aac/libFDK/src/fixpoint_math.cpp

/* -----------------------------------------------------------------------------------------------------------
Software License for The Fraunhofer FDK AAC Codec Library for Android

© Copyright  1995 - 2013 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
----------------------------------------------------------------------------------------------------------- */

/***************************  Fraunhofer IIS FDK Tools  **********************

   Author(s):   M. Gayer
   Description: Fixed point specific mathematical functions

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

#include "fixpoint_math.h"


#define MAX_LD_PRECISION 10
#define LD_PRECISION     10

/* Taylor series coeffcients for ln(1-x), centered at 0 (MacLaurin polinomial). */
#ifndef LDCOEFF_16BIT
LNK_SECTION_CONSTDATA_L1
static const FIXP_DBL ldCoeff[MAX_LD_PRECISION] = {
    FL2FXCONST_DBL(-1.0),
    FL2FXCONST_DBL(-1.0/2.0),
    FL2FXCONST_DBL(-1.0/3.0),
    FL2FXCONST_DBL(-1.0/4.0),
    FL2FXCONST_DBL(-1.0/5.0),
    FL2FXCONST_DBL(-1.0/6.0),
    FL2FXCONST_DBL(-1.0/7.0),
    FL2FXCONST_DBL(-1.0/8.0),
    FL2FXCONST_DBL(-1.0/9.0),
    FL2FXCONST_DBL(-1.0/10.0)
};
#else
LNK_SECTION_CONSTDATA_L1
static const FIXP_SGL ldCoeff[MAX_LD_PRECISION] = {
    FL2FXCONST_SGL(-1.0),
    FL2FXCONST_SGL(-1.0/2.0),
    FL2FXCONST_SGL(-1.0/3.0),
    FL2FXCONST_SGL(-1.0/4.0),
    FL2FXCONST_SGL(-1.0/5.0),
    FL2FXCONST_SGL(-1.0/6.0),
    FL2FXCONST_SGL(-1.0/7.0),
    FL2FXCONST_SGL(-1.0/8.0),
    FL2FXCONST_SGL(-1.0/9.0),
    FL2FXCONST_SGL(-1.0/10.0)
};
#endif

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

  functionname: CalcLdData
  description:  Delivers the Logarithm Dualis ld(op)/LD_DATA_SCALING with polynomial approximation.
  input:        Input op is assumed to be double precision fractional 0 < op < 1.0
                This function does not accept negative values.
  output:       For op == 0, the result is saturated to -1.0
                This function does not return positive values since input values are treated as fractional values.
                It does not make sense to input an integer value into this function (and expect a positive output value)
                since input values are treated as fractional values.

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

LNK_SECTION_CODE_L1
FIXP_DBL CalcLdData(FIXP_DBL op)
{
  return fLog2(op, 0);
}


/*****************************************************************************
  functionname: LdDataVector
*****************************************************************************/
LNK_SECTION_CODE_L1
void LdDataVector(  FIXP_DBL    *srcVector,
                    FIXP_DBL    *destVector,
                    INT         n)
{
    INT i;
    for ( i=0; i<n; i++) {
        destVector[i] = CalcLdData(srcVector[i]);
    }
}



#define MAX_POW2_PRECISION 8
#ifndef SINETABLE_16BIT
	#define POW2_PRECISION MAX_POW2_PRECISION
#else
	#define POW2_PRECISION 5
#endif

/*
  Taylor series coefficients of the function x^2. The first coefficient is
  ommited (equal to 1.0).

