Local coordinates (caret notation) don't work in command blocks facing up or down

If you type /setblock ^ ^ ^1 stone into an command block that is facing up or down, the block will be placed 1 block in positive x, when the command block is facing north, east, south, or west, the block is placed where the command block would place the block where the arrows on the side point, like expected, but when pointing up or down, they do not work.