#ifndef _BGC_MATRICES_H_INCLUDED_
#define _BGC_MATRICES_H_INCLUDED_

// ================== Matrix2x2 ================= //

typedef struct {
    float r1c1, r1c2;
    float r2c1, r2c2;
} BGC_FP32_Matrix2x2;

typedef struct {
    double r1c1, r1c2;
    double r2c1, r2c2;
} BGC_FP64_Matrix2x2;

// ================== Matrix2x3 ================= //

typedef struct {
    float r1c1, r1c2;
    float r2c1, r2c2;
    float r3c1, r3c2;
} BGC_FP32_Matrix2x3;

typedef struct {
    double r1c1, r1c2;
    double r2c1, r2c2;
    double r3c1, r3c2;
} BGC_FP64_Matrix2x3;

// ================== Matrix3x2 ================= //

typedef struct {
    float r1c1, r1c2, r1c3;
    float r2c1, r2c2, r2c3;
} BGC_FP32_Matrix3x2;

typedef struct {
    double r1c1, r1c2, r1c3;
    double r2c1, r2c2, r2c3;
} BGC_FP64_Matrix3x2;

// ================== Matrix3x3 ================= //

typedef struct {
    float r1c1, r1c2, r1c3;
    float r2c1, r2c2, r2c3;
    float r3c1, r3c2, r3c3;
} BGC_FP32_Matrix3x3;

typedef struct {
    double r1c1, r1c2, r1c3;
    double r2c1, r2c2, r2c3;
    double r3c1, r3c2, r3c3;
} BGC_FP64_Matrix3x3;

// ========== Matrix Product 2x2 at 2x2 ========= //

inline void bgc_fp32_multiply_matrix2x2_by_matrix2x2(BGC_FP32_Matrix2x2* product, const BGC_FP32_Matrix2x2* matrix1, const BGC_FP32_Matrix2x2* matrix2)
{
    const float r1c1 = matrix1->r1c1 * matrix2->r1c1 + matrix1->r1c2 * matrix2->r2c1;
    const float r1c2 = matrix1->r1c1 * matrix2->r1c2 + matrix1->r1c2 * matrix2->r2c2;

    const float r2c1 = matrix1->r2c1 * matrix2->r1c1 + matrix1->r2c2 * matrix2->r2c1;
    const float r2c2 = matrix1->r2c1 * matrix2->r1c2 + matrix1->r2c2 * matrix2->r2c2;

    product->r1c1 = r1c1;
    product->r1c2 = r1c2;

    product->r2c1 = r2c1;
    product->r2c2 = r2c2;
}

inline void bgc_fp64_multiply_matrix2x2_by_matrix2x2(BGC_FP64_Matrix2x2* product, const BGC_FP64_Matrix2x2* matrix1, const BGC_FP64_Matrix2x2* matrix2)
{
    const double r1c1 = matrix1->r1c1 * matrix2->r1c1 + matrix1->r1c2 * matrix2->r2c1;
    const double r1c2 = matrix1->r1c1 * matrix2->r1c2 + matrix1->r1c2 * matrix2->r2c2;

    const double r2c1 = matrix1->r2c1 * matrix2->r1c1 + matrix1->r2c2 * matrix2->r2c1;
    const double r2c2 = matrix1->r2c1 * matrix2->r1c2 + matrix1->r2c2 * matrix2->r2c2;

    product->r1c1 = r1c1;
    product->r1c2 = r1c2;

    product->r2c1 = r2c1;
    product->r2c2 = r2c2;
}

// ========== Matrix Product 2x2 at 3x2 ========= //

inline void bgc_fp32_multiply_matrix2x2_by_matrix3x2(BGC_FP32_Matrix3x2* product, const BGC_FP32_Matrix2x2* matrix1, const BGC_FP32_Matrix3x2* matrix2)
{
    const float r1c1 = matrix1->r1c1 * matrix2->r1c1 + matrix1->r1c2 * matrix2->r2c1;
    const float r1c2 = matrix1->r1c1 * matrix2->r1c2 + matrix1->r1c2 * matrix2->r2c2;
    const float r1c3 = matrix1->r1c1 * matrix2->r1c3 + matrix1->r1c2 * matrix2->r2c3;

