450 lines
16 KiB
C
450 lines
16 KiB
C
/* ----------------------------------------------------------------------
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* Project: CMSIS DSP Library
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* Title: arm_dct4_f32.c
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* Description: Processing function of DCT4 & IDCT4 F32
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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 groupTransforms
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*/
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/**
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* @defgroup DCT4_IDCT4 DCT Type IV Functions
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* Representation of signals by minimum number of values is important for storage and transmission.
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* The possibility of large discontinuity between the beginning and end of a period of a signal
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* in DFT can be avoided by extending the signal so that it is even-symmetric.
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* Discrete Cosine Transform (DCT) is constructed such that its energy is heavily concentrated in the lower part of the
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* spectrum and is very widely used in signal and image coding applications.
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* The family of DCTs (DCT type- 1,2,3,4) is the outcome of different combinations of homogeneous boundary conditions.
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* DCT has an excellent energy-packing capability, hence has many applications and in data compression in particular.
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*
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* DCT is essentially the Discrete Fourier Transform(DFT) of an even-extended real signal.
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* Reordering of the input data makes the computation of DCT just a problem of
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* computing the DFT of a real signal with a few additional operations.
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* This approach provides regular, simple, and very efficient DCT algorithms for practical hardware and software implementations.
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*
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* DCT type-II can be implemented using Fast fourier transform (FFT) internally, as the transform is applied on real values, Real FFT can be used.
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* DCT4 is implemented using DCT2 as their implementations are similar except with some added pre-processing and post-processing.
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* DCT2 implementation can be described in the following steps:
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* - Re-ordering input
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* - Calculating Real FFT
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* - Multiplication of weights and Real FFT output and getting real part from the product.
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*
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* This process is explained by the block diagram below:
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* \image html DCT4.gif "Discrete Cosine Transform - type-IV"
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*
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* \par Algorithm:
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* The N-point type-IV DCT is defined as a real, linear transformation by the formula:
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* \image html DCT4Equation.gif
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* where <code>k = 0,1,2,.....N-1</code>
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*\par
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* Its inverse is defined as follows:
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* \image html IDCT4Equation.gif
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* where <code>n = 0,1,2,.....N-1</code>
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*\par
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* The DCT4 matrices become involutory (i.e. they are self-inverse) by multiplying with an overall scale factor of sqrt(2/N).
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* The symmetry of the transform matrix indicates that the fast algorithms for the forward
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* and inverse transform computation are identical.
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* Note that the implementation of Inverse DCT4 and DCT4 is same, hence same process function can be used for both.
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*
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* \par Lengths supported by the transform:
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* As DCT4 internally uses Real FFT, it supports all the lengths 128, 512, 2048 and 8192.
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* The library provides separate functions for Q15, Q31, and floating-point data types.
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* \par Instance Structure
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* The instances for Real FFT and FFT, cosine values table and twiddle factor table are stored in an instance data structure.
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* A separate instance structure must be defined for each transform.
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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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* - Initializes Real FFT as its process function is used internally in DCT4, by calling arm_rfft_init_f32().
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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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* Manually initialize the instance structure as follows:
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* <pre>
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*arm_dct4_instance_f32 S = {N, Nby2, normalize, pTwiddle, pCosFactor, pRfft, pCfft};
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*arm_dct4_instance_q31 S = {N, Nby2, normalize, pTwiddle, pCosFactor, pRfft, pCfft};
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*arm_dct4_instance_q15 S = {N, Nby2, normalize, pTwiddle, pCosFactor, pRfft, pCfft};
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* </pre>
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* where \c N is the length of the DCT4; \c Nby2 is half of the length of the DCT4;
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* \c normalize is normalizing factor used and is equal to <code>sqrt(2/N)</code>;
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* \c pTwiddle points to the twiddle factor table;
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* \c pCosFactor points to the cosFactor table;
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* \c pRfft points to the real FFT instance;
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* \c pCfft points to the complex FFT instance;
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* The CFFT and RFFT structures also needs to be initialized, refer to arm_cfft_radix4_f32()
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* and arm_rfft_f32() respectively for details regarding static initialization.
