File talk:Comparison rounding graphs SMIL.svg

No mistakes in the solid and hollow dots

This composite graph might appear potentially incorrect at first, because round-with-tie-UP has solid dots on the LEFT, while round-UP has solid dots on the RIGHT. But the "reversals" are correct and necessary.

Round-with-tie-UP needs round-DOWN, and round-with-tie-DOWN needs round-UP. (See w:Floor and ceiling functions#Rounding.)

$RoundTieUp(x)=RoundDown(x+0.5)$ ... or ... $floor(x+0.5)$

$RoundTieDown(x)=RoundUp(x-0.5)$ ... or ... $ceil(x-0.5)$

We can write the expressions without the "reversals", but only at the cost of two negations each:

$RoundTieUp(x)=-RoundUp(-x-0.5)$ ... or ... $-ceil(-x-0.5)$

$RoundTieDown(x)=-RoundDown(-x+0.5)$ ... or ... $-floor(-x+0.5)$

We can write the expressions without addition or subtraction, but only at the cost of doubling and halving and using both ceil and floor:

$RoundTieUp(x)=RoundUp(RoundDown(2x)/2)$ ... or ... $ceil(floor(2x)/2)$

$RoundTieDown(x)=RoundDown(RoundUp(2x)/2)$ ... or ... $floor(ceil(2x)/2)$

There might be a better way to present it all, such reordering the entries or using different colors, but the plotted lines are correct. -A876 (talk) 09:39, 28 December 2018 (UTC)