OpenEuphoria

Re: ESL - math.e - rounding

• Posted by "Christian Cuvier" <christian.cuvier at agriculture.gouv.fr> Aug 03, 2005
• 769 views

> Date: Wed, 03 Aug 2005 14:53:22 +0200
> From: "Juergen Luethje" <j.lue at gmx.de>
> Subject: ESL - math.e - rounding
>
>
> 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
>

In theory, we need the 4 rounding modes below. And the Intel FP
architecture supports them all.

[Quoting from Intel FPU documentation]

Table 4-8. Rounding Modes and Encoding of Rounding Control (RC) Field

--------------------------------------------------------------------
   Rounding     ! RC Field !      Setting Description
     Mode       !          !
---------------+----------+----------------------------------------
                !          ! Rounded result is the closest to the
Round to       !  00B     ! infinitely precise result. If two values
nearest (even) !          ! are equally close, the result is the even
                !          ! value (that is, the one with the
                !          ! least-significant bit of zero). Default
---------------+----------+------------------------------------------
Round down     !          ! Rounded result is closest to but no greater
(toward =E2=88=92=E2=88=9E)    !  01B     !than the infinitely precise resu=
lt.
---------------+----------+------------------------------------------
Round up       !          ! Rounded result is closest to but no less
(toward +=E2=88=9E)    ! 10B      !than the infinitely precise result.
---------------+----------+------------------------------------------
Round toward   !          ! Rounded result is closest to but no greater
zero (Truncate)! 11B      !in absolute value than the infinitely precise

                !          !result.
---------------------------------------------------------------------

Commercial rounding is just rounding up, while scientific calculations
use round to nearst more often.

CChris