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*
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* \par Fixed-Point Behavior
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* Care must be taken when using the fixed-point versions of the DCT4 transform functions.
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* In particular, the overflow and saturation behavior of the accumulator used in each function must be considered.
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* Refer to the function specific documentation below for usage guidelines.
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*/
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/**
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* @addtogroup DCT4_IDCT4
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* @{
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*/
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/**
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* @brief Processing function for the floating-point DCT4/IDCT4.
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* @param[in] *S points to an instance of the floating-point DCT4/IDCT4 structure.
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* @param[in] *pState points to state buffer.
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* @param[in,out] *pInlineBuffer points to the in-place input and output buffer.
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* @return none.
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*/
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void arm_dct4_f32(
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const arm_dct4_instance_f32 * S,
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float32_t * pState,
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float32_t * pInlineBuffer)
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{
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uint32_t i; /* Loop counter */
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float32_t *weights = S->pTwiddle; /* Pointer to the Weights table */
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float32_t *cosFact = S->pCosFactor; /* Pointer to the cos factors table */
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float32_t *pS1, *pS2, *pbuff; /* Temporary pointers for input buffer and pState buffer */
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float32_t in; /* Temporary variable */
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/* DCT4 computation involves DCT2 (which is calculated using RFFT)
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* along with some pre-processing and post-processing.
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* Computational procedure is explained as follows:
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* (a) Pre-processing involves multiplying input with cos factor,
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* r(n) = 2 * u(n) * cos(pi*(2*n+1)/(4*n))
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* where,
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* r(n) -- output of preprocessing
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* u(n) -- input to preprocessing(actual Source buffer)
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* (b) Calculation of DCT2 using FFT is divided into three steps:
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* Step1: Re-ordering of even and odd elements of input.
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* Step2: Calculating FFT of the re-ordered input.
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* Step3: Taking the real part of the product of FFT output and weights.
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* (c) Post-processing - DCT4 can be obtained from DCT2 output using the following equation:
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* Y4(k) = Y2(k) - Y4(k-1) and Y4(-1) = Y4(0)
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* where,
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* Y4 -- DCT4 output, Y2 -- DCT2 output
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* (d) Multiplying the output with the normalizing factor sqrt(2/N).
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*/
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/*-------- Pre-processing ------------*/
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/* Multiplying input with cos factor i.e. r(n) = 2 * x(n) * cos(pi*(2*n+1)/(4*n)) */
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arm_scale_f32(pInlineBuffer, 2.0f, pInlineBuffer, S->N);
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arm_mult_f32(pInlineBuffer, cosFact, pInlineBuffer, S->N);
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/* ----------------------------------------------------------------
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* Step1: Re-ordering of even and odd elements as,
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* pState[i] = pInlineBuffer[2*i] and
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* pState[N-i-1] = pInlineBuffer[2*i+1] where i = 0 to N/2
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---------------------------------------------------------------------*/
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/* pS1 initialized to pState */
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pS1 = pState;
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/* pS2 initialized to pState+N-1, so that it points to the end of the state buffer */
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pS2 = pState + (S->N - 1U);
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/* pbuff initialized to input buffer */
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pbuff = pInlineBuffer;
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#if defined (ARM_MATH_DSP)
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/* Run the below code for Cortex-M4 and Cortex-M3 */
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/* Initializing the loop counter to N/2 >> 2 for loop unrolling by 4 */
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i = (uint32_t) S->Nby2 >> 2U;
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/* First part of the processing with loop unrolling. Compute 4 outputs at a time.
