SegMamba/monai/csrc/resample/pushpull_cpu.cpp

/*
Copyright (c) MONAI Consortium
Licensed under the Apache License, Version 2.0 (the "License");
you may not use this file except in compliance with the License.
You may obtain a copy of the License at
    http://www.apache.org/licenses/LICENSE-2.0
Unless required by applicable law or agreed to in writing, software
distributed under the License is distributed on an "AS IS" BASIS,
WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied.
See the License for the specific language governing permissions and
limitations under the License.
*/

// adapted from https://github.com/balbasty/nitorch

// This file implements spline interpolation / sampling and its adjoint
// operations. It corresponds loosely to torch's `GridSampler`.
// It handles boundary conditions and interpolation orders defined in
// `utils/resample_utils.h` and `utils/resample_utils.h`.
// These parameters can be specified per dimension.
// Isotropic 0-th and 1-st order interpolation have their own (faster)
// implementations. Sliding boundary conditions are also implemented
// separately.

// TODO:
// . [DONE] generic 3d
// . [DONE] generic 2d
// . [DONE] generic 1d
// . sliding nearest 3d
// . sliding nearest 2d
// . sliding linear 3d
// . sliding linear 2d
// . sliding generic 3d
// . sliding generic 2d
// . [DONE] spatial gradient mode (without multiplication with output gradient)
// . [DONE] second order gradients (backward pass for spatial gradients)
// . performance tests
// . input bound/inter are always vectors -> clean unused constructors

#include <ATen/ATen.h>
#include <limits>
#include <tuple>
#include "bounds_common.h"
#include "interpolation_common.h"
#include "utils/resample_utils.h"
//#include <cstdio>

// ~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
// CPU-specific parameters
#include <ATen/Parallel.h>
namespace {
// This parameter specifies the minimum number of voxels that should be
// processed on a single processor in the parallel for loop .
int64_t GRAIN_SIZE = static_cast<int64_t>(at::internal::GRAIN_SIZE);
} // namespace

// ~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~

// maximum number of channels
// > not used in mode isotropic nearest/linear
#ifndef MONAI_MAX_NUM_CHANNELS
#define MONAI_MAX_NUM_CHANNELS 1024
#endif

// This parameter allows for a little bit of tolerance when considering
// a coordinate as "out-of-bound" (if !extrapolate)
#define TINY 5e-2

using at::Tensor;
using at::TensorOptions;
using c10::IntArrayRef;

namespace monai {
MONAI_NAMESPACE_DEVICE { // cpu

  namespace { // anonymous namespace > everything inside has internal linkage

  // ~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
  //                        INDEXING UTILS
  // ~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~

  // This class reads and sets all the parameters that will later be used
  // by the algorithm in PushPullImpl. All of this is done outside of the
  // implementation class so that we do not depend on generic types. The
  // point is to pre-allocate all necessary tensors so that we can check
  // if they're all compatible with 32 bit math. If it's the case, we can
  // dispatch to a 32b cuda implementation, which might increase
  // performance. Else, we use 64 bit math to compute offsets.
  // (On CPU, we always use 64 bit offsets because it doesn't make a huge
  // difference. It would be different if we had a vectorized
  // implementation as in PyTorch).
  class PushPullAllocator {
   public:
    static constexpr int64_t max_int32 = std::numeric_limits<int32_t>::max();

    // ~~~ CONSTRUCTORS ~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~

    MONAI_HOST
    PushPullAllocator(
        int dim,
        BoundVectorRef bound,
        InterpolationVectorRef interpolation,
        bool extrapolate,
        bool do_pull,
        bool do_push,
        bool do_count,
        bool do_grad,
        bool do_sgrad)
        : dim(dim),
          bound0(bound.size() > 0 ? bound[0] : BoundType::Replicate),
          bound1(
              bound.size() > 1       ? bound[1]
                  : bound.size() > 0 ? bound[0]
                                     : BoundType::Replicate),
          bound2(
              bound.size() > 2       ? bound[2]
                  : bound.size() > 1 ? bound[1]
                  : bound.size() > 0 ? bound[0]
                                     : BoundType::Replicate),
          interpolation0(interpolation.size() > 0 ? interpolation[0] : InterpolationType::Linear),
          interpolation1(
              interpolation.size() > 1       ? interpolation[1]
                  : interpolation.size() > 0 ? interpolation[0]
                                             : InterpolationType::Linear),
          interpolation2(
              interpolation.size() > 2       ? interpolation[2]
                  : interpolation.size() > 1 ? interpolation[1]
                  : interpolation.size() > 0 ? interpolation[0]
                                             : InterpolationType::Linear),
          extrapolate(extrapolate),
          do_pull(do_pull),
          do_push(do_push),
          do_count(do_count),
          do_grad(do_grad),
          do_sgrad(do_sgrad) {
      iso = interpolation0 == interpolation1 && interpolation0 == interpolation2;
    }

    // ~~~ FUNCTORS ~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~

    // Usually used for pull:
    // - do_pull  -> return source[grid]
    // - do_push  -> fails
    // - do_grad  -> return J(source)[grid]
    // - do_sgrad -> return H(source)[grid]
    MONAI_HOST void ioset(const Tensor& source, const Tensor& grid) {
      init_all();
      init_source(source);
      init_grid(grid);
      init_output();
    }

    // Usually used for pull_backward:
    // - do_pull  -> return source[grid]
    // - do_push  -> return push(target, grid, source.shape)
    // - do_grad  -> return J(source)[grid]
    // - do_sgrad -> return H(source)[grid]
    MONAI_HOST void ioset(const Tensor& source, const Tensor& grid, const Tensor& target) {
      init_all();
      init_source(source);
      init_grid(grid);
      init_target(target);
      init_output();
    }

    // Usually used for push:
    // - do_pull  -> fails
    // - do_push  -> return push(target, grid, source_size)
    // - do_grad  -> fails
    // - do_sgrad -> fails
    MONAI_HOST void ioset(IntArrayRef source_size, const Tensor& grid, const Tensor& target) {
      init_all();
      init_source(source_size);
      init_grid(grid);
      init_target(target);
      init_output();
    }

    // Usually used for count:
    // - do_pull  -> fails
    // - do_push  -> return push(ones, grid, source_size)
    // - do_grad  -> fails
    // - do_sgrad -> fails
    MONAI_HOST void ioset(IntArrayRef source_size, const Tensor& grid) {
      init_all();
      init_source(source_size);
      init_grid(grid);
      init_output();
    }

    // We just check that all tensors that we own are compatible with 32b math
    bool canUse32BitIndexMath(int64_t max_elem = max_int32) const {
      return src_32b_ok && trgt_32b_ok && grid_32b_ok && grad_32b_ok && out_32b_ok;
    }

   private:
    // Copied from aten/src/ATen/native/IndexingUtils.cpp in PyTorch 1.6.
    // It is used to decide to which pointer type we should dispatch to.
    // Basically, we need to make sure that the "furthest" element we need
    // to reach is less than max_elem away.
    static bool tensorCanUse32BitIndexMath(const Tensor& t, int64_t max_elem = max_int32) {
      int64_t elements = t.numel();
      if (elements >= max_elem) {
        return false;
      }
      if (elements == 0) {
        return max_elem > 0;
      }

      int64_t offset = 0;
      int64_t linearId = elements - 1;

      // NOTE: Assumes all strides are positive, which is true for now
      for (int i = t.dim() - 1; i >= 0; --i) {
        int64_t curDimIndex = linearId % t.size(i);
        int64_t curDimOffset = curDimIndex * t.stride(i);
        offset += curDimOffset;
        linearId /= t.size(i);
      }

      if (offset >= max_elem) {
        return false;
      }

      return true;
    }

    // ~~~ COMPONENTS ~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
    MONAI_HOST void init_all();
    MONAI_HOST void init_source(const Tensor& source);
    MONAI_HOST void init_source(IntArrayRef source_size);
    MONAI_HOST void init_grid(const Tensor& grid);
    MONAI_HOST void init_target(const Tensor& target);
    MONAI_HOST void init_output();

    // ~~~ OPTIONS ~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
    int dim; // dimensionality (2 or 3)
    BoundType bound0; // boundary condition  // x|W
    BoundType bound1; // boundary condition  // y|H
    BoundType bound2; // boundary condition  // z|D
    InterpolationType interpolation0; // interpolation order // x|W
    InterpolationType interpolation1; // interpolation order // y|H
    InterpolationType interpolation2; // interpolation order // z|D
    bool iso; // isotropic interpolation?
    bool extrapolate; // compute out-of-bound values
    bool do_pull; // sample a volume
    bool do_push; // splat a volume
    bool do_count; // splatting weights (= jacobian determinant)
    bool do_grad; // backprop: gradient of grid // pull
    bool do_sgrad; // sample spatial gradients

    // ~~~ NAVIGATORS ~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
    std::deque<Tensor> output;
    TensorOptions src_opt;
    TensorOptions grid_opt;
    TensorOptions trgt_opt;
    int64_t N;
    int64_t C;
    int64_t src_X;
    int64_t src_Y;
    int64_t src_Z;
    int64_t trgt_X;
    int64_t trgt_Y;
    int64_t trgt_Z;
    int64_t trgt_K;
    int64_t src_sN;
    int64_t src_sC;
    int64_t src_sX;
    int64_t src_sY;
    int64_t src_sZ;
    bool src_32b_ok;
    void* src_ptr;
    int64_t trgt_sN;
    int64_t trgt_sC;
    int64_t trgt_sX;
    int64_t trgt_sY;
    int64_t trgt_sZ;
    int64_t trgt_sK;
    bool trgt_32b_ok;
    void* trgt_ptr;
    int64_t grid_sN;
    int64_t grid_sC;
    int64_t grid_sX;
    int64_t grid_sY;
    int64_t grid_sZ;
    bool grid_32b_ok;
    void* grid_ptr;
    int64_t out_sN;
    int64_t out_sC;
    int64_t out_sX;
    int64_t out_sY;
    int64_t out_sZ;
    int64_t out_sK; // gradient dimension
    bool out_32b_ok;
    void* out_ptr;
    int64_t grad_sN;
    int64_t grad_sC;
    int64_t grad_sX;
    int64_t grad_sY;
    int64_t grad_sZ;
    bool grad_32b_ok;
    void* grad_ptr;

    // Allow PushPullImpl's constructor to access PushPullAllocator's
    // private members.
    template <typename scalar_t, typename offset_t>
    friend class PushPullImpl;
  };

  // ~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
  //                          INITIALISATION
  // ~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~

  MONAI_HOST
  void PushPullAllocator::init_all() {
    src_opt = grid_opt = trgt_opt = TensorOptions();
    N = C = 1L;
    src_X = src_Y = src_Z = 1L;
    trgt_X = trgt_Y = trgt_Z = 1L;
    trgt_K = 0L;
    src_sN = src_sC = src_sX = src_sY = src_sZ = 0L;
    grid_sN = grid_sC = grid_sX = grid_sY = grid_sZ = 0L;
    grad_sN = grad_sC = grad_sX = grad_sY = grad_sZ = 0L;
    trgt_sN = trgt_sC = trgt_sX = trgt_sY = trgt_sZ = trgt_sK = 0L;
    out_sN = out_sC = out_sX = out_sY = out_sZ = out_sK = 0L;
    src_ptr = trgt_ptr = grid_ptr = out_ptr = grad_ptr = static_cast<float*>(0);
    src_32b_ok = trgt_32b_ok = grid_32b_ok = out_32b_ok = grad_32b_ok = true;
  }

  MONAI_HOST
  void PushPullAllocator::init_source(const Tensor& source) {
    N = source.size(0);
    C = source.size(1);
    src_X = source.size(2);
    src_Y = dim < 2 ? 1L : source.size(3);
    src_Z = dim < 3 ? 1L : source.size(4);
    src_sN = source.stride(0);
    src_sC = source.stride(1);
    src_sX = source.stride(2);
    src_sY = dim < 2 ? 0L : source.stride(3);
    src_sZ = dim < 3 ? 0L : source.stride(4);
    src_ptr = source.data_ptr();
    src_opt = source.options();
    src_32b_ok = tensorCanUse32BitIndexMath(source);
  }

  MONAI_HOST
  void PushPullAllocator::init_source(IntArrayRef source_size) {
    src_X = source_size[0];
    src_Y = dim < 2 ? 1L : source_size[1];
    src_Z = dim < 3 ? 1L : source_size[2];
  }

  MONAI_HOST
  void PushPullAllocator::init_grid(const Tensor& grid) {
    N = grid.size(0);
    trgt_X = grid.size(1);
    trgt_Y = dim < 2 ? 1L : grid.size(2);
    trgt_Z = dim < 3 ? 1L : grid.size(3);
    grid_sN = grid.stride(0);
    grid_sX = grid.stride(1);
    grid_sY = dim < 2 ? 0L : grid.stride(2);
    grid_sZ = dim < 3 ? 0L : grid.stride(3);
    grid_sC = grid.stride(dim == 1 ? 2 : dim == 2 ? 3 : 4);
    grid_ptr = grid.data_ptr();
    grid_opt = grid.options();
    grid_32b_ok = tensorCanUse32BitIndexMath(grid);
  }

