Merging upstream version 127.0.

Signed-off-by: Daniel Baumann <daniel.baumann@progress-linux.org>

3 files changed, 396 insertions, 103 deletions

diff --git a/third_party/aom/aom_dsp/flow_estimation/arm/disflow_neon.c b/third_party/aom/aom_dsp/flow_estimation/arm/disflow_neon.c
index 62729133e3..5758d2887f 100644
--- a/third_party/aom/aom_dsp/flow_estimation/arm/disflow_neon.c
+++ b/third_party/aom/aom_dsp/flow_estimation/arm/disflow_neon.c
@@ -16,36 +16,10 @@
 
 #include "aom_dsp/arm/mem_neon.h"
 #include "aom_dsp/arm/sum_neon.h"
+#include "aom_dsp/flow_estimation/arm/disflow_neon.h"
 #include "config/aom_config.h"
 #include "config/aom_dsp_rtcd.h"
 
-static INLINE void get_cubic_kernel_dbl(double x, double kernel[4]) {
-  // Check that the fractional position is in range.
-  //
-  // Note: x is calculated from, e.g., `u_frac = u - floor(u)`.
-  // Mathematically, this implies that 0 <= x < 1. However, in practice it is
-  // possible to have x == 1 due to floating point rounding. This is fine,
-  // and we still interpolate correctly if we allow x = 1.
-  assert(0 <= x && x <= 1);
-
-  double x2 = x * x;
-  double x3 = x2 * x;
-  kernel[0] = -0.5 * x + x2 - 0.5 * x3;
-  kernel[1] = 1.0 - 2.5 * x2 + 1.5 * x3;
-  kernel[2] = 0.5 * x + 2.0 * x2 - 1.5 * x3;
-  kernel[3] = -0.5 * x2 + 0.5 * x3;
-}
-
-static INLINE void get_cubic_kernel_int(double x, int kernel[4]) {
-  double kernel_dbl[4];
-  get_cubic_kernel_dbl(x, kernel_dbl);
-
-  kernel[0] = (int)rint(kernel_dbl[0] * (1 << DISFLOW_INTERP_BITS));
-  kernel[1] = (int)rint(kernel_dbl[1] * (1 << DISFLOW_INTERP_BITS));
-  kernel[2] = (int)rint(kernel_dbl[2] * (1 << DISFLOW_INTERP_BITS));
-  kernel[3] = (int)rint(kernel_dbl[3] * (1 << DISFLOW_INTERP_BITS));
-}
-
 // 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
@@ -157,82 +131,6 @@ static INLINE void compute_flow_error(const uint8_t *src, const uint8_t *ref,
   }
 }
 
-static INLINE void sobel_filter_x(const uint8_t *src, int src_stride,
-                                  int16_t *dst, int dst_stride) {
-  int16_t tmp[DISFLOW_PATCH_SIZE * (DISFLOW_PATCH_SIZE + 2)];
-
-  // Horizontal filter, using kernel {1, 0, -1}.
-  const uint8_t *src_start = src - 1 * src_stride - 1;
-
-  for (int i = 0; i < DISFLOW_PATCH_SIZE + 2; i++) {
-    uint8x16_t s = vld1q_u8(src_start + i * src_stride);
-    uint8x8_t s0 = vget_low_u8(s);
-    uint8x8_t s2 = vget_low_u8(vextq_u8(s, s, 2));
-
-    // Given that the kernel is {1, 0, -1} the convolution is a simple
-    // subtraction.
-    int16x8_t diff = vreinterpretq_s16_u16(vsubl_u8(s0, s2));
-
-    vst1q_s16(tmp + i * DISFLOW_PATCH_SIZE, diff);
-  }
-
-  // Vertical filter, using kernel {1, 2, 1}.
-  // This kernel can be split into two 2-taps kernels of value {1, 1}.
-  // That way we need only 3 add operations to perform the convolution, one of
-  // which can be reused for the next line.
-  int16x8_t s0 = vld1q_s16(tmp);
-  int16x8_t s1 = vld1q_s16(tmp + DISFLOW_PATCH_SIZE);
-  int16x8_t sum01 = vaddq_s16(s0, s1);
-  for (int i = 0; i < DISFLOW_PATCH_SIZE; i++) {
-    int16x8_t s2 = vld1q_s16(tmp + (i + 2) * DISFLOW_PATCH_SIZE);
-
-    int16x8_t sum12 = vaddq_s16(s1, s2);
-    int16x8_t sum = vaddq_s16(sum01, sum12);
-
-    vst1q_s16(dst + i * dst_stride, sum);
-
-    sum01 = sum12;
-    s1 = s2;
-  }
-}
-
-static INLINE void sobel_filter_y(const uint8_t *src, int src_stride,
-                                  int16_t *dst, int dst_stride) {
-  int16_t tmp[DISFLOW_PATCH_SIZE * (DISFLOW_PATCH_SIZE + 2)];
-
-  // Horizontal filter, using kernel {1, 2, 1}.
