How is GLKit's GLKMatrix "Column Major"?

Question

Premise A

When talking about "Column Major" matrices in linear memory, columns are specified one after another, such that the first 4 entries in memory correspond to the first column in the matrix. "Row Major" matrices, on the other hand, are understood to specify rows one after another, such that the first 4 entries in memory specify the first row of the matrix.

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A GLKMatrix4 looks like this:

union _GLKMatrix4
{
    struct
    {
        float m00, m01, m02, m03;
        float m10, m11, m12, m13;
        float m20, m21, m22, m23;
        float m30, m31, m32, m33;
    };
    float m[16];
}
typedef union _GLKMatrix4 GLKMatrix4;

The documentation on the m member says:

A one-dimensional array of the matrix’s elements in column-major order.

Premise B

A "row" in a GLKMatrix4 is a set of 4 floats declared horizontally ([m00, m01, m02, m03] would be the first "row"). Thus, those entries can be interpreted as mRowCol (m12 would be the entry at row 1, column 2).

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If we look at how those GLKMatrix struct members are laid out based on the order of the declarations, we see:

[m00, m01, m02, m03, m10, m11, m12, m13, m20, m21, m22, m23, ...]

Where the first 4 entries clearly represent the first row of the matrix, not the first column.

Conclusion

m is not actually Column Major, and the docs are wrong.

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Now, I should note that I don't actually believe the conclusion, but the two premises seem pretty reasonable. Really, I distrust premise B the most, but it seems strange to define a "row" to be vertical and a "column" to be horizontal. Can someone explain this?

Answer 1

The declaration is a bit confusing, but the matrix is in column major order. The four rows in the struct represent the columns in the matrix, with m0* being column 0 and m3* being column 3. This is easy to verify, just create a translation matrix and check values m30, m31 and m32 for the translation components.

I am guessing your confusion is coming from the fact that the struct lays out the floats in rows, when they are in fact representing columns.