Version 28 (modified by cowan, 4 years ago) (diff)


The numeric tower

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. 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.

----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, JScheme*, BDC*, XLisp*, Schemik*, VX, SXM*, Inlab, Llava, Sixx, Sizzle, Dfsch*, Stalin (also Elisp*, C*)
-++1Limited-range exact and inexact real numbersNexJ (also Java)
-+++Limited-range exact and inexact numbersS7, Wraith
+-+-Exact integers and inexact real numbersBigloo, Scheme 9, Elk (also ISLisp)
+-++Exact integers, inexact real numbers, and inexact complex numbersSCM
++--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 onlyPsyche, Ikarus, Rep, Dfsch (also Clojure)
++++Full numeric towerRacket, 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.

In my opinion, the reasonable general-purpose towers are --+- (fixnums and flonums), +-+- (fixnums, bignums, and flonums), and ++++ (full).

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.