#ifndef _BGC_VERSOR_H_
#define _BGC_VERSOR_H_

#include <stdint.h>

#include "utilities.h"
#include "angle.h"
#include "vector3.h"
#include "rotation3.h"
#include "matrix3x3.h"
#include "quaternion.h"

#define BGC_SOME_TURN 1
#define BGC_ZERO_TURN 0
#define BGC_OPPOSITE -1

#define BGC_ERROR_PRIMARY_DIRECTION_UNKNOWN -3001
#define BGC_ERROR_PRIMARY_VECTOR_IS_ZERO -3002

#define BGC_ERROR_AUXILIARY_DIRECTION_UNKNOWN -3011
#define BGC_ERROR_AUXILIARY_VECTOR_IS_ZERO -3012

#define BGC_ERROR_DIRECTIONS_PARALLEL -3021
#define BGC_ERROR_VECTORS_PARALLEL -3022

// =================== Types ==================== //

typedef struct {
    float _s0, _x1, _x2, _x3;
} BgcVersorFP32;

typedef struct {
    double _s0, _x1, _x2, _x3;
} BgcVersorFP64;

// ================= Constants ================== //

extern const BgcVersorFP32 BGC_IDLE_VERSOR_FP32;
extern const BgcVersorFP64 BGC_IDLE_VERSOR_FP64;

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

inline void bgc_versor_reset_fp32(BgcVersorFP32* versor)
{
    versor->_s0 = 1.0f;
    versor->_x1 = 0.0f;
    versor->_x2 = 0.0f;
    versor->_x3 = 0.0f;
}

inline void bgc_versor_reset_fp64(BgcVersorFP64* versor)
{
    versor->_s0 = 1.0;
    versor->_x1 = 0.0;
    versor->_x2 = 0.0;
    versor->_x3 = 0.0;
}

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

void _bgc_versor_normalize_fp32(const float square_modulus, BgcVersorFP32* twin);

void _bgc_versor_normalize_fp64(const double square_modulus, BgcVersorFP64* twin);

inline void bgc_versor_set_values_fp32(const float s0, const float x1, const float x2, const float x3, BgcVersorFP32* versor)
{
    versor->_s0 = s0;
    versor->_x1 = x1;
    versor->_x2 = x2;
    versor->_x3 = x3;

    const float square_modulus = (s0 * s0 + x1 * x1) + (x2 * x2 + x3 * x3);

    if (!bgc_is_sqare_unit_fp32(square_modulus)) {
        _bgc_versor_normalize_fp32(square_modulus, versor);
    }
}

inline void bgc_versor_set_values_fp64(const double s0, const double x1, const double x2, const double x3, BgcVersorFP64* versor)
{
    versor->_s0 = s0;
    versor->_x1 = x1;
    versor->_x2 = x2;
    versor->_x3 = x3;

    const double square_modulus = (s0 * s0 + x1 * x1) + (x2 * x2 + x3 * x3);

    if (!bgc_is_sqare_unit_fp64(square_modulus)) {
        _bgc_versor_normalize_fp64(square_modulus, versor);
    }
}

// ================== Set Turn ================== //

void bgc_versor_set_turn_fp32(const float x1, const float x2, const float x3, const float angle, const BgcAngleUnitEnum unit, BgcVersorFP32* result);

void bgc_versor_set_turn_fp64(const double x1, const double x2, const double x3, const double angle, const BgcAngleUnitEnum unit, BgcVersorFP64* result);

// ================ Set Rotation ================ //

inline void bgc_versor_set_rotation_fp32(const BgcRotation3FP32* rotation, BgcVersorFP32* result)
{
    bgc_versor_set_turn_fp32(rotation->axis.x1, rotation->axis.x2, rotation->axis.x3, rotation->radians, BGC_ANGLE_UNIT_RADIANS, result);
}

inline void bgc_versor_set_rotation_fp64(const BgcRotation3FP64* rotation, BgcVersorFP64* result)
{
    bgc_versor_set_turn_fp64(rotation->axis.x1, rotation->axis.x2, rotation->axis.x3, rotation->radians, BGC_ANGLE_UNIT_RADIANS, result);
}

