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See the thread starting at:
http://mail.python.org/pipermail/python-dev/2009-October/092958.html
Eric suggested that we don't need a separate branch for this; sounds
fine to me. It should still be possible to do the backport in stages,
though. Something like the following?
(1) Check in David Gay's code plus necessary build changes,
configuration steps, etc; conversions still use the old code.
(2) Switch to using the new code for float -> string (str, repr, float
formatting) and string -> float conversions (float, complex
constructors, numeric literals in Python code). [Substeps?]
(3) Fix up builtin round function to use the new code.
(4) Make any necessary fixes to the documentation. (Raymond, I assume
you'll take care of the whatsnew changes when the time comes?)
(1), (3) and (4) should be straightforward. (2) is where most of the
work is, I think. I think it should be possible to do the stage (2)
work in pieces without breaking too much.

Some key revision numbers from the py3k short float repr, for reference:
r71663: include Gay's code, build and configure fixes
r71723: backout SSE2 detection code added in r71663
r71665: rewrite of float formatting code to use Gay's code
Backported most of r71663 and r71723 to trunk in:
r75651: Add dtoa.c, dtoa.h, update license.
r75658: configuration changes - detect float endianness,
 add functions to get and set x87 control word, and
 determine when short float repr can be used.
Significant changes from r71663 not yet included:
* Misc/NEWS update
* Lib/test/formatfloat_testcases.txt needs updating to match py3k.

r75666: Add sys.float_repr_style attribute.

r75672: temporarily disable the short float repr while we're putting
 the pieces in place.
When testing, the disablement can be disabled (hah) by defining the 
PY_SHORT_FLOAT_REPR preprocessor symbol, e.g. (on Unix) with
CC='gcc -DPY_SHORT_FLOAT_REPR' ./configure && make

I think the next step on my side is to remove _PyOS_double_to_string,
and make all of the internal code call PyOS_double_to_string. The
distinction is that _PyOS_double_to_string gets passed a buffer and
length, but PyOS_double_to_string returns allocated memory that must be
freed. David Gay's code (_Py_dg_dtoa) returns allocated memory, so
that's the easiest interface to propagate internally.
That's the approach we used in the py3k branch. I'll start work on it.
So Mark's work should be mostly config stuff and hooking up Gay's code
to PyOS_double_to_string. I think it will basically match the py3k version.
The existing _PyOS_double_to_string will become the basis for the
fallback code for use when PY_NO_SHORT_FLOAT_REPR is defined (and it
will then be renamed PyOS_double_to_string and have its signature
changed to match).

One issue occurs to me: should the backport change the behaviour of the 
round function?
In py3k, round consistently uses round-half-to-even for halfway cases.
In trunk, round semi-consistently uses round-half-away-from-zero (and 
this is documented). E.g., round(1.25, 1) will give 1.2 in py3k and 
(usually) 1.3 in trunk.
I definitely want to use Gay's code for round in 2.7, since having round 
work sensibly is part of the motivation for the backport in the first 
place. But this naturally leads to a round-half-to-even version of 
round, since the Python-adapted version of Gay's code isn't capable of 
doing anything other than round-half-to-even at the moment.
Options:
(1) change round in 2.7 to do round-half-to-even. This is easy,
 natural, and means that round will agree with float formatting
 (which does round-half-to-even in both py3k and trunk). But it
 may break existing applications. However: (a) those applications
 would need fixing anyway to work with py3k, and (b) I have little
 sympathy for people depending on behaviour of rounding of
 *binary* floats for halfway *decimal* cases. (Decimal is another
 matter, of course: there it's perfectly reasonable to expect
 guaranteed rounding behaviour.)
 It's more complicated than that, though, since if rounding
 becomes round-half-to-even for floats, it should also change
 for integers, Fractions, etc.
(2) have round stick with round-half-away-from-zero. This may be
 awkward to implement (though I have some half-formed ideas about
 how to make it work), and would lead to round occasionally not
 agreeing with float formatting. For example:
 >>> '{0:.1f}'.format(1.25)
 '1.2'
 >>> round(1.25, 1)
 1.3

Adding tim_one as nosy. He'll no doubt have an opinion on rounding. And
hopefully he'll share it!

Another thing to consider is that in py3k we removed all conversions of
converting 'f' to 'g', such as this, from Objects/unicodeobject.c:
 if (type == 'f' && fabs(x) >= 1e50)
 type = 'g';
Should we also do that as part of this exercise? Or should it be another
issue, or not done at all?

