Georgios Pinitas | def2a85 | 2019-02-21 14:47:56 +0000 | [diff] [blame] | 1 | /* |
| 2 | * Copyright (c) 2019 ARM Limited. |
| 3 | * |
| 4 | * SPDX-License-Identifier: MIT |
| 5 | * |
| 6 | * Permission is hereby granted, free of charge, to any person obtaining a copy |
| 7 | * of this software and associated documentation files (the "Software"), to |
| 8 | * deal in the Software without restriction, including without limitation the |
| 9 | * rights to use, copy, modify, merge, publish, distribute, sublicense, and/or |
| 10 | * sell copies of the Software, and to permit persons to whom the Software is |
| 11 | * furnished to do so, subject to the following conditions: |
| 12 | * |
| 13 | * The above copyright notice and this permission notice shall be included in all |
| 14 | * copies or substantial portions of the Software. |
| 15 | * |
| 16 | * THE SOFTWARE IS PROVIDED "AS IS", WITHOUT WARRANTY OF ANY KIND, EXPRESS OR |
| 17 | * IMPLIED, INCLUDING BUT NOT LIMITED TO THE WARRANTIES OF MERCHANTABILITY, |
| 18 | * FITNESS FOR A PARTICULAR PURPOSE AND NONINFRINGEMENT. IN NO EVENT SHALL THE |
| 19 | * AUTHORS OR COPYRIGHT HOLDERS BE LIABLE FOR ANY CLAIM, DAMAGES OR OTHER |
| 20 | * LIABILITY, WHETHER IN AN ACTION OF CONTRACT, TORT OR OTHERWISE, ARISING FROM, |
| 21 | * OUT OF OR IN CONNECTION WITH THE SOFTWARE OR THE USE OR OTHER DEALINGS IN THE |
| 22 | * SOFTWARE. |
| 23 | */ |
| 24 | #include "DFT.h" |
| 25 | |
| 26 | #include "PadLayer.h" |
| 27 | #include "Permute.h" |
| 28 | #include "Reverse.h" |
| 29 | #include "SliceOperations.h" |
| 30 | |
| 31 | #include <cmath> |
| 32 | |
| 33 | namespace arm_compute |
| 34 | { |
| 35 | namespace test |
| 36 | { |
| 37 | namespace validation |
| 38 | { |
| 39 | namespace reference |
| 40 | { |
| 41 | namespace |
| 42 | { |
| 43 | /** Performs an one dimensional DFT on a given real sequence. |
| 44 | * |
| 45 | * @param[in] src_ptr Pointer to the real input sequence. |
| 46 | * @param[in] N Size of input sequence. |
| 47 | * @param[out] dst_ptr Pointer to the complex output sequence. |
| 48 | * @param[out] K Size of the output sequence |
| 49 | */ |
| 50 | template <typename T> |
| 51 | void rdft_1d_step(const T *src_ptr, size_t N, T *dst_ptr, size_t K) |
| 52 | { |
| 53 | for(unsigned int k = 0; k < K; ++k) |
| 54 | { |
| 55 | float Xr = 0; |
| 56 | float Xi = 0; |
| 57 | for(unsigned int n = 0; n < N; ++n) |
| 58 | { |
| 59 | const float alpha = (2 * M_PI * k * n) / N; |
| 60 | const float val_r = src_ptr[n]; |
| 61 | // Assuming DFT from the R domain thus skipping imaginary calculations |
| 62 | Xr += val_r * cos(alpha); |
| 63 | Xi -= val_r * sin(alpha); |
| 64 | } |
| 65 | |
| 66 | dst_ptr[k * 2] = Xr; |
| 67 | dst_ptr[k * 2 + 1] = Xi; |
| 68 | } |
| 69 | } |
| 70 | |
| 71 | /** Performs an one dimensional DFT on a given complex sequence. |
| 72 | * |
| 73 | * @param[in] src_ptr Pointer to the complex input sequence. |
| 74 | * @param[out] dst_ptr Pointer to the complex output sequence. |
| 75 | * @param[in] N Size of the sequences |
| 76 | */ |
| 77 | template <typename T> |
| 78 | void dft_1d_step(const T *src_ptr, T *dst_ptr, size_t N) |
| 79 | { |
| 80 | for(unsigned int k = 0; k < N; ++k) |
| 81 | { |
| 82 | float Xr = 0; |
| 83 | float Xi = 0; |
| 84 | for(unsigned int n = 0; n < N; ++n) |
| 85 | { |
| 86 | const float alpha = (2 * M_PI * k * n) / N; |
