extended type equality
lazarus / 62-General

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littlepaul476 · 2018-11-21 09:22

Can someone explain to me, why this ended with <NOT OK>? Double or
Real alternatives are <OK>.

Code: Pascal  [Select][+][-]window.onload = function(){var x1 =
document.getElementById("main_content_section"); if (x1) { var x =
document.getElementsByClassName("geshi");for (var i = 0; i var i,j:
extended;begin  i:=23500.0*0.032;  j:=752.0;  if i=j then    <OK> 
else    <NOT OK>;end;
Lazarus 1.8.4. FPC 3.0.4, Win32

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marcov · 2018-11-21 09:28

Floating point math is not exact. 

Extended on 32-bit x86 has more precision, so the deviation from the
exact value suddenly fits extended. If you print i you get

7.51999999999999999944E+0002

There is a lot of information about comparing floating point values on
the internet, I suggest you read it for a background.

https://floating-point-gui.de/errors/comparison/
https://bitbashing.io/comparing-floats.html

The common trick is to compare with a small deviation (if abs(x-y)<eps
then instead of x=y),   free Pascal has a helper routine for that
called samevalue

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littlepaul476 · 2018-11-21 10:28

Thanks for explanation. I checked values under Watch List and both i
and j showed 752. SameValue did the trick, even with default epsilon =
0

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wp · 2018-11-21 10:35

Quote from: littlepaul476 on November 21, 2018, 11:28:36 amSameValue
did the trick, even with default epsilon = 0 
The default value here is misleading. The value 0 signals to use a
standard epsilon depending on the floatingpoint data type. Copied from
math.pp:
Code: Pascal  [Select][+][-]window.onload = function(){var x1 =
document.getElementById("main_content_section"); if (x1) { var x =
document.getElementsByClassName("geshi");for (var i = 0; i Const 
EZeroResolution = 1E-16;  DZeroResolution = 1E-12;  SZeroResolution =
1E-4; function SameValue(const A, B: Extended; Epsilon: Extended):
Boolean;begin  if (Epsilon=0) then   
Epsilon:=Max(Min(Abs(A),Abs(B))*EZeroResolution,EZeroResolution);  if
(A>B) then    Result:=((A-B)<=Epsilon)  else   
Result:=((B-A)<=Epsilon);end;

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srvaldez · 2018-11-21 12:38

I played with this for a while
changing the expression i:=23500.0*0.032; to i:=23500.0*32/1000; made
it work
I thought that casting the literal constant to extended would work,
but it made no difference.

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PascalDragon · 2018-11-21 13:40

Simply don't assume that two floating point values are equal (except
when checking for special values like 0, +/- Infinity and NaN).
Everything else will only lead to problems sooner or later.

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Gammatester · 2018-11-21 14:35

Floating point arithmetic works by rounding the true result to the
next representable floating point number (using the selected precision
and rounding mode).

With double precision you have
Code: [Select]0.032 ->
0.0320000000000000006661338147750939242541790008544921875
0.032*23500 ->
752.00000000000001565414464721470721997320652008056640625
The last number is rounded to 752 and with FPC304/Win7 you really get
OK!

OTH, for extended precision you get
Code: [Select]0.032 ->
0.03199999999999999999867185233870525706834087031893432140350341796875
0.032*23500 -> 751.999999999999999968788529959573541106010452494956552
982330322265625The last number is rounded to
751.999999999999999944488848768742172978818416595458984375, and
therefore you get NOT OK.

Your expression 23500.0*32/1000 works, because all numbers are
(representable as) integers and so the result must be an integer.