[issue5118] '%.2f' % 2.545 doesn't round correctly

[Mark Dickinson]

Mark Dickinson <dickinsm at gmail.com> added the comment:

> print round(2.545, 2) // returns 2.55

Aha!  Yes, that one *is* a bug (see issue #1869), though it's not one that 
I regard as terribly serious, and not one that can be easily solved in all 
cases.

Here's why I don't see it as particularly serious: you're rounding a value 
that's just on the boundary:  2.545+tiny_error should round up, while 
2.545-tiny_error should round down.  But tiny (or not-so-tiny) errors are 
an almost unavoidable part of working with binary floating-point 
arithmetic.  Additionally, whether the binary approximation stored for 
2.545 is less than or greater than the true value depends on many things 
(format of a C double, system C library function used for string-to-double 
conversion, etc.), so in a sense either 2.55 *or* 2.54 can be defended as 
a valid result, and a good numeric programmer won't write code that 
depends on getting one or the other.

Having said that, if you're interested in providing a patch for issue 
#1869 I'd certainly take a look.

If you care about *exact* representations of numbers with a finite number 
of places after the decimal point, you may be interested in Python's 
'decimal' module.

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<http://bugs.python.org/issue5118>
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