/*
 * Copyright (c) 2016, Alliance for Open Media. All rights reserved
 *
 * This source code is subject to the terms of the BSD 2 Clause License and
 * the Alliance for Open Media Patent License 1.0. If the BSD 2 Clause License
 * was not distributed with this source code in the LICENSE file, you can
 * obtain it at www.aomedia.org/license/software. If the Alliance for Open
 * Media Patent License 1.0 was not distributed with this source code in the
 * PATENTS file, you can obtain it at www.aomedia.org/license/patent.
 */

// Dense Inverse Search flow algorithm
// Paper: https://arxiv.org/abs/1603.03590

#include "aom_dsp/aom_dsp_common.h"
#include "aom_dsp/flow_estimation/corner_detect.h"
#include "aom_dsp/flow_estimation/disflow.h"
#include "aom_dsp/pyramid.h"
#include "aom_mem/aom_mem.h"

#include "config/aom_dsp_rtcd.h"

// TODO(rachelbarker):
// Implement specialized functions for upscaling flow fields,
// replacing av1_resize_plane_double().
// Then we can avoid needing to include code from av1/
#include "av1/common/resize.h"

#include <assert.h>

// Number of outermost flow field entries (on each edge) which can't be
// computed, because the patch they correspond to extends outside of the
// frame
// The border is (DISFLOW_PATCH_SIZE >> 1) pixels, which is
// (DISFLOW_PATCH_SIZE >> 1) >> DOWNSAMPLE_SHIFT many flow field entries
#define FLOW_BORDER ((DISFLOW_PATCH_SIZE >> 1) >> DOWNSAMPLE_SHIFT)

// Compare two regions of width x height pixels, one rooted at position
// (x, y) in src and the other at (x + u, y + v) in ref.
// This function returns the sum of squared pixel differences between
// the two regions.
static INLINE void compute_flow_error(const uint8_t *src, const uint8_t *ref,
                                      int width, int height, int stride, int x,
                                      int y, double u, double v, int16_t *dt) {
  // Split offset into integer and fractional parts, and compute cubic
  // interpolation kernels
  const int u_int = (int)floor(u);
  const int v_int = (int)floor(v);
  const double u_frac = u - floor(u);
  const double v_frac = v - floor(v);

  int h_kernel[4];
  int v_kernel[4];
  get_cubic_kernel_int(u_frac, h_kernel);
  get_cubic_kernel_int(v_frac, v_kernel);

  // Storage for intermediate values between the two convolution directions
  int tmp_[DISFLOW_PATCH_SIZE * (DISFLOW_PATCH_SIZE + 3)];
  int *tmp = tmp_ + DISFLOW_PATCH_SIZE;  // Offset by one row

  // Clamp coordinates so that all pixels we fetch will remain within the
  // allocated border region, but allow them to go far enough out that
  // the border pixels' values do not change.
  // Since we are calculating an 8x8 block, the bottom-right pixel
  // in the block has coordinates (x0 + 7, y0 + 7). Then, the cubic
  // interpolation has 4 taps, meaning that the output of pixel
  // (x_w, y_w) depends on the pixels in the range
  // ([x_w - 1, x_w + 2], [y_w - 1, y_w + 2]).
  //
  // Thus the most extreme coordinates which will be fetched are
  // (x0 - 1, y0 - 1) and (x0 + 9, y0 + 9).
  const int x0 = clamp(x + u_int, -9, width);
  const int y0 = clamp(y + v_int, -9, height);

  // Horizontal convolution
  for (int i = -1; i < DISFLOW_PATCH_SIZE + 2; ++i) {
    const int y_w = y0 + i;
    for (int j = 0; j < DISFLOW_PATCH_SIZE; ++j) {
      const int x_w = x0 + j;
      int arr[4];

      arr[0] = (int)ref[y_w * stride + (x_w - 1)];
      arr[1] = (int)ref[y_w * stride + (x_w + 0)];
      arr[2] = (int)ref[y_w * stride + (x_w + 1)];
      arr[3] = (int)ref[y_w * stride + (x_w + 2)];

