#ifndef _BGC_TURN3_H_INCLUDED_
#define _BGC_TURN3_H_INCLUDED_

#include <stdint.h>
#include <math.h>

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

#define BGC_ERROR_TURN3_FIRST_VECTOR_ZERO -3010
#define BGC_ERROR_TURN3_SECOND_VECTOR_ZERO -3011
#define BGC_ERROR_TURN3_VECTORS_OPPOSITE -3012

#define _BGC_ERROR_TURN3_FIRST_PAIR -3020
#define _BGC_ERROR_TURN3_SECOND_PAIR -3030
#define _BGC_ERROR_TURN3_EMPTY_MAIN -1
#define _BGC_ERROR_TURN3_EMPTY_BRANCH -2
#define _BGC_ERROR_TURN3_PAIR_PARALLEL -3

#define BGC_ERROR_TURN3_FIRST_PAIR_ZERO_MAIN -3021
#define BGC_ERROR_TURN3_FIRST_PAIR_ZERO_BRANCH -3022
#define BGC_ERROR_TURN3_FIRST_PAIR_PARALLEL -3023

#define BGC_ERROR_TURN3_SECOND_PAIR_ZERO_MAIN -3031
#define BGC_ERROR_TURN3_SECOND_PAIR_ZERO_BRANCH -3032
#define BGC_ERROR_TURN3_SECOND_PAIR_PARALLEL -3033

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

extern const BGC_FP32_Turn3 BGC_FP32_IDLE_TURN3;
extern const BGC_FP64_Turn3 BGC_FP64_IDLE_TURN3;

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

inline void bgc_fp32_turn3_reset(BGC_FP32_Turn3* const turn)
{
    turn->_versor.s = 1.0f;
    turn->_versor.x = 0.0f;
    turn->_versor.y = 0.0f;
    turn->_versor.z = 0.0f;
}

inline void bgc_fp64_turn3_reset(BGC_FP64_Turn3* const turn)
{
    turn->_versor.s = 1.0;
    turn->_versor.x = 0.0;
    turn->_versor.y = 0.0;
    turn->_versor.z = 0.0;
}

// ============= Private: Normalize ============= //

inline void _bgc_fp32_turn3_normalize(BGC_FP32_Turn3* const turn)
{
    const float square_magnitude = bgc_fp32_quaternion_get_square_magnitude(&turn->_versor);

    if (bgc_fp32_is_square_unit(square_magnitude)) {
        return;
    }

    if (square_magnitude <= BGC_FP32_SQUARE_EPSILON || isnan(square_magnitude)) {
        turn->_versor.s = 1.0f;
        turn->_versor.x = 0.0f;
        turn->_versor.y = 0.0f;
        turn->_versor.z = 0.0f;
        return;
    }

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

    turn->_versor.s *= multiplier;
    turn->_versor.x *= multiplier;
    turn->_versor.y *= multiplier;
    turn->_versor.z *= multiplier;
}

inline void _bgc_fp64_turn3_normalize(BGC_FP64_Turn3* const turn)
{
    const double square_magnitude = bgc_fp64_quaternion_get_square_magnitude(&turn->_versor);

    if (bgc_fp64_is_square_unit(square_magnitude)) {
        return;
    }

    if (square_magnitude <= BGC_FP64_SQUARE_EPSILON || isnan(square_magnitude)) {
        turn->_versor.s = 1.0;
        turn->_versor.x = 0.0;
        turn->_versor.y = 0.0;
        turn->_versor.z = 0.0;
        return;
    }

    const double multiplier = sqrt(1.0 / square_magnitude);

    turn->_versor.s *= multiplier;
    turn->_versor.x *= multiplier;
    turn->_versor.y *= multiplier;
    turn->_versor.z *= multiplier;
}

