/* -----------------------------------------------------------------------------

Software License for The Fraunhofer FDK AAC Codec Library for Android

© Copyright  1995 - 2020 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):   M. Gayer

   Description: Fixed point specific mathematical functions

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

#include "fixpoint_math.h"

/*

 * Hardware specific implementations

 */

/*

 * Fallback implementations

 */

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

  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] = fLog2(srcVector[i], 0);

  }

}

#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

RAM_ALIGN

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

RAM_ALIGN

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: 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.

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

/* Date: 06-JULY-2012 Arthur Tritthart, IIS Fraunhofer Erlangen */

/* Version with 3 table lookup and 1 linear interpolations      */

/* Algorithm: compute power of 2, argument x is in Q7.25 format */

/*  result = 2^(x/64)                                           */

/*  We split exponent (x/64) into 5 components:                 */

/*  integer part:      represented by b31..b25  (exp)           */

/*  fractional part 1: represented by b24..b20  (lookup1)       */

/*  fractional part 2: represented by b19..b15  (lookup2)       */

/*  fractional part 3: represented by b14..b10  (lookup3)       */

/*  fractional part 4: represented by b09..b00  (frac)          */

/*  => result = (lookup1*lookup2*(lookup3+C1*frac)<<3)>>exp     */

/* Due to the fact, that all lookup values contain a factor 0.5 */

/* the result has to be shifted by 3 to the right also.         */

/* Table exp2_tab_long contains the log2 for 0 to 1.0 in steps  */

/* of 1/32, table exp2w_tab_long the log2 for 0 to 1/32 in steps*/

/* of 1/1024, table exp2x_tab_long the log2 for 0 to 1/1024 in  */

/* steps of 1/32768. Since the 2-logarithm of very very small   */

/* negative value is rather linear, we can use interpolation.   */

/* Limitations:                                                 */

/* For x <= 0, the result is fractional positive                */

/* For x > 0, the result is integer in range 1...7FFF.FFFF      */

/* For x < -31/64, we have to clear the result                  */

/* For x = 0, the result is ~1.0 (0x7FFF.FFFF)                  */

/* For x >= 31/64, the result is 0x7FFF.FFFF                    */

/* This table is used for lookup 2^x with   */

/* x in range [0...1.0[ in steps of 1/32 */

LNK_SECTION_DATA_L1

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

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

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

};

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

    functionname: InitLdInt and CalcLdInt

    description:  Create and access table with integer LdData (0 to

LD_INT_TAB_LEN)

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

#ifndef LD_INT_TAB_LEN

#define LD_INT_TAB_LEN \

  193 /* Default tab length. Lower value should be set in fix.h */

#endif

#if (LD_INT_TAB_LEN <= 120)

