Fraunhofer AAC codec.

License boilerplate update to follow.

Change-Id: I2810460c11a58b6d148d84673cc031f3685e79b5

1 files changed, 1395 insertions, 0 deletions

diff --git a/libFDK/src/fft.cpp b/libFDK/src/fft.cpp
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+/***************************  Fraunhofer IIS FDK Tools  **********************
+
+                        (C) Copyright Fraunhofer IIS (2001)
+                               All Rights Reserved
+
+    Please be advised that this software and/or program delivery is
+    Confidential Information of Fraunhofer and subject to and covered by the
+
+    Fraunhofer IIS Software Evaluation Agreement
+    between Google Inc. and  Fraunhofer
+    effective and in full force since March 1, 2012.
+
+    You may use this software and/or program only under the terms and
+    conditions described in the above mentioned Fraunhofer IIS Software
+    Evaluation Agreement. Any other and/or further use requires a separate agreement.
+
+
+   $Id$
+   Author(s):   Josef Hoepfl, DSP Solutions
+   Description: Fix point FFT
+
+   This software and/or program is protected by copyright law and international
+   treaties. Any reproduction or distribution of this software and/or program,
+   or any portion of it, may result in severe civil and criminal penalties, and
+   will be prosecuted to the maximum extent possible under law.
+
+   History:
+   20-APR-2010  A. Tritthart  replaced modulo operations with comparisons in fft15
+                to avoid failures with ARM RVCT 4.0 compiler
+                Tuned fft15 by 18% (Cortex-A8) to 25% (ARM926) by reprogramming
+                with merged loops.
+
+******************************************************************************/
+
+#include "fft.h"
+
+#include "fft_rad2.h"
+#include "FDK_tools_rom.h"
+
+
+
+
+
+#define F3C(x) STC(x)
+
+#define     C31       (F3C(0x91261468))      /* FL2FXCONST_DBL(-0.86602540)   */
+
+/* Performs the FFT of length 3 according to the algorithm after winograd.
+   No scaling of the input vector because the scaling is already done in the rotation vector. */
+static FORCEINLINE void fft3(FIXP_DBL *RESTRICT pDat)
+{
+  FIXP_DBL r1,r2;
+  FIXP_DBL s1,s2;
+  /* real part */
+  r1      = pDat[2] + pDat[4];
+  r2      = fMult((pDat[2] - pDat[4]), C31);
+  pDat[0] = pDat[0] + r1;
+  r1      = pDat[0] - r1 - (r1>>1);
+
+  /* imaginary part */
+  s1      = pDat[3] + pDat[5];
+  s2      = fMult((pDat[3] - pDat[5]), C31);
+  pDat[1] = pDat[1] + s1;
+  s1      = pDat[1] - s1 - (s1>>1);
+
+  /* combination */
+  pDat[2] = r1 - s2;
+  pDat[4] = r1 + s2;
+  pDat[3] = s1 + r2;
+  pDat[5] = s1 - r2;
+}
+
+
+//#define F5C(x) ((FIXP_DBL)x)
+#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 */
+static 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];
+  r4      = pDat[2] - pDat[8];
+  r3      = pDat[4] + pDat[6];
+  r2      = pDat[4] - pDat[6];
+  t       = fMult((r1-r3), C54);
+  r1      = r1 + r3;
+  pDat[0] = pDat[0] + 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];
+  s4      = pDat[3] - pDat[9];
+  s3      = pDat[5] + pDat[7];
+  s2      = pDat[5] - pDat[7];
+  t       = fMult((s1 - s3), C54);
+  s1      = s1 + s3;
+  pDat[1] = pDat[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 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)
+{
+#if FORCE_CRITICAL_CODE_FOR_RVCT4
+  FIXP_DBL  accu;
+  int j;
+#endif
+  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)]; */
+#if FORCE_CRITICAL_CODE_FOR_RVCT4
+  /* This branch generate failures on RVCT 4.0 with ARM926/ARM1136/ARM1176/C-R4, but not on Cortex-A8 */
