/* ----------------------------------------------------------------------
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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_cfft_radix8_f32.c
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*
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* Description: Radix-8 Decimation in Frequency CFFT & CIFFT Floating point processing function
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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 groupTransforms
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*/
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/**
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* @defgroup Radix8_CFFT_CIFFT Radix-8 Complex FFT Functions
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*
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* \par
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* Complex Fast Fourier Transform(CFFT) and Complex Inverse Fast Fourier Transform(CIFFT) is an efficient algorithm to compute Discrete Fourier Transform(DFT) and Inverse Discrete Fourier Transform(IDFT).
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* Computational complexity of CFFT reduces drastically when compared to DFT.
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* \par
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* This set of functions implements CFFT/CIFFT
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* for floating-point data types. The functions operates on in-place buffer which uses same buffer for input and output.
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* Complex input is stored in input buffer in an interleaved fashion.
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*
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* \par
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* The functions operate on blocks of input and output data and each call to the function processes
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* <code>2*fftLen</code> samples through the transform. <code>pSrc</code> points to In-place arrays containing <code>2*fftLen</code> values.
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* \par
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* The <code>pSrc</code> points to the array of in-place buffer of size <code>2*fftLen</code> and inputs and outputs are stored in an interleaved fashion as shown below.
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* <pre> {real[0], imag[0], real[1], imag[1],..} </pre>
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*
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* \par Lengths supported by the transform:
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* \par
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* Internally, the function utilize a Radix-8 decimation in frequency(DIF) algorithm
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* and the size of the FFT supported are of the lengths [ 64, 512, 4096].
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*
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*
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* \par Algorithm:
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*
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* <b>Complex Fast Fourier Transform:</b>
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* \par
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* Input real and imaginary data:
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* <pre>
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* x(n) = xa + j * ya
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* x(n+N/4 ) = xb + j * yb
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* x(n+N/2 ) = xc + j * yc
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* x(n+3N 4) = xd + j * yd
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* </pre>
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* where N is length of FFT
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* \par
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* Output real and imaginary data:
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* <pre>
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* X(4r) = xa'+ j * ya'
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* X(4r+1) = xb'+ j * yb'
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* X(4r+2) = xc'+ j * yc'
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* X(4r+3) = xd'+ j * yd'
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* </pre>
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* \par
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* Twiddle factors for Radix-8 FFT:
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* <pre>
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* Wn = co1 + j * (- si1)
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* W2n = co2 + j * (- si2)
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* W3n = co3 + j * (- si3)
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* </pre>
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*
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* \par
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* \image html CFFT.gif "Radix-8 Decimation-in Frequency Complex Fast Fourier Transform"
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*
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* \par
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* Output from Radix-8 CFFT Results in Digit reversal order. Interchange middle two branches of every butterfly results in Bit reversed output.
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* \par
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* <b> Butterfly CFFT equations:</b>
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* <pre>
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* xa' = xa + xb + xc + xd
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* ya' = ya + yb + yc + yd
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* xc' = (xa+yb-xc-yd)* co1 + (ya-xb-yc+xd)* (si1)
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* yc' = (ya-xb-yc+xd)* co1 - (xa+yb-xc-yd)* (si1)
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* xb' = (xa-xb+xc-xd)* co2 + (ya-yb+yc-yd)* (si2)
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* yb' = (ya-yb+yc-yd)* co2 - (xa-xb+xc-xd)* (si2)
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* xd' = (xa-yb-xc+yd)* co3 + (ya+xb-yc-xd)* (si3)
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* yd' = (ya+xb-yc-xd)* co3 - (xa-yb-xc+yd)* (si3)
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* </pre>
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*
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* \par
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* where <code>fftLen</code> length of CFFT/CIFFT; <code>ifftFlag</code> Flag for selection of CFFT or CIFFT(Set ifftFlag to calculate CIFFT otherwise calculates CFFT);
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* <code>bitReverseFlag</code> Flag for selection of output order(Set bitReverseFlag to output in normal order otherwise output in bit reversed order);
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* <code>pTwiddle</code>points to array of twiddle coefficients; <code>pBitRevTable</code> points to the array of bit reversal table.
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* <code>twidCoefModifier</code> modifier for twiddle factor table which supports all FFT lengths with same table;
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* <code>pBitRevTable</code> modifier for bit reversal table which supports all FFT lengths with same table.
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* <code>onebyfftLen</code> value of 1/fftLen to calculate CIFFT;
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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 CFFT/CIFFT function.
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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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* @brief Core function for the floating-point CFFT butterfly process.
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* @param[in, out] *pSrc points to the in-place buffer of floating-point data type.
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* @param[in] fftLen length of the FFT.
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* @param[in] *pCoef points to the twiddle coefficient buffer.
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* @param[in] twidCoefModifier twiddle coefficient modifier that supports different size FFTs with the same twiddle factor table.
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* @return none.