    const float r2c1 = matrix1->r2c1 * matrix2->r1c1 + matrix1->r2c2 * matrix2->r2c1;
    const float r2c2 = matrix1->r2c1 * matrix2->r1c2 + matrix1->r2c2 * matrix2->r2c2;
    const float r2c3 = matrix1->r2c1 * matrix2->r1c3 + matrix1->r2c2 * matrix2->r2c3;

    product->r1c1 = r1c1;
    product->r1c2 = r1c2;
    product->r1c3 = r1c3;

    product->r2c1 = r2c1;
    product->r2c2 = r2c2;
    product->r2c3 = r2c3;
}

inline void bgc_fp64_multiply_matrix2x2_by_matrix3x2(BGC_FP64_Matrix3x2* product, const BGC_FP64_Matrix2x2* matrix1, const BGC_FP64_Matrix3x2* matrix2)
{
    const double r1c1 = matrix1->r1c1 * matrix2->r1c1 + matrix1->r1c2 * matrix2->r2c1;
    const double r1c2 = matrix1->r1c1 * matrix2->r1c2 + matrix1->r1c2 * matrix2->r2c2;
    const double r1c3 = matrix1->r1c1 * matrix2->r1c3 + matrix1->r1c2 * matrix2->r2c3;

    const double r2c1 = matrix1->r2c1 * matrix2->r1c1 + matrix1->r2c2 * matrix2->r2c1;
    const double r2c2 = matrix1->r2c1 * matrix2->r1c2 + matrix1->r2c2 * matrix2->r2c2;
    const double r2c3 = matrix1->r2c1 * matrix2->r1c3 + matrix1->r2c2 * matrix2->r2c3;

    product->r1c1 = r1c1;
    product->r1c2 = r1c2;
    product->r1c3 = r1c3;

    product->r2c1 = r2c1;
    product->r2c2 = r2c2;
    product->r2c3 = r2c3;
}

// ========== Matrix Product 2x3 at 2x2 ========= //

inline void bgc_fp32_multiply_matrix2x3_by_matrix2x2(BGC_FP32_Matrix2x3* product, const BGC_FP32_Matrix2x3* matrix1, const BGC_FP32_Matrix2x2* matrix2)
{
    const float r1c1 = matrix1->r1c1 * matrix2->r1c1 + matrix1->r1c2 * matrix2->r2c1;
    const float r1c2 = matrix1->r1c1 * matrix2->r1c2 + matrix1->r1c2 * matrix2->r2c2;

    const float r2c1 = matrix1->r2c1 * matrix2->r1c1 + matrix1->r2c2 * matrix2->r2c1;
    const float r2c2 = matrix1->r2c1 * matrix2->r1c2 + matrix1->r2c2 * matrix2->r2c2;

    const float r3c1 = matrix1->r3c1 * matrix2->r1c1 + matrix1->r3c2 * matrix2->r2c1;
    const float r3c2 = matrix1->r3c1 * matrix2->r1c2 + matrix1->r3c2 * matrix2->r2c2;

    product->r1c1 = r1c1;
    product->r1c2 = r1c2;

    product->r2c1 = r2c1;
    product->r2c2 = r2c2;

    product->r3c1 = r3c1;
    product->r3c2 = r3c2;
}

inline void bgc_fp64_multiply_matrix2x3_by_matrix2x2(BGC_FP64_Matrix2x3* product, const BGC_FP64_Matrix2x3* matrix1, const BGC_FP64_Matrix2x2* matrix2)
{
    const double r1c1 = matrix1->r1c1 * matrix2->r1c1 + matrix1->r1c2 * matrix2->r2c1;
    const double r1c2 = matrix1->r1c1 * matrix2->r1c2 + matrix1->r1c2 * matrix2->r2c2;

    const double r2c1 = matrix1->r2c1 * matrix2->r1c1 + matrix1->r2c2 * matrix2->r2c1;
    const double r2c2 = matrix1->r2c1 * matrix2->r1c2 + matrix1->r2c2 * matrix2->r2c2;

