WLED/wled00/wled_math.h

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#ifndef WLED_MATH_H
#define WLED_MATH_H
/*
* Contains some trigonometric functions.
* The ANSI C equivalents are likely faster, but using any sin/cos/tan function incurs a memory penalty of 460 bytes on ESP8266, likely for lookup tables.
* This implementation has no extra static memory usage.
*
* Source of the cos_t() function: https://web.eecs.utk.edu/~azh/blog/cosine.html (cos_taylor_literal_6terms)
*/
#include <Arduino.h> //PI constant
//#define WLED_DEBUG_MATH
#define modd(x, y) ((x) - (int)((x) / (y)) * (y))
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float cos_t(float phi)
{
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float x = modd(phi, TWO_PI);
int8_t sign = 1;
if (x > PI)
{
x -= PI;
sign = -1;
}
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float xx = x * x;
float res = sign * (1 - ((xx) / (2)) + ((xx * xx) / (24)) - ((xx * xx * xx) / (720)) + ((xx * xx * xx * xx) / (40320)) - ((xx * xx * xx * xx * xx) / (3628800)) + ((xx * xx * xx * xx * xx * xx) / (479001600)));
#ifdef WLED_DEBUG_MATH
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Serial.printf("cos: %f,%f,%f,(%f)\n",phi,res,cos(x),res-cos(x));
#endif
return res;
}
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float sin_t(float x) {
float res = cos_t(HALF_PI - x);
#ifdef WLED_DEBUG_MATH
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Serial.printf("sin: %f,%f,%f,(%f)\n",x,res,sin(x),res-sin(x));
#endif
return res;
}
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float tan_t(float x) {
float c = cos_t(x);
if (c==0.0) return 0;
float res = sin_t(x) / c;
#ifdef WLED_DEBUG_MATH
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Serial.printf("tan: %f,%f,%f,(%f)\n",x,res,tan(x),res-tan(x));
#endif
return res;
}
//https://stackoverflow.com/questions/3380628
// Absolute error <= 6.7e-5
float acos_t(float x) {
float negate = float(x < 0);
float xabs = std::abs(x);
float ret = -0.0187293;
ret = ret * xabs;
ret = ret + 0.0742610;
ret = ret * xabs;
ret = ret - 0.2121144;
ret = ret * xabs;
ret = ret + HALF_PI;
ret = ret * sqrt(1.0-xabs);
ret = ret - 2 * negate * ret;
float res = negate * PI + ret;
#ifdef WLED_DEBUG_MATH
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Serial.printf("acos: %f,%f,%f,(%f)\n",x,res,acos(x),res-acos(x));
#endif
return res;
}
float asin_t(float x) {
float res = HALF_PI - acos_t(x);
#ifdef WLED_DEBUG_MATH
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Serial.printf("asin: %f,%f,%f,(%f)\n",x,res,asin(x),res-asin(x));
#endif
return res;
}
//https://stackoverflow.com/a/42542593
#define A 0.0776509570923569
#define B -0.287434475393028
#define C ((HALF_PI/2) - A - B)
//polynominal factors for approximation between 1 and 5
#define C0 0.089494f
#define C1 0.974207f
#define C2 -0.326175f
#define C3 0.05375f
#define C4 -0.003445f
float atan_t(float x) {
bool neg = (x < 0);
#ifdef WLED_DEBUG_MATH
float xinput = x;
#endif
x = std::abs(x);
float res;
if (x > 5.0f) { //atan(x) converges to pi/2 - (1/x) for large values
res = HALF_PI - (1.0f/x);
}
else if (x > 1.0f) { //1 < x < 5
float xx = x * x;
res = (C4*xx*xx)+(C3*xx*x)+(C2*xx)+(C1*x)+C0;
} else { //this approximation is only for x <= 1
float xx = x * x;
res = ((A*xx + B)*xx + C)*x;
}
if (neg) res = -res;
#ifdef WLED_DEBUG_MATH
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Serial.printf("atan: %f,%f,%f,(%f)\n",xinput,res,atan(xinput),res-atan(xinput));
#endif
return res;
}
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float floor_t(float x) {
bool neg = x < 0;
int val = x;
if (neg) val--;
#ifdef WLED_DEBUG_MATH
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Serial.printf("floor: %f,%f,%f\n",x,(float)val,floor(x));
#endif
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return val;
}
float fmod_t(float num, float denom) {
int tquot = num / denom;
float res = num - tquot * denom;
#ifdef WLED_DEBUG_MATH
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Serial.printf("fmod: %f,%f,(%f)\n",res,fmod(num,denom),res-fmod(num,denom));
#endif
return res;
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}
#endif