Fork of mbed-dsp. CMSIS-DSP library of supporting NEON

Dependents:   mbed-os-example-cmsis_dsp_neon

Fork of mbed-dsp by mbed official

Information

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CMSIS-DSP of supporting NEON

What is this ?

A library for CMSIS-DSP of supporting NEON.
We supported the NEON to CMSIS-DSP Ver1.4.3(CMSIS V4.1) that ARM supplied, has achieved the processing speed improvement.
If you use the mbed-dsp library, you can use to replace this library.
CMSIS-DSP of supporting NEON is provied as a library.

Library Creation environment

CMSIS-DSP library of supporting NEON was created by the following environment.

  • Compiler
    ARMCC Version 5.03
  • Compile option switch[C Compiler]
   -DARM_MATH_MATRIX_CHECK -DARM_MATH_ROUNDING -O3 -Otime --cpu=Cortex-A9 --littleend --arm 
   --apcs=/interwork --no_unaligned_access --fpu=vfpv3_fp16 --fpmode=fast --apcs=/hardfp 
   --vectorize --asm
  • Compile option switch[Assembler]
   --cpreproc --cpu=Cortex-A9 --littleend --arm --apcs=/interwork --no_unaligned_access 
   --fpu=vfpv3_fp16 --fpmode=fast --apcs=/hardfp


Effects of NEON support

In the data which passes to each function, large size will be expected more effective than small size.
Also if the data is a multiple of 16, effect will be expected in every function in the CMSIS-DSP.


NEON対応CMSIS-DSP

概要

NEON対応したCMSIS-DSPのライブラリです。
ARM社提供のCMSIS-DSP Ver1.4.3(CMSIS V4.1)をターゲットにNEON対応を行ない、処理速度向上を実現しております。
mbed-dspライブラリを使用している場合は、本ライブラリに置き換えて使用することができます。
NEON対応したCMSIS-DSPはライブラリで提供します。

ライブラリ作成環境

NEON対応CMSIS-DSPライブラリは、以下の環境で作成しています。

  • コンパイラ
    ARMCC Version 5.03
  • コンパイルオプションスイッチ[C Compiler]
   -DARM_MATH_MATRIX_CHECK -DARM_MATH_ROUNDING -O3 -Otime --cpu=Cortex-A9 --littleend --arm 
   --apcs=/interwork --no_unaligned_access --fpu=vfpv3_fp16 --fpmode=fast --apcs=/hardfp 
   --vectorize --asm
  • コンパイルオプションスイッチ[Assembler]
   --cpreproc --cpu=Cortex-A9 --littleend --arm --apcs=/interwork --no_unaligned_access 
   --fpu=vfpv3_fp16 --fpmode=fast --apcs=/hardfp


NEON対応による効果について

CMSIS-DSP内の各関数へ渡すデータは、小さいサイズよりも大きいサイズの方が効果が見込めます。
また、16の倍数のデータであれば、CMSIS-DSP内のどの関数でも効果が見込めます。


