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

[Thaddy]

@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

Oops, you are correct. And I am using bankers rounding all my life (except true standard bankers rounding is usually always on the sixth decimal (to the fifth), balance sheets and current accounts in 1000th' excluded);
I should have known better.

[srcstorm]

You can try this workaround:

Code: Pascal  [Select][+][-]

1. function RoundHalfUpSymmetric(const d: double): integer;
2. begin
3.   result := 0;
4.   if d <> 0.0 then
5.   begin
6.     result := trunc(d);
7.     if abs(frac(d)) >= 0.5 then
8.       if d > 0.0 then
9.         inc(result)
10.       else
11.         dec(result)
12.   end
13. end;
14.  

[Thaddy]

I would write

Code: Pascal  [Select][+][-]

1. d.frac

Provided sysutils is included..

[Mr.Madguy]

I don't know. 0.5 is 1^-2, i.e. it's number, that can be precisely represented by either fixed point or floating point number. It's binary 0.1. That means, Trunc(X + 0.5) should work properly in virtually any situation.

[Thaddy]

I don't know. 0.5 is 1^-2, i.e. it's number, that can be precisely represented by either fixed point or floating point number. It's binary 0.1. That means, Trunc(X + 0.5) should work properly in virtually any situation.

No. Because of the rounding mode of the CPU. Which is configurable. (SetRoundMode)

[Gerhard Fourie]

 I do a lot of technical programming, and "banker's" rounding does not do it for me.

My Delphi "MyUtils.pas" unit contains this function:

      function RoundCorrect(R: Real): LongInt;
      begin
        Result:= Trunc(R);       // extract the integer part
        if Frac(R) >= 0.5 then   // if fractional part >= 0.5 then...
          Result:= Result + 1;   // ...add 1
      end;

[Handoko]

Hello Gerhard Fourie,
Welcome to the forum.

You don't need to write your own function. You can use SetRoundMode just as Thaddy said.
https://www.freepascal.org/docs-html/rtl/math/setroundmode.html

[taazz]

I do a lot of technical programming, and "banker's" rounding does not do it for me.

My Delphi "MyUtils.pas" unit contains this function:

      function RoundCorrect(R: Real): LongInt;
      begin
        Result:= Trunc(R);       // extract the integer part
        if Frac(R) >= 0.5 then   // if fractional part >= 0.5 then...
          Result:= Result + 1;   // ...add 1
      end;

and this works correctly with negative numbers too?

[Handoko]

According to this wiki page, it is correct and called as Round Half Up
https://en.wikipedia.org/wiki/Rounding#Round_half_up

Sorry, I was wrong. Need more samples to test.

According to this page, that code doesn't produce correct result:
https://en.wikipedia.org/wiki/Rounding#Comparison_of_rounding_modes

[Thaddy]

Handoko, lest you forgot, https://www.freepascal.org/docs-html/rtl/math/setroundmode.html.
I gave that already some time ago.

Note that it is the responsibility of the programmer to restore the rounding mode if he needs something else than the default.

[Gerhard Fourie]

I do a lot of technical programming, and "banker's" rounding does not do it for me.

My Delphi "MyUtils.pas" unit contains this function:

      function RoundCorrect(R: Real): LongInt;
      begin
        Result:= Trunc(R);       // extract the integer part
        if Frac(R) >= 0.5 then   // if fractional part >= 0.5 then...
          Result:= Result + 1;   // ...add 1
      end;

and this works correctly with negative numbers too?

You are right, negative numbers need a bit of a correction:

      function RoundCorrect(R: Real): LongInt;
      begin
        Result:= Trunc(R);                          // extract the integer part
        if Abs(Frac(R)) >= 0.5 then                 // if fractional part >= 0.5 then...
          Result := Result + Trunc(2.0 * Frac(R));  // add +1 or -1, depending on R's sign
      end;

PS I wrote this for Delphi5, which to my knowledge did not have 'SetRoundMode' as an option.