#ifndef _BGC_VECTOR3_H_INCLUDED_
#define _BGC_VECTOR3_H_INCLUDED_

#include <math.h>

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

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

inline void bgc_fp32_vector3_reset(BGC_FP32_Vector3* const vector)
{
    vector->x = 0.0f;
    vector->y = 0.0f;
    vector->z = 0.0f;
}

inline void bgc_fp64_vector3_reset(BGC_FP64_Vector3* const vector)
{
    vector->x = 0.0;
    vector->y = 0.0;
    vector->z = 0.0;
}

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

inline void bgc_fp32_vector3_set_values(BGC_FP32_Vector3* const destination, const float x, const float y, const float z)
{
    destination->x = x;
    destination->y = y;
    destination->z = z;
}

inline void bgc_fp64_vector3_set_values(BGC_FP64_Vector3* const destination, const double x, const double y, const double z)
{
    destination->x = x;
    destination->y = y;
    destination->z = z;
}

// ================== Modulus =================== //

inline float bgc_fp32_vector3_get_squared_length(const BGC_FP32_Vector3* const vector)
{
    return vector->x * vector->x + vector->y * vector->y + vector->z * vector->z;
}

inline double bgc_fp64_vector3_get_squared_length(const BGC_FP64_Vector3* const vector)
{
    return vector->x * vector->x + vector->y * vector->y + vector->z * vector->z;
}

inline float bgc_fp32_vector3_get_length(const BGC_FP32_Vector3* const vector)
{
    return sqrtf(bgc_fp32_vector3_get_squared_length(vector));
}

inline double bgc_fp64_vector3_get_length(const BGC_FP64_Vector3* const vector)
{
    return sqrt(bgc_fp64_vector3_get_squared_length(vector));
}

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

inline int bgc_fp32_vector3_is_zero(const BGC_FP32_Vector3* const vector)
{
    return bgc_fp32_vector3_get_squared_length(vector) <= BGC_FP32_SQUARE_EPSILON;
}

inline int bgc_fp64_vector3_is_zero(const BGC_FP64_Vector3* const vector)
{
    return bgc_fp64_vector3_get_squared_length(vector) <= BGC_FP64_SQUARE_EPSILON;
}

inline int bgc_fp32_vector3_is_unit(const BGC_FP32_Vector3* const vector)
{
    return bgc_fp32_is_square_unit(bgc_fp32_vector3_get_squared_length(vector));
}

inline int bgc_fp64_vector3_is_unit(const BGC_FP64_Vector3* const vector)
{
    return bgc_fp64_is_square_unit(bgc_fp64_vector3_get_squared_length(vector));
}

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

inline void bgc_fp32_vector3_copy(BGC_FP32_Vector3* const destination, const BGC_FP32_Vector3* const source)
{
    destination->x = source->x;
    destination->y = source->y;
    destination->z = source->z;
}

inline void bgc_fp64_vector3_copy(BGC_FP64_Vector3* const destination, const BGC_FP64_Vector3* const source)
{
    destination->x = source->x;
    destination->y = source->y;
    destination->z = source->z;
}

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

inline void bgc_fp32_vector3_swap(BGC_FP32_Vector3* const vector1, BGC_FP32_Vector3* const vector2)
{
    const float x = vector2->x;
    const float y = vector2->y;
    const float z = vector2->z;

    vector2->x = vector1->x;
    vector2->y = vector1->y;
    vector2->z = vector1->z;

    vector1->x = x;
    vector1->y = y;
    vector1->z = z;
}

inline void bgc_fp64_vector3_swap(BGC_FP64_Vector3* const vector1, BGC_FP64_Vector3* const vector2)
{
    const double x = vector2->x;
    const double y = vector2->y;
    const double z = vector2->z;

    vector2->x = vector1->x;
    vector2->y = vector1->y;
    vector2->z = vector1->z;

    vector1->x = x;
    vector1->y = y;
    vector1->z = z;
}

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

inline void bgc_fp32_vector3_convert_to_fp64(BGC_FP64_Vector3* const destination, const BGC_FP32_Vector3* const source)
{
    destination->x = source->x;
    destination->y = source->y;
    destination->z = source->z;
}

inline void bgc_fp64_vector3_convert_to_fp32(BGC_FP32_Vector3* const destination, const BGC_FP64_Vector3* const source)
{
    destination->x = (float)source->x;
    destination->y = (float)source->y;
    destination->z = (float)source->z;
}

