/* -----------------------------------------------------------------------------
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Software License for The Fraunhofer FDK AAC Codec Library for Android
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© Copyright 1995 - 2018 Fraunhofer-Gesellschaft zur Förderung der angewandten
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Forschung e.V. All rights reserved.
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1. INTRODUCTION
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The Fraunhofer FDK AAC Codec Library for Android ("FDK AAC Codec") is software
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that implements the MPEG Advanced Audio Coding ("AAC") encoding and decoding
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scheme for digital audio. This FDK AAC Codec software is intended to be used on
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a wide variety of Android devices.
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AAC's HE-AAC and HE-AAC v2 versions are regarded as today's most efficient
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general perceptual audio codecs. AAC-ELD is considered the best-performing
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full-bandwidth communications codec by independent studies and is widely
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deployed. AAC has been standardized by ISO and IEC as part of the MPEG
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specifications.
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Patent licenses for necessary patent claims for the FDK AAC Codec (including
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those of Fraunhofer) may be obtained through Via Licensing
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(www.vialicensing.com) or through the respective patent owners individually for
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the purpose of encoding or decoding bit streams in products that are compliant
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with the ISO/IEC MPEG audio standards. Please note that most manufacturers of
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Android devices already license these patent claims through Via Licensing or
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directly from the patent owners, and therefore FDK AAC Codec software may
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already be covered under those patent licenses when it is used for those
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licensed purposes only.
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Commercially-licensed AAC software libraries, including floating-point versions
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with enhanced sound quality, are also available from Fraunhofer. Users are
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encouraged to check the Fraunhofer website for additional applications
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information and documentation.
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2. COPYRIGHT LICENSE
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Redistribution and use in source and binary forms, with or without modification,
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are permitted without payment of copyright license fees provided that you
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satisfy the following conditions:
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You must retain the complete text of this software license in redistributions of
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the FDK AAC Codec or your modifications thereto in source code form.
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You must retain the complete text of this software license in the documentation
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and/or other materials provided with redistributions of the FDK AAC Codec or
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your modifications thereto in binary form. You must make available free of
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charge copies of the complete source code of the FDK AAC Codec and your
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modifications thereto to recipients of copies in binary form.
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The name of Fraunhofer may not be used to endorse or promote products derived
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from this library without prior written permission.
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You may not charge copyright license fees for anyone to use, copy or distribute
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the FDK AAC Codec software or your modifications thereto.
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Your modified versions of the FDK AAC Codec must carry prominent notices stating
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that you changed the software and the date of any change. For modified versions
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of the FDK AAC Codec, the term "Fraunhofer FDK AAC Codec Library for Android"
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must be replaced by the term "Third-Party Modified Version of the Fraunhofer FDK
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AAC Codec Library for Android."
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3. NO PATENT LICENSE
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NO EXPRESS OR IMPLIED LICENSES TO ANY PATENT CLAIMS, including without
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limitation the patents of Fraunhofer, ARE GRANTED BY THIS SOFTWARE LICENSE.
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Fraunhofer provides no warranty of patent non-infringement with respect to this
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software.
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You may use this FDK AAC Codec software or modifications thereto only for
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purposes that are authorized by appropriate patent licenses.
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4. DISCLAIMER
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This FDK AAC Codec software is provided by Fraunhofer on behalf of the copyright
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holders and contributors "AS IS" and WITHOUT ANY EXPRESS OR IMPLIED WARRANTIES,
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including but not limited to the implied warranties of merchantability and
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fitness for a particular purpose. IN NO EVENT SHALL THE COPYRIGHT HOLDER OR
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CONTRIBUTORS BE LIABLE for any direct, indirect, incidental, special, exemplary,
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or consequential damages, including but not limited to procurement of substitute
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goods or services; loss of use, data, or profits, or business interruption,
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however caused and on any theory of liability, whether in contract, strict
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liability, or tort (including negligence), arising in any way out of the use of
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this software, even if advised of the possibility of such damage.
