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disflow_avx2.c (18781B)

---

/*
* Copyright (c) 2024, 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.
*/

#include <assert.h>
#include <math.h>
#include <immintrin.h>

#include "aom_dsp/aom_dsp_common.h"
#include "aom_dsp/flow_estimation/disflow.h"
#include "aom_dsp/x86/synonyms.h"
#include "aom_dsp/x86/synonyms_avx2.h"

#include "config/aom_dsp_rtcd.h"

#if DISFLOW_PATCH_SIZE != 8
#error "Need to change disflow_avx2.c if DISFLOW_PATCH_SIZE != 8"
#endif

// Compute horizontal and vertical kernels and return them packed into a
// register. The coefficient ordering is:
//   h0, h1, v0, v1, h2, h3, v2, v3
// This is chosen because it takes less work than fully separating the kernels,
// but it is separated enough that we can pick out each coefficient pair in the
// main compute_flow_at_point function
static inline __m128i compute_cubic_kernels(double u, double v) {
 const __m128d x = _mm_set_pd(v, u);

 const __m128d x2 = _mm_mul_pd(x, x);
 const __m128d x3 = _mm_mul_pd(x2, x);

 // Macro to multiply a value v by a constant coefficient c
#define MULC(c, v) _mm_mul_pd(_mm_set1_pd(c), v)

 // Compute floating-point kernel
 // Note: To ensure results are bit-identical to the C code, we need to perform
 // exactly the same sequence of operations here as in the C code.
 __m128d k0 = _mm_sub_pd(_mm_add_pd(MULC(-0.5, x), x2), MULC(0.5, x3));
 __m128d k1 =
     _mm_add_pd(_mm_sub_pd(_mm_set1_pd(1.0), MULC(2.5, x2)), MULC(1.5, x3));
 __m128d k2 =
     _mm_sub_pd(_mm_add_pd(MULC(0.5, x), MULC(2.0, x2)), MULC(1.5, x3));
 __m128d k3 = _mm_add_pd(MULC(-0.5, x2), MULC(0.5, x3));
#undef MULC

 // Integerize
 __m128d prec = _mm_set1_pd((double)(1 << DISFLOW_INTERP_BITS));

 k0 = _mm_round_pd(_mm_mul_pd(k0, prec),
                   _MM_FROUND_TO_NEAREST_INT | _MM_FROUND_NO_EXC);
 k1 = _mm_round_pd(_mm_mul_pd(k1, prec),
                   _MM_FROUND_TO_NEAREST_INT | _MM_FROUND_NO_EXC);
 k2 = _mm_round_pd(_mm_mul_pd(k2, prec),
                   _MM_FROUND_TO_NEAREST_INT | _MM_FROUND_NO_EXC);
 k3 = _mm_round_pd(_mm_mul_pd(k3, prec),
                   _MM_FROUND_TO_NEAREST_INT | _MM_FROUND_NO_EXC);

 const __m128i c0 = _mm_cvtpd_epi32(k0);
 const __m128i c1 = _mm_cvtpd_epi32(k1);
 const __m128i c2 = _mm_cvtpd_epi32(k2);
 const __m128i c3 = _mm_cvtpd_epi32(k3);

 // Rearrange results and convert down to 16 bits, giving the target output
 // ordering
 const __m128i c01 = _mm_unpacklo_epi32(c0, c1);
 const __m128i c23 = _mm_unpacklo_epi32(c2, c3);
 return _mm_packs_epi32(c01, c23);
}

// 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.
//
// TODO(rachelbarker): Test speed/quality impact of using bilinear interpolation
// instad of bicubic interpolation
static inline void compute_flow_vector(const uint8_t *src, const uint8_t *ref,
                                      int width, int height, int stride, int x,
                                      int y, double u, double v,
                                      const int16_t *dx, const int16_t *dy,
                                      int *b) {
 const __m256i zero = _mm256_setzero_si256();

 // Accumulate 8 32-bit partial sums for each element of b
 // These will be flattened at the end.
 __m256i b0_acc = _mm256_setzero_si256();
 __m256i b1_acc = _mm256_setzero_si256();

