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/* ----------------------------------------------------------------------    
* Copyright (C) 2010-2013 ARM Limited. All rights reserved.    
*    
* $Date:        17. January 2013
* $Revision: 	V1.4.1
*    
* Project: 	    CMSIS DSP Library    
* Title:		arm_cos_q15.c    
*    
* Description:	Fast cosine calculation for Q15 values.   
*    
* Target Processor: Cortex-M4/Cortex-M3/Cortex-M0
*  
* Redistribution and use in source and binary forms, with or without 
* modification, are permitted provided that the following conditions
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*     notice, this list of conditions and the following disclaimer.
*   - Redistributions in binary form must reproduce the above copyright
*     notice, this list of conditions and the following disclaimer in
*     the documentation and/or other materials provided with the 
*     distribution.
*   - Neither the name of ARM LIMITED nor the names of its contributors
*     may be used to endorse or promote products derived from this
*     software without specific prior written permission.
*
* THIS SOFTWARE IS PROVIDED BY THE COPYRIGHT HOLDERS AND CONTRIBUTORS
* "AS IS" AND ANY EXPRESS OR IMPLIED WARRANTIES, INCLUDING, BUT NOT
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* FOR A PARTICULAR PURPOSE ARE DISCLAIMED. IN NO EVENT SHALL THE 
* COPYRIGHT OWNER 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;
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* -------------------------------------------------------------------- */

#include "arm_math.h"

/**    
 * @ingroup groupFastMath    
 */

 /**    
 * @addtogroup cos    
 * @{    
 */

/**   
* \par    
 * Table values are in Q15 (1.15 fixed-point format) and generation is done in 
 * three steps.  First,  generate cos values in floating point:    
 * <pre>
 * tableSize = 256;
 * for(n = -1; n < (tableSize + 1); n++)    
 * {    
 *	cosTable[n+1]= cos(2*pi*n/tableSize);    
 * } </pre>     
 * where pi value is  3.14159265358979    
 * \par    
 * Second, convert floating-point to Q15 (fixed-point):    
 *	(cosTable[i] * pow(2, 15))    
 * \par    
 * Finally, round to the nearest integer value:
 * 	cosTable[i] += (cosTable[i] > 0 ? 0.5 :-0.5);    
*/

static const q15_t cosTableQ15[259] = {
  0x7ff6, 0x7fff, 0x7ff6, 0x7fd9, 0x7fa7, 0x7f62, 0x7f0a, 0x7e9d,
  0x7e1e, 0x7d8a, 0x7ce4, 0x7c2a, 0x7b5d, 0x7a7d, 0x798a, 0x7885,
  0x776c, 0x7642, 0x7505, 0x73b6, 0x7255, 0x70e3, 0x6f5f, 0x6dca,
  0x6c24, 0x6a6e, 0x68a7, 0x66d0, 0x64e9, 0x62f2, 0x60ec, 0x5ed7,
  0x5cb4, 0x5a82, 0x5843, 0x55f6, 0x539b, 0x5134, 0x4ec0, 0x4c40,
  0x49b4, 0x471d, 0x447b, 0x41ce, 0x3f17, 0x3c57, 0x398d, 0x36ba,
  0x33df, 0x30fc, 0x2e11, 0x2b1f, 0x2827, 0x2528, 0x2224, 0x1f1a,
  0x1c0c, 0x18f9, 0x15e2, 0x12c8, 0xfab, 0xc8c, 0x96b, 0x648,
  0x324, 0x0, 0xfcdc, 0xf9b8, 0xf695, 0xf374, 0xf055, 0xed38,
  0xea1e, 0xe707, 0xe3f4, 0xe0e6, 0xdddc, 0xdad8, 0xd7d9, 0xd4e1,
  0xd1ef, 0xcf04, 0xcc21, 0xc946, 0xc673, 0xc3a9, 0xc0e9, 0xbe32,
  0xbb85, 0xb8e3, 0xb64c, 0xb3c0, 0xb140, 0xaecc, 0xac65, 0xaa0a,
  0xa7bd, 0xa57e, 0xa34c, 0xa129, 0x9f14, 0x9d0e, 0x9b17, 0x9930,
  0x9759, 0x9592, 0x93dc, 0x9236, 0x90a1, 0x8f1d, 0x8dab, 0x8c4a,
  0x8afb, 0x89be, 0x8894, 0x877b, 0x8676, 0x8583, 0x84a3, 0x83d6,
  0x831c, 0x8276, 0x81e2, 0x8163, 0x80f6, 0x809e, 0x8059, 0x8027,
  0x800a, 0x8000, 0x800a, 0x8027, 0x8059, 0x809e, 0x80f6, 0x8163,
  0x81e2, 0x8276, 0x831c, 0x83d6, 0x84a3, 0x8583, 0x8676, 0x877b,
  0x8894, 0x89be, 0x8afb, 0x8c4a, 0x8dab, 0x8f1d, 0x90a1, 0x9236,
  0x93dc, 0x9592, 0x9759, 0x9930, 0x9b17, 0x9d0e, 0x9f14, 0xa129,
  0xa34c, 0xa57e, 0xa7bd, 0xaa0a, 0xac65, 0xaecc, 0xb140, 0xb3c0,
  0xb64c, 0xb8e3, 0xbb85, 0xbe32, 0xc0e9, 0xc3a9, 0xc673, 0xc946,
  0xcc21, 0xcf04, 0xd1ef, 0xd4e1, 0xd7d9, 0xdad8, 0xdddc, 0xe0e6,
  0xe3f4, 0xe707, 0xea1e, 0xed38, 0xf055, 0xf374, 0xf695, 0xf9b8,
  0xfcdc, 0x0, 0x324, 0x648, 0x96b, 0xc8c, 0xfab, 0x12c8,
  0x15e2, 0x18f9, 0x1c0c, 0x1f1a, 0x2224, 0x2528, 0x2827, 0x2b1f,
  0x2e11, 0x30fc, 0x33df, 0x36ba, 0x398d, 0x3c57, 0x3f17, 0x41ce,
  0x447b, 0x471d, 0x49b4, 0x4c40, 0x4ec0, 0x5134, 0x539b, 0x55f6,
  0x5843, 0x5a82, 0x5cb4, 0x5ed7, 0x60ec, 0x62f2, 0x64e9, 0x66d0,
  0x68a7, 0x6a6e, 0x6c24, 0x6dca, 0x6f5f, 0x70e3, 0x7255, 0x73b6,
  0x7505, 0x7642, 0x776c, 0x7885, 0x798a, 0x7a7d, 0x7b5d, 0x7c2a,
  0x7ce4, 0x7d8a, 0x7e1e, 0x7e9d, 0x7f0a, 0x7f62, 0x7fa7, 0x7fd9,
  0x7ff6, 0x7fff, 0x7ff6
};