// ========= Make Direction Difference ========== //

int bgc_versor_make_direction_difference_fp32(const BgcVector3FP32* start, const BgcVector3FP32* end, BgcVersorFP32* result);

int bgc_versor_make_direction_difference_fp64(const BgcVector3FP64* start, const BgcVector3FP64* end, BgcVersorFP64* result);

// =============== Set Directions =============== //

int bgc_versor_make_basis_difference_fp32(
    const BgcVector3FP32* initial_primary_direction,
    const BgcVector3FP32* initial_auxiliary_direction,
    const BgcVector3FP32* final_primary_direction,
    const BgcVector3FP32* final_auxiliary_direction,
    BgcVersorFP32* result
);

int bgc_versor_make_basis_difference_fp64(
    const BgcVector3FP64* initial_primary_direction,
    const BgcVector3FP64* initial_auxiliary_direction,
    const BgcVector3FP64* final_primary_direction,
    const BgcVector3FP64* final_auxiliary_direction,
    BgcVersorFP64* result
);

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

inline void bgc_versor_copy_fp32(const BgcVersorFP32* source, BgcVersorFP32* destination)
{
    destination->_s0 = source->_s0;
    destination->_x1 = source->_x1;
    destination->_x2 = source->_x2;
    destination->_x3 = source->_x3;
}

inline void bgc_versor_copy_fp64(const BgcVersorFP64* source, BgcVersorFP64* destination)
{
    destination->_s0 = source->_s0;
    destination->_x1 = source->_x1;
    destination->_x2 = source->_x2;
    destination->_x3 = source->_x3;
}

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

inline void bgc_versor_swap_fp32(BgcVersorFP32* versor1, BgcVersorFP32* versor2)
{
    const float s0 = versor1->_s0;
    const float x1 = versor1->_x1;
    const float x2 = versor1->_x2;
    const float x3 = versor1->_x3;

    versor1->_s0 = versor2->_s0;
    versor1->_x1 = versor2->_x1;
    versor1->_x2 = versor2->_x2;
    versor1->_x3 = versor2->_x3;

    versor2->_s0 = s0;
    versor2->_x1 = x1;
    versor2->_x2 = x2;
    versor2->_x3 = x3;
}

inline void bgc_versor_swap_fp64(BgcVersorFP64* versor1, BgcVersorFP64* versor2)
{
    const double s0 = versor1->_s0;
    const double x1 = versor1->_x1;
    const double x2 = versor1->_x2;
    const double x3 = versor1->_x3;

    versor1->_s0 = versor2->_s0;
    versor1->_x1 = versor2->_x1;
    versor1->_x2 = versor2->_x2;
    versor1->_x3 = versor2->_x3;

    versor2->_s0 = s0;
    versor2->_x1 = x1;
    versor2->_x2 = x2;
    versor2->_x3 = x3;
}

// ================= Comparison ================= //

inline int bgc_versor_is_identity_fp32(const BgcVersorFP32* versor)
{
    return versor->_x1 * versor->_x1 + versor->_x2 * versor->_x2 + versor->_x3 * versor->_x3 <= BGC_SQUARE_EPSYLON_FP32;
}

inline int bgc_versor_is_identity_fp64(const BgcVersorFP64* versor)
{
    return versor->_x1 * versor->_x1 + versor->_x2 * versor->_x2 + versor->_x3 * versor->_x3 <= BGC_SQUARE_EPSYLON_FP64;
}