 // 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);

 const __m128i kernels = compute_cubic_kernels(u_frac, v_frac);

 // Storage for intermediate values between the two convolution directions
 // In the AVX2 implementation, this needs a dummy row at the end, because
 // we generate 2 rows at a time but the total number of rows is odd.
 // So we generate one more row than we actually need.
 DECLARE_ALIGNED(32, int16_t,
                 tmp_[DISFLOW_PATCH_SIZE * (DISFLOW_PATCH_SIZE + 4)]);
 int16_t *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

 // Prepare the kernel vectors
 // We split the kernel into two vectors with kernel indices:
 // 0, 1, 0, 1, 0, 1, 0, 1, and
 // 2, 3, 2, 3, 2, 3, 2, 3
 __m256i h_kernel_01 = _mm256_broadcastd_epi32(kernels);
 __m256i h_kernel_23 = _mm256_broadcastd_epi32(_mm_srli_si128(kernels, 8));

 __m256i round_const_h = _mm256_set1_epi32(1 << (DISFLOW_INTERP_BITS - 6 - 1));

 for (int i = -1; i < DISFLOW_PATCH_SIZE + 2; i += 2) {
   const int y_w = y0 + i;
   const uint8_t *ref_row = &ref[y_w * stride + (x0 - 1)];
   int16_t *tmp_row = &tmp[i * DISFLOW_PATCH_SIZE];

   // Load this row of pixels.
   // For an 8x8 patch, we need to load the 8 image pixels + 3 extras,
   // for a total of 11 pixels. Here we load 16 pixels, but only use
   // the first 11.
   __m256i row =
       yy_loadu2_128((__m128i *)(ref_row + stride), (__m128i *)ref_row);

   // Expand pixels to int16s
   // We must use unpacks here, as we have one row in each 128-bit lane
   // and want to handle each of those independently.
   // This is in contrast to _mm256_cvtepu8_epi16(), which takes a single
   // 128-bit input and widens it to 256 bits.
   __m256i px_0to7_i16 = _mm256_unpacklo_epi8(row, zero);
   __m256i px_4to10_i16 =
       _mm256_unpacklo_epi8(_mm256_srli_si256(row, 4), zero);

   // Compute first four outputs
   // input pixels 0, 1, 1, 2, 2, 3, 3, 4
   // * kernel     0, 1, 0, 1, 0, 1, 0, 1
   __m256i px0 =
       _mm256_unpacklo_epi16(px_0to7_i16, _mm256_srli_si256(px_0to7_i16, 2));
   // input pixels 2, 3, 3, 4, 4, 5, 5, 6
   // * kernel     2, 3, 2, 3, 2, 3, 2, 3
   __m256i px1 = _mm256_unpacklo_epi16(_mm256_srli_si256(px_0to7_i16, 4),
                                       _mm256_srli_si256(px_0to7_i16, 6));
   // Convolve with kernel and sum 2x2 boxes to form first 4 outputs
   __m256i sum0 = _mm256_add_epi32(_mm256_madd_epi16(px0, h_kernel_01),
                                   _mm256_madd_epi16(px1, h_kernel_23));

   __m256i out0 = _mm256_srai_epi32(_mm256_add_epi32(sum0, round_const_h),
                                    DISFLOW_INTERP_BITS - 6);

   // Compute second four outputs
   __m256i px2 =
       _mm256_unpacklo_epi16(px_4to10_i16, _mm256_srli_si256(px_4to10_i16, 2));
   __m256i px3 = _mm256_unpacklo_epi16(_mm256_srli_si256(px_4to10_i16, 4),
                                       _mm256_srli_si256(px_4to10_i16, 6));
   __m256i sum1 = _mm256_add_epi32(_mm256_madd_epi16(px2, h_kernel_01),
                                   _mm256_madd_epi16(px3, h_kernel_23));

