591 lines
17 KiB
C
591 lines
17 KiB
C
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/* ----------------------------------------------------------------------
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* Project: CMSIS DSP Library
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* Title: arm_biquad_cascade_df2T_f64.c
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* Description: Processing function for floating-point transposed direct form II Biquad cascade filter
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*
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* $Date: 27. January 2017
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* $Revision: V.1.5.1
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*
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* Target Processor: Cortex-M cores
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* -------------------------------------------------------------------- */
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/*
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* Copyright (C) 2010-2017 ARM Limited or its affiliates. All rights reserved.
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*
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* SPDX-License-Identifier: Apache-2.0
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*
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* Licensed under the Apache License, Version 2.0 (the License); you may
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* not use this file except in compliance with the License.
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* You may obtain a copy of the License at
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*
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* www.apache.org/licenses/LICENSE-2.0
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*
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* Unless required by applicable law or agreed to in writing, software
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* distributed under the License is distributed on an AS IS BASIS, WITHOUT
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* WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied.
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* See the License for the specific language governing permissions and
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* limitations under the License.
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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 BiquadCascadeDF2T Biquad Cascade IIR Filters Using a Direct Form II Transposed Structure
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*
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* This set of functions implements arbitrary order recursive (IIR) filters using a transposed direct form II structure.
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* The filters are implemented as a cascade of second order Biquad sections.
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* These functions provide a slight memory savings as compared to the direct form I Biquad filter functions.
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* Only floating-point data is supported.
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*
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* This function operate on blocks of input and output data and each call to the function
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* processes <code>blockSize</code> samples through the filter.
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* <code>pSrc</code> points to the array of input data and
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* <code>pDst</code> points to the array of output data.
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* Both arrays contain <code>blockSize</code> values.
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*
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* \par Algorithm
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* Each Biquad stage implements a second order filter using the difference equation:
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* <pre>
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* y[n] = b0 * x[n] + d1
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* d1 = b1 * x[n] + a1 * y[n] + d2
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* d2 = b2 * x[n] + a2 * y[n]
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* </pre>
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* where d1 and d2 represent the two state values.
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*
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* \par
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* A Biquad filter using a transposed Direct Form II structure is shown below.
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* \image html BiquadDF2Transposed.gif "Single transposed Direct Form II Biquad"
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* Coefficients <code>b0, b1, and b2 </code> multiply the input signal <code>x[n]</code> and are referred to as the feedforward coefficients.
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* Coefficients <code>a1</code> and <code>a2</code> multiply the output signal <code>y[n]</code> and are referred to as the feedback coefficients.
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* Pay careful attention to the sign of the feedback coefficients.
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* Some design tools flip the sign of the feedback coefficients:
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* <pre>
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* y[n] = b0 * x[n] + d1;
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* d1 = b1 * x[n] - a1 * y[n] + d2;
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* d2 = b2 * x[n] - a2 * y[n];
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* </pre>
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* In this case the feedback coefficients <code>a1</code> and <code>a2</code> must be negated when used with the CMSIS DSP Library.
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*
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* \par
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* Higher order filters are realized as a cascade of second order sections.
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* <code>numStages</code> refers to the number of second order stages used.
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* For example, an 8th order filter would be realized with <code>numStages=4</code> second order stages.
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* A 9th order filter would be realized with <code>numStages=5</code> second order stages with the
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* coefficients for one of the stages configured as a first order filter (<code>b2=0</code> and <code>a2=0</code>).
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*
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* \par
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* <code>pState</code> points to the state variable array.
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* Each Biquad stage has 2 state variables <code>d1</code> and <code>d2</code>.
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* The state variables are arranged in the <code>pState</code> array as:
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* <pre>
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* {d11, d12, d21, d22, ...}
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* </pre>
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* where <code>d1x</code> refers to the state variables for the first Biquad and
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* <code>d2x</code> refers to the state variables for the second Biquad.
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* The state array has a total length of <code>2*numStages</code> values.
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* The state variables are updated after each block of data is processed; the coefficients are untouched.
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*
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* \par
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* The CMSIS library contains Biquad filters in both Direct Form I and transposed Direct Form II.
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* The advantage of the Direct Form I structure is that it is numerically more robust for fixed-point data types.
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* That is why the Direct Form I structure supports Q15 and Q31 data types.
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* 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>.
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* Because of this, the CMSIS library only has a floating-point version of the Direct Form II Biquad.
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* 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.
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*
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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.
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* Coefficient arrays may be shared among several instances while state variable arrays cannot be shared.