// ==================== Add ===================== //

inline void bgc_fp32_vector3_add(BGC_FP32_Vector3* const sum, const BGC_FP32_Vector3* const vector1, const BGC_FP32_Vector3* const vector2)
{
    sum->x = vector1->x + vector2->x;
    sum->y = vector1->y + vector2->y;
    sum->z = vector1->z + vector2->z;
}

inline void bgc_fp64_vector3_add(BGC_FP64_Vector3* const sum, const BGC_FP64_Vector3* const vector1, const BGC_FP64_Vector3* const vector2)
{
    sum->x = vector1->x + vector2->x;
    sum->y = vector1->y + vector2->y;
    sum->z = vector1->z + vector2->z;
}

// ================= Add scaled ================= //

inline void bgc_fp32_vector3_add_scaled(BGC_FP32_Vector3* const sum, const BGC_FP32_Vector3* const basic_vector, const BGC_FP32_Vector3* const scalable_vector, const float scale)
{
    sum->x = basic_vector->x + scalable_vector->x * scale;
    sum->y = basic_vector->y + scalable_vector->y * scale;
    sum->z = basic_vector->z + scalable_vector->z * scale;
}

inline void bgc_fp64_vector3_add_scaled(BGC_FP64_Vector3* const sum, const BGC_FP64_Vector3* const basic_vector, const BGC_FP64_Vector3* const scalable_vector, const double scale)
{
    sum->x = basic_vector->x + scalable_vector->x * scale;
    sum->y = basic_vector->y + scalable_vector->y * scale;
    sum->z = basic_vector->z + scalable_vector->z * scale;
}

// ================== Subtract ================== //

inline void bgc_fp32_vector3_subtract(BGC_FP32_Vector3* const difference, const BGC_FP32_Vector3* const minuend, const BGC_FP32_Vector3* const subtrahend)
{
    difference->x = minuend->x - subtrahend->x;
    difference->y = minuend->y - subtrahend->y;
    difference->z = minuend->z - subtrahend->z;
}

inline void bgc_fp64_vector3_subtract(BGC_FP64_Vector3* const difference, const BGC_FP64_Vector3* const minuend, const BGC_FP64_Vector3* const subtrahend)
{
    difference->x = minuend->x - subtrahend->x;
    difference->y = minuend->y - subtrahend->y;
    difference->z = minuend->z - subtrahend->z;
}

// ============== Subtract Scaled =============== //

inline void bgc_fp32_vector3_subtract_scaled(BGC_FP32_Vector3* const difference, const BGC_FP32_Vector3* const basic_vector, const BGC_FP32_Vector3* const scalable_vector, const float scale)
{
    difference->x = basic_vector->x - scalable_vector->x * scale;
    difference->y = basic_vector->y - scalable_vector->y * scale;
    difference->z = basic_vector->z - scalable_vector->z * scale;
}

inline void bgc_fp64_vector3_subtract_scaled(BGC_FP64_Vector3* const difference, const BGC_FP64_Vector3* const basic_vector, const BGC_FP64_Vector3* const scalable_vector, const double scale)
{
    difference->x = basic_vector->x - scalable_vector->x * scale;
    difference->y = basic_vector->y - scalable_vector->y * scale;
    difference->z = basic_vector->z - scalable_vector->z * scale;
}

// ================== Multiply ================== //

inline void bgc_fp32_vector3_multiply_by_real_number(BGC_FP32_Vector3* const product, const BGC_FP32_Vector3* const multiplicand, const float multiplier)
{
    product->x = multiplicand->x * multiplier;
    product->y = multiplicand->y * multiplier;
    product->z = multiplicand->z * multiplier;
}

inline void bgc_fp64_vector3_multiply_by_real_number(BGC_FP64_Vector3* const product, const BGC_FP64_Vector3* const multiplicand, const double multiplier)
{
    product->x = multiplicand->x * multiplier;
    product->y = multiplicand->y * multiplier;
    product->z = multiplicand->z * multiplier;
}