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** a second loop below computes the remaining 1 to 3 samples. */
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do
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{
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/* Re-ordering of even and odd elements */
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/* pState[i] = pInlineBuffer[2*i] */
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*pS1++ = *pbuff++;
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/* pState[N-i-1] = pInlineBuffer[2*i+1] */
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*pS2-- = *pbuff++;
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*pS1++ = *pbuff++;
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*pS2-- = *pbuff++;
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*pS1++ = *pbuff++;
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*pS2-- = *pbuff++;
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*pS1++ = *pbuff++;
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*pS2-- = *pbuff++;
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/* Decrement the loop counter */
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i--;
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} while (i > 0U);
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/* pbuff initialized to input buffer */
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pbuff = pInlineBuffer;
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/* pS1 initialized to pState */
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pS1 = pState;
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/* Initializing the loop counter to N/4 instead of N for loop unrolling */
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i = (uint32_t) S->N >> 2U;
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/* Processing with loop unrolling 4 times as N is always multiple of 4.
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* Compute 4 outputs at a time */
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do
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{
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/* Writing the re-ordered output back to inplace input buffer */
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*pbuff++ = *pS1++;
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*pbuff++ = *pS1++;
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*pbuff++ = *pS1++;
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*pbuff++ = *pS1++;
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/* Decrement the loop counter */
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i--;
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} while (i > 0U);
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/* ---------------------------------------------------------
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* Step2: Calculate RFFT for N-point input
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* ---------------------------------------------------------- */
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/* pInlineBuffer is real input of length N , pState is the complex output of length 2N */
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arm_rfft_f32(S->pRfft, pInlineBuffer, pState);
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/*----------------------------------------------------------------------
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* Step3: Multiply the FFT output with the weights.
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*----------------------------------------------------------------------*/
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arm_cmplx_mult_cmplx_f32(pState, weights, pState, S->N);
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/* ----------- Post-processing ---------- */
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/* DCT-IV can be obtained from DCT-II by the equation,
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* Y4(k) = Y2(k) - Y4(k-1) and Y4(-1) = Y4(0)
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* Hence, Y4(0) = Y2(0)/2 */
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/* Getting only real part from the output and Converting to DCT-IV */
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/* Initializing the loop counter to N >> 2 for loop unrolling by 4 */
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i = ((uint32_t) S->N - 1U) >> 2U;
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/* pbuff initialized to input buffer. */
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pbuff = pInlineBuffer;
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/* pS1 initialized to pState */
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pS1 = pState;
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/* Calculating Y4(0) from Y2(0) using Y4(0) = Y2(0)/2 */
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in = *pS1++ * (float32_t) 0.5;
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/* input buffer acts as inplace, so output values are stored in the input itself. */
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*pbuff++ = in;
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/* pState pointer is incremented twice as the real values are located alternatively in the array */
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pS1++;
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/* First part of the processing with loop unrolling. Compute 4 outputs at a time.
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** a second loop below computes the remaining 1 to 3 samples. */
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do
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{
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/* Calculating Y4(1) to Y4(N-1) from Y2 using equation Y4(k) = Y2(k) - Y4(k-1) */
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/* pState pointer (pS1) is incremented twice as the real values are located alternatively in the array */
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in = *pS1++ - in;
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*pbuff++ = in;
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/* points to the next real value */
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pS1++;
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in = *pS1++ - in;
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*pbuff++ = in;
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pS1++;
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in = *pS1++ - in;
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*pbuff++ = in;
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pS1++;
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in = *pS1++ - in;
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*pbuff++ = in;
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pS1++;
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/* Decrement the loop counter */
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i--;
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} while (i > 0U);
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/* If the blockSize is not a multiple of 4, compute any remaining output samples here.
