round() ?

```Hello
How can i round float to 2 digits after '.' ?

Thanx

```
 0
user681 (69)
1/19/2004 3:45:03 PM
vc.mfc 33608 articles. 0 followers.

15 Replies
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```Quick and Dirty:

Multiply by 100, add 0.5 (to round up correctly). convert to long, then
back to float, then divide by 100.

This is limited to values that will fit within a long, and is not
efficient.  It is reliable.

also:

float val;

val = val - fmod(val, .01);

Or, the real thing:

char *_fcvt( double value, int count, int *dec, int *sign );
Which is a char string, which you can then feed to atof() and get your
rounded value back.  Alas, beware errors in precision limits!

Balboos

user@domain.invalid wrote:

> Hello
> How can i round float to 2 digits after '.' ?
>
> Thanx
>

```
 0
balboos (139)
1/19/2004 4:01:30 PM
```<user@domain.invalid> wrote in message
news:%232tyyMq3DHA.2144@TK2MSFTNGP10.phx.gbl...
> Hello
> How can i round float to 2 digits after '.' ?
>
> Thanx

I once had to deal with rounding doubles in a financial application (I did
not have fixed precision class), and made following rounding function. You
would better use double to deal with floating point.

#include <cmath>

// Round up to 10 digit precision
double ROUND(double number, int decimals)
{
static const double EPSILON = 1E-10;
static const double RNDFACT[] =
{1E0,1E1,1E2,1E3,1E4,1E5,1E6,1E7,1E8,1E9,1E10};
static const double bnd_with_epsilon_value_pos = 0.5-EPSILON;
static const double bnd_with_epsilon_value_neg = 0.5+EPSILON;

ASSERT(0<=decimals && decimals<=10);
number *= RNDFACT[decimals];
double flr  = floor(number); //  2.8 -> 2   -2.8 -> -3
double rest = number - flr;  //  2.8-2 = 0.8 ; -2.8-(-3) = 0.2
if(
(number>=0.0 && rest>=bnd_with_epsilon_value_pos) ||
(number<0.0 && rest>=bnd_with_epsilon_value_neg)
)
number = ceil(number);
else
number = flr;
return number / RNDFACT[decimals];
}

Tom.

```
 0
1/19/2004 4:56:27 PM
```Be careful with this one. It might be completely removed by the compiler
optimizations ;-)

Jase

"Balboos" <balboos@masonicbrother.com.No.Spam> wrote in message
news:ubTOb.20152\$OM2.4545949@news4.srv.hcvlny.cv.net...
> Quick and Dirty:
>
> Multiply by 100, add 0.5 (to round up correctly). convert to long, then
> back to float, then divide by 100.
>
> This is limited to values that will fit within a long, and is not
> efficient.  It is reliable.
>
> also:
>
> float val;
>
> val = val - fmod(val, .01);
>
> Or, the real thing:
>
> char *_fcvt( double value, int count, int *dec, int *sign );
> Which is a char string, which you can then feed to atof() and get your
> rounded value back.  Alas, beware errors in precision limits!
>
>
> Balboos
>
>
> user@domain.invalid wrote:
>
> > Hello
> > How can i round float to 2 digits after '.' ?
> >
> > Thanx
> >
>

```
 0
jshelley (197)
1/20/2004 4:30:15 AM
``` CString cs;
cs.Format("%.2f", d);
d = atof(cs);

Normand

<user@domain.invalid> a �crit dans le message de news:
#2tyyMq3DHA.2144@TK2MSFTNGP10.phx.gbl...
> Hello
> How can i round float to 2 digits after '.' ?
>
> Thanx
>

```
 0
NoEmail9920 (149)
1/20/2004 6:06:35 AM
```Well whata ya know ;-) I never realised that performed rounding. (yeah...
I've checked it ;-) )

Jase

news:Mz3Pb.9552\$U77.688636@news20.bellglobal.com...
> CString cs;
>  cs.Format("%.2f", d);
>  d = atof(cs);
>
> Normand
>
> <user@domain.invalid> a �crit dans le message de news:
> #2tyyMq3DHA.2144@TK2MSFTNGP10.phx.gbl...
> > Hello
> > How can i round float to 2 digits after '.' ?
> >
> > Thanx
> >
>
>

```
 0
jshelley (197)
1/20/2004 6:43:34 AM
```"Jase" <jshelley@spamblock.enersol.com.au> wrote in message
news:400cce17\$0\$26114\$afc38c87@news.optusnet.com.au...
> Well whata ya know ;-) I never realised that performed rounding. (yeah...
> I've checked it ;-) )

It doesn't round correctly in all cases. You'll see soon enough that for
some numbers, you'll never get the correct rounded number.
I noticed this in a financial application I developed. Formatting does _not_
round correctly in all cases.