// ========== Multiply by Dual Number =========== //

inline void bgc_fp32_vector3_multiply_by_dual_number(BGC_FP32_DualVector3* const product, const BGC_FP32_Vector3* const multiplicand, const BGC_FP32_DualNumber* const multiplier)
{
    const float real_x = multiplicand->x * multiplier->real_part;
    const float real_y = multiplicand->y * multiplier->real_part;
    const float real_z = multiplicand->z * multiplier->real_part;

    const float dual_x = multiplicand->x * multiplier->dual_part;
    const float dual_y = multiplicand->y * multiplier->dual_part;
    const float dual_z = multiplicand->z * multiplier->dual_part;

    product->real_part.x = real_x;
    product->real_part.y = real_y;
    product->real_part.z = real_z;

    product->dual_part.x = dual_x;
    product->dual_part.y = dual_y;
    product->dual_part.z = dual_z;
}

inline void bgc_fp64_vector3_multiply_by_dual_number(BGC_FP64_DualVector3* const product, const BGC_FP64_Vector3* const multiplicand, const BGC_FP64_DualNumber* const multiplier)
{
    const double real_x = multiplicand->x * multiplier->real_part;
    const double real_y = multiplicand->y * multiplier->real_part;
    const double real_z = multiplicand->z * multiplier->real_part;

    const double dual_x = multiplicand->x * multiplier->dual_part;
    const double dual_y = multiplicand->y * multiplier->dual_part;
    const double dual_z = multiplicand->z * multiplier->dual_part;

    product->real_part.x = real_x;
    product->real_part.y = real_y;
    product->real_part.z = real_z;

    product->dual_part.x = dual_x;
    product->dual_part.y = dual_y;
    product->dual_part.z = dual_z;
}

// ====== Restrict Multiply by Dual Number ====== //

inline void _bgc_fp32_restrict_vector3_multiply_by_dual_number(BGC_FP32_DualVector3* restrict const product, const BGC_FP32_Vector3* const multiplicand, const BGC_FP32_DualNumber* const multiplier)
{
    product->real_part.x = multiplicand->x * multiplier->real_part;
    product->real_part.y = multiplicand->y * multiplier->real_part;
    product->real_part.z = multiplicand->z * multiplier->real_part;

    product->dual_part.x = multiplicand->x * multiplier->dual_part;
    product->dual_part.y = multiplicand->y * multiplier->dual_part;
    product->dual_part.z = multiplicand->z * multiplier->dual_part;
}

inline void _bgc_fp64_restrict_vector3_multiply_by_dual_number(BGC_FP64_DualVector3* restrict const product, const BGC_FP64_Vector3* const multiplicand, const BGC_FP64_DualNumber* const multiplier)
{
    product->real_part.x = multiplicand->x * multiplier->real_part;
    product->real_part.y = multiplicand->y * multiplier->real_part;
    product->real_part.z = multiplicand->z * multiplier->real_part;

    product->dual_part.x = multiplicand->x * multiplier->dual_part;
    product->dual_part.y = multiplicand->y * multiplier->dual_part;
    product->dual_part.z = multiplicand->z * multiplier->dual_part;
}

// ============ Left Vector Product ============= //

inline void bgc_fp32_vector3_multiply_by_matrix2x3(BGC_FP32_Vector2* const product, const BGC_FP32_Vector3* const vector, const BGC_FP32_Matrix2x3* const matrix)
{
    product->x = vector->x * matrix->r1c1 + vector->y * matrix->r2c1 + vector->z * matrix->r3c1;
    product->y = vector->x * matrix->r1c2 + vector->y * matrix->r2c2 + vector->z * matrix->r3c2;
}

inline void bgc_fp64_vector3_multiply_by_matrix2x3(BGC_FP64_Vector2* const product, const BGC_FP64_Vector3* const vector, const BGC_FP64_Matrix2x3* const matrix)
{
    product->x = vector->x * matrix->r1c1 + vector->y * matrix->r2c1 + vector->z * matrix->r3c1;
    product->y = vector->x * matrix->r1c2 + vector->y * matrix->r2c2 + vector->z * matrix->r3c2;
}

// ============ Left Vector Product ============= //

inline void bgc_fp32_vector3_multiply_by_matrix3x3(BGC_FP32_Vector3* const product, const BGC_FP32_Vector3* const vector, const BGC_FP32_Matrix3x3* const matrix)
{
    const float x = vector->x * matrix->r1c1 + vector->y * matrix->r2c1 + vector->z * matrix->r3c1;
    const float y = vector->x * matrix->r1c2 + vector->y * matrix->r2c2 + vector->z * matrix->r3c2;
    const float z = vector->x * matrix->r1c3 + vector->y * matrix->r2c3 + vector->z * matrix->r3c3;