LNK_SECTION_CONSTDATA_L1

static const FIXP_DBL ldIntCoeff[] = {

    (FIXP_DBL)0x80000001, (FIXP_DBL)0x00000000, (FIXP_DBL)0x02000000,

    (FIXP_DBL)0x032b8034, (FIXP_DBL)0x04000000, (FIXP_DBL)0x04a4d3c2,

    (FIXP_DBL)0x052b8034, (FIXP_DBL)0x059d5da0, (FIXP_DBL)0x06000000,

    (FIXP_DBL)0x06570069, (FIXP_DBL)0x06a4d3c2, (FIXP_DBL)0x06eb3a9f,

    (FIXP_DBL)0x072b8034, (FIXP_DBL)0x0766a009, (FIXP_DBL)0x079d5da0,

    (FIXP_DBL)0x07d053f7, (FIXP_DBL)0x08000000, (FIXP_DBL)0x082cc7ee,

    (FIXP_DBL)0x08570069, (FIXP_DBL)0x087ef05b, (FIXP_DBL)0x08a4d3c2,

    (FIXP_DBL)0x08c8ddd4, (FIXP_DBL)0x08eb3a9f, (FIXP_DBL)0x090c1050,

    (FIXP_DBL)0x092b8034, (FIXP_DBL)0x0949a785, (FIXP_DBL)0x0966a009,

    (FIXP_DBL)0x0982809d, (FIXP_DBL)0x099d5da0, (FIXP_DBL)0x09b74949,

    (FIXP_DBL)0x09d053f7, (FIXP_DBL)0x09e88c6b, (FIXP_DBL)0x0a000000,

    (FIXP_DBL)0x0a16bad3, (FIXP_DBL)0x0a2cc7ee, (FIXP_DBL)0x0a423162,

    (FIXP_DBL)0x0a570069, (FIXP_DBL)0x0a6b3d79, (FIXP_DBL)0x0a7ef05b,

    (FIXP_DBL)0x0a92203d, (FIXP_DBL)0x0aa4d3c2, (FIXP_DBL)0x0ab7110e,

    (FIXP_DBL)0x0ac8ddd4, (FIXP_DBL)0x0ada3f60, (FIXP_DBL)0x0aeb3a9f,

    (FIXP_DBL)0x0afbd42b, (FIXP_DBL)0x0b0c1050, (FIXP_DBL)0x0b1bf312,

    (FIXP_DBL)0x0b2b8034, (FIXP_DBL)0x0b3abb40, (FIXP_DBL)0x0b49a785,

    (FIXP_DBL)0x0b584822, (FIXP_DBL)0x0b66a009, (FIXP_DBL)0x0b74b1fd,

    (FIXP_DBL)0x0b82809d, (FIXP_DBL)0x0b900e61, (FIXP_DBL)0x0b9d5da0,

    (FIXP_DBL)0x0baa708f, (FIXP_DBL)0x0bb74949, (FIXP_DBL)0x0bc3e9ca,

    (FIXP_DBL)0x0bd053f7, (FIXP_DBL)0x0bdc899b, (FIXP_DBL)0x0be88c6b,

    (FIXP_DBL)0x0bf45e09, (FIXP_DBL)0x0c000000, (FIXP_DBL)0x0c0b73cb,

    (FIXP_DBL)0x0c16bad3, (FIXP_DBL)0x0c21d671, (FIXP_DBL)0x0c2cc7ee,

    (FIXP_DBL)0x0c379085, (FIXP_DBL)0x0c423162, (FIXP_DBL)0x0c4caba8,

    (FIXP_DBL)0x0c570069, (FIXP_DBL)0x0c6130af, (FIXP_DBL)0x0c6b3d79,

    (FIXP_DBL)0x0c7527b9, (FIXP_DBL)0x0c7ef05b, (FIXP_DBL)0x0c88983f,

    (FIXP_DBL)0x0c92203d, (FIXP_DBL)0x0c9b8926, (FIXP_DBL)0x0ca4d3c2,

    (FIXP_DBL)0x0cae00d2, (FIXP_DBL)0x0cb7110e, (FIXP_DBL)0x0cc0052b,

    (FIXP_DBL)0x0cc8ddd4, (FIXP_DBL)0x0cd19bb0, (FIXP_DBL)0x0cda3f60,

    (FIXP_DBL)0x0ce2c97d, (FIXP_DBL)0x0ceb3a9f, (FIXP_DBL)0x0cf39355,

    (FIXP_DBL)0x0cfbd42b, (FIXP_DBL)0x0d03fda9, (FIXP_DBL)0x0d0c1050,

    (FIXP_DBL)0x0d140ca0, (FIXP_DBL)0x0d1bf312, (FIXP_DBL)0x0d23c41d,

    (FIXP_DBL)0x0d2b8034, (FIXP_DBL)0x0d3327c7, (FIXP_DBL)0x0d3abb40,

    (FIXP_DBL)0x0d423b08, (FIXP_DBL)0x0d49a785, (FIXP_DBL)0x0d510118,

    (FIXP_DBL)0x0d584822, (FIXP_DBL)0x0d5f7cff, (FIXP_DBL)0x0d66a009,

    (FIXP_DBL)0x0d6db197, (FIXP_DBL)0x0d74b1fd, (FIXP_DBL)0x0d7ba190,

    (FIXP_DBL)0x0d82809d, (FIXP_DBL)0x0d894f75, (FIXP_DBL)0x0d900e61,

    (FIXP_DBL)0x0d96bdad, (FIXP_DBL)0x0d9d5da0, (FIXP_DBL)0x0da3ee7f,

    (FIXP_DBL)0x0daa708f, (FIXP_DBL)0x0db0e412, (FIXP_DBL)0x0db74949,

    (FIXP_DBL)0x0dbda072, (FIXP_DBL)0x0dc3e9ca, (FIXP_DBL)0x0dca258e};

#elif (LD_INT_TAB_LEN <= 193)

