/* ----------------------------------------------------------------------
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* Copyright (C) 2010-2014 ARM Limited. All rights reserved.
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*
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* $Date: 19. March 2015
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* $Revision: V.1.4.5
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*
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* Project: CMSIS DSP Library
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* Title: arm_lms_f32.c
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*
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* Description: Processing function for the floating-point LMS filter.
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*
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* Target Processor: Cortex-M4/Cortex-M3/Cortex-M0
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*
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* Redistribution and use in source and binary forms, with or without
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* modification, are permitted provided that the following conditions
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* are met:
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* - Redistributions of source code must retain the above copyright
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* notice, this list of conditions and the following disclaimer.
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* - Redistributions in binary form must reproduce the above copyright
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* notice, this list of conditions and the following disclaimer in
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* the documentation and/or other materials provided with the
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* distribution.
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* - Neither the name of ARM LIMITED nor the names of its contributors
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* may be used to endorse or promote products derived from this
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* software without specific prior written permission.
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*
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* THIS SOFTWARE IS PROVIDED BY THE COPYRIGHT HOLDERS AND CONTRIBUTORS
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* "AS IS" AND ANY EXPRESS OR IMPLIED WARRANTIES, INCLUDING, BUT NOT
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* LIMITED TO, THE IMPLIED WARRANTIES OF MERCHANTABILITY AND FITNESS
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* FOR A PARTICULAR PURPOSE ARE DISCLAIMED. IN NO EVENT SHALL THE
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* COPYRIGHT OWNER OR CONTRIBUTORS BE LIABLE FOR ANY DIRECT, INDIRECT,
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* INCIDENTAL, SPECIAL, EXEMPLARY, OR CONSEQUENTIAL DAMAGES (INCLUDING,
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* BUT NOT LIMITED TO, PROCUREMENT OF SUBSTITUTE GOODS OR SERVICES;
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* LOSS OF USE, DATA, OR PROFITS; OR BUSINESS INTERRUPTION) HOWEVER
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* CAUSED AND ON ANY THEORY OF LIABILITY, WHETHER IN CONTRACT, STRICT
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* LIABILITY, OR TORT (INCLUDING NEGLIGENCE OR OTHERWISE) ARISING IN
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* ANY WAY OUT OF THE USE OF THIS SOFTWARE, EVEN IF ADVISED OF THE
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* POSSIBILITY OF SUCH DAMAGE.
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* -------------------------------------------------------------------- */
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#include "arm_math.h"
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/**
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* @ingroup groupFilters
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*/
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/**
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* @defgroup LMS Least Mean Square (LMS) Filters
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*
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* LMS filters are a class of adaptive filters that are able to "learn" an unknown transfer functions.
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* LMS filters use a gradient descent method in which the filter coefficients are updated based on the instantaneous error signal.
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* Adaptive filters are often used in communication systems, equalizers, and noise removal.
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* The CMSIS DSP Library contains LMS filter functions that operate on Q15, Q31, and floating-point data types.
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* The library also contains normalized LMS filters in which the filter coefficient adaptation is indepedent of the level of the input signal.
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*
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* An LMS filter consists of two components as shown below.
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* The first component is a standard transversal or FIR filter.
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* The second component is a coefficient update mechanism.
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* The LMS filter has two input signals.
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* The "input" feeds the FIR filter while the "reference input" corresponds to the desired output of the FIR filter.
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* That is, the FIR filter coefficients are updated so that the output of the FIR filter matches the reference input.
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* The filter coefficient update mechanism is based on the difference between the FIR filter output and the reference input.
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* This "error signal" tends towards zero as the filter adapts.
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* The LMS processing functions accept the input and reference input signals and generate the filter output and error signal.
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* \image html LMS.gif "Internal structure of the Least Mean Square filter"
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*
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* The functions operate on blocks of data and each call to the function processes
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* <code>blockSize</code> samples through the filter.
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* <code>pSrc</code> points to input signal, <code>pRef</code> points to reference signal,
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* <code>pOut</code> points to output signal and <code>pErr</code> points to error signal.