      // Apply kernel and round, keeping 6 extra bits of precision.
      //
      // 6 is the maximum allowable number of extra bits which will avoid
      // the intermediate values overflowing an int16_t. The most extreme
      // intermediate value occurs when:
      // * The input pixels are [0, 255, 255, 0]
      // * u_frac = 0.5
      // In this case, the un-scaled output is 255 * 1.125 = 286.875.
      // As an integer with 6 fractional bits, that is 18360, which fits
      // in an int16_t. But with 7 fractional bits it would be 36720,
      // which is too large.
      tmp[i * DISFLOW_PATCH_SIZE + j] = ROUND_POWER_OF_TWO(
          get_cubic_value_int(arr, h_kernel), FLOW_INTERP_BITS - 6);
    }
  }

  // Vertical convolution
  for (int i = 0; i < DISFLOW_PATCH_SIZE; ++i) {
    for (int j = 0; j < DISFLOW_PATCH_SIZE; ++j) {
      const int *p = &tmp[i * DISFLOW_PATCH_SIZE + j];
      const int arr[4] = { p[-DISFLOW_PATCH_SIZE], p[0], p[DISFLOW_PATCH_SIZE],
                           p[2 * DISFLOW_PATCH_SIZE] };
      const int result = get_cubic_value_int(arr, v_kernel);

      // Apply kernel and round.
      // This time, we have to round off the 6 extra bits which were kept
      // earlier, but we also want to keep DISFLOW_DERIV_SCALE_LOG2 extra bits
      // of precision to match the scale of the dx and dy arrays.
      const int round_bits = FLOW_INTERP_BITS + 6 - DISFLOW_DERIV_SCALE_LOG2;
      const int warped = ROUND_POWER_OF_TWO(result, round_bits);
      const int src_px = src[(x + j) + (y + i) * stride] << 3;
      const int err = warped - src_px;
      dt[i * DISFLOW_PATCH_SIZE + j] = err;
    }
  }
}

static INLINE void sobel_filter(const uint8_t *src, int src_stride,
                                int16_t *dst, int dst_stride, int dir) {
  int16_t tmp_[DISFLOW_PATCH_SIZE * (DISFLOW_PATCH_SIZE + 2)];
  int16_t *tmp = tmp_ + DISFLOW_PATCH_SIZE;

  // Sobel filter kernel
  // This must have an overall scale factor equal to DISFLOW_DERIV_SCALE,
  // in order to produce correctly scaled outputs.
  // To work out the scale factor, we multiply two factors:
  //
  // * For the derivative filter (sobel_a), comparing our filter
  //    image[x - 1] - image[x + 1]
  //   to the standard form
  //    d/dx image[x] = image[x+1] - image[x]
  //   tells us that we're actually calculating -2 * d/dx image[2]
  //
  // * For the smoothing filter (sobel_b), all coefficients are positive
  //   so the scale factor is just the sum of the coefficients
  //
  // Thus we need to make sure that DISFLOW_DERIV_SCALE = 2 * sum(sobel_b)
  // (and take care of the - sign from sobel_a elsewhere)
  static const int16_t sobel_a[3] = { 1, 0, -1 };
  static const int16_t sobel_b[3] = { 1, 2, 1 };
  const int taps = 3;

  // horizontal filter
  const int16_t *h_kernel = dir ? sobel_a : sobel_b;

  for (int y = -1; y < DISFLOW_PATCH_SIZE + 1; ++y) {
    for (int x = 0; x < DISFLOW_PATCH_SIZE; ++x) {
      int sum = 0;
      for (int k = 0; k < taps; ++k) {
        sum += h_kernel[k] * src[y * src_stride + (x + k - 1)];
      }
      tmp[y * DISFLOW_PATCH_SIZE + x] = sum;
    }
  }

  // vertical filter
  const int16_t *v_kernel = dir ? sobel_b : sobel_a;

  for (int y = 0; y < DISFLOW_PATCH_SIZE; ++y) {
    for (int x = 0; x < DISFLOW_PATCH_SIZE; ++x) {
      int sum = 0;
      for (int k = 0; k < taps; ++k) {
        sum += v_kernel[k] * tmp[(y + k - 1) * DISFLOW_PATCH_SIZE + x];
      }
      dst[y * dst_stride + x] = sum;
    }
  }
}

