From fcbec620242a755faa682b8bd924ac5f8cb94661 Mon Sep 17 00:00:00 2001
From: Andrey Pokidov <andrey.pokidov@gmail.com>
Date: Wed, 25 Dec 2024 13:37:23 +0700
Subject: [PATCH] =?UTF-8?q?=D0=9F=D1=80=D0=B8=D0=B0=D0=B2=D0=B5=D0=B4?=
 =?UTF-8?q?=D0=B5=D0=BD=D0=B8=D0=B5=20=D1=82=D0=B0=D0=BD=D0=B3=D0=B5=D0=BD?=
 =?UTF-8?q?=D1=81=D0=B0=20(tangent)=20=D0=BA=20=D0=B5=D0=B4=D0=B8=D0=BD?=
 =?UTF-8?q?=D0=BE=D0=BC=D1=83=20=D0=B2=D0=B8=D0=B4=D1=83=20=D1=81=20=D0=B4?=
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---
 basic-geometry-dev/main.c         |   2 +-
 basic-geometry/basic-geometry.cbp |   4 +
 basic-geometry/tangent.h          | 244 +++++++++++++++++++-----------
 basic-geometry/vector2.h          |  22 ++-
 basic-geometry/versor.h           |  24 ---
 5 files changed, 182 insertions(+), 114 deletions(-)

diff --git a/basic-geometry-dev/main.c b/basic-geometry-dev/main.c
index 2b30542..a9665a9 100644
--- a/basic-geometry-dev/main.c
+++ b/basic-geometry-dev/main.c
@@ -93,7 +93,7 @@ BgFP32Versor * make_random_versors(const unsigned int amount)
 
 void print_versor(const BgFP32Versor* versor)
 {
-    printf("Versor (%f, %f, %f, %f); Delta = %e\n", versor->s0, versor->x1, versor->x2, versor->x3, bg_fp32_versor_get_modulus(versor) - 1.0f);
+    printf("Versor (%f, %f, %f, %f)\n", versor->s0, versor->x1, versor->x2, versor->x3);
 }
 
 void print_vector(const BgFP32Vector3* vector)
diff --git a/basic-geometry/basic-geometry.cbp b/basic-geometry/basic-geometry.cbp
index 1c35dce..d128ff0 100644
--- a/basic-geometry/basic-geometry.cbp
+++ b/basic-geometry/basic-geometry.cbp
@@ -74,6 +74,10 @@
 			<Option compilerVar="CC" />
 		</Unit>
 		<Unit filename="rotation3.h" />
+		<Unit filename="tangent.c">
+			<Option compilerVar="CC" />
+		</Unit>
+		<Unit filename="tangent.h" />
 		<Unit filename="vector2.c">
 			<Option compilerVar="CC" />
 		</Unit>
diff --git a/basic-geometry/tangent.h b/basic-geometry/tangent.h
index a0487eb..95c0388 100644
--- a/basic-geometry/tangent.h
+++ b/basic-geometry/tangent.h
@@ -8,16 +8,30 @@
 #include "vector2.h"
 #include "matrix2x2.h"
 
+// =================== Types ==================== //
+
 typedef struct
 {
-    float _cos, _sin;
+    const float cos, sin;
 } BgFP32Tangent;
 
 typedef struct
 {
-    double _cos, _sin;
+    const double cos, sin;
 } BgFP64Tangent;
 
+// ================= Dark Twins ================= //
+
+typedef struct {
+    float cos, sin;
+} __BgFP32DarkTwinTangent;
+
+typedef struct {
+    double cos, sin;
+} __BgFP64DarkTwinTangent;
+
+// ================= Constants ================== //
+
 extern const BgFP32Tangent BG_FP32_IDLE_TANGENT;
 extern const BgFP64Tangent BG_FP64_IDLE_TANGENT;
 
@@ -25,212 +39,266 @@ extern const BgFP64Tangent BG_FP64_IDLE_TANGENT;
 
 static inline void bg_fp32_tangent_reset(BgFP32Tangent* tangent)
 {
-    tangent->_cos = 1.0f;
-    tangent->_sin = 0.0f;
+    __BgFP32DarkTwinTangent* twin = (__BgFP32DarkTwinTangent*)tangent;
+
+    twin->cos = 1.0f;
+    twin->sin = 0.0f;
 }
 
 static inline void bg_fp64_tangent_reset(BgFP64Tangent* tangent)
 {
-    tangent->_cos = 1.0;
-    tangent->_sin = 0.0;
+    __BgFP64DarkTwinTangent* twin = (__BgFP64DarkTwinTangent*)tangent;
+
+    twin->cos = 1.0;
+    twin->sin = 0.0;
 }
 
