#include <math.h>
#include "./quaternion.h"

extern inline void bgc_fp32_quaternion_reset(BGC_FP32_Quaternion* const quaternion);
extern inline void bgc_fp64_quaternion_reset(BGC_FP64_Quaternion* const quaternion);

extern inline float bgc_fp32_quaternion_get_square_magnitude(const BGC_FP32_Quaternion* const quaternion);
extern inline double bgc_fp64_quaternion_get_square_magnitude(const BGC_FP64_Quaternion* const quaternion);

extern inline float bgc_fp32_quaternion_get_magnitude(const BGC_FP32_Quaternion* const quaternion);
extern inline double bgc_fp64_quaternion_get_magnitude(const BGC_FP64_Quaternion* const quaternion);

extern inline int bgc_fp32_quaternion_is_zero(const BGC_FP32_Quaternion* const quaternion);
extern inline int bgc_fp64_quaternion_is_zero(const BGC_FP64_Quaternion* const quaternion);

extern inline int bgc_fp32_quaternion_is_unit(const BGC_FP32_Quaternion* const quaternion);
extern inline int bgc_fp64_quaternion_is_unit(const BGC_FP64_Quaternion* const quaternion);

extern inline int bgc_fp32_quaternion_is_pure(const BGC_FP32_Quaternion* const quaternion);
extern inline int bgc_fp64_quaternion_is_pure(const BGC_FP64_Quaternion* const quaternion);

extern inline int bgc_fp32_quaternion_is_real(const BGC_FP32_Quaternion* const quaternion);
extern inline int bgc_fp64_quaternion_is_real(const BGC_FP64_Quaternion* const quaternion);

extern inline void bgc_fp32_quaternion_copy(BGC_FP32_Quaternion* const destination, const BGC_FP32_Quaternion* const source);
extern inline void bgc_fp64_quaternion_copy(BGC_FP64_Quaternion* const destination, const BGC_FP64_Quaternion* const source);

extern inline void bgc_fp32_quaternion_swap(BGC_FP32_Quaternion* const quarternion1, BGC_FP32_Quaternion* const quarternion2);
extern inline void bgc_fp64_quaternion_swap(BGC_FP64_Quaternion* const quarternion1, BGC_FP64_Quaternion* const quarternion2);

extern inline void bgc_fp32_quaternion_convert_to_fp64(BGC_FP64_Quaternion* const destination, const BGC_FP32_Quaternion* const source);
extern inline void bgc_fp64_quaternion_convert_to_fp32(BGC_FP32_Quaternion* const destination, const BGC_FP64_Quaternion* const source);

extern inline void bgc_fp32_quaternion_add(BGC_FP32_Quaternion* const sum, const BGC_FP32_Quaternion* const quaternion1, const BGC_FP32_Quaternion* const quaternion2);
extern inline void bgc_fp64_quaternion_add(BGC_FP64_Quaternion* const sum, const BGC_FP64_Quaternion* const quaternion1, const BGC_FP64_Quaternion* const quaternion2);

extern inline void bgc_fp32_quaternion_add_scaled(BGC_FP32_Quaternion* const sum, const BGC_FP32_Quaternion* const basic_quaternion, const BGC_FP32_Quaternion* const scalable_quaternion, const float scale);
extern inline void bgc_fp64_quaternion_add_scaled(BGC_FP64_Quaternion* const sum, const BGC_FP64_Quaternion* const basic_quaternion, const BGC_FP64_Quaternion* const scalable_quaternion, const double scale);

extern inline void bgc_fp32_quaternion_subtract(BGC_FP32_Quaternion* const difference, const BGC_FP32_Quaternion* const minuend, const BGC_FP32_Quaternion* const subtrahend);
extern inline void bgc_fp64_quaternion_subtract(BGC_FP64_Quaternion* const difference, const BGC_FP64_Quaternion* const minuend, const BGC_FP64_Quaternion* const subtrahend);

