This is an analysis of the R5RS provision that the full numeric tower may be subsetted. In this analysis, four boolean feature settings characterize different kinds of numeric towers: exactness-preserving, ratios, inexact, and complex. These refer respectively to the closure of exact numbers under rational operations (except /), exact non-integer values, inexact rationals, and non-real numbers.
There are therefore 16 possible numeric towers. 9 of them are known to have implementations, as shown below. I write + if a feature is present and - if it is absent, and give a general description of the resulting tower and some Scheme implementations that provide it.
exactness-preserving |
ratios |
inexact |
complex |
Description | Implementations |
|---|---|---|---|---|---|
| - | - | - | - | Bounded exact integers only | !SigScheme†, MiniScheme† |
| - | - | + | - | Fixnums and flonums | Plain Chicken 4, Shoe†, TinyScheme†, RScheme, JScheme†, SIOD, BDC†, XLisp†, Schemik†, VX, SXM†, Inlab, Llava, Sixx, Picrin†, Sizzle, Dfsch†, Stalin (also Elisp†, C†) |
| - | + | + | + | Limited-range exact and inexact numbers | S7, Wraith |
| + | - | + | - | Exact integers and inexact real numbers | Bigloo, Scheme 9, Unlikely Scheme††, Elk (also ISLisp) |
| + | - | + | + | Exact integers, inexact real numbers, and complex numbers | SCM, Cyclone |
| + | + | - | - | Exact rational numbers only | Dream, Oaklisp |
| + | + | - | + | Exact numbers only | Owl Lisp |
| + | + | + | - | Real numbers only | Psyche, Ikarus, Rep, Dfsch (also Clojure) |
| + | + | + | + | Full numeric tower | Racket, Gauche, MIT, Gambit, Chicken 4 with the numbers egg, Chicken 5, Scheme48/scsh, Kawa, SISC, Chibi, Guile, Chez, Vicare, Larceny, Ypsilon, Mosh, IronScheme, STklos, KSi, UMB, Spark, Sagittarius (also R6RS, Common Lisp, Pure) |
†These systems are technically exactness-preserving, but silently return the wrong answers when their arithmetic operations overflow. This makes them non-conformant.
††This system provides ratios, but they are so buggy as to be useless: (/ 1 3) => 3/7.
NexJ's numeric tower is undocumented and behaves inconsistently in any case: applying expt to two fixnums, for example, returns a bignum, but adding them returns a potentially incorrect fixnum. Basically it does what Java does.
See also: Complex representations for information on which Schemes support exact, inexact, and mixed-exactness complex numbers.
See also: Float precision for information on the different precisions of inexact numbers that some Schemes support.