Issue #8883 has been updated by marcandre (Marc-Andre Lafortune).


david_macmahon (David MacMahon) wrote:
>  While playing around with this, I see that integer Floats also have some special handling:

Right. Floats are inexact while Integers & Rational are exact, and so are Complex with exact components. Rational(1/1) and 1 should yield the same mathematical result, but with floats that can be tricky.  For example there are infinitely many different bigdecimals that will map to 1.0 (say 1.000....1 and 1.000...2 with enough zeros), but they don't behave exactly the same way, for example if you substract 1), so we can't freely map them.

>  Oddly though, this can result in non-reduced Rationals:
>  
>  $ ruby -r mathn -e 'p [2/2.0, 2/2.5]'
>  [(2/2), 0.8]

Oh oh, that's a bug. It's not even related to 'mathn'. I opened a new issue about this: https://bugs.ruby-lang.org/issues/8894
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Bug #8883: Rational canonicalization unexpectedly converts to Fixnum
https://bugs.ruby-lang.org/issues/8883#change-41732

Author: melquiades (Paul Cantrell)
Status: Rejected
Priority: Normal
Assignee: 
Category: lib
Target version: 
ruby -v: ruby 2.0.0p247 (2013-06-27 revision 41674) [x86_64-darwin12.3.0]
Backport: 1.9.3: UNKNOWN, 2.0.0: UNKNOWN


The documentation for Rational (http://www.ruby-doc.org/core-2.0.0/Rational.html) states that the result of creating or doing arithmetic on Rationals returns Rationals, as one would expect. Examples from the docs:

    Rational(1)      #=> (1/1)
    3.to_r           #=> (3/1)
    Rational(-2, 9) * Rational(-9, 2)  #=> (1/1)

These all work as documented in 1.9. In 2.0, however, they all return Fixnum:

    Rational(1)      #=> 1
    3.to_r           #=> 3
    Rational(-2, 9) * Rational(-9, 2)  #=> 1

This leads to unexpected behavior:

    Rational(2) / Rational(3)  # => 0  ...but returns (2/3) in 1.9

That behavior is potentially dangerous. Math that may *usually* work, but suddenly start suffering from truncation errors depending on intermediate results. For example:

  def should_always_return_one(a, b, c)
    (Rational(a, c) + Rational(b, c)) / (a + b) * c
  end

Under 1.9:

    should_always_return_one(2, 3, 7) #=> (1/1)
    should_always_return_one(2, 4, 7) #=> (1/1)
    should_always_return_one(2, 5, 7) #=> (1/1)
    should_always_return_one(2, 6, 7) #=> (1/1)

Under 2.0:

    should_always_return_one(2, 3, 7) #=> 1
    should_always_return_one(2, 4, 7) #=> 1
    should_always_return_one(2, 5, 7) #=> 0   Oops!
    should_always_return_one(2, 6, 7) #=> 1

Either the docs are wrong, or this is a bug. I vote bug. Whether arithmetic expressions truncate the result should not depend on whether intermediate values just happen to be integers! Such behavior renders Rational almost too dangerous to use in situations where exact results are required. (Yes, I realize that requiring 'mathn' fixes this, but even with such a workaround as an option, this is dangerously broken. See also #2121.) Note that floating point arithmetic does _not_ exhibit this behavior.



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