COMPMID-661: softmax-fp32 optimisation (#14)

Change-Id: I2007af1ed9dcf68065cf412aa50f73a2025b31a6
Reviewed-on: http://mpd-gerrit.cambridge.arm.com/94605
Reviewed-by: Gian Marco Iodice <gianmarco.iodice@arm.com>
Tested-by: Kaizen <jeremy.johnson+kaizengerrit@arm.com>

1 files changed, 487 insertions, 0 deletions

diff --git a/src/core/CL/cl_kernels/softmax_layer.cl b/src/core/CL/cl_kernels/softmax_layer.cl
index 010135eb7b..5bc43ef144 100644
--- a/src/core/CL/cl_kernels/softmax_layer.cl
+++ b/src/core/CL/cl_kernels/softmax_layer.cl
@@ -57,8 +57,36 @@
 
 #endif /* FIXED_POINT_POSITION */
 
+/* Number of workitems in dimension 0. */
+#if !defined(GRID_SIZE)
+#define GRID_SIZE 1
+#endif /* !defined(GRID_SIZE) */
+
+/* Vector size, i.e. number of vector elements. */
+#if VECTOR_SIZE == 2
+__constant VEC_DATA_TYPE(DATA_TYPE, 2) type_min_ = (VEC_DATA_TYPE(DATA_TYPE, 2))(MINVAL);
+__constant uint2 idx__ = (uint2)(0, 1);
+
+#elif VECTOR_SIZE == 4
+__constant VEC_DATA_TYPE(DATA_TYPE, 4) type_min_ = (VEC_DATA_TYPE(DATA_TYPE, 4))(MINVAL);
+__constant uint4 idx__ = (uint4)(0, 1, 2, 3);
+
+#elif VECTOR_SIZE == 8
+__constant VEC_DATA_TYPE(DATA_TYPE, 8) type_min_ = (VEC_DATA_TYPE(DATA_TYPE, 8))(MINVAL);
+__constant uint8 idx__ = (uint8)(0, 1, 2, 3, 4, 5, 6, 7);
+
+#else /* VECTOR_SIZE DEFAULT */
+#define VECTOR_SIZE 16
+#define LOG_VECTOR_SIZE 4
+__constant VEC_DATA_TYPE(DATA_TYPE, 16) type_min_ = (VEC_DATA_TYPE(DATA_TYPE, 16))(MINVAL);
+__constant uint16 idx__ = (uint16)(0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15);
+
+#endif /* VECTOR_SIZE END */
+
+// TODO (COMPMID-661): Remove if the non-fused kernels are removed
 __constant VEC_DATA_TYPE(DATA_TYPE, 16) type_min = (VEC_DATA_TYPE(DATA_TYPE, 16))(MINVAL);
 __constant uint16 idx16 = (uint16)(0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15);
+__constant uint4 idx4   = (uint4)(0, 1, 2, 3);
 
 /** Identifies the maximum value across the 1st dimension.
  *
@@ -277,3 +305,462 @@ __kernel void softmax_layer_norm(
     data = vload16(0, (__global DATA_TYPE *)offset(&src, 0, 0));
     vstore16(DIV_OP(data, sum_val, DATA_TYPE, 16), 0, (__global DATA_TYPE *)offset(&dst, 0, 0));
 }
+
+/** Identifies the maximum value across the 1st dimension and shifts the values of the input tensor by this maximum value,
+ * then gets the exponent of each element as sums all elements across each row.
+ *
+ * @note Datatype must be given as a preprocessor argument using -DDATA_TYPE=type. e.g. -DDATA_TYPE=short
+ * @note Fixed point position must be given as a preprocessor argument using -DFIXED_POINT_POSITION=pos. e.g. DFIXED_POINT_POSITION=4
+ * @note In case the input is not a multiple of VECTOR_SIZE (2,4,8,16) -DNON_MULTIPLE_OF_VECTOR_SIZE must be passed.
+ * @note Beta can be optionally passed at compile time using -DBETA (by default, it is 1.0).
