#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 void _bgc_fp32_versor_get_rotation_matrix(BGC_FP32_Matrix3x3* const matrix, const BGC_FP32_Quaternion* const versor);
extern inline void _bgc_fp64_versor_get_rotation_matrix(BGC_FP64_Matrix3x3* const matrix, const BGC_FP64_Quaternion* const versor);

extern inline void _bgc_fp32_versor_get_reverse_matrix(BGC_FP32_Matrix3x3* const matrix, const BGC_FP32_Quaternion* const versor);
extern inline void _bgc_fp64_versor_get_reverse_matrix(BGC_FP64_Matrix3x3* const matrix, const BGC_FP64_Quaternion* const versor);

extern inline int bgc_fp32_quaternion_get_rotation_matrix(BGC_FP32_Matrix3x3* const rotation, const BGC_FP32_Quaternion* const quaternion);
extern inline int bgc_fp64_quaternion_get_rotation_matrix(BGC_FP64_Matrix3x3* const rotation, const BGC_FP64_Quaternion* const quaternion);

extern inline int bgc_fp32_quaternion_get_reverse_matrix(BGC_FP32_Matrix3x3* const reverse, const BGC_FP32_Quaternion* const quaternion);
extern inline int bgc_fp64_quaternion_get_reverse_matrix(BGC_FP64_Matrix3x3* const reverse, const BGC_FP64_Quaternion* const quaternion);

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;
}