FDK_trigFcts.cpp - Android社区 - https://www.androidos.net.cn/

/* -----------------------------------------------------------------------------------------------------------
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the MPEG Advanced Audio Coding ("AAC") encoding and decoding scheme for digital audio.
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Fraunhofer Institute for Integrated Circuits IIS
Attention: Audio and Multimedia Departments - FDK AAC LL
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----------------------------------------------------------------------------------------------------------- */

/***************************  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;
}

C++程序 | 331行 | 12.32 KB

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