Clarify column-major vs row-major (docs)

[jimon]

Reading gb_math.h source sometimes is really confusing.
Usual math notation for matrix is Aij where i is row and j is column:

A00 A01 A02 A03
A10 A11 A12 A13
A20 A21 A22 A23
A30 A31 A32 A33

Note that this notation is memory-layout free, this is just how matrices are written down on paper in generic science/engineering notation.

Considering this:

typedef union gbMat4 {
	struct { gbVec4 x, y, z, w; };
	gbVec4 col[4];
	float e[16];
} gbMat4;

One can make an assumption that layout is column-major, awesome. But then reading something like this:

gbFloat4 *gb_float44_m(gbMat4 *m)    { return (gbFloat4 *)m; }
...
gbFloat4 *m = gb_float44_m(out);
...
m[0][0] = 1.0f / (aspect*tan_half_fovy);
m[1][1] = 1.0f / (tan_half_fovy);
m[2][2] = -(z_far + z_near) / (z_far - z_near);
m[2][3] = -1.0f;
m[3][2] = -2.0f*z_far*z_near / (z_far - z_near);

Means that m is still column-major, so it's m[j][i] notation instead of m[i][j] as accepted in generic mathematics. We can test it like this :

uint8_t a[16] = // column-major
{
	0x0, 0x1, 0x2, 0x3,
	0x4, 0x5, 0x6, 0x7,
	0x8, 0x9, 0xa, 0xb,
	0xc, 0xd, 0xe, 0xf
};
typedef uint8_t column_t[4];
column_t * c = (column_t*)a;
printf("%x\n", c[2][1]); // prints 9, which means 2 is column, 1 is row

So would be nice to write down some comments in a lib saying this, and maybe introduce some _M(i, j) macro just so algorithms are written down in more mathematics friendly notation, which should enable less error-prone code.

[gingerBill]

I understand your concern but I don't think the operation/macro should be part of the library. I'm not going to close this issue as if others want this, I will reconsider it.