/* * Copyright (c) 2017-2019 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 "helpers.h" #define ADD_OP(a, b) ((a) + (b)) #define SUB_OP(a, b) ((a) - (b)) #define MUL_OP(a, b) ((a) * (b)) #define INVSQRT_OP(a) rsqrt((a)) #define SQCVT_SAT(a) (a) #if defined(VEC_SIZE) && defined(DATA_TYPE) #if defined(FUSED_ACTIVATION) #include "activation_layer.cl" #define ACTIVATION_FUNC(x) ACTIVATION_OP(FUSED_ACTIVATION, x) #else /* defined(FUSED_ACTIVATION) */ #define ACTIVATION_FUNC(x) (x) #endif /* defined(FUSED_ACTIVATION) */ /** Apply batch normalization. * * @param[in] input_ptr Pointer to the first source tensor. Supported data types: F16/F32 * @param[in] input_stride_x Stride of the first source tensor in X dimension (in bytes) * @param[in] input_step_x input_stride_x * number of elements along X processed per workitem(in bytes) * @param[in] input_stride_y Stride of the first source tensor in Y dimension (in bytes) * @param[in] input_step_y input_stride_y * number of elements along Y processed per workitem(in bytes) * @param[in] input_stride_z Stride of the first source tensor in Z dimension (in bytes) * @param[in] input_step_z input_stride_z * number of elements along Z processed per workitem(in bytes) * @param[in] input_offset_first_element_in_bytes The offset of the first element in the first source tensor * @param[out] output_ptr Pointer to the destination tensor. Supported data types: same as @p input_ptr * @param[in] output_stride_x Stride of the destination tensor in X dimension (in bytes) * @param[in] output_step_x output_stride_x * number of elements along X processed per workitem(in bytes) * @param[in] output_stride_y Stride of the destination tensor in Y dimension (in bytes) * @param[in] output_step_y output_stride_y * number of elements along Y processed per workitem(in bytes) * @param[in] output_stride_z Stride of the destination tensor in Z dimension (in bytes) * @param[in] output_step_z output_stride_z * number of elements along Z processed per workitem(in bytes) * @param[in] output_offset_first_element_in_bytes The offset of the first element in the destination tensor * @param[in] mean_ptr Pointer to the mean source tensor. Supported data types: same as @p input_ptr * @param[in] mean_stride_x Stride of the mean source tensor in X dimension (in bytes) * @param[in] mean_step_x mean_stride_x * number of elements along X processed per workitem(in bytes) * @param[in] mean_offset_first_element_in_bytes The offset of the first element in the mean source tensor * @param[in] var_ptr Pointer to the var tensor. Supported data types: same as @p input_ptr * @param[in] var_stride_x Stride of the var tensor in X dimension (in bytes) * @param[in] var_step_x var_stride_x * number of elements along X processed per workitem(in bytes) * @param[in] var_offset_first_element_in_bytes The offset of the first element in the var source tensor * @param[in] beta_ptr Pointer to the beta source tensor. Supported data types: same as @p input_ptr * @param[in] beta_stride_x Stride of the beta source tensor in X dimension (in bytes) * @param[in] beta_step_x beta_stride_x * number of elements along X processed per workitem(in bytes) * @param[in] beta_offset_first_element_in_bytes The offset of the first element in the beta source tensor * @param[in] gamma_ptr Pointer to the gamma source tensor. Supported