  MONAI_HOST
  void PushPullAllocator::init_target(const Tensor& target) {
    N = target.size(0);
    C = target.size(1);
    trgt_X = target.size(2);
    trgt_Y = dim < 2 ? 1L : target.size(3);
    trgt_Z = dim < 3 ? 1L : target.size(4);
    trgt_K = target.dim() == dim + 3 ? target.size(dim == 1 ? 3 : dim == 2 ? 4 : 5) : 0L;
    trgt_sN = target.stride(0);
    trgt_sC = target.stride(1);
    trgt_sX = target.stride(2);
    trgt_sY = dim < 2 ? 0L : target.stride(3);
    trgt_sZ = dim < 3 ? 0L : target.stride(4);
    trgt_sK = target.dim() == dim + 3 ? target.stride(dim == 1 ? 3 : dim == 2 ? 4 : 5) : 0L;
    trgt_ptr = target.data_ptr();
    trgt_opt = target.options();
    trgt_32b_ok = tensorCanUse32BitIndexMath(target);
  }

  MONAI_HOST
  void PushPullAllocator::init_output() {
    output.clear();
    if (do_pull) {
      if (dim == 1)
        output.push_back(at::empty({N, C, trgt_X}, src_opt));
      else if (dim == 2)
        output.push_back(at::empty({N, C, trgt_X, trgt_Y}, src_opt));
      else
        output.push_back(at::empty({N, C, trgt_X, trgt_Y, trgt_Z}, src_opt));
      auto pull = output.back();
      out_sN = pull.stride(0);
      out_sC = pull.stride(1);
      out_sX = pull.stride(2);
      out_sY = dim < 2 ? 0L : pull.stride(3);
      out_sZ = dim < 3 ? 0L : pull.stride(4);
      out_sK = 0L;
      out_ptr = pull.data_ptr();
      out_32b_ok = tensorCanUse32BitIndexMath(pull);
    } else if (do_sgrad) {
      if (dim == 1)
        output.push_back(at::empty({N, C, trgt_X, 1}, src_opt));
      else if (dim == 2)
        output.push_back(at::empty({N, C, trgt_X, trgt_Y, 2}, src_opt));
      else
        output.push_back(at::empty({N, C, trgt_X, trgt_Y, trgt_Z, 3}, src_opt));
      auto sgrad = output.back();
      out_sN = sgrad.stride(0);
      out_sC = sgrad.stride(1);
      out_sX = sgrad.stride(2);
      out_sY = dim < 2 ? 0L : sgrad.stride(3);
      out_sZ = dim < 3 ? 0L : sgrad.stride(4);
      out_sK = sgrad.stride(dim == 1 ? 3 : dim == 2 ? 4 : 5);
      out_ptr = sgrad.data_ptr();
      out_32b_ok = tensorCanUse32BitIndexMath(sgrad);

      if (iso && interpolation0 == InterpolationType::Nearest)
        sgrad.zero_();
      if (iso && interpolation0 == InterpolationType::Linear && dim == 1)
        sgrad.zero_();
    } else if (do_push) {
      if (dim == 1)
        output.push_back(at::zeros({N, C, src_X}, trgt_opt));
      else if (dim == 2)
        output.push_back(at::zeros({N, C, src_X, src_Y}, trgt_opt));
      else
        output.push_back(at::zeros({N, C, src_X, src_Y, src_Z}, trgt_opt));
      auto push = output.back();
      out_sN = push.stride(0);
      out_sC = push.stride(1);
      out_sX = push.stride(2);
      out_sY = dim < 2 ? 0L : push.stride(3);
      out_sZ = dim < 3 ? 0L : push.stride(4);
      out_sK = 0L;
      out_ptr = push.data_ptr();
      out_32b_ok = tensorCanUse32BitIndexMath(push);
    } else if (do_count) {
      if (dim == 1)
        output.push_back(at::zeros({N, 1, src_X}, grid_opt));
      else if (dim == 2)
        output.push_back(at::zeros({N, 1, src_X, src_Y}, grid_opt));
      else
        output.push_back(at::zeros({N, 1, src_X, src_Y, src_Z}, grid_opt));
      auto count = output.back();
      out_sN = count.stride(0);
      out_sC = count.stride(1);
      out_sX = count.stride(2);
      out_sY = dim < 2 ? 0L : count.stride(3);
      out_sZ = dim < 3 ? 0L : count.stride(4);
      out_sK = 0L;
      out_ptr = count.data_ptr();
      out_32b_ok = tensorCanUse32BitIndexMath(count);
    }
    if (do_grad) {
      if (dim == 1)
        output.push_back(at::zeros({N, trgt_X, 1}, grid_opt));
      else if (dim == 2)
        output.push_back(at::zeros({N, trgt_X, trgt_Y, 2}, grid_opt));
      else
        output.push_back(at::zeros({N, trgt_X, trgt_Y, trgt_Z, 3}, grid_opt));
      auto grad = output.back();
      grad_sN = grad.stride(0);
      grad_sX = grad.stride(1);
      grad_sY = dim < 2 ? 0L : grad.stride(2);
      grad_sZ = dim < 3 ? 0L : grad.stride(3);
      grad_sC = grad.stride(dim == 1 ? 2 : dim == 2 ? 3 : 4);
      grad_ptr = grad.data_ptr();
      out_32b_ok = tensorCanUse32BitIndexMath(grad);

      if (iso && interpolation0 == InterpolationType::Nearest)
        grad.zero_();
    }
  }

  // ~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
  //                        GENERIC PUSHPULL CLASS
  // ~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
  // This class implements the bulk of the code.
  // /!\ No type and shape checking is performed here.

  template <typename scalar_t, typename offset_t>
  class PushPullImpl {
   public:
    // ~~~ CONSTRUCTOR ~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
    PushPullImpl(const PushPullAllocator& info)
        : output(info.output),
          dim(info.dim),
          bound0(info.bound0),
          bound1(info.bound1),
          bound2(info.bound2),
          interpolation0(info.interpolation0),
          interpolation1(info.interpolation1),
          interpolation2(info.interpolation1),
          iso(info.iso),
          extrapolate(info.extrapolate),
          do_pull(info.do_pull),
          do_push(info.do_push),
          do_count(info.do_count),
          do_grad(info.do_grad),
          do_sgrad(info.do_sgrad),
          N(static_cast<offset_t>(info.N)),
          C(static_cast<offset_t>(info.C)),
          src_X(static_cast<offset_t>(info.src_X)),
          src_Y(static_cast<offset_t>(info.src_Y)),
          src_Z(static_cast<offset_t>(info.src_Z)),
          trgt_X(static_cast<offset_t>(info.trgt_X)),
          trgt_Y(static_cast<offset_t>(info.trgt_Y)),
          trgt_Z(static_cast<offset_t>(info.trgt_Z)),
          trgt_K(static_cast<offset_t>(info.trgt_K)),
          src_sN(static_cast<offset_t>(info.src_sN)),
          src_sC(static_cast<offset_t>(info.src_sC)),
          src_sX(static_cast<offset_t>(info.src_sX)),
          src_sY(static_cast<offset_t>(info.src_sY)),
          src_sZ(static_cast<offset_t>(info.src_sZ)),
          src_ptr(static_cast<scalar_t*>(info.src_ptr)),
          trgt_sN(static_cast<offset_t>(info.trgt_sN)),
          trgt_sC(static_cast<offset_t>(info.trgt_sC)),
          trgt_sX(static_cast<offset_t>(info.trgt_sX)),
          trgt_sY(static_cast<offset_t>(info.trgt_sY)),
          trgt_sZ(static_cast<offset_t>(info.trgt_sZ)),
          trgt_sK(static_cast<offset_t>(info.trgt_sK)),
          trgt_ptr(static_cast<scalar_t*>(info.trgt_ptr)),
          grid_sN(static_cast<offset_t>(info.grid_sN)),
          grid_sC(static_cast<offset_t>(info.grid_sC)),
          grid_sX(static_cast<offset_t>(info.grid_sX)),
          grid_sY(static_cast<offset_t>(info.grid_sY)),
          grid_sZ(static_cast<offset_t>(info.grid_sZ)),
          grid_ptr(static_cast<scalar_t*>(info.grid_ptr)),
          out_sN(static_cast<offset_t>(info.out_sN)),
          out_sC(static_cast<offset_t>(info.out_sC)),
          out_sX(static_cast<offset_t>(info.out_sX)),
          out_sY(static_cast<offset_t>(info.out_sY)),
          out_sZ(static_cast<offset_t>(info.out_sZ)),
          out_sK(static_cast<offset_t>(info.out_sK)),
          out_ptr(static_cast<scalar_t*>(info.out_ptr)),
          grad_sN(static_cast<offset_t>(info.grad_sN)),
          grad_sC(static_cast<offset_t>(info.grad_sC)),
          grad_sX(static_cast<offset_t>(info.grad_sX)),
          grad_sY(static_cast<offset_t>(info.grad_sY)),
          grad_sZ(static_cast<offset_t>(info.grad_sZ)),
          grad_ptr(static_cast<scalar_t*>(info.grad_ptr)) {}

    // ~~~ PUBLIC VALUE ~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~

    std::deque<Tensor> output;

    // MONAI_HOST MONAI_DEVICE void printInfo() const {
    //   printf("dim: %d\n", dim);
    //   printf("do_pull:  %d\n", do_pull);
    //   printf("do_push:  %d\n", do_push);
    //   printf("do_count: %d\n", do_count);
    //   printf("do_sgrad: %d\n", do_sgrad);
    //   printf("do_grad:  %d\n", do_grad);
    //   printf("bound:         [%d %d %d]\n", static_cast<int>(bound0),
    //     static_cast<int>(bound1), static_cast<int>(bound2));
    //   printf("interpolation: [%d %d %d]\n", static_cast<int>(interpolation0),
    //     static_cast<int>(interpolation1), static_cast<int>(interpolation2));
    //   printf("src:  [%d %d %d]\n", src_Z, src_Y, src_X);
    //   printf("trgt: [%d %d %d (%d)]\n", trgt_Z, trgt_Y, trgt_X, trgt_K);
    //   printf("N: %d\n", N);
    //   printf("C: %d\n", C);
    //   printf("src  -> %lu\n", reinterpret_cast<std::uintptr_t>(src_ptr));
    //   printf("trgt -> %lu\n", reinterpret_cast<std::uintptr_t>(trgt_ptr));
    //   printf("grid -> %lu\n", reinterpret_cast<std::uintptr_t>(grid_ptr));
    //   printf("out  -> %lu\n", reinterpret_cast<std::uintptr_t>(out_ptr));
    //   printf("grad -> %lu\n", reinterpret_cast<std::uintptr_t>(grad_ptr));
    // }

    // ~~~ FUNCTORS ~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~

    // Loop over all voxels
    void loop() const;

    MONAI_HOST MONAI_DEVICE int64_t voxcount() const {
      return N * trgt_X * trgt_Y * trgt_Z;
    }

   private:
    // ~~~ COMPONENTS ~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
    MONAI_DEVICE void check1d(offset_t w, offset_t n) const;
    MONAI_DEVICE void check2d(offset_t w, offset_t h, offset_t n) const;
    MONAI_DEVICE void check3d(offset_t w, offset_t h, offset_t d, offset_t n) const;
    MONAI_DEVICE void interpolate1d(scalar_t x, offset_t w, offset_t n) const;
    MONAI_DEVICE void interpolate1d_nearest(scalar_t x, offset_t w, offset_t n) const;
    MONAI_DEVICE void interpolate1d_linear(scalar_t x, offset_t w, offset_t n) const;
    MONAI_DEVICE void interpolate1d_sliding(scalar_t x, offset_t w, offset_t n) const { /*TODO*/
    }
    MONAI_DEVICE void interpolate1d_sliding_nearest(scalar_t x, offset_t w, offset_t n) const { /*TODO*/
    }
    MONAI_DEVICE void interpolate1d_sliding_linear(scalar_t x, offset_t w, offset_t n) const { /*TODO*/
    }
    MONAI_DEVICE void interpolate2d(scalar_t x, scalar_t y, offset_t w, offset_t h, offset_t n) const;
    MONAI_DEVICE void interpolate2d_nearest(scalar_t x, scalar_t y, offset_t w, offset_t h, offset_t n) const;
    MONAI_DEVICE void interpolate2d_bilinear(scalar_t x, scalar_t y, offset_t w, offset_t h, offset_t n) const;
    MONAI_DEVICE void interpolate2d_sliding(scalar_t x, scalar_t y, offset_t w, offset_t h, offset_t n) const { /*TODO*/
    }
    MONAI_DEVICE void interpolate2d_sliding_nearest(scalar_t x, scalar_t y, offset_t w, offset_t h, offset_t n)
        const { /*TODO*/
    }
    MONAI_DEVICE void interpolate2d_sliding_bilinear(scalar_t x, scalar_t y, offset_t w, offset_t h, offset_t n)
        const { /*TODO*/
    }
    MONAI_DEVICE void interpolate3d(scalar_t x, scalar_t y, scalar_t z, offset_t w, offset_t h, offset_t d, offset_t n)
        const;
    MONAI_DEVICE void interpolate3d_nearest(
        scalar_t x,
        scalar_t y,
        scalar_t z,
        offset_t w,
        offset_t h,
        offset_t d,
        offset_t n) const;
    MONAI_DEVICE void interpolate3d_trilinear(
        scalar_t x,
        scalar_t y,
        scalar_t z,
        offset_t w,
        offset_t h,
        offset_t d,
        offset_t n) const;
    MONAI_DEVICE void interpolate3d_sliding(
        scalar_t x,
        scalar_t y,
        scalar_t z,
        offset_t w,
        offset_t h,
        offset_t d,
        offset_t n) const { /*TODO*/
    }
    MONAI_DEVICE void interpolate3d_sliding_nearest(
        scalar_t x,
        scalar_t y,
        scalar_t z,
        offset_t w,
        offset_t h,
        offset_t d,
        offset_t n) const { /*TODO*/
    }
    MONAI_DEVICE void interpolate3d_sliding_trilinear(
        scalar_t x,
        scalar_t y,
        scalar_t z,
        offset_t w,
        offset_t h,
        offset_t d,
        offset_t n) const { /*TODO*/
    }