-  // This kernel can be split into two 2-taps kernels of value {1, 1}.
-  // That way we need only 3 add operations to perform the convolution.
-  const uint8_t *src_start = src - 1 * src_stride - 1;
-
-  for (int i = 0; i < DISFLOW_PATCH_SIZE + 2; i++) {
-    uint8x16_t s = vld1q_u8(src_start + i * src_stride);
-    uint8x8_t s0 = vget_low_u8(s);
-    uint8x8_t s1 = vget_low_u8(vextq_u8(s, s, 1));
-    uint8x8_t s2 = vget_low_u8(vextq_u8(s, s, 2));
-
-    uint16x8_t sum01 = vaddl_u8(s0, s1);
-    uint16x8_t sum12 = vaddl_u8(s1, s2);
-    uint16x8_t sum = vaddq_u16(sum01, sum12);
-
-    vst1q_s16(tmp + i * DISFLOW_PATCH_SIZE, vreinterpretq_s16_u16(sum));
-  }
-
-  // Vertical filter, using kernel {1, 0, -1}.
-  // Load the whole block at once to avoid redundant loads during convolution.
-  int16x8_t t[10];
-  load_s16_8x10(tmp, DISFLOW_PATCH_SIZE, &t[0], &t[1], &t[2], &t[3], &t[4],
-                &t[5], &t[6], &t[7], &t[8], &t[9]);
-
-  for (int i = 0; i < DISFLOW_PATCH_SIZE; i++) {
-    // Given that the kernel is {1, 0, -1} the convolution is a simple
-    // subtraction.
-    int16x8_t diff = vsubq_s16(t[i], t[i + 2]);
-
-    vst1q_s16(dst + i * dst_stride, diff);
-  }
-}
-
 // Computes the components of the system of equations used to solve for
 // a flow vector.
 //
diff --git a/third_party/aom/aom_dsp/flow_estimation/arm/disflow_neon.h b/third_party/aom/aom_dsp/flow_estimation/arm/disflow_neon.h
new file mode 100644
index 0000000000..d991a13460
--- /dev/null
+++ b/third_party/aom/aom_dsp/flow_estimation/arm/disflow_neon.h
@@ -0,0 +1,127 @@
+/*
+ * 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.
+ */
+
+#ifndef AOM_AOM_DSP_FLOW_ESTIMATION_ARM_DISFLOW_NEON_H_
+#define AOM_AOM_DSP_FLOW_ESTIMATION_ARM_DISFLOW_NEON_H_
+
+#include "aom_dsp/flow_estimation/disflow.h"
+
+#include <arm_neon.h>
+#include <math.h>
+
+#include "aom_dsp/arm/mem_neon.h"
+#include "config/aom_config.h"
+#include "config/aom_dsp_rtcd.h"
+
+static INLINE void get_cubic_kernel_dbl(double x, double kernel[4]) {
+  // Check that the fractional position is in range.
+  //
+  // Note: x is calculated from, e.g., `u_frac = u - floor(u)`.
+  // Mathematically, this implies that 0 <= x < 1. However, in practice it is
+  // possible to have x == 1 due to floating point rounding. This is fine,
+  // and we still interpolate correctly if we allow x = 1.
+  assert(0 <= x && x <= 1);
+
+  double x2 = x * x;
+  double x3 = x2 * x;
+  kernel[0] = -0.5 * x + x2 - 0.5 * x3;
+  kernel[1] = 1.0 - 2.5 * x2 + 1.5 * x3;
+  kernel[2] = 0.5 * x + 2.0 * x2 - 1.5 * x3;
+  kernel[3] = -0.5 * x2 + 0.5 * x3;
+}
+
+static INLINE void get_cubic_kernel_int(double x, int kernel[4]) {
+  double kernel_dbl[4];
+  get_cubic_kernel_dbl(x, kernel_dbl);
+
+  kernel[0] = (int)rint(kernel_dbl[0] * (1 << DISFLOW_INTERP_BITS));
+  kernel[1] = (int)rint(kernel_dbl[1] * (1 << DISFLOW_INTERP_BITS));
+  kernel[2] = (int)rint(kernel_dbl[2] * (1 << DISFLOW_INTERP_BITS));
+  kernel[3] = (int)rint(kernel_dbl[3] * (1 << DISFLOW_INTERP_BITS));
+}
+
+static INLINE void sobel_filter_x(const uint8_t *src, int src_stride,
+                                  int16_t *dst, int dst_stride) {
+  int16_t tmp[DISFLOW_PATCH_SIZE * (DISFLOW_PATCH_SIZE + 2)];
+
+  // Horizontal filter, using kernel {1, 0, -1}.
