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+/*
+ * 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_AOM_DSP_MATHUTILS_H_
+#define AOM_AOM_DSP_MATHUTILS_H_
+
+#include <assert.h>
+#include <math.h>
+#include <string.h>
+
+#include "aom_dsp/aom_dsp_common.h"
+#include "aom_mem/aom_mem.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
+//
+// This process is split into three steps in order to avoid needing to
+// explicitly allocate the A matrix, which may be very large if there
+// are many equations to solve.
+//
+// The process for using this is (in pseudocode):
+//
+// Allocate mat (size n*n), y (size n), a (size n), x (size n)
+// least_squares_init(mat, y, n)
+// for each equation a . x = b {
+//    least_squares_accumulate(mat, y, a, b, n)
+// }
+// least_squares_solve(mat, y, x, n)
+//
+// where:
+// * mat, y are accumulators for the values A'A and A'b respectively,
+// * a, b are the coefficients of each individual equation,
+// * x is the result vector
+// * and n is the problem size
+static INLINE void least_squares_init(double *mat, double *y, int n) {
+  memset(mat, 0, n * n * sizeof(double));
+  memset(y, 0, n * sizeof(double));
+}
+
+// Round the given positive value to nearest integer
+static AOM_FORCE_INLINE int iroundpf(float x) {
+  assert(x >= 0.0);
+  return (int)(x + 0.5f);
+}
+
+static INLINE void least_squares_accumulate(double *mat, double *y,
+                                            const double *a, double b, int n) {
+  for (int i = 0; i < n; i++) {
+    for (int j = 0; j < n; j++) {
+      mat[i * n + j] += a[i] * a[j];
+    }
+  }
+  for (int i = 0; i < n; i++) {
+    y[i] += a[i] * b;
+  }
+}
+
+static INLINE int least_squares_solve(double *mat, double *y, double *x,
+                                      int n) {
+  return linsolve(n, mat, n, y, x);
+}
+
+// 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;
+    }
+  }
+}
+
+static AOM_INLINE float approx_exp(float y) {
+#define A ((1 << 23) / 0.69314718056f)  // (1 << 23) / ln(2)
+#define B \
+  127  // Offset for the exponent according to IEEE floating point standard.
+#define C 60801  // Magic number controls the accuracy of approximation
+  union {
+    float as_float;
+    int32_t as_int32;
+  } container;
+  container.as_int32 = ((int32_t)(y * A)) + ((B << 23) - C);
+  return container.as_float;
+#undef A
+#undef B
+#undef C
+}
+#endif  // AOM_AOM_DSP_MATHUTILS_H_