#ifndef _BGC_QUATERNION_H_INCLUDED_
#define _BGC_QUATERNION_H_INCLUDED_

#include <math.h>

#include "./utilities.h"
#include "./types.h"
#include "./angle.h"
#include "./matrix3x3.h"

// ==================== Reset =================== //

inline void bgc_fp32_quaternion_reset(BGC_FP32_Quaternion* const quaternion)
{
    quaternion->s = 0.0f;
    quaternion->x = 0.0f;
    quaternion->y = 0.0f;
    quaternion->z = 0.0f;
}

inline void bgc_fp64_quaternion_reset(BGC_FP64_Quaternion* const quaternion)
{
    quaternion->s = 0.0;
    quaternion->x = 0.0;
    quaternion->y = 0.0;
    quaternion->z = 0.0;
}

// ================= Make Unit ================== //

inline void bgc_fp32_quaternion_make_unit(BGC_FP32_Quaternion* const quaternion)
{
    quaternion->s = 1.0f;
    quaternion->x = 0.0f;
    quaternion->y = 0.0f;
    quaternion->z = 0.0f;
}

inline void bgc_fp64_quaternion_make_unit(BGC_FP64_Quaternion* const quaternion)
{
    quaternion->s = 1.0;
    quaternion->x = 0.0;
    quaternion->y = 0.0;
    quaternion->z = 0.0;
}

// ==================== Set ===================== //

inline void bgc_fp32_quaternion_set_values(BGC_FP32_Quaternion* const quaternion, const float s, const float x, const float y, const float z)
{
    quaternion->s = s;
    quaternion->x = x;
    quaternion->y = y;
    quaternion->z = z;
}

inline void bgc_fp64_quaternion_set_values(BGC_FP64_Quaternion* const quaternion, const double s, const double x, const double y, const double z)
{
    quaternion->s = s;
    quaternion->x = x;
    quaternion->y = y;
    quaternion->z = z;
}

// ============= Get Square Modulus ============= //

inline float bgc_fp32_quaternion_get_square_magnitude(const BGC_FP32_Quaternion* const quaternion)
{
    return (quaternion->s * quaternion->s + quaternion->x * quaternion->x) + (quaternion->y * quaternion->y + quaternion->z * quaternion->z);
}

inline double bgc_fp64_quaternion_get_square_magnitude(const BGC_FP64_Quaternion* const quaternion)
{
    return (quaternion->s * quaternion->s + quaternion->x * quaternion->x) + (quaternion->y * quaternion->y + quaternion->z * quaternion->z);
}

// ================ Get Modulus ================= //

inline float bgc_fp32_quaternion_get_magnitude(const BGC_FP32_Quaternion* const quaternion)
{
    return sqrtf(bgc_fp32_quaternion_get_square_magnitude(quaternion));
}

inline double bgc_fp64_quaternion_get_magnitude(const BGC_FP64_Quaternion* const quaternion)
{
    return sqrt(bgc_fp64_quaternion_get_square_magnitude(quaternion));
}

// ================== Is Zero =================== //

inline int bgc_fp32_quaternion_is_zero(const BGC_FP32_Quaternion* const quaternion)
{
    return bgc_fp32_quaternion_get_square_magnitude(quaternion) <= BGC_FP32_SQUARE_EPSILON;
}

inline int bgc_fp64_quaternion_is_zero(const BGC_FP64_Quaternion* const quaternion)
{
    return bgc_fp64_quaternion_get_square_magnitude(quaternion) <= BGC_FP64_SQUARE_EPSILON;
}

// ================== Is Unit =================== //

inline int bgc_fp32_quaternion_is_unit(const BGC_FP32_Quaternion* const quaternion)
{
    return bgc_fp32_is_square_unit(bgc_fp32_quaternion_get_square_magnitude(quaternion));
}

inline int bgc_fp64_quaternion_is_unit(const BGC_FP64_Quaternion* const quaternion)
{
    return bgc_fp64_is_square_unit(bgc_fp64_quaternion_get_square_magnitude(quaternion));
}

// ================== Is Pure =================== //

inline int bgc_fp32_quaternion_is_pure(const BGC_FP32_Quaternion* const quaternion)
{
    return bgc_fp32_is_zero(quaternion->s);
}

inline int bgc_fp64_quaternion_is_pure(const BGC_FP64_Quaternion* const quaternion)
{
    return bgc_fp64_is_zero(quaternion->s);
}

// ================== Is Real =================== //

inline int bgc_fp32_quaternion_is_real(const BGC_FP32_Quaternion* const quaternion)
{
    return quaternion->x * quaternion->x + quaternion->y * quaternion->y + quaternion->z * quaternion->z <= BGC_FP32_SQUARE_EPSILON;
}

inline int bgc_fp64_quaternion_is_real(const BGC_FP64_Quaternion* const quaternion)
{
    return quaternion->x * quaternion->x + quaternion->y * quaternion->y + quaternion->z * quaternion->z <= BGC_FP64_SQUARE_EPSILON;
}

// ==================== Copy ==================== //

inline void bgc_fp32_quaternion_copy(BGC_FP32_Quaternion* const destination, const BGC_FP32_Quaternion* const source)
{
    destination->s = source->s;
    destination->x = source->x;
    destination->y = source->y;
    destination->z = source->z;
}

inline void bgc_fp64_quaternion_copy(BGC_FP64_Quaternion* const destination, const BGC_FP64_Quaternion* const source)
{
    destination->s = source->s;
    destination->x = source->x;
    destination->y = source->y;
    destination->z = source->z;
}

// ==================== Swap ==================== //

inline void bgc_fp32_quaternion_swap(BGC_FP32_Quaternion* const quarternion1, BGC_FP32_Quaternion* const quarternion2)
{
    const float s = quarternion2->s;
    const float x = quarternion2->x;
    const float y = quarternion2->y;
    const float z = quarternion2->z;

    quarternion2->s = quarternion1->s;
    quarternion2->x = quarternion1->x;
    quarternion2->y = quarternion1->y;
    quarternion2->z = quarternion1->z;

    quarternion1->s = s;
    quarternion1->x = x;
    quarternion1->y = y;
    quarternion1->z = z;
}

inline void bgc_fp64_quaternion_swap(BGC_FP64_Quaternion* const quarternion1, BGC_FP64_Quaternion* const quarternion2)
{
    const double s = quarternion2->s;
    const double x = quarternion2->x;
    const double y = quarternion2->y;
    const double z = quarternion2->z;

    quarternion2->s = quarternion1->s;
    quarternion2->x = quarternion1->x;
    quarternion2->y = quarternion1->y;
    quarternion2->z = quarternion1->z;

    quarternion1->s = s;
    quarternion1->x = x;
    quarternion1->y = y;
    quarternion1->z = z;
}

// ================== Convert =================== //

inline void bgc_fp32_quaternion_convert_to_fp64(BGC_FP64_Quaternion* const destination, const BGC_FP32_Quaternion* const source)
{
    destination->s = source->s;
    destination->x = source->x;
    destination->y = source->y;
    destination->z = source->z;
}

inline void bgc_fp64_quaternion_convert_to_fp32(BGC_FP32_Quaternion* const destination, const BGC_FP64_Quaternion* const source)
{
    destination->s = (float)source->s;
    destination->x = (float)source->x;
    destination->y = (float)source->y;
    destination->z = (float)source->z;
}

// ==================== Add ===================== //

inline void bgc_fp32_quaternion_add(BGC_FP32_Quaternion* const sum, const BGC_FP32_Quaternion* const quaternion1, const BGC_FP32_Quaternion* const quaternion2)
{
    sum->s = quaternion1->s + quaternion2->s;
    sum->x = quaternion1->x + quaternion2->x;
    sum->y = quaternion1->y + quaternion2->y;
    sum->z = quaternion1->z + quaternion2->z;
}

inline void bgc_fp64_quaternion_add(BGC_FP64_Quaternion* const sum, const BGC_FP64_Quaternion* const quaternion1, const BGC_FP64_Quaternion* const quaternion2)
{
    sum->s = quaternion1->s + quaternion2->s;
    sum->x = quaternion1->x + quaternion2->x;
    sum->y = quaternion1->y + quaternion2->y;
    sum->z = quaternion1->z + quaternion2->z;
}