    // ~~~ OPTIONS ~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
    int dim; // dimensionality (2 or 3)
    BoundType bound0; // boundary condition  // x|W
    BoundType bound1; // boundary condition  // y|H
    BoundType bound2; // boundary condition  // z|D
    InterpolationType interpolation0; // interpolation order // x|W
    InterpolationType interpolation1; // interpolation order // y|H
    InterpolationType interpolation2; // interpolation order // z|D
    bool iso; // isotropic interpolation?
    bool extrapolate; // compute out-of-bound values
    bool do_pull; // sample a volume
    bool do_push; // splat a volume
    bool do_count; // splatting weights (= jacobian determinant)
    bool do_grad; // backprop: gradient of grid // pull
    bool do_sgrad; // sample spatial gradients

    // ~~~ NAVIGATORS ~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
    offset_t N;
    offset_t C;
    offset_t src_X;
    offset_t src_Y;
    offset_t src_Z;
    offset_t trgt_X;
    offset_t trgt_Y;
    offset_t trgt_Z;
    offset_t trgt_K;
    offset_t src_sN;
    offset_t src_sC;
    offset_t src_sX;
    offset_t src_sY;
    offset_t src_sZ;
    scalar_t* src_ptr;
    offset_t trgt_sN;
    offset_t trgt_sC;
    offset_t trgt_sX;
    offset_t trgt_sY;
    offset_t trgt_sZ;
    offset_t trgt_sK;
    scalar_t* trgt_ptr;
    offset_t grid_sN;
    offset_t grid_sC;
    offset_t grid_sX;
    offset_t grid_sY;
    offset_t grid_sZ;
    scalar_t* grid_ptr;
    offset_t out_sN;
    offset_t out_sC;
    offset_t out_sX;
    offset_t out_sY;
    offset_t out_sZ;
    offset_t out_sK; // gradient dimension
    scalar_t* out_ptr;
    offset_t grad_sN;
    offset_t grad_sC;
    offset_t grad_sX;
    offset_t grad_sY;
    offset_t grad_sZ;
    scalar_t* grad_ptr;
  };

  // ~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
  //                             LOOP
  // ~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~

  // This bit loops over all target voxels. We therefore need to
  // convert linear indices to multivariate indices. The way I do it
  // might not be optimal.
  // Note that I parallelize across all voxels (whereas ATen's grid
  // sampler is only parallelized across batches).
  //
  // TODO: check that the default grain size is optimal. We do quite a lot
  // of compute per voxel, so a smaller value might be better suited.
  template <typename scalar_t, typename offset_t>
  MONAI_HOST void PushPullImpl<scalar_t, offset_t>::loop() const {
#if !(AT_PARALLEL_OPENMP)
    if (do_push) {
      // I do not have access to atomic operations so I cannot
      // parallelize across voxels.
      at::parallel_for(0, N, 0, [&](offset_t start, offset_t end) {
        for (offset_t n = start; n < end; ++n) {
          if (dim == 1) {
            for (offset_t w = 0; w < trgt_X; ++w)
              check1d(w, n);
          } else if (dim == 2) {
            for (offset_t h = 0; h < trgt_Y; ++h)
              for (offset_t w = 0; w < trgt_X; ++w)
                check2d(w, h, n);
          } else {
            for (offset_t d = 0; d < trgt_Z; ++d)
              for (offset_t h = 0; h < trgt_Y; ++h)
                for (offset_t w = 0; w < trgt_X; ++w)
                  check3d(w, h, d, n);
          }
        }
      });
      return;
    }

#endif
    // Parallelize across voxels
    offset_t trgt_NXYZ = trgt_Z * trgt_Y * trgt_X * N;
    offset_t trgt_XYZ = trgt_Z * trgt_Y * trgt_X;
    offset_t trgt_YZ = trgt_Z * trgt_Y;
    at::parallel_for(0, trgt_NXYZ, GRAIN_SIZE, [&](offset_t start, offset_t end) {
      offset_t n, w, h, d;
      for (offset_t i = start; i < end; ++i) {
        // Convert index: linear to sub
        n = (i / trgt_XYZ);
        w = (i / trgt_YZ) % trgt_X;
        h = (i / trgt_Z) % trgt_Y;
        d = i % trgt_Z;

        if (dim == 1)
          check1d(w, n);
        else if (dim == 2)
          check2d(w, h, n);
        else
          check3d(w, h, d, n);
      }
    });
  }

  // ~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
  //                        CHECK OUT-OF-BOUND
  // ~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~

  // Here, we:
  // 1) read the [x,y,z] source coordinate for the current target voxel
  // 3) check if the source coordinate is in bounds

  template <typename scalar_t, typename offset_t>
  MONAI_DEVICE void PushPullImpl<scalar_t, offset_t>::check3d(offset_t w, offset_t h, offset_t d, offset_t n) const {
    // get the corresponding input x, y, z co-ordinates from grid
    scalar_t* grid_ptr_NXYZ = grid_ptr + n * grid_sN + w * grid_sX + h * grid_sY + d * grid_sZ;
    scalar_t x = *grid_ptr_NXYZ;
    scalar_t y = grid_ptr_NXYZ[grid_sC];
    scalar_t z = grid_ptr_NXYZ[grid_sC * 2];

    // Check if out-of-bound
    if (!(extrapolate ||
          (inbounds(x, src_X, static_cast<scalar_t>(TINY)) && inbounds(y, src_Y, static_cast<scalar_t>(TINY)) &&
           inbounds(z, src_Z, static_cast<scalar_t>(TINY))))) {
      if (do_pull || do_sgrad) {
        scalar_t* out_ptr_NCXYZ = out_ptr + n * out_sN + w * out_sX + h * out_sY + d * out_sZ;
        for (offset_t c = 0; c < C; ++c, out_ptr_NCXYZ += out_sC) {
          *out_ptr_NCXYZ = static_cast<scalar_t>(0);
          if (do_sgrad) {
            out_ptr_NCXYZ[out_sK] = static_cast<scalar_t>(0);
            out_ptr_NCXYZ[out_sK * 2] = static_cast<scalar_t>(0);
          }
        }
      }
      if (do_grad) {
        scalar_t* grad_ptr_NXYZ = grad_ptr + n * grad_sN + w * grad_sX + h * grad_sY + d * grad_sZ;
        (*grad_ptr_NXYZ) = static_cast<scalar_t>(0);
        grad_ptr_NXYZ[grad_sC] = static_cast<scalar_t>(0);
        grad_ptr_NXYZ[grad_sC * 2] = static_cast<scalar_t>(0);
      }
      return;
    }

    // Next step
    if (bound0 == BoundType::Sliding) {
      if (iso)
        switch (static_cast<int>(interpolation0)) {
          case 0:
            return interpolate3d_sliding_nearest(x, y, z, w, h, d, n);
          case 1:
            return interpolate3d_sliding_trilinear(x, y, z, w, h, d, n);
        }
      return interpolate3d_sliding(x, y, z, w, h, d, n);
    } else {
      if (iso)
        switch (static_cast<int>(interpolation0)) {
          case 0:
            return interpolate3d_nearest(x, y, z, w, h, d, n);
          case 1:
            return interpolate3d_trilinear(x, y, z, w, h, d, n);
        }
      return interpolate3d(x, y, z, w, h, d, n);
    }
  }

  template <typename scalar_t, typename offset_t>
  MONAI_DEVICE void PushPullImpl<scalar_t, offset_t>::check2d(offset_t w, offset_t h, offset_t n) const {
    // get the corresponding input x, y, z co-ordinates from grid
    scalar_t* grid_ptr_NXY = grid_ptr + n * grid_sN + w * grid_sX + h * grid_sY;
    scalar_t x = *grid_ptr_NXY;
    scalar_t y = grid_ptr_NXY[grid_sC];

    // Check if out-of-bound
    if (!(extrapolate ||
          (inbounds(x, src_X, static_cast<scalar_t>(TINY)) && inbounds(y, src_Y, static_cast<scalar_t>(TINY))))) {
      if (do_pull || do_sgrad) {
        scalar_t* out_ptr_NCXY = out_ptr + n * out_sN + w * out_sX + h * out_sY;
        for (offset_t c = 0; c < C; ++c, out_ptr_NCXY += out_sC) {
          *out_ptr_NCXY = static_cast<scalar_t>(0);
          if (do_sgrad)
            out_ptr_NCXY[out_sK] = static_cast<scalar_t>(0);
        }
      }
      if (do_grad) {
        scalar_t* grad_ptr_NXY = grad_ptr + n * grad_sN + w * grad_sX + h * grad_sY;
        (*grad_ptr_NXY) = static_cast<scalar_t>(0);
        grad_ptr_NXY[grad_sC] = static_cast<scalar_t>(0);
      }
      return;
    }

    // Next step
    if (bound0 == BoundType::Sliding) {
      if (iso)
        switch (static_cast<int>(interpolation0)) {
          case 0:
            return interpolate2d_sliding_nearest(x, y, w, h, n);
          case 1:
            return interpolate2d_sliding_bilinear(x, y, w, h, n);
        }
      return interpolate2d_sliding(x, y, w, h, n);
    } else {
      if (iso)
        switch (static_cast<int>(interpolation0)) {
          case 0:
            return interpolate2d_nearest(x, y, w, h, n);
          case 1:
            return interpolate2d_bilinear(x, y, w, h, n);
        }
      return interpolate2d(x, y, w, h, n);
    }
  }

  template <typename scalar_t, typename offset_t>
  MONAI_DEVICE void PushPullImpl<scalar_t, offset_t>::check1d(offset_t w, offset_t n) const {
    // get the corresponding input x, y, z co-ordinates from grid
    scalar_t* grid_ptr_NX = grid_ptr + n * grid_sN + w * grid_sX;
    scalar_t x = *grid_ptr_NX;

    // Check if out-of-bound
    if (!(extrapolate || inbounds(x, src_X, static_cast<scalar_t>(TINY)))) {
      if (do_pull || do_sgrad) {
        scalar_t* out_ptr_NCX = out_ptr + n * out_sN + w * out_sX;
        for (offset_t c = 0; c < C; ++c, out_ptr_NCX += out_sC) {
          *out_ptr_NCX = static_cast<scalar_t>(0);
          if (do_sgrad)
            out_ptr_NCX[out_sK] = static_cast<scalar_t>(0);
        }
      }
      if (do_grad) {
        scalar_t* grad_ptr_NX = grad_ptr + n * grad_sN + w * grad_sX;
        (*grad_ptr_NX) = static_cast<scalar_t>(0);
        grad_ptr_NX[grad_sC] = static_cast<scalar_t>(0);
      }
      return;
    }

    // Next step
    if (bound0 == BoundType::Sliding) {
      if (iso)
        switch (static_cast<int>(interpolation0)) {
          case 0:
            return interpolate1d_sliding_nearest(x, w, n);
          case 1:
            return interpolate1d_sliding_linear(x, w, n);
        }
      return interpolate1d_sliding(x, w, n);
    } else {
      if (iso)
        switch (static_cast<int>(interpolation0)) {
          case 0:
            return interpolate1d_nearest(x, w, n);
          case 1:
            return interpolate1d_linear(x, w, n);
        }
      return interpolate1d(x, w, n);
    }
  }

  // ~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
  //                     GENERIC INTERPOLATION 3D
  // ~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~

  template <typename scalar_t, typename offset_t>
  MONAI_DEVICE void PushPullImpl<scalar_t, offset_t>::interpolate3d(
      scalar_t x,
      scalar_t y,
      scalar_t z,
      offset_t w,
      offset_t h,
      offset_t d,
      offset_t n) const {
    // Get corner pixel values from (x, y, z)
    offset_t bx0, bx1, by0, by1, bz0, bz1;
    interpolation::bounds(interpolation0, x, bx0, bx1);
    interpolation::bounds(interpolation1, y, by0, by1);
    interpolation::bounds(interpolation2, z, bz0, bz1);
    offset_t dbx = bx1 - bx0;
    offset_t dby = by1 - by0;
    offset_t dbz = bz1 - bz0;

    // Pre-compute offsets and target value
    scalar_t* src_ptr_NC0 = src_ptr + n * src_sN;
    scalar_t* out_ptr_NC0 = out_ptr + n * out_sN;
    scalar_t* out_ptr_NCXYZ0 = out_ptr + n * out_sN + w * out_sX + h * out_sY + d * out_sZ;
    scalar_t* trgt_ptr_NCXYZ = trgt_ptr + n * trgt_sN + w * trgt_sX + h * trgt_sY + d * trgt_sZ;
    scalar_t target[3 * MONAI_MAX_NUM_CHANNELS];
    if (trgt_ptr && (do_push || do_grad))
      for (offset_t c = 0; c < C; ++c, trgt_ptr_NCXYZ += trgt_sC) {
        target[c] = *trgt_ptr_NCXYZ;
        if (trgt_K > 0) {
          target[c + C] = trgt_ptr_NCXYZ[trgt_sK];
          target[c + C * 2] = trgt_ptr_NCXYZ[trgt_sK * 2];
        }
      }

