/* ----------------------------------------------------------------------  
* Copyright (C) 2010 ARM Limited. All rights reserved.  
*  
* $Date:        29. November 2010  
* $Revision: 	V1.0.3  
*  
* Project: 	    CMSIS DSP Library  
* Title:	    arm_rfft_f32.c  
*  
* Description:	RFFT & RIFFT Floating point process function  
*  
* Target Processor: Cortex-M4/Cortex-M3
*  
* Version 1.0.3 2010/11/29 
*    Re-organized the CMSIS folders and updated documentation.  
*   
* Version 1.0.2 2010/11/11  
*    Documentation updated.   
*  
* Version 1.0.1 2010/10/05   
*    Production release and review comments incorporated.  
*  
* Version 1.0.0 2010/09/20   
*    Production release and review comments incorporated.  
*  
* Version 0.0.7  2010/06/10   
*    Misra-C changes done  
* -------------------------------------------------------------------- */ 
 
#include "arm_math.h" 
 
/**  
 * @ingroup groupTransforms  
 */ 
 
/**  
 * @defgroup RFFT_RIFFT Real FFT Functions  
 *  
 * \par  
 * Complex FFT/IFFT typically assumes complex input and output. However many applications use real valued data in time domain.   
 * Real FFT/IFFT efficiently process real valued sequences with the advantage of requirement of low memory and with less complexity.  
 *  
 * \par  
 * This set of functions implements Real Fast Fourier Transforms(RFFT) and Real Inverse Fast Fourier Transform(RIFFT)  
 * for Q15, Q31, and floating-point data types.    
 *  
 *  
 * \par Algorithm:  
 *  
 * <b>Real Fast Fourier Transform:</b>  
 * \par  
 * Real FFT of N-point is calculated using CFFT of N/2-point and Split RFFT process as shown below figure.  
 * \par  
 * \image html RFFT.gif "Real Fast Fourier Transform"  
 * \par  
 * The RFFT functions operate on blocks of input and output data and each call to the function processes  
 * <code>fftLenR</code> samples through the transform.  <code>pSrc</code>  points to input array containing <code>fftLenR</code> values.  
 * <code>pDst</code>  points to output array containing <code>2*fftLenR</code> values. \n 
 * Input for real FFT is in the order of   
 * <pre>{real[0], real[1], real[2], real[3], ..}</pre>  
 * Output for real FFT is complex and are in the order of  
 * <pre>{real(0), imag(0), real(1), imag(1), ...}</pre>   
 *  
 * <b>Real Inverse Fast Fourier Transform:</b>  
 * \par  
 * Real IFFT of N-point is calculated using Split RIFFT process and CFFT of N/2-point as shown below figure.  
 * \par  
 * \image html RIFFT.gif "Real Inverse Fast Fourier Transform"  
 * \par  
 * The RIFFT functions operate on blocks of input and output data and each call to the function processes  
 * <code>2*fftLenR</code> samples through the transform.  <code>pSrc</code>  points to input array containing <code>2*fftLenR</code> values.  
 * <code>pDst</code>  points to output array containing <code>fftLenR</code> values. \n  
 * Input for real IFFT is complex and are in the order of 
 * <pre>{real(0), imag(0), real(1), imag(1), ...}</pre> 
 *  Output for real IFFT is real and in the order of   
 * <pre>{real[0], real[1], real[2], real[3], ..}</pre> 
 *  
 * \par Lengths supported by the transform: 
 * \par  
 * Real FFT/IFFT supports the lengths [128, 512, 2048], as it internally uses CFFT/CIFFT.  
 *  
 * \par Instance Structure  
 * A separate instance structure must be defined for each Instance but the twiddle factors can be reused.  
 * There are separate instance structure declarations for each of the 3 supported data types.  
 *  
 * \par Initialization Functions  
 * 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 tables. 
 * - Initializes CFFT data structure fields.   
 * \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 must be manually initialized.  
 * Manually initialize the instance structure as follows:  
 * <pre>  
 *arm_rfft_instance_f32 S = {fftLenReal, fftLenBy2, ifftFlagR, bitReverseFlagR, twidCoefRModifier, pTwiddleAReal, pTwiddleBReal, pCfft};  
 *arm_rfft_instance_q31 S = {fftLenReal, fftLenBy2, ifftFlagR, bitReverseFlagR, twidCoefRModifier, pTwiddleAReal, pTwiddleBReal, pCfft};  
 *arm_rfft_instance_q15 S = {fftLenReal, fftLenBy2, ifftFlagR, bitReverseFlagR, twidCoefRModifier, pTwiddleAReal, pTwiddleBReal, pCfft};  
 * </pre>  
 * where <code>fftLenReal</code> length of RFFT/RIFFT; <code>fftLenBy2</code> length of CFFT/CIFFT.   
 * <code>ifftFlagR</code> Flag for selection of RFFT or RIFFT(Set ifftFlagR to calculate RIFFT otherwise calculates RFFT);  
 * <code>bitReverseFlagR</code> Flag for selection of output order(Set bitReverseFlagR to output in normal order otherwise output in bit reversed order);   
 * <code>twidCoefRModifier</code> modifier for twiddle factor table which supports 128, 512, 2048 RFFT lengths with same table;  
 * <code>pTwiddleAReal</code>points to A array of twiddle coefficients; <code>pTwiddleBReal</code>points to B array of twiddle coefficients;  
 * <code>pCfft</code> points to the CFFT Instance structure. The CFFT structure also needs to be initialized, refer to arm_cfft_radix4_f32() for details regarding  
 * static initialization of cfft structure.  
 *  
 * \par Fixed-Point Behavior  
 * Care must be taken when using the fixed-point versions of the RFFT/RIFFT function.  
 * Refer to the function specific documentation below for usage guidelines.  
 */ 
 
