wiki:NumericTower

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

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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.

exactness-preservingratiosinexactcomplexDescriptionImplementations
----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.