+ *
+ * @param[in]  src_ptr                            Pointer to the source tensor slice. Supported data types: QS8/QS16/F16/F32
+ * @param[in]  src_stride_x                       Stride of the source tensor in X dimension (in bytes)
+ * @param[in]  src_step_x                         src_stride_x * number of elements along X processed per workitem(in bytes)
+ * @param[in]  src_stride_y                       Stride of the source tensor in Y dimension (in bytes)
+ * @param[in]  src_step_y                         src_stride_y * number of elements along Y processed per workitem(in bytes)
+ * @param[in]  src_stride_z                       Stride of the source tensor in Z dimension (in bytes)
+ * @param[in]  src_step_z                         src_stride_z * number of elements along Z processed per workitem(in bytes)
+ * @param[in]  src_offset_first_element_in_bytes  The offset of the first element in the source tensor
+ * @param[in]  maxo_ptr                           Pointer to the max values tensor slice. Supported data types: same as @p src_ptr
+ * @param[in]  maxo_stride_x                      Stride of the max values tensor in X dimension (in bytes)
+ * @param[in]  maxo_step_x                        max_stride_x * number of elements along X processed per workitem(in bytes)
+ * @param[in]  maxo_stride_y                      Stride of the max values tensor in Y dimension (in bytes)
+ * @param[in]  maxo_step_y                        max_stride_y * number of elements along Y processed per workitem(in bytes)
+ * @param[in]  maxo_stride_z                      Stride of the max values tensor in Z dimension (in bytes)
+ * @param[in]  maxo_step_z                        max_stride_z * number of elements along Z processed per workitem(in bytes)
+ * @param[in]  maxo_offset_first_element_in_bytes The offset of the first element in the max values tensor
+ * @param[out] dst_ptr                            Pointer to the destination tensor slice. Supported data types: same as @p src_ptr
+ * @param[in]  dst_stride_x                       Stride of the destination tensor in X dimension (in bytes)
+ * @param[in]  dst_step_x                         dst_stride_x * number of elements along X processed per workitem(in bytes)
+ * @param[in]  dst_stride_y                       Stride of the destination tensor in Y dimension (in bytes)
+ * @param[in]  dst_step_y                         dst_stride_y * number of elements along Y processed per workitem(in bytes)
+ * @param[in]  dst_stride_z                       Stride of the destination tensor in Z dimension (in bytes)
+ * @param[in]  dst_step_z                         dst_stride_z * number of elements along Z processed per workitem(in bytes)
+ * @param[in]  dst_offset_first_element_in_bytes  The offset of the first element in the destination tensor
+ * @param[out] sum_ptr                            Pointer to the sum values tensor slice. Supported data types: same as @p src_ptr
