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

Software License for The Fraunhofer FDK AAC Codec Library for Android

© Copyright  1995 - 2018 Fraunhofer-Gesellschaft zur Förderung der angewandten

Forschung e.V. All rights reserved.

 1.    INTRODUCTION

The Fraunhofer FDK AAC Codec Library for Android ("FDK AAC Codec") is software

that implements the MPEG Advanced Audio Coding ("AAC") encoding and decoding

scheme for digital audio. This FDK AAC Codec software is intended to be used on

a wide variety of Android devices.

AAC's HE-AAC and HE-AAC v2 versions are regarded as today's most efficient

general perceptual audio codecs. AAC-ELD is considered the best-performing

full-bandwidth communications codec by independent studies and is widely

deployed. AAC has been standardized by ISO and IEC as part of the MPEG

specifications.

Patent licenses for necessary patent claims for the FDK AAC Codec (including

those of Fraunhofer) may be obtained through Via Licensing

(www.vialicensing.com) or through the respective patent owners individually for

the purpose of encoding or decoding bit streams in products that are compliant

with the ISO/IEC MPEG audio standards. Please note that most manufacturers of

Android devices already license these patent claims through Via Licensing or

directly from the patent owners, and therefore FDK AAC Codec software may

already be covered under those patent licenses when it is used for those

licensed purposes only.

Commercially-licensed AAC software libraries, including floating-point versions

with enhanced sound quality, are also available from Fraunhofer. Users are

encouraged to check the Fraunhofer website for additional applications

information and documentation.

2.    COPYRIGHT LICENSE

Redistribution and use in source and binary forms, with or without modification,

are permitted without payment of copyright license fees provided that you

satisfy the following conditions:

You must retain the complete text of this software license in redistributions of

the FDK AAC Codec or your modifications thereto in source code form.

You must retain the complete text of this software license in the documentation

and/or other materials provided with redistributions of the FDK AAC Codec or

your modifications thereto in binary form. You must make available free of

charge copies of the complete source code of the FDK AAC Codec and your

modifications thereto to recipients of copies in binary form.

The name of Fraunhofer may not be used to endorse or promote products derived

from this library without prior written permission.

You may not charge copyright license fees for anyone to use, copy or distribute

the FDK AAC Codec software or your modifications thereto.

Your modified versions of the FDK AAC Codec must carry prominent notices stating

that you changed the software and the date of any change. For modified versions

of the FDK AAC Codec, the term "Fraunhofer FDK AAC Codec Library for Android"

must be replaced by the term "Third-Party Modified Version of the Fraunhofer FDK

AAC Codec Library for Android."

3.    NO PATENT LICENSE

NO EXPRESS OR IMPLIED LICENSES TO ANY PATENT CLAIMS, including without

limitation the patents of Fraunhofer, ARE GRANTED BY THIS SOFTWARE LICENSE.

Fraunhofer provides no warranty of patent non-infringement with respect to this

software.

You may use this FDK AAC Codec software or modifications thereto only for

purposes that are authorized by appropriate patent licenses.

4.    DISCLAIMER

This FDK AAC Codec software is provided by Fraunhofer on behalf of the copyright

holders and contributors "AS IS" and WITHOUT ANY EXPRESS OR IMPLIED WARRANTIES,

including but not limited to the implied warranties of merchantability and

fitness for a particular purpose. IN NO EVENT SHALL THE COPYRIGHT HOLDER 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), arising in any way out of the use of

this software, even if advised of the possibility of such damage.

5.    CONTACT INFORMATION

Fraunhofer Institute for Integrated Circuits IIS

Attention: Audio and Multimedia Departments - FDK AAC LL

Am Wolfsmantel 33

91058 Erlangen, Germany

www.iis.fraunhofer.de/amm

amm-info@iis.fraunhofer.de

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

/******************* Library for basic calculation routines ********************

   Author(s):   Josef Hoepfl, DSP Solutions

   Description: Fix point FFT

*******************************************************************************/

#include "fft_rad2.h"

#include "FDK_tools_rom.h"

#define W_PiFOURTH STC(0x5a82799a)

//#define W_PiFOURTH ((FIXP_DBL)(0x5a82799a))

#ifndef SUMDIFF_PIFOURTH

#define SUMDIFF_PIFOURTH(diff, sum, a, b) \

  {                                       \

    FIXP_DBL wa, wb;                      \

    wa = fMultDiv2(a, W_PiFOURTH);        \

    wb = fMultDiv2(b, W_PiFOURTH);        \

    diff = wb - wa;                       \

    sum = wb + wa;                        \

  }

#define SUMDIFF_PIFOURTH16(diff, sum, a, b)       \

  {                                               \

    FIXP_SGL wa, wb;                              \

    wa = FX_DBL2FX_SGL(fMultDiv2(a, W_PiFOURTH)); \

    wb = FX_DBL2FX_SGL(fMultDiv2(b, W_PiFOURTH)); \

    diff = wb - wa;                               \

    sum = wb + wa;                                \

  }

#endif

#define SCALEFACTOR2048 10

#define SCALEFACTOR1024 9

#define SCALEFACTOR512 8

#define SCALEFACTOR256 7

#define SCALEFACTOR128 6

#define SCALEFACTOR64 5

#define SCALEFACTOR32 4

#define SCALEFACTOR16 3

#define SCALEFACTOR8 2

#define SCALEFACTOR4 1

#define SCALEFACTOR2 1

#define SCALEFACTOR3 1

#define SCALEFACTOR5 1

#define SCALEFACTOR6 (SCALEFACTOR2 + SCALEFACTOR3 + 2)

#define SCALEFACTOR7 2

#define SCALEFACTOR9 2

#define SCALEFACTOR10 5

#define SCALEFACTOR12 3

#define SCALEFACTOR15 3

#define SCALEFACTOR18 (SCALEFACTOR2 + SCALEFACTOR9 + 2)

#define SCALEFACTOR20 (SCALEFACTOR4 + SCALEFACTOR5 + 2)