+  pSrc = pInput;
+  pDst = aDst;
+  for(i=0,l=0,k=0; i<N5; i++)
+  {
+    for(j=0; j<N3; j++)
+    {
+      pDst[k]   = pSrc[l];
+      pDst[k+1] = pSrc[l+1];
+      k += 2;
+      l += 2*N5;
+      if (l >= (2*N15))
+        l -= (2*N15);
+    }
+    l += (2*N3);
+    if (l >= (2*N15))
+      l -= (2*N15);
+  }
+  /* Perform 5 times the fft of length 3
+  output3(0:2)   = fft3(input3(0:2));
+  output3(3:5)   = fft3(input3(3:5));
+  output3(6:8)   = fft3(input3(6:8));
+  output3(9:11)  = fft3(input3(9:11));
+  output3(12:14) = fft3(input3(12:14)); */
+  pSrc=aDst;
+  for(i=0; i<N5; i++)
+  {
+    fft3(pSrc);
+    pSrc += (2*N3);
+  }
+
+  /* Scaling of the input vector of the fft5 with the scale factor 0.125 */
+  pSrc=aDst;
+  for(j=0; j<(2*N3*N5); j++)
+  {
+    accu = pSrc[j];
+    /* 2 bit right shift */
+    accu >>= 2;
+    pSrc[j] = accu;
+  }
+#else
+  {
+    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;
+    }
+  }
+#endif
+  /* 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 */
+    }
+  }
+}
+
+#define W_PiFOURTH STC(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;\
+  }
+#endif
+
+/* This version is more overflow save, but less cycle optimal. */
+#define SUMDIFF_EIGTH(x, y, ix, iy, vr, vi, ur, ui) \
+  vr = (x[ 0 + ix]>>1) + (x[16 + ix]>>1);  /* Re A + Re B */ \
+  vi = (x[ 8 + ix]>>1) + (x[24 + ix]>>1);     /* Re C + Re D */ \
+  ur = (x[ 1 + ix]>>1) + (x[17 + ix]>>1);  /* Im A + Im B */ \
+  ui = (x[ 9 + ix]>>1) + (x[25 + ix]>>1);     /* Im C + Im D */ \
+  y[ 0 + iy] = vr + vi;     /* Re A' = ReA + ReB +ReC + ReD */    \
+  y[ 4 + iy] = vr - vi;     /* Re C' = -(ReC+ReD) + (ReA+ReB) */  \
+  y[ 1 + iy] = ur + ui;     /* Im A' = sum of imag values */      \
+  y[ 5 + iy] = ur - ui;     /* Im C' = -Im C -Im D +Im A +Im B */ \
+  vr -= x[16 + ix];              /* Re A - Re B */ \
+  vi = vi - x[24 + ix];          /* Re C - Re D */ \
+  ur -= x[17 + ix];              /* Im A - Im B */ \
+  ui = ui - x[25 + ix];          /* Im C - Im D */ \
+  y[ 2 + iy] = ui + vr;          /* Re B' = Im C - Im D  + Re A - Re B */ \
+  y[ 6 + iy] = vr - ui;          /* Re D' = -Im C + Im D + Re A - Re B */ \
+  y[ 3 + iy] = ur - vi;          /* Im B'= -Re C + Re D + Im A - Im B */  \
+  y[ 7 + iy] = vi + ur;          /* Im D'= Re C - Re D + Im A - Im B */
+
+static const FIXP_SPK fft16_w16[2] = { {{STC(0x7641af3d), STC(0x30fbc54d)}}, {{ STC(0x30fbc54d), STC(0x7641af3d)}} };
+
+LNK_SECTION_CODE_L1
+inline void fft_16(FIXP_DBL *RESTRICT x)
+{
+  FIXP_DBL vr, vi, ur, ui;
+  FIXP_DBL y[32];
+
+  SUMDIFF_EIGTH(x, y, 0,  0, vr, vi, ur, ui);
+  SUMDIFF_EIGTH(x, y, 4,  8, vr, vi, ur, ui);
+  SUMDIFF_EIGTH(x, y, 2, 16, vr, vi, ur, ui);
+  SUMDIFF_EIGTH(x, y, 6, 24, vr, vi, ur, ui);
+
+// xt1 =  0
+// xt2 =  8
+  vr = y[ 8];
+  vi = y[ 9];
+  ur = y[ 0]>>1;
+  ui = y[ 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 = y[13];
+  vi = y[12];
+  ur = y[ 4]>>1;
+  ui = y[ 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 = y[24];
+  vi = y[25];
+  ur = y[16]>>1;
+  ui = y[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 = y[29];
+  vi = y[28];
+  ur = y[20]>>1;
+  ui = y[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, y[10], y[11])
+  //vr = fMultDiv2((y[11] + y[10]),W_PiFOURTH);
+  //vi = fMultDiv2((y[11] - y[10]),W_PiFOURTH);
+  ur = y[ 2];
+  ui = y[ 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, y[14], y[15])
+  ur = y[ 6];
+  ui = y[ 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, y[26], y[27])
+  ur = y[18];
+  ui = y[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, y[30], y[31])
