#ifndef _BGC_QUATERNION_H_
#define _BGC_QUATERNION_H_

#include <math.h>

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

typedef struct {
    float s0, x1, x2, x3;
} BGC_FP32_Quaternion;

typedef struct {
    double s0, x1, x2, x3;
} BGC_FP64_Quaternion;

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

inline void bgc_fp32_quaternion_reset(BGC_FP32_Quaternion* quaternion)
{
    quaternion->s0 = 0.0f;
    quaternion->x1 = 0.0f;
    quaternion->x2 = 0.0f;
    quaternion->x3 = 0.0f;
}

inline void bgc_fp64_quaternion_reset(BGC_FP64_Quaternion* quaternion)
{
    quaternion->s0 = 0.0;
    quaternion->x1 = 0.0;
    quaternion->x2 = 0.0;
    quaternion->x3 = 0.0;
}

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

inline void bgc_fp32_quaternion_make_unit(BGC_FP32_Quaternion* quaternion)
{
    quaternion->s0 = 1.0f;
    quaternion->x1 = 0.0f;
    quaternion->x2 = 0.0f;
    quaternion->x3 = 0.0f;
}

inline void bgc_fp64_quaternion_make_unit(BGC_FP64_Quaternion* quaternion)
{
    quaternion->s0 = 1.0;
    quaternion->x1 = 0.0;
    quaternion->x2 = 0.0;
    quaternion->x3 = 0.0;
}

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

inline void bgc_fp32_quaternion_make(BGC_FP32_Quaternion* quaternion, const float s0, const float x1, const float x2, const float x3)
{
    quaternion->s0 = s0;
    quaternion->x1 = x1;
    quaternion->x2 = x2;
    quaternion->x3 = x3;
}

inline void bgc_fp64_quaternion_make(BGC_FP64_Quaternion* quaternion, const double s0, const double x1, const double x2, const double x3)
{
    quaternion->s0 = s0;
    quaternion->x1 = x1;
    quaternion->x2 = x2;
    quaternion->x3 = x3;
}

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

inline float bgc_fp32_quaternion_get_square_modulus(const BGC_FP32_Quaternion* quaternion)
{
    return (quaternion->s0 * quaternion->s0 + quaternion->x1 * quaternion->x1) + (quaternion->x2 * quaternion->x2 + quaternion->x3 * quaternion->x3);
}

inline double bgc_fp64_quaternion_get_square_modulus(const BGC_FP64_Quaternion* quaternion)
{
    return (quaternion->s0 * quaternion->s0 + quaternion->x1 * quaternion->x1) + (quaternion->x2 * quaternion->x2 + quaternion->x3 * quaternion->x3);
}

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

inline float bgc_fp32_quaternion_get_modulus(const BGC_FP32_Quaternion* quaternion)
{
    return sqrtf(bgc_fp32_quaternion_get_square_modulus(quaternion));
}

inline double bgc_fp64_quaternion_get_modulus(const BGC_FP64_Quaternion* quaternion)
{
    return sqrt(bgc_fp64_quaternion_get_square_modulus(quaternion));
}

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

inline int bgc_fp32_quaternion_is_zero(const BGC_FP32_Quaternion* quaternion)
{
    return bgc_fp32_quaternion_get_square_modulus(quaternion) <= BGC_FP32_SQUARE_EPSILON;
}

inline int bgc_fp64_quaternion_is_zero(const BGC_FP64_Quaternion* quaternion)
{
    return bgc_fp64_quaternion_get_square_modulus(quaternion) <= BGC_FP64_SQUARE_EPSILON;
}

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

inline int bgc_fp32_quaternion_is_unit(const BGC_FP32_Quaternion* quaternion)
{
    return bgc_fp32_is_square_unit(bgc_fp32_quaternion_get_square_modulus(quaternion));
}

inline int bgc_fp64_quaternion_is_unit(const BGC_FP64_Quaternion* quaternion)
{
    return bgc_fp64_is_square_unit(bgc_fp64_quaternion_get_square_modulus(quaternion));
}

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

inline void bgc_fp32_quaternion_copy(BGC_FP32_Quaternion* destination, const BGC_FP32_Quaternion* source)
{
    destination->s0 = source->s0;
    destination->x1 = source->x1;
    destination->x2 = source->x2;
    destination->x3 = source->x3;
}

inline void bgc_fp64_quaternion_copy(BGC_FP64_Quaternion* destination, const BGC_FP64_Quaternion* source)
{
    destination->s0 = source->s0;
    destination->x1 = source->x1;
    destination->x2 = source->x2;
    destination->x3 = source->x3;
}