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5. CONTACT INFORMATION
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Fraunhofer Institute for Integrated Circuits IIS
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Attention: Audio and Multimedia Departments - FDK AAC LL
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Am Wolfsmantel 33
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91058 Erlangen, Germany
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www.iis.fraunhofer.de/amm
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amm-info@iis.fraunhofer.de
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----------------------------------------------------------------------------- */
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/******************* Library for basic calculation routines ********************
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Author(s): Haricharan Lakshman, Manuel Jander
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Description: Trigonometric functions fixed point fractional implementation.
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*******************************************************************************/
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#include "FDK_trigFcts.h"
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#include "fixpoint_math.h"
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#define IMPROVE_ATAN2_ACCURACY 1 /* 0 --> 59 dB SNR 1 --> 65 dB SNR */
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#define MINSFTAB 7
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#define MAXSFTAB 25
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#if IMPROVE_ATAN2_ACCURACY
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static const FIXP_DBL f_atan_expand_range[MAXSFTAB - (MINSFTAB - 1)] = {
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/*****************************************************************************
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*
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* Table holds fixp_atan() output values which are outside of input range
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* of fixp_atan() to improve SNR of fixp_atan2().
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*
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* This Table might also be used in fixp_atan() so there a wider input
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* range can be covered, too.
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*
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*****************************************************************************/
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FL2FXCONST_DBL(7.775862990872099e-001),
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FL2FXCONST_DBL(7.814919928673978e-001),
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FL2FXCONST_DBL(7.834450483314648e-001),
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FL2FXCONST_DBL(7.844216021392089e-001),
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FL2FXCONST_DBL(7.849098823026687e-001),
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FL2FXCONST_DBL(7.851540227918509e-001),
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FL2FXCONST_DBL(7.852760930873737e-001),
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FL2FXCONST_DBL(7.853371282415015e-001),
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FL2FXCONST_DBL(7.853676458193612e-001),
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FL2FXCONST_DBL(7.853829046083906e-001),
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FL2FXCONST_DBL(7.853905340029177e-001),
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FL2FXCONST_DBL(7.853943487001828e-001),
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FL2FXCONST_DBL(7.853962560488155e-001),
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FL2FXCONST_DBL(7.853972097231319e-001),
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FL2FXCONST_DBL(7.853976865602901e-001),
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FL2FXCONST_DBL(7.853979249788692e-001),
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FL2FXCONST_DBL(7.853980441881587e-001),
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FL2FXCONST_DBL(7.853981037928035e-001),
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FL2FXCONST_DBL(7.853981335951259e-001)
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/* pi/4 = 0.785398163397448 = pi/2/ATO_SCALE */
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};
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#endif
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FIXP_DBL fixp_atan2(FIXP_DBL y, FIXP_DBL x) {
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FIXP_DBL q;
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FIXP_DBL at; /* atan out */
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FIXP_DBL at2; /* atan2 out */
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FIXP_DBL ret = FL2FXCONST_DBL(-1.0f);
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INT sf, sfo, stf;
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/* --- division */
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if (y > FL2FXCONST_DBL(0.0f)) {
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if (x > FL2FXCONST_DBL(0.0f)) {
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q = fDivNormHighPrec(y, x, &sf); /* both pos. */
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} else if (x < FL2FXCONST_DBL(0.0f)) {
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q = -fDivNormHighPrec(y, -x, &sf); /* x neg. */
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} else { /* (x == FL2FXCONST_DBL(0.0f)) */
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q = FL2FXCONST_DBL(+1.0f); /* y/x = pos/zero = +Inf */
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sf = 0;
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}
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} else if (y < FL2FXCONST_DBL(0.0f)) {
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if (x > FL2FXCONST_DBL(0.0f)) {
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q = -fDivNormHighPrec(-y, x, &sf); /* y neg. */
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} else if (x < FL2FXCONST_DBL(0.0f)) {