+  ur = y[22];
+  ui = y[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;
+}
+
+#ifndef FUNCTION_fft_32
+static const FIXP_SPK fft32_w32[6] =
+{
+  {{ STC(0x7641af3d), STC(0x30fbc54d)}}, {{ STC(0x30fbc54d), STC(0x7641af3d)}}, {{ STC(0x7d8a5f40), STC(0x18f8b83c)}},
+  {{ STC(0x6a6d98a4), STC(0x471cece7)}}, {{ STC(0x471cece7), STC(0x6a6d98a4)}}, {{ STC(0x18f8b83c), STC(0x7d8a5f40)}}
+};
+
+LNK_SECTION_CODE_L1
+inline void fft_32(FIXP_DBL *x)
+{
+
+#define W_PiFOURTH STC(0x5a82799a)
+
+  FIXP_DBL vr,vi,ur,ui;
+  FIXP_DBL y[64];
+
+  /*
+   * 1+2 stage radix 4
+   */
+
+/////////////////////////////////////////////////////////////////////////////////////////
+
+  // i = 0
+  vr = (x[ 0] + x[32])>>1;  /* Re A + Re B */
+  vi = (x[16] + x[48]);     /* Re C + Re D */
+  ur = (x[ 1] + x[33])>>1;  /* Im A + Im B */
+  ui = (x[17] + x[49]);     /* Im C + Im D */
+
+  y[ 0] = vr + (vi>>1);     /* Re A' = ReA + ReB +ReC + ReD */
+  y[ 4] = vr - (vi>>1);     /* Re C' = -(ReC+ReD) + (ReA+ReB) */
+  y[ 1] = ur + (ui>>1);     /* Im A' = sum of imag values */
+  y[ 5] = ur - (ui>>1);     /* Im C' = -Im C -Im D +Im A +Im B */
+
+  vr -= x[32];              /* Re A - Re B */
+  vi = (vi>>1) - x[48];     /* Re C - Re D */
+  ur -= x[33];              /* Im A - Im B */
+  ui = (ui>>1) - x[49];     /* Im C - Im D */
+
+  y[ 2] = ui + vr;          /* Re B' = Im C - Im D  + Re A - Re B */
+  y[ 6] = vr - ui;          /* Re D' = -Im C + Im D + Re A - Re B */
+  y[ 3] = ur - vi;          /* Im B'= -Re C + Re D + Im A - Im B */
+  y[ 7] = vi + ur;          /* Im D'= Re C - Re D + Im A - Im B */
+
+  //i=8
+  vr = (x[ 8] + x[40])>>1;  /* Re A + Re B */
+  vi = (x[24] + x[56]);     /* Re C + Re D */
+  ur = (x[ 9] + x[41])>>1;  /* Im A + Im B */
+  ui = (x[25] + x[57]);     /* Im C + Im D */
+
+  y[ 8] = vr + (vi>>1);     /* Re A' = ReA + ReB +ReC + ReD */
+  y[12] = vr - (vi>>1);     /* Re C' = -(ReC+ReD) + (ReA+ReB) */
+  y[ 9] = ur + (ui>>1);     /* Im A' = sum of imag values */
+  y[13] = ur - (ui>>1);     /* Im C' = -Im C -Im D +Im A +Im B */
+
+  vr -= x[40];              /* Re A - Re B */
+  vi = (vi>>1) - x[56];     /* Re C - Re D */
+  ur -= x[41];              /* Im A - Im B */
+  ui = (ui>>1) - x[57];     /* Im C - Im D */
+
+  y[10] = ui + vr;          /* Re B' = Im C - Im D  + Re A - Re B */
+  y[14] = vr - ui;          /* Re D' = -Im C + Im D + Re A - Re B */
+  y[11] = ur - vi;          /* Im B'= -Re C + Re D + Im A - Im B */
+  y[15] = vi + ur;          /* Im D'= Re C - Re D + Im A - Im B */
+
+  //i=16
+  vr = (x[ 4] + x[36])>>1;  /* Re A + Re B */
+  vi = (x[20] + x[52]);     /* Re C + Re D */
+  ur = (x[ 5] + x[37])>>1;  /* Im A + Im B */
+  ui = (x[21] + x[53]);     /* Im C + Im D */
+
+  y[16] = vr + (vi>>1);     /* Re A' = ReA + ReB +ReC + ReD */
+  y[20] = vr - (vi>>1);     /* Re C' = -(ReC+ReD) + (ReA+ReB) */
+  y[17] = ur + (ui>>1);     /* Im A' = sum of imag values */
+  y[21] = ur - (ui>>1);     /* Im C' = -Im C -Im D +Im A +Im B */
+
+  vr -= x[36];              /* Re A - Re B */
+  vi = (vi>>1) - x[52];     /* Re C - Re D */
+  ur -= x[37];              /* Im A - Im B */
+  ui = (ui>>1) - x[53];     /* Im C - Im D */
+
+  y[18] = ui + vr;          /* Re B' = Im C - Im D  + Re A - Re B */
+  y[22] = vr - ui;          /* Re D' = -Im C + Im D + Re A - Re B */
+  y[19] = ur - vi;          /* Im B'= -Re C + Re D + Im A - Im B */
+  y[23] = vi + ur;          /* Im D'= Re C - Re D + Im A - Im B */
+
+  //i=24
+  vr = (x[12] + x[44])>>1;  /* Re A + Re B */
+  vi = (x[28] + x[60]);     /* Re C + Re D */