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

inline void bgc_fp32_quaternion_swap(BGC_FP32_Quaternion* quarternion1, BGC_FP32_Quaternion* quarternion2)
{
    const float s0 = quarternion2->s0;
    const float x1 = quarternion2->x1;
    const float x2 = quarternion2->x2;
    const float x3 = quarternion2->x3;

    quarternion2->s0 = quarternion1->s0;
    quarternion2->x1 = quarternion1->x1;
    quarternion2->x2 = quarternion1->x2;
    quarternion2->x3 = quarternion1->x3;

    quarternion1->s0 = s0;
    quarternion1->x1 = x1;
    quarternion1->x2 = x2;
    quarternion1->x3 = x3;
}

inline void bgc_fp64_quaternion_swap(BGC_FP64_Quaternion* quarternion1, BGC_FP64_Quaternion* quarternion2)
{
    const double s0 = quarternion2->s0;
    const double x1 = quarternion2->x1;
    const double x2 = quarternion2->x2;
    const double x3 = quarternion2->x3;

    quarternion2->s0 = quarternion1->s0;
    quarternion2->x1 = quarternion1->x1;
    quarternion2->x2 = quarternion1->x2;
    quarternion2->x3 = quarternion1->x3;

    quarternion1->s0 = s0;
    quarternion1->x1 = x1;
    quarternion1->x2 = x2;
    quarternion1->x3 = x3;
}

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

inline void bgc_fp32_quaternion_convert_to_fp64(BGC_FP64_Quaternion* destination, const BGC_FP32_Quaternion* source)
{
    destination->s0 = source->s0;
    destination->x1 = source->x1;
    destination->x2 = source->x2;
    destination->x3 = source->x3;
}

inline void bgc_fp64_quaternion_convert_to_fp32(BGC_FP32_Quaternion* destination, const BGC_FP64_Quaternion* source)
{
    destination->s0 = (float)source->s0;
    destination->x1 = (float)source->x1;
    destination->x2 = (float)source->x2;
    destination->x3 = (float)source->x3;
}

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

inline void bgc_fp32_quaternion_add(BGC_FP32_Quaternion* sum, const BGC_FP32_Quaternion* quaternion1, const BGC_FP32_Quaternion* quaternion2)
{
    sum->s0 = quaternion1->s0 + quaternion2->s0;
    sum->x1 = quaternion1->x1 + quaternion2->x1;
    sum->x2 = quaternion1->x2 + quaternion2->x2;
    sum->x3 = quaternion1->x3 + quaternion2->x3;
}

inline void bgc_fp64_quaternion_add(BGC_FP64_Quaternion* sum, const BGC_FP64_Quaternion* quaternion1, const BGC_FP64_Quaternion* quaternion2)
{
    sum->s0 = quaternion1->s0 + quaternion2->s0;
    sum->x1 = quaternion1->x1 + quaternion2->x1;
    sum->x2 = quaternion1->x2 + quaternion2->x2;
    sum->x3 = quaternion1->x3 + quaternion2->x3;
}

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

inline void bgc_fp32_quaternion_add_scaled(BGC_FP32_Quaternion* sum, const BGC_FP32_Quaternion* basic_quaternion, const BGC_FP32_Quaternion* scalable_quaternion, const float scale)
{
    sum->s0 = basic_quaternion->s0 + scalable_quaternion->s0 * scale;
    sum->x1 = basic_quaternion->x1 + scalable_quaternion->x1 * scale;
    sum->x2 = basic_quaternion->x2 + scalable_quaternion->x2 * scale;
    sum->x3 = basic_quaternion->x3 + scalable_quaternion->x3 * scale;
}

inline void bgc_fp64_quaternion_add_scaled(BGC_FP64_Quaternion* sum, const BGC_FP64_Quaternion* basic_quaternion, const BGC_FP64_Quaternion* scalable_quaternion, const double scale)
{
    sum->s0 = basic_quaternion->s0 + scalable_quaternion->s0 * scale;
    sum->x1 = basic_quaternion->x1 + scalable_quaternion->x1 * scale;
    sum->x2 = basic_quaternion->x2 + scalable_quaternion->x2 * scale;
    sum->x3 = basic_quaternion->x3 + scalable_quaternion->x3 * scale;
}