+  const uint8_t *src_start = src - 1 * src_stride - 1;
+
+  for (int i = 0; i < DISFLOW_PATCH_SIZE + 2; i++) {
+    uint8x16_t s = vld1q_u8(src_start + i * src_stride);
+    uint8x8_t s0 = vget_low_u8(s);
+    uint8x8_t s2 = vget_low_u8(vextq_u8(s, s, 2));
+
+    // Given that the kernel is {1, 0, -1} the convolution is a simple
+    // subtraction.
+    int16x8_t diff = vreinterpretq_s16_u16(vsubl_u8(s0, s2));
+
+    vst1q_s16(tmp + i * DISFLOW_PATCH_SIZE, diff);
+  }
+
+  // Vertical filter, using kernel {1, 2, 1}.
+  // This kernel can be split into two 2-taps kernels of value {1, 1}.
+  // That way we need only 3 add operations to perform the convolution, one of
+  // which can be reused for the next line.
+  int16x8_t s0 = vld1q_s16(tmp);
+  int16x8_t s1 = vld1q_s16(tmp + DISFLOW_PATCH_SIZE);
+  int16x8_t sum01 = vaddq_s16(s0, s1);
+  for (int i = 0; i < DISFLOW_PATCH_SIZE; i++) {
+    int16x8_t s2 = vld1q_s16(tmp + (i + 2) * DISFLOW_PATCH_SIZE);
+
+    int16x8_t sum12 = vaddq_s16(s1, s2);
+    int16x8_t sum = vaddq_s16(sum01, sum12);
+
+    vst1q_s16(dst + i * dst_stride, sum);
+
+    sum01 = sum12;
+    s1 = s2;
+  }
+}
+
+static INLINE void sobel_filter_y(const uint8_t *src, int src_stride,
+                                  int16_t *dst, int dst_stride) {
+  int16_t tmp[DISFLOW_PATCH_SIZE * (DISFLOW_PATCH_SIZE + 2)];
+
+  // Horizontal filter, using kernel {1, 2, 1}.
+  // This kernel can be split into two 2-taps kernels of value {1, 1}.
+  // That way we need only 3 add operations to perform the convolution.
+  const uint8_t *src_start = src - 1 * src_stride - 1;
+
+  for (int i = 0; i < DISFLOW_PATCH_SIZE + 2; i++) {
+    uint8x16_t s = vld1q_u8(src_start + i * src_stride);
+    uint8x8_t s0 = vget_low_u8(s);
+    uint8x8_t s1 = vget_low_u8(vextq_u8(s, s, 1));
+    uint8x8_t s2 = vget_low_u8(vextq_u8(s, s, 2));
+
+    uint16x8_t sum01 = vaddl_u8(s0, s1);
+    uint16x8_t sum12 = vaddl_u8(s1, s2);
+    uint16x8_t sum = vaddq_u16(sum01, sum12);
+
+    vst1q_s16(tmp + i * DISFLOW_PATCH_SIZE, vreinterpretq_s16_u16(sum));
+  }
+
+  // Vertical filter, using kernel {1, 0, -1}.
+  // Load the whole block at once to avoid redundant loads during convolution.
+  int16x8_t t[10];
+  load_s16_8x10(tmp, DISFLOW_PATCH_SIZE, &t[0], &t[1], &t[2], &t[3], &t[4],
+                &t[5], &t[6], &t[7], &t[8], &t[9]);
+
+  for (int i = 0; i < DISFLOW_PATCH_SIZE; i++) {
+    // Given that the kernel is {1, 0, -1} the convolution is a simple
+    // subtraction.
