text: /* ----------------------------------------------------------------------    
  * Copyright (C) 2010-2014 ARM Limited. All rights reserved.    
  *    
  * $Date:        12. March 2014
  * $Revision: 	V1.4.4
  *    
  * Project: 	    CMSIS DSP Library    
  * Title:	    arm_biquad_cascade_df1_f32.c    
  *    
  * Description:	Processing function for the    
  *               floating-point Biquad cascade DirectFormI(DF1) filter.    
  *    
  * Target Processor: Cortex-M4/Cortex-M3/Cortex-M0
  *  
  * Redistribution and use in source and binary forms, with or without 
  * modification, are permitted provided that the following conditions
  * are met:
  *   - Redistributions of source code must retain the above copyright
  *     notice, this list of conditions and the following disclaimer.
  *   - Redistributions in binary form must reproduce the above copyright
  *     notice, this list of conditions and the following disclaimer in
  *     the documentation and/or other materials provided with the 
  *     distribution.
  *   - Neither the name of ARM LIMITED nor the names of its contributors
  *     may be used to endorse or promote products derived from this
  *     software without specific prior written permission.
  *
  * THIS SOFTWARE IS PROVIDED BY THE COPYRIGHT HOLDERS AND CONTRIBUTORS
  * "AS IS" AND ANY EXPRESS OR IMPLIED WARRANTIES, INCLUDING, BUT NOT
  * LIMITED TO, THE IMPLIED WARRANTIES OF MERCHANTABILITY AND FITNESS
  * FOR A PARTICULAR PURPOSE ARE DISCLAIMED. IN NO EVENT SHALL THE 
  * COPYRIGHT OWNER OR CONTRIBUTORS BE LIABLE FOR ANY DIRECT, INDIRECT,
  * INCIDENTAL, SPECIAL, EXEMPLARY, OR CONSEQUENTIAL DAMAGES (INCLUDING,
  * BUT NOT LIMITED TO, PROCUREMENT OF SUBSTITUTE GOODS OR SERVICES;
  * LOSS OF USE, DATA, OR PROFITS; OR BUSINESS INTERRUPTION) HOWEVER
  * CAUSED AND ON ANY THEORY OF LIABILITY, WHETHER IN CONTRACT, STRICT
  * LIABILITY, OR TORT (INCLUDING NEGLIGENCE OR OTHERWISE) ARISING IN
  * ANY WAY OUT OF THE USE OF THIS SOFTWARE, EVEN IF ADVISED OF THE
  * POSSIBILITY OF SUCH DAMAGE. 
  * -------------------------------------------------------------------- */
  
  #include "arm_math.h"
  
