/* ----------------------------------------------------------------------  
* Copyright (C) 2010 ARM Limited. All rights reserved.  
*  
* $Date:        29. November 2010  
* $Revision: 	V1.0.3  
*  
* Project: 	    CMSIS DSP Library  
* Title:		arm_cos_q31.c  
*  
* Description:	Fast cosine calculation for Q31 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  
 */ 
 
 /**  
 * @addtogroup cos  
 * @{  
 */ 
 
/**  
 * \par  
 * Table Values are in Q31(1.31 Fixed point format) and generation is done in three steps  
 * First Generate cos values in floating point:  
 * 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  
 * \par  
 * Secondly Convert Floating point to Q31(Fixed point):  
 *	(cosTable[i] * pow(2, 31))  
 * \par  
 * Finally Rounding to nearest integer is done  
 * 	cosTable[i] += (cosTable[i] > 0 ? 0.5 :-0.5);  
 */ 
 
 
static const q31_t cosTableQ31[259] = { 
  0x7ff62182, 0x7fffffff, 0x7ff62182, 0x7fd8878e, 0x7fa736b4, 0x7f62368f, 
    0x7f0991c4, 0x7e9d55fc, 
  0x7e1d93ea, 0x7d8a5f40, 0x7ce3ceb2, 0x7c29fbee, 0x7b5d039e, 0x7a7d055b, 
    0x798a23b1, 0x78848414, 
  0x776c4edb, 0x7641af3d, 0x7504d345, 0x73b5ebd1, 0x72552c85, 0x70e2cbc6, 
    0x6f5f02b2, 0x6dca0d14, 
  0x6c242960, 0x6a6d98a4, 0x68a69e81, 0x66cf8120, 0x64e88926, 0x62f201ac, 
    0x60ec3830, 0x5ed77c8a, 
  0x5cb420e0, 0x5a82799a, 0x5842dd54, 0x55f5a4d2, 0x539b2af0, 0x5133cc94, 
    0x4ebfe8a5, 0x4c3fdff4, 
  0x49b41533, 0x471cece7, 0x447acd50, 0x41ce1e65, 0x3f1749b8, 0x3c56ba70, 
    0x398cdd32, 0x36ba2014, 
  0x33def287, 0x30fbc54d, 0x2e110a62, 0x2b1f34eb, 0x2826b928, 0x25280c5e, 
    0x2223a4c5, 0x1f19f97b, 
  0x1c0b826a, 0x18f8b83c, 0x15e21445, 0x12c8106f, 0xfab272b, 0xc8bd35e, 
    0x96a9049, 0x647d97c, 
  0x3242abf, 0x0, 0xfcdbd541, 0xf9b82684, 0xf6956fb7, 0xf3742ca2, 0xf054d8d5, 
    0xed37ef91, 
  0xea1debbb, 0xe70747c4, 0xe3f47d96, 0xe0e60685, 0xdddc5b3b, 0xdad7f3a2, 
    0xd7d946d8, 0xd4e0cb15, 
  0xd1eef59e, 0xcf043ab3, 0xcc210d79, 0xc945dfec, 0xc67322ce, 0xc3a94590, 
    0xc0e8b648, 0xbe31e19b, 
  0xbb8532b0, 0xb8e31319, 0xb64beacd, 0xb3c0200c, 0xb140175b, 0xaecc336c, 
    0xac64d510, 0xaa0a5b2e, 
