[Chicken-janitors] #1016: Numerator and denominator don't work on inexact numbers

[Chicken Trac]

#1016: Numerator and denominator don't work on inexact numbers
------------------------+---------------------------------------------------
 Reporter:  johnwcowan  |       Owner:         
     Type:  defect      |      Status:  new    
 Priority:  major       |   Milestone:  someday
Component:  unknown     |     Version:  4.8.x  
 Keywords:              |  
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 The R5RS and R7RS require that `numerator` and `denominator` work
 correctly on any rational number.  That means that they should accept all
 inexact numbers except infinities and !NaNs and return inexact results.
 This is not currently true either with or without the numbers egg:

 {{{
 #;1> (numerator 5.0)
 5.0
 #;2> (denominator 5.0)
 1
 #;3> (numerator 5.5)

 Error: (numerator) bad argument type - not a rational number: 5.5

         Call history:

         <syntax>          (numerator 5.5)
         <eval>    (numerator 5.5)       <--
 #;4> (denominator 5.5)

 Error: (numerator) bad argument type - not a rational number: 5.5

         Call history:

         <syntax>          (denominator 5.5)
         <eval>    (denominator 5.5)     <--
 }}}

 Whereas in fact:

 1 is correct

 2 should return 1.0

 3 should return 11.0

 4 should return 2.0

 In the numbers egg this is straightforward: use `inexact->exact` to get a
 ratio, use the ratio version of `numerator` or `denominator`, and then use
 `exact->inexact` to force the result to be inexact again.

 Without the numbers egg, we only have flonum arithmetic.  I suggest the
 following algorithm, which preserves the obvious invariant but doesn't
 always give integer results (hey, that's why we call it ''inexact''
 arithmetic):

 {{{
 (define (denominator x)
   (if (integer? x)
     (if (exact? x) 1 1.0)
     (/ (- x (floor x)))))

 (define (numerator x)
   (* x (denominator x)))
 }}}

 Example with these definitions:

 {{{
 #;56> (define pi 3.1415926535898)
 #;57> (numerator pi)
 22.1875399177921
 #;58> (denominator pi)
 7.0625133059307
 }}}

 These algorithms will return NaN if applied to an infinity or NaN.

-- 
Ticket URL: <http://bugs.call-cc.org/ticket/1016>
Chicken Scheme <http://www.call-with-current-continuation.org/>
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