// ================= Add Scaled ================= //

inline void bgc_fp32_quaternion_add_scaled(BGC_FP32_Quaternion* const sum, const BGC_FP32_Quaternion* const basic_quaternion, const BGC_FP32_Quaternion* const scalable_quaternion, const float scale)
{
    sum->s = basic_quaternion->s + scalable_quaternion->s * scale;
    sum->x = basic_quaternion->x + scalable_quaternion->x * scale;
    sum->y = basic_quaternion->y + scalable_quaternion->y * scale;
    sum->z = basic_quaternion->z + scalable_quaternion->z * scale;
}

inline void bgc_fp64_quaternion_add_scaled(BGC_FP64_Quaternion* const sum, const BGC_FP64_Quaternion* const basic_quaternion, const BGC_FP64_Quaternion* const scalable_quaternion, const double scale)
{
    sum->s = basic_quaternion->s + scalable_quaternion->s * scale;
    sum->x = basic_quaternion->x + scalable_quaternion->x * scale;
    sum->y = basic_quaternion->y + scalable_quaternion->y * scale;
    sum->z = basic_quaternion->z + scalable_quaternion->z * scale;
}

// ================== Subtract ================== //

inline void bgc_fp32_quaternion_subtract(BGC_FP32_Quaternion* const difference, const BGC_FP32_Quaternion* const minuend, const BGC_FP32_Quaternion* const subtrahend)
{
    difference->s = minuend->s - subtrahend->s;
    difference->x = minuend->x - subtrahend->x;
    difference->y = minuend->y - subtrahend->y;
    difference->z = minuend->z - subtrahend->z;
}

inline void bgc_fp64_quaternion_subtract(BGC_FP64_Quaternion* const difference, const BGC_FP64_Quaternion* const minuend, const BGC_FP64_Quaternion* const subtrahend)
{
    difference->s = minuend->s - subtrahend->s;
    difference->x = minuend->x - subtrahend->x;
    difference->y = minuend->y - subtrahend->y;
    difference->z = minuend->z - subtrahend->z;
}

// ============== Subtract Scaled =============== //

inline void bgc_fp32_quaternion_subtract_scaled(BGC_FP32_Quaternion* const difference, const BGC_FP32_Quaternion* const basic_quaternion, const BGC_FP32_Quaternion* const scalable_quaternion, const float scale)
{
    difference->s = basic_quaternion->s - scalable_quaternion->s * scale;
    difference->x = basic_quaternion->x - scalable_quaternion->x * scale;
    difference->y = basic_quaternion->y - scalable_quaternion->y * scale;
    difference->z = basic_quaternion->z - scalable_quaternion->z * scale;
}

inline void bgc_fp64_quaternion_subtract_scaled(BGC_FP64_Quaternion* const difference, const BGC_FP64_Quaternion* const basic_quaternion, const BGC_FP64_Quaternion* const scalable_quaternion, const double scale)
{
    difference->s = basic_quaternion->s - scalable_quaternion->s * scale;
    difference->x = basic_quaternion->x - scalable_quaternion->x * scale;
    difference->y = basic_quaternion->y - scalable_quaternion->y * scale;
    difference->z = basic_quaternion->z - scalable_quaternion->z * scale;
}

// ============= Multiply By Number ============= //

inline void bgc_fp32_quaternion_multiply_by_real_number(BGC_FP32_Quaternion* const product, const BGC_FP32_Quaternion* const multiplicand, const float multiplier)
{
    product->s = multiplicand->s * multiplier;
    product->x = multiplicand->x * multiplier;
    product->y = multiplicand->y * multiplier;
    product->z = multiplicand->z * multiplier;
}

inline void bgc_fp64_quaternion_multiply_by_real_number(BGC_FP64_Quaternion* const product, const BGC_FP64_Quaternion* const multiplicand, const double multiplier)
{
    product->s = multiplicand->s * multiplier;
    product->x = multiplicand->x * multiplier;
    product->y = multiplicand->y * multiplier;
    product->z = multiplicand->z * multiplier;
}

// ========== Multiply By Dual Number =========== //

inline void bgc_fp32_quaternion_multiply_by_dual_number(BGC_FP32_DualQuaternion* const product, const BGC_FP32_Quaternion* const multiplicand, const BGC_FP32_DualNumber* const multiplier)
{
    const float real_s = multiplicand->s * multiplier->real_part;
    const float real_x = multiplicand->x * multiplier->real_part;
    const float real_y = multiplicand->y * multiplier->real_part;
    const float real_z = multiplicand->z * multiplier->real_part;

    const float dual_s = multiplicand->s * multiplier->dual_part;
    const float dual_x = multiplicand->x * multiplier->dual_part;
    const float dual_y = multiplicand->y * multiplier->dual_part;
    const float dual_z = multiplicand->z * multiplier->dual_part;

    product->real_part.s = real_s;
    product->real_part.x = real_x;
    product->real_part.y = real_y;
    product->real_part.z = real_z;

    product->dual_part.s = dual_s;
    product->dual_part.x = dual_x;
    product->dual_part.y = dual_y;
    product->dual_part.z = dual_z;
}

inline void bgc_fp64_quaternion_multiply_by_dual_number(BGC_FP64_DualQuaternion* const product, const BGC_FP64_Quaternion* const multiplicand, const BGC_FP64_DualNumber* const multiplier)
{
    const double real_s = multiplicand->s * multiplier->real_part;
    const double real_x = multiplicand->x * multiplier->real_part;
    const double real_y = multiplicand->y * multiplier->real_part;
    const double real_z = multiplicand->z * multiplier->real_part;

    const double dual_s = multiplicand->s * multiplier->dual_part;
    const double dual_x = multiplicand->x * multiplier->dual_part;
    const double dual_y = multiplicand->y * multiplier->dual_part;
    const double dual_z = multiplicand->z * multiplier->dual_part;

    product->real_part.s = real_s;
    product->real_part.x = real_x;
    product->real_part.y = real_y;
    product->real_part.z = real_z;

    product->dual_part.s = dual_s;
    product->dual_part.x = dual_x;
    product->dual_part.y = dual_y;
    product->dual_part.z = dual_z;
}

// ====== Restrict Multiply By Dual Number ====== //

inline void _bgc_fp32_restrict_quaternion_multiply_by_dual_number(BGC_FP32_DualQuaternion* restrict const product, const BGC_FP32_Quaternion* const multiplicand, const BGC_FP32_DualNumber* const multiplier)
{
    product->real_part.s = multiplicand->s * multiplier->real_part;
    product->real_part.x = multiplicand->x * multiplier->real_part;
    product->real_part.y = multiplicand->y * multiplier->real_part;
    product->real_part.z = multiplicand->z * multiplier->real_part;

    product->dual_part.s = multiplicand->s * multiplier->dual_part;
    product->dual_part.x = multiplicand->x * multiplier->dual_part;
    product->dual_part.y = multiplicand->y * multiplier->dual_part;
    product->dual_part.z = multiplicand->z * multiplier->dual_part;
}

inline void _bgc_fp64_restrict_quaternion_multiply_by_dual_number(BGC_FP64_DualQuaternion* restrict const product, const BGC_FP64_Quaternion* const multiplicand, const BGC_FP64_DualNumber* const multiplier)
{
    product->real_part.s = multiplicand->s * multiplier->real_part;
    product->real_part.x = multiplicand->x * multiplier->real_part;
    product->real_part.y = multiplicand->y * multiplier->real_part;
    product->real_part.z = multiplicand->z * multiplier->real_part;

    product->dual_part.s = multiplicand->s * multiplier->dual_part;
    product->dual_part.x = multiplicand->x * multiplier->dual_part;
    product->dual_part.y = multiplicand->y * multiplier->dual_part;
    product->dual_part.z = multiplicand->z * multiplier->dual_part;
}