Revision:
5:a912b042151f
Parent:
4:9cee975aadce
--- a/cmsis_dsp/TransformFunctions/arm_cfft_f32.c	Mon Jun 23 09:30:09 2014 +0100
+++ /dev/null	Thu Jan 01 00:00:00 1970 +0000
@@ -1,616 +0,0 @@
-/* ----------------------------------------------------------------------    
-* Copyright (C) 2010-2013 ARM Limited. All rights reserved.    
-*    
-* $Date:        17. January 2013  
-* $Revision: 	V1.4.1  
-*    
-* Project: 	    CMSIS DSP Library    
-* Title:	    arm_cfft_f32.c   
-*    
-* Description:	Combined Radix Decimation in Frequency CFFT Floating point processing function
-*    
-* Target Processor: Cortex-M4/Cortex-M3/Cortex-M0
-*  
-* Redistribution and use in source and binary forms, with or without 
-* modification, are permitted provided that the following conditions
-* are met:
-*   - Redistributions of source code must retain the above copyright
-*     notice, this list of conditions and the following disclaimer.
-*   - Redistributions in binary form must reproduce the above copyright
-*     notice, this list of conditions and the following disclaimer in
-*     the documentation and/or other materials provided with the 
-*     distribution.
-*   - Neither the name of ARM LIMITED nor the names of its contributors
-*     may be used to endorse or promote products derived from this
-*     software without specific prior written permission.
-*
-* THIS SOFTWARE IS PROVIDED BY THE COPYRIGHT HOLDERS AND CONTRIBUTORS
-* "AS IS" AND ANY EXPRESS OR IMPLIED WARRANTIES, INCLUDING, BUT NOT
-* LIMITED TO, THE IMPLIED WARRANTIES OF MERCHANTABILITY AND FITNESS
-* FOR A PARTICULAR PURPOSE ARE DISCLAIMED. IN NO EVENT SHALL THE 
-* COPYRIGHT OWNER OR CONTRIBUTORS BE LIABLE FOR ANY DIRECT, INDIRECT,
-* INCIDENTAL, SPECIAL, EXEMPLARY, OR CONSEQUENTIAL DAMAGES (INCLUDING,
-* BUT NOT LIMITED TO, PROCUREMENT OF SUBSTITUTE GOODS OR SERVICES;
-* LOSS OF USE, DATA, OR PROFITS; OR BUSINESS INTERRUPTION) HOWEVER
-* CAUSED AND ON ANY THEORY OF LIABILITY, WHETHER IN CONTRACT, STRICT
-* LIABILITY, OR TORT (INCLUDING NEGLIGENCE OR OTHERWISE) ARISING IN
-* ANY WAY OUT OF THE USE OF THIS SOFTWARE, EVEN IF ADVISED OF THE
-* POSSIBILITY OF SUCH DAMAGE.   
-* -------------------------------------------------------------------- */
-
-
-#include "arm_math.h"
-#include "arm_common_tables.h"
-
-extern void arm_radix8_butterfly_f32(
-  float32_t * pSrc,
-  uint16_t fftLen,
-  const float32_t * pCoef,
-  uint16_t twidCoefModifier);
-
-extern void arm_bitreversal_32(
-		uint32_t * pSrc,
-		const uint16_t bitRevLen,
-		const uint16_t * pBitRevTable);
-
-/**   
-* @ingroup groupTransforms   
-*/
-
-/**   
-* @defgroup ComplexFFT Complex FFT Functions   
-*   
-* \par
-* The Fast Fourier Transform (FFT) is an efficient algorithm for computing the
-* Discrete Fourier Transform (DFT).  The FFT can be orders of magnitude faster
-* than the DFT, especially for long lengths.
-* The algorithms described in this section
-* operate on complex data.  A separate set of functions is devoted to handling
-* of real sequences.
-* \par
-* There are separate algorithms for handling floating-point, Q15, and Q31 data
-* types.  The algorithms available for each data type are described next.
-* \par
-* The FFT functions operate in-place.  That is, the array holding the input data
