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[Axiom-developer] Re: [sage-devel] Re: doctest failures due to rounding

From: Tim Daly
Subject: [Axiom-developer] Re: [sage-devel] Re: doctest failures due to rounding errors on Solaris.
Date: Fri, 01 Jan 2010 01:09:06 -0500
User-agent: Thunderbird (Windows/20090302)

William Stein wrote:
On Thu, Dec 31, 2009 at 9:13 PM, Tim Daly <address@hidden> wrote:
Dr. David Kirkby wrote:
rjf wrote:

On Dec 31, 11:15 am, "Dr. David Kirkby" <address@hidden>


The point you are missing is that we want to compare the output what Sage prints
to a human.

The point you are missing is that the following item, which presumably
could be printed by Sage,
is perfectly readable to a human:

6121026514868073 * 2^(-51).

It exactly dictates the bits in an IEEE double-float, and does not
require any conversion from binary
to decimal. It does not need rounding.  This kind of representation
does not have any hidden unprinted digits.  It does not ever need to
be longer because of delicate edge conditions of certain numbers.

It happens to evaluate to
APPROXIMATELY   2.718281828459045

Sure, Sage could print that. It would also be worth printing the sign bit, so we
could verify the values of

1) Sign bit
2) Significand
3) Exponent.

All of those could be correct. But there is still the software which does the
non-trivial task of converting that into the base 10 representation used by
humans. Then in additon to that, there is the software which takes a base 10
number, shows it with the Sage prompt, adding carriage returns etc where
necessary. All of these can go wrong.

I would think in an almost ideal world, the test would be done at a higher
level, using hardware/software which checked what the monitor actually
displayed. That's not quite as easy to do though.

Even better would be some way to scan the brain of the user to see what he/she
believes Sage is showing. Perhaps we use a font that is not very good, so
despite being displayed properly, it misunderstood.

Given most of time people want to see a base 10 representation of a number, and
not a base 2, base 16 or IEE 754 representation, I believe most testing should
be done at the base 10 level.

If there is a reason for testing the IEEE 754 representation as first choice,
then you have yet to convince me of it.



Axiom has the same issues.

My take on this is that what you check depends on the reason you are
If you are generating the output for human use (e.g. a table) then you
want decimal.
If you are generating the output for regression testing (e.g. checking
the answers on
multiple hardware) then you probably want Fateman's solution.


The output is used both for human use and for regression testing.  Its
primary use is human -- it's an example in the Sage reference manual:

   sage: float(e)

This is something a user will look at when reading the documentation
for some function.  It illustrates what happens when they convert the
symbolic constant e to float.


And therein lies the problem. We use a regression that does a comparison of the printed representation of the output of the run with a stored copy of the output.

All of our regression tests were passing until I installed another, unrelated program. Suddenly about 30 regression tests started failing. It turns out that the unrelated program upgraded one of the system libraries. The net effect of that change was to cause the last digit in the output to "wobble" so that some of the table values differ in the nth place (20th, 30th, or thereabouts digit). This caused the regression
comparisons to fail.

Common lisp will give you the exact bit pattern of the float and this value
does not wobble so the text comparison succeeds with both the old and
the new libraries against the bit pattern.

So I can tell you from experience that what you would like to do is not
going to succeed.

Our solution to the human vs regression problem is to include the stable
bit values in the actual compare and keep the human values in a latex
table. This is easy to do with literate input.


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