Re: native floating point sinint

[Michele]

On 08/16/2017 11:24 PM, Colin Macdonald wrote:
> On 2017-08-16 02:22 PM, Colin Macdonald wrote:
> > I wonder if you could take a look at this old pull request:
> >
> > https://github.com/cbm755/octsympy/pull/425
> >
> > My feeling is drop this but I thought you might offer a perspective 
> > after your summer project.
> >
> > Background: the symbolic package inherited a bunch of code from the 
> > specfun pkg.  This included "sinint" and "cosint" implementations.  
> > They were not very good so I replaced them [1] with rather slow, 
> > nonvectorized calls to the SymPy (ultimately the arbitrary precision 
> > python library "mpmath").  The PR is the original specfun code, with 
> > a few failing tests added by me.
> >
> > [1] 
> > https://github.com/cbm755/octsympy/blob/master/inst/%40double/sinint.m
>
> I'm sorry, wrong person!
>
> *Michele*, I meant to refer the above to you!
>
> best,
> Colin

Dear Colin,
I'm giving a look to the functions. Unfortunately seems that there is 
only a series expansion (no continued fraction or other strategies). But 
it is possible to use some relations in order to use expint to compute them.
I took few minutes to try to implement sinint using some of these 
relations (Abramowitz 5.2.19 and 5.2.21).
The result far to be perfect but I think it could be a good starting point.

--
Michele Ginesi

sinint.m
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