path: root/libFDK/src/FDK_trigFcts.cpp

/* -----------------------------------------------------------------------------------------------------------
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
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You must make available free of charge copies of the complete source code of the FDK AAC Codec and your
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respect to this software.

You may use this FDK AAC Codec software or modifications thereto only for purposes that are authorized
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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
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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):   Haricharan Lakshman, Manuel Jander
   Description: Trigonometric functions fixed point fractional implementation.

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

#include "FDK_trigFcts.h"

#include "fixpoint_math.h"




#define IMPROVE_ATAN2_ACCURACY  1  // 0 --> 59 dB SNR     1 --> 65 dB SNR
#define MINSFTAB  7
#define MAXSFTAB 25

#if IMPROVE_ATAN2_ACCURACY
static const FIXP_DBL f_atan_expand_range[MAXSFTAB-(MINSFTAB-1)]  =
{
  /*****************************************************************************
   *
   *  Table holds fixp_atan() output values which are outside of input range
   *  of fixp_atan() to improve SNR of fixp_atan2().
   *
   *  This Table might also be used in fixp_atan() [todo] so there a wider input
   *  range can be covered, too.
   *
   *  Matlab (generate table):
   *    for scl = 7:25            % MINSFTAB .. MAXSFTAB
   *      at=atan(0.5 *(2^scl));  % 0.5 because get in 'middle' area of current scale level 'scl'
   *      at/2                    % div at by ATO_SCALE
   *    end
   *
   *  Table divided by 2=ATO_SCALE  <--  SF=ATO_SF
   *****************************************************************************/
   FL2FXCONST_DBL(7.775862990872099e-001), FL2FXCONST_DBL(7.814919928673978e-001), FL2FXCONST_DBL(7.834450483314648e-001),
   FL2FXCONST_DBL(7.844216021392089e-001), FL2FXCONST_DBL(7.849098823026687e-001), FL2FXCONST_DBL(7.851540227918509e-001),
   FL2FXCONST_DBL(7.852760930873737e-001), FL2FXCONST_DBL(7.853371282415015e-001), FL2FXCONST_DBL(7.853676458193612e-001),
   FL2FXCONST_DBL(7.853829046083906e-001), FL2FXCONST_DBL(7.853905340029177e-001), FL2FXCONST_DBL(7.853943487001828e-001),
   FL2FXCONST_DBL(7.853962560488155e-001), FL2FXCONST_DBL(7.853972097231319e-001), FL2FXCONST_DBL(7.853976865602901e-001),
   FL2FXCONST_DBL(7.853979249788692e-001), FL2FXCONST_DBL(7.853980441881587e-001), FL2FXCONST_DBL(7.853981037928035e-001),
   FL2FXCONST_DBL(7.853981335951259e-001)
   //     pi/4 = 0.785398163397448 = pi/2/ATO_SCALE
};
#endif

FIXP_DBL fixp_atan2(FIXP_DBL y, FIXP_DBL x)
{
    FIXP_DBL q;
    FIXP_DBL at;  // atan  out
    FIXP_DBL at2; // atan2 out
    FIXP_DBL ret = FL2FXCONST_DBL(-1.0f);
    INT sf,sfo,stf;

    // --- division

    if      (y > FL2FXCONST_DBL(0.0f))
    {
        if      (x > FL2FXCONST_DBL(0.0f)) {
                                           q =  fDivNormHighPrec( y, x, &sf); // both pos.
        }
        else if (x < FL2FXCONST_DBL(0.0f)) {
                                           q = -fDivNormHighPrec( y,-x, &sf); // x neg.
        }
        else {//(x ==FL2FXCONST_DBL(0.0f))
                                           q =  FL2FXCONST_DBL(+1.0f);  // y/x = pos/zero = +Inf
                                           sf = 0;
        }
    }
    else if (y < FL2FXCONST_DBL(0.0f))
    {
        if      (x > FL2FXCONST_DBL(0.0f)) {
                                           q = -fDivNormHighPrec(-y, x, &sf); // y neg.
        }
        else if (x < FL2FXCONST_DBL(0.0f)) {
                                           q =  fDivNormHighPrec(-y,-x, &sf); // both neg.
        }
        else {//(x ==FL2FXCONST_DBL(0.0f))
                                           q =  FL2FXCONST_DBL(-1.0f);  // y/x = neg/zero = -Inf
                                           sf = 0;
        }
    }
    else { // (y ==FL2FXCONST_DBL(0.0f))
        q = FL2FXCONST_DBL(0.0f);
        sf = 0;
    }
    sfo = sf;

    // --- atan()

    if  ( sfo > ATI_SF ) {
        // --- could not calc fixp_atan() here bec of input data out of range
        //     ==> therefore give back boundary values