-// ==================== Copy ==================== //
-
-static inline void bg_fp32_tangent_copy(const BgFP32Tangent* from, BgFP32Tangent* to)
-{
-    to->_cos = from->_cos;
-    to->_sin = from->_sin;
-}
-
-static inline void bg_fp64_tangent_copy(const BgFP64Tangent* from, BgFP64Tangent* to)
-{
-    to->_cos = from->_cos;
-    to->_sin = from->_sin;
-}
-
-// ==================== Make ==================== //
+// ==================== Set ===================== //
 
 static inline void bg_fp32_tangent_set_values(const float x1, const float x2, BgFP32Tangent* tangent)
 {
     const float square_module = x1 * x1 + x2 * x2;
 
-    tangent->_cos = x1;
-    tangent->_sin = x2;
+    __BgFP32DarkTwinTangent* twin = (__BgFP32DarkTwinTangent*)tangent;
+
+    twin->cos = x1;
+    twin->sin = x2;
 
     if (1.0f - BG_FP32_TWO_EPSYLON <= square_module && square_module <= 1.0f + BG_FP32_TWO_EPSYLON) {
         return;
     }
 
     if (square_module <= BG_FP32_SQUARE_EPSYLON) {
-        tangent->_cos = 1.0f;
-        tangent->_sin = 0.0f;
+        twin->cos = 1.0f;
+        twin->sin = 0.0f;
         return;
     }
 
     const float multiplier = sqrtf(1.0f / square_module);
 
-    tangent->_cos = x1 * multiplier;
-    tangent->_sin = x2 * multiplier;
+    twin->cos = x1 * multiplier;
+    twin->sin = x2 * multiplier;
 }
 
 static inline void bg_fp64_tangent_set_values(const double x1, const double x2, BgFP64Tangent* tangent)
 {
     const double square_module = x1 * x1 + x2 * x2;
 
-    tangent->_cos = x1;
-    tangent->_sin = x2;
+    __BgFP64DarkTwinTangent* twin = (__BgFP64DarkTwinTangent*)tangent;
+
+    twin->cos = x1;
+    twin->sin = x2;
 
     if (1.0 - BG_FP64_TWO_EPSYLON <= square_module && square_module <= 1.0 + BG_FP64_TWO_EPSYLON) {
         return;
     }
 
     if (square_module <= BG_FP64_SQUARE_EPSYLON) {
-        tangent->_cos = 1.0;
-        tangent->_sin = 0.0;
+        twin->cos = 1.0;
+        twin->sin = 0.0;
         return;
     }
 
     const double multiplier = sqrt(1.0 / square_module);
 
-    tangent->_cos = x1 * multiplier;
-    tangent->_sin = x2 * multiplier;
+    twin->cos = x1 * multiplier;
+    twin->sin = x2 * multiplier;
 }
 
-// ================== Set Angle ================= //
+// ==================== Copy ==================== //
 
-static inline void bg_fp32_tangent_set_angle(const float angle, const angle_unit_t unit, BgFP32Tangent* tangent)
+static inline void bg_fp32_tangent_copy(const BgFP32Tangent* from, BgFP32Tangent* to)
+{
+    __BgFP32DarkTwinTangent* twin = (__BgFP32DarkTwinTangent*)to;
+
+    twin->cos = from->cos;
+    twin->sin = from->sin;
+}
+
+static inline void bg_fp64_tangent_copy(const BgFP64Tangent* from, BgFP64Tangent* to)
+{
+    __BgFP64DarkTwinTangent* twin = (__BgFP64DarkTwinTangent*)to;
+
+    twin->cos = from->cos;
+    twin->sin = from->sin;
+}
+
+// ==================== Swap ==================== //
+
+static inline void bg_fp32_tangent_swap(BgFP32Tangent* tangent1, BgFP32Tangent* tangent2)
+{
+    const float cos = tangent1->cos;
+    const float sin = tangent1->sin;
+
+    __BgFP32DarkTwinTangent* twin1 = (__BgFP32DarkTwinTangent*)tangent1;
+
+    twin1->cos = tangent2->cos;
+    twin1->sin = tangent2->sin;
+
+    __BgFP32DarkTwinTangent* twin2 = (__BgFP32DarkTwinTangent*)tangent2;
+
+    twin2->cos = cos;
+    twin2->sin = sin;
+}
+
+static inline void bg_fp64_tangent_swap(BgFP64Tangent* tangent1, BgFP64Tangent* tangent2)
+{
+    const double cos = tangent1->cos;
+    const double sin = tangent1->sin;
+
+    __BgFP64DarkTwinTangent* twin1 = (__BgFP64DarkTwinTangent*)tangent1;
+
+    twin1->cos = tangent2->cos;
+    twin1->sin = tangent2->sin;
+
+    __BgFP64DarkTwinTangent* twin2 = (__BgFP64DarkTwinTangent*)tangent2;
+
+    twin2->cos = cos;
+    twin2->sin = sin;
+}
+
+// ================== Set Turn ================== //
+
+static inline void bg_fp32_tangent_set_turn(const float angle, const angle_unit_t unit, BgFP32Tangent* tangent)
 {
     const float radians = bg_fp32_angle_to_radians(angle, unit);
 