+  ur = (x[13] + x[45])>>1;  /* Im A + Im B */
+  ui = (x[29] + x[61]);     /* Im C + Im D */
+
+  y[24] = vr + (vi>>1);     /* Re A' = ReA + ReB +ReC + ReD */
+  y[28] = vr - (vi>>1);     /* Re C' = -(ReC+ReD) + (ReA+ReB) */
+  y[25] = ur + (ui>>1);     /* Im A' = sum of imag values */
+  y[29] = ur - (ui>>1);     /* Im C' = -Im C -Im D +Im A +Im B */
+
+  vr -= x[44];              /* Re A - Re B */
+  vi = (vi>>1) - x[60];     /* Re C - Re D */
+  ur -= x[45];              /* Im A - Im B */
+  ui = (ui>>1) - x[61];     /* Im C - Im D */
+
+  y[26] = ui + vr;          /* Re B' = Im C - Im D  + Re A - Re B */
+  y[30] = vr - ui;          /* Re D' = -Im C + Im D + Re A - Re B */
+  y[27] = ur - vi;          /* Im B'= -Re C + Re D + Im A - Im B */
+  y[31] = vi + ur;          /* Im D'= Re C - Re D + Im A - Im B */
+
+  // i = 32
+  vr = (x[ 2] + x[34])>>1;  /* Re A + Re B */
+  vi = (x[18] + x[50]);     /* Re C + Re D */
+  ur = (x[ 3] + x[35])>>1;  /* Im A + Im B */
+  ui = (x[19] + x[51]);     /* Im C + Im D */
+
+  y[32] = vr + (vi>>1);     /* Re A' = ReA + ReB +ReC + ReD */
+  y[36] = vr - (vi>>1);     /* Re C' = -(ReC+ReD) + (ReA+ReB) */
+  y[33] = ur + (ui>>1);     /* Im A' = sum of imag values */
+  y[37] = ur - (ui>>1);     /* Im C' = -Im C -Im D +Im A +Im B */
+
+  vr -= x[34];              /* Re A - Re B */
+  vi = (vi>>1) - x[50];     /* Re C - Re D */
+  ur -= x[35];              /* Im A - Im B */
+  ui = (ui>>1) - x[51];     /* Im C - Im D */
+
+  y[34] = ui + vr;          /* Re B' = Im C - Im D  + Re A - Re B */
+  y[38] = vr - ui;          /* Re D' = -Im C + Im D + Re A - Re B */
+  y[35] = ur - vi;          /* Im B'= -Re C + Re D + Im A - Im B */
+  y[39] = vi + ur;          /* Im D'= Re C - Re D + Im A - Im B */
+
+  //i=40
+  vr = (x[10] + x[42])>>1;  /* Re A + Re B */
+  vi = (x[26] + x[58]);     /* Re C + Re D */
+  ur = (x[11] + x[43])>>1;  /* Im A + Im B */
+  ui = (x[27] + x[59]);     /* Im C + Im D */
+
+  y[40] = vr + (vi>>1);     /* Re A' = ReA + ReB +ReC + ReD */
+  y[44] = vr - (vi>>1);     /* Re C' = -(ReC+ReD) + (ReA+ReB) */
+  y[41] = ur + (ui>>1);     /* Im A' = sum of imag values */
+  y[45] = ur - (ui>>1);     /* Im C' = -Im C -Im D +Im A +Im B */
+
+  vr -= x[42];              /* Re A - Re B */
+  vi = (vi>>1) - x[58];     /* Re C - Re D */
+  ur -= x[43];              /* Im A - Im B */
+  ui = (ui>>1) - x[59];     /* Im C - Im D */
+
+  y[42] = ui + vr;          /* Re B' = Im C - Im D  + Re A - Re B */
+  y[46] = vr - ui;          /* Re D' = -Im C + Im D + Re A - Re B */
+  y[43] = ur - vi;          /* Im B'= -Re C + Re D + Im A - Im B */
+  y[47] = vi + ur;          /* Im D'= Re C - Re D + Im A - Im B */
+
+  //i=48
+  vr = (x[ 6] + x[38])>>1;  /* Re A + Re B */
+  vi = (x[22] + x[54]);     /* Re C + Re D */
+  ur = (x[ 7] + x[39])>>1;  /* Im A + Im B */
+  ui = (x[23] + x[55]);     /* Im C + Im D */
+
+  y[48] = vr + (vi>>1);     /* Re A' = ReA + ReB +ReC + ReD */
+  y[52] = vr - (vi>>1);     /* Re C' = -(ReC+ReD) + (ReA+ReB) */
+  y[49] = ur + (ui>>1);     /* Im A' = sum of imag values */
+  y[53] = ur - (ui>>1);     /* Im C' = -Im C -Im D +Im A +Im B */
+
+  vr -= x[38];              /* Re A - Re B */
+  vi = (vi>>1) - x[54];     /* Re C - Re D */
+  ur -= x[39];              /* Im A - Im B */
+  ui = (ui>>1) - x[55];     /* Im C - Im D */
+
+  y[50] = ui + vr;          /* Re B' = Im C - Im D  + Re A - Re B */
+  y[54] = vr - ui;          /* Re D' = -Im C + Im D + Re A - Re B */
+  y[51] = ur - vi;          /* Im B'= -Re C + Re D + Im A - Im B */
+  y[55] = vi + ur;          /* Im D'= Re C - Re D + Im A - Im B */
