diff options
Diffstat (limited to 'tests/validation/TensorOperations.h')
| -rw-r--r-- | tests/validation/TensorOperations.h | 1370 |
1 files changed, 1370 insertions, 0 deletions
diff --git a/tests/validation/TensorOperations.h b/tests/validation/TensorOperations.h new file mode 100644 index 0000000000..5e27e9d3a0 --- /dev/null +++ b/tests/validation/TensorOperations.h @@ -0,0 +1,1370 @@ +/* + * Copyright (c) 2017 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. + */ +#ifndef __ARM_COMPUTE_TEST_TENSOR_OPERATIONS_H__ +#define __ARM_COMPUTE_TEST_TENSOR_OPERATIONS_H__ + +#include "FixedPoint.h" +#include "Tensor.h" +#include "Types.h" +#include "Utils.h" + +#include "FixedPoint.h" +#include "Types.h" +#include "arm_compute/core/FixedPoint.h" +#include "arm_compute/core/Types.h" +#include "tests/validation/FixedPoint.h" + +#include <algorithm> +#include <array> +#include <cmath> + +namespace arm_compute +{ +namespace test +{ +namespace validation +{ +namespace tensor_operations +{ +namespace +{ +bool is_valid_pixel(int i, int min, int max) +{ + return (i >= min && i < max); +} + +// 3D convolution for floating point type +template <typename T, typename std::enable_if<std::is_floating_point<T>::value, int>::type * = nullptr> +void convolution3d(const T *in, const T *weights, const T *bias, T *out, int xi, int yi, int width_in, int height_in, int depth_in, int width_weights, int height_weights, int8_t fixed_point_position) +{ + const int half_width_weights = width_weights / 2; + const int half_height_weights = height_weights / 2; + + // Reset accumulator + T acc = static_cast<T>(0); + + // Compute a 2D convolution for each IFM and accumulate the result + for(int ifm = 0; ifm < depth_in; ++ifm) + { + // Compute the offset for the input slice + const int offset_slice_in = xi + yi * width_in + ifm * width_in * height_in; + + // Compute 2D convolution + for(int yk = -half_height_weights; yk <= half_height_weights; ++yk) + { + for(int xk = -half_width_weights; xk <= half_width_weights; ++xk) + { + // Check if the pixel is out-of-bound + if(is_valid_pixel(xi + xk, 0, width_in) && is_valid_pixel(yi + yk, 0, height_in)) + { + const int idx = xk + half_width_weights; + const int idy = yk + half_height_weights; + + const T i_value = in[offset_slice_in + xk + yk * width_in]; + const T w_value = weights[idx + idy * width_weights + ifm * width_weights * height_weights]; + + acc += i_value * w_value; + } + } + } + } + + // Accumulate the bias and store the result + *out = acc + (*bias); +} + +// 3D convolution for fixed point type +template <typename T, typename std::enable_if<std::is_integral<T>::value, int>::type * = nullptr> +void convolution3d(const T *in, const T *weights, const T *bias, T *out, int xi, int yi, int width_in, int height_in, int depth_in, int width_weights, int height_weights, + int8_t fixed_point_position) +{ + const int half_width_weights = width_weights / 2; + const int half_height_weights = height_weights / 2; + + using namespace fixed_point_arithmetic; + using promoted_type = typename fixed_point_arithmetic::traits::promote<T>::type; + + // Reset accumulator + fixed_point<promoted_type> acc(0, fixed_point_position); + + // Compute a 2D convolution for each IFM and accumulate the result + for(int ifm = 0; ifm < depth_in; ++ifm) + { + // Compute the offset for the input slice + const int offset_slice_in = xi + yi * width_in + ifm * width_in * height_in; + + // Compute 2D convolution + for(int yk = -half_height_weights; yk <= half_height_weights; ++yk) + { + for(int xk = -half_width_weights; xk <= half_width_weights; ++xk) + { + // Check if the pixel is out-of-bound + if(is_valid_pixel(xi + xk, 0, width_in) && is_valid_pixel(yi + yk, 0, height_in)) + { + const int idx = xk + half_width_weights; + const int idy = yk + half_height_weights; + + const fixed_point<promoted_type> i_value(in[offset_slice_in + xk + yk * width_in], fixed_point_position, true); + const fixed_point<promoted_type> w_value(weights[idx + idy * width_weights + ifm * width_weights * height_weights], fixed_point_position, true); + const fixed_point<promoted_type> iw = i_value * w_value; + acc = iw + acc; + } + } + } + } + + // Get the bias + const fixed_point<promoted_type> b(*bias, fixed_point_position, true); + + // Accumulate the bias and covert back + acc = acc + b; + fixed_point<T> res(acc); + *out = res.raw(); +} + +template <typename T> +void vector_matrix_multiply(const T *in, const T *weights, const T *bias, T *out, int cols_weights, int rows_weights, uint8_t fixed_point_position) +{ + for(int x = 0; x < cols_weights; ++x) + { + T acc = 0.0f; + for(int y = 0; y < rows_weights; ++y) + { + acc += in[y] * weights[x + y * cols_weights]; + } + out[x] = acc + bias[x]; + } +} + +template <> +void vector_matrix_multiply(const int8_t *in, const int8_t *weights, const int8_t *bias, int8_t *out, int cols_weights, int rows_weights, uint8_t fixed_point_position) +{ + using namespace fixed_point_arithmetic; + using promoted_type = typename fixed_point_arithmetic::traits::promote<int8_t>::type; + + for(int x = 0; x < cols_weights; ++x) + { + // Reset accumulator + fixed_point<promoted_type> acc(0, fixed_point_position); + + for(int y = 0; y < rows_weights; ++y) + { + const fixed_point<promoted_type> i_value(in[y], fixed_point_position, true); + const fixed_point<promoted_type> w_value(weights[x + y * cols_weights], fixed_point_position, true); + const fixed_point<promoted_type> iw = i_value * w_value; + acc = iw + acc; + } + + // Get the bias + const fixed_point<int8_t> b(bias[x], fixed_point_position, true); + + // Convert back and accumulate the bias + fixed_point<int8_t> res(acc); + res = res + b; + + // Store the result + out[x] = res.raw(); + } +} + +/** Apply 2D spatial filter on a single element of @p in at coordinates @p coord + * + * - filter sizes have to be odd number + * - Valid region assumed + * - Row major order of filter assumed + * - TO_ZERO rounding policy assumed + * - SATURATE convert policy assumed + * + */ +template <typename T1, typename T2, typename T3> +void apply_2d_spatial_filter(Coordinates coord, const Tensor<T1> &in, Tensor<T3> &out, const TensorShape &filter_shape, const T2 *filter_itr, float scale) +{ + using intermediate_type = typename common_promoted_signed_type<T1, T2, T3>::intermediate_type; + intermediate_type val = 0; + int x = coord.x(); + int y = coord.y(); + for(size_t j = y - filter_shape[1] / 2; j <= y + filter_shape[1] / 2; ++j) + { + for(size_t i = x - filter_shape[0] / 2; i <= x + filter_shape[0] / 2; ++i) + { + coord.set(0, i); + coord.set(1, j); + val += static_cast<intermediate_type>(*filter_itr) * static_cast<intermediate_type>(in[coord2index(in.shape(), coord)]); + ++filter_itr; + } + } + coord.set(0, x); + coord.set(1, y); + double rounded_val = cpp11::trunc(val * static_cast<double>(scale)); + out[coord2index(in.shape(), coord)] = saturate_cast<T3>(rounded_val); +} +} // namespace + +// Integral Image +void integral_image(const Tensor<uint8_t> &in, Tensor<uint32_t> &out) +{ + // Length of dimensions + const size_t width = in.shape().x(); + const size_t height = in.shape().y(); + const size_t depth = in.shape().z() * in.shape()[3] * in.shape()[4] * in.shape()[5]; + + const size_t image_size = width * height; + + for(size_t z = 0; z < depth; ++z) + { + size_t current_image = z * image_size; + + //First element of each image + out[current_image] = in[current_image]; + + // First row of each image (add only pixel on the left) + for(size_t x = 1; x < width; ++x) + { + out[current_image + x] = static_cast<uint32_t>(in[current_image + x]) + out[current_image + x - 1]; + } + + // Subsequent rows + for(size_t y = 1; y < height; ++y) + { + size_t current_row = current_image + (width * y); + + // First element of each row (add only pixel up) + out[current_row] = static_cast<uint32_t>(in[current_row]) + out[current_row - width]; + + // Following row elements + for(size_t x = 1; x < width; ++x) + { + size_t current_pixel = current_row + x; + + // out = in + up(out) + left(out) - up_left(out) + out[current_pixel] = static_cast<uint32_t>(in[current_pixel]) + out[current_pixel - 1] + + out[current_pixel - width] - out[current_pixel - width - 1]; + } + } + } +} + +// Absolute difference +template <typename T1, typename T2, typename T3> +void absolute_difference(const Tensor<T1> &in1, const Tensor<T2> &in2, Tensor<T3> &out) +{ + using intermediate_type = typename common_promoted_signed_type<T1, T2, T3>::intermediate_type; + + for(int i = 0; i < in1.num_elements(); ++i) + { + intermediate_type val = std::abs(static_cast<intermediate_type>(in1[i]) - static_cast<intermediate_type>(in2[i])); + out[i] = saturate_cast<T3>(val); + } +} + +// Accumulate +template <typename T1, typename T2> +void accumulate(const Tensor<T1> &in, Tensor<T2> &out) +{ + using intermediate_type = typename common_promoted_signed_type<T1, T2>::intermediate_type; + + for(int i = 0; i < in.num_elements(); ++i) + { + intermediate_type val = static_cast<intermediate_type>(out[i]) + static_cast<intermediate_type>(in[i]); + out[i] = saturate_cast<T2>(val); + } +} + +// Accumulate squared +template <typename T1, typename T2> +void accumulate_squared(const Tensor<T1> &in, Tensor<T2> &out, uint32_t shift) +{ + if(shift > 15) + { + ARM_COMPUTE_ERROR("Shift in accumulate_squared must be within the range [0, 15]"); + } + using intermediate_type = typename common_promoted_signed_type<T1, T2>::intermediate_type; + intermediate_type denom = 1 << shift; + + for(int i = 0; i < in.num_elements(); ++i) + { + intermediate_type val = static_cast<intermediate_type>(out[i]) + (static_cast<intermediate_type>(in[i]) * static_cast<intermediate_type>(in[i]) / denom); + out[i] = saturate_cast<T2>(val); + } +} + +// Accumulate weighted +template <typename T> +void accumulate_weighted(const Tensor<T> &in, Tensor<T> &out, float alpha) +{ + if(alpha < 0.f || alpha > 1.f) + { + ARM_COMPUTE_ERROR("Weight (alpha) specified in accumulate_weighted must be within the range [0, 1]"); + } + using intermediate_type = typename common_promoted_signed_type<T>::intermediate_type; + + for(int i = 0; i < in.num_elements(); ++i) + { + double val = (1. - static_cast<double>(alpha)) * static_cast<intermediate_type>(out[i]) + static_cast<double>(alpha) * static_cast<intermediate_type>(in[i]); + out[i] = static_cast<T>(val); + } +} + +// Arithmetic addition +template <typename T1, typename T2, typename T3> +void arithmetic_addition(const Tensor<T1> &in1, const Tensor<T2> &in2, Tensor<T3> &out, ConvertPolicy convert_policy) +{ + using intermediate_type = typename common_promoted_signed_type<T1, T2, T3>::intermediate_type; + + for(int i = 0; i < in1.num_elements(); ++i) + { + intermediate_type