  pow2Coeff[i-1] = (1/i!) d^i(2^x)/dx^i, i=1..MAX_POW2_PRECISION
  To evaluate the taylor series around x = 0, the coefficients are: 1/!i * ln(2)^i
 */
#ifndef POW2COEFF_16BIT
LNK_SECTION_CONSTDATA_L1
static const FIXP_DBL pow2Coeff[MAX_POW2_PRECISION] = {
    FL2FXCONST_DBL(0.693147180559945309417232121458177),    /* ln(2)^1 /1! */
    FL2FXCONST_DBL(0.240226506959100712333551263163332),    /* ln(2)^2 /2! */
    FL2FXCONST_DBL(0.0555041086648215799531422637686218),   /* ln(2)^3 /3! */
    FL2FXCONST_DBL(0.00961812910762847716197907157365887),  /* ln(2)^4 /4! */
    FL2FXCONST_DBL(0.00133335581464284434234122219879962),  /* ln(2)^5 /5! */
    FL2FXCONST_DBL(1.54035303933816099544370973327423e-4),  /* ln(2)^6 /6! */
    FL2FXCONST_DBL(1.52527338040598402800254390120096e-5),  /* ln(2)^7 /7! */
    FL2FXCONST_DBL(1.32154867901443094884037582282884e-6)   /* ln(2)^8 /8! */
};
#else
LNK_SECTION_CONSTDATA_L1
static const FIXP_SGL pow2Coeff[MAX_POW2_PRECISION] = {
    FL2FXCONST_SGL(0.693147180559945309417232121458177),    /* ln(2)^1 /1! */
    FL2FXCONST_SGL(0.240226506959100712333551263163332),    /* ln(2)^2 /2! */
    FL2FXCONST_SGL(0.0555041086648215799531422637686218),   /* ln(2)^3 /3! */
    FL2FXCONST_SGL(0.00961812910762847716197907157365887),  /* ln(2)^4 /4! */
    FL2FXCONST_SGL(0.00133335581464284434234122219879962),  /* ln(2)^5 /5! */
    FL2FXCONST_SGL(1.54035303933816099544370973327423e-4),  /* ln(2)^6 /6! */
    FL2FXCONST_SGL(1.52527338040598402800254390120096e-5),  /* ln(2)^7 /7! */
    FL2FXCONST_SGL(1.32154867901443094884037582282884e-6)   /* ln(2)^8 /8! */
};
#endif



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

    functionname: mul_dbl_sgl_rnd
    description:  Multiply with round.
*****************************************************************************/

/* for rounding a dfract to fract */
#define ACCU_R (LONG) 0x00008000

LNK_SECTION_CODE_L1
FIXP_DBL mul_dbl_sgl_rnd (const FIXP_DBL op1, const FIXP_SGL op2)
{
  FIXP_DBL prod;
  LONG v = (LONG)(op1);
  SHORT u = (SHORT)(op2);

  LONG low = u*(v&SGL_MASK);
  low = (low+(ACCU_R>>1)) >> (FRACT_BITS-1);  /* round */
  LONG high = u * ((v>>FRACT_BITS)<<1);

  prod = (LONG)(high+low);

  return((FIXP_DBL)prod);
}


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

  functionname: CalcInvLdData
  description:  Delivers the inverse of function CalcLdData().
                Delivers 2^(op*LD_DATA_SCALING)
  input:        Input op is assumed to be fractional -1.0 < op < 1.0
  output:       For op == 0, the result is MAXVAL_DBL (almost 1.0).
                For negative input values the output should be treated as a positive fractional value.
                For positive input values the output should be treated as a positive integer value.
                This function does not output negative values.

*****************************************************************************/
LNK_SECTION_CODE_L1
/* This table is used for lookup 2^x with   */
/* x in range [0...1.0[ in steps of 1/32 */
LNK_SECTION_DATA_L1 static const UINT exp2_tab_long[32]={
0x40000000,0x4166C34C,0x42D561B4,0x444C0740,
0x45CAE0F2,0x47521CC6,0x48E1E9BA,0x4A7A77D4,
0x4C1BF829,0x4DC69CDD,0x4F7A9930,0x51382182,
0x52FF6B55,0x54D0AD5A,0x56AC1F75,0x5891FAC1,
0x5A82799A,0x5C7DD7A4,0x5E8451D0,0x60962665,
0x62B39509,0x64DCDEC3,0x6712460B,0x69540EC9,
0x6BA27E65,0x6DFDDBCC,0x70666F76,0x72DC8374,
0x75606374,0x77F25CCE,0x7A92BE8B,0x7D41D96E
// 0x80000000
};

/* This table is used for lookup 2^x with   */
/* x in range [0...1/32[ in steps of 1/1024 */
LNK_SECTION_DATA_L1 static const UINT exp2w_tab_long[32]={
0x40000000,0x400B1818,0x4016321B,0x40214E0C,
0x402C6BE9,0x40378BB4,0x4042AD6D,0x404DD113,
0x4058F6A8,0x40641E2B,0x406F479E,0x407A7300,
0x4085A051,0x4090CF92,0x409C00C4,0x40A733E6,
0x40B268FA,0x40BD9FFF,0x40C8D8F5,0x40D413DD,
0x40DF50B8,0x40EA8F86,0x40F5D046,0x410112FA,
0x410C57A2,0x41179E3D,0x4122E6CD,0x412E3152,
0x41397DCC,0x4144CC3B,0x41501CA0,0x415B6EFB,
// 0x4166C34C,
};
/* This table is used for lookup 2^x with   */
/* x in range [0...1/1024[ in steps of 1/32768 */
LNK_SECTION_DATA_L1 static const UINT exp2x_tab_long[32]={
0x40000000,0x400058B9,0x4000B173,0x40010A2D,
0x400162E8,0x4001BBA3,0x4002145F,0x40026D1B,
0x4002C5D8,0x40031E95,0x40037752,0x4003D011,
0x400428CF,0x4004818E,0x4004DA4E,0x4005330E,
0x40058BCE,0x4005E48F,0x40063D51,0x40069613,
0x4006EED5,0x40074798,0x4007A05B,0x4007F91F,
0x400851E4,0x4008AAA8,0x4009036E,0x40095C33,
0x4009B4FA,0x400A0DC0,0x400A6688,0x400ABF4F,
//0x400B1818
};