// ================= Set Values ================= //

inline void bgc_fp32_turn3_set_values(BGC_FP32_Turn3* const turn, const float s, const float x, const float y, const float z)
{
    bgc_fp32_quaternion_set_values(&turn->_versor, s, x, y, z);
    _bgc_fp32_turn3_normalize(turn);
}

inline void bgc_fp64_turn3_set_values(BGC_FP64_Turn3* const turn, const double s, const double x, const double y, const double z)
{
    bgc_fp64_quaternion_set_values(&turn->_versor, s, x, y, z);
    _bgc_fp64_turn3_normalize(turn);
}

// =============== Get Quaternion =============== //

inline void bgc_fp32_turn3_get_quaternion(BGC_FP32_Quaternion* const quaternion, const BGC_FP32_Turn3* const turn)
{
    bgc_fp32_quaternion_copy(quaternion, &turn->_versor);
}

inline void bgc_fp64_turn3_get_quaternion(BGC_FP64_Quaternion* const quaternion, const BGC_FP64_Turn3* const turn)
{
    bgc_fp64_quaternion_copy(quaternion, &turn->_versor);
}

// =============== Set Quaternion =============== //

inline void bgc_fp32_turn3_set_quaternion(BGC_FP32_Turn3* const turn, const BGC_FP32_Quaternion* const quaternion)
{
    bgc_fp32_quaternion_copy(&turn->_versor, quaternion);
    _bgc_fp32_turn3_normalize(turn);
}

inline void bgc_fp64_turn3_set_quaternion(BGC_FP64_Turn3* const turn, const BGC_FP64_Quaternion* const quaternion)
{
    bgc_fp64_quaternion_copy(&turn->_versor, quaternion);
    _bgc_fp64_turn3_normalize(turn);
}

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

float bgc_fp32_turn3_get_rotation(BGC_FP32_Vector3* const axis, const BGC_FP32_Turn3* const turn, const int angle_unit);

double bgc_fp64_turn3_get_rotation(BGC_FP64_Vector3* const axis, const BGC_FP64_Turn3* const turn, const int angle_unit);

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

void bgc_fp32_turn3_set_rotation(BGC_FP32_Turn3* const turn, const float x, const float y, const float z, const float angle, const int angle_unit);

void bgc_fp64_turn3_set_rotation(BGC_FP64_Turn3* const turn, const double x, const double y, const double z, const double angle, const int angle_unit);

// ========= Find Direction Difference ========== //

int bgc_fp32_turn3_find_direction_difference(BGC_FP32_Turn3* const turn, const BGC_FP32_Vector3* const start, const BGC_FP32_Vector3* const end);

int bgc_fp64_turn3_find_direction_difference(BGC_FP64_Turn3* const turn, const BGC_FP64_Vector3* const start, const BGC_FP64_Vector3* const end);

// ======= Find Direction Pair Difference ======= //

int bgc_fp32_turn3_find_pair_difference(
    BGC_FP32_Turn3* const turn,
    const BGC_FP32_Vector3* const first_pair_main,
    const BGC_FP32_Vector3* const first_pair_branch,
    const BGC_FP32_Vector3* const second_pair_main,
    const BGC_FP32_Vector3* const second_pair_branch
);

int bgc_fp64_turn3_find_pair_difference(
    BGC_FP64_Turn3* const turn,
    const BGC_FP64_Vector3* const first_pair_main,
    const BGC_FP64_Vector3* const first_pair_branch,
    const BGC_FP64_Vector3* const second_pair_main,
    const BGC_FP64_Vector3* const second_pair_branch
);

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

inline void bgc_fp32_turn3_copy(BGC_FP32_Turn3* const destination, const BGC_FP32_Turn3* const source)
{
    bgc_fp32_quaternion_copy(&destination->_versor, &source->_versor);
}

inline void bgc_fp64_turn3_copy(BGC_FP64_Turn3* const destination, const BGC_FP64_Turn3* const source)
{
    bgc_fp64_quaternion_copy(&destination->_versor, &source->_versor);
}