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

inline void bgc_versor_convert_fp64_to_fp32(const BgcVersorFP64* source, BgcVersorFP32* destination)
{
    bgc_versor_set_values_fp32(
        (float)source->_s0,
        (float)source->_x1,
        (float)source->_x2,
        (float)source->_x3,
        destination
    );
}

inline void bgc_versor_convert_fp32_to_fp64(const BgcVersorFP32* source, BgcVersorFP64* destination)
{
    bgc_versor_set_values_fp64(
        source->_s0,
        source->_x1,
        source->_x2,
        source->_x3,
        destination
    );
}

// ================== Shorten =================== //

inline void bgc_versor_shorten_fp32(BgcVersorFP32* versor)
{
    if (versor->_s0 < 0.0f) {
        versor->_s0 = -versor->_s0;
        versor->_x1 = -versor->_x1;
        versor->_x2 = -versor->_x2;
        versor->_x3 = -versor->_x3;
    }
}

inline void bgc_versor_shorten_fp64(BgcVersorFP64* versor)
{
    if (versor->_s0 < 0.0) {
        versor->_s0 = -versor->_s0;
        versor->_x1 = -versor->_x1;
        versor->_x2 = -versor->_x2;
        versor->_x3 = -versor->_x3;
    }
}

inline void bgc_versor_get_shortened_fp32(const BgcVersorFP32* versor, BgcVersorFP32* shortened)
{
    if (versor->_s0 >= 0.0f) {
        shortened->_s0 = versor->_s0;
        shortened->_x1 = versor->_x1;
        shortened->_x2 = versor->_x2;
        shortened->_x3 = versor->_x3;
        return;
    }

    shortened->_s0 = -versor->_s0;
    shortened->_x1 = -versor->_x1;
    shortened->_x2 = -versor->_x2;
    shortened->_x3 = -versor->_x3;
}

inline void bgc_versor_get_shortened_fp64(const BgcVersorFP64* versor, BgcVersorFP64* shortened)
{
    if (versor->_s0 >= 0.0) {
        shortened->_s0 = versor->_s0;
        shortened->_x1 = versor->_x1;
        shortened->_x2 = versor->_x2;
        shortened->_x3 = versor->_x3;
        return;
    }

    shortened->_s0 = -versor->_s0;
    shortened->_x1 = -versor->_x1;
    shortened->_x2 = -versor->_x2;
    shortened->_x3 = -versor->_x3;
}

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

inline void bgc_versor_make_opposite_fp32(BgcVersorFP32* versor)
{
    versor->_s0 = -versor->_s0;
    versor->_x1 = -versor->_x1;
    versor->_x2 = -versor->_x2;
    versor->_x3 = -versor->_x3;
}

inline void bgc_versor_make_opposite_fp64(BgcVersorFP64* versor)
{
    versor->_s0 = -versor->_s0;
    versor->_x1 = -versor->_x1;
    versor->_x2 = -versor->_x2;
    versor->_x3 = -versor->_x3;
}

inline void bgc_versor_get_opposite_fp32(const BgcVersorFP32* versor, BgcVersorFP32* opposite)
{
    opposite->_s0 = -versor->_s0;
    opposite->_x1 = -versor->_x1;
    opposite->_x2 = -versor->_x2;
    opposite->_x3 = -versor->_x3;
}

inline void bgc_versor_get_opposite_fp64(const BgcVersorFP64* versor, BgcVersorFP64* opposite)
{
    opposite->_s0 = -versor->_s0;
    opposite->_x1 = -versor->_x1;
    opposite->_x2 = -versor->_x2;
    opposite->_x3 = -versor->_x3;
}

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

inline void bgc_versor_invert_fp32(BgcVersorFP32* versor)
{
    versor->_x1 = -versor->_x1;
    versor->_x2 = -versor->_x2;
    versor->_x3 = -versor->_x3;
}

inline void bgc_versor_invert_fp64(BgcVersorFP64* versor)
{
    versor->_x1 = -versor->_x1;
    versor->_x2 = -versor->_x2;
    versor->_x3 = -versor->_x3;
}

inline void bgc_versor_get_inverse_fp32(const BgcVersorFP32* versor, BgcVersorFP32* inverse)
{
    inverse->_s0 = versor->_s0;
    inverse->_x1 = -versor->_x1;
    inverse->_x2 = -versor->_x2;
    inverse->_x3 = -versor->_x3;
}

inline void bgc_versor_get_inverse_fp64(const BgcVersorFP64* versor, BgcVersorFP64* inverse)
{
    inverse->_s0 = versor->_s0;
    inverse->_x1 = -versor->_x1;
    inverse->_x2 = -versor->_x2;
    inverse->_x3 = -versor->_x3;
}