extern inline void bgc_fp32_quaternion_subtract_scaled(BGC_FP32_Quaternion* const difference, const BGC_FP32_Quaternion* const basic_quaternion, const BGC_FP32_Quaternion* const scalable_quaternion, const float scale);
extern inline void bgc_fp64_quaternion_subtract_scaled(BGC_FP64_Quaternion* const difference, const BGC_FP64_Quaternion* const basic_quaternion, const BGC_FP64_Quaternion* const scalable_quaternion, const double scale);

extern inline void bgc_fp32_quaternion_multiply_by_real_number(BGC_FP32_Quaternion* const product, const BGC_FP32_Quaternion* const multiplicand, const float multiplier);
extern inline void bgc_fp64_quaternion_multiply_by_real_number(BGC_FP64_Quaternion* const product, const BGC_FP64_Quaternion* const multiplicand, const double multiplier);

extern inline void bgc_fp32_quaternion_multiply_by_dual_number(BGC_FP32_DualQuaternion* const product, const BGC_FP32_Quaternion* const multiplicand, const BGC_FP32_DualNumber* const multiplier);
extern inline void bgc_fp64_quaternion_multiply_by_dual_number(BGC_FP64_DualQuaternion* const product, const BGC_FP64_Quaternion* const multiplicand, const BGC_FP64_DualNumber* const multiplier);

extern inline void bgc_fp32_quaternion_multiply_by_quaternion(BGC_FP32_Quaternion* const product, const BGC_FP32_Quaternion* const left, const BGC_FP32_Quaternion* const right);
extern inline void bgc_fp64_quaternion_multiply_by_quaternion(BGC_FP64_Quaternion* const product, const BGC_FP64_Quaternion* const left, const BGC_FP64_Quaternion* const right);

extern inline void bgc_fp32_quaternion_multiply_by_dual_quaternion(BGC_FP32_DualQuaternion* const product, const BGC_FP32_Quaternion* const left, const BGC_FP32_DualQuaternion* const right);
extern inline void bgc_fp64_quaternion_multiply_by_dual_quaternion(BGC_FP64_DualQuaternion* const product, const BGC_FP64_Quaternion* const left, const BGC_FP64_DualQuaternion* const right);

extern inline void bgc_fp32_quaternion_multiply_by_conjugate(BGC_FP32_Quaternion* const product, const BGC_FP32_Quaternion* const left, const BGC_FP32_Quaternion* const right);
extern inline void bgc_fp64_quaternion_multiply_by_conjugate(BGC_FP64_Quaternion* const product, const BGC_FP64_Quaternion* const left, const BGC_FP64_Quaternion* const right);

extern inline void bgc_fp32_conjugate_quaternion_multiply_by_quaternion(BGC_FP32_Quaternion* const product, const BGC_FP32_Quaternion* const left, const BGC_FP32_Quaternion* const right);
extern inline void bgc_fp64_conjugate_quaternion_multiply_by_quaternion(BGC_FP64_Quaternion* const product, const BGC_FP64_Quaternion* const left, const BGC_FP64_Quaternion* const right);

extern inline void bgc_fp32_conjugate_quaternion_multiply_by_conjugate(BGC_FP32_Quaternion* const product, const BGC_FP32_Quaternion* const left, const BGC_FP32_Quaternion* const right);
extern inline void bgc_fp64_conjugate_quaternion_multiply_by_conjugate(BGC_FP64_Quaternion* const product, const BGC_FP64_Quaternion* const left, const BGC_FP64_Quaternion* const right);

extern inline int bgc_fp32_quaternion_divide_by_real_number(BGC_FP32_Quaternion* const quotient, const BGC_FP32_Quaternion* const dividend, const float divisor);
extern inline int bgc_fp64_quaternion_divide_by_real_number(BGC_FP64_Quaternion* const quotient, const BGC_FP64_Quaternion* const dividend, const double divisor);

