#ifndef _BGC_DUAL_QUATERNION_H_INCLUDED_
#define _BGC_DUAL_QUATERNION_H_INCLUDED_

#include "./types.h"
#include "./quaternion.h"

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

inline void bgc_fp32_dual_quaternion_reset(BGC_FP32_DualQuaternion* quaternion)
{
    bgc_fp32_quaternion_reset(&quaternion->real_part);
    bgc_fp32_quaternion_reset(&quaternion->dual_part);
}

inline void bgc_fp64_dual_quaternion_reset(BGC_FP64_DualQuaternion* quaternion)
{
    bgc_fp64_quaternion_reset(&quaternion->real_part);
    bgc_fp64_quaternion_reset(&quaternion->dual_part);
}

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

inline void bgc_fp32_dual_quaternion_copy(BGC_FP32_DualQuaternion* destination, const BGC_FP32_DualQuaternion* source)
{
    bgc_fp32_quaternion_copy(&destination->real_part, &source->real_part);
    bgc_fp32_quaternion_copy(&destination->dual_part, &source->dual_part);
}

inline void bgc_fp64_dual_quaternion_copy(BGC_FP64_DualQuaternion* destination, const BGC_FP64_DualQuaternion* source)
{
    bgc_fp64_quaternion_copy(&destination->real_part, &source->real_part);
    bgc_fp64_quaternion_copy(&destination->dual_part, &source->dual_part);
}

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

inline void bgc_fp32_dual_quaternion_swap(BGC_FP32_DualQuaternion* first, BGC_FP32_DualQuaternion* second)
{
    bgc_fp32_quaternion_swap(&first->real_part, &second->real_part);
    bgc_fp32_quaternion_swap(&first->dual_part, &second->dual_part);
}

inline void bgc_fp64_dual_quaternion_swap(BGC_FP64_DualQuaternion* first, BGC_FP64_DualQuaternion* second)
{
    bgc_fp64_quaternion_swap(&first->real_part, &second->real_part);
    bgc_fp64_quaternion_swap(&first->dual_part, &second->dual_part);
}

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

inline void bgc_fp32_dual_quaternion_convert_to_fp64(BGC_FP64_DualQuaternion* destination, const BGC_FP32_DualQuaternion* source)
{
    bgc_fp32_quaternion_convert_to_fp64(&destination->real_part, &source->real_part);
    bgc_fp32_quaternion_convert_to_fp64(&destination->dual_part, &source->dual_part);
}

inline void bgc_fp64_dual_quaternion_convert_to_fp32(BGC_FP32_DualQuaternion* destination, const BGC_FP64_DualQuaternion* source)
{
    bgc_fp64_quaternion_convert_to_fp32(&destination->real_part, &source->real_part);
    bgc_fp64_quaternion_convert_to_fp32(&destination->dual_part, &source->dual_part);
}

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

inline void bgc_fp32_dual_quaternion_revert(BGC_FP32_DualQuaternion* quaternion)
{
    bgc_fp32_quaternion_revert(&quaternion->real_part);
    bgc_fp32_quaternion_revert(&quaternion->dual_part);
}

inline void bgc_fp64_dual_quaternion_revert(BGC_FP64_DualQuaternion* quaternion)
{
    bgc_fp64_quaternion_revert(&quaternion->real_part);
    bgc_fp64_quaternion_revert(&quaternion->dual_part);
}

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

inline void bgc_fp32_dual_quaternion_get_reverse(BGC_FP32_DualQuaternion* reverse, const BGC_FP32_DualQuaternion* quaternion)
{
    bgc_fp32_quaternion_get_reverse(&reverse->real_part, &quaternion->real_part);
    bgc_fp32_quaternion_get_reverse(&reverse->dual_part, &quaternion->dual_part);
}

inline void bgc_fp64_dual_quaternion_get_reverse(BGC_FP64_DualQuaternion* reverse, const BGC_FP64_DualQuaternion* quaternion)
{
    bgc_fp64_quaternion_get_reverse(&reverse->real_part, &quaternion->real_part);
    bgc_fp64_quaternion_get_reverse(&reverse->dual_part, &quaternion->dual_part);
}

// =================== Invert =================== //

inline int bgc_fp32_dual_quaternion_invert(BGC_FP32_DualQuaternion* quaternion)
{
    if (bgc_fp32_quaternion_get_inverse(&quaternion->real_part, &quaternion->real_part) !== BGC_SUCCESS) {
        return BGC_FAILURE;
    }