// =========== Multiply By Quaternion =========== //

inline void bgc_fp32_quaternion_multiply_by_quaternion(BGC_FP32_Quaternion* const product, const BGC_FP32_Quaternion* const left, const BGC_FP32_Quaternion* const right)
{
    const float s = (left->s * right->s - left->x * right->x) - (left->y * right->y + left->z * right->z);
    const float x = (left->x * right->s + left->s * right->x) - (left->z * right->y - left->y * right->z);
    const float y = (left->y * right->s + left->s * right->y) - (left->x * right->z - left->z * right->x);
    const float z = (left->z * right->s + left->s * right->z) - (left->y * right->x - left->x * right->y);

    product->s = s;
    product->x = x;
    product->y = y;
    product->z = z;
}

inline void bgc_fp64_quaternion_multiply_by_quaternion(BGC_FP64_Quaternion* const product, const BGC_FP64_Quaternion* const left, const BGC_FP64_Quaternion* const right)
{
    const double s = (left->s * right->s - left->x * right->x) - (left->y * right->y + left->z * right->z);
    const double x = (left->x * right->s + left->s * right->x) - (left->z * right->y - left->y * right->z);
    const double y = (left->y * right->s + left->s * right->y) - (left->x * right->z - left->z * right->x);
    const double z = (left->z * right->s + left->s * right->z) - (left->y * right->x - left->x * right->y);

    product->s = s;
    product->x = x;
    product->y = y;
    product->z = z;
}

// ====== Multiply By Conjugate Quaternion ====== //

inline void bgc_fp32_quaternion_multiply_by_conjugate(BGC_FP32_Quaternion* const product, const BGC_FP32_Quaternion* const left, const BGC_FP32_Quaternion* const right)
{
    const float s = (left->s * right->s + left->x * right->x) + (left->y * right->y + left->z * right->z);
    const float x = (left->x * right->s + left->z * right->y) - (left->s * right->x + left->y * right->z);
    const float y = (left->y * right->s + left->x * right->z) - (left->s * right->y + left->z * right->x);
    const float z = (left->z * right->s + left->y * right->x) - (left->s * right->z + left->x * right->y);

    product->s = s;
    product->x = x;
    product->y = y;
    product->z = z;
}

inline void bgc_fp64_quaternion_multiply_by_conjugate(BGC_FP64_Quaternion* const product, const BGC_FP64_Quaternion* const left, const BGC_FP64_Quaternion* const right)
{
    const double s = (left->s * right->s + left->x * right->x) + (left->y * right->y + left->z * right->z);
    const double x = (left->x * right->s + left->z * right->y) - (left->s * right->x + left->y * right->z);
    const double y = (left->y * right->s + left->x * right->z) - (left->s * right->y + left->z * right->x);
    const double z = (left->z * right->s + left->y * right->x) - (left->s * right->z + left->x * right->y);

    product->s = s;
    product->x = x;
    product->y = y;
    product->z = z;
}

// ====== Multiply Conjugate By Quaternion ====== //

inline void bgc_fp32_conjugate_quaternion_multiply_by_quaternion(BGC_FP32_Quaternion* const product, const BGC_FP32_Quaternion* const left, const BGC_FP32_Quaternion* const right)
{
    const float s = (left->s * right->s + left->x * right->x) + (left->y * right->y + left->z * right->z);
    const float x = (left->s * right->x - left->x * right->s) + (left->z * right->y - left->y * right->z);
    const float y = (left->s * right->y - left->y * right->s) + (left->x * right->z - left->z * right->x);
    const float z = (left->s * right->z - left->z * right->s) + (left->y * right->x - left->x * right->y);

    product->s = s;
    product->x = x;
    product->y = y;
    product->z = z;
}

inline void bgc_fp64_conjugate_quaternion_multiply_by_quaternion(BGC_FP64_Quaternion* const product, const BGC_FP64_Quaternion* const left, const BGC_FP64_Quaternion* const right)
{
    const double s = (left->s * right->s + left->x * right->x) + (left->y * right->y + left->z * right->z);
    const double x = (left->s * right->x - left->x * right->s) + (left->z * right->y - left->y * right->z);
    const double y = (left->s * right->y - left->y * right->s) + (left->x * right->z - left->z * right->x);
    const double z = (left->s * right->z - left->z * right->s) + (left->y * right->x - left->x * right->y);

    product->s = s;
    product->x = x;
    product->y = y;
    product->z = z;
}

// ====== Multiply Conjugate By Conjugate ======= //

inline void bgc_fp32_conjugate_quaternion_multiply_by_conjugate(BGC_FP32_Quaternion* const product, const BGC_FP32_Quaternion* const left, const BGC_FP32_Quaternion* const right)
{
    const float s = (left->s * right->s - left->x * right->x) - (left->y * right->y + left->z * right->z);
    const float x = (left->y * right->z - left->z * right->y) - (left->x * right->s + left->s * right->x);
    const float y = (left->z * right->x - left->x * right->z) - (left->y * right->s + left->s * right->y);
    const float z = (left->x * right->y - left->y * right->x) - (left->z * right->s + left->s * right->z);

    product->s = s;
    product->x = x;
    product->y = y;
    product->z = z;
}

inline void bgc_fp64_conjugate_quaternion_multiply_by_conjugate(BGC_FP64_Quaternion* const product, const BGC_FP64_Quaternion* const left, const BGC_FP64_Quaternion* const right)
{
    const double s = (left->s * right->s - left->x * right->x) - (left->y * right->y + left->z * right->z);
    const double x = (left->y * right->z - left->z * right->y) - (left->x * right->s + left->s * right->x);
    const double y = (left->z * right->x - left->x * right->z) - (left->y * right->s + left->s * right->y);
    const double z = (left->x * right->y - left->y * right->x) - (left->z * right->s + left->s * right->z);

    product->s = s;
    product->x = x;
    product->y = y;
    product->z = z;
}

// ====== Restrict Multiply By Quaternion ======= //

inline void _bgc_fp32_restrict_quaternion_multiply_by_quaternion(BGC_FP32_Quaternion* restrict const product, const BGC_FP32_Quaternion* const left, const BGC_FP32_Quaternion* const right)
{
    product->s = (left->s * right->s - left->x * right->x) - (left->y * right->y + left->z * right->z);
    product->x = (left->x * right->s + left->s * right->x) - (left->z * right->y - left->y * right->z);
    product->y = (left->y * right->s + left->s * right->y) - (left->x * right->z - left->z * right->x);
    product->z = (left->z * right->s + left->s * right->z) - (left->y * right->x - left->x * right->y);
}

inline void _bgc_fp64_restrict_quaternion_multiply_by_quaternion(BGC_FP64_Quaternion* restrict const product, const BGC_FP64_Quaternion* const left, const BGC_FP64_Quaternion* const right)
{
    product->s = (left->s * right->s - left->x * right->x) - (left->y * right->y + left->z * right->z);
    product->x = (left->x * right->s + left->s * right->x) - (left->z * right->y - left->y * right->z);
    product->y = (left->y * right->s + left->s * right->y) - (left->x * right->z - left->z * right->x);
    product->z = (left->z * right->s + left->s * right->z) - (left->y * right->x - left->x * right->y);
}

// = Restrict Multiply By Conjugate Quaternion == //

inline void _bgc_fp32_restrict_quaternion_multiply_by_conjugate(BGC_FP32_Quaternion* restrict const product, const BGC_FP32_Quaternion* const left, const BGC_FP32_Quaternion* const right)
{
    product->s = (left->s * right->s + left->x * right->x) + (left->y * right->y + left->z * right->z);
    product->x = (left->x * right->s + left->z * right->y) - (left->s * right->x + left->y * right->z);
    product->y = (left->y * right->s + left->x * right->z) - (left->s * right->y + left->z * right->x);
    product->z = (left->z * right->s + left->y * right->x) - (left->s * right->z + left->x * right->y);
}

inline void _bgc_fp64_restrict_quaternion_multiply_by_conjugate(BGC_FP64_Quaternion* restrict const product, const BGC_FP64_Quaternion* const left, const BGC_FP64_Quaternion* const right)
{
    product->s = (left->s * right->s + left->x * right->x) + (left->y * right->y + left->z * right->z);
    product->x = (left->x * right->s + left->z * right->y) - (left->s * right->x + left->y * right->z);
    product->y = (left->y * right->s + left->x * right->z) - (left->s * right->y + left->z * right->x);
    product->z = (left->z * right->s + left->y * right->x) - (left->s * right->z + left->x * right->y);
}

