arm_cfft_f32.c

/* ----------------------------------------------------------------------    
* Copyright (C) 2010-2014 ARM Limited. All rights reserved.    
*    
* $Date:        19. March 2015 
* $Revision: 	V.1.4.5  
*    
* 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
* Pre-initialized 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:
* \code
* 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;
*   }
* \endcode
* \par Q15 and Q31
* The floating-point complex FFT uses a mixed-radix algorithm.  Multiple radix-4
* stages are performed along with a single radix-2 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
* Pre-initialized 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_q31.  For example:
* \par
* <code>arm_cfft_q31(arm_cfft_sR_q31_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_q31 function follows:
* \code
* const static arm_cfft_instance_q31 *S;
* ...
*   switch (length) {
*     case 16:
*       S = &arm_cfft_sR_q31_len16;
*       break;
*     case 32:
*       S = &arm_cfft_sR_q31_len32;
*       break;
*     case 64:
*       S = &arm_cfft_sR_q31_len64;
*       break;
*     case 128:
*       S = &arm_cfft_sR_q31_len128;
*       break;
*     case 256:
*       S = &arm_cfft_sR_q31_len256;
*       break;
*     case 512:
*       S = &arm_cfft_sR_q31_len512;
*       break;
*     case 1024:
*       S = &arm_cfft_sR_q31_len1024;
*       break;
*     case 2048:
*       S = &arm_cfft_sR_q31_len2048;
*       break;
*     case 4096:
*       S = &arm_cfft_sR_q31_len4096;
*       break;
*   }
* \endcode
* 
*/

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++;
        }
    }
}

/**    
* @} end of ComplexFFT group    
*/