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/* ----------------------------------------------------------------------
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* Copyright (C) 2010 ARM Limited. All rights reserved.
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*
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* $Date: 15. July 2011
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* $Revision: V1.0.10
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*
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* Project: CMSIS DSP Library
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* Title: arm_sin_cos_f32.c
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*
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* Description: Sine and Cosine calculation for floating-point values.
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*
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* Target Processor: Cortex-M4/Cortex-M3/Cortex-M0
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*
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* Version 1.0.10 2011/7/15
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* Big Endian support added and Merged M0 and M3/M4 Source code.
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*
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* Version 1.0.3 2010/11/29
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* Re-organized the CMSIS folders and updated documentation.
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*
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* Version 1.0.2 2010/11/11
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* Documentation updated.
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*
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* Version 1.0.1 2010/10/05
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* Production release and review comments incorporated.
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*
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* Version 1.0.0 2010/09/20
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* Production release and review comments incorporated.
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* -------------------------------------------------------------------- */
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#include "arm_math.h"
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/**
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* @ingroup groupController
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*/
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/**
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* @defgroup SinCos Sine Cosine
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*
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* Computes the trigonometric sine and cosine values using a combination of table lookup
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* and linear interpolation.
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* There are separate functions for Q31 and floating-point data types.
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* The input to the floating-point version is in degrees while the
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* fixed-point Q31 have a scaled input with the range
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* [-1 1) mapping to [-180 180) degrees.
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*
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* The implementation is based on table lookup using 360 values together with linear interpolation.
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* The steps used are:
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* -# Calculation of the nearest integer table index.
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* -# Compute the fractional portion (fract) of the input.