extern inline int bgc_fp32_quaternion_divide_by_quaternion(BGC_FP32_Quaternion* const quotient, const BGC_FP32_Quaternion* const divident, const BGC_FP32_Quaternion* const divisor);
extern inline int bgc_fp64_quaternion_divide_by_quaternion(BGC_FP64_Quaternion* const quotient, const BGC_FP64_Quaternion* const divident, const BGC_FP64_Quaternion* const divisor);

extern inline int bgc_fp32_quaternion_divide_by_conjugate(BGC_FP32_Quaternion* const quotient, const BGC_FP32_Quaternion* const divident, const BGC_FP32_Quaternion* const divisor_to_conjugate);
extern inline int bgc_fp64_quaternion_divide_by_conjugate(BGC_FP64_Quaternion* const quotient, const BGC_FP64_Quaternion* const divident, const BGC_FP64_Quaternion* const divisor_to_conjugate);

extern inline void bgc_fp32_quaternion_get_mean2(BGC_FP32_Quaternion* const mean, const BGC_FP32_Quaternion* const quaternion1, const BGC_FP32_Quaternion* const quaternion2);
extern inline void bgc_fp64_quaternion_get_mean2(BGC_FP64_Quaternion* const mean, const BGC_FP64_Quaternion* const quaternion1, const BGC_FP64_Quaternion* const quaternion2);

extern inline void bgc_fp32_quaternion_get_mean3(BGC_FP32_Quaternion* const mean, const BGC_FP32_Quaternion* const quaternion1, const BGC_FP32_Quaternion* const quaternion2, const BGC_FP32_Quaternion* const quaternion3);
extern inline void bgc_fp64_quaternion_get_mean3(BGC_FP64_Quaternion* const mean, const BGC_FP64_Quaternion* const quaternion1, const BGC_FP64_Quaternion* const quaternion2, const BGC_FP64_Quaternion* const quaternion3);

extern inline void bgc_fp32_quaternion_interpolate(BGC_FP32_Quaternion* const interpolation, const BGC_FP32_Quaternion* const quaternion1, const BGC_FP32_Quaternion* const quaternion2, const float phase);
extern inline void bgc_fp64_quaternion_interpolate(BGC_FP64_Quaternion* const interpolation, const BGC_FP64_Quaternion* const quaternion1, const BGC_FP64_Quaternion* const quaternion2, const double phase);

extern inline float bgc_fp32_quaternion_get_dot_product(const BGC_FP32_Quaternion* const quaternion1, const BGC_FP32_Quaternion* const quaternion2);
extern inline double bgc_fp64_quaternion_get_dot_product(const BGC_FP64_Quaternion* const quaternion1, const BGC_FP64_Quaternion* const quaternion2);

extern inline void bgc_fp32_quaternion_conjugate(BGC_FP32_Quaternion* const quaternion);
extern inline void bgc_fp64_quaternion_conjugate(BGC_FP64_Quaternion* const quaternion);

extern inline void bgc_fp32_quaternion_get_conjugate(BGC_FP32_Quaternion* const conjugate, const BGC_FP32_Quaternion* const quaternion);
extern inline void bgc_fp64_quaternion_get_conjugate(BGC_FP64_Quaternion* const conjugate, const BGC_FP64_Quaternion* const quaternion);

extern inline void bgc_fp32_quaternion_revert(BGC_FP32_Quaternion* const quaternion);
extern inline void bgc_fp64_quaternion_revert(BGC_FP64_Quaternion* const quaternion);

extern inline void bgc_fp32_quaternion_get_reverse(BGC_FP32_Quaternion* const reverse, const BGC_FP32_Quaternion* const quaternion);
extern inline void bgc_fp64_quaternion_get_reverse(BGC_FP64_Quaternion* const reverse, const BGC_FP64_Quaternion* const quaternion);

extern inline int bgc_fp32_quaternion_invert(BGC_FP32_Quaternion* const quaternion);
extern inline int bgc_fp64_quaternion_invert(BGC_FP64_Quaternion* const quaternion);