    BGC_FP32_Quaternion temporary;

    bgc_fp32_quaternion_multiply_by_quaternion(&temporary, &quaternion->real_part, &quaternion->dual_part);
    bgc_fp32_quaternion_multiply_by_quaternion(&quaternion->dual_part, &temporary, &quaternion->real_part);

    bgc_fp32_quaternion_revert(&quaternion->dual_part);

    return BGC_SUCCESS;
}

inline int bgc_fp64_dual_quaternion_invert(BGC_FP64_DualQuaternion* quaternion)
{
    if (bgc_fp64_quaternion_get_inverse(&quaternion->real_part, &quaternion->real_part) !== BGC_SUCCESS) {
        return BGC_FAILURE;
    }

    BGC_FP64_Quaternion temporary;

    bgc_fp64_quaternion_multiply_by_quaternion(&temporary, &quaternion->real_part, &quaternion->dual_part);
    bgc_fp64_quaternion_multiply_by_quaternion(&quaternion->dual_part, &temporary, &quaternion->real_part);

    bgc_fp64_quaternion_revert(&quaternion->dual_part);

    return BGC_SUCCESS;
}

// ================ Get Inverse ================= //

inline int bgc_fp32_dual_quaternion_get_inverse(BGC_FP32_DualQuaternion* inverse, const BGC_FP32_DualQuaternion* quaternion)
{
    if (bgc_fp32_quaternion_get_inverse(&inverse->real_part, &quaternion->real_part) !== BGC_SUCCESS) {
        return BGC_FAILURE;
    }

    BGC_FP32_Quaternion temporary;

    bgc_fp32_quaternion_multiply_by_quaternion(&temporary, &inverse->real_part, &quaternion->dual_part);
    bgc_fp32_quaternion_multiply_by_quaternion(&inverse->dual_part, &temporary, &inverse->real_part);

    bgc_fp32_quaternion_revert(&inverse->dual_part);

    return BGC_SUCCESS;
}

inline int bgc_fp64_dual_quaternion_get_inverse(BGC_FP64_DualQuaternion* inverse, const BGC_FP64_DualQuaternion* quaternion)
{
    if (bgc_fp64_quaternion_get_inverse(&inverse->real_part, &quaternion->real_part) !== BGC_SUCCESS) {
        return BGC_FAILURE;
    }

    BGC_FP64_Quaternion temporary;

    bgc_fp64_quaternion_multiply_by_quaternion(&temporary, &inverse->real_part, &quaternion->dual_part);
    bgc_fp64_quaternion_multiply_by_quaternion(&inverse->dual_part, &temporary, &inverse->real_part);

    bgc_fp64_quaternion_revert(&inverse->dual_part);

    return BGC_SUCCESS;
}

// ============ Component Conjugate ============= //

inline void bgc_fp32_dual_quaternion_component_conjugate(BGC_FP32_DualQuaternion* quaternion)
{
    bgc_fp32_quaternion_conjugate(&quaternion->real_part);
    bgc_fp32_quaternion_conjugate(&quaternion->dual_part);
}

inline void bgc_fp64_dual_quaternion_component_conjugate(BGC_FP64_DualQuaternion* quaternion)
{
    bgc_fp64_quaternion_conjugate(&quaternion->real_part);
    bgc_fp64_quaternion_conjugate(&quaternion->dual_part);
}

// ========== Get Component Conjugate =========== //

inline void bgc_fp32_dual_quaternion_get_component_conjugate(BGC_FP32_DualQuaternion* conjugate, const BGC_FP32_DualQuaternion* quaternion)
{
    bgc_fp32_quaternion_get_conjugate(&conjugate->real_part, &quaternion->real_part);
    bgc_fp32_quaternion_get_conjugate(&conjugate->dual_part, &quaternion->dual_part);
}

inline void bgc_fp64_dual_quaternion_get_component_conjugate(BGC_FP64_DualQuaternion* conjugate, const BGC_FP64_DualQuaternion* quaternion)
{
    bgc_fp64_quaternion_get_conjugate(&conjugate->real_part, &quaternion->real_part);
    bgc_fp64_quaternion_get_conjugate(&conjugate->dual_part, &quaternion->dual_part);
}