+
+  //i=56
+  vr = (x[14] + x[46])>>1;  /* Re A + Re B */
+  vi = (x[30] + x[62]);     /* Re C + Re D */
+  ur = (x[15] + x[47])>>1;  /* Im A + Im B */
+  ui = (x[31] + x[63]);     /* Im C + Im D */
+
+  y[56] = vr + (vi>>1);     /* Re A' = ReA + ReB +ReC + ReD */
+  y[60] = vr - (vi>>1);     /* Re C' = -(ReC+ReD) + (ReA+ReB) */
+  y[57] = ur + (ui>>1);     /* Im A' = sum of imag values */
+  y[61] = ur - (ui>>1);     /* Im C' = -Im C -Im D +Im A +Im B */
+
+  vr -= x[46];              /* Re A - Re B */
+  vi = (vi>>1) - x[62];     /* Re C - Re D */
+  ur -= x[47];              /* Im A - Im B */
+  ui = (ui>>1) - x[63];     /* Im C - Im D */
+
+  y[58] = ui + vr;          /* Re B' = Im C - Im D  + Re A - Re B */
+  y[62] = vr - ui;          /* Re D' = -Im C + Im D + Re A - Re B */
+  y[59] = ur - vi;          /* Im B'= -Re C + Re D + Im A - Im B */
+  y[63] = vi + ur;          /* Im D'= Re C - Re D + Im A - Im B */
+
+
+  FIXP_DBL *xt = &x[0];
+  FIXP_DBL *yt = &y[0];
+
+  int j = 4;
+  do
+  {
+    vr = yt[8];
+    vi = yt[9];
+    ur = yt[0]>>1;
+    ui = yt[1]>>1;
+    xt[ 0] = ur + (vr>>1);
+    xt[ 1] = ui + (vi>>1);
+    xt[ 8] = ur - (vr>>1);
+    xt[ 9] = ui - (vi>>1);
+
+    vr = yt[13];
+    vi = yt[12];
+    ur = yt[4]>>1;
+    ui = yt[5]>>1;
+    xt[ 4] = ur + (vr>>1);
+    xt[ 5] = ui - (vi>>1);
+    xt[12] = ur - (vr>>1);
+    xt[13] = ui + (vi>>1);
+
+    SUMDIFF_PIFOURTH(vi, vr, yt[10], yt[11])
+    ur = yt[2];
+    ui = yt[3];
+    xt[ 2] = (ur>>1) + vr;
+    xt[ 3] = (ui>>1) + vi;
+    xt[10] = (ur>>1) - vr;
+    xt[11] = (ui>>1) - vi;
+
+    SUMDIFF_PIFOURTH(vr, vi, yt[14], yt[15])
+    ur = yt[6];
+    ui = yt[7];
+
+    xt[ 6] = (ur>>1) + vr;
+    xt[ 7] = (ui>>1) - vi;
+    xt[14] = (ur>>1) - vr;
+    xt[15] = (ui>>1) + vi;
+    xt += 16;
+    yt += 16;
+  } while (--j != 0);
+
+  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);
+
+  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);
+
+  vr = x[48];
+  vi = x[49];
+  ur = x[32]>>1;
+  ui = x[33]>>1;
+  x[32] = ur + (vr>>1);
+  x[33] = ui + (vi>>1);
+  x[48] = ur - (vr>>1);
+  x[49] = ui - (vi>>1);
+
+  vi = x[56];
+  vr = x[57];
+  ur = x[40]>>1;
+  ui = x[41]>>1;
+  x[40] = ur + (vr>>1);
+  x[41] = ui - (vi>>1);
+  x[56] = ur - (vr>>1);
+  x[57] = ui + (vi>>1);
+
+  cplxMultDiv2(&vi, &vr, x[19], x[18], fft32_w32[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;
+
+  cplxMultDiv2(&vr, &vi, x[27], x[26], fft32_w32[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;
+
+  cplxMultDiv2(&vi, &vr, x[51], x[50], fft32_w32[0]);
+  ur = x[34];
+  ui = x[35];
+  x[34] = (ur>>1) + vr;
+  x[35] = (ui>>1) + vi;
+  x[50] = (ur>>1) - vr;
+  x[51] = (ui>>1) - vi;
+
+  cplxMultDiv2(&vr, &vi, x[59], x[58], fft32_w32[0]);
+  ur = x[42];
+  ui = x[43];
+  x[42] = (ur>>1) + vr;
+  x[43] = (ui>>1) - vi;
+  x[58] = (ur>>1) - vr;
+  x[59] = (ui>>1) + vi;
+
+  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;
+
+  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;
+
+  SUMDIFF_PIFOURTH(vi, vr, x[52], x[53])
+  ur = x[36];
+  ui = x[37];
+  x[36] = (ur>>1) + vr;
+  x[37] = (ui>>1) + vi;
+  x[52] = (ur>>1) - vr;
+  x[53] = (ui>>1) - vi;
+
+  SUMDIFF_PIFOURTH(vr, vi, x[60], x[61])
+  ur = x[44];
+  ui = x[45];
+  x[44] = (ur>>1) + vr;
+  x[45] = (ui>>1) - vi;
+  x[60] = (ur>>1) - vr;
+  x[61] = (ui>>1) + vi;
+
+
+  cplxMultDiv2(&vi, &vr, x[23], x[22], fft32_w32[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;
+
+  cplxMultDiv2(&vr, &vi, x[31], x[30], fft32_w32[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;
+
