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+
+/* -----------------------------------------------------------------------------------------------------------
+Software License for The Fraunhofer FDK AAC Codec Library for Android
+
+© Copyright  1995 - 2012 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
+----------------------------------------------------------------------------------------------------------- */
+
+/*!
+  \file
+  \brief  FDK Fixed Point Arithmetic Library Interface  
+*/
+
+#ifndef __TRANSCENDENT_H
+#define __TRANSCENDENT_H
+
+#include "sbrdecoder.h"
+#include "sbr_rom.h"
+
+/************************************************************************/
+/*!
+  \brief   Get number of octaves between frequencies a and b
+
+  The Result is scaled with 1/8.
+  The valid range for a and b is 1 to LOG_DUALIS_TABLE_SIZE.
+
+  \return   ld(a/b) / 8
+*/
+/************************************************************************/
+static inline FIXP_SGL FDK_getNumOctavesDiv8(INT a, /*!< lower band */
+                                             INT b) /*!< upper band */
+{
+  return ( (SHORT)((LONG)(CalcLdInt(b) - CalcLdInt(a))>>(FRACT_BITS-3)) );
+}
+
+
+/************************************************************************/
+/*!
+  \brief   Add two values given by mantissa and exponent.
+
+  Mantissas are in fract format with values between 0 and 1. <br>
+  The base for exponents is 2.  Example:  \f$  a = a\_m * 2^{a\_e}  \f$<br>
+*/
+/************************************************************************/
+inline void FDK_add_MantExp(FIXP_SGL a_m, /*!< Mantissa of 1st operand a */
+                     SCHAR     a_e,       /*!< Exponent of 1st operand a */
+                     FIXP_SGL  b_m,       /*!< Mantissa of 2nd operand b */
+                     SCHAR     b_e,       /*!< Exponent of 2nd operand b */
+                     FIXP_SGL *ptrSum_m,  /*!< Mantissa of result */
+                     SCHAR    *ptrSum_e)  /*!< Exponent of result */
+{
+  FIXP_DBL accu;
+  int   shift;
+  int   shiftAbs;
+
+  FIXP_DBL shiftedMantissa;
+  FIXP_DBL otherMantissa;
+
+  /* Equalize exponents of the summands.
+     For the smaller summand, the exponent is adapted and
+     for compensation, the mantissa is shifted right. */
+
+  shift = (int)(a_e - b_e);
+
+  shiftAbs = (shift>0)? shift : -shift;
+  shiftAbs = (shiftAbs < DFRACT_BITS-1)? shiftAbs : DFRACT_BITS-1;
+  shiftedMantissa = (shift>0)? (FX_SGL2FX_DBL(b_m) >> shiftAbs) : (FX_SGL2FX_DBL(a_m) >> shiftAbs);
+  otherMantissa = (shift>0)? FX_SGL2FX_DBL(a_m) : FX_SGL2FX_DBL(b_m);
+  *ptrSum_e = (shift>0)? a_e : b_e;
+
+  accu = (shiftedMantissa >> 1) + (otherMantissa >> 1);
+  /* shift by 1 bit to avoid overflow */
+
+  if ( (accu >= (FL2FXCONST_DBL(0.5f) - (FIXP_DBL)1)) || (accu <= FL2FXCONST_DBL(-0.5f)) )
+    *ptrSum_e += 1;
+  else
+    accu = (shiftedMantissa + otherMantissa);
+
+  *ptrSum_m = FX_DBL2FX_SGL(accu);
+
+}
+
+inline void FDK_add_MantExp(FIXP_DBL a,   /*!< Mantissa of 1st operand a */
+                     SCHAR     a_e,       /*!< Exponent of 1st operand a */
+                     FIXP_DBL  b,         /*!< Mantissa of 2nd operand b */
+                     SCHAR     b_e,       /*!< Exponent of 2nd operand b */
+                     FIXP_DBL *ptrSum,    /*!< Mantissa of result */
+                     SCHAR    *ptrSum_e)  /*!< Exponent of result */
+{
+  FIXP_DBL accu;
+  int   shift;
+  int   shiftAbs;
+
+  FIXP_DBL shiftedMantissa;
+  FIXP_DBL otherMantissa;
+
+  /* Equalize exponents of the summands.
