doubleValue returns incorrect infinities and NaNs and zeroes

[detreville]

With Rational<BigInt> values, incorrect infinities or NaNs or zeroes are returned for doubleValue when the numerators or denominator or both are too large themselves to fit inside a Double, even when the values themselves fit.

It would be great to document this behavior or even to correct for it.

Example test program:

import Foundation
import NumberKit

var x: Rational<BigInt> = 1

while true {
  print("\(x)")
  print("numerator.doubleValue = \(x.numerator.doubleValue)")
  print("denominator.doubleValue = \(x.denominator.doubleValue)")
  print("doubleValue = \(x.doubleValue)")
  if x.doubleValue.isNaN {
    break
  }
  x *= 101
  x /= 100
  print()
}

Example test output:

...

449290712499035178136313067576445965611259479254722670514813444007703755277757233626012171465497954998012097338429625913922663389615772353420792692877397988852736997750126238302536602889821678795213590136955628111947677132802585714228163560288611949064673775051015631052360866493066504213939770088265101/100000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000
numerator.doubleValue = 4.4929071249903515e+302
denominator.doubleValue = 1e+302
doubleValue = 4.492907124990351

45378361962402552991767619825221042526737207404726989721996157844778079283053480596227229318015293454799221831181392217306189002351193007695500061980617196874126436772762750068556196891871989558316572603832518439306715390413061157137044519589149806855532051280152578736288447515799716925607916778914775201/10000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000
numerator.doubleValue = 4.537836196240255e+304
denominator.doubleValue = 1e+304
doubleValue = 4.537836196240256

4583214558202657852168529602347325295200457947877425961921611942322586007588401540218950161119544638934721404949320613947925089237470493777245506260042336884286770114049037756924175886079070945389973832987084362369978254431719176870841496478504130492408737179295410452365133199095771409486399594670392295301/1000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000
numerator.doubleValue = 4.583214558202658e+306
denominator.doubleValue = 1e+306
doubleValue = 4.583214558202658

462904670378468443069021489837079854815246252735620022154082806174581186766428555562113966273074008532406861899881382008740434012984519871501796132264276025312963781518952813449341764493986165484387357131695520599367803697603636863954991144328917179733282455108836455688878453108672912358126359061709621825401/100000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000
numerator.doubleValue = inf
denominator.doubleValue = 1e+308
doubleValue = inf

46753371708225312749971170473545065336339871526297622237562363423632699863409284111773510593580474861773093051888019582882783835311436507021681409358691878556609341933414234158383518213892602713923123070301247580536148173457967323259454105577220635153061527965992482024576723763975964148170762265232671804365501/10000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000
numerator.doubleValue =   inf
denominator.doubleValue = inf
doubleValue = nan