+  cplxMultDiv2(&vi, &vr, x[55], x[54], fft32_w32[1]);
+  ur = x[38];
+  ui = x[39];
+  x[38] = (ur>>1) + vr;
+  x[39] = (ui>>1) + vi;
+  x[54] = (ur>>1) - vr;
+  x[55] = (ui>>1) - vi;
+
+  cplxMultDiv2(&vr, &vi, x[63], x[62], fft32_w32[1]);
+  ur = x[46];
+  ui = x[47];
+
+  x[46] = (ur>>1) + vr;
+  x[47] = (ui>>1) - vi;
+  x[62] = (ur>>1) - vr;
+  x[63] = (ui>>1) + vi;
+
+  vr = x[32];
+  vi = x[33];
+  ur = x[ 0]>>1;
+  ui = x[ 1]>>1;
+  x[ 0] = ur + (vr>>1);
+  x[ 1] = ui + (vi>>1);
+  x[32] = ur - (vr>>1);
+  x[33] = ui - (vi>>1);
+
+  vi = x[48];
+  vr = x[49];
+  ur = x[16]>>1;
+  ui = x[17]>>1;
+  x[16] = ur + (vr>>1);
+  x[17] = ui - (vi>>1);
+  x[48] = ur - (vr>>1);
+  x[49] = ui + (vi>>1);
+
+  cplxMultDiv2(&vi, &vr, x[35], x[34], fft32_w32[2]);
+  ur = x[ 2];
+  ui = x[ 3];
+  x[ 2] = (ur>>1) + vr;
+  x[ 3] = (ui>>1) + vi;
+  x[34] = (ur>>1) - vr;
+  x[35] = (ui>>1) - vi;
+
+  cplxMultDiv2(&vr, &vi, x[51], x[50], fft32_w32[2]);
+  ur = x[18];
+  ui = x[19];
+  x[18] = (ur>>1) + vr;
+  x[19] = (ui>>1) - vi;
+  x[50] = (ur>>1) - vr;
+  x[51] = (ui>>1) + vi;
+
+  cplxMultDiv2(&vi, &vr, x[37], x[36], fft32_w32[0]);
+  ur = x[ 4];
+  ui = x[ 5];
+  x[ 4] = (ur>>1) + vr;
+  x[ 5] = (ui>>1) + vi;
+  x[36] = (ur>>1) - vr;
+  x[37] = (ui>>1) - vi;
+
+  cplxMultDiv2(&vr, &vi, x[53], x[52], fft32_w32[0]);
+  ur = x[20];
+  ui = x[21];
+  x[20] = (ur>>1) + vr;
+  x[21] = (ui>>1) - vi;
+  x[52] = (ur>>1) - vr;
+  x[53] = (ui>>1) + vi;
+
+  cplxMultDiv2(&vi, &vr, x[39], x[38], fft32_w32[3]);
+  ur = x[ 6];
+  ui = x[ 7];
+  x[ 6] = (ur>>1) + vr;
+  x[ 7] = (ui>>1) + vi;
+  x[38] = (ur>>1) - vr;
+  x[39] = (ui>>1) - vi;
+
+  cplxMultDiv2(&vr, &vi, x[55], x[54], fft32_w32[3]);
+  ur = x[22];
+  ui = x[23];
+  x[22] = (ur>>1) + vr;
+  x[23] = (ui>>1) - vi;
+  x[54] = (ur>>1) - vr;
+  x[55] = (ui>>1) + vi;
+
+  SUMDIFF_PIFOURTH(vi, vr, x[40], x[41])
+  ur = x[ 8];
+  ui = x[ 9];
+  x[ 8] = (ur>>1) + vr;
+  x[ 9] = (ui>>1) + vi;
+  x[40] = (ur>>1) - vr;
+  x[41] = (ui>>1) - vi;
+
+  SUMDIFF_PIFOURTH(vr, vi, x[56], x[57])
+  ur = x[24];
+  ui = x[25];
+  x[24] = (ur>>1) + vr;
+  x[25] = (ui>>1) - vi;
+  x[56] = (ur>>1) - vr;
+  x[57] = (ui>>1) + vi;
+
+  cplxMultDiv2(&vi, &vr, x[43], x[42], fft32_w32[4]);
+  ur = x[10];
+  ui = x[11];
+
+  x[10] = (ur>>1) + vr;
+  x[11] = (ui>>1) + vi;
+  x[42] = (ur>>1) - vr;
+  x[43] = (ui>>1) - vi;
+
+  cplxMultDiv2(&vr, &vi, x[59], x[58], fft32_w32[4]);
+  ur = x[26];
+  ui = x[27];
+  x[26] = (ur>>1) + vr;
+  x[27] = (ui>>1) - vi;
+  x[58] = (ur>>1) - vr;
+  x[59] = (ui>>1) + vi;
+
+  cplxMultDiv2(&vi, &vr, x[45], x[44], fft32_w32[1]);
+  ur = x[12];
+  ui = x[13];
+  x[12] = (ur>>1) + vr;
+  x[13] = (ui>>1) + vi;
+  x[44] = (ur>>1) - vr;
+  x[45] = (ui>>1) - vi;
+
+  cplxMultDiv2(&vr, &vi, x[61], x[60], fft32_w32[1]);
+  ur = x[28];
+  ui = x[29];
+  x[28] = (ur>>1) + vr;
+  x[29] = (ui>>1) - vi;
+  x[60] = (ur>>1) - vr;
+  x[61] = (ui>>1) + vi;
+
+  cplxMultDiv2(&vi, &vr, x[47], x[46], fft32_w32[5]);
+  ur = x[14];
+  ui = x[15];
+  x[14] = (ur>>1) + vr;
+  x[15] = (ui>>1) + vi;
+  x[46] = (ur>>1) - vr;
+  x[47] = (ui>>1) - vi;
+
+  cplxMultDiv2(&vr, &vi, x[63], x[62], fft32_w32[5]);
+  ur = x[30];
+  ui = x[31];
+  x[30] = (ur>>1) + vr;
+  x[31] = (ui>>1) - vi;
+  x[62] = (ur>>1) - vr;
+  x[63] = (ui>>1) + vi;
+}
+#endif /* #ifndef FUNCTION_fft_32 */
+
+
+/**
+ * \brief Apply rotation vectors to a data buffer.
+ * \param cl length of each row of input data.
+ * \param l total length of input data.
+ * \param pVecRe real part of rotation ceofficient vector.
+ * \param pVecIm imaginary part of rotation ceofficient vector.
