From: "shyouhei (Shyouhei Urabe)" <shyouhei@...>
Date: 2012-09-19T18:05:09+09:00
Subject: [ruby-core:47590] [ruby-trunk - Bug #7037] float formatting inconsistently rounds half to even


Issue #7037 has been updated by shyouhei (Shyouhei Urabe).


I can't under stand what @nobu says so I did this myself.

@headius mixed two points.

* 1.15 for instance is not exactly representable in floating point number.  So tie-breaking is not the case.
* 1.25 for instance is exact.  This, and only this one in above example, is the tie-breaking, and is rounded to 1.2.  Rounding 1.25 to 1.2 is not inconsistent regarding "half to even".

am I correct?
----------------------------------------
Bug #7037: float formatting inconsistently rounds half to even
https://bugs.ruby-lang.org/issues/7037#change-29514

Author: headius (Charles Nutter)
Status: Closed
Priority: Normal
Assignee: 
Category: core
Target version: 
ruby -v: 2.0.0dev


MRI does not appear to consistently round half to even. I'm not sure what rounding strategy this is, but it rounds xx05 and xx15 to odd for xxx, and other values to even:

irb(main):001:0> "%1.1f" % 1.05
=> "1.1"
irb(main):002:0> "%1.1f" % 1.15
=> "1.1"
irb(main):003:0> "%1.1f" % 1.25
=> "1.2"
irb(main):004:0> "%1.1f" % 1.35
=> "1.4"
irb(main):005:0> "%1.1f" % 1.45
=> "1.4"
irb(main):006:0> "%1.1f" % 1.55
=> "1.6"

None of the tie-breaking strategies I could find (http://en.wikipedia.org/wiki/Rounding#Tie-breaking) seem to support MRI's model.

If MRI is indeed using "half even", xx05 should round to xx0 and xx15 should round to xx2. An example with Java's BigDecimal appears to support this:

irb(main):029:0> java.math.BigDecimal.new('1.05').round(java.math.MathContext.new(2, java.math.RoundingMode::HALF_EVEN)).to_s
=> "1.0"
irb(main):030:0> java.math.BigDecimal.new('1.15').round(java.math.MathContext.new(2, java.math.RoundingMode::HALF_EVEN)).to_s
=> "1.2"
irb(main):031:0> java.math.BigDecimal.new('1.25').round(java.math.MathContext.new(2, java.math.RoundingMode::HALF_EVEN)).to_s
=> "1.2"
irb(main):032:0> java.math.BigDecimal.new('1.35').round(java.math.MathContext.new(2, java.math.RoundingMode::HALF_EVEN)).to_s
=> "1.4"

We would like clarification about the proper rounding tie-breaker strategy to use so we can fix this JRuby issue properly: http://jira.codehaus.org/browse/JRUBY-6889


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