#ifndef _BGC_DUAL_VECTOR3_H_INCLUDED_
#define _BGC_DUAL_VECTOR3_H_INCLUDED_

#include "./types.h"
#include "./vector3.h"

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

inline void bgc_fp32_dual_vector3_reset(BGC_FP32_DualVector3* const vector)
{
    bgc_fp32_vector3_reset(&vector->real_part);
    bgc_fp32_vector3_reset(&vector->dual_part);
}

inline void bgc_fp64_dual_vector3_reset(BGC_FP64_DualVector3* const vector)
{
    bgc_fp64_vector3_reset(&vector->real_part);
    bgc_fp64_vector3_reset(&vector->dual_part);
}

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

inline void bgc_fp32_dual_vector3_copy(BGC_FP32_DualVector3* const destination, const BGC_FP32_DualVector3* const source)
{
    bgc_fp32_vector3_copy(&destination->real_part, &source->real_part);
    bgc_fp32_vector3_copy(&destination->dual_part, &source->dual_part);
}

inline void bgc_fp64_dual_vector3_copy(BGC_FP64_DualVector3* const destination, const BGC_FP64_DualVector3* const source)
{
    bgc_fp64_vector3_copy(&destination->real_part, &source->real_part);
    bgc_fp64_vector3_copy(&destination->dual_part, &source->dual_part);
}

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

inline void bgc_fp32_dual_vector3_swap(BGC_FP32_DualVector3* const first, BGC_FP32_DualVector3* const second)
{
    bgc_fp32_vector3_swap(&first->real_part, &second->real_part);
    bgc_fp32_vector3_swap(&first->dual_part, &second->dual_part);
}

inline void bgc_fp64_dual_vector3_swap(BGC_FP64_DualVector3* const first, BGC_FP64_DualVector3* const second)
{
    bgc_fp64_vector3_swap(&first->real_part, &second->real_part);
    bgc_fp64_vector3_swap(&first->dual_part, &second->dual_part);
}

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

inline void bgc_fp32_dual_vector3_convert_to_fp64(BGC_FP64_DualVector3* const destination, const BGC_FP32_DualVector3* const source)
{
    bgc_fp32_vector3_convert_to_fp64(&destination->real_part, &source->real_part);
    bgc_fp32_vector3_convert_to_fp64(&destination->dual_part, &source->dual_part);
}

inline void bgc_fp64_dual_vector3_convert_to_fp32(BGC_FP32_DualVector3* const destination, const BGC_FP64_DualVector3* const source)
{
    bgc_fp64_vector3_convert_to_fp32(&destination->real_part, &source->real_part);
    bgc_fp64_vector3_convert_to_fp32(&destination->dual_part, &source->dual_part);
}

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

inline void bgc_fp32_dual_vector3_revert(BGC_FP32_DualVector3* const vector)
{
    bgc_fp32_vector3_revert(&vector->real_part);
    bgc_fp32_vector3_revert(&vector->dual_part);
}

inline void bgc_fp64_dual_vector3_revert(BGC_FP64_DualVector3* const vector)
{
    bgc_fp64_vector3_revert(&vector->real_part);
    bgc_fp64_vector3_revert(&vector->dual_part);
}

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

inline void bgc_fp32_dual_vector3_get_reverse(BGC_FP32_DualVector3* const reverse, const BGC_FP32_DualVector3* const vector)
{
    bgc_fp32_vector3_get_reverse(&reverse->real_part, &vector->real_part);
    bgc_fp32_vector3_get_reverse(&reverse->dual_part, &vector->dual_part);
}

inline void bgc_fp64_dual_vector3_get_reverse(BGC_FP64_DualVector3* const reverse, const BGC_FP64_DualVector3* const vector)
{
    bgc_fp64_vector3_get_reverse(&reverse->real_part, &vector->real_part);
    bgc_fp64_vector3_get_reverse(&reverse->dual_part, &vector->dual_part);
}

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

inline void bgc_fp32_dual_vector3_add(BGC_FP32_DualVector3* const sum, const BGC_FP32_DualVector3* const first, const BGC_FP32_DualVector3* const second)
{
    bgc_fp32_vector3_add(&sum->real_part, &first->real_part, &second->real_part);
    bgc_fp32_vector3_add(&sum->dual_part, &first->dual_part, &second->dual_part);
}

inline void bgc_fp64_dual_vector3_add(BGC_FP64_DualVector3* const sum, const BGC_FP64_DualVector3* const first, const BGC_FP64_DualVector3* const second)
{
    bgc_fp64_vector3_add(&sum->real_part, &first->real_part, &second->real_part);
    bgc_fp64_vector3_add(&sum->dual_part, &first->dual_part, &second->dual_part);
}

