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

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

extern inline void bgc_fp32_quaternion_make_unit(BGC_FP32_Quaternion* quaternion);
extern inline void bgc_fp64_quaternion_make_unit(BGC_FP64_Quaternion* quaternion);

extern inline void bgc_fp32_quaternion_make(const float s0, const float x1, const float x2, const float x3, BGC_FP32_Quaternion* quaternion);
extern inline void bgc_fp64_quaternion_make(const double s0, const double x1, const double x2, const double x3, BGC_FP64_Quaternion* quaternion);

extern inline float bgc_fp32_quaternion_get_square_modulus(const BGC_FP32_Quaternion* quaternion);
extern inline double bgc_fp64_quaternion_get_square_modulus(const BGC_FP64_Quaternion* quaternion);

extern inline float bgc_fp32_quaternion_get_modulus(const BGC_FP32_Quaternion* quaternion);
extern inline double bgc_fp64_quaternion_get_modulus(const BGC_FP64_Quaternion* quaternion);

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

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

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

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

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

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

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

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

extern inline void bgc_fp32_quaternion_get_product(const BGC_FP32_Quaternion* left, const BGC_FP32_Quaternion* right, BGC_FP32_Quaternion* product);
extern inline void bgc_fp64_quaternion_get_product(const BGC_FP64_Quaternion* left, const BGC_FP64_Quaternion* right, BGC_FP64_Quaternion* product);

extern inline void bgc_fp32_quaternion_multiply(const BGC_FP32_Quaternion* multiplicand, const float multipier, BGC_FP32_Quaternion* product);
extern inline void bgc_fp64_quaternion_multiply(const BGC_FP64_Quaternion* multiplicand, const double multipier, BGC_FP64_Quaternion* product);

extern inline int bgc_fp32_quaternion_get_ratio(const BGC_FP32_Quaternion* divident, const BGC_FP32_Quaternion* divisor, BGC_FP32_Quaternion* quotient);
extern inline int bgc_fp64_quaternion_get_ratio(const BGC_FP64_Quaternion* divident, const BGC_FP64_Quaternion* divisor, BGC_FP64_Quaternion* quotient);

extern inline void bgc_fp32_quaternion_divide(const BGC_FP32_Quaternion* dividend, const float divisor, BGC_FP32_Quaternion* quotient);
extern inline void bgc_fp64_quaternion_divide(const BGC_FP64_Quaternion* dividend, const double divisor, BGC_FP64_Quaternion* quotient);

extern inline void bgc_fp32_quaternion_get_mean2(const BGC_FP32_Quaternion* vector1, const BGC_FP32_Quaternion* vector2, BGC_FP32_Quaternion* mean);
extern inline void bgc_fp64_quaternion_get_mean2(const BGC_FP64_Quaternion* vector1, const BGC_FP64_Quaternion* vector2, BGC_FP64_Quaternion* mean);

extern inline void bgc_fp32_quaternion_get_mean3(const BGC_FP32_Quaternion* vector1, const BGC_FP32_Quaternion* vector2, const BGC_FP32_Quaternion* vector3, BGC_FP32_Quaternion* mean);
extern inline void bgc_fp64_quaternion_get_mean3(const BGC_FP64_Quaternion* vector1, const BGC_FP64_Quaternion* vector2, const BGC_FP64_Quaternion* vector3, BGC_FP64_Quaternion* mean);

extern inline void bgc_fp32_quaternion_interpolate(const BGC_FP32_Quaternion* vector1, const BGC_FP32_Quaternion* vector2, const float phase, BGC_FP32_Quaternion* interpolation);
extern inline void bgc_fp64_quaternion_interpolate(const BGC_FP64_Quaternion* vector1, const BGC_FP64_Quaternion* vector2, const double phase, BGC_FP64_Quaternion* interpolation);

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

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

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

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

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

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

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

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

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

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

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

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

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

int bgc_fp32_quaternion_get_exponation(const BGC_FP32_Quaternion* base, const float exponent, BGC_FP32_Quaternion* power)
{
    const float s0s0 = base->s0 * base->s0;
    const float x1x1 = base->x1 * base->x1;
    const float x2x2 = base->x2 * base->x2;
    const float x3x3 = base->x3 * base->x3;

    const float square_vector = x1x1 + (x2x2 + x3x3);
    const float square_modulus = (s0s0 + x1x1) + (x2x2 + x3x3);

    // isnan(square_modulus) means checking for NaN value at square_modulus
    if (isnan(square_modulus)) {
        return 0;
    }

    if (square_vector <= BGC_FP32_SQUARE_EPSYLON) {
        if (base->s0 < 0.0f) {
            return 0;
        }

        power->s0 = powf(base->s0, exponent);
        power->x1 = 0.0f;
        power->x2 = 0.0f;
        power->x3 = 0.0f;

        return 1;
    }

    const float vector_modulus = sqrtf(square_vector);
    const float power_angle = atan2f(vector_modulus, base->s0) * exponent;
    const float power_modulus = powf(square_modulus, 0.5f * exponent);
    const float multiplier = power_modulus * sinf(power_angle) / vector_modulus;

    power->s0 = power_modulus * cosf(power_angle);
    power->x1 = base->x1 * multiplier;
    power->x2 = base->x2 * multiplier;
    power->x3 = base->x3 * multiplier;

    return 1;
}

int bgc_fp64_quaternion_get_exponation(const BGC_FP64_Quaternion* base, const double exponent, BGC_FP64_Quaternion* power)
{
    const double s0s0 = base->s0 * base->s0;
    const double x1x1 = base->x1 * base->x1;
    const double x2x2 = base->x2 * base->x2;
    const double x3x3 = base->x3 * base->x3;

    const double square_vector = x1x1 + (x2x2 + x3x3);
    const double square_modulus = (s0s0 + x1x1) + (x2x2 + x3x3);

    // isnan(square_modulus) means checking for NaN value at square_modulus
    if (isnan(square_modulus)) {
        return 0;
    }

    if (square_vector <= BGC_FP64_SQUARE_EPSYLON) {
        if (base->s0 < 0.0) {
            return 0;
        }

        power->s0 = pow(base->s0, exponent);
        power->x1 = 0.0;
        power->x2 = 0.0;
        power->x3 = 0.0;

        return 1;
    }

    const double vector_modulus = sqrt(square_vector);
    const double power_angle = atan2(vector_modulus, base->s0) * exponent;
    const double power_modulus = pow(square_modulus, 0.5 * exponent);
    const double multiplier = power_modulus * sin(power_angle) / vector_modulus;

    power->s0 = power_modulus * cos(power_angle);
    power->x1 = base->x1 * multiplier;
    power->x2 = base->x2 * multiplier;
    power->x3 = base->x3 * multiplier;

    return 1;
}