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Speed improvements, commented legacy _t trig functions

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- speed improvement: by default M_TWOPI is treated as a double float
- directly calling sin16_t in cos_approx() saves a lot of overhead
This commit is contained in:
Damian Schneider
2024-11-26 20:32:39 +01:00
parent 98a6907976
commit 1a8aaa3b26
1 changed files with 14 additions and 9 deletions
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23
wled00/wled_math.cpp
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@@ -10,14 +10,17 @@
//#define WLED_DEBUG_MATH //#define WLED_DEBUG_MATH
#define modd(x, y) ((x) - (int)((x) / (y)) * (y)) // Note: cos_t, sin_t and tan_t are very accurate but slow
// Note: cos_t, sin_t and tan_t are very accurate but may be slow
// the math.h functions use several kB of flash and are to be avoided if possible // the math.h functions use several kB of flash and are to be avoided if possible
// sin16_t / cos16_t are faster and much more accurate than the fastled variants // sin16_t / cos16_t are faster and much more accurate than the fastled variants
// sin_approx and cos_approx are float wrappers for sin16_t/cos16_t and have an accuracy better than +/-0.0015 compared to sinf() // sin_approx and cos_approx are float wrappers for sin16_t/cos16_t and have an accuracy better than +/-0.0015 compared to sinf()
// sin8_t / cos8_t are fastled replacements and use sin16_t / cos16_t. Slightly slower than fastled version but very accurate // sin8_t / cos8_t are fastled replacements and use sin16_t / cos16_t. Slightly slower than fastled version but very accurate
// Taylor series approximations, replaced with Bhaskara I's approximation
/*
#define modd(x, y) ((x) - (int)((x) / (y)) * (y))
float cos_t(float phi) float cos_t(float phi)
{ {
float x = modd(phi, M_TWOPI); float x = modd(phi, M_TWOPI);
@@ -54,6 +57,7 @@ float tan_t(float x) {
#endif #endif
return res; return res;
} }
*/
// 16-bit, integer based Bhaskara I's sine approximation: 16*x*(pi - x) / (5*pi^2 - 4*x*(pi - x)) // 16-bit, integer based Bhaskara I's sine approximation: 16*x*(pi - x) / (5*pi^2 - 4*x*(pi - x))
// input is 16bit unsigned (0-65535), output is 16bit signed (-32767 to +32767) // input is 16bit unsigned (0-65535), output is 16bit signed (-32767 to +32767)
@@ -85,17 +89,18 @@ uint8_t cos8_t(uint8_t theta) {
return sin8_t(theta + 64); //cos(x) = sin(x+pi/2) return sin8_t(theta + 64); //cos(x) = sin(x+pi/2)
} }
float sin_approx(float theta) float sin_approx(float theta) {
{ uint16_t scaled_theta = (int)(theta * (float)(0xFFFF / M_TWOPI)); // note: do not cast negative float to uint! cast to int first (undefined on C3)
uint16_t scaled_theta = (int)(theta * (0xFFFF / M_TWOPI)); // note: do not cast negative float to uint! cast to int first (undefined on C3)
int32_t result = sin16_t(scaled_theta); int32_t result = sin16_t(scaled_theta);
float sin = float(result) / 0x7FFF; float sin = float(result) / 0x7FFF;
return sin; return sin;
} }
float cos_approx(float theta) float cos_approx(float theta) {
{ uint16_t scaled_theta = (int)(theta * (float)(0xFFFF / M_TWOPI)); // note: do not cast negative float to uint! cast to int first (undefined on C3)
return sin_approx(theta + M_PI_2); int32_t result = sin16_t(scaled_theta + 16384);
float cos = float(result) / 0x7FFF;
return cos;
} }
float tan_approx(float x) { float tan_approx(float x) {