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

inline void bgc_fp32_turn3_swap(BGC_FP32_Turn3* const turn1, BGC_FP32_Turn3* const turn2)
{
    bgc_fp32_quaternion_swap(&turn1->_versor, &turn2->_versor);
}

inline void bgc_fp64_turn3_swap(BGC_FP64_Turn3* const turn1, BGC_FP64_Turn3* const turn2)
{
    bgc_fp64_quaternion_swap(&turn1->_versor, &turn2->_versor);
}

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

inline int bgc_fp32_turn3_is_idle(const BGC_FP32_Turn3* const turn)
{
    return bgc_fp32_quaternion_is_real(&turn->_versor);
}

inline int bgc_fp64_turn3_is_idle(const BGC_FP64_Turn3* const turn)
{
    return bgc_fp64_quaternion_is_real(&turn->_versor);
}

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

inline void bgc_fp32_turn3_convert_to_fp64(BGC_FP64_Turn3* const destination, const BGC_FP32_Turn3* const source)
{
    bgc_fp32_quaternion_convert_to_fp64(&destination->_versor, &source->_versor);
    _bgc_fp64_turn3_normalize(destination);

}

inline void bgc_fp64_turn3_convert_to_fp32(BGC_FP32_Turn3* const destination, const BGC_FP64_Turn3* const source)
{
    bgc_fp64_quaternion_convert_to_fp32(&destination->_versor, &source->_versor);
    _bgc_fp32_turn3_normalize(destination);
}

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

inline void bgc_fp32_turn3_shorten(BGC_FP32_Turn3* const turn)
{
    if (turn->_versor.s < 0.0f) {
        bgc_fp32_quaternion_revert(&turn->_versor);
    }
}

inline void bgc_fp64_turn3_shorten(BGC_FP64_Turn3* const turn)
{
    if (turn->_versor.s < 0.0) {
        bgc_fp64_quaternion_revert(&turn->_versor);
    }
}

inline void bgc_fp32_turn3_get_shortened(BGC_FP32_Turn3* const shortened, const BGC_FP32_Turn3* const turn)
{
    if (turn->_versor.s >= 0.0f) {
        bgc_fp32_quaternion_copy(&shortened->_versor, &turn->_versor);
    }
    else {
        bgc_fp32_quaternion_get_reverse(&shortened->_versor, &turn->_versor);
    }
}

inline void bgc_fp64_turn3_get_shortened(BGC_FP64_Turn3* const shortened, const BGC_FP64_Turn3* const turn)
{
    if (turn->_versor.s >= 0.0) {
        bgc_fp64_quaternion_copy(&shortened->_versor, &turn->_versor);
    }
    else {
        bgc_fp64_quaternion_get_reverse(&shortened->_versor, &turn->_versor);
    }
}

// ================= Alternate ================== //

inline void bgc_fp32_turn3_alternate(BGC_FP32_Turn3* const turn)
{
    bgc_fp32_quaternion_revert(&turn->_versor);
}

inline void bgc_fp64_turn3_alternate(BGC_FP64_Turn3* const turn)
{
    bgc_fp64_quaternion_revert(&turn->_versor);
}

inline void bgc_fp32_turn3_get_alternative(BGC_FP32_Turn3* const alternative, const BGC_FP32_Turn3* const turn)
{
    bgc_fp32_quaternion_get_reverse(&alternative->_versor, &turn->_versor);
}

inline void bgc_fp64_turn3_get_alternative(BGC_FP64_Turn3* const alternative, const BGC_FP64_Turn3* const turn)
{
    bgc_fp64_quaternion_get_reverse(&alternative->_versor, &turn->_versor);
}