  /**    
   * @ingroup groupFilters    
   */
  
  /**    
   * @defgroup BiquadCascadeDF1 Biquad Cascade IIR Filters Using Direct Form I Structure    
   *    
   * This set of functions implements arbitrary order recursive (IIR) filters.    
   * The filters are implemented as a cascade of second order Biquad sections.    
   * The functions support Q15, Q31 and floating-point data types.  
   * Fast version of Q15 and Q31 also supported on CortexM4 and Cortex-M3.    
   *    
   * The functions operate on blocks of input and output data and each call to the function    
   * processes <code>blockSize</code> samples through the filter.    
   * <code>pSrc</code> points to the array of input data and    
   * <code>pDst</code> points to the array of output data.    
   * Both arrays contain <code>blockSize</code> values.    
   *    
   * \par Algorithm    
   * Each Biquad stage implements a second order filter using the difference equation:    
   * <pre>    
   *     y[n] = b0 * x[n] + b1 * x[n-1] + b2 * x[n-2] + a1 * y[n-1] + a2 * y[n-2]    
   * </pre>    
   * A Direct Form I algorithm is used with 5 coefficients and 4 state variables per stage.    
   * \image html Biquad.gif "Single Biquad filter stage"    
   * Coefficients <code>b0, b1 and b2 </code> multiply the input signal <code>x[n]</code> and are referred to as the feedforward coefficients.    
   * Coefficients <code>a1</code> and <code>a2</code> multiply the output signal <code>y[n]</code> and are referred to as the feedback coefficients.    
   * Pay careful attention to the sign of the feedback coefficients.    
   * Some design tools use the difference equation    
   * <pre>    
   *     y[n] = b0 * x[n] + b1 * x[n-1] + b2 * x[n-2] - a1 * y[n-1] - a2 * y[n-2]    
   * </pre>    
   * In this case the feedback coefficients <code>a1</code> and <code>a2</code> must be negated when used with the CMSIS DSP Library.    
   *    
   * \par    
   * Higher order filters are realized as a cascade of second order sections.    
   * <code>numStages</code> refers to the number of second order stages used.    
   * For example, an 8th order filter would be realized with <code>numStages=4</code> second order stages.    
   * \image html BiquadCascade.gif "8th order filter using a cascade of Biquad stages"    
   * A 9th order filter would be realized with <code>numStages=5</code> second order stages with the coefficients for one of the stages configured as a first order filter (<code>b2=0</code> and <code>a2=0</code>).    
   *    
   * \par    
   * The <code>pState</code> points to state variables 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>    
   *    
   * \par    
   * 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 Instance Structure    
   * The coefficients and state variables for a filter are stored together in an instance data structure.    
   * A separate instance structure must be defined for each filter.    
   * Coefficient arrays may be shared among several instances while state variable arrays cannot be shared.    
   * There are separate instance structure declarations for each of the 3 supported data types.    
   *    
   * \par Init Functions    
   * There is also an associated initialization function for each data type.    
   * The initialization function performs following operations:    
   * - Sets the values of the internal structure fields.    
   * - Zeros out the values in the state buffer.    
   * To do this manually without calling the init function, assign the follow subfields of the instance structure:
   * numStages, pCoeffs, pState. Also set all of the values in pState to zero. 
   *    
   * \par    
   * Use of the initialization function is optional.    
   * However, if the initialization function is used, then the instance structure cannot be placed into a const data section.    
   * To place an instance structure into a const data section, the instance structure must be manually initialized.    
   * Set the values in the state buffer to zeros before static initialization.    
   * The code below statically initializes each of the 3 different data type filter instance structures    
   * <pre>    
   *     arm_biquad_casd_df1_inst_f32 S1 = {numStages, pState, pCoeffs};    
   *     arm_biquad_casd_df1_inst_q15 S2 = {numStages, pState, pCoeffs, postShift};    
   *     arm_biquad_casd_df1_inst_q31 S3 = {numStages, pState, pCoeffs, postShift};    
   * </pre>    
   * where <code>numStages</code> is the number of Biquad stages in the filter; <code>pState</code> is the address of the state buffer;    
   * <code>pCoeffs</code> is the address of the coefficient buffer; <code>postShift</code> shift to be applied.    
   *    
   * \par Fixed-Point Behavior    
   * Care must be taken when using the Q15 and Q31 versions of the Biquad Cascade filter functions.    
   * Following issues must be considered:    
   * - Scaling of coefficients    
   * - Filter gain    
   * - Overflow and saturation    
   *    
   * \par    
   * <b>Scaling of coefficients: </b>    
   * Filter coefficients are represented as fractional values and    
   * coefficients are restricted to lie in the range <code>[-1 +1)</code>.    
   * The fixed-point functions have an additional scaling parameter <code>postShift</code>    
   * which allow the filter coefficients to exceed the range <code>[+1 -1)</code>.    
   * At the output of the filter's accumulator is a shift register which shifts the result by <code>postShift</code> bits.    
   * \image html BiquadPostshift.gif "Fixed-point Biquad with shift by postShift bits after accumulator"    
   * This essentially scales the filter coefficients by <code>2^postShift</code>.    
   * For example, to realize the coefficients    
   * <pre>    
   *    {1.5, -0.8, 1.2, 1.6, -0.9}    
   * </pre>    
   * set the pCoeffs array to:    
   * <pre>    
   *    {0.75, -0.4, 0.6, 0.8, -0.45}    
   * </pre>    
   * and set <code>postShift=1</code>    
   *    
   * \par    
   * <b>Filter gain: </b>    
   * The frequency response of a Biquad filter is a function of its coefficients.    
   * It is possible for the gain through the filter to exceed 1.0 meaning that the filter increases the amplitude of certain frequencies.    
   * This means that an input signal with amplitude < 1.0 may result in an output > 1.0 and these are saturated or overflowed based on the implementation of the filter.    
   * To avoid this behavior the filter needs to be scaled down such that its peak gain < 1.0 or the input signal must be scaled down so that the combination of input and filter are never overflowed.    
   *    
   * \par    
   * <b>Overflow and saturation: </b>    
   * For Q15 and Q31 versions, it is described separately as part of the function specific documentation below.    
   */
  