LNK_SECTION_CODE_L1 FIXP_DBL CalcInvLdData(FIXP_DBL x)
{
  int set_zero = (x <  FL2FXCONST_DBL(-31.0/64.0))? 0 : 1;
  int set_max  = (x >= FL2FXCONST_DBL( 31.0/64.0)) | (x == FL2FXCONST_DBL(0.0));

  FIXP_SGL frac = (FIXP_SGL)(LONG)(x & 0x3FF);
  UINT index3 = (UINT)(LONG)(x >> 10) & 0x1F;
  UINT index2 = (UINT)(LONG)(x >> 15) & 0x1F; 
  UINT index1 = (UINT)(LONG)(x >> 20) & 0x1F;
  int exp  = (x >  FL2FXCONST_DBL(0.0f)) ? (31 - (int)(x>>25)) : (int)(-(x>>25));

  UINT lookup1 = exp2_tab_long[index1]*set_zero;
  UINT lookup2 = exp2w_tab_long[index2];
  UINT lookup3 = exp2x_tab_long[index3];
  UINT lookup3f = lookup3 + (UINT)(LONG)fMultDiv2((FIXP_DBL)(0x0016302F),(FIXP_SGL)frac);
  
  UINT lookup12 = (UINT)(LONG)fMult((FIXP_DBL)lookup1,  (FIXP_DBL) lookup2);
  UINT lookup   = (UINT)(LONG)fMult((FIXP_DBL)lookup12, (FIXP_DBL) lookup3f);

  FIXP_DBL retVal = (lookup<<3) >> exp;

  if (set_max)
    retVal=FL2FXCONST_DBL(1.0f);

  return retVal;
}





/*****************************************************************************
    functionname: InitLdInt and CalcLdInt
    description:  Create and access table with integer LdData (0 to 193)
*****************************************************************************/