LNK_SECTION_CONSTDATA_L1

static const FIXP_DBL ldIntCoeff[] = {

    (FIXP_DBL)0x80000001, (FIXP_DBL)0x00000000, (FIXP_DBL)0x02000000,

    (FIXP_DBL)0x032b8034, (FIXP_DBL)0x04000000, (FIXP_DBL)0x04a4d3c2,

    (FIXP_DBL)0x052b8034, (FIXP_DBL)0x059d5da0, (FIXP_DBL)0x06000000,

    (FIXP_DBL)0x06570069, (FIXP_DBL)0x06a4d3c2, (FIXP_DBL)0x06eb3a9f,

    (FIXP_DBL)0x072b8034, (FIXP_DBL)0x0766a009, (FIXP_DBL)0x079d5da0,

    (FIXP_DBL)0x07d053f7, (FIXP_DBL)0x08000000, (FIXP_DBL)0x082cc7ee,

    (FIXP_DBL)0x08570069, (FIXP_DBL)0x087ef05b, (FIXP_DBL)0x08a4d3c2,

    (FIXP_DBL)0x08c8ddd4, (FIXP_DBL)0x08eb3a9f, (FIXP_DBL)0x090c1050,

    (FIXP_DBL)0x092b8034, (FIXP_DBL)0x0949a785, (FIXP_DBL)0x0966a009,

    (FIXP_DBL)0x0982809d, (FIXP_DBL)0x099d5da0, (FIXP_DBL)0x09b74949,

    (FIXP_DBL)0x09d053f7, (FIXP_DBL)0x09e88c6b, (FIXP_DBL)0x0a000000,

    (FIXP_DBL)0x0a16bad3, (FIXP_DBL)0x0a2cc7ee, (FIXP_DBL)0x0a423162,

    (FIXP_DBL)0x0a570069, (FIXP_DBL)0x0a6b3d79, (FIXP_DBL)0x0a7ef05b,

    (FIXP_DBL)0x0a92203d, (FIXP_DBL)0x0aa4d3c2, (FIXP_DBL)0x0ab7110e,

    (FIXP_DBL)0x0ac8ddd4, (FIXP_DBL)0x0ada3f60, (FIXP_DBL)0x0aeb3a9f,

    (FIXP_DBL)0x0afbd42b, (FIXP_DBL)0x0b0c1050, (FIXP_DBL)0x0b1bf312,

    (FIXP_DBL)0x0b2b8034, (FIXP_DBL)0x0b3abb40, (FIXP_DBL)0x0b49a785,

    (FIXP_DBL)0x0b584822, (FIXP_DBL)0x0b66a009, (FIXP_DBL)0x0b74b1fd,

    (FIXP_DBL)0x0b82809d, (FIXP_DBL)0x0b900e61, (FIXP_DBL)0x0b9d5da0,

    (FIXP_DBL)0x0baa708f, (FIXP_DBL)0x0bb74949, (FIXP_DBL)0x0bc3e9ca,

    (FIXP_DBL)0x0bd053f7, (FIXP_DBL)0x0bdc899b, (FIXP_DBL)0x0be88c6b,

    (FIXP_DBL)0x0bf45e09, (FIXP_DBL)0x0c000000, (FIXP_DBL)0x0c0b73cb,

    (FIXP_DBL)0x0c16bad3, (FIXP_DBL)0x0c21d671, (FIXP_DBL)0x0c2cc7ee,

    (FIXP_DBL)0x0c379085, (FIXP_DBL)0x0c423162, (FIXP_DBL)0x0c4caba8,

    (FIXP_DBL)0x0c570069, (FIXP_DBL)0x0c6130af, (FIXP_DBL)0x0c6b3d79,

    (FIXP_DBL)0x0c7527b9, (FIXP_DBL)0x0c7ef05b, (FIXP_DBL)0x0c88983f,

    (FIXP_DBL)0x0c92203d, (FIXP_DBL)0x0c9b8926, (FIXP_DBL)0x0ca4d3c2,

    (FIXP_DBL)0x0cae00d2, (FIXP_DBL)0x0cb7110e, (FIXP_DBL)0x0cc0052b,

    (FIXP_DBL)0x0cc8ddd4, (FIXP_DBL)0x0cd19bb0, (FIXP_DBL)0x0cda3f60,

    (FIXP_DBL)0x0ce2c97d, (FIXP_DBL)0x0ceb3a9f, (FIXP_DBL)0x0cf39355,

    (FIXP_DBL)0x0cfbd42b, (FIXP_DBL)0x0d03fda9, (FIXP_DBL)0x0d0c1050,

    (FIXP_DBL)0x0d140ca0, (FIXP_DBL)0x0d1bf312, (FIXP_DBL)0x0d23c41d,

