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Source for wiki NonFiniteNumbers version 3

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127.11.51.1

NonFiniteNumbers

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== Syntax ==

Here's how various Schemes deal with syntax for non-finite inexact numbers.  "Standard syntax" means what R6RS prescribes: `+inf.0` for positive infinity, `-inf.0` for negative infinity, and both `+nan.0` and `-nan.0` for NaN.

Racket, Gauche, Chicken (with or without the numbers egg), Scheme48, Guile, Kawa, Chez, !Ikarus/Vicare, Larceny, Ypsilon, Mosh, !IronScheme, STklos, Spark, Sagittarius accept and print the standard syntax.

Gambit, Bigloo, Chibi accept and print the standard syntax, except that they do not accept `-nan.0`.

!SigScheme, Scheme 9, Dream, Oaklisp, Owl Lisp are excluded because they do not have inexact non-finite numbers.

The following table concisely describes the other Schemes in the test suite.  "Std syntax" is "yes" if the Scheme can read the standard syntax, "print" shows what `(let* ((i (* 1.0e200 1.0e200)) (n (- i i))) (list i (- i) n))` prints, and "own syntax" is "yes" if the Scheme can reread what it prints.  The implementations are listed in roughly decreasing order of standardosity.

||Scheme||std syntax||prints||own syntax||
||KSi||yes||`(+inf.0 -inf.0 nan.0)`||yes||
||NexJ||yes||`(Infinity -Infinity NaN)`||no||
||VX||yes||`(inf. -inf. -nan.)`||no||
||SCM||*||`(+inf.0 -inf.0 0/0)`||yes||
||S7||no||`(inf.0 -inf.0 -nan.0)`||no||
||SXM||no||`(inf.0 -inf.0 -nan.0)`||no||
||Inlab||no||`(inf.0 -inf.0 -nan.0)`||no||
||UMB||no||`(inf.0 -inf.0 -nan)`||no||
||Shoe||no||`(inf -inf -nan)`||no||
||!TinyScheme||no||`(inf -inf -nan)`||no||
||XLisp||no||`(inf -inf -nan)`||no||
||Schemik||no||`(inf -inf -nan)`||no||
||scsh||no||`(inf. -inf. -nan.)`||no||
||Rep||no||`(inf. -inf. -nan.)`||no||
||RScheme||no||`(inf. -inf. -nan.)`||no||
||Elk||no||`(inf -inf -nan.0)`||no||
||SISC||no||`(infinity.0 -infinity.0 nan.0)`||no||
||BDC||no||`(Infinity -Infinity NaN)`||no||
||MIT||no||`(#[+inf] #[-inf] #[NaN])`||no||

[*] Accepts `+inf.0` and `-inf.0` but not `+nan.0` or `-nan.0`

== NaN equivalence ==

The following implementations return `#t` for `(eqv +nan.0 +nan.0)`: Chez, Gambit, Guile, !Ikarus/Vicare, Kawa, Larceny, Racket, STklos, Sagittarius.

The following implementations return `#f` for `(eqv +nan.0 +nan.0)`: Bigloo, Chibi, Chicken, Gauche, MIT Scheme, Scheme48.

== Infinity examples ==

These are the R6RS examples involving `+inf.0` and `-inf.0` (already accounted for verbally in the "Implementation extensions" section of R7RS):

{{{
(complex? +inf.0)    => #t     ; infinities are real but not rational
(real? -inf.0)       => #t
(rational? -inf.0)   => #f
(integer? -inf.0)    => #f

(inexact? +inf.0)    => #t     ; infinities are inexact

(= +inf.0 +inf.0)    => #t     ; infinities are signed
(= -inf.0 +inf.0)    => #f
(= -inf.0 -inf.0)    => #t
(positive? +inf.0)   => #t
(negative? -inf.0)   => #t
(abs -inf.0)         => +inf.0

(finite? +inf.0)     => #f     ; infinities are infinite
(infinite? +inf.0)   => #t

; infinities are maximal
(max +inf.0 x)       => +inf.0 where x is real
(min -inf.0 x)       => -inf.0 where x is real
(< -inf.0 x +inf.0)) => #t where x is real and finite
(> +inf.0 x -inf.0)) => #t where x is real and finite
(floor +inf.0)       => +inf.0
(ceiling -inf.0)     => -inf.0

; infinities are sticky
(+ +inf.0 x)         => +inf.0 where x is real and finite
(+ -inf.0 x)         => -inf.0 where x is real and finite
(+ +inf.0 +inf.0)    => +inf.0

(+ +inf.0 -inf.0)    => +nan.0 ; sum of oppositely signed infinities is NaN
(- +inf.0 +inf.0)    => +nan.0

(* 5 +inf.0)         => +inf.0 ; infinities are sticky
(* -5 +inf.0)        => -inf.0
(* +inf.0 +inf.0)    => +inf.0
(* +inf.0 -inf.0)    => -inf.0

(/ 0.0)              => +inf.0 ; infinities are reciprocals of zero
(/ 1.0 0)            => +inf.0
(/ -1 0.0)           => -inf.0
(/ +inf.0)           => 0.0
(/ -inf.0)           => -0.0 if distinct from 0.0

(rationalize +inf.0 3)      => +inf.0
(rationalize +inf.0 +inf.0) => +nan.0
(rationalize 3 +inf.0)      => 0.0

(exp +inf.0)         => +inf.0
(exp -inf.0)         => 0.0
(log +inf.0)         => +inf.0
(log 0.0)            => -inf.0
(log -inf.0)         => +inf.0+3.141592653589793i ; approximately
(atan -inf.0)        => -1.5707963267948965 ; approximately
(atan +inf.0)        => 1.5707963267948965 ; approximately

(sqrt +inf.0)        => +inf.0
(sqrt -inf.0)        => +inf.0i

(angle +inf.0)       => 0.0
(angle -inf.0)       => 3.141592653589793
(magnitude (make-rectangular x y)) => +inf.0 where x or y or both are infinite
}}}

== NaN examples ==

These are the R6RS examples involving !NaNs (already accounted for verbally in the "Implementation extensions" section of R7RS):

{{{
(number? +nan.0)   => #t ; NaN is real but not rational
(complex? +nan.0)  => #t
(real? +nan.0)     => #t
(rational? +nan.0) => #f

; NaN compares #f to anything
(= +nan.0 z)       => #f where z numeric
(< +nan.0 x)       => #f where x real
(> +nan.0 x)       => #f where x real

(zero? +nan.0)     => #f ; NaN is unsigned
(positive? +nan.0) => #f
(negative? +nan.0) => #f

; NaN is mostly sticky
(* 0 +inf.0)       => 0 or +nan.0
(* 0 +nan.0)       => 0 or +nan.0
(+ +nan.0 x)       => +nan.0 where x real
(* +nan.0 x)       => +nan.0 where x real and not exact 0

; Sum of +inf.0 and -inf.0 is NaN
(+ +inf.0 -inf.0)  => +nan.0
(- +inf.0 +inf.0)  => +nan.0

; 0/0 is NaN unless both 0s are exact
(/ 0 0.0) => +nan.0
(/ 0.0 0) => +nan.0
(/ 0.0 0.0) => +nan.0

(round +nan.0)     => +nan.0 ; Nan rounds (etc.) to NaN

(rationalize +inf.0 +inf.0) => +nan.0 ; Rationalizing infinity to nearest infinity is NaN
}}}

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2014-12-28 10:07:53

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