/*--------------------------------------------------------------------  
 *		Internal functions prototypes  
 *--------------------------------------------------------------------*/ 
 
void arm_split_rfft_f32( 
  float32_t * pSrc, 
  uint32_t fftLen, 
  float32_t * pATable, 
  float32_t * pBTable, 
  float32_t * pDst, 
  uint32_t modifier); 
void arm_split_rifft_f32( 
  float32_t * pSrc, 
  uint32_t fftLen, 
  float32_t * pATable, 
  float32_t * pBTable, 
  float32_t * pDst, 
  uint32_t modifier); 
 
/**  
 * @addtogroup RFFT_RIFFT  
 * @{  
 */ 
 
/**  
 * @brief Processing function for the floating-point RFFT/RIFFT. 
 * @param[in]  *S    points to an instance of the floating-point RFFT/RIFFT structure. 
 * @param[in]  *pSrc points to the input buffer. 
 * @param[out] *pDst points to the output buffer. 
 * @return none. 
 */ 
 
void arm_rfft_f32( 
  const arm_rfft_instance_f32 * S, 
  float32_t * pSrc, 
  float32_t * pDst) 
{ 
  const arm_cfft_radix4_instance_f32 *S_CFFT = S->pCfft; 
 
 
  /* Calculation of Real IFFT of input */ 
  if(S->ifftFlagR == 1u) 
  { 
    /*  Real IFFT core process */ 
    arm_split_rifft_f32(pSrc, S->fftLenBy2, S->pTwiddleAReal, 
                        S->pTwiddleBReal, pDst, S->twidCoefRModifier); 
 
 
    /* Complex radix-4 IFFT process */ 
    arm_radix4_butterfly_inverse_f32(pDst, S_CFFT->fftLen, 
                                     S_CFFT->pTwiddle, 
                                     S_CFFT->twidCoefModifier, 
                                     S_CFFT->onebyfftLen); 
 
    /* Bit reversal process */ 
    if(S->bitReverseFlagR == 1u) 
    { 
      arm_bitreversal_f32(pDst, S_CFFT->fftLen, 
                          S_CFFT->bitRevFactor, S_CFFT->pBitRevTable); 
    } 
  } 
  else 
  { 
 
    /* Calculation of RFFT of input */ 
 
    /* Complex radix-4 FFT process */ 
    arm_radix4_butterfly_f32(pSrc, S_CFFT->fftLen, 
                             S_CFFT->pTwiddle, S_CFFT->twidCoefModifier); 
 