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

inline void bgc_fp32_quaternion_subtract(BGC_FP32_Quaternion* difference, const BGC_FP32_Quaternion* minuend, const BGC_FP32_Quaternion* subtrahend)
{
    difference->s0 = minuend->s0 - subtrahend->s0;
    difference->x1 = minuend->x1 - subtrahend->x1;
    difference->x2 = minuend->x2 - subtrahend->x2;
    difference->x3 = minuend->x3 - subtrahend->x3;
}

inline void bgc_fp64_quaternion_subtract(BGC_FP64_Quaternion* difference, const BGC_FP64_Quaternion* minuend, const BGC_FP64_Quaternion* subtrahend)
{
    difference->s0 = minuend->s0 - subtrahend->s0;
    difference->x1 = minuend->x1 - subtrahend->x1;
    difference->x2 = minuend->x2 - subtrahend->x2;
    difference->x3 = minuend->x3 - subtrahend->x3;
}

// ================== Multiply ================== //

inline void bgc_fp32_quaternion_get_product(BGC_FP32_Quaternion* product, const BGC_FP32_Quaternion* left, const BGC_FP32_Quaternion* right)
{
    const float s0 = (left->s0 * right->s0 - left->x1 * right->x1) - (left->x2 * right->x2 + left->x3 * right->x3);
    const float x1 = (left->x1 * right->s0 + left->s0 * right->x1) - (left->x3 * right->x2 - left->x2 * right->x3);
    const float x2 = (left->x2 * right->s0 + left->s0 * right->x2) - (left->x1 * right->x3 - left->x3 * right->x1);
    const float x3 = (left->x3 * right->s0 + left->s0 * right->x3) - (left->x2 * right->x1 - left->x1 * right->x2);

    product->s0 = s0;
    product->x1 = x1;
    product->x2 = x2;
    product->x3 = x3;
}

inline void bgc_fp64_quaternion_get_product(BGC_FP64_Quaternion* product, const BGC_FP64_Quaternion* left, const BGC_FP64_Quaternion* right)
{
    const double s0 = (left->s0 * right->s0 - left->x1 * right->x1) - (left->x2 * right->x2 + left->x3 * right->x3);
    const double x1 = (left->x1 * right->s0 + left->s0 * right->x1) - (left->x3 * right->x2 - left->x2 * right->x3);
    const double x2 = (left->x2 * right->s0 + left->s0 * right->x2) - (left->x1 * right->x3 - left->x3 * right->x1);
    const double x3 = (left->x3 * right->s0 + left->s0 * right->x3) - (left->x2 * right->x1 - left->x1 * right->x2);

    product->s0 = s0;
    product->x1 = x1;
    product->x2 = x2;
    product->x3 = x3;
}

inline void bgc_fp32_quaternion_multiply(BGC_FP32_Quaternion* product, const BGC_FP32_Quaternion* multiplicand, const float multipier)
{
    product->s0 = multiplicand->s0 * multipier;
    product->x1 = multiplicand->x1 * multipier;
    product->x2 = multiplicand->x2 * multipier;
    product->x3 = multiplicand->x3 * multipier;
}

inline void bgc_fp64_quaternion_multiply(BGC_FP64_Quaternion* product, const BGC_FP64_Quaternion* multiplicand, const double multipier)
{
    product->s0 = multiplicand->s0 * multipier;
    product->x1 = multiplicand->x1 * multipier;
    product->x2 = multiplicand->x2 * multipier;
    product->x3 = multiplicand->x3 * multipier;
}

// =================== Divide =================== //

inline int bgc_fp32_quaternion_get_ratio(BGC_FP32_Quaternion* quotient, const BGC_FP32_Quaternion* divident, const BGC_FP32_Quaternion* divisor)
{
    const float square_modulus = bgc_fp32_quaternion_get_square_modulus(divisor);

    if (square_modulus <= BGC_FP32_SQUARE_EPSILON || isnan(square_modulus)) {
        return 0;
    }

    const float s0 = (divident->s0 * divisor->s0 + divident->x1 * divisor->x1) + (divident->x2 * divisor->x2 + divident->x3 * divisor->x3);
    const float x1 = (divident->x1 * divisor->s0 + divident->x3 * divisor->x2) - (divident->s0 * divisor->x1 + divident->x2 * divisor->x3);
    const float x2 = (divident->x2 * divisor->s0 + divident->x1 * divisor->x3) - (divident->s0 * divisor->x2 + divident->x3 * divisor->x1);
    const float x3 = (divident->x3 * divisor->s0 + divident->x2 * divisor->x1) - (divident->s0 * divisor->x3 + divident->x1 * divisor->x2);

    const float multiplicand = 1.0f / square_modulus;

    quotient->s0 = s0 * multiplicand;
    quotient->x1 = x1 * multiplicand;
    quotient->x2 = x2 * multiplicand;
    quotient->x3 = x3 * multiplicand;

    return 1;
}

inline int bgc_fp64_quaternion_get_ratio(BGC_FP64_Quaternion* quotient, const BGC_FP64_Quaternion* divident, const BGC_FP64_Quaternion* divisor)
{
    const double square_modulus = bgc_fp64_quaternion_get_square_modulus(divisor);

