DSP/Source/FilteringFunctions/arm_lms_f32.c - third_party/github/STMicroelectronics/cmsis_core - Git at Google

 /* ----------------------------------------------------------------------
  * Project:      CMSIS DSP Library
  * Title:        arm_lms_f32.c
  * Description:  Processing function for the floating-point LMS filter
  *
  * $Date:        18. March 2019
  * $Revision:    V1.6.0
  *
  * Target Processor: Cortex-M cores
  * -------------------------------------------------------------------- */
 /*
  * Copyright (C) 2010-2019 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 "arm_math.h"

 /**
   @ingroup groupFilters
  */

 /**
   @defgroup LMS Least Mean Square (LMS) Filters

   LMS filters are a class of adaptive filters that are able to "learn" an unknown transfer functions.
   LMS filters use a gradient descent method in which the filter coefficients are updated based on the instantaneous error signal.
   Adaptive filters are often used in communication systems, equalizers, and noise removal.
   The CMSIS DSP Library contains LMS filter functions that operate on Q15, Q31, and floating-point data types.
   The library also contains normalized LMS filters in which the filter coefficient adaptation is indepedent of the level of the input signal.

   An LMS filter consists of two components as shown below.
   The first component is a standard transversal or FIR filter.
   The second component is a coefficient update mechanism.
   The LMS filter has two input signals.
   The "input" feeds the FIR filter while the "reference input" corresponds to the desired output of the FIR filter.
   That is, the FIR filter coefficients are updated so that the output of the FIR filter matches the reference input.
   The filter coefficient update mechanism is based on the difference between the FIR filter output and the reference input.
   This "error signal" tends towards zero as the filter adapts.
   The LMS processing functions accept the input and reference input signals and generate the filter output and error signal.
   \image html LMS.gif "Internal structure of the Least Mean Square filter"

   The functions operate on blocks of data and each call to the function processes
   <code>blockSize</code> samples through the filter.
   <code>pSrc</code> points to input signal, <code>pRef</code> points to reference signal,
   <code>pOut</code> points to output signal and <code>pErr</code> points to error signal.
   All arrays contain <code>blockSize</code> values.

   The functions operate on a block-by-block basis.
   Internally, the filter coefficients <code>b[n]</code> are updated on a sample-by-sample basis.
   The convergence of the LMS filter is slower compared to the normalized LMS algorithm.

   @par           Algorithm
                    The output signal <code>y[n]</code> is computed by a standard FIR filter:
   <pre>
       y[n] = b[0] * x[n] + b[1] * x[n-1] + b[2] * x[n-2] + ...+ b[numTaps-1] * x[n-numTaps+1]
   </pre>

   @par
                    The error signal equals the difference between the reference signal <code>d[n]</code> and the filter output:
   <pre>
       e[n] = d[n] - y[n].
   </pre>

   @par
                    After each sample of the error signal is computed, the filter coefficients <code>b[k]</code> are updated on a sample-by-sample basis:
   <pre>
       b[k] = b[k] + e[n] * mu * x[n-k],  for k=0, 1, ..., numTaps-1
   </pre>
                    where <code>mu</code> is the step size and controls the rate of coefficient convergence.
   @par
                    In the APIs, <code>pCoeffs</code> points to a coefficient array of size <code>numTaps</code>.
                    Coefficients are stored in time reversed order.
   @par
   <pre>
      {b[numTaps-1], b[numTaps-2], b[N-2], ..., b[1], b[0]}
   </pre>
   @par
                    <code>pState</code> points to a state array of size <code>numTaps + blockSize - 1</code>.
                    Samples in the state buffer are stored in the order:
   @par
   <pre>
      {x[n-numTaps+1], x[n-numTaps], x[n-numTaps-1], x[n-numTaps-2]....x[0], x[1], ..., x[blockSize-1]}
   </pre>
   @par
                    Note that the length of the state buffer exceeds the length of the coefficient array by <code>blockSize-1</code> samples.
                    The increased state buffer length allows circular addressing, which is traditionally used in FIR filters,
                    to be avoided and yields a significant speed improvement.
                    The state variables are updated after each block of data is processed.
   @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 and
                    coefficient and state arrays cannot be shared among instances.
                    There are separate instance structure declarations for each of the 3 supported data types.

