#ifndef _GEOMETRY_VERSOR_H_
#define _GEOMETRY_VERSOR_H_

#include <stdint.h>

#include "basis.h"
#include "vector3.h"
#include "rotation3.h"
#include "matrix3x3.h"

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

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

extern const SPVersor SP_IDLE_VERSOR;
extern const DPVersor DP_IDLE_VERSOR;

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

static inline void sp_versor_reset(SPVersor* versor)
{
    versor->_s0 = 1.0f;
    versor->_x1 = 0.0f;
    versor->_x2 = 0.0f;
    versor->_x3 = 0.0f;
}

static inline void dp_versor_reset(DPVersor* versor)
{
    versor->_s0 = 1.0;
    versor->_x1 = 0.0;
    versor->_x2 = 0.0;
    versor->_x3 = 0.0;
}

// ============== Get Scalar Part =============== //

static inline float sp_get_scalar_part(const SPVersor* versor)
{
    return versor->_s0;
}

static inline double dp_get_scalar_part(const DPVersor* versor)
{
    return versor->_s0;
}

// ============== Get Vector Part =============== //

static inline void sp_get_vector_part(const SPVersor* versor, SPVector3 * result)
{
    result->x1 = versor->_x1;
    result->x2 = versor->_x2;
    result->x3 = versor->_x3;
}

static inline void dp_get_vector_part(const DPVersor* versor, DPVector3 * result)
{
    result->x1 = versor->_x1;
    result->x2 = versor->_x2;
    result->x3 = versor->_x3;
}

// =================== Get x1 =================== //

static inline float sp_get_x1(const SPVersor* versor)
{
    return versor->_x1;
}

static inline double dp_get_x1(const DPVersor* versor)
{
    return versor->_x1;
}

// =================== Get x2 =================== //

static inline float sp_get_x2(const SPVersor* versor)
{
    return versor->_x2;
}

static inline double dp_get_x2(const DPVersor* versor)
{
    return versor->_x2;
}

// =================== Get x3 =================== //


static inline float sp_get_x3(const SPVersor* versor)
{
    return versor->_x3;
}

static inline double dp_get_x3(const DPVersor* versor)
{
    return versor->_x3;
}

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

void __sp_versor_normalize(const float square_module, SPVersor* versor);

void __dp_versor_normalize(const double square_module, DPVersor* versor);

static inline void sp_versor_set(const float s0, const float x1, const float x2, const float x3, SPVersor* result)
{
    result->_s0 = s0;
    result->_x1 = x1;
    result->_x2 = x2;
    result->_x3 = x3;

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

    if (square_module < 1.0f - SP_TWO_EPSYLON || 1.0f + SP_TWO_EPSYLON < square_module) {
        __sp_versor_normalize(square_module, result);
    }
}

static inline void dp_versor_set(const double s0, const double x1, const double x2, const double x3, DPVersor* result)
{
    result->_s0 = s0;
    result->_x1 = x1;
    result->_x2 = x2;
    result->_x3 = x3;

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

    if (square_module < 1.0 - DP_TWO_EPSYLON || 1.0 + DP_TWO_EPSYLON < square_module) {
        __dp_versor_normalize(square_module, result);
    }
}

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

static inline void sp_versor_copy(const SPVersor* from, SPVersor* to)
{
    to->_s0 = from->_s0;
    to->_x1 = from->_x1;
    to->_x2 = from->_x2;
    to->_x3 = from->_x3;
}

static inline void dp_versor_copy(const DPVersor* from, DPVersor* to)
{
    to->_s0 = from->_s0;
    to->_x1 = from->_x1;
    to->_x2 = from->_x2;
    to->_x3 = from->_x3;
}

// ==================== Make ==================== //

void sp_versor_make_from_crude_turn(const float x1, const float x2, const float x3, const float angle, const angle_unit_t unit, SPVersor* result);

void dp_versor_make_from_crude_turn(const double x1, const double x2, const double x3, const double angle, const angle_unit_t unit, DPVersor* result);

static inline void sp_versor_make_from_turn(const SPVector3* axis, const float angle, const angle_unit_t unit, SPVersor* result)
{
    sp_versor_make_from_crude_turn(axis->x1, axis->x2, axis->x3, angle, unit, result);
}

static inline void dp_versor_make_from_turn(const DPVector3* axis, const double angle, const angle_unit_t unit, DPVersor* result)
{
    dp_versor_make_from_crude_turn(axis->x1, axis->x2, axis->x3, angle, unit, result);
}

static inline void sp_versor_make_from_rotation(const SPRotation3* rotation, SPVersor* result)
{
    sp_versor_make_from_crude_turn(rotation->axis.x1, rotation->axis.x2, rotation->axis.x3, rotation->radians, ANGLE_UNIT_RADIANS, result);
}

static inline void dp_versor_make_from_rotation(const DPRotation3* rotation, DPVersor* result)
{
    dp_versor_make_from_crude_turn(rotation->axis.x1, rotation->axis.x2, rotation->axis.x3, rotation->radians, ANGLE_UNIT_RADIANS, result);
}

