| /* |
| * Copyright (c) 2019 ARM Limited. |
| * |
| * SPDX-License-Identifier: MIT |
| * |
| * Permission is hereby granted, free of charge, to any person obtaining a copy |
| * of this software and associated documentation files (the "Software"), to |
| * deal in the Software without restriction, including without limitation the |
| * rights to use, copy, modify, merge, publish, distribute, sublicense, and/or |
| * sell copies of the Software, and to permit persons to whom the Software is |
| * furnished to do so, subject to the following conditions: |
| * |
| * The above copyright notice and this permission notice shall be included in all |
| * copies or substantial portions of the Software. |
| * |
| * THE SOFTWARE IS PROVIDED "AS IS", WITHOUT WARRANTY OF ANY KIND, EXPRESS OR |
| * IMPLIED, INCLUDING BUT NOT LIMITED TO THE WARRANTIES OF MERCHANTABILITY, |
| * FITNESS FOR A PARTICULAR PURPOSE AND NONINFRINGEMENT. IN NO EVENT SHALL THE |
| * AUTHORS OR COPYRIGHT HOLDERS BE LIABLE FOR ANY CLAIM, DAMAGES OR OTHER |
| * LIABILITY, WHETHER IN AN ACTION OF CONTRACT, TORT OR OTHERWISE, ARISING FROM, |
| * OUT OF OR IN CONNECTION WITH THE SOFTWARE OR THE USE OR OTHER DEALINGS IN THE |
| * SOFTWARE. |
| */ |
| #include "DFT.h" |
| |
| #include "PadLayer.h" |
| #include "Permute.h" |
| #include "Reverse.h" |
| #include "SliceOperations.h" |
| |
| #include <cmath> |
| |
| namespace arm_compute |
| { |
| namespace test |
| { |
| namespace validation |
| { |
| namespace reference |
| { |
| namespace |
| { |
| /** Performs an one dimensional DFT on a given real sequence. |
| * |
| * @param[in] src_ptr Pointer to the real input sequence. |
| * @param[in] N Size of input sequence. |
| * @param[out] dst_ptr Pointer to the complex output sequence. |
| * @param[out] K Size of the output sequence |
| */ |
| template <typename T> |
| void rdft_1d_step(const T *src_ptr, size_t N, T *dst_ptr, size_t K) |
| { |
| for(unsigned int k = 0; k < K; ++k) |
| { |
| float Xr = 0; |
| float Xi = 0; |
| for(unsigned int n = 0; n < N; ++n) |
| { |
| const float alpha = (2 * M_PI * k * n) / N; |
| const float val_r = src_ptr[n]; |
| // Assuming DFT from the R domain thus skipping imaginary calculations |
| Xr += val_r * cos(alpha); |
| Xi -= val_r * sin(alpha); |
| } |
| |
| dst_ptr[k * 2] = Xr; |
| dst_ptr[k * 2 + 1] = Xi; |
| } |
| } |
| |
| /** Performs an one dimensional DFT on a given complex sequence. |
| * |
| * @param[in] src_ptr Pointer to the complex input sequence. |
| * @param[out] dst_ptr Pointer to the complex output sequence. |
| * @param[in] N Size of the sequences |
| */ |
| template <typename T> |
| void dft_1d_step(const T *src_ptr, T *dst_ptr, size_t N) |
| { |
| for(unsigned int k = 0; k < N; ++k) |
| { |
| float Xr = 0; |
| float Xi = 0; |
| for(unsigned int n = 0; n < N; ++n) |
| { |
| const float alpha = (2 * M_PI * k * n) / N; |
| const float val_r = src_ptr[2 * n]; |
| const float val_i = src_ptr[2 * n + 1]; |
| const float cos_alpha = cos(alpha); |
| const float sin_alpha = sin(alpha); |
| |
| Xr += val_r * cos_alpha + val_i * sin_alpha; |
| Xi += val_i * cos_alpha - val_r * sin_alpha; |
| } |
| |
| dst_ptr[k * 2] = Xr; |
| dst_ptr[k * 2 + 1] = Xi; |
| } |
| } |
| |
| /** Performs an one dimensional inverse DFT on a given real sequence. |
| * |
| * @param[in] src_ptr Pointer to the real input sequence. |
| * @param[in] K Size of input sequence. |
| * @param[out] dst_ptr Pointer to the complex output sequence. |
| * @param[out] N Size of the output sequence |
| */ |
| template <typename T> |
| void irdft_1d_step(const T *src_ptr, size_t K, T *dst_ptr, size_t N) |
