text: /* ----------------------------------------------------------------------
   * Project:      CMSIS DSP Library
   * Title:        arm_biquad_cascade_df1_init_f16.c
   * Description:  Floating-point Biquad cascade DirectFormI(DF1) filter initialization function
   *
   * $Date:        23 April 2021
   * $Revision:    V1.9.0
   *
   * Target Processor: Cortex-M and Cortex-A cores
   * -------------------------------------------------------------------- */
  /*
   * Copyright (C) 2010-2021 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.
   */
  
  #include "dsp/filtering_functions_f16.h"
  
  #if defined(ARM_FLOAT16_SUPPORTED)
  /**
    @ingroup groupFilters
   */
  
  /**
    @addtogroup BiquadCascadeDF1
    @{
   */
  
  /**
    @brief         Initialization function for the floating-point Biquad cascade filter.
    @param[in,out] S           points to an instance of the floating-point Biquad cascade structure.
    @param[in]     numStages   number of 2nd order stages in the filter.
    @param[in]     pCoeffs     points to the filter coefficients.
    @param[in]     pState      points to the state buffer.
    @return        none
  
    @par           Coefficient and State Ordering
                     The coefficients are stored in the array <code>pCoeffs</code> in the following order:
    <pre>
        {b10, b11, b12, a11, a12, b20, b21, b22, a21, a22, ...}
    </pre>
  
    @par
                     where <code>b1x</code> and <code>a1x</code> are the coefficients for the first stage,
                     <code>b2x</code> and <code>a2x</code> are the coefficients for the second stage,
                     and so on. The <code>pCoeffs</code> array contains a total of <code>5*numStages</code> values.
    @par
                     The <code>pState</code> is a pointer to state array.
                     Each Biquad stage has 4 state variables <code>x[n-1], x[n-2], y[n-1],</code> and <code>y[n-2]</code>.
                     The state variables are arranged in the <code>pState</code> array as:
    <pre>
        {x[n-1], x[n-2], y[n-1], y[n-2]}
    </pre>
                     The 4 state variables for stage 1 are first, then the 4 state variables for stage 2, and so on.
                     The state array has a total length of <code>4*numStages</code> values.
                     The state variables are updated after each block of data is processed; the coefficients are untouched.
   
    @par             For MVE code, an additional buffer of modified coefficients is required.
                     Its size is numStages and each element of this buffer has type arm_biquad_mod_coef_f16.
                     So, its total size is 96*numStages float16_t elements.
  
                     The initialization function which must be used is arm_biquad_cascade_df1_mve_init_f16.
   */
  
  
  void arm_biquad_cascade_df1_init_f16(
          arm_biquad_casd_df1_inst_f16 * S,
          uint8_t numStages,
    const float16_t * pCoeffs,
          float16_t * pState)
  {
    /* Assign filter stages */
    S->numStages = numStages;
  
    /* Assign coefficient pointer */
    S->pCoeffs = pCoeffs;
  
    /* Clear state buffer and size is always 4 * numStages */
    memset(pState, 0, (4U * (uint32_t) numStages) * sizeof(float16_t));
  
    /* Assign state pointer */
    S->pState = pState;
  }
  
  #if defined(ARM_MATH_MVE_FLOAT16) && !defined(ARM_MATH_AUTOVECTORIZE)
  
  /*
  
  The computation of the coefficients is done in float32 otherwise the
  resulting filter is too different from the expected one.
  