    // Initialize output
    scalar_t* out_ptr_NCXYZ = out_ptr_NCXYZ0;
    if (do_pull || do_sgrad) {
      for (offset_t c = 0; c < C; ++c, out_ptr_NCXYZ += out_sC) {
        *out_ptr_NCXYZ = static_cast<scalar_t>(0);
        if (do_sgrad) {
          out_ptr_NCXYZ[out_sK] = static_cast<scalar_t>(0);
          out_ptr_NCXYZ[out_sK * 2] = static_cast<scalar_t>(0);
        }
      }
    }

    // Pre-compute indices/weights/grad
    scalar_t wx[8], wy[8], wz[8]; // B-spline weights
    scalar_t gx[8], gy[8], gz[8]; // B-spline derivatives
    scalar_t hx[8], hy[8], hz[8]; // B-spline 2nd derivatives
    offset_t ix[8], iy[8], iz[8]; // Warped indices
    uint8_t sx[8], sy[8], sz[8]; // Warped indices

    {
      scalar_t *owz = static_cast<scalar_t*>(wz), *ogz = static_cast<scalar_t*>(gz), *ohz = static_cast<scalar_t*>(hz);
      offset_t* oiz = static_cast<offset_t*>(iz);
      uint8_t* osz = static_cast<uint8_t*>(sz);
      for (offset_t bz = bz0; bz <= bz1; ++bz) {
        scalar_t dz = z - bz;
        *(owz++) = interpolation::fastweight(interpolation2, dz);
        if (do_grad || do_sgrad)
          *(ogz++) = interpolation::fastgrad(interpolation2, dz);
        if (do_grad && trgt_sK > 1)
          *(ohz++) = interpolation::fasthess(interpolation2, dz);
        *(osz++) = bound::sign(bound2, bz, src_Z);
        *(oiz++) = bound::index(bound2, bz, src_Z);
      }
    }
    {
      scalar_t *owy = static_cast<scalar_t*>(wy), *ogy = static_cast<scalar_t*>(gy), *ohy = static_cast<scalar_t*>(hy);
      offset_t* oiy = static_cast<offset_t*>(iy);
      uint8_t* osy = static_cast<uint8_t*>(sy);
      for (offset_t by = by0; by <= by1; ++by) {
        scalar_t dy = y - by;
        *(owy++) = interpolation::fastweight(interpolation1, dy);
        if (do_grad || do_sgrad)
          *(ogy++) = interpolation::fastgrad(interpolation1, dy);
        if (do_grad && trgt_sK > 1)
          *(ohy++) = interpolation::fasthess(interpolation1, dy);
        *(osy++) = bound::sign(bound1, by, src_Y);
        *(oiy++) = bound::index(bound1, by, src_Y);
      }
    }
    {
      scalar_t *owx = static_cast<scalar_t*>(wx), *ogx = static_cast<scalar_t*>(gx), *ohx = static_cast<scalar_t*>(hx);
      offset_t* oix = static_cast<offset_t*>(ix);
      uint8_t* osx = static_cast<uint8_t*>(sx);
      for (offset_t bx = bx0; bx <= bx1; ++bx) {
        scalar_t dx = x - bx;
        *(owx++) = interpolation::fastweight(interpolation0, dx);
        if (do_grad || do_sgrad)
          *(ogx++) = interpolation::fastgrad(interpolation0, dx);
        if (do_grad && trgt_sK > 1)
          *(ohx++) = interpolation::fasthess(interpolation0, dx);
        *(osx++) = bound::sign(bound0, bx, src_X);
        *(oix++) = bound::index(bound0, bx, src_X);
      }
    }

    // Convolve coefficients with basis functions
    scalar_t ogx, ogy, ogz;
    ogx = ogy = ogz = static_cast<scalar_t>(0);
    for (offset_t k = 0; k <= dbz; ++k) {
      offset_t ooz = iz[k] * out_sZ;
      offset_t osz = iz[k] * src_sZ;
      uint8_t szz = sz[k];
      scalar_t wzz = wz[k];
      scalar_t gzz = gz[k];
      scalar_t hzz = hz[k];
      for (offset_t j = 0; j <= dby; ++j) {
        offset_t ooyz = ooz + iy[j] * out_sY;
        offset_t osyz = osz + iy[j] * src_sY;
        uint8_t syz = szz * sy[j];
        scalar_t wyy = wy[j];
        scalar_t gyy = gy[j];
        scalar_t hyy = hy[j];
        for (offset_t i = 0; i <= dbx; ++i) {
          offset_t ooxyz = ooyz + ix[i] * out_sX;
          offset_t osxyz = osyz + ix[i] * src_sX;
          uint8_t sxyz = syz * sx[i];
          scalar_t wxx = wx[i];
          scalar_t gxx = gx[i];
          scalar_t hxx = hx[i];

          // ~~~~~~~~~~~~~~~~~~~~~~~~~~~ Pull ~~~~~~~~~~~~~~~~~~~~~~~~~~~~
          if (do_pull) {
            scalar_t* src_ptr_NC = src_ptr_NC0;
            scalar_t* out_ptr_NCXYZ = out_ptr_NCXYZ0;
            for (offset_t c = 0; c < C; ++c, out_ptr_NCXYZ += out_sC, src_ptr_NC += src_sC)
              *out_ptr_NCXYZ += bound::get(src_ptr_NC, osxyz, sxyz) * (wxx * wyy * wzz);
          }

          // ~~~~~~~~~~~~~~~~~~~~~~~~~~~ SGrad ~~~~~~~~~~~~~~~~~~~~~~~~~~~
          else if (do_sgrad) {
            scalar_t* src_ptr_NC = src_ptr_NC0;
            scalar_t* out_ptr_NCXYZ = out_ptr_NCXYZ0;
            for (offset_t c = 0; c < C; ++c, out_ptr_NCXYZ += out_sC, src_ptr_NC += src_sC) {
              scalar_t src = bound::get(src_ptr_NC, osxyz, sxyz);
              *out_ptr_NCXYZ += src * (gxx * wyy * wzz);
              out_ptr_NCXYZ[out_sK] += src * (wxx * gyy * wzz);
              out_ptr_NCXYZ[2 * out_sK] += src * (wxx * wyy * gzz);
            }
          }

          // ~~~~~~~~~~~~~~~~~~~~~~~~~~~ Push ~~~~~~~~~~~~~~~~~~~~~~~~~~~~
          else if (do_push) {
            if (trgt_K == 0) {
              // Diff w.r.t. push/pull
              scalar_t* out_ptr_NC = out_ptr_NC0;
              for (offset_t c = 0; c < C; ++c, out_ptr_NC += out_sC)
                bound::add(out_ptr_NC, ooxyz, (wxx * wyy * wzz) * target[c], sxyz);
            } else {
              // Diff w.r.t. sgrad
              scalar_t* out_ptr_NC = out_ptr_NC0;
              for (offset_t c = 0; c < C; ++c, out_ptr_NC += out_sC) {
                scalar_t val = (gxx * wyy * wzz) * target[c] + (wxx * gyy * wzz) * target[c + C] +
                    (wxx * wyy * gzz) * target[c + C * 2];
                bound::add(out_ptr_NC, ooxyz, val, sxyz);
              }
            }
          }

          // ~~~~~~~~~~~~~~~~~~~~~~~~~~~ Count ~~~~~~~~~~~~~~~~~~~~~~~~~~~
          else if (do_count) {
            bound::add(out_ptr_NC0, ooxyz, (wxx * wyy * wzz), sxyz);
          }

          // ~~~~~~~~~~~~~~~~~~~~~~~~~~~ Grad ~~~~~~~~~~~~~~~~~~~~~~~~~~~~
          if (do_grad) {
            if (trgt_K == 0) {
              // Diff w.r.t. pull/push
              scalar_t* src_ptr_NC = src_ptr_NC0;
              scalar_t dot = static_cast<scalar_t>(0);
              for (offset_t c = 0; c < C; ++c, src_ptr_NC += src_sC) {
                scalar_t src = bound::get(src_ptr_NC, osxyz, sxyz);
                dot += (trgt_ptr ? src * target[c] : src);
                // trgt_ptr == 0 in the backward pass of 'count'
              }
              ogx += (gxx * wyy * wzz) * dot;
              ogy += (wxx * gyy * wzz) * dot;
              ogz += (wxx * wyy * gzz) * dot;
            } else {
              // Diff w.r.t. sgrad
              scalar_t* src_ptr_NC = src_ptr_NC0;
              scalar_t dot0, dot1, dot2;
              dot0 = dot1 = dot2 = static_cast<scalar_t>(0);
              for (offset_t c = 0; c < C; ++c, src_ptr_NC += src_sC) {
                scalar_t src = bound::get(src_ptr_NC, osxyz, sxyz);
                dot0 += src * target[c];
                dot1 += src * target[c + C];
                dot2 += src * target[c + C * 2];
              }
              ogx += (hxx * wyy * wzz) * dot0 + (gxx * gyy * wzz) * dot1 + (gxx * wyy * gzz) * dot2;
              ogy += (gxx * gyy * wzz) * dot0 + (wxx * hyy * wzz) * dot1 + (wxx * gyy * gzz) * dot2;
              ogz += (gxx * wyy * gzz) * dot0 + (wxx * gyy * gzz) * dot1 + (wxx * wyy * hzz) * dot2;
            }
          }

        } // x
      } // y
    } // z

    // ~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~ Grad ~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
    if (do_grad) {
      scalar_t* grad_ptr_NXYZ = grad_ptr + n * grad_sN + w * grad_sX + h * grad_sY + d * grad_sZ;
      (*grad_ptr_NXYZ) = ogx;
      grad_ptr_NXYZ[grad_sC] = ogy;
      grad_ptr_NXYZ[grad_sC * 2] = ogz;
    }
  }

  // ~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
  //                     GENERIC INTERPOLATION 2D
  // ~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~

  template <typename scalar_t, typename offset_t>
  MONAI_DEVICE void PushPullImpl<scalar_t, offset_t>::interpolate2d(
      scalar_t x,
      scalar_t y,
      offset_t w,
      offset_t h,
      offset_t n) const {
    // Get corner pixel values from (x, y)
    offset_t bx0, bx1, by0, by1;
    interpolation::bounds(interpolation0, x, bx0, bx1);
    interpolation::bounds(interpolation1, y, by0, by1);
    offset_t dbx = bx1 - bx0;
    offset_t dby = by1 - by0;

    // Pre-compute offsets and target value
    scalar_t* src_ptr_NC0 = src_ptr + n * src_sN;
    scalar_t* out_ptr_NC0 = out_ptr + n * out_sN;
    scalar_t* out_ptr_NCXY0 = out_ptr + n * out_sN + w * out_sX + h * out_sY;
    scalar_t* trgt_ptr_NCXY = trgt_ptr + n * trgt_sN + w * trgt_sX + h * trgt_sY;
    scalar_t target[2 * MONAI_MAX_NUM_CHANNELS];
    if (trgt_ptr && (do_push || do_grad))
      for (offset_t c = 0; c < C; ++c, trgt_ptr_NCXY += trgt_sC) {
        target[c] = *trgt_ptr_NCXY;
        if (trgt_K > 0) {
          target[c + C] = trgt_ptr_NCXY[trgt_sK];
        }
      }

    // Initialize output
    scalar_t* out_ptr_NCXY = out_ptr_NCXY0;
    if (do_pull || do_sgrad) {
      for (offset_t c = 0; c < C; ++c, out_ptr_NCXY += out_sC) {
        *out_ptr_NCXY = static_cast<scalar_t>(0);
        if (do_sgrad) {
          out_ptr_NCXY[out_sK] = static_cast<scalar_t>(0);
        }
      }
    }

    // Pre-compute indices/weights/grad
    scalar_t wx[8], wy[8]; // B-spline weights
    scalar_t gx[8], gy[8]; // B-spline derivatives
    scalar_t hx[8], hy[8]; // B-spline 2nd derivatives
    offset_t ix[8], iy[8]; // Warped indices
    uint8_t sx[8], sy[8]; // Warped indices

    {
      scalar_t *owy = static_cast<scalar_t*>(wy), *ogy = static_cast<scalar_t*>(gy), *ohy = static_cast<scalar_t*>(hy);
      offset_t* oiy = static_cast<offset_t*>(iy);
      uint8_t* osy = static_cast<uint8_t*>(sy);
      for (offset_t by = by0; by <= by1; ++by) {
        scalar_t dy = y - by;
        *(owy++) = interpolation::fastweight(interpolation1, dy);
        if (do_grad || do_sgrad)
          *(ogy++) = interpolation::fastgrad(interpolation1, dy);
        if (do_grad && trgt_sK > 1)
          *(ohy++) = interpolation::fasthess(interpolation1, dy);
        *(osy++) = bound::sign(bound1, by, src_Y);
        *(oiy++) = bound::index(bound1, by, src_Y);
      }
    }
    {
      scalar_t *owx = static_cast<scalar_t*>(wx), *ogx = static_cast<scalar_t*>(gx), *ohx = static_cast<scalar_t*>(hx);
      offset_t* oix = static_cast<offset_t*>(ix);
      uint8_t* osx = static_cast<uint8_t*>(sx);
      for (offset_t bx = bx0; bx <= bx1; ++bx) {
        scalar_t dx = x - bx;
        *(owx++) = interpolation::fastweight(interpolation0, dx);
        if (do_grad || do_sgrad)
          *(ogx++) = interpolation::fastgrad(interpolation0, dx);
        if (do_grad && trgt_sK > 1)
          *(ohx++) = interpolation::fasthess(interpolation0, dx);
        *(osx++) = bound::sign(bound0, bx, src_X);
        *(oix++) = bound::index(bound0, bx, src_X);
      }
    }

