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