Date: Wed, 13 Jul 2005 09:58:01 +0200 From: John Oxley <john@yoafrica.com> To: Nikolas Britton <nikolas.britton@gmail.com> Cc: questions@freebsd.org Subject: Re: Whats up with KCalc? Message-ID: <20050713075801.GC8552@yoafrica.com> In-Reply-To: <ef10de9a05071223136515c381@mail.gmail.com> References: <ef10de9a05071203165b346ce1@mail.gmail.com> <200507120941.12027.ean@hedron.org> <42D3D25A.9040107@speechpro.com> <200507121110.01535.ean@hedron.org> <ef10de9a05071213443f407987@mail.gmail.com> <ef10de9a05071223136515c381@mail.gmail.com>
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On Wed, Jul 13, 2005 at 01:13:24AM -0500, Nikolas Britton wrote:
> On 7/12/05, Nikolas Britton <nikolas.britton@gmail.com> wrote:
> Ok... this thing is WAY OFF... if you type in 85.49 and then hit the +
> key the thing automatically jumps to
> 85.48999999999999488409230252727866172791!!! My SuSE box shows "85.49"
> but if you copy and paste the number into a text editor it shows
> 85.48999... too.
IANA Mathematician, but my guess would be that there is a rounding
error. KCalc as you have all said uses 96bit long double precision.
This means that floating point numbers are stored as 96bit doubles.
And yes 46 is a floating point (46.000). My varsity days are a bit
hazy, but I believe a double is stored as X bits ^ Y bits. Not sure of
the ratios of X and Y though. This means you can only get a certain
accuracy. If X is 8 for example, the accuracy is 1/(268435456) =~
3.725290e-09.
Therefore your smallest unit number is that and any other number will be
a multiple of that, raised to a power which is where the Y bits comes
in. Oh I forgot to mention that X+Y = 96.
This is probably a very bad explanation and hopefully someone can do it
better :)
-John
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