+     For the smaller summand, the exponent is adapted and
+     for compensation, the mantissa is shifted right. */
+
+  shift = (int)(a_e - b_e);
+
+  shiftAbs = (shift>0)? shift : -shift;
+  shiftAbs = (shiftAbs < DFRACT_BITS-1)? shiftAbs : DFRACT_BITS-1;
+  shiftedMantissa = (shift>0)? (b >> shiftAbs) : (a >> shiftAbs);
+  otherMantissa = (shift>0)? a : b;
+  *ptrSum_e = (shift>0)? a_e : b_e;
+
+  accu = (shiftedMantissa >> 1) + (otherMantissa >> 1);
+  /* shift by 1 bit to avoid overflow */
+
+  if ( (accu >= (FL2FXCONST_DBL(0.5f) - (FIXP_DBL)1)) || (accu <= FL2FXCONST_DBL(-0.5f)) )
+    *ptrSum_e += 1;
+  else
+    accu = (shiftedMantissa + otherMantissa);
+
+  *ptrSum = accu;
+
+}
+
+/************************************************************************/
+/*!
+  \brief   Divide two values given by mantissa and exponent.
+
+  Mantissas are in fract format with values between 0 and 1. <br>
+  The base for exponents is 2.  Example:  \f$  a = a\_m * 2^{a\_e}  \f$<br>
+
+  For performance reasons, the division is based on a table lookup
+  which limits accuracy.
+*/
+/************************************************************************/
+static inline void FDK_divide_MantExp(FIXP_SGL a_m,           /*!< Mantissa of dividend a */
+                                      SCHAR     a_e,          /*!< Exponent of dividend a */
+                                      FIXP_SGL  b_m,          /*!< Mantissa of divisor b */
+                                      SCHAR     b_e,          /*!< Exponent of divisor b */
+                                      FIXP_SGL *ptrResult_m,  /*!< Mantissa of quotient a/b */
+                                      SCHAR    *ptrResult_e)  /*!< Exponent of quotient a/b */
+
+{
+  int preShift, postShift, index, shift;
+  FIXP_DBL ratio_m;
+  FIXP_SGL  bInv_m = FL2FXCONST_SGL(0.0f);
+
+  preShift = CntLeadingZeros(FX_SGL2FX_DBL(b_m));
+
+  /*
+    Shift b into the range from 0..INV_TABLE_SIZE-1,
+
+    E.g. 10 bits must be skipped for INV_TABLE_BITS 8:
+    - leave 8 bits as index for table
+    - skip sign bit,
+    - skip first bit of mantissa, because this is always the same (>0.5)
+
+    We are dealing with energies, so we need not care
+    about negative numbers
+  */
+
+  /*
+    The first interval has half width so the lowest bit of the index is
+    needed for a doubled resolution.
