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cleanup and improvement to sin_appros()
-replaced all PI references with M_PI version -there is no need to do the angle-modulo in float, casting it to an integer does the same BUT it has to be cast to an `int` first, see comment.
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@ -15,17 +15,17 @@
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// Note: cos_t, sin_t and tan_t are very accurate but may be slow
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// the math.h functions use several kB of flash and are to be avoided if possible
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// sin16_t / cos16_t are faster and much more accurate than the fastled variants
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// sin_approx and cos_approx are float wrappers for sin16_t/cos16_t and have an accuracy of +/-0.0015 compared to sinf()
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// sin_approx and cos_approx are float wrappers for sin16_t/cos16_t and have an accuracy better than +/-0.0015 compared to sinf()
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// sin8_t / cos8_t are fastled replacements and use sin16_t / cos16_t. Slightly slower than fastled version but very accurate
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float cos_t(float phi)
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{
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float x = modd(phi, TWO_PI);
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float x = modd(phi, M_TWOPI);
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if (x < 0) x = -1 * x;
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int8_t sign = 1;
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if (x > PI)
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if (x > M_PI)
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{
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x -= PI;
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x -= M_PI;
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sign = -1;
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}
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float xx = x * x;
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@ -38,7 +38,7 @@ float cos_t(float phi)
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}
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float sin_t(float phi) {
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float res = cos_t(HALF_PI - phi);
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float res = cos_t(M_PI_2 - phi);
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#ifdef WLED_DEBUG_MATH
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Serial.printf("sin: %f,%f,%f,(%f)\n",x,res,sin(x),res-sin(x));
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#endif
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@ -87,9 +87,7 @@ uint8_t cos8_t(uint8_t theta) {
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float sin_approx(float theta)
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{
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theta = modd(theta, TWO_PI); // modulo: bring to -2pi to 2pi range
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if(theta < 0) theta += TWO_PI; // 0-2pi range
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uint16_t scaled_theta = (uint16_t)(theta * (0xFFFF / TWO_PI));
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uint16_t scaled_theta = (int)(theta * (0xFFFF / M_TWOPI)); // note: do not cast negative float to uint! cast to int first (undefined on C3)
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int32_t result = sin16_t(scaled_theta);
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float sin = float(result) / 0x7FFF;
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return sin;
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@ -118,10 +116,10 @@ float atan2_t(float y, float x) {
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float angle;
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if(x < 0) {
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r = -r;
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angle = M_PI/2.0f + M_PI/4.f;
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angle = M_PI_2 + M_PI_4;
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}
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else
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angle = M_PI/2.0f - M_PI/4.f;
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angle = M_PI_2 - M_PI_4;
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float add = (ATAN2_CONST_A * (r * r) - ATAN2_CONST_B) * r;
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angle += add;
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@ -140,10 +138,10 @@ float acos_t(float x) {
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ret = ret * xabs;
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ret = ret - 0.2121144f;
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ret = ret * xabs;
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ret = ret + HALF_PI;
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ret = ret + M_PI_2;
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ret = ret * sqrt(1.0f-xabs);
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ret = ret - 2 * negate * ret;
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float res = negate * PI + ret;
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float res = negate * M_PI + ret;
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#ifdef WLED_DEBUG_MATH
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Serial.printf("acos: %f,%f,%f,(%f)\n",x,res,acos(x),res-acos(x));
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#endif
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@ -151,7 +149,7 @@ float acos_t(float x) {
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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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float res = M_PI_2 - acos_t(x);
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#ifdef WLED_DEBUG_MATH
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Serial.printf("asin: %f,%f,%f,(%f)\n",x,res,asin(x),res-asin(x));
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#endif
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@ -167,7 +165,7 @@ float atan_t(float x) {
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//For A/B/C, see https://stackoverflow.com/a/42542593
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static const double A { 0.0776509570923569 };
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static const double B { -0.287434475393028 };
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static const double C { ((HALF_PI/2) - A - B) };
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static const double C { ((M_PI_4) - A - B) };
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// polynominal factors for approximation between 1 and 5
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static const float C0 { 0.089494f };
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static const float C1 { 0.974207f };
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@ -182,7 +180,7 @@ float atan_t(float x) {
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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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res = M_PI_2 - (1.0f/x);
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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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