A command-value generation apparatus includes: a segmentation unit to segment a machining program into execution units to generate segment machining programs; a parallel computation unit, including a plurality of arithmetic units, to execute the segment machining programs on a per execution unit basis in parallel and generate a segment command for each of the execution units, the segment command being a group of interpolation points on the tool path; and a command-value generation unit to generate a tool travel command from the segment command for each of the execution units. The segment machining programs are separate from one another by at least one segmentation point. The segment machining programs includes a forward segment machining program located forward of the segmentation point, and a rearward segment machining program located rearward of the segmentation point.