// =============== Dual Conjugate =============== //

inline void bgc_fp32_dual_quaternion_dual_conjugate(BGC_FP32_DualQuaternion* quaternion)
{
    bgc_fp32_quaternion_revert(&quaternion->dual_part);
}

inline void bgc_fp64_dual_quaternion_dual_conjugate(BGC_FP64_DualQuaternion* quaternion)
{
    bgc_fp64_quaternion_revert(&quaternion->dual_part);
}

// ============= Get Dual Conjugate ============= //

inline void bgc_fp32_dual_quaternion_get_dual_conjugate(BGC_FP32_DualQuaternion* conjugate, const BGC_FP32_DualQuaternion* quaternion)
{
    bgc_fp32_quaternion_copy(&conjugate->real_part, &quaternion->real_part);
    bgc_fp32_quaternion_get_reverse(&conjugate->real_part, &quaternion->dual_part);
}

inline void bgc_fp64_dual_quaternion_get_dual_conjugate(BGC_FP64_DualQuaternion* conjugate, const BGC_FP64_DualQuaternion* quaternion)
{
    bgc_fp64_quaternion_copy(&conjugate->real_part, &quaternion->real_part);
    bgc_fp64_quaternion_get_reverse(&conjugate->real_part, &quaternion->dual_part);
}

// ============== Fully Conjugate =============== //

inline void bgc_fp32_dual_quaternion_fully_conjugate(BGC_FP32_DualQuaternion* quaternion)
{
    quaternion->real_part.x1 = -quaternion->real_part.x1;
    quaternion->real_part.x2 = -quaternion->real_part.x2;
    quaternion->real_part.x3 = -quaternion->real_part.x3;

    quaternion->dual_part.s0 = -quaternion->dual_part.s0;
}

inline void bgc_fp64_dual_quaternion_fully_conjugate(BGC_FP64_DualQuaternion* quaternion)
{
    quaternion->real_part.x1 = -quaternion->real_part.x1;
    quaternion->real_part.x2 = -quaternion->real_part.x2;
    quaternion->real_part.x3 = -quaternion->real_part.x3;

    quaternion->dual_part.s0 = -quaternion->dual_part.s0;
}

// ============ Get Fully Conjugate ============= //

inline void bgc_fp32_dual_quaternion_get_fully_conjugate(BGC_FP32_DualQuaternion* conjugate, const BGC_FP32_DualQuaternion* quaternion)
{
    conjugate->real_part.s0 =  quaternion->real_part.s0;
    conjugate->real_part.x1 = -quaternion->real_part.x1;
    conjugate->real_part.x2 = -quaternion->real_part.x2;
    conjugate->real_part.x3 = -quaternion->real_part.x3;

    conjugate->dual_part.s0 = -quaternion->dual_part.s0;
    conjugate->dual_part.x1 =  quaternion->dual_part.x1;
    conjugate->dual_part.x2 =  quaternion->dual_part.x2;
    conjugate->dual_part.x3 =  quaternion->dual_part.x3;
}

inline void bgc_fp64_dual_quaternion_get_fully_conjugate(BGC_FP64_DualQuaternion* conjugate, const BGC_FP64_DualQuaternion* quaternion)
{
    conjugate->real_part.s0 =  quaternion->real_part.s0;
    conjugate->real_part.x1 = -quaternion->real_part.x1;
    conjugate->real_part.x2 = -quaternion->real_part.x2;
    conjugate->real_part.x3 = -quaternion->real_part.x3;

    conjugate->dual_part.s0 = -quaternion->dual_part.s0;
    conjugate->dual_part.x1 =  quaternion->dual_part.x1;
    conjugate->dual_part.x2 =  quaternion->dual_part.x2;
    conjugate->dual_part.x3 =  quaternion->dual_part.x3;
}

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

inline void bgc_fp32_dual_quaternion_add(BGC_FP32_DualQuaternion* sum, const BGC_FP32_DualQuaternion* first, const BGC_FP32_DualQuaternion* second)
{
    bgc_fp32_quaternion_add(&sum->real_part, &first->real_part, &second->real_part);
    bgc_fp32_quaternion_add(&sum->dual_part, &first->dual_part, &second->dual_part);
}

inline void bgc_fp64_dual_quaternion_add(BGC_FP64_DualQuaternion* sum, const BGC_FP64_DualQuaternion* first, const BGC_FP64_DualQuaternion* second)
{
    bgc_fp64_quaternion_add(&sum->real_part, &first->real_part, &second->real_part);
    bgc_fp64_quaternion_add(&sum->dual_part, &first->dual_part, &second->dual_part);
}

