Well, 8427.0229, that's what I want.
But what I get is 8427.0224
And that's what I don't unterstand.
- Original Message -
From: Bernd Oppolzer via fpc-pascal
To: Bart via fpc-pascal
Sent: Sunday, January 28, 2024, 10:13:07
Subject: [fpc-pascal] Floating point question
To simplify the problem further:
the addition of 12 /24.0 and the subtraction of 0.5 should be removed, IMO,
because both can be done with floats without loss of precision (0.5 can
be represented exactly in float).
So the problem can be reproduced IMO with this small Pascal program:
program TESTDBL1 ;
var TT : REAL ;
begin (* HAUPTPROGRAMM *)
TT := 8427 + 33 / 1440.0 ;
WRITELN ( 'tt=' , TT : 20 : 20 ) ;
end (* HAUPTPROGRAMM *) .
With my compiler, REAL is always DOUBLE, and the computation is carried
out by a P-Code interpreter
(or call it just-in-time compiler - much like Java), which is written in C.
The result is:
tt=8427.022916667879
and it is the same, no matter if I use this simplified computation or
the original
tt := (8427 - 0.5) + (12 / 24.0) + (33 / 1440.0);
My value is between the two other values:
tt=8427.022916668000
tt=8427.022916667879
ee=8427.022916625000
The problem now is:
the printout of my value suggest an accuracy which in fact is not there,
because with double, you can trust
only the first 16 decimal digits ... after that, all is speculative
a.k.a. wrong. That's why FPC IMO rounds at this
place, prints the 8, and then only zeroes.
The extended format internally has more hex digits and therefore can
reliably show more decimal digits.
But the last two are wrong, too (the exact value is 6... period).
HTH,
kind regards
Bernd
Am 27.01.2024 um 22:53 schrieb Bart via fpc-pascal:
> On Sat, Jan 27, 2024 at 6:23 PM Thomas Kurz via fpc-pascal
> wrote:
>> Hmmm... I don't think I can understand that. If the precision of "double"
>> were that bad, it wouldn't be possible to store dates up to a precision of
>> milliseconds in a TDateTime. I have a discrepancy of 40 seconds here.
> Consider the following simplified program:
>
> var
>tt: double;
>ee: extended;
> begin
>tt := (8427 - Double(0.5)) + (12/ Double(24.0)) +
> (33/Double(1440.0)) + (0/Double(86400.0));
>ee := (8427 - Extended(0.5)) + (12/ Extended(24.0)) +
> (33/Extended(1440.0)) + (0/Extended(86400.0));
>writeln('tt=',tt:20:20);
>writeln('ee=',ee:20:20);
> end.
> ===
> Now see what it outputs:
> C:\Users\Bart\LazarusProjecten\ConsoleProjecten>fpc test.pas
> Free Pascal Compiler version 3.2.2 [2021/05/15] for i386
> ...
> C:\Users\Bart\LazarusProjecten\ConsoleProjecten>test
> tt=8427.022916668000
> ee=8427.022916625000
> C:\Users\Bart\LazarusProjecten\ConsoleProjecten>fpc -Px86_64 test.pas
> Free Pascal Compiler version 3.2.2 [2021/05/15] for x86_64
> ..
> C:\Users\Bart\LazarusProjecten\ConsoleProjecten>test
> tt=8427.022916668000
> ee=8427.022916668000
> On Win64 both values are the same, because there Extended = Double.
> On Win32 the Extended version is a bit closer to the exact solution:
> 8427 - 1/2 + 1/2 + 33/1440 = 8427 + 11/480
> Simple as that.
> Bart
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