+ * @param[in]  sum_stride_x                       Stride of the sum values tensor in X dimension (in bytes)
+ * @param[in]  sum_step_x                         sum_stride_x * number of elements along X processed per workitem(in bytes)
+ * @param[in]  sum_stride_y                       Stride of the sum values tensor in Y dimension (in bytes)
+ * @param[in]  sum_step_y                         sum_stride_z * number of elements along Z processed per workitem(in bytes)
+ * @param[in]  sum_stride_z                       Stride of the sum values tensor in Z dimension (in bytes)
+ * @param[in]  sum_step_z                         sum_stride_z * number of elements along Z processed per workitem(in bytes)
+ * @param[in]  sum_offset_first_element_in_bytes  The offset of the first element in the sum values tensor
+ * @param[in]  width                              Input image width
+ */
+__kernel void softmax_layer_max_shift_exp_sum_serial(
+    TENSOR3D_DECLARATION(src),
+    TENSOR3D_DECLARATION(maxo),
+    TENSOR3D_DECLARATION(dst),
+    TENSOR3D_DECLARATION(sum),
+    uint width)
+{
+    Image src  = CONVERT_TENSOR3D_TO_IMAGE_STRUCT(src);
+    Image dst  = CONVERT_TENSOR3D_TO_IMAGE_STRUCT(dst);
+    Image maxo = CONVERT_TENSOR3D_TO_IMAGE_STRUCT(maxo);
+    Image sum  = CONVERT_TENSOR3D_TO_IMAGE_STRUCT(sum);
+
+#ifdef BETA
+    // Initialize beta
+    VEC_DATA_TYPE(DATA_TYPE, VECTOR_SIZE)
+    beta = (VEC_DATA_TYPE(DATA_TYPE, VECTOR_SIZE))BETA_VAL;
+#endif /* BETA */
+
+    // Initialize local maximum
+    VEC_DATA_TYPE(DATA_TYPE, VECTOR_SIZE)
+    max_val_vec = (VEC_DATA_TYPE(DATA_TYPE, VECTOR_SIZE))type_min_;
+
+    // Calculate max of row
+    const uint width_ = width >> LOG_VECTOR_SIZE;
+    for(uint i = 0; i < width_; i++)
+    {
+        VEC_DATA_TYPE(DATA_TYPE, VECTOR_SIZE)
+        data_max    = VLOAD(VECTOR_SIZE)(0, (__global DATA_TYPE *)offset(&src, i << LOG_VECTOR_SIZE, 0));
+        max_val_vec = MAX_OP(data_max, max_val_vec, DATA_TYPE, VECTOR_SIZE);
+    }
+
+#ifdef NON_MULTIPLE_OF_VECTOR_SIZE
+    VEC_DATA_TYPE(DATA_TYPE, VECTOR_SIZE)
+    data_max = VLOAD(VECTOR_SIZE)(0, (__global DATA_TYPE *)offset(&src, width_ << LOG_VECTOR_SIZE, 0));
+    VEC_DATA_TYPE(SELECT_DATA_TYPE, VECTOR_SIZE)
+    widx        = CONVERT((EXPAND((CL_VEC_DATA_TYPE(uint, VECTOR_SIZE)))(width_ << LOG_VECTOR_SIZE) + idx__) < width, VEC_DATA_TYPE(SELECT_DATA_TYPE, VECTOR_SIZE));
+    max_val_vec = MAX_OP(max_val_vec, select(type_min_, data_max, widx), DATA_TYPE, VECTOR_SIZE);
+#endif /* NON_MULTIPLE_OF_VECTOR_SIZE */
+
+    // Perform max reduction
+#if VECTOR_SIZE == 16
+    max_val_vec.s01234567 = MAX_OP(max_val_vec.s01234567, max_val_vec.s89ABCDEF, DATA_TYPE, 8);
+#endif /* VECTOR SIZE 16 END */
+#if VECTOR_SIZE >= 8
+    max_val_vec.s0123 = MAX_OP(max_val_vec.s0123, max_val_vec.s4567, DATA_TYPE, 4);
+#endif /* VECTOR SIZE 8 END */
+#if VECTOR_SIZE >= 4
+    max_val_vec.s01 = MAX_OP(max_val_vec.s01, max_val_vec.s23, DATA_TYPE, 2);
+#endif /* VECTOR SIZE 4 END */
