#include <math.h>

#include "angle.h"
#include "versor.h"

const BgFP32Versor BG_FP32_IDLE_VERSOR = { 1.0f, 0.0f, 0.0f, 0.0f };

const BgFP64Versor BG_FP64_IDLE_VERSOR = { 1.0, 0.0, 0.0, 0.0 };

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

void bg_fp32_versor_set_values(const float s0, const float x1, const float x2, const float x3, BgFP32Versor* versor)
{
    __BgFP32DarkTwinVersor* twin = (__BgFP32DarkTwinVersor*)versor;

    twin->s0 = s0;
    twin->x1 = x1;
    twin->x2 = x2;
    twin->x3 = x3;

    const float square_modulus = (s0 * s0 + x1 * x1) + (x2 * x2 + x3 * x3);

    if (1.0f - BG_FP32_TWO_EPSYLON <= square_modulus && square_modulus <= 1.0f + BG_FP32_TWO_EPSYLON) {
        return;
    }

    if (square_modulus <= BG_FP32_SQUARE_EPSYLON) {
        twin->s0 = 1.0f;
        twin->x1 = 0.0f;
        twin->x2 = 0.0f;
        twin->x3 = 0.0f;
        return;
    }

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

    twin->s0 *= multiplier;
    twin->x1 *= multiplier;
    twin->x2 *= multiplier;
    twin->x3 *= multiplier;
}

void bg_fp64_versor_set_values(const double s0, const double x1, const double x2, const double x3, BgFP64Versor* versor)
{
    __BgFP64DarkTwinVersor* twin = (__BgFP64DarkTwinVersor*)versor;

    twin->s0 = s0;
    twin->x1 = x1;
    twin->x2 = x2;
    twin->x3 = x3;

    const double square_modulus = (s0 * s0 + x1 * x1) + (x2 * x2 + x3 * x3);

    if (1.0 - BG_FP64_TWO_EPSYLON <= square_modulus && square_modulus <= 1.0 + BG_FP64_TWO_EPSYLON) {
        return;
    }

    if (square_modulus <= BG_FP64_SQUARE_EPSYLON) {
        twin->s0 = 1.0;
        twin->x1 = 0.0;
        twin->x2 = 0.0;
        twin->x3 = 0.0;
        return;
    }

    const double multiplier = sqrt(1.0 / square_modulus);

    twin->s0 *= multiplier;
    twin->x1 *= multiplier;
    twin->x2 *= multiplier;
    twin->x3 *= multiplier;
}

// =============== Set Crude Turn =============== //

void bg_fp32_versor_set_crude_turn(const float x1, const float x2, const float x3, const float angle, const angle_unit_t unit, BgFP32Versor* result)
{
    const float square_vector = x1 * x1 + x2 * x2 + x3 * x3;

    if (square_vector <= BG_FP32_SQUARE_EPSYLON) {
        bg_fp32_versor_reset(result);
        return;
    }

    const float half_angle = bg_fp32_angle_to_radians(0.5f * angle, unit);

    const float sine = sinf(half_angle);

    if (-BG_FP32_EPSYLON <= sine && sine <= BG_FP32_EPSYLON) {
        bg_fp32_versor_reset(result);
        return;
    }

    const float multiplier = sine / sqrtf(square_vector);

    bg_fp32_versor_set_values(cosf(half_angle), x1 * multiplier, x2 * multiplier, x3 * multiplier, result);
}

void bg_fp64_versor_set_crude_turn(const double x1, const double x2, const double x3, const double angle, const angle_unit_t unit, BgFP64Versor* result)
{
    const double square_vector = x1 * x1 + x2 * x2 + x3 * x3;

    if (square_vector <= BG_FP64_SQUARE_EPSYLON) {
        bg_fp64_versor_reset(result);
        return;
    }

    const double half_angle = bg_fp64_angle_to_radians(0.5 * angle, unit);

    const double sine = sin(half_angle);

    if (-BG_FP64_EPSYLON <= sine && sine <= BG_FP64_EPSYLON) {
        bg_fp64_versor_reset(result);
        return;
    }

    const double multiplier = sine / sqrt(square_vector);

    bg_fp64_versor_set_values(cos(half_angle), x1 * multiplier, x2 * multiplier, x3 * multiplier, result);
}