    (FIXP_DBL)0x0d2b8034, (FIXP_DBL)0x0d3327c7, (FIXP_DBL)0x0d3abb40,

    (FIXP_DBL)0x0d423b08, (FIXP_DBL)0x0d49a785, (FIXP_DBL)0x0d510118,

    (FIXP_DBL)0x0d584822, (FIXP_DBL)0x0d5f7cff, (FIXP_DBL)0x0d66a009,

    (FIXP_DBL)0x0d6db197, (FIXP_DBL)0x0d74b1fd, (FIXP_DBL)0x0d7ba190,

    (FIXP_DBL)0x0d82809d, (FIXP_DBL)0x0d894f75, (FIXP_DBL)0x0d900e61,

    (FIXP_DBL)0x0d96bdad, (FIXP_DBL)0x0d9d5da0, (FIXP_DBL)0x0da3ee7f,

    (FIXP_DBL)0x0daa708f, (FIXP_DBL)0x0db0e412, (FIXP_DBL)0x0db74949,

    (FIXP_DBL)0x0dbda072, (FIXP_DBL)0x0dc3e9ca, (FIXP_DBL)0x0dca258e,

    (FIXP_DBL)0x0dd053f7, (FIXP_DBL)0x0dd6753e, (FIXP_DBL)0x0ddc899b,

    (FIXP_DBL)0x0de29143, (FIXP_DBL)0x0de88c6b, (FIXP_DBL)0x0dee7b47,

    (FIXP_DBL)0x0df45e09, (FIXP_DBL)0x0dfa34e1, (FIXP_DBL)0x0e000000,

    (FIXP_DBL)0x0e05bf94, (FIXP_DBL)0x0e0b73cb, (FIXP_DBL)0x0e111cd2,

    (FIXP_DBL)0x0e16bad3, (FIXP_DBL)0x0e1c4dfb, (FIXP_DBL)0x0e21d671,

    (FIXP_DBL)0x0e275460, (FIXP_DBL)0x0e2cc7ee, (FIXP_DBL)0x0e323143,

    (FIXP_DBL)0x0e379085, (FIXP_DBL)0x0e3ce5d8, (FIXP_DBL)0x0e423162,

    (FIXP_DBL)0x0e477346, (FIXP_DBL)0x0e4caba8, (FIXP_DBL)0x0e51daa8,

    (FIXP_DBL)0x0e570069, (FIXP_DBL)0x0e5c1d0b, (FIXP_DBL)0x0e6130af,

    (FIXP_DBL)0x0e663b74, (FIXP_DBL)0x0e6b3d79, (FIXP_DBL)0x0e7036db,

    (FIXP_DBL)0x0e7527b9, (FIXP_DBL)0x0e7a1030, (FIXP_DBL)0x0e7ef05b,

    (FIXP_DBL)0x0e83c857, (FIXP_DBL)0x0e88983f, (FIXP_DBL)0x0e8d602e,

    (FIXP_DBL)0x0e92203d, (FIXP_DBL)0x0e96d888, (FIXP_DBL)0x0e9b8926,

    (FIXP_DBL)0x0ea03232, (FIXP_DBL)0x0ea4d3c2, (FIXP_DBL)0x0ea96df0,

    (FIXP_DBL)0x0eae00d2, (FIXP_DBL)0x0eb28c7f, (FIXP_DBL)0x0eb7110e,

    (FIXP_DBL)0x0ebb8e96, (FIXP_DBL)0x0ec0052b, (FIXP_DBL)0x0ec474e4,

    (FIXP_DBL)0x0ec8ddd4, (FIXP_DBL)0x0ecd4012, (FIXP_DBL)0x0ed19bb0,

    (FIXP_DBL)0x0ed5f0c4, (FIXP_DBL)0x0eda3f60, (FIXP_DBL)0x0ede8797,

    (FIXP_DBL)0x0ee2c97d, (FIXP_DBL)0x0ee70525, (FIXP_DBL)0x0eeb3a9f,

    (FIXP_DBL)0x0eef69ff, (FIXP_DBL)0x0ef39355, (FIXP_DBL)0x0ef7b6b4,

    (FIXP_DBL)0x0efbd42b, (FIXP_DBL)0x0effebcd, (FIXP_DBL)0x0f03fda9,

    (FIXP_DBL)0x0f0809cf, (FIXP_DBL)0x0f0c1050, (FIXP_DBL)0x0f10113b,

    (FIXP_DBL)0x0f140ca0, (FIXP_DBL)0x0f18028d, (FIXP_DBL)0x0f1bf312,

    (FIXP_DBL)0x0f1fde3d, (FIXP_DBL)0x0f23c41d, (FIXP_DBL)0x0f27a4c0,

    (FIXP_DBL)0x0f2b8034};