data types: same as @p input_ptr * @param[in] gamma_stride_x Stride of the gamma source tensor in X dimension (in bytes) * @param[in] gamma_step_x gamma_stride_x * number of elements along X processed per workitem(in bytes) * @param[in] gamma_offset_first_element_in_bytes The offset of the first element in the gamma source tensor * @param[in] epsilon Epsilon parameter in the batch normalization equation */ __kernel void batchnormalization_layer_nchw(TENSOR3D_DECLARATION(input), #ifndef IN_PLACE TENSOR3D_DECLARATION(output), #endif /* not IN_PLACE */ VECTOR_DECLARATION(mean), VECTOR_DECLARATION(var), #ifndef USE_DEFAULT_BETA VECTOR_DECLARATION(beta), #endif /* USE_DEFAULT_BETA */ #ifndef USE_DEFAULT_GAMMA VECTOR_DECLARATION(gamma), #endif /* USE_DEFAULT_GAMMA */ float epsilon) { Tensor3D in = CONVERT_TO_TENSOR3D_STRUCT(input); #ifdef IN_PLACE Tensor3D out = in; #else /* IN_PLACE */ Tensor3D out = CONVERT_TO_TENSOR3D_STRUCT(output); #endif /* IN_PLACE */ Vector mean = CONVERT_TO_VECTOR_STRUCT(mean); Vector var = CONVERT_TO_VECTOR_STRUCT(var); #ifndef USE_DEFAULT_BETA Vector beta = CONVERT_TO_VECTOR_STRUCT(beta); #endif /* USE_DEFAULT_BETA */ #ifndef USE_DEFAULT_GAMMA Vector gamma = CONVERT_TO_VECTOR_STRUCT(gamma); #endif /* USE_DEFAULT_GAMMA */ VEC_DATA_TYPE(DATA_TYPE, VEC_SIZE) data = 0; VEC_DATA_TYPE(DATA_TYPE, VEC_SIZE) denominator = 0; VEC_DATA_TYPE(DATA_TYPE, VEC_SIZE) numerator = 0; VEC_DATA_TYPE(DATA_TYPE, VEC_SIZE) x_bar = 0; VEC_DATA_TYPE(DATA_TYPE, VEC_SIZE) res = 0; const int current_slice = get_global_id(2); data = VLOAD(VEC_SIZE)(0, (__global DATA_TYPE *)in.ptr); denominator = *((__global DATA_TYPE *)(var.ptr + current_slice * var.stride_x)); denominator = INVSQRT_OP(ADD_OP(denominator, ((VEC_DATA_TYPE(DATA_TYPE, VEC_SIZE))SQCVT_SAT(epsilon)))); // Calculate x bar and store results numerator = *((__global DATA_TYPE *)(mean.ptr + current_slice * mean.stride_x)); numerator = SUB_OP(data, numerator); x_bar = MUL_OP(numerator, denominator); #ifndef USE_DEFAULT_GAMMA VEC_DATA_TYPE(DATA_TYPE, VEC_SIZE) gamma_vec = *((__global DATA_TYPE *)(gamma.ptr + current_slice * gamma.stride_x)); res = MUL_OP(gamma_vec, x_bar); #else /* USE_DEFAULT_GAMMA */ // gamma is equal to 1, no need to perform multiplications res = x_bar; #endif /* USE_DEFAULT_GAMMA */ #ifndef USE_DEFAULT_BETA VEC_DATA_TYPE(DATA_TYPE, VEC_SIZE) beta_vec = *((__global DATA_TYPE *)(beta.ptr + current_slice * beta.stride_x)); // beta is not zero, hence we need to perform the addition res = ADD_OP(res, beta_vec); #endif /* USE_DEFAULT_BETA */ res = ACTIVATION_FUNC(res); VSTORE(VEC_SIZE) (res, 0, (__global DATA_TYPE *)out.ptr); } /** Apply batch normalization on tensors with NHWC format. * * @param[in] input_ptr Pointer to the first source tensor. Supported data types: F16/F32 * @param[in] input_stride_x Stride of the first source tensor in X dimension (in bytes) * @param[in] input_step_x input_stride_x * number of elements along X processed per workitem(in bytes) * @param[in] input_stride_y Stride of the first source tensor in Y dimension (in bytes) * @param[in] input_step_y input_stride_y * number of elements along Y processed per workitem(in bytes) * @param[in] input_stride_z Stride of the first source tensor in Z dimension (in bytes) * @param[in] input_step_z input_stride_z * number of elements along Z processed