    // Convolve coefficients with basis functions
    scalar_t ogx, ogy;
    ogx = ogy = static_cast<scalar_t>(0);
    for (offset_t j = 0; j <= dby; ++j) {
      offset_t ooy = iy[j] * out_sY;
      offset_t osy = iy[j] * src_sY;
      uint8_t syy = sy[j];
      scalar_t wyy = wy[j];
      scalar_t gyy = gy[j];
      scalar_t hyy = hy[j];
      for (offset_t i = 0; i <= dbx; ++i) {
        offset_t ooxy = ooy + ix[i] * out_sX;
        offset_t osxy = osy + ix[i] * src_sX;
        uint8_t sxy = syy * sx[i];
        scalar_t wxx = wx[i];
        scalar_t gxx = gx[i];
        scalar_t hxx = hx[i];

        // ~~~~~~~~~~~~~~~~~~~~~~~~~~~~ Pull ~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
        if (do_pull) {
          scalar_t* src_ptr_NC = src_ptr_NC0;
          scalar_t* out_ptr_NCXY = out_ptr_NCXY0;
          for (offset_t c = 0; c < C; ++c, out_ptr_NCXY += out_sC, src_ptr_NC += src_sC)
            *out_ptr_NCXY += bound::get(src_ptr_NC, osxy, sxy) * (wxx * wyy);
        }

        // ~~~~~~~~~~~~~~~~~~~~~~~~~~~~ SGrad ~~~~~~~~~~~~~~~~~~~~~~~~~~~~
        else if (do_sgrad) {
          scalar_t* src_ptr_NC = src_ptr_NC0;
          scalar_t* out_ptr_NCXY = out_ptr_NCXY0;
          for (offset_t c = 0; c < C; ++c, out_ptr_NCXY += out_sC, src_ptr_NC += src_sC) {
            scalar_t src = bound::get(src_ptr_NC, osxy, sxy);
            *out_ptr_NCXY += src * (gxx * wyy);
            out_ptr_NCXY[out_sK] += src * (wxx * gyy);
          }
        }

        // ~~~~~~~~~~~~~~~~~~~~~~~~~~~~ Push ~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
        else if (do_push) {
          if (trgt_K == 0) {
            // Diff w.r.t. push/pull
            scalar_t* out_ptr_NC = out_ptr_NC0;
            for (offset_t c = 0; c < C; ++c, out_ptr_NC += out_sC)
              bound::add(out_ptr_NC, ooxy, (wxx * wyy) * target[c], sxy);
          } else {
            // Diff w.r.t. sgrad
            scalar_t* out_ptr_NC = out_ptr_NC0;
            for (offset_t c = 0; c < C; ++c, out_ptr_NC += out_sC) {
              scalar_t val = (gxx * wyy) * target[c] + (wxx * gyy) * target[c + C];
              bound::add(out_ptr_NC, ooxy, val, sxy);
            }
          }
        }

        // ~~~~~~~~~~~~~~~~~~~~~~~~~~~~ Count ~~~~~~~~~~~~~~~~~~~~~~~~~~~~
        else if (do_count) {
          bound::add(out_ptr_NC0, ooxy, (wxx * wyy), sxy);
        }

        // ~~~~~~~~~~~~~~~~~~~~~~~~~~~~ Grad ~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
        if (do_grad) {
          if (trgt_K == 0) {
            // Diff w.r.t. pull/push
            scalar_t* src_ptr_NC = src_ptr_NC0;
            scalar_t dot = static_cast<scalar_t>(0);
            for (offset_t c = 0; c < C; ++c, src_ptr_NC += src_sC) {
              scalar_t src = bound::get(src_ptr_NC, osxy, sxy);
              dot += (trgt_ptr ? src * target[c] : src);
              // trgt_ptr == 0 in the backward pass of 'count'
            }
            ogx += (gxx * wyy) * dot;
            ogy += (wxx * gyy) * dot;
          } else {
            // Diff w.r.t. sgrad
            scalar_t* src_ptr_NC = src_ptr_NC0;
            scalar_t dot0, dot1;
            dot0 = dot1 = static_cast<scalar_t>(0);
            for (offset_t c = 0; c < C; ++c, src_ptr_NC += src_sC) {
              scalar_t src = bound::get(src_ptr_NC, osxy, sxy);
              dot0 += src * target[c];
              dot1 += src * target[c + C];
            }
            ogx += (hxx * wyy) * dot0 + (gxx * gyy) * dot1;
            ogy += (gxx * gyy) * dot0 + (wxx * hyy) * dot1;
          }
        }

      } // x
    } // y

    // ~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~ Grad ~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
    if (do_grad) {
      scalar_t* grad_ptr_NXY = grad_ptr + n * grad_sN + w * grad_sX + h * grad_sY;
      (*grad_ptr_NXY) = ogx;
      grad_ptr_NXY[grad_sC] = ogy;
    }
  }

  // ~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
  //                     GENERIC INTERPOLATION 1D
  // ~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~

  template <typename scalar_t, typename offset_t>
  MONAI_DEVICE void PushPullImpl<scalar_t, offset_t>::interpolate1d(scalar_t x, offset_t w, offset_t n) const {
    // Get corner pixel values from (x, y)
    offset_t bx0, bx1;
    interpolation::bounds(interpolation0, x, bx0, bx1);
    offset_t dbx = bx1 - bx0;

    // Pre-compute offsets and target value
    scalar_t* src_ptr_NC0 = src_ptr + n * src_sN;
    scalar_t* out_ptr_NC0 = out_ptr + n * out_sN;
    scalar_t* out_ptr_NCX0 = out_ptr + n * out_sN + w * out_sX;
    scalar_t* trgt_ptr_NCX = trgt_ptr + n * trgt_sN + w * trgt_sX;
    scalar_t target[2 * MONAI_MAX_NUM_CHANNELS];
    if (trgt_ptr && (do_push || do_grad))
      for (offset_t c = 0; c < C; ++c, trgt_ptr_NCX += trgt_sC) {
        target[c] = *trgt_ptr_NCX;
        if (trgt_K > 0) {
          target[c + C] = trgt_ptr_NCX[trgt_sK];
        }
      }

    // Initialize output
    scalar_t* out_ptr_NCX = out_ptr_NCX0;
    if (do_pull || do_sgrad) {
      for (offset_t c = 0; c < C; ++c, out_ptr_NCX += out_sC) {
        *out_ptr_NCX = static_cast<scalar_t>(0);
        if (do_sgrad) {
          out_ptr_NCX[out_sK] = static_cast<scalar_t>(0);
        }
      }
    }

    // Pre-compute indices/weights/grad
    scalar_t wx[8]; // B-spline weights
    scalar_t gx[8]; // B-spline derivatives
    scalar_t hx[8]; // B-spline 2nd derivatives
    offset_t ix[8]; // Warped indices
    uint8_t sx[8]; // Warped indices

    {
      scalar_t *owx = static_cast<scalar_t*>(wx), *ogx = static_cast<scalar_t*>(gx), *ohx = static_cast<scalar_t*>(hx);
      offset_t* oix = static_cast<offset_t*>(ix);
      uint8_t* osx = static_cast<uint8_t*>(sx);
      for (offset_t bx = bx0; bx <= bx1; ++bx) {
        scalar_t dx = x - bx;
        *(owx++) = interpolation::fastweight(interpolation0, dx);
        if (do_grad || do_sgrad)
          *(ogx++) = interpolation::fastgrad(interpolation0, dx);
        if (do_grad && trgt_sK > 1)
          *(ohx++) = interpolation::fasthess(interpolation0, dx);
        *(osx++) = bound::sign(bound0, bx, src_X);
        *(oix++) = bound::index(bound0, bx, src_X);
      }
    }

    // Convolve coefficients with basis functions
    scalar_t ogx;
    ogx = static_cast<scalar_t>(0);
    for (offset_t i = 0; i <= dbx; ++i) {
      offset_t oox = ix[i] * out_sX;
      offset_t osx = ix[i] * src_sX;
      uint8_t sxx = sx[i];
      scalar_t wxx = wx[i];
      scalar_t gxx = gx[i];
      scalar_t hxx = hx[i];

      // ~~~~~~~~~~~~~~~~~~~~~~~~~~~~ Pull ~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
      if (do_pull) {
        scalar_t* src_ptr_NC = src_ptr_NC0;
        scalar_t* out_ptr_NCX = out_ptr_NCX0;
        for (offset_t c = 0; c < C; ++c, out_ptr_NCX += out_sC, src_ptr_NC += src_sC)
          *out_ptr_NCX += bound::get(src_ptr_NC, osx, sxx) * wxx;
      }

      // ~~~~~~~~~~~~~~~~~~~~~~~~~~~~ SGrad ~~~~~~~~~~~~~~~~~~~~~~~~~~~~
      else if (do_sgrad) {
        scalar_t* src_ptr_NC = src_ptr_NC0;
        scalar_t* out_ptr_NCX = out_ptr_NCX0;
        for (offset_t c = 0; c < C; ++c, out_ptr_NCX += out_sC, src_ptr_NC += src_sC) {
          scalar_t src = bound::get(src_ptr_NC, osx, sxx);
          *out_ptr_NCX += src * gxx;
        }
      }

      // ~~~~~~~~~~~~~~~~~~~~~~~~~~~~ Push ~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
      else if (do_push) {
        if (trgt_K == 0) {
          // Diff w.r.t. push/pull
          scalar_t* out_ptr_NC = out_ptr_NC0;
          for (offset_t c = 0; c < C; ++c, out_ptr_NC += out_sC)
            bound::add(out_ptr_NC, oox, wxx * target[c], sxx);
        } else {
          // Diff w.r.t. sgrad
          scalar_t* out_ptr_NC = out_ptr_NC0;
          for (offset_t c = 0; c < C; ++c, out_ptr_NC += out_sC) {
            scalar_t val = gxx * target[c];
            bound::add(out_ptr_NC, oox, val, sxx);
          }
        }
      }

      // ~~~~~~~~~~~~~~~~~~~~~~~~~~~~ Count ~~~~~~~~~~~~~~~~~~~~~~~~~~~~
      else if (do_count) {
        bound::add(out_ptr_NC0, oox, wxx, sxx);
      }

      // ~~~~~~~~~~~~~~~~~~~~~~~~~~~~ Grad ~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
      if (do_grad) {
        if (trgt_K == 0) {
          // Diff w.r.t. pull/push
          scalar_t* src_ptr_NC = src_ptr_NC0;
          scalar_t dot = static_cast<scalar_t>(0);
          for (offset_t c = 0; c < C; ++c, src_ptr_NC += src_sC) {
            scalar_t src = bound::get(src_ptr_NC, osx, sxx);
            dot += (trgt_ptr ? src * target[c] : src);
            // trgt_ptr == 0 in the backward pass of 'count'
          }
          ogx += gxx * dot;
        } else {
          // Diff w.r.t. sgrad
          scalar_t* src_ptr_NC = src_ptr_NC0;
          scalar_t dot;
          dot = static_cast<scalar_t>(0);
          for (offset_t c = 0; c < C; ++c, src_ptr_NC += src_sC) {
            scalar_t src = bound::get(src_ptr_NC, osx, sxx);
            dot += src * target[c];
          }
          ogx += hxx * dot;
        }
      }

    } // x

    // ~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~ Grad ~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
    if (do_grad) {
      scalar_t* grad_ptr_NX = grad_ptr + n * grad_sN + w * grad_sX;
      (*grad_ptr_NX) = ogx;
    }
  }

  // ~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
  //                     LINEAR INTERPOLATION 3D
  // ~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~

  template <typename scalar_t, typename offset_t>
  MONAI_DEVICE void PushPullImpl<scalar_t, offset_t>::interpolate3d_trilinear(
      scalar_t x,
      scalar_t y,
      scalar_t z,
      offset_t w,
      offset_t h,
      offset_t d,
      offset_t n) const {
    // Get corner pixel values from (x, y, z)
    offset_t ix0 = static_cast<offset_t>(std::floor(x));
    offset_t iy0 = static_cast<offset_t>(std::floor(y));
    offset_t iz0 = static_cast<offset_t>(std::floor(z));

    // Interpolation weights (inversely proportional to distance)
    scalar_t dx1 = x - ix0;
    scalar_t dy1 = y - iy0;
    scalar_t dz1 = z - iz0;
    scalar_t dx0 = 1. - dx1;
    scalar_t dy0 = 1. - dy1;
    scalar_t dz0 = 1. - dz1;
    scalar_t w000 = dx0 * dy0 * dz0;
    scalar_t w100 = dx1 * dy0 * dz0;
    scalar_t w010 = dx0 * dy1 * dz0;
    scalar_t w001 = dx0 * dy0 * dz1;
    scalar_t w110 = dx1 * dy1 * dz0;
    scalar_t w011 = dx0 * dy1 * dz1;
    scalar_t w101 = dx1 * dy0 * dz1;
    scalar_t w111 = dx1 * dy1 * dz1;

    // Sign (/!\ compute sign before warping indices)
    int8_t sx1 = bound::sign(bound0, ix0 + 1, src_X);
    int8_t sy1 = bound::sign(bound1, iy0 + 1, src_Y);
    int8_t sz1 = bound::sign(bound2, iz0 + 1, src_Z);
    int8_t sx0 = bound::sign(bound0, ix0, src_X);
    int8_t sy0 = bound::sign(bound1, iy0, src_Y);
    int8_t sz0 = bound::sign(bound2, iz0, src_Z);
    int8_t s000 = sx0 * sy0 * sz0;
    int8_t s100 = sx1 * sy0 * sz0;
    int8_t s010 = sx0 * sy1 * sz0;
    int8_t s001 = sx0 * sy0 * sz1;
    int8_t s110 = sx1 * sy1 * sz0;
    int8_t s011 = sx0 * sy1 * sz1;
    int8_t s101 = sx1 * sy0 * sz1;
    int8_t s111 = sx1 * sy1 * sz1;