   @par           Initialization Functions
                    There is also an associated initialization function for each data type.
                    The initialization function performs the 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:
                    numTaps, pCoeffs, mu, postShift (not for f32), 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_lms_instance_f32 S = {numTaps, pState, pCoeffs, mu};
      arm_lms_instance_q31 S = {numTaps, pState, pCoeffs, mu, postShift};
      arm_lms_instance_q15 S = {numTaps, pState, pCoeffs, mu, postShift};
   </pre>
                  where <code>numTaps</code> is the number of filter coefficients in the filter; <code>pState</code> is the address of the state buffer;
                  <code>pCoeffs</code> is the address of the coefficient buffer; <code>mu</code> is the step size parameter; and <code>postShift</code> is the shift applied to coefficients.

   @par           Fixed-Point Behavior
                    Care must be taken when using the Q15 and Q31 versions of the LMS filter.
                    The following issues must be considered:
                    - Scaling of coefficients
                    - Overflow and saturation

   @par           Scaling of Coefficients
                    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>.
                    At the output of the filter's accumulator is a shift register which shifts the result by <code>postShift</code> bits.
                    This essentially scales the filter coefficients by <code>2^postShift</code> and
                    allows the filter coefficients to exceed the range <code>[+1 -1)</code>.
                    The value of <code>postShift</code> is set by the user based on the expected gain through the system being modeled.

   @par           Overflow and Saturation
                    Overflow and saturation behavior of the fixed-point Q15 and Q31 versions are
                    described separately as part of the function specific documentation below.
  */

 /**
   @addtogroup LMS
   @{
  */

 /**
   @brief         Processing function for floating-point LMS filter.
   @param[in]     S          points to an instance of the floating-point LMS filter structure
   @param[in]     pSrc       points to the block of input data
   @param[in]     pRef       points to the block of reference data
   @param[out]    pOut       points to the block of output data
   @param[out]    pErr       points to the block of error data
   @param[in]     blockSize  number of samples to process
   @return        none
  */
 #if defined(ARM_MATH_NEON)
 void arm_lms_f32(
   const arm_lms_instance_f32 * S,
   const float32_t * pSrc,
   float32_t * pRef,
   float32_t * pOut,
   float32_t * pErr,
   uint32_t blockSize)
 {
   float32_t *pState = S->pState;                 /* State pointer */
   float32_t *pCoeffs = S->pCoeffs;               /* Coefficient pointer */
   float32_t *pStateCurnt;                        /* Points to the current sample of the state */
   float32_t *px, *pb;                            /* Temporary pointers for state and coefficient buffers */
   float32_t mu = S->mu;                          /* Adaptive factor */
   uint32_t numTaps = S->numTaps;                 /* Number of filter coefficients in the filter */
   uint32_t tapCnt, blkCnt;                       /* Loop counters */
   float32_t sum, e, d;                           /* accumulator, error, reference data sample */
   float32_t w = 0.0f;                            /* weight factor */

   float32x4_t tempV, sumV, xV, bV;
   float32x2_t tempV2;

   e = 0.0f;
   d = 0.0f;

   /* S->pState points to state array which contains previous frame (numTaps - 1) samples */
   /* pStateCurnt points to the location where the new input data should be written */
   pStateCurnt = &(S->pState[(numTaps - 1U)]);

   blkCnt = blockSize;

   while (blkCnt > 0U)
   {
     /* Copy the new input sample into the state buffer */
     *pStateCurnt++ = *pSrc++;

     /* Initialize pState pointer */
     px = pState;

     /* Initialize coeff pointer */
     pb = (pCoeffs);

     /* Set the accumulator to zero */
     sum = 0.0f;
     sumV = vdupq_n_f32(0.0);

     /* Process 4 taps at a time. */
     tapCnt = numTaps >> 2;

     while (tapCnt > 0U)
     {
       /* Perform the multiply-accumulate */
       xV = vld1q_f32(px);
       bV = vld1q_f32(pb);
       sumV = vmlaq_f32(sumV, xV, bV);

       px += 4;
       pb += 4;