#define SCALEFACTOR21 (SCALEFACTOR3 + SCALEFACTOR7 + 2)

#define SCALEFACTOR24 (SCALEFACTOR2 + SCALEFACTOR12 + 2)

#define SCALEFACTOR30 (SCALEFACTOR2 + SCALEFACTOR15 + 2)

#define SCALEFACTOR40 (SCALEFACTOR5 + SCALEFACTOR8 + 2)

#define SCALEFACTOR48 (SCALEFACTOR4 + SCALEFACTOR12 + 2)

#define SCALEFACTOR60 (SCALEFACTOR4 + SCALEFACTOR15 + 2)

#define SCALEFACTOR80 (SCALEFACTOR5 + SCALEFACTOR16 + 2)

#define SCALEFACTOR96 (SCALEFACTOR3 + SCALEFACTOR32 + 2)

#define SCALEFACTOR120 (SCALEFACTOR8 + SCALEFACTOR15 + 2)

#define SCALEFACTOR160 (SCALEFACTOR10 + SCALEFACTOR16 + 2)

#define SCALEFACTOR168 (SCALEFACTOR21 + SCALEFACTOR8 + 2)

#define SCALEFACTOR192 (SCALEFACTOR12 + SCALEFACTOR16 + 2)

#define SCALEFACTOR240 (SCALEFACTOR16 + SCALEFACTOR15 + 2)

#define SCALEFACTOR320 (SCALEFACTOR10 + SCALEFACTOR32 + 2)

#define SCALEFACTOR336 (SCALEFACTOR21 + SCALEFACTOR16 + 2)

#define SCALEFACTOR384 (SCALEFACTOR12 + SCALEFACTOR32 + 2)

#define SCALEFACTOR480 (SCALEFACTOR32 + SCALEFACTOR15 + 2)

#include "fft.h"

#ifndef FUNCTION_fft2

/* Performs the FFT of length 2. Input vector unscaled, output vector scaled

 * with factor 0.5 */

static FDK_FORCEINLINE void fft2(FIXP_DBL *RESTRICT pDat) {

  FIXP_DBL r1, i1;

  FIXP_DBL r2, i2;

  /* real part */

  r1 = pDat[2];

  r2 = pDat[0];

  /* imaginary part */

  i1 = pDat[3];

  i2 = pDat[1];

  /* real part */

  pDat[0] = (r2 + r1) >> 1;

  pDat[2] = (r2 - r1) >> 1;

  /* imaginary part */

  pDat[1] = (i2 + i1) >> 1;

  pDat[3] = (i2 - i1) >> 1;

}

#endif /* FUNCTION_fft2 */

#define C31 (STC(0x91261468)) /* FL2FXCONST_DBL(-0.86602540) = -sqrt(3)/2  */

#ifndef FUNCTION_fft3

/* Performs the FFT of length 3 according to the algorithm after winograd. */

static FDK_FORCEINLINE void fft3(FIXP_DBL *RESTRICT pDat) {

  FIXP_DBL r1, r2;

  FIXP_DBL s1, s2;

  FIXP_DBL pD;

  /* real part */

  r1 = pDat[2] + pDat[4];

  r2 = fMultDiv2((pDat[2] - pDat[4]), C31);

  pD = pDat[0] >> 1;

  pDat[0] = pD + (r1 >> 1);

  r1 = pD - (r1 >> 2);

  /* imaginary part */

  s1 = pDat[3] + pDat[5];

  s2 = fMultDiv2((pDat[3] - pDat[5]), C31);

  pD = pDat[1] >> 1;

  pDat[1] = pD + (s1 >> 1);

  s1 = pD - (s1 >> 2);

  /* combination */

  pDat[2] = r1 - s2;

  pDat[4] = r1 + s2;

  pDat[3] = s1 + r2;

  pDat[5] = s1 - r2;

}

#endif /* #ifndef FUNCTION_fft3 */

#define F5C(x) STC(x)

#define C51 (F5C(0x79bc3854)) /* FL2FXCONST_DBL( 0.95105652)   */

#define C52 (F5C(0x9d839db0)) /* FL2FXCONST_DBL(-1.53884180/2) */

#define C53 (F5C(0xd18053ce)) /* FL2FXCONST_DBL(-0.36327126)   */

#define C54 (F5C(0x478dde64)) /* FL2FXCONST_DBL( 0.55901699)   */

#define C55 (F5C(0xb0000001)) /* FL2FXCONST_DBL(-1.25/2)       */

/* performs the FFT of length 5 according to the algorithm after winograd */

/* This version works with a prescale of 2 instead of 3 */

static FDK_FORCEINLINE void fft5(FIXP_DBL *RESTRICT pDat) {

  FIXP_DBL r1, r2, r3, r4;

  FIXP_DBL s1, s2, s3, s4;

  FIXP_DBL t;

  /* real part */

  r1 = (pDat[2] + pDat[8]) >> 1;

  r4 = (pDat[2] - pDat[8]) >> 1;

  r3 = (pDat[4] + pDat[6]) >> 1;

  r2 = (pDat[4] - pDat[6]) >> 1;

  t = fMult((r1 - r3), C54);

  r1 = r1 + r3;

  pDat[0] = (pDat[0] >> 1) + r1;

  /* Bit shift left because of the constant C55 which was scaled with the factor

     0.5 because of the representation of the values as fracts */

  r1 = pDat[0] + (fMultDiv2(r1, C55) << (2));

  r3 = r1 - t;

  r1 = r1 + t;

  t = fMult((r4 + r2), C51);

  /* Bit shift left because of the constant C55 which was scaled with the factor

     0.5 because of the representation of the values as fracts */

  r4 = t + (fMultDiv2(r4, C52) << (2));

  r2 = t + fMult(r2, C53);

  /* imaginary part */

  s1 = (pDat[3] + pDat[9]) >> 1;

  s4 = (pDat[3] - pDat[9]) >> 1;

  s3 = (pDat[5] + pDat[7]) >> 1;

  s2 = (pDat[5] - pDat[7]) >> 1;

  t = fMult((s1 - s3), C54);

  s1 = s1 + s3;

  pDat[1] = (pDat[1] >> 1) + s1;

