#ifndef _BASIC_GEOMETRY_QUATERNION_H_
#define _BASIC_GEOMETRY_QUATERNION_H_

#include <math.h>

#include "basis.h"
#include "angle.h"
#include "matrix3x3.h"

typedef struct {
    float s0, x1, x2, x3;
} quaternion_fp32_t;

typedef struct {
    double s0, x1, x2, x3;
} quaternion_fp64_t;

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

inline void quaternion_reset_fp32(quaternion_fp32_t * quaternion)
{
    quaternion->s0 = 0.0f;
    quaternion->x1 = 0.0f;
    quaternion->x2 = 0.0f;
    quaternion->x3 = 0.0f;
}

inline void quaternion_reset_fp64(quaternion_fp64_t * quaternion)
{
    quaternion->s0 = 0.0;
    quaternion->x1 = 0.0;
    quaternion->x2 = 0.0;
    quaternion->x3 = 0.0;
}

// ================== Set Unit ================== //

inline void quaternion_fp32_set_identity(quaternion_fp32_t * quaternion)
{
    quaternion->s0 = 1.0f;
    quaternion->x1 = 0.0f;
    quaternion->x2 = 0.0f;
    quaternion->x3 = 0.0f;
}

inline void quaternion_fp64_set_identity(quaternion_fp64_t * quaternion)
{
    quaternion->s0 = 1.0;
    quaternion->x1 = 0.0;
    quaternion->x2 = 0.0;
    quaternion->x3 = 0.0;
}

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

inline void quaternion_fp32_set_values(const float s0, const float x1, const float x2, const float x3, quaternion_fp32_t * quaternion)
{
    quaternion->s0 = s0;
    quaternion->x1 = x1;
    quaternion->x2 = x2;
    quaternion->x3 = x3;
}

inline void quaternion_fp64_set_values(const double s0, const double x1, const double x2, const double x3, quaternion_fp64_t * quaternion)
{
    quaternion->s0 = s0;
    quaternion->x1 = x1;
    quaternion->x2 = x2;
    quaternion->x3 = x3;
}

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

inline void quaternion_copy_fp32(const quaternion_fp32_t* from, quaternion_fp32_t* to)
{
    to->s0 = from->s0;
    to->x1 = from->x1;
    to->x2 = from->x2;
    to->x3 = from->x3;
}

inline void quaternion_copy_fp64(const quaternion_fp64_t* from, quaternion_fp64_t* to)
{
    to->s0 = from->s0;
    to->x1 = from->x1;
    to->x2 = from->x2;
    to->x3 = from->x3;
}

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

inline void quaternion_swap_fp32(quaternion_fp32_t* quarternion1, quaternion_fp32_t* quarternion2)
{
    const float s0 = quarternion2->s0;
    const float x1 = quarternion2->x1;
    const float x2 = quarternion2->x2;
    const float x3 = quarternion2->x3;

    quarternion2->s0 = quarternion1->s0;
    quarternion2->x1 = quarternion1->x1;
    quarternion2->x2 = quarternion1->x2;
    quarternion2->x3 = quarternion1->x3;

    quarternion1->s0 = s0;
    quarternion1->x1 = x1;
    quarternion1->x2 = x2;
    quarternion1->x3 = x3;
}

inline void quaternion_swap_fp64(quaternion_fp64_t* quarternion1, quaternion_fp64_t* quarternion2)
{
    const double s0 = quarternion2->s0;
    const double x1 = quarternion2->x1;
    const double x2 = quarternion2->x2;
    const double x3 = quarternion2->x3;

    quarternion2->s0 = quarternion1->s0;
    quarternion2->x1 = quarternion1->x1;
    quarternion2->x2 = quarternion1->x2;
    quarternion2->x3 = quarternion1->x3;

    quarternion1->s0 = s0;
    quarternion1->x1 = x1;
    quarternion1->x2 = x2;
    quarternion1->x3 = x3;
}

// ============= Copy to twin type ============== //

inline void quaternion_fp32_set_from_fp64(const quaternion_fp64_t* quaternion, quaternion_fp32_t* result)
{
    result->s0 = (float) quaternion->s0;
    result->x1 = (float) quaternion->x1;
    result->x2 = (float) quaternion->x2;
    result->x3 = (float) quaternion->x3;
}

inline void quaternion_fp64_set_from_fp32(const quaternion_fp32_t* quaternion, quaternion_fp64_t* result)
{
    result->s0 = quaternion->s0;
    result->x1 = quaternion->x1;
    result->x2 = quaternion->x2;
    result->x3 = quaternion->x3;
}