    if (square_modulus <= BGC_FP64_SQUARE_EPSILON || isnan(square_modulus)) {
        return 0;
    }

    const double s0 = (divident->s0 * divisor->s0 + divident->x1 * divisor->x1) + (divident->x2 * divisor->x2 + divident->x3 * divisor->x3);
    const double x1 = (divident->x1 * divisor->s0 + divident->x3 * divisor->x2) - (divident->s0 * divisor->x1 + divident->x2 * divisor->x3);
    const double x2 = (divident->x2 * divisor->s0 + divident->x1 * divisor->x3) - (divident->s0 * divisor->x2 + divident->x3 * divisor->x1);
    const double x3 = (divident->x3 * divisor->s0 + divident->x2 * divisor->x1) - (divident->s0 * divisor->x3 + divident->x1 * divisor->x2);

    const double multiplicand = 1.0 / square_modulus;

    quotient->s0 = s0 * multiplicand;
    quotient->x1 = x1 * multiplicand;
    quotient->x2 = x2 * multiplicand;
    quotient->x3 = x3 * multiplicand;

    return 1;
}

inline void bgc_fp32_quaternion_divide(BGC_FP32_Quaternion* quotient, const BGC_FP32_Quaternion* dividend, const float divisor)
{
    bgc_fp32_quaternion_multiply(quotient, dividend, 1.0f / divisor);
}

inline void bgc_fp64_quaternion_divide(BGC_FP64_Quaternion* quotient, const BGC_FP64_Quaternion* dividend, const double divisor)
{
    bgc_fp64_quaternion_multiply(quotient, dividend, 1.0 / divisor);
}

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

inline void bgc_fp32_quaternion_get_mean2(BGC_FP32_Quaternion* mean, const BGC_FP32_Quaternion* quaternion1, const BGC_FP32_Quaternion* quaternion2)
{
    mean->s0 = (quaternion1->s0 + quaternion2->s0) * 0.5f;
    mean->x1 = (quaternion1->x1 + quaternion2->x1) * 0.5f;
    mean->x2 = (quaternion1->x2 + quaternion2->x2) * 0.5f;
    mean->x3 = (quaternion1->x3 + quaternion2->x3) * 0.5f;
}

inline void bgc_fp64_quaternion_get_mean2(BGC_FP64_Quaternion* mean, const BGC_FP64_Quaternion* quaternion1, const BGC_FP64_Quaternion* quaternion2)
{
    mean->s0 = (quaternion1->s0 + quaternion2->s0) * 0.5f;
    mean->x1 = (quaternion1->x1 + quaternion2->x1) * 0.5f;
    mean->x2 = (quaternion1->x2 + quaternion2->x2) * 0.5f;
    mean->x3 = (quaternion1->x3 + quaternion2->x3) * 0.5f;
}

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

inline void bgc_fp32_quaternion_get_mean3(BGC_FP32_Quaternion* mean, const BGC_FP32_Quaternion* quaternion1, const BGC_FP32_Quaternion* quaternion2, const BGC_FP32_Quaternion* quaternion3)
{
    mean->s0 = (quaternion1->s0 + quaternion2->s0 + quaternion3->s0) * BGC_FP32_ONE_THIRD;
    mean->x1 = (quaternion1->x1 + quaternion2->x1 + quaternion3->x1) * BGC_FP32_ONE_THIRD;
    mean->x2 = (quaternion1->x2 + quaternion2->x2 + quaternion3->x2) * BGC_FP32_ONE_THIRD;
    mean->x3 = (quaternion1->x3 + quaternion2->x3 + quaternion3->x3) * BGC_FP32_ONE_THIRD;
}

inline void bgc_fp64_quaternion_get_mean3(BGC_FP64_Quaternion* mean, const BGC_FP64_Quaternion* quaternion1, const BGC_FP64_Quaternion* quaternion2, const BGC_FP64_Quaternion* quaternion3)
{
    mean->s0 = (quaternion1->s0 + quaternion2->s0 + quaternion3->s0) * BGC_FP64_ONE_THIRD;
    mean->x1 = (quaternion1->x1 + quaternion2->x1 + quaternion3->x1) * BGC_FP64_ONE_THIRD;
    mean->x2 = (quaternion1->x2 + quaternion2->x2 + quaternion3->x2) * BGC_FP64_ONE_THIRD;
    mean->x3 = (quaternion1->x3 + quaternion2->x3 + quaternion3->x3) * BGC_FP64_ONE_THIRD;
}