+ */
+static inline void fft_apply_rot_vector(FIXP_DBL *RESTRICT pData, const int cl, const int l, const FIXP_STB *pVecRe, const FIXP_STB *pVecIm)
+{
+  FIXP_DBL re, im;
+  FIXP_STB vre, vim;
+
+  int i, c;
+
+  for(i=0; i<cl; i++) {
+    re  = pData[2*i];
+    im  = pData[2*i+1];
+
+    pData[2*i]   = re>>2; /* * 0.25 */
+    pData[2*i+1] = im>>2; /* * 0.25 */
+  }
+  for(; i<l; i+=cl)
+  {
+    re  = pData[2*i];
+    im  = pData[2*i+1];
+
+    pData[2*i]   = re>>2; /* * 0.25 */
+    pData[2*i+1] = im>>2; /* * 0.25 */
+
+    for (c=i+1; c<i+cl; c++)
+    {
+      re  = pData[2*c]>>1;
+      im  = pData[2*c+1]>>1;
+      vre = *pVecRe++;
+      vim = *pVecIm++;
+
+      cplxMultDiv2(&pData[2*c+1], &pData[2*c], im, re, vre, vim);
+    }
+  }
+}
+
+#define FFT_TWO_STAGE_MACRO_ENABLE
+
+
+#ifdef FFT_TWO_STAGE_MACRO_ENABLE
+
+#define fftN2(pInput, length, dim1, dim2, fft_func1, fft_func2, RotVectorReal, RotVectorImag) \
+{ \
+  int       i, j; \
+ \
+  C_ALLOC_SCRATCH_START(aDst, FIXP_DBL, length*2); \
+  C_ALLOC_SCRATCH_START(aDst2, FIXP_DBL, dim2*2); \
+ \
+  FDK_ASSERT(length == dim1*dim2); \
+ \
+  /* Perform dim2 times the fft of length dim1. The input samples are at the address of pSrc and the \
+  output samples are at the address of pDst. The input vector for the fft of length dim1 is built \
+  of the interleaved samples in pSrc, the output samples are stored consecutively. \
+  */ \
+  { \
+    const FIXP_DBL* pSrc = pInput; \
+    FIXP_DBL  *RESTRICT pDst = aDst; \
+    \
+    for(i=0; i<dim2; i++) \
+    { \
+      for(j=0; j<dim1; j++) \
+      { \
+        pDst[2*j]   = pSrc[2*j*dim2]; \
+        pDst[2*j+1] = pSrc[2*j*dim2+1]; \
+      } \
+      \
+      fft_func1(pDst); \
+      pSrc += 2; \
+      pDst = pDst + 2*dim1; \
+    } \
+  } \
+  \
+  /* Perform the modulation of the output of the fft of length dim1 */ \
+  fft_apply_rot_vector(aDst, dim1, length, RotVectorReal, RotVectorImag); \
+  \
+  /* Perform dim1 times the fft of length dim2. 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 dim2 is built \
+  of the interleaved samples in aDst, the output samples are stored consecutively at the address \
+  of pInput. \
+  */ \
+  { \
+    const FIXP_DBL* pSrc       = aDst; \
+    FIXP_DBL *RESTRICT pDst    = aDst2; \
+    FIXP_DBL *RESTRICT pDstOut = pInput; \
+    \
+    for(i=0; i<dim1; i++) \
+    { \
+      for(j=0; j<dim2; j++) \
+      { \
+        pDst[2*j]   = pSrc[2*j*dim1]; \
+        pDst[2*j+1] = pSrc[2*j*dim1+1]; \
+      } \
+      \
+      fft_func2(pDst); \
+      \
+      for(j=0; j<dim2; j++) \
+      { \
+        pDstOut[2*j*dim1]   = pDst[2*j]; \
+        pDstOut[2*j*dim1+1] = pDst[2*j+1]; \
+      } \
+      pSrc += 2; \
+      pDstOut += 2; \
+    } \
+  } \
+  \
+  C_ALLOC_SCRATCH_END(aDst2, FIXP_DBL, dim2*2); \
+  C_ALLOC_SCRATCH_END(aDst, FIXP_DBL, length*2); \
+} \
+
+#else /* FFT_TWO_STAGE_MACRO_ENABLE */
+
+/* select either switch case of function pointer. */
+//#define FFT_TWO_STAGE_SWITCH_CASE
+
+static inline void fftN2(
+        FIXP_DBL *pInput,
+        const int length,
+        const int dim1,
+        const int dim2,
+        void (* const fft1)(FIXP_DBL *),
+        void (* const fft2)(FIXP_DBL *),
+        const FIXP_STB *RotVectorReal,
+        const FIXP_STB *RotVectorImag
+        )
+{
+  /* The real part of the input samples are at the addresses with even indices and the imaginary
+  part of the input samples are at the addresses with odd indices. The output samples are stored
+  at the address of pInput
+  */
+  FIXP_DBL  *pSrc, *pDst, *pDstOut;
+  int       i, j;
+
+  C_ALLOC_SCRATCH_START(aDst, FIXP_DBL, length*2);
+  C_ALLOC_SCRATCH_START(aDst2, FIXP_DBL, dim2*2);
+     
+  FDK_ASSERT(length == dim1*dim2);
+
+  /* Perform dim2 times the fft of length dim1. The input samples are at the address of pSrc and the
+  output samples are at the address of pDst. The input vector for the fft of length dim1 is built
+  of the interleaved samples in pSrc, the output samples are stored consecutively.
+  */
+  pSrc = pInput;
+  pDst = aDst;
+  for(i=0; i<length/dim1; i++)
+  {
+    for(j=0; j<length/dim2; j++)
+    {
+      pDst[2*j]   = pSrc[2*j*dim2];
+      pDst[2*j+1] = pSrc[2*j*dim2+1];
+    }
+
+    /* fft of size dim1 */
+#ifndef FFT_TWO_STAGE_SWITCH_CASE
+    fft1(pDst);
+#else
+    switch (dim1) {
+      case 3: fft3(pDst); break;
+      case 4: fft_4(pDst); break;
+      case 5: fft5(pDst); break;
+      case 8: fft_8(pDst); break;
+      case 15: fft15(pDst); break;
+      case 16: fft_16(pDst); break;
+      case 32: fft_32(pDst); break;
+      /*case 64: fft_64(pDst); break;*/
+      case 128: fft_128(pDst); break;
+    }
+#endif
+    pSrc += 2;
+    pDst = pDst + 2*length/dim2;
+  }
+
+  /* Perform the modulation of the output of the fft of length dim1 */
+  pSrc=aDst;
+  fft_apply_rot_vector(pSrc, length/dim2, length, RotVectorReal, RotVectorImag);
+
+  /* Perform dim1 times the fft of length dim2. 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 dim2 is built
+  of the interleaved samples in aDst, the output samples are stored consecutively at the address
+  of pInput.