+    max_val_vec.s0 = MAX_OP(max_val_vec.s0, max_val_vec.s1, DATA_TYPE, 1);
+    // Store result
+    *((__global DATA_TYPE *)maxo.ptr) = max_val_vec.s0;
+
+    /* Second section */
+
+    // Load max value of 1D logits vector (row)
+    DATA_TYPE max_val = *((__global DATA_TYPE *)offset(&maxo, 0, 0));
+
+    // Set sum vector
+    VEC_DATA_TYPE(DATA_TYPE, VECTOR_SIZE)
+    sum1D = 0;
+
+    // Shift values, exp and sum
+    for(uint i = 0; i < width_; i++)
+    {
+        VEC_DATA_TYPE(DATA_TYPE, VECTOR_SIZE)
+        data = VLOAD(VECTOR_SIZE)(0, (__global DATA_TYPE *)offset(&src, i << LOG_VECTOR_SIZE, 0));
+        data = SUB_OP(data, max_val, DATA_TYPE, VECTOR_SIZE);
+#ifdef BETA
+        data = MUL_OP(data, beta, DATA_TYPE, VECTOR_SIZE);
+#endif /* BETA */
+        data = EXP_OP(data, DATA_TYPE, VECTOR_SIZE);
+        VSTORE(VECTOR_SIZE)
+        (data, 0, (__global DATA_TYPE *)offset(&dst, i << LOG_VECTOR_SIZE, 0));
+        sum1D = ADD_OP(sum1D, data, DATA_TYPE, VECTOR_SIZE);
+    }
+
+#ifdef NON_MULTIPLE_OF_VECTOR_SIZE
+    VEC_DATA_TYPE(DATA_TYPE, VECTOR_SIZE)
+    data = VLOAD(VECTOR_SIZE)(0, (__global DATA_TYPE *)offset(&src, width_ << LOG_VECTOR_SIZE, 0));
+    data = SUB_OP(data, max_val, DATA_TYPE, VECTOR_SIZE);
+#ifdef BETA
+    data = MUL_OP(data, beta, DATA_TYPE, VECTOR_SIZE);
+#endif /* BETA */
+    data = EXP_OP(data, DATA_TYPE, VECTOR_SIZE);
+    widx = CONVERT((EXPAND((CL_VEC_DATA_TYPE(uint, VECTOR_SIZE)))(width_ << LOG_VECTOR_SIZE) + idx__) < width, VEC_DATA_TYPE(SELECT_DATA_TYPE, VECTOR_SIZE));
+    data = select(0, data, widx);
+    VSTORE(VECTOR_SIZE)
+    (data, 0, (__global DATA_TYPE *)offset(&dst, width_ << LOG_VECTOR_SIZE, 0));
+    sum1D = ADD_OP(sum1D, data, DATA_TYPE, VECTOR_SIZE);
+#endif /* NON_MULTIPLE_OF_VECTOR_SIZE */
+
+    // Perform sum reduction
+#if VECTOR_SIZE == 16
+    sum1D.s01234567 = ADD_OP(sum1D.s01234567, sum1D.s89ABCDEF, DATA_TYPE, 8);
+#endif /* VECTOR SIZE 16 END */
+#if VECTOR_SIZE >= 8
+    sum1D.s0123 = ADD_OP(sum1D.s0123, sum1D.s4567, DATA_TYPE, 4);
+#endif /* VECTOR SIZE 8 END */
+#if VECTOR_SIZE >= 4
+    sum1D.s01 = ADD_OP(sum1D.s01, sum1D.s23, DATA_TYPE, 2);
+#endif /* VECTOR SIZE 4 END */
+    sum1D.s0 = ADD_OP(sum1D.s0, sum1D.s1, DATA_TYPE, 1);
+
+    // Calculate and store result
+    *((__global DATA_TYPE *)sum.ptr) = sum1D.s0;
+}
+
+/** Identifies the maximum value across the 1st dimension and shifts the values of the input tensor by this maximum value,
+ * then gets the exponent of each element as sums all elements across each row.
+ *
+ * @note Datatype must be given as a preprocessor argument using -DDATA_TYPE=type. e.g. -DDATA_TYPE=short
+ * @note Fixed point position must be given as a preprocessor argument using -DFIXED_POINT_POSITION=pos. e.g. DFIXED_POINT_POSITION=4
+ * @note In case the input is not a multiple of VECTOR_SIZE (2,4,8,16) -DNON_MULTIPLE_OF_VECTOR_SIZE must be passed.
+ * @note Beta can be optionally passed at compile time using -DBETA (by default, it is 1.0).