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* All arrays contain <code>blockSize</code> values.
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*
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* The functions operate on a block-by-block basis.
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* Internally, the filter coefficients <code>b[n]</code> are updated on a sample-by-sample basis.
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* The convergence of the LMS filter is slower compared to the normalized LMS algorithm.
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*
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* \par Algorithm:
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* The output signal <code>y[n]</code> is computed by a standard FIR filter:
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* <pre>
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* y[n] = b[0] * x[n] + b[1] * x[n-1] + b[2] * x[n-2] + ...+ b[numTaps-1] * x[n-numTaps+1]
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* </pre>
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*
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* \par
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* The error signal equals the difference between the reference signal <code>d[n]</code> and the filter output:
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* <pre>
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* e[n] = d[n] - y[n].
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* </pre>
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*
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* \par
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* After each sample of the error signal is computed, the filter coefficients <code>b[k]</code> are updated on a sample-by-sample basis:
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* <pre>
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* b[k] = b[k] + e[n] * mu * x[n-k], for k=0, 1, ..., numTaps-1
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* </pre>
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* where <code>mu</code> is the step size and controls the rate of coefficient convergence.
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*\par
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* In the APIs, <code>pCoeffs</code> points to a coefficient array of size <code>numTaps</code>.
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* Coefficients are stored in time reversed order.
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* \par
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* <pre>
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* {b[numTaps-1], b[numTaps-2], b[N-2], ..., b[1], b[0]}
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* </pre>
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* \par
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* <code>pState</code> points to a state array of size <code>numTaps + blockSize - 1</code>.
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* Samples in the state buffer are stored in the order:
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* \par
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* <pre>
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* {x[n-numTaps+1], x[n-numTaps], x[n-numTaps-1], x[n-numTaps-2]....x[0], x[1], ..., x[blockSize-1]}
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* </pre>
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* \par
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* Note that the length of the state buffer exceeds the length of the coefficient array by <code>blockSize-1</code> samples.
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* The increased state buffer length allows circular addressing, which is traditionally used in FIR filters,
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* to be avoided and yields a significant speed improvement.
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* The state variables are updated after each block of data is processed.
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* \par Instance Structure
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* The coefficients and state variables for a filter are stored together in an instance data structure.
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* A separate instance structure must be defined for each filter and
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* coefficient and state arrays cannot be shared among instances.
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* There are separate instance structure declarations for each of the 3 supported data types.
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*
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* \par Initialization Functions
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* There is also an associated initialization function for each data type.
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* The initialization function performs the following operations:
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* - Sets the values of the internal structure fields.
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* - Zeros out the values in the state buffer.
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* To do this manually without calling the init function, assign the follow subfields of the instance structure:
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* numTaps, pCoeffs, mu, postShift (not for f32), pState. Also set all of the values in pState to zero.
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*
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* \par
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* Use of the initialization function is optional.
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* However, if the initialization function is used, then the instance structure cannot be placed into a const data section.
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* To place an instance structure into a const data section, the instance structure must be manually initialized.
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* Set the values in the state buffer to zeros before static initialization.
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* The code below statically initializes each of the 3 different data type filter instance structures
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* <pre>
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* arm_lms_instance_f32 S = {numTaps, pState, pCoeffs, mu};
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* arm_lms_instance_q31 S = {numTaps, pState, pCoeffs, mu, postShift};
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* arm_lms_instance_q15 S = {numTaps, pState, pCoeffs, mu, postShift};
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* </pre>
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* where <code>numTaps</code> is the number of filter coefficients in the filter; <code>pState</code> is the address of the state buffer;
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* <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.
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*
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* \par Fixed-Point Behavior:
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* Care must be taken when using the Q15 and Q31 versions of the LMS filter.
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* The following issues must be considered:
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* - Scaling of coefficients
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* - Overflow and saturation
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*
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* \par Scaling of Coefficients:
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* Filter coefficients are represented as fractional values and
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* coefficients are restricted to lie in the range <code>[-1 +1)</code>.