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*
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* \par Init Functions
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* There is also an associated initialization function.
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* The initialization function performs 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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* numStages, pCoeffs, 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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* For example, to statically initialize the instance structure use
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* <pre>
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* arm_biquad_cascade_df2T_instance_f64 S1 = {numStages, pState, pCoeffs};
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* </pre>
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* where <code>numStages</code> is the number of Biquad stages 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;
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*
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*/
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/**
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* @addtogroup BiquadCascadeDF2T
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* @{
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*/
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/**
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* @brief Processing function for the floating-point transposed direct form II Biquad cascade filter.
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* @param[in] *S points to an instance of the filter data structure.
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* @param[in] *pSrc points to the block of input data.
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* @param[out] *pDst points to the block of output 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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LOW_OPTIMIZATION_ENTER
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void arm_biquad_cascade_df2T_f64(
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const arm_biquad_cascade_df2T_instance_f64 * S,
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float64_t * pSrc,
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float64_t * pDst,
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uint32_t blockSize)
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{
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float64_t *pIn = pSrc; /* source pointer */
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float64_t *pOut = pDst; /* destination pointer */
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float64_t *pState = S->pState; /* State pointer */
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float64_t *pCoeffs = S->pCoeffs; /* coefficient pointer */
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float64_t acc1; /* accumulator */
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float64_t b0, b1, b2, a1, a2; /* Filter coefficients */
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float64_t Xn1; /* temporary input */
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float64_t d1, d2; /* state variables */
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uint32_t sample, stage = S->numStages; /* loop counters */
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#if defined(ARM_MATH_CM7)
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float64_t Xn2, Xn3, Xn4, Xn5, Xn6, Xn7, Xn8; /* Input State variables */
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float64_t Xn9, Xn10, Xn11, Xn12, Xn13, Xn14, Xn15, Xn16;
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float64_t acc2, acc3, acc4, acc5, acc6, acc7; /* Simulates the accumulator */
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float64_t acc8, acc9, acc10, acc11, acc12, acc13, acc14, acc15, acc16;
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do
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{
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/* Reading the coefficients */
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b0 = pCoeffs[0];
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b1 = pCoeffs[1];
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b2 = pCoeffs[2];
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a1 = pCoeffs[3];
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/* Apply loop unrolling and compute 16 output values simultaneously. */
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sample = blockSize >> 4U;
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a2 = pCoeffs[4];
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/*Reading the state values */
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d1 = pState[0];
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d2 = pState[1];
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pCoeffs += 5U;
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/* First part of the processing with loop unrolling. Compute 16 outputs at a time.
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** a second loop below computes the remaining 1 to 15 samples. */
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while (sample > 0U) {
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/* y[n] = b0 * x[n] + d1 */
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/* d1 = b1 * x[n] + a1 * y[n] + d2 */
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/* d2 = b2 * x[n] + a2 * y[n] */
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/* Read the first 2 inputs. 2 cycles */
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Xn1 = pIn[0 ];
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Xn2 = pIn[1 ];
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/* Sample 1. 5 cycles */
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Xn3 = pIn[2 ];
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acc1 = b0 * Xn1 + d1;
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Xn4 = pIn[3 ];
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d1 = b1 * Xn1 + d2;
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Xn5 = pIn[4 ];
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d2 = b2 * Xn1;
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Xn6 = pIn[5 ];
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d1 += a1 * acc1;
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Xn7 = pIn[6 ];
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d2 += a2 * acc1;