       /* Decrement the loop counter */
       tapCnt--;
     }
     tempV2 = vpadd_f32(vget_low_f32(sumV),vget_high_f32(sumV));
     sum = tempV2[0] + tempV2[1];


     /* If the filter length is not a multiple of 4, compute the remaining filter taps */
     tapCnt = numTaps % 0x4U;

     while (tapCnt > 0U)
     {
       /* Perform the multiply-accumulate */
       sum += (*px++) * (*pb++);

       /* Decrement the loop counter */
       tapCnt--;
     }

     /* The result in the accumulator, store in the destination buffer. */
     *pOut++ = sum;

     /* Compute and store error */
     d = (float32_t) (*pRef++);
     e = d - sum;
     *pErr++ = e;

     /* Calculation of Weighting factor for the updating filter coefficients */
     w = e * mu;

     /* Initialize pState pointer */
     px = pState;

     /* Initialize coeff pointer */
     pb = (pCoeffs);

     /* Process 4 taps at a time. */
     tapCnt = numTaps >> 2;

     /* Update filter coefficients */
     while (tapCnt > 0U)
     {
       /* Perform the multiply-accumulate */
       xV = vld1q_f32(px);
       bV = vld1q_f32(pb);
       px += 4;
       bV = vmlaq_n_f32(bV,xV,w);

       vst1q_f32(pb,bV);
       pb += 4;


       /* Decrement the loop counter */
       tapCnt--;
     }

     /* If the filter length is not a multiple of 4, compute the remaining filter taps */
     tapCnt = numTaps % 0x4U;

     while (tapCnt > 0U)
     {
       /* Perform the multiply-accumulate */
       *pb = *pb + (w * (*px++));
       pb++;

       /* Decrement the loop counter */
       tapCnt--;
     }

     /* Advance state pointer by 1 for the next sample */
     pState = pState + 1;

     /* Decrement the loop counter */
     blkCnt--;
   }


   /* Processing is complete. Now copy the last numTaps - 1 samples to the
      satrt of the state buffer. This prepares the state buffer for the
      next function call. */

   /* Points to the start of the pState buffer */
   pStateCurnt = S->pState;

   /* Process 4 taps at a time for (numTaps - 1U) samples copy */
   tapCnt = (numTaps - 1U) >> 2U;

   /* copy data */
   while (tapCnt > 0U)
   {
     tempV = vld1q_f32(pState);
     vst1q_f32(pStateCurnt,tempV);
     pState += 4;
     pStateCurnt += 4;

     /* Decrement the loop counter */
     tapCnt--;
   }

   /* Calculate remaining number of copies */
   tapCnt = (numTaps - 1U) % 0x4U;

   /* Copy the remaining q31_t data */
   while (tapCnt > 0U)
   {
     *pStateCurnt++ = *pState++;

     /* Decrement the loop counter */
     tapCnt--;
   }


 }
 #else
 void arm_lms_f32(
   const arm_lms_instance_f32 * S,
   const float32_t * pSrc,
         float32_t * pRef,
         float32_t * pOut,
         float32_t * pErr,
         uint32_t blockSize)
 {
         float32_t *pState = S->pState;                 /* State pointer */
         float32_t *pCoeffs = S->pCoeffs;               /* Coefficient pointer */
         float32_t *pStateCurnt;                        /* Points to the current sample of the state */
         float32_t *px, *pb;                            /* Temporary pointers for state and coefficient buffers */
         float32_t mu = S->mu;                          /* Adaptive factor */
         float32_t acc, e;                              /* Accumulator, error */
         float32_t w;                                   /* Weight factor */
         uint32_t numTaps = S->numTaps;                 /* Number of filter coefficients in the filter */
         uint32_t tapCnt, blkCnt;                       /* Loop counters */

   /* Initializations of error,  difference, Coefficient update */
   e = 0.0f;
   w = 0.0f;

