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+/* -----------------------------------------------------------------------------
+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):
+
+   Description:
+
+*******************************************************************************/
+
+/*!
+  \file   dct.cpp
+  \brief  DCT Implementations
+  Library functions to calculate standard DCTs. This will most likely be
+  replaced by hand-optimized functions for the specific target processor.
+
+  Three different implementations of the dct type II and the dct type III
+  transforms are provided.
+
+  By default implementations which are based on a single, standard complex
+  FFT-kernel are used (dctII_f() and dctIII_f()). These are specifically helpful
+  in cases where optimized FFT libraries are already available. The FFT used in
+  these implementation is FFT rad2 from FDK_tools.
+
+  Of course, one might also use DCT-libraries should they be available. The DCT
+  and DST type IV implementations are only available in a version based on a
+  complex FFT kernel.
+*/
+
+#include "dct.h"
+
+#include "FDK_tools_rom.h"
+#include "fft.h"
+
+void dct_getTables(const FIXP_WTP **ptwiddle, const FIXP_STP **sin_twiddle,
+                   int *sin_step, int length) {
+  const FIXP_WTP *twiddle;
+  int ld2_length;
+
+  /* Get ld2 of length - 2 + 1
+      -2: because first table entry is window of size 4
+      +1: because we already include +1 because of ceil(log2(length)) */
+  ld2_length = DFRACT_BITS - 1 - fNormz((FIXP_DBL)length) - 1;
+
+  /* Extract sort of "eigenvalue" (the 4 left most bits) of length. */
+  switch ((length) >> (ld2_length - 1)) {
+    case 0x4: /* radix 2 */
+      *sin_twiddle = SineTable1024;
+      *sin_step = 1 << (10 - ld2_length);
+      twiddle = windowSlopes[0][0][ld2_length - 1];
+      break;
+    case 0x7: /* 10 ms */
+      *sin_twiddle = SineTable480;
+      *sin_step = 1 << (8 - ld2_length);
+      twiddle = windowSlopes[0][1][ld2_length];
+      break;
+    case 0x6: /* 3/4 of radix 2 */
+      *sin_twiddle = SineTable384;
+      *sin_step = 1 << (8 - ld2_length);
+      twiddle = windowSlopes[0][2][ld2_length];
+      break;
+    case 0x5: /* 5/16 of radix 2*/
+      *sin_twiddle = SineTable80;
+      *sin_step = 1 << (6 - ld2_length);
+      twiddle = windowSlopes[0][3][ld2_length];
+      break;
+    default:
+      *sin_twiddle = NULL;
+      *sin_step = 0;
+      twiddle = NULL;
+      break;
+  }
+
+  if (ptwiddle != NULL) {
+    FDK_ASSERT(twiddle != NULL);
+    *ptwiddle = twiddle;
+  }
+
+  FDK_ASSERT(*sin_step > 0);
+}
+
+#if !defined(FUNCTION_dct_III)
+void dct_III(FIXP_DBL *pDat, /*!< pointer to input/output */
+             FIXP_DBL *tmp,  /*!< pointer to temporal working buffer */
+             int L,          /*!< lenght of transform */
+             int *pDat_e) {
+  const FIXP_WTP *sin_twiddle;
+  int i;
+  FIXP_DBL xr, accu1, accu2;
+  int inc, index;
+  int M = L >> 1;
+
+  FDK_ASSERT(L % 4 == 0);
+  dct_getTables(NULL, &sin_twiddle, &inc, L);
+  inc >>= 1;
+
+  FIXP_DBL *pTmp_0 = &tmp[2];
+  FIXP_DBL *pTmp_1 = &tmp[(M - 1) * 2];
+
+  index = 4 * inc;
+
+  /* This loop performs multiplication for index i (i*inc) */
