Sparse conditional constant propagation is an optimization frequently utilized in compilers after conversion to static single assignment form (SSA). It simultaneously removes dead code and propagates constants throughout a program. It must be noted, however, that it is strictly more powerful than applying dead code elimination and constant propagation in any order or any number of repetitions. A diagram of the operation of an ideal compiler. ... In compilers, static single assignment form, more often abbreviated SSA form or just SSA, is an intermediate representation in which every variable is assigned exactly once. ... In computer programming, dead code typically consists of blocks of programming instructions or entire routines that will never be accessed because all calls to them have been removed, or code that cannot be reached because it is guarded by a control structure that probably must always transfer control somewhere else. ... Constant folding, in computing, is the process of simplifying expressions at compile-time which consist only of constants, which are usually simple literals like 2. ... Dead code elimination is a technique used in computer science to reduce program size by removing code which can never be executed. ... Constant folding, in computing, is the process of simplifying expressions at compile-time which consist only of constants, which are usually simple literals like 2. ...

The algorithm operates by performing abstract interpretation of the code in SSA form. During abstract interpretation, it typically uses a flat lattice of constants for values and a global environment mapping SSA variables to values in this lattice. The crux of the algorithm comes in how it handles the interpretation of branch instructions. When encountered, the condition for a branch is evaluated as best as possible given the precision of the abstract values bound to variables in the condition. It may be the case that the values are perfectly precise (neither top nor bottom) and hence, abstract execution can decide in which direction to branch. If the values are not constant, or a variable in the condition is undefined, then both branch directions must be taken to remain conservative. Abstract interpretation is a theory of sound approximation of the semantics of computer programs, based on monotonic functions over ordered sets, especially execution of a computer program which gains information about its semantics (e. ...

Upon completion of the abstract interpretation, instructions which were never reached are marked as dead code. SSA variables found to have constant values may then be inlined at--propagated to--their point of use.

References

Cooper, Keith D. and Torczon, Linda. Engineering a Compiler. Morgan Kaufmann. 2005.