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Source for wiki NumericTower version 17

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cowan

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66.108.19.185

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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.  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
||-||-||-||-||-||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 without the `numbers` egg, 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 operations overflow.

See NumericTowerManisComments for Vincent Manis's comments on an earlier version of this page.

See also ComplexRepresentations.

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2012-04-04 11:48:16