    product->x = x;
    product->y = y;
    product->z = z;
}

inline void bgc_fp64_vector3_multiply_by_matrix3x3(BGC_FP64_Vector3* const product, const BGC_FP64_Vector3* const vector, const BGC_FP64_Matrix3x3* const matrix)
{
    const double x = vector->x * matrix->r1c1 + vector->y * matrix->r2c1 + vector->z * matrix->r3c1;
    const double y = vector->x * matrix->r1c2 + vector->y * matrix->r2c2 + vector->z * matrix->r3c2;
    const double z = vector->x * matrix->r1c3 + vector->y * matrix->r2c3 + vector->z * matrix->r3c3;

    product->x = x;
    product->y = y;
    product->z = z;
}

// =================== Divide =================== //

inline int bgc_fp32_vector3_divide_by_real_number(BGC_FP32_Vector3* const quotient, const BGC_FP32_Vector3* const dividend, const float divisor)
{
    if (bgc_fp32_is_zero(divisor) || isnan(divisor)) {
        return BGC_FAILURE;
    }

    bgc_fp32_vector3_multiply_by_real_number(quotient, dividend, 1.0f / divisor);

    return BGC_SUCCESS;
}

inline int bgc_fp64_vector3_divide_by_real_number(BGC_FP64_Vector3* const quotient, const BGC_FP64_Vector3* const dividend, const double divisor)
{
    if (bgc_fp64_is_zero(divisor) || isnan(divisor)) {
        return BGC_FAILURE;
    }

    bgc_fp64_vector3_multiply_by_real_number(quotient, dividend, 1.0 / divisor);

    return BGC_SUCCESS;
}

// ================== Average2 ================== //

inline void bgc_fp32_vector3_get_mean2(BGC_FP32_Vector3* const mean, const BGC_FP32_Vector3* const vector1, const BGC_FP32_Vector3* const vector2)
{
    mean->x = (vector1->x + vector2->x) * 0.5f;
    mean->y = (vector1->y + vector2->y) * 0.5f;
    mean->z = (vector1->z + vector2->z) * 0.5f;
}

inline void bgc_fp64_vector3_get_mean2(BGC_FP64_Vector3* const mean, const BGC_FP64_Vector3* const vector1, const BGC_FP64_Vector3* const vector2)
{
    mean->x = (vector1->x + vector2->x) * 0.5;
    mean->y = (vector1->y + vector2->y) * 0.5;
    mean->z = (vector1->z + vector2->z) * 0.5;
}

// ================== Average3 ================== //

inline void bgc_fp32_vector3_get_mean3(BGC_FP32_Vector3* const mean, const BGC_FP32_Vector3* const vector1, const BGC_FP32_Vector3* const vector2, const BGC_FP32_Vector3* const vector3)
{
    mean->x = (vector1->x + vector2->x + vector3->x) * BGC_FP32_ONE_THIRD;
    mean->y = (vector1->y + vector2->y + vector3->y) * BGC_FP32_ONE_THIRD;
    mean->z = (vector1->z + vector2->z + vector3->z) * BGC_FP32_ONE_THIRD;
}

inline void bgc_fp64_vector3_get_mean3(BGC_FP64_Vector3* const mean, const BGC_FP64_Vector3* const vector1, const BGC_FP64_Vector3* const vector2, const BGC_FP64_Vector3* const vector3)
{
    mean->x = (vector1->x + vector2->x + vector3->x) * BGC_FP64_ONE_THIRD;
    mean->y = (vector1->y + vector2->y + vector3->y) * BGC_FP64_ONE_THIRD;
    mean->z = (vector1->z + vector2->z + vector3->z) * BGC_FP64_ONE_THIRD;
}

// =================== Linear =================== //

inline void bgc_fp32_vector3_interpolate(BGC_FP32_Vector3* const interpolation, const BGC_FP32_Vector3* const first, const BGC_FP32_Vector3* const second, const float phase)
{
    const float counter_phase = 1.0f - phase;

    interpolation->x = first->x * counter_phase + second->x * phase;
    interpolation->y = first->y * counter_phase + second->y * phase;
    interpolation->z = first->z * counter_phase + second->z * phase;
}

inline void bgc_fp64_vector3_interpolate(BGC_FP64_Vector3* const interpolation, const BGC_FP64_Vector3* const first, const BGC_FP64_Vector3* const second, const double phase)
{
    const double counter_phase = 1.0 - phase;

    interpolation->x = first->x * counter_phase + second->x * phase;
    interpolation->y = first->y * counter_phase + second->y * phase;
    interpolation->z = first->z * counter_phase + second->z * phase;
}

