[phobos] Proposed changes to std.math + introduce std.mathspecial

[David Simcha]

On Wed, Nov 17, 2010 at 4:09 PM, Don Clugston <dclugston at googlemail.com>wrote:

> I have a pile of functions I wrote for Tango, most of which are part
> of C99. I'd like to move them into Phobos. In the process, I'd like to
> clean up a few things in std.math.
>
> The main idea is that a new module, std.mathspecial, will contain
> mathematical Special Functions. In the long term, there could be quite
> a large number of these, but I think it will still be OK to have all
> of them declared in a single module.
> The implementations of these functions will mostly reside in
> std.internal.math.XXX. In many cases, the implementations are quite
> large.
>
> std.math will be restricted to low-level operations and "high school"
> mathematics.
>

Vote++.  I think Phobos could use more math stuff.


>
> (1) Add two necessary functions to std.math:
>
> // Rounds x to the nearest int or long using the currently selected
> rounding mode
> // (MUCH faster than cast(int)).
>

Why isn't this the default, i.e. why doesn't cast(int) do this?

> int rndint(real x)
> long rndlong(real x)
>
> (2) Delete etc.gamma
>

Good, didn't know it was there.

>
> (3) Create a new module std.mathspecial.
>
> Move the following functions from std.math into std.mathspecial:
> erf()
> erfc()
> lgamma() -----> name changes to logGamma(real x)
> tgamma() ---> name changes to gamma(real x).
> BTW The 't' in the C name exists for extremely silly historical reasons.
>
> std.math will retain alias for these functions, before they are
> eventually deprecated.
>
> (4) Add implementations of those functions into
> std.internal.math.gammafunction
> Also add:
> real sgnGamma(real x);    // the sign of gamma(x), always used with
> logGamma.
> real digamma(x);   //  The digamma function
> real beta(real x, real y);    // the beta function
>
> I'm not sure about the naming for the other functions. I will leave
> that for a later discussion.
> They include:
> * Distribution functions for the normal, F, chi-square, students-T, gamma,
> beta,
> poisson, binomial, and negative binomial distributions.
>

Vote++.  I'm sick of maintaining the D2 ports of this stuff myself for
dstats.  It also makes the licensing status of dstats slightly screwy since
I initially got them from Tango.  (I was smart enough, though, to clearly
mark the tainted parts for future removal.)


> * Cylindrical Bessel functions
> real cylBessel_j0(real x)  real cylBessel_y0(real x)
> real cylBessel_j1(real x)  real cylBessel_y1(real x)
> real cylBessel_jn(int n, real x )  real cylBessel_yn(int n, real x)
>

I've got no clue what these even are, but given that they're just math
functions that are orthogonal to the rest of the standard library, I don't
see any harm in adding them.
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