    LNK_SECTION_CONSTDATA_L1
    static const FIXP_DBL ldIntCoeff[] = {
      0x80000001, 0x00000000, 0x02000000, 0x032b8034, 0x04000000, 0x04a4d3c2, 0x052b8034, 0x059d5da0,
      0x06000000, 0x06570069, 0x06a4d3c2, 0x06eb3a9f, 0x072b8034, 0x0766a009, 0x079d5da0, 0x07d053f7,
      0x08000000, 0x082cc7ee, 0x08570069, 0x087ef05b, 0x08a4d3c2, 0x08c8ddd4, 0x08eb3a9f, 0x090c1050,
      0x092b8034, 0x0949a785, 0x0966a009, 0x0982809d, 0x099d5da0, 0x09b74949, 0x09d053f7, 0x09e88c6b,
      0x0a000000, 0x0a16bad3, 0x0a2cc7ee, 0x0a423162, 0x0a570069, 0x0a6b3d79, 0x0a7ef05b, 0x0a92203d,
      0x0aa4d3c2, 0x0ab7110e, 0x0ac8ddd4, 0x0ada3f60, 0x0aeb3a9f, 0x0afbd42b, 0x0b0c1050, 0x0b1bf312,
      0x0b2b8034, 0x0b3abb40, 0x0b49a785, 0x0b584822, 0x0b66a009, 0x0b74b1fd, 0x0b82809d, 0x0b900e61,
      0x0b9d5da0, 0x0baa708f, 0x0bb74949, 0x0bc3e9ca, 0x0bd053f7, 0x0bdc899b, 0x0be88c6b, 0x0bf45e09,
      0x0c000000, 0x0c0b73cb, 0x0c16bad3, 0x0c21d671, 0x0c2cc7ee, 0x0c379085, 0x0c423162, 0x0c4caba8,
      0x0c570069, 0x0c6130af, 0x0c6b3d79, 0x0c7527b9, 0x0c7ef05b, 0x0c88983f, 0x0c92203d, 0x0c9b8926,
      0x0ca4d3c2, 0x0cae00d2, 0x0cb7110e, 0x0cc0052b, 0x0cc8ddd4, 0x0cd19bb0, 0x0cda3f60, 0x0ce2c97d,
      0x0ceb3a9f, 0x0cf39355, 0x0cfbd42b, 0x0d03fda9, 0x0d0c1050, 0x0d140ca0, 0x0d1bf312, 0x0d23c41d,
      0x0d2b8034, 0x0d3327c7, 0x0d3abb40, 0x0d423b08, 0x0d49a785, 0x0d510118, 0x0d584822, 0x0d5f7cff,
      0x0d66a009, 0x0d6db197, 0x0d74b1fd, 0x0d7ba190, 0x0d82809d, 0x0d894f75, 0x0d900e61, 0x0d96bdad,
      0x0d9d5da0, 0x0da3ee7f, 0x0daa708f, 0x0db0e412, 0x0db74949, 0x0dbda072, 0x0dc3e9ca, 0x0dca258e,
      0x0dd053f7, 0x0dd6753e, 0x0ddc899b, 0x0de29143, 0x0de88c6b, 0x0dee7b47, 0x0df45e09, 0x0dfa34e1,
      0x0e000000, 0x0e05bf94, 0x0e0b73cb, 0x0e111cd2, 0x0e16bad3, 0x0e1c4dfb, 0x0e21d671, 0x0e275460,
      0x0e2cc7ee, 0x0e323143, 0x0e379085, 0x0e3ce5d8, 0x0e423162, 0x0e477346, 0x0e4caba8, 0x0e51daa8,
      0x0e570069, 0x0e5c1d0b, 0x0e6130af, 0x0e663b74, 0x0e6b3d79, 0x0e7036db, 0x0e7527b9, 0x0e7a1030,
      0x0e7ef05b, 0x0e83c857, 0x0e88983f, 0x0e8d602e, 0x0e92203d, 0x0e96d888, 0x0e9b8926, 0x0ea03232,
      0x0ea4d3c2, 0x0ea96df0, 0x0eae00d2, 0x0eb28c7f, 0x0eb7110e, 0x0ebb8e96, 0x0ec0052b, 0x0ec474e4,
      0x0ec8ddd4, 0x0ecd4012, 0x0ed19bb0, 0x0ed5f0c4, 0x0eda3f60, 0x0ede8797, 0x0ee2c97d, 0x0ee70525,
      0x0eeb3a9f, 0x0eef69ff, 0x0ef39355, 0x0ef7b6b4, 0x0efbd42b, 0x0effebcd, 0x0f03fda9, 0x0f0809cf,
      0x0f0c1050, 0x0f10113b, 0x0f140ca0, 0x0f18028d, 0x0f1bf312, 0x0f1fde3d, 0x0f23c41d, 0x0f27a4c0,
      0x0f2b8034
    };


  LNK_SECTION_INITCODE
  void InitLdInt()
  {
    /* nothing to do! Use preinitialized logarithm table */
  }



LNK_SECTION_CODE_L1
FIXP_DBL CalcLdInt(INT i)
{
  /* calculates ld(op)/LD_DATA_SCALING */
  /* op is assumed to be an integer value between 1 and 193 */

  FDK_ASSERT((193>0) && ((FIXP_DBL)ldIntCoeff[0]==(FIXP_DBL)0x80000001)); /* tab has to be initialized */

  if ((i>0)&&(i<193))
    return ldIntCoeff[i];
  else
  {
    return (0);
  }
}


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

    functionname: invSqrtNorm2
    description:  delivers 1/sqrt(op) normalized to .5...1 and the shift value of the OUTPUT

*****************************************************************************/
#define SQRT_BITS           7
#define SQRT_VALUES       128
#define SQRT_BITS_MASK   0x7f