| 87 | const float val_r = src_ptr[2 * n]; |
| 88 | const float val_i = src_ptr[2 * n + 1]; |
| 89 | const float cos_alpha = cos(alpha); |
| 90 | const float sin_alpha = sin(alpha); |
| 91 | |
| 92 | Xr += val_r * cos_alpha + val_i * sin_alpha; |
| 93 | Xi += val_i * cos_alpha - val_r * sin_alpha; |
| 94 | } |
| 95 | |
| 96 | dst_ptr[k * 2] = Xr; |
| 97 | dst_ptr[k * 2 + 1] = Xi; |
| 98 | } |
| 99 | } |
| 100 | |
| 101 | /** Performs an one dimensional inverse DFT on a given real sequence. |
| 102 | * |
| 103 | * @param[in] src_ptr Pointer to the real input sequence. |
| 104 | * @param[in] K Size of input sequence. |
| 105 | * @param[out] dst_ptr Pointer to the complex output sequence. |
| 106 | * @param[out] N Size of the output sequence |
| 107 | */ |
| 108 | template <typename T> |
| 109 | void irdft_1d_step(const T *src_ptr, size_t K, T *dst_ptr, size_t N) |
| 110 | { |
| 111 | const bool is_odd = N % 2; |
| 112 | const unsigned int Nleft = N - K; |
| 113 | const int tail_start = is_odd ? K - 1 : K - 2; |
| 114 | |
| 115 | for(unsigned int n = 0; n < N; ++n) |
| 116 | { |
| 117 | float xr = 0; |
| 118 | for(unsigned int k = 0; k < K; ++k) |
| 119 | { |
| 120 | const float alpha = (2 * M_PI * k * n) / N; |
| 121 | xr += src_ptr[2 * k] * cos(alpha) - src_ptr[2 * k + 1] * sin(alpha); |
| 122 | } |
| 123 | |
| 124 | unsigned int j = tail_start; |
| 125 | for(unsigned int k = 0; k < Nleft; ++k) |
| 126 | { |
| 127 | const float alpha = (2 * M_PI * (k + K) * n) / N; |
| 128 | xr += src_ptr[2 * j] * cos(alpha) + src_ptr[2 * j + 1] * sin(alpha); |
| 129 | --j; |
| 130 | } |
| 131 | |
| 132 | dst_ptr[n] = xr; |
| 133 | } |
| 134 | } |
| 135 | |
| 136 | /** Performs an one dimensional inverse DFT on a given complex sequence. |
| 137 | * |
| 138 | * @param[in] src_ptr Pointer to the complex input sequence. |
| 139 | * @param[out] dst_ptr Pointer to the complex output sequence. |
| 140 | * @param[in] N Size of the sequences |
| 141 | */ |
| 142 | template <typename T> |
| 143 | void idft_1d_step(const T *src_ptr, T *dst_ptr, size_t N) |
| 144 | { |
| 145 | for(unsigned int n = 0; n < N; ++n) |
| 146 | { |
| 147 | float xr = 0; |
| 148 | float xi = 0; |
| 149 | for(unsigned int k = 0; k < N; ++k) |
| 150 | { |
| 151 | const float alpha = (2 * M_PI * k * n) / N; |
| 152 | const float cos_alpha = cos(alpha); |
| 153 | const float sin_alpha = sin(alpha); |
| 154 | const float val_r = src_ptr[2 * k]; |
| 155 | const float val_i = src_ptr[2 * k + 1]; |
| 156 | |
| 157 | xr += val_r * cos_alpha - val_i * sin_alpha; |
| 158 | xi += val_i * cos_alpha + val_r * sin_alpha; |
| 159 | } |
| 160 | |
| 161 | dst_ptr[2 * n] = xr; |
| 162 | dst_ptr[2 * n + 1] = xi; |
| 163 | } |
| 164 | } |
| 165 | |
| 166 | template <typename T> |
| 167 | SimpleTensor<T> rdft_1d_core(const SimpleTensor<T> &src, FFTDirection direction, bool is_odd) |
| 168 | { |
| 169 | // Performs only rdft |
| 170 | ARM_COMPUTE_ERROR_ON(direction == FFTDirection::Forward && src.num_channels() != 1); |
| 171 | ARM_COMPUTE_ERROR_ON(direction == FFTDirection::Inverse && src.num_channels() != 2); |
| 172 | |
| 173 | const unsigned int inverse_tail = is_odd ? 1 : 0; |
| 174 | const unsigned int N = src.shape()[0]; |
| 175 | const unsigned int K = direction == FFTDirection::Forward ? N / 2 + 1 : (N - 1) * 2 + inverse_tail; |