-* will also be used to hold the corresponding result.  The input data is complex
-* and contains <code>2*fftLen</code> interleaved values as shown below.
-* <pre> {real[0], imag[0], real[1], imag[1],..} </pre>
-* The FFT result will be contained in the same array and the frequency domain
-* values will have the same interleaving.
-*
-* \par Floating-point
-* The floating-point complex FFT uses a mixed-radix algorithm.  Multiple radix-8
-* stages are performed along with a single radix-2 or radix-4 stage, as needed.
-* The algorithm supports lengths of [16, 32, 64, ..., 4096] and each length uses
-* a different twiddle factor table.  
-* \par
-* The function uses the standard FFT definition and output values may grow by a
-* factor of <code>fftLen</code> when computing the forward transform.  The
-* inverse transform includes a scale of <code>1/fftLen</code> as part of the
-* calculation and this matches the textbook definition of the inverse FFT.
-* \par
-* Preinitialized data structures containing twiddle factors and bit reversal
-* tables are provided and defined in <code>arm_const_structs.h</code>.  Include 
-* this header in your function and then pass one of the constant structures as 
-* an argument to arm_cfft_f32.  For example:
-* \par
-* <code>arm_cfft_f32(arm_cfft_sR_f32_len64, pSrc, 1, 1)</code>
-* \par
-* computes a 64-point inverse complex FFT including bit reversal.
-* The data structures are treated as constant data and not modified during the
-* calculation.  The same data structure can be reused for multiple transforms
-* including mixing forward and inverse transforms.
-* \par
-* Earlier releases of the library provided separate radix-2 and radix-4
-* algorithms that operated on floating-point data.  These functions are still
-* provided but are deprecated.  The older functions are slower and less general
-* than the new functions.
-* \par
-* An example of initialization of the constants for the arm_cfft_f32 function follows:
-* \par
-* const static arm_cfft_instance_f32 *S;
-* ...
-*		switch (length) {
-*    		case 16:
-*    			S = & arm_cfft_sR_f32_len16;
-*    		break;
-*    		case 32:
-*    			S = & arm_cfft_sR_f32_len32;
-*    		break;
-*			case 64:
-*    			S = & arm_cfft_sR_f32_len64;
-*    		break;
-*    		case 128:
-*    			S = & arm_cfft_sR_f32_len128;
-*    		break;
-*    		case 256:
-*    			S = & arm_cfft_sR_f32_len256;
-*    		break;
-*    		case 512:
-*    			S = & arm_cfft_sR_f32_len512;
-*    		break;
-*    		case 1024:
-*    			S = & arm_cfft_sR_f32_len1024;
-*    		break;
-*    		case 2048:
-*    			S = & arm_cfft_sR_f32_len2048;
-*    		break;
-*    		case 4096:
-*    			S = & arm_cfft_sR_f32_len4096;
-*    		break;
-*			}
-* \par Q15 and Q31
-* The library provides radix-2 and radix-4 FFT algorithms for fixed-point data.  The
-* radix-2 algorithm supports lengths of [16, 32, 64, ..., 4096].  The radix-4
-* algorithm supports lengths of [16, 64, 256, ..., 4096].  When possible, you
-* should use the radix-4 algorithm since it is faster than the radix-2 of the
-* same length.
-* \par
-* The forward FFTs include scaling in order to prevent results from overflowing.
-* Intermediate results are scaled down during each butterfly stage.  In the
-* radix-2 algorithm, a scale of 0.5 is applied during each butterfly.  In the