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

void bgc_versor_get_exponation_fp32(const BgcVersorFP32* base, const float exponent, BgcVersorFP32* power);

void bgc_versor_get_exponation_fp64(const BgcVersorFP64* base, const double exponent, BgcVersorFP64* power);

// ================ Combination ================= //

inline void bgc_versor_combine_fp32(const BgcVersorFP32* second, const BgcVersorFP32* first, BgcVersorFP32* result)
{
    bgc_versor_set_values_fp32(
        (second->_s0 * first->_s0 - second->_x1 * first->_x1) - (second->_x2 * first->_x2 + second->_x3 * first->_x3),
        (second->_x1 * first->_s0 + second->_s0 * first->_x1) - (second->_x3 * first->_x2 - second->_x2 * first->_x3),
        (second->_x2 * first->_s0 + second->_s0 * first->_x2) - (second->_x1 * first->_x3 - second->_x3 * first->_x1),
        (second->_x3 * first->_s0 + second->_s0 * first->_x3) - (second->_x2 * first->_x1 - second->_x1 * first->_x2),
        result
    );
}

inline void bgc_versor_combine_fp64(const BgcVersorFP64* second, const BgcVersorFP64* first, BgcVersorFP64* result)
{
    bgc_versor_set_values_fp64(
        (second->_s0 * first->_s0 - second->_x1 * first->_x1) - (second->_x2 * first->_x2 + second->_x3 * first->_x3),
        (second->_x1 * first->_s0 + second->_s0 * first->_x1) - (second->_x3 * first->_x2 - second->_x2 * first->_x3),
        (second->_x2 * first->_s0 + second->_s0 * first->_x2) - (second->_x1 * first->_x3 - second->_x3 * first->_x1),
        (second->_x3 * first->_s0 + second->_s0 * first->_x3) - (second->_x2 * first->_x1 - second->_x1 * first->_x2),
        result
    );
}

// ============ Combination of three ============ //

inline void bgc_versor_combine3_fp32(const BgcVersorFP32* third, const BgcVersorFP32* second, const BgcVersorFP32* first, BgcVersorFP32* result)
{
    const float s0 = (second->_s0 * first->_s0 - second->_x1 * first->_x1) - (second->_x2 * first->_x2 + second->_x3 * first->_x3);
    const float x1 = (second->_x1 * first->_s0 + second->_s0 * first->_x1) - (second->_x3 * first->_x2 - second->_x2 * first->_x3);
    const float x2 = (second->_x2 * first->_s0 + second->_s0 * first->_x2) - (second->_x1 * first->_x3 - second->_x3 * first->_x1);
    const float x3 = (second->_x3 * first->_s0 + second->_s0 * first->_x3) - (second->_x2 * first->_x1 - second->_x1 * first->_x2);

    bgc_versor_set_values_fp32(
        (third->_s0 * s0 - third->_x1 * x1) - (third->_x2 * x2 + third->_x3 * x3),
        (third->_x1 * s0 + third->_s0 * x1) - (third->_x3 * x2 - third->_x2 * x3),
        (third->_x2 * s0 + third->_s0 * x2) - (third->_x1 * x3 - third->_x3 * x1),
        (third->_x3 * s0 + third->_s0 * x3) - (third->_x2 * x1 - third->_x1 * x2),
        result
    );
}

