## 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