-* radix-4 algorithm, a scale of 0.25 is applied.  The scaling applies to both
-* the forward and the inverse FFTs.  Thus the forward FFT contains an additional
-* scale factor of <code>1/fftLen</code> as compared to the standard textbook
-* definition of the FFT.  The inverse FFT also scales down during each butterfly
-* stage and this corresponds to the standard textbook definition.
-* \par
-* A separate instance structure must be defined for each transform used but
-* twiddle factor and bit reversal tables can be reused.
-* \par 
-* There is also an associated initialization function for each data type.   
-* The initialization function performs the following operations:   
-* - Sets the values of the internal structure fields.   
-* - Initializes twiddle factor table and bit reversal table pointers.
-* \par   
-* Use of the initialization function is optional.   
-* However, if the initialization function is used, then the instance structure 
-* cannot be placed into a const data section. To place an instance structure 
-* into a const data section, the instance structure should be manually 
-* initialized as follows:
-* <pre>   
-*arm_cfft_radix2_instance_q31 S = {fftLen, ifftFlag, bitReverseFlag, pTwiddle, pBitRevTable, twidCoefModifier, bitRevFactor};   
-*arm_cfft_radix2_instance_q15 S = {fftLen, ifftFlag, bitReverseFlag, pTwiddle, pBitRevTable, twidCoefModifier, bitRevFactor};   
-*arm_cfft_radix4_instance_q31 S = {fftLen, ifftFlag, bitReverseFlag, pTwiddle, pBitRevTable, twidCoefModifier, bitRevFactor};    
-*arm_cfft_radix4_instance_q15 S = {fftLen, ifftFlag, bitReverseFlag, pTwiddle, pBitRevTable, twidCoefModifier, bitRevFactor};    
-*arm_cfft_instance_f32 S = {fftLen, pTwiddle, pBitRevTable, bitRevLength};
-* </pre>   
-* \par   
-* where <code>fftLen</code> length of CFFT/CIFFT; <code>ifftFlag</code> Flag for
-* selection of forward or inverse transform.  When ifftFlag is set the inverse
-* transform is calculated.
-* <code>bitReverseFlag</code> Flag for selection of output order (Set bitReverseFlag to output in normal order otherwise output in bit reversed order);    
-* <code>pTwiddle</code>points to array of twiddle coefficients; <code>pBitRevTable</code> points to the bit reversal table.   
-* <code>twidCoefModifier</code> modifier for twiddle factor table which supports all FFT lengths with same table;    
-* <code>pBitRevTable</code> modifier for bit reversal table which supports all FFT lengths with same table.   
-* <code>onebyfftLen</code> value of 1/fftLen to calculate CIFFT;
-* \par
-* The Q15 and Q31 FFT functions use a large bit reversal and twiddle factor
-* table.  The tables are defined for the maximum length transform and a subset
-* of the coefficients are used in shorter transforms.
-* 
-*/
-
-void arm_cfft_radix8by2_f32( arm_cfft_instance_f32 * S, float32_t * p1) 
-{
-   uint32_t    L  = S->fftLen;
-   float32_t * pCol1, * pCol2, * pMid1, * pMid2;
-   float32_t * p2 = p1 + L;
-   const float32_t * tw = (float32_t *) S->pTwiddle;
-   float32_t t1[4], t2[4], t3[4], t4[4], twR, twI;
-   float32_t m0, m1, m2, m3;
-   uint32_t l;
-
-   pCol1 = p1;
-   pCol2 = p2;
-
-   //    Define new length
-   L >>= 1;
-   //    Initialize mid pointers
-   pMid1 = p1 + L;
-   pMid2 = p2 + L;