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* -# Fetch the value corresponding to \c index from sine table to \c y0 and also value from \c index+1 to \c y1.
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* -# Sine value is computed as <code> *psinVal = y0 + (fract * (y1 - y0))</code>.
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* -# Fetch the value corresponding to \c index from cosine table to \c y0 and also value from \c index+1 to \c y1.
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* -# Cosine value is computed as <code> *pcosVal = y0 + (fract * (y1 - y0))</code>.
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*/
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/**
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* @addtogroup SinCos
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* @{
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*/
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/**
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* \par
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* Cosine Table is generated from following loop
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* <pre>for(i = 0; i < 360; i++)
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* {
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* cosTable[i]= cos((i-180) * PI/180.0);
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* } </pre>
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*/
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static const float32_t cosTable[360] = {
|
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-0.999847695156391270f, -0.999390827019095760f, -0.998629534754573830f,
|
|
|
-0.997564050259824200f, -0.996194698091745550f, -0.994521895368273290f,
|
|
|
-0.992546151641321980f, -0.990268068741570250f,
|
|
|
-0.987688340595137660f, -0.984807753012208020f, -0.981627183447663980f,
|
|
|
-0.978147600733805690f, -0.974370064785235250f, -0.970295726275996470f,
|
|
|
-0.965925826289068200f, -0.961261695938318670f,
|
|
|
-0.956304755963035440f, -0.951056516295153530f, -0.945518575599316740f,
|
|
|
-0.939692620785908320f, -0.933580426497201740f, -0.927183854566787310f,
|
|
|
-0.920504853452440150f, -0.913545457642600760f,
|
|
|
-0.906307787036649940f, -0.898794046299167040f, -0.891006524188367790f,
|
|
|
-0.882947592858926770f, -0.874619707139395740f, -0.866025403784438710f,
|
|
|
-0.857167300702112220f, -0.848048096156425960f,
|
|
|
-0.838670567945424160f, -0.829037572555041620f, -0.819152044288991580f,
|
|
|
-0.809016994374947340f, -0.798635510047292940f, -0.788010753606721900f,
|
|
|
-0.777145961456970680f, -0.766044443118977900f,
|
|
|
-0.754709580222772010f, -0.743144825477394130f, -0.731353701619170460f,
|
|
|
-0.719339800338651300f, -0.707106781186547460f, -0.694658370458997030f,
|
|
|
-0.681998360062498370f, -0.669130606358858240f,
|
|
|
-0.656059028990507500f, -0.642787609686539360f, -0.629320391049837280f,
|
|
|
-0.615661475325658290f, -0.601815023152048380f, -0.587785252292473030f,
|
|
|
-0.573576436351045830f, -0.559192903470746680f,
|
|
|
-0.544639035015027080f, -0.529919264233204790f, -0.515038074910054270f,
|
|
|
-0.499999999999999780f, -0.484809620246337000f, -0.469471562785890530f,
|
|
|
-0.453990499739546750f, -0.438371146789077510f,
|
|
|
-0.422618261740699330f, -0.406736643075800100f, -0.390731128489273600f,
|
|
|
-0.374606593415912070f, -0.358367949545300270f, -0.342020143325668710f,
|
|
|
-0.325568154457156420f, -0.309016994374947340f,
|
|
|
-0.292371704722736660f, -0.275637355816999050f, -0.258819045102520850f,
|
|
|
-0.241921895599667790f, -0.224951054343864810f, -0.207911690817759120f,
|
|
|
-0.190808995376544800f, -0.173648177666930300f,
|
|
|
-0.156434465040231040f, -0.139173100960065350f, -0.121869343405147370f,
|
|
|
-0.104528463267653330f, -0.087155742747658235f, -0.069756473744125330f,
|
|
|
-0.052335956242943620f, -0.034899496702500733f,
|
|
|
-0.017452406437283477f, 0.000000000000000061f, 0.017452406437283376f,
|
|