You'll be better of using my method, it rounds correctly (at least, I
haven't found a number for which it doesn't round correctly).

Tom.

> Jase
>
> "Normand" <NoEmail@Please.com> wrote in message
> news:Mz3Pb.9552\$U77.688636@news20.bellglobal.com...
> > CString cs;
> >  cs.Format("%.2f", d);
> >  d = atof(cs);
> >
> > Normand
> >
> > <user@domain.invalid> a �crit dans le message de news:
> > #2tyyMq3DHA.2144@TK2MSFTNGP10.phx.gbl...
> > > Hello
> > > How can i round float to 2 digits after '.' ?
> > >
> > > Thanx
> > >
> >
> >
>
>

```
 0
1/20/2004 9:50:32 AM
```Do you have any details about it,  I mean examples or explanations?
Is it the same with sprintf?

"TT (Tom Tempelaere)" <_N_OSPAMtiti____@hotmail.comMAPSO_N_> a �crit dans le
message de news: IR6Pb.20762\$Gf2.3930205@phobos.telenet-ops.be...
> "Jase" <jshelley@spamblock.enersol.com.au> wrote in message
> news:400cce17\$0\$26114\$afc38c87@news.optusnet.com.au...
> > Well whata ya know ;-) I never realised that performed rounding.
(yeah...
> > I've checked it ;-) )
>
> It doesn't round correctly in all cases. You'll see soon enough that for
> some numbers, you'll never get the correct rounded number.
> I noticed this in a financial application I developed. Formatting does
_not_
> round correctly in all cases.
>
> You'll be better of using my method, it rounds correctly (at least, I
> haven't found a number for which it doesn't round correctly).
>
> Tom.
>
> > Jase
> >
> > "Normand" <NoEmail@Please.com> wrote in message
> > news:Mz3Pb.9552\$U77.688636@news20.bellglobal.com...
> > > CString cs;
> > >  cs.Format("%.2f", d);
> > >  d = atof(cs);
> > >
> > > Normand
> > >
> > > <user@domain.invalid> a �crit dans le message de news:
> > > #2tyyMq3DHA.2144@TK2MSFTNGP10.phx.gbl...
> > > > Hello
> > > > How can i round float to 2 digits after '.' ?
> > > >
> > > > Thanx
> > > >
> > >
> > >
> >
> >
>
>

```
 0
NoEmail9920 (149)
1/20/2004 3:58:47 PM
```"Normand" <NoEmail@Please.com> wrote in message
news:_ecPb.12385\$U77.748201@news20.bellglobal.com...
> Do you have any details about it,  I mean examples or explanations?
> Is it the same with sprintf?

There are a lot of numbers that don't round correctly using formatting. I
cannot remember one, it is at least 5 years ago since I had those problems
;-)
But I am very sure that formatting doesn't round correctly in all cases.

And I am sure that my rounding function is 99.9999999...% correct in
rounding any number to 2 digits after the comma. I know this from experience
because since I made and used the rounding function, I had no more rounding
problems. This is a financial application though, and most of the time,
numbers are rounded to 2 or 4 digits after the comma. The rounding function
may prove unstable for eg 10 or more digit rounding, or when rounding
extremely large values.

You (& everybody else) are free to copy and use my rounding function, but
use it wisely.

HTH,
Tom.

