text: /* ----------------------------------------------------------------------   
  * Copyright (C) 2010-2014 ARM Limited. All rights reserved.   
  *   
  * $Date:        31. July 2014 
  * $Revision: 	V1.4.4  
  *   
  * Project: 	    CMSIS DSP Library   
  * Title:	    arm_cfft_radix2_f32.c   
  *   
  * Description:	Radix-2 Decimation in Frequency CFFT & CIFFT 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"
  
  void arm_radix2_butterfly_f32(
    float32_t * pSrc,
    uint32_t fftLen,
    float32_t * pCoef,
    uint16_t twidCoefModifier);
  
  void arm_radix2_butterfly_inverse_f32(
    float32_t * pSrc,
    uint32_t fftLen,
    float32_t * pCoef,
    uint16_t twidCoefModifier,
    float32_t onebyfftLen);
  
  extern void arm_bitreversal_f32(
      float32_t * pSrc,
      uint16_t fftSize,
      uint16_t bitRevFactor,
      uint16_t * pBitRevTab);
  
  /**   
  * @ingroup groupTransforms   
  */
  
  /**   
  * @addtogroup ComplexFFT   
  * @{   
  */
  
  /**   
  * @details
  * @brief Radix-2 CFFT/CIFFT.
  * @deprecated Do not use this function.  It has been superseded by \ref arm_cfft_f32 and will be removed
  * in the future.
  * @param[in]      *S    points to an instance of the floating-point Radix-2 CFFT/CIFFT structure.  
  * @param[in, out] *pSrc points to the complex data buffer of size <code>2*fftLen</code>. Processing occurs in-place.  
  * @return none.
  */
  
  void arm_cfft_radix2_f32(
  const arm_cfft_radix2_instance_f32 * S,
  float32_t * pSrc)
  {
  
     if(S->ifftFlag == 1u)
     {
        /*  Complex IFFT radix-2  */
        arm_radix2_butterfly_inverse_f32(pSrc, S->fftLen, S->pTwiddle,
        S->twidCoefModifier, S->onebyfftLen);
     }
     else
     {
        /*  Complex FFT radix-2  */
        arm_radix2_butterfly_f32(pSrc, S->fftLen, S->pTwiddle,
        S->twidCoefModifier);
     }
  
     if(S->bitReverseFlag == 1u)
     {
        /*  Bit Reversal */
        arm_bitreversal_f32(pSrc, S->fftLen, S->bitRevFactor, S->pBitRevTable);
     }
  
  }
  
  
  /**    
  * @} end of ComplexFFT group    
  */
  
  
  
  /* ----------------------------------------------------------------------    
  ** Internal helper function used by the FFTs    
  ** ------------------------------------------------------------------- */
  
  /*    
  * @brief  Core function for the floating-point CFFT butterfly process.   
  * @param[in, out] *pSrc            points to the in-place buffer of floating-point data type.   
  * @param[in]      fftLen           length of the FFT.   
  * @param[in]      *pCoef           points to the twiddle coefficient buffer.   
  * @param[in]      twidCoefModifier twiddle coefficient modifier that supports different size FFTs with the same twiddle factor table.   
  * @return none.   
  */
  
  void arm_radix2_butterfly_f32(
  float32_t * pSrc,
  uint32_t fftLen,
  float32_t * pCoef,
  uint16_t twidCoefModifier)
  {
  
     uint32_t i, j, k, l;
     uint32_t n1, n2, ia;
     float32_t xt, yt, cosVal, sinVal;
     float32_t p0, p1, p2, p3;
     float32_t a0, a1;
  
  #ifndef ARM_MATH_CM0_FAMILY
  
     /*  Initializations for the first stage */
     n2 = fftLen >> 1;
     ia = 0;
     i = 0;
  
     // loop for groups 
     for (k = n2; k > 0; k--)
     {
        cosVal = pCoef[ia * 2];
        sinVal = pCoef[(ia * 2) + 1];
  
        /*  Twiddle coefficients index modifier */
        ia += twidCoefModifier;
  
        /*  index calculation for the input as, */
        /*  pSrc[i + 0], pSrc[i + fftLen/1] */
        l = i + n2;
  
        /*  Butterfly implementation */
        a0 = pSrc[2 * i] + pSrc[2 * l];
        xt = pSrc[2 * i] - pSrc[2 * l];
  
        yt = pSrc[2 * i + 1] - pSrc[2 * l + 1];
        a1 = pSrc[2 * l + 1] + pSrc[2 * i + 1];
        
        p0 = xt * cosVal;
        p1 = yt * sinVal;
        p2 = yt * cosVal;
        p3 = xt * sinVal;  
        
        pSrc[2 * i]     = a0;   
        pSrc[2 * i + 1] = a1;       
        
        pSrc[2 * l]     = p0 + p1;
        pSrc[2 * l + 1] = p2 - p3;
        
        i++;
     }                             // groups loop end 
  
     twidCoefModifier <<= 1u;
  