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

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

    interpolation->s0 = quaternion1->s0 * counter_phase + quaternion2->s0 * phase;
    interpolation->x1 = quaternion1->x1 * counter_phase + quaternion2->x1 * phase;
    interpolation->x2 = quaternion1->x2 * counter_phase + quaternion2->x2 * phase;
    interpolation->x3 = quaternion1->x3 * counter_phase + quaternion2->x3 * phase;
}

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

    interpolation->s0 = quaternion1->s0 * counter_phase + quaternion2->s0 * phase;
    interpolation->x1 = quaternion1->x1 * counter_phase + quaternion2->x1 * phase;
    interpolation->x2 = quaternion1->x2 * counter_phase + quaternion2->x2 * phase;
    interpolation->x3 = quaternion1->x3 * counter_phase + quaternion2->x3 * phase;
}

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

inline void bgc_fp32_quaternion_conjugate(BGC_FP32_Quaternion* quaternion)
{
    quaternion->x1 = -quaternion->x1;
    quaternion->x2 = -quaternion->x2;
    quaternion->x3 = -quaternion->x3;
}

inline void bgc_fp64_quaternion_conjugate(BGC_FP64_Quaternion* quaternion)
{
    quaternion->x1 = -quaternion->x1;
    quaternion->x2 = -quaternion->x2;
    quaternion->x3 = -quaternion->x3;
}

inline void bgc_fp32_quaternion_get_conjugate(BGC_FP32_Quaternion* conjugate, const BGC_FP32_Quaternion* quaternion)
{
    conjugate->s0 = quaternion->s0;
    conjugate->x1 = -quaternion->x1;
    conjugate->x2 = -quaternion->x2;
    conjugate->x3 = -quaternion->x3;
}

inline void bgc_fp64_quaternion_get_conjugate(BGC_FP64_Quaternion* conjugate, const BGC_FP64_Quaternion* quaternion)
{
    conjugate->s0 = quaternion->s0;
    conjugate->x1 = -quaternion->x1;
    conjugate->x2 = -quaternion->x2;
    conjugate->x3 = -quaternion->x3;
}

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

inline void bgc_fp32_quaternion_revert(BGC_FP32_Quaternion* quaternion)
{
    quaternion->s0 = -quaternion->s0;
    quaternion->x1 = -quaternion->x1;
    quaternion->x2 = -quaternion->x2;
    quaternion->x3 = -quaternion->x3;
}

inline void bgc_fp64_quaternion_revert(BGC_FP64_Quaternion* quaternion)
{
    quaternion->s0 = -quaternion->s0;
    quaternion->x1 = -quaternion->x1;
    quaternion->x2 = -quaternion->x2;
    quaternion->x3 = -quaternion->x3;
}

inline void bgc_fp32_quaternion_get_reverse(BGC_FP32_Quaternion* reverse, const BGC_FP32_Quaternion* quaternion)
{
    reverse->s0 = -quaternion->s0;
    reverse->x1 = -quaternion->x1;
    reverse->x2 = -quaternion->x2;
    reverse->x3 = -quaternion->x3;
}

inline void bgc_fp64_quaternion_get_reverse(BGC_FP64_Quaternion* reverse, const BGC_FP64_Quaternion* quaternion)
{
    reverse->s0 = -quaternion->s0;
    reverse->x1 = -quaternion->x1;
    reverse->x2 = -quaternion->x2;
    reverse->x3 = -quaternion->x3;
}

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

inline int bgc_fp32_quaternion_get_inverse(BGC_FP32_Quaternion* inverse, const BGC_FP32_Quaternion* quaternion)
{
    const float square_modulus = bgc_fp32_quaternion_get_square_modulus(quaternion);

    if (square_modulus <= BGC_FP32_SQUARE_EPSILON || isnan(square_modulus)) {
        return 0;
    }

    const float multiplicand = 1.0f / square_modulus;

    inverse->s0 = quaternion->s0 * multiplicand;
    inverse->x1 = -quaternion->x1 * multiplicand;
    inverse->x2 = -quaternion->x2 * multiplicand;
    inverse->x3 = -quaternion->x3 * multiplicand;

    return 1;
}

inline int bgc_fp64_quaternion_get_inverse(BGC_FP64_Quaternion* inverse, const BGC_FP64_Quaternion* quaternion)
{
    const double square_modulus = bgc_fp64_quaternion_get_square_modulus(quaternion);

    if (square_modulus <= BGC_FP64_SQUARE_EPSILON || isnan(square_modulus)) {
        return 0;
    }

    const double multiplicand = 1.0 / square_modulus;

    inverse->s0 = quaternion->s0 * multiplicand;
    inverse->x1 = -quaternion->x1 * multiplicand;
    inverse->x2 = -quaternion->x2 * multiplicand;
    inverse->x3 = -quaternion->x3 * multiplicand;

    return 1;
}

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

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

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

inline int bgc_fp32_quaternion_normalize(BGC_FP32_Quaternion* quaternion)
{
    const float square_modulus = bgc_fp32_quaternion_get_square_modulus(quaternion);

    if (bgc_fp32_is_square_unit(square_modulus)) {
        return 1;
    }

    if (square_modulus <= BGC_FP32_SQUARE_EPSILON || isnan(square_modulus)) {
        return 0;
    }