> "TT (Tom Tempelaere)" <_N_OSPAMtiti____@hotmail.comMAPSO_N_> a �crit dans
le
> message de news: IR6Pb.20762\$Gf2.3930205@phobos.telenet-ops.be...
> > "Jase" <jshelley@spamblock.enersol.com.au> wrote in message
> > news:400cce17\$0\$26114\$afc38c87@news.optusnet.com.au...
> > > Well whata ya know ;-) I never realised that performed rounding.
> (yeah...
> > > I've checked it ;-) )
> >
> > It doesn't round correctly in all cases. You'll see soon enough that for
> > some numbers, you'll never get the correct rounded number.
> > I noticed this in a financial application I developed. Formatting does
> _not_
> > round correctly in all cases.
> >
> > You'll be better of using my method, it rounds correctly (at least, I
> > haven't found a number for which it doesn't round correctly).
> >
> > Tom.
> >
> > > Jase
> > >
> > > "Normand" <NoEmail@Please.com> wrote in message
> > > news:Mz3Pb.9552\$U77.688636@news20.bellglobal.com...
> > > > CString cs;
> > > >  cs.Format("%.2f", d);
> > > >  d = atof(cs);
> > > >
> > > > Normand
> > > >
> > > > <user@domain.invalid> a �crit dans le message de news:
> > > > #2tyyMq3DHA.2144@TK2MSFTNGP10.phx.gbl...
> > > > > Hello
> > > > > How can i round float to 2 digits after '.' ?
> > > > >
> > > > > Thanx
> > > > >
> > > >
> > > >
> > >
> > >
> >
> >
>
>

```
 0
1/20/2004 5:05:06 PM
```On Tue, 20 Jan 2004 10:58:47 -0500, "Normand" <NoEmail@Please.com> wrote:

>Do you have any details about it,  I mean examples or explanations?
>Is it the same with sprintf?

Top posting is evil. Now I can't make comments in line.

The printing functions do not round incorrectly. If I am not mistaken
they round using "round even" rule (available in FPU). In this method,
they round a mid value (.5) up or down to the even number...and yes,
it's usually the same with sprintf().

2.5 rounds to 2.0 and 3.5 rounds to 4.0

The advantage of this is that rounding errors are statistically
canceled. The average of a sum of rounded numbers will be very
close to the rounded average of the sum of the unrounded numbers.

The average of {2.5,3.5} is 3.0
The average of {2,4} is 3.0
The average of {3,4} (TT's way} is 3.5!

You can get this automatically, efficiently, and with scaling
from System.Math.Round().

Here is a simpler form of TT's method:

double Round(double number, int decimals){
double factor=Math.Pow(10,decimals);
return Math.Floor(number*factor+0.4999999999)/factor;
}

....note that the choice to make digits beyond 1E-10 insignificant is
based on an arbitrary choice.

TT wants ROUND(2.5) = 3.0 and ROUND(-2.5) = -3.0. That's probably ok
for what he's doing but it's not always the right one. It just happens
to work the way he wants it to.

It's inconsistent.
Positive numbers at the mid point are rounded to a larger value, while
negative numbers at a midpoint are rounded to smaller value.

regards,

bullshark

>
>"TT (Tom Tempelaere)" <_N_OSPAMtiti____@hotmail.comMAPSO_N_> a �crit dans le
>message de news: IR6Pb.20762\$Gf2.3930205@phobos.telenet-ops.be...
>> "Jase" <jshelley@spamblock.enersol.com.au> wrote in message
>> news:400cce17\$0\$26114\$afc38c87@news.optusnet.com.au...
>> > Well whata ya know ;-) I never realised that performed rounding.
>(yeah...
>> > I've checked it ;-) )
>>
>> It doesn't round correctly in all cases. You'll see soon enough that for
>> some numbers, you'll never get the correct rounded number.
>> I noticed this in a financial application I developed. Formatting does
>_not_
>> round correctly in all cases.
>>
>> You'll be better of using my method, it rounds correctly (at least, I
>> haven't found a number for which it doesn't round correctly).
>>
>> Tom.
>>
>> > Jase
>> >
>> > "Normand" <NoEmail@Please.com> wrote in message
>> > news:Mz3Pb.9552\$U77.688636@news20.bellglobal.com...
>> > > CString cs;
>> > >  cs.Format("%.2f", d);
>> > >  d = atof(cs);
>> > >
>> > > Normand
>> > >
>> > > <user@domain.invalid> a �crit dans le message de news:
>> > > #2tyyMq3DHA.2144@TK2MSFTNGP10.phx.gbl...
>> > > > Hello
>> > > > How can i round float to 2 digits after '.' ?
>> > > >
>> > > > Thanx
>> > > >
>> > >
>> > >
>> >
>> >
>>
>>
>

```
 0
bullshark (19)
1/20/2004 7:23:20 PM
```On Tue, 20 Jan 2004 19:23:20 GMT, bullshark <bullshark@scubadiving.com> wrote:
>Top posting is evil. Now I can't make comments in line.

