nifty_gridder.cc 14.1 KB
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#include <pybind11/pybind11.h>
#include <pybind11/numpy.h>
#include <iostream>
#include <algorithm>

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#ifdef __GNUC__
#define RESTRICT __restrict__
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#define NOINLINE __attribute__ ((noinline))
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#else
#define RESTRICT
#endif

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using namespace std;

namespace py = pybind11;

namespace {

constexpr double pi = 3.141592653589793238462643383279502884197;

static const uint16_t utab[] = {
#define Z(a) 0x##a##0, 0x##a##1, 0x##a##4, 0x##a##5
#define Y(a) Z(a##0), Z(a##1), Z(a##4), Z(a##5)
#define X(a) Y(a##0), Y(a##1), Y(a##4), Y(a##5)
X(0),X(1),X(4),X(5)
#undef X
#undef Y
#undef Z
};

uint32_t coord2morton2D_32 (uint32_t x, uint32_t y)
  {
  typedef uint32_t I;
  return  (I)(utab[x&0xff])     | ((I)(utab[(x>>8)&0xff])<<16)
       | ((I)(utab[y&0xff])<<1) | ((I)(utab[(y>>8)&0xff])<<17);
  }

static const uint8_t m2p2D_1[4][4] = {
{ 4, 1, 11, 2},{0,15, 5, 6},{10,9,3,12},{14,7,13,8}};
static uint8_t m2p2D_3[4][64];
static const uint8_t p2m2D_1[4][4] = {
{ 4, 1, 3, 10},{0,6,7,13},{15,9,8,2},{11,14,12,5}};
static uint8_t p2m2D_3[4][64];
static int peano2d_done=0;

static void init_peano2d (void)
  {
  peano2d_done=1;

  for (int d=0; d<4; ++d)
    for (uint32_t p=0; p<64; ++p)
      {
      unsigned rot = d;
      uint32_t v = p<<26;
      uint32_t res = 0;
      for (int i=0; i<3; ++i)
        {
        unsigned tab=m2p2D_1[rot][v>>30];
        v<<=2;
        res = (res<<2) | (tab&0x3);
        rot = tab>>2;
        }
      m2p2D_3[d][p]=res|(rot<<6);
      }
  for (int d=0; d<4; ++d)
    for (uint32_t p=0; p<64; ++p)
      {
      unsigned rot = d;
      uint32_t v = p<<26;
      uint32_t res = 0;
      for (int i=0; i<3; ++i)
        {
        unsigned tab=p2m2D_1[rot][v>>30];
        v<<=2;
        res = (res<<2) | (tab&0x3);
        rot = tab>>2;
        }
      p2m2D_3[d][p]=res|(rot<<6);
      }
  }

uint32_t morton2peano2D_32(uint32_t v, int bits)
  {
  if (!peano2d_done) init_peano2d();
  unsigned rot = 0;
  uint32_t res = 0;
  v<<=32-(bits<<1);
  int i=0;
  for (; i<bits-2; i+=3)
    {
    unsigned tab=m2p2D_3[rot][v>>26];
    v<<=6;
    res = (res<<6) | (tab&0x3fu);
    rot = tab>>6;
    }
  for (; i<bits; ++i)
    {
    unsigned tab=m2p2D_1[rot][v>>30];
    v<<=2;
    res = (res<<2) | (tab&0x3);
    rot = tab>>2;
    }
  return res;
  }

void myassert(bool cond, const char *msg)
  {
  if (cond) return;
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  throw runtime_error(msg);
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  }

template<typename It, typename Comp> class IdxComp__
  {
  private:
    It begin;
    Comp comp;
  public:
    IdxComp__ (It begin_, Comp comp_): begin(begin_), comp(comp_) {}
    bool operator() (std::size_t a, std::size_t b) const
      { return comp(*(begin+a),*(begin+b)); }
  };
/*! Performs an indirect sort on the supplied iterator range and returns in
    \a idx a \a vector containing the indices of the smallest, second smallest,
    third smallest, etc. element, according to \a comp. */
template<typename It, typename T2, typename Comp>
  inline void buildIndex (It begin, It end, std::vector<T2> &idx, Comp comp)
  {
  using namespace std;
  T2 num=end-begin;
  idx.resize(num);
  for (T2 i=0; i<num; ++i) idx[i] = i;
  sort (idx.begin(),idx.end(),IdxComp__<It,Comp>(begin,comp));
  }