-
-   // do two dot Fourier transform
-   for ( l = L >> 2; l > 0; l-- ) 
-   {
-      t1[0] = p1[0];
-      t1[1] = p1[1];
-      t1[2] = p1[2];
-      t1[3] = p1[3];
-
-      t2[0] = p2[0];
-      t2[1] = p2[1];
-      t2[2] = p2[2];
-      t2[3] = p2[3];
-
-      t3[0] = pMid1[0];
-      t3[1] = pMid1[1];
-      t3[2] = pMid1[2];
-      t3[3] = pMid1[3];
-
-      t4[0] = pMid2[0];
-      t4[1] = pMid2[1];
-      t4[2] = pMid2[2];
-      t4[3] = pMid2[3];
-
-      *p1++ = t1[0] + t2[0];
-      *p1++ = t1[1] + t2[1];
-      *p1++ = t1[2] + t2[2];
-      *p1++ = t1[3] + t2[3];    // col 1
-
-      t2[0] = t1[0] - t2[0];
-      t2[1] = t1[1] - t2[1];
-      t2[2] = t1[2] - t2[2];
-      t2[3] = t1[3] - t2[3];    // for col 2
-
-      *pMid1++ = t3[0] + t4[0];
-      *pMid1++ = t3[1] + t4[1];
-      *pMid1++ = t3[2] + t4[2];
-      *pMid1++ = t3[3] + t4[3]; // col 1
-
-      t4[0] = t4[0] - t3[0];
-      t4[1] = t4[1] - t3[1];
-      t4[2] = t4[2] - t3[2];
-      t4[3] = t4[3] - t3[3];    // for col 2
-
-      twR = *tw++;
-      twI = *tw++;
-
-      // multiply by twiddle factors
-      m0 = t2[0] * twR;
-      m1 = t2[1] * twI;
-      m2 = t2[1] * twR;
-      m3 = t2[0] * twI;
-      
-      // R  =  R  *  Tr - I * Ti
-      *p2++ = m0 + m1;
-      // I  =  I  *  Tr + R * Ti
-      *p2++ = m2 - m3;
-      
-      // use vertical symmetry
-	  //  0.9988 - 0.0491i <==> -0.0491 - 0.9988i
-      m0 = t4[0] * twI;
-      m1 = t4[1] * twR;
-      m2 = t4[1] * twI;
-      m3 = t4[0] * twR;
-      
-      *pMid2++ = m0 - m1;
-      *pMid2++ = m2 + m3;
-
-      twR = *tw++;
-      twI = *tw++;
-      
-      m0 = t2[2] * twR;
-      m1 = t2[3] * twI;
-      m2 = t2[3] * twR;
-      m3 = t2[2] * twI;
-      
-      *p2++ = m0 + m1;
-      *p2++ = m2 - m3;
-         
-      m0 = t4[2] * twI;
-      m1 = t4[3] * twR;
-      m2 = t4[3] * twI;
-      m3 = t4[2] * twR;
-      
-      *pMid2++ = m0 - m1;
-      *pMid2++ = m2 + m3;
-   }
-
-   // first col
-   arm_radix8_butterfly_f32( pCol1, L, (float32_t *) S->pTwiddle, 2u);
-   // second col
-   arm_radix8_butterfly_f32( pCol2, L, (float32_t *) S->pTwiddle, 2u);
-   
-}
-
-void arm_cfft_radix8by4_f32( arm_cfft_instance_f32 * S, float32_t * p1) 
-{
-   uint32_t    L  = S->fftLen >> 1;
-   float32_t * pCol1, *pCol2, *pCol3, *pCol4, *pEnd1, *pEnd2, *pEnd3, *pEnd4;
-	const float32_t *tw2, *tw3, *tw4;
-   float32_t * p2 = p1 + L;
-   float32_t * p3 = p2 + L;
-   float32_t * p4 = p3 + L;
-   float32_t t2[4], t3[4], t4[4], twR, twI;
-   float32_t p1ap3_0, p1sp3_0, p1ap3_1, p1sp3_1;
-   float32_t m0, m1, m2, m3;
-   uint32_t l, twMod2, twMod3, twMod4;
-
-   pCol1 = p1;         // points to real values by default
-   pCol2 = p2;
-   pCol3 = p3;
-   pCol4 = p4;
-   pEnd1 = p2 - 1;     // points to imaginary values by default
-   pEnd2 = p3 - 1;
-   pEnd3 = p4 - 1;
-   pEnd4 = pEnd3 + L;
-   
-   tw2 = tw3 = tw4 = (float32_t *) S->pTwiddle;
-   
-   L >>= 1;
-
-   // do four dot Fourier transform
-
-   twMod2 = 2;
-   twMod3 = 4;
-   twMod4 = 6;
-
-   // TOP
-   p1ap3_0 = p1[0] + p3[0];
-   p1sp3_0 = p1[0] - p3[0];
-   p1ap3_1 = p1[1] + p3[1];
-   p1sp3_1 = p1[1] - p3[1];
-
-   // col 2
-   t2[0] = p1sp3_0 + p2[1] - p4[1];
-   t2[1] = p1sp3_1 - p2[0] + p4[0];
-   // col 3
-   t3[0] = p1ap3_0 - p2[0] - p4[0];
