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#ifndef GRIDDER_CXX_H
#define GRIDDER_CXX_H

/*
 *  This file is part of nifty_gridder.
 *
 *  nifty_gridder is free software; you can redistribute it and/or modify
 *  it under the terms of the GNU General Public License as published by
 *  the Free Software Foundation; either version 2 of the License, or
 *  (at your option) any later version.
 *
 *  nifty_gridder is distributed in the hope that it will be useful,
 *  but WITHOUT ANY WARRANTY; without even the implied warranty of
 *  MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE.  See the
 *  GNU General Public License for more details.
 *
 *  You should have received a copy of the GNU General Public License
 *  along with nifty_gridder; if not, write to the Free Software
 *  Foundation, Inc., 51 Franklin St, Fifth Floor, Boston, MA  02110-1301  USA
 */

/* Copyright (C) 2019 Max-Planck-Society
   Author: Martin Reinecke */

#include <iostream>
#include <algorithm>
#include <cstdlib>
#include <cmath>
#include <vector>

#include "pocketfft_hdronly.h"
#include <array>

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namespace gridder {

using namespace std;

template<typename T, size_t ndim> class mav
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  {
  static_assert((ndim>0) && (ndim<3), "only supports 1D and 2D arrays");

  private:
    T *d;
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    array<size_t, ndim> shp;
    array<ptrdiff_t, ndim> str;
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  public:
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    mav(T *d_, const array<size_t,ndim> &shp_,
        const array<ptrdiff_t,ndim> &str_)
      : d(d_), shp(shp_), str(str_) {}
    mav(T *d_, const array<size_t,ndim> &shp_)
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      : d(d_), shp(shp_)
      {
      str[ndim-1]=1;
      for (size_t d=2; d<=ndim; ++d)
        str[ndim-d] = str[ndim-d+1]*shp[ndim-d+1];
      }
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    operator mav<const T, ndim>() const
      { return mav<const T, ndim>(d,shp,str); }
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    T &operator[](size_t i)
      { return operator()(i); }
    const T &operator[](size_t i) const
      { return operator()(i); }
    T &operator()(size_t i)
      {
      static_assert(ndim==1, "ndim must be 1");
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      return d[str[0]*i];
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      }
    const T &operator()(size_t i) const
      {
      static_assert(ndim==1, "ndim must be 1");
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      return d[str[0]*i];
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      }
    T &operator()(size_t i, size_t j)
      {
      static_assert(ndim==2, "ndim must be 2");
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      return d[str[0]*i + str[1]*j];
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      }
    const T &operator()(size_t i, size_t j) const
      {
      static_assert(ndim==2, "ndim must be 2");
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      return d[str[0]*i + str[1]*j];
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      }
    size_t shape(size_t i) const { return shp[i]; }
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    const array<size_t,ndim> &shape() const { return shp; }
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    size_t size() const
      {
      size_t res=1;
      for (auto v: shp) res*=v;
      return res;
      }
    size_t stride(size_t i) const { return str[i]; }
    T *data()
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      { return d; }
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    const T *data() const
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      { return d; }
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  };

//
// basic utilities
//

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

template<size_t ndim> void checkShape
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  (const array<size_t, ndim> &shp1, const array<size_t, ndim> &shp2)
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  {
  for (size_t i=0; i<ndim; ++i)
    myassert(shp1[i]==shp2[i], "shape mismatch");
  }

/*! 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. */
template<typename T> inline T fmodulo (T v1, T v2)
  {
  if (v1>=0)
    return (v1<v2) ? v1 : fmod(v1,v2);
  T tmp=fmod(v1,v2)+v2;
  return (tmp==v2) ? T(0) : tmp;
  }

static size_t nthreads = 1;

void set_nthreads(size_t nthreads_)
  {
  myassert(nthreads_>=1, "nthreads must be >= 1");
  nthreads = nthreads_;
  }

size_t get_nthreads()
  { return nthreads; }

//
// Utilities for Gauss-Legendre quadrature
//

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

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void legendre_prep(int n, vector<double> &x, vector<double> &w)
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  {
  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 num_threads(nthreads)
{
  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;
      myassert(++j<100, "convergence problem");
      }

