## Backport #3803

### BigDecimal::ROUND_HALF_DOWN/ROUND_HALF_EVEN behave incorrectly (disagree with JRuby and the rest of the world)

**Description**

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The incorrect behaviour is that all fractional values between 0.5 (inclusive) and 0.6 (non-inclusive) are subject to the rounding policy for 'half', whereas it should only be applied for fractional values exactly equal to 0.5.

This means that, for example, 0.59 is rounded down to 0 by ROUND_HALF_DOWN and ROUND_HALF_EVEN:

>> BigDecimal.new("0.59").round(0, BigDecimal::ROUND_HALF_DOWN).to_s('F') => "0.0" >> BigDecimal.new("0.56").round(0, BigDecimal::ROUND_HALF_EVEN).to_s('F') => "0.0"

The behaviour is actually specified this way in the RDoc:

ROUND_HALF_DOWN: round up if the appropriate digit >= 6, otherwise truncate

But this is most definitely not what most people would expect from 'round half down' (see eg: http://en.wikipedia.org/wiki/Rounding#Round_half_down ). I would expect it to only round down if the fractional part is less than or *exactly equal* to 0.5. It needs to take into account more than just the first decimal digit to do this; while the first decimal digit of 0.59 may be 5, it is not equal to 0.5 and hence should not be subject to the 'half down' rounding policy. (Note that ROUND_HALF_UP still works correctly, since the correct behaviour here can indeed be implemented by only inspecting the first decimal digit; but this is not the case for ROUND_HALF_DOWN or in general for ROUND_HALF_EVEN)

Rather misleadingly, ROUND_HALF_EVEN is specified as being "banker's rounding":

ROUND_HALF_EVEN: round towards the even neighbor (Banker’s rounding)

But since it incorrectly applies the 'half towards even' policy not just to 0.5, but to all values in the [0.5, 0.6) interval, it is not "banker's rounding" as this is usually defined, and is surely a biased rounding policy, which is exactly what banker's rounding is seeking to avoid (see eg http://en.wikipedia.org/wiki/Rounding#Round_half_to_even )

I note (as just one example) that Java's BigDecimal specifies and implements ROUND_HALF_DOWN in the correct way: http://download-llnw.oracle.com/javase/6/docs/api/java/math/BigDecimal.html#ROUND_HALF_DOWN

Rounding mode to round towards "nearest neighbor" unless both neighbors are equidistant, in which case round down.

And that JRuby's BigDecimal appears to be based on this, hence is correct and hence disagrees with MRI when (for example) applying ROUND_HALF_DOWN to 0.59:

irb(main):004:0> RUBY_PLATFORM => "java" irb(main):005:0> BigDecimal.new("0.59").round(0, BigDecimal::ROUND_HALF_DOWN).to_s('F') => "1.0"

Backport to 1.8.7 would be nice if this gets fixed.

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**Related issues**

### Associated revisions

- ext/bigdecimal/bigdecimal.c: fix rounding algorithms for half-down and half-even. This change is based on the patch created by Matthew Willson, the reporter of this bug. [Bug #3803]
- test/bigdecimal/test_bigdecimal.rb: add tests for above changes.

- ext/bigdecimal/bigdecimal.c: fix rounding algorithms for half-down and half-even. This change is based on the patch created by Matthew Willson, the reporter of this bug. [Bug #3803]
- test/bigdecimal/test_bigdecimal.rb: add tests for above changes.

### History

#### #1 Updated by Shyouhei Urabe over 5 years ago

**Status**changed from*Open*to*Assigned***Assignee**set to*Kenta Murata*

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#### #2 Updated by Kenta Murata over 5 years ago

**Target version**set to*1.9.3***Category**set to*ext*

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This is bugs of BigDecimal, which have not been noticed for a long time.

Thank you very much for your report.

While I will correct these bugs in a few days,

if you have appropriate patches, I want to review and incorporate them.

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#### #3 Updated by Matthew Willson over 5 years ago

**File**ruby_bigdecimal_round_half.patch added**File**ruby_bigdecimal_round_half_with_comments.patch added

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#### #4 Updated by Matthew Willson over 5 years ago

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Thanks Kenta, yeah that would be great if you get a moment to review the attached patch. I included a regression test and a fix to the rdoc comments. It fixes the issue for me.

The version with comments includes some comments I added to help me figure out what's going on there, the other patch is more minimal.

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#### #5 Updated by Matthew Willson over 5 years ago

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(I should say the patch is against SVN trunk)

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#### #6 Updated by Kenta Murata over 5 years ago

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Thank you for attaching your patches.

I'll review them tonight.

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#### #7 Updated by Kenta Murata over 5 years ago

**% Done**changed from*0*to*100***Status**changed from*Assigned*to*Closed*

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This issue was solved with changeset r29293.

Matthew, thank you for reporting this issue.

Your contribution to Ruby is greatly appreciated.

May Ruby be with you.

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#### #8 Updated by Shane Emmons almost 5 years ago

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Why isn't this being back-ported into 1.8.7 and 1.9.2? This is a rather critical bug to anyone working with financial transactions. It seems like this is an obvious bug that should be fixed in all currently maintained branches.

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#### #9 Updated by Kenta Murata almost 5 years ago

**Tracker**changed from*Bug*to*Backport***Status**changed from*Closed*to*Assigned***Assignee**changed from*Kenta Murata*to*Yuki Sonoda*

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#### #10 [ruby-core:35540] Updated by Kenta Murata almost 5 years ago

**Target version**changed from*1.9.3*to*1.9.2*

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#### #11 Updated by Kenta Murata over 4 years ago

**Status**changed from*Assigned*to*Closed*

This issue was solved with changeset r29293.

Matthew, thank you for reporting this issue.

Your contribution to Ruby is greatly appreciated.

May Ruby be with you.

- ext/bigdecimal/bigdecimal.c: fix rounding algorithms for half-down and half-even. This change is based on the patch created by Matthew Willson, the reporter of this bug. [Bug #3803]
- test/bigdecimal/test_bigdecimal.rb: add tests for above changes.

#### #12 Updated by Yui NARUSE over 4 years ago

**Target version**deleted ()*1.9.2*