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/* Sample 2. 5 cycles */
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Xn8 = pIn[7 ];
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acc2 = b0 * Xn2 + d1;
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Xn9 = pIn[8 ];
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d1 = b1 * Xn2 + d2;
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Xn10 = pIn[9 ];
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d2 = b2 * Xn2;
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Xn11 = pIn[10];
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d1 += a1 * acc2;
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Xn12 = pIn[11];
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d2 += a2 * acc2;
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/* Sample 3. 5 cycles */
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Xn13 = pIn[12];
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acc3 = b0 * Xn3 + d1;
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Xn14 = pIn[13];
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d1 = b1 * Xn3 + d2;
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Xn15 = pIn[14];
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d2 = b2 * Xn3;
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Xn16 = pIn[15];
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d1 += a1 * acc3;
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pIn += 16;
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d2 += a2 * acc3;
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/* Sample 4. 5 cycles */
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acc4 = b0 * Xn4 + d1;
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d1 = b1 * Xn4 + d2;
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d2 = b2 * Xn4;
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d1 += a1 * acc4;
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d2 += a2 * acc4;
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/* Sample 5. 5 cycles */
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acc5 = b0 * Xn5 + d1;
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d1 = b1 * Xn5 + d2;
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d2 = b2 * Xn5;
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d1 += a1 * acc5;
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d2 += a2 * acc5;
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/* Sample 6. 5 cycles */
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acc6 = b0 * Xn6 + d1;
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d1 = b1 * Xn6 + d2;
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d2 = b2 * Xn6;
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d1 += a1 * acc6;
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d2 += a2 * acc6;
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/* Sample 7. 5 cycles */
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acc7 = b0 * Xn7 + d1;
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d1 = b1 * Xn7 + d2;
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d2 = b2 * Xn7;
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d1 += a1 * acc7;
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d2 += a2 * acc7;
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/* Sample 8. 5 cycles */
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acc8 = b0 * Xn8 + d1;
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d1 = b1 * Xn8 + d2;
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d2 = b2 * Xn8;
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d1 += a1 * acc8;
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d2 += a2 * acc8;
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/* Sample 9. 5 cycles */
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acc9 = b0 * Xn9 + d1;
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d1 = b1 * Xn9 + d2;
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d2 = b2 * Xn9;
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d1 += a1 * acc9;
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d2 += a2 * acc9;
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/* Sample 10. 5 cycles */
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acc10 = b0 * Xn10 + d1;
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d1 = b1 * Xn10 + d2;
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d2 = b2 * Xn10;
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d1 += a1 * acc10;
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d2 += a2 * acc10;
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/* Sample 11. 5 cycles */
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acc11 = b0 * Xn11 + d1;
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d1 = b1 * Xn11 + d2;
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d2 = b2 * Xn11;
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d1 += a1 * acc11;
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d2 += a2 * acc11;
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/* Sample 12. 5 cycles */
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acc12 = b0 * Xn12 + d1;
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d1 = b1 * Xn12 + d2;
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d2 = b2 * Xn12;
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d1 += a1 * acc12;
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d2 += a2 * acc12;
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/* Sample 13. 5 cycles */
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acc13 = b0 * Xn13 + d1;
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d1 = b1 * Xn13 + d2;
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d2 = b2 * Xn13;
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pOut[0 ] = acc1 ;
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d1 += a1 * acc13;
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pOut[1 ] = acc2 ;
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d2 += a2 * acc13;
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/* Sample 14. 5 cycles */
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pOut[2 ] = acc3 ;
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acc14 = b0 * Xn14 + d1;
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pOut[3 ] = acc4 ;
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d1 = b1 * Xn14 + d2;
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pOut[4 ] = acc5 ;
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d2 = b2 * Xn14;
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pOut[5 ] = acc6 ;