-    tangent->_cos = cosf(radians);
-    tangent->_sin = sinf(radians);
+    __BgFP32DarkTwinTangent* twin = (__BgFP32DarkTwinTangent*)tangent;
+
+    twin->cos = cosf(radians);
+    twin->sin = sinf(radians);
 }
 
-static inline void bg_fp64_tangent_set_angle(const double angle, const angle_unit_t unit, BgFP64Tangent* tangent)
+static inline void bg_fp64_tangent_set_turn(const double angle, const angle_unit_t unit, BgFP64Tangent* tangent)
 {
     const double radians = bg_fp64_angle_to_radians(angle, unit);
 
-    tangent->_cos = cos(radians);
-    tangent->_sin = sin(radians);
+    __BgFP64DarkTwinTangent* twin = (__BgFP64DarkTwinTangent*)tangent;
+
+    twin->cos = cos(radians);
+    twin->sin = sin(radians);
 }
 
 // ============= Copy to twin type ============== //
 
-static inline void bg_fp32_tangent_copy_to_double(const BgFP32Tangent* from, BgFP64Tangent* to)
+static inline void bg_fp32_tangent_set_from_fp64(const BgFP64Tangent* from, BgFP32Tangent* to)
 {
-    bg_fp64_tangent_set_values((double)from->_cos, (double)from->_sin, to);
+    bg_fp32_tangent_set_values((float)from->cos, (float)from->sin, to);
 }
 
-static inline void bg_fp64_tangent_copy_to_single(const BgFP64Tangent* from, BgFP32Tangent* to)
+static inline void bg_fp64_tangent_set_from_fp32(const BgFP32Tangent* from, BgFP64Tangent* to)
 {
-    bg_fp32_tangent_set_values((float)from->_cos, (float)from->_sin, to);
+    bg_fp64_tangent_set_values((double)from->cos, (double)from->sin, to);
 }
 
 // ================= Inversion ================== //
 
 static inline void bg_fp32_tangent_invert(BgFP32Tangent* tangent)
 {
-    tangent->_sin = -tangent->_sin;
+    ((__BgFP32DarkTwinTangent*)tangent)->sin = -tangent->sin;
 }
 
 static inline void bg_fp64_tangent_invert(BgFP64Tangent* tangent)
 {
-    tangent->_sin = -tangent->_sin;
+    ((__BgFP64DarkTwinTangent*)tangent)->sin = -tangent->sin;
 }
 
 // ================ Set Inverted ================ //
 
 static inline void bg_fp32_tangent_set_inverted(const BgFP32Tangent* tangent, BgFP32Tangent* result)
 {
-    result->_cos = tangent->_cos;
-    result->_sin = -tangent->_sin;
+    __BgFP32DarkTwinTangent* twin = (__BgFP32DarkTwinTangent*)result;
+
+    twin->cos = tangent->cos;
+    twin->sin = -tangent->sin;
 }
 
 static inline void bg_fp64_tangent_set_inverted(const BgFP64Tangent* tangent, BgFP64Tangent* result)
 {
-    result->_cos = tangent->_cos;
-    result->_sin = -tangent->_sin;
+    __BgFP64DarkTwinTangent* twin = (__BgFP64DarkTwinTangent*)result;
+
+    twin->cos = tangent->cos;
+    twin->sin = -tangent->sin;
 }
 