  0xa7bd22ac, 0xa57d8666, 0xa34bdf20, 0xa1288376, 0x9f13c7d0, 0x9d0dfe54, 
    0x9b1776da, 0x99307ee0, 
  0x9759617f, 0x9592675c, 0x93dbd6a0, 0x9235f2ec, 0x90a0fd4e, 0x8f1d343a, 
    0x8daad37b, 0x8c4a142f, 
  0x8afb2cbb, 0x89be50c3, 0x8893b125, 0x877b7bec, 0x8675dc4f, 0x8582faa5, 
    0x84a2fc62, 0x83d60412, 
  0x831c314e, 0x8275a0c0, 0x81e26c16, 0x8162aa04, 0x80f66e3c, 0x809dc971, 
    0x8058c94c, 0x80277872, 
  0x8009de7e, 0x80000000, 0x8009de7e, 0x80277872, 0x8058c94c, 0x809dc971, 
    0x80f66e3c, 0x8162aa04, 
  0x81e26c16, 0x8275a0c0, 0x831c314e, 0x83d60412, 0x84a2fc62, 0x8582faa5, 
    0x8675dc4f, 0x877b7bec, 
  0x8893b125, 0x89be50c3, 0x8afb2cbb, 0x8c4a142f, 0x8daad37b, 0x8f1d343a, 
    0x90a0fd4e, 0x9235f2ec, 
  0x93dbd6a0, 0x9592675c, 0x9759617f, 0x99307ee0, 0x9b1776da, 0x9d0dfe54, 
    0x9f13c7d0, 0xa1288376, 
  0xa34bdf20, 0xa57d8666, 0xa7bd22ac, 0xaa0a5b2e, 0xac64d510, 0xaecc336c, 
    0xb140175b, 0xb3c0200c, 
  0xb64beacd, 0xb8e31319, 0xbb8532b0, 0xbe31e19b, 0xc0e8b648, 0xc3a94590, 
    0xc67322ce, 0xc945dfec, 
  0xcc210d79, 0xcf043ab3, 0xd1eef59e, 0xd4e0cb15, 0xd7d946d8, 0xdad7f3a2, 
    0xdddc5b3b, 0xe0e60685, 
  0xe3f47d96, 0xe70747c4, 0xea1debbb, 0xed37ef91, 0xf054d8d5, 0xf3742ca2, 
    0xf6956fb7, 0xf9b82684, 
  0xfcdbd541, 0x0, 0x3242abf, 0x647d97c, 0x96a9049, 0xc8bd35e, 0xfab272b, 
    0x12c8106f, 
  0x15e21445, 0x18f8b83c, 0x1c0b826a, 0x1f19f97b, 0x2223a4c5, 0x25280c5e, 
    0x2826b928, 0x2b1f34eb, 
  0x2e110a62, 0x30fbc54d, 0x33def287, 0x36ba2014, 0x398cdd32, 0x3c56ba70, 
    0x3f1749b8, 0x41ce1e65, 
  0x447acd50, 0x471cece7, 0x49b41533, 0x4c3fdff4, 0x4ebfe8a5, 0x5133cc94, 
    0x539b2af0, 0x55f5a4d2, 
  0x5842dd54, 0x5a82799a, 0x5cb420e0, 0x5ed77c8a, 0x60ec3830, 0x62f201ac, 
    0x64e88926, 0x66cf8120, 
  0x68a69e81, 0x6a6d98a4, 0x6c242960, 0x6dca0d14, 0x6f5f02b2, 0x70e2cbc6, 
    0x72552c85, 0x73b5ebd1, 
  0x7504d345, 0x7641af3d, 0x776c4edb, 0x78848414, 0x798a23b1, 0x7a7d055b, 
    0x7b5d039e, 0x7c29fbee, 
  0x7ce3ceb2, 0x7d8a5f40, 0x7e1d93ea, 0x7e9d55fc, 0x7f0991c4, 0x7f62368f, 
    0x7fa736b4, 0x7fd8878e, 
  0x7ff62182, 0x7fffffff, 0x7ff62182 
}; 
 