+  */
+  shift = (FRACT_BITS - 2 - INV_TABLE_BITS - preShift);
+
+  index = (shift<0)? (LONG)b_m << (-shift) : (LONG)b_m >> shift;
+
+
+  /* The index has INV_TABLE_BITS +1 valid bits here. Clear the other bits. */
+  index &= (1 << (INV_TABLE_BITS+1)) - 1;
+
+    /* Remove offset of half an interval */
+  index--;
+
+    /* Now the lowest bit is shifted out */
+  index = index >> 1;
+
+    /* Fetch inversed mantissa from table: */
+  bInv_m = (index<0)? bInv_m : FDK_sbrDecoder_invTable[index];
+
+    /* Multiply a with the inverse of b: */
+  ratio_m = (index<0)? FX_SGL2FX_DBL(a_m >> 1) : fMultDiv2(bInv_m,a_m);
+
+  postShift = CntLeadingZeros(ratio_m)-1;
+
+  *ptrResult_m = FX_DBL2FX_SGL(ratio_m << postShift);
+  *ptrResult_e = a_e - b_e + 1 + preShift - postShift;
+}
+
+static inline void FDK_divide_MantExp(FIXP_DBL a_m,           /*!< Mantissa of dividend a */
+                                      SCHAR     a_e,          /*!< Exponent of dividend a */
+                                      FIXP_DBL  b_m,          /*!< Mantissa of divisor b */
+                                      SCHAR     b_e,          /*!< Exponent of divisor b */
+                                      FIXP_DBL *ptrResult_m,  /*!< Mantissa of quotient a/b */
+                                      SCHAR    *ptrResult_e)  /*!< Exponent of quotient a/b */
+
+{
+  int preShift, postShift, index, shift;
+  FIXP_DBL ratio_m;
+  FIXP_SGL  bInv_m = FL2FXCONST_SGL(0.0f);
+
+  preShift = CntLeadingZeros(b_m);
+
+  /*
+    Shift b into the range from 0..INV_TABLE_SIZE-1,
+
+    E.g. 10 bits must be skipped for INV_TABLE_BITS 8:
+    - leave 8 bits as index for table
+    - skip sign bit,
+    - skip first bit of mantissa, because this is always the same (>0.5)
+
+    We are dealing with energies, so we need not care
+    about negative numbers
+  */
+
+  /*
+    The first interval has half width so the lowest bit of the index is
+    needed for a doubled resolution.
+  */
+  shift = (DFRACT_BITS - 2 - INV_TABLE_BITS - preShift);
+
+  index = (shift<0)? (LONG)b_m << (-shift) : (LONG)b_m >> shift;
+
+
+  /* The index has INV_TABLE_BITS +1 valid bits here. Clear the other bits. */
+  index &= (1 << (INV_TABLE_BITS+1)) - 1;
+
+    /* Remove offset of half an interval */
+  index--;
+
+    /* Now the lowest bit is shifted out */
+  index = index >> 1;
+
+    /* Fetch inversed mantissa from table: */
+  bInv_m = (index<0)? bInv_m : FDK_sbrDecoder_invTable[index];
+
+    /* Multiply a with the inverse of b: */
+  ratio_m = (index<0)? (a_m >> 1) : fMultDiv2(bInv_m,a_m);
+
+  postShift = CntLeadingZeros(ratio_m)-1;
+
+  *ptrResult_m = ratio_m << postShift;
+  *ptrResult_e = a_e - b_e + 1 + preShift - postShift;
+}
+
+/*!
+  \brief   Calculate the squareroot of a number given by mantissa and exponent
+
+  Mantissa is in fract format with values between 0 and 1. <br>
+  The base for the exponent is 2.  Example:  \f$  a = a\_m * 2^{a\_e}  \f$<br>
+  The operand is addressed via pointers and will be overwritten with the result.
+
+  For performance reasons, the square root is based on a table lookup
+  which limits accuracy.
+*/
+static inline void FDK_sqrt_MantExp(FIXP_DBL *mantissa,    /*!< Pointer to mantissa */
+                                    SCHAR    *exponent,
+                                    const SCHAR *destScale)
+{
+  FIXP_DBL input_m = *mantissa;
+  int   input_e = (int) *exponent;
+  FIXP_DBL result = FL2FXCONST_DBL(0.0f);
+  int    result_e = -FRACT_BITS;
+
+  /* Call lookup square root, which does internally normalization. */
+  result   = sqrtFixp_lookup(input_m, &input_e);
+  result_e = input_e;
+
+  /* Write result */
+  if (exponent==destScale) {
+    *mantissa = result;
+    *exponent = result_e;
+  } else {
+    int shift = result_e - *destScale;
+    *mantissa = (shift>=0) ? result << (INT)fixMin(DFRACT_BITS-1,shift)
+                           : result >> (INT)fixMin(DFRACT_BITS-1,-shift);
+    *exponent = *destScale;
+  }
+}
+
+
+#endif