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Date: Thu, 30 Oct 2003 23:00:54 +0200
From: "Eli Zaretskii" <eliz AT elta DOT co DOT il>
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To: djgpp AT delorie DOT com
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	=?iso-8859-15?Q?Rafael_Garc=EDa?= on Thu, 30 Oct 2003 14:07:52 +0100)
Subject: Re: double with only 13 digit precision?
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> From: =?iso-8859-15?Q?Rafael_Garc=EDa?= <rafael AT geninfor DOT com>
> Newsgroups: comp.os.msdos.djgpp
> Date: Thu, 30 Oct 2003 14:07:52 +0100
> 
> I thought type double had at least 15 decimal digits of precision

It does.

> but I have found I can get a result with only 13 precise digits. Can
> anyone please explain that result?

This is expected, since

   a - b = a*(1 - b/a)

and, for the case in point, where a and b are close to each other and
thus b/a is on the order of magnitude of one, the precision of this
expression is |a|*10^(-16).  |a| is 4*10^3, so you get 10^(-13) of
absolute pecision.

In other words, this happens because the precision of FP arithmetics
is 10^(-16) relative to the magnitude of the original operands.