hardware/arduino/sam/system/CMSIS/CMSIS/DSP_Lib/Source/FastMathFunctions/arm_cos_f32.c

/* ----------------------------------------------------------------------   
* Copyright (C) 2010 ARM Limited. All rights reserved.   
*   
* $Date:        15. July 2011  
* $Revision: 	V1.0.10  
*   
* Project: 	    CMSIS DSP Library   
* Title:		arm_cos_f32.c   
*   
* Description:	Fast cosine calculation for floating-point values.  
*   
* Target Processor: Cortex-M4/Cortex-M3/Cortex-M0
*  
* 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   
 */

/**   
 * @defgroup cos Cosine   
 *   
 * Computes the trigonometric cosine function using a combination of table lookup  
 * and cubic interpolation.  There are separate functions for  
 * Q15, Q31, and floating-point data types.  
 * The input to the floating-point version is in radians while the  
 * fixed-point Q15 and Q31 have a scaled input with the range  
 * [0 1) mapping to [0 2*pi).  
 *  
 * The implementation is based on table lookup using 256 values together with cubic interpolation.  
 * The steps used are:  
 *  -# Calculation of the nearest integer table index  
 *  -# Fetch the four table values a, b, c, and d    
 *  -# Compute the fractional portion (fract) of the table index.  
 *  -# Calculation of wa, wb, wc, wd   
 *  -# The final result equals <code>a*wa + b*wb + c*wc + d*wd</code>  
 *  
 * where  
 * <pre>   
 *    a=Table[index-1];   
 *    b=Table[index+0];   
 *    c=Table[index+1];   
 *    d=Table[index+2];   
 * </pre>  
 * and  
 * <pre>   
 *    wa=-(1/6)*fract.^3 + (1/2)*fract.^2 - (1/3)*fract;   
 *    wb=(1/2)*fract.^3 - fract.^2 - (1/2)*fract + 1;   
 *    wc=-(1/2)*fract.^3+(1/2)*fract.^2+fract;   
 *    wd=(1/6)*fract.^3 - (1/6)*fract;   
 * </pre>   
 */

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


/**   
* \par   
* <b>Example code for Generation of Cos Table:</b>  
* tableSize = 256;   
* <pre>for(n = -1; n < (tableSize + 1); n++)   
* {   
*	cosTable[n+1]= cos(2*pi*n/tableSize);   
* } </pre>   
* where pi value is  3.14159265358979   
*/