/*! Performs an indirect sort on the supplied iterator range and returns in
    \a idx a \a vector containing the indices of the smallest, second smallest,
    third smallest, etc. element. */
template<typename It, typename T2> inline void buildIndex (It begin, It end,
  std::vector<T2> &idx)
  {
  using namespace std;
  typedef typename iterator_traits<It>::value_type T;
  buildIndex(begin,end,idx,less<T>());
  }

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/*! Returns the remainder of the division \a v1/v2.
    The result is non-negative.
    \a v1 can be positive or negative; \a v2 must be positive. */
inline double fmodulo (double v1, double v2)
  {
  if (v1>=0)
    return (v1<v2) ? v1 : fmod(v1,v2);
  double tmp=fmod(v1,v2)+v2;
  return (tmp==v2) ? 0. : tmp;
//  return (v1>=0) ? ((v1<v2) ? v1 : fmod(v1,v2)) : (fmod(v1,v2)+v2);
  }

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static inline double one_minus_x2 (double x)
  { return (fabs(x)>0.1) ? (1.+x)*(1.-x) : 1.-x*x; }

void legendre_prep(int n, vector<double> &x, vector<double> &w)
  {
  constexpr double pi = 3.141592653589793238462643383279502884197;
  constexpr double eps = 3e-14;
  int m = (n+1)>>1;
  x.resize(m);
  w.resize(m);

  double t0 = 1 - (1-1./n) / (8.*n*n);
  double t1 = 1./(4.*n+2.);

#pragma omp parallel
{
  int i;
#pragma omp for schedule(dynamic,100)
  for (i=1; i<=m; ++i)
    {
    double x0 = cos(pi * ((i<<2)-1) * t1) * t0;

    int dobreak=0;
    int j=0;
    double dpdx;
    while(1)
      {
      double P_1 = 1.0;
      double P0 = x0;
      double dx, x1;

      for (int k=2; k<=n; k++)
        {
        double P_2 = P_1;
        P_1 = P0;
//        P0 = ((2*k-1)*x0*P_1-(k-1)*P_2)/k;
        P0 = x0*P_1 + (k-1.)/k * (x0*P_1-P_2);
        }

      dpdx = (P_1 - x0*P0) * n / one_minus_x2(x0);

      /* Newton step */
      x1 = x0 - P0/dpdx;
      dx = x0-x1;
      x0 = x1;
      if (dobreak) break;

      if (abs(dx)<=eps) dobreak=1;
      if (++j>=100) throw runtime_error("convergence problem");
      }

    x[m-i] = x0;
    w[m-i] = 2. / (one_minus_x2(x0) * dpdx * dpdx);
    }
} // end of parallel region
  }

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using a_i_c = py::array_t<int, py::array::c_style | py::array::forcecast>;
using a_d_c = py::array_t<double, py::array::c_style | py::array::forcecast>;
using a_c_c = py::array_t<complex<double>,
  py::array::c_style | py::array::forcecast>;

a_i_c peanoindex(const a_d_c &uv_, int nu, int nv)
  {
  myassert(uv_.ndim()==2, "uv array must be 2D");
  myassert(uv_.shape(1)==2, "uv.shape[1] must be 2");
  int nvis = uv_.shape(0);
  auto uv = uv_.data();

