Systematic doctest for function return type

[zimmermann6]

sage: sinh(CIF(1))
[1.1752011936438013 .. 1.1752011936438017]
sage: asinh(CIF(1))
0.881373587019543

The second command should return a (complex) interval.

Also:

sage: asin(CIF(0.6))
...
TypeError: unable to convert '0.59999999999999998?' to a real number

Depends on #24318
Depends on #24329
Depends on #24604

CC: @jdemeyer

Component: symbolics

Author: Ralf Stephan

Branch/Commit: u/rws/24299 @ 0b52ecd

Reviewer: Paul Zimmermann

Issue created by migration from https://trac.sagemath.org/ticket/24299

[rwst]

comment:2

That's a symbolic function evaluation issue, not the fault of CIF.

[rwst]

comment:3

As an explanation, the handling of inexact function arguments has several layers. The fallback layer (if the arg has no suitable member function and exact evaluation has no tricks) is to call the helper functions in libs/pynac/pynac.pyx which use member functions of RR and CC. There is in most cases no automatic back-conversion to the argument type so, as fallback, you at least get Real/ComplexField elements.

There is work ongoing in Pynac to use arb instead of RR and CC because of speed and ease of conversion to e.g. interval field elements. It's just that inverse hyperbolic functions are still waiting for it. Of course one could state it's the responsibility of CIF to implement inverse hyperbolic functions (and inverse trig functions, for that matter) but I'm not holding my breath. CIF is a math programming exercise, Pynac tries to solve real calculus problems, so we'll implement it in Pynac-0.7.14.

[rwst]

Dependencies: #24317

[rwst]

Changed dependencies from #24317 to #24318, pynac-0.7.14

[rwst]

Branch: u/rws/bugs_with_inverse_trig_and_hyperbolic_functions_of_cif_argument

[rwst]

New commits:

0dad6ad

24299: Bugs with inverse trig and hyperbolic functions of CIF argument

[rwst]

Author: Ralf Stephan

[rwst]

Commit: 0dad6ad

[rwst]

Changed dependencies from #24318, pynac-0.7.14 to #24318, #24329

[zimmermann6]

comment:9

I'd like to review this, but I see only non-regression tests in commit ​0dad6ad, and no changes in the source code. How could the results change?

[rwst]

comment:10

Replying to @zimmermann6:

I'd like to review this, but I see only non-regression tests in commit ​0dad6ad, and no changes in the source code. How could the results change?

Functions can be either coded in Python (BuiltinFunction) or C++ (GinacFunction in Pynac). FP evaluation first looks if CIF has a member for asinh and, as there isn't, the function's evalf member is called. As trig and hyperbolic functions are GinacFunctions the changes needed to be done in Pynac, and they became effect with #24329 which was introduced in beta0 I think. So, in order to see the doctests fail you need to go back to 8.1.

[zimmermann6]

comment:11

I'm not sure about this:

sage: acoth(CIF(0.6))
0.693147180559945?

since we get with CC:

sage: acoth(CC(0.6))
0.693147180559945 - 1.57079632679490*I

[zimmermann6]

Reviewer: Paul Zimmermann

[rwst]

comment:12

Agreed, still buggy.

[rwst]

comment:13

I did a systematic search and found these additional issues:

sage: log_gamma(complex(1.7))
-0.09580769740706588
sage: psi(complex(1.7))
0.2085478748734939

Also dickman_rho can't handle anything other than float.

The code I used will go into tests/symbolic-functions.py.

[rwst]

Changed branch from u/rws/bugs_with_inverse_trig_and_hyperbolic_functions_of_cif_argument to u/rws/24299

[rwst]

Changed commit from 0dad6ad to 0b52ecd

[rwst]

New commits:

0b52ecd

24299: Systematic doctest for function return type

[rwst]

Changed dependencies from #24318, #24329 to #24318, #24329, #24604

[rwst]

comment:16

Replying to @zimmermann6:

I'm not sure about this:

sage: acoth(CIF(0.6))
0.693147180559945?

This one is now fixed in Pynac-0.7.16.

[rwst]

comment:17

Now with Pynac-0.7.16 still failing.

[rwst]

comment:18

Update: the correct arccoth(RR(0.7))-->CC, elliptic_eu(7,CC(1.7)), jacobi_am(7,CC(1.7)) are flagged wrong. Still failing: dickman_rho(all types).