text: /*
   * Copyright (C) 2010-2018 Arm Limited or its affiliates. All rights reserved.
   *
   * SPDX-License-Identifier: Apache-2.0
   *
   * Licensed under the Apache License, Version 2.0 (the License); you may
   * not use this file except in compliance with the License.
   * You may obtain a copy of the License at
   *
   * www.apache.org/licenses/LICENSE-2.0
   *
   * Unless required by applicable law or agreed to in writing, software
   * distributed under the License is distributed on an AS IS BASIS, WITHOUT
   * WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied.
   * See the License for the specific language governing permissions and
   * limitations under the License.
   */
  
  /* ----------------------------------------------------------------------
   * Project:      CMSIS NN Library
   * Title:        arm_softmax_q15.c
   * Description:  Q15 softmax function
   *
   * $Date:        20. February 2018
   * $Revision:    V.1.0.0
   *
   * Target Processor:  Cortex-M cores
   *
   * -------------------------------------------------------------------- */
  
  #include "arm_math.h"
  #include "arm_nnfunctions.h"
  
  /**
   *  @ingroup groupNN
   */
  
  /**
   * @addtogroup Softmax
   * @{
   */
  
  /**
   * @brief Q15 softmax function
   * @param[in]       vec_in      pointer to input vector
   * @param[in]       dim_vec     input vector dimention
   * @param[out]      p_out       pointer to output vector
   * @return none.
   *
   * @details
   *
   *  Here, instead of typical e based softmax, we use
   *  2-based softmax, i.e.,:
   *
   *  y_i = 2^(x_i) / sum(2^x_j)
   *
   *  The relative output will be different here.
   *  But mathematically, the gradient will be the same
   *  with a log(2) scaling factor.
   *
   */
  
  void arm_softmax_q15(const q15_t* vec_in, const uint16_t dim_vec, q15_t* p_out)
  {
      q31_t   sum;
      int16_t i;
      uint8_t shift;
      q31_t   base;
      base = -1 * 0x100000;
      for (i = 0; i < dim_vec; i++) {
          if (vec_in[i] > base) {
              base = vec_in[i];
          }
      }
  
      /* we ignore really small values
       * anyway, they will be 0 after shrinking
       * to q15_t
       */
      base = base - 16;
  
      sum = 0;
  
      for (i = 0; i < dim_vec; i++) {
          if (vec_in[i] > base) {
              shift = (uint8_t)__USAT(vec_in[i] - base, 5);
              sum += 0x1 << shift;
          }
      }
  
      /* This is effectively (0x1 << 32) / sum */
      int64_t div_base    = 0x100000000LL;
      int     output_base = (int32_t)(div_base / sum);
  
      /* Final confidence will be output_base >> ( 17 - (vec_in[i] - base) )
       * so 32768 (0x1<<15) -> 100% confidence when sum = 0x1 << 16, output_base = 0x1 << 16
       * and vec_in[i]-base = 16
       */
      for (i = 0; i < dim_vec; i++) {
          if (vec_in[i] > base) {
              /* Here minimum value of 17+base-vec[i] will be 1 */
              shift    = (uint8_t)__USAT(17 + base - vec_in[i], 5);
              p_out[i] = (q15_t)__SSAT((output_base >> shift), 16);
          } else {
              p_out[i] = 0;
          }
      }
  }
  
  /**
   * @} end of Softmax group
   */
  