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Is there an official specification for the round function in Haskell? In GHCi version 7.0.3 I see the following behaviour:

ghci> round (0.5 :: Double)
0
ghci> round (1.5 :: Double)
2

Since both 0.5 and 1.5 are representable exactly as floating point numbers, I expected to see the same behaviour as in Python:

>>> round(0.5)
1.0
>>> round(1.5)
2.0

Is there a rationale for the difference, or is it a quirk of GHCi?

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Note that Python 3 behaves in the same way as GHCi here. – Mark Dickinson May 24 '12 at 16:36
    
Interesting, thanks. Do you happen to know why IEEE specifies rounding to the even number? It seems unintuitive to me - either of round up or round away from zero would make more sense. – Chris Taylor May 24 '12 at 16:54
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I suppose it makes it more likely that rounding errors will cancel out if you round a bunch of numbers and then sum them up... – Chris Taylor May 24 '12 at 16:56
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@ChrisTaylor Yes, it's to avoid bias introduced by rounding. It's often called 'Banker's rounding' (though, iirc, in the EU, round-half-away-from-zero is mandatory for financial applications). With round-half-away-from-zero, it cancels out only if the values are half negative and half positive, with half-to-even, it cancels out more often. – Daniel Fischer May 24 '12 at 17:46
    
It's my understanding that rounding to the even number is the scientific standard. Rounding up is common in grade school for some reason but is otherwise just another convention. – amr Dec 11 '12 at 4:30
up vote 21 down vote accepted

It's in the specification. You can see it in section 6.4.6 of the Haskell report:

round x returns the nearest integer to x, the even integer if x is equidistant between two integers.

As pointed out by @dflemstr, this is in accordance with the IEEE Standard for Floating-Point Arithmetic.

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This is according to the IEEE 754 floating point rounding mode standard. – dflemstr May 24 '12 at 13:44
    
Here's the code for round if anyone is interested: hackage.haskell.org/packages/archive/base/latest/doc/html/sr‌​c/… the check for even is quite obvious there. – Poindexter May 24 '12 at 13:45
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FWIW, for comparison, the python round() is a wrapper around the C99 round() function, which on an implementation that follows C99 Annex F rounds ties away from zero. – janneb May 24 '12 at 13:56

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