// =================== Revert =================== //

inline void bgc_fp32_turn3_revert(BGC_FP32_Turn3* const turn)
{
    bgc_fp32_quaternion_conjugate(&turn->_versor);
}

inline void bgc_fp64_turn3_revert(BGC_FP64_Turn3* const turn)
{
    bgc_fp64_quaternion_conjugate(&turn->_versor);
}

inline void bgc_fp32_turn3_get_reverse(BGC_FP32_Turn3* const inverse, const BGC_FP32_Turn3* const turn)
{
    bgc_fp32_quaternion_get_conjugate(&inverse->_versor, &turn->_versor);
}

inline void bgc_fp64_turn3_get_reverse(BGC_FP64_Turn3* const inverse, const BGC_FP64_Turn3* const turn)
{
    bgc_fp64_quaternion_get_conjugate(&inverse->_versor, &turn->_versor);
}

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

void bgc_fp32_turn3_get_power(BGC_FP32_Turn3* const power, const BGC_FP32_Turn3* const base, const float exponent);

void bgc_fp64_turn3_get_power(BGC_FP64_Turn3* const power, const BGC_FP64_Turn3* const base, const double exponent);

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

inline void bgc_fp32_turn3_combine(BGC_FP32_Turn3* const combination, const BGC_FP32_Turn3* const first, const BGC_FP32_Turn3* const second)
{
    bgc_fp32_quaternion_multiply_by_quaternion(&combination->_versor, &second->_versor, &first->_versor);
    _bgc_fp32_turn3_normalize(combination);
}

inline void bgc_fp64_turn3_combine(BGC_FP64_Turn3* const combination, const BGC_FP64_Turn3* const first, const BGC_FP64_Turn3* const second)
{
    bgc_fp64_quaternion_multiply_by_quaternion(&combination->_versor, &second->_versor, &first->_versor);
    _bgc_fp64_turn3_normalize(combination);
}

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

inline void bgc_fp32_turn3_combine3(BGC_FP32_Turn3* const combination, const BGC_FP32_Turn3* const first, const BGC_FP32_Turn3* const second, const BGC_FP32_Turn3* const third)
{
    BGC_FP32_Quaternion product;

    _bgc_fp32_restrict_quaternion_multiply_by_quaternion(&product, &second->_versor, &first->_versor);

    bgc_fp32_quaternion_multiply_by_quaternion(&combination->_versor, &third->_versor, &product);

    _bgc_fp32_turn3_normalize(combination);
}

inline void bgc_fp64_turn3_combine3(BGC_FP64_Turn3* const combination, const BGC_FP64_Turn3* const first, const BGC_FP64_Turn3* const second, const BGC_FP64_Turn3* const third)
{
    BGC_FP64_Quaternion product;

    _bgc_fp64_restrict_quaternion_multiply_by_quaternion(&product, &second->_versor, &first->_versor);

    bgc_fp64_quaternion_multiply_by_quaternion(&combination->_versor, &third->_versor, &product);

    _bgc_fp64_turn3_normalize(combination);
}

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

inline void bgc_fp32_turn3_exclude(BGC_FP32_Turn3* const difference, const BGC_FP32_Turn3* const base, const BGC_FP32_Turn3* const excludant)
{
    bgc_fp32_quaternion_multiply_by_conjugate(&difference->_versor, &base->_versor, &excludant->_versor);

    _bgc_fp32_turn3_normalize(difference);
}

inline void bgc_fp64_turn3_exclude(BGC_FP64_Turn3* const difference, const BGC_FP64_Turn3* const base, const BGC_FP64_Turn3* const excludant)
{
    bgc_fp64_quaternion_multiply_by_conjugate(&difference->_versor, &base->_versor, &excludant->_versor);

    _bgc_fp64_turn3_normalize(difference);
}

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

void bgc_fp32_turn3_spherically_interpolate(BGC_FP32_Turn3* const interpolation, const BGC_FP32_Turn3* const start, const BGC_FP32_Turn3* const end, const float phase);

void bgc_fp64_turn3_spherically_interpolate(BGC_FP64_Turn3* const interpolation, const BGC_FP64_Turn3* const start, const BGC_FP64_Turn3* const end, const double phase);