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* The fixed-point functions have an additional scaling parameter <code>postShift</code>.
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* At the output of the filter's accumulator is a shift register which shifts the result by <code>postShift</code> bits.
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* This essentially scales the filter coefficients by <code>2^postShift</code> and
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* allows the filter coefficients to exceed the range <code>[+1 -1)</code>.
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* The value of <code>postShift</code> is set by the user based on the expected gain through the system being modeled.
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*
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* \par Overflow and Saturation:
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* Overflow and saturation behavior of the fixed-point Q15 and Q31 versions are
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* described separately as part of the function specific documentation below.
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*/
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/**
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* @addtogroup LMS
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* @{
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*/
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/**
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* @details
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* This function operates on floating-point data types.
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*
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* @brief Processing function for floating-point LMS filter.
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* @param[in] *S points to an instance of the floating-point LMS filter structure.
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* @param[in] *pSrc points to the block of input data.
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* @param[in] *pRef points to the block of reference data.
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* @param[out] *pOut points to the block of output data.
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* @param[out] *pErr points to the block of error data.
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* @param[in] blockSize number of samples to process.
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* @return none.
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*/
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void arm_lms_f32(
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const arm_lms_instance_f32 * S,
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float32_t * pSrc,
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float32_t * pRef,
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float32_t * pOut,
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float32_t * pErr,
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uint32_t blockSize)
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{
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float32_t *pState = S->pState; /* State pointer */
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float32_t *pCoeffs = S->pCoeffs; /* Coefficient pointer */
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float32_t *pStateCurnt; /* Points to the current sample of the state */
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float32_t *px, *pb; /* Temporary pointers for state and coefficient buffers */
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float32_t mu = S->mu; /* Adaptive factor */
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uint32_t numTaps = S->numTaps; /* Number of filter coefficients in the filter */
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uint32_t tapCnt, blkCnt; /* Loop counters */
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float32_t sum, e, d; /* accumulator, error, reference data sample */
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float32_t w = 0.0f; /* weight factor */
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e = 0.0f;
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d = 0.0f;
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/* S->pState points to state array which contains previous frame (numTaps - 1) samples */
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/* pStateCurnt points to the location where the new input data should be written */
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pStateCurnt = &(S->pState[(numTaps - 1u)]);
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blkCnt = blockSize;
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#ifndef ARM_MATH_CM0_FAMILY
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/* Run the below code for Cortex-M4 and Cortex-M3 */
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while(blkCnt > 0u)
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{
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/* Copy the new input sample into the state buffer */
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*pStateCurnt++ = *pSrc++;
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/* Initialize pState pointer */
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px = pState;
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/* Initialize coeff pointer */
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pb = (pCoeffs);
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/* Set the accumulator to zero */
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sum = 0.0f;
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/* Loop unrolling. Process 4 taps at a time. */
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tapCnt = numTaps >> 2;
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while(tapCnt > 0u)
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{
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/* Perform the multiply-accumulate */
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sum += (*px++) * (*pb++);
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sum += (*px++) * (*pb++);
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sum += (*px++) * (*pb++);
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sum += (*px++) * (*pb++);
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/* Decrement the loop counter */
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tapCnt--;
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}
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/* If the filter length is not a multiple of 4, compute the remaining filter taps */
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tapCnt = numTaps % 0x4u;
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while(tapCnt > 0u)
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{
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/* Perform the multiply-accumulate */
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sum += (*px++) * (*pb++);
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/* Decrement the loop counter */
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tapCnt--;
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}
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/* The result in the accumulator, store in the destination buffer. */
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*pOut++ = sum;
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/* Compute and store error */
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d = (float32_t) (*pRef++);
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e = d - sum;
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*pErr++ = e;
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/* Calculation of Weighting factor for the updating filter coefficients */
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w = e * mu;
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/* Initialize pState pointer */
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px = pState;
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/* Initialize coeff pointer */
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pb = (pCoeffs);
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/* Loop unrolling. Process 4 taps at a time. */
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tapCnt = numTaps >> 2;
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/* Update filter coefficients */
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while(tapCnt > 0u)
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{
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/* Perform the multiply-accumulate */
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*pb = *pb + (w * (*px++));
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pb++;