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** No loop unrolling is used. */
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i = ((uint32_t) S->N - 1U) % 0x4U;
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while (i > 0U)
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{
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/* Calculating Y4(1) to Y4(N-1) from Y2 using equation Y4(k) = Y2(k) - Y4(k-1) */
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/* pState pointer (pS1) is incremented twice as the real values are located alternatively in the array */
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in = *pS1++ - in;
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*pbuff++ = in;
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/* points to the next real value */
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pS1++;
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/* Decrement the loop counter */
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i--;
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}
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/*------------ Normalizing the output by multiplying with the normalizing factor ----------*/
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/* Initializing the loop counter to N/4 instead of N for loop unrolling */
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i = (uint32_t) S->N >> 2U;
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/* pbuff initialized to the pInlineBuffer(now contains the output values) */
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pbuff = pInlineBuffer;
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/* Processing with loop unrolling 4 times as N is always multiple of 4. Compute 4 outputs at a time */
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do
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{
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/* Multiplying pInlineBuffer with the normalizing factor sqrt(2/N) */
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in = *pbuff;
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*pbuff++ = in * S->normalize;
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in = *pbuff;
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*pbuff++ = in * S->normalize;
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in = *pbuff;
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*pbuff++ = in * S->normalize;
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in = *pbuff;
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*pbuff++ = in * S->normalize;
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/* Decrement the loop counter */
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i--;
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} while (i > 0U);
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#else
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/* Run the below code for Cortex-M0 */
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/* Initializing the loop counter to N/2 */
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i = (uint32_t) S->Nby2;
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do
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{
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/* Re-ordering of even and odd elements */
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/* pState[i] = pInlineBuffer[2*i] */
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*pS1++ = *pbuff++;
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/* pState[N-i-1] = pInlineBuffer[2*i+1] */
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*pS2-- = *pbuff++;
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/* Decrement the loop counter */
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i--;
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} while (i > 0U);
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/* pbuff initialized to input buffer */
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pbuff = pInlineBuffer;
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/* pS1 initialized to pState */
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pS1 = pState;
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/* Initializing the loop counter */
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i = (uint32_t) S->N;
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do
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{
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/* Writing the re-ordered output back to inplace input buffer */
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*pbuff++ = *pS1++;
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/* Decrement the loop counter */
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i--;
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} while (i > 0U);
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/* ---------------------------------------------------------
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* Step2: Calculate RFFT for N-point input
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* ---------------------------------------------------------- */
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/* pInlineBuffer is real input of length N , pState is the complex output of length 2N */
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arm_rfft_f32(S->pRfft, pInlineBuffer, pState);
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/*----------------------------------------------------------------------
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* Step3: Multiply the FFT output with the weights.
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*----------------------------------------------------------------------*/
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arm_cmplx_mult_cmplx_f32(pState, weights, pState, S->N);
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/* ----------- Post-processing ---------- */
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/* DCT-IV can be obtained from DCT-II by the equation,
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* Y4(k) = Y2(k) - Y4(k-1) and Y4(-1) = Y4(0)
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* Hence, Y4(0) = Y2(0)/2 */
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/* Getting only real part from the output and Converting to DCT-IV */
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/* pbuff initialized to input buffer. */
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pbuff = pInlineBuffer;
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/* pS1 initialized to pState */
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pS1 = pState;
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/* Calculating Y4(0) from Y2(0) using Y4(0) = Y2(0)/2 */
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in = *pS1++ * (float32_t) 0.5;
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/* input buffer acts as inplace, so output values are stored in the input itself. */
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*pbuff++ = in;
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/* pState pointer is incremented twice as the real values are located alternatively in the array */
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pS1++;
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/* Initializing the loop counter */
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i = ((uint32_t) S->N - 1U);
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do
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{
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/* Calculating Y4(1) to Y4(N-1) from Y2 using equation Y4(k) = Y2(k) - Y4(k-1) */
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/* pState pointer (pS1) is incremented twice as the real values are located alternatively in the array */
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in = *pS1++ - in;
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*pbuff++ = in;
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/* points to the next real value */
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pS1++;
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/* Decrement the loop counter */
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i--;
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} while (i > 0U);
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/*------------ Normalizing the output by multiplying with the normalizing factor ----------*/
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/* Initializing the loop counter */
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i = (uint32_t) S->N;
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/* pbuff initialized to the pInlineBuffer(now contains the output values) */
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pbuff = pInlineBuffer;
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do
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{
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/* Multiplying pInlineBuffer with the normalizing factor sqrt(2/N) */
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in = *pbuff;
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*pbuff++ = in * S->normalize;
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/* Decrement the loop counter */
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i--;
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} while (i > 0U);
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#endif /* #if defined (ARM_MATH_DSP) */
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}
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/**
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* @} end of DCT4_IDCT4 group
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*/
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