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*/
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void arm_radix8_butterfly_f32(
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float32_t * pSrc,
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uint16_t fftLen,
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const float32_t * pCoef,
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uint16_t twidCoefModifier)
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{
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uint32_t ia1, ia2, ia3, ia4, ia5, ia6, ia7;
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uint32_t i1, i2, i3, i4, i5, i6, i7, i8;
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uint32_t id;
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uint32_t n1, n2, j;
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float32_t r1, r2, r3, r4, r5, r6, r7, r8;
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float32_t t1, t2;
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float32_t s1, s2, s3, s4, s5, s6, s7, s8;
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float32_t p1, p2, p3, p4;
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float32_t co2, co3, co4, co5, co6, co7, co8;
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float32_t si2, si3, si4, si5, si6, si7, si8;
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const float32_t C81 = 0.70710678118f;
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n2 = fftLen;
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do
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{
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n1 = n2;
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n2 = n2 >> 3;
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i1 = 0;
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do
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{
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i2 = i1 + n2;
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i3 = i2 + n2;
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i4 = i3 + n2;
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i5 = i4 + n2;
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i6 = i5 + n2;
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i7 = i6 + n2;
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i8 = i7 + n2;
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r1 = pSrc[2 * i1] + pSrc[2 * i5];
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r5 = pSrc[2 * i1] - pSrc[2 * i5];
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r2 = pSrc[2 * i2] + pSrc[2 * i6];
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r6 = pSrc[2 * i2] - pSrc[2 * i6];
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r3 = pSrc[2 * i3] + pSrc[2 * i7];
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r7 = pSrc[2 * i3] - pSrc[2 * i7];
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r4 = pSrc[2 * i4] + pSrc[2 * i8];
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r8 = pSrc[2 * i4] - pSrc[2 * i8];
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t1 = r1 - r3;
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r1 = r1 + r3;
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r3 = r2 - r4;
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r2 = r2 + r4;
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pSrc[2 * i1] = r1 + r2;
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pSrc[2 * i5] = r1 - r2;
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r1 = pSrc[2 * i1 + 1] + pSrc[2 * i5 + 1];
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s5 = pSrc[2 * i1 + 1] - pSrc[2 * i5 + 1];
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r2 = pSrc[2 * i2 + 1] + pSrc[2 * i6 + 1];
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s6 = pSrc[2 * i2 + 1] - pSrc[2 * i6 + 1];
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s3 = pSrc[2 * i3 + 1] + pSrc[2 * i7 + 1];
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s7 = pSrc[2 * i3 + 1] - pSrc[2 * i7 + 1];
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r4 = pSrc[2 * i4 + 1] + pSrc[2 * i8 + 1];
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s8 = pSrc[2 * i4 + 1] - pSrc[2 * i8 + 1];
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t2 = r1 - s3;
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r1 = r1 + s3;
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s3 = r2 - r4;
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r2 = r2 + r4;
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pSrc[2 * i1 + 1] = r1 + r2;
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pSrc[2 * i5 + 1] = r1 - r2;
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pSrc[2 * i3] = t1 + s3;
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pSrc[2 * i7] = t1 - s3;
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pSrc[2 * i3 + 1] = t2 - r3;
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pSrc[2 * i7 + 1] = t2 + r3;
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r1 = (r6 - r8) * C81;
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r6 = (r6 + r8) * C81;
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r2 = (s6 - s8) * C81;
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s6 = (s6 + s8) * C81;
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t1 = r5 - r1;
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r5 = r5 + r1;
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r8 = r7 - r6;
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r7 = r7 + r6;
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t2 = s5 - r2;
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s5 = s5 + r2;
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s8 = s7 - s6;
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s7 = s7 + s6;
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pSrc[2 * i2] = r5 + s7;
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pSrc[2 * i8] = r5 - s7;
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pSrc[2 * i6] = t1 + s8;
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pSrc[2 * i4] = t1 - s8;
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pSrc[2 * i2 + 1] = s5 - r7;
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pSrc[2 * i8 + 1] = s5 + r7;
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pSrc[2 * i6 + 1] = t2 - r8;
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pSrc[2 * i4 + 1] = t2 + r8;
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i1 += n1;
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} while(i1 < fftLen);
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if(n2 < 8)
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break;
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ia1 = 0;
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j = 1;
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do
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{
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/* index calculation for the coefficients */
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id = ia1 + twidCoefModifier;
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ia1 = id;
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ia2 = ia1 + id;
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ia3 = ia2 + id;
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ia4 = ia3 + id;
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ia5 = ia4 + id;
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ia6 = ia5 + id;
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ia7 = ia6 + id;
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co2 = pCoef[2 * ia1];
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co3 = pCoef[2 * ia2];
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co4 = pCoef[2 * ia3];
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co5 = pCoef[2 * ia4];
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co6 = pCoef[2 * ia5];
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co7 = pCoef[2 * ia6];
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co8 = pCoef[2 * ia7];
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si2 = pCoef[2 * ia1 + 1];
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si3 = pCoef[2 * ia2 + 1];
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si4 = pCoef[2 * ia3 + 1];
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si5 = pCoef[2 * ia4 + 1];
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si6 = pCoef[2 * ia5 + 1];