inline void bgc_versor_combine3_fp64(const BgcVersorFP64* third, const BgcVersorFP64* second, const BgcVersorFP64* first, BgcVersorFP64* result)
{
    const double s0 = (second->_s0 * first->_s0 - second->_x1 * first->_x1) - (second->_x2 * first->_x2 + second->_x3 * first->_x3);
    const double x1 = (second->_x1 * first->_s0 + second->_s0 * first->_x1) - (second->_x3 * first->_x2 - second->_x2 * first->_x3);
    const double x2 = (second->_x2 * first->_s0 + second->_s0 * first->_x2) - (second->_x1 * first->_x3 - second->_x3 * first->_x1);
    const double x3 = (second->_x3 * first->_s0 + second->_s0 * first->_x3) - (second->_x2 * first->_x1 - second->_x1 * first->_x2);

    bgc_versor_set_values_fp64(
        (third->_s0 * s0 - third->_x1 * x1) - (third->_x2 * x2 + third->_x3 * x3),
        (third->_x1 * s0 + third->_s0 * x1) - (third->_x3 * x2 - third->_x2 * x3),
        (third->_x2 * s0 + third->_s0 * x2) - (third->_x1 * x3 - third->_x3 * x1),
        (third->_x3 * s0 + third->_s0 * x3) - (third->_x2 * x1 - third->_x1 * x2),
        result
    );
}

// ================= Exclusion ================== //

inline void bgc_versor_exclude_fp32(const BgcVersorFP32* base, const BgcVersorFP32* excludant, BgcVersorFP32* difference)
{
    bgc_versor_set_values_fp32(
        (base->_s0 * excludant->_s0 + base->_x1 * excludant->_x1) + (base->_x2 * excludant->_x2 + base->_x3 * excludant->_x3),
        (base->_x1 * excludant->_s0 + base->_x3 * excludant->_x2) - (base->_s0 * excludant->_x1 + base->_x2 * excludant->_x3),
        (base->_x2 * excludant->_s0 + base->_x1 * excludant->_x3) - (base->_s0 * excludant->_x2 + base->_x3 * excludant->_x1),
        (base->_x3 * excludant->_s0 + base->_x2 * excludant->_x1) - (base->_s0 * excludant->_x3 + base->_x1 * excludant->_x2),
        difference
    );
}

inline void bgc_versor_exclude_fp64(const BgcVersorFP64* base, const BgcVersorFP64* excludant, BgcVersorFP64* difference)
{
    bgc_versor_set_values_fp64(
        (base->_s0 * excludant->_s0 + base->_x1 * excludant->_x1) + (base->_x2 * excludant->_x2 + base->_x3 * excludant->_x3),
        (base->_x1 * excludant->_s0 + base->_x3 * excludant->_x2) - (base->_s0 * excludant->_x1 + base->_x2 * excludant->_x3),
        (base->_x2 * excludant->_s0 + base->_x1 * excludant->_x3) - (base->_s0 * excludant->_x2 + base->_x3 * excludant->_x1),
        (base->_x3 * excludant->_s0 + base->_x2 * excludant->_x1) - (base->_s0 * excludant->_x3 + base->_x1 * excludant->_x2),
        difference
    );
}

// ============ Sphere Interpolation ============ //

void bgc_versor_spherically_interpolate_fp32(const BgcVersorFP32* start, const BgcVersorFP32* end, const float phase, BgcVersorFP32* result);

void bgc_versor_spherically_interpolate_fp64(const BgcVersorFP64* start, const BgcVersorFP64* end, const double phase, BgcVersorFP64* result);

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

void bgc_versor_get_rotation_fp32(const BgcVersorFP32* versor, BgcRotation3FP32* result);

void bgc_versor_get_rotation_fp64(const BgcVersorFP64* versor, BgcRotation3FP64* result);

