#9937: PARI real precision is broken in many ways
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Reporter: jdemeyer | Owner: was
Type: defect | Status: new
Priority: major | Milestone: sage-4.6
Component: interfaces | Keywords: pari gp real precision
set_real_precision
Author: | Upstream: N/A
Reviewer: | Merged:
Work_issues: |
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Changes (by jdemeyer):
* keywords: pari gp real precision => pari gp real precision
set_real_precision
Old description:
> The following do not work as they should (try these examples with a
> freshly started copy of Sage, such that everything is default).
>
> {{{
> # Default: 2 significant words (while we really should get only 1)
> sage: pari('Pi').debug()
> [&=0000000004fc9620] REAL(lg=4):0400000000000004
> (+,expo=1):6000000000000001 c90fdaa22168c234 c4c6628b80dc1cd1
>
> # Change precision and then change it back: we get 1 word
> sage: n = pari.get_real_precision(); pari.set_real_precision(100);
> pari.set_real_precision(n);
> sage: pari('Pi').debug()
> [&=00000000012bf200] REAL(lg=3):0400000000000003
> (+,expo=1):6000000000000001 c90fdaa22168c235
> }}}
>
> {{{
> # set_real_precision() doesn't do anything for library functions:
> sage: pari.set_real_precision(1000);
> sage: pari.euler().debug()
> [&=0000000004f75e20] REAL(lg=3):0400000000000003
> (+,expo=-1):5fffffffffffffff 93c467e37db0c7a5
> }}}
>
> Dependencies: #9898, #9893
New description:
The following do not work as they should (try these examples with a
freshly started copy of Sage, such that everything is default).
This is definately a bug with the initialization of the precision:
{{{
# Default: 2 significant words (while we really should get only 1)
sage: pari('Pi').debug()
[&=0000000004fc9620] REAL(lg=4):0400000000000004
(+,expo=1):6000000000000001 c90fdaa22168c234 c4c6628b80dc1cd1
# Change precision and then change it back: we get 1 word
sage: n = pari.get_real_precision(); pari.set_real_precision(100);
pari.set_real_precision(n);
sage: pari('Pi').debug()
[&=00000000012bf200] REAL(lg=3):0400000000000003
(+,expo=1):6000000000000001 c90fdaa22168c235
}}}
{{{set_real_precision()}}} seems to affect essentially only the precision
for evaluating strings in PARI and not much else:
{{{
sage: pari.set_real_precision(1000);
sage: pari.euler().debug()
[&=0000000004f75e20] REAL(lg=3):0400000000000003
(+,expo=-1):5fffffffffffffff 93c467e37db0c7a5
}}}
This last behaviour is actually documented in
{{{sage/libs/pari/gen.pyx}}}:
> Unless otherwise indicated in the docstring, most Pari functions
> that return inexact objects use the precision of their arguments to
> decide the precision of the computation. However, if some of these
> arguments happen to be exact numbers (integers, rationals, etc.),
> an optional parameter indicates the precision (in bits) to which
> these arguments should be converted before the computation. If this
> precision parameter is missing, the '''default precision of 53 bits'''
is
> used.
In other words, the default precision is an unchangable 53 bits. I would
expect {{{set_real_precision()}}} to change this. This is also trivial to
implement since the global variable {{{prec}}} is already there (and
initialized once and for all to 53).
Dependencies: #9898, #9893
--
--
Ticket URL: <http://trac.sagemath.org/sage_trac/ticket/9937#comment:2>
Sage <http://www.sagemath.org>
Sage: Creating a Viable Open Source Alternative to Magma, Maple, Mathematica,
and MATLAB
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