OpenEuphoria

Re: ESL - math.e - rounding

• Posted by "Juergen Luethje" <j.lue at gmx.de> Aug 03, 2005
• 734 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?
>
>
> 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.

Same for me. That was the only way of rounding that I learned at
school. But there actually is the IEEE standard that I mentioned.
And for instance PowerBASIC's round() function works according to it.

> Except, how does it work for negative numbers? Does it round towards + or -?

Sorry, I forgot about that. As far as I know (math experts might want to
correct me) round_half_even() works the same as for positive numbers,
and round_half_up() always rounds up the absolute value:

-- 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

------------------------------------------------------------------------

> Alexander Toresson wrote:
>> round_half_up() would be roof() in qb.
>> There's also a function called floor() in qb, which always rounds down.

Alexander, what do you mean with "qb"? QBasic? Quick Basic?
In all languages that I know which have a floor() function, floor() does
the same as Euphoria's floor() does. The opposite of floor() normally is
called ceil().
It sounds to me that we are talking about different things here.

> 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.
>
> Just like peek() and poke() make me feel like a pervert.
>
> How about
> round_up(num, places)
> round_down(num, places)
> round_even(num, places)

For almost all cases, there are rules when to round up, and when to
round down, which a round function should know and apply automatically.
The only problem arises when the (n+1)th digit is '5', and no more
digits are following. I never heard of a function round_half_down().
And this should not be confused with floor() or ceil().

> 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?

Both proposed rounding functions normally work the way probably everyone
would expect a rounding function to work. The only interesting point is,
when the (n+1)th digit is '5', and no more digits are following.
*If* Euphoria works with 15 decimal places internally (this is just a
guess), then of course it wouldn't make sense to write e.g.
    ? round_half_up(x, 20)

Regards,
   Juergen