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

static inline int sp_versor_is_idle(const SPVersor* versor)
{
    return 1.0f - SP_EPSYLON <= versor->_s0 || versor->_s0 <= -(1.0 - SP_EPSYLON);
}

static inline int dp_versor_is_idle(const DPVersor* versor)
{
    return 1.0 - DP_EPSYLON <= versor->_s0 || versor->_s0 <= -(1.0 - DP_EPSYLON);
}

// ============= Copy to twin type ============== //

static inline void sp_versor_from_double(const DPVersor* versor, SPVersor* result)
{
    sp_versor_set(
        (float)versor->_s0,
        (float)versor->_x1,
        (float)versor->_x2,
        (float)versor->_x3,
        result
    );
}

static inline void dp_versor_from_single(const SPVersor* versor, DPVersor* result)
{
    dp_versor_set(
        (double)versor->_s0,
        (double)versor->_x1,
        (double)versor->_x2,
        (double)versor->_x3,
        result
    );
}

// ================= Inversion ================== //

static inline void sp_versor_invert(SPVersor* versor)
{
    versor->_x1 = -versor->_x1;
    versor->_x2 = -versor->_x2;
    versor->_x3 = -versor->_x3;
}

static inline void dp_versor_invert(DPVersor* versor)
{
    versor->_x1 = -versor->_x1;
    versor->_x2 = -versor->_x2;
    versor->_x3 = -versor->_x3;
}

// ================ Make Inverted =============== //

static inline void sp_versor_make_inverted(const SPVersor* versor, SPVersor* result)
{
    result->_s0 = versor->_s0;
    result->_x1 = -versor->_x1;
    result->_x2 = -versor->_x2;
    result->_x3 = -versor->_x3;
}

static inline void dp_versor_make_inverted(const DPVersor* versor, DPVersor* result)
{
    result->_s0 = versor->_s0;
    result->_x1 = -versor->_x1;
    result->_x2 = -versor->_x2;
    result->_x3 = -versor->_x3;
}

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

static inline void sp_versor_combine(const SPVersor* second, const SPVersor* first, SPVersor* 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);

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

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

    if (square_module < 1.0f - SP_TWO_EPSYLON || 1.0f + SP_TWO_EPSYLON < square_module) {
        __sp_versor_normalize(square_module, result);
    }
}

static inline void dp_versor_combine(const DPVersor* second, const DPVersor* first, DPVersor* 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);

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

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

    if (square_module < 1.0 - DP_TWO_EPSYLON || 1.0 + DP_TWO_EPSYLON < square_module) {
        __dp_versor_normalize(square_module, result);
    }
}

// ================= Rotation3 ================== //

void sp_versor_get_rotation(const SPVersor* versor, SPRotation3* result);

void dp_versor_get_rotation(const DPVersor* versor, DPRotation3* result);

// =========== Make Rotation Matrix3x3 ========== //

static inline void sp_versor_make_matrix(const SPVersor* versor, SPMatrix3x3* 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 = 2.0f * versor->_s0 * versor->_x1;
    const float s0x2 = 2.0f * versor->_s0 * versor->_x2;
    const float s0x3 = 2.0f * versor->_s0 * versor->_x3;

    const float x1x2 = 2.0f * versor->_x1 * versor->_x2;
    const float x1x3 = 2.0f * versor->_x1 * versor->_x3;
    const float x2x3 = 2.0f * versor->_x2 * versor->_x3;

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

    matrix->r1c2 = x1x2 - s0x3;
    matrix->r2c3 = x2x3 - s0x1;
    matrix->r3c1 = x1x3 - s0x2;

