#2567: import MPFR_PREC_MAX from mpfr.h instead of hard coding it to the 32 bit
limit
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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 zimmerma):
> 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.
yes in a previous version MPFR did use the Chudnovsky series, but it only
gives a fixed number of terms per iteration, whereas the current AGM-based
code doubles the accuracy at each iteration, thus is asymptotically
better. Also when the division in GMP is really O(M(n)) the current MPFR
code should be much faster. However we should use the Chudnovsky series
for small precision and the AGM for large precision.
--
Ticket URL: <http://trac.sagemath.org/sage_trac/ticket/2567#comment:8>
Sage <http://sagemath.org/>
Sage - Open Source Mathematical Software: Building the Car Instead of
Reinventing the Wheel
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