| 176 | const unsigned int num_channels = direction == FFTDirection::Forward ? 2 : 1; |
| 177 | |
| 178 | TensorShape dst_shape = src.shape(); |
| 179 | dst_shape.set(0, K); |
| 180 | |
| 181 | SimpleTensor<T> dst(dst_shape, src.data_type(), num_channels); |
| 182 | |
| 183 | const unsigned int upper_dims = src.shape().total_size_upper(1); |
| 184 | for(unsigned int du = 0; du < upper_dims; ++du) |
| 185 | { |
| 186 | const T *src_row_ptr = src.data() + du * N * src.num_channels(); |
| 187 | T *dst_row_ptr = dst.data() + du * K * dst.num_channels(); |
| 188 | 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); |
| 189 | } |
| 190 | |
| 191 | return dst; |
| 192 | } |
| 193 | |
| 194 | template <typename T> |
| 195 | SimpleTensor<T> dft_1d_core(const SimpleTensor<T> &src, FFTDirection direction) |
| 196 | { |
| 197 | ARM_COMPUTE_ERROR_ON(src.num_channels() != 2); |
| 198 | |
| 199 | const unsigned int N = src.shape()[0]; |
| 200 | |
| 201 | SimpleTensor<T> dst(src.shape(), src.data_type(), src.num_channels()); |
| 202 | |
| 203 | const unsigned int upper_dims = src.shape().total_size_upper(1); |
| 204 | for(unsigned int du = 0; du < upper_dims; ++du) |
| 205 | { |
| 206 | const T *src_row_ptr = src.data() + du * N * src.num_channels(); |
| 207 | T *dst_row_ptr = dst.data() + du * N * dst.num_channels(); |
| 208 | direction == FFTDirection::Forward ? dft_1d_step(src_row_ptr, dst_row_ptr, N) : idft_1d_step(src_row_ptr, dst_row_ptr, N); |
| 209 | } |
| 210 | |
| 211 | return dst; |
| 212 | } |
| 213 | |
| 214 | /** Scale a tensor by a given scaling factor. |
| 215 | * |
| 216 | * @param[in,out] tensor Tensor to scale. |
| 217 | * @param[in] scaling_factor Scaling to scale the tensor data with. |
| 218 | */ |
| 219 | template <typename T> |
| 220 | void scale(SimpleTensor<T> &tensor, T scaling_factor) |
| 221 | { |
| 222 | const int total_elements = tensor.num_elements() * tensor.num_channels(); |
| 223 | T *data_ptr = tensor.data(); |
| 224 | for(int i = 0; i < total_elements; ++i) |
| 225 | { |
| 226 | data_ptr[i] /= scaling_factor; |
| 227 | } |
| 228 | } |
| 229 | |
| 230 | /** Performs a complex element-wise multiplication with reduction across the channels axis. |
| 231 | * |
| 232 | * @param[in] input Input tensor. |
| 233 | * @param[in] weights Weights tensor. |
| 234 | * |
| 235 | * @return Output tensor. |
| 236 | */ |
| 237 | template <typename T> |
| 238 | SimpleTensor<T> complex_mul_and_reduce(const SimpleTensor<T> &input, const SimpleTensor<T> &weights) |
| 239 | { |
| 240 | const int W = input.shape().x(); |
| 241 | const int H = input.shape().y(); |
| 242 | const int Ci = input.shape().z(); |
| 243 | const int Co = weights.shape()[3]; |
| 244 | const int N = input.shape().total_size() / (W * H * Ci); |
| 245 | |
| 246 | TensorShape output_shape = input.shape(); |
| 247 | output_shape.set(2, Co); |
| 248 | SimpleTensor<T> dst(output_shape, input.data_type(), input.num_channels()); |
| 249 | |
| 250 | // MemSet dst memory to zero |
| 251 | std::memset(dst.data(), 0, dst.size()); |
| 252 | |
| 253 | for(int b = 0; b < N; ++b) |
| 254 | { |
| 255 | for(int co = 0; co < Co; ++co) |
| 256 | { |
| 257 | for(int ci = 0; ci < Ci; ++ci) |
| 258 | { |
| 259 | for(int h = 0; h < H; ++h) |
| 260 | { |
| 261 | for(int w = 0; w < W; ++w) |
| 262 | { |
| 263 | size_t i_index = w + h * W + ci * H * W + b * H * W * Ci; |