+    int16x8_t diff = vsubq_s16(t[i], t[i + 2]);
+
+    vst1q_s16(dst + i * dst_stride, diff);
+  }
+}
+
+#endif  // AOM_AOM_DSP_FLOW_ESTIMATION_ARM_DISFLOW_NEON_H_
diff --git a/third_party/aom/aom_dsp/flow_estimation/arm/disflow_sve.c b/third_party/aom/aom_dsp/flow_estimation/arm/disflow_sve.c
new file mode 100644
index 0000000000..7b01e90d12
--- /dev/null
+++ b/third_party/aom/aom_dsp/flow_estimation/arm/disflow_sve.c
@@ -0,0 +1,268 @@
+/*
+ * 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 "aom_dsp/flow_estimation/disflow.h"
+
+#include <arm_neon.h>
+#include <arm_sve.h>
+#include <math.h>
+
+#include "aom_dsp/arm/aom_neon_sve_bridge.h"
+#include "aom_dsp/arm/mem_neon.h"
+#include "aom_dsp/arm/sum_neon.h"
+#include "aom_dsp/flow_estimation/arm/disflow_neon.h"
+#include "config/aom_config.h"
+#include "config/aom_dsp_rtcd.h"
+
+DECLARE_ALIGNED(16, static const uint16_t, kDeinterleaveTbl[8]) = {
+  0, 2, 4, 6, 1, 3, 5, 7,
+};
+
+// 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);
+
+  int16_t tmp_[DISFLOW_PATCH_SIZE * (DISFLOW_PATCH_SIZE + 3)];
+
+  // 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.
+  const uint8_t *ref_start = ref + (y0 - 1) * stride + (x0 - 1);
+  const int16x4_t h_kernel_s16 = vmovn_s32(vld1q_s32(h_kernel));
+  const int16x8_t h_filter = vcombine_s16(h_kernel_s16, vdup_n_s16(0));
+  const uint16x8_t idx = vld1q_u16(kDeinterleaveTbl);
+
+  for (int i = 0; i < DISFLOW_PATCH_SIZE + 3; ++i) {
+    svuint16_t r0 = svld1ub_u16(svptrue_b16(), ref_start + i * stride + 0);
+    svuint16_t r1 = svld1ub_u16(svptrue_b16(), ref_start + i * stride + 1);
+    svuint16_t r2 = svld1ub_u16(svptrue_b16(), ref_start + i * stride + 2);
+    svuint16_t r3 = svld1ub_u16(svptrue_b16(), ref_start + i * stride + 3);
+
+    int16x8_t s0 = vreinterpretq_s16_u16(svget_neonq_u16(r0));
+    int16x8_t s1 = vreinterpretq_s16_u16(svget_neonq_u16(r1));
+    int16x8_t s2 = vreinterpretq_s16_u16(svget_neonq_u16(r2));
+    int16x8_t s3 = vreinterpretq_s16_u16(svget_neonq_u16(r3));
+
+    int64x2_t sum04 = aom_svdot_lane_s16(vdupq_n_s64(0), s0, h_filter, 0);
+    int64x2_t sum15 = aom_svdot_lane_s16(vdupq_n_s64(0), s1, h_filter, 0);
+    int64x2_t sum26 = aom_svdot_lane_s16(vdupq_n_s64(0), s2, h_filter, 0);
+    int64x2_t sum37 = aom_svdot_lane_s16(vdupq_n_s64(0), s3, h_filter, 0);
+
+    int32x4_t res0 = vcombine_s32(vmovn_s64(sum04), vmovn_s64(sum15));
+    int32x4_t res1 = vcombine_s32(vmovn_s64(sum26), vmovn_s64(sum37));
+
+    // 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.
+    int16x8_t res = vcombine_s16(vrshrn_n_s32(res0, DISFLOW_INTERP_BITS - 6),
+                                 vrshrn_n_s32(res1, DISFLOW_INTERP_BITS - 6));
+
+    res = aom_tbl_s16(res, idx);
+
+    vst1q_s16(tmp_ + i * DISFLOW_PATCH_SIZE, res);
+  }
+
+  // Vertical convolution.
+  int16x4_t v_filter = vmovn_s32(vld1q_s32(v_kernel));
+  int16_t *tmp_start = tmp_ + DISFLOW_PATCH_SIZE;
+
+  for (int i = 0; i < DISFLOW_PATCH_SIZE; ++i) {
+    int16x8_t t0 = vld1q_s16(tmp_start + (i - 1) * DISFLOW_PATCH_SIZE);
+    int16x8_t t1 = vld1q_s16(tmp_start + i * DISFLOW_PATCH_SIZE);
+    int16x8_t t2 = vld1q_s16(tmp_start + (i + 1) * DISFLOW_PATCH_SIZE);
+    int16x8_t t3 = vld1q_s16(tmp_start + (i + 2) * DISFLOW_PATCH_SIZE);
+
+    int32x4_t sum_lo = vmull_lane_s16(vget_low_s16(t0), v_filter, 0);
+    sum_lo = vmlal_lane_s16(sum_lo, vget_low_s16(t1), v_filter, 1);
+    sum_lo = vmlal_lane_s16(sum_lo, vget_low_s16(t2), v_filter, 2);
+    sum_lo = vmlal_lane_s16(sum_lo, vget_low_s16(t3), v_filter, 3);
+
+    int32x4_t sum_hi = vmull_lane_s16(vget_high_s16(t0), v_filter, 0);
+    sum_hi = vmlal_lane_s16(sum_hi, vget_high_s16(t1), v_filter, 1);
+    sum_hi = vmlal_lane_s16(sum_hi, vget_high_s16(t2), v_filter, 2);
+    sum_hi = vmlal_lane_s16(sum_hi, vget_high_s16(t3), v_filter, 3);
+
+    uint8x8_t s = vld1_u8(src + (i + y) * stride + x);
+    int16x8_t s_s16 = vreinterpretq_s16_u16(vshll_n_u8(s, 3));
+
+    // 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.
