From: Yui NARUSE <naruse@...>
Date: 2011-09-09T18:24:50+09:00
Subject: [ruby-core:39422] [Ruby 1.9 - Bug #5273] Float#round returns the wrong floats for higher precision


Issue #5273 has been updated by Yui NARUSE.


This seems not a bug:
printf "%.40f\n", 2.5e-22 #=> 0.0000000000000000000002499999999999999769

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Bug #5273: Float#round returns the wrong floats for higher precision
http://redmine.ruby-lang.org/issues/5273

Author: Marc-Andre Lafortune
Status: Open
Priority: Normal
Assignee: 
Category: core
Target version: 1.9.3
ruby -v: r33186


Float#round returns the wrong floats for higher precision.

Rounding can be off:
    2.5e-22.round(22) # => 2.0e-22

It can also return values that have extra decimals:
    2.5e-31.round(31) # => 3.0000000000000003e-31
    2.5e-36.round(36) # => 2.9999999999999998e-36

Both errors can occur at the same time too:
2.5e-39.round(39) # => 2.0000000000000002e-39

I believe these errors occur only for ndigits >= 22. For ndigits > 22, 10**(-ndigits) is not an exact Float (as 5 ** 23 won't fit in the 53 bits of a double's mantissa). For ndigits < 22, there should be enough bits left to avoid rounding errors.

For ndigits >= 22, the algorithm to use should be similar to the one used to convert doubles to string.

Hopefully, this is the last bug for #round with a given precision.


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