Numerical noise on devel/sage-main/sage/symbolic/expression.pyx computing sinh(1)

[drkirkby]

Whilst there is no complete 64-bit build of Sage on Solaris x86, a sufficiently large part of Sage does build (with a few changes) on Solaris 10 x86. When built on 'fulvia', a Dell Optiplex with Xeon processors, there was a numerical noise issue - see #9099

sage -t  -long devel/sage/sage/symbolic/expression.pyx
**********************************************************************
File "/home/palmieri/fulvia/sage-4.5.2.rc0/devel/sage-main/sage/symbolic/expression.pyx", line 498\
3:
    sage: maxima('sinh(1.0)')
Expected:
    1.175201193643801
Got:
    1.175201193643802

A computation with Mathematica, using 60 digits of precision gives

In[2]:= N[Sinh[1],60]

Out[2]= 1.17520119364380145688238185059560081515571798133409587022957

The absolute error on Solaris x86 is slightly higher than seen on some other systems, but this is still a perfectly acceptable result.

This should be fairly easy to fix. I'll make a patch later today

Dave

[drkirkby]

I just realise the second failure shown on #9099

Expected:
    0.881373587019543
Got:
    .8813735870195429

is the same file (devel/sage-main/sage/symbolic/expression.pyx) as this simple numerical noise issue. Hopefully be solved too. That's a less obvious problem to solve though.

Any ideas anyone?

[drkirkby]

Solves the numerical noise issue computing sinh(1.0). The archsinh case is more complex, and will be on another ticket.

[jhpalmieri]

It's not very pretty, but

abs(float(maxima('asinh(1.0)')) - 0.881373587019543) < 1e-15

or

maxima('abs(asinh(1.0) - 0.881373587019543)') < 1e-15

work for the other test. Or:

sage: float(maxima('asinh(1.0)'))
0.8813735870195429...

[jhpalmieri]

Or replace "float" with "RR", etc.

[drkirkby]

Yes, we can get this to pass, but that is just covering up a bug, as the number should never be printed as .8813735870195429 It is a numerically correct result, but it is not printed the way one would expect a piece of software to print the number. Carl Witty is of the opinion this is either a Maxima or ECL bug

​http://groups.google.com/group/sage-devel/msg/aa318e11e84afe8d?hl=en

I think its better to leave the asinh(1.0) case failing. It will be a constant reminder we need to get a real solution, not hack the doctest to get it to pass.

Ultimately, I feel the doctest has discovered a bug, which is what a good test should do.

Dave

[drkirkby]

I created #9693 to resolve the leading zero problem and are going to copy the problem to the ECL and Maxima mailing lists, to see if we get any response.

Dave

[cremona]

This looks fine to me and passed tests (in that file) on both 32-bit and 64-bit ubuntu.

[drkirkby]

Replying to cremona:

This looks fine to me and passed tests (in that file) on both 32-bit and 64-bit ubuntu.

Thank you for the review John.

Dave