atan2 und atan als Look-Up-Table

THE_ONE

Hallo!

Ich bin gerade dabei die Implementierung des Arcus Tangens als Lookuptable zu machen, für einen Mikrokontroller ist das nämlich ziemlich rechenaufwendig.

Benötigen tue ich eigentlich den atan2 aber der greift ja auf den normalen atan zurück.

Ich habe hier eine Implementierung des Atan2s:

float atan_2(int y, int x) {
	float result;

	if(abs(x) > abs(y))
		result = atan_1(y/x);
	else
	{
		result = atan_1(x/y);
		if(result < 0)
			result = -M_PI/2 - result;
		else
			result = M_PI/2 - result;
	}

	if (x < 0)
		if(y < 0)
			result = result - M_PI;
		else
			result = result + M_PI;

	return result;
}

Stimmt es, dass durch das erste IF sichergestellt wird dass die Werte für den atan_1 nie über 1 gehen (d.h. die Division ergibt nur werte zwischen 0 und 1)?
Dann brauche ich nämlich in der Lookuptable nur die Werte zwischen 0 und 1 speichern, d.h. z.B. dass der Wert von atan(23) eigentlich uninteressant da 23 nicht möglich ist, korrekt?

MFG THE_ONE

Hallo,

THE_ONE schrieb:

Hallo!

Stimmt es, dass durch das erste IF sichergestellt wird dass die Werte für den atan_1 nie über 1 gehen (d.h. die Division ergibt nur werte zwischen 0 und 1)?
Dann brauche ich nämlich in der Lookuptable nur die Werte zwischen 0 und 1 speichern, d.h. z.B. dass der Wert von atan(23) eigentlich uninteressant da 23 nicht möglich ist, korrekt?

Ja, das ist korrekt. Um genauer zu sein, gilt:

-0,78539816339744830961566084581988... < atan_1(x) < 0,78539816339744830961566084581988...

für -1 < x < 1, da atan_1 auf diesem Intervall streng monoton steigend ist, wie der Mathematiker es ausdrücken würde. Da atan_1(-x) = -atan_1(x) genügt es also, Werte zwischen Null und der oben angegebenen positiven Grenze in der Lookup-Table zu halten.

MfG,

Probe-Nutzer

THE_ONE

Hallo!

Hier nun meine Lösung:

#include "atantable.h"