  /* Bit shift left because of the constant C55 which was scaled with the factor

     0.5 because of the representation of the values as fracts */

  s1 = pDat[1] + (fMultDiv2(s1, C55) << (2));

  s3 = s1 - t;

  s1 = s1 + t;

  t = fMult((s4 + s2), C51);

  /* Bit shift left because of the constant C55 which was scaled with the factor

     0.5 because of the representation of the values as fracts */

  s4 = t + (fMultDiv2(s4, C52) << (2));

  s2 = t + fMult(s2, C53);

  /* combination */

  pDat[2] = r1 + s2;

  pDat[8] = r1 - s2;

  pDat[4] = r3 - s4;

  pDat[6] = r3 + s4;

  pDat[3] = s1 - r2;

  pDat[9] = s1 + r2;

  pDat[5] = s3 + r4;

  pDat[7] = s3 - r4;

}

#define F5C(x) STC(x)

#define C51 (F5C(0x79bc3854)) /* FL2FXCONST_DBL( 0.95105652)   */

#define C52 (F5C(0x9d839db0)) /* FL2FXCONST_DBL(-1.53884180/2) */

#define C53 (F5C(0xd18053ce)) /* FL2FXCONST_DBL(-0.36327126)   */

#define C54 (F5C(0x478dde64)) /* FL2FXCONST_DBL( 0.55901699)   */

#define C55 (F5C(0xb0000001)) /* FL2FXCONST_DBL(-1.25/2)       */

/**

 * \brief    Function performs a complex 10-point FFT

 *           The FFT is performed inplace. The result of the FFT

 *           is scaled by SCALEFACTOR10 bits.

 *

 *           WOPS FLC version:                    1093 cycles

 *           WOPS with 32x16 bit multiplications:  196 cycles

 *

 * \param    [i/o] re    real input / output

 * \param    [i/o] im    imag input / output

 * \param    [i  ] s     stride real and imag input / output

 *

 * \return   void

 */

static void fft10(FIXP_DBL *x)  // FIXP_DBL *re, FIXP_DBL *im, FIXP_SGL s)

{

  FIXP_DBL t;

  FIXP_DBL x0, x1, x2, x3, x4;

  FIXP_DBL r1, r2, r3, r4;

  FIXP_DBL s1, s2, s3, s4;

  FIXP_DBL y00, y01, y02, y03, y04, y05, y06, y07, y08, y09;

  FIXP_DBL y10, y11, y12, y13, y14, y15, y16, y17, y18, y19;

  const int s = 1;  // stride factor

  /* 2 fft5 stages */

  /* real part */

  x0 = (x[s * 0] >> SCALEFACTOR10);

  x1 = (x[s * 4] >> SCALEFACTOR10);

  x2 = (x[s * 8] >> SCALEFACTOR10);

  x3 = (x[s * 12] >> SCALEFACTOR10);

  x4 = (x[s * 16] >> SCALEFACTOR10);

  r1 = (x3 + x2);

  r4 = (x3 - x2);

  r3 = (x1 + x4);

  r2 = (x1 - x4);

  t = fMult((r1 - r3), C54);

  r1 = (r1 + r3);

  y00 = (x0 + r1);

  r1 = (y00 + ((fMult(r1, C55) << 1)));

  r3 = (r1 - t);

  r1 = (r1 + t);

  t = fMult((r4 + r2), C51);

  r4 = (t + (fMult(r4, C52) << 1));

  r2 = (t + fMult(r2, C53));

  /* imaginary part */

  x0 = (x[s * 0 + 1] >> SCALEFACTOR10);

  x1 = (x[s * 4 + 1] >> SCALEFACTOR10);

  x2 = (x[s * 8 + 1] >> SCALEFACTOR10);

  x3 = (x[s * 12 + 1] >> SCALEFACTOR10);

  x4 = (x[s * 16 + 1] >> SCALEFACTOR10);

  s1 = (x3 + x2);

  s4 = (x3 - x2);

  s3 = (x1 + x4);

  s2 = (x1 - x4);

  t = fMult((s1 - s3), C54);

  s1 = (s1 + s3);

  y01 = (x0 + s1);

  s1 = (y01 + (fMult(s1, C55) << 1));

  s3 = (s1 - t);

  s1 = (s1 + t);

  t = fMult((s4 + s2), C51);

  s4 = (t + (fMult(s4, C52) << 1));

  s2 = (t + fMult(s2, C53));

  /* combination */

  y04 = (r1 + s2);

  y16 = (r1 - s2);

  y08 = (r3 - s4);

  y12 = (r3 + s4);

  y05 = (s1 - r2);

  y17 = (s1 + r2);

  y09 = (s3 + r4);

  y13 = (s3 - r4);

  /* real part */

  x0 = (x[s * 10] >> SCALEFACTOR10);

  x1 = (x[s * 2] >> SCALEFACTOR10);

  x2 = (x[s * 6] >> SCALEFACTOR10);

  x3 = (x[s * 14] >> SCALEFACTOR10);

  x4 = (x[s * 18] >> SCALEFACTOR10);

  r1 = (x1 + x4);

  r4 = (x1 - x4);

  r3 = (x3 + x2);

  r2 = (x3 - x2);

  t = fMult((r1 - r3), C54);

  r1 = (r1 + r3);

  y02 = (x0 + r1);

  r1 = (y02 + ((fMult(r1, C55) << 1)));

  r3 = (r1 - t);

  r1 = (r1 + t);

  t = fMult(((r4 + r2)), C51);

  r4 = (t + (fMult(r4, C52) << 1));

  r2 = (t + fMult(r2, C53));