-   t3[1] = p1ap3_1 - p2[1] - p4[1];
-   // col 4
-   t4[0] = p1sp3_0 - p2[1] + p4[1];
-   t4[1] = p1sp3_1 + p2[0] - p4[0];
-   // col 1
-   *p1++ = p1ap3_0 + p2[0] + p4[0];
-   *p1++ = p1ap3_1 + p2[1] + p4[1];
-
-   // Twiddle factors are ones
-   *p2++ = t2[0];
-   *p2++ = t2[1];
-   *p3++ = t3[0];
-   *p3++ = t3[1];
-   *p4++ = t4[0];
-   *p4++ = t4[1];
-   
-   tw2 += twMod2;
-   tw3 += twMod3;
-   tw4 += twMod4;
-   
-   for (l = (L - 2) >> 1; l > 0; l-- ) 
-   {
-
-      // TOP
-      p1ap3_0 = p1[0] + p3[0];
-      p1sp3_0 = p1[0] - p3[0];
-      p1ap3_1 = p1[1] + p3[1];
-      p1sp3_1 = p1[1] - p3[1];
-      // col 2
-      t2[0] = p1sp3_0 + p2[1] - p4[1];
-      t2[1] = p1sp3_1 - p2[0] + p4[0];
-      // col 3
-      t3[0] = p1ap3_0 - p2[0] - p4[0];
-      t3[1] = p1ap3_1 - p2[1] - p4[1];
-      // col 4
-      t4[0] = p1sp3_0 - p2[1] + p4[1];
-      t4[1] = p1sp3_1 + p2[0] - p4[0];
-      // col 1 - top
-      *p1++ = p1ap3_0 + p2[0] + p4[0];
-      *p1++ = p1ap3_1 + p2[1] + p4[1];
-
-      // BOTTOM
-      p1ap3_1 = pEnd1[-1] + pEnd3[-1];
-      p1sp3_1 = pEnd1[-1] - pEnd3[-1];
-      p1ap3_0 = pEnd1[0] + pEnd3[0];
-      p1sp3_0 = pEnd1[0] - pEnd3[0];
-      // col 2
-      t2[2] = pEnd2[0]  - pEnd4[0] + p1sp3_1;
-      t2[3] = pEnd1[0] - pEnd3[0] - pEnd2[-1] + pEnd4[-1];
-      // col 3
-      t3[2] = p1ap3_1 - pEnd2[-1] - pEnd4[-1];
-      t3[3] = p1ap3_0 - pEnd2[0]  - pEnd4[0];
-      // col 4
-      t4[2] = pEnd2[0]  - pEnd4[0]  - p1sp3_1;
-      t4[3] = pEnd4[-1] - pEnd2[-1] - p1sp3_0;
-      // col 1 - Bottom
-      *pEnd1-- = p1ap3_0 + pEnd2[0] + pEnd4[0];
-      *pEnd1-- = p1ap3_1 + pEnd2[-1] + pEnd4[-1];
-
-      // COL 2
-      // read twiddle factors
-      twR = *tw2++;
-      twI = *tw2++;
-      // multiply by twiddle factors
-      //  let    Z1 = a + i(b),   Z2 = c + i(d)
-      //   =>  Z1 * Z2  =  (a*c - b*d) + i(b*c + a*d)
-      // Top
-      m0 = t2[0] * twR;
-      m1 = t2[1] * twI;
-      m2 = t2[1] * twR;
-      m3 = t2[0] * twI;
-      
-      *p2++ = m0 + m1;
-      *p2++ = m2 - m3;
-      // use vertical symmetry col 2
-      // 0.9997 - 0.0245i  <==>  0.0245 - 0.9997i
-      // Bottom
-      m0 = t2[3] * twI;
-      m1 = t2[2] * twR;
-      m2 = t2[2] * twI;
-      m3 = t2[3] * twR;
-      
-      *pEnd2-- = m0 - m1;
-      *pEnd2-- = m2 + m3;
-
-      // COL 3
-      twR = tw3[0];
-      twI = tw3[1];
-      tw3 += twMod3;
-      // Top
-      m0 = t3[0] * twR;
-      m1 = t3[1] * twI;
-      m2 = t3[1] * twR;
-      m3 = t3[0] * twI;
-      
-      *p3++ = m0 + m1;
-      *p3++ = m2 - m3;
-      // use vertical symmetry col 3
-      // 0.9988 - 0.0491i  <==>  -0.9988 - 0.0491i
-      // Bottom
-      m0 = -t3[3] * twR;
-      m1 = t3[2] * twI;
-      m2 = t3[2] * twR;
-      m3 = t3[3] * twI;
-      
-      *pEnd3-- = m0 - m1;
-      *pEnd3-- = m3 - m2;
-      
-      // COL 4
-      twR = tw4[0];
-      twI = tw4[1];
-      tw4 += twMod4;
-      // Top
-      m0 = t4[0] * twR;
-      m1 = t4[1] * twI;
-      m2 = t4[1] * twR;
-      m3 = t4[0] * twI;
-      
-      *p4++ = m0 + m1;
-      *p4++ = m2 - m3;
-      // use vertical symmetry col 4
-      // 0.9973 - 0.0736i  <==>  -0.0736 + 0.9973i
-      // Bottom
-      m0 = t4[3] * twI;
-      m1 = t4[2] * twR;
-      m2 = t4[2] * twI;
