This is an analysis of the R5RS provision that the full numeric tower may be subsetted. 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. Nine 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
|
- |
- |
- |
- |
A "toy" tower with bounded exact integers only (possibly appropriate where no numerical work will be done) |
SigScheme* |
|
- |
- |
+ |
- |
Fixnums and flonums (all arithmetic runs in essentially constant time) |
Plain Chicken, Shoe*, TinyScheme*, RScheme, BDC*, XLisp*, Schemik*, VX, SXM*, Inlab, Sixx, Sizzle (also Elisp*, C*) |
|
- |
- |
+ |
+ |
Fixnums, flonums, and inexact complex numbers (all arithmetic runs in essentially constant time) |
Stalin |
|
- |
+ |
+ |
+ |
Limited-range exact and inexact numbers |
S7, Wraith |
|
+ |
- |
+ |
- |
Exact integers and inexact real numbers (a good all-round compromise) |
Bigloo, Scheme 9, Elk (also ISLisp) |
|
+ |
- |
+ |
+ |
Exact integers, inexact real numbers, and inexact complex numbers |
SCM |
|
+ |
+ |
- |
- |
Exact rational numbers only (reasonable for some purposes, but will often run very slowly without inexact support, so unsuitable for scientific-type work) |
Dream, Oaklisp, Owl Lisp |
|
+ |
+ |
+ |
- |
Real numbers only |
Psyche, Ikarus, Rep, Elk (also Clojure) |
|
+ |
+ |
+ |
+ |
Full numeric tower |
Racket, Gauche, MIT, Gambit, Chicken with the numbers egg, Scheme48/scsh, Kawa, SISC, Chibi, Guile, Chez, Vicare, Larceny, Ypsilon, Mosh, IronScheme, STklos, KSi, UMB, Spark (also R6RS, Common Lisp, Pure) |
*These systems are technically exactness-preserving, but silently return the wrong answers when their arithmetic operations overflow.
See NumericTowerManisComments for Vincent Manis's comments on an earlier version of this page.
See also ComplexRepresentations for information on which Schemes support exact, inexact, and mixed-exactness complex numbers.
See also FloatPrecision for information on the different precisions of inexact numbers that some Schemes support.