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

static inline void dp_versor_make_matrix(const DPVersor* versor, DPMatrix3x3* 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 = 2.0 * versor->_s0 * versor->_x1;
    const double s0x2 = 2.0 * versor->_s0 * versor->_x2;
    const double s0x3 = 2.0 * versor->_s0 * versor->_x3;

    const double x1x2 = 2.0 * versor->_x1 * versor->_x2;
    const double x1x3 = 2.0 * versor->_x1 * versor->_x3;
    const double x2x3 = 2.0 * versor->_x2 * versor->_x3;

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

    matrix->r1c2 = x1x2 - s0x3;
    matrix->r2c3 = x2x3 - s0x1;
    matrix->r3c1 = x1x3 - s0x2;

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

// =========== Make Reverse Matrix3x3 =========== //

static inline void sp_versor_make_reverse_matrix(const SPVersor* versor, SPMatrix3x3* 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 = 2.0f * versor->_s0 * versor->_x1;
    const float s0x2 = 2.0f * versor->_s0 * versor->_x2;
    const float s0x3 = 2.0f * versor->_s0 * versor->_x3;

    const float x1x2 = 2.0f * versor->_x1 * versor->_x2;
    const float x1x3 = 2.0f * versor->_x1 * versor->_x3;
    const float x2x3 = 2.0f * versor->_x2 * versor->_x3;

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

    matrix->r1c2 = x1x2 + s0x3;
    matrix->r2c3 = x2x3 + s0x1;
    matrix->r3c1 = x1x3 + s0x2;

    matrix->r2c1 = x1x2 - s0x3;
    matrix->r3c2 = x2x3 - s0x1;
    matrix->r1c3 = x1x3 - s0x2;
}

static inline void dp_versor_make_reverse_matrix(const DPVersor* versor, DPMatrix3x3* 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 = 2.0 * versor->_s0 * versor->_x1;
    const double s0x2 = 2.0 * versor->_s0 * versor->_x2;
    const double s0x3 = 2.0 * versor->_s0 * versor->_x3;

    const double x1x2 = 2.0 * versor->_x1 * versor->_x2;
    const double x1x3 = 2.0 * versor->_x1 * versor->_x3;
    const double x2x3 = 2.0 * versor->_x2 * versor->_x3;

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

    matrix->r1c2 = x1x2 + s0x3;
    matrix->r2c3 = x2x3 + s0x1;
    matrix->r3c1 = x1x3 + s0x2;

    matrix->r2c1 = x1x2 - s0x3;
    matrix->r3c2 = x2x3 - s0x1;
    matrix->r1c3 = x1x3 - s0x2;
}

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

static inline void sp_versor_turn(const SPVersor* versor, const SPVector3* vector, SPVector3* 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;
}

static inline void dp_versor_turn(const DPVersor* versor, const DPVector3* vector, DPVector3* 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;
}

// ================ Turn2 Vector ================ //

static inline void sp_versor_turn2(const SPVersor* versor, const SPVector3* vector, SPVector3* result)
{
    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 = 2.0f * versor->_s0 * versor->_x1;
    const float s0x2 = 2.0f * versor->_s0 * versor->_x2;
    const float s0x3 = 2.0f * versor->_s0 * versor->_x3;

    const float x1x2 = 2.0f * versor->_x1 * versor->_x2;
    const float x1x3 = 2.0f * versor->_x1 * versor->_x3;
    const float x2x3 = 2.0f * versor->_x2 * versor->_x3;

    const float r2c1 = x1x2 + s0x3;
    const float r3c2 = x2x3 + s0x1;
    const float r1c3 = x1x3 + s0x2;

    const float r1c1 = (s0s0 + x1x1) - (x2x2 + x3x3);
    const float r2c2 = (s0s0 + x2x2) - (x1x1 + x3x3);
    const float r3c3 = (s0s0 + x3x3) - (x1x1 + x2x2);

    const float r1c2 = x1x2 - s0x3;
    const float r2c3 = x2x3 - s0x1;
    const float r3c1 = x1x3 - s0x2;

    const float x1 = r1c1 * vector->x1 + r1c2 * vector->x2 + r1c3 * vector->x3;
    const float x2 = r2c1 * vector->x1 + r2c2 * vector->x2 + r2c3 * vector->x3;
    const float x3 = r3c1 * vector->x1 + r3c2 * vector->x2 + r3c3 * vector->x3;