float atanfield1[] = {0,0.001,0.002,0.003,0.004,0.005,0.0059999,0.0069999,0.0079998,0.0089998,0.0099997,0.011,0.011999,0.012999,0.013999,0.014999,0.015999,0.016998,0.017998,0.018998,0.019997,0.020997,0.021996,0.022996,0.023995,0.024995,0.025994,0.026993,0.027993,0.028992,0.029991,0.03099,0.031989,0.032988,0.033987,0.034986,0.035984,0.036983,0.037982,0.03898,0.039979,0.040977,0.041975,0.042974,0.043972,0.04497,0.045968,0.046965,0.047963,0.048961,0.049958,0.050956,0.051953,0.05295,0.053948,0.054945,0.055942,0.056938,0.057935,0.058932,0.059928,0.060925,0.061921,0.062917,0.063913,0.064909,0.065904,0.0669,0.067895,0.068891,0.069886,0.070881,0.071876,0.072871,0.073865,0.07486,0.075854,0.076848,0.077842,0.078836,0.07983,0.080824,0.081817,0.08281,0.083803,0.084796,0.085789,0.086781,0.087774,0.088766,0.089758,0.09075,0.091742,0.092733,0.093725,0.094716,0.095707,0.096697,0.097688,0.098678,0.099669,0.10066,0.10165,0.10264,0.10363,0.10462,0.10561,0.10659,0.10758,0.10857,0.10956,0.11055,0.11154,0.11252,0.11351,0.1145,0.11548,0.11647,0.11746,0.11844,0.11943,0.12041,0.1214,0.12239,0.12337,0.12435,0.12534,0.12632,0.12731,0.12829,0.12928,0.13026,0.13124,0.13222,0.13321,0.13419,0.13517,0.13615,0.13713,0.13812,0.1391,0.14008,0.14106,0.14204,0.14302,0.144,0.14498,0.14595,0.14693,0.14791,0.14889,0.14987,0.15085,0.15182,0.1528,0.15378,0.15475,0.15573,0.1567,0.15768,0.15866,0.15963,0.1606,0.16158,0.16255,0.16353,0.1645,0.16547,0.16645,0.16742,0.16839,0.16936,0.17033,0.1713,0.17228,0.17325,0.17422,0.17519,0.17616,0.17712,0.17809,0.17906,0.18003,0.181,0.18196,0.18293,0.1839,0.18486,0.18583,0.1868,0.18776,0.18873,0.18969,0.19066,0.19162,0.19258,0.19355,0.19451,0.19547,0.19643,0.1974,0.19836,0.19932,0.20028,0.20124,0.2022,0.20316,0.20412,0.20508,0.20603,0.20699,0.20795,0.20891,0.20986,0.21082,0.21178,0.21273,0.21369,0.21464,0.2156,0.21655,0.2175,0.21846,0.21941,0.22036,0.22131,0.22227,0.22322,0.22417,0.22512,0.22607,0.22702,0.22797,0.22892,0.22986,0.23081,0.23176,0.23271,0.23365,0.2346,0.23554,0.23649,0.23744,0.23838,0.23932,0.24027,0.24121,0.24215,0.2431,0.24404,0.24498,0.24592,0.24686,0.2478,0.24874,0.24968,0.25062,0.25156,0.25249,0.25343,0.25437,0.2553,0.25624,0.25718,0.25811,0.25905,0.25998,0.26091,0.26185,0.26278,0.26371,0.26464,0.26558,0.26651,0.26744,0.26837,0.2693,0.27022,0.27115,0.27208,0.27301,0.27394,0.27486,0.27579,0.27671,0.27764,0.27856,0.27949,0.28041,0.28133,0.28226,0.28318,0.2841,0.28502,0.28594,0.28686,0.28778,0.2887,0.28962,0.29054,0.29146,0.29237,0.29329,0.29421,0.29512,0.29604,0.29695,0.29787,0.29878,0.29969,0.30061,0.30152,0.30243,0.30334,0.30425,0.30516,0.30607,0.30698,0.30789,0.3088,0.3097,0.31061,0.31152,0.31242,0.31333,0.31423,0.31514,0.31604,0.31694,0.31785,0.31875,0.31965,0.32055,0.32145,0.32235,0.32325,0.32415,0.32505,0.32594,0.32684,0.32774,0.32863,0.32953,0.33043,0.33132,0.33221,0.33311,0.334,0.33489,0.33578,0.33667,0.33757,0.33846,0.33934,0.34023,0.34112,0.34201,0.3429,0.34378,0.34467,0.34556,0.34644,0.34732,0.34821