From: "Apache" <apache@digitalkingdom.org>
Date: Fri, 11 Dec 2015 14:47:36 -0800
To: webmaster@lojban.org, curtis289@att.net
Subject: [jvsw] Definition Added At Word ji'i'u -- By krtisfranks
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 Content preview:  In jbovlaste, the user krtisfranks has added a definition
   of "ji'i'u" in the language "English". New Data: Definition: mekso at-most-4-ary
    operator: a rounding function; ordered input list is $(x,n,m,t)$ and the
   output is $b^(-t) *$ round($b^t * x$), with rounding preference $n$ where
   the fractional part being 1/2 maps $b^t * x$ to the nearest integer of form
    $2Z+m$, for base b and an integer Z [...] 
 
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In jbovlaste, the user krtisfranks has added a
definition of "ji'i'u" in the language "English".

New Data:

=09Definition:
=09=09mekso at-most-4-ary operator: a rounding function; ordered input =
list is $(x,n,m,t)$ and the output is $b^(-t) *$ round($b^t * x$), with=
 rounding preference $n$ where the fractional part being 1/2 maps $b^t =
* x$ to the nearest integer of form $2Z+m$, for base b and an integer Z

=09Notes:
=09=09x must be a real number; n must be exactly one of exactly the fol=
lowing: -1, 0, 1; m must be 0 xor 1 if defined at all; t must be an int=
eger if defined at all. n does not have a contextless default value. m =
is defined iff n =3D 0; if m is undefined, then its slot is automatical=
ly and implicitly deleted from this word in that context (so the operat=
or is at-most-3-ary and a third argument would fill the 't' slot under =
the condition that t is defined). If m is defined, then its contextless=
 default value is m =3D 0. It first determines the base being used for =
interpretation of digit strings (determined by context or by explicit s=
pecification (JUHAU)); this determination takes place even before input=
s are accepted; let this base be represented by b throughout this descr=
iption. If the base is not a positional system wherein each digit repre=
sents a corresponding multiple of a fixed natural number raised to the =
power of its position (as determined relative to the radix point) and w=
herein the overall number is the sum of these results/representands, th=
en t is defined; if the base is sufficiently bad or unclear, then t is =
undefined; if t is undefined, then its slot is automatically and implic=
itly deleted from this word in that context (so the operator is at-most=
-3-ary and its input acceptance is terminated by the n or m slot, which=
ever one is later yet defined). If t is defined, then its contextless d=
efault value is t =3D 0.  The rounding function, determined by n, is pe=
rformed (b^(t))*x. If n =3D 1, then the rounding function is the ceilin=
g function: (b^(t))*x is mapped to the least integer that is greater th=
an or equal to it.  If n =3D -1, then the rounding function is the floo=
r function: (b^(t))*x is mapped to the greatest integer that is less th=
an or equal to it. These integers are both determined by the ordering a=
nd metric. If n =3D 0, then the rounding function maps (b^(t))*x to the=
 integer that minimizes the metric distance between itself and (b^(t))*=
x if a unique such integer exists (id est: (b^(t))*x is mapped to the n=
earest integer, where "nearest"-ness is determined according to the ord=
er and metric); if no such unique integer exists, then (b^(t))*x is map=
ped to the unique integer among these aforementioned options for which =
there exists an integer Z such that 2Z+m is the integer in question; if=
 no unique such integer exists, then the function is undefined. Thus n =
=3D 0 produces the commonly used unbiased nearest-integer rounding func=
tion.  In each of these cases, the output of the rounding function is t=
hen multiplied by b^(-t).  Thus, it rounds at the $t$th digit. The orde=
r on, and the operators and metric endowing, the metric space and field=
 of all real numbers is determined by context or by explicit specificat=
ion.

=09Jargon:
=09=09

=09Gloss Keywords:
=09=09Word: rounding function, In Sense: rounds at given digit
=09=09Word: nearest integer function, In Sense:=20
=09=09Word: ceiling function, In Sense:=20
=09=09Word: floor function, In Sense:=20

=09Place Keywords:


You can go to <http://jbovlaste.lojban.org/dict/ji'i'u> to see it.