  int npmax = max(nu, nv);
  int nbits = 0;
  for (int istart = npmax-1; istart!=0; istart>>=1, ++nbits);
  vector<int> ipeano(nvis);
  for (int i=0; i<nvis; ++i)
    {
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    auto u = fmodulo(uv[2*i], 1.)*nu;
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    auto iu = min(nu-1, int(u));
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    auto v = fmodulo(uv[2*i+1], 1.)*nv;
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    auto iv = min(nv-1, int(v));
    ipeano[i] = morton2peano2D_32(coord2morton2D_32(iu,iv),nbits);
    }
  vector<int> newind;
  buildIndex(ipeano.begin(), ipeano.end(), newind);
  int odim[] = {nvis};
  a_i_c res(odim);
  auto iout = res.mutable_data();
  for (int i=0; i<nvis; ++i)
    iout[i] = newind[i];
  return res;
  }

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int get_w(double epsilon)
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  {
  static const vector<double> maxmaperr { 1e8, 0.32, 0.021, 6.2e-4,
    1.08e-5, 1.25e-7, 8.25e-10, 5.70e-12, 1.22e-13, 2.48e-15, 4.82e-17,
    6.74e-19, 5.41e-21, 4.41e-23, 7.88e-25, 3.9e-26 };

  double epssq = epsilon*epsilon;

  for (size_t i=1; i<maxmaperr.size(); ++i)
    if (epssq>maxmaperr[i]) return i;
  throw runtime_error("requested epsilon too small - minimum is 2e-13");
  }
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class Helper
  {
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  protected:
    int nu, nv;
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  public:
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    int w;
    double beta;
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  protected:
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    int nsafe, su;
  public:
    int sv;
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    vector<double> kernel;
    int iu0, iv0; // start index of the current visibility
    int bu0, bv0; // start index of the current buffer

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    void NOINLINE update(double u_in, double v_in)
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      {
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      auto u = fmodulo(u_in, 1.)*nu;
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      iu0 = int(u-w*0.5 + 1 + nu) - nu;
      if (iu0+w>nu+nsafe) iu0 = nu+nsafe-w;
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      auto v = fmodulo(v_in, 1.)*nv;
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      iv0 = int(v-w*0.5 + 1 + nv) - nv;
      if (iv0+w>nv+nsafe) iv0 = nv+nsafe-w;
      double xw=2./w;
      for (int i=0; i<w; ++i)
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        {
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        kernel[i  ] = xw*(iu0+i-u);
        kernel[i+w] = xw*(iv0+i-v);
        }
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      for (auto &k : kernel)
        k = exp(beta*sqrt(1.-k*k));
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      }

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    bool need_to_move() const
      { return (iu0<bu0) || (iv0<bv0) || (iu0+w>bu0+su) || (iv0+w>bv0+sv); }
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    void update_position()
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      {
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      bu0=max(-nsafe, min(nu+nsafe-su, iu0+nsafe-su/2));
      bv0=max(-nsafe, min(nv+nsafe-sv, iv0+nsafe-sv/2));
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      }

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  protected:
    Helper(int nu_, int nv_, double epsilon)
      : nu(nu_), nv(nv_),
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        w(get_w(epsilon)), beta(2.3*w), nsafe((w+1)/2),
        su(min(max(2*w,80), nu)), sv(min(max(2*w,80), nv)),
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        kernel(2*w),
        bu0(-1000000), bv0(-1000000)
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      {
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      if (min(nu,nv)<2*nsafe) throw runtime_error("grid dimensions too small");
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      }
  };

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class WriteHelper: public Helper
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  {
  private:
    vector<complex<double>> data;
    complex<double> *grid;

    void dump()
      {
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      if (bu0<-nsafe) return; // nothing written into buffer yet
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#pragma omp critical
{
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      int idxu = (bu0+nu)%nu;
      int idxv0 = (bv0+nv)%nv;
      for (int iu=0; iu<su; ++iu)
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        {
        int idxv = idxv0;
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        for (int iv=0; iv<sv; ++iv)
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          {
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          grid[idxu*nv + idxv] += data[iu*sv + iv];
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          if (++idxv>=nv) idxv=0;
          }
        if (++idxu>=nu) idxu=0;
        }
}
      }