   /* S->pState points to state array which contains previous frame (numTaps - 1) samples */
   /* pStateCurnt points to the location where the new input data should be written */
   pStateCurnt = &(S->pState[(numTaps - 1U)]);

   /* initialise loop count */
   blkCnt = blockSize;

   while (blkCnt > 0U)
   {
     /* Copy the new input sample into the state buffer */
     *pStateCurnt++ = *pSrc++;

     /* Initialize pState pointer */
     px = pState;

     /* Initialize coefficient pointer */
     pb = pCoeffs;

     /* Set the accumulator to zero */
     acc = 0.0f;

 #if defined (ARM_MATH_LOOPUNROLL)

     /* Loop unrolling: Compute 4 taps at a time. */
     tapCnt = numTaps >> 2U;

     while (tapCnt > 0U)
     {
       /* Perform the multiply-accumulate */
       acc += (*px++) * (*pb++);

       acc += (*px++) * (*pb++);

       acc += (*px++) * (*pb++);

       acc += (*px++) * (*pb++);

       /* Decrement loop counter */
       tapCnt--;
     }

     /* Loop unrolling: Compute remaining taps */
     tapCnt = numTaps % 0x4U;

 #else

     /* Initialize tapCnt with number of samples */
     tapCnt = numTaps;

 #endif /* #if defined (ARM_MATH_LOOPUNROLL) */

     while (tapCnt > 0U)
     {
       /* Perform the multiply-accumulate */
       acc += (*px++) * (*pb++);

       /* Decrement the loop counter */
       tapCnt--;
     }

     /* Store the result from accumulator into the destination buffer. */
     *pOut++ = acc;

     /* Compute and store error */
     e = (float32_t) *pRef++ - acc;
     *pErr++ = e;

     /* Calculation of Weighting factor for updating filter coefficients */
     w = e * mu;

     /* Initialize pState pointer */
     /* Advance state pointer by 1 for the next sample */
     px = pState++;

     /* Initialize coefficient pointer */
     pb = pCoeffs;

 #if defined (ARM_MATH_LOOPUNROLL)

     /* Loop unrolling: Compute 4 taps at a time. */
     tapCnt = numTaps >> 2U;

     /* Update filter coefficients */
     while (tapCnt > 0U)
     {
       /* Perform the multiply-accumulate */
       *pb += w * (*px++);
       pb++;

       *pb += w * (*px++);
       pb++;

       *pb += w * (*px++);
       pb++;

       *pb += w * (*px++);
       pb++;

       /* Decrement loop counter */
       tapCnt--;
     }

     /* Loop unrolling: Compute remaining taps */
     tapCnt = numTaps % 0x4U;

 #else

     /* Initialize tapCnt with number of samples */
     tapCnt = numTaps;

 #endif /* #if defined (ARM_MATH_LOOPUNROLL) */

     while (tapCnt > 0U)
     {
       /* Perform the multiply-accumulate */
       *pb += w * (*px++);
       pb++;

       /* Decrement loop counter */
       tapCnt--;
     }

     /* Decrement loop counter */
     blkCnt--;
   }

   /* Processing is complete.
      Now copy the last numTaps - 1 samples to the start of the state buffer.
      This prepares the state buffer for the next function call. */

   /* Points to the start of the pState buffer */
   pStateCurnt = S->pState;

   /* copy data */
 #if defined (ARM_MATH_LOOPUNROLL)

   /* Loop unrolling: Compute 4 taps at a time. */
   tapCnt = (numTaps - 1U) >> 2U;

   while (tapCnt > 0U)
   {
     *pStateCurnt++ = *pState++;
     *pStateCurnt++ = *pState++;
     *pStateCurnt++ = *pState++;
     *pStateCurnt++ = *pState++;

     /* Decrement loop counter */
     tapCnt--;
   }

   /* Loop unrolling: Compute remaining taps */
   tapCnt = (numTaps - 1U) % 0x4U;

 #else

   /* Initialize tapCnt with number of samples */
   tapCnt = (numTaps - 1U);

 #endif /* #if defined (ARM_MATH_LOOPUNROLL) */

   while (tapCnt > 0U)
   {
     *pStateCurnt++ = *pState++;