// ======== Multiply By Dual Quaternion ========= //

inline void bgc_fp32_quaternion_multiply_by_dual_quaternion(BGC_FP32_DualQuaternion* const product, const BGC_FP32_Quaternion* const left, const BGC_FP32_DualQuaternion* const right)
{
    bgc_fp32_quaternion_multiply_by_quaternion(&product->real_part, left, &right->real_part);
    bgc_fp32_quaternion_multiply_by_quaternion(&product->dual_part, left, &right->dual_part);
}

inline void bgc_fp64_quaternion_multiply_by_dual_quaternion(BGC_FP64_DualQuaternion* const product, const BGC_FP64_Quaternion* const left, const BGC_FP64_DualQuaternion* const right)
{
    bgc_fp64_quaternion_multiply_by_quaternion(&product->real_part, left, &right->real_part);
    bgc_fp64_quaternion_multiply_by_quaternion(&product->dual_part, left, &right->dual_part);
}

// ============== Divide By Number ============== //

inline int bgc_fp32_quaternion_divide_by_real_number(BGC_FP32_Quaternion* const quotient, const BGC_FP32_Quaternion* const dividend, const float divisor)
{
    if (bgc_fp32_is_zero(divisor) || isnan(divisor)) {
        return BGC_FAILURE;
    }

    bgc_fp32_quaternion_multiply_by_real_number(quotient, dividend, 1.0f / divisor);

    return BGC_SUCCESS;
}

inline int bgc_fp64_quaternion_divide_by_real_number(BGC_FP64_Quaternion* const quotient, const BGC_FP64_Quaternion* const dividend, const double divisor)
{
    if (bgc_fp64_is_zero(divisor) || isnan(divisor)) {
        return BGC_FAILURE;
    }

    bgc_fp64_quaternion_multiply_by_real_number(quotient, dividend, 1.0 / divisor);

    return BGC_SUCCESS;
}

// ============ Divide By Quaternion ============ //

inline int bgc_fp32_quaternion_divide_by_quaternion(BGC_FP32_Quaternion* const quotient, const BGC_FP32_Quaternion* const divident, const BGC_FP32_Quaternion* const divisor)
{
    const float square_modulus = bgc_fp32_quaternion_get_square_magnitude(divisor);

    if (square_modulus <= BGC_FP32_SQUARE_EPSILON || isnan(square_modulus)) {
        return BGC_FAILURE;
    }

    bgc_fp32_quaternion_multiply_by_conjugate(quotient, divident, divisor);
    bgc_fp32_quaternion_multiply_by_real_number(quotient, quotient, 1.0f / square_modulus);

    return BGC_SUCCESS;
}

inline int bgc_fp64_quaternion_divide_by_quaternion(BGC_FP64_Quaternion* const quotient, const BGC_FP64_Quaternion* const divident, const BGC_FP64_Quaternion* const divisor)
{
    const double square_modulus = bgc_fp64_quaternion_get_square_magnitude(divisor);

    if (square_modulus <= BGC_FP64_SQUARE_EPSILON || isnan(square_modulus)) {
        return BGC_FAILURE;
    }

    bgc_fp64_quaternion_multiply_by_conjugate(quotient, divident, divisor);
    bgc_fp64_quaternion_multiply_by_real_number(quotient, quotient, 1.0 / square_modulus);

    return BGC_SUCCESS;
}

// ======= Divide By Conjugate Quaternion ======= //

inline int bgc_fp32_quaternion_divide_by_conjugate(BGC_FP32_Quaternion* const quotient, const BGC_FP32_Quaternion* const divident, const BGC_FP32_Quaternion* const divisor_to_conjugate)
{
    const float square_modulus = bgc_fp32_quaternion_get_square_magnitude(divisor_to_conjugate);

    if (square_modulus <= BGC_FP32_SQUARE_EPSILON || isnan(square_modulus)) {
        return BGC_FAILURE;
    }

    bgc_fp32_quaternion_multiply_by_quaternion(quotient, divisor_to_conjugate, divisor_to_conjugate);
    bgc_fp32_quaternion_multiply_by_real_number(quotient, quotient, 1.0f / square_modulus);

    return BGC_SUCCESS;
}

inline int bgc_fp64_quaternion_divide_by_conjugate(BGC_FP64_Quaternion* const quotient, const BGC_FP64_Quaternion* const divident, const BGC_FP64_Quaternion* const divisor_to_conjugate)
{
    const double square_modulus = bgc_fp64_quaternion_get_square_magnitude(divisor_to_conjugate);

    if (square_modulus <= BGC_FP64_SQUARE_EPSILON || isnan(square_modulus)) {
        return BGC_FAILURE;
    }

    bgc_fp64_quaternion_multiply_by_quaternion(quotient, divisor_to_conjugate, divisor_to_conjugate);
    bgc_fp64_quaternion_multiply_by_real_number(quotient, quotient, 1.0 / square_modulus);

    return BGC_SUCCESS;
}

// ================ Mean of Two ================= //

inline void bgc_fp32_quaternion_get_mean2(BGC_FP32_Quaternion* const mean, const BGC_FP32_Quaternion* const quaternion1, const BGC_FP32_Quaternion* const quaternion2)
{
    mean->s = (quaternion1->s + quaternion2->s) * 0.5f;
    mean->x = (quaternion1->x + quaternion2->x) * 0.5f;
    mean->y = (quaternion1->y + quaternion2->y) * 0.5f;
    mean->z = (quaternion1->z + quaternion2->z) * 0.5f;
}

inline void bgc_fp64_quaternion_get_mean2(BGC_FP64_Quaternion* const mean, const BGC_FP64_Quaternion* const quaternion1, const BGC_FP64_Quaternion* const quaternion2)
{
    mean->s = (quaternion1->s + quaternion2->s) * 0.5f;
    mean->x = (quaternion1->x + quaternion2->x) * 0.5f;
    mean->y = (quaternion1->y + quaternion2->y) * 0.5f;
    mean->z = (quaternion1->z + quaternion2->z) * 0.5f;
}

// =============== Mean of Three ================ //

inline void bgc_fp32_quaternion_get_mean3(BGC_FP32_Quaternion* const mean, const BGC_FP32_Quaternion* const quaternion1, const BGC_FP32_Quaternion* const quaternion2, const BGC_FP32_Quaternion* const quaternion3)
{
    mean->s = (quaternion1->s + quaternion2->s + quaternion3->s) * BGC_FP32_ONE_THIRD;
    mean->x = (quaternion1->x + quaternion2->x + quaternion3->x) * BGC_FP32_ONE_THIRD;
    mean->y = (quaternion1->y + quaternion2->y + quaternion3->y) * BGC_FP32_ONE_THIRD;
    mean->z = (quaternion1->z + quaternion2->z + quaternion3->z) * BGC_FP32_ONE_THIRD;
}

inline void bgc_fp64_quaternion_get_mean3(BGC_FP64_Quaternion* const mean, const BGC_FP64_Quaternion* const quaternion1, const BGC_FP64_Quaternion* const quaternion2, const BGC_FP64_Quaternion* const quaternion3)
{
    mean->s = (quaternion1->s + quaternion2->s + quaternion3->s) * BGC_FP64_ONE_THIRD;
    mean->x = (quaternion1->x + quaternion2->x + quaternion3->x) * BGC_FP64_ONE_THIRD;
    mean->y = (quaternion1->y + quaternion2->y + quaternion3->y) * BGC_FP64_ONE_THIRD;
    mean->z = (quaternion1->z + quaternion2->z + quaternion3->z) * BGC_FP64_ONE_THIRD;
}

// ============ Linear Interpolation ============ //

inline void bgc_fp32_quaternion_interpolate(BGC_FP32_Quaternion* const interpolation, const BGC_FP32_Quaternion* const quaternion1, const BGC_FP32_Quaternion* const quaternion2, const float phase)
{
    const float counter_phase = 1.0f - phase;

    interpolation->s = quaternion1->s * counter_phase + quaternion2->s * phase;
    interpolation->x = quaternion1->x * counter_phase + quaternion2->x * phase;
    interpolation->y = quaternion1->y * counter_phase + quaternion2->y * phase;
    interpolation->z = quaternion1->z * counter_phase + quaternion2->z * phase;
}

inline void bgc_fp64_quaternion_interpolate(BGC_FP64_Quaternion* const interpolation, const BGC_FP64_Quaternion* const quaternion1, const BGC_FP64_Quaternion* const quaternion2, const double phase)
{
    const double counter_phase = 1.0 - phase;

    interpolation->s = quaternion1->s * counter_phase + quaternion2->s * phase;
    interpolation->x = quaternion1->x * counter_phase + quaternion2->x * phase;
    interpolation->y = quaternion1->y * counter_phase + quaternion2->y * phase;
    interpolation->z = quaternion1->z * counter_phase + quaternion2->z * phase;
}