  /**    
   * @addtogroup BiquadCascadeDF1    
   * @{    
   */
  
  /**    
   * @param[in]  *S         points to an instance of the floating-point Biquad cascade structure.    
   * @param[in]  *pSrc      points to the block of input data.    
   * @param[out] *pDst      points to the block of output data.    
   * @param[in]  blockSize  number of samples to process per call.    
   * @return     none.    
   *    
   */
  
  void arm_biquad_cascade_df1_f32(
    const arm_biquad_casd_df1_inst_f32 * S,
    float32_t * pSrc,
    float32_t * pDst,
    uint32_t blockSize)
  {
    float32_t *pIn = pSrc;                         /*  source pointer            */
    float32_t *pOut = pDst;                        /*  destination pointer       */
    float32_t *pState = S->pState;                 /*  pState pointer            */
    float32_t *pCoeffs = S->pCoeffs;               /*  coefficient pointer       */
    float32_t acc;                                 /*  Simulates the accumulator */
    float32_t b0, b1, b2, a1, a2;                  /*  Filter coefficients       */
    float32_t Xn1, Xn2, Yn1, Yn2;                  /*  Filter pState variables   */
    float32_t Xn;                                  /*  temporary input           */
    uint32_t sample, stage = S->numStages;         /*  loop counters             */
  
  
  #ifndef ARM_MATH_CM0_FAMILY
  
    /* Run the below code for Cortex-M4 and Cortex-M3 */
  
    do
    {
      /* Reading the coefficients */
      b0 = *pCoeffs++;
      b1 = *pCoeffs++;
      b2 = *pCoeffs++;
      a1 = *pCoeffs++;
      a2 = *pCoeffs++;
  
      /* Reading the pState values */
      Xn1 = pState[0];
      Xn2 = pState[1];
      Yn1 = pState[2];
      Yn2 = pState[3];
  
      /* Apply loop unrolling and compute 4 output values simultaneously. */
      /*      The variable acc hold output values that are being computed:    
       *    
       *    acc =  b0 * x[n] + b1 * x[n-1] + b2 * x[n-2] + a1 * y[n-1]   + a2 * y[n-2]    
       *    acc =  b0 * x[n] + b1 * x[n-1] + b2 * x[n-2] + a1 * y[n-1]   + a2 * y[n-2]    
       *    acc =  b0 * x[n] + b1 * x[n-1] + b2 * x[n-2] + a1 * y[n-1]   + a2 * y[n-2]    
       *    acc =  b0 * x[n] + b1 * x[n-1] + b2 * x[n-2] + a1 * y[n-1]   + a2 * y[n-2]    
       */
  
      sample = blockSize >> 2u;
  
      /* First part of the processing with loop unrolling.  Compute 4 outputs at a time.    
       ** a second loop below computes the remaining 1 to 3 samples. */
      while(sample > 0u)
      {
        /* Read the first input */
        Xn = *pIn++;
  
        /* acc =  b0 * x[n] + b1 * x[n-1] + b2 * x[n-2] + a1 * y[n-1] + a2 * y[n-2] */
        Yn2 = (b0 * Xn) + (b1 * Xn1) + (b2 * Xn2) + (a1 * Yn1) + (a2 * Yn2);
  
        /* Store the result in the accumulator in the destination buffer. */
        *pOut++ = Yn2;
  
        /* Every time after the output is computed state should be updated. */
        /* The states should be updated as:  */
        /* Xn2 = Xn1    */
        /* Xn1 = Xn     */
        /* Yn2 = Yn1    */
        /* Yn1 = acc   */
  
        /* Read the second input */
        Xn2 = *pIn++;
  
        /* acc =  b0 * x[n] + b1 * x[n-1] + b2 * x[n-2] + a1 * y[n-1] + a2 * y[n-2] */
        Yn1 = (b0 * Xn2) + (b1 * Xn) + (b2 * Xn1) + (a1 * Yn2) + (a2 * Yn1);
  
        /* Store the result in the accumulator in the destination buffer. */
        *pOut++ = Yn1;
  
        /* Every time after the output is computed state should be updated. */
        /* The states should be updated as:  */
        /* Xn2 = Xn1    */
        /* Xn1 = Xn     */
        /* Yn2 = Yn1    */
        /* Yn1 = acc   */
  
        /* Read the third input */
        Xn1 = *pIn++;
  
        /* acc =  b0 * x[n] + b1 * x[n-1] + b2 * x[n-2] + a1 * y[n-1] + a2 * y[n-2] */
        Yn2 = (b0 * Xn1) + (b1 * Xn2) + (b2 * Xn) + (a1 * Yn1) + (a2 * Yn2);
  
        /* Store the result in the accumulator in the destination buffer. */
        *pOut++ = Yn2;
  
        /* Every time after the output is computed state should be updated. */
        /* The states should be updated as: */
        /* Xn2 = Xn1    */
        /* Xn1 = Xn     */
        /* Yn2 = Yn1    */
        /* Yn1 = acc   */
  
        /* Read the forth input */
        Xn = *pIn++;
  