For some reason I'll never understand, agent showed me in the C# group

The comments still apply, the formula is the same, the reduced method
is just:

double Round(double number, int decimals){
double factor=pow(10,decimals);
return floor(number*factor+0.499999999)/factor;
}

The C-Library doesn't  provide the round even method, but you can do it
anyway, using _controlfp() API call, if you want it.

regards

bullshark

You may now resume regularly scheduled programming.

```
 0
bullshark (19)
1/20/2004 7:40:51 PM
```"bullshark" <bullshark@scubadiving.com> wrote in message
news:gvpq00t466j6mgvuon15kdp5prur76q8ai@4ax.com...
> On Tue, 20 Jan 2004 10:58:47 -0500, "Normand" <NoEmail@Please.com> wrote:
>
> >Do you have any details about it,  I mean examples or explanations?
> >Is it the same with sprintf?
>
> Top posting is evil. Now I can't make comments in line.

Trueness.

> The printing functions do not round incorrectly.

From my experience, I can certainly tell that this is not true. I don't
recall the exact number I was having problems with, sorry. But (at least in
MFC/VS6) formatting doesn't round correctly in all cases. I'm not talking
about negative vs positive numbers, I'm talking about numbers that have no
exact representation.

> If I am not mistaken
> they round using "round even" rule (available in FPU). In this method,
> they round a mid value (.5) up or down to the even number...and yes,
> it's usually the same with sprintf().

At first I tried using format, with rounding errors as a result (MFC/VS6).

> You can get this automatically, efficiently, and with scaling
> from System.Math.Round().

That is probably .net code, you are posting in an MFC newsgroup.

> Here is a simpler form of TT's method:
>
> double Round(double number, int decimals){
>   double factor=Math.Pow(10,decimals);
>   return Math.Floor(number*factor+0.4999999999)/factor;
> }

I don't know if this yields the exact same results in all cases. Actually, I
doubt it.

> ...note that the choice to make digits beyond 1E-10 insignificant is
> based on an arbitrary choice.

Indeed, it was an observation in my application that I would never need
digits beyound 10 digits.

> TT wants ROUND(2.5) = 3.0 and ROUND(-2.5) = -3.0. That's probably ok
> for what he's doing but it's not always the right one.

It may not be, but (1) it is mathematically sound and is what is expected -
symmetric, (2) desirable for financial applications;

(1) + (2): client needs to pay 2.515 euro. From the clients perspective he
needs to pay 2.515, or rounded 2.52. From his account 2.52 is subtracted. If
you work with debit & credit terms, you never need negative numbers - no
problems there. If you do not (eg as an optimization), you will have to use
negative numbers when representing debit amounts. In this case
rounding -2.515 rounded should yield -2.52, _not_ -2.51!

> It just happens
> to work the way he wants it to.
> It's inconsistent.
> Positive numbers at the mid point are rounded to a larger value, while
> negative numbers at a midpoint are rounded to smaller value.

That's the whole point. I can't think of _any_ application that would rather
have -2.515 rounded to -2.51.

> regards,
> bullshark

Kind regards,
Tom.

> >
> >"TT (Tom Tempelaere)" <_N_OSPAMtiti____@hotmail.comMAPSO_N_> a �crit dans
le
> >message de news: IR6Pb.20762\$Gf2.3930205@phobos.telenet-ops.be...
> >> "Jase" <jshelley@spamblock.enersol.com.au> wrote in message
> >> news:400cce17\$0\$26114\$afc38c87@news.optusnet.com.au...
> >> > Well whata ya know ;-) I never realised that performed rounding.
> >(yeah...
> >> > I've checked it ;-) )
> >>
> >> It doesn't round correctly in all cases. You'll see soon enough that
for
> >> some numbers, you'll never get the correct rounded number.
> >> I noticed this in a financial application I developed. Formatting does
> >_not_
> >> round correctly in all cases.
> >>
> >> You'll be better of using my method, it rounds correctly (at least, I
> >> haven't found a number for which it doesn't round correctly).
> >>
> >> Tom.
> >>
> >> > Jase
> >> >
> >> > "Normand" <NoEmail@Please.com> wrote in message
> >> > news:Mz3Pb.9552\$U77.688636@news20.bellglobal.com...
> >> > > CString cs;
> >> > >  cs.Format("%.2f", d);
> >> > >  d = atof(cs);
> >> > >
> >> > > Normand
> >> > >
> >> > > <user@domain.invalid> a �crit dans le message de news:
> >> > > #2tyyMq3DHA.2144@TK2MSFTNGP10.phx.gbl...
> >> > > > Hello
> >> > > > How can i round float to 2 digits after '.' ?
> >> > > >
> >> > > > Thanx
> >> > > >
> >> > >
> >> > >
> >> >
> >> >
> >>
> >>
> >
>

```
 0
1/20/2004 11:27:58 PM
```Back in the good old days, we disabled the optimizer whenever the
mathematical needs were critical (had to be done right).  What is
needed, of course, is the following:

