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Source for wiki NumericTower version 28

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cowan

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127.10.177.1

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NumericTower

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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-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, JScheme*, BDC*, XLisp*, Schemik*, VX, SXM*, Inlab, Llava, Sixx, Sizzle, Dfsch*, Stalin (also Elisp*, C*)||
||-||+||+||1||Limited-range exact and inexact real numbers||NexJ (also Java)||
||-||+||+||+||Limited-range exact and inexact numbers||S7, Wraith||
||+||-||+||-||Exact integers and inexact real numbers||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, Dfsch (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.

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.

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2013-11-04 03:46:57