// ================== Negative ================== //

inline void bgc_fp32_vector3_revert(BGC_FP32_Vector3* const vector)
{
    vector->x = -vector->x;
    vector->y = -vector->y;
    vector->z = -vector->z;
}

inline void bgc_fp64_vector3_revert(BGC_FP64_Vector3* const vector)
{
    vector->x = -vector->x;
    vector->y = -vector->y;
    vector->z = -vector->z;
}

inline void bgc_fp32_vector3_get_reverse(BGC_FP32_Vector3* const reverse, const BGC_FP32_Vector3* const vector)
{
    reverse->x = -vector->x;
    reverse->y = -vector->y;
    reverse->z = -vector->z;
}

inline void bgc_fp64_vector3_get_reverse(BGC_FP64_Vector3* const reverse, const BGC_FP64_Vector3* const vector)
{
    reverse->x = -vector->x;
    reverse->y = -vector->y;
    reverse->z = -vector->z;
}

// ================= Normalize ================== //

inline int bgc_fp32_vector3_normalize(BGC_FP32_Vector3* const vector)
{
    const float square_modulus = bgc_fp32_vector3_get_squared_length(vector);

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

    if (bgc_fp32_is_square_unit(square_modulus)) {
        return BGC_SUCCESS;
    }

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

    vector->x *= multiplier;
    vector->y *= multiplier;
    vector->z *= multiplier;

    return BGC_SUCCESS;
}

inline int bgc_fp64_vector3_normalize(BGC_FP64_Vector3* const vector)
{
    const double square_modulus = bgc_fp64_vector3_get_squared_length(vector);

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

    if (bgc_fp64_is_square_unit(square_modulus)) {
        return BGC_SUCCESS;
    }

    const double multiplier = sqrt(1.0 / square_modulus);

    vector->x *= multiplier;
    vector->y *= multiplier;
    vector->z *= multiplier;

    return BGC_SUCCESS;
}

inline int bgc_fp32_vector3_get_normalized(BGC_FP32_Vector3* const normalized, const BGC_FP32_Vector3* const vector)
{
    const float square_modulus = bgc_fp32_vector3_get_squared_length(vector);

    if (square_modulus <= BGC_FP32_SQUARE_EPSILON || isnan(square_modulus)) {
        bgc_fp32_vector3_reset(normalized);
        return BGC_FAILURE;
    }

    if (bgc_fp32_is_square_unit(square_modulus)) {
        bgc_fp32_vector3_copy(normalized, vector);
        return BGC_SUCCESS;
    }

    bgc_fp32_vector3_multiply_by_real_number(normalized, vector, sqrtf(1.0f / square_modulus));
    return BGC_SUCCESS;
}

inline int bgc_fp64_vector3_get_normalized(BGC_FP64_Vector3* const normalized, const BGC_FP64_Vector3* const vector)
{
    const double square_modulus = bgc_fp64_vector3_get_squared_length(vector);

    if (square_modulus <= BGC_FP64_SQUARE_EPSILON || isnan(square_modulus)) {
        bgc_fp64_vector3_reset(normalized);
        return BGC_FAILURE;
    }

    if (bgc_fp64_is_square_unit(square_modulus)) {
        bgc_fp64_vector3_copy(normalized, vector);
        return BGC_SUCCESS;
    }

    bgc_fp64_vector3_multiply_by_real_number(normalized, vector, sqrt(1.0 / square_modulus));
    return BGC_SUCCESS;
}

// =============== Scalar Product =============== //

inline float bgc_fp32_vector3_get_dot_product(const BGC_FP32_Vector3* const vector1, const BGC_FP32_Vector3* const vector2)
{
    return vector1->x * vector2->x + vector1->y * vector2->y + vector1->z * vector2->z;
}

inline double bgc_fp64_vector3_get_dot_product(const BGC_FP64_Vector3* const vector1, const BGC_FP64_Vector3* const vector2)
{
    return vector1->x * vector2->x + vector1->y * vector2->y + vector1->z * vector2->z;
}