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

inline void bgc_versor_get_rotation_matrix_fp32(const BgcVersorFP32* versor, BgcMatrix3x3FP32* matrix)
{
    const float s0s0 = versor->_s0 * versor->_s0;
    const float x1x1 = versor->_x1 * versor->_x1;
    const float x2x2 = versor->_x2 * versor->_x2;
    const float x3x3 = versor->_x3 * versor->_x3;

    const float s0x1 = versor->_s0 * versor->_x1;
    const float s0x2 = versor->_s0 * versor->_x2;
    const float s0x3 = versor->_s0 * versor->_x3;
    const float x1x2 = versor->_x1 * versor->_x2;
    const float x1x3 = versor->_x1 * versor->_x3;
    const float x2x3 = versor->_x2 * versor->_x3;

    matrix->r1c1 = (s0s0 + x1x1) - (x2x2 + x3x3);
    matrix->r2c2 = (s0s0 + x2x2) - (x1x1 + x3x3);
    matrix->r3c3 = (s0s0 + x3x3) - (x1x1 + x2x2);

    matrix->r1c2 = 2.0f * (x1x2 - s0x3);
    matrix->r2c3 = 2.0f * (x2x3 - s0x1);
    matrix->r3c1 = 2.0f * (x1x3 - s0x2);

    matrix->r2c1 = 2.0f * (x1x2 + s0x3);
    matrix->r3c2 = 2.0f * (x2x3 + s0x1);
    matrix->r1c3 = 2.0f * (x1x3 + s0x2);
}

inline void bgc_versor_get_rotation_matrix_fp64(const BgcVersorFP64* versor, BgcMatrix3x3FP64* matrix)
{
    const double s0s0 = versor->_s0 * versor->_s0;
    const double x1x1 = versor->_x1 * versor->_x1;
    const double x2x2 = versor->_x2 * versor->_x2;
    const double x3x3 = versor->_x3 * versor->_x3;

    const double s0x1 = versor->_s0 * versor->_x1;
    const double s0x2 = versor->_s0 * versor->_x2;
    const double s0x3 = versor->_s0 * versor->_x3;
    const double x1x2 = versor->_x1 * versor->_x2;
    const double x1x3 = versor->_x1 * versor->_x3;
    const double x2x3 = versor->_x2 * versor->_x3;

    matrix->r1c1 = (s0s0 + x1x1) - (x2x2 + x3x3);
    matrix->r2c2 = (s0s0 + x2x2) - (x1x1 + x3x3);
    matrix->r3c3 = (s0s0 + x3x3) - (x1x1 + x2x2);

    matrix->r1c2 = 2.0 * (x1x2 - s0x3);
    matrix->r2c3 = 2.0 * (x2x3 - s0x1);
    matrix->r3c1 = 2.0 * (x1x3 - s0x2);

    matrix->r2c1 = 2.0 * (x1x2 + s0x3);
    matrix->r3c2 = 2.0 * (x2x3 + s0x1);
    matrix->r1c3 = 2.0 * (x1x3 + s0x2);
}

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

inline void bgc_versor_get_reverse_matrix_fp32(const BgcVersorFP32* versor, BgcMatrix3x3FP32* matrix)
{
    const float s0s0 = versor->_s0 * versor->_s0;
    const float x1x1 = versor->_x1 * versor->_x1;
    const float x2x2 = versor->_x2 * versor->_x2;
    const float x3x3 = versor->_x3 * versor->_x3;

    const float s0x1 = versor->_s0 * versor->_x1;
    const float s0x2 = versor->_s0 * versor->_x2;
    const float s0x3 = versor->_s0 * versor->_x3;
    const float x1x2 = versor->_x1 * versor->_x2;
    const float x1x3 = versor->_x1 * versor->_x3;
    const float x2x3 = versor->_x2 * versor->_x3;

    matrix->r1c1 = (s0s0 + x1x1) - (x2x2 + x3x3);
    matrix->r2c2 = (s0s0 + x2x2) - (x1x1 + x3x3);
    matrix->r3c3 = (s0s0 + x3x3) - (x1x1 + x2x2);