+  for (i = 1; i<M>> 1; i++, pTmp_0 += 2, pTmp_1 -= 2) {
+    FIXP_DBL accu3, accu4, accu5, accu6;
+
+    cplxMultDiv2(&accu2, &accu1, pDat[L - i], pDat[i], sin_twiddle[i * inc]);
+    cplxMultDiv2(&accu4, &accu3, pDat[M + i], pDat[M - i],
+                 sin_twiddle[(M - i) * inc]);
+    accu3 >>= 1;
+    accu4 >>= 1;
+
+    /* This method is better for ARM926, that uses operand2 shifted right by 1
+     * always */
+    if (2 * i < (M / 2)) {
+      cplxMultDiv2(&accu6, &accu5, (accu3 - (accu1 >> 1)),
+                   ((accu2 >> 1) + accu4), sin_twiddle[index]);
+    } else {
+      cplxMultDiv2(&accu6, &accu5, ((accu2 >> 1) + accu4),
+                   (accu3 - (accu1 >> 1)), sin_twiddle[index]);
+      accu6 = -accu6;
+    }
+    xr = (accu1 >> 1) + accu3;
+    pTmp_0[0] = (xr >> 1) - accu5;
+    pTmp_1[0] = (xr >> 1) + accu5;
+
+    xr = (accu2 >> 1) - accu4;
+    pTmp_0[1] = (xr >> 1) - accu6;
+    pTmp_1[1] = -((xr >> 1) + accu6);
+
+    /* Create index helper variables for (4*i)*inc indexed equivalent values of
+     * short tables. */
+    if (2 * i < ((M / 2) - 1)) {
+      index += 4 * inc;
+    } else if (2 * i >= ((M / 2))) {
+      index -= 4 * inc;
+    }
+  }
+
+  xr = fMultDiv2(pDat[M], sin_twiddle[M * inc].v.re); /* cos((PI/(2*L))*M); */
+  tmp[0] = ((pDat[0] >> 1) + xr) >> 1;
+  tmp[1] = ((pDat[0] >> 1) - xr) >> 1;
+
+  cplxMultDiv2(&accu2, &accu1, pDat[L - (M / 2)], pDat[M / 2],
+               sin_twiddle[M * inc / 2]);
+  tmp[M] = accu1 >> 1;
+  tmp[M + 1] = accu2 >> 1;
+
+  /* dit_fft expects 1 bit scaled input values */
+  fft(M, tmp, pDat_e);
+
+  /* ARM926: 12 cycles per 2-iteration, no overhead code by compiler */
+  pTmp_1 = &tmp[L];
+  for (i = M >> 1; i--;) {
+    FIXP_DBL tmp1, tmp2, tmp3, tmp4;
+    tmp1 = *tmp++;
+    tmp2 = *tmp++;
+    tmp3 = *--pTmp_1;
+    tmp4 = *--pTmp_1;
+    *pDat++ = tmp1;
+    *pDat++ = tmp3;
+    *pDat++ = tmp2;
+    *pDat++ = tmp4;
+  }
+
+  *pDat_e += 2;
+}
+
+void dst_III(FIXP_DBL *pDat, /*!< pointer to input/output */
+             FIXP_DBL *tmp,  /*!< pointer to temporal working buffer */
+             int L,          /*!< lenght of transform */
+             int *pDat_e) {
+  int L2 = L >> 1;
+  int i;
+  FIXP_DBL t;
+
+  /* note: DCT III is reused here, direct DST III implementation might be more
+   * efficient */
+
+  /* mirror input */
+  for (i = 0; i < L2; i++) {
+    t = pDat[i];
+    pDat[i] = pDat[L - 1 - i];
+    pDat[L - 1 - i] = t;
+  }
+
+  /* DCT-III */
+  dct_III(pDat, tmp, L, pDat_e);
+
+  /* flip signs at odd indices */
+  for (i = 1; i < L; i += 2) pDat[i] = -pDat[i];
+}
+
+#endif
+
+#if !defined(FUNCTION_dct_II)
+void dct_II(
+    FIXP_DBL *pDat, /*!< pointer to input/output */
+    FIXP_DBL *tmp,  /*!< pointer to temporal working buffer */
+    int L, /*!< lenght of transform (has to be a multiple of 8 (or 4 in case
+              DCT_II_L_MULTIPLE_OF_4_SUPPORT is defined) */
+    int *pDat_e) {
+  const FIXP_WTP *sin_twiddle;
+  FIXP_DBL accu1, accu2;
+  FIXP_DBL *pTmp_0, *pTmp_1;
+
+  int i;
+  int inc, index = 0;
+  int M = L >> 1;
+
+  FDK_ASSERT(L % 4 == 0);
+  dct_getTables(NULL, &sin_twiddle, &inc, L);
+  inc >>= 1;
+
