Hey thats cool. Thank you very much!
Since I have been only working with normal Julia numbers: Do you know a
root finding algorithm which directly uses ACB or ARB numbers? (So in
principle I dont need to convert back directly)
Am Samstag, 28. Mai 2016 16:30:57 UTC+2 schrieb Fredrik Johansson:
>
> On Sat, May 28, 2016 at 4:02 PM, digxx <diger...@hotmail.com <javascript:>>
> wrote:
> > maybe one more thing. How can I extract the number from this form
> [0.1234...
> > +- 12341e-12341] + i*0 to a normal number such that I can work with it
> in
> > later calculations
>
> You can do this:
>
> julia> Float64(real(hyp1f1(R(1), R(1), R(1))))
> 2.718281828459045
>
> Looks like conversion to BigFloat has not been implemented yet (though
> conversion from a BigFloat works). But it can be done with a few lines
> of code:
>
> julia> function bf(x::arb)
> mid = ccall((:arb_mid_ptr, :libarb), Ptr{Void}, (Ptr{arb}, ),
> &x)
> y = BigFloat()
> ccall((:arf_get_mpfr, :libarb), Int, (Ptr{BigFloat},
> Ptr{Void}, Int), &y, mid, 0)
> return y
> end
> bf (generic function with 1 method)
>
> julia> x = hyp1f1(R(1), R(1), R(1));
>
> julia> bf(real(x))
> 2.718281828459045235360287471352662497747295538978622980871818032370215364509352
>
>
>
> julia> bf(imag(x))
> 0.000000000000000000000000000000000000000000000000000000000000000000000000000000
>
>
>
> Another thing worth pointing out is that R(128) can give results with
> much less than 128 bits of accuracy in the final result. You can check
> the number of accurate bits like this:
>
> julia> accuracy_bits(x)
> 126
>
> If the accuracy is too low, you can try again with higher precision.
> Here's an example:
>
> julia> x = hyp1f1(R(-100), R(1), R(20))
> [1854.0367 +/- 4.44e-5] + i*0
>
> julia> accuracy_bits(x)
> 26
>
> julia> R2 = AcbField(256);
>
> julia> x = hyp1f1(R2(-100), R2(1), R2(20))
> [1854.0367283243398148762134198258916179287877866 +/- 4.48e-44] + i*0
>
> julia> accuracy_bits(x)
> 154
>
> So you can easily write a hyp1f1 wrapper for BigFloat that
> automatically doubles the precision until the result is guaranteed to
> be accurate to any accuracy you want.
>
> Fredrik
>
