Round to nearest integer or round up if exactly in middle?

[Kallaste]

Hello,

I know of the function

Code: [Select]

Round(X: Real): Longint which rounds to the nearest whole number unless the input is exactly in the middle of two integers, in which case it will use "banker's rounding" and round to the nearest even integer. Is there a way to tell it not to use banker's rounding, but to simply round up in this case?

If not, I need to figure out the simplest way to get the digits to the right of the decimal place of the input value (i.e., is modulus the simplest way or is there a built in function?) so that I can round it up myself if they are equal to .5. Does anyone have any advice?

Thanks.

[Phil]

know of the function

Code: [Select]

Round(X: Real): Longint which rounds to the nearest whole number unless the input is exactly in the middle of two integers, in which case it will use "banker's rounding" and round to the nearest even integer. Is there a way to tell it not to use banker's rounding, but to simply round up in this case?

I think the ancient Str procedure can be used. If I recall correctly, I don't think it uses banker's rounding. Test to be sure.

http://www.freepascal.org/docs-html/rtl/system/str.html

[Kallaste]

Ha, it works! See, this is why it is good to ask questions on forums. I never would have known about that function. Thank you!

[Mr.Madguy]

I don't know. Something like this is usually used:

Code: Pascal  [Select][+][-]

1. function MyRound(AReal:Real):Integer;
2. begin
3.   if AReal > 0 then begin
4.     Result := Trunc(AReal + 0.5);
5.   end
6.   else begin
7.     Result := Trunc(AReal - 0.5);
8.   end;
9. end;
10.  

[ASerge]

Is there a way to tell it not to use banker's rounding, but to simply round up in this case?

Math.SetRoundMode(rmUp). Example:

Code: Pascal  [Select][+][-]

1. {$APPTYPE CONSOLE}
2. program Project1;
3.  
4. uses Math;
5.  
6. var
7.   L, U: LongInt;
8.   D: Double;
9. begin
10.   D := 6.5;
11.   L := Round(D);
12.   Math.SetRoundMode(rmUp);
13.   U := Round(D);
14.   Writeln('D=', D:0:2, ' L=', L, ' U=', U);
15.   Readln;
16. end.

[Mr.Madguy]

Is there a way to tell it not to use banker's rounding, but to simply round up in this case?

Math.SetRoundMode(rmUp). Example:

Code: Pascal  [Select][+][-]

1. {$APPTYPE CONSOLE}
2. program Project1;
3.  
4. uses Math;
5.  
6. var
7.   L, U: LongInt;
8.   D: Double;
9. begin
10.   D := 6.5;
11.   L := Round(D);
12.   Math.SetRoundMode(rmUp);
13.   U := Round(D);
14.   Writeln('D=', D:0:2, ' L=', L, ' U=', U);
15.   Readln;
16. end.

Yeah, and now try 6.3.

[ASerge]

Yeah, and now try 6.3.

Sorry, missed "if they are equal to .5".

[User137]

Odd, is it the roundmode not working or does it mean something else?

Code: Pascal  [Select][+][-]

1. procedure TForm1.FormCreate(Sender: TObject);
2. begin
3.   Math.SetRoundMode(rmUp);
4.   memo1.Lines.Add('5.5: '+inttostr(round(5.5)));
5.   memo1.Lines.Add('6.5: '+inttostr(round(6.5)));
6.   memo1.Lines.Add('7.5: '+inttostr(round(7.5)));
7.   memo1.Lines.Add('8.5: '+inttostr(round(8.5)));
8. end;

Code: Pascal  [Select][+][-]

1. 5.5: 6
2. 6.5: 6
3. 7.5: 8
4. 8.5: 8

With MyRound() by Mr.Madguy i get:

Code: Pascal  [Select][+][-]

1. 5.5: 6
2. 6.5: 7
3. 7.5: 8
4. 8.5: 9

[Thaddy]

That looks like a bug... I tested it with FPC trunk and get the same rather funny results...

[Mr.Madguy]

Odd, is it the roundmode not working or does it mean something else?

Code: Pascal  [Select][+][-]

1. procedure TForm1.FormCreate(Sender: TObject);
2. begin
3.   Math.SetRoundMode(rmUp);
4.   memo1.Lines.Add('5.5: '+inttostr(round(5.5)));
5.   memo1.Lines.Add('6.5: '+inttostr(round(6.5)));
6.   memo1.Lines.Add('7.5: '+inttostr(round(7.5)));
7.   memo1.Lines.Add('8.5: '+inttostr(round(8.5)));
8. end;

Code: Pascal  [Select][+][-]

1. 5.5: 6
2. 6.5: 6
3. 7.5: 8
4. 8.5: 8

Strange, but it should work like Ceil.

[balazsszekely]

@Thaddy
It's not a bug: "In the case of .5, the algorithm uses "banker's rounding": .5 values are always rounded towards the even number. "
http://www.freepascal.org/docs-html/rtl/system/round.html

[rvk]

It's not a bug: "In the case of .5, the algorithm uses "banker's rounding": .5 values are always rounded towards the even number. "
http://www.freepascal.org/docs-html/rtl/system/round.html

And when exactly is the setting of SetRoundMode() used?

[Mr.Madguy]

Lol. FPC simply precalculates round(constant) value and therefore doesn't respect SetRoundMode.

This doesn't work:

Code: Pascal  [Select][+][-]

1.   Math.SetRoundMode(rmUp);
2.   Memo1.Lines.Add('6.5: '+IntToStr(round(6.5)));
3.  

Cuz it's being "optimized" into:

Code: Pascal  [Select][+][-]

1.   Math.SetRoundMode(rmUp);
2.   Memo1.Lines.Add('6.5: '+IntToStr(6));
3.  

This works:

Code: Pascal  [Select][+][-]

1.   Math.SetRoundMode(rmUp);
2.   X := 6.5;//Double
3.   Y := Round(X);//Integer
4.   Memo1.Lines.Add('6.5: '+IntToStr(Y));
5.  

[rvk]

Yeah, that's real neat.
With the example:

Code: Pascal  [Select][+][-]

1. procedure TForm1.FormCreate(Sender: TObject);
2. var
3.   Y: Double;
4. begin
5.   Math.SetRoundMode(rmUp);
6.   Y := 5.5; memo1.Lines.Add('5.5: '+inttostr(round(Y)) + ' or as constant ' + inttostr(round(5.5)));
7.   Y := 6.5; memo1.Lines.Add('6.5: '+inttostr(round(Y)) + ' or as constant ' + inttostr(round(6.5)));
8.   Y := 7.5; memo1.Lines.Add('7.5: '+inttostr(round(Y)) + ' or as constant ' + inttostr(round(7.5)));
9.   Y := 8.5; memo1.Lines.Add('8.5: '+inttostr(round(Y)) + ' or as constant ' + inttostr(round(8.5)));
10. end;

Code: [Select]

5.5: 6 or as constant 6
6.5: 7 or as constant 6
7.5: 8 or as constant 8
8.5: 9 or as constant 8
Something to be noted in the documentation.

[Handoko]

@Thaddy
It's not a bug: "In the case of .5, the algorithm uses "banker's rounding": .5 values are always rounded towards the even number. "
http://www.freepascal.org/docs-html/rtl/system/round.html

Banker's Rounding is also called as Round-Half-Even, it is commonly used for financial calculations. Read more here:
http://www.eetimes.com/document.asp?doc_id=1274485
http://mathematica.stackexchange.com/questions/2116/why-round-to-even-integers