// ================= Rotation3 ================== //

void bg_fp32_versor_get_rotation(const BgFP32Versor* versor, BgFP32Rotation3* result)
{
    if (versor == 0 || result == 0) {
        return;
    }

    if (versor->s0 <= -(1.0f - BG_FP32_EPSYLON) || 1.0f - BG_FP32_EPSYLON <= versor->s0) {
        bg_fp32_rotation_reset(result);
        return;
    }

    const float square_vector = versor->x1 * versor->x1 + versor->x2 * versor->x2 + versor->x3 * versor->x3;

    result->radians = 2.0f * acosf(versor->s0 / sqrtf(versor->s0 * versor->s0 + square_vector));

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

    result->axis.x1 = versor->x1 * multiplier;
    result->axis.x2 = versor->x2 * multiplier;
    result->axis.x3 = versor->x3 * multiplier;
}

void bg_fp64_versor_get_rotation(const BgFP64Versor* versor, BgFP64Rotation3* result)
{
    if (versor == 0 || result == 0) {
        return;
    }

    if (versor->s0 <= -(1.0 - BG_FP64_EPSYLON) || 1.0 - BG_FP64_EPSYLON <= versor->s0) {
        bg_fp64_rotation_reset(result);
        return;
    }

    const double square_vector = versor->x1 * versor->x1 + versor->x2 * versor->x2 + versor->x3 * versor->x3;

    result->radians = 2.0 * acos(versor->s0 / sqrt(versor->s0 * versor->s0 + square_vector));

    const double multiplier = sqrt(1.0 / square_vector);

    result->axis.x1 = versor->x1 * multiplier;
    result->axis.x2 = versor->x2 * multiplier;
    result->axis.x3 = versor->x3 * multiplier;
}

// ================ Combination ================= //

void bg_fp32_versor_combine(const BgFP32Versor* second, const BgFP32Versor* first, BgFP32Versor* result)
{
    const float s0 = (second->s0 * first->s0 - second->x1 * first->x1) - (second->x2 * first->x2 + second->x3 * first->x3);
    const float x1 = (second->x1 * first->s0 + second->s0 * first->x1) - (second->x3 * first->x2 - second->x2 * first->x3);
    const float x2 = (second->x2 * first->s0 + second->s0 * first->x2) - (second->x1 * first->x3 - second->x3 * first->x1);
    const float x3 = (second->x3 * first->s0 + second->s0 * first->x3) - (second->x2 * first->x1 - second->x1 * first->x2);

    const float square_modulus = (s0 * s0 + x1 * x1) + (x2 * x2 + x3 * x3);

    __BgFP32DarkTwinVersor* twin = (__BgFP32DarkTwinVersor*)result;

    twin->s0 = s0;
    twin->x1 = x1;
    twin->x2 = x2;
    twin->x3 = x3;

    if (1.0f - BG_FP32_TWO_EPSYLON <= square_modulus && square_modulus <= 1.0f + BG_FP32_TWO_EPSYLON) {
        return;
    }

    if (square_modulus <= BG_FP32_SQUARE_EPSYLON) {
        twin->s0 = 1.0f;
        twin->x1 = 0.0f;
        twin->x2 = 0.0f;
        twin->x3 = 0.0f;
        return;
    }

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

    twin->s0 *= multiplier;
    twin->x1 *= multiplier;
    twin->x2 *= multiplier;
    twin->x3 *= multiplier;
}

void bg_fp64_versor_combine(const BgFP64Versor* second, const BgFP64Versor* first, BgFP64Versor* result)
{
    const double s0 = (second->s0 * first->s0 - second->x1 * first->x1) - (second->x2 * first->x2 + second->x3 * first->x3);
    const double x1 = (second->x1 * first->s0 + second->s0 * first->x1) - (second->x3 * first->x2 - second->x2 * first->x3);
    const double x2 = (second->x2 * first->s0 + second->s0 * first->x2) - (second->x1 * first->x3 - second->x3 * first->x1);
    const double x3 = (second->x3 * first->s0 + second->s0 * first->x3) - (second->x2 * first->x1 - second->x1 * first->x2);

    const double square_modulus = (s0 * s0 + x1 * x1) + (x2 * x2 + x3 * x3);