    matrix->r1c2 = 2.0f * (x1x2 + s0x3);
    matrix->r2c3 = 2.0f * (x2x3 + s0x1);
    matrix->r3c1 = 2.0f * (x1x3 + s0x2);

    matrix->r2c1 = 2.0f * (x1x2 - s0x3);
    matrix->r3c2 = 2.0f * (x2x3 - s0x1);
    matrix->r1c3 = 2.0f * (x1x3 - s0x2);
}

inline void bgc_versor_get_reverse_matrix_fp64(const BgcVersorFP64* versor, BgcMatrix3x3FP64* matrix)
{
    const double s0s0 = versor->_s0 * versor->_s0;
    const double x1x1 = versor->_x1 * versor->_x1;
    const double x2x2 = versor->_x2 * versor->_x2;
    const double x3x3 = versor->_x3 * versor->_x3;

    const double s0x1 = versor->_s0 * versor->_x1;
    const double s0x2 = versor->_s0 * versor->_x2;
    const double s0x3 = versor->_s0 * versor->_x3;
    const double x1x2 = versor->_x1 * versor->_x2;
    const double x1x3 = versor->_x1 * versor->_x3;
    const double x2x3 = versor->_x2 * versor->_x3;

    matrix->r1c1 = (s0s0 + x1x1) - (x2x2 + x3x3);
    matrix->r2c2 = (s0s0 + x2x2) - (x1x1 + x3x3);
    matrix->r3c3 = (s0s0 + x3x3) - (x1x1 + x2x2);

    matrix->r1c2 = 2.0 * (x1x2 + s0x3);
    matrix->r2c3 = 2.0 * (x2x3 + s0x1);
    matrix->r3c1 = 2.0 * (x1x3 + s0x2);

    matrix->r2c1 = 2.0 * (x1x2 - s0x3);
    matrix->r3c2 = 2.0 * (x2x3 - s0x1);
    matrix->r1c3 = 2.0 * (x1x3 - s0x2);
}

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

inline void bgc_versor_get_both_matrices_fp32(const BgcVersorFP32* versor, BgcMatrix3x3FP32* rotation, BgcMatrix3x3FP32* reverse)
{
    bgc_versor_get_reverse_matrix_fp32(versor, reverse);
    bgc_matrix3x3_transpose_fp32(reverse, rotation);
}

inline void bgc_versor_get_both_matrices_fp64(const BgcVersorFP64* versor, BgcMatrix3x3FP64* rotation, BgcMatrix3x3FP64* reverse)
{
    bgc_versor_get_reverse_matrix_fp64(versor, reverse);
    bgc_matrix3x3_transpose_fp64(reverse, rotation);
}

// ================ Turn Vector ================= //

inline void bgc_versor_turn_vector_fp32(const BgcVersorFP32* versor, const BgcVector3FP32* vector, BgcVector3FP32* result)
{
    const float tx1 = 2.0f * (versor->_x2 * vector->x3 - versor->_x3 * vector->x2);
    const float tx2 = 2.0f * (versor->_x3 * vector->x1 - versor->_x1 * vector->x3);
    const float tx3 = 2.0f * (versor->_x1 * vector->x2 - versor->_x2 * vector->x1);

    const float x1 = (vector->x1 + tx1 * versor->_s0) + (versor->_x2 * tx3 - versor->_x3 * tx2);
    const float x2 = (vector->x2 + tx2 * versor->_s0) + (versor->_x3 * tx1 - versor->_x1 * tx3);
    const float x3 = (vector->x3 + tx3 * versor->_s0) + (versor->_x1 * tx2 - versor->_x2 * tx1);

    result->x1 = x1;
    result->x2 = x2;
    result->x3 = x3;
}

inline void bgc_versor_turn_vector_fp64(const BgcVersorFP64* versor, const BgcVector3FP64* vector, BgcVector3FP64* result)
{
    const double tx1 = 2.0 * (versor->_x2 * vector->x3 - versor->_x3 * vector->x2);
    const double tx2 = 2.0 * (versor->_x3 * vector->x1 - versor->_x1 * vector->x3);
    const double tx3 = 2.0 * (versor->_x1 * vector->x2 - versor->_x2 * vector->x1);