extern inline int bgc_fp32_quaternion_get_inverse(BGC_FP32_Quaternion* const inverse, const BGC_FP32_Quaternion* const quaternion);
extern inline int bgc_fp64_quaternion_get_inverse(BGC_FP64_Quaternion* const inverse, const BGC_FP64_Quaternion* const quaternion);

extern inline int bgc_fp32_quaternion_normalize(BGC_FP32_Quaternion* const quaternion);
extern inline int bgc_fp64_quaternion_normalize(BGC_FP64_Quaternion* const quaternion);

extern inline int bgc_fp32_quaternion_get_normalized(BGC_FP32_Quaternion* const normalized, const BGC_FP32_Quaternion* const quaternion);
extern inline int bgc_fp64_quaternion_get_normalized(BGC_FP64_Quaternion* const normalized, const BGC_FP64_Quaternion* const quaternion);

extern inline void _bgc_fp32_versor_turn_vector(BGC_FP32_Vector3* const turned_vector, const BGC_FP32_Quaternion* const quaternion, const BGC_FP32_Vector3* const original_vector);
extern inline void _bgc_fp64_versor_turn_vector(BGC_FP64_Vector3* const turned_vector, const BGC_FP64_Quaternion* const quaternion, const BGC_FP64_Vector3* const original_vector);

extern inline void _bgc_fp32_versor_turn_vector_back(BGC_FP32_Vector3* const turned_vector, const BGC_FP32_Quaternion* const quaternion, const BGC_FP32_Vector3* const original_vector);
extern inline void _bgc_fp64_versor_turn_vector_back(BGC_FP64_Vector3* const turned_vector, const BGC_FP64_Quaternion* const quaternion, const BGC_FP64_Vector3* const original_vector);

extern inline int bgc_fp32_quaternion_turn_vector(BGC_FP32_Vector3* const turned_vector, const BGC_FP32_Quaternion* const quaternion, const BGC_FP32_Vector3* const original_vector);
extern inline int bgc_fp64_quaternion_turn_vector(BGC_FP64_Vector3* const turned_vector, const BGC_FP64_Quaternion* const quaternion, const BGC_FP64_Vector3* const original_vector);

extern inline int bgc_fp32_quaternion_turn_vector_back(BGC_FP32_Vector3* const turned_vector, const BGC_FP32_Quaternion* const quaternion, const BGC_FP32_Vector3* const original_vector);
extern inline int bgc_fp64_quaternion_turn_vector_back(BGC_FP64_Vector3* const turned_vector, const BGC_FP64_Quaternion* const quaternion, const BGC_FP64_Vector3* const original_vector);

extern inline int bgc_fp32_quaternion_get_both_matrices(BGC_FP32_Matrix3x3* const rotation, BGC_FP32_Matrix3x3* const reverse, const BGC_FP32_Quaternion* const quaternion);
extern inline int bgc_fp64_quaternion_get_both_matrices(BGC_FP64_Matrix3x3* const rotation, BGC_FP64_Matrix3x3* const reverse, const BGC_FP64_Quaternion* const quaternion);

extern inline int bgc_fp32_quaternion_are_close(const BGC_FP32_Quaternion* const quaternion1, const BGC_FP32_Quaternion* const quaternion2);
extern inline int bgc_fp64_quaternion_are_close(const BGC_FP64_Quaternion* const quaternion1, const BGC_FP64_Quaternion* const quaternion2);

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

int bgc_fp32_quaternion_get_power(BGC_FP32_Quaternion* const power, const BGC_FP32_Quaternion* const base, const float exponent)
{
    const float ss = base->s * base->s;
    const float xx = base->x * base->x;
    const float yy = base->y * base->y;
    const float zz = base->z * base->z;

