Adding upstream version 110.0.1.upstream/110.0.1upstream

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

1 files changed, 359 insertions, 0 deletions

diff --git a/third_party/aom/av1/encoder/mathutils.h b/third_party/aom/av1/encoder/mathutils.h
new file mode 100644
index 0000000000..64f9361767
--- /dev/null
+++ b/third_party/aom/av1/encoder/mathutils.h
@@ -0,0 +1,359 @@
+/*
+ * Copyright (c) 2017, 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_AV1_ENCODER_MATHUTILS_H_
+#define AOM_AV1_ENCODER_MATHUTILS_H_
+
+#include <memory.h>
+#include <math.h>
+#include <stdio.h>
+#include <stdlib.h>
+#include <assert.h>
+
+static const double TINY_NEAR_ZERO = 1.0E-16;
+
+// Solves Ax = b, where x and b are column vectors of size nx1 and A is nxn
+static INLINE int linsolve(int n, double *A, int stride, double *b, double *x) {
+  int i, j, k;
+  double c;
+  // Forward elimination
+  for (k = 0; k < n - 1; k++) {
+    // Bring the largest magnitude to the diagonal position
+    for (i = n - 1; i > k; i--) {
+      if (fabs(A[(i - 1) * stride + k]) < fabs(A[i * stride + k])) {
+        for (j = 0; j < n; j++) {
+          c = A[i * stride + j];
+          A[i * stride + j] = A[(i - 1) * stride + j];
+          A[(i - 1) * stride + j] = c;
+        }
+        c = b[i];
+        b[i] = b[i - 1];
+        b[i - 1] = c;
+      }
+    }
+    for (i = k; i < n - 1; i++) {
+      if (fabs(A[k * stride + k]) < TINY_NEAR_ZERO) return 0;
+      c = A[(i + 1) * stride + k] / A[k * stride + k];
+      for (j = 0; j < n; j++) A[(i + 1) * stride + j] -= c * A[k * stride + j];
+      b[i + 1] -= c * b[k];
+    }
+  }
+  // Backward substitution
+  for (i = n - 1; i >= 0; i--) {
+    if (fabs(A[i * stride + i]) < TINY_NEAR_ZERO) return 0;
+    c = 0;
+    for (j = i + 1; j <= n - 1; j++) c += A[i * stride + j] * x[j];
+    x[i] = (b[i] - c) / A[i * stride + i];
+  }
+
+  return 1;
+}
+
+////////////////////////////////////////////////////////////////////////////////
+// Least-squares
+// Solves for n-dim x in a least squares sense to minimize |Ax - b|^2
+// The solution is simply x = (A'A)^-1 A'b or simply the solution for
+// the system: A'A x = A'b
+static INLINE int least_squares(int n, double *A, int rows, int stride,
+                                double *b, double *scratch, double *x) {
+  int i, j, k;
+  double *scratch_ = NULL;
+  double *AtA, *Atb;
+  if (!scratch) {
+    scratch_ = (double *)aom_malloc(sizeof(*scratch) * n * (n + 1));
+    scratch = scratch_;
+  }
+  AtA = scratch;
+  Atb = scratch + n * n;
+
+  for (i = 0; i < n; ++i) {
+    for (j = i; j < n; ++j) {
+      AtA[i * n + j] = 0.0;
+      for (k = 0; k < rows; ++k)
+        AtA[i * n + j] += A[k * stride + i] * A[k * stride + j];
+      AtA[j * n + i] = AtA[i * n + j];
+    }
+    Atb[i] = 0;
+    for (k = 0; k < rows; ++k) Atb[i] += A[k * stride + i] * b[k];
+  }
+  int ret = linsolve(n, AtA, n, Atb, x);
+  if (scratch_) aom_free(scratch_);
+  return ret;
+}
+
+// Matrix multiply
+static INLINE void multiply_mat(const double *m1, const double *m2, double *res,
+                                const int m1_rows, const int inner_dim,
+                                const int m2_cols) {
+  double sum;
+
+  int row, col, inner;
+  for (row = 0; row < m1_rows; ++row) {
+    for (col = 0; col < m2_cols; ++col) {
+      sum = 0;
+      for (inner = 0; inner < inner_dim; ++inner)
+        sum += m1[row * inner_dim + inner] * m2[inner * m2_cols + col];
+      *(res++) = sum;
+    }
+  }
+}
+
+//
+// The functions below are needed only for homography computation
+// Remove if the homography models are not used.