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

    quaternion->s0 *= multiplier;
    quaternion->x1 *= multiplier;
    quaternion->x2 *= multiplier;
    quaternion->x3 *= multiplier;

    return 1;
}

inline int bgc_fp64_quaternion_normalize(BGC_FP64_Quaternion* quaternion)
{
    const double square_modulus = bgc_fp64_quaternion_get_square_modulus(quaternion);

    if (bgc_fp64_is_square_unit(square_modulus)) {
        return 1;
    }

    if (square_modulus <= BGC_FP64_SQUARE_EPSILON || isnan(square_modulus)) {
        return 0;
    }

    const double multiplier = sqrt(1.0 / square_modulus);

    quaternion->s0 *= multiplier;
    quaternion->x1 *= multiplier;
    quaternion->x2 *= multiplier;
    quaternion->x3 *= multiplier;

    return 1;
}

inline int bgc_fp32_quaternion_get_normalized(BGC_FP32_Quaternion* normalized, const BGC_FP32_Quaternion* quaternion)
{
    const float square_modulus = bgc_fp32_quaternion_get_square_modulus(quaternion);

    if (bgc_fp32_is_square_unit(square_modulus)) {
        bgc_fp32_quaternion_copy(normalized, quaternion);
        return 1;
    }

    if (square_modulus <= BGC_FP32_SQUARE_EPSILON || isnan(square_modulus)) {
        bgc_fp32_quaternion_reset(normalized);
        return 0;
    }

    bgc_fp32_quaternion_multiply(normalized, quaternion, sqrtf(1.0f / square_modulus));
    return 1;
}

inline int bgc_fp64_quaternion_get_normalized(BGC_FP64_Quaternion* normalized, const BGC_FP64_Quaternion* quaternion)
{
    const double square_modulus = bgc_fp64_quaternion_get_square_modulus(quaternion);

    if (bgc_fp64_is_square_unit(square_modulus)) {
        bgc_fp64_quaternion_copy(normalized, quaternion);
        return 1;
    }

    if (square_modulus <= BGC_FP64_SQUARE_EPSILON || isnan(square_modulus)) {
        bgc_fp64_quaternion_reset(normalized);
        return 0;
    }

    bgc_fp64_quaternion_multiply(normalized, quaternion, sqrt(1.0 / square_modulus));
    return 1;
}

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

int bgc_fp32_quaternion_get_exponation(BGC_FP32_Quaternion* power, const BGC_FP32_Quaternion* base, const float exponent);

int bgc_fp64_quaternion_get_exponation(BGC_FP64_Quaternion* power, const BGC_FP64_Quaternion* base, const double exponent);

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

inline int bgc_fp32_quaternion_get_rotation_matrix(BGC_FP32_Matrix3x3* rotation, const BGC_FP32_Quaternion* quaternion)
{
    const float s0s0 = quaternion->s0 * quaternion->s0;
    const float x1x1 = quaternion->x1 * quaternion->x1;
    const float x2x2 = quaternion->x2 * quaternion->x2;
    const float x3x3 = quaternion->x3 * quaternion->x3;

    const float square_modulus = (s0s0 + x1x1) + (x2x2 + x3x3);

    if (square_modulus <= BGC_FP32_SQUARE_EPSILON || isnan(square_modulus))
    {
        bgc_fp32_matrix3x3_make_identity(rotation);
        return 0;
    }

    const float corrector1 = 1.0f / square_modulus;

    const float s0x1 = quaternion->s0 * quaternion->x1;
    const float s0x2 = quaternion->s0 * quaternion->x2;
    const float s0x3 = quaternion->s0 * quaternion->x3;
    const float x1x2 = quaternion->x1 * quaternion->x2;
    const float x1x3 = quaternion->x1 * quaternion->x3;
    const float x2x3 = quaternion->x2 * quaternion->x3;

    const float corrector2 = 2.0f * corrector1;

