From 37efbe333c0d5cd247fc3799fd15f3fe41f0f7cd Mon Sep 17 00:00:00 2001
From: teridax <sven.vogel123@web.de>
Date: Thu, 1 Jun 2023 18:29:58 +0200
Subject: [PATCH] Added `hypot`, `sqrt` and `sgn` function.

---
 library.c | 58 +++++++++++++++++++++++++++++++++++++++++++++++++
 library.h | 65 +++++++++++++++++++++++++++++++++++++++++++++++++++++++
 2 files changed, 123 insertions(+)

diff --git a/library.c b/library.c
index 95ca696..8f768dd 100644
--- a/library.c
+++ b/library.c
@@ -1,5 +1,9 @@
 #include "library.h"
 
+float sgn(const float x) {
+    return x < 0 ? -1 : 1;
+}
+
 long long fac(const long long x) {
     long long prod = 1;
     for (long long i = 2; i <= x; i++) {
@@ -8,6 +12,16 @@ long long fac(const long long x) {
     return prod;
 }
 
+long long fib(const long long n) {
+    long long sum = 0;
+    long long prev = 0;
+    for (long long i = 1LL; i <= n; i++) {
+        sum += prev;
+        prev = i - 1;
+    }
+    return sum;
+}
+
 inline float trunc(const float x) {
     return (float)(int)(x);
 }
@@ -49,6 +63,18 @@ float exp(const float x) {
     return sum;
 }
 
+float sqrt(const float x) {
+    float a = x;
+    for (int i = 0; i < SQRT_NEWTON_ITERATIONS; i++) {
+        a = 0.5f * (x/a + a);
+    }
+    return a;
+}
+
+float hypot(const float x, const float y) {
+    return x + 0.5f * y * y / x;
+}
+
 float sin(const float x) {
     float sign = -1;
     float prod = 1;
@@ -73,3 +99,35 @@ inline float cos(const float x) {
 inline float tan(const float x) {
     return sin(x)/cos(x);
 }
+
+inline float csc(const float x) {
+    return 1.0f / sin(x);
+}
+
+inline float sec(const float x) {
+    return 1.0f / cos(x);
+}
+
+inline float cot(const float x) {
+    return tan(PI * 0.5f - x);
+}
+
+float arctan(const float x) {
+    const float a = 0.6204500718160764f;
+    const float b = 0.6204500718160764f;
+    const float c = 0.9031580043522688f;
+
+    return a * x / (b + sqrt(c + x * x));
+}
+
+inline float arccot(const float x) {
+    return PI * 0.5f - arctan(x);
+}
+
+float atan2(const float x, const float y) {
+    return arctan(y/x);
+}
+
+float arcsin(const float x) {
+
+}
\ No newline at end of file
diff --git a/library.h b/library.h
index dae226f..ba4cd14 100644
--- a/library.h
+++ b/library.h
@@ -2,9 +2,18 @@
 #define COMMON_MATH_LIBRARY_H
 
 #define TAYLOR_SERIES_DEGREE 34
+#define SQRT_NEWTON_ITERATIONS 26
 
 const float PI = 3.1415926535897932384626433f;
 
+/**
+ * Computes the sign of the parameter x.
+ * Returns 1 if x >= 0 and -1 if x < 0
+ * @param x
+ * @return
+ */
+float sgn(float x);
+
 /**
  * Compute the factorial of parameter x.
  * This function only properly works on natural numbers.
@@ -15,6 +24,16 @@ const float PI = 3.1415926535897932384626433f;
  */
 long long fac(long long x);
 
+/**
+ * Computes the n-th element of the fibonacci sequence.
+ * This function only properly works on natural numbers.
+ * The implementation is an iterative one and is only limited by the size
+ * of the type used in the calculation.
+ * @param n the n-th element to compute
+ * @return the n-th fibonacci number
+ */
+long long fib(long long n);
+
 /**
  * Truncates the parameter x.
  * In other words this function will cut of the fraction part of the number x.
@@ -73,6 +92,22 @@ float mod(float x, float y);
  */
 float exp(float x);
 
+/**
+ * Approximate the sqrt of x using the newton's method.
+ * Precision an be optimized via SQRT_NEWTON_ITERATIONS
+ * @param x
+ * @return sqrt(x)
+ */
+float sqrt(float x);
+
+/**
+ * Approximate the hypotenuse of x and y (sqrt(x²+y²)) using the babylonian method.
+ * @param x
+ * @param y
+ * @return sqrt(x²+y²)
+ */
+float hypot(float x, float y);
+
 /**
  * Computes the sine of x.
  * @param x
@@ -94,4 +129,34 @@ float cos(float x);
  */
 float tan(float x);
 
+/**
+ * Computes an approximation of the cosecant of parameter x.
+ * @param x
+ * @return csc(x)
+ */
+float csc(float x);
+
+/**
+ * Computes an approximation of the secant of parameter x.
+ * @param x
+ * @return sec(x)
+ */
+float sec(float x);
+
+/**
+ * Computes an approximation of the cotangent of parameter x.
+ * @param x
+ * @return cot(x)
+ */
+float cot(float x);
+
+/**
+ * Approximates the inverse of the tangent of x
+ * @param x
+ * @return
+ */
+float arctan(float x);
+
+
+
 #endif //COMMON_MATH_LIBRARY_H