|
0.034899496702501080f, 0.052335956242943966f, 0.069756473744125455f,
|
|
|
0.087155742747658138f, 0.104528463267653460f,
|
|
|
0.121869343405147490f, 0.139173100960065690f, 0.156434465040230920f,
|
|
|
0.173648177666930410f, 0.190808995376544920f, 0.207911690817759450f,
|
|
|
0.224951054343864920f, 0.241921895599667900f,
|
|
|
0.258819045102520740f, 0.275637355816999160f, 0.292371704722736770f,
|
|
|
0.309016994374947450f, 0.325568154457156760f, 0.342020143325668820f,
|
|
|
0.358367949545300380f, 0.374606593415911960f,
|
|
|
0.390731128489273940f, 0.406736643075800210f, 0.422618261740699440f,
|
|
|
0.438371146789077460f, 0.453990499739546860f, 0.469471562785890860f,
|
|
|
0.484809620246337110f, 0.500000000000000110f,
|
|
|
0.515038074910054380f, 0.529919264233204900f, 0.544639035015027200f,
|
|
|
0.559192903470746790f, 0.573576436351046050f, 0.587785252292473140f,
|
|
|
0.601815023152048270f, 0.615661475325658290f,
|
|
|
0.629320391049837500f, 0.642787609686539360f, 0.656059028990507280f,
|
|
|
0.669130606358858240f, 0.681998360062498480f, 0.694658370458997370f,
|
|
|
0.707106781186547570f, 0.719339800338651190f,
|
|
|
0.731353701619170570f, 0.743144825477394240f, 0.754709580222772010f,
|
|
|
0.766044443118978010f, 0.777145961456970900f, 0.788010753606722010f,
|
|
|
0.798635510047292830f, 0.809016994374947450f,
|
|
|
0.819152044288991800f, 0.829037572555041620f, 0.838670567945424050f,
|
|
|
0.848048096156425960f, 0.857167300702112330f, 0.866025403784438710f,
|
|
|
0.874619707139395740f, 0.882947592858926990f,
|
|
|
0.891006524188367900f, 0.898794046299167040f, 0.906307787036649940f,
|
|
|
0.913545457642600870f, 0.920504853452440370f, 0.927183854566787420f,
|
|
|
0.933580426497201740f, 0.939692620785908430f,
|
|
|
0.945518575599316850f, 0.951056516295153530f, 0.956304755963035440f,
|
|
|
0.961261695938318890f, 0.965925826289068310f, 0.970295726275996470f,
|
|
|
0.974370064785235250f, 0.978147600733805690f,
|
|
|
0.981627183447663980f, 0.984807753012208020f, 0.987688340595137770f,
|
|
|
0.990268068741570360f, 0.992546151641321980f, 0.994521895368273290f,
|
|
|
0.996194698091745550f, 0.997564050259824200f,
|
|
|
0.998629534754573830f, 0.999390827019095760f, 0.999847695156391270f,
|
|
|
1.000000000000000000f, 0.999847695156391270f, 0.999390827019095760f,
|
|
|
0.998629534754573830f, 0.997564050259824200f,
|
|
|
0.996194698091745550f, 0.994521895368273290f, 0.992546151641321980f,
|
|
|
0.990268068741570360f, 0.987688340595137770f, 0.984807753012208020f,
|
|
|
0.981627183447663980f, 0.978147600733805690f,
|
|
|
0.974370064785235250f, 0.970295726275996470f, 0.965925826289068310f,
|
|
|
0.961261695938318890f, 0.956304755963035440f, 0.951056516295153530f,
|
|
|
0.945518575599316850f, 0.939692620785908430f,
|
|
|
0.933580426497201740f, 0.927183854566787420f, 0.920504853452440370f,
|
|
|
0.913545457642600870f, 0.906307787036649940f, 0.898794046299167040f,
|
|
|
0.891006524188367900f, 0.882947592858926990f,
|
|
|
0.874619707139395740f, 0.866025403784438710f, 0.857167300702112330f,
|
|
|
0.848048096156425960f, 0.838670567945424050f, 0.829037572555041620f,
|
|
|
0.819152044288991800f, 0.809016994374947450f,
|
|
|
0.798635510047292830f, 0.788010753606722010f, 0.777145961456970900f,
|
|
|
0.766044443118978010f, 0.754709580222772010f, 0.743144825477394240f,
|
|
|
0.731353701619170570f, 0.719339800338651190f,
|
|
|
0.707106781186547570f, 0.694658370458997370f, 0.681998360062498480f,
|
|
|
0.669130606358858240f, 0.656059028990507280f, 0.642787609686539360f,
|
|
|
0.629320391049837500f, 0.615661475325658290f,
|
|
|
0.601815023152048270f, 0.587785252292473140f, 0.573576436351046050f,
|
|
|
0.559192903470746790f, 0.544639035015027200f, 0.529919264233204900f,
|
|
|
0.515038074910054380f, 0.500000000000000110f,
|
|
|
0.484809620246337110f, 0.469471562785890860f, 0.453990499739546860f,
|
|
|
0.438371146789077460f, 0.422618261740699440f, 0.406736643075800210f,
|
|
|
0.390731128489273940f, 0.374606593415911960f,
|
|
|