// ================= Inversion ================== //

inline void quaternion_fp32_conjugate(quaternion_fp32_t* quaternion)
{
    quaternion->x1 = -quaternion->x1;
    quaternion->x2 = -quaternion->x2;
    quaternion->x3 = -quaternion->x3;
}

inline void quaternion_fp64_conjugate(quaternion_fp64_t* quaternion)
{
    quaternion->x1 = -quaternion->x1;
    quaternion->x2 = -quaternion->x2;
    quaternion->x3 = -quaternion->x3;
}

// ================ Set Conjugate =============== //

inline void quaternion_fp32_set_conjugate(const quaternion_fp32_t* quaternion, quaternion_fp32_t* result)
{
    result->s0 = quaternion->s0;
    result->x1 = -quaternion->x1;
    result->x2 = -quaternion->x2;
    result->x3 = -quaternion->x3;
}

inline void quaternion_fp64_set_conjugate(const quaternion_fp64_t* quaternion, quaternion_fp64_t* result)
{
    result->s0 = quaternion->s0;
    result->x1 = -quaternion->x1;
    result->x2 = -quaternion->x2;
    result->x3 = -quaternion->x3;
}

// ================ Set Conjugate =============== //

inline void quaternion_fp32_set_conjugate_fp64(const quaternion_fp64_t* quaternion, quaternion_fp32_t* result)
{
    result->s0 = (float) quaternion->s0;
    result->x1 = (float) -quaternion->x1;
    result->x2 = (float) -quaternion->x2;
    result->x3 = (float) -quaternion->x3;
}

inline void quaternion_fp64_set_conjugate_fp32(const quaternion_fp32_t* quaternion, quaternion_fp64_t* result)
{
    result->s0 = quaternion->s0;
    result->x1 = -quaternion->x1;
    result->x2 = -quaternion->x2;
    result->x3 = -quaternion->x3;
}

// ============= Get Square Modulus ============= //

inline float quaternion_get_square_modulus_fp32(const quaternion_fp32_t* quaternion)
{
    return (quaternion->s0 * quaternion->s0 + quaternion->x1 * quaternion->x1) + (quaternion->x2 * quaternion->x2 + quaternion->x3 * quaternion->x3);
}

inline double quaternion_get_square_modulus_fp64(const quaternion_fp64_t* quaternion)
{
    return (quaternion->s0 * quaternion->s0 + quaternion->x1 * quaternion->x1) + (quaternion->x2 * quaternion->x2 + quaternion->x3 * quaternion->x3);
}

// ================ Get Modulus ================= //

inline float quaternion_get_modulus_fp32(const quaternion_fp32_t* quaternion)
{
    return sqrtf(quaternion_get_square_modulus_fp32(quaternion));
}

inline double quaternion_get_modulus_fp64(const quaternion_fp64_t* quaternion)
{
    return sqrt(quaternion_get_square_modulus_fp64(quaternion));
}

// =============== Normalization ================ //

inline int quaternion_fp32_normalize(quaternion_fp32_t* quaternion)
{
    const float square_modulus = quaternion_get_square_modulus_fp32(quaternion);

    if (1.0f - FP32_TWO_EPSYLON <= square_modulus && square_modulus <= 1.0f + FP32_TWO_EPSYLON) {
        return 1;
    }

    if (square_modulus <= FP32_SQUARE_EPSYLON) {
        quaternion_reset_fp32(quaternion);
        return 0;
    }