LNK_SECTION_CONSTDATA_L1
static const FIXP_DBL invSqrtTab[SQRT_VALUES] = {
  0x5a827999, 0x5a287e03, 0x59cf8cbb, 0x5977a0ab, 0x5920b4de, 0x58cac480, 0x5875cade, 0x5821c364,
  0x57cea99c, 0x577c792f, 0x572b2ddf, 0x56dac38d, 0x568b3631, 0x563c81df, 0x55eea2c3, 0x55a19521,
  0x55555555, 0x5509dfd0, 0x54bf311a, 0x547545d0, 0x542c1aa3, 0x53e3ac5a, 0x539bf7cc, 0x5354f9e6,
  0x530eafa4, 0x52c91617, 0x52842a5e, 0x523fe9ab, 0x51fc513f, 0x51b95e6b, 0x51770e8e, 0x51355f19,
  0x50f44d88, 0x50b3d768, 0x5073fa4f, 0x5034b3e6, 0x4ff601df, 0x4fb7e1f9, 0x4f7a5201, 0x4f3d4fce,
  0x4f00d943, 0x4ec4ec4e, 0x4e8986e9, 0x4e4ea718, 0x4e144ae8, 0x4dda7072, 0x4da115d9, 0x4d683948,
  0x4d2fd8f4, 0x4cf7f31b, 0x4cc08604, 0x4c898fff, 0x4c530f64, 0x4c1d0293, 0x4be767f5, 0x4bb23df9,
  0x4b7d8317, 0x4b4935ce, 0x4b1554a6, 0x4ae1de2a, 0x4aaed0f0, 0x4a7c2b92, 0x4a49ecb3, 0x4a1812fa,
  0x49e69d16, 0x49b589bb, 0x4984d7a4, 0x49548591, 0x49249249, 0x48f4fc96, 0x48c5c34a, 0x4896e53c,
  0x48686147, 0x483a364c, 0x480c6331, 0x47dee6e0, 0x47b1c049, 0x4784ee5f, 0x4758701c, 0x472c447c,
  0x47006a80, 0x46d4e130, 0x46a9a793, 0x467ebcb9, 0x46541fb3, 0x4629cf98, 0x45ffcb80, 0x45d61289,
  0x45aca3d5, 0x45837e88, 0x455aa1ca, 0x45320cc8, 0x4509beb0, 0x44e1b6b4, 0x44b9f40b, 0x449275ec,
  0x446b3b95, 0x44444444, 0x441d8f3b, 0x43f71bbe, 0x43d0e917, 0x43aaf68e, 0x43854373, 0x435fcf14,
  0x433a98c5, 0x43159fdb, 0x42f0e3ae, 0x42cc6397, 0x42a81ef5, 0x42841527, 0x4260458d, 0x423caf8c,
  0x4219528b, 0x41f62df1, 0x41d3412a, 0x41b08ba1, 0x418e0cc7, 0x416bc40d, 0x4149b0e4, 0x4127d2c3,
  0x41062920, 0x40e4b374, 0x40c3713a, 0x40a261ef, 0x40818511, 0x4060da21, 0x404060a1, 0x40201814
};

LNK_SECTION_INITCODE
void InitInvSqrtTab()
{
  /* nothing to do !
     use preinitialized square root table
  */
}



#if !defined(FUNCTION_invSqrtNorm2)
/*****************************************************************************
  delivers 1/sqrt(op) normalized to .5...1 and the shift value of the OUTPUT,
  i.e. the denormalized result is 1/sqrt(op) = invSqrtNorm(op) * 2^(shift)
  uses Newton-iteration for approximation
      Q(n+1) = Q(n) + Q(n) * (0.5 - 2 * V * Q(n)^2)
      with Q = 0.5* V ^-0.5; 0.5 <= V < 1.0
*****************************************************************************/
FIXP_DBL invSqrtNorm2(FIXP_DBL op, INT *shift)
{

  FIXP_DBL val = op ;
  FIXP_DBL reg1, reg2, regtmp ;

  if (val == FL2FXCONST_DBL(0.0)) {
    *shift = 1 ;
    return((LONG)1);  /* minimum positive value */
  }


  /* normalize input, calculate shift value */
  FDK_ASSERT(val > FL2FXCONST_DBL(0.0));
  *shift = fNormz(val) - 1;  /* CountLeadingBits() is not necessary here since test value is always > 0 */
  val <<=*shift ;  /* normalized input V */
  *shift+=2 ;      /* bias for exponent */

  /* Newton iteration of 1/sqrt(V) */
  reg1 = invSqrtTab[ (INT)(val>>(DFRACT_BITS-1-(SQRT_BITS+1))) & SQRT_BITS_MASK ];
  reg2 = FL2FXCONST_DBL(0.0625f);   /* 0.5 >> 3 */

  regtmp= fPow2Div2(reg1);              /* a = Q^2 */
  regtmp= reg2 - fMultDiv2(regtmp, val);      /* b = 0.5 - 2 * V * Q^2 */
  reg1 += (fMultDiv2(regtmp, reg1)<<4);       /* Q = Q + Q*b */