+ *
+ * @param[in]  src_ptr                            Pointer to the source tensor slice. Supported data types: QS8/QS16/F16/F32
+ * @param[in]  src_stride_x                       Stride of the source tensor in X dimension (in bytes)
+ * @param[in]  src_step_x                         src_stride_x * number of elements along X processed per workitem(in bytes)
+ * @param[in]  src_stride_y                       Stride of the source tensor in Y dimension (in bytes)
+ * @param[in]  src_step_y                         src_stride_y * number of elements along Y processed per workitem(in bytes)
+ * @param[in]  src_stride_z                       Stride of the source tensor in Z dimension (in bytes)
+ * @param[in]  src_step_z                         src_stride_z * number of elements along Z processed per workitem(in bytes)
+ * @param[in]  src_offset_first_element_in_bytes  The offset of the first element in the source tensor
+ * @param[in]  maxo_ptr                           Pointer to the max values tensor slice. Supported data types: same as @p src_ptr
+ * @param[in]  maxo_stride_x                      Stride of the max values tensor in X dimension (in bytes)
+ * @param[in]  maxo_step_x                        max_stride_x * number of elements along X processed per workitem(in bytes)
+ * @param[in]  maxo_stride_y                      Stride of the max values tensor in Y dimension (in bytes)
+ * @param[in]  maxo_step_y                        max_stride_y * number of elements along Y processed per workitem(in bytes)
+ * @param[in]  maxo_stride_z                      Stride of the max values tensor in Z dimension (in bytes)
+ * @param[in]  maxo_step_z                        max_stride_z * number of elements along Z processed per workitem(in bytes)
+ * @param[in]  maxo_offset_first_element_in_bytes The offset of the first element in the max values tensor
+ * @param[out] dst_ptr                            Pointer to the destination tensor slice. Supported data types: same as @p src_ptr
+ * @param[in]  dst_stride_x                       Stride of the destination tensor in X dimension (in bytes)
+ * @param[in]  dst_step_x                         dst_stride_x * number of elements along X processed per workitem(in bytes)
+ * @param[in]  dst_stride_y                       Stride of the destination tensor in Y dimension (in bytes)
+ * @param[in]  dst_step_y                         dst_stride_y * number of elements along Y processed per workitem(in bytes)
+ * @param[in]  dst_stride_z                       Stride of the destination tensor in Z dimension (in bytes)
+ * @param[in]  dst_step_z                         dst_stride_z * number of elements along Z processed per workitem(in bytes)
+ * @param[in]  dst_offset_first_element_in_bytes  The offset of the first element in the destination tensor
+ * @param[out] sum_ptr                            Pointer to the sum values tensor slice. Supported data types: same as @p src_ptr
+ * @param[in]  sum_stride_x                       Stride of the sum values tensor in X dimension (in bytes)
+ * @param[in]  sum_step_x                         sum_stride_x * number of elements along X processed per workitem(in bytes)
+ * @param[in]  sum_stride_y                       Stride of the sum values tensor in Y dimension (in bytes)
+ * @param[in]  sum_step_y                         sum_stride_z * number of elements along Z processed per workitem(in bytes)
+ * @param[in]  sum_stride_z                       Stride of the sum values tensor in Z dimension (in bytes)
+ * @param[in]  sum_step_z                         sum_stride_z * number of elements along Z processed per workitem(in bytes)
+ * @param[in]  sum_offset_first_element_in_bytes  The offset of the first element in the sum values tensor
+ * @param[in]  width                              Input image width
+ */
+__kernel void softmax_layer_max_shift_exp_sum_parallel(
+    TENSOR3D_DECLARATION(src),
+    TENSOR3D_DECLARATION(maxo),
+    TENSOR3D_DECLARATION(dst),
+    TENSOR3D_DECLARATION(sum),
+    uint width)
+{
+    Image src  = CONVERT_TENSOR3D_TO_IMAGE_STRUCT(src);
+    Image dst  = CONVERT_TENSOR3D_TO_IMAGE_STRUCT(dst);
+    Image maxo = CONVERT_TENSOR3D_TO_IMAGE_STRUCT(maxo);
+    Image sum  = CONVERT_TENSOR3D_TO_IMAGE_STRUCT(sum);
+
+    const uint lid = get_local_id(0);
+
+#ifdef BETA
+    // Initialize beta
+    VEC_DATA_TYPE(DATA_TYPE, 4)
+    beta = (VEC_DATA_TYPE(DATA_TYPE, 4))BETA;
+#endif /* BETA */
+
+    // Define one temporary vector per work-item.