0.358367949545300380f, 0.342020143325668820f, 0.325568154457156760f,
|
|
|
0.309016994374947450f, 0.292371704722736770f, 0.275637355816999160f,
|
|
|
0.258819045102520740f, 0.241921895599667900f,
|
|
|
0.224951054343864920f, 0.207911690817759450f, 0.190808995376544920f,
|
|
|
0.173648177666930410f, 0.156434465040230920f, 0.139173100960065690f,
|
|
|
0.121869343405147490f, 0.104528463267653460f,
|
|
|
0.087155742747658138f, 0.069756473744125455f, 0.052335956242943966f,
|
|
|
0.034899496702501080f, 0.017452406437283376f, 0.000000000000000061f,
|
|
|
-0.017452406437283477f, -0.034899496702500733f,
|
|
|
-0.052335956242943620f, -0.069756473744125330f, -0.087155742747658235f,
|
|
|
-0.104528463267653330f, -0.121869343405147370f, -0.139173100960065350f,
|
|
|
-0.156434465040231040f, -0.173648177666930300f,
|
|
|
-0.190808995376544800f, -0.207911690817759120f, -0.224951054343864810f,
|
|
|
-0.241921895599667790f, -0.258819045102520850f, -0.275637355816999050f,
|
|
|
-0.292371704722736660f, -0.309016994374947340f,
|
|
|
-0.325568154457156420f, -0.342020143325668710f, -0.358367949545300270f,
|
|
|
-0.374606593415912070f, -0.390731128489273600f, -0.406736643075800100f,
|
|
|
-0.422618261740699330f, -0.438371146789077510f,
|
|
|
-0.453990499739546750f, -0.469471562785890530f, -0.484809620246337000f,
|
|
|
-0.499999999999999780f, -0.515038074910054270f, -0.529919264233204790f,
|
|
|
-0.544639035015027080f, -0.559192903470746680f,
|
|
|
-0.573576436351045830f, -0.587785252292473030f, -0.601815023152048380f,
|
|
|
-0.615661475325658290f, -0.629320391049837280f, -0.642787609686539360f,
|
|
|
-0.656059028990507500f, -0.669130606358858240f,
|
|
|
-0.681998360062498370f, -0.694658370458997030f, -0.707106781186547460f,
|
|
|
-0.719339800338651300f, -0.731353701619170460f, -0.743144825477394130f,
|
|
|
-0.754709580222772010f, -0.766044443118977900f,
|
|
|
-0.777145961456970680f, -0.788010753606721900f, -0.798635510047292940f,
|
|
|
-0.809016994374947340f, -0.819152044288991580f, -0.829037572555041620f,
|
|
|
-0.838670567945424160f, -0.848048096156425960f,
|
|
|
-0.857167300702112220f, -0.866025403784438710f, -0.874619707139395740f,
|
|
|
-0.882947592858926770f, -0.891006524188367790f, -0.898794046299167040f,
|
|
|
-0.906307787036649940f, -0.913545457642600760f,
|
|
|
-0.920504853452440150f, -0.927183854566787310f, -0.933580426497201740f,
|
|
|
-0.939692620785908320f, -0.945518575599316740f, -0.951056516295153530f,
|
|
|
-0.956304755963035440f, -0.961261695938318670f,
|
|
|
-0.965925826289068200f, -0.970295726275996470f, -0.974370064785235250f,
|
|
|
-0.978147600733805690f, -0.981627183447663980f, -0.984807753012208020f,
|
|
|
-0.987688340595137660f, -0.990268068741570250f,
|
|
|
-0.992546151641321980f, -0.994521895368273290f, -0.996194698091745550f,
|
|
|
-0.997564050259824200f, -0.998629534754573830f, -0.999390827019095760f,
|
|
|
-0.999847695156391270f, -1.000000000000000000f
|
|
|
};
|
|
|
|
|
|
/**
|
|
|
* \par
|
|
|
* Sine Table is generated from following loop
|
|
|
* <pre>for(i = 0; i < 360; i++)
|
|
|
* {
|
|
|
* sinTable[i]= sin((i-180) * PI/180.0);
|
|
|
* } </pre>
|
|
|
*/
|
|
|
|
|
|
|
|
|
static const float32_t sinTable[360] = {
|
|
|
-0.017452406437283439f, -0.034899496702500699f, -0.052335956242943807f,
|
|
|
-0.069756473744125524f, -0.087155742747658638f, -0.104528463267653730f,
|
|
|
-0.121869343405147550f, -0.139173100960065740f,
|
|
|
-0.156434465040230980f, -0.173648177666930280f, -0.190808995376544970f,
|
|
|
-0.207911690817759310f, -0.224951054343864780f, -0.241921895599667730f,
|
|
|
-0.258819045102521020f, -0.275637355816999660f,
|
|
|
-0.292371704722737050f, -0.309016994374947510f, -0.325568154457156980f,
|
|
|
-0.342020143325668880f, -0.358367949545300210f, -0.374606593415912240f,
|
|
|
-0.390731128489274160f, -0.406736643075800430f,
|
|
|
-0.422618261740699500f, -0.438371146789077290f, -0.453990499739546860f,
|
|
|
-0.469471562785891080f, -0.484809620246337170f, -0.499999999999999940f,
|
|
|