  public:
    complex<double> *p0;
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    WriteHelper(int nu_, int nv_, double epsilon, complex<double> *grid_)
      : Helper(nu_, nv_, epsilon), data(su*sv, 0.), grid(grid_) {}
    ~WriteHelper() { dump(); }
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    void prep_write(double u_in, double v_in)
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      {
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      update(u_in, v_in);
      if (need_to_move())
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        {
        dump();
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        update_position();
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        fill(data.begin(), data.end(), 0.);
        }
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      p0 = data.data() + sv*(iu0-bu0) + iv0-bv0;
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      }
  };

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class ReadHelper: public Helper
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  {
  private:
    vector<complex<double>> data;
    const complex<double> *grid;

    void load()
      {
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      int idxu = (bu0+nu)%nu;
      int idxv0 = (bv0+nv)%nv;
      for (int iu=0; iu<su; ++iu)
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        {
        int idxv = idxv0;
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        for (int iv=0; iv<sv; ++iv)
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          {
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          data[iu*sv + iv] = grid[idxu*nv + idxv];
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          if (++idxv>=nv) idxv=0;
          }
        if (++idxu>=nu) idxu=0;
        }
      }

  public:
    const complex<double> *p0;
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    ReadHelper(int nu_, int nv_, double epsilon, const complex<double> *grid_)
      : Helper(nu_, nv_, epsilon), data(su*sv,0.), grid(grid_), p0(nullptr) {}
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    void prep_read(double u_in, double v_in)
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      {
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      update(u_in, v_in);
      if (need_to_move())
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        {
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        update_position();
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        load();
        }
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      p0 = data.data() + sv*(iu0-bu0) + iv0-bv0;
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      }
  };

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a_d_c complex2hartley (const a_c_c &grid_)
  {
  myassert(grid_.ndim()==2, "grid array must be 2D");
  int nu = grid_.shape(0), nv = grid_.shape(1);
  auto grid = grid_.data();

  int odim[] = {nu,nv};
  a_d_c res(odim);
  auto grid2 = res.mutable_data();
  for (int u=0; u<nu; ++u)
    {
    int xu = (u==0) ? 0 : nu-u;
    for (int v=0; v<nv; ++v)
      {
      int xv = (v==0) ? 0 : nv-v;
      int i1 = u*nv+v;
      int i2 = xu*nv+xv;
      grid2[i1] = 0.5*(grid[i1].real()+grid[i1].imag()+
                       grid[i2].real()-grid[i2].imag());
      }
    }
  return res;
  }

a_d_c to_grid (const a_d_c &uv_, const a_c_c &vis_,
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               int nu, int nv, double epsilon)
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  {
  myassert(uv_.ndim()==2, "uv array must be 2D");
  myassert(uv_.shape(1)==2, "uv.shape[1] must be 2");
  int nvis = uv_.shape(0);
  myassert(vis_.ndim()==1, "vis array must be 1D");
  myassert(vis_.shape(0)==nvis, "array size mismatch");
  auto uv = uv_.data();
  auto vis = vis_.data();

  int odim[] = {nu,nv};
  a_c_c res(odim);
  auto grid = res.mutable_data();
  for (int i=0; i<nu*nv; ++i) grid[i] = 0.;

#pragma omp parallel
{
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  WriteHelper hlp(nu, nv, epsilon, grid);
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  double emb = exp(-2*hlp.beta);
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  // Loop over sampling points
#pragma omp for schedule(dynamic,10000)
  for (int ipart=0; ipart<nvis; ++ipart)
    {
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    hlp.prep_write(uv[2*ipart], uv[2*ipart+1]);
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    auto * RESTRICT ptr = hlp.p0;
    int w = hlp.w;
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    auto v = vis[ipart]*emb;
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    const double * RESTRICT ku = hlp.kernel.data();
    const double * RESTRICT kv = hlp.kernel.data()+hlp.w;
    for (int cu=0; cu<w; ++cu)
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      {
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      complex<double> tmp = v*ku[cu];
      for (int cv=0; cv<w; ++cv)
        ptr[cv] += tmp*kv[cv];
      ptr+=hlp.sv;
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      }
    }
} // end of parallel region
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  return complex2hartley(res);
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  }