   // Round by just enough bits that the result is
   // guaranteed to fit into an i16. Then the next stage can use 16 x 16 -> 32
   // bit multiplies, which should be a fair bit faster than 32 x 32 -> 32
   // as it does now
   // This means shifting down so we have 6 extra bits, for a maximum value
   // of +18360, which can occur if u_frac == 0.5 and the input pixels are
   // {0, 255, 255, 0}.
   __m256i out1 = _mm256_srai_epi32(_mm256_add_epi32(sum1, round_const_h),
                                    DISFLOW_INTERP_BITS - 6);

   _mm256_storeu_si256((__m256i *)tmp_row, _mm256_packs_epi32(out0, out1));
 }

 // Vertical convolution
 const int round_bits = DISFLOW_INTERP_BITS + 6 - DISFLOW_DERIV_SCALE_LOG2;
 __m256i round_const_v = _mm256_set1_epi32(1 << (round_bits - 1));

 __m256i v_kernel_01 = _mm256_broadcastd_epi32(_mm_srli_si128(kernels, 4));
 __m256i v_kernel_23 = _mm256_broadcastd_epi32(_mm_srli_si128(kernels, 12));

 for (int i = 0; i < DISFLOW_PATCH_SIZE; i += 2) {
   int16_t *tmp_row = &tmp[i * DISFLOW_PATCH_SIZE];

   // Load 5 rows of 8 x 16-bit values, and pack into 4 registers
   // holding rows {0, 1}, {1, 2}, {2, 3}, {3, 4}
   __m128i row0 = _mm_loadu_si128((__m128i *)(tmp_row - DISFLOW_PATCH_SIZE));
   __m128i row1 = _mm_loadu_si128((__m128i *)tmp_row);
   __m128i row2 = _mm_loadu_si128((__m128i *)(tmp_row + DISFLOW_PATCH_SIZE));
   __m128i row3 =
       _mm_loadu_si128((__m128i *)(tmp_row + 2 * DISFLOW_PATCH_SIZE));
   __m128i row4 =
       _mm_loadu_si128((__m128i *)(tmp_row + 3 * DISFLOW_PATCH_SIZE));

   __m256i px0 = _mm256_set_m128i(row1, row0);
   __m256i px1 = _mm256_set_m128i(row2, row1);
   __m256i px2 = _mm256_set_m128i(row3, row2);
   __m256i px3 = _mm256_set_m128i(row4, row3);

   // We want to calculate px0 * v_kernel[0] + px1 * v_kernel[1] + ... ,
   // but each multiply expands its output to 32 bits. So we need to be
   // a little clever about how we do this
   __m256i sum0 = _mm256_add_epi32(
       _mm256_madd_epi16(_mm256_unpacklo_epi16(px0, px1), v_kernel_01),
       _mm256_madd_epi16(_mm256_unpacklo_epi16(px2, px3), v_kernel_23));
   __m256i sum1 = _mm256_add_epi32(
       _mm256_madd_epi16(_mm256_unpackhi_epi16(px0, px1), v_kernel_01),
       _mm256_madd_epi16(_mm256_unpackhi_epi16(px2, px3), v_kernel_23));

   __m256i sum0_rounded =
       _mm256_srai_epi32(_mm256_add_epi32(sum0, round_const_v), round_bits);
   __m256i sum1_rounded =
       _mm256_srai_epi32(_mm256_add_epi32(sum1, round_const_v), round_bits);

   __m256i warped = _mm256_packs_epi32(sum0_rounded, sum1_rounded);
   __m128i src_pixels_u8 = xx_loadu_2x64(&src[(y + i + 1) * stride + x],
                                         &src[(y + i) * stride + x]);
   __m256i src_pixels =
       _mm256_slli_epi16(_mm256_cvtepu8_epi16(src_pixels_u8), 3);

   // Calculate delta from the target patch
   __m256i dt = _mm256_sub_epi16(warped, src_pixels);