-0.515038074910054380f, -0.529919264233204900f,
|
|
|
-0.544639035015026860f, -0.559192903470746900f, -0.573576436351046380f,
|
|
|
-0.587785252292473250f, -0.601815023152048160f, -0.615661475325658400f,
|
|
|
-0.629320391049837720f, -0.642787609686539470f,
|
|
|
-0.656059028990507280f, -0.669130606358858350f, -0.681998360062498590f,
|
|
|
-0.694658370458997140f, -0.707106781186547570f, -0.719339800338651410f,
|
|
|
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0.000000000000000000f, 0.017452406437283512f, 0.034899496702500969f,
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0.052335956242943828f, 0.069756473744125302f,
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0.087155742747658166f, 0.104528463267653460f, 0.121869343405147480f,
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0.139173100960065440f, 0.156434465040230870f, 0.173648177666930330f,
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0.190808995376544800f, 0.207911690817759310f,
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0.224951054343865000f, 0.241921895599667730f, 0.258819045102520740f,
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0.275637355816999160f, 0.292371704722736770f, 0.309016994374947400f,
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0.325568154457156640f, 0.342020143325668710f,
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0.358367949545300270f, 0.374606593415912010f, 0.390731128489273720f,
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0.406736643075800150f, 0.422618261740699440f, 0.438371146789077400f,
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0.453990499739546750f, 0.469471562785890810f,
|
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0.484809620246337060f, 0.499999999999999940f, 0.515038074910054160f,
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0.529919264233204900f, 0.544639035015027080f, 0.559192903470746900f,
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0.573576436351046050f, 0.587785252292473140f,
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0.601815023152048270f, 0.615661475325658180f, 0.629320391049837390f,
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0.681998360062498480f, 0.694658370458997250f,
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0.777145961456970790f, 0.788010753606722010f,
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0.857167300702112220f, 0.866025403784438600f,
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0.920504853452440260f, 0.927183854566787420f,
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0.951056516295153530f, 0.956304755963035440f, 0.961261695938318890f,
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0.965925826289068310f, 0.970295726275996470f,
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0.974370064785235250f, 0.978147600733805580f, 0.981627183447663980f,
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0.984807753012208020f, 0.987688340595137770f, 0.990268068741570250f,
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0.992546151641321980f, 0.994521895368273290f,
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0.996194698091745550f, 0.997564050259824200f, 0.998629534754573830f,
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0.999390827019095760f, 0.999847695156391270f, 1.000000000000000000f,
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0.999847695156391270f, 0.999390827019095760f,
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0.998629534754573830f, 0.997564050259824200f, 0.996194698091745550f,
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0.994521895368273400f, 0.992546151641322090f, 0.990268068741570360f,
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0.987688340595137660f, 0.984807753012208020f,
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0.981627183447663980f, 0.978147600733805690f, 0.974370064785235250f,
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0.970295726275996470f, 0.965925826289068310f, 0.961261695938318890f,