    rotation->row1_col1 = corrector1 * ((s0s0 + x1x1) - (x2x2 + x3x3));
    rotation->row2_col2 = corrector1 * ((s0s0 + x2x2) - (x1x1 + x3x3));
    rotation->row3_col3 = corrector1 * ((s0s0 + x3x3) - (x1x1 + x2x2));

    rotation->row1_col2 = corrector2 * (x1x2 - s0x3);
    rotation->row2_col3 = corrector2 * (x2x3 - s0x1);
    rotation->row3_col1 = corrector2 * (x1x3 - s0x2);

    rotation->row2_col1 = corrector2 * (x1x2 + s0x3);
    rotation->row3_col2 = corrector2 * (x2x3 + s0x1);
    rotation->row1_col3 = corrector2 * (x1x3 + s0x2);

    return 1;
}

inline int bgc_fp64_quaternion_get_rotation_matrix(BGC_FP64_Matrix3x3* rotation, const BGC_FP64_Quaternion* quaternion)
{
    const double s0s0 = quaternion->s0 * quaternion->s0;
    const double x1x1 = quaternion->x1 * quaternion->x1;
    const double x2x2 = quaternion->x2 * quaternion->x2;
    const double x3x3 = quaternion->x3 * quaternion->x3;

    const double square_modulus = (s0s0 + x1x1) + (x2x2 + x3x3);

    if (square_modulus <= BGC_FP64_SQUARE_EPSILON || isnan(square_modulus))
    {
        bgc_fp64_matrix3x3_make_identity(rotation);
        return 0;
    }

    const double corrector1 = 1.0f / square_modulus;

    const double s0x1 = quaternion->s0 * quaternion->x1;
    const double s0x2 = quaternion->s0 * quaternion->x2;
    const double s0x3 = quaternion->s0 * quaternion->x3;
    const double x1x2 = quaternion->x1 * quaternion->x2;
    const double x1x3 = quaternion->x1 * quaternion->x3;
    const double x2x3 = quaternion->x2 * quaternion->x3;

    const double corrector2 = 2.0f * corrector1;

    rotation->row1_col1 = corrector1 * ((s0s0 + x1x1) - (x2x2 + x3x3));
    rotation->row2_col2 = corrector1 * ((s0s0 + x2x2) - (x1x1 + x3x3));
    rotation->row3_col3 = corrector1 * ((s0s0 + x3x3) - (x1x1 + x2x2));

    rotation->row1_col2 = corrector2 * (x1x2 - s0x3);
    rotation->row2_col3 = corrector2 * (x2x3 - s0x1);
    rotation->row3_col1 = corrector2 * (x1x3 - s0x2);

    rotation->row2_col1 = corrector2 * (x1x2 + s0x3);
    rotation->row3_col2 = corrector2 * (x2x3 + s0x1);
    rotation->row1_col3 = corrector2 * (x1x3 + s0x2);

    return 1;
}

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

inline int bgc_fp32_quaternion_get_reverse_matrix(BGC_FP32_Matrix3x3* reverse, const BGC_FP32_Quaternion* quaternion)
{
    const float s0s0 = quaternion->s0 * quaternion->s0;
    const float x1x1 = quaternion->x1 * quaternion->x1;
    const float x2x2 = quaternion->x2 * quaternion->x2;
    const float x3x3 = quaternion->x3 * quaternion->x3;

    const float square_modulus = (s0s0 + x1x1) + (x2x2 + x3x3);

    if (square_modulus <= BGC_FP32_SQUARE_EPSILON || isnan(square_modulus))
    {
        bgc_fp32_matrix3x3_make_identity(reverse);
        return 0;
    }

    const float corrector1 = 1.0f / square_modulus;

    const float s0x1 = quaternion->s0 * quaternion->x1;
    const float s0x2 = quaternion->s0 * quaternion->x2;
    const float s0x3 = quaternion->s0 * quaternion->x3;
    const float x1x2 = quaternion->x1 * quaternion->x2;
    const float x1x3 = quaternion->x1 * quaternion->x3;
    const float x2x3 = quaternion->x2 * quaternion->x3;

    const float corrector2 = 2.0f * corrector1;

    reverse->row1_col1 = corrector1 * ((s0s0 + x1x1) - (x2x2 + x3x3));
    reverse->row2_col2 = corrector1 * ((s0s0 + x2x2) - (x1x1 + x3x3));
    reverse->row3_col3 = corrector1 * ((s0s0 + x3x3) - (x1x1 + x2x2));

    reverse->row1_col2 = corrector2 * (x1x2 + s0x3);
    reverse->row2_col3 = corrector2 * (x2x3 + s0x1);
    reverse->row3_col1 = corrector2 * (x1x3 + s0x2);