#else

#error "ldInt table size too small"

#endif

LNK_SECTION_INITCODE

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

}

#if (LD_INT_TAB_LEN != 0)

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 LD_INT_TAB_LEN */

  FDK_ASSERT((LD_INT_TAB_LEN > 0) &&

             ((FIXP_DBL)ldIntCoeff[0] ==

              (FIXP_DBL)0x80000001)); /* tab has to be initialized */

  if ((i > 0) && (i < LD_INT_TAB_LEN))

    return ldIntCoeff[i];

  else {

    return (0);

  }

}

#endif /* (LD_INT_TAB_LEN!=0)  */

#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;

  if ((f1 == (FIXP_DBL)MINVAL_DBL) && (f2 == (FIXP_DBL)MINVAL_DBL)) {

    product = -((FIXP_DBL)MINVAL_DBL >> 1);

    *result_e = -(norm_f1 + norm_f2 - 1);

  } else {

    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_fDivNormSigned

FIXP_DBL fDivNormSigned(FIXP_DBL num, FIXP_DBL denom) {

  INT e;

  FIXP_DBL res;

  int sign;

  if (denom == (FIXP_DBL)0) {

    return (FIXP_DBL)MAXVAL_DBL;

  }

  sign = ((num >= (FIXP_DBL)0) != (denom >= (FIXP_DBL)0));

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

  /* Saturate since we must output a value with exponent 0 */

  if ((e > 0) && (fAbs(res) >= FL2FXCONST_DBL(0.5))) {

    if (sign) {

      res = (FIXP_DBL)MINVAL_DBL;

    } else {

      res = (FIXP_DBL)MAXVAL_DBL;

    }

  } else {

    res = scaleValue(res, e);

  }

  return res;

}

FIXP_DBL fDivNormSigned(FIXP_DBL L_num, FIXP_DBL L_denum, INT *result_e) {

  FIXP_DBL div;

  INT norm_num, norm_den;

  int sign;

  sign = ((L_num >= (FIXP_DBL)0) != (L_denum >= (FIXP_DBL)0));

  if (L_num == (FIXP_DBL)0) {

    *result_e = 0;

    return ((FIXP_DBL)0);

  }

  if (L_denum == (FIXP_DBL)0) {

    *result_e = 14;

    return ((FIXP_DBL)MAXVAL_DBL);

  }

  norm_num = CountLeadingBits(L_num);

  L_num = L_num << norm_num;

  L_num = L_num >> 2;

  L_num = fAbs(L_num);

  *result_e = -norm_num + 1;

  norm_den = CountLeadingBits(L_denum);

  L_denum = L_denum << norm_den;

  L_denum = L_denum >> 1;

  L_denum = fAbs(L_denum);

  *result_e -= -norm_den;

  div = schur_div(L_num, L_denum, FRACT_BITS);

  if (sign) {

    div = -div;

  }

  return div;

}

#endif /* FUNCTION_fDivNormSigned */

#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 */

#ifndef FUNCTION_fPow

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);

  }

  /* "+ 1" compensates fMultAddDiv2() of the polynomial evaluation below. */

  *result_e = int_part + 1;

  /* 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);

    }

  }

  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;

  if (base_m <= (FIXP_DBL)0) {

    result = (FIXP_DBL)0;

    *result_e = 0;

    return 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;

}

#endif /* FUNCTION_fPow */

#ifndef FUNCTION_fLog2

FIXP_DBL CalcLog2(FIXP_DBL base_m, INT base_e, INT *result_e) {

  return fLog2(base_m, base_e, result_e);

}

#endif /* FUNCTION_fLog2 */

INT fixp_floorToInt(FIXP_DBL f_inp, INT sf) {

  FDK_ASSERT(sf >= 0);

  INT floorInt = (INT)(f_inp >> ((DFRACT_BITS - 1) - sf));

  return floorInt;

}

FIXP_DBL fixp_floor(FIXP_DBL f_inp, INT sf) {

  FDK_ASSERT(sf >= 0);

  INT floorInt = fixp_floorToInt(f_inp, sf);

