floating point - Haskell ranges and floats

Question

Why is the behavior of the Haskell range notation different for floats than for integers and chars?

Prelude> [1, 3 .. 10] :: [Int]
[1,3,5,7,9] 
Prelude> [1, 3 .. 10] :: [Float]
[1.0,3.0,5.0,7.0,9.0,11.0]
Prelude> ['a', 'c' .. 'f']
"ace"

I would understand it if the last element was close to the upper bound, but this is obviously not a rounding issue.

Answer 1

The syntax [e1, e2 .. e3] is really syntactic sugar for enumFromThenTo e1 e2 e3, which is a function in the Enum typeclass.

The Haskell standard defines its semantics as follows:

For the types Int and Integer, the enumeration functions have the following meaning:

• The sequence enumFrom e1 is the list [e1,e1 + 1,e1 + 2,…].
• The sequence enumFromThen e1 e2 is the list [e1,e1 + i,e1 + 2i,…], where the increment, i, is e2 ? e1. The increment may be zero or negative. If the increment is zero, all the list elements are the same.
• The sequence enumFromTo e1 e3 is the list [e1,e1 + 1,e1 + 2,…e3]. The list is empty if e1 > e3.
• The sequence enumFromThenTo e1 e2 e3 is the list [e1,e1 + i,e1 + 2i,…e3], where the increment, i, is e2 ? e1. If the increment is positive or zero, the list terminates when the next element would be greater than e3; the list is empty if e1 > e3. If the increment is negative, the list terminates when the next element would be less than e3; the list is empty if e1 < e3.

This is pretty much what you'd expect, but the Float and Double instances are defined differently:

For Float and Double, the semantics of the enumFrom family is given by the rules for Int above, except that the list terminates when the elements become greater than e3 + i∕2 for positive increment i, or when they become less than e3 + i∕2 for negative i.

I'm not really sure what the justification for this is, so the only answer I can give you is that it is that way because it's defined that way in the standard.

You can work around this by enumerating using integers and converting to Float afterward.

Prelude> map fromIntegral [1, 3 .. 10] :: [Float]
[1.0,3.0,5.0,7.0,9.0]