| 264 | size_t w_index = w + h * W + ci * H * W + co * H * W * Ci; |
| 265 | size_t o_index = w + h * W + co * H * W + b * H * W * Co; |
| 266 | const Coordinates i_coords = index2coords(input.shape(), i_index); |
| 267 | const Coordinates w_coords = index2coords(weights.shape(), w_index); |
| 268 | const Coordinates o_coords = index2coords(dst.shape(), o_index); |
| 269 | |
| 270 | auto i_ptr = static_cast<const T *>(input(i_coords)); |
| 271 | auto w_ptr = static_cast<const T *>(weights(w_coords)); |
| 272 | auto o_ptr = static_cast<T *>(dst(o_coords)); |
| 273 | |
| 274 | const T Rin = i_ptr[0]; |
| 275 | const T Iin = i_ptr[1]; |
| 276 | const T Rw = w_ptr[0]; |
| 277 | const T Iw = w_ptr[1]; |
| 278 | |
| 279 | o_ptr[0] += Rin * Rw - Iin * Iw; |
| 280 | o_ptr[1] += Rin * Iw + Rw * Iin; |
| 281 | } |
| 282 | } |
| 283 | } |
| 284 | } |
| 285 | } |
| 286 | return dst; |
| 287 | } |
| 288 | } // namespace |
| 289 | |
| 290 | template <typename T> |
| 291 | SimpleTensor<T> rdft_1d(const SimpleTensor<T> &src) |
| 292 | { |
| 293 | return rdft_1d_core(src, FFTDirection::Forward, false); |
| 294 | } |
| 295 | |
| 296 | template <typename T> |
| 297 | SimpleTensor<T> ridft_1d(const SimpleTensor<T> &src, bool is_odd) |
| 298 | { |
| 299 | auto dst = rdft_1d_core(src, FFTDirection::Inverse, is_odd); |
| 300 | |
| 301 | const T scaling_factor = dst.shape()[0]; |
| 302 | scale(dst, scaling_factor); |
| 303 | |
| 304 | return dst; |
| 305 | } |
| 306 | |
| 307 | template <typename T> |
| 308 | SimpleTensor<T> dft_1d(const SimpleTensor<T> &src, FFTDirection direction) |
| 309 | { |
| 310 | auto dst = dft_1d_core(src, direction); |
| 311 | if(direction == FFTDirection::Inverse) |
| 312 | { |
| 313 | const T scaling_factor = dst.shape()[0]; |
| 314 | scale(dst, scaling_factor); |
| 315 | } |
| 316 | return dst; |
| 317 | } |
| 318 | |
| 319 | template <typename T> |
| 320 | SimpleTensor<T> rdft_2d(const SimpleTensor<T> &src) |
| 321 | { |
| 322 | ARM_COMPUTE_ERROR_ON(src.num_channels() != 1); |
| 323 | constexpr FFTDirection direction = FFTDirection::Forward; |
| 324 | |
| 325 | auto first_pass = rdft_1d_core(src, direction, false); |
| 326 | auto transposed = permute(first_pass, PermutationVector(1U, 0U)); |
| 327 | auto second_pass = dft_1d_core(transposed, direction); |
| 328 | return permute(second_pass, PermutationVector(1U, 0U)); |
| 329 | } |
| 330 | |
| 331 | template <typename T> |
| 332 | SimpleTensor<T> ridft_2d(const SimpleTensor<T> &src, bool is_odd) |
| 333 | { |
| 334 | ARM_COMPUTE_ERROR_ON(src.num_channels() != 2); |
| 335 | constexpr FFTDirection direction = FFTDirection::Inverse; |
| 336 | |
| 337 | auto transposed = permute(src, PermutationVector(1U, 0U)); |
| 338 | auto first_pass = dft_1d_core(transposed, direction); |
| 339 | auto transposed_2 = permute(first_pass, PermutationVector(1U, 0U)); |
| 340 | auto dst = rdft_1d_core(transposed_2, direction, is_odd); |
| 341 | |
| 342 | const T scaling_factor = dst.shape()[0] * dst.shape()[1]; |
| 343 | scale(dst, scaling_factor); |
| 344 | return dst; |
| 345 | } |
| 346 | |
| 347 | template <typename T> |
| 348 | SimpleTensor<T> dft_2d(const SimpleTensor<T> &src, FFTDirection direction) |
| 349 | { |
| 350 | ARM_COMPUTE_ERROR_ON(src.num_channels() != 2); |
| 351 | |
| 352 | if(direction == FFTDirection::Forward) |
| 353 | { |
