text: /* ----------------------------------------------------------------------   
  * Copyright (C) 2010 ARM Limited. All rights reserved.   
  *   
  * $Date:        15. July 2011  
  * $Revision: 	V1.0.10  
  *   
  * Project: 	    CMSIS DSP Library   
  * Title:	    arm_biquad_cascade_df2T_f32.c   
  *   
  * Description:  Processing function for the floating-point transposed   
  *               direct form II Biquad cascade filter.  
  *   
  * Target Processor: Cortex-M4/Cortex-M3/Cortex-M0
  *  
  * Version 1.0.10 2011/7/15 
  *    Big Endian support added and Merged M0 and M3/M4 Source code.  
  *   
  * Version 1.0.3 2010/11/29  
  *    Re-organized the CMSIS folders and updated documentation.   
  *    
  * Version 1.0.2 2010/11/11   
  *    Documentation updated.    
  *   
  * Version 1.0.1 2010/10/05    
  *    Production release and review comments incorporated.   
  *   
  * Version 1.0.0 2010/09/20    
  *    Production release and review comments incorporated   
  *   
  * Version 0.0.7  2010/06/10    
  *    Misra-C changes done   
  * -------------------------------------------------------------------- */
   /**
   * Support and FAQ: visit <a href="http://www.atmel.com/design-support/">Atmel Support</a>
   */
  
  #include "arm_math.h"
  
  /**   
   * @ingroup groupFilters   
   */
  
  /**   
   * @defgroup BiquadCascadeDF2T Biquad Cascade IIR Filters Using a Direct Form II Transposed Structure   
   *   
   * This set of functions implements arbitrary order recursive (IIR) filters using a transposed direct form II structure.   
   * The filters are implemented as a cascade of second order Biquad sections.   
   * These functions provide a slight memory savings as compared to the direct form I Biquad filter functions.  
   * Only floating-point data is supported.   
   *   
   * This function 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] + d1   
   *    d1 = b1 * x[n] + a1 * y[n] + d2   
   *    d2 = b2 * x[n] + a2 * y[n]   
   * </pre>   
   * where d1 and d2 represent the two state values.   
   *   
   * \par   
   * A Biquad filter using a transposed Direct Form II structure is shown below.   
   * \image html BiquadDF2Transposed.gif "Single transposed Direct Form II Biquad"   
   * 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 flip the sign of the feedback coefficients:   
   * <pre>   
   *    y[n] = b0 * x[n] + d1;   
   *    d1 = b1 * x[n] - a1 * y[n] + d2;   
   *    d2 = b2 * x[n] - a2 * y[n];   
   * </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.   
   * 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   
   * <code>pState</code> points to the state variable array.   
   * Each Biquad stage has 2 state variables <code>d1</code> and <code>d2</code>.   
   * The state variables are arranged in the <code>pState</code> array as:   
   * <pre>   
   *     {d11, d12, d21, d22, ...}   
   * </pre>   
   * where <code>d1x</code> refers to the state variables for the first Biquad and   
   * <code>d2x</code> refers to the state variables for the second Biquad.   
   * The state array has a total length of <code>2*numStages</code> values.   
   * The state variables are updated after each block of data is processed; the coefficients are untouched.   
   *   
   * \par   
   * The CMSIS library contains Biquad filters in both Direct Form I and transposed Direct Form II.   
   * The advantage of the Direct Form I structure is that it is numerically more robust for fixed-point data types.   
   * That is why the Direct Form I structure supports Q15 and Q31 data types.   
   * The transposed Direct Form II structure, on the other hand, requires a wide dynamic range for the state variables <code>d1</code> and <code>d2</code>.   
   * Because of this, the CMSIS library only has a floating-point version of the Direct Form II Biquad.   
   * The advantage of the Direct Form II Biquad is that it requires half the number of state variables, 2 rather than 4, per Biquad stage.   
   *   
   * \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.   
   *   
   * \par Init Functions   
   * There is also an associated initialization function.  
   * The initialization function performs following operations:   
   * - Sets the values of the internal structure fields.   
   * - Zeros out the values in the state buffer.   
   *   
   * \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.   
   * For example, to statically initialize the instance structure use   
   * <pre>   
   *     arm_biquad_cascade_df2T_instance_f32 S1 = {numStages, pState, pCoeffs};   
   * </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;    
   *   
   */
  
  /**   
   * @addtogroup BiquadCascadeDF2T   
   * @{   
   */
  
  /**  
   * @brief Processing function for the floating-point transposed direct form II Biquad cascade filter.  
   * @param[in]  *S        points to an instance of the filter data 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.  
   * @return none.  
   */
  
  void arm_biquad_cascade_df2T_f32(
    const arm_biquad_cascade_df2T_instance_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;                 /*  State pointer            */
    float32_t *pCoeffs = S->pCoeffs;               /*  coefficient pointer       */
    float32_t acc0;                                /*  Simulates the accumulator */
    float32_t b0, b1, b2, a1, a2;                  /*  Filter coefficients       */
    float32_t Xn;                                  /*  temporary input           */
    float32_t d1, d2;                              /*  state variables          */
    uint32_t sample, stage = S->numStages;         /*  loop counters             */
  