    /* Bit reversal process */ 
    if(S->bitReverseFlagR == 1u) 
    { 
      arm_bitreversal_f32(pSrc, S_CFFT->fftLen, 
                          S_CFFT->bitRevFactor, S_CFFT->pBitRevTable); 
    } 
 
 
    /*  Real FFT core process */ 
    arm_split_rfft_f32(pSrc, S->fftLenBy2, S->pTwiddleAReal, 
                       S->pTwiddleBReal, pDst, S->twidCoefRModifier); 
  } 
 
} 
 
/**  
   * @} end of RFFT_RIFFT group  
   */ 
 
/**  
 * @brief  Core Real FFT process  
 * @param[in]   *pSrc 				points to the input buffer.  
 * @param[in]   fftLen  			length of FFT.  
 * @param[in]   *pATable 			points to the twiddle Coef A buffer.  
 * @param[in]   *pBTable 			points to the twiddle Coef B buffer.  
 * @param[out]  *pDst 				points to the output buffer.  
 * @param[in]   modifier 	        twiddle coefficient modifier that supports different size FFTs with the same twiddle factor table. 
 * @return none.  
 */ 
 
void arm_split_rfft_f32( 
  float32_t * pSrc, 
  uint32_t fftLen, 
  float32_t * pATable, 
  float32_t * pBTable, 
  float32_t * pDst, 
  uint32_t modifier) 
{ 
  uint32_t i;                                    /* Loop Counter */ 
  float32_t outR, outI;                          /* Temporary variables for output */ 
  float32_t *pCoefA, *pCoefB;                    /* Temporary pointers for twiddle factors */ 
  float32_t CoefA1, CoefA2, CoefB1;              /* Temporary variables for twiddle coefficients */ 
  float32_t *pDst1 = &pDst[2], *pDst2 = &pDst[(4u * fftLen) - 1u];      /* temp pointers for output buffer */ 
  float32_t *pSrc1 = &pSrc[2], *pSrc2 = &pSrc[(2u * fftLen) - 1u];      /* temp pointers for input buffer */ 
 
 
  pSrc[2u * fftLen] = pSrc[0]; 
  pSrc[(2u * fftLen) + 1u] = pSrc[1]; 
 
  /* Init coefficient pointers */ 
  pCoefA = &pATable[modifier * 2u]; 
  pCoefB = &pBTable[modifier * 2u]; 
 
  i = fftLen - 1u; 
 
  while(i > 0u) 
  { 
    /*  
       outR = (pSrc[2 * i] * pATable[2 * i] - pSrc[2 * i + 1] * pATable[2 * i + 1]  
       + pSrc[2 * n - 2 * i] * pBTable[2 * i] +  
       pSrc[2 * n - 2 * i + 1] * pBTable[2 * i + 1]);  
     */ 
 
    /* outI = (pIn[2 * i + 1] * pATable[2 * i] + pIn[2 * i] * pATable[2 * i + 1] +  
       pIn[2 * n - 2 * i] * pBTable[2 * i + 1] -  
       pIn[2 * n - 2 * i + 1] * pBTable[2 * i]); */ 
 
    /* read pATable[2 * i] */ 
    CoefA1 = *pCoefA++; 
    /* pATable[2 * i + 1] */ 
    CoefA2 = *pCoefA; 
 
    /* pSrc[2 * i] * pATable[2 * i] */ 
    outR = *pSrc1 * CoefA1; 
    /* pSrc[2 * i] * CoefA2 */ 
    outI = *pSrc1++ * CoefA2; 
 
    /* (pSrc[2 * i + 1] + pSrc[2 * fftLen - 2 * i + 1]) * CoefA2 */ 
    outR -= (*pSrc1 + *pSrc2) * CoefA2; 
    /* pSrc[2 * i + 1] * CoefA1 */ 
    outI += *pSrc1++ * CoefA1; 
 
    CoefB1 = *pCoefB; 
 
    /* pSrc[2 * fftLen - 2 * i + 1] * CoefB1 */ 
    outI -= *pSrc2-- * CoefB1; 
    /* pSrc[2 * fftLen - 2 * i] * CoefA2 */ 
    outI -= *pSrc2 * CoefA2; 
 
    /* pSrc[2 * fftLen - 2 * i] * CoefB1 */ 
    outR += *pSrc2-- * CoefB1; 
 
