# [Haskell-beginners] How to improve the accuracy of floating point calculation?

Mateusz Kowalczyk fuuzetsu at fuuzetsu.co.uk
Wed Feb 6 01:47:32 CET 2013

```I thought that KC was asking why is 0.5 not displayed as 0.5 when it's
supported by the IEEE754. Even if that wasn't question, it is my
question now.

IEEE754 is capable of representing 0.5 with perfect precision; in fact,
it would be `00111111000000000000000000000000'.

My question is why [0.1, 0.2 .. 1.0] comes up with an imprecise
midpoint:
[0.1,0.2,0.30000000000000004,0.4000000000000001,0.5000000000000001,0.6000000000000001,0.7000000000000001,0.8,0.9,1.0]

My initial guess is that the expansion is done by working out the
difference between the first two elements and using that to generate the
rest. This also makes me question why 0.1 is shown properly when it
can't be represented precisely in IEEE754. Quickly rolling own list
generation function:

*Main> let f x y = x : f y (y + y - x)
*Main> take 10 \$ f 0.1 0.2
[0.1,0.2,0.30000000000000004,0.4000000000000001,0.5000000000000001,0.6000000000000001,0.7000000000000001,0.8,0.9,1.0]

reveals the same result as the short-hand which would imply that it's
exactly what it's doing (for the simple case). My question for why can
0.1 be shown properly still stands in this case.

On 06/02/13 00:12, Darren Grant wrote:
> I'm not sure how CReal implements its values, but IEEE754 also supports
> decimal formats preferred for accuracy in many applications. Take a look:
>
>    http://en.wikipedia.org/wiki/IEEE_floating_point
>
>
> Cheers,
> d
>
>
>
>
> On Tue, Feb 5, 2013 at 3:24 PM, Patrick Mylund Nielsen
>
>     http://floating-point-gui.de/
>     http://floating-point-gui.de/formats/fp/
>
>     http://en.wikipedia.org/wiki/Floating_point#Accuracy_problems
>
>
>     On Wed, Feb 6, 2013 at 12:08 AM, KC <kc1956 at gmail.com
>     <mailto:kc1956 at gmail.com>> wrote:
>
>         0.1 cannot be represented exactly in floating point.
>
>         0.5 can be represented exactly.  Why?
>
>
>         On Tue, Feb 5, 2013 at 2:41 PM, yi lu
>         <zhiwudazhanjiangshi at gmail.com
>         <mailto:zhiwudazhanjiangshi at gmail.com>> wrote:
>         > Hi,
>         >
>         > I found that in ghci, I input
>         > [0.1,0.2..2]
>         > and run, I get a result of
>         >
>         >
>         [0.1,0.2,0.30000000000000004,0.4000000000000001,0.5000000000000001,0.6000000000000001,0.7000000000000001,0.8,0.9,1.0,1.1,1.2000000000000002,1.3000000000000003,1.4000000000000004,1.5000000000000004,1.6000000000000005,1.7000000000000006,1.8000000000000007,1.9000000000000008,2.000000000000001]
>         >
>         > But, as you know, it is not the exact answer.
>         >
>         > So, I wonder if there is something I can do to achieve a
>         better performance
>         > and get [0.1,0.2,0.3,0.4..] as the result.
>         >
>         > Thanks.
>         >
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>         >
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>
>
>         --
>         --
>         Regards,
>         KC
>
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