OpenEuphoria

Re: ESL - math.e - rounding

• Posted by Alexander Toresson <alexander.toresson at gmail.com> Aug 03, 2005
• 763 views

Jason Gade wrote:
> 
> Juergen Luethje wrote:
> > 
> > Hi all,
> > 
> > here are some thoughts concerning ESL rounding functions.
> > 
> > Any function for rounding a number should take a second argument that
> > denotes the number of digital places that we want the result to have,
> > e.g.
> >     round(77.123456, 3) = 77.123
> > 
> > There is an IEEE standard for rounding. A *different* way of rounding
> > is what we call in German "kaufmaennisches Runden".
> > Translated word by word to English, this would be "commercial rounding".
> > Does this (or a similar) term exist in English?
> >      round_half_even(x,n)     -- according to IEEE
> >      round_half_up(x,n)       -- "kaufmaennisches Runden"
> > 
> > 
> > Both functions sometimes return different results, when the (n+1)th
> > decimal place of x equals 5:
> >      round_half_even()        -- rounds to nearest even value
> >      round_half_up()          -- always rounds up  ( surprise!  )
> > 
> > -- Example
> > x = 7.125
> > round_half_even(x,2)    -->  7.12
> > round_half_up(x,2)      -->  7.13
> > 
> > x = 7.135
> > round_half_even(x,2)    -->  7.14
> > round_half_up(x,2)      -->  7.14
> > 
> > 
> > What do you all think?
> > 
> > Regards,
> >    Juergen
> > 
> > -- 
> > Have you read a good program lately?
> > 
> > 
> Not being a memember of the IEEE standards committee, round_half_up() would be
> the
> behavior I expect from a rounding function. That was the way I was always
> taught to
> round.
> 
> Except, how does it work for negative numbers? Does it round towards + or -?
> 
> 
> Alexander Toresson wrote:
> > round_half_up() would be roof() in qb.
> > There's also a function called floor() in qb, which always rounds down.
> 
> It would be nice to have different words for this. For one Euphoria already
> has a floor()
> function, for two it sounds like I'm building a house instead of a program.

Oh, yes, it's round() (which rounds to the nearest integer) and roof() that I
always have to reimplement.

> Just like peek() and poke() make me feel like a pervert.

Lol, yes, and peek4u() is even worse :)

> How about
> round_up(num, places)
> round_down(num, places)
> round_even(num, places)

That's a good propotion.

> Also, how do these functions work on numbers with very large exponents? Such
> as 7.135e15?
> Are they only for numbers within 15 significant figures of 0?
> 

Well, I don't think it would work very well to round 7.135e15 to the nearest
integer, because 64-bit floats are starting to become inaccurate with that many
decimals. I recommend checking out the following great article about the
bottlenecks of floats:

http://www.cfxweb.net/modules.php?name=News&file=article&sid=1312&mode=&order=0&thold=0

Regards, Alexander Toresson