File content as of revision 0:1014af42efd9:

/* ----------------------------------------------------------------------  
* Copyright (C) 2010 ARM Limited. All rights reserved.  
*  
* $Date:        29. November 2010  
* $Revision: 	V1.0.3  
*  
* Project: 	    CMSIS DSP Library  
* Title:		arm_cos_f32.c  
*  
* Description:	Fast cosine calculation for floating-point values. 
*  
* Target Processor: Cortex-M4/Cortex-M3
*  
* 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  
 */