#2567: remove limitation on computing digits of pi using mpfr
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Reporter: was | Owner: somebody
Type: defect | Status: new
Priority: major | Milestone: sage-3.4.1
Component: basic arithmetic | Resolution:
Keywords: |
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Comment (by fredrik.johansson):
In mpmath on an Athlon 3700+ 2.21 GHz, 1 GB RAM,
10**6 digits took 5.96 seconds (4.77 calc, 1.19 convert)
10**7 digits took 109.45 seconds (82.16 calc, 27.28 convert)
10**8 digits took 2184.68 seconds (1634.65 calc, 550.02 convert)
I can't compare with MPFR on the same computer at the moment, due to
network problems. (With an old version of sage, 3.0.2, %time
str(pi.n(10**6*log(10.,2))) takes 43.06 s, but I don't trust that number).
This is the result reported by Ondrej a few months ago:
{{{
E.g. in sympy+gmpy:
In [3]: time a = pi.evalf(10**6)
CPU times: user 5.13 s, sys: 0.04 s, total: 5.17 s
Wall time: 5.19 s
Sage 3.1.1:
sage: time a = pi.n(digits=10**6)
CPU times: user 14.06 s, sys: 0.06 s, total: 14.12 s
Wall time: 14.34 s
}}}
> This is without using the new FFT code we designed with Gaudry and
Kruppa, which should give a twofold speedup. Anyway if mpmath can compute
100 million digits in less than 15 minutes, I am really impressed!
Mpmath relies directly on multiplication of GMP mpz's. If it is faster
than MPFR, that is entirely due to using a better formula. Before using
the Chudnovsky series, mpmath used AGM which has better theoretical
complexity but was 3x slower up to at least 1M digits.
--
Ticket URL: <http://trac.sagemath.org/sage_trac/ticket/2567#comment:6>
Sage <http://sagemath.org/>
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