A processor comprising: a plurality of packed data registers; a decode unit to decode an instruction, wherein the instruction is to indicate a source packed data operand that is to include a plurality of Morton coordinates, a dimensionality of a multi-dimensional space having points that the Morton coordinates are to be mapped to, a given dimension of the multi-dimensional space, and a destination storage location, the source packed data operand having a plurality of data elements each including one of the plurality of Morton coordinates; and an execution unit coupled with the packed data registers and the decode unit, the execution unit, in response to the decode unit decoding the instruction, to store a result packed data operand in the destination storage location, wherein the result packed data operand is to include a plurality of Morton coordinates, the result packet data operand having a plurality of data elements each including a corresponding one of the Morton coordinates of the source packed data operand, wherein the execution unit is to generate each Morton coordinate of the result packed data operand such that Morton coordinate is to be mapped to a point in the multi-dimensional space that differs from a point that the corresponding Morton coordinate of the source packed data operand is to be mapped to by a fixed change in the given dimension being a unit decrement in the given dimension indicated by the instruction, by: setting all lowest order zeroed bits corresponding to the given dimension of each corresponding Morton coordinate of the source packed data operand, which are lower order than each lowest order set bit corresponding to the given dimension of each Morton coordinate of the source packed data operand; and clearing the lowest order set bit corresponding to the given dimension of each Morton coordinate of the source packed data operand. a plurality of packed data registers; a decode unit to decode an instruction, wherein the instruction is to indicate a source packed data operand that is to include a plurality of Morton coordinates, a dimensionality of a multi-dimensional space having points that the Morton coordinates are to be mapped to, a given dimension of the multi-dimensional space, and a destination storage location, the source packed data operand having a plurality of data elements each including one of the plurality of Morton coordinates; and an execution unit coupled with the packed data registers and the decode unit, the execution unit, in response to the decode unit decoding the instruction, to store a result packed data operand in the destination storage location, wherein the result packed data operand is to include a plurality of Morton coordinates, the result packet data operand having a plurality of data elements each including a corresponding one of the Morton coordinates of the source packed data operand, wherein the execution unit is to generate each Morton coordinate of the result packed data operand such that Morton coordinate is to be mapped to a point in the multi-dimensional space that differs from a point that the corresponding Morton coordinate of the source packed data operand is to be mapped to by a fixed change in the given dimension being a unit decrement in the given dimension indicated by the instruction, by: setting all lowest order zeroed bits corresponding to the given dimension of each corresponding Morton coordinate of the source packed data operand, which are lower order than each lowest order set bit corresponding to the given dimension of each Morton coordinate of the source packed data operand; and clearing the lowest order set bit corresponding to the given dimension of each Morton coordinate of the source packed data operand. setting all lowest order zeroed bits corresponding to the given dimension of each corresponding Morton coordinate of the source packed data operand, which are lower order than each lowest order set bit corresponding to the given dimension of each Morton coordinate of the source packed data operand; and clearing the lowest order set bit corresponding to the given dimension of each Morton coordinate of the source packed data operand.