// ================= Add Scaled ================= //

inline void bgc_fp32_dual_vector3_add_scaled(BGC_FP32_DualVector3* const sum, const BGC_FP32_DualVector3* const base_vector, const BGC_FP32_DualVector3* const scalable_vector, const float scale)
{
    bgc_fp32_vector3_add_scaled(&sum->real_part, &base_vector->real_part, &scalable_vector->real_part, scale);
    bgc_fp32_vector3_add_scaled(&sum->dual_part, &base_vector->dual_part, &scalable_vector->dual_part, scale);
}

inline void bgc_fp64_dual_vector3_add_scaled(BGC_FP64_DualVector3* const sum, const BGC_FP64_DualVector3* const base_vector, const BGC_FP64_DualVector3* const scalable_vector, const double scale)
{
    bgc_fp64_vector3_add_scaled(&sum->real_part, &base_vector->real_part, &scalable_vector->real_part, scale);
    bgc_fp64_vector3_add_scaled(&sum->dual_part, &base_vector->dual_part, &scalable_vector->dual_part, scale);
}

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

inline void bgc_fp32_dual_vector3_subtract(BGC_FP32_DualVector3* const difference, const BGC_FP32_DualVector3* const minuend, const BGC_FP32_DualVector3* const subtrahend)
{
    bgc_fp32_vector3_subtract(&difference->real_part, &minuend->real_part, &subtrahend->real_part);
    bgc_fp32_vector3_subtract(&difference->dual_part, &minuend->dual_part, &subtrahend->dual_part);
}

inline void bgc_fp64_dual_vector3_subtract(BGC_FP64_DualVector3* const difference, const BGC_FP64_DualVector3* const minuend, const BGC_FP64_DualVector3* const subtrahend)
{
    bgc_fp64_vector3_subtract(&difference->real_part, &minuend->real_part, &subtrahend->real_part);
    bgc_fp64_vector3_subtract(&difference->dual_part, &minuend->dual_part, &subtrahend->dual_part);
}

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

inline void bgc_fp32_dual_vector3_subtract_scaled(BGC_FP32_DualVector3* const difference, const BGC_FP32_DualVector3* const base_vector, const BGC_FP32_DualVector3* const scalable_vector, const float scale)
{
    bgc_fp32_vector3_subtract_scaled(&difference->real_part, &base_vector->real_part, &scalable_vector->real_part, scale);
    bgc_fp32_vector3_subtract_scaled(&difference->dual_part, &base_vector->dual_part, &scalable_vector->dual_part, scale);
}

inline void bgc_fp64_dual_vector3_subtract_scaled(BGC_FP64_DualVector3* const difference, const BGC_FP64_DualVector3* const base_vector, const BGC_FP64_DualVector3* const scalable_vector, const double scale)
{
    bgc_fp64_vector3_subtract_scaled(&difference->real_part, &base_vector->real_part, &scalable_vector->real_part, scale);
    bgc_fp64_vector3_subtract_scaled(&difference->dual_part, &base_vector->dual_part, &scalable_vector->dual_part, scale);
}

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

inline void bgc_fp32_dual_vector3_multiply_by_real_number(BGC_FP32_DualVector3* const product, const BGC_FP32_DualVector3* const multiplicand, const float multiplier)
{
    bgc_fp32_vector3_multiply_by_real_number(&product->real_part, &multiplicand->real_part, multiplier);
    bgc_fp32_vector3_multiply_by_real_number(&product->dual_part, &multiplicand->dual_part, multiplier);
}

inline void bgc_fp64_dual_vector3_multiply_by_real_number(BGC_FP64_DualVector3* const product, const BGC_FP64_DualVector3* const multiplicand, const double multiplier)
{
    bgc_fp64_vector3_multiply_by_real_number(&product->real_part, &multiplicand->real_part, multiplier);
    bgc_fp64_vector3_multiply_by_real_number(&product->dual_part, &multiplicand->dual_part, multiplier);
}