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q = fDivNormHighPrec(-y, -x, &sf); /* both neg. */
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} else { /* (x == FL2FXCONST_DBL(0.0f)) */
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q = FL2FXCONST_DBL(-1.0f); /* y/x = neg/zero = -Inf */
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sf = 0;
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}
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} else { /* (y == FL2FXCONST_DBL(0.0f)) */
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q = FL2FXCONST_DBL(0.0f);
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sf = 0;
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}
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sfo = sf;
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/* --- atan() */
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if (sfo > ATI_SF) {
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/* --- could not calc fixp_atan() here bec of input data out of range */
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/* ==> therefore give back boundary values */
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#if IMPROVE_ATAN2_ACCURACY
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if (sfo > MAXSFTAB) sfo = MAXSFTAB;
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#endif
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if (q > FL2FXCONST_DBL(0.0f)) {
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#if IMPROVE_ATAN2_ACCURACY
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at = +f_atan_expand_range[sfo - ATI_SF - 1];
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#else
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at = FL2FXCONST_DBL(+M_PI / 2 / ATO_SCALE);
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#endif
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} else if (q < FL2FXCONST_DBL(0.0f)) {
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#if IMPROVE_ATAN2_ACCURACY
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at = -f_atan_expand_range[sfo - ATI_SF - 1];
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#else
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at = FL2FXCONST_DBL(-M_PI / 2 / ATO_SCALE);
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#endif
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} else { /* q == FL2FXCONST_DBL(0.0f) */
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at = FL2FXCONST_DBL(0.0f);
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}
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} else {
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/* --- calc of fixp_atan() is possible; input data within range */
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/* ==> set q on fixed scale level as desired from fixp_atan() */
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stf = sfo - ATI_SF;
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if (stf > 0)
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q = q << (INT)fMin(stf, DFRACT_BITS - 1);
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else
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q = q >> (INT)fMin(-stf, DFRACT_BITS - 1);
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at = fixp_atan(q); /* ATO_SF */
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}
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// --- atan2()
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at2 = at >> (AT2O_SF - ATO_SF); // now AT2O_SF for atan2
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if (x > FL2FXCONST_DBL(0.0f)) {
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ret = at2;
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} else if (x < FL2FXCONST_DBL(0.0f)) {
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if (y >= FL2FXCONST_DBL(0.0f)) {
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ret = at2 + FL2FXCONST_DBL(M_PI / AT2O_SCALE);
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} else {
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ret = at2 - FL2FXCONST_DBL(M_PI / AT2O_SCALE);
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}
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} else {
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// x == 0
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if (y > FL2FXCONST_DBL(0.0f)) {
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ret = FL2FXCONST_DBL(+M_PI / 2 / AT2O_SCALE);
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} else if (y < FL2FXCONST_DBL(0.0f)) {
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ret = FL2FXCONST_DBL(-M_PI / 2 / AT2O_SCALE);
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} else if (y == FL2FXCONST_DBL(0.0f)) {
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ret = FL2FXCONST_DBL(0.0f);
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}
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}
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return ret;
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}
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FIXP_DBL fixp_atan(FIXP_DBL x) {
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INT sign;
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FIXP_DBL result, temp;
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/* SNR of fixp_atan() = 56 dB */
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FIXP_DBL P281 = (FIXP_DBL)0x00013000; // 0.281 in q18
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FIXP_DBL ONEP571 = (FIXP_DBL)0x6487ef00; // 1.571 in q30
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if (x < FIXP_DBL(0)) {
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sign = 1;
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x = -x;
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} else {
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sign = 0;
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}
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FDK_ASSERT(FL2FXCONST_DBL(1.0 / 64.0) == Q(Q_ATANINP));
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/* calc of arctan */
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if (x < FL2FXCONST_DBL(1.0 / 64.0))
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/*
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Chebyshev polynomial approximation of atan(x)