     /* Decrement loop counter */
     tapCnt--;
   }

 }
 #endif /* #if defined(ARM_MATH_NEON) */

 /**
   @} end of LMS group
  */
	/* ----------------------------------------------------------------------
	* Project: CMSIS DSP Library
	* Title: arm_lms_f32.c
	* Description: Processing function for the floating-point LMS filter
	*
	* $Date: 18. March 2019
	* $Revision: V1.6.0
	*
	* Target Processor: Cortex-M cores
	* -------------------------------------------------------------------- */
	/*
	* Copyright (C) 2010-2019 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 "arm_math.h"

	/**
	@ingroup groupFilters
	*/

	/**
	@defgroup LMS Least Mean Square (LMS) Filters

	LMS filters are a class of adaptive filters that are able to "learn" an unknown transfer functions.
	LMS filters use a gradient descent method in which the filter coefficients are updated based on the instantaneous error signal.
	Adaptive filters are often used in communication systems, equalizers, and noise removal.
	The CMSIS DSP Library contains LMS filter functions that operate on Q15, Q31, and floating-point data types.
	The library also contains normalized LMS filters in which the filter coefficient adaptation is indepedent of the level of the input signal.

	An LMS filter consists of two components as shown below.
	The first component is a standard transversal or FIR filter.
	The second component is a coefficient update mechanism.
	The LMS filter has two input signals.
	The "input" feeds the FIR filter while the "reference input" corresponds to the desired output of the FIR filter.
	That is, the FIR filter coefficients are updated so that the output of the FIR filter matches the reference input.
	The filter coefficient update mechanism is based on the difference between the FIR filter output and the reference input.
	This "error signal" tends towards zero as the filter adapts.
	The LMS processing functions accept the input and reference input signals and generate the filter output and error signal.
	\image html LMS.gif "Internal structure of the Least Mean Square filter"

	The functions operate on blocks of data and each call to the function processes
	<code>blockSize</code> samples through the filter.
	<code>pSrc</code> points to input signal, <code>pRef</code> points to reference signal,
	<code>pOut</code> points to output signal and <code>pErr</code> points to error signal.
	All arrays contain <code>blockSize</code> values.

	The functions operate on a block-by-block basis.
	Internally, the filter coefficients <code>b[n]</code> are updated on a sample-by-sample basis.
	The convergence of the LMS filter is slower compared to the normalized LMS algorithm.

	@par Algorithm
	The output signal <code>y[n]</code> is computed by a standard FIR filter:
	<pre>
	y[n] = b[0] * x[n] + b[1] * x[n-1] + b[2] * x[n-2] + ...+ b[numTaps-1] * x[n-numTaps+1]
	</pre>

	@par
	The error signal equals the difference between the reference signal <code>d[n]</code> and the filter output:
	<pre>
	e[n] = d[n] - y[n].
	</pre>

	@par
	After each sample of the error signal is computed, the filter coefficients <code>b[k]</code> are updated on a sample-by-sample basis:
	<pre>
	b[k] = b[k] + e[n] * mu * x[n-k], for k=0, 1, ..., numTaps-1
	</pre>
	where <code>mu</code> is the step size and controls the rate of coefficient convergence.
	@par
	In the APIs, <code>pCoeffs</code> points to a coefficient array of size <code>numTaps</code>.
	Coefficients are stored in time reversed order.
	@par
	<pre>
	{b[numTaps-1], b[numTaps-2], b[N-2], ..., b[1], b[0]}
	</pre>
	@par
	<code>pState</code> points to a state array of size <code>numTaps + blockSize - 1</code>.
	Samples in the state buffer are stored in the order:
	@par
	<pre>
	{x[n-numTaps+1], x[n-numTaps], x[n-numTaps-1], x[n-numTaps-2]....x[0], x[1], ..., x[blockSize-1]}
	</pre>
	@par
	Note that the length of the state buffer exceeds the length of the coefficient array by <code>blockSize-1</code> samples.
	The increased state buffer length allows circular addressing, which is traditionally used in FIR filters,
	to be avoided and yields a significant speed improvement.
	The state variables are updated after each block of data is processed.
	@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 and
	coefficient and state arrays cannot be shared among instances.
	There are separate instance structure declarations for each of the 3 supported data types.