 // ============== Rotation Matrix =============== //
 
 static inline void bg_fp32_tangent_make_rotation_matrix(const BgFP32Tangent* tangent, BgFP32Matrix2x2* matrix)
 {
-    matrix->r1c1 = tangent->_cos;
-    matrix->r1c2 = -tangent->_sin;
-    matrix->r2c1 = tangent->_sin;
-    matrix->r2c2 = tangent->_cos;
+    matrix->r1c1 = tangent->cos;
+    matrix->r1c2 = -tangent->sin;
+    matrix->r2c1 = tangent->sin;
+    matrix->r2c2 = tangent->cos;
 }
 
 static inline void bg_fp64_tangent_make_rotation_matrix(const BgFP64Tangent* tangent, BgFP64Matrix2x2* matrix)
 {
-    matrix->r1c1 = tangent->_cos;
-    matrix->r1c2 = -tangent->_sin;
-    matrix->r2c1 = tangent->_sin;
-    matrix->r2c2 = tangent->_cos;
+    matrix->r1c1 = tangent->cos;
+    matrix->r1c2 = -tangent->sin;
+    matrix->r2c1 = tangent->sin;
+    matrix->r2c2 = tangent->cos;
 }
 
 // ============== Reverse Matrix ================ //
 
 static inline void bg_fp32_tangent_make_reverse_matrix(const BgFP32Tangent* tangent, BgFP32Matrix2x2* matrix)
 {
-    matrix->r1c1 = tangent->_cos;
-    matrix->r1c2 = tangent->_sin;
-    matrix->r2c1 = -tangent->_sin;
-    matrix->r2c2 = tangent->_cos;
+    matrix->r1c1 = tangent->cos;
+    matrix->r1c2 = tangent->sin;
+    matrix->r2c1 = -tangent->sin;
+    matrix->r2c2 = tangent->cos;
 }
 
 static inline void bg_fp64_tangent_make_reverse_matrix(const BgFP64Tangent* tangent, BgFP64Matrix2x2* matrix)
 {
-    matrix->r1c1 = tangent->_cos;
-    matrix->r1c2 = tangent->_sin;
-    matrix->r2c1 = -tangent->_sin;
-    matrix->r2c2 = tangent->_cos;
+    matrix->r1c1 = tangent->cos;
+    matrix->r1c2 = tangent->sin;
+    matrix->r2c1 = -tangent->sin;
+    matrix->r2c2 = tangent->cos;
 }
 
 // =================== Angle =================== //
 
 static inline float bg_fp32_tangent_get_angle(const BgFP32Tangent* tangent, const angle_unit_t unit)
 {
-    if (tangent->_cos >= 1.0f - BG_FP32_TWO_EPSYLON) {
+    if (tangent->cos >= 1.0f - BG_FP32_TWO_EPSYLON) {
         return 0.0f;
     }
 
-    if (tangent->_cos <= -1.0f + BG_FP32_TWO_EPSYLON) {
+    if (tangent->cos <= -1.0f + BG_FP32_TWO_EPSYLON) {
         return bg_fp32_angle_get_half_circle(unit);
     }
 
-    if (tangent->_sin >= 1.0f - BG_FP32_TWO_EPSYLON) {
+    if (tangent->sin >= 1.0f - BG_FP32_TWO_EPSYLON) {
         return bg_fp32_angle_get_quater_circle(unit);
     }
 
-    if (tangent->_sin <= -1.0f + BG_FP32_TWO_EPSYLON) {
+    if (tangent->sin <= -1.0f + BG_FP32_TWO_EPSYLON) {
         return 0.75f * bg_fp32_angle_get_full_circle(unit);
     }
 
-    return bg_fp32_radians_to_units(atan2f(tangent->_cos, tangent->_sin), unit);
+    return bg_fp32_radians_to_units(atan2f(tangent->cos, tangent->sin), unit);
 }
 
 static inline double bg_fp64_tangent_get_angle(const BgFP64Tangent* tangent, const angle_unit_t unit)
 {
-    if (tangent->_cos >= 1.0 - BG_FP64_TWO_EPSYLON) {
+    if (tangent->cos >= 1.0 - BG_FP64_TWO_EPSYLON) {
         return 0.0;
     }
 
-    if (tangent->_cos <= -1.0 + BG_FP64_TWO_EPSYLON) {
+    if (tangent->cos <= -1.0 + BG_FP64_TWO_EPSYLON) {
         return bg_fp64_angle_get_half_circle(unit);
     }
 
