RFC: Fixing floating point conversions.
Nick Bowler
nbowler at elliptictech.com
Thu Feb 25 10:40:48 EST 2010
Currently, Haskell does not provide any mechanism for converting one
floating type to another, since realToFrac appears to be fundamentally
broken in this regard. For details on that matter, see the discussion
at http://hackage.haskell.org/trac/ghc/ticket/3676. Essentially,
realToFrac does not preserve floating values which are not representable
as a Rational.
I'd like to start discussing improvements to this situation by
submitting some ideas which I have considered for comments. First
though, two proposals:
* Codify a requirement that Double values are a superset of Float
values. C demands this, as it makes it possible to define Float to
Double conversions as value-preserving. I couldn't find such a
statement in the report; idea #1 below requires this.
* Define toRational as throwing an exception on non-finite input.
Infinities magically turning into integers is simply not nice. I
personally feel that floating types should not be instances of the
Real class, but that discussion can be saved for another day.
*** Idea #0 ***
Fix realToFrac.
This seems to be impossible without highly undesirable consequences, see
the trac ticket linked above for details.
*** Idea #1 ***
Add two methods to the RealFloat class:
toDouble :: RealFloat a => a -> Double
fromDouble :: RealFloat a => Double -> a
and a function:
toFloating :: (RealFloat a, RealFloat b) => a -> b
toFloating = fromDouble . toDouble
Advantages:
* No extensions (other than this one) beyond Haskell 98 are required.
* Simple to define instances, exactly two functions per floating type.
* Trivial to implement.
Disadvantages:
* It encodes directly into the RealFloat class the knowledge that
Double can represent values of any other floating type. This
makes it difficult or impossible to create new floating types later.
*** Idea #2 ***
Similar to #1, except using a "generic" type instead of Double.
Define a new type, call it FloatConvert, which represents "rational plus
other values". Something along the lines of:
data FloatConvert
= FCZero Bool -- Signed zero
| FCInfinity Bool -- Signed infinity
| FCNaN Integer -- Generic NaN
| FCFinite Rational -- Finite, non-zero value
Add two new methods to the RealFloat class:
toFloatConvert :: RealFloat a => a -> FloatConvert
fromFloatConvert :: RealFloat a => FloatConvert -> a
and a function:
toFloating :: (RealFloat a, RealFloat b) => a -> b
toFloating = fromFloatConvert . toFloatConvert
Advantages:
* No extensions (other than this one) beyond Haskell 98 are required.
* Simple to define instances, exactly two functions per floating type.
* Easy to add floating types to the language, and easy for users to
define their own in libraries.
Disadvantages:
* A data type whose sole purpose is to convert floating types seems
like a wart.
* While the free-form encoding of NaN values will allow conversion
from a type to itself to be the identity function, it may make
it tricky to perform the "ideal" conversion between different
types.
*** Idea #3 ***
Use a multi-parameter type class:
class FloatConvert a b where
toFloating :: a -> b
Advantages:
* Can define any conversion imaginable without constraints.
* Straightforward to add floating types to the language.
Disadvantages:
* Requires multi-parameter type classes.
* Not practical for library authors to define their own instances
of this class except in special circumstances, since it requires
knowledge of all other floating types.
Of these three ideas, I think #2 (or something similar) is the most
workable. What do others think?
--
Nick Bowler, Elliptic Technologies (http://www.elliptictech.com/)
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