// =============== Triple Product =============== //

inline float bgc_fp32_vector3_get_triple_product(const BGC_FP32_Vector3* const vector1, const BGC_FP32_Vector3* const vector2, const BGC_FP32_Vector3* const vector3)
{
    return vector1->x * (vector2->y * vector3->z - vector2->z * vector3->y)
         + vector1->y * (vector2->z * vector3->x - vector2->x * vector3->z)
         + vector1->z * (vector2->x * vector3->y - vector2->y * vector3->x);
}

inline double bgc_fp64_vector3_get_triple_product(const BGC_FP64_Vector3* const vector1, const BGC_FP64_Vector3* const vector2, const BGC_FP64_Vector3* const vector3)
{
    return vector1->x * (vector2->y * vector3->z - vector2->z * vector3->y)
         + vector1->y * (vector2->z * vector3->x - vector2->x * vector3->z)
         + vector1->z * (vector2->x * vector3->y - vector2->y * vector3->x);
}

// =========== Restrict Cross Product =========== //

inline void _bgc_fp32_restrict_vector3_get_cross_product(BGC_FP32_Vector3* restrict const product, const BGC_FP32_Vector3* const vector1, const BGC_FP32_Vector3* const vector2)
{
    product->x = vector1->y * vector2->z - vector1->z * vector2->y;
    product->y = vector1->z * vector2->x - vector1->x * vector2->z;
    product->z = vector1->x * vector2->y - vector1->y * vector2->x;
}

inline void _bgc_fp64_restrict_vector3_get_cross_product(BGC_FP64_Vector3* restrict const product, const BGC_FP64_Vector3* const vector1, const BGC_FP64_Vector3* const vector2)
{
    product->x = vector1->y * vector2->z - vector1->z * vector2->y;
    product->y = vector1->z * vector2->x - vector1->x * vector2->z;
    product->z = vector1->x * vector2->y - vector1->y * vector2->x;
}

// =============== Cross Product ================ //

inline void bgc_fp32_vector3_get_cross_product(BGC_FP32_Vector3* const product, const BGC_FP32_Vector3* const vector1, const BGC_FP32_Vector3* const vector2)
{
    const float x = vector1->y * vector2->z - vector1->z * vector2->y;
    const float y = vector1->z * vector2->x - vector1->x * vector2->z;
    const float z = vector1->x * vector2->y - vector1->y * vector2->x;

    product->x = x;
    product->y = y;
    product->z = z;
}

inline void bgc_fp64_vector3_get_cross_product(BGC_FP64_Vector3* const product, const BGC_FP64_Vector3* const vector1, const BGC_FP64_Vector3* const vector2)
{
    const double x = vector1->y * vector2->z - vector1->z * vector2->y;
    const double y = vector1->z * vector2->x - vector1->x * vector2->z;
    const double z = vector1->x * vector2->y - vector1->y * vector2->x;

    product->x = x;
    product->y = y;
    product->z = z;
}

// ============ Double Cross Product ============ //

// [a x [b x c]] = b * (a, c) - c * (a, b)
inline void bgc_fp32_vector3_get_double_cross(BGC_FP32_Vector3* const product, const BGC_FP32_Vector3* const vector1, const BGC_FP32_Vector3* const vector2, const BGC_FP32_Vector3* const vector3)
{
    const float ac = bgc_fp32_vector3_get_dot_product(vector1, vector3);
    const float ab = bgc_fp32_vector3_get_dot_product(vector1, vector2);

    product->x = vector2->x * ac - vector3->x * ab;
    product->y = vector2->y * ac - vector3->y * ab;
    product->z = vector2->z * ac - vector3->z * ab;
}

// [a x [b x c]] = b * (a, c) - c * (a, b)
inline void bgc_fp64_vector3_get_double_cross(BGC_FP64_Vector3* const product, const BGC_FP64_Vector3* const vector1, const BGC_FP64_Vector3* const vector2, const BGC_FP64_Vector3* const vector3)
{
    const double ac = bgc_fp64_vector3_get_dot_product(vector1, vector3);
    const double ab = bgc_fp64_vector3_get_dot_product(vector1, vector2);

    product->x = vector2->x * ac - vector3->x * ab;
    product->y = vector2->y * ac - vector3->y * ab;
    product->z = vector2->z * ac - vector3->z * ab;
}