    /* write output */ 
    *pDst1++ = outR; 
    *pDst1++ = outI; 
 
    /* write complex conjugate output */ 
    *pDst2-- = -outI; 
    *pDst2-- = outR; 
 
    /* update coefficient pointer */ 
    pCoefB = pCoefB + (modifier * 2u); 
    pCoefA = pCoefA + ((modifier * 2u) - 1u); 
 
    i--; 
 
  } 
 
  pDst[2u * fftLen] = pSrc[0] - pSrc[1]; 
  pDst[(2u * fftLen) + 1u] = 0.0f; 
 
  pDst[0] = pSrc[0] + pSrc[1]; 
  pDst[1] = 0.0f; 
 
} 
 
 
/**  
 * @brief  Core Real IFFT process  
 * @param[in]   *pSrc 				points to the input buffer.  
 * @param[in]   fftLen  			length of FFT. 
 * @param[in]   *pATable 			points to the twiddle Coef A buffer. 
 * @param[in]   *pBTable 			points to the twiddle Coef B buffer. 
 * @param[out]  *pDst 				points to the output buffer. 
 * @param[in]   modifier 	        twiddle coefficient modifier that supports different size FFTs with the same twiddle factor table.  
 * @return none.  
 */ 
 
void arm_split_rifft_f32( 
  float32_t * pSrc, 
  uint32_t fftLen, 
  float32_t * pATable, 
  float32_t * pBTable, 
  float32_t * pDst, 
  uint32_t modifier) 
{ 
  float32_t outR, outI;                          /* Temporary variables for output */ 
  float32_t *pCoefA, *pCoefB;                    /* Temporary pointers for twiddle factors */ 
  float32_t CoefA1, CoefA2, CoefB1;              /* Temporary variables for twiddle coefficients */ 
  float32_t *pSrc1 = &pSrc[0], *pSrc2 = &pSrc[(2u * fftLen) + 1u]; 
 
  pCoefA = &pATable[0]; 
  pCoefB = &pBTable[0]; 
 
  while(fftLen > 0u) 
  { 
    /*  
       outR = (pIn[2 * i] * pATable[2 * i] + pIn[2 * i + 1] * pATable[2 * i + 1] +  
       pIn[2 * n - 2 * i] * pBTable[2 * i] -  
       pIn[2 * n - 2 * i + 1] * pBTable[2 * i + 1]);  
 
       outI = (pIn[2 * i + 1] * pATable[2 * i] - pIn[2 * i] * pATable[2 * i + 1] -  
       pIn[2 * n - 2 * i] * pBTable[2 * i + 1] -  
       pIn[2 * n - 2 * i + 1] * pBTable[2 * i]);  
 
     */ 
 
    CoefA1 = *pCoefA++; 
    CoefA2 = *pCoefA; 
 
    /* outR = (pSrc[2 * i] * CoefA1 */ 
    outR = *pSrc1 * CoefA1; 
 
    /* - pSrc[2 * i] * CoefA2 */ 
    outI = -(*pSrc1++) * CoefA2; 
 
    /* (pSrc[2 * i + 1] + pSrc[2 * fftLen - 2 * i + 1]) * CoefA2 */ 
    outR += (*pSrc1 + *pSrc2) * CoefA2; 
 
    /* pSrc[2 * i + 1] * CoefA1 */ 
    outI += (*pSrc1++) * CoefA1; 
 
    CoefB1 = *pCoefB; 
 
    /* - pSrc[2 * fftLen - 2 * i + 1] * CoefB1 */ 
    outI -= *pSrc2-- * CoefB1; 
 
    /* pSrc[2 * fftLen - 2 * i] * CoefB1 */ 
    outR += *pSrc2 * CoefB1; 
 
    /* pSrc[2 * fftLen - 2 * i] * CoefA2 */ 
    outI += *pSrc2-- * CoefA2; 
 
    /* write output */ 
    *pDst++ = outR; 
    *pDst++ = outI; 
 
    /* update coefficient pointer */ 
    pCoefB = pCoefB + (modifier * 2u); 
    pCoefA = pCoefA + ((modifier * 2u) - 1u); 
 
    /* Decrement loop count */ 
    fftLen--; 
  } 
 
}