#include "matrix.h"


// remove from sequence 0, 1, 2, 3, two numbers, see following
// example:
//   r0 = 1, r1 = 2
// initial sequence:
//   0, 1, 2, 3
// remove number at place r0 (1 for ex):
//   0, 2, 3
// remove number at place r1 (2 for ex):
//   0, 2
// so result for index0(1, 2) is 0
//       and for index1(1, 2) is 2
//
// r1\r0 :  0    1    2    3
// ---------------------------
//    -- : _123 0_23 01_3 012_
//     0 : _.23 ._23 .1_3 .12_
//     1 : _1.3 0_.3 0._3 0.2_
//     2 : _12. 0_2. 01_. 01._
// ---------------------------
//     0 :  23   23   13   12
//     1 :  13   03   03   02
//     2 :  12   02   01   01

static inline int index0(int r0, int r1)
	{ return r1 ? (r0 ? 0 : 1) : (r0 > 1 ? 1 : 2); }
static inline int index1(int r0, int r1)
	{ return r1 < 2 ? (r0 < 3 ? 3 : 2) : (r0 > 1 ? 1 : 2); }
static inline int index0(int r)
	{ return r > 0 ? 0 : 1; }
static inline int index1(int r)
	{ return r > 1 ? 1 : 2; }
static inline int index2(int r)
	{ return r > 2 ? 2 : 3; }

static inline Real det2(const Matrix4 &m, int r, int c, int rr, int cc) {
	const int r0 = index0(r, rr);
	const int r1 = index1(r, rr);
	const int c0 = index0(c, cc);
	const int c1 = index1(c, cc);
	return m[r0][c0]*m[r1][c1] - m[r0][c1]*m[r1][c0];
}

static inline Real det3(const Matrix4 &m, int r, int c) {
	const int r0 = index0(r);
	return m[r0][index0(c)] * det2(m, r, c, 0, 0)
	     - m[r0][index1(c)] * det2(m, r, c, 0, 1)
		 + m[r0][index2(c)] * det2(m, r, c, 0, 2);
}


Real
Matrix4::det() const
	{ return m00*det3(*this, 0, 0) - m01*det3(*this, 0, 1) + m02*det3(*this, 0, 2) - m03*det3(*this, 0, 3); }

Matrix4
Matrix4::inverted() const {
	Vector4 dv(
		 det3(*this, 0, 0),
		-det3(*this, 0, 1),
		 det3(*this, 0, 2),
		-det3(*this, 0, 3) );
	Real d = m00*dv.x + m01*dv.y + m02*dv.z + m03*dv.w;
	if (fabs(d) <= real_precision)
		return zero();

	d = 1.0/d;
	return Matrix4(
		Vector4(dv.x, -det3(*this, 1, 0), det3(*this, 2, 0), -det3(*this, 3, 0))*d,
		Vector4(dv.y,  det3(*this, 1, 1),-det3(*this, 2, 1),  det3(*this, 3, 1))*d,
		Vector4(dv.z, -det3(*this, 1, 2), det3(*this, 2, 2), -det3(*this, 3, 2))*d,
		Vector4(dv.w,  det3(*this, 1, 3),-det3(*this, 2, 3),  det3(*this, 3, 3))*d );
}