| 354 | auto first_pass = dft_1d_core(src, direction); |
| 355 | auto transposed = permute(first_pass, PermutationVector(1U, 0U)); |
| 356 | auto second_pass = dft_1d_core(transposed, direction); |
| 357 | return permute(second_pass, PermutationVector(1U, 0U)); |
| 358 | } |
| 359 | else |
| 360 | { |
| 361 | auto transposed = permute(src, PermutationVector(1U, 0U)); |
| 362 | auto first_pass = dft_1d_core(transposed, direction); |
| 363 | auto transposed_2 = permute(first_pass, PermutationVector(1U, 0U)); |
| 364 | auto dst = dft_1d_core(transposed_2, direction); |
| 365 | |
| 366 | const T scaling_factor = dst.shape()[0] * dst.shape()[1]; |
| 367 | scale(dst, scaling_factor); |
| 368 | |
| 369 | return dst; |
| 370 | } |
| 371 | } |
| 372 | |
| 373 | template <typename T> |
| 374 | SimpleTensor<T> conv2d_dft(const SimpleTensor<T> &src, const SimpleTensor<T> &w, const PadStrideInfo &conv_info) |
| 375 | { |
| 376 | // Pad input to full padding |
| 377 | const PaddingList padding_in = { { 0, w.shape()[0] - 1 }, { 0, w.shape()[1] - 1 } }; |
| 378 | auto padded_src = pad_layer(src, padding_in); |
| 379 | |
| 380 | // Flip weights |
| 381 | std::vector<uint32_t> axis_v = { 0, 1 }; |
| 382 | SimpleTensor<uint32_t> axis{ TensorShape(2U), DataType::U32 }; |
| 383 | std::copy(axis_v.begin(), axis_v.begin() + axis.shape().x(), axis.data()); |
| 384 | auto flipped_w = reverse(w, axis); |
| 385 | |
| 386 | // Pad weights to have the same size as input |
| 387 | const PaddingList paddings_w = { { 0, src.shape()[0] - 1 }, { 0, src.shape()[1] - 1 } }; |
| 388 | auto padded_w = pad_layer(flipped_w, paddings_w); |
| 389 | |
| 390 | // Transform input and weights to frequency domain |
| 391 | auto Fsrc = rdft_2d(padded_src); |
| 392 | auto Fw = rdft_2d(padded_w); |
| 393 | |
| 394 | // Perform dot product |
| 395 | auto Fdst = complex_mul_and_reduce(Fsrc, Fw); |
| 396 | |
| 397 | // Transform output back to frequency domain |
| 398 | auto conv_res = ridft_2d(Fdst); |
| 399 | |
| 400 | // Slice output |
| 401 | const int start_left = w.shape().x() - conv_info.pad_left() - 1; |
| 402 | const int start_top = w.shape().y() - conv_info.pad_top() - 1; |
| 403 | const int end_right = conv_res.shape().x() - (w.shape().x() - conv_info.pad_right() - 1); |
| 404 | const int end_botton = conv_res.shape().y() - (w.shape().y() - conv_info.pad_bottom() - 1); |
| 405 | return slice(conv_res, Coordinates(start_left, start_top), Coordinates(end_right, end_botton)); |
| 406 | } |
| 407 | |
| 408 | template SimpleTensor<float> rdft_1d(const SimpleTensor<float> &src); |
| 409 | template SimpleTensor<float> ridft_1d(const SimpleTensor<float> &src, bool is_odd); |
| 410 | template SimpleTensor<float> dft_1d(const SimpleTensor<float> &src, FFTDirection direction); |
| 411 | |
| 412 | template SimpleTensor<float> rdft_2d(const SimpleTensor<float> &src); |
| 413 | template SimpleTensor<float> ridft_2d(const SimpleTensor<float> &src, bool is_odd); |
| 414 | template SimpleTensor<float> dft_2d(const SimpleTensor<float> &src, FFTDirection direction); |
| 415 | |
| 416 | template SimpleTensor<float> conv2d_dft(const SimpleTensor<float> &src, const SimpleTensor<float> &w, const PadStrideInfo &conv_info); |
| 417 | } // namespace reference |
| 418 | } // namespace validation |
| 419 | } // namespace test |
| 420 | } // namespace arm_compute |