     // loop for stage 
     for (k = n2; k > 2; k = k >> 1)
     {
        n1 = n2;
        n2 = n2 >> 1;
        ia = 0;
  
        // loop for groups 
        j = 0;
        do
        {
           cosVal = pCoef[ia * 2];
           sinVal = pCoef[(ia * 2) + 1];
           ia += twidCoefModifier;
  
           // loop for butterfly 
           i = j;
           do
           {
              l = i + n2;
              a0 = pSrc[2 * i] + pSrc[2 * l];
              xt = pSrc[2 * i] - pSrc[2 * l];
  
              yt = pSrc[2 * i + 1] - pSrc[2 * l + 1];
              a1 = pSrc[2 * l + 1] + pSrc[2 * i + 1];
              
              p0 = xt * cosVal;
              p1 = yt * sinVal;
              p2 = yt * cosVal;
              p3 = xt * sinVal;  
              
              pSrc[2 * i] = a0;   
              pSrc[2 * i + 1] = a1;       
              
              pSrc[2 * l]     = p0 + p1;
              pSrc[2 * l + 1] = p2 - p3;
              
              i += n1;
           } while( i < fftLen );                        // butterfly loop end 
           j++;
        } while( j < n2);                          // groups loop end 
        twidCoefModifier <<= 1u;
     }                             // stages loop end 
  
     // loop for butterfly 
     for (i = 0; i < fftLen; i += 2)
     {
        a0 = pSrc[2 * i] + pSrc[2 * i + 2];
        xt = pSrc[2 * i] - pSrc[2 * i + 2];
  
        yt = pSrc[2 * i + 1] - pSrc[2 * i + 3];
        a1 = pSrc[2 * i + 3] + pSrc[2 * i + 1];
        
        pSrc[2 * i] = a0;   
        pSrc[2 * i + 1] = a1;
        pSrc[2 * i + 2] = xt;
        pSrc[2 * i + 3] = yt;
     }                             // groups loop end 
  
  #else
   
     n2 = fftLen;
  
     // loop for stage 
     for (k = fftLen; k > 1; k = k >> 1)
     {
        n1 = n2;
        n2 = n2 >> 1;
        ia = 0;
  
        // loop for groups 
        j = 0;
        do
        {
           cosVal = pCoef[ia * 2];
           sinVal = pCoef[(ia * 2) + 1];
           ia += twidCoefModifier;
  
           // loop for butterfly 
           i = j;
           do
           {
              l = i + n2;
              a0 = pSrc[2 * i] + pSrc[2 * l];
              xt = pSrc[2 * i] - pSrc[2 * l];
  
              yt = pSrc[2 * i + 1] - pSrc[2 * l + 1];
              a1 = pSrc[2 * l + 1] + pSrc[2 * i + 1];
              
              p0 = xt * cosVal;
              p1 = yt * sinVal;
              p2 = yt * cosVal;
              p3 = xt * sinVal;  
              
              pSrc[2 * i] = a0;   
              pSrc[2 * i + 1] = a1;       
              
              pSrc[2 * l]     = p0 + p1;
              pSrc[2 * l + 1] = p2 - p3;
              
              i += n1;
           } while(i < fftLen);
           j++;
        } while(j < n2);
        twidCoefModifier <<= 1u;
     }
  
  #endif //    #ifndef ARM_MATH_CM0_FAMILY
  
  }
  
  
  void arm_radix2_butterfly_inverse_f32(
  float32_t * pSrc,
  uint32_t fftLen,
  float32_t * pCoef,
  uint16_t twidCoefModifier,
  float32_t onebyfftLen)
  {
  
     uint32_t i, j, k, l;
     uint32_t n1, n2, ia;
     float32_t xt, yt, cosVal, sinVal;
     float32_t p0, p1, p2, p3;
     float32_t a0, a1;
  
  #ifndef ARM_MATH_CM0_FAMILY
  
     n2 = fftLen >> 1;
     ia = 0;
  
     // loop for groups 
     for (i = 0; i < n2; i++)
     {
        cosVal = pCoef[ia * 2];
        sinVal = pCoef[(ia * 2) + 1];
        ia += twidCoefModifier;
  
        l = i + n2;
        a0 = pSrc[2 * i] + pSrc[2 * l];
        xt = pSrc[2 * i] - pSrc[2 * l];
  
        yt = pSrc[2 * i + 1] - pSrc[2 * l + 1];
        a1 = pSrc[2 * l + 1] + pSrc[2 * i + 1];
        
        p0 = xt * cosVal;
        p1 = yt * sinVal;
        p2 = yt * cosVal;
        p3 = xt * sinVal;  
        
        pSrc[2 * i] = a0;   
        pSrc[2 * i + 1] = a1;       
        
        pSrc[2 * l]     = p0 - p1;
        pSrc[2 * l + 1] = p2 + p3;  
     }                             // groups loop end 
  
     twidCoefModifier <<= 1u;
  