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

inline void bgc_fp32_dual_quaternion_add_scaled(BGC_FP32_DualQuaternion* sum, const BGC_FP32_DualQuaternion* base_quaternion, const BGC_FP32_DualQuaternion* scalable_quaternion, const float scale)
{
    bgc_fp32_quaternion_add_scaled(&sum->real_part, &base_quaternion->real_part, &scalable_quaternion->real_part, scale);
    bgc_fp32_quaternion_add_scaled(&sum->dual_part, &base_quaternion->dual_part, &scalable_quaternion->dual_part, scale);
}

inline void bgc_fp64_dual_quaternion_add_scaled(BGC_FP64_DualQuaternion* sum, const BGC_FP64_DualQuaternion* base_quaternion, const BGC_FP64_DualQuaternion* scalable_quaternion, const double scale)
{
    bgc_fp64_quaternion_add_scaled(&sum->real_part, &base_quaternion->real_part, &scalable_quaternion->real_part, scale);
    bgc_fp64_quaternion_add_scaled(&sum->dual_part, &base_quaternion->dual_part, &scalable_quaternion->dual_part, scale);
}

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

inline void bgc_fp32_dual_quaternion_subtract(BGC_FP32_DualQuaternion* difference, const BGC_FP32_DualQuaternion* minuend, const BGC_FP32_DualQuaternion* subtrahend)
{
    bgc_fp32_quaternion_subtract(&difference->real_part, &minuend->real_part, &subtrahend->real_part);
    bgc_fp32_quaternion_subtract(&difference->dual_part, &minuend->dual_part, &subtrahend->dual_part);
}

inline void bgc_fp64_dual_quaternion_subtract(BGC_FP64_DualQuaternion* difference, const BGC_FP64_DualQuaternion* minuend, const BGC_FP64_DualQuaternion* subtrahend)
{
    bgc_fp64_quaternion_subtract(&difference->real_part, &minuend->real_part, &subtrahend->real_part);
    bgc_fp64_quaternion_subtract(&difference->dual_part, &minuend->dual_part, &subtrahend->dual_part);
}

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

inline void bgc_fp32_dual_quaternion_subtract_scaled(BGC_FP32_DualQuaternion* difference, const BGC_FP32_DualQuaternion* base_quaternion, const BGC_FP32_DualQuaternion* scalable_quaternion, const float scale)
{
    bgc_fp32_quaternion_subtract_scaled(&difference->real_part, &base_quaternion->real_part, &scalable_quaternion->real_part, scale);
    bgc_fp32_quaternion_subtract_scaled(&difference->dual_part, &base_quaternion->dual_part, &scalable_quaternion->dual_part, scale);
}

inline void bgc_fp64_dual_quaternion_subtract_scaled(BGC_FP64_DualQuaternion* difference, const BGC_FP64_DualQuaternion* base_quaternion, const BGC_FP64_DualQuaternion* scalable_quaternion, const double scale)
{
    bgc_fp64_quaternion_subtract_scaled(&difference->real_part, &base_quaternion->real_part, &scalable_quaternion->real_part, scale);
    bgc_fp64_quaternion_subtract_scaled(&difference->dual_part, &base_quaternion->dual_part, &scalable_quaternion->dual_part, scale);
}

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

inline void bgc_fp32_dual_quaternion_multiply_by_real_number(BGC_FP32_DualQuaternion* product, const BGC_FP32_DualQuaternion* multiplicand, const float multiplier)
{
    bgc_fp32_quaternion_multiply_by_real(&product->real_part, &multiplicand->real_part, multiplier);
    bgc_fp32_quaternion_multiply_by_real(&product->dual_part, &multiplicand->dual_part, multiplier);
}

inline void bgc_fp64_dual_quaternion_multiply_by_real_number(BGC_FP64_DualQuaternion* product, const BGC_FP64_DualQuaternion* multiplicand, const double multiplier)
{
    bgc_fp64_quaternion_multiply_by_real(&product->real_part, &multiplicand->real_part, multiplier);
    bgc_fp64_quaternion_multiply_by_real(&product->dual_part, &multiplicand->dual_part, multiplier);
}

