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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"
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 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_
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