));
exvector rest_vars(vars);
rest_vars.pop_back();
while (rdeg >= bdeg) {
ex term, rcoeff = r.coeff(x, rdeg);
if (!divide_in_z_p(rcoeff, blcoeff, term, rest_vars, p))
break;
term = (term*power(x, rdeg - bdeg)).expand();
v.push_back(term);
r = (r - term*eb).expand();
if (p != 0)
r = r.smod(numeric(p));
if (r.is_zero()) {
q = (new add(v))->setflag(status_flags::dynallocated);
return true;
}
rdeg = r.degree(x);
}
return false;
}
void CContextContactsDetailView::HandleCreateMessageL()
{
TInt idx = iContainer->get_current_item_idx();
const MPbkFieldData& fielddata=iItem->PbkFieldAt(idx);
TPbkFieldId id = fielddata.PbkFieldId();
const TPbkContactItemField * field = iItem->FindField(id, idx);
TAddressSelectorF selector = SmsSelectorL;
TMessageSenderF sender = &CMessaging::MessageSenderL;
TPbkFieldFilterF filter = SmsFieldFilterL;
TInt warningResource = R_CONTACTS_NO_SMS;
auto_ptr<CArrayFixFlat<TUid> > disabled_mtms( new (ELeave) CArrayFixFlat< TUid >(4) );
const CPbkFieldInfo &info=field->FieldInfo();
TBool is_address_field=EFalse;
auto_ptr<CDesCArrayFlat> recip( new (ELeave) CDesCArrayFlat(1));
auto_ptr<CDesCArrayFlat> alias( new (ELeave) CDesCArrayFlat(1));
auto_ptr<HBufC> title(iItem->GetContactTitleL());
alias->AppendL(*title);
if (!info.IsPhoneNumberField()) {
disabled_mtms->AppendL(KSenduiMtmSmsUid);
} else {
is_address_field=ETrue;
}
if (!info.IsPhoneNumberField() && !info.IsMmsField() ) {
disabled_mtms->AppendL(KSenduiMtmMmsUid);
} else {
is_address_field=ETrue;
}
if (!info.IsEmailField()) {
disabled_mtms->AppendL(KSenduiMtmSmtpUid);
} else {
is_address_field=ETrue;
}
if (!is_address_field) disabled_mtms->Reset();
else recip->AppendL( fielddata.PbkFieldText() );
disabled_mtms->AppendL(KSenduiMtmIrUid);
disabled_mtms->AppendL(KSenduiMtmBtUid);
TUid mtm=iMessaging->iSendAppUi->ShowSendQueryL(0, TSendingCapabilities(KCapabilitiesForAllServices),
disabled_mtms.get(), _L("Send Message"));
if (mtm==KNullUid) return;
if (is_address_field) {
iMessaging->MessageSenderL(recip.get(), alias.get(), mtm);
} else {
if (mtm==KSenduiMtmSmtpUid) {
selector=EmailSelectorL;
filter=EmailFieldFilterL;
warningResource=R_CONTACTS_NO_EMAIL;
} else if (mtm!=KSenduiMtmSmsUid) {
selector=MmsSelectorL;
filter=MmsFieldFilterL;
warningResource=R_CONTACTS_NO_MMS;
}
iMessaging->CreateSingleMessageL( iItem->Id(), selector, sender, mtm );
}
}
static inline void SV_PackEntity(
int edictIdx,
edict_t* ent,
SendTable* pSendTable,
EntityChange_t changeType,
CFrameSnapshot *pSnapshot )
{
int iSerialNum = pSnapshot->m_Entities[ edictIdx ].m_nSerialNumber;
// Check to see if this entity specifies its changes.
// If so, then try to early out making the fullpack
bool bUsedPrev = false;
if ( changeType == ENTITY_CHANGE_NONE )
{
// Now this may not work if we didn't previously send a packet;
// if not, then we gotta compute it
bUsedPrev = framesnapshot->UsePreviouslySentPacket( pSnapshot, edictIdx, iSerialNum );
}
if ( !bUsedPrev || sv_debugmanualmode.GetInt() )
{
// First encode the entity's data.
char packedData[MAX_PACKEDENTITY_DATA];
bf_write writeBuf( "SV_PackEntity->writeBuf", packedData, sizeof( packedData ) );
// (avoid constructor overhead).
unsigned char tempData[ sizeof( CSendProxyRecipients ) * MAX_DATATABLE_PROXIES ];
CUtlMemory< CSendProxyRecipients > recip( (CSendProxyRecipients*)tempData, pSendTable->GetNumDataTableProxies() );
if( !SendTable_Encode( pSendTable, ent->m_pEnt, &writeBuf, NULL, edictIdx, &recip ) )
{
Host_Error( "SV_PackEntity: SendTable_Encode returned false (ent %d).\n", edictIdx );
}
SV_EnsureInstanceBaseline( edictIdx, packedData, writeBuf.GetNumBytesWritten() );
int nFlatProps = SendTable_GetNumFlatProps( pSendTable );
IChangeFrameList *pChangeFrame;
// If this entity was previously in there, then it should have a valid IChangeFrameList
// which we can delta against to figure out which properties have changed.
//
// If not, then we want to setup a new IChangeFrameList.