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

//
// Start of real gridder functionality
//

size_t get_supp(double epsilon)
  {
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  static const vector<double> maxmaperr { 1e8, 0.32, 0.021, 6.2e-4,
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    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;
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  throw runtime_error("requested epsilon too small - minimum is 2e-13");
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  }

template<typename T> class EC_Kernel
  {
  protected:
    size_t supp;
    T beta, emb_;

  public:
    EC_Kernel(size_t supp_)
      : supp(supp_), beta(2.3*supp_), emb_(exp(-beta)) {}
    T operator()(T v) const { return exp(beta*(sqrt(T(1)-v*v)-T(1))); }
    T val_no_emb(T v) const { return exp(beta*sqrt(T(1)-v*v)); }
    T emb() const { return emb_; }
  };

template<typename T> class EC_Kernel_with_correction: public EC_Kernel<T>
  {
  protected:
    static constexpr T pi = T(3.141592653589793238462643383279502884197L);
    int p;
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    vector<T> x, wgt, psi;
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    using EC_Kernel<T>::supp;

  public:
    using EC_Kernel<T>::operator();
    EC_Kernel_with_correction(size_t supp_)
      : EC_Kernel<T>(supp_), p(int(1.5*supp_+2))
      {
      legendre_prep(2*p,x,wgt);
      psi=x;
      for (auto &v:psi)
        v=operator()(v);
      }
    /* Compute correction factors for the ES gridding kernel
       This implementation follows eqs. (3.8) to (3.10) of Barnett et al. 2018 */
    T corfac(T v) const
      {
      T tmp=0;
      for (int i=0; i<p; ++i)
        tmp += wgt[i]*psi[i]*cos(pi*supp*v*x[i]);
      return T(1)/(supp*tmp);
      }
  };
/* Compute correction factors for the ES gridding kernel
   This implementation follows eqs. (3.8) to (3.10) of Barnett et al. 2018 */
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vector<double> correction_factors (size_t n, size_t nval, size_t supp)
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  {
  EC_Kernel_with_correction<double> kernel(supp);
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  vector<double> res(nval);
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  double xn = 1./n;
#pragma omp parallel for schedule(static) num_threads(nthreads)
  for (size_t k=0; k<nval; ++k)
    res[k] = kernel.corfac(k*xn);
  return res;
  }

template<typename T> struct UVW
  {
  T u, v, w;
  UVW () {}
  UVW (T u_, T v_, T w_) : u(u_), v(v_), w(w_) {}
  UVW operator* (T fct) const
    { return UVW(u*fct, v*fct, w*fct); }
  };

template<typename T> class Baselines
  {
  protected:
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    vector<UVW<T>> coord;
    vector<T> f_over_c;
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    size_t nrows, nchan;

  public:
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    Baselines(const mav<const T,2> &coord_, const mav<const T,1> &freq)
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      {
      constexpr double speedOfLight = 299792458.;
      myassert(coord_.shape(1)==3, "dimension mismatch");
      nrows = coord_.shape(0);
      nchan = freq.shape(0);
      myassert(nrows*nchan<(size_t(1)<<32), "too many entries in MS");
      f_over_c.resize(nchan);
      for (size_t i=0; i<nchan; ++i)
        f_over_c[i] = freq(i)/speedOfLight;
      coord.resize(nrows);
      for (size_t i=0; i<coord.size(); ++i)
        coord[i] = UVW<T>(coord_(i,0), coord_(i,1), coord_(i,2));
      }

    UVW<T> effectiveCoord(uint32_t index) const
      {
      size_t irow = index/nchan;
      size_t ichan = index-nchan*irow;
      return coord[irow]*f_over_c[ichan];
      }
    UVW<T> effectiveCoord(size_t irow, size_t ichan) const
      { return coord[irow]*f_over_c[ichan]; }
    size_t Nrows() const { return nrows; }
    size_t Nchannels() const { return nchan; }

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    void effectiveUVW(const mav<const uint32_t,1> &idx, mav<T,2> &res) const
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      {
      size_t nvis = idx.shape(0);
      myassert(res.shape(0)==nvis, "shape mismatch");
      myassert(res.shape(1)==3, "shape mismatch");
      for (size_t i=0; i<nvis; i++)
        {
        auto uvw = effectiveCoord(idx(i));
        res(i,0) = uvw.u;
        res(i,1) = uvw.v;
        res(i,2) = uvw.w;
        }
      }