  /* imaginary part */

  x0 = (x[s * 10 + 1] >> SCALEFACTOR10);

  x1 = (x[s * 2 + 1] >> SCALEFACTOR10);

  x2 = (x[s * 6 + 1] >> SCALEFACTOR10);

  x3 = (x[s * 14 + 1] >> SCALEFACTOR10);

  x4 = (x[s * 18 + 1] >> SCALEFACTOR10);

  s1 = (x1 + x4);

  s4 = (x1 - x4);

  s3 = (x3 + x2);

  s2 = (x3 - x2);

  t = fMult((s1 - s3), C54);

  s1 = (s1 + s3);

  y03 = (x0 + s1);

  s1 = (y03 + (fMult(s1, C55) << 1));

  s3 = (s1 - t);

  s1 = (s1 + t);

  t = fMult((s4 + s2), C51);

  s4 = (t + (fMult(s4, C52) << 1));

  s2 = (t + fMult(s2, C53));

  /* combination */

  y06 = (r1 + s2);

  y18 = (r1 - s2);

  y10 = (r3 - s4);

  y14 = (r3 + s4);

  y07 = (s1 - r2);

  y19 = (s1 + r2);

  y11 = (s3 + r4);

  y15 = (s3 - r4);

  /* 5 fft2 stages */

  x[s * 0] = (y00 + y02);

  x[s * 0 + 1] = (y01 + y03);

  x[s * 10] = (y00 - y02);

  x[s * 10 + 1] = (y01 - y03);

  x[s * 4] = (y04 + y06);

  x[s * 4 + 1] = (y05 + y07);

  x[s * 14] = (y04 - y06);

  x[s * 14 + 1] = (y05 - y07);

  x[s * 8] = (y08 + y10);

  x[s * 8 + 1] = (y09 + y11);

  x[s * 18] = (y08 - y10);

  x[s * 18 + 1] = (y09 - y11);

  x[s * 12] = (y12 + y14);

  x[s * 12 + 1] = (y13 + y15);

  x[s * 2] = (y12 - y14);

  x[s * 2 + 1] = (y13 - y15);

  x[s * 16] = (y16 + y18);

  x[s * 16 + 1] = (y17 + y19);

  x[s * 6] = (y16 - y18);

  x[s * 6 + 1] = (y17 - y19);

}

#ifndef FUNCTION_fft12

#define FUNCTION_fft12

#undef C31

#define C31 (STC(0x91261468)) /* FL2FXCONST_DBL(-0.86602540) = -sqrt(3)/2  */

static inline void fft12(FIXP_DBL *pInput) {

  FIXP_DBL aDst[24];

  FIXP_DBL *pSrc, *pDst;

  int i;

  pSrc = pInput;

  pDst = aDst;

  FIXP_DBL r1, r2, s1, s2, pD;

  /* First 3*2 samples are shifted right by 2 before output */

  r1 = pSrc[8] + pSrc[16];

  r2 = fMultDiv2((pSrc[8] - pSrc[16]), C31);

  pD = pSrc[0] >> 1;

  pDst[0] = (pD + (r1 >> 1)) >> 1;

  r1 = pD - (r1 >> 2);

  /* imaginary part */

  s1 = pSrc[9] + pSrc[17];

  s2 = fMultDiv2((pSrc[9] - pSrc[17]), C31);

  pD = pSrc[1] >> 1;

  pDst[1] = (pD + (s1 >> 1)) >> 1;

  s1 = pD - (s1 >> 2);

  /* combination */

  pDst[2] = (r1 - s2) >> 1;

  pDst[3] = (s1 + r2) >> 1;

  pDst[4] = (r1 + s2) >> 1;

  pDst[5] = (s1 - r2) >> 1;

  pSrc += 2;

  pDst += 6;

  const FIXP_STB *pVecRe = RotVectorReal12;

  const FIXP_STB *pVecIm = RotVectorImag12;

  FIXP_DBL re, im;

  FIXP_STB vre, vim;

  for (i = 0; i < 2; i++) {

    /* sample 0,1 are shifted right by 2 before output */

    /* sample 2,3 4,5 are shifted right by 1 and complex multiplied before

     * output */

    r1 = pSrc[8] + pSrc[16];

    r2 = fMultDiv2((pSrc[8] - pSrc[16]), C31);

    pD = pSrc[0] >> 1;

    pDst[0] = (pD + (r1 >> 1)) >> 1;

    r1 = pD - (r1 >> 2);

    /* imaginary part */

    s1 = pSrc[9] + pSrc[17];

    s2 = fMultDiv2((pSrc[9] - pSrc[17]), C31);

    pD = pSrc[1] >> 1;

    pDst[1] = (pD + (s1 >> 1)) >> 1;

    s1 = pD - (s1 >> 2);

    /* combination */

    re = (r1 - s2) >> 0;

    im = (s1 + r2) >> 0;

    vre = *pVecRe++;

    vim = *pVecIm++;

    cplxMultDiv2(&pDst[3], &pDst[2], im, re, vre, vim);

    re = (r1 + s2) >> 0;

    im = (s1 - r2) >> 0;

    vre = *pVecRe++;

    vim = *pVecIm++;

    cplxMultDiv2(&pDst[5], &pDst[4], im, re, vre, vim);

    pDst += 6;

    pSrc += 2;

  }

  /* sample 0,1 are shifted right by 2 before output */

  /* sample 2,3 is shifted right by 1 and complex multiplied with (0.0,+1.0) */

  /* sample 4,5 is shifted right by 1 and complex multiplied with (-1.0,0.0) */

  r1 = pSrc[8] + pSrc[16];

  r2 = fMultDiv2((pSrc[8] - pSrc[16]), C31);

  pD = pSrc[0] >> 1;

  pDst[0] = (pD + (r1 >> 1)) >> 1;

  r1 = pD - (r1 >> 2);

  /* imaginary part */

  s1 = pSrc[9] + pSrc[17];

  s2 = fMultDiv2((pSrc[9] - pSrc[17]), C31);

  pD = pSrc[1] >> 1;

  pDst[1] = (pD + (s1 >> 1)) >> 1;

  s1 = pD - (s1 >> 2);

  /* combination */

  pDst[2] = (s1 + r2) >> 1;

  pDst[3] = (s2 - r1) >> 1;

  pDst[4] = -((r1 + s2) >> 1);

  pDst[5] = (r2 - s1) >> 1;

  /* Perform 3 times the fft of length 4. The input samples are at the address

  of aDst and the output samples are at the address of pInput. The input vector

  for the fft of length 4 is built of the interleaved samples in aDst, the

  output samples are stored consecutively at the address of pInput.

