/* ----------------------------------------------------------------------
* Copyright (C) 2010-2013 ARM Limited. All rights reserved.
*
* $Date: 17. January 2013
* $Revision: V1.4.1
*
* 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
*
* Redistribution and use in source and binary forms, with or without
* modification, are permitted provided that the following conditions
* are met:
* - Redistributions of source code must retain the above copyright
* 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
* LIMITED TO, THE IMPLIED WARRANTIES OF MERCHANTABILITY AND FITNESS
* 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;
* LOSS OF USE, DATA, OR PROFITS; OR BUSINESS INTERRUPTION) HOWEVER
* CAUSED AND ON ANY THEORY OF LIABILITY, WHETHER IN CONTRACT, STRICT
* LIABILITY, OR TORT (INCLUDING NEGLIGENCE OR OTHERWISE) ARISING IN
* ANY WAY OUT OF THE USE OF THIS SOFTWARE, EVEN IF ADVISED OF THE
* POSSIBILITY OF SUCH DAMAGE.
* -------------------------------------------------------------------- */
#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 +0.9999] mapping to [0 2*pi). The fixed-point range is chosen so that a
* value of 2*pi wraps around to 0.
*
* 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 a*wa + b*wb + c*wc + d*wd
*
* where
*
* a=Table[index-1];
* b=Table[index+0];
* c=Table[index+1];
* d=Table[index+2];
*
* and
*
* 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;
*
*/
/**
* @addtogroup cos
* @{
*/
/**
* \par
* Example code for Generation of Cos Table:
*
* tableSize = 256;
* for(n = -1; n < (tableSize + 2); n++)
* {
* cosTable[n+1]= cos(2*pi*n/tableSize);
* }
* where pi value is 3.14159265358979
*/
static const float32_t cosTable[260] = {
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,
0.998795449733734130f
};
/**
* @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;
int32_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;
float32_t fractsq, fractby2, fractby6, fractby3, fractsqby2;
float32_t oneminusfractby2;
float32_t frby2xfrsq, frby6xfrsq;
/* 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;
/* Checking min and max index of table */
if(index < 0)
{
index = 0;
}
else if(index > 256)
{
index = 256;
}
/* Initialise table pointer */
tablePtr = (float32_t *) & cosTable[index];
/* Read four nearest values of input value from the cos table */
a = tablePtr[0];
b = tablePtr[1];
c = tablePtr[2];
d = tablePtr[3];
/* Cubic interpolation process */
fractsq = fract * fract;
fractby2 = fract * 0.5f;
fractby6 = fract * 0.166666667f;
fractby3 = fract * 0.3333333333333f;
fractsqby2 = fractsq * 0.5f;
frby2xfrsq = (fractby2) * fractsq;
frby6xfrsq = (fractby6) * fractsq;
oneminusfractby2 = 1.0f - fractby2;
wb = fractsqby2 - fractby3;
wc = (fractsqby2 + fract);
wa = wb - frby6xfrsq;
wb = frby2xfrsq - fractsq;
cosVal = wa * a;
wc = wc - frby2xfrsq;
wd = (frby6xfrsq) - fractby6;
wb = wb + oneminusfractby2;
/* Calculate cos value */
cosVal = (cosVal + (b * wb)) + ((c * wc) + (d * wd));
/* Return the output value */
return (cosVal);
}
/**
* @} end of cos group
*/