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/* ----------------------------------------------------------------------

 * Project:      CMSIS DSP Library

 * Title:        arm_cfft_f32.c

 * Description:  Combined Radix Decimation in Frequency CFFT Floating point processing function

 *

 * $Date:        27. January 2017

 * $Revision:    V.1.5.1

 *

 * Target Processor: Cortex-M cores

 * -------------------------------------------------------------------- */

/*

 * Copyright (C) 2010-2017 ARM Limited or its affiliates. All rights reserved.

 *

 * SPDX-License-Identifier: Apache-2.0

 *

 * Licensed under the Apache License, Version 2.0 (the License); you may

 * not use this file except in compliance with the License.

 * You may obtain a copy of the License at

 *

 * www.apache.org/licenses/LICENSE-2.0

 *

 * Unless required by applicable law or agreed to in writing, software

 * distributed under the License is distributed on an AS IS BASIS, WITHOUT

 * WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied.

 * See the License for the specific language governing permissions and

 * limitations under the License.

 */

#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

*/