// ============== Get Dot Product =============== //

inline float bgc_fp32_quaternion_get_dot_product(const BGC_FP32_Quaternion* const quaternion1, const BGC_FP32_Quaternion* const quaternion2)
{
    return (quaternion1->s * quaternion2->s + quaternion1->x * quaternion2->x) + (quaternion1->y * quaternion2->y + quaternion1->z * quaternion2->z);
}

inline double bgc_fp64_quaternion_get_dot_product(const BGC_FP64_Quaternion* const quaternion1, const BGC_FP64_Quaternion* const quaternion2)
{
    return (quaternion1->s * quaternion2->s + quaternion1->x * quaternion2->x) + (quaternion1->y * quaternion2->y + quaternion1->z * quaternion2->z);
}

// ================= Conjugate ================== //

inline void bgc_fp32_quaternion_conjugate(BGC_FP32_Quaternion* const quaternion)
{
    quaternion->x = -quaternion->x;
    quaternion->y = -quaternion->y;
    quaternion->z = -quaternion->z;
}

inline void bgc_fp64_quaternion_conjugate(BGC_FP64_Quaternion* const quaternion)
{
    quaternion->x = -quaternion->x;
    quaternion->y = -quaternion->y;
    quaternion->z = -quaternion->z;
}

inline void bgc_fp32_quaternion_get_conjugate(BGC_FP32_Quaternion* const conjugate, const BGC_FP32_Quaternion* const quaternion)
{
    conjugate->s = quaternion->s;
    conjugate->x = -quaternion->x;
    conjugate->y = -quaternion->y;
    conjugate->z = -quaternion->z;
}

inline void bgc_fp64_quaternion_get_conjugate(BGC_FP64_Quaternion* const conjugate, const BGC_FP64_Quaternion* const quaternion)
{
    conjugate->s = quaternion->s;
    conjugate->x = -quaternion->x;
    conjugate->y = -quaternion->y;
    conjugate->z = -quaternion->z;
}

// ================== Negative ================== //

inline void bgc_fp32_quaternion_revert(BGC_FP32_Quaternion* const quaternion)
{
    quaternion->s = -quaternion->s;
    quaternion->x = -quaternion->x;
    quaternion->y = -quaternion->y;
    quaternion->z = -quaternion->z;
}

inline void bgc_fp64_quaternion_revert(BGC_FP64_Quaternion* const quaternion)
{
    quaternion->s = -quaternion->s;
    quaternion->x = -quaternion->x;
    quaternion->y = -quaternion->y;
    quaternion->z = -quaternion->z;
}

inline void bgc_fp32_quaternion_get_reverse(BGC_FP32_Quaternion* const reverse, const BGC_FP32_Quaternion* const quaternion)
{
    reverse->s = -quaternion->s;
    reverse->x = -quaternion->x;
    reverse->y = -quaternion->y;
    reverse->z = -quaternion->z;
}

inline void bgc_fp64_quaternion_get_reverse(BGC_FP64_Quaternion* const reverse, const BGC_FP64_Quaternion* const quaternion)
{
    reverse->s = -quaternion->s;
    reverse->x = -quaternion->x;
    reverse->y = -quaternion->y;
    reverse->z = -quaternion->z;
}

// =================== Invert =================== //

inline int bgc_fp32_quaternion_get_inverse(BGC_FP32_Quaternion* const inverse, const BGC_FP32_Quaternion* const quaternion)
{
    const float square_modulus = bgc_fp32_quaternion_get_square_magnitude(quaternion);

    if (square_modulus <= BGC_FP32_SQUARE_EPSILON || isnan(square_modulus)) {
        return BGC_FAILURE;
    }

    const float multiplicand = 1.0f / square_modulus;

    inverse->s = quaternion->s * multiplicand;
    inverse->x = -quaternion->x * multiplicand;
    inverse->y = -quaternion->y * multiplicand;
    inverse->z = -quaternion->z * multiplicand;

    return BGC_SUCCESS;
}

inline int bgc_fp64_quaternion_get_inverse(BGC_FP64_Quaternion* const inverse, const BGC_FP64_Quaternion* const quaternion)
{
    const double square_modulus = bgc_fp64_quaternion_get_square_magnitude(quaternion);

    if (square_modulus <= BGC_FP64_SQUARE_EPSILON || isnan(square_modulus)) {
        return BGC_FAILURE;
    }

    const double multiplicand = 1.0 / square_modulus;

    inverse->s = quaternion->s * multiplicand;
    inverse->x = -quaternion->x * multiplicand;
    inverse->y = -quaternion->y * multiplicand;
    inverse->z = -quaternion->z * multiplicand;

    return BGC_SUCCESS;
}

inline int bgc_fp32_quaternion_invert(BGC_FP32_Quaternion* const quaternion)
{
    return bgc_fp32_quaternion_get_inverse(quaternion, quaternion);
}

inline int bgc_fp64_quaternion_invert(BGC_FP64_Quaternion* const quaternion)
{
    return bgc_fp64_quaternion_get_inverse(quaternion, quaternion);
}

// ================= Normalize ================== //

inline int bgc_fp32_quaternion_normalize(BGC_FP32_Quaternion* const quaternion)
{
    const float square_modulus = bgc_fp32_quaternion_get_square_magnitude(quaternion);

    if (square_modulus <= BGC_FP32_SQUARE_EPSILON || isnan(square_modulus)) {
        return BGC_FAILURE;
    }

    if (bgc_fp32_is_square_unit(square_modulus)) {
        return BGC_SUCCESS;
    }

    const float multiplier = sqrtf(1.0f / square_modulus);

    quaternion->s *= multiplier;
    quaternion->x *= multiplier;
    quaternion->y *= multiplier;
    quaternion->z *= multiplier;

    return BGC_SUCCESS;
}

inline int bgc_fp64_quaternion_normalize(BGC_FP64_Quaternion* const quaternion)
{
    const double square_modulus = bgc_fp64_quaternion_get_square_magnitude(quaternion);

    if (square_modulus <= BGC_FP64_SQUARE_EPSILON || isnan(square_modulus)) {
        return BGC_FAILURE;
    }

    if (bgc_fp64_is_square_unit(square_modulus)) {
        return BGC_SUCCESS;
    }

    const double multiplier = sqrt(1.0 / square_modulus);

    quaternion->s *= multiplier;
    quaternion->x *= multiplier;
    quaternion->y *= multiplier;
    quaternion->z *= multiplier;

    return BGC_SUCCESS;
}

inline int bgc_fp32_quaternion_get_normalized(BGC_FP32_Quaternion* const normalized, const BGC_FP32_Quaternion* const quaternion)
{
    const float square_modulus = bgc_fp32_quaternion_get_square_magnitude(quaternion);

    if (square_modulus <= BGC_FP32_SQUARE_EPSILON || isnan(square_modulus)) {
        bgc_fp32_quaternion_reset(normalized);
        return BGC_FAILURE;
    }

    if (bgc_fp32_is_square_unit(square_modulus)) {
        bgc_fp32_quaternion_copy(normalized, quaternion);
        return BGC_SUCCESS;
    }

    bgc_fp32_quaternion_multiply_by_real_number(normalized, quaternion, sqrtf(1.0f / square_modulus));
    return BGC_SUCCESS;
}

inline int bgc_fp64_quaternion_get_normalized(BGC_FP64_Quaternion* const normalized, const BGC_FP64_Quaternion* const quaternion)
{
    const double square_modulus = bgc_fp64_quaternion_get_square_magnitude(quaternion);

    if (square_modulus <= BGC_FP64_SQUARE_EPSILON || isnan(square_modulus)) {
        bgc_fp64_quaternion_reset(normalized);
        return BGC_FAILURE;
    }

    if (bgc_fp64_is_square_unit(square_modulus)) {
        bgc_fp64_quaternion_copy(normalized, quaternion);
        return BGC_SUCCESS;
    }

    bgc_fp64_quaternion_multiply_by_real_number(normalized, quaternion, sqrt(1.0 / square_modulus));
    return BGC_SUCCESS;
}

