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+/* -----------------------------------------------------------------------------
+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
+}