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

inline void bgc_fp32_dual_vector3_multiply_by_dual_number(BGC_FP32_DualVector3* const product, const BGC_FP32_DualVector3* const multiplicand, const BGC_FP32_DualNumber* multiplier)
{
    BGC_FP32_Vector3 dual_part;

    bgc_fp32_vector3_multiply_by_real_number(&dual_part, &multiplicand->dual_part, multiplier->real_part);
    bgc_fp32_vector3_add_scaled(&dual_part, &dual_part, &multiplicand->real_part, multiplier->dual_part);

    bgc_fp32_vector3_multiply_by_real_number(&product->real_part, &multiplicand->real_part, multiplier->real_part);
    bgc_fp32_vector3_copy(&product->dual_part, &dual_part);
}

inline void bgc_fp64_dual_vector3_multiply_by_dual_number(BGC_FP64_DualVector3* const product, const BGC_FP64_DualVector3* const multiplicand, const BGC_FP64_DualNumber* multiplier)
{
    BGC_FP64_Vector3 dual_part;

    bgc_fp64_vector3_multiply_by_real_number(&dual_part, &multiplicand->dual_part, multiplier->real_part);
    bgc_fp64_vector3_add_scaled(&dual_part, &dual_part, &multiplicand->real_part, multiplier->dual_part);

    bgc_fp64_vector3_multiply_by_real_number(&product->real_part, &multiplicand->real_part, multiplier->real_part);
    bgc_fp64_vector3_copy(&product->dual_part, &dual_part);
}

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

inline void bgc_fp32_dual_vector3_multiply_by_conjugate_dual_number(BGC_FP32_DualVector3* const product, const BGC_FP32_DualVector3* const multiplicand, const BGC_FP32_DualNumber* const multiplier_to_conjugate)
{
    BGC_FP32_Vector3 dual_part;

    bgc_fp32_vector3_multiply_by_real_number(&dual_part, &multiplicand->dual_part, multiplier_to_conjugate->real_part);
    bgc_fp32_vector3_subtract_scaled(&dual_part, &dual_part, &multiplicand->real_part, multiplier_to_conjugate->dual_part);

    bgc_fp32_vector3_multiply_by_real_number(&product->real_part, &multiplicand->real_part, multiplier_to_conjugate->real_part);
    bgc_fp32_vector3_copy(&product->dual_part, &dual_part);
}

inline void bgc_fp64_dual_vector3_multiply_by_conjugate_dual_number(BGC_FP64_DualVector3* const product, const BGC_FP64_DualVector3* const multiplicand, const BGC_FP64_DualNumber* const multiplier_to_conjugate)
{
    BGC_FP64_Vector3 dual_part;

    bgc_fp64_vector3_multiply_by_real_number(&dual_part, &multiplicand->dual_part, multiplier_to_conjugate->real_part);
    bgc_fp64_vector3_subtract_scaled(&dual_part, &dual_part, &multiplicand->real_part, multiplier_to_conjugate->dual_part);

    bgc_fp64_vector3_multiply_by_real_number(&product->real_part, &multiplicand->real_part, multiplier_to_conjugate->real_part);
    bgc_fp64_vector3_copy(&product->dual_part, &dual_part);
}

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

inline void bgc_fp32_dual_vector3_multiply_by_matrix3x3(BGC_FP32_DualVector3* const product, const BGC_FP32_DualVector3* const vector, const BGC_FP32_Matrix3x3* const matrix)
{
    const float real_x = vector->real_part.x * matrix->r1c1 + vector->real_part.y * matrix->r2c1 + vector->real_part.z * matrix->r3c1;
    const float real_y = vector->real_part.x * matrix->r1c2 + vector->real_part.y * matrix->r2c2 + vector->real_part.z * matrix->r3c2;
    const float real_z = vector->real_part.x * matrix->r1c3 + vector->real_part.y * matrix->r2c3 + vector->real_part.z * matrix->r3c3;

    const float dual_x = vector->real_part.x * matrix->r1c1 + vector->real_part.y * matrix->r2c1 + vector->real_part.z * matrix->r3c1;
    const float dual_y = vector->real_part.x * matrix->r1c2 + vector->real_part.y * matrix->r2c2 + vector->real_part.z * matrix->r3c2;
    const float dual_z = vector->real_part.x * matrix->r1c3 + vector->real_part.y * matrix->r2c3 + vector->real_part.z * matrix->r3c3;