-      m3 = t4[3] * twR;
-      
-      *pEnd4-- = m0 - m1;
-      *pEnd4-- = m2 + m3;
-   }
-
-   //MIDDLE
-   // Twiddle factors are 
-   //  1.0000  0.7071-0.7071i  -1.0000i  -0.7071-0.7071i
-   p1ap3_0 = p1[0] + p3[0];
-   p1sp3_0 = p1[0] - p3[0];
-   p1ap3_1 = p1[1] + p3[1];
-   p1sp3_1 = p1[1] - p3[1];
-
-   // col 2
-   t2[0] = p1sp3_0 + p2[1] - p4[1];
-   t2[1] = p1sp3_1 - p2[0] + p4[0];
-   // col 3
-   t3[0] = p1ap3_0 - p2[0] - p4[0];
-   t3[1] = p1ap3_1 - p2[1] - p4[1];
-   // col 4
-   t4[0] = p1sp3_0 - p2[1] + p4[1];
-   t4[1] = p1sp3_1 + p2[0] - p4[0];
-   // col 1 - Top
-   *p1++ = p1ap3_0 + p2[0] + p4[0];
-   *p1++ = p1ap3_1 + p2[1] + p4[1];
-   
-   // COL 2
-   twR = tw2[0];
-   twI = tw2[1];
-   
-   m0 = t2[0] * twR;
-   m1 = t2[1] * twI;
-   m2 = t2[1] * twR;
-   m3 = t2[0] * twI;
-   
-   *p2++ = m0 + m1;
-   *p2++ = m2 - m3;
-      // COL 3
-   twR = tw3[0];
-   twI = tw3[1];
-   
-   m0 = t3[0] * twR;
-   m1 = t3[1] * twI;
-   m2 = t3[1] * twR;
-   m3 = t3[0] * twI;
-   
-   *p3++ = m0 + m1;
-   *p3++ = m2 - m3;
-   // COL 4
-   twR = tw4[0];
-   twI = tw4[1];
-   
-   m0 = t4[0] * twR;
-   m1 = t4[1] * twI;
-   m2 = t4[1] * twR;
-   m3 = t4[0] * twI;
-   
-   *p4++ = m0 + m1;
-   *p4++ = m2 - m3;
-
-   // first col
-   arm_radix8_butterfly_f32( pCol1, L, (float32_t *) S->pTwiddle, 4u);
-   // second col
-   arm_radix8_butterfly_f32( pCol2, L, (float32_t *) S->pTwiddle, 4u);
-   // third col
-   arm_radix8_butterfly_f32( pCol3, L, (float32_t *) S->pTwiddle, 4u);
-   // fourth col
-   arm_radix8_butterfly_f32( pCol4, L, (float32_t *) S->pTwiddle, 4u);
-
-}
-
-/**
-* @addtogroup ComplexFFT   
-* @{   
-*/
-
-/**   
-* @details   
-* @brief       Processing function for the floating-point complex FFT.
-* @param[in]      *S    points to an instance of the floating-point CFFT structure.  
-* @param[in, out] *p1   points to the complex data buffer of size <code>2*fftLen</code>. Processing occurs in-place.  
-* @param[in]     ifftFlag       flag that selects forward (ifftFlag=0) or inverse (ifftFlag=1) transform.  
-* @param[in]     bitReverseFlag flag that enables (bitReverseFlag=1) or disables (bitReverseFlag=0) bit reversal of output.  
-* @return none.  
-*/
-
-void arm_cfft_f32( 
-   const arm_cfft_instance_f32 * S, 
-   float32_t * p1,
-   uint8_t ifftFlag,
-   uint8_t bitReverseFlag)
-{
-
-   uint32_t  L = S->fftLen, l;
-   float32_t invL, * pSrc;
-
-  if(ifftFlag == 1u)
-  {
-	  /*  Conjugate input data  */
-	  pSrc = p1 + 1;
-	  for(l=0; l<L; l++) {
-		  *pSrc = -*pSrc;
-		   pSrc += 2;
-	  }
-  }
-
-		switch (L) {
-		case 16: 
-		case 128:
-		case 1024:
-			 arm_cfft_radix8by2_f32  ( (arm_cfft_instance_f32 *) S, p1);
-			 break;
-		case 32:
-		case 256:
-		case 2048:
-			 arm_cfft_radix8by4_f32  ( (arm_cfft_instance_f32 *) S, p1);
-			 break;
-		case 64:
-		case 512:
-		case 4096:
-          arm_radix8_butterfly_f32( p1, L, (float32_t *) S->pTwiddle, 1);
-			 break;
-		}  
-
-	if( bitReverseFlag )
-		arm_bitreversal_32((uint32_t*)p1,S->bitRevLength,S->pBitRevTable);
-
-  if(ifftFlag == 1u)
-  {
-	  invL = 1.0f/(float32_t)L;
-	  /*  Conjugate and scale output data */
-	  pSrc = p1;
-	  for(l=0; l<L; l++) {
-  		 *pSrc++ *=   invL ;
-		 *pSrc  = -(*pSrc) * invL;
-                 pSrc++;
-	  }
-  }
-}
-