+    __local VEC_DATA_TYPE(DATA_TYPE, 4) tmp_local[GRID_SIZE];
+    __local DATA_TYPE max_local;
+
+    __constant VEC_DATA_TYPE(DATA_TYPE, 4) type_min4 = (VEC_DATA_TYPE(DATA_TYPE, 4))(MINVAL);
+    VEC_DATA_TYPE(DATA_TYPE, 4)
+    max_val_vec = (VEC_DATA_TYPE(DATA_TYPE, 4))type_min4;
+    // Number of elements per work-item.
+    const uint row = width / GRID_SIZE;
+    // Number of iterations per work-item.
+    const uint width_ = row >> 2;
+    // Calculate max of row
+    uint i = 0;
+    for(; i < width_; i++)
+    {
+        VEC_DATA_TYPE(DATA_TYPE, 4)
+        data_max    = VLOAD(4)(0, (__global DATA_TYPE *)offset(&src, i * GRID_SIZE * 4, 0));
+        max_val_vec = MAX_OP(data_max, max_val_vec, DATA_TYPE, 4);
+    }
+#ifdef NON_MULTIPLE_OF_GRID_SIZE
+    // How many work-items needed to complete the computation.
+    //TODO: Optimize this calculation (avoid %).
+    int boundary_workitems = (width % (GRID_SIZE * 4)) / 4;
+    if(lid < boundary_workitems)
+    {
+        VEC_DATA_TYPE(DATA_TYPE, 4)
+        data_max    = VLOAD(4)(0, (__global DATA_TYPE *)offset(&src, i * GRID_SIZE * 4, 0));
+        max_val_vec = MAX_OP(data_max, max_val_vec, DATA_TYPE, 4);
+    }
+#ifdef NON_MULTIPLE_OF_VECTOR_SIZE
+    if(boundary_workitems == 0)
+    {
+        boundary_workitems = GRID_SIZE;
+        i--;
+    }
+    if(lid == (boundary_workitems - 1))
+    {
+        // Handle non multiple of 4
+        VEC_DATA_TYPE(DATA_TYPE, 4)
+        data_max = VLOAD(4)(0, (__global DATA_TYPE *)offset(&src, (GRID_SIZE * i * 4) + 4, 0));
+        VEC_DATA_TYPE(SELECT_DATA_TYPE, 4)
+        widx        = CONVERT(((uint4)(GRID_SIZE * i * 4) + boundary_workitems * 4 + idx4) < width, VEC_DATA_TYPE(SELECT_DATA_TYPE, 4));
+        max_val_vec = MAX_OP(max_val_vec, select(type_min_, data_max, widx), DATA_TYPE, 4);
+    }
+#endif /* NON_MULTIPLE_OF_VECTOR_SIZE */
+#endif /* NON_MULTIPLE_OF_GRID_SIZE */
+    tmp_local[lid] = max_val_vec;
+
+    barrier(CLK_LOCAL_MEM_FENCE);
+
+    if(GRID_SIZE >= 256)
+    {
+        if(lid < 128)
+        {
+            tmp_local[lid] = MAX_OP(tmp_local[lid + 128], tmp_local[lid], DATA_TYPE, 4);
+        }
+        barrier(CLK_LOCAL_MEM_FENCE);
+    }
+    if(GRID_SIZE >= 128)
+    {
+        if(lid < 64)
+        {
+            tmp_local[lid] = MAX_OP(tmp_local[lid + 64], tmp_local[lid], DATA_TYPE, 4);
+        }
+        barrier(CLK_LOCAL_MEM_FENCE);
+    }
+    if(GRID_SIZE >= 64)
+    {
+        if(lid < 32)
+        {
+            tmp_local[lid] = MAX_OP(tmp_local[lid + 32], tmp_local[lid], DATA_TYPE, 4);
+        }
+        barrier(CLK_LOCAL_MEM_FENCE);
+    }
+    if(GRID_SIZE >= 32)
+    {
+        if(lid < 16)
+        {
