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

Software License for The Fraunhofer FDK AAC Codec Library for Android

© Copyright  1995 - 2018 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):   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() so there a wider input

     *  range can be covered, too.

     *

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

    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 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;

  }

  FDK_ASSERT(FL2FXCONST_DBL(1.0 / 64.0) == Q(Q_ATANINP));

  /* calc of arctan */

  if (x < FL2FXCONST_DBL(1.0 / 64.0))

  /*

    Chebyshev polynomial approximation of atan(x)

    5th-order approximation: atan(x) = a1*x + a2*x^3 + a3*x^5 = x(a1 + x^2*(a2 +

    a3*x^2)); a1 = 0.9949493661166540f, a2 = 0.2870606355326520f, a3 =

    0.0780371764464410f; 7th-order approximation: atan(x) = a1*x + a2*x^3 +

    a3*x^5 + a3*x^7 = x(a1 + x^2*(a2 + x^2*(a3 + a4*x^2))); a1 =

    0.9991334482227801, a2 = -0.3205332923816640, a3 = 0.1449824901444650, a4 =

    -0.0382544649702990; 7th-order approximation in use (the most accurate

    solution)

  */

  {

    x <<= ATI_SF;

    FIXP_DBL x2 = fPow2(x);

    temp = fMultAddDiv2((FL2FXCONST_DBL(0.1449824901444650f) >> 1), x2,

                        FL2FXCONST_DBL(-0.0382544649702990));

    temp = fMultAddDiv2((FL2FXCONST_DBL(-0.3205332923816640f) >> 2), x2, temp);

    temp = fMultAddDiv2((FL2FXCONST_DBL(0.9991334482227801f) >> 3), x2, temp);

    result = fMult(x, (temp << 2));

  } 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 {

    /* Other approximation for |x| > 1.28 */

    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);

#ifdef SINETABLE_16BIT

  return cosine - error;

#else

  /* Undo downscaling by 1 which was done at fixp_sin_cos_residual_inline */

  return SATURATE_LEFT_SHIFT(cosine - error, 1, DFRACT_BITS);

#endif

}

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);

#ifdef SINETABLE_16BIT

  return sine + error;

#else

  return SATURATE_LEFT_SHIFT(sine + error, 1, DFRACT_BITS);

#endif

}

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);

#ifdef SINETABLE_16BIT

  *cos = cosine - error0;

  *sin = sine + error1;

#else

  *cos = SATURATE_LEFT_SHIFT(cosine - error0, 1, DFRACT_BITS);

  *sin = SATURATE_LEFT_SHIFT(sine + error1, 1, DFRACT_BITS);

#endif

}