    // Warp indices
    offset_t ix1, iy1, iz1;
    ix1 = bound::index(bound0, ix0 + 1, src_X);
    iy1 = bound::index(bound1, iy0 + 1, src_Y);
    iz1 = bound::index(bound2, iz0 + 1, src_Z);
    ix0 = bound::index(bound0, ix0, src_X);
    iy0 = bound::index(bound1, iy0, src_Y);
    iz0 = bound::index(bound2, iz0, src_Z);

    offset_t o000, o100, o010, o001, o110, o011, o101, o111;

    if (do_pull || do_grad || do_sgrad) {
      // Offsets into source volume
      o000 = ix0 * src_sX + iy0 * src_sY + iz0 * src_sZ;
      o100 = ix1 * src_sX + iy0 * src_sY + iz0 * src_sZ;
      o010 = ix0 * src_sX + iy1 * src_sY + iz0 * src_sZ;
      o001 = ix0 * src_sX + iy0 * src_sY + iz1 * src_sZ;
      o110 = ix1 * src_sX + iy1 * src_sY + iz0 * src_sZ;
      o011 = ix0 * src_sX + iy1 * src_sY + iz1 * src_sZ;
      o101 = ix1 * src_sX + iy0 * src_sY + iz1 * src_sZ;
      o111 = ix1 * src_sX + iy1 * src_sY + iz1 * src_sZ;
    } else if (!(do_push || do_count)) {
      o000 = o100 = o010 = o001 = o110 = o011 = o101 = o111 = 0;
    }

    // ~~~~~~~~~~~~~~~~~~~~~~~~~~ Grid gradient ~~~~~~~~~~~~~~~~~~~~~~~~~~
    if (do_grad) {
      scalar_t gx = static_cast<scalar_t>(0);
      scalar_t gy = static_cast<scalar_t>(0);
      scalar_t gz = static_cast<scalar_t>(0);
      scalar_t* trgt_ptr_NCXYZ = trgt_ptr + n * trgt_sN + w * trgt_sX + h * trgt_sY + d * trgt_sZ;
      scalar_t* src_ptr_NC = src_ptr + n * src_sN;

      if (trgt_K == 0) {
        // backward w.r.t. push/pull
        for (offset_t c = 0; c < C; ++c, trgt_ptr_NCXYZ += trgt_sC, src_ptr_NC += src_sC) {
          scalar_t src;
          scalar_t trgt = trgt_ptr ? *trgt_ptr_NCXYZ : static_cast<scalar_t>(1);
          // ^ trgt_ptr == 0 during the backward pass of count
          src = bound::get(src_ptr_NC, o000, s000);
          if (trgt_ptr)
            src *= trgt;
          gx -= dy0 * dz0 * src;
          gy -= dx0 * dz0 * src;
          gz -= dx0 * dy0 * src;
          src = bound::get(src_ptr_NC, o100, s100);
          if (trgt_ptr)
            src *= trgt;
          gx += dy0 * dz0 * src;
          gy -= dx1 * dz0 * src;
          gz -= dx1 * dy0 * src;
          src = bound::get(src_ptr_NC, o010, s010);
          if (trgt_ptr)
            src *= trgt;
          gx -= dy1 * dz0 * src;
          gy += dx0 * dz0 * src;
          gz -= dx0 * dy1 * src;
          src = bound::get(src_ptr_NC, o110, s110);
          if (trgt_ptr)
            src *= trgt;
          gx += dy1 * dz0 * src;
          gy += dx1 * dz0 * src;
          gz -= dx1 * dy1 * src;
          src = bound::get(src_ptr_NC, o001, s001);
          if (trgt_ptr)
            src *= trgt;
          gx -= dy0 * dz1 * src;
          gy -= dx0 * dz1 * src;
          gz += dx0 * dy0 * src;
          src = bound::get(src_ptr_NC, o101, s101);
          if (trgt_ptr)
            src *= trgt;
          gx += dy0 * dz1 * src;
          gy -= dx1 * dz1 * src;
          gz += dx1 * dy0 * src;
          src = bound::get(src_ptr_NC, o011, s011);
          if (trgt_ptr)
            src *= trgt;
          gx -= dy1 * dz1 * src;
          gy += dx0 * dz1 * src;
          gz += dx0 * dy1 * src;
          src = bound::get(src_ptr_NC, o111, s111);
          if (trgt_ptr)
            src *= trgt;
          gx += dy1 * dz1 * src;
          gy += dx1 * dz1 * src;
          gz += dx1 * dy1 * src;
        }
      } else {
        // backward w.r.t. sgrad
        for (offset_t c = 0; c < C; ++c, trgt_ptr_NCXYZ += trgt_sC, src_ptr_NC += src_sC) {
          scalar_t src;
          scalar_t trgt0 = *trgt_ptr_NCXYZ, trgt1 = trgt_ptr_NCXYZ[trgt_sK], trgt2 = trgt_ptr_NCXYZ[trgt_sK * 2];
          src = bound::get(src_ptr_NC, o000, s000);
          gx += (dz0 * trgt1 + dy0 * trgt2) * src;
          gy += (dz0 * trgt0 + dx0 * trgt2) * src;
          gz += (dy0 * trgt0 + dx0 * trgt1) * src;
          src = bound::get(src_ptr_NC, o100, s100);
          gx += (-dz0 * trgt1 - dy0 * trgt2) * src;
          gy += (-dz0 * trgt0 + dx1 * trgt2) * src;
          gz += (-dy0 * trgt0 + dx1 * trgt1) * src;
          src = bound::get(src_ptr_NC, o010, s010);
          gx += (-dz0 * trgt1 + dy1 * trgt2) * src;
          gy += (-dz0 * trgt0 - dx0 * trgt2) * src;
          gz += (dy1 * trgt0 - dx0 * trgt1) * src;
          src = bound::get(src_ptr_NC, o110, s110);
          gx += (dz0 * trgt1 - dy1 * trgt2) * src;
          gy += (dz0 * trgt0 - dx1 * trgt2) * src;
          gz += (-dy1 * trgt0 - dx1 * trgt1) * src;
          src = bound::get(src_ptr_NC, o001, s001);
          gx += (dz1 * trgt1 - dy0 * trgt2) * src;
          gy += (dz1 * trgt0 - dx0 * trgt2) * src;
          gz += (-dy0 * trgt0 - dx0 * trgt1) * src;
          src = bound::get(src_ptr_NC, o101, s101);
          gx += (-dz1 * trgt1 + dy0 * trgt2) * src;
          gy += (-dz1 * trgt0 - dx1 * trgt2) * src;
          gz += (dy0 * trgt0 - dx1 * trgt1) * src;
          src = bound::get(src_ptr_NC, o011, s011);
          gx += (-dz1 * trgt1 - dy1 * trgt2) * src;
          gy += (-dz1 * trgt0 + dx0 * trgt2) * src;
          gz += (-dy1 * trgt0 + dx0 * trgt1) * src;
          src = bound::get(src_ptr_NC, o111, s111);
          gx += (dz1 * trgt1 + dy1 * trgt2) * src;
          gy += (dz1 * trgt0 + dx1 * trgt2) * src;
          gz += (dy1 * trgt0 + dx1 * trgt1) * src;
        }
      }

      scalar_t* grad_ptr_NXYZ = grad_ptr + n * grad_sN + w * grad_sX + h * grad_sY + d * grad_sZ;
      (*grad_ptr_NXYZ) = gx;
      grad_ptr_NXYZ[grad_sC] = gy;
      grad_ptr_NXYZ[grad_sC * 2] = gz;
    }
    if (do_push || do_count) {
      // Offsets into 'push' volume
      o000 = ix0 * out_sX + iy0 * out_sY + iz0 * out_sZ;
      o100 = ix1 * out_sX + iy0 * out_sY + iz0 * out_sZ;
      o010 = ix0 * out_sX + iy1 * out_sY + iz0 * out_sZ;
      o001 = ix0 * out_sX + iy0 * out_sY + iz1 * out_sZ;
      o110 = ix1 * out_sX + iy1 * out_sY + iz0 * out_sZ;
      o011 = ix0 * out_sX + iy1 * out_sY + iz1 * out_sZ;
      o101 = ix1 * out_sX + iy0 * out_sY + iz1 * out_sZ;
      o111 = ix1 * out_sX + iy1 * out_sY + iz1 * out_sZ;
    }
    // ~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~ Pull ~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
    if (do_pull) {
      scalar_t* out_ptr_NCXYZ = out_ptr + n * out_sN + w * out_sX + h * out_sY + d * out_sZ;
      scalar_t* src_ptr_NC = src_ptr + n * src_sN;
      for (offset_t c = 0; c < C; ++c, out_ptr_NCXYZ += out_sC, src_ptr_NC += src_sC) {
        *out_ptr_NCXYZ = bound::get(src_ptr_NC, o000, s000) * w000 + bound::get(src_ptr_NC, o100, s100) * w100 +
            bound::get(src_ptr_NC, o010, s010) * w010 + bound::get(src_ptr_NC, o110, s110) * w110 +
            bound::get(src_ptr_NC, o001, s001) * w001 + bound::get(src_ptr_NC, o101, s101) * w101 +
            bound::get(src_ptr_NC, o011, s011) * w011 + bound::get(src_ptr_NC, o111, s111) * w111;
      }
    }
    // ~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~ SGrad ~~~~~~~~~~~~~~~~~~~~~ ~~~~~~~~~
    else if (do_sgrad) {
      scalar_t* out_ptr_NCXYZ = out_ptr + n * out_sN + w * out_sX + h * out_sY + d * out_sZ;
      scalar_t* src_ptr_NC = src_ptr + n * src_sN;

      for (offset_t c = 0; c < C; ++c, out_ptr_NCXYZ += out_sC, src_ptr_NC += src_sC) {
        scalar_t src000 = bound::get(src_ptr_NC, o000, s000);
        scalar_t src100 = bound::get(src_ptr_NC, o100, s100);
        scalar_t src010 = bound::get(src_ptr_NC, o010, s010);
        scalar_t src110 = bound::get(src_ptr_NC, o110, s110);
        scalar_t src001 = bound::get(src_ptr_NC, o001, s001);
        scalar_t src101 = bound::get(src_ptr_NC, o101, s101);
        scalar_t src011 = bound::get(src_ptr_NC, o011, s011);
        scalar_t src111 = bound::get(src_ptr_NC, o111, s111);
        *out_ptr_NCXYZ = -dy0 * dz0 * src000 + dy0 * dz0 * src100 - dy1 * dz0 * src010 + dy1 * dz0 * src110 -
            dy0 * dz1 * src001 + dy0 * dz1 * src101 - dy1 * dz1 * src011 + dy1 * dz1 * src111;
        out_ptr_NCXYZ[out_sK] = -dx0 * dz0 * src000 - dx1 * dz0 * src100 + dx0 * dz0 * src010 + dx1 * dz0 * src110 -
            dx0 * dz1 * src001 - dx1 * dz1 * src101 + dx0 * dz1 * src011 + dx1 * dz1 * src111;
        out_ptr_NCXYZ[out_sK * 2] = -dx0 * dy0 * src000 - dx1 * dy0 * src100 - dx0 * dy1 * src010 - dx1 * dy1 * src110 +
            dx0 * dy0 * src001 + dx1 * dy0 * src101 + dx0 * dy1 * src011 + dx1 * dy1 * src111;
      }
    }
    // ~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~ Push ~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
    else if (do_push) {
      // Offsets into 'push' volume
      o000 = ix0 * out_sX + iy0 * out_sY + iz0 * out_sZ;
      o100 = ix1 * out_sX + iy0 * out_sY + iz0 * out_sZ;
      o010 = ix0 * out_sX + iy1 * out_sY + iz0 * out_sZ;
      o001 = ix0 * out_sX + iy0 * out_sY + iz1 * out_sZ;
      o110 = ix1 * out_sX + iy1 * out_sY + iz0 * out_sZ;
      o011 = ix0 * out_sX + iy1 * out_sY + iz1 * out_sZ;
      o101 = ix1 * out_sX + iy0 * out_sY + iz1 * out_sZ;
      o111 = ix1 * out_sX + iy1 * out_sY + iz1 * out_sZ;
      scalar_t* trgt_ptr_NCXYZ = trgt_ptr + n * trgt_sN + w * trgt_sX + h * trgt_sY + d * trgt_sZ;
      scalar_t* out_ptr_NC = out_ptr + n * out_sN;
      if (trgt_K == 0) {
        // Diff w.r.t. push/pull
        for (offset_t c = 0; c < C; ++c, trgt_ptr_NCXYZ += trgt_sC, out_ptr_NC += out_sC) {
          scalar_t trgt = *trgt_ptr_NCXYZ;
          bound::add(out_ptr_NC, o000, w000 * trgt, s000);
          bound::add(out_ptr_NC, o100, w100 * trgt, s100);
          bound::add(out_ptr_NC, o010, w010 * trgt, s010);
          bound::add(out_ptr_NC, o110, w110 * trgt, s110);
          bound::add(out_ptr_NC, o001, w001 * trgt, s001);
          bound::add(out_ptr_NC, o101, w101 * trgt, s101);
          bound::add(out_ptr_NC, o011, w011 * trgt, s011);
          bound::add(out_ptr_NC, o111, w111 * trgt, s111);
        }
      } else {
        // Diff w.r.t. sgrad
        scalar_t val;
        for (offset_t c = 0; c < C; ++c, trgt_ptr_NCXYZ += trgt_sC, out_ptr_NC += out_sC) {
          scalar_t trgt0 = *trgt_ptr_NCXYZ, trgt1 = trgt_ptr_NCXYZ[trgt_sK], trgt2 = trgt_ptr_NCXYZ[trgt_sK * 2];
          val = -dy0 * dz0 * trgt0 - dx0 * dz0 * trgt1 - dx0 * dy0 * trgt2;
          bound::add(out_ptr_NC, o000, val, s000);
          val = dy0 * dz0 * trgt0 - dx1 * dz0 * trgt1 - dx1 * dy0 * trgt2;
          bound::add(out_ptr_NC, o100, val, s100);
          val = -dy1 * dz0 * trgt0 + dx0 * dz0 * trgt1 - dx0 * dy1 * trgt2;
          bound::add(out_ptr_NC, o010, val, s010);
          val = dy1 * dz0 * trgt0 + dx1 * dz0 * trgt1 - dx1 * dy1 * trgt2;
          bound::add(out_ptr_NC, o110, val, s110);
          val = -dy0 * dz1 * trgt0 - dx0 * dz1 * trgt1 + dx0 * dy0 * trgt2;
          bound::add(out_ptr_NC, o001, val, s001);
          val = dy0 * dz1 * trgt0 - dx1 * dz1 * trgt1 + dx1 * dy0 * trgt2;
          bound::add(out_ptr_NC, o101, val, s101);
          val = -dy1 * dz1 * trgt0 + dx0 * dz1 * trgt1 + dx0 * dy1 * trgt2;
          bound::add(out_ptr_NC, o011, val, s011);
          val = dy1 * dz1 * trgt0 + dx1 * dz1 * trgt1 + dx1 * dy1 * trgt2;
          bound::add(out_ptr_NC, o111, val, s111);
        }
      }
    }
    // ~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~ Push ~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
    else if (do_count) {
      scalar_t* out_ptr_N = out_ptr + n * out_sN;
      bound::add(out_ptr_N, o000, w000, s000);
      bound::add(out_ptr_N, o100, w100, s100);
      bound::add(out_ptr_N, o010, w010, s010);
      bound::add(out_ptr_N, o110, w110, s110);
      bound::add(out_ptr_N, o001, w001, s001);
      bound::add(out_ptr_N, o101, w101, s101);
      bound::add(out_ptr_N, o011, w011, s011);
      bound::add(out_ptr_N, o111, w111, s111);
    }
  }