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

    // isnan(square_modulus) means checking for NaN value at square_modulus
    if (isnan(square_modulus)) {
        return BGC_FAILURE;
    }

    if (square_vector <= BGC_FP32_SQUARE_EPSILON) {
        if (base->s < 0.0f) {
            return BGC_FAILURE;
        }

        power->s = powf(base->s, exponent);
        power->x = 0.0f;
        power->y = 0.0f;
        power->z = 0.0f;

        return BGC_SUCCESS;
    }

    const float vector_modulus = sqrtf(square_vector);
    const float power_angle = atan2f(vector_modulus, base->s) * exponent;
    const float power_modulus = powf(square_modulus, 0.5f * exponent);
    const float multiplier = power_modulus * sinf(power_angle) / vector_modulus;

    power->s = power_modulus * cosf(power_angle);
    power->x = base->x * multiplier;
    power->y = base->y * multiplier;
    power->z = base->z * multiplier;

    return BGC_SUCCESS;
}

int bgc_fp64_quaternion_get_power(BGC_FP64_Quaternion* const power, const BGC_FP64_Quaternion* const base, const double exponent)
{
    const double ss = base->s * base->s;
    const double xx = base->x * base->x;
    const double yy = base->y * base->y;
    const double zz = base->z * base->z;

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

    // isnan(square_modulus) means checking for NaN value at square_modulus
    if (isnan(square_modulus)) {
        return BGC_FAILURE;
    }

    if (square_vector <= BGC_FP64_SQUARE_EPSILON) {
        if (base->s < 0.0) {
            return BGC_FAILURE;
        }

        power->s = pow(base->s, exponent);
        power->x = 0.0;
        power->y = 0.0;
        power->z = 0.0;

        return BGC_SUCCESS;
    }

    const double vector_modulus = sqrt(square_vector);
    const double power_angle = atan2(vector_modulus, base->s) * exponent;
    const double power_modulus = pow(square_modulus, 0.5 * exponent);
    const double multiplier = power_modulus * sin(power_angle) / vector_modulus;

    power->s = power_modulus * cos(power_angle);
    power->x = base->x * multiplier;
    power->y = base->y * multiplier;
    power->z = base->z * multiplier;

    return BGC_SUCCESS;
}

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

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

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

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

    const float corrector1 = 1.0f / square_modulus;

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

    const float corrector2 = 2.0f * corrector1;

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

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

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

    return BGC_SUCCESS;
}

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

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

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

    const double corrector1 = 1.0 / square_modulus;

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

    const double corrector2 = 2.0 * corrector1;

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

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

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

    return BGC_SUCCESS;
}

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

int bgc_fp32_quaternion_set_rotation_matrix(BGC_FP32_Quaternion* const quaternion, const BGC_FP32_Matrix3x3* const matrix)
{
    if (!bgc_fp32_matrix3x3_is_rotation(matrix)) {
        return BGC_FAILURE;
    }

    const float ss_4 = (1 + matrix->r1c1) + (matrix->r2c2 + matrix->r3c3);
    const float xx_4 = (1 + matrix->r1c1) - (matrix->r2c2 + matrix->r3c3);
    const float yy_4 = (1 + matrix->r2c2) - (matrix->r1c1 + matrix->r3c3);
    const float zz_4 = (1 + matrix->r3c3) - (matrix->r1c1 + matrix->r2c2);

    const float sx_4 = matrix->r3c2 - matrix->r2c3;
    const float sy_4 = matrix->r1c3 - matrix->r3c1;
    const float sz_4 = matrix->r2c1 - matrix->r1c2;

    const float yz_4 = matrix->r3c2 + matrix->r2c3;
    const float xz_4 = matrix->r1c3 + matrix->r3c1;
    const float xy_4 = matrix->r2c1 + matrix->r1c2;

    float max = ss_4;
    int index = 0;

    if (xx_4 > max) {
        max = xx_4;
        index = 1;
    }

    if (yy_4 > max) {
        max = yy_4;
        index = 2;
    }

    if (zz_4 > max) {
        max = zz_4;
        index = 3;
    }

    switch (index) {
    case 0:
        quaternion->s = ss_4;
        quaternion->x = sx_4;
        quaternion->y = sy_4;
        quaternion->z = sz_4;
        break;