// =============== Get Exponation =============== //

int bgc_fp32_quaternion_get_power(BGC_FP32_Quaternion* const power, const BGC_FP32_Quaternion* const base, const float exponent);

int bgc_fp64_quaternion_get_power(BGC_FP64_Quaternion* const power, const BGC_FP64_Quaternion* const base, const double exponent);

// ============== Raw Turn Vector3 ============== //

// An internal function
inline void _bgc_fp32_versor_turn_vector(BGC_FP32_Vector3* const turned_vector, const BGC_FP32_Quaternion* const quaternion, const BGC_FP32_Vector3* const original_vector)
{
    const float tx = 2.0f * (quaternion->y * original_vector->z - quaternion->z * original_vector->y);
    const float ty = 2.0f * (quaternion->z * original_vector->x - quaternion->x * original_vector->z);
    const float tz = 2.0f * (quaternion->x * original_vector->y - quaternion->y * original_vector->x);

    const float x = (original_vector->x + tx * quaternion->s) + (quaternion->y * tz - quaternion->z * ty);
    const float y = (original_vector->y + ty * quaternion->s) + (quaternion->z * tx - quaternion->x * tz);
    const float z = (original_vector->z + tz * quaternion->s) + (quaternion->x * ty - quaternion->y * tx);

    turned_vector->x = x;
    turned_vector->y = y;
    turned_vector->z = z;
}

// An internal function
inline void _bgc_fp64_versor_turn_vector(BGC_FP64_Vector3* const turned_vector, const BGC_FP64_Quaternion* const quaternion, const BGC_FP64_Vector3* const original_vector)
{
    const double tx = 2.0f * (quaternion->y * original_vector->z - quaternion->z * original_vector->y);
    const double ty = 2.0f * (quaternion->z * original_vector->x - quaternion->x * original_vector->z);
    const double tz = 2.0f * (quaternion->x * original_vector->y - quaternion->y * original_vector->x);

    const double x = (original_vector->x + tx * quaternion->s) + (quaternion->y * tz - quaternion->z * ty);
    const double y = (original_vector->y + ty * quaternion->s) + (quaternion->z * tx - quaternion->x * tz);
    const double z = (original_vector->z + tz * quaternion->s) + (quaternion->x * ty - quaternion->y * tx);

    turned_vector->x = x;
    turned_vector->y = y;
    turned_vector->z = z;
}

// ========= Raw Turn Vector3 Backwards ========= //

// An internal function
inline void _bgc_fp32_versor_turn_vector_back(BGC_FP32_Vector3* const turned_vector, const BGC_FP32_Quaternion* const quaternion, const BGC_FP32_Vector3* const original_vector)
{
    const float tx = 2.0f * (quaternion->y * original_vector->z - quaternion->z * original_vector->y);
    const float ty = 2.0f * (quaternion->z * original_vector->x - quaternion->x * original_vector->z);
    const float tz = 2.0f * (quaternion->x * original_vector->y - quaternion->y * original_vector->x);

    const float x = (original_vector->x + tx * quaternion->s) + (quaternion->y * tz - quaternion->z * ty);
    const float y = (original_vector->y + ty * quaternion->s) + (quaternion->z * tx - quaternion->x * tz);
    const float z = (original_vector->z + tz * quaternion->s) + (quaternion->x * ty - quaternion->y * tx);

    turned_vector->x = x;
    turned_vector->y = y;
    turned_vector->z = z;
}

// An internal function
inline void _bgc_fp64_versor_turn_vector_back(BGC_FP64_Vector3* const turned_vector, const BGC_FP64_Quaternion* const quaternion, const BGC_FP64_Vector3* const original_vector)
{
    const double tx = 2.0f * (quaternion->y * original_vector->z - quaternion->z * original_vector->y);
    const double ty = 2.0f * (quaternion->z * original_vector->x - quaternion->x * original_vector->z);
    const double tz = 2.0f * (quaternion->x * original_vector->y - quaternion->y * original_vector->x);

    const double x = (original_vector->x + tx * quaternion->s) + (quaternion->y * tz - quaternion->z * ty);
    const double y = (original_vector->y + ty * quaternion->s) + (quaternion->z * tx - quaternion->x * tz);
    const double z = (original_vector->z + tz * quaternion->s) + (quaternion->x * ty - quaternion->y * tx);

    turned_vector->x = x;
    turned_vector->y = y;
    turned_vector->z = z;
}

// ================ Turn Vector3 ================ //

inline int bgc_fp32_quaternion_turn_vector(BGC_FP32_Vector3* const turned_vector, const BGC_FP32_Quaternion* const quaternion, const BGC_FP32_Vector3* const original_vector)
{
    const float square_modulus = bgc_fp32_quaternion_get_square_magnitude(quaternion);

    if (square_modulus < BGC_FP32_SQUARE_EPSILON || isnan(square_modulus)) {
        return BGC_FAILURE;
    }

    const float multiplier = 2.0f / square_modulus;

    const float tx = multiplier * (quaternion->y * original_vector->z - quaternion->z * original_vector->y);
    const float ty = multiplier * (quaternion->z * original_vector->x - quaternion->x * original_vector->z);
    const float tz = multiplier * (quaternion->x * original_vector->y - quaternion->y * original_vector->x);

    const float x = (original_vector->x + tx * quaternion->s) + (quaternion->y * tz - quaternion->z * ty);
    const float y = (original_vector->y + ty * quaternion->s) + (quaternion->z * tx - quaternion->x * tz);
    const float z = (original_vector->z + tz * quaternion->s) + (quaternion->x * ty - quaternion->y * tx);

    turned_vector->x = x;
    turned_vector->y = y;
    turned_vector->z = z;


    return BGC_SUCCESS;
}

inline int bgc_fp64_quaternion_turn_vector(BGC_FP64_Vector3* const turned_vector, const BGC_FP64_Quaternion* const quaternion, const BGC_FP64_Vector3* const original_vector)
{
    const double square_modulus = bgc_fp64_quaternion_get_square_magnitude(quaternion);

    if (square_modulus < BGC_FP64_SQUARE_EPSILON || isnan(square_modulus)) {
        return BGC_FAILURE;
    }

    const double multiplier = 2.0 / square_modulus;

    const double tx = multiplier * (quaternion->y * original_vector->z - quaternion->z * original_vector->y);
    const double ty = multiplier * (quaternion->z * original_vector->x - quaternion->x * original_vector->z);
    const double tz = multiplier * (quaternion->x * original_vector->y - quaternion->y * original_vector->x);

    const double x = (original_vector->x + tx * quaternion->s) + (quaternion->y * tz - quaternion->z * ty);
    const double y = (original_vector->y + ty * quaternion->s) + (quaternion->z * tx - quaternion->x * tz);
    const double z = (original_vector->z + tz * quaternion->s) + (quaternion->x * ty - quaternion->y * tx);

    turned_vector->x = x;
    turned_vector->y = y;
    turned_vector->z = z;


    return BGC_SUCCESS;
}

// =========== Turn Vector3 Backwards =========== //

inline int bgc_fp32_quaternion_turn_vector_back(BGC_FP32_Vector3* const turned_vector, const BGC_FP32_Quaternion* const quaternion, const BGC_FP32_Vector3* const original_vector)
{
    const float square_modulus = bgc_fp32_quaternion_get_square_magnitude(quaternion);

    if (square_modulus < BGC_FP32_SQUARE_EPSILON || isnan(square_modulus)) {
        return BGC_FAILURE;
    }

    const float multiplier = 2.0f / square_modulus;

    const float tx = multiplier * (quaternion->y * original_vector->z - quaternion->z * original_vector->y);
    const float ty = multiplier * (quaternion->z * original_vector->x - quaternion->x * original_vector->z);
    const float tz = multiplier * (quaternion->x * original_vector->y - quaternion->y * original_vector->x);

    const float x = (original_vector->x - tx * quaternion->s) + (quaternion->y * tz - quaternion->z * ty);
    const float y = (original_vector->y - ty * quaternion->s) + (quaternion->z * tx - quaternion->x * tz);
    const float z = (original_vector->z - tz * quaternion->s) + (quaternion->x * ty - quaternion->y * tx);

    turned_vector->x = x;
    turned_vector->y = y;
    turned_vector->z = z;


