Implemented the fast inverse sqrt algoritm

Used in all vector normalization functions instead of `1/sqrt(x)`.

Author: iWas-Coder

src/carbon_math.c

@@ -178,6 +178,16 @@ f32 carbon_math_sqrt(f32 x) {
 #endif
 }
 
+f32 carbon_math_rsqrt(f32 x) {
+  // Fast Inverse Square Root algorithm
+  f32 x2 = x/2, y = x;
+  i32 i = *((i32 *) &y);      // evil floating point bit level hacking
+  i = 0x5f3759df - (i >> 1);  // what the fuck?
+  y = *((f32 *) &i);
+  y *= (1.5 - (x2 * y * y));
+  return y;
+}
+
 i32 carbon_math_imod(i32 x, i32 y) {
   CBN_ASSERT(y && "division by 0 is not defined");
   return (x%y + y) % y;

src/carbon_math.h

@@ -151,6 +151,13 @@ CBNDEF f32 carbon_math_snap(f32 x, f32 dx);
  */
 CBNDEF f32 carbon_math_sqrt(f32 x);
 
+/**
+ * @brief Returns the reciprocal (multiplicative inverse) of the square root of a specified number.
+ * @param x The number.
+ * @return An approximation of 1/√x, provided x ≥ 0.
+ */
+CBNDEF f32 carbon_math_rsqrt(f32 x);
+
 /**
  * @brief Performs a true modulo operation for integers.
  * @param x The dividend.

src/carbon_math_quat.c

@@ -47,9 +47,9 @@ f32 carbon_math_quat_len(CBN_Quat q) {
 }
 
 CBN_Quat carbon_math_quat_norm(CBN_Quat q) {
-  f32 len = carbon_math_quat_len(q);
-  if (!len) return q;
-  return carbon_math_quat_scale(q, 1/len);
+  f32 sqlen = carbon_math_quat_len_squared(q);
+  if (sqlen <= CARBON_EPS_SQ) return q;
+  return carbon_math_quat_scale(q, carbon_math_rsqrt(sqlen));
 }
 
 CBN_Quat carbon_math_quat_inv(CBN_Quat q) {

src/carbon_math_vec2.c

@@ -38,7 +38,7 @@ f32 carbon_math_vec2_len(CBN_Vec2 v) {
 CBN_Vec2 carbon_math_vec2_norm(CBN_Vec2 v) {
   f32 sqlen = carbon_math_vec2_len_squared(v);
   if (sqlen <= CARBON_EPS_SQ) return v;
-  return carbon_math_vec2_scale(v, 1/carbon_math_sqrt(sqlen));
+  return carbon_math_vec2_scale(v, carbon_math_rsqrt(sqlen));
 }
 
 CBN_Vec2 carbon_math_vec2_lerp(CBN_Vec2 u, CBN_Vec2 v, f32 t) {

src/carbon_math_vec3.c

@@ -42,7 +42,7 @@ f32 carbon_math_vec3_len(CBN_Vec3 v) {
 CBN_Vec3 carbon_math_vec3_norm(CBN_Vec3 v) {
   f32 sqlen = carbon_math_vec3_len_squared(v);
   if (sqlen <= CARBON_EPS_SQ) return v;
-  return carbon_math_vec3_scale(v, 1/carbon_math_sqrt(sqlen));
+  return carbon_math_vec3_scale(v, carbon_math_rsqrt(sqlen));
 }
 
 char *carbon_math_vec3_to_cstr(CBN_Vec3 v) {