static const float32_t cosTable[259] = {
  0.999698817729949950f, 1.000000000000000000f, 0.999698817729949950f,
  0.998795449733734130f, 0.997290432453155520f, 0.995184719562530520f,
  0.992479562759399410f, 0.989176511764526370f,
  0.985277652740478520f, 0.980785250663757320f, 0.975702106952667240f,
  0.970031261444091800f, 0.963776051998138430f, 0.956940352916717530f,
  0.949528157711029050f, 0.941544055938720700f,
  0.932992815971374510f, 0.923879504203796390f, 0.914209783077239990f,
  0.903989315032958980f, 0.893224298954010010f, 0.881921291351318360f,
  0.870086967945098880f, 0.857728600502014160f,
  0.844853579998016360f, 0.831469595432281490f, 0.817584812641143800f,
  0.803207516670227050f, 0.788346409797668460f, 0.773010432720184330f,
  0.757208824157714840f, 0.740951120853424070f,
  0.724247097969055180f, 0.707106769084930420f, 0.689540565013885500f,
  0.671558976173400880f, 0.653172850608825680f, 0.634393274784088130f,
  0.615231573581695560f, 0.595699310302734380f,
  0.575808167457580570f, 0.555570244789123540f, 0.534997642040252690f,
  0.514102756977081300f, 0.492898195981979370f, 0.471396744251251220f,
  0.449611335992813110f, 0.427555084228515630f,
  0.405241310596466060f, 0.382683426141738890f, 0.359895050525665280f,
  0.336889863014221190f, 0.313681751489639280f, 0.290284663438797000f,
  0.266712754964828490f, 0.242980182170867920f,
  0.219101235270500180f, 0.195090323686599730f, 0.170961886644363400f,
  0.146730467677116390f, 0.122410677373409270f, 0.098017141222953796f,
  0.073564566671848297f, 0.049067676067352295f,
  0.024541229009628296f, 0.000000000000000061f, -0.024541229009628296f,
  -0.049067676067352295f, -0.073564566671848297f, -0.098017141222953796f,
  -0.122410677373409270f, -0.146730467677116390f,
  -0.170961886644363400f, -0.195090323686599730f, -0.219101235270500180f,
  -0.242980182170867920f, -0.266712754964828490f, -0.290284663438797000f,
  -0.313681751489639280f, -0.336889863014221190f,
  -0.359895050525665280f, -0.382683426141738890f, -0.405241310596466060f,
  -0.427555084228515630f, -0.449611335992813110f, -0.471396744251251220f,
  -0.492898195981979370f, -0.514102756977081300f,
  -0.534997642040252690f, -0.555570244789123540f, -0.575808167457580570f,
  -0.595699310302734380f, -0.615231573581695560f, -0.634393274784088130f,
  -0.653172850608825680f, -0.671558976173400880f,
  -0.689540565013885500f, -0.707106769084930420f, -0.724247097969055180f,
  -0.740951120853424070f, -0.757208824157714840f, -0.773010432720184330f,
  -0.788346409797668460f, -0.803207516670227050f,
  -0.817584812641143800f, -0.831469595432281490f, -0.844853579998016360f,
  -0.857728600502014160f, -0.870086967945098880f, -0.881921291351318360f,
  -0.893224298954010010f, -0.903989315032958980f,
  -0.914209783077239990f, -0.923879504203796390f, -0.932992815971374510f,
  -0.941544055938720700f, -0.949528157711029050f, -0.956940352916717530f,
  -0.963776051998138430f, -0.970031261444091800f,
  -0.975702106952667240f, -0.980785250663757320f, -0.985277652740478520f,
  -0.989176511764526370f, -0.992479562759399410f, -0.995184719562530520f,
  -0.997290432453155520f, -0.998795449733734130f,
  -0.999698817729949950f, -1.000000000000000000f, -0.999698817729949950f,
  -0.998795449733734130f, -0.997290432453155520f, -0.995184719562530520f,
  -0.992479562759399410f, -0.989176511764526370f,
  -0.985277652740478520f, -0.980785250663757320f, -0.975702106952667240f,
  -0.970031261444091800f, -0.963776051998138430f, -0.956940352916717530f,
  -0.949528157711029050f, -0.941544055938720700f,
  -0.932992815971374510f, -0.923879504203796390f, -0.914209783077239990f,
  -0.903989315032958980f, -0.893224298954010010f, -0.881921291351318360f,
  -0.870086967945098880f, -0.857728600502014160f,
  -0.844853579998016360f, -0.831469595432281490f, -0.817584812641143800f,
  -0.803207516670227050f, -0.788346409797668460f, -0.773010432720184330f,
  -0.757208824157714840f, -0.740951120853424070f,
  -0.724247097969055180f, -0.707106769084930420f, -0.689540565013885500f,
  -0.671558976173400880f, -0.653172850608825680f, -0.634393274784088130f,
  -0.615231573581695560f, -0.595699310302734380f,
  -0.575808167457580570f, -0.555570244789123540f, -0.534997642040252690f,
  -0.514102756977081300f, -0.492898195981979370f, -0.471396744251251220f,
  -0.449611335992813110f, -0.427555084228515630f,
  -0.405241310596466060f, -0.382683426141738890f, -0.359895050525665280f,
  -0.336889863014221190f, -0.313681751489639280f, -0.290284663438797000f,
  -0.266712754964828490f, -0.242980182170867920f,
  -0.219101235270500180f, -0.195090323686599730f, -0.170961886644363400f,
  -0.146730467677116390f, -0.122410677373409270f, -0.098017141222953796f,
  -0.073564566671848297f, -0.049067676067352295f,
  -0.024541229009628296f, -0.000000000000000184f, 0.024541229009628296f,
  0.049067676067352295f, 0.073564566671848297f, 0.098017141222953796f,
  0.122410677373409270f, 0.146730467677116390f,
  0.170961886644363400f, 0.195090323686599730f, 0.219101235270500180f,
  0.242980182170867920f, 0.266712754964828490f, 0.290284663438797000f,
  0.313681751489639280f, 0.336889863014221190f,
  0.359895050525665280f, 0.382683426141738890f, 0.405241310596466060f,
  0.427555084228515630f, 0.449611335992813110f, 0.471396744251251220f,
  0.492898195981979370f, 0.514102756977081300f,
  0.534997642040252690f, 0.555570244789123540f, 0.575808167457580570f,
  0.595699310302734380f, 0.615231573581695560f, 0.634393274784088130f,
  0.653172850608825680f, 0.671558976173400880f,
  0.689540565013885500f, 0.707106769084930420f, 0.724247097969055180f,
  0.740951120853424070f, 0.757208824157714840f, 0.773010432720184330f,
  0.788346409797668460f, 0.803207516670227050f,
  0.817584812641143800f, 0.831469595432281490f, 0.844853579998016360f,
  0.857728600502014160f, 0.870086967945098880f, 0.881921291351318360f,
  0.893224298954010010f, 0.903989315032958980f,
  0.914209783077239990f, 0.923879504203796390f, 0.932992815971374510f,
  0.941544055938720700f, 0.949528157711029050f, 0.956940352916717530f,
  0.963776051998138430f, 0.970031261444091800f,
  0.975702106952667240f, 0.980785250663757320f, 0.985277652740478520f,
  0.989176511764526370f, 0.992479562759399410f, 0.995184719562530520f,
  0.997290432453155520f, 0.998795449733734130f,
  0.999698817729949950f, 1.000000000000000000f, 0.999698817729949950f
};