	@par Initialization Functions
	There is also an associated initialization function for each data type.
	The initialization function performs the 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:
	numTaps, pCoeffs, mu, postShift (not for f32), 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_lms_instance_f32 S = {numTaps, pState, pCoeffs, mu};
	arm_lms_instance_q31 S = {numTaps, pState, pCoeffs, mu, postShift};
	arm_lms_instance_q15 S = {numTaps, pState, pCoeffs, mu, postShift};
	</pre>
	where <code>numTaps</code> is the number of filter coefficients in the filter; <code>pState</code> is the address of the state buffer;
	<code>pCoeffs</code> is the address of the coefficient buffer; <code>mu</code> is the step size parameter; and <code>postShift</code> is the shift applied to coefficients.

	@par Fixed-Point Behavior
	Care must be taken when using the Q15 and Q31 versions of the LMS filter.
	The following issues must be considered:
	- Scaling of coefficients
	- Overflow and saturation

	@par Scaling of Coefficients
	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>.
	At the output of the filter's accumulator is a shift register which shifts the result by <code>postShift</code> bits.
	This essentially scales the filter coefficients by <code>2^postShift</code> and
	allows the filter coefficients to exceed the range <code>[+1 -1)</code>.
	The value of <code>postShift</code> is set by the user based on the expected gain through the system being modeled.

	@par Overflow and Saturation
	Overflow and saturation behavior of the fixed-point Q15 and Q31 versions are
	described separately as part of the function specific documentation below.
	*/

	/**
	@addtogroup LMS
	@{
	*/

	/**
	@brief Processing function for floating-point LMS filter.
	@param[in] S points to an instance of the floating-point LMS filter structure
	@param[in] pSrc points to the block of input data
	@param[in] pRef points to the block of reference data
	@param[out] pOut points to the block of output data
	@param[out] pErr points to the block of error data
	@param[in] blockSize number of samples to process
	@return none
	*/
	#if defined(ARM_MATH_NEON)
	void arm_lms_f32(
	const arm_lms_instance_f32 * S,
	const float32_t * pSrc,
	float32_t * pRef,
	float32_t * pOut,
	float32_t * pErr,
	uint32_t blockSize)
	{
	float32_t pState = S->pState; / State pointer */
	float32_t pCoeffs = S->pCoeffs; / Coefficient pointer */
	float32_t pStateCurnt; / Points to the current sample of the state */
	float32_t px, pb; /* Temporary pointers for state and coefficient buffers */
	float32_t mu = S->mu; /* Adaptive factor */
	uint32_t numTaps = S->numTaps; /* Number of filter coefficients in the filter */
	uint32_t tapCnt, blkCnt; /* Loop counters */
	float32_t sum, e, d; /* accumulator, error, reference data sample */
	float32_t w = 0.0f; /* weight factor */

	float32x4_t tempV, sumV, xV, bV;
	float32x2_t tempV2;

	e = 0.0f;
	d = 0.0f;

	/* S->pState points to state array which contains previous frame (numTaps - 1) samples */
	/* pStateCurnt points to the location where the new input data should be written */
	pStateCurnt = &(S->pState[(numTaps - 1U)]);

	blkCnt = blockSize;

	while (blkCnt > 0U)
	{
	/* Copy the new input sample into the state buffer */
	pStateCurnt++ = pSrc++;

	/* Initialize pState pointer */
	px = pState;

	/* Initialize coeff pointer */
	pb = (pCoeffs);

	/* Set the accumulator to zero */
	sum = 0.0f;
	sumV = vdupq_n_f32(0.0);

	/* Process 4 taps at a time. */
	tapCnt = numTaps >> 2;

	while (tapCnt > 0U)
	{
	/* Perform the multiply-accumulate */
	xV = vld1q_f32(px);
	bV = vld1q_f32(pb);
	sumV = vmlaq_f32(sumV, xV, bV);

	px += 4;
	pb += 4;