  FIXP_DBL f_floor = (FIXP_DBL)(floorInt << ((DFRACT_BITS - 1) - sf));

  return f_floor;

}

INT fixp_ceilToInt(FIXP_DBL f_inp, INT sf)  // sf  mantissaBits left of dot

{

  FDK_ASSERT(sf >= 0);

  INT sx = (DFRACT_BITS - 1) - sf;  // sx  mantissaBits right of dot

  INT inpINT = (INT)f_inp;

  INT mask = (0x1 << sx) - 1;

  INT ceilInt = (INT)(f_inp >> sx);

  if (inpINT & mask) {

    ceilInt++;  // increment only, if there is at least one set mantissaBit

                // right of dot [in inpINT]

  }

  return ceilInt;

}

FIXP_DBL fixp_ceil(FIXP_DBL f_inp, INT sf) {

  FDK_ASSERT(sf >= 0);

  INT sx = (DFRACT_BITS - 1) - sf;

  INT ceilInt = fixp_ceilToInt(f_inp, sf);

  ULONG mask = (ULONG)0x1 << (DFRACT_BITS - 1);  // 0x80000000

  ceilInt = ceilInt

            << sx;  // no fract warn bec. shift into saturation done on int side

  if ((f_inp > FL2FXCONST_DBL(0.0f)) && (ceilInt & mask)) {

    --ceilInt;

  }

  FIXP_DBL f_ceil = (FIXP_DBL)ceilInt;

  return f_ceil;

}

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

   fixp_truncateToInt()

     Just remove the fractional part which is located right of decimal point

     Same as which is done when a float is casted to (INT) :

     result_INTtype = (INT)b_floatTypeInput;

   returns INT

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

INT fixp_truncateToInt(FIXP_DBL f_inp, INT sf)  // sf  mantissaBits left  of dot

                                                // (without sign)  e.g. at width

                                                // 32 this would be [sign]7.

                                                // supposed sf equals 8.

{

  FDK_ASSERT(sf >= 0);

  INT sx = (DFRACT_BITS - 1) - sf;  // sx  mantissaBits right of dot

                                    // at width 32 this would be        .24

                                    // supposed sf equals 8.

  INT fbaccu = (INT)f_inp;

  INT mask = (0x1 << sx);

  if ((fbaccu < 0) && (fbaccu & (mask - 1))) {

    fbaccu = fbaccu + mask;

  }

  fbaccu = fbaccu >> sx;

  return fbaccu;

}

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

   fixp_truncate()

     Just remove the fractional part which is located right of decimal point

   returns FIXP_DBL

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

FIXP_DBL fixp_truncate(FIXP_DBL f_inp, INT sf) {

  FDK_ASSERT(sf >= 0);

  INT truncateInt = fixp_truncateToInt(f_inp, sf);

  FIXP_DBL f_truncate = (FIXP_DBL)(truncateInt << ((DFRACT_BITS - 1) - sf));

  return f_truncate;

}

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

  fixp_roundToInt()

    round [typical rounding]

    See fct roundRef() [which is the reference]

  returns INT

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

INT fixp_roundToInt(FIXP_DBL f_inp, INT sf) {

  FDK_ASSERT(sf >= 0);

  INT sx = DFRACT_BITS - 1 - sf;

  INT inp = (INT)f_inp;

  INT mask1 = (0x1 << (sx - 1));

  INT mask2 = (0x1 << (sx)) - 1;

  INT mask3 = 0x7FFFFFFF;

  INT iam = inp & mask2;

  INT rnd;

  if ((inp < 0) && !(iam == mask1))

    rnd = inp + mask1;

  else if ((inp > 0) && !(inp == mask3))

    rnd = inp + mask1;

  else

    rnd = inp;

  rnd = rnd >> sx;

  if (inp == mask3) rnd++;

  return rnd;

}

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

  fixp_round()

    round [typical rounding]

    See fct roundRef() [which is the reference]

  returns FIXP_DBL

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

FIXP_DBL fixp_round(FIXP_DBL f_inp, INT sf) {

  FDK_ASSERT(sf >= 0);

  INT sx = DFRACT_BITS - 1 - sf;

  INT r = fixp_roundToInt(f_inp, sf);

  ULONG mask = (ULONG)0x1 << (DFRACT_BITS - 1);  // 0x80000000

  r = r << sx;

  if ((f_inp > FL2FXCONST_DBL(0.0f)) && (r & mask)) {

    --r;

  }

  FIXP_DBL f_round = (FIXP_DBL)r;

  return f_round;

}