    __BgFP64DarkTwinVersor* twin = (__BgFP64DarkTwinVersor*)result;

    twin->s0 = s0;
    twin->x1 = x1;
    twin->x2 = x2;
    twin->x3 = x3;

    if (1.0 - BG_FP64_TWO_EPSYLON <= square_modulus && square_modulus <= 1.0 + BG_FP64_TWO_EPSYLON) {
        return;
    }

    if (square_modulus <= BG_FP64_SQUARE_EPSYLON) {
        twin->s0 = 1.0;
        twin->x1 = 0.0;
        twin->x2 = 0.0;
        twin->x3 = 0.0;
        return;
    }

    const double multiplier = sqrt(1.0 / square_modulus);

    twin->s0 *= multiplier;
    twin->x1 *= multiplier;
    twin->x2 *= multiplier;
    twin->x3 *= multiplier;
}

// =========== Make Rotation Matrix3x3 ========== //

void bg_fp32_versor_get_rotation_matrix(const BgFP32Versor* versor, BgFP32Matrix3x3* matrix)
{
    const float s0s0 = versor->s0 * versor->s0;
    const float x1x1 = versor->x1 * versor->x1;
    const float x2x2 = versor->x2 * versor->x2;
    const float x3x3 = versor->x3 * versor->x3;

    const float s0x1 = 2.0f * versor->s0 * versor->x1;
    const float s0x2 = 2.0f * versor->s0 * versor->x2;
    const float s0x3 = 2.0f * versor->s0 * versor->x3;

    const float x1x2 = 2.0f * versor->x1 * versor->x2;
    const float x1x3 = 2.0f * versor->x1 * versor->x3;
    const float x2x3 = 2.0f * versor->x2 * versor->x3;

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

    matrix->r1c2 = x1x2 - s0x3;
    matrix->r2c3 = x2x3 - s0x1;
    matrix->r3c1 = x1x3 - s0x2;

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

void bg_fp64_versor_get_rotation_matrix(const BgFP64Versor* versor, BgFP64Matrix3x3* matrix)
{
    const double s0s0 = versor->s0 * versor->s0;
    const double x1x1 = versor->x1 * versor->x1;
    const double x2x2 = versor->x2 * versor->x2;
    const double x3x3 = versor->x3 * versor->x3;

    const double s0x1 = 2.0 * versor->s0 * versor->x1;
    const double s0x2 = 2.0 * versor->s0 * versor->x2;
    const double s0x3 = 2.0 * versor->s0 * versor->x3;

    const double x1x2 = 2.0 * versor->x1 * versor->x2;
    const double x1x3 = 2.0 * versor->x1 * versor->x3;
    const double x2x3 = 2.0 * versor->x2 * versor->x3;

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

    matrix->r1c2 = x1x2 - s0x3;
    matrix->r2c3 = x2x3 - s0x1;
    matrix->r3c1 = x1x3 - s0x2;

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

// =========== Make Reverse Matrix3x3 =========== //

void bg_fp32_versor_get_reverse_matrix(const BgFP32Versor* versor, BgFP32Matrix3x3* matrix)
{
    const float s0s0 = versor->s0 * versor->s0;
    const float x1x1 = versor->x1 * versor->x1;
    const float x2x2 = versor->x2 * versor->x2;
    const float x3x3 = versor->x3 * versor->x3;

    const float s0x1 = 2.0f * versor->s0 * versor->x1;
    const float s0x2 = 2.0f * versor->s0 * versor->x2;
    const float s0x3 = 2.0f * versor->s0 * versor->x3;

    const float x1x2 = 2.0f * versor->x1 * versor->x2;
    const float x1x3 = 2.0f * versor->x1 * versor->x3;
    const float x2x3 = 2.0f * versor->x2 * versor->x3;

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

    matrix->r1c2 = x1x2 + s0x3;
    matrix->r2c3 = x2x3 + s0x1;
    matrix->r3c1 = x1x3 + s0x2;

    matrix->r2c1 = x1x2 - s0x3;
    matrix->r3c2 = x2x3 - s0x1;
    matrix->r1c3 = x1x3 - s0x2;
}

void bg_fp64_versor_get_reverse_matrix(const BgFP64Versor* versor, BgFP64Matrix3x3* matrix)
{
    const double s0s0 = versor->s0 * versor->s0;
    const double x1x1 = versor->x1 * versor->x1;
    const double x2x2 = versor->x2 * versor->x2;
    const double x3x3 = versor->x3 * versor->x3;

    const double s0x1 = 2.0 * versor->s0 * versor->x1;
    const double s0x2 = 2.0 * versor->s0 * versor->x2;
    const double s0x3 = 2.0 * versor->s0 * versor->x3;

    const double x1x2 = 2.0 * versor->x1 * versor->x2;
    const double x1x3 = 2.0 * versor->x1 * versor->x3;
    const double x2x3 = 2.0 * versor->x2 * versor->x3;