PackedEntity *pPrevFrame = framesnapshot->GetPreviouslySentPacket( edictIdx, pSnapshot->m_Entities[ edictIdx ].m_nSerialNumber );
if ( pPrevFrame )
{
// Calculate a delta.
bf_read bfPrev( "SV_PackEntity->bfPrev", pPrevFrame->LockData(), pPrevFrame->GetNumBytes() );
bf_read bfNew( "SV_PackEntity->bfNew", packedData, writeBuf.GetNumBytesWritten() );
int deltaProps[MAX_DATATABLE_PROPS];
int nChanges = SendTable_CalcDelta(
pSendTable,
pPrevFrame->LockData(), pPrevFrame->GetNumBits(),
packedData, writeBuf.GetNumBitsWritten(),
deltaProps,
ARRAYSIZE( deltaProps ),
edictIdx
);
// If it's non-manual-mode, but we detect that there are no changes here, then just
// use the previous pSnapshot if it's available (as though the entity were manual mode).
// It would be interesting to hook here and see how many non-manual-mode entities
// are winding up with no changes.
if ( nChanges == 0 )
{
if ( changeType == ENTITY_CHANGE_NONE )
{
for ( int iDeltaProp=0; iDeltaProp < nChanges; iDeltaProp++ )
{
Msg( "Entity %d (class '%s') reported ENTITY_CHANGE_NONE but '%s' changed.\n",
edictIdx,
STRING( ent->classname ),
pSendTable->GetProp( deltaProps[iDeltaProp] )->GetName() );
}
}
else
{
if ( pPrevFrame->CompareRecipients( recip ) )
{
if ( framesnapshot->UsePreviouslySentPacket( pSnapshot, edictIdx, iSerialNum ) )
return;
}
}
}
// Ok, now snag the changeframe from the previous frame and update the 'last frame changed'
// for the properties in the delta.
pChangeFrame = pPrevFrame->SnagChangeFrameList();
ErrorIfNot( pChangeFrame && pChangeFrame->GetNumProps() == nFlatProps,
("SV_PackEntity: SnagChangeFrameList returned null")
);
pChangeFrame->SetChangeTick( deltaProps, nChanges, pSnapshot->m_nTickNumber );
}
else
{
// Ok, init the change frames for the first time.
pChangeFrame = AllocChangeFrameList( nFlatProps, pSnapshot->m_nTickNumber );
}
// Now make a PackedEntity and store the new packed data in there.
PackedEntity *pCurFrame = framesnapshot->CreatePackedEntity( pSnapshot, edictIdx );
pCurFrame->SetChangeFrameList( pChangeFrame );
pCurFrame->m_nEntityIndex = edictIdx;
pCurFrame->m_pSendTable = pSendTable;
pCurFrame->AllocAndCopyPadded( packedData, writeBuf.GetNumBytesWritten(), &g_PackedDataAllocator );
pCurFrame->SetRecipients( recip );
}
}
doubledouble cosh(const doubledouble& x) { doubledouble t=exp(x); return 0.5*(t+recip(t)); }
// hyperbolic
doubledouble sinh(const doubledouble& x) {
if (fabs(x.h())<1.0e-5) { // avoid cancellation in e^x-e^(-x), use Taylor series...
doubledouble q=sqr(x); return x*(1+q/6*(1+q/20*(1+q/42))); }
doubledouble t=exp(x);
return 0.5*(t-recip(t));
}
matrix_pf * NullSpace(BerlekampMatrix* b_mtx, int *r_ret)
{
int deg = b_mtx->GetDegree();
int prime_char = b_mtx->PrimeBase();
matrix_pf *v = new matrix_pf(0,deg,0,deg);
int *c = new int[deg];
PrimeFieldElem b_val;
int i, j, k, k1, r, s;
bool dependence_found;
for(i=0; i<deg; i++) c[i]=-1;
r=0;
for( k=0; k<deg; k++)
{
dependence_found = false;
for( j=0; j<deg; j++)
{
if( (*b_mtx)[k][j] == 0 ) continue;
if( c[j] >= 0 ) continue;
//---------------------------------
// multiply column by -1/B[k,j]
b_val = neg(recip( (*b_mtx)[k][j]));
for( k1=0; k1<deg; k1++)
(*b_mtx)[k1][j] *= b_val;
//---------------------------------------
// add B[k,i] times column j to column i
// for all i .ne. j
for( i=0; i<deg; i++)
{
if( (i==j) || ((*b_mtx)[k][i] == 0) ) continue;
b_val = (*b_mtx)[k][i];
for( k1=0; k1<deg; k1++)
{
(*b_mtx)[k1][i] += b_val * (*b_mtx)[k1][j];
}
}
c[j] = k;
dependence_found = true;
break;
} // end of loop over j
if( !dependence_found )
{
for( j=0; j<deg; j++)
{
(*v)[r][j] = PrimeFieldElem(prime_char,0);
for( s=0; s<deg; s++)
{
if( c[s] == j ) (*v)[r][j] = (*b_mtx)[k][s];
}
if( j==k ) (*v)[r][j] = PrimeFieldElem(prime_char,1);
}
r++;
}
} // end of loop over k
*r_ret = r;
return(v);
};
int main(int, char**) {
int x = 3;
return int(int(www) * recip(x));
}
// Newton-Raphson refinements of the low-precision ops
vr recip2(const vr &a) { vr b=recip(a); return (imm(2)-a*b)*b; }