71 lines
1.6 KiB
C
71 lines
1.6 KiB
C
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#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 modd(x, y) ((x) - (int)((x) / (y)) * (y))
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double cos_t(double 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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double xx = x * x;
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return 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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}
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double sin_t(double x) {
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return cos_t(HALF_PI - x);
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}
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double tan_t(double x) {
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double c = cos_t(x);
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if (c==0.0) return 0;
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return sin_t(x) / c;
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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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x = std::abs(x);
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float ret = -0.0187293;
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ret = ret * x;
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ret = ret + 0.0742610;
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ret = ret * x;
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ret = ret - 0.2121144;
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ret = ret * x;
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ret = ret + HALF_PI;
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ret = ret * sqrt(1.0-x);
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ret = ret - 2 * negate * ret;
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return negate * PI + ret;
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}
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float asin_t(float x) {
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return HALF_PI - acos_t(x);
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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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double atan_t(double x) {
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double xx = x * x;
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return ((A*xx + B)*xx + C)*x;
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}
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#endif
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