  */

  pSrc = aDst;

  pDst = pInput;

  for (i = 0; i < 3; i++) {

    /* inline FFT4 merged with incoming resorting loop */

    FIXP_DBL a00, a10, a20, a30, tmp0, tmp1;

    a00 = (pSrc[0] + pSrc[12]) >> 1; /* Re A + Re B */

    a10 = (pSrc[6] + pSrc[18]) >> 1; /* Re C + Re D */

    a20 = (pSrc[1] + pSrc[13]) >> 1; /* Im A + Im B */

    a30 = (pSrc[7] + pSrc[19]) >> 1; /* Im C + Im D */

    pDst[0] = a00 + a10; /* Re A' = Re A + Re B + Re C + Re D */

    pDst[1] = a20 + a30; /* Im A' = Im A + Im B + Im C + Im D */

    tmp0 = a00 - pSrc[12]; /* Re A - Re B */

    tmp1 = a20 - pSrc[13]; /* Im A - Im B */

    pDst[12] = a00 - a10; /* Re C' = Re A + Re B - Re C - Re D */

    pDst[13] = a20 - a30; /* Im C' = Im A + Im B - Im C - Im D */

    a10 = a10 - pSrc[18]; /* Re C - Re D */

    a30 = a30 - pSrc[19]; /* Im C - Im D */

    pDst[6] = tmp0 + a30;  /* Re B' = Re A - Re B + Im C - Im D */

    pDst[18] = tmp0 - a30; /* Re D' = Re A - Re B - Im C + Im D */

    pDst[7] = tmp1 - a10;  /* Im B' = Im A - Im B - Re C + Re D */

    pDst[19] = tmp1 + a10; /* Im D' = Im A - Im B + Re C - Re D */

    pSrc += 2;

    pDst += 2;

  }

}

#endif /* FUNCTION_fft12 */

#ifndef FUNCTION_fft15

#define N3 3

#define N5 5

#define N6 6

#define N15 15

/* Performs the FFT of length 15. It is split into FFTs of length 3 and

 * length 5. */

static inline void fft15(FIXP_DBL *pInput) {

  FIXP_DBL aDst[2 * N15];

  FIXP_DBL aDst1[2 * N15];

  int i, k, l;

  /* Sort input vector for fft's of length 3

  input3(0:2)   = [input(0) input(5) input(10)];

  input3(3:5)   = [input(3) input(8) input(13)];

  input3(6:8)   = [input(6) input(11) input(1)];

  input3(9:11)  = [input(9) input(14) input(4)];

  input3(12:14) = [input(12) input(2) input(7)]; */

  {

    const FIXP_DBL *pSrc = pInput;

    FIXP_DBL *RESTRICT pDst = aDst;

    /* Merge 3 loops into one, skip call of fft3 */

    for (i = 0, l = 0, k = 0; i < N5; i++, k += 6) {

      pDst[k + 0] = pSrc[l];

      pDst[k + 1] = pSrc[l + 1];

      l += 2 * N5;

      if (l >= (2 * N15)) l -= (2 * N15);

      pDst[k + 2] = pSrc[l];

      pDst[k + 3] = pSrc[l + 1];

      l += 2 * N5;

      if (l >= (2 * N15)) l -= (2 * N15);

      pDst[k + 4] = pSrc[l];

      pDst[k + 5] = pSrc[l + 1];

      l += (2 * N5) + (2 * N3);

      if (l >= (2 * N15)) l -= (2 * N15);

      /* fft3 merged with shift right by 2 loop */

      FIXP_DBL r1, r2, r3;

      FIXP_DBL s1, s2;

      /* real part */

      r1 = pDst[k + 2] + pDst[k + 4];

      r2 = fMult((pDst[k + 2] - pDst[k + 4]), C31);

      s1 = pDst[k + 0];

      pDst[k + 0] = (s1 + r1) >> 2;

      r1 = s1 - (r1 >> 1);

      /* imaginary part */

      s1 = pDst[k + 3] + pDst[k + 5];

      s2 = fMult((pDst[k + 3] - pDst[k + 5]), C31);

      r3 = pDst[k + 1];

      pDst[k + 1] = (r3 + s1) >> 2;

      s1 = r3 - (s1 >> 1);

      /* combination */

      pDst[k + 2] = (r1 - s2) >> 2;

      pDst[k + 4] = (r1 + s2) >> 2;

      pDst[k + 3] = (s1 + r2) >> 2;

      pDst[k + 5] = (s1 - r2) >> 2;

    }

  }

  /* Sort input vector for fft's of length 5

  input5(0:4)   = [output3(0) output3(3) output3(6) output3(9) output3(12)];

  input5(5:9)   = [output3(1) output3(4) output3(7) output3(10) output3(13)];

  input5(10:14) = [output3(2) output3(5) output3(8) output3(11) output3(14)]; */

  /* Merge 2 loops into one, brings about 10% */

  {

    const FIXP_DBL *pSrc = aDst;

    FIXP_DBL *RESTRICT pDst = aDst1;

    for (i = 0, l = 0, k = 0; i < N3; i++, k += 10) {

      l = 2 * i;

      pDst[k + 0] = pSrc[l + 0];

      pDst[k + 1] = pSrc[l + 1];

      pDst[k + 2] = pSrc[l + 0 + (2 * N3)];

      pDst[k + 3] = pSrc[l + 1 + (2 * N3)];

      pDst[k + 4] = pSrc[l + 0 + (4 * N3)];

      pDst[k + 5] = pSrc[l + 1 + (4 * N3)];

      pDst[k + 6] = pSrc[l + 0 + (6 * N3)];

      pDst[k + 7] = pSrc[l + 1 + (6 * N3)];

      pDst[k + 8] = pSrc[l + 0 + (8 * N3)];

      pDst[k + 9] = pSrc[l + 1 + (8 * N3)];

      fft5(&pDst[k]);