   // Load 2x8 elements each of dx and dt, to pair with the 2x8 elements of dt
   // that we have just computed. Then compute 2x8 partial sums of dx * dt
   // and dy * dt, implicitly sum to give 2x4 partial sums of each, and
   // accumulate.
   __m256i dx_row = _mm256_loadu_si256((__m256i *)&dx[i * DISFLOW_PATCH_SIZE]);
   __m256i dy_row = _mm256_loadu_si256((__m256i *)&dy[i * DISFLOW_PATCH_SIZE]);
   b0_acc = _mm256_add_epi32(b0_acc, _mm256_madd_epi16(dx_row, dt));
   b1_acc = _mm256_add_epi32(b1_acc, _mm256_madd_epi16(dy_row, dt));
 }

 // Flatten the two sets of partial sums to find the final value of b
 // We need to set b[0] = sum(b0_acc), b[1] = sum(b1_acc).
 // We need to do 14 additions in total; a `hadd` instruction can take care
 // of eight of them, then a vertical sum can do four more, leaving two
 // scalar additions.
 __m256i partial_sum_256 = _mm256_hadd_epi32(b0_acc, b1_acc);
 __m128i partial_sum =
     _mm_add_epi32(_mm256_extracti128_si256(partial_sum_256, 0),
                   _mm256_extracti128_si256(partial_sum_256, 1));
 b[0] = _mm_extract_epi32(partial_sum, 0) + _mm_extract_epi32(partial_sum, 1);
 b[1] = _mm_extract_epi32(partial_sum, 2) + _mm_extract_epi32(partial_sum, 3);
}

// Compute the x and y gradients of the source patch in a single pass,
// and store into dx and dy respectively.
static inline void sobel_filter(const uint8_t *src, int src_stride, int16_t *dx,
                               int16_t *dy) {
 const __m256i zero = _mm256_setzero_si256();

 // Loop setup: Load the first two rows (of 10 input rows) and apply
 // the horizontal parts of the two filters
 __m256i row_m1_0 =
     yy_loadu2_128((__m128i *)(src - 1), (__m128i *)(src - src_stride - 1));
 __m256i row_m1_0_a = _mm256_unpacklo_epi8(row_m1_0, zero);
 __m256i row_m1_0_b =
     _mm256_unpacklo_epi8(_mm256_srli_si256(row_m1_0, 1), zero);
 __m256i row_m1_0_c =
     _mm256_unpacklo_epi8(_mm256_srli_si256(row_m1_0, 2), zero);

 __m256i row_m1_0_hsmooth =
     _mm256_add_epi16(_mm256_add_epi16(row_m1_0_a, row_m1_0_c),
                      _mm256_slli_epi16(row_m1_0_b, 1));
 __m256i row_m1_0_hdiff = _mm256_sub_epi16(row_m1_0_a, row_m1_0_c);

 // Main loop: For each pair of output rows (i, i+1):
 // * Load rows (i+1, i+2) and apply both horizontal filters
 // * Apply vertical filters and store results
 // * Shift rows for next iteration
 for (int i = 0; i < DISFLOW_PATCH_SIZE; i += 2) {
   // Load rows (i+1, i+2) and apply both horizontal filters
   const __m256i row_p1_p2 =
       yy_loadu2_128((__m128i *)(src + (i + 2) * src_stride - 1),
                     (__m128i *)(src + (i + 1) * src_stride - 1));
   const __m256i row_p1_p2_a = _mm256_unpacklo_epi8(row_p1_p2, zero);
   const __m256i row_p1_p2_b =
       _mm256_unpacklo_epi8(_mm256_srli_si256(row_p1_p2, 1), zero);
   const __m256i row_p1_p2_c =
       _mm256_unpacklo_epi8(_mm256_srli_si256(row_p1_p2, 2), zero);

   const __m256i row_p1_p2_hsmooth =
       _mm256_add_epi16(_mm256_add_epi16(row_p1_p2_a, row_p1_p2_c),
                        _mm256_slli_epi16(row_p1_p2_b, 1));
   const __m256i row_p1_p2_hdiff = _mm256_sub_epi16(row_p1_p2_a, row_p1_p2_c);