    reverse->row2_col1 = corrector2 * (x1x2 - s0x3);
    reverse->row3_col2 = corrector2 * (x2x3 - s0x1);
    reverse->row1_col3 = corrector2 * (x1x3 - s0x2);

    return 1;
}

inline int bgc_fp64_quaternion_get_reverse_matrix(BGC_FP64_Matrix3x3* reverse, const BGC_FP64_Quaternion* quaternion)
{
    const double s0s0 = quaternion->s0 * quaternion->s0;
    const double x1x1 = quaternion->x1 * quaternion->x1;
    const double x2x2 = quaternion->x2 * quaternion->x2;
    const double x3x3 = quaternion->x3 * quaternion->x3;

    const double square_modulus = (s0s0 + x1x1) + (x2x2 + x3x3);

    if (square_modulus <= BGC_FP64_SQUARE_EPSILON || isnan(square_modulus))
    {
        bgc_fp64_matrix3x3_make_identity(reverse);
        return 0;
    }

    const double corrector1 = 1.0f / square_modulus;

    const double s0x1 = quaternion->s0 * quaternion->x1;
    const double s0x2 = quaternion->s0 * quaternion->x2;
    const double s0x3 = quaternion->s0 * quaternion->x3;
    const double x1x2 = quaternion->x1 * quaternion->x2;
    const double x1x3 = quaternion->x1 * quaternion->x3;
    const double x2x3 = quaternion->x2 * quaternion->x3;

    const double corrector2 = 2.0f * corrector1;

    reverse->row1_col1 = corrector1 * ((s0s0 + x1x1) - (x2x2 + x3x3));
    reverse->row2_col2 = corrector1 * ((s0s0 + x2x2) - (x1x1 + x3x3));
    reverse->row3_col3 = corrector1 * ((s0s0 + x3x3) - (x1x1 + x2x2));

    reverse->row1_col2 = corrector2 * (x1x2 + s0x3);
    reverse->row2_col3 = corrector2 * (x2x3 + s0x1);
    reverse->row3_col1 = corrector2 * (x1x3 + s0x2);

    reverse->row2_col1 = corrector2 * (x1x2 - s0x3);
    reverse->row3_col2 = corrector2 * (x2x3 - s0x1);
    reverse->row1_col3 = corrector2 * (x1x3 - s0x2);

    return 1;
}

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

inline int bgc_fp32_quaternion_get_both_matrices(BGC_FP32_Matrix3x3* rotation, BGC_FP32_Matrix3x3* reverse, const BGC_FP32_Quaternion* quaternion)
{
    if (bgc_fp32_quaternion_get_reverse_matrix(reverse, quaternion)) {
        bgc_fp32_matrix3x3_get_transposed(rotation, reverse);
        return 1;
    }

    return 0;
}

inline int bgc_fp64_quaternion_get_both_matrices(BGC_FP64_Matrix3x3* rotation, BGC_FP64_Matrix3x3* reverse, const BGC_FP64_Quaternion* quaternion)
{
    if (bgc_fp64_quaternion_get_reverse_matrix(reverse, quaternion)) {
        bgc_fp64_matrix3x3_get_transposed(rotation, reverse);
        return 1;
    }

    return 0;
}

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

inline int bgc_fp32_quaternion_are_close(const BGC_FP32_Quaternion* quaternion1, const BGC_FP32_Quaternion* quaternion2)
{
    const float ds0 = quaternion1->s0 - quaternion2->s0;
    const float dx1 = quaternion1->x1 - quaternion2->x1;
    const float dx2 = quaternion1->x2 - quaternion2->x2;
    const float dx3 = quaternion1->x3 - quaternion2->x3;

    const float square_modulus1 = bgc_fp32_quaternion_get_square_modulus(quaternion1);
    const float square_modulus2 = bgc_fp32_quaternion_get_square_modulus(quaternion2);
    const float square_distance = (ds0 * ds0 + dx1 * dx1) + (dx2 * dx2 + dx3 * dx3);

    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* quaternion1, const BGC_FP64_Quaternion* quaternion2)
{
    const double ds0 = quaternion1->s0 - quaternion2->s0;
    const double dx1 = quaternion1->x1 - quaternion2->x1;
    const double dx2 = quaternion1->x2 - quaternion2->x2;
    const double dx3 = quaternion1->x3 - quaternion2->x3;

    const double square_modulus1 = bgc_fp64_quaternion_get_square_modulus(quaternion1);
    const double square_modulus2 = bgc_fp64_quaternion_get_square_modulus(quaternion2);
    const double square_distance = (ds0 * ds0 + dx1 * dx1) + (dx2 * dx2 + dx3 * dx3);

    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