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

    quaternion->s0 *= multiplier;
    quaternion->x1 *= multiplier;
    quaternion->x2 *= multiplier;
    quaternion->x3 *= multiplier;

    return 1;
}

inline int quaternion_fp64_normalize(quaternion_fp64_t* quaternion)
{
    const double square_modulus = quaternion_get_square_modulus_fp64(quaternion);

    if (1.0 - FP64_TWO_EPSYLON <= square_modulus && square_modulus <= 1.0 + FP64_TWO_EPSYLON) {
        return 1;
    }

    if (square_modulus <= FP32_SQUARE_EPSYLON) {
        quaternion_reset_fp64(quaternion);
        return 0;
    }

    const double multiplier = sqrt(1.0 / square_modulus);

    quaternion->s0 *= multiplier;
    quaternion->x1 *= multiplier;
    quaternion->x2 *= multiplier;
    quaternion->x3 *= multiplier;

    return 1;
}

// ============ Make Rotation Matrix ============ //

inline void quaternion_fp32_get_rotation_matrix(const quaternion_fp32_t* quaternion, matrix3x3_fp32_t* matrix)
{
    const float s0s0 = quaternion->s0 * quaternion->s0;
    const float x1x1 = quaternion->x1 * quaternion->x1;
    const float x2x2 = quaternion->x2 * quaternion->x2;
    const float x3x3 = quaternion->x3 * quaternion->x3;

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

    if (-FP32_EPSYLON <= square_modulus && square_modulus <= FP32_EPSYLON)
    {
        matrix3x3_fp32_set_to_identity(matrix);
        return;
    }

    const float corrector1 = 1.0f / square_modulus;
    const float corrector2 = 2.0f * corrector1;

    const float s0x1 = quaternion->s0 * quaternion->x1;
    const float s0x2 = quaternion->s0 * quaternion->x2;
    const float s0x3 = quaternion->s0 * quaternion->x3;
    const float x1x2 = quaternion->x1 * quaternion->x2;
    const float x1x3 = quaternion->x1 * quaternion->x3;
    const float x2x3 = quaternion->x2 * quaternion->x3;

    matrix->r1c1 = corrector1 * ((s0s0 + x1x1) - (x2x2 + x3x3));
    matrix->r2c2 = corrector1 * ((s0s0 + x2x2) - (x1x1 + x3x3));
    matrix->r3c3 = corrector1 * ((s0s0 + x3x3) - (x1x1 + x2x2));

    matrix->r1c2 = corrector2 * (x1x2 - s0x3);
    matrix->r2c3 = corrector2 * (x2x3 - s0x1);
    matrix->r3c1 = corrector2 * (x1x3 - s0x2);

    matrix->r2c1 = corrector2 * (x1x2 + s0x3);
    matrix->r3c2 = corrector2 * (x2x3 + s0x1);
    matrix->r1c3 = corrector2 * (x1x3 + s0x2);
}

inline void quaternion_fp64_get_rotation_matrix(const quaternion_fp64_t* quaternion, matrix3x3_fp64_t* matrix)
{
    const double s0s0 = quaternion->s0 * quaternion->s0;
    const double x1x1 = quaternion->x1 * quaternion->x1;
    const double x2x2 = quaternion->x2 * quaternion->x2;
    const double x3x3 = quaternion->x3 * quaternion->x3;

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

    if (-FP64_EPSYLON <= square_modulus && square_modulus <= FP64_EPSYLON)
    {
        matrix3x3_fp64_set_to_identity(matrix);
        return;
    }

    const double corrector1 = 1.0f / square_modulus;
    const double corrector2 = 2.0f * corrector1;

    const double s0x1 = quaternion->s0 * quaternion->x1;
    const double s0x2 = quaternion->s0 * quaternion->x2;
    const double s0x3 = quaternion->s0 * quaternion->x3;
    const double x1x2 = quaternion->x1 * quaternion->x2;
    const double x1x3 = quaternion->x1 * quaternion->x3;
    const double x2x3 = quaternion->x2 * quaternion->x3;

    matrix->r1c1 = corrector1 * ((s0s0 + x1x1) - (x2x2 + x3x3));
    matrix->r2c2 = corrector1 * ((s0s0 + x2x2) - (x1x1 + x3x3));
    matrix->r3c3 = corrector1 * ((s0s0 + x3x3) - (x1x1 + x2x2));

    matrix->r1c2 = corrector2 * (x1x2 - s0x3);
    matrix->r2c3 = corrector2 * (x2x3 - s0x1);
    matrix->r3c1 = corrector2 * (x1x3 - s0x2);

    matrix->r2c1 = corrector2 * (x1x2 + s0x3);
    matrix->r3c2 = corrector2 * (x2x3 + s0x1);
    matrix->r1c3 = corrector2 * (x1x3 + s0x2);
}

