ji'i'u'u VUhU experimental cmavo

mekso, at-most-5-ary; rounding function. (See notes).

This word is mathematically equivalent to "ji'i'u", except that every occurrence of "abs(x)" in its definition is here replaced simply with "x" and every occurrence of "sgn(x)" in its definition is here replaced with "1". In other words, where "ji'i'u" really rounds toward or away from 0, this word rounds toward negative or positive infinity. The behaviors coincide for nonnegative x, but differ for x < 0; for example, for x < 0, a 'negative-type' rounding for "ji'i'u" would round toward 0, which is actually an increase in value (just decrease in absolute value) while remaining negative, whereas a 'negative-type' rounding here would round toward negative infinity, which is a decrease in value (but an increase in absolute value) while remaining negative. This function corresponds more closely with a simple floor or ceiling function, but can be annoying in certain common contexts due to the need to define behavior involving it piecewisely for negative x.

In notes:

ji'i'u (exp!)
mekso, at-most-5-ary operator: a rounding function; ordered input list is (x,n,t,m,b) and the output is sgn(x) bt roundn (b(-t) abs(x)), with rounding preference n and where the fractional part of b(-t) abs(x) being equal to 1/2 causes the roundn ( ) function to map b(-t) abs(x) to the nearest integer of form 2Z+m, for base b (determined by context if not explicitly input) and some integer Z (determined by context).