Floating point problems

[Jan-Willem Maessen]

On Aug 30, 2006, at 6:04 PM, Lennart Augustsson wrote:

>
> On Aug 30, 2006, at 14:58 , David Roundy wrote:
>
>> On Wed, Aug 30, 2006 at 07:38:35PM +0100, Jamie Brandon wrote:
>>> I recently defied my supervisor and used Haskell to write my
>>> coursework instead of C. All went well until I needed floating point
>>> and started having odd results. As far as I can tell it isn't
>>> substantially affecting my results but it is rather embarrassing
>>> after slagging off C so much. Here are some examples:
>>>
>>>         *Main> 0.2 + 0.1
>>>         0.30000000000000004
>>>         *Main> 0.200000000000000 + 0.100000000000000000
>>>         0.30000000000000004
>>>         *Main> 0.3 + 0.1
>>>         0.4
>>>         *Main> 0.2 + 0.1
>>>         0.30000000000000004
>>>         *Main> it + 0.1
>>>         0.4
>>>
>>> I assume this is a result of the discrepancy between binary and  
>>> decimal
>>> representations of the numbers. Is there any way around? For a  
>>> start, it
>>> would be nice to have a simple way to get 0.1 + 0.2 == 0.3  =  True
>>>
>>> This is with GHC 6.4.1 and GCC 4.0.3
>>
>> The trouble here is that ghci is printing more digits than it really
>> ought to be printing.
>
> No, I don't think it is.  Ghci is printing the number that is  
> closest of all numbers in decimal notation to the Double in  
> question (i.e., 0.1+0.2).  Printing it with fewer decimals would  
> yield a different number if it was read back.

I always wondered why we didn't instead ask for "the number that has  
the fewest digits of significand which converts to the Double in  
question."  Of course, for doubles with a single ulp of difference,  
that's still an awfully long decimal.

I feel like I looked into this once when I was trying to understand  
the bignum-heavy Read instance for Double in the report, and ended up  
with a nasty headache and some fixed-point code which used cute hacks  
and seemed to work with limited testing and the vagaries of gcc as a  
back end.

-Jan-Willem Maessen

>
> 	-- Lennart
>
>
>
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