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diff --git a/chapters/tensor_ops.adoc b/chapters/tensor_ops.adoc index 47768d4..b3f6f5a 100644 --- a/chapters/tensor_ops.adoc +++ b/chapters/tensor_ops.adoc @@ -333,6 +333,70 @@ for_each(0 <= n<N, 0 <= oy < OH, 0 <= ox < OW; 0 <= c < C, 0 <= m < M) { |MI, MT|floating-point|float_t|float_t|float_t |=== +==== FFT2D + +Performs a batched complex 2D Fast Fourier Transform over the input. +The complex input values are constructed from the corresponding values in the input_real and input_imag tensors. +The resulting values in the output are split into the output_real and output_imag tensors. +No normalization is applied on either the forward or inverse versions of the operation. + +// output[h][w] = \sum_{m=0}^{H-1}\sum_{n=0}^{W-1}input[m][n] * \exp\left(-2\pi i\left(\frac{mh}{H} + \frac{nw}{W}\right)\right) + +.Calculation for the forward FFT2D calculation (direction=false) +image::forward_fft2d.svg["forward FFT definition", align="center"] + +// output[h][w] = \sum_{m=0}^{H-1}\sum_{n=0}^{W-1}input[m][n] * \exp\left(2\pi i\left(\frac{mh}{H} + \frac{nw}{W}\right)\right) + +.Calculation for the inverse FFT2D calculation (direction=true) +image::inverse_fft2d.svg["inverse FFT definition", align="center"] + +*Arguments:* + +|=== +|Argument|Type|Name|Shape|Description + +|Input|in_out_t*|input_real|[N,H,W]|Real part of the complex input. H,W must be powers of two. +|Input|in_out_t*|input_imag|[N,H,W]|Imaginary part of the complex input. H,W must be powers of two. +|Attribute|bool_t|inverse|-|false for forward FFT, true for inverse FFT +|Output|in_out_t*|output_real|[N,H,W]|Real part of the complex output +|Output|in_out_t*|output_imag|[N,H,W]|Imaginary part of the complex output. +|=== + +*Operation Function* + +[source,c++] +---- +ERROR_IF(!power_of_two(H)); +ERROR_IF(!power_of_two(W)); + +float sign_val = 1.0; + +if (inverse) { + sign_val = -1.0; +} + +for_each(0 <= n < N, 0 <= oy < H, 0 <= ox < W) { + in_out_t sum_real = 0.0; + in_out_t sum_imag = 0.0; + for_each(0 <= iy < H, 0 <= ix < W) { + in_out_t val_real = tensor_read<in_out_t>(input_real, [N,H,W], [n,iy,ix]); + in_out_t val_imag = tensor_read<in_out_t>(input_imag, [N,H,W], [n,iy,ix]); + float_t a = sign_val * 2 * pi() * ((iy * oy) / H + (ix * ox) / W); + sum_real += val_real * cos(a) + val_imag * sin(a); + sum_imag += -val_real * sin(a) + val_imag * cos(a); + } + tensor_write<in_out_t>(output_real, [N,H,W], [n,oy,ox], sum_real); + tensor_write<in_out_t>(output_imag, [N,H,W], [n,oy,ox], sum_imag); +} +---- + +*Supported Data Types:* + +|=== +|Profile|Mode|in_out_t +|MI,MT|floating-point|float +|=== + ==== FULLY_CONNECTED Performs a fully connected network. @@ -479,6 +543,54 @@ for_each(0 <= n < N, 0 <= oy < H, 0 <= ox < W, 0 <= c < C ) { |MI, MT|floating-point|float_t |=== +==== RFFT2D + +Performs a batched 2D real-valued Fast Fourier Transform over the input where the input tensor consists of real values producing complex valued output. +The complex output values will be split into the output_real and output_imag tensor arguments. +RFFT2D takes advantage of Hermitian symmetry to only calculate the first half of the output. +Imaginary values with locations h=0,H/2 or w=0,W/2 are zero. + +image::forward_fft2d.svg["forward FFT definition", align="center"] + +*Arguments:* + +|=== +|Argument|Type|Name|Shape|Description + +|Input|in_out_t*|input|[N,H,W]|Real input. H,W must be powers of two. +|Output|in_out_t*|output_real|[N,H/2 + 1,W/2 + 1]|Real part of the complex output +|Output|in_out_t*|output_imag|[N,H/2 + 1,W/2 + 1]|Imaginary part of the complex output. +|=== + +*Operation Function* + +[source,c++] +---- +ERROR_IF(!power_of_two(H)); +ERROR_IF(!power_of_two(W)); + +for_each(0 <= n < N, 0 <= oy < H/2 + 1, 0 <= ox < W/2 + 1) { + in_out_t sum_real = 0.0; + in_out_t sum_imag = 0.0; + for_each(0 <= iy < H, 0 <= ix < W) { + in_out_t val_real = tensor_read<in_out_t>(input_real, [N,H,W], [n,iy,ix]); + float_t a = 2 * pi() * ((iy * oy) / H + (ix * ox) / W); + sum_real += val_real * cos(a); + sum_imag += -val_real * sin(a); + } + tensor_write<in_out_t>(output_real, [N,H,W], [n,oy,ox], sum_real); + tensor_write<in_out_t>(output_imag, [N,H,W], [n,oy,ox], sum_imag); +} +---- + +*Supported Data Types:* + +|=== +|Profile|Mode|in_out_t +|MI,MT|floating-point|float +|=== + + ==== TRANSPOSE_CONV2D Performs a 2D transposed convolution over the given tensor input, using the weights tensor. |