+    sum_lo = vrshrq_n_s32(sum_lo,
+                          DISFLOW_INTERP_BITS + 6 - DISFLOW_DERIV_SCALE_LOG2);
+    sum_hi = vrshrq_n_s32(sum_hi,
+                          DISFLOW_INTERP_BITS + 6 - DISFLOW_DERIV_SCALE_LOG2);
+    int32x4_t err_lo = vsubw_s16(sum_lo, vget_low_s16(s_s16));
+    int32x4_t err_hi = vsubw_s16(sum_hi, vget_high_s16(s_s16));
+    vst1q_s16(dt + i * DISFLOW_PATCH_SIZE,
+              vcombine_s16(vmovn_s32(err_lo), vmovn_s32(err_hi)));
+  }
+}
+
+// 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_inv) {
+  int64x2_t sum[3] = { vdupq_n_s64(0), vdupq_n_s64(0), vdupq_n_s64(0) };
+
+  for (int i = 0; i < DISFLOW_PATCH_SIZE; i++) {
+    int16x8_t x = vld1q_s16(dx + i * dx_stride);
+    int16x8_t y = vld1q_s16(dy + i * dy_stride);
+
+    sum[0] = aom_sdotq_s16(sum[0], x, x);
+    sum[1] = aom_sdotq_s16(sum[1], x, y);
+    sum[2] = aom_sdotq_s16(sum[2], y, y);
+  }
+
+  sum[0] = vpaddq_s64(sum[0], sum[1]);
+  sum[2] = vpaddq_s64(sum[1], sum[2]);
+  int32x4_t res = vcombine_s32(vmovn_s64(sum[0]), vmovn_s64(sum[2]));
+
+  // 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.
+
+  double M0 = (double)vgetq_lane_s32(res, 0) + 1;
+  double M1 = (double)vgetq_lane_s32(res, 1);
+  double M2 = (double)vgetq_lane_s32(res, 2);
+  double M3 = (double)vgetq_lane_s32(res, 3) + 1;
+
+  // Invert matrix M.
+  double det = (M0 * M3) - (M1 * M2);
+  assert(det >= 1);
+  const double det_inv = 1 / det;
+
+  M_inv[0] = M3 * det_inv;
+  M_inv[1] = -M1 * det_inv;
+  M_inv[2] = -M2 * det_inv;
+  M_inv[3] = M0 * det_inv;
+}
+
+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) {
+  int64x2_t b_s64[2] = { vdupq_n_s64(0), vdupq_n_s64(0) };
+
+  for (int i = 0; i < DISFLOW_PATCH_SIZE; i++) {
+    int16x8_t dx16 = vld1q_s16(dx + i * dx_stride);
+    int16x8_t dy16 = vld1q_s16(dy + i * dy_stride);
+    int16x8_t dt16 = vld1q_s16(dt + i * dt_stride);
+
+    b_s64[0] = aom_sdotq_s16(b_s64[0], dx16, dt16);
+    b_s64[1] = aom_sdotq_s16(b_s64[1], dy16, dt16);
+  }
+
+  b_s64[0] = vpaddq_s64(b_s64[0], b_s64[1]);
+  vst1_s32(b, vmovn_s64(b_s64[0]));
+}
+
+void aom_compute_flow_at_point_sve(const uint8_t *src, const uint8_t *ref,
+                                   int x, int y, int width, int height,
+                                   int stride, double *u, double *v) {
+  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_x(src_patch, stride, dx, DISFLOW_PATCH_SIZE);
+  sobel_filter_y(src_patch, stride, dy, DISFLOW_PATCH_SIZE);
+
+  compute_flow_matrix(dx, DISFLOW_PATCH_SIZE, dy, DISFLOW_PATCH_SIZE, M_inv);
+
+  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;
+    }
+  }
+}