    const double r3c1 = matrix1->r3c1 * matrix2->r1c1 + matrix1->r3c2 * matrix2->r2c1;
    const double r3c2 = matrix1->r3c1 * matrix2->r1c2 + matrix1->r3c2 * matrix2->r2c2;

    product->r1c1 = r1c1;
    product->r1c2 = r1c2;

    product->r2c1 = r2c1;
    product->r2c2 = r2c2;

    product->r3c1 = r3c1;
    product->r3c2 = r3c2;
}

// ========== Matrix Product 2x3 at 3x2 ========= //

inline void bgc_fp32_multiply_matrix2x3_by_matrix3x2(BGC_FP32_Matrix3x3* product, const BGC_FP32_Matrix2x3* matrix1, const BGC_FP32_Matrix3x2* matrix2)
{
    product->r1c1 = matrix1->r1c1 * matrix2->r1c1 + matrix1->r1c2 * matrix2->r2c1;
    product->r1c2 = matrix1->r1c1 * matrix2->r1c2 + matrix1->r1c2 * matrix2->r2c2;
    product->r1c3 = matrix1->r1c1 * matrix2->r1c3 + matrix1->r1c2 * matrix2->r2c3;

    product->r2c1 = matrix1->r2c1 * matrix2->r1c1 + matrix1->r2c2 * matrix2->r2c1;
    product->r2c2 = matrix1->r2c1 * matrix2->r1c2 + matrix1->r2c2 * matrix2->r2c2;
    product->r2c3 = matrix1->r2c1 * matrix2->r1c3 + matrix1->r2c2 * matrix2->r2c3;

    product->r3c1 = matrix1->r3c1 * matrix2->r1c1 + matrix1->r3c2 * matrix2->r2c1;
    product->r3c2 = matrix1->r3c1 * matrix2->r1c2 + matrix1->r3c2 * matrix2->r2c2;
    product->r3c3 = matrix1->r3c1 * matrix2->r1c3 + matrix1->r3c2 * matrix2->r2c3;
}

inline void bgc_fp64_multiply_matrix2x3_by_matrix3x2(BGC_FP64_Matrix3x3* product, const BGC_FP64_Matrix2x3* matrix1, const BGC_FP64_Matrix3x2* matrix2)
{
    product->r1c1 = matrix1->r1c1 * matrix2->r1c1 + matrix1->r1c2 * matrix2->r2c1;
    product->r1c2 = matrix1->r1c1 * matrix2->r1c2 + matrix1->r1c2 * matrix2->r2c2;
    product->r1c3 = matrix1->r1c1 * matrix2->r1c3 + matrix1->r1c2 * matrix2->r2c3;

    product->r2c1 = matrix1->r2c1 * matrix2->r1c1 + matrix1->r2c2 * matrix2->r2c1;
    product->r2c2 = matrix1->r2c1 * matrix2->r1c2 + matrix1->r2c2 * matrix2->r2c2;
    product->r2c3 = matrix1->r2c1 * matrix2->r1c3 + matrix1->r2c2 * matrix2->r2c3;

    product->r3c1 = matrix1->r3c1 * matrix2->r1c1 + matrix1->r3c2 * matrix2->r2c1;
    product->r3c2 = matrix1->r3c1 * matrix2->r1c2 + matrix1->r3c2 * matrix2->r2c2;
    product->r3c3 = matrix1->r3c1 * matrix2->r1c3 + matrix1->r3c2 * matrix2->r2c3;
}

// ========== Matrix Product 3x2 at 2x3 ========= //

inline void bgc_fp32_multiply_matrix3x2_by_matrix2x3(BGC_FP32_Matrix2x2* product, const BGC_FP32_Matrix3x2* matrix1, const BGC_FP32_Matrix2x3* matrix2)
{
    product->r1c1 = matrix1->r1c1 * matrix2->r1c1 + matrix1->r1c2 * matrix2->r2c1 + matrix1->r1c3 * matrix2->r3c1;
    product->r1c2 = matrix1->r1c1 * matrix2->r1c2 + matrix1->r1c2 * matrix2->r2c2 + matrix1->r1c3 * matrix2->r3c2;