-    if (tangent->_sin >= 1.0 - BG_FP64_TWO_EPSYLON) {
+    if (tangent->sin >= 1.0 - BG_FP64_TWO_EPSYLON) {
         return bg_fp64_angle_get_quater_circle(unit);
     }
 
-    if (tangent->_sin <= -1.0 + BG_FP64_TWO_EPSYLON) {
+    if (tangent->sin <= -1.0 + BG_FP64_TWO_EPSYLON) {
         return 0.75 * bg_fp64_angle_get_full_circle(unit);
     }
 
-    return bg_fp64_radians_to_units(atan2(tangent->_cos, tangent->_sin), unit);
+    return bg_fp64_radians_to_units(atan2(tangent->cos, tangent->sin), unit);
 }
 
 // ================ Combination ================= //
@@ -238,8 +306,8 @@ static inline double bg_fp64_tangent_get_angle(const BgFP64Tangent* tangent, con
 static inline void bg_fp32_tangent_combine(const BgFP32Tangent* tangent1, const BgFP32Tangent* tangent2, BgFP32Tangent* result)
 {
     bg_fp32_tangent_set_values(
-        tangent1->_cos * tangent2->_cos - tangent1->_sin * tangent2->_sin,
-        tangent1->_cos * tangent2->_sin + tangent1->_sin * tangent2->_cos,
+        tangent1->cos * tangent2->cos - tangent1->sin * tangent2->sin,
+        tangent1->cos * tangent2->sin + tangent1->sin * tangent2->cos,
         result
     );
 }
@@ -247,8 +315,8 @@ static inline void bg_fp32_tangent_combine(const BgFP32Tangent* tangent1, const
 static inline void bg_fp64_tangent_combine(const BgFP64Tangent* tangent1, const BgFP64Tangent* tangent2, BgFP64Tangent* result)
 {
     bg_fp64_tangent_set_values(
-        tangent1->_cos * tangent2->_cos - tangent1->_sin * tangent2->_sin,
-        tangent1->_cos * tangent2->_sin + tangent1->_sin * tangent2->_cos,
+        tangent1->cos * tangent2->cos - tangent1->sin * tangent2->sin,
+        tangent1->cos * tangent2->sin + tangent1->sin * tangent2->cos,
         result
     );
 }
@@ -257,8 +325,8 @@ static inline void bg_fp64_tangent_combine(const BgFP64Tangent* tangent1, const
 
 static inline void bg_fp32_tangent_turn(const BgFP32Tangent* tangent, const BgFP32Vector2* vector, BgFP32Vector2* result)
 {
-    const float x1 = tangent->_cos * vector->x1 - tangent->_sin * vector->x2;
-    const float x2 = tangent->_sin * vector->x1 + tangent->_cos * vector->x2;
+    const float x1 = tangent->cos * vector->x1 - tangent->sin * vector->x2;
+    const float x2 = tangent->sin * vector->x1 + tangent->cos * vector->x2;
 
     result->x1 = x1;
     result->x2 = x2;
@@ -266,8 +334,8 @@ static inline void bg_fp32_tangent_turn(const BgFP32Tangent* tangent, const BgFP
 
 static inline void bg_fp64_tangent_turn(const BgFP64Tangent* tangent, const BgFP64Vector2* vector, BgFP64Vector2* result)
 {
-    const double x1 = tangent->_cos * vector->x1 - tangent->_sin * vector->x2;
-    const double x2 = tangent->_sin * vector->x1 + tangent->_cos * vector->x2;
+    const double x1 = tangent->cos * vector->x1 - tangent->sin * vector->x2;
+    const double x2 = tangent->sin * vector->x1 + tangent->cos * vector->x2;
 
     result->x1 = x1;
     result->x2 = x2;
@@ -277,8 +345,8 @@ static inline void bg_fp64_tangent_turn(const BgFP64Tangent* tangent, const BgFP
 
 static inline void bg_fp32_tangent_turn_back(const BgFP32Tangent* tangent, const BgFP32Vector2* vector, BgFP32Vector2* result)
 {
-    const float x1 = tangent->_sin * vector->x2 + tangent->_cos * vector->x1;
-    const float x2 = tangent->_cos * vector->x2 - tangent->_sin * vector->x1;
+    const float x1 = tangent->sin * vector->x2 + tangent->cos * vector->x1;
+    const float x2 = tangent->cos * vector->x2 - tangent->sin * vector->x1;
 