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si7 = pCoef[2 * ia6 + 1];
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si8 = pCoef[2 * ia7 + 1];
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i1 = j;
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do
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{
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/* index calculation for the input */
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i2 = i1 + n2;
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i3 = i2 + n2;
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i4 = i3 + n2;
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i5 = i4 + n2;
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i6 = i5 + n2;
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i7 = i6 + n2;
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i8 = i7 + n2;
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r1 = pSrc[2 * i1] + pSrc[2 * i5];
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r5 = pSrc[2 * i1] - pSrc[2 * i5];
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r2 = pSrc[2 * i2] + pSrc[2 * i6];
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r6 = pSrc[2 * i2] - pSrc[2 * i6];
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r3 = pSrc[2 * i3] + pSrc[2 * i7];
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r7 = pSrc[2 * i3] - pSrc[2 * i7];
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r4 = pSrc[2 * i4] + pSrc[2 * i8];
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r8 = pSrc[2 * i4] - pSrc[2 * i8];
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t1 = r1 - r3;
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r1 = r1 + r3;
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r3 = r2 - r4;
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r2 = r2 + r4;
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pSrc[2 * i1] = r1 + r2;
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r2 = r1 - r2;
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s1 = pSrc[2 * i1 + 1] + pSrc[2 * i5 + 1];
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s5 = pSrc[2 * i1 + 1] - pSrc[2 * i5 + 1];
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s2 = pSrc[2 * i2 + 1] + pSrc[2 * i6 + 1];
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s6 = pSrc[2 * i2 + 1] - pSrc[2 * i6 + 1];
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s3 = pSrc[2 * i3 + 1] + pSrc[2 * i7 + 1];
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s7 = pSrc[2 * i3 + 1] - pSrc[2 * i7 + 1];
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s4 = pSrc[2 * i4 + 1] + pSrc[2 * i8 + 1];
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s8 = pSrc[2 * i4 + 1] - pSrc[2 * i8 + 1];
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t2 = s1 - s3;
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s1 = s1 + s3;
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s3 = s2 - s4;
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s2 = s2 + s4;
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r1 = t1 + s3;
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t1 = t1 - s3;
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pSrc[2 * i1 + 1] = s1 + s2;
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s2 = s1 - s2;
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s1 = t2 - r3;
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t2 = t2 + r3;
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p1 = co5 * r2;
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p2 = si5 * s2;
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p3 = co5 * s2;
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p4 = si5 * r2;
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pSrc[2 * i5] = p1 + p2;
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pSrc[2 * i5 + 1] = p3 - p4;
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p1 = co3 * r1;
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p2 = si3 * s1;
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p3 = co3 * s1;
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p4 = si3 * r1;
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pSrc[2 * i3] = p1 + p2;
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pSrc[2 * i3 + 1] = p3 - p4;
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p1 = co7 * t1;
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p2 = si7 * t2;
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p3 = co7 * t2;
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p4 = si7 * t1;
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pSrc[2 * i7] = p1 + p2;
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pSrc[2 * i7 + 1] = p3 - p4;
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r1 = (r6 - r8) * C81;
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r6 = (r6 + r8) * C81;
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s1 = (s6 - s8) * C81;
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s6 = (s6 + s8) * C81;
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t1 = r5 - r1;
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r5 = r5 + r1;
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r8 = r7 - r6;
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r7 = r7 + r6;
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t2 = s5 - s1;
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s5 = s5 + s1;
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s8 = s7 - s6;
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s7 = s7 + s6;
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r1 = r5 + s7;
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r5 = r5 - s7;
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r6 = t1 + s8;
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t1 = t1 - s8;
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s1 = s5 - r7;
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s5 = s5 + r7;
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s6 = t2 - r8;
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t2 = t2 + r8;
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p1 = co2 * r1;
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p2 = si2 * s1;
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p3 = co2 * s1;
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p4 = si2 * r1;
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pSrc[2 * i2] = p1 + p2;
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pSrc[2 * i2 + 1] = p3 - p4;
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p1 = co8 * r5;
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p2 = si8 * s5;
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p3 = co8 * s5;
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p4 = si8 * r5;
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pSrc[2 * i8] = p1 + p2;
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pSrc[2 * i8 + 1] = p3 - p4;
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p1 = co6 * r6;
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p2 = si6 * s6;
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p3 = co6 * s6;
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p4 = si6 * r6;
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pSrc[2 * i6] = p1 + p2;
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pSrc[2 * i6 + 1] = p3 - p4;
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p1 = co4 * t1;
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p2 = si4 * t2;
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p3 = co4 * t2;
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p4 = si4 * t1;
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pSrc[2 * i4] = p1 + p2;
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pSrc[2 * i4 + 1] = p3 - p4;
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i1 += n1;
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} while(i1 < fftLen);
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j++;
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} while(j < n2);
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twidCoefModifier <<= 3;
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} while(n2 > 7);
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}
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/**
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* @} end of Radix8_CFFT_CIFFT group
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*/
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