per workitem(in bytes) * @param[in] input_offset_first_element_in_bytes The offset of the first element in the first source tensor * @param[out] output_ptr Pointer to the destination tensor. Supported data types: same as @p input_ptr * @param[in] output_stride_x Stride of the destination tensor in X dimension (in bytes) * @param[in] output_step_x output_stride_x * number of elements along X processed per workitem(in bytes) * @param[in] output_stride_y Stride of the destination tensor in Y dimension (in bytes) * @param[in] output_step_y output_stride_y * number of elements along Y processed per workitem(in bytes) * @param[in] output_stride_z Stride of the destination tensor in Z dimension (in bytes) * @param[in] output_step_z output_stride_z * number of elements along Z processed per workitem(in bytes) * @param[in] output_offset_first_element_in_bytes The offset of the first element in the destination tensor * @param[in] mean_ptr Pointer to the mean source tensor. Supported data types: same as @p input_ptr * @param[in] mean_stride_x Stride of the mean source tensor in X dimension (in bytes) * @param[in] mean_step_x mean_stride_x * number of elements along X processed per workitem(in bytes) * @param[in] mean_offset_first_element_in_bytes The offset of the first element in the mean source tensor * @param[in] var_ptr Pointer to the var tensor. Supported data types: same as @p input_ptr * @param[in] var_stride_x Stride of the var tensor in X dimension (in bytes) * @param[in] var_step_x var_stride_x * number of elements along X processed per workitem(in bytes) * @param[in] var_offset_first_element_in_bytes The offset of the first element in the var source tensor * @param[in] beta_ptr Pointer to the beta source tensor. Supported data types: same as @p input_ptr * @param[in] beta_stride_x Stride of the beta source tensor in X dimension (in bytes) * @param[in] beta_step_x beta_stride_x * number of elements along X processed per workitem(in bytes) * @param[in] beta_offset_first_element_in_bytes The offset of the first element in the beta source tensor * @param[in] gamma_ptr Pointer to the gamma source tensor. Supported data types: same as @p input_ptr * @param[in] gamma_stride_x Stride of the gamma source tensor in X dimension (in bytes) * @param[in] gamma_step_x gamma_stride_x * number of elements along X processed per workitem(in bytes) * @param[in] gamma_offset_first_element_in_bytes The offset of the first element in the gamma source tensor * @param[in] epsilon Epsilon parameter in the batch normalization equation */ __kernel void batchnormalization_layer_nhwc(TENSOR3D_DECLARATION(input), #ifndef IN_PLACE TENSOR3D_DECLARATION(output), #endif /* not IN_PLACE */ VECTOR_DECLARATION(mean), VECTOR_DECLARATION(var), #ifndef USE_DEFAULT_BETA VECTOR_DECLARATION(beta), #endif /* USE_DEFAULT_BETA */ #ifndef USE_DEFAULT_GAMMA VECTOR_DECLARATION(gamma), #endif /* USE_DEFAULT_GAMMA */ float epsilon) { Tensor3D in = CONVERT_TO_TENSOR3D_STRUCT(input); #ifdef IN_PLACE Tensor3D out = in; #else /* IN_PLACE */ Tensor3D out = CONVERT_TO_TENSOR3D_STRUCT(output); #endif /* IN_PLACE */ Vector mean = CONVERT_TO_VECTOR_STRUCT(mean); Vector var = CONVERT_TO_VECTOR_STRUCT(var); #ifndef USE_DEFAULT_BETA Vector beta = CONVERT_TO_VECTOR_STRUCT(beta); #endif /* USE_DEFAULT_BETA */ #ifndef USE_DEFAULT_GAMMA Vector