// =-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-==-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-= //
//  »Project«   Teikitu Gaming System (TgS) (∂)
//  »File«      TgS Common - Math API [Matrix] [F] [F].h_inc
//  »Author«    Andrew Aye (EMail: mailto:andrew.aye@gmail.com, Web: http://www.andrewaye.com)
//  »Version«   4.0
// ------------------------------------------------------------------------------------------------------------------------------ //
//  Copyright: © 2002-2010, Andrew Aye.  All Rights Reserved.
//  This software is free for non-commercial use. Redistribution and use in source and binary forms, with or without modification,
//  are permitted provided that the following conditions are met: 
//    Redistributions of source code must retain this copyright notice, this list of conditions and the following disclaimers. 
//    Redistributions in binary form must reproduce this copyright notice, this list of conditions and the following
//      disclaimers in the documentation and other materials provided with the distribution. 
//  Neither the names of the copyright owner nor the names of its contributors may be used to endorse or promote products derived
//  from this software without specific prior written permission. 
//  The intellectual property rights of the algorithms used reside with Andrew Aye.  You may not use this software, in whole or
//  in part, in support of any commercial product without the express written consent of the author.
//  There is no warranty or other guarantee of fitness of this software for any purpose. It is provided solely "as is".
// =-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-==-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-= //
// == Math ====================================================================================================================== //

// General Matrix Implementation

                                            // Per-Vector Arithmetic Operations
TgINLINE TgVOID                             M(F_ADD_MM)( M(PCU_TgMAT), M(CPCU_TgMAT), M(CPCU_TgMAT) );
TgINLINE TgVOID                             M(F_MUL_MM)( M(PCU_TgMAT), M(CPCU_TgMAT), M(CPCU_TgMAT) );
TgINLINE TgVOID                             M(F_MUL_SM)( M(PCU_TgMAT), const TYPE, M(CPCU_TgMAT) );
TgINLINE TgVOID                             M(F_MUL_MS)( M(PCU_TgMAT), M(CPCU_TgMAT), const TYPE );
TgINLINE TgVOID                             M(F_DIV_MM)( M(PCU_TgMAT), M(CPCU_TgMAT), M(CPCU_TgMAT) );
TgINLINE TgVOID                             M(F_DIV_SM)( M(PCU_TgMAT), const TYPE, M(CPCU_TgMAT) );
TgINLINE TgVOID                             M(F_DIV_MS)( M(PCU_TgMAT), M(CPCU_TgMAT), const TYPE );
TgINLINE TgVOID                             M(F_SUB_MM)( M(PCU_TgMAT), M(CPCU_TgMAT), M(CPCU_TgMAT) );
TgINLINE TgVOID                             M(F_NEG_MM)( M(PCU_TgMAT), M(CPCU_TgMAT) );


// Matrix Specific Implementation

                                            // Load/Set Operations
TgINLINE TgVOID                             M(F_CLI)( M(PCU_TgMAT) );

                                            // Matrix Arithmetic Operations
TgINLINE TgVOID                             M(F_CAT)( M(PCU_TgMAT), M(CPCU_TgMAT), M(CPCU_TgMAT) );

                                            // Inverse Functions
TgINLINE TgVOID                             M(F_INV_DET)( M(PCU_TgMAT), const TYPE, M(CPCU_TgMAT) );
TgINLINE TgVOID                             M(F_INV)( M(PCU_TgMAT), M(CPCU_TgMAT) );
TgINLINE TYPE                               M(F_DET)( M(CPCU_TgMAT) );

                                            // Transformation
TgINLINE V4(TgVEC)                          M(F_TX_V4)( M(CPCU_TgMAT), V4(CPCU_TgVEC) );

                                            // Get Basis
TgINLINE V4(TgVEC)                          M(F_GET_COL_0_V4)( M(CPCU_TgMAT) );
TgINLINE V4(TgVEC)                          M(F_GET_COL_1_V4)( M(CPCU_TgMAT) );
TgINLINE V4(TgVEC)                          M(F_GET_COL_2_V4)( M(CPCU_TgMAT) );
TgINLINE V4(TgVEC)                          M(F_GET_COL_3_V4)( M(CPCU_TgMAT) );




// -.-.-.-.-.-.-.-.-.-.-.-.-.-.-.-.-.-.-.-.-.-.-.-.-.-.-.-.-.-.-.-.-.-.-.-.-.-.-.-.-.-.-.-.-.-.-.-.-.-.-.-.-.-.-.-.-.-.-.-.-.-.-. //
//  Scalar Function
// -.-.-.-.-.-.-.-.-.-.-.-.-.-.-.-.-.-.-.-.-.-.-.-.-.-.-.-.-.-.-.-.-.-.-.-.-.-.-.-.-.-.-.-.-.-.-.-.-.-.-.-.-.-.-.-.-.-.-.-.-.-.-. //

// Scalar - General Matrix Implementation

                                            // Set Rotation [[0..2][0..2]]
TgINLINE TgVOID                             M(F_SET_EUL_V3)( M(PCU_TgMAT), V3(CPCU_TgVEC) );
TgINLINE TgVOID                             M(F_SET_EUL_V4)( M(PCU_TgMAT), V4(CPCU_TgVEC) );
TgINLINE TgVOID                             M(F_SET_EUL_ELEM)( M(PCU_TgMAT), const TYPE, const TYPE, const TYPE );
TgINLINE TgVOID                             M(F_SET_ELX)( M(PCU_TgMAT), const TYPE );
TgINLINE TgVOID                             M(F_SET_ELY)( M(PCU_TgMAT), const TYPE );
TgINLINE TgVOID                             M(F_SET_ELZ)( M(PCU_TgMAT), const TYPE );
TgINLINE TgVOID                             M(F_SET_ROT)( M(PCU_TgMAT), V4(CPCU_TgVEC) );

// Scalar - Matrix Specific Implementation

                                            // Validation
TgINLINE TgBOOL                             M(F_NaN)( M(CPCU_TgMAT) );

                                            // Init Rotation [[0..2][0..2]]
TgINLINE TgVOID                             M(F_INIT_EUL_V3)( M(PCU_TgMAT), V3(CPCU_TgVEC) );
TgINLINE TgVOID                             M(F_INIT_EUL_V4)( M(PCU_TgMAT), V4(CPCU_TgVEC) );
TgINLINE TgVOID                             M(F_INIT_EUL_ELEM)( M(PCU_TgMAT), const TYPE, const TYPE, const TYPE );
TgINLINE TgVOID                             M(F_INIT_ELX)( M(PCU_TgMAT), const TYPE );
TgINLINE TgVOID                             M(F_INIT_ELY)( M(PCU_TgMAT), const TYPE );
TgINLINE TgVOID                             M(F_INIT_ELZ)( M(PCU_TgMAT), const TYPE );
TgINLINE TgVOID                             M(F_INIT_ROT)( M(PCU_TgMAT), V4(CPCU_TgVEC) );

                                            // Get Basis
TgINLINE V3(TgVEC)                          M(F_GET_COL_0_V3)( M(CPCU_TgMAT) );
TgINLINE V3(TgVEC)                          M(F_GET_COL_1_V3)( M(CPCU_TgMAT) );
TgINLINE V3(TgVEC)                          M(F_GET_COL_2_V3)( M(CPCU_TgMAT) );
TgINLINE V3(TgVEC)                          M(F_GET_COL_3_V3)( M(CPCU_TgMAT) );