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

inline void bgc_fp32_dual_quaternion_multiply_by_dual_number(BGC_FP32_DualQuaternion* product, const BGC_FP32_DualQuaternion* multiplicand, const BGC_FP32_DualNumber* multiplier)
{
    BGC_FP32_Quaternion dual_part;

    bgc_fp32_quaternion_multiply_by_real(&dual_part, &multiplicand->dual_part, multiplier->real_part);
    bgc_fp32_quaternion_add_scaled(&dual_part, &dual_part, &multiplicand->real_part, multiplier->dual_part);

    bgc_fp32_quaternion_multiply_by_real(&product->real_part, &multiplicand->real_part, multiplier->real_part);
    bgc_fp32_quaternion_copy(&product->dual_part, &dual_part);
}

inline void bgc_fp64_dual_quaternion_multiply_by_dual_number(BGC_FP64_DualQuaternion* product, const BGC_FP64_DualQuaternion* multiplicand, const BGC_FP64_DualNumber* multiplier)
{
    BGC_FP64_Quaternion dual_part;

    bgc_fp64_quaternion_multiply_by_real(&dual_part, &multiplicand->dual_part, multiplier->real_part);
    bgc_fp64_quaternion_add_scaled(&dual_part, &dual_part, &multiplicand->real_part, multiplier->dual_part);

    bgc_fp64_quaternion_multiply_by_real(&product->real_part, &multiplicand->real_part, multiplier->real_part);
    bgc_fp64_quaternion_copy(&product->dual_part, &dual_part);
}

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

inline void bgc_fp32_dual_quaternion_multiply_by_conjugate_dual_number(BGC_FP32_DualQuaternion* product, const BGC_FP32_DualQuaternion* multiplicand, const BGC_FP32_DualNumber* multiplier_to_conjugate)
{
    BGC_FP32_Quaternion dual_part;

    bgc_fp32_quaternion_multiply_by_real(&dual_part, &multiplicand->dual_part, multiplier_to_conjugate->real_part);
    bgc_fp32_quaternion_subtract_scaled(&dual_part, &dual_part, &multiplicand->real_part, multiplier_to_conjugate->dual_part);

    bgc_fp32_quaternion_multiply_by_real(&product->real_part, &multiplicand->real_part, multiplier_to_conjugate->real_part);
    bgc_fp32_quaternion_copy(&product->dual_part, &dual_part);
}

inline void bgc_fp64_dual_quaternion_multiply_by_conjugate_dual_number(BGC_FP64_DualQuaternion* product, const BGC_FP64_DualQuaternion* multiplicand, const BGC_FP64_DualNumber* multiplier_to_conjugate)
{
    BGC_FP64_Quaternion dual_part;

    bgc_fp64_quaternion_multiply_by_real(&dual_part, &multiplicand->dual_part, multiplier_to_conjugate->real_part);
    bgc_fp64_quaternion_subtract_scaled(&dual_part, &dual_part, &multiplicand->real_part, multiplier_to_conjugate->dual_part);

    bgc_fp64_quaternion_multiply_by_real(&product->real_part, &multiplicand->real_part, multiplier_to_conjugate->real_part);
    bgc_fp64_quaternion_copy(&product->dual_part, &dual_part);
}

// ====== Multiply by (Regular) Quaternion ====== //

inline void bgc_fp32_dual_quaternion_multiply_by_quaternion(BGC_FP32_DualQuaternion* product, const BGC_FP32_DualQuaternion* multiplicand, const BGC_FP32_Quaternion* multiplier)
{
    bgc_fp32_quaternion_multiply_by_quaternion(&product->real_part, &multiplicand->real_part, multiplier);
    bgc_fp32_quaternion_multiply_by_quaternion(&product->dual_part, &multiplicand->dual_part, multiplier);
}

inline void bgc_fp64_dual_quaternion_multiply_by_quaternion(BGC_FP64_DualQuaternion* product, const BGC_FP64_DualQuaternion* multiplicand, const BGC_FP64_Quaternion* multiplier)
{
    bgc_fp64_quaternion_multiply_by_quaternion(&product->real_part, &multiplicand->real_part, multiplier);
    bgc_fp64_quaternion_multiply_by_quaternion(&product->dual_part, &multiplicand->dual_part, multiplier);
}