/**   
 * @brief Fast approximation to the trigonometric cosine function for Q15 data.   
 * @param[in] x Scaled input value in radians.   
 * @return  cos(x).   
 *   
 * The Q15 input value is in the range [0 +0.9999] and is mapped to a radian
 * value in the range [0 2*pi).
 */

q15_t arm_cos_q15(
  q15_t x)
{
  q31_t cosVal;                                  /* Temporary variable for output */
  q15_t *tablePtr;                               /* Pointer to table */
  q15_t in, in2;                                 /* Temporary variables for input */
  q31_t wa, wb, wc, wd;                          /* Cubic interpolation coefficients */
  q15_t a, b, c, d;                              /* Four nearest output values */
  q15_t fract, fractCube, fractSquare;           /* Variables for fractional value */
  q15_t oneBy6 = 0x1555;                         /* Fixed point value of 1/6 */
  q15_t tableSpacing = TABLE_SPACING_Q15;        /* Table spacing */
  int32_t index;                                 /* Index variable */

  in = x;

  /* Calculate the nearest index */
  index = (int32_t) in / tableSpacing;

  /* Calculate the nearest value of input */
  in2 = (q15_t) index *tableSpacing;

  /* Calculation of fractional value */
  fract = (in - in2) << 8;

  /* fractSquare = fract * fract */
  fractSquare = (q15_t) ((fract * fract) >> 15);

  /* fractCube = fract * fract * fract */
  fractCube = (q15_t) ((fractSquare * fract) >> 15);

  /* Checking min and max index of table */
  if(index < 0)
  {
    index = 0;
  }
  else if(index > 256)
  {
    index = 256;
  }

  /* Initialise table pointer */
  tablePtr = (q15_t *) & cosTableQ15[index];

  /* Cubic interpolation process */
  /* Calculation of wa */
  /* wa = -(oneBy6)*fractCube + (fractSquare >> 1u) - (0x2AAA)*fract; */
  wa = (q31_t) oneBy6 *fractCube;
  wa += (q31_t) 0x2AAA *fract;
  wa = -(wa >> 15);
  wa += (fractSquare >> 1u);

  /* Read first nearest value of output from the cos table */
  a = *tablePtr++;

  /* cosVal = a * wa */
  cosVal = a * wa;

  /* Calculation of wb */
  wb = (((fractCube >> 1u) - fractSquare) - (fract >> 1u)) + 0x7FFF;

  /* Read second nearest value of output from the cos table */
  b = *tablePtr++;

  /*      cosVal += b*wb */
  cosVal += b * wb;

  /* Calculation of wc */
  wc = -(q31_t) fractCube + fractSquare;
  wc = (wc >> 1u) + fract;

  /* Read third nearest value of output from the cos table */
  c = *tablePtr++;

  /* cosVal += c*wc */
  cosVal += c * wc;

  /* Calculation of wd */
  /* wd = (oneBy6)*fractCube - (oneBy6)*fract; */
  fractCube = fractCube - fract;
  wd = ((q15_t) (((q31_t) oneBy6 * fractCube) >> 15));

  /* Read fourth nearest value of output from the cos table */
  d = *tablePtr++;

  /* cosVal += d*wd; */
  cosVal += d * wd;

  /* Convert output value in 1.15(q15) format and saturate */
  cosVal = __SSAT((cosVal >> 15), 16);

  /* Return the output value in 1.15(q15) format */
  return ((q15_t) cosVal);

}

/**    
 * @} end of cos group    
 */