gamma = CONVERT_TO_VECTOR_STRUCT(gamma); #endif /* USE_DEFAULT_GAMMA */ VEC_DATA_TYPE(DATA_TYPE, VEC_SIZE) data = 0; VEC_DATA_TYPE(DATA_TYPE, VEC_SIZE) denominator = 0; VEC_DATA_TYPE(DATA_TYPE, VEC_SIZE) numerator = 0; VEC_DATA_TYPE(DATA_TYPE, VEC_SIZE) x_bar = 0; VEC_DATA_TYPE(DATA_TYPE, VEC_SIZE) res = 0; const int current_slice = get_global_id(0); data = VLOAD(VEC_SIZE)(0, (__global DATA_TYPE *)in.ptr); denominator = VLOAD(VEC_SIZE)(0, (__global DATA_TYPE *)(var.ptr + current_slice * VEC_SIZE * var.stride_x)); denominator = INVSQRT_OP(ADD_OP(denominator, ((VEC_DATA_TYPE(DATA_TYPE, VEC_SIZE))SQCVT_SAT(epsilon)))); // Calculate x bar and store results numerator = VLOAD(VEC_SIZE)(0, (__global DATA_TYPE *)(mean.ptr + current_slice * VEC_SIZE * mean.stride_x)); numerator = SUB_OP(data, numerator); x_bar = MUL_OP(numerator, denominator); #ifndef USE_DEFAULT_GAMMA VEC_DATA_TYPE(DATA_TYPE, VEC_SIZE) gamma_vec = VLOAD(VEC_SIZE)(0, (__global DATA_TYPE *)(gamma.ptr + current_slice * VEC_SIZE * gamma.stride_x)); res = MUL_OP(gamma_vec, x_bar); #else /* USE_DEFAULT_GAMMA */ // gamma is equal to 1, no need to perform multiplications res = x_bar; #endif /* USE_DEFAULT_GAMMA */ #ifndef USE_DEFAULT_BETA VEC_DATA_TYPE(DATA_TYPE, VEC_SIZE) beta_vec = VLOAD(VEC_SIZE)(0, (__global DATA_TYPE *)(beta.ptr + current_slice * VEC_SIZE * beta.stride_x)); // beta is not zero, hence we need to perform the addition res = ADD_OP(res, beta_vec); #endif /* USE_DEFAULT_BETA */ res = ACTIVATION_FUNC(res); VSTORE(VEC_SIZE) (res, 0, (__global DATA_TYPE *)out.ptr); } #endif /* defined(VEC_SIZE) && defined(DATA_TYPE) */ #if defined(NUM_CHANNELS) && defined(DATA_TYPE) && defined(EPSILON) /** Fuse batchnorm parameters to convolution layer parameters * * @attention Data type should be passed using the -DDATA_TYPE compile flag, e.g. -DDATA_TYPE=float * @attention Input tensor depth should be given as a preprocessor argument using -DNUM_CHANNELS=size. e.g. -DNUM_CHANNELS=16 * @attention Batch normalization epsilon parameter should be given as a preprocessor argument with -DEPSILON=value. e.g. -DEPSILON=0.001f * * @param[in] conv_w_ptr Pointer to the source tensor. Supported data types: F16/F32 * @param[in] conv_w_stride_x Stride of the source tensor in X dimension (in bytes) * @param[in] conv_w_step_x input_stride_x * number of elements along X processed per workitem(in bytes) * @param[in] conv_w_stride_y Stride of the source tensor in Y dimension (in bytes) * @param[in] conv_w_step_y input_stride_y * number of elements along Y processed per workitem(in bytes) * @param[in] conv_w_stride_z Stride of the source tensor in Z dimension (in bytes) * @param[in] conv_w_step_z input_stride_z * number of elements along Z processed per workitem(in bytes) * @param[in] conv_w_stride_w Stride of the source tensor in W dimension (in bytes) * @param[in] conv_w_step_w input_stride_w * number of elements along W processed per workitem(in bytes) * @param[in] conv_w_offset_first_element_in_bytes The offset of the first element in the source tensor * @param[in] bn_mean_ptr Pointer to the mean source tensor. Supported data types: same as @p input_ptr * @param[in] bn_mean_stride_x Stride of the mean source tensor in X dimension (in bytes) * @param[in] bn_mean_step_x bn_mean_stride_x * number of elements along X processed per workitem(in