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    template<typename T2> void ms2vis(const mav<const T2,2> &ms,
      const mav<const uint32_t,1> &idx, mav<T2,1> &vis) const
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      {
      myassert(ms.shape(0)==nrows, "shape mismatch");
      myassert(ms.shape(1)==nchan, "shape mismatch");
      size_t nvis = idx.shape(0);
      myassert(vis.shape(0)==nvis, "shape mismatch");
#pragma omp parallel for num_threads(nthreads)
      for (size_t i=0; i<nvis; ++i)
        {
        auto t = idx(i);
        auto row = t/nchan;
        auto chan = t-row*nchan;
        vis[i] = ms(row, chan);
        }
      }

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    template<typename T2> void vis2ms(const mav<const T2,1> &vis,
      const mav<const uint32_t,1> &idx, mav<T2,2> &ms) const
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      {
      size_t nvis = vis.shape(0);
      myassert(idx.shape(0)==nvis, "shape mismatch");
      myassert(ms.shape(0)==nrows, "shape mismatch");
      myassert(ms.shape(1)==nchan, "shape mismatch");
#pragma omp parallel for num_threads(nthreads)
      for (size_t i=0; i<nvis; ++i)
        {
        auto t = idx(i);
        auto row = t/nchan;
        auto chan = t-row*nchan;
        ms(row, chan) += vis(i);
        }
      }
  };

template<typename T> class GridderConfig
  {
  protected:
    size_t nx_dirty, ny_dirty;
    double eps, psx, psy;
    size_t supp, nsafe, nu, nv;
    T beta;
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    vector<T> cfu, cfv;
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    complex<T> wscreen(double x, double y, double w, bool adjoint) const
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      {
      constexpr double pi = 3.141592653589793238462643383279502884197;
#if 1
      double eps = sqrt(x+y);
      double s = sin(eps);
      double nm1 = -s*s/(1.+cos(eps));
#else
      double nm1 = (-x-y)/(sqrt(1.-x-y)+1);
#endif
      double n = nm1+1., xn = 1./n;
      double phase = 2*pi*w*nm1;
      if (adjoint) phase *= -1;
      return complex<T>(cos(phase)*xn, sin(phase)*xn);
      }

  public:
    GridderConfig(size_t nxdirty, size_t nydirty, double epsilon,
      double pixsize_x, double pixsize_y)
      : nx_dirty(nxdirty), ny_dirty(nydirty), eps(epsilon),
        psx(pixsize_x), psy(pixsize_y),
        supp(get_supp(epsilon)), nsafe((supp+1)/2),
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        nu(max(2*nsafe,2*nx_dirty)), nv(max(2*nsafe,2*ny_dirty)),
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        beta(2.3*supp),
        cfu(nx_dirty), cfv(ny_dirty)
      {
      myassert((nx_dirty&1)==0, "nx_dirty must be even");
      myassert((ny_dirty&1)==0, "ny_dirty must be even");
      myassert(epsilon>0, "epsilon must be positive");
      myassert(pixsize_x>0, "pixsize_x must be positive");
      myassert(pixsize_y>0, "pixsize_y must be positive");

      auto tmp = correction_factors(nu, nx_dirty/2+1, supp);
      cfu[nx_dirty/2]=tmp[0];
      cfu[0]=tmp[nx_dirty/2];
      for (size_t i=1; i<nx_dirty/2; ++i)
        cfu[nx_dirty/2-i] = cfu[nx_dirty/2+i] = tmp[i];
      tmp = correction_factors(nv, ny_dirty/2+1, supp);
      cfv[ny_dirty/2]=tmp[0];
      cfv[0]=tmp[ny_dirty/2];
      for (size_t i=1; i<ny_dirty/2; ++i)
        cfv[ny_dirty/2-i] = cfv[ny_dirty/2+i] = tmp[i];
      }
    size_t Nxdirty() const { return nx_dirty; }
    size_t Nydirty() const { return ny_dirty; }
    double Epsilon() const { return eps; }
    double Pixsize_x() const { return psx; }
    double Pixsize_y() const { return psy; }
    size_t Nu() const { return nu; }
    size_t Nv() const { return nv; }
    size_t Supp() const { return supp; }
    size_t Nsafe() const { return nsafe; }
    T Beta() const { return beta; }

