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/* ----------------------------------------------------------------------    
* Copyright (C) 2010 ARM Limited. All rights reserved.    
*    
* $Date:        15. February 2012  
* $Revision:     V1.1.0  
*    
* 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 1.1.0 2012/02/15 
*    Updated with more optimizations, bug fixes and minor API changes.  
*   
* 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    
* -------------------------------------------------------------------- */

#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;                                /*  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

  float32_t Xn1, Xn2;                            /*  Input State variables     */
  float32_t acc1;                                /*  accumulator               */



  /* 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)
    {

      /* y[n] = b0 * x[n] + d1 */
      /* d1 = b1 * x[n] + a1 * y[n] + d2 */
      /* d2 = b2 * x[n] + a2 * y[n] */

      /* Read the first input */
      Xn1 = *pIn++;

      /* y[n] = b0 * x[n] + d1 */
      acc0 = (b0 * Xn1) + d1;

      /* d1 = b1 * x[n] + d2 */
      d1 = (b1 * Xn1) + d2;

      /* d2 = b2 * x[n] */
      d2 = (b2 * Xn1);

      /* Read the second input */
      Xn2 = *pIn++;

      /* d1 = b1 * x[n] + a1 * y[n] */
      d1 = (a1 * acc0) + d1;

      /* Store the result in the accumulator in the destination buffer. */
      *pOut++ = acc0;

      d2 = (a2 * acc0) + d2;

      /* y[n] = b0 * x[n] + d1 */
      acc1 = (b0 * Xn2) + d1;

      /* Read the third input */
      Xn1 = *pIn++;

      d1 = (b1 * Xn2) + d2;

      d2 = (b2 * Xn2);

      /* Store the result in the accumulator in the destination buffer. */
      *pOut++ = acc1;

      d1 = (a1 * acc1) + d1;

      d2 = (a2 * acc1) + d2;

      /* y[n] = b0 * x[n] + d1 */
      acc0 = (b0 * Xn1) + d1;

      d1 = (b1 * Xn1) + d2;

      d2 = (b2 * Xn1);

      /* Read the fourth input */
      Xn2 = *pIn++;

      d1 = (a1 * acc0) + d1;

      /* Store the result in the accumulator in the destination buffer. */
      *pOut++ = acc0;

      d2 = (a2 * acc0) + d2;

      /* y[n] = b0 * x[n] + d1 */
      acc1 = (b0 * Xn2) + d1;

      d1 = (b1 * Xn2) + d2;

      d2 = (b2 * Xn2);

      /* Store the result in the accumulator in the destination buffer. */
      *pOut++ = acc1;

      d1 = (a1 * acc1) + d1;

      d2 = (a2 * acc1) + d2;

      /* 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       
   */