Proposed patch makes following things:

1. Rewrite error messages in float.as_integer_ratio() and Python implementation of Decimal.as_integer_ratio() in more general form, not mentioning as_integer_ratio(), as in C implementation of Decimal.as_integer_ratio().

2. Use Decimal.as_integer_ratio() to convert Decimal to Fraction.

3. Get rid of additional checks in Fraction constructor that raise errors with appropriate messages, since new error messages from as_integer_ratio() are appropriate enough.

This speeds up creating a Fraction from float and Decimal 2 to 3 times.

Any particular reason for the lower-casing of "Cannot" to "cannot" in the exception messages?

Otherwise, LGTM.

Any particular reason for the lower-casing of "Cannot" to "cannot" in the exception messages?

Only for matching current messages in C implementation of Decimal.as_integer_ratio(). As well as non-distinguishing positive and negative infinities, NaN and sNaN. If this is desirable, exception messages in C implementation of Decimal.as_integer_ratio() should be changed too.

Both versions are fine with me. The lowercase "cannot do ..." is more
pervasive in the source tree:

$ grep -R '"cannot' | wc -l
293
$ grep -R '"Cannot' | wc -l
150

If we change it, let's change all occurrences in _pydecimal and
_decimal/docstrings.h to uppercase (e.g. in __floor__, __round__,
__ceil__).

From my non-native speaker's point of view, I'd use lowercase if
the sentence doesn't end with a full stop, uppercase otherwise.

When I started here I was told that error messages in Python
usually don't have a full stop. ;)

Yes, this already was discussed in bpo-22364. The lowercase form wins with the score 4:1 (see msg226790, error messages use not only double quotes).

The question is wherever we should distinguish different sorts of infinities and NaNs (I think this is not needed).

Sorry for the bikeshedding, but I find this interesting:

Poly/ML (Cambridge), ghci (Glasgow) and OCaml (INRIA) appear to
use error messages without a full stop but starting in uppercase.

SML/NJ (Bell Labs) uses lowercase (and no full stop).

Perhaps this is a British/European vs. American issue?

Regarding int/-inf: I don't think it's important to distiguish
between them.

I wonder if it is a (programming) language specific thing. On the other hand, I don't know what those langauges error messages look like, but Python's normally follow a colon (ValueError: ....) where not having the message capitalized is more natural (whether or not there is a full stop at the end), at least in American English.

Serhiy: to me, the patch also looks good, we can certainly change
any error messages later.

Back to the bikeshedding:

Poly/ML:
========

f;
Error-Value or constructor (f) has not been declared Found near f
Static errors (pass2)

ghci
====
Prelude> f

<interactive>:2:1: Not in scope: `f'

OCaml
=====

# f;;
Error: Unbound value f

SML/NJ
======

• f;
  stdIn:1.2 Error: unbound variable or constructor: f

Basically the European languages start in uppercase after the
first relevant colon (or hyphen in the case of Poly/ML).

New changeset 284026a8af9e by Serhiy Storchaka in branch 'default':
Issue bpo-25971: Optimized creating Fractions from floats by 2 times and from
https://hg.python.org/cpython/rev/284026a8af9e

Thank you all for your review.