abs tol unable to handle non-real numerical noise #36631
Description
E.g.
--- a/src/sage/doctest/parsing.py
+++ b/src/sage/doctest/parsing.py
@@ -1461,7 +1461,7 @@ class SageOutputChecker(doctest.OutputChecker):
...
RuntimeError
sage: 1 # abs tol 2
- -0.5
+ -0.5+0.0001*I
sage: print("0.9999") # rel tol 1e-4
1.0
sage: print("1.00001") # abs tol 1e-5gives
sage -t --warn-long 20.5 --random-seed=37938279076849498617774420336933883040 src/sage/doctest/parsing.py
**********************************************************************
File "src/sage/doctest/parsing.py", line 1463, in sage.doctest.parsing.SageOutputChecker.check_output
Failed example:
1 # abs tol 2
Expected:
-0.5+0.0001*I
Got:
1
**********************************************************************
1 item had failures:
1 of 55 in sage.doctest.parsing.SageOutputChecker.check_output
[322 tests, 1 failure, 0.17 s]
----------------------------------------------------------------------
sage -t --warn-long 20.5 --random-seed=37938279076849498617774420336933883040 src/sage/doctest/parsing.py # 1 doctest failed
Indeed, RIF is used as data to check tolerances, no wonder things go wrong here.
By right, one needs a complex abs tol and rel tol.
Originally posted by @dimpase in #36509 (comment)