// ============ Make Reverse Matrix ============= //

inline void quaternion_fp32_get_reverse_matrix(const quaternion_fp32_t* quaternion, matrix3x3_fp32_t* matrix)
{
    const float s0s0 = quaternion->s0 * quaternion->s0;
    const float x1x1 = quaternion->x1 * quaternion->x1;
    const float x2x2 = quaternion->x2 * quaternion->x2;
    const float x3x3 = quaternion->x3 * quaternion->x3;

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

    if (-FP32_EPSYLON <= square_modulus && square_modulus <= FP32_EPSYLON)
    {
        matrix3x3_fp32_set_to_identity(matrix);
        return;
    }

    const float corrector1 = 1.0f / square_modulus;
    const float corrector2 = 2.0f * corrector1;

    const float s0x1 = quaternion->s0 * quaternion->x1;
    const float s0x2 = quaternion->s0 * quaternion->x2;
    const float s0x3 = quaternion->s0 * quaternion->x3;
    const float x1x2 = quaternion->x1 * quaternion->x2;
    const float x1x3 = quaternion->x1 * quaternion->x3;
    const float x2x3 = quaternion->x2 * quaternion->x3;

    matrix->r1c1 = corrector1 * ((s0s0 + x1x1) - (x2x2 + x3x3));
    matrix->r2c2 = corrector1 * ((s0s0 + x2x2) - (x1x1 + x3x3));
    matrix->r3c3 = corrector1 * ((s0s0 + x3x3) - (x1x1 + x2x2));

    matrix->r1c2 = corrector2 * (x1x2 + s0x3);
    matrix->r2c3 = corrector2 * (x2x3 + s0x1);
    matrix->r3c1 = corrector2 * (x1x3 + s0x2);

    matrix->r2c1 = corrector2 * (x1x2 - s0x3);
    matrix->r3c2 = corrector2 * (x2x3 - s0x1);
    matrix->r1c3 = corrector2 * (x1x3 - s0x2);
}

inline void quaternion_fp64_get_reverse_matrix(const quaternion_fp64_t* quaternion, matrix3x3_fp64_t* matrix)
{
    const double s0s0 = quaternion->s0 * quaternion->s0;
    const double x1x1 = quaternion->x1 * quaternion->x1;
    const double x2x2 = quaternion->x2 * quaternion->x2;
    const double x3x3 = quaternion->x3 * quaternion->x3;

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

    if (-FP64_EPSYLON <= square_modulus && square_modulus <= FP64_EPSYLON)
    {
        matrix3x3_fp64_set_to_identity(matrix);
        return;
    }

    const double corrector1 = 1.0f / square_modulus;
    const double corrector2 = 2.0f * corrector1;

    const double s0x1 = quaternion->s0 * quaternion->x1;
    const double s0x2 = quaternion->s0 * quaternion->x2;
    const double s0x3 = quaternion->s0 * quaternion->x3;
    const double x1x2 = quaternion->x1 * quaternion->x2;
    const double x1x3 = quaternion->x1 * quaternion->x3;
    const double x2x3 = quaternion->x2 * quaternion->x3;

    matrix->r1c1 = corrector1 * ((s0s0 + x1x1) - (x2x2 + x3x3));
    matrix->r2c2 = corrector1 * ((s0s0 + x2x2) - (x1x1 + x3x3));
    matrix->r3c3 = corrector1 * ((s0s0 + x3x3) - (x1x1 + x2x2));

    matrix->r1c2 = corrector2 * (x1x2 + s0x3);
    matrix->r2c3 = corrector2 * (x2x3 + s0x1);
    matrix->r3c1 = corrector2 * (x1x3 + s0x2);

    matrix->r2c1 = corrector2 * (x1x2 - s0x3);
    matrix->r3c2 = corrector2 * (x2x3 - s0x1);
    matrix->r1c3 = corrector2 * (x1x3 - s0x2);
}

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

inline void quaternion_fp32_add(const quaternion_fp32_t * quaternion1, const quaternion_fp32_t * quaternion2, quaternion_fp32_t * result)
{
    result->s0 = quaternion1->s0 + quaternion2->s0;
    result->x1 = quaternion1->x1 + quaternion2->x1;
    result->x2 = quaternion1->x2 + quaternion2->x2;
    result->x3 = quaternion1->x3 + quaternion2->x3;
}

inline void quaternion_fp64_add(const quaternion_fp64_t * quaternion1, const quaternion_fp64_t * quaternion2, quaternion_fp64_t * result)
{
    result->s0 = quaternion1->s0 + quaternion2->s0;
    result->x1 = quaternion1->x1 + quaternion2->x1;
    result->x2 = quaternion1->x2 + quaternion2->x2;
    result->x3 = quaternion1->x3 + quaternion2->x3;
}