  // ~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
  //                     LINEAR INTERPOLATION 2D
  // ~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~

  template <typename scalar_t, typename offset_t>
  MONAI_DEVICE void PushPullImpl<scalar_t, offset_t>::interpolate2d_bilinear(
      scalar_t x,
      scalar_t y,
      offset_t w,
      offset_t h,
      offset_t n) const {
    // Get corner pixel values from (x, y, z)
    offset_t ix0 = static_cast<offset_t>(std::floor(x));
    offset_t iy0 = static_cast<offset_t>(std::floor(y));

    // Interpolation weights (inversely proportional to distance)
    scalar_t dx1 = x - ix0;
    scalar_t dy1 = y - iy0;
    scalar_t dx0 = 1. - dx1;
    scalar_t dy0 = 1. - dy1;
    scalar_t w00 = dx0 * dy0;
    scalar_t w10 = dx1 * dy0;
    scalar_t w01 = dx0 * dy1;
    scalar_t w11 = dx1 * dy1;

    // Sign (/!\ compute sign before warping indices)
    int8_t sx1 = bound::sign(bound0, ix0 + 1, src_X);
    int8_t sy1 = bound::sign(bound1, iy0 + 1, src_Y);
    int8_t sx0 = bound::sign(bound0, ix0, src_X);
    int8_t sy0 = bound::sign(bound1, iy0, src_Y);
    int8_t s00 = sx0 * sy0;
    int8_t s10 = sx1 * sy0;
    int8_t s01 = sx0 * sy1;
    int8_t s11 = sx1 * sy1;

    // Warp indices
    offset_t ix1, iy1;
    ix1 = bound::index(bound0, ix0 + 1, src_X);
    iy1 = bound::index(bound1, iy0 + 1, src_Y);
    ix0 = bound::index(bound0, ix0, src_X);
    iy0 = bound::index(bound1, iy0, src_Y);

    offset_t o00, o10, o01, o11;
    if (do_pull || do_grad || do_sgrad) {
      // Offsets into source volume
      o00 = ix0 * src_sX + iy0 * src_sY;
      o10 = ix1 * src_sX + iy0 * src_sY;
      o01 = ix0 * src_sX + iy1 * src_sY;
      o11 = ix1 * src_sX + iy1 * src_sY;
    } else if (!(do_push || do_count)) {
      o00 = o10 = o01 = o11 = 0;
    }

    // ~~~~~~~~~~~~~~~~~~~~~~~~~~ Grid gradient ~~~~~~~~~~~~~~~~~~~~~~~~~~
    if (do_grad) {
      scalar_t gx = static_cast<scalar_t>(0);
      scalar_t gy = static_cast<scalar_t>(0);
      scalar_t* trgt_ptr_NCXY = trgt_ptr + n * trgt_sN + w * trgt_sX + h * trgt_sY;
      scalar_t* src_ptr_NC = src_ptr + n * src_sN;

      if (trgt_K == 0) {
        // backward w.r.t. push/pull
        for (offset_t c = 0; c < C; ++c, trgt_ptr_NCXY += trgt_sC, src_ptr_NC += src_sC) {
          scalar_t src;
          scalar_t trgt = trgt_ptr ? *trgt_ptr_NCXY : static_cast<scalar_t>(1);
          // ^ trgt_ptr == 0 during the backward pass of count
          src = bound::get(src_ptr_NC, o00, s00);
          if (trgt_ptr)
            src *= trgt;
          gx -= dy0 * src;
          gy -= dx0 * src;
          src = bound::get(src_ptr_NC, o10, s10);
          if (trgt_ptr)
            src *= trgt;
          gx += dy0 * src;
          gy -= dx1 * src;
          src = bound::get(src_ptr_NC, o01, s01);
          if (trgt_ptr)
            src *= trgt;
          gx -= dy1 * src;
          gy += dx0 * src;
          src = bound::get(src_ptr_NC, o11, s11);
          if (trgt_ptr)
            src *= trgt;
          gx += dy1 * src;
          gy += dx1 * src;
        }
      } else {
        // backward w.r.t. sgrad
        for (offset_t c = 0; c < C; ++c, trgt_ptr_NCXY += trgt_sC, src_ptr_NC += src_sC) {
          scalar_t src;
          scalar_t trgt0 = *trgt_ptr_NCXY, trgt1 = trgt_ptr_NCXY[trgt_sK];
          src = bound::get(src_ptr_NC, o00, s00);
          gx += trgt1 * src;
          gy += trgt0 * src;
          src = bound::get(src_ptr_NC, o10, s10);
          gx -= trgt1 * src;
          gy -= trgt0 * src;
          src = bound::get(src_ptr_NC, o01, s01);
          gx -= trgt1 * src;
          gy -= trgt0 * src;
          src = bound::get(src_ptr_NC, o11, s11);
          gx += trgt1 * src;
          gy += trgt0 * src;
        }
      }

      scalar_t* grad_ptr_NXY = grad_ptr + n * grad_sN + w * grad_sX + h * grad_sY;
      (*grad_ptr_NXY) = gx;
      grad_ptr_NXY[grad_sC] = gy;
    }
    if (do_push || do_count) {
      // Offsets into 'push' volume
      o00 = ix0 * out_sX + iy0 * out_sY;
      o10 = ix1 * out_sX + iy0 * out_sY;
      o01 = ix0 * out_sX + iy1 * out_sY;
      o11 = ix1 * out_sX + iy1 * out_sY;
    }
    // ~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~ Pull ~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
    if (do_pull) {
      scalar_t* out_ptr_NCXY = out_ptr + n * out_sN + w * out_sX + h * out_sY;
      scalar_t* src_ptr_NC = src_ptr + n * src_sN;
      for (offset_t c = 0; c < C; ++c, out_ptr_NCXY += out_sC, src_ptr_NC += src_sC) {
        *out_ptr_NCXY = bound::get(src_ptr_NC, o00, s00) * w00 + bound::get(src_ptr_NC, o10, s10) * w10 +
            bound::get(src_ptr_NC, o01, s01) * w01 + bound::get(src_ptr_NC, o11, s11) * w11;
      }
    }
    // ~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~ SGrad ~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
    else if (do_sgrad) {
      scalar_t* out_ptr_NCXY = out_ptr + n * out_sN + w * out_sX + h * out_sY;
      scalar_t* src_ptr_NC = src_ptr + n * src_sN;

      for (offset_t c = 0; c < C; ++c, out_ptr_NCXY += out_sC, src_ptr_NC += src_sC) {
        scalar_t src00 = bound::get(src_ptr_NC, o00, s00);
        scalar_t src10 = bound::get(src_ptr_NC, o10, s10);
        scalar_t src01 = bound::get(src_ptr_NC, o01, s01);
        scalar_t src11 = bound::get(src_ptr_NC, o11, s11);
        *out_ptr_NCXY = -dy0 * src00 + dy0 * src10 - dy1 * src01 + dy1 * src11;
        out_ptr_NCXY[out_sK] = -dx0 * src00 - dx1 * src10 + dx0 * src01 + dx1 * src11;
      }
    }
    // ~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~ Push ~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
    else if (do_push) {
      scalar_t* trgt_ptr_NCXY = trgt_ptr + n * trgt_sN + w * trgt_sX + h * trgt_sY;
      scalar_t* out_ptr_NC = out_ptr + n * out_sN;
      if (trgt_K == 0) {
        // Diff w.r.t. push/pull
        for (offset_t c = 0; c < C; ++c, trgt_ptr_NCXY += trgt_sC, out_ptr_NC += out_sC) {
          scalar_t trgt = *trgt_ptr_NCXY;
          bound::add(out_ptr_NC, o00, w00 * trgt, s00);
          bound::add(out_ptr_NC, o10, w10 * trgt, s10);
          bound::add(out_ptr_NC, o01, w01 * trgt, s01);
          bound::add(out_ptr_NC, o11, w11 * trgt, s11);
        }
      } else {
        // Diff w.r.t. sgrad
        scalar_t val;
        for (offset_t c = 0; c < C; ++c, trgt_ptr_NCXY += trgt_sC, out_ptr_NC += out_sC) {
          scalar_t trgt0 = *trgt_ptr_NCXY, trgt1 = trgt_ptr_NCXY[trgt_sK];
          val = -dy0 * trgt0 - dx0 * trgt1;
          bound::add(out_ptr_NC, o00, val, s00);
          val = dy0 * trgt0 - dx1 * trgt1;
          bound::add(out_ptr_NC, o10, val, s10);
          val = -dy1 * trgt0 + dx0 * trgt1;
          bound::add(out_ptr_NC, o01, val, s01);
          val = dy1 * trgt0 + dx1 * trgt1;
          bound::add(out_ptr_NC, o11, val, s11);
        }
      }
    }
    // ~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~ Push ~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
    else if (do_count) {
      scalar_t* out_ptr_N = out_ptr + n * out_sN;
      bound::add(out_ptr_N, o00, w00, s00);
      bound::add(out_ptr_N, o10, w10, s10);
      bound::add(out_ptr_N, o01, w01, s01);
      bound::add(out_ptr_N, o11, w11, s11);
    }
  }

  // ~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
  //                     LINEAR INTERPOLATION 1D
  // ~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~

  template <typename scalar_t, typename offset_t>
  MONAI_DEVICE void PushPullImpl<scalar_t, offset_t>::interpolate1d_linear(scalar_t x, offset_t w, offset_t n) const {
    // Get corner pixel values from (x)
    offset_t ix0 = static_cast<offset_t>(std::floor(x));

    // Interpolation weights (inversely proportional to distance)
    scalar_t w1 = x - ix0;
    scalar_t w0 = 1. - w1;

    // Sign (/!\ compute sign before warping indices)
    int8_t s1 = bound::sign(bound0, ix0 + 1, src_X);
    int8_t s0 = bound::sign(bound0, ix0, src_X);

    // Warp indices
    offset_t ix1;
    ix1 = bound::index(bound0, ix0 + 1, src_X);
    ix0 = bound::index(bound0, ix0, src_X);

    offset_t o0, o1;
    if (do_pull || do_grad || do_sgrad) {
      // Offsets into source volume
      o0 = ix0 * src_sX;
      o1 = ix1 * src_sX;
    } else if (!(do_push || do_count)) {
      o0 = o1 = 0;
    }

