Make RealBallField useful

[mmezzarobba]

After #17194, implement more comprehensive Arb bindings as part of RealBallField/RealBall.

[fredrik.johansson]

Regarding the "What is going on?!" comment: transcendental functions are not quite deterministic due to internal caches. In this case, doing something that results in an internal recomputation of log(2) to higher precision leads to a slightly more accurate value later on.

This is something that I could fix with a bit of effort.

In any case, output could also change slightly between versions due to changes in algorithms. That's an inherent drawback of doing doctests this way...

[mmezzarobba]

Replying to fredrik.johansson:

Regarding the "What is going on?!" comment: transcendental functions are not quite deterministic due to internal caches. In this case, doing something that results in an internal recomputation of log(2) to higher precision leads to a slightly more accurate value later on.

Good to know, I wasn't aware of that.

This is something that I could fix with a bit of effort.

Unless you have other users that need it, I don't think it is worth the effort.

In any case, output could also change slightly between versions due to changes in algorithms. That's an inherent drawback of doing doctests this way...

Yes. But I thought I'd first go with a version that tested the exact output, and we could always make something more sophisticated later on if some of the outputs really changed.

Thanks for your comments!

[cheuberg]

Two remarks:

• Shouldn't we use bint for those C functions returning an integer which is meant as a boolean? In that case, bool could be omitted in the Python methods.

• Should we really expose a function is_nonzero? We have to implement __nonzero__ anyway.

[mmezzarobba]

Replying to cheuberg:

Two remarks:

• Shouldn't we use bint for those C functions returning an integer which is meant as a boolean? In that case, bool could be omitted in the Python methods.

Yes, indeed, thanks. I just copied the C prototypes without thinking...

• Should we really expose a function is_nonzero? We have to implement nonzero anyway.

RIF intervals implement __nonzero__ with the meaning of "not exactly zero". So I think we need both if we want to stay compatible with them. But then I'm not sure doing things that way in RIF was the wisest choice in the first place...

[cheuberg]

Replying to mmezzarobba:

Replying to cheuberg:

• Should we really expose a function is_nonzero? We have to implement __nonzero__ anyway.

RIF intervals implement __nonzero__ with the meaning of "not exactly zero". So I think we need both if we want to stay compatible with them. But then I'm not sure doing things that way in RIF was the wisest choice in the first place...

I think we should not have methods __nonzero__ and is_nonzero with different behaviour.

[cheuberg]

#17194 needs to be merged. It would be good to merge #17811 and to replace its doctest by a simpler variant using the arithmetic operations introduced here.

[git]

Branch pushed to git repo; I updated commit sha1. This was a forced push. Last 10 new commits:

​760e2e2	RBF: separate conversions from initialization of elements
​464c601	RealBall: def accuracy
​e3453ce	rst syntax fixes
​624a609	RBF: more conversions
​26d4130	RealBall: better error handling
​ef6d130	RealBall: simple predicates
​dd15270	RealBall: more comparisons
​d1c6169	RealBall: contains()
​b54dd6c	RealBall: sqrt and friends
​2eec53a	RealBall: elementary functions

[git]

Branch pushed to git repo; I updated commit sha1. This was a forced push. Last 10 new commits:

​fae4e89	RBF: separate conversions from initialization of elements
​01af6a9	RealBall: def accuracy
​b1d45da	rst syntax fixes
​0101f43	RBF: more conversions
​cd8b230	RealBall: better error handling
​6ff081a	RealBall: simple predicates
​1af1a53	RealBall: more comparisons
​5e00b8d	RealBall: contains()
​b76df7f	RealBall: sqrt and friends
​0b34a7a	RealBall: elementary functions

[git]

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

​2f2e95e	RealBall: "return nonzero" → "return True" (for consistency)
​d65e84e	RealBall: rename arc-trig functions
​ca2f5f9	RealBall: adapt tests do deal with nondeterministic output
​1c8de12	RealBall: minor changes to docstrings and comments

[mmezzarobba]

Last 10 new commits:

​b518474	RealBall: contains()
​d28e6c2	RealBall: sqrt and friends
​8ea7a07	RealBall: elementary functions
​39c7c96	RealBall: "return nonzero" → "return True" (for consistency)
​17bf841	RealBall: rename arc-trig functions
​f8e2db9	RealBall: adapt tests do deal with nondeterministic output
​71a82e7	RealBall: minor changes to docstrings and comments
​9732629	RealBall: fix comparisons involving special values
​91591bf	RealBall: some special functions
​54340f0	RealBallField: some ball function of non-ball arguments

[git]

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

​9ab0759

RealBall: polylogs

[git]

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

​6d44ccb

RealBall: more functions

[git]

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

​5a14202

RealBall: changing my mind about nan1 == nan2 when nan1 is nan2

[git]

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

​f5ed6b1	RealBallField: misc Parent stuff
​5d13026	RealBall: TODO

[git]

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

​528fcda

RealBall: mid, rad as balls

[git]

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

​6808761

RealBall: fix an incorrect statement copied from the arb documentation

[git]

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

​7f24576

RealBall: remove duplicate methods introduced by mistake

[git]

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

​b952f49	RealBall: comparisons with symbolic ±∞
​4eed560	RealBall: floor(), ceil()

[git]

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

​28d63d8

RealBall: allow RealNumbers as radii

[git]

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

​b8036f2	real_arb: let's no longer call the bindings elementary :-)
​19aee15	Fix coercion RBF → InfinityRing when arb is not installed

[git]

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

​88d770d

real_arb: rst syntax fixes

[git]

Branch pushed to git repo; I updated commit sha1. This was a forced push. Last 10 new commits:

​edf95ab	RealBall: mid, rad as balls
​9469ce3	RealBall: fix an incorrect statement copied from the arb documentation
​5183126	RealBall: remove duplicate methods introduced by mistake
​8c1df6b	RealBall: comparisons with symbolic ±∞
​be93dba	RealBall: floor(), ceil()
​36801c6	RealBall: allow RealNumbers as radii
​9e06cce	real_arb: let's no longer call the bindings elementary :-)
​a6d68c6	Fix coercion RBF → InfinityRing when arb is not installed
​4046200	real_arb: rst syntax fixes
​0f67513	real_arb: mark all tests as optional

[git]

Branch pushed to git repo; I updated commit sha1. This was a forced push. New commits:

​1c6aa0c	RealBall: improve conversion to MPFI intervals
​2dd40b7	real_arb: mark all tests as optional

[git]

Branch pushed to git repo; I updated commit sha1. This was a forced push. New commits:

​760c2d5	real_arb: let's no longer call the bindings rudimentary :-)
​91dddf9	Fix coercion RBF → InfinityRing when arb is not installed
​b4f922b	real_arb: rst syntax fixes
​1134261	RealBall: improve conversion to MPFI intervals
​441f1c4	RealBall: remove superfluous bool() added back by mistake
​37bcb77	real_arb: mark all tests as optional

[fredrik.johansson]

Looks good to me.

Btw, I'm unable to build the reference manual, but this is presumably some problem with my Sage install and unrelated to this ticket.

[mmezzarobba]

Thanks for the review!

[vbraun]

Reviewer name is supposed to be the real name, not the trac account name