#9937: PARI real precision is broken in many ways
--------------------------+-------------------------------------------------
Reporter: jdemeyer | Owner: was
Type: defect | Status: needs_work
Priority: major | Milestone: sage-pending
Component: interfaces | Keywords: pari gp real precision
set_real_precision
Work_issues: | Upstream: N/A
Reviewer: | Author: Jeroen Demeyer
Merged: | Dependencies: #11130, #11321
--------------------------+-------------------------------------------------
Changes (by jdemeyer):
* dependencies: => #11130, #11321
* milestone: sage-4.7.2 => sage-pending
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).
>
> 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(50);
> sage: pari('Euler') # Precision changes
> 0.57721566490153286060651209008240243104215933593992
> sage: pari.euler() # Precision does NOT change
> 0.5772156649015328607
> }}}
>
> 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).
>
> Depends on #11130.
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(50);
sage: pari('Euler') # Precision changes
0.57721566490153286060651209008240243104215933593992
sage: pari.euler() # Precision does NOT change
0.5772156649015328607
}}}
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).
--
--
Ticket URL: <http://trac.sagemath.org/sage_trac/ticket/9937#comment:10>
Sage <http://www.sagemath.org>
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