	/* Decrement the loop counter */
	tapCnt--;
	}
	tempV2 = vpadd_f32(vget_low_f32(sumV),vget_high_f32(sumV));
	sum = tempV2[0] + tempV2[1];


	/* If the filter length is not a multiple of 4, compute the remaining filter taps */
	tapCnt = numTaps % 0x4U;

	while (tapCnt > 0U)
	{
	/* Perform the multiply-accumulate */
	sum += (px++) (*pb++);

	/* Decrement the loop counter */
	tapCnt--;
	}

	/* The result in the accumulator, store in the destination buffer. */
	*pOut++ = sum;

	/* Compute and store error */
	d = (float32_t) (*pRef++);
	e = d - sum;
	*pErr++ = e;

	/* Calculation of Weighting factor for the updating filter coefficients */
	w = e * mu;

	/* Initialize pState pointer */
	px = pState;

	/* Initialize coeff pointer */
	pb = (pCoeffs);

	/* Process 4 taps at a time. */
	tapCnt = numTaps >> 2;

	/* Update filter coefficients */
	while (tapCnt > 0U)
	{
	/* Perform the multiply-accumulate */
	xV = vld1q_f32(px);
	bV = vld1q_f32(pb);
	px += 4;
	bV = vmlaq_n_f32(bV,xV,w);

	vst1q_f32(pb,bV);
	pb += 4;


	/* Decrement the loop counter */
	tapCnt--;
	}

	/* If the filter length is not a multiple of 4, compute the remaining filter taps */
	tapCnt = numTaps % 0x4U;

	while (tapCnt > 0U)
	{
	/* Perform the multiply-accumulate */
	pb = pb + (w * (*px++));
	pb++;

	/* Decrement the loop counter */
	tapCnt--;
	}

	/* Advance state pointer by 1 for the next sample */
	pState = pState + 1;

	/* Decrement the loop counter */
	blkCnt--;
	}


	/* Processing is complete. Now copy the last numTaps - 1 samples to the
	satrt of the state buffer. This prepares the state buffer for the
	next function call. */

	/* Points to the start of the pState buffer */
	pStateCurnt = S->pState;

	/* Process 4 taps at a time for (numTaps - 1U) samples copy */
	tapCnt = (numTaps - 1U) >> 2U;

	/* copy data */
	while (tapCnt > 0U)
	{
	tempV = vld1q_f32(pState);
	vst1q_f32(pStateCurnt,tempV);
	pState += 4;
	pStateCurnt += 4;

	/* Decrement the loop counter */
	tapCnt--;
	}

	/* Calculate remaining number of copies */
	tapCnt = (numTaps - 1U) % 0x4U;

	/* Copy the remaining q31_t data */
	while (tapCnt > 0U)
	{
	pStateCurnt++ = pState++;

	/* Decrement the loop counter */
	tapCnt--;
	}


	}
	#else
	void arm_lms_f32(
	const arm_lms_instance_f32 * S,
	const float32_t * pSrc,
	float32_t * pRef,
	float32_t * pOut,
	float32_t * pErr,
	uint32_t blockSize)
	{
	float32_t pState = S->pState; / State pointer */
	float32_t pCoeffs = S->pCoeffs; / Coefficient pointer */
	float32_t pStateCurnt; / Points to the current sample of the state */
	float32_t px, pb; /* Temporary pointers for state and coefficient buffers */
	float32_t mu = S->mu; /* Adaptive factor */
	float32_t acc, e; /* Accumulator, error */
	float32_t w; /* Weight factor */
	uint32_t numTaps = S->numTaps; /* Number of filter coefficients in the filter */
	uint32_t tapCnt, blkCnt; /* Loop counters */

	/* Initializations of error, difference, Coefficient update */
	e = 0.0f;
	w = 0.0f;

	/* S->pState points to state array which contains previous frame (numTaps - 1) samples */
	/* pStateCurnt points to the location where the new input data should be written */
	pStateCurnt = &(S->pState[(numTaps - 1U)]);