     // loop for stage 
     for (k = fftLen / 2; k > 2; k = k >> 1)
     {
        n1 = n2;
        n2 = n2 >> 1;
        ia = 0;
  
        // loop for groups 
        j = 0;
        do
        {
           cosVal = pCoef[ia * 2];
           sinVal = pCoef[(ia * 2) + 1];
           ia += twidCoefModifier;
  
           // loop for butterfly 
           i = j;
           do
           {
              l = i + n2;
              a0 = pSrc[2 * i] + pSrc[2 * l];
              xt = pSrc[2 * i] - pSrc[2 * l];
  
              yt = pSrc[2 * i + 1] - pSrc[2 * l + 1];
              a1 = pSrc[2 * l + 1] + pSrc[2 * i + 1];
              
              p0 = xt * cosVal;
              p1 = yt * sinVal;
              p2 = yt * cosVal;
              p3 = xt * sinVal;  
              
              pSrc[2 * i] = a0;   
              pSrc[2 * i + 1] = a1;       
              
              pSrc[2 * l]     = p0 - p1;
              pSrc[2 * l + 1] = p2 + p3; 
  
              i += n1;
           } while( i < fftLen );                 // butterfly loop end 
           j++;
        } while(j < n2);                      // groups loop end 
  
        twidCoefModifier <<= 1u;
     }                             // stages loop end 
  
     // loop for butterfly 
     for (i = 0; i < fftLen; i += 2)
     {   
        a0 = pSrc[2 * i] + pSrc[2 * i + 2];
        xt = pSrc[2 * i] - pSrc[2 * i + 2];
        
        a1 = pSrc[2 * i + 3] + pSrc[2 * i + 1];
        yt = pSrc[2 * i + 1] - pSrc[2 * i + 3];
        
        p0 = a0 * onebyfftLen;
        p2 = xt * onebyfftLen;
        p1 = a1 * onebyfftLen;
        p3 = yt * onebyfftLen; 
        
        pSrc[2 * i] = p0;
        pSrc[2 * i + 1] = p1;  
        pSrc[2 * i + 2] = p2;       
        pSrc[2 * i + 3] = p3;
     }                             // butterfly loop end 
  
  #else
  
     n2 = fftLen;
  
     // loop for stage 
     for (k = fftLen; k > 2; k = k >> 1)
     {
        n1 = n2;
        n2 = n2 >> 1;
        ia = 0;
  
        // loop for groups 
        j = 0;
        do
        {
           cosVal = pCoef[ia * 2];
           sinVal = pCoef[(ia * 2) + 1];
           ia = ia + twidCoefModifier;
  
           // loop for butterfly 
           i = j;
           do
           {
              l = i + n2;
              a0 = pSrc[2 * i] + pSrc[2 * l];
              xt = pSrc[2 * i] - pSrc[2 * l];
  
              yt = pSrc[2 * i + 1] - pSrc[2 * l + 1];
              a1 = pSrc[2 * l + 1] + pSrc[2 * i + 1];
              
              p0 = xt * cosVal;
              p1 = yt * sinVal;
              p2 = yt * cosVal;
              p3 = xt * sinVal;  
              
              pSrc[2 * i] = a0;   
              pSrc[2 * i + 1] = a1;       
              
              pSrc[2 * l]     = p0 - p1;
              pSrc[2 * l + 1] = p2 + p3;  
              
              i += n1;
           } while( i < fftLen );                    // butterfly loop end 
           j++;
        } while( j < n2 );                      // groups loop end 
  
        twidCoefModifier = twidCoefModifier << 1u;
     }                             // stages loop end 
  
     n1 = n2;
     n2 = n2 >> 1;
  
     // loop for butterfly 
     for (i = 0; i < fftLen; i += n1)
     {
        l = i + n2;
        
        a0 = pSrc[2 * i] + pSrc[2 * l];
        xt = pSrc[2 * i] - pSrc[2 * l];
        
        a1 = pSrc[2 * l + 1] + pSrc[2 * i + 1];
        yt = pSrc[2 * i + 1] - pSrc[2 * l + 1];
        
        p0 = a0 * onebyfftLen;
        p2 = xt * onebyfftLen;
        p1 = a1 * onebyfftLen;
        p3 = yt * onebyfftLen; 
        
        pSrc[2 * i] = p0;
        pSrc[2u * l] = p2;
       
        pSrc[2 * i + 1] = p1;    
        pSrc[2u * l + 1u] = p3;
     }                             // butterfly loop end 
  
  #endif //      #ifndef ARM_MATH_CM0_FAMILY
  
  }
  