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atan.cpp
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#include <math.h>
//
// xiezhq@shanghaitech.edu.cn && wanghe@shanghaitech.edu.cn
/* Reference:
[1] Abhisek Ukil, Vishal H Shah, Bernhard Deck,
"Fast Computation of arctangent Functions for Embedded Applications: A
Comparative Analysis" IEEE International Symposium on Industrial Electronics,
Pages: 1206 - 1211, DOI: 10.1109/ISIE.2011.5984330, 2011
[2] Sreeraman Rajan, Sichun Wang, Robert Inkol, and Alain Joyal
"Efficient Approximations for the Arctangent Function"
IEEE SIGNAL PROCESSING MAGAZINE [108] MAY 2006
*/
float LUT[102] = {
0, 0.0099996664, 0.019997334, 0.029991005, 0.039978687,
0.049958397, 0.059928156, 0.069885999, 0.079829983, 0.089758173,
0.099668652, 0.10955953, 0.11942893, 0.12927501, 0.13909595,
0.14888994, 0.15865526, 0.16839015, 0.17809294, 0.18776195,
0.19739556, 0.20699219, 0.21655031, 0.22606839, 0.23554498,
0.24497867, 0.25436807, 0.26371184, 0.27300870, 0.28225741,
0.29145679, 0.30060568, 0.30970293, 0.31874755, 0.32773849,
0.33667481, 0.34555557, 0.35437992, 0.36314702, 0.37185606,
0.38050637, 0.38909724, 0.39762798, 0.40609807, 0.41450688,
0.42285392, 0.43113875, 0.43936089, 0.44751999, 0.45561564,
0.46364760, 0.47161558, 0.47951928, 0.48735857, 0.49513325,
0.50284320, 0.51048833, 0.51806855, 0.52558380, 0.53303409,
0.54041952, 0.54774004, 0.55499572, 0.56218672, 0.56931317,
0.57637525, 0.58337301, 0.59030676, 0.59717667, 0.60398299,
0.61072594, 0.61740589, 0.62402308, 0.63057774, 0.63707036,
0.64350110, 0.64987046, 0.65617871, 0.66242629, 0.66861355,
0.67474097, 0.68080884, 0.68681765, 0.69276786, 0.69865984,
0.70449406, 0.71027100, 0.71599114, 0.72165483, 0.72726268,
0.73281509, 0.73831260, 0.74375558, 0.74914461, 0.75448018,
0.75976276, 0.76499283, 0.77017093, 0.77529752, 0.78037310,
0.78539819, 0.79037325};
double LUT_d[102] = {
0, 0.00999966668666524, 0.0199973339731505, 0.0299910048568779, 0.0399786871232900,
0.0499583957219428, 0.0599281551212079, 0.0698860016346425, 0.0798299857122373, 0.0897581741899505,
0.0996686524911620, 0.109559526773944, 0.119428926018338, 0.129275004048143, 0.139095941482071,
0.148889947609497, 0.158655262186401, 0.168390157147530, 0.178092938231198, 0.187761946513593,
0.197395559849881, 0.206992194219821, 0.216550304976089, 0.226068387993884, 0.235544980720863,
0.244978663126864, 0.254368058553266, 0.263711834462266, 0.273008703086711, 0.282257421981491,
0.291456794477867, 0.300605670042395, 0.309702944542456, 0.318747560420644, 0.327738506780556,
0.336674819386727, 0.345555580581712, 0.354379919123438, 0.363147009946176, 0.371856073848581,
0.380506377112365, 0.389097231055278, 0.397627991522129, 0.406098058317616, 0.414506874584786,
0.422853926132941, 0.431138740718782, 0.439360887284591, 0.447519975157170, 0.455615653211225,
0.463647609000806, 0.471615567862328, 0.479519291992596, 0.487358579505190, 0.495133263468404,
0.502843210927861, 0.510488321916776, 0.518068528456721, 0.525583793551610, 0.533034110177490,
0.540419500270584, 0.547740013715902, 0.554995727338587, 0.562186743900029, 0.569313191100662,
0.576375220591184, 0.583373006993856, 0.590306746935372, 0.597176658092678, 0.603982978252998,
0.610725964389209, 0.617405891751573, 0.624023052976757, 0.630577757214935, 0.637070329275684,
0.643501108793284, 0.649870449411948, 0.656178717991395, 0.662426293833151, 0.668613567927821,
0.674740942223553, 0.680808828915828, 0.686817649758645, 0.692767835397122, 0.698659824721463,
0.704494064242218, 0.710271007486686, 0.715991114416300, 0.721654850864761, 0.727262687996690,
0.732815101786507, 0.738312572517228, 0.743755584298860, 0.749144624606017, 0.754480183834406,
0.759762754875771, 0.764992832710910, 0.770170914020331, 0.775297496812126, 0.780373080066636,
0.785398163397448, 0.790373246728302
};
float atan_fast(float x){
/*
A fast look-up method with enough accuracy
*/
if (x > 0) {
if (x <= 1) {
int index = round(x * 100);
return LUT[index];
} else {
float re_x = 1 / x;
int index = round(re_x * 100);
return (M_PI_2 - LUT[index]);
}
} else {
if (x >= -1) {
float abs_x = -x;
int index = round(abs_x * 100);
return -(LUT[index]);
} else {
float re_x = 1 / (-x);
int index = round(re_x * 100);
return (LUT[index] - M_PI_2);
}
}
}
float atan_single(float x) {
/*
Linear interpolation is used for higher accuracy
*/
if (x >= 0) {
if (x <= 1) {
int index = round(x * 100);
return (LUT[index] + (x * 100 - index) * (LUT[index + 1] - LUT[index]));
} else {
float re_x = 1 / x;
int index = round(re_x * 100);
return (M_PI_2 - (LUT[index] + (re_x * 100 - index) * (LUT[index + 1] - LUT[index])));
// No recursive is better here
}
} else {
if (x >= -1) {
float abs_x = -x;
int index = round(abs_x * 100);
return -(LUT[index] + (abs_x * 100 - index) * (LUT[index + 1] - LUT[index]));
} else {
float re_x = 1 / (-x);
int index = round(re_x * 100);
return (LUT[index] + (re_x * 100 - index) * (LUT[index+1] - LUT[index])) - M_PI_2;
}
}
}
double atan_double(double x) {
/*
More precise look-up table is used for higher accuracy
*/
if (x >= 0) {
if (x <= 1) {
int index = round(x * 100);
return (LUT_d[index] + (x * 100 - index) * (LUT_d[index + 1] - LUT_d[index]));
} else {
double re_x = 1 / x;
int index = round(re_x * 100);
return (M_PI_2 - (LUT_d[index] + (re_x * 100 - index) * (LUT_d[index + 1] - LUT_d[index])));
// No recursive is better here
}
} else {
if (x >= -1) {
double abs_x = -x;
int index = round(abs_x * 100);
return -(LUT_d[index] + (abs_x * 100 - index) * (LUT_d[index + 1] - LUT_d[index]));
} else {
double re_x = 1 / (-x);
int index = round(re_x * 100);
return (LUT_d[index] + (re_x * 100 - index) * (LUT_d[index+1] - LUT_d[index])) - M_PI_2;
}
}
}