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    void apply_taper(const mav<const T,2> &img, mav<T,2> &img2, bool divide) const
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      {
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      checkShape(img.shape(), {nx_dirty, ny_dirty});
      checkShape(img2.shape(), {nx_dirty, ny_dirty});
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      if (divide)
        for (size_t i=0; i<nx_dirty; ++i)
          for (size_t j=0; j<ny_dirty; ++j)
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            img2(i,j) = img(i,j)/(cfu[i]*cfv[j]);
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      else
        for (size_t i=0; i<nx_dirty; ++i)
          for (size_t j=0; j<ny_dirty; ++j)
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            img2(i,j) = img(i,j)*cfu[i]*cfv[j];
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      }

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    void grid2dirty_c(const mav<const complex<T>,2> &grid, mav<complex<T>,2> &dirty) const
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      {
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      checkShape(grid.shape(), {nu,nv});
      checkShape(dirty.shape(), {nx_dirty,ny_dirty});
      vector<complex<T>> tmpdat(nu*nv);
      auto tmp=mav<complex<T>,2>(tmpdat.data(),{nu,nv},{nv,1});
      constexpr auto sc = sizeof(complex<T>);
      pocketfft::c2c({nu,nv},{grid.stride(0)*sc,grid.stride(1)*sc},
        {tmp.stride(0)*sc, tmp.stride(1)*sc}, {0,1}, pocketfft::BACKWARD,
        grid.data(), tmp.data(), T(1), nthreads);
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      for (size_t i=0; i<nx_dirty; ++i)
        for (size_t j=0; j<ny_dirty; ++j)
          {
          size_t i2 = nu-nx_dirty/2+i;
          if (i2>=nu) i2-=nu;
          size_t j2 = nv-ny_dirty/2+j;
          if (j2>=nv) j2-=nv;
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          dirty(i,j) = tmp(i2,j2)*cfu[i]*cfv[j];
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          }
      }
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#if 0
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    pyarr_c<complex<T>> dirty2grid_c(const pyarr_c<complex<T>> &dirty) const
      {
      checkArray(dirty, "dirty", {nx_dirty, ny_dirty});
      auto pdirty = dirty.data();
      auto tmp = makeArray<complex<T>>({nu, nv});
      auto ptmp = tmp.mutable_data();
      pocketfft::stride_t strides{tmp.strides(0),tmp.strides(1)};
      {
      py::gil_scoped_release release;
      for (size_t i=0; i<nu*nv; ++i)
        ptmp[i] = 0.;
      for (size_t i=0; i<nx_dirty; ++i)
        for (size_t j=0; j<ny_dirty; ++j)
          {
          size_t i2 = nu-nx_dirty/2+i;
          if (i2>=nu) i2-=nu;
          size_t j2 = nv-ny_dirty/2+j;
          if (j2>=nv) j2-=nv;
          ptmp[nv*i2+j2] = pdirty[ny_dirty*i + j]*cfu[i]*cfv[j];
          }
      pocketfft::c2c({nu,nv}, strides, strides, {0,1}, pocketfft::FORWARD,
        ptmp, ptmp, T(1), nthreads);
      }
      return tmp;
      }
#endif
    inline void getpix(T u_in, T v_in, T &u, T &v, int &iu0, int &iv0) const
      {
      u=fmodulo(u_in*psx, T(1))*nu,
      iu0 = int(u-supp*0.5 + 1 + nu) - nu;
      if (iu0+supp>nu+nsafe) iu0 = nu+nsafe-supp;
      v=fmodulo(v_in*psy, T(1))*nv;
      iv0 = int(v-supp*0.5 + 1 + nv) - nv;
      if (iv0+supp>nv+nsafe) iv0 = nv+nsafe-supp;
      }
#if 0
    pyarr_c<complex<T>> apply_wscreen(const pyarr_c<complex<T>> &dirty_, double w, bool adjoint) const
      {
      checkArray(dirty_, "dirty", {nx_dirty, ny_dirty});
      auto dirty = dirty_.data();
      auto res_ = makeArray<complex<T>>({nx_dirty, ny_dirty});
      auto res = res_.mutable_data();
      double x0 = -0.5*nx_dirty*psx,
             y0 = -0.5*ny_dirty*psy;
      {
      py::gil_scoped_release release;
#pragma omp parallel num_threads(nthreads)
{
#pragma omp for schedule(static)
      for (size_t i=0; i<=nx_dirty/2; ++i)
        {
        double fx = x0+i*psx;
        fx *= fx;
        for (size_t j=0; j<=ny_dirty/2; ++j)
          {
          double fy = y0+j*psy;
          auto ws = wscreen(fx, fy*fy, w, adjoint);
          res[ny_dirty*i+j] = dirty[ny_dirty*i+j]*ws; // lower left
          size_t i2 = nx_dirty-i, j2 = ny_dirty-j;
          if ((i>0)&&(i<i2))
            {
            res[ny_dirty*i2+j] = dirty[ny_dirty*i2+j]*ws; // lower right
            if ((j>0)&&(j<j2))
              res[ny_dirty*i2+j2] = dirty[ny_dirty*i2+j2]*ws; // upper right
            }
          if ((j>0)&&(j<j2))
            res[ny_dirty*i+j2] = dirty[ny_dirty*i+j2]*ws; // upper left
          }
        }
}
      }
      return res_;
      }
#endif
  };

