>>> float.fromhex('0x0.8p-1074')
0.0
>>> float.fromhex('0x.8p-1074')
5e-324

One of them is obviously wrong. It's the second one, because:
- The smallest denormal is 0x1p-1074
- Therefore, 0x0.8p-1074 is a tie for rounding purposes.
- The digit in the last place is even because the number is zero, and there is a tie, which implies rounding down.

Thanks for the report! I can reproduce the issue, and agree with your analysis.

The bug is in this line:

https://github.com/python/cpython/blob/3db42fc5aca320b0cac1895bc3cb731235ede794/Objects/floatobject.c#L1467

which reads:

            (half_eps == 8 && (HEX_DIGIT(key_digit+1) & 1) != 0))

In the buggy case, key_digit=0 and the HEX_DIGIT macro is trying to retrieve the value of the second-to-least significant hex digit in the coefficient, to decide whether it's odd or not. For the "0x0.8" case it retrieves the "0". For the "0x.8" case, it retrieves the "x" and tries to interpret it as a hex digit.

Even worse, if we exclude the "0x" prefix, as in `float.fromhex(".8p-1074")`, `HEX_DIGIT(1)` is accessing memory that doesn't belong to the string.

New changeset 60b93d9e4922eeae25052bc15909d1f4152babde by Mark Dickinson in branch 'main':
bpo-44954: Fix wrong result in float.fromhex corner case (GH-27834)
https://github.com/python/cpython/commit/60b93d9e4922eeae25052bc15909d1f4152babde

New changeset 7ef0673de48958bc3a75af5f152564bd2dffa8dd by Miss Islington (bot) in branch '3.9':
bpo-44954: Fix wrong result in float.fromhex corner case (GH-27834) (GH-27855)
https://github.com/python/cpython/commit/7ef0673de48958bc3a75af5f152564bd2dffa8dd

Fixed in the main branch and in 3.9; 3.10 is very close to release, so the backport PR for 3.10 may have to wait for 3.10.1 (which wouldn't really be a problem, given that this bug has apparently lain unnoticed since Python 2.7). That's Pablo's call, of course.

@Pedro Thanks again for the report! Just out of curiosity, how did you manage to find this?

New changeset 838b0e975fc2c106508eb27d19a9548533ac1e55 by Miss Islington (bot) in branch '3.10':
bpo-44954: Fix wrong result in float.fromhex corner case (GH-27834)
https://github.com/python/cpython/commit/838b0e975fc2c106508eb27d19a9548533ac1e55

All fixed! Closing.

> @Pedro Thanks again for the report! Just out of curiosity, how did you manage to find this?

I'm writing a C strtod implementation and I was adding corner cases to the unit testing (now published here: https://codeberg.org/pgimeno/ACSL/src/branch/master/tests/test-strtod.c). Sometimes I get confused by whether to add one or subtract one to the exponent as digits are moved, and since I have an interactive Python shell always open as a calculator, I used it to make sure that the test I was writing had the correct exponent. But the result I got was not the one I expected, and upon verification, I soon became convinced that it was a bug, so I dug a bit more (at first I didn't notice it only happened if the leading zero was left out) and finally submitted the bug.

Thanks for the quick fix, by the way.