Re: gnu software bugs - long double

[Mischa Baars <mjbaars1977 at gmail dot com>]

On 11/02/2013 09:11 PM, David Given wrote:
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> On 02/11/13 19:48, Mischa Baars wrote:
> [...]
> > I have written a couple of new trigonometric functions for use in
> > the library, and actually I need this to function properly.
> The point is that 1.1 simply cannot be represented precisely as a IEEE
> floating point number, for precisely the same reasons that 1/3 cannot
> be represented precisely as a decimal number (1.3333...). This is
> intrinsic to the way that floating point numbers work. If you try,
> you'll get the closest number that IEEE floats *can* represent.
>
> If you really need a completely precise representation of 1.1, then
> you're not going to be able to use IEEE floats --- you'll have to use
> decimals or some sort of fractional representation instead. I don't
> know if gcc can help you with those, but there are endless helper
> libraries that will do both for you. They're usually pretty slow, though.

You are mistaken :)

Indeed some rational numbers can only be represented up to a certain 
number of bits, like 1 / 3. Others can be exactly represented, like 1 / 8.

All real numbers, and therefore all rational numbers, can be represented 
up to a certain number of bits.

Converting 1.1 from string to double should not be a problem.

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