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*pb = *pb + (w * (*px++));
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pb++;
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*pb = *pb + (w * (*px++));
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pb++;
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*pb = *pb + (w * (*px++));
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pb++;
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/* Decrement the loop counter */
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tapCnt--;
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}
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/* If the filter length is not a multiple of 4, compute the remaining filter taps */
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tapCnt = numTaps % 0x4u;
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while(tapCnt > 0u)
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{
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/* Perform the multiply-accumulate */
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*pb = *pb + (w * (*px++));
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pb++;
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/* Decrement the loop counter */
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tapCnt--;
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}
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/* Advance state pointer by 1 for the next sample */
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pState = pState + 1;
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/* Decrement the loop counter */
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blkCnt--;
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}
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/* Processing is complete. Now copy the last numTaps - 1 samples to the
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satrt of the state buffer. This prepares the state buffer for the
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next function call. */
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/* Points to the start of the pState buffer */
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pStateCurnt = S->pState;
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/* Loop unrolling for (numTaps - 1u) samples copy */
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tapCnt = (numTaps - 1u) >> 2u;
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/* copy data */
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while(tapCnt > 0u)
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{
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*pStateCurnt++ = *pState++;
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*pStateCurnt++ = *pState++;
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*pStateCurnt++ = *pState++;
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*pStateCurnt++ = *pState++;
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/* Decrement the loop counter */
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tapCnt--;
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}
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/* Calculate remaining number of copies */
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tapCnt = (numTaps - 1u) % 0x4u;
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/* Copy the remaining q31_t data */
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while(tapCnt > 0u)
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{
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*pStateCurnt++ = *pState++;
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/* Decrement the loop counter */
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tapCnt--;
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}
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#else
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/* Run the below code for Cortex-M0 */
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while(blkCnt > 0u)
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{
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/* Copy the new input sample into the state buffer */
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*pStateCurnt++ = *pSrc++;
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/* Initialize pState pointer */
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px = pState;
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/* Initialize pCoeffs pointer */
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pb = pCoeffs;
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/* Set the accumulator to zero */
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sum = 0.0f;
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/* Loop over numTaps number of values */
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tapCnt = numTaps;
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while(tapCnt > 0u)
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{
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/* Perform the multiply-accumulate */
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sum += (*px++) * (*pb++);
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/* Decrement the loop counter */
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tapCnt--;
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}
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/* The result is stored in the destination buffer. */
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*pOut++ = sum;
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/* Compute and store error */
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d = (float32_t) (*pRef++);
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e = d - sum;
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*pErr++ = e;
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/* Weighting factor for the LMS version */
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w = e * mu;
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/* Initialize pState pointer */
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px = pState;
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/* Initialize pCoeffs pointer */
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pb = pCoeffs;
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/* Loop over numTaps number of values */
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tapCnt = numTaps;
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while(tapCnt > 0u)
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{
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/* Perform the multiply-accumulate */
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*pb = *pb + (w * (*px++));
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pb++;
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/* Decrement the loop counter */
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tapCnt--;
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}
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/* Advance state pointer by 1 for the next sample */
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pState = pState + 1;
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/* Decrement the loop counter */
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blkCnt--;
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}
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/* Processing is complete. Now copy the last numTaps - 1 samples to the
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* start of the state buffer. This prepares the state buffer for the
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* next function call. */
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/* Points to the start of the pState buffer */
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pStateCurnt = S->pState;
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/* Copy (numTaps - 1u) samples */
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tapCnt = (numTaps - 1u);
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/* Copy the data */
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while(tapCnt > 0u)
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{
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*pStateCurnt++ = *pState++;
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/* Decrement the loop counter */
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tapCnt--;
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}
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#endif /* #ifndef ARM_MATH_CM0_FAMILY */
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}
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/**
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* @} end of LMS group
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*/
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