# Random testing¶

Some Sage modules do random testing in their doctests; that is, they construct test cases using a random number generator. To get the broadest possible test coverage, we want everybody who runs the doctests to use a different random seed; but we also want to be able to reproduce the problems when debugging. This module provides a decorator to help write random testers that meet these goals.

sage.misc.random_testing.random_testing(fn)

This decorator helps create random testers. These can be run as part of the standard Sage test suite; everybody who runs the test will use a different random number seed, so many different random tests will eventually be run.

INPUT:

• fn - The function that we are wrapping for random testing.

The resulting function will take two additional arguments, seed (default None) and print_seed (default False). The result will set the random number seed to the given seed value (or to a truly random value, if seed is not specified), then call the original function. If print_seed is true, then the seed will be printed before calling the original function. If the original function raises an exception, then the random seed that was used will be displayed, along with a message entreating the user to submit a bug report. All other arguments will be passed through to the original function.

Here is a set of recommendations for using this wrapper.

The function to be tested should take arguments specifying the difficulty of the test (size of the test cases, number of iterations, etc.), as well as an argument verbose (defaulting to false). With verbose true, it should print the values being tested. Suppose test_foo() takes an argument for number of iterations. Then the doctests could be:

test_foo(2, verbose=True, seed=0)
test_foo(10)
test_foo(100) # long time


The first doctest, with the specified seed and verbose=True, simply verifies that the tests really are reproducible (that test_foo is correctly using the randstate framework). The next two tests use truly random seeds, and will print out the seed used if the test fails (raises an exception).

If you want a very long-running test using this setup, you should do something like:

for _ in xrange(10^10): test_foo(100)


test_foo(10^12)


If the test fails after several hours, the latter snippet would make you rerun the test for several hours while reproducing and debugging the problem. With the former snippet, you only need to rerun test_foo(100) with a known-failing random seed.

See sage.misc.random_testing.test_add_commutes() for a simple example using this decorator, and sage.rings.tests for realistic uses.

Setting print_seed to true is useless in doctests, because the random seed printed will never match the expected doctest result (and using # random means the doctest framework will never report an error even if one happens). However, it is useful if you have a random test that sometimes segfaults. The normal print-the-random-seed-on-exceptions won’t work then, so you can run:

while True: test_foo(print_seed=True)


and look at the last seed that was printed before it crashed.

TESTS:

sage: from sage.misc.random_testing import random_testing
sage: def foo(verbose=False):
...       'oh look, a docstring'
...       n = ZZ.random_element(2^50)
...       if verbose:
...           print "Random value: %s" % n
...       assert(n == 49681376900427)
sage: foo = random_testing(foo)
sage: foo(seed=0, verbose=True)
Random value: 49681376900427
sage: foo(seed=15, verbose=True)
Random value: 1049538412064764
Random testing has revealed a problem in foo
Please report this bug!  You may be the first
person in the world to have seen this problem.
Random seed: 15
AssertionError()
sage: foo() # random
Random testing has revealed a problem in foo
Please report this bug!  You may be the first
person in the world to have seen this problem.
Random seed: 272500700755151445506092479579811710040
AssertionError()
sage: foo.__doc__
'oh look, a docstring'
sage: foo.__name__
'foo'
sage: def bar(): pass
sage: bar = random_testing(bar)
sage: bar(print_seed=True) # random
Random seed: 262841091890156346923539765543814146051


This is a simple demonstration of the random_testing() decorator and its recommended usage.

We test that addition is commutative over rationals.

EXAMPLES:

sage: from sage.misc.random_testing import test_add_commutes
a == -4, b == 0 ...
Passes!
a == -1/2, b == -1/95 ...
Passes!


This example demonstrates a failing random_testing() test, and shows how to reproduce the error.

DO NOT USE THIS AS AN EXAMPLE OF HOW TO USE random_testing()! Instead, look at sage.misc.random_testing.test_add_commutes().

We test that a+b == a*b, for a, b rational. This is of course false, so the test will almost always fail.

EXAMPLES:

sage: from sage.misc.random_testing import test_add_is_mul


We start by testing that we get reproducible results when setting seed to 0.

sage: test_add_is_mul(2, verbose=True, seed=0)
a == -4, b == 0 ...
Random testing has revealed a problem in test_add_is_mul
Please report this bug!  You may be the first
person in the world to have seen this problem.
Random seed: 0
AssertionError()


Normally in a @random_testing doctest, we would leave off the verbose=True and the # random. We put it in here so that we can verify that we are seeing the exact same error when we reproduce the error below.

sage: test_add_is_mul(10, verbose=True) # random
a == -2/7, b == 1 ...
Random testing has revealed a problem in test_add_is_mul
Please report this bug!  You may be the first
person in the world to have seen this problem.
Random seed: 216390410596009428782506007128692114173
AssertionError()


OK, now assume that some user has reported a test_add_is_mul() failure. We can specify the same random_seed that was found in the bug report, and we will get the exact same failure so that we can debug the “problem”.

sage: test_add_is_mul(10, verbose=True, seed=216390410596009428782506007128692114173)
a == -2/7, b == 1 ...
Random testing has revealed a problem in test_add_is_mul
Please report this bug!  You may be the first
person in the world to have seen this problem.