+            tmp_local[lid] = MAX_OP(tmp_local[lid + 16], tmp_local[lid], DATA_TYPE, 4);
+        }
+        barrier(CLK_LOCAL_MEM_FENCE);
+    }
+    if(GRID_SIZE >= 16)
+    {
+        if(lid < 8)
+        {
+            tmp_local[lid] = MAX_OP(tmp_local[lid + 8], tmp_local[lid], DATA_TYPE, 4);
+        }
+        barrier(CLK_LOCAL_MEM_FENCE);
+    }
+    if(GRID_SIZE >= 8)
+    {
+        if(lid < 4)
+        {
+            tmp_local[lid] = MAX_OP(tmp_local[lid + 4], tmp_local[lid], DATA_TYPE, 4);
+        }
+        barrier(CLK_LOCAL_MEM_FENCE);
+    }
+    if(GRID_SIZE >= 4)
+    {
+        if(lid < 2)
+        {
+            tmp_local[lid] = MAX_OP(tmp_local[lid + 2], tmp_local[lid], DATA_TYPE, 4);
+        }
+        barrier(CLK_LOCAL_MEM_FENCE);
+    }
+    if(lid == 0)
+    {
+        max_val_vec     = MAX_OP(tmp_local[lid + 1], tmp_local[lid], DATA_TYPE, 4);
+        max_val_vec.s01 = MAX_OP(max_val_vec.s01, max_val_vec.s23, DATA_TYPE, 2);
+        max_val_vec.s0  = MAX_OP(max_val_vec.s0, max_val_vec.s1, DATA_TYPE, 1);
+        max_local       = max_val_vec.s0;
+    }
+    barrier(CLK_LOCAL_MEM_FENCE);
+
+    /* Second section */
+
+    // Set sum vector
+    VEC_DATA_TYPE(DATA_TYPE, 4)
+    sum1D             = 0;
+    DATA_TYPE max_val = max_local;
+
+    // Shift values, exp and sum
+    for(i = 0; i < width_; i++)
+    {
+        VEC_DATA_TYPE(DATA_TYPE, 4)
+        data = VLOAD(4)(0, (__global DATA_TYPE *)offset(&src, i * GRID_SIZE * 4, 0));
+        data = SUB_OP(data, max_val, DATA_TYPE, 4);
+#ifdef BETA
+        data = MUL_OP(data, beta, DATA_TYPE, 4);
+#endif /* BETA */
+        data = EXP_OP(data, DATA_TYPE, 4);
+        VSTORE(4)
+        (data, 0, (__global DATA_TYPE *)offset(&dst, i * GRID_SIZE * 4, 0));
+        sum1D = ADD_OP(sum1D, data, DATA_TYPE, 4);
+    }
+#ifdef NON_MULTIPLE_OF_GRID_SIZE
+    //TODO: Optimize the calculation (avoid %).
+    boundary_workitems = (width % (GRID_SIZE * 4)) / 4;
+    if(lid < boundary_workitems)
+    {
+        VEC_DATA_TYPE(DATA_TYPE, 4)
+        data = VLOAD(4)(0, (__global DATA_TYPE *)offset(&src, i * GRID_SIZE * 4, 0));
+        data = SUB_OP(data, max_val, DATA_TYPE, 4);
+#ifdef BETA
+        data = MUL_OP(data, beta, DATA_TYPE, 4);
+#endif /* BETA */
+        data = EXP_OP(data, DATA_TYPE, 4);
+        VSTORE(4)
+        (data, 0, (__global DATA_TYPE *)offset(&dst, i * GRID_SIZE * 4, 0));
+        sum1D = ADD_OP(sum1D, data, DATA_TYPE, 4);
+    }
+#ifdef NON_MULTIPLE_OF_VECTOR_SIZE
+    if(boundary_workitems == 0)
+    {
+        boundary_workitems = GRID_SIZE;
+        i--;
+    }
+    if(lid == (boundary_workitems - 1))
+    {
+        // Handle non multiple of vector size ((GRID_SIZE * i * 4) + 4, 0); move 4 float positions ahead, *4 is due to the stride