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d1 += a1 * acc14;
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pOut[6 ] = acc7 ;
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d2 += a2 * acc14;
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/* Sample 15. 5 cycles */
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pOut[7 ] = acc8 ;
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pOut[8 ] = acc9 ;
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acc15 = b0 * Xn15 + d1;
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pOut[9 ] = acc10;
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d1 = b1 * Xn15 + d2;
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pOut[10] = acc11;
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d2 = b2 * Xn15;
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pOut[11] = acc12;
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d1 += a1 * acc15;
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pOut[12] = acc13;
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d2 += a2 * acc15;
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/* Sample 16. 5 cycles */
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pOut[13] = acc14;
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acc16 = b0 * Xn16 + d1;
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pOut[14] = acc15;
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d1 = b1 * Xn16 + d2;
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pOut[15] = acc16;
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d2 = b2 * Xn16;
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sample--;
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d1 += a1 * acc16;
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pOut += 16;
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d2 += a2 * acc16;
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}
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sample = blockSize & 0xFu;
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while (sample > 0U) {
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Xn1 = *pIn;
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acc1 = b0 * Xn1 + d1;
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pIn++;
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d1 = b1 * Xn1 + d2;
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*pOut = acc1;
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d2 = b2 * Xn1;
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pOut++;
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d1 += a1 * acc1;
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sample--;
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d2 += a2 * acc1;
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}
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/* Store the updated state variables back into the state array */
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pState[0] = d1;
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/* The current stage input is given as the output to the next stage */
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pIn = pDst;
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pState[1] = d2;
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/* decrement the loop counter */
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stage--;
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pState += 2U;
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/*Reset the output working pointer */
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pOut = pDst;
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} while (stage > 0U);
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#elif defined(ARM_MATH_CM0_FAMILY)
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/* Run the below code for Cortex-M0 */
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do
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{
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/* Reading the coefficients */
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b0 = *pCoeffs++;
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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 */
|
||
|
Xn1 = *pIn++;
|
||
|
|
||
|
/* y[n] = b0 * x[n] + d1 */
|
||
|
acc1 = (b0 * Xn1) + d1;
|
||
|
|
||
|
/* Store the result in the accumulator in the destination buffer. */
|
||
|
*pOut++ = acc1;
|
||
|
|
||
|
/* Every time after the output is computed state should be updated. */
|
||
|
/* d1 = b1 * x[n] + a1 * y[n] + d2 */
|
||
|
d1 = ((b1 * Xn1) + (a1 * acc1)) + d2;
|
||
|
|
||
|
/* d2 = b2 * x[n] + a2 * y[n] */
|
||
|
d2 = (b2 * Xn1) + (a2 * acc1);
|
||
|
|
||
|
/* 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
|
||
|
|
||
|
float64_t Xn2, Xn3, Xn4; /* Input State variables */
|
||
|
float64_t acc2, acc3, acc4; /* accumulator */
|
||
|
|
||
|
|
||
|
float64_t p0, p1, p2, p3, p4, A1;
|
||
|
|
||
|
/* 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 four inputs */
|
||
|
Xn1 = pIn[0];
|
||
|
Xn2 = pIn[1];
|
||
|
Xn3 = pIn[2];
|
||
|
Xn4 = pIn[3];
|
||
|
pIn += 4;
|
||
|
|
||
|
p0 = b0 * Xn1;
|
||
|
p1 = b1 * Xn1;
|
||
|
acc1 = p0 + d1;
|
||
|
p0 = b0 * Xn2;
|
||
|
p3 = a1 * acc1;
|
||
|
p2 = b2 * Xn1;
|
||
|
A1 = p1 + p3;
|
||
|
p4 = a2 * acc1;
|
||
|
d1 = A1 + d2;
|
||
|
d2 = p2 + p4;
|
||
|
|
||
|
p1 = b1 * Xn2;
|
||
|
acc2 = p0 + d1;
|
||
|
p0 = b0 * Xn3;
|
||
|
p3 = a1 * acc2;
|
||
|
p2 = b2 * Xn2;
|
||
|
A1 = p1 + p3;
|
||
|
p4 = a2 * acc2;
|
||
|
d1 = A1 + d2;
|
||
|
d2 = p2 + p4;
|
||
|
|
||
|
p1 = b1 * Xn3;
|
||
|
acc3 = p0 + d1;
|
||
|
p0 = b0 * Xn4;
|
||
|
p3 = a1 * acc3;
|
||
|
p2 = b2 * Xn3;
|
||
|
A1 = p1 + p3;
|
||
|
p4 = a2 * acc3;
|
||
|
d1 = A1 + d2;
|
||
|
d2 = p2 + p4;
|
||
|
|
||
|
acc4 = p0 + d1;
|
||
|
p1 = b1 * Xn4;
|
||
|
p3 = a1 * acc4;
|
||
|
p2 = b2 * Xn4;
|
||
|
A1 = p1 + p3;
|
||
|
p4 = a2 * acc4;
|
||
|
d1 = A1 + d2;
|
||
|
d2 = p2 + p4;
|
||
|
|
||
|
pOut[0] = acc1;
|
||
|
pOut[1] = acc2;
|
||
|
pOut[2] = acc3;
|
||
|
pOut[3] = acc4;
|
||
|
pOut += 4;
|
||
|
|
||
|
sample--;
|
||
|
}
|
||
|
|
||
|
sample = blockSize & 0x3U;
|
||
|
while (sample > 0U) {
|
||
|
Xn1 = *pIn++;
|
||
|
|
||
|
p0 = b0 * Xn1;
|
||
|
p1 = b1 * Xn1;
|
||
|
acc1 = p0 + d1;
|
||
|
p3 = a1 * acc1;
|
||
|
p2 = b2 * Xn1;
|
||
|
A1 = p1 + p3;
|
||
|
p4 = a2 * acc1;
|
||
|
d1 = A1 + d2;
|
||
|
d2 = p2 + p4;
|
||
|
|
||
|
*pOut++ = acc1;
|
||
|
|
||
|
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
|
||
|
|
||
|
}
|
||
|
LOW_OPTIMIZATION_EXIT
|
||
|
|
||
|
/**
|
||
|
* @} end of BiquadCascadeDF2T group
|
||
|
*/
|