// Computes the components of the system of equations used to solve for
// a flow vector.
//
// The flow equations are a least-squares system, derived as follows:
//
// For each pixel in the patch, we calculate the current error `dt`,
// and the x and y gradients `dx` and `dy` of the source patch.
// This means that, to first order, the squared error for this pixel is
//
//    (dt + u * dx + v * dy)^2
//
// where (u, v) are the incremental changes to the flow vector.
//
// We then want to find the values of u and v which minimize the sum
// of the squared error across all pixels. Conveniently, this fits exactly
// into the form of a least squares problem, with one equation
//
//   u * dx + v * dy = -dt
//
// for each pixel.
//
// Summing across all pixels in a square window of size DISFLOW_PATCH_SIZE,
// and absorbing the - sign elsewhere, this results in the least squares system
//
//   M = |sum(dx * dx)  sum(dx * dy)|
//       |sum(dx * dy)  sum(dy * dy)|
//
//   b = |sum(dx * dt)|
//       |sum(dy * dt)|
static INLINE void compute_flow_matrix(const int16_t *dx, int dx_stride,
                                       const int16_t *dy, int dy_stride,
                                       double *M) {
  int tmp[4] = { 0 };

  for (int i = 0; i < DISFLOW_PATCH_SIZE; i++) {
    for (int j = 0; j < DISFLOW_PATCH_SIZE; j++) {
      tmp[0] += dx[i * dx_stride + j] * dx[i * dx_stride + j];
      tmp[1] += dx[i * dx_stride + j] * dy[i * dy_stride + j];
      // Don't compute tmp[2], as it should be equal to tmp[1]
      tmp[3] += dy[i * dy_stride + j] * dy[i * dy_stride + j];
    }
  }

  // Apply regularization
  // We follow the standard regularization method of adding `k * I` before
  // inverting. This ensures that the matrix will be invertible.
  //
  // Setting the regularization strength k to 1 seems to work well here, as
  // typical values coming from the other equations are very large (1e5 to
  // 1e6, with an upper limit of around 6e7, at the time of writing).
  // It also preserves the property that all matrix values are whole numbers,
  // which is convenient for integerized SIMD implementation.
  tmp[0] += 1;
  tmp[3] += 1;

  tmp[2] = tmp[1];

  M[0] = (double)tmp[0];
  M[1] = (double)tmp[1];
  M[2] = (double)tmp[2];
  M[3] = (double)tmp[3];
}

static INLINE void compute_flow_vector(const int16_t *dx, int dx_stride,
                                       const int16_t *dy, int dy_stride,
                                       const int16_t *dt, int dt_stride,
                                       int *b) {
  memset(b, 0, 2 * sizeof(*b));

  for (int i = 0; i < DISFLOW_PATCH_SIZE; i++) {
    for (int j = 0; j < DISFLOW_PATCH_SIZE; j++) {
      b[0] += dx[i * dx_stride + j] * dt[i * dt_stride + j];
      b[1] += dy[i * dy_stride + j] * dt[i * dt_stride + j];
    }
  }
}

// Try to invert the matrix M
// Returns a success indication:
// true => M was successfully inverted into M_inv
// false => M is degenerate (or too close to it), and could not be inverted
static INLINE bool invert_2x2(const double *M, double *M_inv) {
  double det = (M[0] * M[3]) - (M[1] * M[2]);
  if (fabs(det) < 1e-5) {
    return false;
  }
  const double det_inv = 1 / det;

  M_inv[0] = M[3] * det_inv;
  M_inv[1] = -M[1] * det_inv;
  M_inv[2] = -M[2] * det_inv;
  M_inv[3] = M[0] * det_inv;
  return true;
}

void aom_compute_flow_at_point_c(const uint8_t *src, const uint8_t *ref, int x,
                                 int y, int width, int height, int stride,
                                 double *u, double *v) {
  double M[4];
  double M_inv[4];
  int b[2];
  int16_t dt[DISFLOW_PATCH_SIZE * DISFLOW_PATCH_SIZE];
  int16_t dx[DISFLOW_PATCH_SIZE * DISFLOW_PATCH_SIZE];
  int16_t dy[DISFLOW_PATCH_SIZE * DISFLOW_PATCH_SIZE];