+1 on backporting the 'f' and 'g' work also.
We will be well served by getting the two
code bases ins-sync with one another.
Eliminating obscure differences makes it easier
to port code from 2.x to 3.x

r75720: Backport py3k version of pystrtod.c to trunk. There are still
 some (necessary) differences between the two versions, which
 should become unnecessary once everything else is hooked up.
 The differences should be re-examined later.

[Eric, on removing f to g conversions]
> Should we also do that as part of this exercise? Or should it be another
> issue, or not done at all?
I'd definitely like to remove the f to g conversion in trunk. I don't 
see any great need to open a separate issue for that. (Was there one 
already for the py3k removal?)

Found it: issue #5859 was opened for the removal of the f -> g conversion 
in py3k. We could just add a note to that issue.

r75730: backport pystrtod.h
r75731: Fix floatobject.c to use PyOS_string_to_double.

r75739: Fix complexobject.c to use PyOS_string_to_double.

r75743: Fix cPickle.c to use PyOS_string_to_double.

r75745: Fix stropmodule.c to use PyOS_string_to_double.

r75824: Fix ast.c to use PyOS_string_to_double.

r75846: Fix marshal.c to use PyOS_string_to_double.

r75913: Fix _json.c to use PyOS_string_to_double. Change made after
consulting with Bob Ippolito.
This completes the removal of calls to PyOS_ascii_strtod.

The next job is to deprecate PyOS_ascii_atof and PyOS_ascii_strtod, I 
think. I'll get to work on that.

r75979: Deprecate PyOS_ascii_atof and PyOS_ascii_strtod; document
 PyOS_double_to_string.

Here's a patch for correctly-rounded round in trunk. This patch doesn't 
change the rounding behaviour between 2.6 and 2.7: it's still doing 
round-half-away-from-zero instead of round-half-even. It was necessary to 
detect and treat halfway cases specially to make this work. Removing this 
special case code would be easy, so we can decide later whether it's worth 
changing round to do round-half-to-even for 2.7.
I want to let this sit for a couple of days before I apply it.

r76373: Backport round.

Short float repr is now enabled in r76379.
Misc/NEWS entries added/updated in r76411.

r76465 removes the fixed-length buffer for formatting floats, hence
removes the restriction on the precision. This should make removal of 
the %f -> %g switch straightforward.

r76474: Remove %f -> %g switch.

I think we're pretty much done here.
I'd still like to produce a more complete set of float formatting test 
cases at some point (for both trunk and py3k), but that's a separate 
activity.
Eric, Raymond: can you spot anything we've missed?

Thanks for tackling the last few bits, Mark. I think we're done,
although I admit I haven't verified what state the documentation is in.
I suggest we close this issue and if any problems occur open them as new
issues.

Thanks, Eric.
The only remaining documentation issues I'm aware of are in 
Doc/tutorial/floatingpoint.rst. I think Raymond is going to update this 
to match the py3k version.
I'll call this done, then! Thanks for all your help.

Wondered if you guys had heard of some recent advances in the state of the art in this field. I'm sure you have, but thought I'd link it here anywhere.
Quote taken from this article (which links to relevant papers):
http://www.serpentine.com/blog/2011/06/29/here-be-dragons-advances-in-problems-you-didnt-even-know-you-had/
In 2010, Florian Loitsch published a wonderful paper in PLDI, "Printing floating-point numbers quickly and accurately with integers", which represents the biggest step in this field in 20 years: he mostly figured out how to use machine integers to perform accurate rendering! Why do I say "mostly"? Because although Loitsch's "Grisu3" algorithm is very fast, it gives up on about 0.5% of numbers, in which case you have to fall back to Dragon4 or a derivative.
If you're a language runtime author, the Grisu algorithms are a big deal: Grisu3 is about 5 times faster than the algorithm used by printf in GNU libc, for instance. A few language implementors have already taken note: Google hired Loitsch, and the Grisu family acts as the default rendering algorithms in both the V8 and Mozilla Javascript engines (replacing David Gay's 17-year-old dtoa code). Loitsch has kindly released implementations of his Grisu algorithms as a library named double-conversion.

Hadn't seen that. Interesting!

Thanks for the link :-)

I've filed issue12450 to track this last idea.