If the bracing is parallel to the beam, it isn't cross bracing. I don't know what it is, this is a very confusing description. Cross bracing by definition is bracing applied between two structural elements, i.e. joists, at an angle to the structural elements. If it is at approximately 45 degrees, it is commonly referred to as X bracing.
Cross bracing serves several purposes. First, it connects two structural elements, and effectively increases the moment of inertia in the plane of the bracing. This increases the lateral stiffness and strength of the structure. It has no effect on the span length, which by definition is the unsupported length of a structural element between two supports.
Cross bracing on long, slender columns has the effect of reducing the effective length of the column. This only applies to vertical structural elements (columns), this discussion is not applicable to horizontal beams, which rarely act as columns, at least in residential applications.
Cross bracing on horizontal elements has the effect of reducing the effective length of the beam in the horizontal plane of the cross bracing, which reduces the effective length of the beam for purposes of lateral buckling analysis. This is important in bridge applications, where large lateral loads on slender I beam elements can and do routinely occur, and lateral buckling is a potential problem. I have never seen a case of lateral buckling in residential applications, however with the increased use of I joists it is a theoretical possibility, and there are guidelines published by manufacturers of I joist products regarding the need for cross bracing, which typically must be installed before allowing workers to walk on I joists.