/**  
 * @brief  Fast approximation to the trigonometric cosine function for floating-point data.  
 * @param[in] x input value in radians.  
 * @return cos(x).  
 */

float32_t arm_cos_f32(
  float32_t x)
{
  float32_t cosVal, fract, in;
  uint32_t index;
  uint32_t tableSize = (uint32_t) TABLE_SIZE;
  float32_t wa, wb, wc, wd;
  float32_t a, b, c, d;
  float32_t *tablePtr;
  int32_t n;

  /* input x is in radians */
  /* Scale the input to [0 1] range from [0 2*PI] , divide input by 2*pi */
  in = x * 0.159154943092f;

  /* Calculation of floor value of input */
  n = (int32_t) in;

  /* Make negative values towards -infinity */
  if(x < 0.0f)
  {
    n = n - 1;
  }

  /* Map input value to [0 1] */
  in = in - (float32_t) n;

  /* Calculation of index of the table */
  index = (uint32_t) (tableSize * in);

  /* fractional value calculation */
  fract = ((float32_t) tableSize * in) - (float32_t) index;

  /* Initialise table pointer */
  tablePtr = (float32_t *) & cosTable[index];

  /* Read four nearest values of input value from the cos table */
  a = *tablePtr++;
  b = *tablePtr++;
  c = *tablePtr++;
  d = *tablePtr++;

  /* Cubic interpolation process */
  wa = -(((0.166666667f) * fract) * (fract * fract)) +
    (((0.5f) * (fract * fract)) - ((0.3333333333333f) * fract));
  wb = ((((0.5f) * fract) * (fract * fract)) - (fract * fract)) +
    (-((0.5f) * fract) + 1.0f);
  wc = -(((0.5f) * fract) * (fract * fract)) +
    (((0.5f) * (fract * fract)) + fract);
  wd = (((0.166666667f) * fract) * (fract * fract)) -
    ((0.166666667f) * fract);

  /* Calculate cos value */
  cosVal = ((a * wa) + (b * wb)) + ((c * wc) + (d * wd));

  /* Return the output value */
  return (cosVal);

}

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