#pragma KEEP_YOUR_GRUBBY_OPTIMIZING_PAWS_OFF_THIS_BLOCK
.... clever mathematical code ...

"When I use a word, it means precisely what I wish it to mean - neither
more nor less"  Humpty Dumpty (Through the Looking Glass)

Balboos

P.S.  Thanks, again, to the group for the help with the Property Sheets

Jase wrote:
> Be careful with this one. It might be completely removed by the compiler
> optimizations ;-)
>
> Jase
>
> "Balboos" <balboos@masonicbrother.com.No.Spam> wrote in message
> news:ubTOb.20152\$OM2.4545949@news4.srv.hcvlny.cv.net...
>
>>Quick and Dirty:
>>
>>Multiply by 100, add 0.5 (to round up correctly). convert to long, then
>>back to float, then divide by 100.
>>
>>This is limited to values that will fit within a long, and is not
>>efficient.  It is reliable.
>>
>>also:
>>
>>float val;
>>
>>val = val - fmod(val, .01);
>>
>>Or, the real thing:
>>
>>char *_fcvt( double value, int count, int *dec, int *sign );
>>Which is a char string, which you can then feed to atof() and get your
>>rounded value back.  Alas, beware errors in precision limits!
>>
>>
>>Balboos
>>
>>
>>user@domain.invalid wrote:
>>
>>
>>>Hello
>>>How can i round float to 2 digits after '.' ?
>>>
>>>Thanx
>>>
>>
>
>

```
 0
balboos (139)
1/21/2004 12:05:21 AM
```Back in the good old days, we disabled the optimizer whenever the
mathematical needs were critical (had to be done right).  What is
needed, of course, is the following:

#pragma KEEP_YOUR_GRUBBY_OPTIMIZING_PAWS_OFF_THIS_BLOCK
.... unusually clever mathematical code ...

"When I use a word, it means precisely what I wish it to mean - neither
more nor less"  Humpty Dumpty (Through the Looking Glass)

Balboos

P.S.  Thanks, again, to the group for the help with the Property Sheets

Jase wrote:

> Be careful with this one. It might be completely removed by the compiler
> optimizations ;-)
>
> Jase
>
> "Balboos" <balboos@masonicbrother.com.No.Spam> wrote in message
> news:ubTOb.20152\$OM2.4545949@news4.srv.hcvlny.cv.net...
>
>>Quick and Dirty:
>>
>>Multiply by 100, add 0.5 (to round up correctly). convert to long, then
>>back to float, then divide by 100.
>>
>>This is limited to values that will fit within a long, and is not
>>efficient.  It is reliable.
>>
>>also:
>>
>>float val;
>>
>>val = val - fmod(val, .01);
>>
>>Or, the real thing:
>>
>>char *_fcvt( double value, int count, int *dec, int *sign );
>>Which is a char string, which you can then feed to atof() and get your
>>rounded value back.  Alas, beware errors in precision limits!
>>
>>
>>Balboos
>>
>>
>>user@domain.invalid wrote:
>>
>>
>>>Hello
>>>How can i round float to 2 digits after '.' ?
>>>
>>>Thanx
>>>
>>
>
>

```
 0
balboos (139)
1/21/2004 12:12:17 AM
```> double Round(double number, int decimals){
>   double factor=pow(10,decimals);
>   return floor(number*factor+0.499999999)/factor;
> }
>
> The C-Library doesn't  provide the round even method, but you can do it
> anyway, using _controlfp() API call, if you want it.