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

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

inline void bgc_fp64_dual_vector3_multiply_by_matrix3x3(BGC_FP64_DualVector3* const product, const BGC_FP64_DualVector3* const vector, const BGC_FP64_Matrix3x3* const matrix)
{
    const double real_x = vector->real_part.x * matrix->r1c1 + vector->real_part.y * matrix->r2c1 + vector->real_part.z * matrix->r3c1;
    const double real_y = vector->real_part.x * matrix->r1c2 + vector->real_part.y * matrix->r2c2 + vector->real_part.z * matrix->r3c2;
    const double real_z = vector->real_part.x * matrix->r1c3 + vector->real_part.y * matrix->r2c3 + vector->real_part.z * matrix->r3c3;

    const double dual_x = vector->real_part.x * matrix->r1c1 + vector->real_part.y * matrix->r2c1 + vector->real_part.z * matrix->r3c1;
    const double dual_y = vector->real_part.x * matrix->r1c2 + vector->real_part.y * matrix->r2c2 + vector->real_part.z * matrix->r3c2;
    const double dual_z = vector->real_part.x * matrix->r1c3 + vector->real_part.y * matrix->r2c3 + vector->real_part.z * matrix->r3c3;

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

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

// ===== Restrict Left Dual Vector Product ====== //

inline void _bgc_fp32_restrict_dual_vector3_multiply_by_matrix3x3(BGC_FP32_DualVector3* restrict const product, const BGC_FP32_DualVector3* const vector, const BGC_FP32_Matrix3x3* const matrix)
{
    product->real_part.x = vector->real_part.x * matrix->r1c1 + vector->real_part.y * matrix->r2c1 + vector->real_part.z * matrix->r3c1;
    product->real_part.y = vector->real_part.x * matrix->r1c2 + vector->real_part.y * matrix->r2c2 + vector->real_part.z * matrix->r3c2;
    product->real_part.z = vector->real_part.x * matrix->r1c3 + vector->real_part.y * matrix->r2c3 + vector->real_part.z * matrix->r3c3;

    product->real_part.x = vector->real_part.x * matrix->r1c1 + vector->real_part.y * matrix->r2c1 + vector->real_part.z * matrix->r3c1;
    product->real_part.y = vector->real_part.x * matrix->r1c2 + vector->real_part.y * matrix->r2c2 + vector->real_part.z * matrix->r3c2;
    product->real_part.z = vector->real_part.x * matrix->r1c3 + vector->real_part.y * matrix->r2c3 + vector->real_part.z * matrix->r3c3;
}

inline void _bgc_fp64_restrict_dual_vector3_multiply_by_matrix3x3(BGC_FP64_DualVector3* restrict const product, const BGC_FP64_DualVector3* const vector, const BGC_FP64_Matrix3x3* const matrix)
{
    product->real_part.x = vector->real_part.x * matrix->r1c1 + vector->real_part.y * matrix->r2c1 + vector->real_part.z * matrix->r3c1;
    product->real_part.y = vector->real_part.x * matrix->r1c2 + vector->real_part.y * matrix->r2c2 + vector->real_part.z * matrix->r3c2;
    product->real_part.z = vector->real_part.x * matrix->r1c3 + vector->real_part.y * matrix->r2c3 + vector->real_part.z * matrix->r3c3;

    product->real_part.x = vector->real_part.x * matrix->r1c1 + vector->real_part.y * matrix->r2c1 + vector->real_part.z * matrix->r3c1;
    product->real_part.y = vector->real_part.x * matrix->r1c2 + vector->real_part.y * matrix->r2c2 + vector->real_part.z * matrix->r3c2;
    product->real_part.z = vector->real_part.x * matrix->r1c3 + vector->real_part.y * matrix->r2c3 + vector->real_part.z * matrix->r3c3;
}