// ====== Multiply by Conjugate Quaternion ====== //

inline void bgc_fp32_dual_quaternion_multiply_by_conjugate_quaternion(BGC_FP32_DualQuaternion* product, const BGC_FP32_DualQuaternion* multiplicand, const BGC_FP32_Quaternion* multiplier_to_conjugate)
{
    bgc_fp32_quaternion_multiply_by_conjugate(&product->real_part, &multiplicand->real_part, multiplier_to_conjugate);
    bgc_fp32_quaternion_multiply_by_conjugate(&product->dual_part, &multiplicand->dual_part, multiplier_to_conjugate);
}

inline void bgc_fp64_dual_quaternion_multiply_by_conjugate_quaternion(BGC_FP64_DualQuaternion* product, const BGC_FP64_DualQuaternion* multiplicand, const BGC_FP64_Quaternion* multiplier_to_conjugate)
{
    bgc_fp64_quaternion_multiply_by_conjugate(&product->real_part, &multiplicand->real_part, multiplier_to_conjugate);
    bgc_fp64_quaternion_multiply_by_conjugate(&product->dual_part, &multiplicand->dual_part, multiplier_to_conjugate);
}

// ======== Multiply by Dual Quaternion ========= //

inline void bgc_fp32_dual_quaternion_multiply_by_dual_quaternion(BGC_FP32_DualQuaternion* product, const BGC_FP32_DualQuaternion* left, const BGC_FP32_DualQuaternion* right)
{
    BGC_FP32_Quaternion dual_part1, dual_part2;

    bgc_fp32_quaternion_multiply_by_quaternion(&dual_part1, &left->real_part, &right->dual_part);
    bgc_fp32_quaternion_multiply_by_quaternion(&dual_part2, &left->dual_part, &right->real_part);

    bgc_fp32_quaternion_multiply_by_quaternion(&product->real_part, &left->real_part, &right->real_part);
    bgc_fp32_quaternion_add(&product->dual_part, &dual_part1, &dual_part2);
}

inline void bgc_fp64_dual_quaternion_multiply_by_dual_quaternion(BGC_FP64_DualQuaternion* product, const BGC_FP64_DualQuaternion* left, const BGC_FP64_DualQuaternion* right)
{
    BGC_FP64_Quaternion dual_part1, dual_part2;

    bgc_fp64_quaternion_multiply_by_quaternion(&dual_part1, &left->real_part, &right->dual_part);
    bgc_fp64_quaternion_multiply_by_quaternion(&dual_part2, &left->dual_part, &right->real_part);

    bgc_fp64_quaternion_multiply_by_quaternion(&product->real_part, &left->real_part, &right->real_part);
    bgc_fp64_quaternion_add(&product->dual_part, &dual_part1, &dual_part2);
}

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

inline int bgc_fp32_dual_quaternion_divide_by_real_number(BGC_FP32_DualQuaternion* quotient, const BGC_FP32_DualQuaternion* dividend, const float divisor)
{
    if (bgc_fp32_is_zero(divisor)) {
        return BGC_FAILURE;
    }

    const float multiplier = 1.0f / divisor;

    bgc_fp32_quaternion_multiply_by_real(&quotient->real_part, &dividend->real_part, multiplier);
    bgc_fp32_quaternion_multiply_by_real(&quotient->dual_part, &dividend->dual_part, multiplier);

    return BGC_SUCCESS;
}

inline int bgc_fp64_dual_quaternion_divide_by_real_number(BGC_FP64_DualQuaternion* quotient, const BGC_FP64_DualQuaternion* dividend, const double divisor)
{
    if (bgc_fp64_is_zero(divisor)) {
        return BGC_FAILURE;
    }

    const double multiplier = 1.0 / divisor;

    bgc_fp64_quaternion_multiply_by_real(&quotient->real_part, &dividend->real_part, multiplier);
    bgc_fp64_quaternion_multiply_by_real(&quotient->dual_part, &dividend->dual_part, multiplier);

    return BGC_SUCCESS;
}

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

inline int bgc_fp32_dual_quaternion_divide_by_dual_number(BGC_FP32_DualQuaternion* quotient, const BGC_FP32_DualQuaternion* dividend, const BGC_FP32_DualNumber* divisor)
{
    const float square_modulus = divisor->real_part * divisor->real_part;

