Optimize initialization of RealIntervalFieldElement

[jdemeyer]

Profiling #19288 showed that this was a significant bottleneck.

[jdemeyer]

New commits:

​048b036	Implement conversion of interval fields to real/complex fields
​752c401	Use the new conversions in qqbar
​6e2b88b	Optimize initialization of RealIntervalFieldElement

[git]

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

​40ff569

Add conversion from RealDoubleElement and float

[vdelecroix]

field.zero() should be faster than field(0) (not much though).

[jdemeyer]

Replying to vdelecroix:

field.zero() should be faster than field(0) (not much though).

I intentionally use field(0) because I need to mutate the number. field.zero() is probably cached and that would break things.

Ideally, I would use ComplexNumber.__new__() but that's not properly supported. The way I'm writing RealIntervalFieldElement.__cinit__() should be done for more element classes. But I didn't feel like rewriting also the ComplexNumber constructor here.

[mmezzarobba]

Not a bug introduced here, but since you are cleaning up this code: I think

       elif isinstance(x, str):
           s = str(x).replace('..', ',').replace(' ','').replace('+infinity', '@inf@').replace('-infinity','-@inf@')
           if mpfi_set_str(self.value, s, base):
               raise TypeError("unable to convert {!r} to real interval".format(x))

should be

       elif isinstance(x, basestring):
           ...

or at least

       elif isinstance(x, (str, unicode)):
           ...

[mmezzarobba]

Also, do you know if this branch is really used anywhere?

           # try coercing to real
           try:
               ra = self._parent._lower_field()(x)
               rb = self._parent._upper_field()(x)

I'm far from convinced that conversions of sage objects to real fields with directed rounding really return upper/lower bounds...

[mmezzarobba]

Positive review since the above comments are about peripheral issues, but feel free to make further changes if you agree with my comments.

[git]

Branch pushed to git repo; I updated commit sha1 and set ticket back to needs_review. New commits:

​842a66b

Fix a few details

[jdemeyer]

Replying to mmezzarobba:

Also, do you know if this branch is really used anywhere?

It's used at least for constants, and it even works correctly:

sage: RIF(pi).endpoints()
(3.14159265358979, 3.14159265358980)
sage: RIF.pi().endpoints()
(3.14159265358979, 3.14159265358980)