RealDoubleFieldElement without GSL: Add missing methods

[mkoeppe]

Follow-up on #32677: Observed in the context of #32432 (sagemath-polyhedra):

   AttributeError: 'sage.rings.real_double.RealDoubleElement' object has no attribute 'sin'
   AttributeError: 'sage.rings.real_double.RealDoubleElement' object has no attribute '_pow_'

In this ticket, we provide simple implementations for these methods (whose implementation using GSL was moved to a subclass in #32677)

Depends on #32963

CC: @sagetrac-tmonteil

Component: refactoring

Author: Matthias Koeppe

Issue created by migration from https://trac.sagemath.org/ticket/32779

[mkoeppe]

Dependencies: #32677

[mkoeppe]

Branch: u/mkoeppe/realdoublefieldelement_without_gsl__add_missing_methods

[sagetrac-git]

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

ac0b0fe

RealDoubleElement.cos, tan, _pow_: New implementations without GSL

[sagetrac-git]

Commit: ac0b0fe

[sagetrac-git]

Changed commit from ac0b0fe to d447c2b

[sagetrac-git]

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

d447c2b

RealDoubleElement: In doctests for methods redefined by RealDoubleElement_gsl, invoke methods defined here explicitly

[sagetrac-git]

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

46a680c	RealDoubleElement: Move methods arccos, arcsin, arctan, sech, csch, coth back here from RealDoubleElement_gsl
566326a	RealDoubleElement._pow_: Fix up declaration
8c82df5	RealDoubleElement: Add remaining trig/hyp functions

[sagetrac-git]

Changed commit from d447c2b to 8c82df5

[mkoeppe]

Author: Matthias Koeppe

[dimpase]

comment:7

I get

$ ./sage -tp src/sage/rings/real_double.pyx
Running doctests with ID 2021-12-03-18-09-42-15c43c30.
Git branch: wipprimec
Using --optional=build,dochtml,e_antic,gentoo,normaliz,pip,pynormaliz,sage,sage.geometry.polyhedron,sage.rings.real_double,sage_spkg
Doctesting 1 file using 4 threads.
sage -t --warn-long 58.0 --random-seed=69902574013687066773814734789326488934 src/sage/rings/real_double.pyx
**********************************************************************
File "src/sage/rings/real_double.pyx", line 2081, in sage.rings.real_double.RealDoubleElement._pow_
Failed example:
    RealDoubleElement._pow_(RDF(0), RDF(-1))
Expected:
    Traceback (most recent call last):
    ...
    ZeroDivisionError: 0.0 cannot be raised to a negative power
Got:
    +infinity
**********************************************************************
File "src/sage/rings/real_double.pyx", line 2089, in sage.rings.real_double.RealDoubleElement._pow_
Failed example:
    RealDoubleElement._pow_(RDF(-1), RDF(0.5))
Expected:
    Traceback (most recent call last):
    ...
    ValueError: negative number cannot be raised to a fractional power
Got:
    NaN
**********************************************************************
File "src/sage/rings/real_double.pyx", line 2104, in sage.rings.real_double.RealDoubleElement.cos
Failed example:
    RealDoubleElement.cos(t)
Expected:
    6.123233995736757e-17
Got:
    6.123233995736766e-17
**********************************************************************
File "src/sage/rings/real_double.pyx", line 2132, in sage.rings.real_double.RealDoubleElement.tan
Failed example:
    RealDoubleElement.tan(q)
Expected:
    0.5773502691896256
Got:
    0.5773502691896257
**********************************************************************
3 items had failures:
   2 of  12 in sage.rings.real_double.RealDoubleElement._pow_
   1 of   4 in sage.rings.real_double.RealDoubleElement.cos
   1 of   6 in sage.rings.real_double.RealDoubleElement.tan
    [373 tests, 4 failures, 0.26 s]
----------------------------------------------------------------------
sage -t --warn-long 58.0 --random-seed=69902574013687066773814734789326488934 src/sage/rings/real_double.pyx  # 4 doctests failed
----------------------------------------------------------------------
Total time for all tests: 0.4 seconds
    cpu time: 0.3 seconds
    cumulative wall time: 0.3 seconds
Pytest is not installed, skip checking tests that rely on it.

two of these are trivial numerical noise, but the other two return NaNs/infinites, not throwing exceptions any more. Is this what we need?

[mkoeppe]

comment:8

RDF is not terribly consistent regarding exceptions vs. infinities/NaNs. For example:

sage: RDF(1.0)/RDF(0.0)
+infinity
sage: RDF(0.0)/RDF(0.0)
NaN

[mkoeppe]

comment:9

The code that raises these exceptions seems to come from #24247.

[mkoeppe]

comment:10

I've opened #32963 for this

[mkoeppe]

Changed dependencies from #32677 to #32963

[mkoeppe]

Removed branch from issue description; replaced by PR #35158