,0.34909,0.34997,0.35086,0.35174,0.35262,0.3535,0.35438,0.35526,0.35614,0.35702,0.35789,0.35877,0.35965,0.36052,0.3614,0.36227,0.36315,0.36402,0.36489,0.36577,0.36664,0.36751,0.36838,0.36925,0.37012,0.37099,0.37186,0.37272,0.37359,0.37446,0.37532,0.37619,0.37705,0.37792,0.37878,0.37964,0.38051,0.38137,0.38223,0.38309,0.38395,0.38481,0.38567,0.38653,0.38738,0.38824,0.3891,0.38995,0.39081,0.39166,0.39252,0.39337,0.39422,0.39508,0.39593,0.39678,0.39763,0.39848,0.39933,0.40018,0.40102,0.40187,0.40272,0.40356,0.40441,0.40525,0.4061,0.40694,0.40778,0.40863,0.40947,0.41031,0.41115,0.41199,0.41283,0.41367,0.41451,0.41534,0.41618,0.41702,0.41785,0.41869,0.41952,0.42036,0.42119,0.42202,0.42285,0.42369,0.42452,0.42535,0.42618,0.427,0.42783,0.42866,0.42949,0.43031,0.43114,0.43196,0.43279,0.43361,0.43444,0.43526,0.43608,0.4369,0.43772,0.43854,0.43936,0.44018,0.441,0.44182,0.44263,0.44345,0.44426,0.44508,0.44589,0.44671,0.44752,0.44833,0.44914,0.44996,0.45077,0.45158,0.45239,0.45319,0.454,0.45481,0.45562,0.45642,0.45723,0.45803,0.45884,0.45964,0.46044,0.46124,0.46205,0.46285,0.46365,0.46445,0.46525,0.46604,0.46684,0.46764,0.46844,0.46923,0.47003,0.47082,0.47162,0.47241,0.4732,0.47399,0.47478,0.47558,0.47637,0.47715,0.47794,0.47873,0.47952,0.48031,0.48109,0.48188,0.48266,0.48345,0.48423,0.48501,0.4858,0.48658,0.48736,0.48814,0.48892,0.4897,0.49048,0.49125,0.49203,0.49281,0.49358,0.49436,0.49513,0.49591,0.49668,0.49745,0.49823,0.499,0.49977,0.50054,0.50131,0.50208,0.50284,0.50361,0.50438,0.50514,0.50591,0.50667,0.50744,0.5082,0.50896,0.50973,0.51049,0.51125,0.51201,0.51277,0.51353,0.51429,0.51504,0.5158,0.51656,0.51731,0.51807,0.51882,0.51958,0.52033,0.52108,0.52183,0.52259,0.52334,0.52409,0.52484,0.52558,0.52633,0.52708,0.52783,0.52857,0.52932,0.53006,0.53081,0.53155,0.53229,0.53303,0.53378,0.53452,0.53526,0.536,0.53673,0.53747,0.53821,0.53895,0.53968,0.54042,0.54115,0.54189,0.54262,0.54336,0.54409,0.54482,0.54555,0.54628,0.54701,0.54774,0.54847,0.5492,0.54992,0.55065,0.55138,0.5521,0.55283,0.55355,0.55427,0.555,0.55572,0.55644,0.55716,0.55788,0.5586,0.55932,0.56004,0.56075,0.56147,0.56219,0.5629,0.56362,0.56433,0.56505,0.56576,0.56647,0.56718,0.56789,0.5686,0.56931,0.57002,0.57073,0.57144,0.57215,0.57285,0.57356,0.57426,0.57497,0.57567,0.57638,0.57708,0.57778,0.57848,0.57918,0.57988,0.58058,0.58128,0.58198,0.58268,0.58337,0.58407,0.58476,0.58546,0.58615,0.58685,0.58754,0.58823,0.58893,0.58962,0.59031,0.591,0.59169,0.59237,0.59306,0.59375,0.59444,0.59512,0.59581,0.59649,0.59718,0.59786,0.59854,0.59923,0.59991,0.60059,0.60127,0.60195,0.60263,0.60331,0.60398,0.60466,0.60534,0.60601,0.60669,0.60736,0.60804,0.60871,0.60938,0.61005,0.61073,0.6114,0.61207,0.61274,0.61341,0.61407,0.61474,0.61541,0.61607,0.61674,0.61741,0.61807,0.61873,0.6194,0.62006,0.62072,0.62138,0.62204,0.6227,0.62336,0.62402,0.62468,0.62534,0.626,0.62665,0.62731,0.62796,0.62862,0.62927,0.62993,0.63058,0.63123,0.63188,0.63253,0.63318,0.63383,0.63448,0.63513,0.63578,0.63