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0.956304755963035550f, 0.951056516295153640f,
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0.945518575599316850f, 0.939692620785908430f, 0.933580426497201740f,
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0.927183854566787420f, 0.920504853452440370f, 0.913545457642600980f,
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0.906307787036650050f, 0.898794046299166930f,
|
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0.891006524188367900f, 0.882947592858927100f, 0.874619707139395850f,
|
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0.866025403784438710f, 0.857167300702112330f, 0.848048096156426070f,
|
|
|
0.838670567945424050f, 0.829037572555041740f,
|
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|
0.819152044288992020f, 0.809016994374947450f, 0.798635510047292720f,
|
|
|
0.788010753606722010f, 0.777145961456971010f, 0.766044443118978010f,
|
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0.754709580222771790f, 0.743144825477394240f,
|
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|
0.731353701619170570f, 0.719339800338651410f, 0.707106781186547570f,
|
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0.694658370458997140f, 0.681998360062498590f, 0.669130606358858350f,
|
|
|
0.656059028990507280f, 0.642787609686539470f,
|
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|
0.629320391049837720f, 0.615661475325658400f, 0.601815023152048160f,
|
|
|
0.587785252292473250f, 0.573576436351046380f, 0.559192903470746900f,
|
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|
0.544639035015026860f, 0.529919264233204900f,
|
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|
0.515038074910054380f, 0.499999999999999940f, 0.484809620246337170f,
|
|
|
0.469471562785891080f, 0.453990499739546860f, 0.438371146789077290f,
|
|
|
0.422618261740699500f, 0.406736643075800430f,
|
|
|
0.390731128489274160f, 0.374606593415912240f, 0.358367949545300210f,
|
|
|
0.342020143325668880f, 0.325568154457156980f, 0.309016994374947510f,
|
|
|
0.292371704722737050f, 0.275637355816999660f,
|
|
|
0.258819045102521020f, 0.241921895599667730f, 0.224951054343864780f,
|
|
|
0.207911690817759310f, 0.190808995376544970f, 0.173648177666930280f,
|
|
|
0.156434465040230980f, 0.139173100960065740f,
|
|
|
0.121869343405147550f, 0.104528463267653730f, 0.087155742747658638f,
|
|
|
0.069756473744125524f, 0.052335956242943807f, 0.034899496702500699f,
|
|
|
0.017452406437283439f, 0.000000000000000122f
|
|
|
};
|
|
|
|
|
|
|
|
|
/**
|
|
|
* @brief Floating-point sin_cos function.
|
|
|
* @param[in] theta input value in degrees
|
|
|
* @param[out] *pSinVal points to the processed sine output.
|
|
|
* @param[out] *pCosVal points to the processed cos output.
|
|
|
* @return none.
|
|
|
*/
|
|
|
|
|
|
|
|
|
void arm_sin_cos_f32(
|
|
|
float32_t theta,
|
|
|
float32_t * pSinVal,
|
|
|
float32_t * pCosVal)
|
|
|
{
|
|
|
uint32_t i; /* Index for reading nearwst output values */
|
|
|
float32_t x1 = -179.0f; /* Initial input value */
|
|
|
float32_t y0, y1; /* nearest output values */
|
|
|
float32_t fract; /* fractional part of input */
|
|
|
|
|
|
/* Calculation of fractional part */
|
|
|
if(theta > 0.0f)
|
|
|
{
|
|
|
fract = theta - (float32_t) ((int32_t) theta);
|
|
|
}
|
|
|
else
|
|
|
{
|
|
|
fract = (theta - (float32_t) ((int32_t) theta)) + 1.0f;
|
|
|
}
|
|
|
|
|
|
/* index calculation for reading nearest output values */
|
|
|
i = (uint32_t) (theta - x1);
|
|
|
|
|
|
/* reading nearest sine output values */
|
|
|
y0 = sinTable[i];
|
|
|
y1 = sinTable[i + 1u];
|
|
|
|
|
|
/* Calculation of sine value */
|
|
|
*pSinVal = y0 + (fract * (y1 - y0));
|
|
|
|
|
|
/* reading nearest cosine output values */
|
|
|
y0 = cosTable[i];
|
|
|
y1 = cosTable[i + 1u];
|
|
|
|
|
|
/* Calculation of cosine value */
|
|
|
*pCosVal = y0 + (fract * (y1 - y0));
|
|
|
|
|
|
}
|
|
|
|
|
|
/**
|
|
|
* @} end of SinCos group
|
|
|
*/
|
|
|
|