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

    bgc_fp32_dual_quaternion_multiply_by_conjugate_dual_number(quotient, dividend, divisor);
    bgc_fp32_dual_quaternion_multiply_by_real_number(quotient, quotient, 1.0f / square_modulus);

    return BGC_SUCCESS;
}

inline int bgc_fp64_dual_quaternion_divide_by_dual_number(BGC_FP64_DualQuaternion* quotient, const BGC_FP64_DualQuaternion* dividend, const BGC_FP64_DualNumber* divisor)
{
    const double square_modulus = divisor->real_part * divisor->real_part;

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

    bgc_fp64_dual_quaternion_multiply_by_conjugate_dual_number(quotient, dividend, divisor);
    bgc_fp64_dual_quaternion_multiply_by_real_number(quotient, quotient, 1.0 / square_modulus);

    return BGC_SUCCESS;
}

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

inline int bgc_fp32_dual_quaternion_divide_by_conjugate_dual_number(BGC_FP32_DualQuaternion* quotient, const BGC_FP32_DualQuaternion* dividend, const BGC_FP32_DualNumber* 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_quaternion_multiply_by_dual_number(quotient, dividend, divisor_to_conjugate);
    bgc_fp32_dual_quaternion_multiply_by_real_number(quotient, quotient, 1.0f / square_modulus);

    return BGC_SUCCESS;
}

inline int bgc_fp64_dual_quaternion_divide_by_conjugate_dual_number(BGC_FP64_DualQuaternion* quotient, const BGC_FP64_DualQuaternion* dividend, const BGC_FP64_DualNumber* 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_quaternion_multiply_by_dual_number(quotient, dividend, divisor_to_conjugate);
    bgc_fp64_dual_quaternion_multiply_by_real_number(quotient, quotient, 1.0 / square_modulus);

    return BGC_SUCCESS;
}

// ======= Divide by (Regular) Quaternion ======= //

inline int bgc_fp32_dual_quaternion_divide_by_quaternion(BGC_FP32_DualQuaternion* quotient, const BGC_FP32_DualQuaternion* dividend, const BGC_FP32_Quaternion* divisor)
{
    const float square_magnitude = bgc_fp32_quaternion_get_square_magnitude(divisor);

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

    const float multiplier = 1.0f / square_magnitude;

    bgc_fp32_quaternion_multiply_by_conjugate(&quotient->real_part, &dividend->real_part, divisor);
    bgc_fp32_quaternion_multiply_by_conjugate(&quotient->dual_part, &dividend->dual_part, divisor);

    bgc_fp32_quaternion_multiply_by_real(&quotient->real_part, &quotient->real_part, multiplier);
    bgc_fp32_quaternion_multiply_by_real(&quotient->dual_part, &quotient->dual_part, multiplier);

    return BGC_SUCCESS;
}

inline int bgc_fp64_dual_quaternion_divide_by_quaternion(BGC_FP64_DualQuaternion* quotient, const BGC_FP64_DualQuaternion* dividend, const BGC_FP64_Quaternion* divisor)
{
    const double square_magnitude = bgc_fp64_quaternion_get_square_magnitude(divisor);

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

    const double multiplier = 1.0 / square_magnitude;

    bgc_fp64_quaternion_multiply_by_conjugate(&quotient->real_part, &dividend->real_part, divisor);
    bgc_fp64_quaternion_multiply_by_conjugate(&quotient->dual_part, &dividend->dual_part, divisor);

    bgc_fp64_quaternion_multiply_by_real(&quotient->real_part, &quotient->real_part, multiplier);
    bgc_fp64_quaternion_multiply_by_real(&quotient->dual_part, &quotient->dual_part, multiplier);

    return BGC_SUCCESS;
}

// ======= Divide by Conjugate Quaternion ======= //

inline int bgc_fp32_dual_quaternion_divide_by_conjugate_quaternion(BGC_FP32_DualQuaternion* quotient, const BGC_FP32_DualQuaternion* dividend, const BGC_FP32_Quaternion* divisor_to_conjugate)
{
    const float square_magnitude = bgc_fp32_quaternion_get_square_magnitude(divisor_to_conjugate);