| { |
| const bool is_odd = N % 2; |
| const unsigned int Nleft = N - K; |
| const int tail_start = is_odd ? K - 1 : K - 2; |
| |
| for(unsigned int n = 0; n < N; ++n) |
| { |
| float xr = 0; |
| for(unsigned int k = 0; k < K; ++k) |
| { |
| const float alpha = (2 * M_PI * k * n) / N; |
| xr += src_ptr[2 * k] * cos(alpha) - src_ptr[2 * k + 1] * sin(alpha); |
| } |
| |
| unsigned int j = tail_start; |
| for(unsigned int k = 0; k < Nleft; ++k) |
| { |
| const float alpha = (2 * M_PI * (k + K) * n) / N; |
| xr += src_ptr[2 * j] * cos(alpha) + src_ptr[2 * j + 1] * sin(alpha); |
| --j; |
| } |
| |
| dst_ptr[n] = xr; |
| } |
| } |
| |
| /** Performs an one dimensional inverse DFT on a given complex sequence. |
| * |
| * @param[in] src_ptr Pointer to the complex input sequence. |
| * @param[out] dst_ptr Pointer to the complex output sequence. |
| * @param[in] N Size of the sequences |
| */ |
| template <typename T> |
| void idft_1d_step(const T *src_ptr, T *dst_ptr, size_t N) |
| { |
| for(unsigned int n = 0; n < N; ++n) |
| { |
| float xr = 0; |
| float xi = 0; |
| for(unsigned int k = 0; k < N; ++k) |
| { |
| const float alpha = (2 * M_PI * k * n) / N; |
| const float cos_alpha = cos(alpha); |
| const float sin_alpha = sin(alpha); |
| const float val_r = src_ptr[2 * k]; |
| const float val_i = src_ptr[2 * k + 1]; |
| |
| xr += val_r * cos_alpha - val_i * sin_alpha; |
| xi += val_i * cos_alpha + val_r * sin_alpha; |
| } |
| |
| dst_ptr[2 * n] = xr; |
| dst_ptr[2 * n + 1] = xi; |
| } |
| } |
| |
| template <typename T> |
| SimpleTensor<T> rdft_1d_core(const SimpleTensor<T> &src, FFTDirection direction, bool is_odd) |
| { |
| // Performs only rdft |
| ARM_COMPUTE_ERROR_ON(direction == FFTDirection::Forward && src.num_channels() != 1); |
| ARM_COMPUTE_ERROR_ON(direction == FFTDirection::Inverse && src.num_channels() != 2); |
| |
| const unsigned int inverse_tail = is_odd ? 1 : 0; |
| const unsigned int N = src.shape()[0]; |
| const unsigned int K = direction == FFTDirection::Forward ? N / 2 + 1 : (N - 1) * 2 + inverse_tail; |
| const unsigned int num_channels = direction == FFTDirection::Forward ? 2 : 1; |
| |
| TensorShape dst_shape = src.shape(); |
| dst_shape.set(0, K); |
| |
| SimpleTensor<T> dst(dst_shape, src.data_type(), num_channels); |
| |
| const unsigned int upper_dims = src.shape().total_size_upper(1); |
| for(unsigned int du = 0; du < upper_dims; ++du) |
| { |
| const T *src_row_ptr = src.data() + du * N * src.num_channels(); |
| T *dst_row_ptr = dst.data() + du * K * dst.num_channels(); |
| direction == FFTDirection::Forward ? rdft_1d_step(src_row_ptr, N, dst_row_ptr, K) : irdft_1d_step(src_row_ptr, N, dst_row_ptr, K); |
| } |
| |
| return dst; |
| } |
| |
| template <typename T> |
| SimpleTensor<T> dft_1d_core(const SimpleTensor<T> &src, FFTDirection direction) |
| { |
| ARM_COMPUTE_ERROR_ON(src.num_channels() != 2); |
| |
| const unsigned int N = src.shape()[0]; |
| |
| SimpleTensor<T> dst(src.shape(), src.data_type(), src.num_channels()); |
| |
| const unsigned int upper_dims = src.shape().total_size_upper(1); |
| for(unsigned int du = 0; du < upper_dims; ++du) |
| { |
| const T *src_row_ptr = src.data() + du * N * src.num_channels(); |
| T *dst_row_ptr = dst.data() + du * N * dst.num_channels(); |
| direction == FFTDirection::Forward ? dft_1d_step(src_row_ptr, dst_row_ptr, N) : idft_1d_step(src_row_ptr, dst_row_ptr, N); |
| } |
| |
| return dst; |
| } |
| |
| /** Scale a tensor by a given scaling factor. |
| * |
| * @param[in,out] tensor Tensor to scale. |
| * @param[in] scaling_factor Scaling to scale the tensor data with. |
