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<p>Thanks a lot for the input Charles and Thomas,</p>
<p>I am not familiar with either <a
href="https://en.wikipedia.org/wiki/Horner%27s_method">Horner</a>
or <a href="https://en.wikipedia.org/wiki/Clenshaw_algorithm">Clenshaw</a>,
but I do see the mentions now on <i>Section 6 - Evaluating the
series</i> pages 6 and 7 of the papers.<br>
I implemented the simpler basic approach from section 3 / page 3,
which also happened to more easily correspond to the existing PROJ
implementation.</p>
<p>I can definitely try to understand all this, with the help of
this Rust Geodesy code and the GeographicLib code, and have a go
at updating my proposed implementation for improved accuracy and
performance.</p>
<p>Kind regards,</p>
<p>-Jerome</p>
<div class="moz-cite-prefix">On 9/11/24 12:18 PM, Thomas Knudsen
wrote:<br>
</div>
<blockquote type="cite"
cite="mid:CAH0YoEMiYpNxR1LNYFxh9BqjM=NWWaiJKFZV_2yoe+kb__uy2g@mail.gmail.com">
<pre class="moz-quote-pre" wrap="">I totally agree with Charles regarding using Horner for polynomial
evaluation and Clenshaw for the trig series - for accuracy and speed.
I implemented all the material from Charles' preprint
<a class="moz-txt-link-freetext" href="https://arxiv.org/pdf/2212.05818">https://arxiv.org/pdf/2212.05818</a> for Rust Geodesy, when the preprint
appeared about 1½ years ago.
And although (being an experiment) my handling of the raw coefficients
is rather clumsy, at least it gave me a reason to revise my PROJ horner
and clenshaw implementations (which in turn were based on material from
Poder & Engsager: "Some Conformal Mappings...").
So Jérôme, perhaps take a look at the functions "taylor" and "fourier"
over at <a class="moz-txt-link-freetext" href="https://github.com/busstoptaktik/geodesy/blob/main/src/math/series.rs">https://github.com/busstoptaktik/geodesy/blob/main/src/math/series.rs</a>
While written in Rust, translating to C++ should be rather trivial,
and they may be easier to follow than my decade-old versions already
in the PROJ code base.
</pre>
</blockquote>
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