bytes) * @param[in] bn_mean_offset_first_element_in_bytes The offset of the first element in the mean source tensor * @param[in] bn_var_ptr Pointer to the var tensor. Supported data types: same as @p input_ptr * @param[in] bn_var_stride_x Stride of the var tensor in X dimension (in bytes) * @param[in] bn_var_step_x bn_var_stride_x * number of elements along X processed per workitem(in bytes) * @param[in] bn_var_offset_first_element_in_bytes The offset of the first element in the var source tensor * @param[out] fused_w_ptr Pointer to the destination weights tensors. Supported data types: same as @p input_ptr * @param[in] fused_w_stride_x Stride of the destination tensor in X dimension (in bytes) * @param[in] fused_w_step_x fused_w_stride_x * number of elements along X processed per workitem(in bytes) * @param[in] fused_w_stride_y Stride of the destination tensor in Y dimension (in bytes) * @param[in] fused_w_step_y fused_w_stride_y * number of elements along Y processed per workitem(in bytes) * @param[in] fused_w_stride_z Stride of the destination tensor in Z dimension (in bytes) * @param[in] fused_w_step_z fused_w_stride_z * number of elements along Z processed per workitem(in bytes) * @param[in] fused_w_stride_w Stride of the destination tensor in W dimension (in bytes) * @param[in] fused_w_step_w fused_w_stride_w * number of elements along W processed per workitem(in bytes) * @param[in] fused_w_offset_first_element_in_bytes The offset of the first element in the destination tensor * @param[in] fused_b_ptr Pointer to the destination bias tensor. Supported data types: same as @p input_ptr * @param[in] fused_b_stride_x Stride of the bias source tensor in X dimension (in bytes) * @param[in] fused_b_step_x fused_b_stride_x * number of elements along X processed per workitem(in bytes) * @param[in] fused_b_offset_first_element_in_bytes The offset of the first element in the destination tensor * @param[in] conv_b_ptr Pointer to the source bias tensor. Supported data types: same as @p input_ptr * @param[in] conv_b_stride_x Stride of the beta source tensor in X dimension (in bytes) * @param[in] conv_b_step_x conv_b_beta_stride_x * number of elements along X processed per workitem(in bytes) * @param[in] conv_b_offset_first_element_in_bytes The offset of the first element in the source bias tensor * @param[in] bn_beta_ptr Pointer to the beta source tensor. Supported data types: same as @p input_ptr * @param[in] bn_beta_stride_x Stride of the beta source tensor in X dimension (in bytes) * @param[in] bn_beta_step_x bn_beta_stride_x * number of elements along X processed per workitem(in bytes) * @param[in] bn_beta_offset_first_element_in_bytes The offset of the first element in the beta source tensor * @param[in] bn_gamma_ptr Pointer to the gamma source tensor. Supported data types: same as @p input_ptr * @param[in] bn_gamma_stride_x Stride of the gamma source tensor in X dimension (in bytes) * @param[in] bn_gamma_step_x bn_gamma_stride_x * number of elements along X processed per workitem(in bytes) * @param[in] bn_gamma_offset_first_element_in_bytes The offset of the first element in the gamma source tensor * @param[in] epsilon Epsilon parameter in the batch normalization equation */ __kernel void fuse_batchnormalization_layer(TENSOR4D_DECLARATION(conv_w), VECTOR_DECLARATION(bn_mean), VECTOR_DECLARATION(bn_var) #ifndef