float equality

[spir]

On 02/20/2011 06:17 AM, Jonathan M Davis wrote:
> On Saturday 19 February 2011 20:46:50 Walter Bright wrote:
>> bearophile wrote:
>>> Walter:
>>>> That'll just trade one set of problems for another.
>>>
>>> But the second set of problems may be smaller :-)
>>
>> There's a total lack of evidence for that. Furthermore,
>>
>> 1. Roundoff error is not of a fixed magnitude.
>>
>> 2. A user may choose to ignore roundoff errors, but that is not the
>> prerogative of the language.
>>
>> 3. What is an acceptable amount of roundoff error is not decidable by the
>> language.
>>
>> 4. At Boeing doing design work, I've seen what happens when engineers
>> ignore roundoff errors. It ain't pretty. It ain't safe. It ain't correct.
>
> Honestly, the more that I learn about and deal with floating point numbers, the
> more I wonder why we don't just use fixed point. Obviously that can be a bit
> limiting for the size of the number (on either side of the decimal) -
> particularly in 32-bit land - but with 64-bit numbers, it sounds increasingly
> reasonable given all of the issues with floating point values. Ideally, I
> suppose, you'd have both, but the CPU specifically supports floating point (I
> don't know about fixed point), and I don't think that I've ever used a language
> which really had fixed point values (unless you count integers as fixed point with
> no digits to the right of the decimal).

I don't see how fixed point would solve common issues with floats. Would you 
expand a bit on this?

For me, the source of the issue is inaccurate and unintuitive "translations" 
from/to decimal and binary. For instance (using python just for example):

>>> 0.1
0.10000000000000001
>>> 0.7
0.69999999999999996
>>> 0.3
0.29999999999999999

To solve this, one may use rationals (representing 0.1 by 1/10) or decimals 
(representing decimal digits, each eg by half a byte). Both are costly, indeed.
I may ignore some other points, solved by fixed point arithmetics.

Denis
-- 
_________________
vita es estrany
spir.wikidot.com