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5th-order approximation: atan(x) = a1*x + a2*x^3 + a3*x^5 = x(a1 + x^2*(a2 +
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a3*x^2)); a1 = 0.9949493661166540f, a2 = 0.2870606355326520f, a3 =
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0.0780371764464410f; 7th-order approximation: atan(x) = a1*x + a2*x^3 +
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a3*x^5 + a3*x^7 = x(a1 + x^2*(a2 + x^2*(a3 + a4*x^2))); a1 =
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0.9991334482227801, a2 = -0.3205332923816640, a3 = 0.1449824901444650, a4 =
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-0.0382544649702990; 7th-order approximation in use (the most accurate
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solution)
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*/
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{
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x <<= ATI_SF;
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FIXP_DBL x2 = fPow2(x);
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temp = fMultAddDiv2((FL2FXCONST_DBL(0.1449824901444650f) >> 1), x2,
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FL2FXCONST_DBL(-0.0382544649702990));
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temp = fMultAddDiv2((FL2FXCONST_DBL(-0.3205332923816640f) >> 2), x2, temp);
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temp = fMultAddDiv2((FL2FXCONST_DBL(0.9991334482227801f) >> 3), x2, temp);
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result = fMult(x, (temp << 2));
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} else if (x < FL2FXCONST_DBL(1.28 / 64.0)) {
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FIXP_DBL delta_fix;
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FIXP_DBL PI_BY_4 = FL2FXCONST_DBL(3.1415926 / 4.0) >> 1; /* pi/4 in q30 */
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delta_fix = (x - FL2FXCONST_DBL(1.0 / 64.0)) << 5; /* q30 */
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result = PI_BY_4 + (delta_fix >> 1) - (fPow2Div2(delta_fix));
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} else {
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/* Other approximation for |x| > 1.28 */
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INT res_e;
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temp = fPow2Div2(x); /* q25 * q25 - (DFRACT_BITS-1) - 1 = q18 */
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temp = temp + P281; /* q18 + q18 = q18 */
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result = fDivNorm(x, temp, &res_e);
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result = scaleValue(result,
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(Q_ATANOUT - Q_ATANINP + 18 - DFRACT_BITS + 1) + res_e);
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result = ONEP571 - result; /* q30 + q30 = q30 */
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}
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if (sign) {
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result = -result;
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}
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return (result);
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}
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#include "FDK_tools_rom.h"
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FIXP_DBL fixp_cos(FIXP_DBL x, int scale) {
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FIXP_DBL residual, error, sine, cosine;
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residual = fixp_sin_cos_residual_inline(x, scale, &sine, &cosine);
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error = fMult(sine, residual);
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#ifdef SINETABLE_16BIT
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return cosine - error;
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#else
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/* Undo downscaling by 1 which was done at fixp_sin_cos_residual_inline */
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return SATURATE_LEFT_SHIFT(cosine - error, 1, DFRACT_BITS);
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#endif
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}
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FIXP_DBL fixp_sin(FIXP_DBL x, int scale) {
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FIXP_DBL residual, error, sine, cosine;
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residual = fixp_sin_cos_residual_inline(x, scale, &sine, &cosine);
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error = fMult(cosine, residual);
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#ifdef SINETABLE_16BIT
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return sine + error;
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#else
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return SATURATE_LEFT_SHIFT(sine + error, 1, DFRACT_BITS);
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#endif
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}
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void fixp_cos_sin(FIXP_DBL x, int scale, FIXP_DBL *cos, FIXP_DBL *sin) {
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FIXP_DBL residual, error0, error1, sine, cosine;
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residual = fixp_sin_cos_residual_inline(x, scale, &sine, &cosine);
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error0 = fMult(sine, residual);
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error1 = fMult(cosine, residual);
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#ifdef SINETABLE_16BIT
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*cos = cosine - error0;
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*sin = sine + error1;
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#else
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*cos = SATURATE_LEFT_SHIFT(cosine - error0, 1, DFRACT_BITS);
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*sin = SATURATE_LEFT_SHIFT(sine + error1, 1, DFRACT_BITS);
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#endif
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}
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