  */
  static void generateCoefsFastBiquadF16(float16_t b0, float16_t b1, float16_t b2, float16_t a1, float16_t a2,
                                  arm_biquad_mod_coef_f16 * newCoef)
  {
      float32_t coeffs[8][12] = {
          {0.0f, 0.0f, 0.0f, 0.0f, 0.0f, 0.0f, 0.0f, (float32_t)b0, (float32_t)b1, (float32_t)b2, (float32_t)a1, (float32_t)a2},
          {0.0f, 0.0f, 0.0f, 0.0f, 0.0f, 0.0f, (float32_t)b0, (float32_t)b1, (float32_t)b2, 0.0f, (float32_t)a2, 0.0f},
          {0.0f, 0.0f, 0.0f, 0.0f, 0.0f, (float32_t)b0, (float32_t)b1, (float32_t)b2, 0.0f, 0.0f, 0.0f, 0.0f},
          {0.0f, 0.0f, 0.0f, 0.0f, (float32_t)b0, (float32_t)b1, (float32_t)b2, 0.0f, 0.0f, 0.0f, 0.0f, 0.0f},
          {0.0f, 0.0f, 0.0f, (float32_t)b0, (float32_t)b1, (float32_t)b2, 0.0f, 0.0f, 0.0f, 0.0f, 0.0f, 0.0f},
          {0.0f, 0.0f, (float32_t)b0, (float32_t)b1, (float32_t)b2, 0.0f, 0.0f, 0.0f, 0.0f, 0.0f, 0.0f, 0.0f},
          {0.0f, (float32_t)b0, (float32_t)b1, (float32_t)b2, 0.0f, 0.0f, 0.0f, 0.0f, 0.0f, 0.0f, 0.0f, 0.0f},
          {(float32_t)b0, (float32_t)b1, (float32_t)b2, 0.0f, 0.0f, 0.0f, 0.0f, 0.0f, 0.0f, 0.0f, 0.0f, 0.0f}
      };
  
      for (int i = 0; i < 12; i++)
      {
          coeffs[1][i] += ((float32_t)a1 * coeffs[0][i]);
          coeffs[2][i] += ((float32_t)a1 * coeffs[1][i]) + ((float32_t)a2 * coeffs[0][i]);
          coeffs[3][i] += ((float32_t)a1 * coeffs[2][i]) + ((float32_t)a2 * coeffs[1][i]);
          coeffs[4][i] += ((float32_t)a1 * coeffs[3][i]) + ((float32_t)a2 * coeffs[2][i]);
          coeffs[5][i] += ((float32_t)a1 * coeffs[4][i]) + ((float32_t)a2 * coeffs[3][i]);
          coeffs[6][i] += ((float32_t)a1 * coeffs[5][i]) + ((float32_t)a2 * coeffs[4][i]);
          coeffs[7][i] += ((float32_t)a1 * coeffs[6][i]) + ((float32_t)a2 * coeffs[5][i]);
  
          /*
           * transpose
           */
          newCoef->coeffs[i][0] = (float16_t) coeffs[0][i];
          newCoef->coeffs[i][1] = (float16_t) coeffs[1][i];
          newCoef->coeffs[i][2] = (float16_t) coeffs[2][i];
          newCoef->coeffs[i][3] = (float16_t) coeffs[3][i];
          newCoef->coeffs[i][4] = (float16_t) coeffs[4][i];
          newCoef->coeffs[i][5] = (float16_t) coeffs[5][i];
          newCoef->coeffs[i][6] = (float16_t) coeffs[6][i];
          newCoef->coeffs[i][7] = (float16_t) coeffs[7][i];
  
      }
  }
  
  void arm_biquad_cascade_df1_mve_init_f16(arm_biquad_casd_df1_inst_f16 * S,
                                           uint8_t numStages,
                                           const float16_t * pCoeffs, 
                                           arm_biquad_mod_coef_f16 * pCoeffsMod, 
                                           float16_t * pState)
  {
      arm_biquad_cascade_df1_init_f16(S, numStages, (float16_t *)pCoeffsMod, pState);
  
      /* Generate SIMD friendly modified coefs */
      for (int i = 0; i < numStages; i++)
      {
          generateCoefsFastBiquadF16(pCoeffs[0], pCoeffs[1], pCoeffs[2], pCoeffs[3], pCoeffs[4], pCoeffsMod);
          pCoeffs += 5;
          pCoeffsMod++;
      }
  }
  
  #endif
  
  /**
    @} end of BiquadCascadeDF1 group
   */
  #endif /* #if defined(ARMfloat16_t_SUPPORTED) */
  