        #if IMPROVE_ATAN2_ACCURACY
        if (sfo > MAXSFTAB) sfo = MAXSFTAB;
        #endif

        if      (  q > FL2FXCONST_DBL(0.0f) ) {
           #if IMPROVE_ATAN2_ACCURACY
            at = +f_atan_expand_range[sfo-ATI_SF-1];
           #else
            at = FL2FXCONST_DBL( +M_PI/2 / ATO_SCALE);
           #endif
        }
        else if (  q < FL2FXCONST_DBL(0.0f) ) {
           #if IMPROVE_ATAN2_ACCURACY
            at = -f_atan_expand_range[sfo-ATI_SF-1];
           #else
            at = FL2FXCONST_DBL( -M_PI/2 / ATO_SCALE);
           #endif
        }
        else {  // q== FL2FXCONST_DBL(0.0f)
            at = FL2FXCONST_DBL( 0.0f );
        }
    }else{
        // --- calc of fixp_atan() is possible; input data within range
        //     ==> set q on fixed scale level as desired from fixp_atan()
        stf = sfo - ATI_SF;
        if (stf > 0)  q = q << (INT)fMin( stf,DFRACT_BITS-1);
        else          q = q >> (INT)fMin(-stf,DFRACT_BITS-1);
        at = fixp_atan(q);  // ATO_SF
    }

    // --- atan2()

    at2 = at >> (AT2O_SF - ATO_SF); // now AT2O_SF for atan2
    if      (  x > FL2FXCONST_DBL(0.0f) ) {
        ret = at2;
    }
    else if (  x < FL2FXCONST_DBL(0.0f) ) {
        if (  y >= FL2FXCONST_DBL(0.0f) ) {
            ret = at2 + FL2FXCONST_DBL( M_PI / AT2O_SCALE);
        } else {
            ret = at2 - FL2FXCONST_DBL( M_PI / AT2O_SCALE);
        }
    }
    else {
        // x == 0
        if      ( y >  FL2FXCONST_DBL(0.0f) ) {
            ret = FL2FXCONST_DBL( +M_PI/2 / AT2O_SCALE);
        }
        else if ( y <  FL2FXCONST_DBL(0.0f) ) {
            ret = FL2FXCONST_DBL( -M_PI/2 / AT2O_SCALE);
        }
        else if ( y == FL2FXCONST_DBL(0.0f) ) {
            ret = FL2FXCONST_DBL(0.0f);
        }
    }
    return ret;
}


FIXP_DBL fixp_atan(FIXP_DBL x)
{
    INT sign;
    FIXP_DBL result, temp;

    // SNR of fixp_atan() = 56 dB
    FIXP_DBL ONEBY3P56  = (FIXP_DBL)0x26800000; // 1.0/3.56 in q31
    FIXP_DBL P281       = (FIXP_DBL)0x00013000; // 0.281 in q18
    FIXP_DBL ONEP571    = (FIXP_DBL)0x6487ef00; // 1.571 in q30

    if (x < FIXP_DBL(0)) {
      sign = 1;
      x = - x ;
    } else {
      sign = 0;
    }

    /* calc of arctan */
    if(x < ( Q(Q_ATANINP)-FL2FXCONST_DBL(0.00395)) )
    {
        INT res_e;

        temp = fPow2(x);            // q25 * q25 - (DFRACT_BITS-1) = q19
        temp = fMult(temp, ONEBY3P56);      // q19 * q31 - (DFRACT_BITS-1) = q19
        temp = temp + Q(19);                // q19 + q19 = q19
        result = fDivNorm(x, temp, &res_e);
        result = scaleValue(result, (Q_ATANOUT-Q_ATANINP+19-DFRACT_BITS+1) + res_e  );
    }
    else if( x < FL2FXCONST_DBL(1.28/64.0) )
    {
        FIXP_DBL delta_fix;
        FIXP_DBL PI_BY_4 = FL2FXCONST_DBL(3.1415926/4.0) >> 1; /* pi/4 in q30 */

        delta_fix = (x - FL2FXCONST_DBL(1.0/64.0)) << 5; /* q30 */
        result = PI_BY_4 + (delta_fix >> 1) - (fPow2Div2(delta_fix));
    }
    else
    {
        INT res_e;

        temp = fPow2Div2(x);        // q25 * q25 - (DFRACT_BITS-1) - 1 = q18
        temp = temp + P281;                 // q18 + q18 = q18
        result = fDivNorm(x, temp, &res_e);
        result = scaleValue(result, (Q_ATANOUT-Q_ATANINP+18-DFRACT_BITS+1) + res_e );
        result = ONEP571 - result;          // q30 + q30 = q30
    }
    if (sign) {
      result = -result;
    }

    return(result);
}



#include "FDK_tools_rom.h"

FIXP_DBL fixp_cos(FIXP_DBL x, int scale)
{
    FIXP_DBL residual, error, sine, cosine;
    
    residual = fixp_sin_cos_residual_inline(x, scale, &sine, &cosine);
    error = fMult(sine, residual);

    return cosine - error;
}

FIXP_DBL fixp_sin(FIXP_DBL x, int scale)
{
    FIXP_DBL residual, error, sine, cosine;
    
    residual = fixp_sin_cos_residual_inline(x, scale, &sine, &cosine);
    error = fMult(cosine, residual);

    return sine + error;
}

void fixp_cos_sin (FIXP_DBL x, int scale, FIXP_DBL *cos, FIXP_DBL *sin)
{
    FIXP_DBL residual, error0, error1, sine, cosine;
    
    residual = fixp_sin_cos_residual_inline(x, scale, &sine, &cosine);
    error0 = fMult(sine, residual);
    error1 = fMult(cosine, residual);
    *cos  = cosine - error0;
    *sin  = sine + error1;
}