Doctest tolerance: allow spaces and use intervals

[jdemeyer]

The doctesting framework should ignore whitespace before numbers and between the sign and the number when testing with (abs|rel) tol. There are two reasons why:

1. The spacing of matrices is unpredictable. You could have

   [1.0 0.0]
   [1.0 0.0]
   

vs

[0.999999 0.0]
[     1.0 0.0]

Note the added space between [ and 1.0.

2. Complex numbers or polynomials

   1.0 + 1e-16*I
   

vs

1.0 - 1e-16*I

Here you want to compare + 1e-16 and - 1e-16 with the sign for your tolerance computations.

After some consideration, I decided it actually makes a lot of sense to use interval arithmetic for doctest tolerances, this is implemented on this ticket.

[git]

Branch pushed to git repo; I updated commit sha1. This was a forced push. New commits:

​46301ac

Doctest tolerance: allow spaces

[git]

Branch pushed to git repo; I updated commit sha1. This was a forced push. New commits:

​291a442

Doctest tolerance: allow spaces

[jdemeyer]

Paul Zimmermann: this needs a minor change to a French book doctest. When using # tol, you may no longer split doctest results like

1.5 -
2.3

The minus sign may not be on its own line, you need to write

1.5
- 2.3

[zimmerma]

in the source of the french book, I've changed to:

  [0.347521510119 + 0.566550553398*I, 0.347521510119 - 0.566550553398*I,
  0.345023776962 + 0.439908702386*I, 0.345023776962 - 0.439908702386*I,
  -0.517257614325 + 0.512958206789*I,
  -0.517257614325 - 0.512958206789*I, -1.36699716455, -9.98357818097]

which uses the same number of lines, and should not make any overfull hbox. Is that ok?

Paul

[jdemeyer]

Replying to zimmerma:

in the source of the french book, I've changed to:

  [0.347521510119 + 0.566550553398*I, 0.347521510119 - 0.566550553398*I,
  0.345023776962 + 0.439908702386*I, 0.345023776962 - 0.439908702386*I,
  -0.517257614325 + 0.512958206789*I,
  -0.517257614325 - 0.512958206789*I, -1.36699716455, -9.98357818097]

which uses the same number of lines, and should not make any overfull hbox. Is that ok?

Yes, that would be good. However, note that Sage itself actually formats the results as in my patch, with one value per line.

[zimmerma]

ok, however in our book we allow ourselves not to follow 100% the Sage output format, up to spaces and line breaks, to save some vertical space.

Paul

[jdemeyer]

Fun fact: this ticket relies on functionality added in 2006:

src/sage/ext/mpfr.pyx

@@ -602 +602 @@
             d = parent(x.denominator())
             mpfr_div(self.value, n.value, d.value, parent.rnd)
         else:
-            s = str(x)
+            s = str(x).replace(' ','')
             if mpfr_set_str(self.value, s, base, parent.rnd):
                 if s == 'NaN' or s == '@NaN@':
                     mpfr_set_nan(self.value)

[git]

Branch pushed to git repo; I updated commit sha1. New commits:

​dde3a3a

Use intervals for doctest tolerances

[git]

Branch pushed to git repo; I updated commit sha1. New commits:

​59b511e

Add tolerance test file

[vbraun]

This looks good to me. How about renaming the tolerance.rst to must_fail.rst or so and have an explanatory sentence about what is going on at the top. I fear that somebody will sooner or later "fix" the failing doctests if its not clear ;-)

[git]

Branch pushed to git repo; I updated commit sha1. New commits:

​1f858c7

Add comment that we test failing tests

[vbraun]

Doctests fail because the line numbers are shifted, e.g. ​http://build.sagemath.org/sage/builders/%20%20fast%20Volker%20Desktop%20%28Fedora%2020%20x86_64%29%20incremental/builds/416/steps/shell_4/logs/stdio