IN_PLACE_W , TENSOR4D_DECLARATION(fused_w) #endif /* not IN_PLACE_W */ #ifndef IN_PLACE_B , VECTOR_DECLARATION(fused_b) #endif /* not IN_PLACE_B */ #ifdef HAS_BIAS , VECTOR_DECLARATION(conv_b) #endif /* HAS_BIAS */ #ifndef USE_DEFAULT_BETA , VECTOR_DECLARATION(bn_beta) #endif /* USE_DEFAULT_BETA */ #ifndef USE_DEFAULT_GAMMA , VECTOR_DECLARATION(bn_gamma) #endif /* USE_DEFAULT_GAMMA */ ) { Tensor4D conv_w = CONVERT_TO_TENSOR4D_STRUCT(conv_w, NUM_CHANNELS); Vector bn_mean = CONVERT_TO_VECTOR_STRUCT_NO_STEP(bn_mean); Vector bn_var = CONVERT_TO_VECTOR_STRUCT_NO_STEP(bn_var); // Conditional ops #ifdef HAS_BIAS Vector conv_b = CONVERT_TO_VECTOR_STRUCT_NO_STEP(conv_b); #endif /* HAS_BIAS */ #ifndef USE_DEFAULT_BETA Vector bn_beta = CONVERT_TO_VECTOR_STRUCT_NO_STEP(bn_beta); #endif /* USE_DEFAULT_BETA */ #ifndef USE_DEFAULT_GAMMA Vector bn_gamma = CONVERT_TO_VECTOR_STRUCT_NO_STEP(bn_gamma); #endif /* USE_DEFAULT_GAMMA */ // In-place ops #ifdef IN_PLACE_W Tensor4D fused_w = conv_w; uint fused_w_stride_x = conv_w_stride_x; #else /* IN_PLACE_W */ Tensor4D fused_w = CONVERT_TO_TENSOR4D_STRUCT(fused_w, NUM_CHANNELS); #endif /* IN_PLACE_W */ #ifdef IN_PLACE_B Vector fused_b = conv_b; #else /* IN_PLACE_B */ Vector fused_b = CONVERT_TO_VECTOR_STRUCT_NO_STEP(fused_b); #endif /* IN_PLACE_B */ const int current_slice = get_global_id(2) / NUM_CHANNELS; #if defined(VEC_SIZE) && defined(LAST_ACCESSED_X) // Check if access on width gets out of bounds // If it does shift access vector to access elements within bounds const int xi = (int)(get_global_id(0) * VEC_SIZE); conv_w.ptr -= max(xi - (int)LAST_ACCESSED_X, 0) * conv_w_stride_x; fused_w.ptr -= max(xi - (int)LAST_ACCESSED_X, 0) * fused_w_stride_x; // Load W VEC_DATA_TYPE(DATA_TYPE, VEC_SIZE) wn = VLOAD(VEC_SIZE)(0, (__global DATA_TYPE *)conv_w.ptr); #else // !defined(VEC_SIZE) || !defined(LAST_ACCESSED_X) DATA_TYPE wn = *((__global DATA_TYPE *)(conv_w.ptr)); #endif // defined(VEC_SIZE) && defined(LAST_ACCESSED_X) // rvar = 1 / sqrt(var + epsilon) const DATA_TYPE var = *((__global DATA_TYPE *)(bn_var.ptr + current_slice * bn_var.stride_x)); const DATA_TYPE rvar = INVSQRT_OP(ADD_OP(var, SQCVT_SAT((float)EPSILON))); wn *= rvar; // Load b const DATA_TYPE mean = *((__global DATA_TYPE *)(bn_mean.ptr + current_slice * bn_mean.stride_x)); DATA_TYPE bn = 0; #ifdef HAS_BIAS bn = *((__global DATA_TYPE *)(conv_b.ptr + current_slice * conv_b.stride_x)); #endif /* HAS_BIAS */ bn = (bn - mean) * rvar; #ifndef USE_DEFAULT_GAMMA const DATA_TYPE gamma_scalar = *((__global DATA_TYPE *)(bn_gamma.ptr + current_slice * bn_gamma.stride_x)); wn *= gamma_scalar; bn *= gamma_scalar; #endif /* USE_DEFAULT_GAMMA */ #ifndef USE_DEFAULT_BETA const DATA_TYPE beta_scalar = *((__global DATA_TYPE *)(bn_beta.ptr + current_slice * bn_beta.stride_x)); bn += beta_scalar; #endif /* USE_DEFAULT_BETA */ #if defined(VEC_SIZE) && defined(LAST_ACCESSED_X) // Store updated weights VSTORE(VEC_SIZE) (wn, 0, (__global DATA_TYPE *)fused_w.ptr); #else // !defined(VEC_SIZE) || !defined(LAST_ACCESSED_X) *((__global DATA_TYPE *)(fused_w.ptr)) = wn; #endif // defined(VEC_SIZE) && defined(LAST_ACCESSED_X) // Store updated bias *((__global DATA_TYPE *)(fused_b.ptr + current_slice * fused_b.stride_x)) = bn; } #endif /* defined(NUM_CHANNELS) && defined(DATA_TYPE) && defined(EPSILON) */