bug in j0f()

[Steve Kargl]

On Tue, Dec 02, 2014 at 04:29:08PM -0800, Steve Kargl wrote:
> On Tue, Dec 02, 2014 at 04:09:41PM -0800, Steve Kargl wrote:
> > On Tue, Dec 02, 2014 at 01:43:25PM -0800, Steve Kargl wrote:
> > > Anyone object to the following patch?
> > > 
> > > Index: e_j0f.c
> > > ===================================================================
> > > --- e_j0f.c	(revision 275211)
> > > +++ e_j0f.c	(working copy)
> > > @@ -62,7 +62,7 @@
> > >  	 * j0(x) = 1/sqrt(pi) * (P(0,x)*cc - Q(0,x)*ss) / sqrt(x)
> > >  	 * y0(x) = 1/sqrt(pi) * (P(0,x)*ss + Q(0,x)*cc) / sqrt(x)
> > >  	 */
> > > -		if(ix>0x80000000) z = (invsqrtpi*cc)/sqrtf(x);
> > > +		if(ix>0x4b800000) z = (invsqrtpi*cc)/sqrtf(x);
> > 
> > Exhaustive testing in the range 0x1p38 to 0x1p100 
> > indicated at the constant should be 0x54000000.
> > 
> 
> Note, a similar wrong condition exists within y0f().  I have
> not tested y0f(), but propose making a similar change in y0f()
> as well.
> 

While I'm monologuing, I might as well point out that the
rational approximations in j0f (and y0f and most likely
j1f and y1f) are over-specified.  I suspect that the 
polynomials in the rational approximation can be reduced
by one or two terms.

-- 
Steve