Missing digits in numerical_approx

[Jérôme Tremblay]

Using n() sometimes returns the wrong number of digits

This is correct:

sage: a = n(golden_ratio, digits=5000)
sage: len(str(a))
5001

This is not:

sage: a = n(golden_ratio, digits=5000000)
sage: len(str(a))
4999989

Any clue?

Jerome Tremblay
LaCIM, UQAM

[Harald Schilly]

Via "n??" I looked at the code. There is a line

prec = int((digits+1) * 3.32192) + 1

where the 3.32… is an approximation to log_2(10). I highly suspect that's the source of it. Make the trailing 2 a 3 and it should give you more than the requested number of digits.

sage: n(log(10,2), prec=100)

3.3219280948873623478703194295…

H

[D. S. McNeil]

I think problems caused by the log(10,2) ~ 3.32192 assumption occur in
several places throughout Sage, and it's the source of at least one
bug report (http://trac.sagemath.org/sage_trac/ticket/10164). The
following all look suspicious to me:

misc/functional.py: prec = int((digits+1) * 3.32192) + 1
rings/complex_interval.pyx: bits =
max(int(3.32192*len(s_real)),int(3.32192*len(s_imag)))
rings/complex_number.pyx: bits =
max(int(3.32192*len(s_real)),int(3.32192*len(s_imag)))
rings/real_mpfi.pyx: bits = int(3.32192*len(s))
rings/real_mpfr.pyx: bits = int(3.32192*sigfigs)+1
symbolic/expression.pyx: prec = int((digits+1) * 3.32192) + 1

Doug

[William Stein]

2011/12/14 Jérôme Tremblay <trembla...@uqam.ca>:

> Using n() sometimes returns the wrong number of digits
>
> This is correct:
>
> sage: a = n(golden_ratio, digits=5000)
> sage: len(str(a))
> 5001
>
> This is not:
>
> sage: a = n(golden_ratio, digits=5000000)
> sage: len(str(a))
> 4999989
>
> Any clue?

My first guess is that the problem might come from the fact that str
truncates the last few digits. However, even with that disabled,
there are still not enough digits:

sage: len(a.str(truncate=False))
4999992

(Only 3 more)

Somebody needs to open a ticket.

-- William

[Sébastien Labbé]

> Somebody needs to open a ticket.

http://trac.sagemath.org/sage_trac/ticket/12163