+        VEC_DATA_TYPE(DATA_TYPE, 4)
+        data = VLOAD(4)(0, (__global DATA_TYPE *)offset(&src, (GRID_SIZE * i * 4) + 4, 0));
+        data = SUB_OP(data, max_val, DATA_TYPE, 4);
+#ifdef BETA
+        data = MUL_OP(data, beta, DATA_TYPE, 4);
+#endif /* BETA */
+        data = EXP_OP(data, DATA_TYPE, 4);
+        VEC_DATA_TYPE(SELECT_DATA_TYPE, 4)
+        widx = CONVERT(((uint4)(GRID_SIZE * i * 4) + boundary_workitems * 4 + idx4) < width, VEC_DATA_TYPE(SELECT_DATA_TYPE, 4));
+        data = select(0, data, widx);
+        VSTORE(4)
+        (data, 0, (__global DATA_TYPE *)offset(&dst, (GRID_SIZE * i * 4) + 4, 0));
+        sum1D = ADD_OP(sum1D, data, DATA_TYPE, 4);
+    }
+#endif /* NON_MULTIPLE_OF_VECTOR_SIZE */
+#endif /* NON_MULTIPLE_OF_GRID_SIZE */
+    tmp_local[lid] = sum1D;
+
+    barrier(CLK_LOCAL_MEM_FENCE);
+
+    if(GRID_SIZE >= 256)
+    {
+        if(lid < 128)
+        {
+            tmp_local[lid] = ADD_OP(tmp_local[lid + 128], tmp_local[lid], DATA_TYPE, 4);
+        }
+        barrier(CLK_LOCAL_MEM_FENCE);
+    }
+    if(GRID_SIZE >= 128)
+    {
+        if(lid < 64)
+        {
+            tmp_local[lid] = ADD_OP(tmp_local[lid + 64], tmp_local[lid], DATA_TYPE, 4);
+        }
+        barrier(CLK_LOCAL_MEM_FENCE);
+    }
+    if(GRID_SIZE >= 64)
+    {
+        if(lid < 32)
+        {
+            tmp_local[lid] = ADD_OP(tmp_local[lid + 32], tmp_local[lid], DATA_TYPE, 4);
+        }
+        barrier(CLK_LOCAL_MEM_FENCE);
+    }
+    if(GRID_SIZE >= 32)
+    {
+        if(lid < 16)
+        {
+            tmp_local[lid] = ADD_OP(tmp_local[lid + 16], tmp_local[lid], DATA_TYPE, 4);
+        }
+        barrier(CLK_LOCAL_MEM_FENCE);
+    }
+    if(GRID_SIZE >= 16)
+    {
+        if(lid < 8)
+        {
+            tmp_local[lid] = ADD_OP(tmp_local[lid + 8], tmp_local[lid], DATA_TYPE, 4);
+        }
+        barrier(CLK_LOCAL_MEM_FENCE);
+    }
+    if(GRID_SIZE >= 8)
+    {
+        if(lid < 4)
+        {
+            tmp_local[lid] = ADD_OP(tmp_local[lid + 4], tmp_local[lid], DATA_TYPE, 4);
+        }
+        barrier(CLK_LOCAL_MEM_FENCE);
+    }
+    if(GRID_SIZE >= 4)
+    {
+        if(lid < 2)
+        {
+            tmp_local[lid] = ADD_OP(tmp_local[lid + 2], tmp_local[lid], DATA_TYPE, 4);
+        }
+        barrier(CLK_LOCAL_MEM_FENCE);
+    }
+    if(lid == 0)
+    {
+        sum1D = ADD_OP(tmp_local[lid + 1], tmp_local[lid], DATA_TYPE, 4);
+        // Perform max reduction
+        sum1D.s01                        = ADD_OP(sum1D.s01, sum1D.s23, DATA_TYPE, 2);
+        sum1D.s0                         = ADD_OP(sum1D.s0, sum1D.s1, DATA_TYPE, 1);
+        *((__global DATA_TYPE *)sum.ptr) = sum1D.s0;
+    }
+}