RE: [boost] 3j, 6j 9j symbol (was Special functions, Quaternions, Octonions)

From: Paul A. Bristow (pbristow_at_[hidden])
Date: 2001-04-15 04:02:35

If ultimate accuracy and portability is important
(portability is most important to BOOSTers I suspect)

It may still be best to calculate the coefficients
using higher accuracy than the compiler can do.

(You may lose one least significant bit on every operator used,
and perhaps two or three if rooting, several if powing).

(NTL also does integer arithmetic, and conversion to
floating point with 150-bit (50 decimal digits) accuracy).

But I have no desire to create unncessary work for myself!

Paul

> -----Original Message-----
> From: Peter Schmitteckert (boost) [mailto:boost_at_[hidden]]
> Sent: Thursday, April 12, 2001 5:42 PM
> To: boost_at_[hidden]
> Subject: Re: [boost] 3j, 6j 9j symbol (was Special functions,
> Quaternions, Octonions)
>
>
> Salut,
>
> On Thursday 12 April 2001 13:31, you wrote:
> [...]
> > > BTW: Looking at this package I wondered if someone is working
> > >      on Clebsch-Gordon coefficients and 3j, 6j and 9j symbols?
> >
> > If these are easily computed, I may be able to use NTL very
> high accuracy
> > to calculate then for 128-bit floating point use like math constants.
> >
> > Paul
>
> It's just a terrible mess of +,-,*,/ and a few sqrts.
> Most of the calculation can be done using integers,
> but currently I only needed special 3j symbols for
> which explicit formulas are known.
> Please note that 3j symbols are not just number but real valued functions
> taking 6 integer parameters,
> e.g. ClebschGordon_3j( j1, m1, j2, m2, j3, m3) ; j_i>=0; abs(m_i) <= j_i
> corresponding to the coupling of two angular moments to a third one.
>
> Best wishes,
> Peter
>
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