  
  #ifndef ARM_MATH_CM0
  
    /* 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 state values */
      d1 = pState[0];
      d2 = pState[1];
  
      /* Apply loop unrolling and compute 4 output values simultaneously. */
      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++;
  
        /* y[n] = b0 * x[n] + d1 */
        acc0 = (b0 * Xn) + d1;
  
        /* Store the result in the accumulator in the destination buffer. */
        *pOut++ = acc0;
  
        /* Every time after the output is computed state should be updated. */
        /* d1 = b1 * x[n] + a1 * y[n] + d2 */
        d1 = ((b1 * Xn) + (a1 * acc0)) + d2;
  
        /* d2 = b2 * x[n] + a2 * y[n] */
        d2 = (b2 * Xn) + (a2 * acc0);
  
        /* Read the second input */
        Xn = *pIn++;
  
        /* y[n] = b0 * x[n] + d1 */
        acc0 = (b0 * Xn) + d1;
  
        /* Store the result in the accumulator in the destination buffer. */
        *pOut++ = acc0;
  
        /* Every time after the output is computed state should be updated. */
        /* d1 = b1 * x[n] + a1 * y[n] + d2 */
        d1 = ((b1 * Xn) + (a1 * acc0)) + d2;
  
        /* d2 = b2 * x[n] + a2 * y[n] */
        d2 = (b2 * Xn) + (a2 * acc0);
  
        /* Read the third input */
        Xn = *pIn++;
  
        /* y[n] = b0 * x[n] + d1 */
        acc0 = (b0 * Xn) + d1;
  
        /* Store the result in the accumulator in the destination buffer. */
        *pOut++ = acc0;
  
        /* Every time after the output is computed state should be updated. */
        /* d1 = b1 * x[n] + a1 * y[n] + d2 */
        d1 = ((b1 * Xn) + (a1 * acc0)) + d2;
  
        /* d2 = b2 * x[n] + a2 * y[n] */
        d2 = (b2 * Xn) + (a2 * acc0);
  
        /* Read the fourth input */
        Xn = *pIn++;
  
        /* y[n] = b0 * x[n] + d1 */
        acc0 = (b0 * Xn) + d1;
  
        /* Store the result in the accumulator in the destination buffer. */
        *pOut++ = acc0;
  
        /* Every time after the output is computed state should be updated. */
        /* d1 = b1 * x[n] + a1 * y[n] + d2 */
        d1 = (b1 * Xn) + (a1 * acc0) + d2;
  
        /* d2 = b2 * x[n] + a2 * y[n] */
        d2 = (b2 * Xn) + (a2 * acc0);
  
        /* 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++;
  
        /* y[n] = b0 * x[n] + d1 */
        acc0 = (b0 * Xn) + d1;
  
        /* Store the result in the accumulator in the destination buffer. */
        *pOut++ = acc0;
  
        /* Every time after the output is computed state should be updated. */
        /* d1 = b1 * x[n] + a1 * y[n] + d2 */
        d1 = ((b1 * Xn) + (a1 * acc0)) + d2;
  
        /* d2 = b2 * x[n] + a2 * y[n] */
        d2 = (b2 * Xn) + (a2 * acc0);
  
        /* decrement the loop counter */
        sample--;
      }
  
      /* Store the updated state variables back into the state array */
      *pState++ = d1;
      *pState++ = d2;
  
      /* The current stage input is given as the output to the next stage */
      pIn = pDst;
  
      /*Reset the output working 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 state values */
      d1 = pState[0];
      d2 = pState[1];
  
  
      sample = blockSize;
  
      while(sample > 0u)
      {
        /* Read the input */
        Xn = *pIn++;
  
        /* y[n] = b0 * x[n] + d1 */
        acc0 = (b0 * Xn) + d1;
  
        /* Store the result in the accumulator in the destination buffer. */
        *pOut++ = acc0;
  
        /* Every time after the output is computed state should be updated. */
        /* d1 = b1 * x[n] + a1 * y[n] + d2 */
        d1 = ((b1 * Xn) + (a1 * acc0)) + d2;
  
        /* d2 = b2 * x[n] + a2 * y[n] */
        d2 = (b2 * Xn) + (a2 * acc0);
  
        /* decrement the loop counter */
        sample--;
      }
  
      /* Store the updated state variables back into the state array */
      *pState++ = d1;
      *pState++ = d2;
  
      /* The current stage input is given as the output to the next stage */
      pIn = pDst;
  
      /*Reset the output working pointer */
      pOut = pDst;
  
      /* decrement the loop counter */
      stage--;
  
    } while(stage > 0u);
  
  #endif /*  #ifndef ARM_MATH_CM0         */
  
  }
  
  
    /**   
     * @} end of BiquadCascadeDF2T group   
     */
  