+  */
+  pSrc    = aDst;
+  pDst    = aDst2;
+  pDstOut = pInput;
+  for(i=0; i<length/dim2; i++)
+  {
+    for(j=0; j<length/dim1; j++)
+    {
+      pDst[2*j]   = pSrc[2*j*dim1];
+      pDst[2*j+1] = pSrc[2*j*dim1+1];
+    }
+
+#ifndef FFT_TWO_STAGE_SWITCH_CASE
+    fft2(pDst);
+#else
+    switch (dim2) {
+      case 3: fft3(pDst); break;
+      case 4: fft_4(pDst); break;
+      case 5: fft5(pDst); break;
+      case 8: fft_8(pDst); break;
+      case 15: fft15(pDst); break;
+      case 16: fft_16(pDst); break;
+      case 32: fft_32(pDst); break;
+      /*case 64: fft_64(pDst); break;*/
+      case 128: fft_128(pDst); break;
+    }
+#endif
+
+    for(j=0; j<length/dim1; j++)
+    {
+      pDstOut[2*j*dim1]   = pDst[2*j];
+      pDstOut[2*j*dim1+1] = pDst[2*j+1];
+    }
+    pSrc += 2;
+    pDstOut += 2;
+  }
+
+  C_ALLOC_SCRATCH_END(aDst2, FIXP_DBL, dim2*2);
+  C_ALLOC_SCRATCH_END(aDst, FIXP_DBL, length*2);
+}
+
+#endif /* FFT_TWO_STAGE_MACRO_ENABLE */
+
+
+
+
+
+
+
+
+
+
+
+
+#define SCALEFACTOR60         5
+/**
+The function performs the fft of length 60. It is splittet into fft's of length 4 and fft's of
+length 15. Between the fft's a modolation is calculated.
+*/
+static inline void fft60(FIXP_DBL *pInput, INT *pScalefactor)
+{
+  fftN2(
+          pInput, 60, 4, 15, 
+          fft_4, fft15,
+          RotVectorReal60, RotVectorImag60
+          );
+  *pScalefactor += SCALEFACTOR60;
+}
+
+
+
+/* Fallback implementation in case of no better implementation available. */
+
+#define SCALEFACTOR240        7
+
+/**
+The function performs the fft of length 240. It is splittet into fft's of length 16 and fft's of
+length 15. Between the fft's a modulation is calculated.
+*/
+static inline void fft240(FIXP_DBL *pInput, INT *pScalefactor)
+{
+  fftN2(
+          pInput, 240, 16, 15, 
+          fft_16, fft15,
+          RotVectorReal240, RotVectorImag240
+          );
+  *pScalefactor += SCALEFACTOR240;
+}
+
+
+#define SCALEFACTOR480        8
+#define N32                   32
+#define TABLE_SIZE_16        (32/2)
+
+/**
+The function performs the fft of length 480. It is splittet into fft's of length 32 and fft's of
+length 15. Between the fft's a modulation is calculated.
+*/
+static inline void fft480(FIXP_DBL *pInput, INT *pScalefactor)
+{
+  fftN2(
+          pInput, 480, 32, 15, 
+          fft_32, fft15,
+          RotVectorReal480, RotVectorImag480
+          );
+  *pScalefactor += SCALEFACTOR480;
+}
+
+void fft(int length, FIXP_DBL *pInput, INT *pScalefactor)
+{
+  if (length == 32)
+  {
+      fft_32(pInput);
+      *pScalefactor += SCALEFACTOR32;
+  }
+  else
+  {
+  
+  switch (length) {
+    case 16:
+      fft_16(pInput);
+      *pScalefactor += SCALEFACTOR16;
+      break;
+    case 8:
+      fft_8(pInput);
+      *pScalefactor += SCALEFACTOR8;
+      break;
+    case 3:
+      fft3(pInput);
+      break;
+    case 4:
+      fft_4(pInput);
+      *pScalefactor += SCALEFACTOR4;
+      break;
+    case 5:
+      fft5(pInput);
+      break;
+    case 15:
+      fft15(pInput);
+      *pScalefactor += 2;
+      break;
+    case 60:
+      fft60(pInput, pScalefactor);
+      break;
+    case 64:
+      dit_fft(pInput, 6, SineTable512, 512);
+      *pScalefactor += SCALEFACTOR64;
+      break;
+    case 240:
+      fft240(pInput, pScalefactor);
+      break;
+    case 256:
+      dit_fft(pInput, 8, SineTable512, 512);
+      *pScalefactor += SCALEFACTOR256;
+      break;
+    case 480:
+      fft480(pInput, pScalefactor);
+      break;
+    case 512:
+      dit_fft(pInput, 9, SineTable512, 512);
+      *pScalefactor += SCALEFACTOR512;
+      break;
+    default:
+      FDK_ASSERT(0); /* FFT length not supported! */
+      break;
+  }
+  }
+}
+
+
+void ifft(int length, FIXP_DBL *pInput, INT *scalefactor)
+{
+  switch (length) {
+    default:
+      FDK_ASSERT(0); /* IFFT length not supported! */
+      break;
+  }
+}
+
+