+  {
+    for (i = 0; i < M; i++) {
+      tmp[i] = pDat[2 * i] >> 1; /* dit_fft expects 1 bit scaled input values */
+      tmp[L - 1 - i] =
+          pDat[2 * i + 1] >> 1; /* dit_fft expects 1 bit scaled input values */
+    }
+  }
+
+  fft(M, tmp, pDat_e);
+
+  pTmp_0 = &tmp[2];
+  pTmp_1 = &tmp[(M - 1) * 2];
+
+  index = inc * 4;
+
+  for (i = 1; i<M>> 1; i++, pTmp_0 += 2, pTmp_1 -= 2) {
+    FIXP_DBL a1, a2;
+    FIXP_DBL accu3, accu4;
+
+    a1 = ((pTmp_0[1] >> 1) + (pTmp_1[1] >> 1));
+    a2 = ((pTmp_1[0] >> 1) - (pTmp_0[0] >> 1));
+
+    if (2 * i < (M / 2)) {
+      cplxMultDiv2(&accu1, &accu2, a2, a1, sin_twiddle[index]);
+    } else {
+      cplxMultDiv2(&accu1, &accu2, a1, a2, sin_twiddle[index]);
+      accu1 = -accu1;
+    }
+    accu1 <<= 1;
+    accu2 <<= 1;
+
+    a1 = ((pTmp_0[0] >> 1) + (pTmp_1[0] >> 1));
+    a2 = ((pTmp_0[1] >> 1) - (pTmp_1[1] >> 1));
+
+    cplxMultDiv2(&accu3, &accu4, (a1 + accu2), -(accu1 + a2),
+                 sin_twiddle[i * inc]);
+    pDat[L - i] = accu4;
+    pDat[i] = accu3;
+
+    cplxMultDiv2(&accu3, &accu4, (a1 - accu2), -(accu1 - a2),
+                 sin_twiddle[(M - i) * inc]);
+    pDat[M + i] = accu4;
+    pDat[M - i] = accu3;
+
+    /* Create index helper variables for (4*i)*inc indexed equivalent values of
+     * short tables. */
+    if (2 * i < ((M / 2) - 1)) {
+      index += 4 * inc;
+    } else if (2 * i >= ((M / 2))) {
+      index -= 4 * inc;
+    }
+  }
+
+  cplxMultDiv2(&accu1, &accu2, tmp[M], tmp[M + 1], sin_twiddle[(M / 2) * inc]);
+  pDat[L - (M / 2)] = accu2;
+  pDat[M / 2] = accu1;
+
+  pDat[0] = (tmp[0] >> 1) + (tmp[1] >> 1);
+  pDat[M] = fMult(((tmp[0] >> 1) - (tmp[1] >> 1)),
+                  sin_twiddle[M * inc].v.re); /* cos((PI/(2*L))*M); */
+
+  *pDat_e += 2;
+}
+#endif
+
+#if !defined(FUNCTION_dct_IV)
+
+void dct_IV(FIXP_DBL *pDat, int L, int *pDat_e) {
+  int sin_step = 0;
+  int M = L >> 1;
+
+  const FIXP_WTP *twiddle;
+  const FIXP_STP *sin_twiddle;
+
+  FDK_ASSERT(L >= 4);
+
+  FDK_ASSERT(L >= 4);
+
+  dct_getTables(&twiddle, &sin_twiddle, &sin_step, L);
+
+  {
+    FIXP_DBL *RESTRICT pDat_0 = &pDat[0];
+    FIXP_DBL *RESTRICT pDat_1 = &pDat[L - 2];
+    int i;
+
+    /* 29 cycles on ARM926 */
+    for (i = 0; i < M - 1; i += 2, pDat_0 += 2, pDat_1 -= 2) {
+      FIXP_DBL accu1, accu2, accu3, accu4;
+
+      accu1 = pDat_1[1];
+      accu2 = pDat_0[0];
+      accu3 = pDat_0[1];
+      accu4 = pDat_1[0];
+
+      cplxMultDiv2(&accu1, &accu2, accu1, accu2, twiddle[i]);
+      cplxMultDiv2(&accu3, &accu4, accu4, accu3, twiddle[i + 1]);
+
+      pDat_0[0] = accu2 >> 1;
+      pDat_0[1] = accu1 >> 1;
+      pDat_1[0] = accu4 >> 1;
+      pDat_1[1] = -(accu3 >> 1);
+    }
+    if (M & 1) {
+      FIXP_DBL accu1, accu2;
+
+      accu1 = pDat_1[1];
+      accu2 = pDat_0[0];
+
+      cplxMultDiv2(&accu1, &accu2, accu1, accu2, twiddle[i]);
+
+      pDat_0[0] = accu2 >> 1;
+      pDat_0[1] = accu1 >> 1;
+    }
+  }
+
+  fft(M, pDat, pDat_e);
+
+  {
+    FIXP_DBL *RESTRICT pDat_0 = &pDat[0];
+    FIXP_DBL *RESTRICT pDat_1 = &pDat[L - 2];
+    FIXP_DBL accu1, accu2, accu3, accu4;
+    int idx, i;
+
+    /* Sin and Cos values are 0.0f and 1.0f */
+    accu1 = pDat_1[0];
