Fraunhofer AAC codec.

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+/****************************************************************************
+
+                     (C) Copyright Fraunhofer IIS (2004)
+                               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.
+
+
+   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.
+
+ $Id$
+
+*******************************************************************************/
+/*!
+  \file
+  \brief  FDK Fixed Point Arithmetic Library Interface $Revision: 36841 $
+*/
+
+/*!
+  \mainpage Fixed Point Arithmetic Library Documentation
+
+  Information in this SDK is subject to change without notice. Companies,
+  names, and data used in examples herein are fictitious unless otherwise
+  noted.
+
+  Product and corporate names may be trademarks or registered trademarks
+  of other companies. They are used for explanation only, with no intent
+  to infringe.
+
+  No part of this publication may be reproduced or utilized in any form or
+  by any means, electronic or mechanical, including photocopying and
+  microfilm, without permission in writing from the publisher.
+*/
+
+#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