642,0.63707,0.63772,0.63836,0.63901,0.63965,0.64029,0.64094,0.64158,0.64222,0.64286,0.6435,0.64414,0.64478,0.64542,0.64606,0.64669,0.64733,0.64797,0.6486,0.64924,0.64987,0.6505,0.65114,0.65177,0.6524,0.65303,0.65366,0.65429,0.65492,0.65555,0.65618,0.65681,0.65743,0.65806,0.65869,0.65931,0.65993,0.66056,0.66118,0.6618,0.66243,0.66305,0.66367,0.66429,0.66491,0.66553,0.66615,0.66676,0.66738,0.668,0.66861,0.66923,0.66984,0.67046,0.67107,0.67168,0.6723,0.67291,0.67352,0.67413,0.67474,0.67535,0.67596,0.67657,0.67718,0.67778,0.67839,0.67899,0.6796,0.6802,0.68081,0.68141,0.68202,0.68262,0.68322,0.68382,0.68442,0.68502,0.68562,0.68622,0.68682,0.68742,0.68801,0.68861,0.6892,0.6898,0.69039,0.69099,0.69158,0.69218,0.69277,0.69336,0.69395,0.69454,0.69513,0.69572,0.69631,0.6969,0.69749,0.69807,0.69866,0.69925,0.69983,0.70042,0.701,0.70158,0.70217,0.70275,0.70333,0.70391,0.70449,0.70507,0.70565,0.70623,0.70681,0.70739,0.70797,0.70854,0.70912,0.7097,0.71027,0.71085,0.71142,0.71199,0.71257,0.71314,0.71371,0.71428,0.71485,0.71542,0.71599,0.71656,0.71713,0.7177,0.71826,0.71883,0.7194,0.71996,0.72053,0.72109,0.72165,0.72222,0.72278,0.72334,0.7239,0.72447,0.72503,0.72559,0.72615,0.7267,0.72726,0.72782,0.72838,0.72893,0.72949,0.73005,0.7306,0.73116,0.73171,0.73226,0.73282,0.73337,0.73392,0.73447,0.73502,0.73557,0.73612,0.73667,0.73722,0.73777,0.73831,0.73886,0.73941,0.73995,0.7405,0.74104,0.74158,0.74213,0.74267,0.74321,0.74376,0.7443,0.74484,0.74538,0.74592,0.74646,0.747,0.74753,0.74807,0.74861,0.74914,0.74968,0.75022,0.75075,0.75129,0.75182,0.75235,0.75289,0.75342,0.75395,0.75448,0.75501,0.75554,0.75607,0.7566,0.75713,0.75766,0.75818,0.75871,0.75924,0.75976,0.76029,0.76081,0.76134,0.76186,0.76238,0.76291,0.76343,0.76395,0.76447,0.76499,0.76551,0.76603,0.76655,0.76707,0.76759,0.76811,0.76862,0.76914,0.76966,0.77017,0.77069,0.7712,0.77171,0.77223,0.77274,0.77325,0.77376,0.77428,0.77479,0.7753,0.77581,0.77632,0.77683,0.77733,0.77784,0.77835,0.77886,0.77936,0.77987,0.78037,0.78088,0.78138,0.78189,0.78239,0.78289,0.78339,0.7839,0.7844,0.7849,0.7854};

float atan_1(int y,int x)
{
	int index;
	int vorz;
	float erg;

	vorz = 1;
	if (((x < 0) && (y < 0)) || ((x > 0) && (y > 0)))  {vorz = 0;}
	else x = -x;

	/*atan of y/x */
	index =(int) (((y*10000)/x+5)/10); //+5 for rounding
	//printf("%s%d%s%d%s%d\n","index=",index," x= ",x," y= ",y);

	erg = atanfield1[index];

	if (vorz == 0 ) return erg; 
	else return -erg;
}

float atan_2(int y, int x) {
	float result;

	if(abs(x) > abs(y))
		result = atan_1(y,x);
	else
	{
		result = atan_1(x,y);
		if(result < 0)
			result = -M_PI/2 - result;
		else
			result = M_PI/2 - result;
	}

	if (x < 0)
		if(y < 0)
			result = result - M_PI;
		else
			result = result + M_PI;

	return result;
}

und das h file dazu:

#if !defined __ATAN_TABLE__
#define __ATAN_TABLE__

#define M_PI 3.14159265f

float atan_1(int y,int x);
float atan_2(int y, int x); 

#endif

ich hoffe das es passt, wenn nicht bitte melden!

Lg THE_ONE