    }

  }

  /* Sort output vector of length 15

  output = [out5(0)  out5(6)  out5(12) out5(3)  out5(9)

            out5(10) out5(1)  out5(7)  out5(13) out5(4)

            out5(5)  out5(11) out5(2)  out5(8)  out5(14)]; */

  /* optimize clumsy loop, brings about 5% */

  {

    const FIXP_DBL *pSrc = aDst1;

    FIXP_DBL *RESTRICT pDst = pInput;

    for (i = 0, l = 0, k = 0; i < N3; i++, k += 10) {

      pDst[k + 0] = pSrc[l];

      pDst[k + 1] = pSrc[l + 1];

      l += (2 * N6);

      if (l >= (2 * N15)) l -= (2 * N15);

      pDst[k + 2] = pSrc[l];

      pDst[k + 3] = pSrc[l + 1];

      l += (2 * N6);

      if (l >= (2 * N15)) l -= (2 * N15);

      pDst[k + 4] = pSrc[l];

      pDst[k + 5] = pSrc[l + 1];

      l += (2 * N6);

      if (l >= (2 * N15)) l -= (2 * N15);

      pDst[k + 6] = pSrc[l];

      pDst[k + 7] = pSrc[l + 1];

      l += (2 * N6);

      if (l >= (2 * N15)) l -= (2 * N15);

      pDst[k + 8] = pSrc[l];

      pDst[k + 9] = pSrc[l + 1];

      l += 2; /* no modulo check needed, it cannot occur */

    }

  }

}

#endif /* FUNCTION_fft15 */

/*

 Select shift placement.

 Some processors like ARM may shift "for free" in combination with an addition

 or substraction, but others don't so either combining shift with +/- or reduce

 the total amount or shift operations is optimal

 */

#if !defined(__arm__)

#define SHIFT_A >> 1

#define SHIFT_B

#else

#define SHIFT_A

#define SHIFT_B >> 1

#endif

#ifndef FUNCTION_fft_16 /* we check, if fft_16 (FIXP_DBL *) is not yet defined \

                         */

/* This defines prevents this array to be declared twice, if 16-bit fft is

 * enabled too */

#define FUNCTION_DATA_fft_16_w16

static const FIXP_STP fft16_w16[2] = {STCP(0x7641af3d, 0x30fbc54d),

                                      STCP(0x30fbc54d, 0x7641af3d)};

LNK_SECTION_CODE_L1

inline void fft_16(FIXP_DBL *RESTRICT x) {

  FIXP_DBL vr, ur;

  FIXP_DBL vr2, ur2;

  FIXP_DBL vr3, ur3;

  FIXP_DBL vr4, ur4;

  FIXP_DBL vi, ui;

  FIXP_DBL vi2, ui2;

  FIXP_DBL vi3, ui3;

