How does this simple fragment shader function work?

[Nick Wiggill]

This code is used in a DoF blur fragment shader I found online (I am trying to make one of my own):

uniform sampler2D gdepth; //<- the depth buffer? How/where is this set?
float getDepth(vec2 coord)
{
    return 2.0 * near * far / (far + near - (2.0 * texture2D(gdepth, coord).x - 1.0) * (far - near)); //is gdepth equivalent to gl_FragCoord.z?
}

How do the mathematics in this depth retrieval function work? I assume it's converting from screen to world space. The terms look strikingly like those found in the projection matrix I ended up using in my CPU-side code:

public static Matrix4 getProjectionMatrix(float fovYDeg, float aspectRatio, float near, float far)
{
    Matrix4 result = new Matrix4();
 
    float fovYRad = fovYDeg * (float)PI / 180f; 
    float e = 1f/(float)(tan(fovYRad / 2)); //focal length
 
    result.val[Matrix4.M00] = e / aspectRatio;
    result.val[Matrix4.M11] = e;
    result.val[Matrix4.M22] = (far + near) / (near - far);
    result.val[Matrix4.M23] = (2 * far * near) / (near - far);
    result.val[Matrix4.M32] = -1f;
    result.val[Matrix4.M33] = 0f;
 
    return result;
}

I really can't just keep letting this stuff go over my head.

PS. The original shader code is here.