Hi Eike,
Merry Christmas and a happy New Year to you.
Eike Rathke schrieb:
Hi Regina,
On Wednesday, 2008-12-17 16:22:09 +0100, Regina Henschel wrote:
Mathematically FISHER(x)=atanh(x). But the OOo function ATANH() uses the
same insufficient algorithm as FISHER. Therefore ATANH() has to be
changed too. The best solution, using a build-in function, is not
available: atanh() is a C99 function and therefore not available in MSVC
compiler. The code itself is rather simple, there are two possible
methods:
(1) atanh(x)=0.5*log1p(2*x/(1-x))
(2) Use the first five summands of the power series for |x|<0.01, which
would be atanh(x)=x(1+x²*(1/3+x²*(1/5+x²*(1/7+x²*1/9)))) and use
atanh(x)=0.5*ln((1+x)/(1-x)) in the other cases.
I trust you that the results would be identical ;-)
In general they are, but to test, which cut value to use and how many
summands are needed, is tedious. If there will be a reason for to make
the solution independed of log1p, the algorithm can be changed.
I think #1
would be best, for simplicity.
I have used (1)
You could also profile some ten thousand
calls or so with a sample range of values to determine if any of the two
approaches would have significant performance benefits over the other.
I found no difference in performance.
1. Should atanh be implemented to ::rtl::math like it has been done for
log1p and expm1?
Yes, that would be cleanest. Please file an issue similar to i97091
It is issue 97467. Although I do not really understand the things you
have done for expm1 and log1p, I have tried to mimic them. Perhaps when
code freeze is over, you have some time to explain it?
The related changes for ATANH, FISHER and FISHERINV are in issue 97468.
A quick look at ASINH shows, that it has similar deficiencies. But that
will be a new project.
kind regards
Regina
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