  /* calculate the output exponent = input exp/2 */
  if (*shift & 0x00000001) { /* odd shift values ? */
    reg2 = FL2FXCONST_DBL(0.707106781186547524400844362104849f); /* 1/sqrt(2); */
    reg1 = fMultDiv2(reg1, reg2) << 2;
  }

  *shift = *shift>>1;

  return(reg1);
}
#endif /* !defined(FUNCTION_invSqrtNorm2) */

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

    functionname: sqrtFixp
    description:  delivers sqrt(op)

*****************************************************************************/
FIXP_DBL sqrtFixp(FIXP_DBL op)
{
  INT tmp_exp = 0;
  FIXP_DBL tmp_inv = invSqrtNorm2(op, &tmp_exp);

  FDK_ASSERT(tmp_exp > 0) ;
  return( (FIXP_DBL) ( fMultDiv2( (op<<(tmp_exp-1)), tmp_inv ) << 2 ));
}


#if !defined(FUNCTION_schur_div)
/*****************************************************************************

    functionname: schur_div
    description:  delivers op1/op2 with op3-bit accuracy

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


FIXP_DBL schur_div(FIXP_DBL num, FIXP_DBL denum, INT count)
{
    INT L_num   = (LONG)num>>1;
    INT L_denum = (LONG)denum>>1;
    INT div     = 0;
    INT k       = count;

    FDK_ASSERT (num>=(FIXP_DBL)0);
    FDK_ASSERT (denum>(FIXP_DBL)0);
    FDK_ASSERT (num <= denum);

    if (L_num != 0)
        while (--k)
        {
            div   <<= 1;
            L_num <<= 1;
            if (L_num >= L_denum)
            {
                L_num -= L_denum;
                div++;
            }
        }
    return (FIXP_DBL)(div << (DFRACT_BITS - count));
}


#endif /* !defined(FUNCTION_schur_div) */


#ifndef FUNCTION_fMultNorm
FIXP_DBL fMultNorm(FIXP_DBL f1, FIXP_DBL f2, INT *result_e)
{
    INT    product = 0;
    INT    norm_f1, norm_f2;

    if (  (f1 == (FIXP_DBL)0) || (f2 == (FIXP_DBL)0) ) {
        *result_e = 0;
        return (FIXP_DBL)0;
    }
    norm_f1 = CountLeadingBits(f1);
    f1 = f1 << norm_f1;
    norm_f2 = CountLeadingBits(f2);
    f2 = f2 << norm_f2;

    product = fMult(f1, f2);
    *result_e  = - (norm_f1 + norm_f2);

    return (FIXP_DBL)product;
}
#endif

#ifndef FUNCTION_fDivNorm
FIXP_DBL fDivNorm(FIXP_DBL L_num, FIXP_DBL L_denum, INT *result_e)
{
    FIXP_DBL div;
    INT norm_num, norm_den;

    FDK_ASSERT (L_num   >= (FIXP_DBL)0);
    FDK_ASSERT (L_denum >  (FIXP_DBL)0);

    if(L_num == (FIXP_DBL)0)
    {
        *result_e = 0;
        return ((FIXP_DBL)0);
    }

    norm_num = CountLeadingBits(L_num);
    L_num = L_num << norm_num;
    L_num = L_num >> 1;
    *result_e = - norm_num + 1;

    norm_den = CountLeadingBits(L_denum);
    L_denum = L_denum << norm_den;
    *result_e -= - norm_den;

    div = schur_div(L_num, L_denum, FRACT_BITS);

    return div;
}
#endif /* !FUNCTION_fDivNorm */

#ifndef FUNCTION_fDivNorm
FIXP_DBL fDivNorm(FIXP_DBL num, FIXP_DBL denom)
{
    INT e;
    FIXP_DBL res;

    FDK_ASSERT (denom >= num);

    res = fDivNorm(num, denom, &e);

    /* Avoid overflow since we must output a value with exponent 0
       there is no other choice than saturating to almost 1.0f */
    if(res == (FIXP_DBL)(1<<(DFRACT_BITS-2)) && e == 1)
    {
        res = (FIXP_DBL)MAXVAL_DBL;
    }
    else
    {
        res = scaleValue(res, e);
    }

    return res;
}
#endif /* !FUNCTION_fDivNorm */

#ifndef FUNCTION_fDivNormHighPrec
FIXP_DBL fDivNormHighPrec(FIXP_DBL num, FIXP_DBL denom, INT *result_e)
{
    FIXP_DBL div;
    INT norm_num, norm_den;

