added full stack of inverse trigonmetric functions

This commit is contained in:
Sven Vogel 2023-06-01 19:54:11 +02:00
parent 37efbe333c
commit 9273c738c8
2 changed files with 84 additions and 7 deletions

View File

@ -1,9 +1,14 @@
#include "library.h" #include "library.h"
#include <inttypes.h>
float sgn(const float x) { float sgn(const float x) {
return x < 0 ? -1 : 1; return x < 0 ? -1 : 1;
} }
float signum(const float x) {
return x < 0 ? -1.0f : (x == 0.0f ? 0.0f : 1.0f);
}
long long fac(const long long x) { long long fac(const long long x) {
long long prod = 1; long long prod = 1;
for (long long i = 2; i <= x; i++) { for (long long i = 2; i <= x; i++) {
@ -112,7 +117,7 @@ inline float cot(const float x) {
return tan(PI * 0.5f - x); return tan(PI * 0.5f - x);
} }
float arctan(const float x) { float atan(const float x) {
const float a = 0.6204500718160764f; const float a = 0.6204500718160764f;
const float b = 0.6204500718160764f; const float b = 0.6204500718160764f;
const float c = 0.9031580043522688f; const float c = 0.9031580043522688f;
@ -120,14 +125,35 @@ float arctan(const float x) {
return a * x / (b + sqrt(c + x * x)); return a * x / (b + sqrt(c + x * x));
} }
inline float arccot(const float x) { inline float acot(const float x) {
return PI * 0.5f - arctan(x); return PI * 0.5f - atan(x);
} }
float atan2(const float x, const float y) { inline float acsc(const float x) {
return arctan(y/x); return asin(1/x);
} }
float arcsin(const float x) { inline float asec(const float x) {
return asin(-1/x) + PI * 0.5f;
}
float asin(const float x) {
return atan(x * inv_sqrt((1 + x) * (1 - x)));
}
float acos(const float x) {
return asin(-x) + PI * 0.5f;
}
float inv_sqrt(const float x) {
union {
float f;
uint32_t i;
} conv = { .f = x };
conv.i = 0x5f1ffff9 - (conv.i >> 1);
for (int k = 0; k < INV_SQRT_NEWTON_STEPS; k++)
conv.f *= 0.703952253f * (2.38924456f - x * conv.f * conv.f);
return conv.f;
} }

View File

@ -3,6 +3,7 @@
#define TAYLOR_SERIES_DEGREE 34 #define TAYLOR_SERIES_DEGREE 34
#define SQRT_NEWTON_ITERATIONS 26 #define SQRT_NEWTON_ITERATIONS 26
#define INV_SQRT_NEWTON_STEPS 2
const float PI = 3.1415926535897932384626433f; const float PI = 3.1415926535897932384626433f;
@ -14,6 +15,14 @@ const float PI = 3.1415926535897932384626433f;
*/ */
float sgn(float x); float sgn(float x);
/**
* Computes the signum of the parameter x.
* Returns 1 if x > 0, 0 if x equals 0 and -1 if x < 0
* @param x
* @return
*/
float signum(float x);
/** /**
* Compute the factorial of parameter x. * Compute the factorial of parameter x.
* This function only properly works on natural numbers. * This function only properly works on natural numbers.
@ -155,8 +164,50 @@ float cot(float x);
* @param x * @param x
* @return * @return
*/ */
float arctan(float x); float atan(float x);
/**
* Approximates the inverse of the sine of x
* @param x
* @return
*/
float asin(float x);
/**
* Approximates the inverse of the cosine of x
* @param x
* @return
*/
float acos(float x);
/**
* Approximates the inverse of the cotangent of x
* @param x
* @return
*/
float acot(float x);
/**
* Approximates the inverse of the cosecant of x
* @param x
* @return
*/
float acsc(float x);
/**
* Approximates the inverse of the secant of x
* @param x
* @return
*/
float asec(float x);
/**
* Approximate the inverse square root.
* This implementation is based on the algorithm introduced in the Quake game with
* various improvements.
* @param x
* @return 1/sqrt(x)
*/
float inv_sqrt(float x);
#endif //COMMON_MATH_LIBRARY_H #endif //COMMON_MATH_LIBRARY_H