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Diffstat (limited to 'third_party/aom/aom_dsp/mathutils.h')
| -rw-r--r-- | third_party/aom/aom_dsp/mathutils.h | 145 |
1 files changed, 145 insertions, 0 deletions
diff --git a/third_party/aom/aom_dsp/mathutils.h b/third_party/aom/aom_dsp/mathutils.h new file mode 100644 index 0000000000..cbb6cf491f --- /dev/null +++ b/third_party/aom/aom_dsp/mathutils.h @@ -0,0 +1,145 @@ +/* + * 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_ |