File content as of revision 2:da51fb522205:

/* ----------------------------------------------------------------------    
* Copyright (C) 2010 ARM Limited. All rights reserved.    
*    
* $Date:        15. February 2012  
* $Revision: 	V1.1.0  
*    
* Project: 	    CMSIS DSP Library    
* Title:		arm_sin_q15.c    
*    
* Description:	Fast sine calculation for Q15 values.   
*    
* Target Processor: Cortex-M4/Cortex-M3/Cortex-M0
*  
* Version 1.1.0 2012/02/15 
*    Updated with more optimizations, bug fixes and minor API changes.  
*   
* Version 1.0.10 2011/7/15  
*    Big Endian support added and Merged M0 and M3/M4 Source code.   
*    
* Version 1.0.3 2010/11/29   
*    Re-organized the CMSIS folders and updated documentation.    
*     
* Version 1.0.2 2010/11/11    
*    Documentation updated.     
*    
* Version 1.0.1 2010/10/05     
*    Production release and review comments incorporated.    
*    
* Version 1.0.0 2010/09/20     
*    Production release and review comments incorporated.    
* -------------------------------------------------------------------- */

#include "arm_math.h"

/**    
 * @ingroup groupFastMath    
 */

 /**    
 * @addtogroup sin    
 * @{    
 */


/**    
 * \par    
 * Example code for Generation of Q15 Sin Table:   
 * \par    
 * <pre>tableSize = 256;    
 * for(n = -1; n < (tableSize + 1); n++)    
 * {    
 *	sinTable[n+1]=sin(2*pi*n/tableSize);    
 * } </pre>    
 * where pi value is  3.14159265358979    
 * \par    
 * Convert Floating point to Q15(Fixed point):    
 *	(sinTable[i] * pow(2, 15))    
 * \par    
 * rounding to nearest integer is done    
 * 	sinTable[i] += (sinTable[i] > 0 ? 0.5 :-0.5);    
 */


static const q15_t sinTableQ15[259] = {
  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, 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
};


/**   
 * @brief Fast approximation to the trigonometric sine function for Q15 data.   
 * @param[in] x Scaled input value in radians.   
 * @return  sin(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), Here range excludes 2*pi.   
 */

q15_t arm_sin_q15(
  q15_t x)
{
  q31_t sinVal;                                  /* Temporary variables output */
  q15_t *tablePtr;                               /* Pointer to table */
  q15_t fract, in, in2;                          /* Temporary variables for input, output */
  q31_t wa, wb, wc, wd;                          /* Cubic interpolation coefficients */
  q15_t a, b, c, d;                              /* Four nearest output values */
  q15_t fractCube, fractSquare;                  /* Temporary values 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 *) & sinTableQ15[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 += ((q31_t) fractSquare >> 1u);

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

  /* sinVal = a * wa */
  sinVal = a * wa;

  /* Calculation of wb */
  wb = (((q31_t) fractCube >> 1u) - (q31_t) fractSquare) -
    (((q31_t) fract >> 1u) - 0x7FFF);

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

  /*      sinVal += b*wb */
  sinVal += b * wb;


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

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

  /* sinVal += c*wc */
  sinVal += 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 sin table */
  d = *tablePtr++;

  /* sinVal += d*wd; */
  sinVal += d * wd;

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

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

}

/**    
 * @} end of sin group    
 */