The IEEE/ANSI standard for Scheme requires implementations to be properly tail recursive. This ensures that portable code can rely upon the space efficiency of continuation-passing style and other idioms. On its face, proper tail recursion concerns the efficiency of procedure calls that occur within a tail context. When examined closely, proper tail recursion also depends upon the fact that garbage collection can be asymptotically more space-efficient than Algol-like stack allocation. Proper tail recursion is not the same as ad hoc tail call optimization in stack-based languages. Proper tail recursion often precludes stack allocation of variables, but yields a well-defined asymptotic space complexity that can be relied upon by portable programs. This paper offers a formal and implementation-independent definition of proper tail recursion for Scheme. It also shows how an entire family of reference implementations can be used to characterize related safe-for-space properties, and proves ...

Converting decimal scientific notation into binary floating point is nontrivial, but this conversion can be performed with the best possible accuracy without sacrificing efficiency. 1.

Abstract. Scheme and Smalltalk continuations may have unlimited extent. This means that a purely stack-based implementation of continuations, as suffices for most languages, is inadequate. We review several implementation strategies for continuations and compare their performance using instruction counts for the normal case and continuation-intensive synthetic benchmarks for other scenarios, including coroutines and multitasking. All of the strategies constrain a compiler in some way, resulting in indirect costs that are hard to measure directly. We use related measurements on a set of benchmarks to calculate upper bounds for these indirect costs.