Hi Jori,
> Date: Mon, 17 Feb 2014 14:56:56 +0200 (EET)
> From: Jori Mantysalo
>=20
> On Mon, 17 Feb 2014, Zimmermann Paul wrote:
>=20
> > On my computer, computing gamma(Pi^2) to 1 bits takes about 1.4s (f=
or the
> > first computation, when Bernoulli numb
a last update: MPFR now uses the Von Staudt=E2=80=93Clausen theorem to comp=
ute
Bernoulli numbers (thanks to Fredrik Johansson for pointing out this formul=
a).
On my computer, computing gamma(Pi^2) to 1 bits takes about 1.4s (for t=
he
first computation, when Bernoulli numbers are not cached)
an update on this: we now cache Bernoulli numbers in MPFR, and the time to
compute 1000 times gamma(pi^2) at precision 1000 bits has decreased to 0.4s
on my computer (was 2.9s before). In comparison, Pari/GP (which also does
cache Bernoulli numbers) takes 0.5s.
Best regards,
Paul Zimmermann
--
Y
Dear Jori,
> And reason is of course clear, as Fredrik Johansson wrote "If you cache
> Bernoulli numbers, - -".
in fact there is another reason: the MPFR code computes the Bernoulli numbers
exactly, as integers B(2n)*(2n+1)!, whereas Pari/GP computes a floating-point
approximation. For 10
William,
thank you for putting me in cc.
> From: William Stein
> Date: Wed, 12 Feb 2014 06:01:29 -0800
>
> On Wed, Feb 12, 2014 at 4:55 AM, wrote:
> > Ah, I see what you mean. If that's the case then I understand. How does
> > one find out if this is true?
>
> 1. It is *NOT* true.
Nils,
> Date: Mon, 6 Jan 2014 13:18:07 -0800 (PST)
> From: Nils Bruin
>
> On Monday, January 6, 2014 12:46:19 PM UTC-8, Zimmermann Paul wrote:
>
> > What about getting rid of real literals?
> >
>
> I think they exist mainly to let
>
> RealF
Hi,
[since I am not subscribed to sage-devel, please keep me in cc]
the concept of real literals, which was intended (as far as I understand)
to keep exactly track of inputs like "1e-20", leads to the following:
sage: a=RealField(53)(1e-20)
sage: Reals(200)(a)
1.00
Peter,
> I think a case could be made for having two versions of the current RR: one
> like the current one (more like a model of the extended real line) and one
> where overflow or division by zero raises an exception instead of returning
> +/- infinity (more like a model of the usual r
William,
[please forward to sage-devel since I'm not sure I'm allowed to post there]
> The implementation of RR and CC in Sage are a very direct wrapping of
> MPFR, which is the most well-thought out efficient implementation of
> floating point real numbers I've ever seen. It is worth vis
Jean-Pierre,
[please forward to sage-devel, since I'm not subscribed, thus my mail will
be rejected]
thank you for forwarding us that message:
> Date: Fri, 20 Sep 2013 11:36:26 -0700 (PDT)
> From: Jean-Pierre Flori
> Cc: Zimmermann Paul
>
> [1:multipart/alternati
this is now ticket http://trac.sagemath.org/sage_trac/ticket/14466
Paul
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