  vr = (x[0] >> 1) + (x[16] >> 1);       /* Re A + Re B */

  ur = (x[1] >> 1) + (x[17] >> 1);       /* Im A + Im B */

  vi = (x[8] SHIFT_A) + (x[24] SHIFT_A); /* Re C + Re D */

  ui = (x[9] SHIFT_A) + (x[25] SHIFT_A); /* Im C + Im D */

  x[0] = vr + (vi SHIFT_B);              /* Re A' = ReA + ReB +ReC + ReD */

  x[1] = ur + (ui SHIFT_B);              /* Im A' = sum of imag values */

  vr2 = (x[4] >> 1) + (x[20] >> 1); /* Re A + Re B */

  ur2 = (x[5] >> 1) + (x[21] >> 1); /* Im A + Im B */

  x[4] = vr - (vi SHIFT_B); /* Re C' = -(ReC+ReD) + (ReA+ReB) */

  x[5] = ur - (ui SHIFT_B); /* Im C' = -Im C -Im D +Im A +Im B */

  vr -= x[16];              /* Re A - Re B */

  vi = (vi SHIFT_B)-x[24];  /* Re C - Re D */

  ur -= x[17];              /* Im A - Im B */

  ui = (ui SHIFT_B)-x[25];  /* Im C - Im D */

  vr3 = (x[2] >> 1) + (x[18] >> 1); /* Re A + Re B */

  ur3 = (x[3] >> 1) + (x[19] >> 1); /* Im A + Im B */

  x[2] = ui + vr; /* Re B' = Im C - Im D  + Re A - Re B */

  x[3] = ur - vi; /* Im B'= -Re C + Re D + Im A - Im B */

  vr4 = (x[6] >> 1) + (x[22] >> 1); /* Re A + Re B */

  ur4 = (x[7] >> 1) + (x[23] >> 1); /* Im A + Im B */

  x[6] = vr - ui; /* Re D' = -Im C + Im D + Re A - Re B */

  x[7] = vi + ur; /* Im D'= Re C - Re D + Im A - Im B */

  vi2 = (x[12] SHIFT_A) + (x[28] SHIFT_A); /* Re C + Re D */

  ui2 = (x[13] SHIFT_A) + (x[29] SHIFT_A); /* Im C + Im D */

  x[8] = vr2 + (vi2 SHIFT_B);              /* Re A' = ReA + ReB +ReC + ReD */

  x[9] = ur2 + (ui2 SHIFT_B);              /* Im A' = sum of imag values */

  x[12] = vr2 - (vi2 SHIFT_B);             /* Re C' = -(ReC+ReD) + (ReA+ReB) */

  x[13] = ur2 - (ui2 SHIFT_B);             /* Im C' = -Im C -Im D +Im A +Im B */

  vr2 -= x[20];                            /* Re A - Re B */

  ur2 -= x[21];                            /* Im A - Im B */

  vi2 = (vi2 SHIFT_B)-x[28];               /* Re C - Re D */

  ui2 = (ui2 SHIFT_B)-x[29];               /* Im C - Im D */

  vi = (x[10] SHIFT_A) + (x[26] SHIFT_A); /* Re C + Re D */

  ui = (x[11] SHIFT_A) + (x[27] SHIFT_A); /* Im C + Im D */

  x[10] = ui2 + vr2; /* Re B' = Im C - Im D  + Re A - Re B */

  x[11] = ur2 - vi2; /* Im B'= -Re C + Re D + Im A - Im B */

  vi3 = (x[14] SHIFT_A) + (x[30] SHIFT_A); /* Re C + Re D */

  ui3 = (x[15] SHIFT_A) + (x[31] SHIFT_A); /* Im C + Im D */

  x[14] = vr2 - ui2; /* Re D' = -Im C + Im D + Re A - Re B */

  x[15] = vi2 + ur2; /* Im D'= Re C - Re D + Im A - Im B */

  x[16] = vr3 + (vi SHIFT_B); /* Re A' = ReA + ReB +ReC + ReD */

  x[17] = ur3 + (ui SHIFT_B); /* Im A' = sum of imag values */

  x[20] = vr3 - (vi SHIFT_B); /* Re C' = -(ReC+ReD) + (ReA+ReB) */

  x[21] = ur3 - (ui SHIFT_B); /* Im C' = -Im C -Im D +Im A +Im B */

  vr3 -= x[18];               /* Re A - Re B */

  ur3 -= x[19];               /* Im A - Im B */

  vi = (vi SHIFT_B)-x[26];    /* Re C - Re D */

  ui = (ui SHIFT_B)-x[27];    /* Im C - Im D */

  x[18] = ui + vr3;           /* Re B' = Im C - Im D  + Re A - Re B */

  x[19] = ur3 - vi;           /* Im B'= -Re C + Re D + Im A - Im B */

  x[24] = vr4 + (vi3 SHIFT_B); /* Re A' = ReA + ReB +ReC + ReD */

  x[28] = vr4 - (vi3 SHIFT_B); /* Re C' = -(ReC+ReD) + (ReA+ReB) */

  x[25] = ur4 + (ui3 SHIFT_B); /* Im A' = sum of imag values */

  x[29] = ur4 - (ui3 SHIFT_B); /* Im C' = -Im C -Im D +Im A +Im B */

  vr4 -= x[22];                /* Re A - Re B */

  ur4 -= x[23];                /* Im A - Im B */

  x[22] = vr3 - ui; /* Re D' = -Im C + Im D + Re A - Re B */

  x[23] = vi + ur3; /* Im D'= Re C - Re D + Im A - Im B */

  vi3 = (vi3 SHIFT_B)-x[30]; /* Re C - Re D */

  ui3 = (ui3 SHIFT_B)-x[31]; /* Im C - Im D */

  x[26] = ui3 + vr4;         /* Re B' = Im C - Im D  + Re A - Re B */

  x[30] = vr4 - ui3;         /* Re D' = -Im C + Im D + Re A - Re B */

  x[27] = ur4 - vi3;         /* Im B'= -Re C + Re D + Im A - Im B */

  x[31] = vi3 + ur4;         /* Im D'= Re C - Re D + Im A - Im B */

  // xt1 =  0

  // xt2 =  8

  vr = x[8];

  vi = x[9];

  ur = x[0] >> 1;

  ui = x[1] >> 1;

  x[0] = ur + (vr >> 1);

  x[1] = ui + (vi >> 1);

  x[8] = ur - (vr >> 1);

  x[9] = ui - (vi >> 1);

  // xt1 =  4

  // xt2 = 12

  vr = x[13];

  vi = x[12];

  ur = x[4] >> 1;

  ui = x[5] >> 1;

  x[4] = ur + (vr >> 1);

  x[5] = ui - (vi >> 1);

  x[12] = ur - (vr >> 1);

  x[13] = ui + (vi >> 1);

  // xt1 = 16

  // xt2 = 24

  vr = x[24];

  vi = x[25];

  ur = x[16] >> 1;

  ui = x[17] >> 1;

  x[16] = ur + (vr >> 1);

  x[17] = ui + (vi >> 1);

  x[24] = ur - (vr >> 1);

  x[25] = ui - (vi >> 1);

  // xt1 = 20

  // xt2 = 28

  vr = x[29];

  vi = x[28];

  ur = x[20] >> 1;

  ui = x[21] >> 1;

  x[20] = ur + (vr >> 1);

  x[21] = ui - (vi >> 1);

  x[28] = ur - (vr >> 1);

  x[29] = ui + (vi >> 1);

  // xt1 =  2

  // xt2 = 10

  SUMDIFF_PIFOURTH(vi, vr, x[10], x[11])

  // vr = fMultDiv2((x[11] + x[10]),W_PiFOURTH);

  // vi = fMultDiv2((x[11] - x[10]),W_PiFOURTH);

  ur = x[2];

  ui = x[3];

  x[2] = (ur >> 1) + vr;

  x[3] = (ui >> 1) + vi;

  x[10] = (ur >> 1) - vr;

  x[11] = (ui >> 1) - vi;

  // xt1 =  6

  // xt2 = 14

  SUMDIFF_PIFOURTH(vr, vi, x[14], x[15])

  ur = x[6];

  ui = x[7];

  x[6] = (ur >> 1) + vr;

  x[7] = (ui >> 1) - vi;

  x[14] = (ur >> 1) - vr;

  x[15] = (ui >> 1) + vi;

  // xt1 = 18

  // xt2 = 26

  SUMDIFF_PIFOURTH(vi, vr, x[26], x[27])

  ur = x[18];

  ui = x[19];

  x[18] = (ur >> 1) + vr;

  x[19] = (ui >> 1) + vi;

  x[26] = (ur >> 1) - vr;

  x[27] = (ui >> 1) - vi;

  // xt1 = 22

  // xt2 = 30

  SUMDIFF_PIFOURTH(vr, vi, x[30], x[31])

  ur = x[22];

  ui = x[23];

  x[22] = (ur >> 1) + vr;

  x[23] = (ui >> 1) - vi;

  x[30] = (ur >> 1) - vr;

  x[31] = (ui >> 1) + vi;