    product->r2c1 = matrix1->r2c1 * matrix2->r1c1 + matrix1->r2c2 * matrix2->r2c1 + matrix1->r2c3 * matrix2->r3c1;
    product->r2c2 = matrix1->r2c1 * matrix2->r1c2 + matrix1->r2c2 * matrix2->r2c2 + matrix1->r2c3 * matrix2->r3c2;
}

inline void bgc_fp64_multiply_matrix3x2_by_matrix2x3(BGC_FP64_Matrix2x2* product, const BGC_FP64_Matrix3x2* matrix1, const BGC_FP64_Matrix2x3* matrix2)
{
    product->r1c1 = matrix1->r1c1 * matrix2->r1c1 + matrix1->r1c2 * matrix2->r2c1 + matrix1->r1c3 * matrix2->r3c1;
    product->r1c2 = matrix1->r1c1 * matrix2->r1c2 + matrix1->r1c2 * matrix2->r2c2 + matrix1->r1c3 * matrix2->r3c2;

    product->r2c1 = matrix1->r2c1 * matrix2->r1c1 + matrix1->r2c2 * matrix2->r2c1 + matrix1->r2c3 * matrix2->r3c1;
    product->r2c2 = matrix1->r2c1 * matrix2->r1c2 + matrix1->r2c2 * matrix2->r2c2 + matrix1->r2c3 * matrix2->r3c2;
}

// ========== Matrix Product 3x2 at 3x3 ========= //

inline void bgc_fp32_multiply_matrix3x2_by_matrix3x3(BGC_FP32_Matrix3x2* product, const BGC_FP32_Matrix3x2* matrix1, const BGC_FP32_Matrix3x3* matrix2)
{
    const float r1c1 = matrix1->r1c1 * matrix2->r1c1 + matrix1->r1c2 * matrix2->r2c1 + matrix1->r1c3 * matrix2->r3c1;
    const float r1c2 = matrix1->r1c1 * matrix2->r1c2 + matrix1->r1c2 * matrix2->r2c2 + matrix1->r1c3 * matrix2->r3c2;
    const float r1c3 = matrix1->r1c1 * matrix2->r1c3 + matrix1->r1c2 * matrix2->r2c3 + matrix1->r1c3 * matrix2->r3c3;

    const float r2c1 = matrix1->r2c1 * matrix2->r1c1 + matrix1->r2c2 * matrix2->r2c1 + matrix1->r2c3 * matrix2->r3c1;
    const float r2c2 = matrix1->r2c1 * matrix2->r1c2 + matrix1->r2c2 * matrix2->r2c2 + matrix1->r2c3 * matrix2->r3c2;
    const float r2c3 = matrix1->r2c1 * matrix2->r1c3 + matrix1->r2c2 * matrix2->r2c3 + matrix1->r2c3 * matrix2->r3c3;

    product->r1c1 = r1c1;
    product->r1c2 = r1c2;
    product->r1c3 = r1c3;

    product->r2c1 = r2c1;
    product->r2c2 = r2c2;
    product->r2c3 = r2c3;
}

inline void bgc_fp64_multiply_matrix3x2_by_matrix3x3(BGC_FP64_Matrix3x2* product, const BGC_FP64_Matrix3x2* matrix1, const BGC_FP64_Matrix3x3* matrix2)
{
    const double r1c1 = matrix1->r1c1 * matrix2->r1c1 + matrix1->r1c2 * matrix2->r2c1 + matrix1->r1c3 * matrix2->r3c1;
    const double r1c2 = matrix1->r1c1 * matrix2->r1c2 + matrix1->r1c2 * matrix2->r2c2 + matrix1->r1c3 * matrix2->r3c2;
    const double r1c3 = matrix1->r1c1 * matrix2->r1c3 + matrix1->r1c2 * matrix2->r2c3 + matrix1->r1c3 * matrix2->r3c3;

    const double r2c1 = matrix1->r2c1 * matrix2->r1c1 + matrix1->r2c2 * matrix2->r2c1 + matrix1->r2c3 * matrix2->r3c1;
    const double r2c2 = matrix1->r2c1 * matrix2->r1c2 + matrix1->r2c2 * matrix2->r2c2 + matrix1->r2c3 * matrix2->r3c2;
    const double r2c3 = matrix1->r2c1 * matrix2->r1c3 + matrix1->r2c2 * matrix2->r2c3 + matrix1->r2c3 * matrix2->r3c3;