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

    const float multiplier = 1.0f / square_magnitude;

    bgc_fp32_quaternion_multiply_by_quaternion(&quotient->real_part, &dividend->real_part, divisor_to_conjugate);
    bgc_fp32_quaternion_multiply_by_quaternion(&quotient->dual_part, &dividend->dual_part, divisor_to_conjugate);

    bgc_fp32_quaternion_multiply_by_real(&quotient->real_part, &quotient->real_part, multiplier);
    bgc_fp32_quaternion_multiply_by_real(&quotient->dual_part, &quotient->dual_part, multiplier);

    return BGC_SUCCESS;
}

inline int bgc_fp64_dual_quaternion_divide_by_conjugate_quaternion(BGC_FP64_DualQuaternion* quotient, const BGC_FP64_DualQuaternion* dividend, const BGC_FP64_Quaternion* divisor_to_conjugate)
{
    const double square_magnitude = bgc_fp64_quaternion_get_square_magnitude(divisor_to_conjugate);

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

    const double multiplier = 1.0 / square_magnitude;

    bgc_fp64_quaternion_multiply_by_quaternion(&quotient->real_part, &dividend->real_part, divisor_to_conjugate);
    bgc_fp64_quaternion_multiply_by_quaternion(&quotient->dual_part, &dividend->dual_part, divisor_to_conjugate);

    bgc_fp64_quaternion_multiply_by_real(&quotient->real_part, &quotient->real_part, multiplier);
    bgc_fp64_quaternion_multiply_by_real(&quotient->dual_part, &quotient->dual_part, multiplier);

    return BGC_SUCCESS;
}

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

inline void bgc_fp32_dual_quaternion_get_mean2(BGC_FP32_DualQuaternion* mean, const BGC_FP32_DualQuaternion* quaternion1, const BGC_FP32_DualQuaternion* quaternion2)
{
    bgc_fp32_quaternion_get_mean2(&mean->real_part, &quaternion1->real_part, &quaternion2->real_part);
    bgc_fp32_quaternion_get_mean2(&mean->dual_part, &quaternion1->dual_part, &quaternion2->dual_part);
}

inline void bgc_fp64_dual_quaternion_get_mean2(BGC_FP64_DualQuaternion* mean, const BGC_FP64_DualQuaternion* quaternion1, const BGC_FP64_DualQuaternion* quaternion2)
{
    bgc_fp64_quaternion_get_mean2(&mean->real_part, &quaternion1->real_part, &quaternion2->real_part);
    bgc_fp64_quaternion_get_mean2(&mean->dual_part, &quaternion1->dual_part, &quaternion2->dual_part);
}

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

inline void bgc_fp32_dual_quaternion_get_mean3(BGC_FP32_DualQuaternion* mean, const BGC_FP32_DualQuaternion* quaternion1, const BGC_FP32_DualQuaternion* quaternion2, const BGC_FP32_DualQuaternion* quaternion3)
{
    bgc_fp32_quaternion_get_mean3(&mean->real_part, &quaternion1->real_part, &quaternion2->real_part, &quaternion3->real_part);
    bgc_fp32_quaternion_get_mean3(&mean->dual_part, &quaternion1->dual_part, &quaternion2->dual_part, &quaternion3->dual_part);
}

inline void bgc_fp64_dual_quaternion_get_mean3(BGC_FP64_DualQuaternion* mean, const BGC_FP64_DualQuaternion* quaternion1, const BGC_FP64_DualQuaternion* quaternion2, const BGC_FP64_DualQuaternion* quaternion3)
{
    bgc_fp64_quaternion_get_mean3(&mean->real_part, &quaternion1->real_part, &quaternion2->real_part, &quaternion3->real_part);
    bgc_fp64_quaternion_get_mean3(&mean->dual_part, &quaternion1->dual_part, &quaternion2->dual_part, &quaternion3->dual_part);
}

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

inline void bgc_fp32_dual_quaternion_interpolate(BGC_FP32_DualQuaternion* interpolation, const BGC_FP32_DualQuaternion* first, const BGC_FP32_DualQuaternion* second, const float phase)
{
    bgc_fp32_quaternion_interpolate(&interpolation->real_part, &first->real_part, &second->real_part, phase);
    bgc_fp32_quaternion_interpolate(&interpolation->dual_part, &first->dual_part, &second->dual_part, phase);
}

inline void bgc_fp64_dual_quaternion_interpolate(BGC_FP64_DualQuaternion* interpolation, const BGC_FP64_DualQuaternion* first, const BGC_FP64_DualQuaternion* second, const double phase)
{
    bgc_fp64_quaternion_interpolate(&interpolation->real_part, &first->real_part, &second->real_part, phase);
    bgc_fp64_quaternion_interpolate(&interpolation->dual_part, &first->dual_part, &second->dual_part, phase);
}

#endif