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a_c_c hartley2complex (const a_d_c &grid_)
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  {
  myassert(grid_.ndim()==2, "grid array must be 2D");
  int nu = grid_.shape(0), nv = grid_.shape(1);
  auto grid = grid_.data();

  int odim[] = {nu,nv};
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  a_c_c res(odim);
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  auto grid2 = res.mutable_data();
  for (int u=0; u<nu; ++u)
    {
    int xu = (u==0) ? 0 : nu-u;
    for (int v=0; v<nv; ++v)
      {
      int xv = (v==0) ? 0 : nv-v;
      int i1 = u*nv+v;
      int i2 = xu*nv+xv;
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      double v1 = 0.5*grid[i1];
      double v2 = 0.5*grid[i2];
      grid2[i1] = complex<double>(v1+v2, v1-v2);
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      }
    }
  return res;
  }

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a_c_c from_grid (const a_d_c &uv_, const a_d_c &grid0_, double epsilon)
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  {
  myassert(uv_.ndim()==2, "uv array must be 2D");
  myassert(uv_.shape(1)==2, "uv.shape[1] must be 2");
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  myassert(grid0_.ndim()==2, "grid array must be 2D");
  auto grid_ = hartley2complex(grid0_);
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  int nvis = uv_.shape(0);
  auto uv = uv_.data();
  auto grid = grid_.data();

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  int nu=grid_.shape(0),
      nv=grid_.shape(1);
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  int odim[] = {nvis};
  a_c_c res(odim);
  auto vis = res.mutable_data();

  // Loop over sampling points
#pragma omp parallel
{
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  ReadHelper hlp(nu, nv, epsilon, grid);
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  double emb = exp(-2*hlp.beta);
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#pragma omp for schedule(dynamic,10000)
  for (int ipart=0; ipart<nvis; ++ipart)
    {
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    hlp.prep_read(uv[2*ipart], uv[2*ipart+1]);
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    complex<double> r = 0.;
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    auto * RESTRICT ptr = hlp.p0;
    int w = hlp.w;
    const double * RESTRICT ku = hlp.kernel.data();
    const double * RESTRICT kv = hlp.kernel.data()+hlp.w;
    for (int cu=0; cu<w; ++cu)
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      {
      complex<double> tmp = 0.;
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      for (int cv=0; cv<w; ++cv)
        tmp += ptr[cv] * kv[cv];
      r += tmp*ku[cu];
      ptr += hlp.sv;
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      }
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    vis[ipart] = r*emb;
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    }
}
  return res;
  }

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a_d_c correction_factors (size_t n, size_t nval, double epsilon)
  {
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  auto w = get_w(epsilon);
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  auto beta = 2.3*w;
  auto p = int(1.5*w+2);
  double alpha = pi*w/n;
  vector<double> x, wgt;
  legendre_prep(2*p,x,wgt);
  auto psi = x;
  for (auto &v:psi)
    v = exp(beta*(sqrt(1-v*v)-1.));
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  int odim[] = {int(nval)};
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  a_d_c res(odim);
  auto val = res.mutable_data();
  for (size_t k=0; k<nval; ++k)
    {
    double tmp=0;
    for (int i=0; i<p; ++i)
      tmp += wgt[i]*psi[i]*cos(alpha*k*x[i]);
    val[k] = 1./(w*tmp);
    }
  return res;
  }

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} // unnamed namespace

PYBIND11_MODULE(nifty_gridder, m)
  {
  m.def("peanoindex",&peanoindex);
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  m.def("get_w",&get_w);
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  m.def("to_grid",&to_grid);
  m.def("from_grid",&from_grid);
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  m.def("correction_factors",&correction_factors);
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  }