    const double x1 = (vector->x1 + tx1 * versor->_s0) + (versor->_x2 * tx3 - versor->_x3 * tx2);
    const double x2 = (vector->x2 + tx2 * versor->_s0) + (versor->_x3 * tx1 - versor->_x1 * tx3);
    const double x3 = (vector->x3 + tx3 * versor->_s0) + (versor->_x1 * tx2 - versor->_x2 * tx1);

    result->x1 = x1;
    result->x2 = x2;
    result->x3 = x3;
}

// ============== Turn Vector Back ============== //

inline void bgc_versor_turn_vector_back_fp32(const BgcVersorFP32* versor, const BgcVector3FP32* vector, BgcVector3FP32* result)
{
    const float tx1 = 2.0f * (versor->_x2 * vector->x3 - versor->_x3 * vector->x2);
    const float tx2 = 2.0f * (versor->_x3 * vector->x1 - versor->_x1 * vector->x3);
    const float tx3 = 2.0f * (versor->_x1 * vector->x2 - versor->_x2 * vector->x1);

    const float x1 = (vector->x1 - tx1 * versor->_s0) + (versor->_x2 * tx3 - versor->_x3 * tx2);
    const float x2 = (vector->x2 - tx2 * versor->_s0) + (versor->_x3 * tx1 - versor->_x1 * tx3);
    const float x3 = (vector->x3 - tx3 * versor->_s0) + (versor->_x1 * tx2 - versor->_x2 * tx1);

    result->x1 = x1;
    result->x2 = x2;
    result->x3 = x3;
}

inline void bgc_versor_turn_vector_back_fp64(const BgcVersorFP64* versor, const BgcVector3FP64* vector, BgcVector3FP64* result)
{
    const double tx1 = 2.0 * (versor->_x2 * vector->x3 - versor->_x3 * vector->x2);
    const double tx2 = 2.0 * (versor->_x3 * vector->x1 - versor->_x1 * vector->x3);
    const double tx3 = 2.0 * (versor->_x1 * vector->x2 - versor->_x2 * vector->x1);

    const double x1 = (vector->x1 - tx1 * versor->_s0) + (versor->_x2 * tx3 - versor->_x3 * tx2);
    const double x2 = (vector->x2 - tx2 * versor->_s0) + (versor->_x3 * tx1 - versor->_x1 * tx3);
    const double x3 = (vector->x3 - tx3 * versor->_s0) + (versor->_x1 * tx2 - versor->_x2 * tx1);

    result->x1 = x1;
    result->x2 = x2;
    result->x3 = x3;
}

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

inline int bgc_versor_are_close_fp32(const BgcVersorFP32* versor1, const BgcVersorFP32* versor2)
{
    const float ds0 = versor1->_s0 - versor2->_s0;
    const float dx1 = versor1->_x1 - versor2->_x1;
    const float dx2 = versor1->_x2 - versor2->_x2;
    const float dx3 = versor1->_x3 - versor2->_x3;

    return (ds0 * ds0 + dx1 * dx1) + (dx2 * dx2 + dx3 * dx3) <= BGC_SQUARE_EPSYLON_FP32;
}

inline int bgc_versor_are_close_fp64(const BgcVersorFP64* versor1, const BgcVersorFP64* versor2)
{
    const double ds0 = versor1->_s0 - versor2->_s0;
    const double dx1 = versor1->_x1 - versor2->_x1;
    const double dx2 = versor1->_x2 - versor2->_x2;
    const double dx3 = versor1->_x3 - versor2->_x3;

    return (ds0 * ds0 + dx1 * dx1) + (dx2 * dx2 + dx3 * dx3) <= BGC_SQUARE_EPSYLON_FP64;
}

#endif