    product->r1c1 = r1c1;
    product->r1c2 = r1c2;
    product->r1c3 = r1c3;

    product->r2c1 = r2c1;
    product->r2c2 = r2c2;
    product->r2c3 = r2c3;
}

// ========== Matrix Product 3x3 at 2x3 ========= //

inline void bgc_fp32_multiply_matrix3x3_by_matrix2x3(BGC_FP32_Matrix2x3* product, const BGC_FP32_Matrix3x3* matrix1, const BGC_FP32_Matrix2x3* matrix2)
{
    const float r1c1 = matrix1->r1c1 * matrix2->r1c1 + matrix1->r1c2 * matrix2->r2c1 + matrix1->r1c3 * matrix2->r3c1;
    const float r1c2 = matrix1->r1c1 * matrix2->r1c2 + matrix1->r1c2 * matrix2->r2c2 + matrix1->r1c3 * matrix2->r3c2;

    const float r2c1 = matrix1->r2c1 * matrix2->r1c1 + matrix1->r2c2 * matrix2->r2c1 + matrix1->r2c3 * matrix2->r3c1;
    const float r2c2 = matrix1->r2c1 * matrix2->r1c2 + matrix1->r2c2 * matrix2->r2c2 + matrix1->r2c3 * matrix2->r3c2;

    const float r3c1 = matrix1->r3c1 * matrix2->r1c1 + matrix1->r3c2 * matrix2->r2c1 + matrix1->r3c3 * matrix2->r3c1;
    const float r3c2 = matrix1->r3c1 * matrix2->r1c2 + matrix1->r3c2 * matrix2->r2c2 + matrix1->r3c3 * matrix2->r3c2;

    product->r1c1 = r1c1;
    product->r1c2 = r1c2;

    product->r2c1 = r2c1;
    product->r2c2 = r2c2;

    product->r3c1 = r3c1;
    product->r3c2 = r3c2;
}

inline void bgc_fp64_multiply_matrix3x3_by_matrix2x3(BGC_FP64_Matrix2x3* product, const BGC_FP64_Matrix3x3* matrix1, const BGC_FP64_Matrix2x3* matrix2)
{
    const double r1c1 = matrix1->r1c1 * matrix2->r1c1 + matrix1->r1c2 * matrix2->r2c1 + matrix1->r1c3 * matrix2->r3c1;
    const double r1c2 = matrix1->r1c1 * matrix2->r1c2 + matrix1->r1c2 * matrix2->r2c2 + matrix1->r1c3 * matrix2->r3c2;

    const double r2c1 = matrix1->r2c1 * matrix2->r1c1 + matrix1->r2c2 * matrix2->r2c1 + matrix1->r2c3 * matrix2->r3c1;
    const double r2c2 = matrix1->r2c1 * matrix2->r1c2 + matrix1->r2c2 * matrix2->r2c2 + matrix1->r2c3 * matrix2->r3c2;

    const double r3c1 = matrix1->r3c1 * matrix2->r1c1 + matrix1->r3c2 * matrix2->r2c1 + matrix1->r3c3 * matrix2->r3c1;
    const double r3c2 = matrix1->r3c1 * matrix2->r1c2 + matrix1->r3c2 * matrix2->r2c2 + matrix1->r3c3 * matrix2->r3c2;

    product->r1c1 = r1c1;
    product->r1c2 = r1c2;

    product->r2c1 = r2c1;
    product->r2c2 = r2c2;

    product->r3c1 = r3c1;
    product->r3c2 = r3c2;
}

// ========== Matrix Product 3x3 at 3x3 ========= //

inline void bgc_fp32_multiply_matrix3x3_by_matrix3x3(BGC_FP32_Matrix3x3* product, const BGC_FP32_Matrix3x3* matrix1, const BGC_FP32_Matrix3x3* matrix2)
{
    const float r1c1 = matrix1->r1c1 * matrix2->r1c1 + matrix1->r1c2 * matrix2->r2c1 + matrix1->r1c3 * matrix2->r3c1;
    const float r1c2 = matrix1->r1c1 * matrix2->r1c2 + matrix1->r1c2 * matrix2->r2c2 + matrix1->r1c3 * matrix2->r3c2;
    const float r1c3 = matrix1->r1c1 * matrix2->r1c3 + matrix1->r1c2 * matrix2->r2c3 + matrix1->r1c3 * matrix2->r3c3;