constexpr int logsquare=4;

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template<typename T, typename T2=complex<T>> class Helper
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  {
  private:
    const GridderConfig<T> &gconf;
    int nu, nv, nsafe, supp;
    T beta;
    const T2 *grid_r;
    T2 *grid_w;
    int su, sv;
    int iu0, iv0; // start index of the current visibility
    int bu0, bv0; // start index of the current buffer

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    vector<T2> rbuf, wbuf;
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    void dump() const
      {
      if (bu0<-nsafe) return; // nothing written into buffer yet

#pragma omp critical (gridder_writing_to_grid)
{
      int idxu = (bu0+nu)%nu;
      int idxv0 = (bv0+nv)%nv;
      for (int iu=0; iu<su; ++iu)
        {
        int idxv = idxv0;
        for (int iv=0; iv<sv; ++iv)
          {
          grid_w[idxu*nv + idxv] += wbuf[iu*sv + iv];
          if (++idxv>=nv) idxv=0;
          }
        if (++idxu>=nu) idxu=0;
        }
}
      }

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

  public:
    const T2 *p0r;
    T2 *p0w;
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    vector<T> kernel;
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    Helper(const GridderConfig<T> &gconf_, const T2 *grid_r_, T2 *grid_w_)
      : gconf(gconf_), nu(gconf.Nu()), nv(gconf.Nv()), nsafe(gconf.Nsafe()),
        supp(gconf.Supp()), beta(gconf.Beta()), grid_r(grid_r_),
        grid_w(grid_w_), su(2*nsafe+(1<<logsquare)), sv(2*nsafe+(1<<logsquare)),
        bu0(-1000000), bv0(-1000000),
        rbuf(su*sv*(grid_r!=nullptr),T(0)),
        wbuf(su*sv*(grid_w!=nullptr),T(0)),
        kernel(2*supp)
      {}
    ~Helper() { if (grid_w) dump(); }

    int lineJump() const { return sv; }

    void prep(T u_in, T v_in)
      {
      T u, v;
      gconf.getpix(u_in, v_in, u, v, iu0, iv0);
      T xsupp=T(2)/supp;
      auto x0 = xsupp*(iu0-u);
      auto y0 = xsupp*(iv0-v);
      for (int i=0; i<supp; ++i)
        {
        auto x = x0+i*xsupp;
        kernel[i  ] = beta*sqrt(T(1)-x*x);
        auto y = y0+i*xsupp;
        kernel[i+supp] = beta*sqrt(T(1)-y*y);
        }
      for (auto &k : kernel)
        k = exp(k);

      if ((iu0<bu0) || (iv0<bv0) || (iu0+supp>bu0+su) || (iv0+supp>bv0+sv))
        {
        if (grid_w) { dump(); fill(wbuf.begin(), wbuf.end(), T(0)); }
        bu0=((((iu0+nsafe)>>logsquare)<<logsquare))-nsafe;
        bv0=((((iv0+nsafe)>>logsquare)<<logsquare))-nsafe;
        if (grid_r) load();
        }
      p0r = grid_r ? rbuf.data() + sv*(iu0-bu0) + iv0-bv0 : nullptr;
      p0w = grid_w ? wbuf.data() + sv*(iu0-bu0) + iv0-bv0 : nullptr;
      }
  };

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} // namespace gridder

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#endif