        /* acc =  b0 * x[n] + b1 * x[n-1] + b2 * x[n-2] + a1 * y[n-1] + a2 * y[n-2] */
        Yn1 = (b0 * Xn) + (b1 * Xn1) + (b2 * Xn2) + (a1 * Yn2) + (a2 * Yn1);
  
        /* Store the result in the accumulator in the destination buffer. */
        *pOut++ = Yn1;
  
        /* Every time after the output is computed state should be updated. */
        /* The states should be updated as:  */
        /* Xn2 = Xn1    */
        /* Xn1 = Xn     */
        /* Yn2 = Yn1    */
        /* Yn1 = acc   */
        Xn2 = Xn1;
        Xn1 = Xn;
  
        /* decrement the loop counter */
        sample--;
  
      }
  
      /* If the blockSize is not a multiple of 4, compute any remaining output samples here.    
       ** No loop unrolling is used. */
      sample = blockSize & 0x3u;
  
      while(sample > 0u)
      {
        /* Read the input */
        Xn = *pIn++;
  
        /* acc =  b0 * x[n] + b1 * x[n-1] + b2 * x[n-2] + a1 * y[n-1] + a2 * y[n-2] */
        acc = (b0 * Xn) + (b1 * Xn1) + (b2 * Xn2) + (a1 * Yn1) + (a2 * Yn2);
  
        /* Store the result in the accumulator in the destination buffer. */
        *pOut++ = acc;
  
        /* Every time after the output is computed state should be updated. */
        /* The states should be updated as:    */
        /* Xn2 = Xn1    */
        /* Xn1 = Xn     */
        /* Yn2 = Yn1    */
        /* Yn1 = acc   */
        Xn2 = Xn1;
        Xn1 = Xn;
        Yn2 = Yn1;
        Yn1 = acc;
  
        /* decrement the loop counter */
        sample--;
  
      }
  
      /*  Store the updated state variables back into the pState array */
      *pState++ = Xn1;
      *pState++ = Xn2;
      *pState++ = Yn1;
      *pState++ = Yn2;
  
      /*  The first stage goes from the input buffer to the output buffer. */
      /*  Subsequent numStages  occur in-place in the output buffer */
      pIn = pDst;
  
      /* Reset the output pointer */
      pOut = pDst;
  
      /* decrement the loop counter */
      stage--;
  
    } while(stage > 0u);
  
  #else
  
    /* Run the below code for Cortex-M0 */
  
    do
    {
      /* Reading the coefficients */
      b0 = *pCoeffs++;
      b1 = *pCoeffs++;
      b2 = *pCoeffs++;
      a1 = *pCoeffs++;
      a2 = *pCoeffs++;
  
      /* Reading the pState values */
      Xn1 = pState[0];
      Xn2 = pState[1];
      Yn1 = pState[2];
      Yn2 = pState[3];
  
      /*      The variables acc holds the output value that is computed:        
       *    acc =  b0 * x[n] + b1 * x[n-1] + b2 * x[n-2] + a1 * y[n-1]   + a2 * y[n-2]        
       */
  
      sample = blockSize;
  
      while(sample > 0u)
      {
        /* Read the input */
        Xn = *pIn++;
  
        /* acc =  b0 * x[n] + b1 * x[n-1] + b2 * x[n-2] + a1 * y[n-1] + a2 * y[n-2] */
        acc = (b0 * Xn) + (b1 * Xn1) + (b2 * Xn2) + (a1 * Yn1) + (a2 * Yn2);
  
        /* Store the result in the accumulator in the destination buffer. */
        *pOut++ = acc;
  
        /* Every time after the output is computed state should be updated. */
        /* The states should be updated as:    */
        /* Xn2 = Xn1    */
        /* Xn1 = Xn     */
        /* Yn2 = Yn1    */
        /* Yn1 = acc   */
        Xn2 = Xn1;
        Xn1 = Xn;
        Yn2 = Yn1;
        Yn1 = acc;
  
        /* decrement the loop counter */
        sample--;
      }
  
      /*  Store the updated state variables back into the pState array */
      *pState++ = Xn1;
      *pState++ = Xn2;
      *pState++ = Yn1;
      *pState++ = Yn2;
  
      /*  The first stage goes from the input buffer to the output buffer. */
      /*  Subsequent numStages  occur in-place in the output buffer */
      pIn = pDst;
  
      /* Reset the output pointer */
      pOut = pDst;
  
      /* decrement the loop counter */
      stage--;
  
    } while(stage > 0u);
  
  #endif /*   #ifndef ARM_MATH_CM0_FAMILY         */
  
  }
  
  
    /**    
     * @} end of BiquadCascadeDF1 group    
     */
  