   // Apply vertical filters and store results
   // dx = vertical smooth(horizontal diff(input))
   // dy = vertical diff(horizontal smooth(input))
   const __m256i row_0_p1_hdiff =
       _mm256_permute2x128_si256(row_m1_0_hdiff, row_p1_p2_hdiff, 0x21);
   const __m256i dx_row =
       _mm256_add_epi16(_mm256_add_epi16(row_m1_0_hdiff, row_p1_p2_hdiff),
                        _mm256_slli_epi16(row_0_p1_hdiff, 1));
   const __m256i dy_row =
       _mm256_sub_epi16(row_m1_0_hsmooth, row_p1_p2_hsmooth);

   _mm256_storeu_si256((__m256i *)(dx + i * DISFLOW_PATCH_SIZE), dx_row);
   _mm256_storeu_si256((__m256i *)(dy + i * DISFLOW_PATCH_SIZE), dy_row);

   // Shift rows for next iteration
   // This allows a lot of work to be reused, reducing the number of
   // horizontal filtering operations from 2*3*8 = 48 to 2*10 = 20
   row_m1_0_hsmooth = row_p1_p2_hsmooth;
   row_m1_0_hdiff = row_p1_p2_hdiff;
 }
}

static inline void compute_flow_matrix(const int16_t *dx, int dx_stride,
                                      const int16_t *dy, int dy_stride,
                                      double *M) {
 __m256i acc[4] = { 0 };

 for (int i = 0; i < DISFLOW_PATCH_SIZE; i += 2) {
   __m256i dx_row = _mm256_loadu_si256((__m256i *)&dx[i * dx_stride]);
   __m256i dy_row = _mm256_loadu_si256((__m256i *)&dy[i * dy_stride]);

   acc[0] = _mm256_add_epi32(acc[0], _mm256_madd_epi16(dx_row, dx_row));
   acc[1] = _mm256_add_epi32(acc[1], _mm256_madd_epi16(dx_row, dy_row));
   // Don't compute acc[2], as it should be equal to acc[1]
   acc[3] = _mm256_add_epi32(acc[3], _mm256_madd_epi16(dy_row, dy_row));
 }

 // Condense sums
 __m256i partial_sum_0 = _mm256_hadd_epi32(acc[0], acc[1]);
 __m256i partial_sum_1 = _mm256_hadd_epi32(acc[1], acc[3]);
 __m256i result_256 = _mm256_hadd_epi32(partial_sum_0, partial_sum_1);
 __m128i result = _mm_add_epi32(_mm256_extracti128_si256(result_256, 0),
                                _mm256_extracti128_si256(result_256, 1));

 // 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.
 result = _mm_add_epi32(result, _mm_set_epi32(1, 0, 0, 1));

 // Convert results to doubles and store
 _mm256_storeu_pd(M, _mm256_cvtepi32_pd(result));
}

// Try to invert the matrix M
// Note: Due to the nature of how a least-squares matrix is constructed, all of
// the eigenvalues will be >= 0, and therefore det M >= 0 as well.
// The regularization term `+ k * I` further ensures that det M >= k^2.
// As mentioned in compute_flow_matrix(), here we use k = 1, so det M >= 1.
// So we don't have to worry about non-invertible matrices here.
static inline void invert_2x2(const double *M, double *M_inv) {
 double det = (M[0] * M[3]) - (M[1] * M[2]);
 assert(det >= 1);
 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;
}

void aom_compute_flow_at_point_avx2(const uint8_t *src, const uint8_t *ref,
                                   int x, int y, int width, int height,
                                   int stride, double *u, double *v) {
 DECLARE_ALIGNED(32, double, M[4]);
 DECLARE_ALIGNED(32, double, M_inv[4]);
 DECLARE_ALIGNED(32, int16_t, dx[DISFLOW_PATCH_SIZE * DISFLOW_PATCH_SIZE]);
 DECLARE_ALIGNED(32, int16_t, dy[DISFLOW_PATCH_SIZE * DISFLOW_PATCH_SIZE]);
 int b[2];

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

 compute_flow_matrix(dx, DISFLOW_PATCH_SIZE, dy, DISFLOW_PATCH_SIZE, M);
 invert_2x2(M, M_inv);

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