    return BGC_SUCCESS;
}

inline int bgc_fp64_quaternion_turn_vector_back(BGC_FP64_Vector3* const turned_vector, const BGC_FP64_Quaternion* const quaternion, const BGC_FP64_Vector3* const original_vector)
{
    const double square_modulus = bgc_fp64_quaternion_get_square_magnitude(quaternion);

    if (square_modulus < BGC_FP64_SQUARE_EPSILON || isnan(square_modulus)) {
        return BGC_FAILURE;
    }

    const double multiplier = 2.0 / square_modulus;

    const double tx = multiplier * (quaternion->y * original_vector->z - quaternion->z * original_vector->y);
    const double ty = multiplier * (quaternion->z * original_vector->x - quaternion->x * original_vector->z);
    const double tz = multiplier * (quaternion->x * original_vector->y - quaternion->y * original_vector->x);

    const double x = (original_vector->x - tx * quaternion->s) + (quaternion->y * tz - quaternion->z * ty);
    const double y = (original_vector->y - ty * quaternion->s) + (quaternion->z * tx - quaternion->x * tz);
    const double z = (original_vector->z - tz * quaternion->s) + (quaternion->x * ty - quaternion->y * tx);

    turned_vector->x = x;
    turned_vector->y = y;
    turned_vector->z = z;


    return BGC_SUCCESS;
}

// ========= Get Versor Rotation Matrix ========= //

inline void _bgc_fp32_versor_get_rotation_matrix(BGC_FP32_Matrix3x3* const matrix, const BGC_FP32_Quaternion* const versor)
{
    const float ss = versor->s * versor->s;
    const float xx = versor->x * versor->x;
    const float yy = versor->y * versor->y;
    const float zz = versor->z * versor->z;

    const float sx = versor->s * versor->x;
    const float sy = versor->s * versor->y;
    const float sz = versor->s * versor->z;

    const float xy = versor->x * versor->y;
    const float xz = versor->x * versor->z;

    const float yz = versor->y * versor->z;

    matrix->r1c1 = ((ss + xx) - (yy + zz));
    matrix->r2c2 = ((ss + yy) - (xx + zz));
    matrix->r3c3 = ((ss + zz) - (xx + yy));

    matrix->r1c2 = 2.0f * (xy - sz);
    matrix->r2c3 = 2.0f * (yz - sx);
    matrix->r3c1 = 2.0f * (xz - sy);

    matrix->r2c1 = 2.0f * (xy + sz);
    matrix->r3c2 = 2.0f * (yz + sx);
    matrix->r1c3 = 2.0f * (xz + sy);
}

inline void _bgc_fp64_versor_get_rotation_matrix(BGC_FP64_Matrix3x3* const matrix, const BGC_FP64_Quaternion* const versor)
{
    const double ss = versor->s * versor->s;
    const double xx = versor->x * versor->x;
    const double yy = versor->y * versor->y;
    const double zz = versor->z * versor->z;

    const double sx = versor->s * versor->x;
    const double sy = versor->s * versor->y;
    const double sz = versor->s * versor->z;

    const double xy = versor->x * versor->y;
    const double xz = versor->x * versor->z;

    const double yz = versor->y * versor->z;

    matrix->r1c1 = ((ss + xx) - (yy + zz));
    matrix->r2c2 = ((ss + yy) - (xx + zz));
    matrix->r3c3 = ((ss + zz) - (xx + yy));

    matrix->r1c2 = 2.0 * (xy - sz);
    matrix->r2c3 = 2.0 * (yz - sx);
    matrix->r3c1 = 2.0 * (xz - sy);

    matrix->r2c1 = 2.0 * (xy + sz);
    matrix->r3c2 = 2.0 * (yz + sx);
    matrix->r1c3 = 2.0 * (xz + sy);
}

// ========= Get Versor Reverse Matrix ========== //

inline void _bgc_fp32_versor_get_reverse_matrix(BGC_FP32_Matrix3x3* const matrix, const BGC_FP32_Quaternion* const versor)
{
    const float ss = versor->s * versor->s;
    const float xx = versor->x * versor->x;
    const float yy = versor->y * versor->y;
    const float zz = versor->z * versor->z;

    const float sx = versor->s * versor->x;
    const float sy = versor->s * versor->y;
    const float sz = versor->s * versor->z;

    const float xy = versor->x * versor->y;
    const float xz = versor->x * versor->z;

    const float yz = versor->y * versor->z;

    matrix->r1c1 = ((ss + xx) - (yy + zz));
    matrix->r2c2 = ((ss + yy) - (xx + zz));
    matrix->r3c3 = ((ss + zz) - (xx + yy));

    matrix->r1c2 = 2.0f * (xy + sz);
    matrix->r2c3 = 2.0f * (yz + sx);
    matrix->r3c1 = 2.0f * (xz + sy);

    matrix->r2c1 = 2.0f * (xy - sz);
    matrix->r3c2 = 2.0f * (yz - sx);
    matrix->r1c3 = 2.0f * (xz - sy);
}

inline void _bgc_fp64_versor_get_reverse_matrix(BGC_FP64_Matrix3x3* const matrix, const BGC_FP64_Quaternion* const versor)
{
    const double ss = versor->s * versor->s;
    const double xx = versor->x * versor->x;
    const double yy = versor->y * versor->y;
    const double zz = versor->z * versor->z;

    const double sx = versor->s * versor->x;
    const double sy = versor->s * versor->y;
    const double sz = versor->s * versor->z;

    const double xy = versor->x * versor->y;
    const double xz = versor->x * versor->z;

    const double yz = versor->y * versor->z;

    matrix->r1c1 = ((ss + xx) - (yy + zz));
    matrix->r2c2 = ((ss + yy) - (xx + zz));
    matrix->r3c3 = ((ss + zz) - (xx + yy));

    matrix->r1c2 = 2.0 * (xy + sz);
    matrix->r2c3 = 2.0 * (yz + sx);
    matrix->r3c1 = 2.0 * (xz + sy);

    matrix->r2c1 = 2.0 * (xy - sz);
    matrix->r3c2 = 2.0 * (yz - sx);
    matrix->r1c3 = 2.0 * (xz - sy);
}

// ============ Get Rotation Matrix ============= //

inline int bgc_fp32_quaternion_get_rotation_matrix(BGC_FP32_Matrix3x3* const rotation, const BGC_FP32_Quaternion* const quaternion)
{
    const float ss = quaternion->s * quaternion->s;
    const float xx = quaternion->x * quaternion->x;
    const float yy = quaternion->y * quaternion->y;
    const float zz = quaternion->z * quaternion->z;

    const float square_modulus = (ss + xx) + (yy + zz);

    if (square_modulus <= BGC_FP32_SQUARE_EPSILON || isnan(square_modulus))
    {
        bgc_fp32_matrix3x3_make_identity(rotation);
        return BGC_FAILURE;
    }

    const float corrector1 = 1.0f / square_modulus;

    const float sx = quaternion->s * quaternion->x;
    const float sy = quaternion->s * quaternion->y;
    const float sz = quaternion->s * quaternion->z;
    const float xy = quaternion->x * quaternion->y;
    const float xz = quaternion->x * quaternion->z;
    const float yz = quaternion->y * quaternion->z;

    const float corrector2 = 2.0f * corrector1;

    rotation->r1c1 = corrector1 * ((ss + xx) - (yy + zz));
    rotation->r2c2 = corrector1 * ((ss + yy) - (xx + zz));
    rotation->r3c3 = corrector1 * ((ss + zz) - (xx + yy));

    rotation->r1c2 = corrector2 * (xy - sz);
    rotation->r2c3 = corrector2 * (yz - sx);
    rotation->r3c1 = corrector2 * (xz - sy);

    rotation->r2c1 = corrector2 * (xy + sz);
    rotation->r3c2 = corrector2 * (yz + sx);
    rotation->r1c3 = corrector2 * (xz + sy);

    return BGC_SUCCESS;
}

inline int bgc_fp64_quaternion_get_rotation_matrix(BGC_FP64_Matrix3x3* const rotation, const BGC_FP64_Quaternion* const quaternion)
{
    const double ss = quaternion->s * quaternion->s;
    const double xx = quaternion->x * quaternion->x;
    const double yy = quaternion->y * quaternion->y;
    const double zz = quaternion->z * quaternion->z;