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

static inline void dp_versor_turn2(const DPVersor* versor, const DPVector3* vector, DPVector3* result)
{
    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 = 2.0f * versor->_s0 * versor->_x1;
    const double s0x2 = 2.0f * versor->_s0 * versor->_x2;
    const double s0x3 = 2.0f * versor->_s0 * versor->_x3;

    const double x1x2 = 2.0f * versor->_x1 * versor->_x2;
    const double x1x3 = 2.0f * versor->_x1 * versor->_x3;
    const double x2x3 = 2.0f * versor->_x2 * versor->_x3;

    const double r2c1 = x1x2 + s0x3;
    const double r3c2 = x2x3 + s0x1;
    const double r1c3 = x1x3 + s0x2;

    const double r1c1 = (s0s0 + x1x1) - (x2x2 + x3x3);
    const double r2c2 = (s0s0 + x2x2) - (x1x1 + x3x3);
    const double r3c3 = (s0s0 + x3x3) - (x1x1 + x2x2);

    const double r1c2 = x1x2 - s0x3;
    const double r2c3 = x2x3 - s0x1;
    const double r3c1 = x1x3 - s0x2;

    const double x1 = r1c1 * vector->x1 + r1c2 * vector->x2 + r1c3 * vector->x3;
    const double x2 = r2c1 * vector->x1 + r2c2 * vector->x2 + r2c3 * vector->x3;
    const double x3 = r3c1 * vector->x1 + r3c2 * vector->x2 + r3c3 * vector->x3;

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

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

static inline void sp_versor_turn_back(const SPVersor* versor, const SPVector3* vector, SPVector3* 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;
}

static inline void dp_versor_turn_back(const DPVersor* versor, const DPVector3* vector, DPVector3* 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 Back2 ============= //

static inline void sp_versor_turn_back2(const SPVersor* versor, const SPVector3* vector, SPVector3* result)
{
    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 = 2.0f * versor->_s0 * versor->_x1;
    const float s0x2 = 2.0f * versor->_s0 * versor->_x2;
    const float s0x3 = 2.0f * versor->_s0 * versor->_x3;

    const float x1x2 = 2.0f * versor->_x1 * versor->_x2;
    const float x1x3 = 2.0f * versor->_x1 * versor->_x3;
    const float x2x3 = 2.0f * versor->_x2 * versor->_x3;

    const float r1c2 = x1x2 + s0x3;
    const float r2c3 = x2x3 + s0x1;
    const float r3c1 = x1x3 + s0x2;

    const float r1c1 = (s0s0 + x1x1) - (x2x2 + x3x3);
    const float r2c2 = (s0s0 + x2x2) - (x1x1 + x3x3);
    const float r3c3 = (s0s0 + x3x3) - (x1x1 + x2x2);

    const float r2c1 = x1x2 - s0x3;
    const float r3c2 = x2x3 - s0x1;
    const float r1c3 = x1x3 - s0x2;

    const float x1 = r1c1 * vector->x1 + r1c2 * vector->x2 + r1c3 * vector->x3;
    const float x2 = r2c1 * vector->x1 + r2c2 * vector->x2 + r2c3 * vector->x3;
    const float x3 = r3c1 * vector->x1 + r3c2 * vector->x2 + r3c3 * vector->x3;

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

static inline void dp_versor_turn_back2(const DPVersor* versor, const DPVector3* vector, DPVector3* result)
{
    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 = 2.0f * versor->_s0 * versor->_x1;
    const double s0x2 = 2.0f * versor->_s0 * versor->_x2;
    const double s0x3 = 2.0f * versor->_s0 * versor->_x3;

    const double x1x2 = 2.0f * versor->_x1 * versor->_x2;
    const double x1x3 = 2.0f * versor->_x1 * versor->_x3;
    const double x2x3 = 2.0f * versor->_x2 * versor->_x3;

    const double r1c2 = x1x2 + s0x3;
    const double r2c3 = x2x3 + s0x1;
    const double r3c1 = x1x3 + s0x2;

    const double r1c1 = (s0s0 + x1x1) - (x2x2 + x3x3);
    const double r2c2 = (s0s0 + x2x2) - (x1x1 + x3x3);
    const double r3c3 = (s0s0 + x3x3) - (x1x1 + x2x2);

    const double r2c1 = x1x2 - s0x3;
    const double r3c2 = x2x3 - s0x1;
    const double r1c3 = x1x3 - s0x2;

    const double x1 = r1c1 * vector->x1 + r1c2 * vector->x2 + r1c3 * vector->x3;
    const double x2 = r2c1 * vector->x1 + r2c2 * vector->x2 + r2c3 * vector->x3;
    const double x3 = r3c1 * vector->x1 + r3c2 * vector->x2 + r3c3 * vector->x3;

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

#endif