    FDK_ASSERT (num   >= (FIXP_DBL)0);
    FDK_ASSERT (denom >  (FIXP_DBL)0);

    if(num == (FIXP_DBL)0)
    {
        *result_e = 0;
        return ((FIXP_DBL)0);
    }

    norm_num = CountLeadingBits(num);
    num = num << norm_num;
    num = num >> 1;
    *result_e = - norm_num + 1;

    norm_den = CountLeadingBits(denom);
    denom = denom << norm_den;
    *result_e -=  - norm_den;

    div = schur_div(num, denom, 31);
    return div;
}
#endif /* !FUNCTION_fDivNormHighPrec */



FIXP_DBL CalcLog2(FIXP_DBL base_m, INT base_e, INT *result_e)
{
  return fLog2(base_m, base_e, result_e);
}

FIXP_DBL f2Pow(
        const FIXP_DBL exp_m, const INT exp_e,
        INT *result_e
        )
{
  FIXP_DBL frac_part, result_m;
  INT int_part;

  if (exp_e > 0)
  {
      INT exp_bits = DFRACT_BITS-1 - exp_e;
      int_part = exp_m >> exp_bits;
      frac_part = exp_m - (FIXP_DBL)(int_part << exp_bits);
      frac_part = frac_part << exp_e;
  }
  else
  {
      int_part = 0;
      frac_part = exp_m >> -exp_e;
  }

  /* Best accuracy is around 0, so try to get there with the fractional part. */
  if( frac_part > FL2FXCONST_DBL(0.5f) )
  {
      int_part = int_part + 1;
      frac_part = frac_part + FL2FXCONST_DBL(-1.0f);
  }
  if( frac_part < FL2FXCONST_DBL(-0.5f) )
  {
      int_part = int_part - 1;
      frac_part = -(FL2FXCONST_DBL(-1.0f) - frac_part);
  }

  /* Evaluate taylor polynomial which approximates 2^x */
  {
    FIXP_DBL p;

    /* result_m ~= 2^frac_part */
    p = frac_part;
    /* First taylor series coefficient a_0 = 1.0, scaled by 0.5 due to fMultDiv2(). */
    result_m = FL2FXCONST_DBL(1.0f/2.0f);
    for (INT i = 0; i < POW2_PRECISION; i++) {
      /* next taylor series term: a_i * x^i, x=0 */
      result_m = fMultAddDiv2(result_m, pow2Coeff[i], p);
      p  = fMult(p, frac_part);
    }
  }

  /* "+ 1" compensates fMultAddDiv2() of the polynomial evaluation above. */
  *result_e = int_part + 1;

  return result_m;
}

FIXP_DBL f2Pow(
        const FIXP_DBL exp_m, const INT exp_e
        )
{
  FIXP_DBL result_m;
  INT result_e;

  result_m = f2Pow(exp_m, exp_e, &result_e);
  result_e = fixMin(DFRACT_BITS-1,fixMax(-(DFRACT_BITS-1),result_e));

  return scaleValue(result_m, result_e);
}

FIXP_DBL fPow(
        FIXP_DBL base_m, INT base_e,
        FIXP_DBL exp_m, INT exp_e,
        INT *result_e
        )
{
    INT ans_lg2_e, baselg2_e;
    FIXP_DBL base_lg2, ans_lg2, result;

    /* Calc log2 of base */
    base_lg2 = fLog2(base_m, base_e, &baselg2_e);

    /* Prepare exp */
    {
      INT leadingBits;

      leadingBits = CountLeadingBits(fAbs(exp_m));
      exp_m = exp_m << leadingBits;
      exp_e -= leadingBits;
    }

    /* Calc base pow exp */
    ans_lg2 = fMult(base_lg2, exp_m);
    ans_lg2_e = exp_e + baselg2_e;

    /* Calc antilog */
    result = f2Pow(ans_lg2, ans_lg2_e, result_e);

    return result;
}

FIXP_DBL fLdPow(
        FIXP_DBL baseLd_m,
        INT baseLd_e,
        FIXP_DBL exp_m, INT exp_e,
        INT *result_e
        )
{
    INT ans_lg2_e;
    FIXP_DBL ans_lg2, result;

    /* Prepare exp */
    {
      INT leadingBits;

      leadingBits = CountLeadingBits(fAbs(exp_m));
      exp_m = exp_m << leadingBits;
      exp_e -= leadingBits;
    }