     result->x1 = x1;
     result->x2 = x2;
@@ -286,8 +354,8 @@ static inline void bg_fp32_tangent_turn_back(const BgFP32Tangent* tangent, const
 
 static inline void bg_fp64_tangent_turn_back(const BgFP64Tangent* tangent, const BgFP64Vector2* vector, BgFP64Vector2* result)
 {
-    const double x1 = tangent->_sin * vector->x2 + tangent->_cos * vector->x1;
-    const double x2 = tangent->_cos * vector->x2 - tangent->_sin * vector->x1;
+    const double x1 = tangent->sin * vector->x2 + tangent->cos * vector->x1;
+    const double x2 = tangent->cos * vector->x2 - tangent->sin * vector->x1;
 
     result->x1 = x1;
     result->x2 = x2;
diff --git a/basic-geometry/vector2.h b/basic-geometry/vector2.h
index dda4d10..425abd0 100644
--- a/basic-geometry/vector2.h
+++ b/basic-geometry/vector2.h
@@ -289,11 +289,31 @@ static inline float bg_fp32_vector2_cross_product(const BgFP32Vector2* vector1,
     return vector1->x1 * vector2->x2 - vector1->x2 * vector2->x1;
 }
 
-static inline double bg_fp64_vector2_cross_product(const BgFP64Vector2* vector1, const BgFP64Vector2* vector2, BgFP64Vector2* result)
+static inline double bg_fp64_vector2_cross_product(const BgFP64Vector2* vector1, const BgFP64Vector2* vector2)
 {
     return vector1->x1 * vector2->x2 - vector1->x2 * vector2->x1;
 }
 
+// ============== Complex Product =============== //
+
+static inline void bg_fp32_vector2_complex_product(const BgFP32Vector2* vector1, const BgFP32Vector2* vector2, BgFP32Vector2* result)
+{
+    const float x1 = vector1->x1 * vector2->x1 - vector1->x2 * vector2->x2;
+    const float x2 = vector1->x1 * vector2->x2 + vector1->x2 * vector2->x1;
+
+    result->x1 = x1;
+    result->x2 = x2;
+}
+
+static inline void bg_fp64_vector2_complex_product(const BgFP64Vector2* vector1, const BgFP64Vector2* vector2, BgFP64Vector2* result)
+{
+    const double x1 = vector1->x1 * vector2->x1 - vector1->x2 * vector2->x2;
+    const double x2 = vector1->x1 * vector2->x2 + vector1->x2 * vector2->x1;
+
+    result->x1 = x1;
+    result->x2 = x2;
+}
+
 // =============== Normalization ================ //
 
 static inline int bg_fp32_vector2_normalize(BgFP32Vector2* vector)
diff --git a/basic-geometry/versor.h b/basic-geometry/versor.h
index b05e72c..6eff522 100644
--- a/basic-geometry/versor.h
+++ b/basic-geometry/versor.h
@@ -218,30 +218,6 @@ static inline void bg_fp64_versor_set_rotation(const BgFP64Rotation3* rotation,
     bg_fp64_versor_set_crude_turn(rotation->axis.x1, rotation->axis.x2, rotation->axis.x3, rotation->radians, BG_ANGLE_UNIT_RADIANS, result);
 }
 
-// =============== Square modulus =============== //
-
-static inline float bg_fp32_versor_get_square_modulus(const BgFP32Versor* versor)
-{
-    return (versor->s0 * versor->s0 + versor->x1 * versor->x1) + (versor->x2 * versor->x2 + versor->x3 * versor->x3);
-}
-
-static inline double bg_fp64_versor_get_square_modulus(const BgFP64Versor* versor)
-{
-    return (versor->s0 * versor->s0 + versor->x1 * versor->x1) + (versor->x2 * versor->x2 + versor->x3 * versor->x3);
-}
-
-// =================== Modulus ================== //
-
-static inline float bg_fp32_versor_get_modulus(const BgFP32Versor* versor)
-{
-    return sqrtf(bg_fp32_versor_get_square_modulus(versor));
-}
-
-static inline double bg_fp64_versor_get_modulus(const BgFP64Versor* versor)
-{
-    return sqrt(bg_fp64_versor_get_square_modulus(versor));
-}
-
 // ================= Comparison ================= //
 
 static inline int bg_fp32_versor_is_idle(const BgFP32Versor* versor)