// ====== Alternative Double Cross Product ====== //

// [[a x b] x c] = - [c x [a x b]] = -(a * (c, b) - b * (c, a)) = b * (a, c) - a * (b, c)
inline void bgc_fp32_vector3_get_alternative_double_cross(BGC_FP32_Vector3* const product, const BGC_FP32_Vector3* const vector1, const BGC_FP32_Vector3* const vector2, const BGC_FP32_Vector3* const vector3)
{
    const float ac = bgc_fp32_vector3_get_dot_product(vector1, vector3);
    const float bc = bgc_fp32_vector3_get_dot_product(vector2, vector3);

    product->x = vector2->x * ac - vector1->x * bc;
    product->y = vector2->y * ac - vector1->y * bc;
    product->z = vector2->z * ac - vector1->z * bc;
}

// [[a x b] x c] = - [c x [a x b]] = -(a * (b, c) - b * (a, c)) = b * (a, c) - a * (b, c)
inline void bgc_fp64_vector3_get_alternative_double_cross(BGC_FP64_Vector3* const product, const BGC_FP64_Vector3* const vector1, const BGC_FP64_Vector3* const vector2, const BGC_FP64_Vector3* const vector3)
{
    const double ac = bgc_fp64_vector3_get_dot_product(vector1, vector3);
    const double bc = bgc_fp64_vector3_get_dot_product(vector2, vector3);

    product->x = vector2->x * ac - vector1->x * bc;
    product->y = vector2->y * ac - vector1->y * bc;
    product->z = vector2->z * ac - vector1->z * bc;
}

// =================== Angle ==================== //

float bgc_fp32_vector3_get_angle(const BGC_FP32_Vector3* const vector1, const BGC_FP32_Vector3* const vector2, const int angle_unit);

double bgc_fp64_vector3_get_angle(const BGC_FP64_Vector3* const vector1, const BGC_FP64_Vector3* const vector2, const int angle_unit);

// =============== Square Distance ============== //

inline float bgc_fp32_vector3_get_square_distance(const BGC_FP32_Vector3* const vector1, const BGC_FP32_Vector3* const vector2)
{
    const float dx = (vector1->x - vector2->x);
    const float dy = (vector1->y - vector2->y);
    const float dz = (vector1->z - vector2->z);

    return dx * dx + dy * dy + dz * dz;
}

inline double bgc_fp64_vector3_get_square_distance(const BGC_FP64_Vector3* const vector1, const BGC_FP64_Vector3* const vector2)
{
    const double dx = (vector1->x - vector2->x);
    const double dy = (vector1->y - vector2->y);
    const double dz = (vector1->z - vector2->z);

    return dx * dx + dy * dy + dz * dz;
}

// ================== Distance ================== //

inline float bgc_fp32_vector3_get_distance(const BGC_FP32_Vector3* const vector1, const BGC_FP32_Vector3* const vector2)
{
    return sqrtf(bgc_fp32_vector3_get_square_distance(vector1, vector2));
}

inline double bgc_fp64_vector3_get_distance(const BGC_FP64_Vector3* const vector1, const BGC_FP64_Vector3* const vector2)
{
    return sqrt(bgc_fp64_vector3_get_square_distance(vector1, vector2));
}

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

inline int bgc_fp32_vector3_are_close_enough(const BGC_FP32_Vector3* const vector1, const BGC_FP32_Vector3* const vector2, const float distance_limit)
{
    return bgc_fp32_vector3_get_square_distance(vector1, vector2) <= distance_limit * distance_limit;
}

inline int bgc_fp64_vector3_are_close_enough(const BGC_FP64_Vector3* const vector1, const BGC_FP64_Vector3* const vector2, const double distance_limit)
{
    return bgc_fp64_vector3_get_square_distance(vector1, vector2) <= distance_limit * distance_limit;
}

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

inline int bgc_fp32_vector3_are_close(const BGC_FP32_Vector3* const vector1, const BGC_FP32_Vector3* const vector2)
{
    const float square_modulus1 = bgc_fp32_vector3_get_squared_length(vector1);
    const float square_modulus2 = bgc_fp32_vector3_get_squared_length(vector2);
    const float square_distance = bgc_fp32_vector3_get_square_distance(vector1, vector2);

    if (square_modulus1 <= BGC_FP32_EPSILON_EFFECTIVENESS_LIMIT || square_modulus2 <= BGC_FP32_EPSILON_EFFECTIVENESS_LIMIT) {
        return square_distance <= BGC_FP32_SQUARE_EPSILON;
    }

    return square_distance <= BGC_FP32_SQUARE_EPSILON * square_modulus1 && square_distance <= BGC_FP32_SQUARE_EPSILON * square_modulus2;
}