/** 
 * @brief Fast approximation to the trigonometric cosine function for Q31 data. 
 * @param[in] x Scaled input value in radians. 
 * @return  cos(x). 
 * 
 * The Q31 input value is in the range [0 +1) and is mapped to a radian value in the range [0 2*pi). 
 */ 
 
q31_t arm_cos_q31( 
  q31_t x) 
{ 
  q31_t cosVal, fract, in, in2;                  /* Temporary variables for input, output */ 
  q31_t wa, wb, wc, wd;                          /* Cubic interpolation coefficients */ 
  q31_t a, b, c, d;                              /* Four nearest output values */ 
  q31_t *tablePtr;                               /* Pointer to table */ 
  q31_t fractCube, fractSquare;                  /* Temporary values for fractional value */ 
  q31_t oneBy6 = 0x15555555;                     /* Fixed point value of 1/6 */ 
  q31_t tableSpacing = TABLE_SPACING_Q31;        /* Table spacing */ 
  q31_t temp;                                    /* Temporary variable for intermediate process */ 
  uint32_t index;                                /* Index variable */ 
 
  in = x; 
 
  /* Calculate the nearest index */ 
  index = in / tableSpacing; 
 
  /* Calculate the nearest value of input */ 
  in2 = ((q31_t) index) * tableSpacing; 
 
  /* Calculation of fractional value */ 
  fract = (in - in2) << 8; 
 
  /* fractSquare = fract * fract */ 
  fractSquare = ((q31_t) (((q63_t) fract * fract) >> 32)); 
  fractSquare = fractSquare << 1; 
 
  /* fractCube = fract * fract * fract */ 
  fractCube = ((q31_t) (((q63_t) fractSquare * fract) >> 32)); 
  fractCube = fractCube << 1; 
 
  /* Initialise table pointer */ 
  tablePtr = (q31_t *) & cosTableQ31[index]; 
 
  /* Cubic interpolation process */ 
  /* Calculation of wa */ 
  /* wa = -(oneBy6)*fractCube + (fractSquare >> 1u) - (0x2AAAAAAA)*fract; */ 
  wa = ((q31_t) (((q63_t) oneBy6 * fractCube) >> 32)); 
  temp = 0x2AAAAAAA; 
  wa = (q31_t) ((((q63_t) wa << 32) + ((q63_t) temp * fract)) >> 32); 
  wa = -(wa << 1u); 
  wa += (fractSquare >> 1u); 
 
  /* Read first nearest value of output from the cos table */ 
  a = *tablePtr++; 
 
  /* cosVal = a*wa */ 
  cosVal = ((q31_t) (((q63_t) a * wa) >> 32)); 
 
  /* q31(1.31) Fixed point value of 1 */ 
  temp = 0x7FFFFFFF; 
 
  /* Calculation of wb */ 
  wb = ((fractCube >> 1u) - (fractSquare + (fract >> 1u))) + temp; 
  /* Read second nearest value of output from the cos table */ 
  b = *tablePtr++; 
 
  /*      cosVal += b*wb */ 
  cosVal = (q31_t) ((((q63_t) cosVal << 32) + ((q63_t) b * (wb))) >> 32); 
 
  /* Calculation of wc */ 
  wc = -fractCube + fractSquare; 
  wc = (wc >> 1u) + fract; 
  /* Read third nearest values of output value from the cos table */ 
  c = *tablePtr++; 
 
  /*      cosVal += c*wc */ 
  cosVal = (q31_t) ((((q63_t) cosVal << 32) + ((q63_t) c * (wc))) >> 32); 
 
  /* Calculation of wd */ 
  /* wd = (oneBy6)*fractCube - (oneBy6)*fract; */ 
  fractCube = fractCube - fract; 
  wd = ((q31_t) (((q63_t) oneBy6 * fractCube) >> 32)); 
  wd = (wd << 1u); 
 
  /* Read fourth nearest value of output from the cos table */ 
  d = *tablePtr++; 
 
  /* cosVal += d*wd; */ 
  cosVal = (q31_t) ((((q63_t) cosVal << 32) + ((q63_t) d * (wd))) >> 32); 
 
  /* convert cosVal in 2.30 format to 1.31 format */ 
  return (cosVal << 1u); 
 
} 
 
/**  
 * @} end of cos group  
 */ 