    // ~~~~~~~~~~~~~~~~~~~~~~~~~~ Grid gradient ~~~~~~~~~~~~~~~~~~~~~~~~~~
    if (do_grad) {
      if (trgt_K == 0) {
        // backward w.r.t. push/pull
        scalar_t gx = static_cast<scalar_t>(0);
        scalar_t* trgt_ptr_NCX = trgt_ptr + n * trgt_sN + w * trgt_sX;
        scalar_t* src_ptr_NC = src_ptr + n * src_sN;

        for (offset_t c = 0; c < C; ++c, trgt_ptr_NCX += trgt_sC, src_ptr_NC += src_sC) {
          scalar_t src;
          scalar_t trgt = trgt_ptr ? *trgt_ptr_NCX : static_cast<scalar_t>(1);
          // ^ trgt_ptr == 0 during the backward pass of count
          src = bound::get(src_ptr_NC, o0, s0);
          if (trgt_ptr)
            src *= trgt;
          gx -= src;
          src = bound::get(src_ptr_NC, o1, s1);
          if (trgt_ptr)
            src *= trgt;
          gx += src;
        }

        scalar_t* grad_ptr_NX = grad_ptr + n * grad_sN + w * grad_sX;
        (*grad_ptr_NX) = gx;
      } else {
        // backward w.r.t. sgrad
        // -> zero (make sure this is done at initialization)
      }
    }
    if (do_push || do_count) {
      // Offsets into 'push' volume
      o0 = ix0 * out_sX;
      o1 = ix1 * out_sX;
    }
    // ~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~ Pull ~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
    if (do_pull) {
      scalar_t* out_ptr_NCX = out_ptr + n * out_sN + w * out_sX;
      scalar_t* src_ptr_NC = src_ptr + n * src_sN;
      for (offset_t c = 0; c < C; ++c, out_ptr_NCX += out_sC, src_ptr_NC += src_sC) {
        *out_ptr_NCX = bound::get(src_ptr_NC, o0, s0) * w0 + bound::get(src_ptr_NC, o1, s1) * w1;
      }
    }
    // ~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~ SGrad ~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
    else if (do_sgrad) {
      scalar_t* out_ptr_NCX = out_ptr + n * out_sN + w * out_sX;
      scalar_t* src_ptr_NC = src_ptr + n * src_sN;

      for (offset_t c = 0; c < C; ++c, out_ptr_NCX += out_sC, src_ptr_NC += src_sC) {
        *out_ptr_NCX = bound::get(src_ptr_NC, o1, s1) - bound::get(src_ptr_NC, o0, s0);
      }
    }
    // ~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~ Push ~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
    else if (do_push) {
      scalar_t* trgt_ptr_NCX = trgt_ptr + n * trgt_sN + w * trgt_sX;
      scalar_t* out_ptr_NC = out_ptr + n * out_sN;
      if (trgt_K == 0) {
        // Diff w.r.t. push/pull
        for (offset_t c = 0; c < C; ++c, trgt_ptr_NCX += trgt_sC, out_ptr_NC += out_sC) {
          scalar_t trgt = *trgt_ptr_NCX;
          bound::add(out_ptr_NC, o0, w0 * trgt, s0);
          bound::add(out_ptr_NC, o1, w1 * trgt, s1);
        }
      } else {
        // Diff w.r.t. sgrad
        for (offset_t c = 0; c < C; ++c, trgt_ptr_NCX += trgt_sC, out_ptr_NC += out_sC) {
          scalar_t trgt0 = *trgt_ptr_NCX;
          bound::add(out_ptr_NC, o0, -trgt0, s0);
          bound::add(out_ptr_NC, o1, trgt0, s1);
        }
      }
    }
    // ~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~ Push ~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
    else if (do_count) {
      scalar_t* out_ptr_N = out_ptr + n * out_sN;
      bound::add(out_ptr_N, o0, w0, s0);
      bound::add(out_ptr_N, o1, w1, s1);
    }
  }

  // ~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
  //                  NEAREST NEIGHBOR INTERPOLATION 3D
  // ~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~

  template <typename scalar_t, typename offset_t>
  MONAI_DEVICE void PushPullImpl<scalar_t, offset_t>::interpolate3d_nearest(
      scalar_t x,
      scalar_t y,
      scalar_t z,
      offset_t w,
      offset_t h,
      offset_t d,
      offset_t n) const {
    offset_t ix = static_cast<offset_t>(std::round(x));
    offset_t iy = static_cast<offset_t>(std::round(y));
    offset_t iz = static_cast<offset_t>(std::round(z));

    // Boundary condition (/!\ compute sign before warping indices)
    int8_t sx = bound::sign(bound0, ix, src_X);
    int8_t sy = bound::sign(bound1, iy, src_Y);
    int8_t sz = bound::sign(bound2, iz, src_Z);
    ix = bound::index(bound0, ix, src_X);
    iy = bound::index(bound1, iy, src_Y);
    iz = bound::index(bound2, iz, src_Z);

    // Sign
    int8_t s = sz * sy * sx;

    if (do_pull) {
      offset_t o = iz * src_sZ + iy * src_sY + ix * src_sX;
      scalar_t* out_ptr_NCXYZ = out_ptr + n * out_sN + w * out_sX + h * out_sY + d * out_sZ;
      scalar_t* src_ptr_NC = src_ptr + n * src_sN;
      for (offset_t c = 0; c < C; ++c, out_ptr_NCXYZ += out_sC, src_ptr_NC += src_sC)
        *out_ptr_NCXYZ = bound::get(src_ptr_NC, o, s);
    } else if (do_push && trgt_K == 0) {
      offset_t o = iz * out_sZ + iy * out_sY + ix * out_sX;
      scalar_t* trgt_ptr_NCXYZ = trgt_ptr + n * trgt_sN + w * trgt_sX + h * trgt_sY + d * trgt_sZ;
      scalar_t* out_ptr_NC = out_ptr + n * out_sN;
      for (offset_t c = 0; c < C; ++c, trgt_ptr_NCXYZ += trgt_sC, out_ptr_NC += out_sC)
        bound::add(out_ptr_NC, o, *trgt_ptr_NCXYZ, s);
    } else if (do_count) {
      offset_t o = iz * out_sZ + iy * out_sY + ix * out_sX;
      scalar_t* out_ptr_NC = out_ptr + n * out_sN;
      for (offset_t c = 0; c < C; ++c, out_ptr_NC += out_sC)
        bound::add(out_ptr_NC, o, static_cast<scalar_t>(1), s);
    }
  }

  // ~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
  //                  NEAREST NEIGHBOR INTERPOLATION 2D
  // ~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~

  template <typename scalar_t, typename offset_t>
  MONAI_DEVICE void PushPullImpl<scalar_t, offset_t>::interpolate2d_nearest(
      scalar_t x,
      scalar_t y,
      offset_t w,
      offset_t h,
      offset_t n) const {
    offset_t ix = static_cast<offset_t>(std::round(x));
    offset_t iy = static_cast<offset_t>(std::round(y));

    // Boundary condition (/!\ compute sign before warping indices)
    int8_t sx = bound::sign(bound0, ix, src_X);
    int8_t sy = bound::sign(bound1, iy, src_Y);
    ix = bound::index(bound0, ix, src_X);
    iy = bound::index(bound1, iy, src_Y);

    // Sign
    int8_t s = sy * sx;

    if (do_pull) {
      offset_t o = iy * src_sY + ix * src_sX;
      scalar_t* out_ptr_NCXY = out_ptr + n * out_sN + w * out_sX + h * out_sY;
      scalar_t* src_ptr_NC = src_ptr + n * src_sN;
      for (offset_t c = 0; c < C; ++c, out_ptr_NCXY += out_sC, src_ptr_NC += src_sC)
        *out_ptr_NCXY = bound::get(src_ptr_NC, o, s);
    } else if (do_push && trgt_K == 0) {
      offset_t o = iy * out_sY + ix * out_sX;
      scalar_t* trgt_ptr_NCXY = trgt_ptr + n * trgt_sN + w * trgt_sX + h * trgt_sY;
      scalar_t* out_ptr_NC = out_ptr + n * out_sN;
      for (offset_t c = 0; c < C; ++c, trgt_ptr_NCXY += trgt_sC, out_ptr_NC += out_sC)
        bound::add(out_ptr_NC, o, *trgt_ptr_NCXY, s);
    } else if (do_count) {
      offset_t o = iy * out_sY + ix * out_sX;
      scalar_t* out_ptr_NC = out_ptr + n * out_sN;
      for (offset_t c = 0; c < C; ++c, out_ptr_NC += out_sC)
        bound::add(out_ptr_NC, o, static_cast<scalar_t>(1), s);
    }
  }

  // ~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
  //                  NEAREST NEIGHBOR INTERPOLATION 1D
  // ~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~

  template <typename scalar_t, typename offset_t>
  MONAI_DEVICE void PushPullImpl<scalar_t, offset_t>::interpolate1d_nearest(scalar_t x, offset_t w, offset_t n) const {
    offset_t i = static_cast<offset_t>(std::round(x));

    // Boundary condition (/!\ compute sign before warping indices)
    int8_t s = bound::sign(bound0, i, src_X);
    i = bound::index(bound0, i, src_X);

    if (do_pull) {
      offset_t o = i * src_sX;
      scalar_t* out_ptr_NCX = out_ptr + n * out_sN + w * out_sX;
      scalar_t* src_ptr_NC = src_ptr + n * src_sN;
      for (offset_t c = 0; c < C; ++c, out_ptr_NCX += out_sC, src_ptr_NC += src_sC)
        *out_ptr_NCX = bound::get(src_ptr_NC, o, s);
    } else if (do_push && trgt_K == 0) {
      offset_t o = i * out_sX;
      scalar_t* trgt_ptr_NCX = trgt_ptr + n * trgt_sN + w * trgt_sX;
      scalar_t* out_ptr_NC = out_ptr + n * out_sN;
      for (offset_t c = 0; c < C; ++c, trgt_ptr_NCX += trgt_sC, out_ptr_NC += out_sC)
        bound::add(out_ptr_NC, o, *trgt_ptr_NCX, s);
    } else if (do_count) {
      offset_t o = i * out_sX;
      scalar_t* out_ptr_NC = out_ptr + n * out_sN;
      for (offset_t c = 0; c < C; ++c, out_ptr_NC += out_sC)
        bound::add(out_ptr_NC, o, static_cast<scalar_t>(1), s);
    }
  }

  // ~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
  //            LINEAR INTERPOLATION 3D + SLIDING BOUNDARY
  // ~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
  // TODO

  // ~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
  //                  CUDA KERNEL (MUST BE OUT OF CLASS)
  // ~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~

  } // namespace

  // ~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
  //                    FUNCTIONAL FORM WITH DISPATCH
  // ~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~

#define PUSHPULL_INSTANTIATE3(BoundType0, InterpolationType0, SourceType0) \
  template std::deque<Tensor> pushpull(                                    \
      const SourceType0&,                                                  \
      const Tensor&,                                                       \
      const Tensor&,                                                       \
      BoundType0,                                                          \
      InterpolationType0,                                                  \
      bool,                                                                \
      bool,                                                                \
      bool,                                                                \
      bool,                                                                \
      bool,                                                                \
      bool);                                                               \
  template std::deque<Tensor> pushpull(                                    \
      const SourceType0&, const Tensor&, BoundType0, InterpolationType0, bool, bool, bool, bool, bool, bool)
#define PUSHPULL_INSTANTIATE2(BoundType0, InterpolationType0)         \
  PUSHPULL_INSTANTIATE3(BoundType0, InterpolationType0, IntArrayRef); \
  PUSHPULL_INSTANTIATE3(BoundType0, InterpolationType0, Tensor)
#define PUSHPULL_INSTANTIATE1(BoundType0)               \
  PUSHPULL_INSTANTIATE2(BoundType0, InterpolationType); \
  PUSHPULL_INSTANTIATE2(BoundType0, InterpolationVectorRef)
#define PUSHPULL_INSTANTIATE        \
  PUSHPULL_INSTANTIATE1(BoundType); \
  PUSHPULL_INSTANTIATE1(BoundVectorRef)

  // Two arguments (source, grid)
  // > `bound` and `interpolation` can be single arguments or vectors.
  template <typename BoundType, typename InterpolationType, typename SourceType>
  MONAI_HOST std::deque<Tensor> pushpull(
      const SourceType& source,
      const Tensor& grid,
      BoundType bound,
      InterpolationType interpolation,
      bool extrapolate,
      bool do_pull,
      bool do_push,
      bool do_count,
      bool do_grad,
      bool do_sgrad) {
    PushPullAllocator info(
        grid.dim() - 2, bound, interpolation, extrapolate, do_pull, do_push, do_count, do_grad, do_sgrad);
    info.ioset(source, grid);

    return AT_DISPATCH_FLOATING_TYPES(grid.scalar_type(), "pushpull", [&] {
      PushPullImpl<scalar_t, int64_t> algo(info);
      algo.loop();
      return algo.output;
    });
  }

  // Three arguments (source, grid, target)
  // > `bound` and `interpolation` can be single arguments or vectors.
  // > `source` can be a tensor or a vector of dimensions.
  template <typename BoundType, typename InterpolationType, typename SourceType>
  MONAI_HOST std::deque<Tensor> pushpull(
      const SourceType& source,
      const Tensor& grid,
      const Tensor& target,
      BoundType bound,
      InterpolationType interpolation,
      bool extrapolate,
      bool do_pull,
      bool do_push,
      bool do_count,
      bool do_grad,
      bool do_sgrad) {
    PushPullAllocator info(
        grid.dim() - 2, bound, interpolation, extrapolate, do_pull, do_push, do_count, do_grad, do_sgrad);
    info.ioset(source, grid, target);

    return AT_DISPATCH_FLOATING_TYPES(grid.scalar_type(), "pushpull", [&] {
      PushPullImpl<scalar_t, int64_t> algo(info);
      algo.loop();
      return algo.output;
    });
  }

  PUSHPULL_INSTANTIATE;

} // namespace cpu
} // namespace monai