    /* Calc base pow exp */
    ans_lg2 = fMult(baseLd_m, exp_m);
    ans_lg2_e = exp_e + baseLd_e;

    /* Calc antilog */
    result = f2Pow(ans_lg2, ans_lg2_e, result_e);

    return result;
}

FIXP_DBL fLdPow(
        FIXP_DBL baseLd_m, INT baseLd_e,
        FIXP_DBL exp_m, INT exp_e
        )
{
  FIXP_DBL result_m;
  int result_e;

  result_m = fLdPow(baseLd_m, baseLd_e, exp_m, exp_e, &result_e);

  return SATURATE_SHIFT(result_m, -result_e, DFRACT_BITS);
}

FIXP_DBL fPowInt(
        FIXP_DBL base_m, INT base_e,
        INT exp,
        INT *pResult_e
        )
{
  FIXP_DBL result;

  if (exp != 0) {
    INT result_e = 0;

    if (base_m != (FIXP_DBL)0) {
      {
        INT leadingBits;
        leadingBits = CountLeadingBits( base_m );
        base_m <<= leadingBits;
        base_e -= leadingBits;
      }

      result = base_m;

      {
        int i;
        for (i = 1; i < fAbs(exp); i++) {
          result = fMult(result, base_m);
        }
      }

      if (exp < 0) {
        /* 1.0 / ans */
        result = fDivNorm( FL2FXCONST_DBL(0.5f), result, &result_e );
        result_e++;
      } else {
        int ansScale = CountLeadingBits( result );
        result <<= ansScale;
        result_e -= ansScale;
      }

      result_e += exp * base_e;

    } else {
      result = (FIXP_DBL)0;
    }
    *pResult_e = result_e;
  }
  else {
    result =  FL2FXCONST_DBL(0.5f);
    *pResult_e = 1;
  }

  return result;
}

FIXP_DBL fLog2(FIXP_DBL x_m, INT x_e, INT *result_e)
{
  FIXP_DBL result_m;

  /* Short cut for zero and negative numbers. */
  if ( x_m <= FL2FXCONST_DBL(0.0f) ) {
    *result_e = DFRACT_BITS-1;
    return FL2FXCONST_DBL(-1.0f);
  }

  /* Calculate log2() */
  {
    FIXP_DBL px2_m, x2_m;

    /* Move input value x_m * 2^x_e toward 1.0, where the taylor approximation
       of the function log(1-x) centered at 0 is most accurate. */
    {
      INT b_norm;

      b_norm = fNormz(x_m)-1;
      x2_m = x_m << b_norm;
      x_e = x_e - b_norm;
    }

    /* map x from log(x) domain to log(1-x) domain. */
    x2_m = - (x2_m + FL2FXCONST_DBL(-1.0) );

    /* Taylor polinomial approximation of ln(1-x) */
    result_m  = FL2FXCONST_DBL(0.0);
    px2_m = x2_m;
    for (int i=0; i<LD_PRECISION; i++) {
      result_m = fMultAddDiv2(result_m, ldCoeff[i], px2_m);
      px2_m = fMult(px2_m, x2_m);
    }
    /* Multiply result with 1/ln(2) = 1.0 + 0.442695040888 (get log2(x) from ln(x) result). */
    result_m = fMultAddDiv2(result_m, result_m, FL2FXCONST_DBL(2.0*0.4426950408889634073599246810019));

    /* Add exponent part. log2(x_m * 2^x_e) = log2(x_m) + x_e */
    if (x_e != 0)
    {
      int enorm;

      enorm = DFRACT_BITS - fNorm((FIXP_DBL)x_e);
      /* The -1 in the right shift of result_m compensates the fMultDiv2() above in the taylor polinomial evaluation loop.*/
      result_m = (result_m >> (enorm-1)) + ((FIXP_DBL)x_e << (DFRACT_BITS-1-enorm));

      *result_e = enorm;
    } else {
      /* 1 compensates the fMultDiv2() above in the taylor polinomial evaluation loop.*/
      *result_e = 1;
    }
  }

  return result_m;
}

FIXP_DBL fLog2(FIXP_DBL x_m, INT x_e)
{
  if ( x_m <= FL2FXCONST_DBL(0.0f) ) {
    x_m = FL2FXCONST_DBL(-1.0f);
  }
  else {
    INT result_e;
    x_m = fLog2(x_m, x_e, &result_e);
    x_m = scaleValue(x_m, result_e-LD_DATA_SHIFT);
  }
  return  x_m;
}