+//
+///////////////////////////////////////////////////////////////////////////////
+// svdcmp
+// Adopted from Numerical Recipes in C
+
+static INLINE double sign(double a, double b) {
+  return ((b) >= 0 ? fabs(a) : -fabs(a));
+}
+
+static INLINE double pythag(double a, double b) {
+  double ct;
+  const double absa = fabs(a);
+  const double absb = fabs(b);
+
+  if (absa > absb) {
+    ct = absb / absa;
+    return absa * sqrt(1.0 + ct * ct);
+  } else {
+    ct = absa / absb;
+    return (absb == 0) ? 0 : absb * sqrt(1.0 + ct * ct);
+  }
+}
+
+static INLINE int svdcmp(double **u, int m, int n, double w[], double **v) {
+  const int max_its = 30;
+  int flag, i, its, j, jj, k, l, nm;
+  double anorm, c, f, g, h, s, scale, x, y, z;
+  double *rv1 = (double *)aom_malloc(sizeof(*rv1) * (n + 1));
+  g = scale = anorm = 0.0;
+  for (i = 0; i < n; i++) {
+    l = i + 1;
+    rv1[i] = scale * g;
+    g = s = scale = 0.0;
+    if (i < m) {
+      for (k = i; k < m; k++) scale += fabs(u[k][i]);
+      if (scale != 0.) {
+        for (k = i; k < m; k++) {
+          u[k][i] /= scale;
+          s += u[k][i] * u[k][i];
+        }
+        f = u[i][i];
+        g = -sign(sqrt(s), f);
+        h = f * g - s;
+        u[i][i] = f - g;
+        for (j = l; j < n; j++) {
+          for (s = 0.0, k = i; k < m; k++) s += u[k][i] * u[k][j];
+          f = s / h;
+          for (k = i; k < m; k++) u[k][j] += f * u[k][i];
+        }
+        for (k = i; k < m; k++) u[k][i] *= scale;
+      }
+    }
+    w[i] = scale * g;
+    g = s = scale = 0.0;
+    if (i < m && i != n - 1) {
+      for (k = l; k < n; k++) scale += fabs(u[i][k]);
+      if (scale != 0.) {
+        for (k = l; k < n; k++) {
+          u[i][k] /= scale;
+          s += u[i][k] * u[i][k];
+        }
+        f = u[i][l];
+        g = -sign(sqrt(s), f);
+        h = f * g - s;
+        u[i][l] = f - g;
+        for (k = l; k < n; k++) rv1[k] = u[i][k] / h;
+        for (j = l; j < m; j++) {
+          for (s = 0.0, k = l; k < n; k++) s += u[j][k] * u[i][k];
+          for (k = l; k < n; k++) u[j][k] += s * rv1[k];
+        }
+        for (k = l; k < n; k++) u[i][k] *= scale;
+      }
+    }
+    anorm = fmax(anorm, (fabs(w[i]) + fabs(rv1[i])));
+  }
+
+  for (i = n - 1; i >= 0; i--) {
+    if (i < n - 1) {
+      if (g != 0.) {
+        for (j = l; j < n; j++) v[j][i] = (u[i][j] / u[i][l]) / g;
+        for (j = l; j < n; j++) {
+          for (s = 0.0, k = l; k < n; k++) s += u[i][k] * v[k][j];
+          for (k = l; k < n; k++) v[k][j] += s * v[k][i];
+        }
+      }
+      for (j = l; j < n; j++) v[i][j] = v[j][i] = 0.0;
+    }
+    v[i][i] = 1.0;
+    g = rv1[i];
+    l = i;
+  }
+  for (i = AOMMIN(m, n) - 1; i >= 0; i--) {
+    l = i + 1;
+    g = w[i];
+    for (j = l; j < n; j++) u[i][j] = 0.0;
+    if (g != 0.) {
+      g = 1.0 / g;
+      for (j = l; j < n; j++) {
+        for (s = 0.0, k = l; k < m; k++) s += u[k][i] * u[k][j];
+        f = (s / u[i][i]) * g;
+        for (k = i; k < m; k++) u[k][j] += f * u[k][i];
+      }
+      for (j = i; j < m; j++) u[j][i] *= g;
+    } else {
+      for (j = i; j < m; j++) u[j][i] = 0.0;
+    }
+    ++u[i][i];
+  }
+  for (k = n - 1; k >= 0; k--) {
+    for (its = 0; its < max_its; its++) {
+      flag = 1;
