[fpc-devel] Rounding inconsistent (critical)

[Chris Cheney]

Date sent:      	Mon, 2 Oct 2006 12:59:45 +0200
From:           	"Graeme Geldenhuys" <graemeg.lists at gmail.com>
To:             	"FPC developers' list" <fpc-devel at lists.freepascal.org>
Subject:        	Re: [fpc-devel] Rounding inconsistent (critical)
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> I also ran the exact example given on the Wikipedia site and I also got errors.
> 
>   AssertEquals('Failing on 1', '3.02', FormatFloat('0.00', 3.016));
>   AssertEquals('Failing on 2', '3.01', FormatFloat('0.00', 3.013));
>   AssertEquals('Failing on 3', '3.02', FormatFloat('0.00', 3.015));
>   AssertEquals('Failing on 4', '3.04', FormatFloat('0.00', 3.045));
>   AssertEquals('Failing on 5', '3.05', FormatFloat('0.00', 3.04501));
> 
> 
> Test 1: Passed
> Test 2: Passed
> Test 3: Passed
> Test 4: Failing on 4 expected: <3.04> but was: <3.05>
> Test 5: Passed

See, for example, 

http://support.microsoft.com/default.aspx?scid=kb;EN-US;q42980

(there are plenty of other web sites explaining this sort of thing)

The short version is that very few numbers expressed as a decimal 
fraction are representable ACCURATELY on a computer.

BTW Delphi uses Banker's Rounding by default.