  // xt1 =  0

  // xt2 = 16

  vr = x[16];

  vi = x[17];

  ur = x[0] >> 1;

  ui = x[1] >> 1;

  x[0] = ur + (vr >> 1);

  x[1] = ui + (vi >> 1);

  x[16] = ur - (vr >> 1);

  x[17] = ui - (vi >> 1);

  // xt1 =  8

  // xt2 = 24

  vi = x[24];

  vr = x[25];

  ur = x[8] >> 1;

  ui = x[9] >> 1;

  x[8] = ur + (vr >> 1);

  x[9] = ui - (vi >> 1);

  x[24] = ur - (vr >> 1);

  x[25] = ui + (vi >> 1);

  // xt1 =  2

  // xt2 = 18

  cplxMultDiv2(&vi, &vr, x[19], x[18], fft16_w16[0]);

  ur = x[2];

  ui = x[3];

  x[2] = (ur >> 1) + vr;

  x[3] = (ui >> 1) + vi;

  x[18] = (ur >> 1) - vr;

  x[19] = (ui >> 1) - vi;

  // xt1 = 10

  // xt2 = 26

  cplxMultDiv2(&vr, &vi, x[27], x[26], fft16_w16[0]);

  ur = x[10];

  ui = x[11];

  x[10] = (ur >> 1) + vr;

  x[11] = (ui >> 1) - vi;

  x[26] = (ur >> 1) - vr;

  x[27] = (ui >> 1) + vi;

  // xt1 =  4

  // xt2 = 20

  SUMDIFF_PIFOURTH(vi, vr, x[20], x[21])

  ur = x[4];

  ui = x[5];

  x[4] = (ur >> 1) + vr;

  x[5] = (ui >> 1) + vi;

  x[20] = (ur >> 1) - vr;

  x[21] = (ui >> 1) - vi;

  // xt1 = 12

  // xt2 = 28

  SUMDIFF_PIFOURTH(vr, vi, x[28], x[29])

  ur = x[12];

  ui = x[13];

  x[12] = (ur >> 1) + vr;

  x[13] = (ui >> 1) - vi;

  x[28] = (ur >> 1) - vr;

  x[29] = (ui >> 1) + vi;

  // xt1 =  6

  // xt2 = 22

  cplxMultDiv2(&vi, &vr, x[23], x[22], fft16_w16[1]);

  ur = x[6];

  ui = x[7];

  x[6] = (ur >> 1) + vr;

  x[7] = (ui >> 1) + vi;

  x[22] = (ur >> 1) - vr;

  x[23] = (ui >> 1) - vi;

  // xt1 = 14

  // xt2 = 30

  cplxMultDiv2(&vr, &vi, x[31], x[30], fft16_w16[1]);

  ur = x[14];

  ui = x[15];

  x[14] = (ur >> 1) + vr;

  x[15] = (ui >> 1) - vi;

  x[30] = (ur >> 1) - vr;

  x[31] = (ui >> 1) + vi;

}

#endif /* FUNCTION_fft_16 */

#ifndef FUNCTION_fft_32

static const FIXP_STP fft32_w32[6] = {

    STCP(0x7641af3d, 0x30fbc54d), STCP(0x30fbc54d, 0x7641af3d),

    STCP(0x7d8a5f40, 0x18f8b83c), STCP(0x6a6d98a4, 0x471cece7),

    STCP(0x471cece7, 0x6a6d98a4), STCP(0x18f8b83c, 0x7d8a5f40)};

#define W_PiFOURTH STC(0x5a82799a)

LNK_SECTION_CODE_L1

inline void fft_32(FIXP_DBL *const _x) {

  /*

   * 1+2 stage radix 4

   */

  /////////////////////////////////////////////////////////////////////////////////////////

  {

    FIXP_DBL *const x = _x;

    FIXP_DBL vi, ui;

    FIXP_DBL vi2, ui2;

    FIXP_DBL vi3, ui3;

    FIXP_DBL vr, ur;

    FIXP_DBL vr2, ur2;

    FIXP_DBL vr3, ur3;

    FIXP_DBL vr4, ur4;

    // i = 0

    vr = (x[0] + x[32]) >> 1;     /* Re A + Re B */

    ur = (x[1] + x[33]) >> 1;     /* Im A + Im B */

    vi = (x[16] + x[48]) SHIFT_A; /* Re C + Re D */

    ui = (x[17] + x[49]) SHIFT_A; /* Im C + Im D */

    x[0] = vr + (vi SHIFT_B); /* Re A' = ReA + ReB +ReC + ReD */

    x[1] = ur + (ui SHIFT_B); /* Im A' = sum of imag values */

    vr2 = (x[4] + x[36]) >> 1; /* Re A + Re B */

    ur2 = (x[5] + x[37]) >> 1; /* Im A + Im B */

    x[4] = vr - (vi SHIFT_B); /* Re C' = -(ReC+ReD) + (ReA+ReB) */

    x[5] = ur - (ui SHIFT_B); /* Im C' = -Im C -Im D +Im A +Im B */

    vr -= x[32];             /* Re A - Re B */

    ur -= x[33];             /* Im A - Im B */

    vi = (vi SHIFT_B)-x[48]; /* Re C - Re D */

    ui = (ui SHIFT_B)-x[49]; /* Im C - Im D */

    vr3 = (x[2] + x[34]) >> 1; /* Re A + Re B */

    ur3 = (x[3] + x[35]) >> 1; /* Im A + Im B */

    x[2] = ui + vr; /* Re B' = Im C - Im D  + Re A - Re B */

    x[3] = ur - vi; /* Im B'= -Re C + Re D + Im A - Im B */

    vr4 = (x[6] + x[38]) >> 1; /* Re A + Re B */

    ur4 = (x[7] + x[39]) >> 1; /* Im A + Im B */

    x[6] = vr - ui; /* Re D' = -Im C + Im D + Re A - Re B */