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

inline void quaternion_fp32_subtract(const quaternion_fp32_t * minuend, const quaternion_fp32_t * subtrahend, quaternion_fp32_t * difference)
{
    difference->s0 = minuend->s0 - subtrahend->s0;
    difference->x1 = minuend->x1 - subtrahend->x1;
    difference->x2 = minuend->x2 - subtrahend->x2;
    difference->x3 = minuend->x3 - subtrahend->x3;
}

inline void quaternion_fp64_subtract(const quaternion_fp64_t * minuend, const quaternion_fp64_t * subtrahend, quaternion_fp64_t * difference)
{
    difference->s0 = minuend->s0 - subtrahend->s0;
    difference->x1 = minuend->x1 - subtrahend->x1;
    difference->x2 = minuend->x2 - subtrahend->x2;
    difference->x3 = minuend->x3 - subtrahend->x3;
}

// =============== Multiplication =============== //

inline void quaternion_fp32_multiply(const quaternion_fp32_t* multiplicand, const float multipier, quaternion_fp32_t* product)
{
    product->s0 = multiplicand->s0 * multipier;
    product->x1 = multiplicand->x1 * multipier;
    product->x2 = multiplicand->x2 * multipier;
    product->x3 = multiplicand->x3 * multipier;
}

inline void quaternion_fp64_multiply(const quaternion_fp64_t* multiplicand, const double multipier, quaternion_fp64_t* product)
{
    product->s0 = multiplicand->s0 * multipier;
    product->x1 = multiplicand->x1 * multipier;
    product->x2 = multiplicand->x2 * multipier;
    product->x3 = multiplicand->x3 * multipier;
}

// ================== Division ================== //

inline void quaternion_fp32_divide(const quaternion_fp32_t* dividend, const float divisor, quaternion_fp32_t* quotient)
{
    quaternion_fp32_multiply(dividend, 1.0f / divisor, quotient);
}

inline void quaternion_fp64_divide(const quaternion_fp64_t* dividend, const double divisor, quaternion_fp64_t* quotient)
{
    quaternion_fp64_multiply(dividend, 1.0 / divisor, quotient);
}

// ================== Product =================== //

inline void quaternion_fp32_get_product(const quaternion_fp32_t* left, const quaternion_fp32_t* right, quaternion_fp32_t* product)
{
    const float s0 = (left->s0 * right->s0 - left->x1 * right->x1) - (left->x2 * right->x2 + left->x3 * right->x3);
    const float x1 = (left->x1 * right->s0 + left->s0 * right->x1) - (left->x3 * right->x2 - left->x2 * right->x3);
    const float x2 = (left->x2 * right->s0 + left->s0 * right->x2) - (left->x1 * right->x3 - left->x3 * right->x1);
    const float x3 = (left->x3 * right->s0 + left->s0 * right->x3) - (left->x2 * right->x1 - left->x1 * right->x2);

    product->s0 = s0;
    product->x1 = x1;
    product->x2 = x2;
    product->x3 = x3;
}

inline void quaternion_fp64_get_product(const quaternion_fp64_t* left, const quaternion_fp64_t* right, quaternion_fp64_t* product)
{
    const double s0 = (left->s0 * right->s0 - left->x1 * right->x1) - (left->x2 * right->x2 + left->x3 * right->x3);
    const double x1 = (left->x1 * right->s0 + left->s0 * right->x1) - (left->x3 * right->x2 - left->x2 * right->x3);
    const double x2 = (left->x2 * right->s0 + left->s0 * right->x2) - (left->x1 * right->x3 - left->x3 * right->x1);
    const double x3 = (left->x3 * right->s0 + left->s0 * right->x3) - (left->x2 * right->x1 - left->x1 * right->x2);

    product->s0 = s0;
    product->x1 = x1;
    product->x2 = x2;
    product->x3 = x3;
}

#endif // _GEOMETRY_QUATERNION_H_