val = static_cast<intermediate_type>(in1[i]) + static_cast<intermediate_type>(in2[i]); + out[i] = (convert_policy == ConvertPolicy::SATURATE) ? saturate_cast<T3>(val) : static_cast<T3>(val); + } +} + +// Arithmetic Subtraction +template <typename T1, typename T2, typename T3> +void arithmetic_subtraction(const Tensor<T1> &in1, const Tensor<T2> &in2, Tensor<T3> &out, ConvertPolicy convert_policy) +{ + using intermediate_type = typename common_promoted_signed_type<T1, T2, T3>::intermediate_type; + + for(int i = 0; i < in1.num_elements(); ++i) + { + intermediate_type val = static_cast<intermediate_type>(in1[i]) - static_cast<intermediate_type>(in2[i]); + out[i] = (convert_policy == ConvertPolicy::SATURATE) ? saturate_cast<T3>(val) : static_cast<T3>(val); + } +} + +// Bitwise and +template <typename T, typename = typename std::enable_if<std::is_integral<T>::value>::type> +void bitwise_and(const Tensor<T> &in1, const Tensor<T> &in2, Tensor<T> &out) +{ + for(int i = 0; i < in1.num_elements(); ++i) + { + out[i] = in1[i] & in2[i]; + } +} + +// Bitwise or +template <typename T, typename = typename std::enable_if<std::is_integral<T>::value>::type> +void bitwise_or(const Tensor<T> &in1, const Tensor<T> &in2, Tensor<T> &out) +{ + for(int i = 0; i < in1.num_elements(); ++i) + { + out[i] = in1[i] | in2[i]; + } +} + +// Bitwise xor +template <typename T, typename = typename std::enable_if<std::is_integral<T>::value>::type> +void bitwise_xor(const Tensor<T> &in1, const Tensor<T> &in2, Tensor<T> &out) +{ + for(int i = 0; i < in1.num_elements(); ++i) + { + out[i] = in1[i] ^ in2[i]; + } +} + +// Bitwise not +template <typename T, typename = typename std::enable_if<std::is_integral<T>::value>::type> +void bitwise_not(const Tensor<T> &in, Tensor<T> &out) +{ + for(int i = 0; i < in.num_elements(); ++i) + { + out[i] = ~in[i]; + } +} + +// 3-by-3 box filter +template <typename T, typename = typename std::enable_if<std::is_integral<T>::value>::type> +void box3x3(const Tensor<T> &in, Tensor<T> &out) +{ + const std::array<T, 9> filter{ { 1, 1, 1, 1, 1, 1, 1, 1, 1 } }; + float scale = 1.f / static_cast<float>(filter.size()); + const ValidRegion valid_region = shape_to_valid_region_undefined_border(in.shape(), BorderSize(1)); + for(int element_idx = 0; element_idx < in.num_elements(); ++element_idx) + { + const Coordinates id = index2coord(in.shape(), element_idx); + if(is_in_valid_region(valid_region, id)) + { + apply_2d_spatial_filter(id, in, out, TensorShape(3U, 3U), filter.data(), scale); + } + } +} + +// Depth conversion +template <typename T1, typename T2> +void depth_convert(const Tensor<T1> &in, Tensor<T2> &out, ConvertPolicy policy, uint32_t shift) +{ + ARM_COMPUTE_ERROR("The conversion is not supported"); +} + +template <> +void depth_convert<int8_t, float>(const Tensor<int8_t> &in, Tensor<float> &out, ConvertPolicy policy, uint32_t shift) +{ + const int8_t fixed_point_position = static_cast<int8_t>(in.fixed_point_position()); + for(int i = 0; i < in.num_elements(); ++i) + { + out[i] = static_cast<float>(in[i]) * (1.0f / (1 << fixed_point_position)); + } +} + +template <> +void depth_convert<float, int8_t>(const Tensor<float> &in, Tensor<int8_t> &out, ConvertPolicy policy, uint32_t shift) +{ + const int8_t fixed_point_position = static_cast<int8_t>(in.fixed_point_position()); + for(int i = 0; i < in.num_elements(); ++i) + { + float val = in[i] * (1 << fixed_point_position) + 0.5f; + out[i] = ((policy == ConvertPolicy::SATURATE) ? saturate_cast<int8_t>(val) : static_cast<int8_t>(val)); + } +} + +template <> +void depth_convert<uint8_t, uint16_t>(const Tensor<uint8_t> &in, Tensor<uint16_t> &out, ConvertPolicy policy, uint32_t shift) +{ + for(int i = 0; i < in.num_elements(); ++i) + { + out[i] = static_cast<uint16_t>(in[i]) << shift; + } +} + +template <> +void depth_convert<uint8_t, int16_t>(const Tensor<uint8_t> &in, Tensor<int16_t> &out, ConvertPolicy policy, uint32_t shift) +{ + for(int i = 0; i < in.num_elements(); ++i) + { + out[i] = static_cast<int16_t>(in[i]) << shift; + } +} + +template <> +void depth_convert<uint8_t, int32_t>(const Tensor<uint8_t> &in, Tensor<int32_t> &out, ConvertPolicy policy, uint32_t shift) +{ + for(int i = 0; i < in.num_elements(); ++i) + { + out[i] = static_cast<int32_t>(in[i]) << shift; + } +} + +template <> +void depth_convert<uint16_t, uint8_t>(const Tensor<uint16_t> &in, Tensor<uint8_t> &out, ConvertPolicy policy, uint32_t shift) +{ + for(int i = 0; i < in.num_elements(); ++i) + { + uint16_t val = in[i] >> shift; + out[i] = ((policy == ConvertPolicy::SATURATE) ? saturate_cast<uint8_t>(val) : static_cast<uint8_t>(val)); + } +} + +template <> +void depth_convert<uint16_t, uint32_t>(const Tensor<uint16_t> &in, Tensor<uint32_t> &out, ConvertPolicy policy, uint32_t shift) +{ + for(int i = 0; i < in.num_elements(); ++i) + { + out[i] = static_cast<uint32_t>(in[i]) << shift; + } +} + +template <> +void depth_convert<int16_t, uint8_t>(const Tensor<int16_t> &in, Tensor<uint8_t> &out, ConvertPolicy policy, uint32_t shift) +{ + for(int i = 0; i < in.num_elements(); ++i) + { + int16_t val = in[i] >> shift; + out[i] = ((policy == ConvertPolicy::SATURATE) ? saturate_cast<uint8_t>(val) : static_cast<uint8_t>(val)); + } +} +template <> +void depth_convert<int16_t, int32_t>(const Tensor<int16_t> &in, Tensor<int32_t> &out, ConvertPolicy policy, uint32_t