+    accu2 = pDat_1[1];
+
+    pDat_1[1] = -pDat_0[1];
+
+    /* 28 cycles for ARM926 */
+    for (idx = sin_step, i = 1; i<(M + 1)>> 1; i++, idx += sin_step) {
+      FIXP_STP twd = sin_twiddle[idx];
+      cplxMult(&accu3, &accu4, accu1, accu2, twd);
+      pDat_0[1] = accu3;
+      pDat_1[0] = accu4;
+
+      pDat_0 += 2;
+      pDat_1 -= 2;
+
+      cplxMult(&accu3, &accu4, pDat_0[1], pDat_0[0], twd);
+
+      accu1 = pDat_1[0];
+      accu2 = pDat_1[1];
+
+      pDat_1[1] = -accu3;
+      pDat_0[0] = accu4;
+    }
+
+    if ((M & 1) == 0) {
+      /* Last Sin and Cos value pair are the same */
+      accu1 = fMult(accu1, WTC(0x5a82799a));
+      accu2 = fMult(accu2, WTC(0x5a82799a));
+
+      pDat_1[0] = accu1 + accu2;
+      pDat_0[1] = accu1 - accu2;
+    }
+  }
+
+  /* Add twiddeling scale. */
+  *pDat_e += 2;
+}
+#endif /* defined (FUNCTION_dct_IV) */
+
+#if !defined(FUNCTION_dst_IV)
+void dst_IV(FIXP_DBL *pDat, int L, int *pDat_e) {
+  int sin_step = 0;
+  int M = L >> 1;
+
+  const FIXP_WTP *twiddle;
+  const FIXP_STP *sin_twiddle;
+
+  FDK_ASSERT(L >= 4);
+
+  FDK_ASSERT(L >= 4);
+
+  dct_getTables(&twiddle, &sin_twiddle, &sin_step, L);
+
+  {
+    FIXP_DBL *RESTRICT pDat_0 = &pDat[0];
+    FIXP_DBL *RESTRICT pDat_1 = &pDat[L - 2];
+    int i;
+
+    /* 34 cycles on ARM926 */
+    for (i = 0; i < M - 1; i += 2, pDat_0 += 2, pDat_1 -= 2) {
+      FIXP_DBL accu1, accu2, accu3, accu4;
+
+      accu1 = pDat_1[1];
+      accu2 = -pDat_0[0];
+      accu3 = pDat_0[1];
+      accu4 = -pDat_1[0];
+
+      cplxMultDiv2(&accu1, &accu2, accu1, accu2, twiddle[i]);
+      cplxMultDiv2(&accu3, &accu4, accu4, accu3, twiddle[i + 1]);
+
+      pDat_0[0] = accu2 >> 1;
+      pDat_0[1] = accu1 >> 1;
+      pDat_1[0] = accu4 >> 1;
+      pDat_1[1] = -(accu3 >> 1);
+    }
+    if (M & 1) {
+      FIXP_DBL accu1, accu2;
+
+      accu1 = pDat_1[1];
+      accu2 = -pDat_0[0];
+
+      cplxMultDiv2(&accu1, &accu2, accu1, accu2, twiddle[i]);
+
+      pDat_0[0] = accu2 >> 1;
+      pDat_0[1] = accu1 >> 1;
+    }
+  }
+
+  fft(M, pDat, pDat_e);
+
+  {
+    FIXP_DBL *RESTRICT pDat_0;
+    FIXP_DBL *RESTRICT pDat_1;
+    FIXP_DBL accu1, accu2, accu3, accu4;
+    int idx, i;
+
+    pDat_0 = &pDat[0];
+    pDat_1 = &pDat[L - 2];
+
+    /* Sin and Cos values are 0.0f and 1.0f */
+    accu1 = pDat_1[0];
+    accu2 = pDat_1[1];
+
+    pDat_1[1] = -pDat_0[0];
+    pDat_0[0] = pDat_0[1];
+
+    for (idx = sin_step, i = 1; i<(M + 1)>> 1; i++, idx += sin_step) {
+      FIXP_STP twd = sin_twiddle[idx];
+
+      cplxMult(&accu3, &accu4, accu1, accu2, twd);
+      pDat_1[0] = -accu3;
+      pDat_0[1] = -accu4;
+
+      pDat_0 += 2;
+      pDat_1 -= 2;
+
+      cplxMult(&accu3, &accu4, pDat_0[1], pDat_0[0], twd);
+
+      accu1 = pDat_1[0];
+      accu2 = pDat_1[1];
+
+      pDat_0[0] = accu3;
+      pDat_1[1] = -accu4;
+    }
+
+    if ((M & 1) == 0) {
+      /* Last Sin and Cos value pair are the same */
+      accu1 = fMult(accu1, WTC(0x5a82799a));
+      accu2 = fMult(accu2, WTC(0x5a82799a));
+
+      pDat_0[1] = -accu1 - accu2;
+      pDat_1[0] = accu2 - accu1;
+    }
+  }
+
+  /* Add twiddeling scale. */
+  *pDat_e += 2;
+}
+#endif /* !defined(FUNCTION_dst_IV) */