    const double square_modulus = (ss + xx) + (yy + zz);

    if (square_modulus <= BGC_FP64_SQUARE_EPSILON || isnan(square_modulus))
    {
        bgc_fp64_matrix3x3_make_identity(rotation);
        return BGC_FAILURE;
    }

    const double corrector1 = 1.0f / square_modulus;

    const double sx = quaternion->s * quaternion->x;
    const double sy = quaternion->s * quaternion->y;
    const double sz = quaternion->s * quaternion->z;
    const double xy = quaternion->x * quaternion->y;
    const double xz = quaternion->x * quaternion->z;
    const double yz = quaternion->y * quaternion->z;

    const double corrector2 = 2.0f * corrector1;

    rotation->r1c1 = corrector1 * ((ss + xx) - (yy + zz));
    rotation->r2c2 = corrector1 * ((ss + yy) - (xx + zz));
    rotation->r3c3 = corrector1 * ((ss + zz) - (xx + yy));

    rotation->r1c2 = corrector2 * (xy - sz);
    rotation->r2c3 = corrector2 * (yz - sx);
    rotation->r3c1 = corrector2 * (xz - sy);

    rotation->r2c1 = corrector2 * (xy + sz);
    rotation->r3c2 = corrector2 * (yz + sx);
    rotation->r1c3 = corrector2 * (xz + sy);

    return BGC_SUCCESS;
}

// ============= Get Reverse Matrix ============= //

inline int bgc_fp32_quaternion_get_reverse_matrix(BGC_FP32_Matrix3x3* const reverse, const BGC_FP32_Quaternion* const quaternion)
{
    const float ss = quaternion->s * quaternion->s;
    const float xx = quaternion->x * quaternion->x;
    const float yy = quaternion->y * quaternion->y;
    const float zz = quaternion->z * quaternion->z;

    const float square_modulus = (ss + xx) + (yy + zz);

    if (square_modulus <= BGC_FP32_SQUARE_EPSILON || isnan(square_modulus))
    {
        bgc_fp32_matrix3x3_make_identity(reverse);
        return BGC_FAILURE;
    }

    const float corrector1 = 1.0f / square_modulus;

    const float sx = quaternion->s * quaternion->x;
    const float sy = quaternion->s * quaternion->y;
    const float sz = quaternion->s * quaternion->z;
    const float xy = quaternion->x * quaternion->y;
    const float xz = quaternion->x * quaternion->z;
    const float yz = quaternion->y * quaternion->z;

    const float corrector2 = 2.0f * corrector1;

    reverse->r1c1 = corrector1 * ((ss + xx) - (yy + zz));
    reverse->r2c2 = corrector1 * ((ss + yy) - (xx + zz));
    reverse->r3c3 = corrector1 * ((ss + zz) - (xx + yy));

    reverse->r1c2 = corrector2 * (xy + sz);
    reverse->r2c3 = corrector2 * (yz + sx);
    reverse->r3c1 = corrector2 * (xz + sy);

    reverse->r2c1 = corrector2 * (xy - sz);
    reverse->r3c2 = corrector2 * (yz - sx);
    reverse->r1c3 = corrector2 * (xz - sy);

    return BGC_SUCCESS;
}

inline int bgc_fp64_quaternion_get_reverse_matrix(BGC_FP64_Matrix3x3* const reverse, const BGC_FP64_Quaternion* const quaternion)
{
    const double ss = quaternion->s * quaternion->s;
    const double xx = quaternion->x * quaternion->x;
    const double yy = quaternion->y * quaternion->y;
    const double zz = quaternion->z * quaternion->z;

    const double square_modulus = (ss + xx) + (yy + zz);

    if (square_modulus <= BGC_FP64_SQUARE_EPSILON || isnan(square_modulus))
    {
        bgc_fp64_matrix3x3_make_identity(reverse);
        return BGC_FAILURE;
    }

    const double corrector1 = 1.0f / square_modulus;

    const double sx = quaternion->s * quaternion->x;
    const double sy = quaternion->s * quaternion->y;
    const double sz = quaternion->s * quaternion->z;
    const double xy = quaternion->x * quaternion->y;
    const double xz = quaternion->x * quaternion->z;
    const double yz = quaternion->y * quaternion->z;

    const double corrector2 = 2.0f * corrector1;

    reverse->r1c1 = corrector1 * ((ss + xx) - (yy + zz));
    reverse->r2c2 = corrector1 * ((ss + yy) - (xx + zz));
    reverse->r3c3 = corrector1 * ((ss + zz) - (xx + yy));

    reverse->r1c2 = corrector2 * (xy + sz);
    reverse->r2c3 = corrector2 * (yz + sx);
    reverse->r3c1 = corrector2 * (xz + sy);

    reverse->r2c1 = corrector2 * (xy - sz);
    reverse->r3c2 = corrector2 * (yz - sx);
    reverse->r1c3 = corrector2 * (xz - sy);

    return BGC_SUCCESS;
}

// ============= Get Both Matrixes ============== //

inline int bgc_fp32_quaternion_get_both_matrices(BGC_FP32_Matrix3x3* const rotation, BGC_FP32_Matrix3x3* const reverse, const BGC_FP32_Quaternion* const quaternion)
{
    if (bgc_fp32_quaternion_get_reverse_matrix(reverse, quaternion) != BGC_SUCCESS) {
        return BGC_FAILURE;
    }

    bgc_fp32_matrix3x3_get_transposed(rotation, reverse);
    return BGC_SUCCESS;
}

inline int bgc_fp64_quaternion_get_both_matrices(BGC_FP64_Matrix3x3* const rotation, BGC_FP64_Matrix3x3* const reverse, const BGC_FP64_Quaternion* const quaternion)
{
    if (bgc_fp64_quaternion_get_reverse_matrix(reverse, quaternion) != BGC_SUCCESS) {
        return BGC_FAILURE;
    }

    bgc_fp64_matrix3x3_get_transposed(rotation, reverse);
    return BGC_SUCCESS;
}

// ================== Are Close ================= //

inline int bgc_fp32_quaternion_are_close(const BGC_FP32_Quaternion* const quaternion1, const BGC_FP32_Quaternion* const quaternion2)
{
    const float ds = quaternion1->s - quaternion2->s;
    const float dx = quaternion1->x - quaternion2->x;
    const float dy = quaternion1->y - quaternion2->y;
    const float dz = quaternion1->z - quaternion2->z;

    const float square_modulus1 = bgc_fp32_quaternion_get_square_magnitude(quaternion1);
    const float square_modulus2 = bgc_fp32_quaternion_get_square_magnitude(quaternion2);
    const float square_distance = (ds * ds + dx * dx) + (dy * dy + dz * dz);

    if (square_modulus1 <= BGC_FP32_EPSILON_EFFECTIVENESS_LIMIT || square_modulus2 <= BGC_FP32_EPSILON_EFFECTIVENESS_LIMIT) {
        return square_distance <= BGC_FP32_SQUARE_EPSILON;
    }

    return square_distance <= BGC_FP32_SQUARE_EPSILON * square_modulus1 && square_distance <= BGC_FP32_SQUARE_EPSILON * square_modulus2;
}

inline int bgc_fp64_quaternion_are_close(const BGC_FP64_Quaternion* const quaternion1, const BGC_FP64_Quaternion* const quaternion2)
{
    const double ds = quaternion1->s - quaternion2->s;
    const double dx = quaternion1->x - quaternion2->x;
    const double dy = quaternion1->y - quaternion2->y;
    const double dz = quaternion1->z - quaternion2->z;

    const double square_modulus1 = bgc_fp64_quaternion_get_square_magnitude(quaternion1);
    const double square_modulus2 = bgc_fp64_quaternion_get_square_magnitude(quaternion2);
    const double square_distance = (ds * ds + dx * dx) + (dy * dy + dz * dz);

    if (square_modulus1 <= BGC_FP64_EPSILON_EFFECTIVENESS_LIMIT || square_modulus2 <= BGC_FP64_EPSILON_EFFECTIVENESS_LIMIT) {
        return square_distance <= BGC_FP64_SQUARE_EPSILON;
    }

    return square_distance <= BGC_FP64_SQUARE_EPSILON * square_modulus1 && square_distance <= BGC_FP64_SQUARE_EPSILON * square_modulus2;
}

#endif