	/* initialise loop count */
	blkCnt = blockSize;

	while (blkCnt > 0U)
	{
	/* Copy the new input sample into the state buffer */
	pStateCurnt++ = pSrc++;

	/* Initialize pState pointer */
	px = pState;

	/* Initialize coefficient pointer */
	pb = pCoeffs;

	/* Set the accumulator to zero */
	acc = 0.0f;

	#if defined (ARM_MATH_LOOPUNROLL)

	/* Loop unrolling: Compute 4 taps at a time. */
	tapCnt = numTaps >> 2U;

	while (tapCnt > 0U)
	{
	/* Perform the multiply-accumulate */
	acc += (px++) (*pb++);

	acc += (px++) (*pb++);

	acc += (px++) (*pb++);

	acc += (px++) (*pb++);

	/* Decrement loop counter */
	tapCnt--;
	}

	/* Loop unrolling: Compute remaining taps */
	tapCnt = numTaps % 0x4U;

	#else

	/* Initialize tapCnt with number of samples */
	tapCnt = numTaps;

	#endif /* #if defined (ARM_MATH_LOOPUNROLL) */

	while (tapCnt > 0U)
	{
	/* Perform the multiply-accumulate */
	acc += (px++) (*pb++);

	/* Decrement the loop counter */
	tapCnt--;
	}

	/* Store the result from accumulator into the destination buffer. */
	*pOut++ = acc;

	/* Compute and store error */
	e = (float32_t) *pRef++ - acc;
	*pErr++ = e;

	/* Calculation of Weighting factor for updating filter coefficients */
	w = e * mu;

	/* Initialize pState pointer */
	/* Advance state pointer by 1 for the next sample */
	px = pState++;

	/* Initialize coefficient pointer */
	pb = pCoeffs;

	#if defined (ARM_MATH_LOOPUNROLL)

	/* Loop unrolling: Compute 4 taps at a time. */
	tapCnt = numTaps >> 2U;

	/* Update filter coefficients */
	while (tapCnt > 0U)
	{
	/* Perform the multiply-accumulate */
	pb += w (*px++);
	pb++;

	pb += w (*px++);
	pb++;

	pb += w (*px++);
	pb++;

	pb += w (*px++);
	pb++;

	/* Decrement loop counter */
	tapCnt--;
	}

	/* Loop unrolling: Compute remaining taps */
	tapCnt = numTaps % 0x4U;

	#else

	/* Initialize tapCnt with number of samples */
	tapCnt = numTaps;

	#endif /* #if defined (ARM_MATH_LOOPUNROLL) */

	while (tapCnt > 0U)
	{
	/* Perform the multiply-accumulate */
	pb += w (*px++);
	pb++;

	/* Decrement loop counter */
	tapCnt--;
	}

	/* Decrement loop counter */
	blkCnt--;
	}

	/* Processing is complete.
	Now copy the last numTaps - 1 samples to the start of the state buffer.
	This prepares the state buffer for the next function call. */

	/* Points to the start of the pState buffer */
	pStateCurnt = S->pState;

	/* copy data */
	#if defined (ARM_MATH_LOOPUNROLL)

	/* Loop unrolling: Compute 4 taps at a time. */
	tapCnt = (numTaps - 1U) >> 2U;

	while (tapCnt > 0U)
	{
	pStateCurnt++ = pState++;
	pStateCurnt++ = pState++;
	pStateCurnt++ = pState++;
	pStateCurnt++ = pState++;

	/* Decrement loop counter */
	tapCnt--;
	}

	/* Loop unrolling: Compute remaining taps */
	tapCnt = (numTaps - 1U) % 0x4U;

	#else

	/* Initialize tapCnt with number of samples */
	tapCnt = (numTaps - 1U);

	#endif /* #if defined (ARM_MATH_LOOPUNROLL) */

	while (tapCnt > 0U)
	{
	pStateCurnt++ = pState++;

	/* Decrement loop counter */
	tapCnt--;
	}

	}
	#endif /* #if defined(ARM_MATH_NEON) */

	/**
	@} end of LMS group
	*/