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

inline int bgc_fp32_dual_vector3_divide_by_real_number(BGC_FP32_DualVector3* const quotient, const BGC_FP32_DualVector3* const dividend, const float divisor)
{
    if (bgc_fp32_is_zero(divisor)) {
        return BGC_FAILURE;
    }

    const float multiplier = 1.0f / divisor;

    bgc_fp32_vector3_multiply_by_real_number(&quotient->real_part, &dividend->real_part, multiplier);
    bgc_fp32_vector3_multiply_by_real_number(&quotient->dual_part, &dividend->dual_part, multiplier);

    return BGC_SUCCESS;
}

inline int bgc_fp64_dual_vector3_divide_by_real_number(BGC_FP64_DualVector3* const quotient, const BGC_FP64_DualVector3* const dividend, const double divisor)
{
    if (bgc_fp64_is_zero(divisor)) {
        return BGC_FAILURE;
    }

    const double multiplier = 1.0 / divisor;

    bgc_fp64_vector3_multiply_by_real_number(&quotient->real_part, &dividend->real_part, multiplier);
    bgc_fp64_vector3_multiply_by_real_number(&quotient->dual_part, &dividend->dual_part, multiplier);

    return BGC_SUCCESS;
}

// =========== Divide by Dual Number ============ //

inline int bgc_fp32_dual_vector3_divide_by_dual_number(BGC_FP32_DualVector3* const quotient, const BGC_FP32_DualVector3* const dividend, const BGC_FP32_DualNumber* const divisor)
{
    const float square_modulus = divisor->real_part * divisor->real_part;

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

    bgc_fp32_dual_vector3_multiply_by_conjugate_dual_number(quotient, dividend, divisor);
    bgc_fp32_dual_vector3_multiply_by_real_number(quotient, quotient, 1.0f / square_modulus);

    return BGC_SUCCESS;
}

inline int bgc_fp64_dual_vector3_divide_by_dual_number(BGC_FP64_DualVector3* const quotient, const BGC_FP64_DualVector3* const dividend, const BGC_FP64_DualNumber* const divisor)
{
    const double square_modulus = divisor->real_part * divisor->real_part;

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

    bgc_fp64_dual_vector3_multiply_by_conjugate_dual_number(quotient, dividend, divisor);
    bgc_fp64_dual_vector3_multiply_by_real_number(quotient, quotient, 1.0 / square_modulus);

    return BGC_SUCCESS;
}

// ====== Divide by Conjugate Dual Number ======= //

inline int bgc_fp32_dual_vector3_divide_by_conjugate_dual_number(BGC_FP32_DualVector3* const quotient, const BGC_FP32_DualVector3* const dividend, const BGC_FP32_DualNumber* const divisor_to_conjugate)
{
    const float square_modulus = divisor_to_conjugate->real_part * divisor_to_conjugate->real_part;

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

    bgc_fp32_dual_vector3_multiply_by_dual_number(quotient, dividend, divisor_to_conjugate);
    bgc_fp32_dual_vector3_multiply_by_real_number(quotient, quotient, 1.0f / square_modulus);

    return BGC_SUCCESS;
}

inline int bgc_fp64_dual_vector3_divide_by_conjugate_dual_number(BGC_FP64_DualVector3* const quotient, const BGC_FP64_DualVector3* const dividend, const BGC_FP64_DualNumber* const divisor_to_conjugate)
{
    const double square_modulus = divisor_to_conjugate->real_part * divisor_to_conjugate->real_part;

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

    bgc_fp64_dual_vector3_multiply_by_dual_number(quotient, dividend, divisor_to_conjugate);
    bgc_fp64_dual_vector3_multiply_by_real_number(quotient, quotient, 1.0 / square_modulus);

    return BGC_SUCCESS;
}

// ================ Mean of Two ================= //

inline void bgc_fp32_dual_vector3_get_mean2(BGC_FP32_DualVector3* const mean, const BGC_FP32_DualVector3* const first, const BGC_FP32_DualVector3* const second)
{
    bgc_fp32_vector3_get_mean2(&mean->real_part, &first->real_part, &second->real_part);
    bgc_fp32_vector3_get_mean2(&mean->dual_part, &first->dual_part, &second->dual_part);
}

inline void bgc_fp64_dual_vector3_get_mean2(BGC_FP64_DualVector3* const mean, const BGC_FP64_DualVector3* const first, const BGC_FP64_DualVector3* const second)
{
    bgc_fp64_vector3_get_mean2(&mean->real_part, &first->real_part, &second->real_part);
    bgc_fp64_vector3_get_mean2(&mean->dual_part, &first->dual_part, &second->dual_part);
}