    case 1:
        quaternion->s = sx_4;
        quaternion->x = xx_4;
        quaternion->y = xy_4;
        quaternion->z = xz_4;
        break;

    case 2:
        quaternion->s = sy_4;
        quaternion->x = xy_4;
        quaternion->y = yy_4;
        quaternion->z = yz_4;
        break;

    case 3:
        quaternion->s = sz_4;
        quaternion->x = xz_4;
        quaternion->y = yz_4;
        quaternion->z = zz_4;
        break;
    }

    if (quaternion->s < 0.0f) {
        quaternion->s = -quaternion->s;
        quaternion->x = -quaternion->x;
        quaternion->y = -quaternion->y;
        quaternion->z = -quaternion->z;
    }

    const float multiplicator = sqrtf(1.0f / bgc_fp32_quaternion_get_square_magnitude(quaternion));

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

    return BGC_SUCCESS;
}

int bgc_fp64_quaternion_set_rotation_matrix(BGC_FP64_Quaternion* const quaternion, const BGC_FP64_Matrix3x3* const matrix)
{
    if (!bgc_fp64_matrix3x3_is_rotation(matrix)) {
        return BGC_FAILURE;
    }

    const double ss_4 = (1 + matrix->r1c1) + (matrix->r2c2 + matrix->r3c3);
    const double xx_4 = (1 + matrix->r1c1) - (matrix->r2c2 - matrix->r3c3);
    const double yy_4 = (1 + matrix->r2c2) - (matrix->r1c1 - matrix->r3c3);
    const double zz_4 = (1 + matrix->r3c3) - (matrix->r1c1 - matrix->r2c2);

    const double sx_4 = matrix->r3c2 - matrix->r2c3;
    const double sy_4 = matrix->r1c3 - matrix->r3c1;
    const double sz_4 = matrix->r2c1 - matrix->r1c2;

    const double yz_4 = matrix->r3c2 + matrix->r2c3;
    const double xz_4 = matrix->r1c3 + matrix->r3c1;
    const double xy_4 = matrix->r2c1 + matrix->r1c2;

    double max = ss_4;
    int index = 0;

    if (xx_4 > max) {
        max = xx_4;
        index = 1;
    }

    if (yy_4 > max) {
        max = yy_4;
        index = 2;
    }

    if (zz_4 > max) {
        max = zz_4;
        index = 3;
    }

    switch (index) {
    case 0:
        quaternion->s = ss_4;
        quaternion->x = sx_4;
        quaternion->y = sy_4;
        quaternion->z = sz_4;
        break;

    case 1:
        quaternion->s = sx_4;
        quaternion->x = xx_4;
        quaternion->y = xy_4;
        quaternion->z = xz_4;
        break;

    case 2:
        quaternion->s = sy_4;
        quaternion->x = xy_4;
        quaternion->y = yy_4;
        quaternion->z = yz_4;
        break;

    case 3:
        quaternion->s = sz_4;
        quaternion->x = xz_4;
        quaternion->y = yz_4;
        quaternion->z = zz_4;
        break;
    }

    if (quaternion->s < 0.0) {
        quaternion->s = -quaternion->s;
        quaternion->x = -quaternion->x;
        quaternion->y = -quaternion->y;
        quaternion->z = -quaternion->z;
    }

    const double multiplicator = sqrt(1.0 / bgc_fp64_quaternion_get_square_magnitude(quaternion));

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

    return BGC_SUCCESS;
}

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

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

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

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

    const float corrector1 = 1.0f / square_modulus;

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

    const float corrector2 = 2.0f * corrector1;

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

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

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

    return BGC_SUCCESS;
}

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

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

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

    const double corrector1 = 1.0 / square_modulus;

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

    const double corrector2 = 2.0 * corrector1;

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

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

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

    return BGC_SUCCESS;
}