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

    matrix->r1c2 = x1x2 + s0x3;
    matrix->r2c3 = x2x3 + s0x1;
    matrix->r3c1 = x1x3 + s0x2;

    matrix->r2c1 = x1x2 - s0x3;
    matrix->r3c2 = x2x3 - s0x1;
    matrix->r1c3 = x1x3 - s0x2;
}

// ================ Turn Vector ================= //

void bg_fp32_versor_turn(const BgFP32Versor* versor, const BgFP32Vector3* vector, BgFP32Vector3* result)
{
    const float tx1 = 2.0f * (versor->x2 * vector->x3 - versor->x3 * vector->x2);
    const float tx2 = 2.0f * (versor->x3 * vector->x1 - versor->x1 * vector->x3);
    const float tx3 = 2.0f * (versor->x1 * vector->x2 - versor->x2 * vector->x1);

    const float x1 = (vector->x1 + tx1 * versor->s0) + (versor->x2 * tx3 - versor->x3 * tx2);
    const float x2 = (vector->x2 + tx2 * versor->s0) + (versor->x3 * tx1 - versor->x1 * tx3);
    const float x3 = (vector->x3 + tx3 * versor->s0) + (versor->x1 * tx2 - versor->x2 * tx1);

    result->x1 = x1;
    result->x2 = x2;
    result->x3 = x3;
}

void bg_fp64_versor_turn(const BgFP64Versor* versor, const BgFP64Vector3* vector, BgFP64Vector3* result)
{
    const double tx1 = 2.0 * (versor->x2 * vector->x3 - versor->x3 * vector->x2);
    const double tx2 = 2.0 * (versor->x3 * vector->x1 - versor->x1 * vector->x3);
    const double tx3 = 2.0 * (versor->x1 * vector->x2 - versor->x2 * vector->x1);

    const double x1 = (vector->x1 + tx1 * versor->s0) + (versor->x2 * tx3 - versor->x3 * tx2);
    const double x2 = (vector->x2 + tx2 * versor->s0) + (versor->x3 * tx1 - versor->x1 * tx3);
    const double x3 = (vector->x3 + tx3 * versor->s0) + (versor->x1 * tx2 - versor->x2 * tx1);

    result->x1 = x1;
    result->x2 = x2;
    result->x3 = x3;
}

// ============== Turn Vector Back ============== //

void bg_fp32_versor_turn_back(const BgFP32Versor* versor, const BgFP32Vector3* vector, BgFP32Vector3* result)
{
    const float tx1 = 2.0f * (versor->x2 * vector->x3 - versor->x3 * vector->x2);
    const float tx2 = 2.0f * (versor->x3 * vector->x1 - versor->x1 * vector->x3);
    const float tx3 = 2.0f * (versor->x1 * vector->x2 - versor->x2 * vector->x1);

    const float x1 = (vector->x1 - tx1 * versor->s0) + (versor->x2 * tx3 - versor->x3 * tx2);
    const float x2 = (vector->x2 - tx2 * versor->s0) + (versor->x3 * tx1 - versor->x1 * tx3);
    const float x3 = (vector->x3 - tx3 * versor->s0) + (versor->x1 * tx2 - versor->x2 * tx1);

    result->x1 = x1;
    result->x2 = x2;
    result->x3 = x3;
}

void bg_fp64_versor_turn_back(const BgFP64Versor* versor, const BgFP64Vector3* vector, BgFP64Vector3* result)
{
    const double tx1 = 2.0 * (versor->x2 * vector->x3 - versor->x3 * vector->x2);
    const double tx2 = 2.0 * (versor->x3 * vector->x1 - versor->x1 * vector->x3);
    const double tx3 = 2.0 * (versor->x1 * vector->x2 - versor->x2 * vector->x1);

    const double x1 = (vector->x1 - tx1 * versor->s0) + (versor->x2 * tx3 - versor->x3 * tx2);
    const double x2 = (vector->x2 - tx2 * versor->s0) + (versor->x3 * tx1 - versor->x1 * tx3);
    const double x3 = (vector->x3 - tx3 * versor->s0) + (versor->x1 * tx2 - versor->x2 * tx1);

    result->x1 = x1;
    result->x2 = x2;
    result->x3 = x3;
}