shift) +{ + for(int i = 0; i < in.num_elements(); ++i) + { + out[i] = static_cast<int32_t>(in[i]) << shift; + } +} + +// Matrix multiplication for floating point type +template <typename T, typename std::enable_if<std::is_floating_point<T>::value, int>::type * = nullptr> +void gemm(const Tensor<T> &in1, const Tensor<T> &in2, const Tensor<T> &in3, Tensor<T> &out, float alpha, float beta) +{ + const int M = out.shape().y(); + const int N = out.shape().x(); + const int K = in1.shape().x(); + + for(int r = 0; r < M; ++r) + { + for(int c = 0; c < N; ++c) + { + T acc = 0.0f; + + for(int k = 0; k < K; ++k) + { + const T a0 = in1[r * K + k]; + const T b0 = in2[k * N + c]; + + acc += a0 * b0; + } + + // Finalize the result: A * B * alpha + C * beta + const T c0 = in3[c + r * N]; + out[c + r * N] = alpha * acc + beta * c0; + } + } +} + +// Matrix multiplication for fixed point type +template <typename T, typename std::enable_if<std::is_integral<T>::value, int>::type * = nullptr> +void gemm(const Tensor<T> &in1, const Tensor<T> &in2, const Tensor<T> &in3, Tensor<T> &out, float alpha, float beta) +{ + using namespace fixed_point_arithmetic; + + using promoted_type = typename fixed_point_arithmetic::traits::promote<T>::type; + + const int M = out.shape().y(); + const int N = out.shape().x(); + const int K = in1.shape().x(); + const int8_t fixed_point_position = static_cast<int8_t>(in1.fixed_point_position()); + + const fixed_point<T> alpha_q(alpha, fixed_point_position); + const fixed_point<T> beta_q(beta, fixed_point_position); + + for(int r = 0; r < M; ++r) + { + for(int c = 0; c < N; ++c) + { + fixed_point<promoted_type> acc_q(0, fixed_point_position); + + for(int k = 0; k < K; ++k) + { + const fixed_point<promoted_type> a0_q(in1[r * K + k], fixed_point_position, true); + const fixed_point<promoted_type> b0_q(in2[k * N + c], fixed_point_position, true); + const fixed_point<promoted_type> axb_q = a0_q * b0_q; + + acc_q = axb_q + acc_q; + } + + // Finalize the result: A * B * alpha + C * beta + const fixed_point<T> c0_q(in3[c + r * N], fixed_point_position, true); + + fixed_point<T> res_q(acc_q); + res_q = alpha_q * res_q; + res_q = (c0_q * beta_q) + res_q; + + // Store the result + out[c + r * N] = res_q.raw(); + } + } +} + +// Pixel-wise multiplication +template <typename T1, typename T2, typename T3> +void pixel_wise_multiplication(const Tensor<T1> &in1, const Tensor<T2> &in2, Tensor<T3> &out, float scale, ConvertPolicy convert_policy, RoundingPolicy rounding_policy) +{ + if(scale < 0) + { + ARM_COMPUTE_ERROR("Scale of pixel-wise multiplication must be non-negative"); + } + using intermediate_type = typename common_promoted_signed_type<T1, T2, T3>::intermediate_type; + for(int i = 0; i < in1.num_elements(); ++i) + { + double val = static_cast<intermediate_type>(in1[i]) * static_cast<intermediate_type>(in2[i]) * static_cast<double>(scale); + if(std::is_floating_point<T3>::value) + { + out[i] = val; + } + else + { + double rounded_val = 0; + switch(rounding_policy) + { + case(RoundingPolicy::TO_ZERO): + rounded_val = cpp11::trunc(val); + break; + case(RoundingPolicy::TO_NEAREST_UP): + rounded_val = cpp11::round_half_up(val); + break; + case(RoundingPolicy::TO_NEAREST_EVEN): + rounded_val = cpp11::round_half_even(val); + break; + default: + ARM_COMPUTE_ERROR("Unsupported rounding policy"); + } + out[i] = (convert_policy == ConvertPolicy::SATURATE) ? saturate_cast<T3>(rounded_val) : static_cast<T3>(rounded_val); + } + } +} + +// Fixed-point Pixel-wise Multiplication +template <typename T, typename = typename std::enable_if<std::is_integral<T>::value>::type> +void fixed_point_pixel_wise_multiplication(const Tensor<T> &in1, const Tensor<T> &in2, Tensor<T> &out, int scale, ConvertPolicy convert_policy, RoundingPolicy rounding_policy) +{ + using namespace fixed_point_arithmetic; + + const int fixed_point_position = in1.fixed_point_position(); + + ARM_COMPUTE_ERROR_ON_MSG(in1.data_type() != in2.data_type() || in1.data_type() != out.data_type(), + "Tensors must all have the same DataType"); + ARM_COMPUTE_ERROR_ON_MSG(fixed_point_position != in2.fixed_point_position() || fixed_point_position != out.fixed_point_position(), + "Fixed-point position must be the same for both inputs and outputs"); + + // Validate fixed_point_position + ARM_COMPUTE_ERROR_ON((in1.data_type() == DataType::QS8) && (fixed_point_position == 0 || fixed_point_position > 7)); + ARM_COMPUTE_ERROR_ON((in1.data_type() == DataType::QS16) && (fixed_point_position == 0 || fixed_point_position > 15)); + + fixed_point<T> fp_scale(scale, fixed_point_position); + const bool is_sat = convert_policy == ConvertPolicy::SATURATE; + const bool do_scaling = scale != 1; + + for(int i = 0; i < in1.num_elements(); ++i) + { + fixed_point<T> val1(in1[i], fixed_point_position, true); + fixed_point<T> val2(in2[i], fixed_point_position, true); + fixed_point<T> res = (is_sat) ? val1 * val2 : mul<OverflowPolicy::WRAP>(val1, val2); + if(do_scaling) + { + res = (is_sat) ? res * fp_scale : mul<OverflowPolicy::WRAP>(res, fp_scale); + } + out[i] = res.raw(); + } +} + +// Threshold +template <typename T> +void threshold(const Tensor<T> &in, Tensor<T> &out, uint8_t threshold, uint8_t false_value, uint8_t true_value, ThresholdType type, uint8_t upper) +{ + switch(type) + { + case ThresholdType::BINARY: + for(int i = 0; i < in.num_elements(); ++i) + { + out[i] = ((in[i] > threshold) ? true_value : false_value); + } + break; + case ThresholdType::RANGE: + for(int i = 0; i < in.num_elements(); ++i) + { + if(in[i] > upper) + { + out[i] = false_value; + } + else if(in[i] < threshold) + { + out[i] = false_value; + } + else + { + out[i] = true_value; + } + } + break; + default: + ARM_COMPUTE_ERROR("Thresholding type not recognised"); + break; + } +} + +// Activation Layer for floating point type +template <typename T, typename std::enable_if<std::is_floating_point<T>::value, int>::type * = nullptr> +void activation_layer(const Tensor<T> &in, Tensor<T> &out, ActivationLayerInfo act_info) +{ + const T a = static_cast<T>(act_info.a()); + const T b = static_cast<T>(act_info.b()); + + for(int i = 0; i < in.num_elements(); ++i) + { + T x = in[i]; + switch(act_info.activation()) + { + case ActivationLayerInfo::ActivationFunction::ABS: + out[i] = std::abs(x); + break; + case ActivationLayerInfo::ActivationFunction::BOUNDED_RELU: + out[i] = std::min<T>(a, std::max<T>(0, x)); + break; + case ActivationLayerInfo::ActivationFunction::LINEAR: + out[i] = a * x + b; + break; + case ActivationLayerInfo::ActivationFunction::LOGISTIC: + out[i] = static_cast<T>(1) / (static_cast<T>(1) + std::exp(-x)); + break; + case ActivationLayerInfo::ActivationFunction::RELU: + out[i] = std::max<T>(0, x); + break; + case ActivationLayerInfo::ActivationFunction::SOFT_RELU: + out[i] = std::log(static_cast<T>(1) + std::exp(x)); + break; + case ActivationLayerInfo::ActivationFunction::SQRT: + out[i] = std::sqrt(x); + break; + case ActivationLayerInfo::ActivationFunction::SQUARE: + out[i] = x * x; + break; + case ActivationLayerInfo::ActivationFunction::TANH: + out[i] = a * std::tanh(b * x); + break; + default: + ARM_COMPUTE_ERROR("Activation function not recognised"); + break; + } + } +} + +// Activation Layer for fixed point type +template <typename T, typename std::enable_if<std::is_integral<T>::value, int>::type * = nullptr> +void activation_layer(const Tensor<T> &in, Tensor<T> &out, ActivationLayerInfo act_info) +{ + using namespace fixed_point_arithmetic; + int fixed_point_position = in.fixed_point_position(); + ActivationLayerInfo::ActivationFunction act_func = act_info.activation(); + const fixed_point<T> a(act_info.a(), fixed_point_position); + const fixed_point<T> b(act_info.b(), fixed_point_position); + const fixed_point<T> const_0(0, fixed_point_position); + const fixed_point<T> const_1(1, fixed_point_position); + + for(int i = 0; i < in.num_elements(); ++i) + { + fixed_point<T> x(in[i], fixed_point_position, true); + switch(act_func) + { + case ActivationLayerInfo::ActivationFunction::ABS: + out[i] = abs(x).raw(); + break; + case ActivationLayerInfo::ActivationFunction::BOUNDED_RELU: + out[i] = min(a, max(const_0, x)).raw(); + break; + case ActivationLayerInfo::ActivationFunction::LINEAR: + out[i] = add(b, mul(a, x)).raw(); + break; + case ActivationLayerInfo::ActivationFunction::LOGISTIC: + out[i] = (const_1 / (const_1 + exp(-x))).raw(); + break; + case ActivationLayerInfo::ActivationFunction::RELU: + out[i] = max(const_0, x).raw(); + break; + case ActivationLayerInfo::ActivationFunction::SOFT_RELU: + out[i] = log(const_1 + exp(x)).raw(); + break; + case ActivationLayerInfo::ActivationFunction::SQRT: + out[i] = (const_1 / inv_sqrt(x)).raw(); + break; + case ActivationLayerInfo::ActivationFunction::SQUARE: + out[i] = mul(x, x).raw(); + break; + case ActivationLayerInfo::ActivationFunction::TANH: + out[i] = tanh(x).raw(); + break; + default: + ARM_COMPUTE_ERROR("Activation function not recognised"); + break; + } + } +} + +// Batch Normalization Layer for fixed point type +template <typename T, typename std::enable_if<std::is_integral<T>::value, int>::type * = nullptr> +void batch_normalization_layer(const Tensor<T> &in, Tensor<T> &out, const Tensor<T> &mean, const Tensor<T> &var, const Tensor<T> &beta, const Tensor<T> &gamma, float epsilon, int fixed_point_position) +{ + const int cols = static_cast<int>(in.shape()[0]); + const int rows = static_cast<int>(in.shape()[1]); + const int depth = static_cast<int>(in.shape()[2]); + int upper_dims = in.shape().total_size() / (cols * rows * depth); + + for(int r = 0; r < upper_dims; ++r) + { + for(int i = 0; i < depth; ++i) + { + for(int k = 0; k < rows; ++k) + { + for(int l = 0; l < cols; ++l) + { + const int pos = l + k * cols + i * rows * cols + r * cols * rows * depth; + fixed_point_arithmetic::fixed_point<T> in_qs8(in[pos], fixed_point_position, true); + fixed_point_arithmetic::fixed_point<T> var_qs8(var[i], fixed_point_position, true); + fixed_point_arithmetic::fixed_point<T> mean_qs8(mean[i], fixed_point_position, true); + fixed_point_arithmetic::fixed_point<T> beta_qs8(beta[i], fixed_point_position, true); + fixed_point_arithmetic::fixed_point<T> gamma_qs8(gamma[i], fixed_point_position, true); + fixed_point_arithmetic::fixed_point<T> epsilon_qs8(epsilon, fixed_point_position); + + auto denominator = fixed_point_arithmetic::inv_sqrt(var_qs8 + epsilon_qs8); + auto numerator = in_qs8 - mean_qs8; + auto x_bar = numerator * denominator; + x_bar = beta_qs8 + x_bar * gamma_qs8; + out[pos] = x_bar.raw(); + } + } + } + } +} + +// Batch Normalization Layer for floating point type +template <typename T, typename std::enable_if<std::is_floating_point<T>::value, int>::type * = nullptr> +void batch_normalization_layer(const Tensor<T> &in, Tensor<T> &out, const Tensor<T> &mean, const Tensor<T> &var, const Tensor<T> &beta, const Tensor<T> &gamma, float epsilon, int fixed_point_position) +{ + const int cols = static_cast<int>(in.shape()[0]); + const int rows = static_cast<int>(in.shape()[1]); + const int depth = static_cast<int>(in.shape()[2]); + int upper_dims = in.shape().total_size() / (cols * rows * depth); + + for(int r = 0; r < upper_dims; ++r) + { + for(int i = 0; i < depth; ++i) + { + for(int k = 0; k < rows; ++k) + { + for(int l = 0; l < cols; ++l) + { + const int pos = l + k * cols + i * rows * cols + r * cols * rows * depth; + const float denominator = sqrt(var[i] + epsilon); + const float numerator = in[pos] - mean[i]; + const float x_bar = numerator / denominator; + out[pos] = beta[i] + x_bar * gamma[i]; + } + } + } + } +} + +// Convolution layer +template <typename T> +void convolution_layer(const Tensor<T> &in, const Tensor<T> &weights, const Tensor<T> &bias, Tensor<T> &out, const PadStrideInfo &conv_info) +{ + const int width_in = in.shape().x(); + const int height_in = in.shape().y(); + const int depth_in = in.shape().z(); + const int width_out = out.shape().x(); + const int height_out = out.shape().y(); + const int depth_out = out.shape().z(); + const int width_weights = weights.shape().x(); + const int height_weights = weights.shape().y(); + const int depth_weights = weights.shape().z(); + const int pad_xi = std::min(static_cast<int>(conv_info.pad().first), width_weights / 2); + const int pad_yi = std::min(static_cast<int>(conv_info.pad().second), height_weights / 2); + const int start_xi = width_weights / 2 - pad_xi; + const int start_yi = height_weights / 2 - pad_yi; + const int end_xi = width_in - start_xi; + const int end_yi = height_in - start_yi; + const int stride_xi = conv_info.stride().first; + const int stride_yi = conv_info.stride().second; + const int num_batches = in.shape().total_size() / (width_in * height_in * depth_in); + + for(int r = 0; r < num_batches; ++r) + { + for(int yi = start_yi; yi < end_yi; yi += stride_yi) + { + for(int xi = start_xi; xi < end_xi; xi += stride_xi) + { + for(int ofm = 0; ofm < depth_out; ++ofm) + { + // Compute input and output offsets + const int offset_in = r * width_in * height_in * depth_in; + const int xo = (xi - start_xi) / stride_xi; + const int yo = (yi - start_yi) / stride_yi; + const int offset_out = xo + yo * width_out + ofm * width_out * height_out + r * width_out * height_out * depth_out; + + // Compute 3D convolution + convolution3d(in.data() + offset_in, + weights.data() + ofm * width_weights * height_weights * depth_weights, + bias.data() + ofm, + out.data() + offset_out, + xi, yi, + width_in, height_in, depth_in, + width_weights, height_weights, + static_cast<int8_t>(in.fixed_point_position())); + } + } + } + } +} + +// Fully connected layer +template <typename T> +void fully_connected_layer(const Tensor<T> &in, const Tensor<T> &weights, const Tensor<T> &bias, Tensor<T> &out) +{ + ARM_COMPUTE_ERROR_ON(weights.shape().x() != out.shape().x()); + ARM_COMPUTE_ERROR_ON(weights.shape().y() != in.shape().x() * in.shape().y() * in.shape().z()); + const int cols_weights = weights.shape().x(); + const int rows_weights = weights.shape().y(); + const int num_batches = in.shape().total_size() / rows_weights; + + for(int k = 0; k < num_batches; ++k) + { + vector_matrix_multiply<T>(in.data() + k * rows_weights, + weights.data(), + bias.data(), + out.data() + k * cols_weights, + cols_weights, + rows_weights, + in.fixed_point_position()); + } +} + +// Normalization Layer for floating point type +template <typename T, typename std::enable_if<std::is_floating_point<T>::value, int>::type * = nullptr> +void normalization_layer(const Tensor<T> &in, Tensor<T> &out, NormalizationLayerInfo norm_info) +{ + const uint32_t norm_size = norm_info.norm_size(); + NormType type = norm_info.type(); + float beta = norm_info.beta(); + uint32_t kappa = norm_info.kappa(); + + const int cols = static_cast<int>(in.shape()[0]); + const int rows = static_cast<int>(in.shape()[1]); + const int depth = static_cast<int>(in.shape()[2]); + int upper_dims = in.shape().total_size() / (cols * rows); + + float coeff = norm_info.scale_coeff(); + int radius_cols = norm_size / 2; + // IN_MAP_1D and CROSS_MAP normalize over a single axis only + int radius_rows = (NormType::IN_MAP_2D == type) ? norm_size / 2 : 0; + + if(type == NormType::CROSS_MAP) + { + // Remove also depth from upper dimensions since it is the axes we want + // to use for normalization + upper_dims /= depth; + for(int r = 0; r < upper_dims; ++r) + { + for(int i = 0; i < rows; ++i) + { + for(int k = 0; k < cols; ++k) + { + for(int l = 0; l < depth; ++l) + { + float accumulated_scale = 0.f; + for(int j = -radius_cols; j <= radius_cols; ++j) + { + const int z = l + j; + if(z >= 0 && z < depth) + { + const T value = in[k + i * cols + z * rows * cols + r * cols * rows * depth]; + accumulated_scale += value * value; + } + } + out[k + i * cols + l * rows * cols + r * cols * rows * depth] = kappa + accumulated_scale * coeff; + } + } + } + } + } + else + { + for(int r = 0; r < upper_dims; ++r) + { + for(int i = 0; i < rows; ++i) + { + for(int k = 0; k < cols; ++k) + { + float accumulated_scale = 0.f; + for(int j = -radius_rows; j <= radius_rows; ++j) + { + const int y = i + j; + for(int l = -radius_cols; l <= radius_cols; ++l) + { + const int x = k + l; + if((x >= 0 && y >= 0) && (x < cols && y < rows)) + { + const T value = in[x + y * cols + r * cols * rows]; + accumulated_scale += value * value; + } + } + } + out[k + i * cols + r * cols * rows] = kappa + accumulated_scale * coeff; + } + } + } + } + + if(beta == 1.f) + { + for(int i = 0; i < out.num_elements(); ++i) + { + out[i] = in[i] / out[i]; + } + } + else if(beta == 0.5f) + { + for(int i = 0; i < out.num_elements(); ++i) + { + out[i] = in[i] / std::sqrt(out[i]); + } + } + else + { + for(int i = 0; i < out.num_elements(); ++i) + { + out[i] = in[i] * std::exp(std::log(out[i]) * -beta); + } + } +} +// Normalization Layer for fixed-point types +template <typename T, typename std::enable_if<std::is_integral<T>::value, int>::type * = nullptr> +void normalization_layer(const Tensor<T> &in, Tensor<T> &out, NormalizationLayerInfo norm_info) +{ + using namespace fixed_point_arithmetic; + + const int fixed_point_position = in.fixed_point_position(); + + const uint32_t norm_size = norm_info.norm_size(); + NormType type = norm_info.type(); + fixed_point<T> beta(norm_info.beta(), fixed_point_position); + fixed_point<T> kappa(norm_info.kappa(), fixed_point_position); + + const int cols = static_cast<int>(in.shape()[0]); + const int rows = static_cast<int>(in.shape()[1]); + const int depth = static_cast<int>(in.shape()[2]); + int upper_dims = in.shape().total_size() / (cols * rows); + + fixed_point<T> coeff(norm_info.scale_coeff(), fixed_point_position); + int radius_cols = norm_size / 2; + // IN_MAP_1D and CROSS_MAP normalize over a single axis only + int radius_rows = (NormType::IN_MAP_2D == type) ? norm_size / 2 : 0; + + if(type == NormType::CROSS_MAP) + { + // Remove also depth from upper dimensions since it is the axes we want + // to use for normalization + upper_dims /= depth; + for(int r = 0; r < upper_dims; ++r) + { + for(int i = 0; i < rows; ++i) + { + for(int k = 0; k < cols; ++k) + { + for(int l = 0; l < depth; ++l) + { + fixed_point<T> accumulated_scale(0.f, fixed_point_position); + for(int j = -radius_cols; j <= radius_cols; ++j) + { + const int z = l + j; + if(z >= 0 && z < depth) + { + const T value = in[k + i * cols + z * rows * cols + r * cols * rows * depth]; + const fixed_point<T> fp_value(value, fixed_point_position, true); + accumulated_scale = add(accumulated_scale, mul(fp_value, fp_value)); + } + } + accumulated_scale = add(kappa, mul(accumulated_scale, coeff)); + out[k + i * cols + l * rows * cols + r * cols * rows * depth] = accumulated_scale.raw(); + } + } + } + } + } + else + { + for(int r = 0; r < upper_dims; ++r) + { + for(int i = 0; i < rows; ++i) + { + for(int k = 0; k < cols; ++k) + { + fixed_point<T> accumulated_scale(0.f, fixed_point_position); + for(int j = -radius_rows; j <= radius_rows; ++j) + { + const int y = i + j; + for(int l = -radius_cols; l <= radius_cols; ++l) + { + const int x = k + l; + if((x >= 0 && y >= 0) && (x < cols && y < rows)) + { + const T value = in[x + y * cols + r * cols * rows]; + const fixed_point<T> fp_value(value, fixed_point_position, true); + accumulated_scale = add(accumulated_scale, mul(fp_value, fp_value)); + } + } + } + accumulated_scale = add(kappa, mul(accumulated_scale, coeff)); + out[k + i * cols + r * cols * rows] = accumulated_scale.raw(); + } + } + } + } + + if(norm_info.beta() == 1.f) + { + for(int i = 0; i < out.num_elements(); ++i) + { + fixed_point<T> res = div(fixed_point<T>(in[i], fixed_point_position, true), fixed_point<T>(out[i], fixed_point_position, true)); + out[i] = res.raw(); + } + } + else + { + const fixed_point<T> beta(norm_info.beta(), fixed_point_position); + for(int i = 0; i < out.num_elements(); ++i) + { + fixed_point<T> res = pow(fixed_point<T>(out[i], fixed_point_position, true), beta); + res = div(fixed_point<T>(in[i], fixed_point_position, true), res); + out[i] = res.raw(); + } + } +} + +// Pooling layer +template <typename T> +void pooling_layer(const Tensor<T> &in, Tensor<T> &out, PoolingLayerInfo pool_info, int fixed_point_position) +{ + const int pool_size = pool_info.pool_size(); + PoolingType type = pool_info.pool_type(); + int pool_stride_x = 0; + int pool_stride_y = 0; + int pad_x = 0; + int pad_y = 0; + std::tie(pool_stride_x, pool_stride_y) = pool_info.pad_stride_info().stride(); + std::tie(pad_x, pad_y) = pool_info.pad_stride_info().pad(); + + const int cols_in = static_cast<int>(in.shape()[0]); + const int rows_in = static_cast<int>(in.shape()[1]); + + const int cols_out = static_cast<int>(out.shape()[0]); + const int rows_out = static_cast<int>(out.shape()[1]); + + int upper_dims = in.shape().total_size() / (cols_in * rows_in); + + int pooled_height = static_cast<int>(ceil(static_cast<float>(rows_in + 2 * pad_x - pool_size) / pool_stride_x)) + 1; + int pooled_width = static_cast<int>(ceil(static_cast<float>(cols_in + 2 * pad_y - pool_size) / pool_stride_y)) + 1; + + if((pooled_height - 1) * pool_stride_x >= rows_in + pad_x) + { + --pooled_height; + } + if((pooled_width - 1) * pool_stride_y >= cols_in + pad_y) + { + --pooled_width; + } + + if(type == PoolingType::MAX) + { + for(int r = 0; r < upper_dims; ++r) + { + for(int i = 0; i < pooled_height; ++i) + { + for(int k = 0; k < pooled_width; ++k) + { + int hstart = i * pool_stride_x - pad_x; + int wstart = k * pool_stride_y - pad_y; + int hend = std::min(hstart + pool_size, rows_in); + int wend = std::min(wstart + pool_size, cols_in); + hstart = std::max(hstart, 0); + wstart = std::max(wstart, 0); + + T max_val = std::numeric_limits<T>::lowest(); + for(int y = hstart; y < hend; ++y) + { + for(int x = wstart; x < wend; ++x) + { + T val = in[r * cols_in * rows_in + y * cols_in + x]; + if(val > max_val) + { + max_val = val; + } + } + } + + out[r * rows_out * cols_out + i * pooled_width + k] = max_val; + } + } + } + } + else // Average pooling + { + for(int r = 0; r < upper_dims; ++r) + { + for(int i = 0; i < pooled_height; ++i) + { + for(int k = 0; k < pooled_width; ++k) + { + T avg_val = 0; + + int hstart = i * pool_stride_x - pad_x; + int wstart = k * pool_stride_y - pad_y; + int hend = std::min(hstart + pool_size, cols_in + pad_x); + int wend = std::min(wstart + pool_size, rows_in + pad_y); + int pool = (hend - hstart) * (wend - wstart); + hstart = std::max(hstart, 0); + wstart = std::max(wstart, 0); + hend = std::min(hend, rows_in); + wend = std::min(wend, cols_in); + + if(std::is_floating_point<T>::value) + { + for(int y = hstart; y < hend; ++y) + { + for(int x = wstart; x < wend; ++x) + { + avg_val += in[r * cols_in * rows_in + y * cols_in + x]; + } + } + out[r * rows_out * cols_out + i * pooled_width + k] = avg_val / pool; + } + else + { + static std::array<qint8_t, 10> scale_values_q8 = + { { 0x0, 0x0, 0x40, 0x2A, 0x20, 0x19, 0x15, 0x12, 0x10, 0xE } }; + + for(int y = hstart; y < hend; ++y) + { + for(int x = wstart; x < wend; ++x) + { + avg_val = sqadd_qs8(avg_val, in[r * cols_in * rows_in + y * cols_in + x]); + } + } + out[r * rows_out * cols_out + i * pooled_width + k] = sqmul_qs8(avg_val, (scale_values_q8[pool] >> (7 - fixed_point_position)), fixed_point_position); + } + } + } + } + } +} + +// Softmax Layer +template <typename T, typename std::enable_if<std::is_floating_point<T>::value, int>::type * = nullptr> +void softmax_layer(const Tensor<T> &in, Tensor<T> &out) +{ + const int cols = static_cast<int>(in.shape()[0]); + const int upper_dims = in.shape().total_size() / cols; + for(int r = 0; r < upper_dims; ++r) + { + // Find max + T max = std::numeric_limits<T>::lowest(); + for(int c = 0; c < cols; ++c) + { + const T x = in[r * cols + c]; + if(x > max) + { + max = x; + } + } + + // Regularize + T sum = 0; + for(int c = 0; c < cols; ++c) + { + const T res = exp(in[r * cols + c] - max); + out[r * cols + c] = res; + sum += res; + } + + // Normalize + const T norm_val = 1 / sum; + for(int c = 0; c < cols; ++c) + { + out[r * cols + c] *= norm_val; + } + } +} +template <typename T, typename std::enable_if<std::is_integral<T>::value, int>::type * = nullptr> +void softmax_layer(const Tensor<T> &in, Tensor<T> &out) +{ + using namespace fixed_point_arithmetic; + using promoted_T = typename test::traits::promote<T>::type; + + const int fixed_point_position = in.fixed_point_position(); + const int cols = static_cast<int>(in.shape()[0]); + const int upper_dims = in.shape().total_size() / cols; + + for(int r = 0; r < upper_dims; ++r) + { + // Find max + fixed_point<T> max(std::numeric_limits<T>::lowest(), fixed_point_position, true); + for(int c = 0; c < cols; ++c) + { + const fixed_point<T> x(in[r * cols + c], fixed_point_position, true); + if(x > max) + { + max = x; + } + } + + // Regularize + fixed_point<promoted_T> sum(0, fixed_point_position); + for(int c = 0; c < cols; ++c) + { + const fixed_point<T> x(in[r * cols + c], fixed_point_position, true); + fixed_point<T> res = exp(x - max); + out[r * cols + c] = res.raw(); + sum = add(sum, static_cast<fixed_point<promoted_T>>(res)); + } + + // Normalize + fixed_point<T> sat_sum(sum); + for(int c = 0; c < cols; ++c) + { + const fixed_point<T> x(out[r * cols + c], fixed_point_position, true); + out[r * cols + c] = div(x, sat_sum).raw(); + } + } +} + +// Fixed point operations +template <typename T> +void fixed_point_operation(const Tensor<T> &in, Tensor<T> &out, FixedPointOp op) +{ + int p = in.fixed_point_position(); + switch(op) + { + case FixedPointOp::EXP: + for(int i = 0; i < in.num_elements(); ++i) + { + out[i] = fixed_point_arithmetic::exp(fixed_point_arithmetic::fixed_point<T>(in[i], p, true)).raw(); + } + break; + case FixedPointOp::LOG: + for(int i = 0; i < in.num_elements(); ++i) + { + out[i] = fixed_point_arithmetic::log(fixed_point_arithmetic::fixed_point<T>(in[i], p, true)).raw(); + } + break; + case FixedPointOp::INV_SQRT: + for(int i = 0; i < in.num_elements(); ++i) + { + out[i] = fixed_point_arithmetic::inv_sqrt(fixed_point_arithmetic::fixed_point<T>(in[i], p, true)).raw(); + } + break; + case FixedPointOp::RECIPROCAL: + for(int i = 0; i < in.num_elements(); ++i) + { + out[i] = fixed_point_arithmetic::div(fixed_point_arithmetic::fixed_point<T>(1, p), fixed_point_arithmetic::fixed_point<T>(in[i], p, true)).raw(); + } + break; + default: + ARM_COMPUTE_ERROR("Fixed point operation not supported"); + break; + } +} + +// Tensor print +template <typename T> +void print(const Tensor<T> &in, std::ostream &out) +{ + out << "\n"; + for(int i = 0; i < in.num_elements(); ++i) + { + out << in[i] << " "; + } + out << "\n"; +} +} // namespace tensor_operations +} // namespace validation +} // namespace test +} // namespace arm_compute + +#endif /* __ARM_COMPUTE_TEST_TENSOR_OPERATIONS_H__ */ |