#17122: bessel_Y is off by 3 ulps
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Reporter: zimmerma | Owner:
Type: defect | Status: new
Priority: major | Milestone: sage-6.4
Component: basic arithmetic | Resolution:
Keywords: | Merged in:
Authors: | Reviewers:
Report Upstream: N/A | Work issues:
Branch: | Commit:
Dependencies: | Stopgaps:
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Old description:
> consider the following with Sage 6.0:
> {{{
> sage: R=RealField(113)
> sage: a=R("1.414213562373095048801688724209698177")
> sage: b=bessel_Y(0,a)
> sage: c=R(bessel_Y(0,RealField(200)(a)))
> sage: (b-c)/c.ulp()
> -3.00000000000000000000000000000000
> sage: b
> -7.44623881999333920107530266264974e-7
> sage: c
> -7.44623881999333920107530266264973e-7
> }}}
> Given that MPFR provides correct rounding for bessel_Y (mpfr_y0) this
> should not happen.
New description:
consider the following with Sage 6.0:
{{{
sage: R=RealField(113)
sage: a=R("8.935761195587725798762818805462843676e-01")
sage: b=bessel_Y(0,a)
sage: c=R(bessel_Y(0,RealField(200)(a)))
sage: (b-c)/c.ulp()
-3.00000000000000000000000000000000
sage: b
-7.44623881999333920107530266264974e-7
sage: c
-7.44623881999333920107530266264973e-7
}}}
Given that MPFR provides correct rounding for bessel_Y (mpfr_y0) this
should not happen.
--
Comment (by zimmerma):
sorry, the value of {{{a}}} was wrong, I changed it in the description.
Indeed MPFR can only handle integer n for Y(n,x), but it would better to
call it in that case,
since it guarantees correct rounding (and thus numerical reproducibility).
--
Ticket URL: <http://trac.sagemath.org/ticket/17122#comment:2>
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