variable analysis. Alias classification and pointer analysis in the presence of pointers, it is difficult to make any optimizations at all, since potentially any variable can have been changed when a memory location is assigned to. By specifying which pointers can alias which variables, unrelated pointers can be ignored. Dead-store elimination removal of assignments to variables that are not subsequently read, either because the lifetime of the variable ends or because of a subsequent assignment that will overwrite the first value. SSA-based optimizations These optimizations are intended to be done after transforming the program into a special form called Static Single Assignment, in which every variable is assigned in only one place. Although some function without SSA, they are most effective with SSA. Many optimizations listed in other sections also benefit with no special changes, such as register allocation. Global value numbering GVN eliminates redundancy by constructing a value graph of the program, and then determining which values are computed by equivalent expressions. GVN is able to identify some redundancy that common subexpression elimination cannot, and vice versa. Sparse conditional constant propagation Combines constant propagation, constant folding, and dead-code elimination, and improves upon what is possible by running them separately. This optimization symbolically executes the program, simultaneously propagating constant values and eliminating portions of the control-flow graph that this makes unreachable. Code generator optimizations Register allocation The most frequently used variables should be kept in processor registers for fastest access. To find which variables to put in registers, an interference-graph is created. Each variable is a vertex and when two variables are used at the same time (have an intersecting liverange) they have an edge between them. This graph is colored using for example Chaitin's algorithm using the same number of colors as there are registers. If the coloring fails one variable is "spilled" to memory and the coloring is retried. Instruction selection Most architectures, particularly CISC architectures and those with many addressing modes, offer several different ways of performing a particular operation, using entirely different sequences of instructions. The job of the instruction selector is to do a good job overall of choosing which instructions to implement which operators in the low-level intermediate representation with. For example, on many processors in the 68000 family and on the x86 architecture, complex addressing modes can be used in statements like "lea 25(a1,d5*4), a0", allowing a single instruction to perform a significant