    const float r2c1 = matrix1->r2c1 * matrix2->r1c1 + matrix1->r2c2 * matrix2->r2c1 + matrix1->r2c3 * matrix2->r3c1;
    const float r2c2 = matrix1->r2c1 * matrix2->r1c2 + matrix1->r2c2 * matrix2->r2c2 + matrix1->r2c3 * matrix2->r3c2;
    const float r2c3 = matrix1->r2c1 * matrix2->r1c3 + matrix1->r2c2 * matrix2->r2c3 + matrix1->r2c3 * matrix2->r3c3;

    const float r3c1 = matrix1->r3c1 * matrix2->r1c1 + matrix1->r3c2 * matrix2->r2c1 + matrix1->r3c3 * matrix2->r3c1;
    const float r3c2 = matrix1->r3c1 * matrix2->r1c2 + matrix1->r3c2 * matrix2->r2c2 + matrix1->r3c3 * matrix2->r3c2;
    const float r3c3 = matrix1->r3c1 * matrix2->r1c3 + matrix1->r3c2 * matrix2->r2c3 + matrix1->r3c3 * matrix2->r3c3;

    product->r1c1 = r1c1;
    product->r1c2 = r1c2;
    product->r1c3 = r1c3;

    product->r2c1 = r2c1;
    product->r2c2 = r2c2;
    product->r2c3 = r2c3;

    product->r3c1 = r3c1;
    product->r3c2 = r3c2;
    product->r3c3 = r3c3;
}

inline void bgc_fp64_multiply_matrix3x3_by_matrix3x3(BGC_FP64_Matrix3x3* product, const BGC_FP64_Matrix3x3* matrix1, const BGC_FP64_Matrix3x3* matrix2)
{
    const double r1c1 = matrix1->r1c1 * matrix2->r1c1 + matrix1->r1c2 * matrix2->r2c1 + matrix1->r1c3 * matrix2->r3c1;
    const double r1c2 = matrix1->r1c1 * matrix2->r1c2 + matrix1->r1c2 * matrix2->r2c2 + matrix1->r1c3 * matrix2->r3c2;
    const double r1c3 = matrix1->r1c1 * matrix2->r1c3 + matrix1->r1c2 * matrix2->r2c3 + matrix1->r1c3 * matrix2->r3c3;

    const double r2c1 = matrix1->r2c1 * matrix2->r1c1 + matrix1->r2c2 * matrix2->r2c1 + matrix1->r2c3 * matrix2->r3c1;
    const double r2c2 = matrix1->r2c1 * matrix2->r1c2 + matrix1->r2c2 * matrix2->r2c2 + matrix1->r2c3 * matrix2->r3c2;
    const double r2c3 = matrix1->r2c1 * matrix2->r1c3 + matrix1->r2c2 * matrix2->r2c3 + matrix1->r2c3 * matrix2->r3c3;

    const double r3c1 = matrix1->r3c1 * matrix2->r1c1 + matrix1->r3c2 * matrix2->r2c1 + matrix1->r3c3 * matrix2->r3c1;
    const double r3c2 = matrix1->r3c1 * matrix2->r1c2 + matrix1->r3c2 * matrix2->r2c2 + matrix1->r3c3 * matrix2->r3c2;
    const double r3c3 = matrix1->r3c1 * matrix2->r1c3 + matrix1->r3c2 * matrix2->r2c3 + matrix1->r3c3 * matrix2->r3c3;

    product->r1c1 = r1c1;
    product->r1c2 = r1c2;
    product->r1c3 = r1c3;

    product->r2c1 = r2c1;
    product->r2c2 = r2c2;
    product->r2c3 = r2c3;

    product->r3c1 = r3c1;
    product->r3c2 = r3c2;
    product->r3c3 = r3c3;
}

#endif // _BGC_MATRIX_TYPES_H_