+      for (l = k; l >= 0; l--) {
+        nm = l - 1;
+        if ((double)(fabs(rv1[l]) + anorm) == anorm || nm < 0) {
+          flag = 0;
+          break;
+        }
+        if ((double)(fabs(w[nm]) + anorm) == anorm) break;
+      }
+      if (flag) {
+        c = 0.0;
+        s = 1.0;
+        for (i = l; i <= k; i++) {
+          f = s * rv1[i];
+          rv1[i] = c * rv1[i];
+          if ((double)(fabs(f) + anorm) == anorm) break;
+          g = w[i];
+          h = pythag(f, g);
+          w[i] = h;
+          h = 1.0 / h;
+          c = g * h;
+          s = -f * h;
+          for (j = 0; j < m; j++) {
+            y = u[j][nm];
+            z = u[j][i];
+            u[j][nm] = y * c + z * s;
+            u[j][i] = z * c - y * s;
+          }
+        }
+      }
+      z = w[k];
+      if (l == k) {
+        if (z < 0.0) {
+          w[k] = -z;
+          for (j = 0; j < n; j++) v[j][k] = -v[j][k];
+        }
+        break;
+      }
+      if (its == max_its - 1) {
+        aom_free(rv1);
+        return 1;
+      }
+      assert(k > 0);
+      x = w[l];
+      nm = k - 1;
+      y = w[nm];
+      g = rv1[nm];
+      h = rv1[k];
+      f = ((y - z) * (y + z) + (g - h) * (g + h)) / (2.0 * h * y);
+      g = pythag(f, 1.0);
+      f = ((x - z) * (x + z) + h * ((y / (f + sign(g, f))) - h)) / x;
+      c = s = 1.0;
+      for (j = l; j <= nm; j++) {
+        i = j + 1;
+        g = rv1[i];
+        y = w[i];
+        h = s * g;
+        g = c * g;
+        z = pythag(f, h);
+        rv1[j] = z;
+        c = f / z;
+        s = h / z;
+        f = x * c + g * s;
+        g = g * c - x * s;
+        h = y * s;
+        y *= c;
+        for (jj = 0; jj < n; jj++) {
+          x = v[jj][j];
+          z = v[jj][i];
+          v[jj][j] = x * c + z * s;
+          v[jj][i] = z * c - x * s;
+        }
+        z = pythag(f, h);
+        w[j] = z;
+        if (z != 0.) {
+          z = 1.0 / z;
+          c = f * z;
+          s = h * z;
+        }
+        f = c * g + s * y;
+        x = c * y - s * g;
+        for (jj = 0; jj < m; jj++) {
+          y = u[jj][j];
+          z = u[jj][i];
+          u[jj][j] = y * c + z * s;
+          u[jj][i] = z * c - y * s;
+        }
+      }
+      rv1[l] = 0.0;
+      rv1[k] = f;
+      w[k] = x;
+    }
+  }
+  aom_free(rv1);
+  return 0;
+}
+
+static INLINE int SVD(double *U, double *W, double *V, double *matx, int M,
+                      int N) {
+  // Assumes allocation for U is MxN
+  double **nrU = (double **)aom_malloc((M) * sizeof(*nrU));
+  double **nrV = (double **)aom_malloc((N) * sizeof(*nrV));
+  int problem, i;
+
+  problem = !(nrU && nrV);
+  if (!problem) {
+    for (i = 0; i < M; i++) {
+      nrU[i] = &U[i * N];
+    }
+    for (i = 0; i < N; i++) {
+      nrV[i] = &V[i * N];
+    }
+  } else {
+    if (nrU) aom_free(nrU);
+    if (nrV) aom_free(nrV);
+    return 1;
+  }
+
+  /* copy from given matx into nrU */
+  for (i = 0; i < M; i++) {
+    memcpy(&(nrU[i][0]), matx + N * i, N * sizeof(*matx));
+  }
+
+  /* HERE IT IS: do SVD */
+  if (svdcmp(nrU, M, N, W, nrV)) {
+    aom_free(nrU);
+    aom_free(nrV);
+    return 1;
+  }
+
+  /* aom_free Numerical Recipes arrays */
+  aom_free(nrU);
+  aom_free(nrV);
+
+  return 0;
+}
+
+#endif  // AOM_AV1_ENCODER_MATHUTILS_H_