modernize complex_mpfr

[videlec]

Similarly to #24457 for real numbers we perform some cleaning for complex numbers in view of #17713/#24457.

step 1

• complex_field.py complex_number.pyx -> complex_mpfr.pyx #24483: move sage.rings.complex_field to sage.rings.complex_mpfr
• change the string representation from Complex Field with XX bits of precision to Complex Floating-point Field with XX bits of precision
• (possibly) get rid of the factory ComplexField by making the class ComplexField_class inherits from UniqueRepresentation
• rename CompleNumber/ComplexField into ComplexFloatingPoint/ComplexFloatingPointField
• remove the attribute _prec of ComplexNumber (a mpfr_t carries its precision that can be obtained with mpfr_get_prec)
• deprecate is_ComplexNumber(x)/is_ComplexField(x) in favor of isinstance(x, ComplexFloatingPoint)/isinstance(x, ComplexFloatingPointField)
• actually initialize the mpfr_t pointers in __cinit__ as it is the case for real floating point numbers in real_mpfr.pyx
• clarify the behavior of rounding (currently there is a global (sic) variable taking care of it)
• Deprecate CC in favor of CFF

see also task ticket #17713

Depends on #24483
Depends on #24457

CC: @mezzarobba @jpflori

Component: basic arithmetic

Author: Vincent Delecroix

Issue created by migration from https://trac.sagemath.org/ticket/24489

[jdemeyer]

comment:4

If you are going to do serious refactoring, here is a different proposal: deprecate complex_mpfr altogether and use complex_mpc instead as the default complex floating point field.

[videlec]

comment:5

Replying to @jdemeyer:

If you are going to do serious refactoring, here is a different proposal: deprecate complex_mpfr altogether and use complex_mpc instead as the default complex floating point field.

+1. I wanted to do that at some point but Marc Mezzarobba claimed that the mpfr version was faster and hence still needed. I will be more than happy to recycle this ticket in order to do this!

Though the branch in #24483 is still useful to liberate the module sage.rings.complex_field needed for #24456.

[jdemeyer]

comment:6

+1. I wanted to do that at some point but Marc Mezzarobba claimed that the mpfr version was faster and hence still needed.

Please keep in mind #24353 which will almost certainly change timings. Unfortunately, that ticket is current stalled because it breaks MPFI. If there is a proper release of MPC, maybe I'll try to patch MPFI in Sage.

[videlec]

Changed dependencies from #24483 to #24483, #24457

[videlec]

comment:10

Replying to @videlec:

Replying to @jdemeyer:

+1. I wanted to do that at some point but Marc Mezzarobba claimed that the mpfr version was faster and hence still needed. I will be more than happy to recycle this ticket in order to do this!

My bad: it was JP Flori.

[jpflori]

comment:12

Yes it used to be the case, and Paul Zimmerman improved MPC but my last souvenir is that for basic operations Sage's complex_mpfr was still faster than complex_mpc surely because it does not handle special cases (NaN, infinities, and i don't know what) gracefully.

Things can have changed but there is only one way to knwom: benchmark both implementations, and I don't think I have any time for this.

On a side note, I would think it is a very good idea to get rid of complex_mpfr if we can.

[jdemeyer]

comment:13

Replying to @jpflori:

because it does not handle special cases (NaN, infinities, and i don't know what) gracefully.

Certainly not because of that reason. First of all, checking for a special value is really trivial compared to dealing with Python objects. You need to work with least ~100 bits of precision to have a sensible benchmark because otherwise you are only benchmarking the Python overhead anyway.

[jdemeyer]

comment:14

Replying to @jpflori:

my last souvenir is that for basic operations Sage's complex_mpfr was still faster than complex_mpc

Of course it's always going to be faster. But that's not the point. If you really want speed, use CDF.

The thing that we should focus on is the correctness. With MPC, you are guaranteed that the answer that you receive is as good as it can be. With MPFR complex numbers, we are using some arbitrary formulas and we hope that everything works. On the one hand, we use an arbitrary-precision library but we cannot say whether the many bits that you get are actually meaningful.