  // Compute gradients within this patch
  const uint8_t *src_patch = &src[y * stride + x];
  sobel_filter(src_patch, stride, dx, DISFLOW_PATCH_SIZE, 1);
  sobel_filter(src_patch, stride, dy, DISFLOW_PATCH_SIZE, 0);

  compute_flow_matrix(dx, DISFLOW_PATCH_SIZE, dy, DISFLOW_PATCH_SIZE, M);
  bool valid = invert_2x2(M, M_inv);
  if (!valid) {
    // Unable to refine this point at this level
    return;
  }

  for (int itr = 0; itr < DISFLOW_MAX_ITR; itr++) {
    compute_flow_error(src, ref, width, height, stride, x, y, *u, *v, dt);
    compute_flow_vector(dx, DISFLOW_PATCH_SIZE, dy, DISFLOW_PATCH_SIZE, dt,
                        DISFLOW_PATCH_SIZE, b);

    // Solve flow equations to find a better estimate for the flow vector
    // at this point
    const double step_u = M_inv[0] * b[0] + M_inv[1] * b[1];
    const double step_v = M_inv[2] * b[0] + M_inv[3] * b[1];
    *u += fclamp(step_u * DISFLOW_STEP_SIZE, -2, 2);
    *v += fclamp(step_v * DISFLOW_STEP_SIZE, -2, 2);

    if (fabs(step_u) + fabs(step_v) < DISFLOW_STEP_SIZE_THRESOLD) {
      // Stop iteration when we're close to convergence
      break;
    }
  }
}

static void fill_flow_field_borders(double *flow, int width, int height,
                                    int stride) {
  // Calculate the bounds of the rectangle which was filled in by
  // compute_flow_field() before calling this function.
  // These indices are inclusive on both ends.
  const int left_index = FLOW_BORDER;
  const int right_index = (width - FLOW_BORDER - 1);
  const int top_index = FLOW_BORDER;
  const int bottom_index = (height - FLOW_BORDER - 1);

  // Left area
  for (int i = top_index; i <= bottom_index; i += 1) {
    double *row = flow + i * stride;
    const double left = row[left_index];
    for (int j = 0; j < left_index; j++) {
      row[j] = left;
    }
  }

  // Right area
  for (int i = top_index; i <= bottom_index; i += 1) {
    double *row = flow + i * stride;
    const double right = row[right_index];
    for (int j = right_index + 1; j < width; j++) {
      row[j] = right;
    }
  }

  // Top area
  const double *top_row = flow + top_index * stride;
  for (int i = 0; i < top_index; i++) {
    double *row = flow + i * stride;
    memcpy(row, top_row, width * sizeof(*row));
  }

  // Bottom area
  const double *bottom_row = flow + bottom_index * stride;
  for (int i = bottom_index + 1; i < height; i++) {
    double *row = flow + i * stride;
    memcpy(row, bottom_row, width * sizeof(*row));
  }
}

// make sure flow_u and flow_v start at 0
static void compute_flow_field(const ImagePyramid *src_pyr,
                               const ImagePyramid *ref_pyr, FlowField *flow) {
  assert(src_pyr->n_levels == ref_pyr->n_levels);

  double *flow_u = flow->u;
  double *flow_v = flow->v;

  const size_t flow_size = flow->stride * (size_t)flow->height;
  double *u_upscale = aom_calloc(flow_size, sizeof(*u_upscale));
  double *v_upscale = aom_calloc(flow_size, sizeof(*v_upscale));

  // Compute flow field from coarsest to finest level of the pyramid
  for (int level = src_pyr->n_levels - 1; level >= 0; --level) {
    const PyramidLayer *cur_layer = &src_pyr->layers[level];
    const int cur_width = cur_layer->width;
    const int cur_height = cur_layer->height;
    const int cur_stride = cur_layer->stride;

    const uint8_t *src_buffer = cur_layer->buffer;
    const uint8_t *ref_buffer = ref_pyr->layers[level].buffer;

    const int cur_flow_width = cur_width >> DOWNSAMPLE_SHIFT;
    const int cur_flow_height = cur_height >> DOWNSAMPLE_SHIFT;
    const int cur_flow_stride = flow->stride;

    for (int i = FLOW_BORDER; i < cur_flow_height - FLOW_BORDER; i += 1) {
      for (int j = FLOW_BORDER; j < cur_flow_width - FLOW_BORDER; j += 1) {
        const int flow_field_idx = i * cur_flow_stride + j;

