template<class TV> void SparseMatrix::
multiply_helper(RawArray<const TV> x,RawArray<TV> result) const
{
const int rows = this->rows();
GEODE_ASSERT(columns()<=x.size() && rows<=result.size());
RawArray<const int> offsets = J.offsets;
RawArray<const int> J_flat = J.flat;
RawArray<const T> A_flat = A.flat;
for(int i=0;i<rows;i++){
int end=offsets[i+1];TV sum=TV();
for(int index=offsets[i];index<end;index++) sum+=A_flat[index]*x[J_flat[index]];
result[i]=sum;}
result.slice(rows,result.size()).zero();
}
static void spatial_sort(RawArray<Perturbed2> X, const int leaf_size, Random& random) {
const int n = X.size();
if (n<=leaf_size)
return;
// We determine the subdivision axis using inexact computation, which is okay since neither the result nor
// the asymptotic worst case complexity depends upon any properties of the spatial_sort whatsoever.
const Box<EV> box = bounding_box(X.project<EV,&Perturbed2::value_>());
const int axis = box.sizes().argmax();
// We use exact arithmetic to perform the partition, which is important in case many points are coincident
const int mid = axis==0 ? spatial_partition<0>(X,random)
: spatial_partition<1>(X,random);
// Recursely sort both halves
spatial_sort(X.slice(0,mid),leaf_size,random);
spatial_sort(X.slice(mid,n),leaf_size,random);
}
static inline RawArray<mp_limb_t> sqrt_helper(RawArray<mp_limb_t> result, RawArray<const mp_limb_t> x) {
const auto s = result.slice(0,(1+x.size())/2);
mpn_sqrtrem(s.data(),0,x.data(),x.size());
return trim(s);
}