| */ |
| template <typename T> |
| void scale(SimpleTensor<T> &tensor, T scaling_factor) |
| { |
| const int total_elements = tensor.num_elements() * tensor.num_channels(); |
| T *data_ptr = tensor.data(); |
| for(int i = 0; i < total_elements; ++i) |
| { |
| data_ptr[i] /= scaling_factor; |
| } |
| } |
| |
| /** Performs a complex element-wise multiplication with reduction across the channels axis. |
| * |
| * @param[in] input Input tensor. |
| * @param[in] weights Weights tensor. |
| * |
| * @return Output tensor. |
| */ |
| template <typename T> |
| SimpleTensor<T> complex_mul_and_reduce(const SimpleTensor<T> &input, const SimpleTensor<T> &weights) |
| { |
| const uint32_t W = input.shape().x(); |
| const uint32_t H = input.shape().y(); |
| const uint32_t Ci = input.shape().z(); |
| const uint32_t Co = weights.shape()[3]; |
| const uint32_t N = input.shape().total_size() / (W * H * Ci); |
| |
| TensorShape output_shape = input.shape(); |
| output_shape.set(2, Co); |
| SimpleTensor<T> dst(output_shape, input.data_type(), input.num_channels()); |
| |
| // MemSet dst memory to zero |
| std::memset(dst.data(), 0, dst.size()); |
| |
| for(uint32_t b = 0; b < N; ++b) |
| { |
| for(uint32_t co = 0; co < Co; ++co) |
| { |
| for(uint32_t ci = 0; ci < Ci; ++ci) |
| { |
| for(uint32_t h = 0; h < H; ++h) |
| { |
| for(uint32_t w = 0; w < W; ++w) |
| { |
| const uint32_t i_index = w + h * W + ci * H * W + b * H * W * Ci; |
| const uint32_t w_index = w + h * W + ci * H * W + co * H * W * Ci; |
| const uint32_t o_index = w + h * W + co * H * W + b * H * W * Co; |
| const Coordinates i_coords = index2coords(input.shape(), i_index); |
| const Coordinates w_coords = index2coords(weights.shape(), w_index); |
| const Coordinates o_coords = index2coords(dst.shape(), o_index); |
| |
| auto i_ptr = static_cast<const T *>(input(i_coords)); |
| auto w_ptr = static_cast<const T *>(weights(w_coords)); |
| auto o_ptr = static_cast<T *>(dst(o_coords)); |
| |
| const T Rin = i_ptr[0]; |
| const T Iin = i_ptr[1]; |
| const T Rw = w_ptr[0]; |
| const T Iw = w_ptr[1]; |
| |
| o_ptr[0] += Rin * Rw - Iin * Iw; |
| o_ptr[1] += Rin * Iw + Rw * Iin; |
| } |
| } |
| } |
| } |
| } |
| return dst; |
| } |
| } // namespace |
| |
| template <typename T> |
| SimpleTensor<T> rdft_1d(const SimpleTensor<T> &src) |
| { |
| return rdft_1d_core(src, FFTDirection::Forward, false); |
| } |
| |
| template <typename T> |
| SimpleTensor<T> ridft_1d(const SimpleTensor<T> &src, bool is_odd) |
| { |
| auto dst = rdft_1d_core(src, FFTDirection::Inverse, is_odd); |
| |
| const T scaling_factor = dst.shape()[0]; |
| scale(dst, scaling_factor); |
| |
| return dst; |
| } |
| |
| template <typename T> |
| SimpleTensor<T> dft_1d(const SimpleTensor<T> &src, FFTDirection direction) |
| { |
| auto dst = dft_1d_core(src, direction); |
| if(direction == FFTDirection::Inverse) |
| { |
| const T scaling_factor = dst.shape()[0]; |
| scale(dst, scaling_factor); |
| } |
| return dst; |
| } |
| |
| template <typename T> |
| SimpleTensor<T> rdft_2d(const SimpleTensor<T> &src) |
| { |
| ARM_COMPUTE_ERROR_ON(src.num_channels() != 1); |
| constexpr FFTDirection direction = FFTDirection::Forward; |
| |
| auto first_pass = rdft_1d_core(src, direction, false); |
| auto transposed = permute(first_pass, PermutationVector(1U, 0U)); |
| auto second_pass = dft_1d_core(transposed, direction); |
| return permute(second_pass, PermutationVector(1U, 0U)); |
| } |
| |
| template <typename T> |
| SimpleTensor<T> ridft_2d(const SimpleTensor<T> &src, bool is_odd) |
| { |
| ARM_COMPUTE_ERROR_ON(src.num_channels() != 2); |
