Introduce random-seed option to allow fuzzing of doctests

[gh-kliem]

This is the first step towards #29935.

We introduce an option for doctests: --random-seed.

This allows specifying which seed to use for tests involving randomness.

The seed is displayed in the test log:

sage -t --long --random-seed=9876543210 src/sage/all.py 
...
Doctesting 1 file.
sage -t --long --random-seed=9876543210 src/sage/all.py
    [16 tests, 0.73 s]
----------------------------------------------------------------------
All tests passed!
----------------------------------------------------------------------
Total time for all tests: 0.8 seconds
    cpu time: 0.7 seconds
    cumulative wall time: 0.7 seconds

which makes it easy to re-run tests with the same seed.

The seed defaults to 0 for now:

sage -t --long src/sage/all.py 
...
Doctesting 1 file.
sage -t --long --random-seed=0 src/sage/all.py
    [16 tests, 0.73 s]
----------------------------------------------------------------------
All tests passed!
----------------------------------------------------------------------
Total time for all tests: 0.8 seconds
    cpu time: 0.7 seconds
    cumulative wall time: 0.7 seconds

but the plan in #29935 is to eventually have the random seed itself picked at random by default.

[gh-kliem]

New commits:

​da1c6be	start from a "random" random seed for doctesting
​b7b836d	make random seed reproducible
​eedbe5e	document random_seed
​998b1b9	default random seed 0 for now

[git]

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

​23ed583	fix doctest in hyperbolic_space/hyperbolic_point
​5283dc4	use abs tol flag
​7b244c0	modify doctests to the extend that they hold with fuzz
​228f379	Merge branch 'public/29936' of git://trac.sagemath.org/sage into public/29962
​5c7e562	fix double description of hypercube
​e1bf211	remove set_random_seed
​0e7a998	Merge branch 'public/29904' of git://trac.sagemath.org/sage into public/29962
​b6a5dc7	fix random test in geometry/linear_expression

[git]

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

[git]

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

​1d7b00e

dash instead of underscore for command line options

[gh-mwageringel]

Overall, this looks good to me. The following changes seem to be needed:

-    sage: subprocess.call(["sage", "-t", "--warn-long", "0", "--random-seed=0", -random_seed.rst"], **kwds)  # long time
+    sage: subprocess.call(["sage", "-t", "--warn-long", "0", "--random-seed=0", "random_seed.rst"], **kwds)  # long time

-  - ``--random_seed[=seed]`` -- random seed for fuzzing doctests
+  - ``--random-seed[=seed]`` -- random seed for fuzzing doctests

[mkoeppe]

The branch adds this to the documentation, which is not true for this ticket:

--- a/src/doc/en/developer/doctesting.rst
+++ b/src/doc/en/developer/doctesting.rst
...
+Doctests start from a random seed::
+
+    [kliem@sage sage-9.2]$ sage -t src/sage/doctest/tests/random_seed.rst
...
+    sage -t --warn-long 89.5 --random-seed=112986622569797306072457879734474628454 src/sage/doctest/tests/random_seed.rst
+    **********************************************************************

[gh-kliem]

New commits:

​b31e2d5	Merge branch 'public/29962' of git://trac.sagemath.org/sage into public/29962-reb
​2f30dd9	small fixes
​b62f781	doctests do not start from a random seed by default yet

[mkoeppe]

From my side this is a positive review - if patchbot is green

[gh-mwageringel]

Thanks. This successfully passes ptestlong.

[gh-kliem]

Thank you.

[vbraun]

Merge conflict

[gh-kliem]

sage -t --long --all passes for me.

---

New commits:

​1d99129

fix merge conflict

[gh-kliem]

Thank you.

[slelievre]

What random seeds are allowed? Any integer? Of any sign? Arbitrarily large?

[gh-kliem]

This is how we will eventually get the random seeds.

sage: import sage.misc.randstate as randstate                                   
sage: randstate.set_random_seed()                                               
sage: randstate.initial_seed()                                                  
11032378495085541661748859066830408537

At least that's the plan for now. Any random seed that you can feed into set_random_seed should work.

(Edit: But I wouldn't be surprised if there are bugs somewhere with some strange random seed. There is no way, you can avoid all of them. But at least you can prepare for rather probable cases.)

[slelievre]

The random_seed docstring says seed "must be coercible to a Python long".

Is that from -2**127 to 2**127 - 1? Or are 32-bit and 64-bit systems different there?

Also isn't "long" a Python 2 concept, with only "int" existing in Python 3?

Could we document the admissible range in a follow-up ticket, for non-experts like me?

[slelievre]

And thanks for the work on varying random seeds when testing!

[gh-kliem]

I added this issue to #29935.

The idea was that once all parts of Sage are ready for it, the default would be to select a "random" random seed.