From 9273c738c84d060efee4592c9c92e12955121be8 Mon Sep 17 00:00:00 2001
From: teridax <sven.vogel123@web.de>
Date: Thu, 1 Jun 2023 19:54:11 +0200
Subject: [PATCH] added full stack of inverse trigonmetric functions

---
 library.c | 38 ++++++++++++++++++++++++++++++++------
 library.h | 53 ++++++++++++++++++++++++++++++++++++++++++++++++++++-
 2 files changed, 84 insertions(+), 7 deletions(-)

diff --git a/library.c b/library.c
index 8f768dd..3d5a30e 100644
--- a/library.c
+++ b/library.c
@@ -1,9 +1,14 @@
 #include "library.h"
+#include <inttypes.h>
 
 float sgn(const float x) {
     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 prod = 1;
     for (long long i = 2; i <= x; i++) {
@@ -112,7 +117,7 @@ inline float cot(const float x) {
     return tan(PI * 0.5f - x);
 }
 
-float arctan(const float x) {
+float atan(const float x) {
     const float a = 0.6204500718160764f;
     const float b = 0.6204500718160764f;
     const float c = 0.9031580043522688f;
@@ -120,14 +125,35 @@ float arctan(const float x) {
     return a * x / (b + sqrt(c + x * x));
 }
 
-inline float arccot(const float x) {
-    return PI * 0.5f - arctan(x);
+inline float acot(const float x) {
+    return PI * 0.5f - atan(x);
 }
 
-float atan2(const float x, const float y) {
-    return arctan(y/x);
+inline float acsc(const float 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;
 }
\ No newline at end of file
diff --git a/library.h b/library.h
index ba4cd14..15fb1ec 100644
--- a/library.h
+++ b/library.h
@@ -3,6 +3,7 @@
 
 #define TAYLOR_SERIES_DEGREE 34
 #define SQRT_NEWTON_ITERATIONS 26
+#define INV_SQRT_NEWTON_STEPS 2
 
 const float PI = 3.1415926535897932384626433f;
 
@@ -14,6 +15,14 @@ const float PI = 3.1415926535897932384626433f;
  */
 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.
  * This function only properly works on natural numbers.
@@ -155,8 +164,50 @@ float cot(float x);
  * @param x
  * @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