RE: John's asinh split versus convert-to-sortable...
I like this reformulation, it only used sqrt which is usually very fast.
-----Original Message-----
From: stds-1788@xxxxxxxx [mailto:stds-1788@xxxxxxxx] On Behalf Of Dan Zuras Intervals
Sent: Thursday, March 22, 2012 12:49 AM
To: stds-1788@xxxxxxxxxxxxxxxxx
Cc: Dan Zuras Intervals
Subject: John's asinh split versus convert-to-sortable...
Folks,
I think if you look at John's split based on asinh,
you will find that it already contains, at level 1,
all the properties you are seeking in a convert-to-
sortable split. And none of the faults associated
with a split defined at level 2 only.
To review, I will formulate it as follows:
split(x,y):
u = asinh(x); v = asinh(y);
t = (u + v)/2;
return s = sinh(t);
where John's fully general split with the scale
parameter L is L*split(a/L,b/L). On can use these
definitions:
asinh(z) = ln(z + sqrt(1 + z^2))
sinh(z) = (exp(z) - exp(-z))/2
To turn that into:
split(x,y):
u = x + sqrt(1 + x^2);
v = y + sqrt(1 + y^2);
t = sqrt(u*v);
return s = (t - 1/t)/2;
...