| constexpr FFTDirection direction = FFTDirection::Inverse; |
| |
| auto transposed = permute(src, PermutationVector(1U, 0U)); |
| auto first_pass = dft_1d_core(transposed, direction); |
| auto transposed_2 = permute(first_pass, PermutationVector(1U, 0U)); |
| auto dst = rdft_1d_core(transposed_2, direction, is_odd); |
| |
| const T scaling_factor = dst.shape()[0] * dst.shape()[1]; |
| scale(dst, scaling_factor); |
| return dst; |
| } |
| |
| template <typename T> |
| SimpleTensor<T> dft_2d(const SimpleTensor<T> &src, FFTDirection direction) |
| { |
| ARM_COMPUTE_ERROR_ON(src.num_channels() != 2); |
| |
| if(direction == FFTDirection::Forward) |
| { |
| auto first_pass = dft_1d_core(src, direction); |
| auto transposed = permute(first_pass, PermutationVector(1U, 0U)); |
| auto second_pass = dft_1d_core(transposed, direction); |
| return permute(second_pass, PermutationVector(1U, 0U)); |
| } |
| else |
| { |
| auto transposed = permute(src, PermutationVector(1U, 0U)); |
| auto first_pass = dft_1d_core(transposed, direction); |
| auto transposed_2 = permute(first_pass, PermutationVector(1U, 0U)); |
| auto dst = dft_1d_core(transposed_2, direction); |
| |
| const T scaling_factor = dst.shape()[0] * dst.shape()[1]; |
| scale(dst, scaling_factor); |
| |
| return dst; |
| } |
| } |
| |
| template <typename T> |
| SimpleTensor<T> conv2d_dft(const SimpleTensor<T> &src, const SimpleTensor<T> &w, const PadStrideInfo &conv_info) |
| { |
| // Pad input to full padding |
| const PaddingList padding_in = { { 0, w.shape()[0] - 1 }, { 0, w.shape()[1] - 1 } }; |
| auto padded_src = pad_layer(src, padding_in); |
| |
| // Flip weights |
| std::vector<uint32_t> axis_v = { 0, 1 }; |
| SimpleTensor<uint32_t> axis{ TensorShape(2U), DataType::U32 }; |
| std::copy(axis_v.begin(), axis_v.begin() + axis.shape().x(), axis.data()); |
| auto flipped_w = reverse(w, axis); |
| |
| // Pad weights to have the same size as input |
| const PaddingList paddings_w = { { 0, src.shape()[0] - 1 }, { 0, src.shape()[1] - 1 } }; |
| auto padded_w = pad_layer(flipped_w, paddings_w); |
| |
| // Transform input and weights to frequency domain |
| auto Fsrc = rdft_2d(padded_src); |
| auto Fw = rdft_2d(padded_w); |
| |
| // Perform dot product |
| auto Fdst = complex_mul_and_reduce(Fsrc, Fw); |
| |
| // Transform output back to frequency domain |
| auto conv_res = ridft_2d(Fdst); |
| |
| // Slice output |
| const int start_left = w.shape().x() - conv_info.pad_left() - 1; |
| const int start_top = w.shape().y() - conv_info.pad_top() - 1; |
| const int end_right = conv_res.shape().x() - (w.shape().x() - conv_info.pad_right() - 1); |
| const int end_botton = conv_res.shape().y() - (w.shape().y() - conv_info.pad_bottom() - 1); |
| return slice(conv_res, Coordinates(start_left, start_top), Coordinates(end_right, end_botton)); |
| } |
| |
| template SimpleTensor<float> rdft_1d(const SimpleTensor<float> &src); |
| template SimpleTensor<float> ridft_1d(const SimpleTensor<float> &src, bool is_odd); |
| template SimpleTensor<float> dft_1d(const SimpleTensor<float> &src, FFTDirection direction); |
| |
| template SimpleTensor<float> rdft_2d(const SimpleTensor<float> &src); |
| template SimpleTensor<float> ridft_2d(const SimpleTensor<float> &src, bool is_odd); |
| template SimpleTensor<float> dft_2d(const SimpleTensor<float> &src, FFTDirection direction); |
| |
| template SimpleTensor<float> conv2d_dft(const SimpleTensor<float> &src, const SimpleTensor<float> &w, const PadStrideInfo &conv_info); |
| } // namespace reference |
| } // namespace validation |
| } // namespace test |
| } // namespace arm_compute |