inline int bgc_fp64_vector3_are_close(const BGC_FP64_Vector3* const vector1, const BGC_FP64_Vector3* const vector2)
{
    const double square_modulus1 = bgc_fp64_vector3_get_squared_length(vector1);
    const double square_modulus2 = bgc_fp64_vector3_get_squared_length(vector2);
    const double square_distance = bgc_fp64_vector3_get_square_distance(vector1, vector2);

    if (square_modulus1 <= BGC_FP64_EPSILON_EFFECTIVENESS_LIMIT || square_modulus2 <= BGC_FP64_EPSILON_EFFECTIVENESS_LIMIT) {
        return square_distance <= BGC_FP64_SQUARE_EPSILON;
    }

    return square_distance <= BGC_FP64_SQUARE_EPSILON * square_modulus1 && square_distance <= BGC_FP64_SQUARE_EPSILON * square_modulus2;
}

// ================== Parallel ================== //

inline int bgc_fp32_vector3_are_parallel(const BGC_FP32_Vector3* const vector1, const BGC_FP32_Vector3* const vector2)
{
    const float square_modulus1 = bgc_fp32_vector3_get_squared_length(vector1);
    const float square_modulus2 = bgc_fp32_vector3_get_squared_length(vector2);

    if (square_modulus1 <= BGC_FP32_SQUARE_EPSILON || square_modulus2 <= BGC_FP32_SQUARE_EPSILON) {
        return 1;
    }

    BGC_FP32_Vector3 product;

    _bgc_fp32_restrict_vector3_get_cross_product(&product, vector1, vector2);

    return bgc_fp32_vector3_get_squared_length(&product) <= BGC_FP32_SQUARE_EPSILON * square_modulus1 * square_modulus2;
}

inline int bgc_fp64_vector3_are_parallel(const BGC_FP64_Vector3* const vector1, const BGC_FP64_Vector3* const vector2)
{
    const double square_modulus1 = bgc_fp64_vector3_get_squared_length(vector1);
    const double square_modulus2 = bgc_fp64_vector3_get_squared_length(vector2);

    if (square_modulus1 <= BGC_FP64_SQUARE_EPSILON || square_modulus2 <= BGC_FP64_SQUARE_EPSILON) {
        return 1;
    }

    BGC_FP64_Vector3 product;

    _bgc_fp64_restrict_vector3_get_cross_product(&product, vector1, vector2);

    return bgc_fp64_vector3_get_squared_length(&product) <= BGC_FP64_SQUARE_EPSILON * square_modulus1 * square_modulus2;
}

// ================= Orthogonal ================= //

inline int bgc_fp32_vector3_are_orthogonal(const BGC_FP32_Vector3* const vector1, const BGC_FP32_Vector3* const vector2)
{
    const float square_modulus1 = bgc_fp32_vector3_get_squared_length(vector1);
    const float square_modulus2 = bgc_fp32_vector3_get_squared_length(vector2);

    if (square_modulus1 <= BGC_FP32_SQUARE_EPSILON || square_modulus2 <= BGC_FP32_SQUARE_EPSILON) {
        return 1;
    }

    const float scalar_product = bgc_fp32_vector3_get_dot_product(vector1, vector2);

    return scalar_product * scalar_product <= BGC_FP32_SQUARE_EPSILON * square_modulus1 * square_modulus2;
}

inline int bgc_fp64_vector3_are_orthogonal(const BGC_FP64_Vector3* const vector1, const BGC_FP64_Vector3* const vector2)
{
    const double square_modulus1 = bgc_fp64_vector3_get_squared_length(vector1);
    const double square_modulus2 = bgc_fp64_vector3_get_squared_length(vector2);

    if (square_modulus1 <= BGC_FP64_SQUARE_EPSILON || square_modulus2 <= BGC_FP64_SQUARE_EPSILON) {
        return 1;
    }

    const double scalar_product = bgc_fp64_vector3_get_dot_product(vector1, vector2);

    return scalar_product * scalar_product <= BGC_FP64_SQUARE_EPSILON * square_modulus1 * square_modulus2;
}

// ================== Attitude ================== //

int bgc_fp32_vector3_get_attitude(const BGC_FP32_Vector3* const vector1, const BGC_FP32_Vector3* const vector2);

int bgc_fp64_vector3_get_attitude(const BGC_FP64_Vector3* const vector1, const BGC_FP64_Vector3* const vector2);

#endif