        // Calculate the position of a patch of size DISFLOW_PATCH_SIZE pixels,
        // which is centered on the region covered by this flow field entry
        const int patch_center_x =
            (j << DOWNSAMPLE_SHIFT) + UPSAMPLE_CENTER_OFFSET;  // In pixels
        const int patch_center_y =
            (i << DOWNSAMPLE_SHIFT) + UPSAMPLE_CENTER_OFFSET;  // In pixels
        const int patch_tl_x = patch_center_x - DISFLOW_PATCH_CENTER;
        const int patch_tl_y = patch_center_y - DISFLOW_PATCH_CENTER;
        assert(patch_tl_x >= 0);
        assert(patch_tl_y >= 0);

        aom_compute_flow_at_point(src_buffer, ref_buffer, patch_tl_x,
                                  patch_tl_y, cur_width, cur_height, cur_stride,
                                  &flow_u[flow_field_idx],
                                  &flow_v[flow_field_idx]);
      }
    }

    // Fill in the areas which we haven't explicitly computed, with copies
    // of the outermost values which we did compute
    fill_flow_field_borders(flow_u, cur_flow_width, cur_flow_height,
                            cur_flow_stride);
    fill_flow_field_borders(flow_v, cur_flow_width, cur_flow_height,
                            cur_flow_stride);

    if (level > 0) {
      const int upscale_flow_width = cur_flow_width << 1;
      const int upscale_flow_height = cur_flow_height << 1;
      const int upscale_stride = flow->stride;

      av1_resize_plane_double(flow_u, cur_flow_height, cur_flow_width,
                              cur_flow_stride, u_upscale, upscale_flow_height,
                              upscale_flow_width, upscale_stride);
      av1_resize_plane_double(flow_v, cur_flow_height, cur_flow_width,
                              cur_flow_stride, v_upscale, upscale_flow_height,
                              upscale_flow_width, upscale_stride);

      // Multiply all flow vectors by 2.
      // When we move down a pyramid level, the image resolution doubles.
      // Thus we need to double all vectors in order for them to represent
      // the same translation at the next level down
      for (int i = 0; i < upscale_flow_height; i++) {
        for (int j = 0; j < upscale_flow_width; j++) {
          const int index = i * upscale_stride + j;
          flow_u[index] = u_upscale[index] * 2.0;
          flow_v[index] = v_upscale[index] * 2.0;
        }
      }

      // If we didn't fill in the rightmost column or bottommost row during
      // upsampling (in order to keep the ratio to exactly 2), fill them
      // in here by copying the next closest column/row
      const PyramidLayer *next_layer = &src_pyr->layers[level - 1];
      const int next_flow_width = next_layer->width >> DOWNSAMPLE_SHIFT;
      const int next_flow_height = next_layer->height >> DOWNSAMPLE_SHIFT;

      // Rightmost column
      if (next_flow_width > upscale_flow_width) {
        assert(next_flow_width == upscale_flow_width + 1);
        for (int i = 0; i < upscale_flow_height; i++) {
          const int index = i * upscale_stride + upscale_flow_width;
          flow_u[index] = flow_u[index - 1];
          flow_v[index] = flow_v[index - 1];
        }
      }

      // Bottommost row
      if (next_flow_height > upscale_flow_height) {
        assert(next_flow_height == upscale_flow_height + 1);
        for (int j = 0; j < next_flow_width; j++) {
          const int index = upscale_flow_height * upscale_stride + j;
          flow_u[index] = flow_u[index - upscale_stride];
          flow_v[index] = flow_v[index - upscale_stride];
        }
      }
    }
  }
  aom_free(u_upscale);
  aom_free(v_upscale);
}

FlowField *aom_compute_flow_field(YV12_BUFFER_CONFIG *src,
                                  YV12_BUFFER_CONFIG *ref, int bit_depth) {
  // Precompute information we will need about each frame
  ImagePyramid *src_pyramid = src->y_pyramid;
  ImagePyramid *ref_pyramid = ref->y_pyramid;
  aom_compute_pyramid(src, bit_depth, src_pyramid);
  aom_compute_pyramid(ref, bit_depth, ref_pyramid);

  const int src_width = src_pyramid->layers[0].width;
  const int src_height = src_pyramid->layers[0].height;
  assert(ref_pyramid->layers[0].width == src_width);
  assert(ref_pyramid->layers[0].height == src_height);

  FlowField *flow = aom_alloc_flow_field(src_width, src_height);

  compute_flow_field(src_pyramid, ref_pyramid, flow);

  return flow;
}