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

inline void bgc_fp32_turn3_get_rotation_matrix(BGC_FP32_Matrix3x3* const matrix, const BGC_FP32_Turn3* const turn)
{
    _bgc_fp32_versor_get_rotation_matrix(matrix, &turn->_versor);
}

inline void bgc_fp64_turn3_get_rotation_matrix(BGC_FP64_Matrix3x3* const matrix, const BGC_FP64_Turn3* const turn)
{
    _bgc_fp64_versor_get_rotation_matrix(matrix, &turn->_versor);
}

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

inline void bgc_fp32_turn3_get_reverse_matrix(BGC_FP32_Matrix3x3* const matrix, const BGC_FP32_Turn3* const turn)
{
    _bgc_fp32_versor_get_reverse_matrix(matrix, &turn->_versor);
}

inline void bgc_fp64_turn3_get_reverse_matrix(BGC_FP64_Matrix3x3* const matrix, const BGC_FP64_Turn3* const turn)
{
    _bgc_fp64_versor_get_reverse_matrix(matrix, &turn->_versor);
}

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

inline void bgc_fp32_turn3_get_both_matrices(BGC_FP32_Matrix3x3* const rotation, BGC_FP32_Matrix3x3* const reverse, const BGC_FP32_Turn3* const turn)
{
    _bgc_fp32_versor_get_reverse_matrix(reverse, &turn->_versor);
    bgc_fp32_matrix3x3_get_transposed(rotation, reverse);
}

inline void bgc_fp64_turn3_get_both_matrices(BGC_FP64_Matrix3x3* const rotation, BGC_FP64_Matrix3x3* const reverse, const BGC_FP64_Turn3* const turn)
{
    _bgc_fp64_versor_get_reverse_matrix(reverse, &turn->_versor);
    bgc_fp64_matrix3x3_get_transposed(rotation, reverse);
}

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

inline void bgc_fp32_turn3_vector(BGC_FP32_Vector3* const turned_vector, const BGC_FP32_Turn3* const turn, const BGC_FP32_Vector3* const original_vector)
{
    _bgc_fp32_versor_turn_vector(turned_vector, &turn->_versor, original_vector);
}

inline void bgc_fp64_turn3_vector(BGC_FP64_Vector3* const turned_vector, const BGC_FP64_Turn3* const turn, const BGC_FP64_Vector3* const original_vector)
{
    _bgc_fp64_versor_turn_vector(turned_vector, &turn->_versor, original_vector);
}

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

inline void bgc_fp32_turn3_vector_back(BGC_FP32_Vector3* const turned_vector, const BGC_FP32_Turn3* const turn, const BGC_FP32_Vector3* const original_vector)
{
    _bgc_fp32_versor_turn_vector_back(turned_vector, &turn->_versor, original_vector);
}

inline void bgc_fp64_turn3_vector_back(BGC_FP64_Vector3* const turned_vector, const BGC_FP64_Turn3* const turn, const BGC_FP64_Vector3* const original_vector)
{
    _bgc_fp64_versor_turn_vector_back(turned_vector, &turn->_versor, original_vector);
}

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

inline int bgc_fp32_turn3_are_close(const BGC_FP32_Turn3* const turn1, const BGC_FP32_Turn3* const turn2)
{
    BGC_FP32_Quaternion difference;
    bgc_fp32_quaternion_subtract(&difference, &turn1->_versor, &turn2->_versor);
    return bgc_fp32_quaternion_get_square_magnitude(&difference) <= BGC_FP32_SQUARE_EPSILON;
}

inline int bgc_fp64_turn3_are_close(const BGC_FP64_Turn3* const turn1, const BGC_FP64_Turn3* const turn2)
{
    BGC_FP64_Quaternion difference;
    bgc_fp64_quaternion_subtract(&difference, &turn1->_versor, &turn2->_versor);
    return bgc_fp64_quaternion_get_square_magnitude(&difference) <= BGC_FP64_SQUARE_EPSILON;
}

#endif