// =============== Mean of Three ================ //

inline void bgc_fp32_dual_vector3_get_mean3(BGC_FP32_DualVector3* const mean, const BGC_FP32_DualVector3* const first, const BGC_FP32_DualVector3* const second, const BGC_FP32_DualVector3* const third)
{
    bgc_fp32_vector3_get_mean3(&mean->real_part, &first->real_part, &second->real_part, &third->real_part);
    bgc_fp32_vector3_get_mean3(&mean->dual_part, &first->dual_part, &second->dual_part, &third->dual_part);
}

inline void bgc_fp64_dual_vector3_get_mean3(BGC_FP64_DualVector3* const mean, const BGC_FP64_DualVector3* const first, const BGC_FP64_DualVector3* const second, const BGC_FP64_DualVector3* const third)
{
    bgc_fp64_vector3_get_mean3(&mean->real_part, &first->real_part, &second->real_part, &third->real_part);
    bgc_fp64_vector3_get_mean3(&mean->dual_part, &first->dual_part, &second->dual_part, &third->dual_part);
}

// ============ Linear Interpolation ============ //

inline void bgc_fp32_dual_vector3_interpolate(BGC_FP32_DualVector3* const interpolation, const BGC_FP32_DualVector3* const first, const BGC_FP32_DualVector3* const second, const float phase)
{
    bgc_fp32_vector3_interpolate(&interpolation->real_part, &first->real_part, &second->real_part, phase);
    bgc_fp32_vector3_interpolate(&interpolation->dual_part, &first->dual_part, &second->dual_part, phase);
}

inline void bgc_fp64_dual_vector3_interpolate(BGC_FP64_DualVector3* const interpolation, const BGC_FP64_DualVector3* const first, const BGC_FP64_DualVector3* const second, const double phase)
{
    bgc_fp64_vector3_interpolate(&interpolation->real_part, &first->real_part, &second->real_part, phase);
    bgc_fp64_vector3_interpolate(&interpolation->dual_part, &first->dual_part, &second->dual_part, phase);
}

// ================ Dot Product ================= //

inline void bgc_fp32_dual_vector3_get_dot_product(BGC_FP32_DualNumber* const product, const BGC_FP32_DualVector3* const first, const BGC_FP32_DualVector3* const second)
{
    product->real_part = bgc_fp32_vector3_get_dot_product(&first->real_part, &second->real_part);
    product->dual_part = bgc_fp32_vector3_get_dot_product(&first->dual_part, &second->real_part) + bgc_fp32_vector3_get_dot_product(&first->real_part, &second->dual_part);
}

inline void bgc_fp64_dual_vector3_get_dot_product(BGC_FP64_DualNumber* const product, const BGC_FP64_DualVector3* const first, const BGC_FP64_DualVector3* const second)
{
    product->real_part = bgc_fp64_vector3_get_dot_product(&first->real_part, &second->real_part);
    product->dual_part = bgc_fp64_vector3_get_dot_product(&first->dual_part, &second->real_part) + bgc_fp64_vector3_get_dot_product(&first->real_part, &second->dual_part);
}

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

inline void bgc_fp32_dual_vector3_get_cross_product(BGC_FP32_DualVector3* const product, const BGC_FP32_DualVector3* const first, const BGC_FP32_DualVector3* const second)
{
    BGC_FP32_Vector3 part1, part2;

    _bgc_fp32_restrict_vector3_get_cross_product(&part1, &first->dual_part, &second->real_part);
    _bgc_fp32_restrict_vector3_get_cross_product(&part2, &first->real_part, &second->dual_part);

    bgc_fp32_vector3_get_cross_product(&product->real_part, &first->real_part, &second->real_part);
    bgc_fp32_vector3_add(&product->dual_part, &part1, &part2);
}

inline void bgc_fp64_dual_vector3_get_cross_product(BGC_FP64_DualVector3* const product, const BGC_FP64_DualVector3* const first, const BGC_FP64_DualVector3* const second)
{
    BGC_FP64_Vector3 part1, part2;

    _bgc_fp64_restrict_vector3_get_cross_product(&part1, &first->dual_part, &second->real_part);
    _bgc_fp64_restrict_vector3_get_cross_product(&part2, &first->real_part, &second->dual_part);

    bgc_fp64_vector3_get_cross_product(&product->real_part, &first->real_part, &second->real_part);
    bgc_fp64_vector3_add(&product->dual_part, &part1, &part2);
}

#endif