This is an analysis of the R5RS provision that the full numeric tower may be subsetted. Five boolean feature settings characterize different kinds of numeric towers: exactness-preserving, ratios, inexact, and complex, and exact-complex. These refer respectively to the closure of exact numbers under rational operations (except /), exact non-integer values, inexact rationals, non-real numbers, and exact non-real numbers. Of course, exact-complex can only be true if complex is true.
So here are some numeric towers that have implementations. I use + if a feature is present and - if it is absent, and give a general description of the resulting tower.
||exactness-preserving||ratios||inexact||complex||exact-complex||Description||Examples
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- |
- |
- |
- |
- |
A "toy" tower with fixnums (bounded exact integers) only. Possibly appropriate where no numerical work will be done. |
SigScheme |
|
- |
- |
+ |
- |
- |
A fixnum-flonum Scheme where all numbers are real and all arithmetic happens in essentially constant time. |
Chicken (default numbers), Shoe*, TinyScheme*, RScheme, BDC*, XLisp*, Schemik*, VX, SXM*, Inlab, Sixx, Sizzle (also Elisp*, C*) |
|
- |
- |
+ |
+ |
- |
The complex-number equivalent of the preceding. |
Stalin |
|
- |
+ |
+ |
+ |
- |
Limited-range exact and inexact numbers. |
Scheme 7 |
|
- |
+ |
+ |
+ |
+ |
Limited-range exact and inexact numbers, including exact non-reals. |
Wraith |
|
+ |
- |
+ |
- |
- |
Exact integers and inexact real numbers, a good all-round compromise. |
Bigloo, Scheme 9, Elk (also ISLisp) |
|
+ |
- |
+ |
+ |
- |
The same as the preceding, but with inexact complex numbers as well. |
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 |
|
+ |
+ |
+ |
- |
- |
Full numeric tower with real numbers only. |
Psyche, Ikarus, Rep, Elk (also Clojure) |
|
+ |
+ |
+ |
+ |
- |
Full numeric tower with inexact complex numbers only. |
Gauche, Guile, SISC, KSi, UMB |
|
+ |
+ |
+ |
+ |
+ |
Full numeric tower with both exact and inexact complex numbers. |
Racket, MIT, Gambit, Chicken with the numbers egg, Scheme48/scsh, Kawa, Chibi, Chez, Vicare, Larceny, Ypsilon, Mosh, IronScheme, STklos, Spark (also Common Lisp) |
*These systems are technically exactness-preserving but don't return the right answers when their arithmetic overflows.
See NumericTowerManisComments for Vincent Manis's comments on an earlier version of this page.
See also ComplexRepresentations.