Re: [libreoffice-users] ROUND function consistency

I just performed a bit of a test.
Cells across.
A1| =RANDBETWEEN(0,100000)/100  # simulate dollar and cent amounts 
between 0.00 and $1000.00
B1| =A1*0.15                    # simulate a tax of 15% on the amounts in A
C1| =ROUND(B1,2)                # round the tax amount to 2 places 
(whole cents) using the Calc ROUND function
D1| =VBRND(B1,2)                # round the tax to 2 places using a 
macro function that uses the VBA compatible round function (bankers 
rounding)
E1| =INT(B1*100+0.5)/100        # round the tax the old school way.

Function VBRND(c,d)
VBRND = round(c,d)
End Function

I then copied this row down another 999 rows and performed some 
summation at the bottom of the 1000 results. I regenerated the random 
values in A ten times and recorded the summations below.

(sum RNDBETWEEN) * 0.15 	sum (RNDBETWEEN * 0.15) 	Sum ROUND() 	ABS error 
ROUND()
	sum VBRND() 	ABS error VBRND()	sum int(val*100+0.5)/100 	ABS Error old 
school
75056.829 	75056.829 	75057.07 	0.24100000000908 	75056.74 	0.089000 
75057.07 	0.24100000000908
75388.419 	75388.419 	75388.59 	0.171000000002095 	75388.4 	0.019000 
75388.59 	0.171000000002095
74833.6095 	74833.6095 	74833.83 	0.220499999995809 	74833.44 	0.169500 
74833.83 	0.220499999995809
73028.487 	73028.487 	73028.76 	0.273000000001048 	73028.42 	0.067000 
73028.76 	0.273000000001048
73042.698 	73042.698 	73042.95 	0.251999999993131 	73042.69 	0.008000 
73042.95 	0.251999999993131
74173.5075 	74173.5075 	74173.8 	0.292499999995925 	74173.46 	0.047500 
74173.8 	0.292499999995925
75420.3825 	75420.3825 	75420.64 	0.257499999992433 	75420.4 	0.017500 
75420.64 	0.257499999992433
74621.5965 	74621.5965 	74621.85 	0.25350000000617 	74621.55 	0.046500 
74621.85 	0.25350000000617
75481.0995 	75481.0995 	75481.41 	0.310500000006868 	75481.12 	0.020500 
75481.41 	0.310500000006868
73694.1585 	73694.1585 	73694.39 	0.231499999994412 	73694.03 	0.128500 
73694.39 	0.231499999994412

        
	Av. Err. 	0.250299999999697 	Av. Err. 	0.061300 	Av. Err. 
0.250299999999697

        
        Std. Dev.       0.038875        Std. Dev.       0.053381        Std. Dev.       0.038875




I found that the average magnitude of the error was least with the 
bankers rounding although this ad a little more spread. Bankers rounding 
also had less bias.

Steve

On 05/06/2022 21:55, Michael D. Setzer II wrote:
> One windows excell page mentions that it uses the
> banking rounding method, which I believe is the round to
> nearest even. So, using that method 12.125 would round
> to 12.12, while 12.135 would round to 12.14..
> With this method if next digit is 1,2,3,4 the number
> rounds down. If it is 6,7,8,9 it rounds up. If 0 it does
> nothing, but if it is 5, it has to check if the key pervious
> digit is an even or old number. If it is even, then it rounds
> down, if odd it rounds up.
>
> The regular LibreOffice round uses the standard round
> function.
>
> Usually, the standard round is used, but know that some
> government regulations require the banking/roundeven
> or roundodd method.
>
> Was surprized that excell's would default to banking?
> Note sure why they don't provide one for each method, or
> have an option to set.
>
>
>
> On 5 Jun 2022 at 11:37, Johnny Rosenberg wrote:
>
> From:                   Johnny Rosenberg
> <gurus.knugum@gmail.com>
> Date sent:              Sun, 5 Jun 2022 11:37:04 +0200
> Subject:                Re: [libreoffice-users] ROUND function
> consistency
> To:                     LibreOffice Användare
> <users@global.libreoffice.org>
>
> > Looks like a bug to me. 12.125 returns 12.12, but 12.1251 returns 12.13.
> > Both should return the same.
> > I guess this bug should be reported.
> > Meanwhile, you can make your own function that you can use. Here are two
> > different suggestions.
> >
> > 1: This one use the Calc built-in ROUND() cell function. Place it in "My
> > macros & dialogs". VBA compatibility mode is not needed.
> >
> > Public Function faRound(x As Double, d As Integer)
> > Dim Calc
> > Calc=createUnoService("com.sun.star.sheet.FunctionAccess")
> > faRound=Calc.callFunction("ROUND", Array(x, d))
> > End Function
> >
> > 2: This one use the method we learned at school:
> > Public Function fRound(x As Double, d As Integer)
> > fRound=Int(10^d*x+.5)/10^d
> > End Function
> >
> > Test:
> > Print afRound(12.125, 2)
> > Result: 12.13
> >
> > Print fRound(12.125, 2)
> > Result: 12.13
> >
> > Print fRound(12.125, 1)
> > Result: 12.1
> >
> > ... and so on.
> >
> > Kind regards
> >
> > Johnny Rosenberg
> >
> > Den sön 5 juni 2022 kl 04:46 skrev Steve Edmonds <steve.edmonds@ptglobal.com
> > > :
> > > I have just put a basic macro together so it will calculate income tax
> > > due from our local tax rates.
> > > I needed to round the tax to the nearest cent so taking the easy route I
> > > added Option VBASupport 1 to use the available VB round function.
> > >
> > > I then noticed that the VB round function with say round(12.125,2)
> > > rounds down to 12.12 and the LO inbuilt spread sheet function ROUND with
> > > ROUND(12.125,2) rounds up to 12.13.
> > >
> > > Is rounding in this situation arbitrary or is there some some convention
> > > for consistency.
> > >
> > > Steve
> > >
> > >
> > > --
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> +------------------------------------------------------------+
>   Michael D. Setzer II - Computer Science Instructor
> (Retired)
>   mailto:mikes@guam.net                             
>   mailto:msetzerii@gmail.com
>   Guam - Where America's Day Begins
>   G4L Disk Imaging Project maintainer
>   http://sourceforge.net/projects/g4l/
> +------------------------------------------------------------+

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