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http://issues.apache.org/jira/browse/MATH-151?page=comments#action_12415733 ]
Luc Maisonobe commented on MATH-151:
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The point is neither on the rounding method not on the scale factor, it is
rather on the initial number itself.
39.245 has no exact representation in IEE754. it lies between two representable
numbers (I forgot 4 bits in my previous post):
0x139f5c28f5c28f * 2^-47 < 39.245 < 0x139f5c28f5c290 * 2^-47
or 0x27.3eb851eb851e < 39.245 < 27.3eb851eb8520
or 39.2449999999999974420461512636... < 39.245 <
39.2450000000000045474735088646...
When we talk about 39.245, we refer to the decimal representation that was
parsed either by some data input function using something like
Double.parseDouble(String) or we refer to a litteral value in the Java code,
which in fact is also parsed at compilation time, probably also by
double.parseDouble(String) or a similar function. The virtual machine doesn't
see the 39.245 real number we want, it sees either 0x27.3EB851EB851E or
x27.3EB851EB8520 depending on the parsing behaviour. This is not a Java-related
problem, it is also true for languages like C, C++, fortran, whatever.
In the case discussed here, the value was the low one (i.e. 0x27.3EB851EB851E,
or 39.2449999999999974420461...). The parsing method did a good job here in my
opinion as this number is the closest one to the real number we wanted (the
error is about 2.55e-15 and it would have been 4.54e-15 if the other
alternative were chosen).
Going back to the initial problem, and assuming we now start from
39.2449999999999974420461..., we want to round this number 2 digits after the
decimal point. MathUtils.round answer is 39.24 (really
39.2400000000000019895...), which is "only" 0.0049999999999954525264... away
from out number. Answering 39.25 (which CAN be represented exactly in IEEE754)
would be "0.005000000000002557953848..." away. The initial number is not
exactly at a 0.5 * 10^-n boundary, so switching between ROUND_HALF_DOWN,
ROUND_HALF_UP or ROUND_HALF_EVEN does not change anything (I have checked this).
> MathUtils.round incorrect result
> --------------------------------
>
> Key: MATH-151
> URL: http://issues.apache.org/jira/browse/MATH-151
> Project: Commons Math
> Type: Bug
> Versions: 1.1 Final
> Environment: Win2K, Sun JDK1.5.0_05 b05
> Reporter: Buza Zoltán
>
> MathUtils.round(39.245, 2) results 39.24, however it should be 39.25, with
> default rounding mode BigDecimal.ROUND_HALF_UP.
> I found that internally MathUtils.round multiplies the given number by
> 10^scale.
> 39.245 * 100.0 results 3924.49999...5 , and after this the calculation is
> not correct any more.
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