Round to nearest integer strange results

haskell floating-point

14,860

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.

14,860

Chris Taylor

I'm broadly interested in very applied math. I try to apply ideas from mathematics, statistics, machine learning, formal systems and computer science to solve real-world problems. Mostly in applied finance/quantitative trading, but in other areas if the mood takes me.

Updated on July 11, 2022

Comments

Chris Taylor almost 2 years
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?
- Mark Dickinson almost 12 years
  
  Note that Python 3 behaves in the same way as GHCi here.
- Chris Taylor almost 12 years
  
  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...
- Daniel Fischer almost 12 years
  
  @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.
- amr over 11 years
  
  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.
dflemstr almost 12 years

This is according to the IEEE 754 floating point rounding mode standard.
Poindexter almost 12 years

Here's the code for round if anyone is interested: hackage.haskell.org/packages/archive/base/latest/doc/html/sr‌c/… the check for even is quite obvious there.
janneb almost 12 years

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.
SwiftsNamesake over 6 years

@Poindexter The link is dead. Long live the link!