This is my roundung rountine. I never noticed any problems with it.

double round(const double& inValue)
{
double xShift = inValue - .5;
double nShift = fix(xShift);
if (xShift == nShift)
{
if (nShift == 2.*fix(nShift/2.))
xShift -= .25;		// nShift even, round off
else
xShift += .25;		// nShift odd, round up
}
return ceil(xShift);
}
```
 0
1/21/2004 10:26:26 AM
```On Tue, 20 Jan 2004 23:27:58 GMT, "TT \(Tom Tempelaere\)" <_N_OSPAMtiti____@hotmail.comMAPSO_N_> wrote:

>> If I am not mistaken
>> they round using "round even" rule (available in FPU). In this method,
>> they round a mid value (.5) up or down to the even number...and yes,
>> it's usually the same with sprintf().
>
>At first I tried using format, with rounding errors as a result (MFC/VS6).

The round even rule is an ieee standard 754 section 4...not an error.

>
>I don't know if this yields the exact same results in all cases. Actually, I
>doubt it.

big ooops there. I didn't think hard enough about effects of epsilon
and FPU inexactness...I did try it, but happened to pick happy numbers.

Would this do the same?

int signed=number<0;
double factor=pow(10.0,decimals);
number=floor(fabs(number)*factor+0.5)/factor;
return signed?-number:number;

....even with the pow call it's almost as fast (14% rounded (c:),
but in either case insignificant. With the addition of static factors
its the same speed (at least over 18Million reps). There's nothing wrong
with your code, it's just a little arcane and easily broken if the ASSERT
is off. It also can't do something like:

round(256751335.12345,-3) (nearest 1000 = 256751000.000000

>It may not be, but (1) it is mathematically sound and is what is expected -
>symmetric, (2) desirable for financial applications;

It may be desirable for financial applications, but floating point is not.
As to "mathematically sound", a matter of opinion. Reconsider the averages example.

>
>(1) + (2): client needs to pay 2.515 euro. From the clients perspective he
>needs to pay 2.515, or rounded 2.52. From his account 2.52 is subtracted. If
>you work with debit & credit terms, you never need negative numbers - no
>problems there. If you do not (eg as an optimization), you will have to use
>negative numbers when representing debit amounts. In this case
>rounding -2.515 rounded should yield -2.52, _not_ -2.51!

1) the round even rule would round 2.515 to 2.52
2) a bank that always rounds mid values away from zero stands to
gain a half on some transactions, or lose a half point on others.
Transaction flows in high volumes can cause large overages/shortfalls
and unaccountable discrepancies. Round even rule makes all the numbers
add up all the time to within 1 occurrence of rounding tolerance.
3) negative numbers get the same treatment as positive.
i.e. abs(roundEven(-num))==roundEven(num), but as you point out,
sensible financial apps do not use signed numbers, so the sign issue
should be immaterial.

>That's the whole point. I can't think of _any_ application that would rather
>have -2.515 rounded to -2.51.

You haven't worked with statistics programs, or scientific applications?
The point of round even is that it doesn't skew data or make it dirty.
Errors introduced by rounding with round even are self-cancelling. In
scientific calculations it is generally considered mandatory to follow
the round even rule. Otherwise computations based on printed materials
( necessarily rounded ) hardly work out.

BTW, which way to round mid-value numbers in financial applications is
a matter of accounting policy and occasionally law, but not one of fact.

e.g. NIST rounding rules for SI Units (a very explicit round-even)
http://www.physics.nist.gov/Pubs/SP811/appenB.html
....can be found in section B-7.

Round-even is supported by the Intel FPU (round near), so it is very efficient
when used, and it's widespread demand obvious by it's inclusion.
In fact, it's the only 'round' (as we think of it) supported. Everything
else is chop/floor/ceil. Your application uses it by default as the
FPU converts in and out of 80-bit(internal) format to double and float.

I would say the sprintf libs don't round incorrectly, they just don't
round the way you expected.

The roundEven can be had on WinIntel with:

double ieeeRound(double num){
/* MS defaults fpu control word to round near (_RC_NEAR)*/
__asm{     //don't know how to do this in C
FLD num
FRNDINT
}
}

Variability of round behavior is probably the reason StdC libs don't
provide a round method.

regards,

bullshark
```
 0
bullshark (19)
1/21/2004 6:14:45 PM

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