On 2 June 2015 at 04:08,
The Haskell 2010 report defines, in chapter 9, round :: (Real a, Fractional a, Integral b) => a -> b
round x = let (n, r) = properFraction x -- n = truncate x, r = x-n (same sign as x) m = if r < 0 then n - 1 else n + 1 in case signum (abs r - 0.5) of -1 -> n -- round in if |r| < 0.5 1 -> m -- round out if |r| > 0.5 0 -> if even n then n else m
(commented and slightly rearranged). The traditional definition of rounding to integer, so traditional that it is actually given in the OED, is basically
round x = truncate (x + signum x * 0.5)
There was a discussion of rounding recently in another mailing list and I put together this table:
* Round x.5 OUT Ada, Algol W, C, COBOL, Fortran, Matlab, Pascal, PL/I, Python, Quintus Prolog, Smalltalk. The pre-computing tradition.
* Round x.5 to EVEN Common Lisp, R, Haskell, SML, F#, Wolfram Language.
* Round x.5 UP to positive infinity Java, JavaScript, ISO Prolog, Algol 60
* Rounding of x.5 UNSPECIFIED Algol 68, IMP 77
What I was wondering was whether anyone on this list knew why Haskell has the break-ties-to-even definition instead of the traditional break-ties-out one. (And please don't say that it is to get statistical unbiasedness, because given the kinds of data distribution I see, it _isn't_ unbiased.)
This is pure conjecture, but reading about "round half to even" on Wikipedia (http://en.wikipedia.org/wiki/Rounding#Round_half_to_even) shows that it has the most aliases of all tie-breaking strategies, it is also the rounding used in IEEE 754. /M -- Magnus Therning OpenPGP: 0xAB4DFBA4 email: magnus@therning.org jabber: magnus@therning.org twitter: magthe http://therning.org/magnus