add inf and nan to math module #67374

ethanfurman · 2015-01-07T16:33:44Z

BPO	23185
Nosy	@malemburg, @gvanrossum, @rhettinger, @mdickinson, @pitrou, @vstinner, @ericvsmith, @ethanfurman, @serhiy-storchaka
Files	math_inf_nan.patch math_inf_nan2.patch math_inf_nan3.patch math_inf_nan4.patch

^{Note: these values reflect the state of the issue at the time it was migrated and might not reflect the current state.}

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GitHub fields:

assignee = 'https://github.com/mdickinson'
closed_at = <Date 2015-01-11.11:56:31.326>
created_at = <Date 2015-01-07.16:33:44.317>
labels = ['easy', 'type-feature', 'library']
title = 'add inf and nan to math module'
updated_at = <Date 2015-01-13.09:37:33.819>
user = 'https://github.com/ethanfurman'

bugs.python.org fields:

activity = <Date 2015-01-13.09:37:33.819>
actor = 'mark.dickinson'
assignee = 'mark.dickinson'
closed = True
closed_date = <Date 2015-01-11.11:56:31.326>
closer = 'mark.dickinson'
components = ['Library (Lib)']
creation = <Date 2015-01-07.16:33:44.317>
creator = 'ethan.furman'
dependencies = []
files = ['37633', '37634', '37635', '37647']
hgrepos = []
issue_num = 23185
keywords = ['patch', 'easy']
message_count = 26.0
messages = ['233580', '233581', '233582', '233583', '233585', '233588', '233591', '233593', '233594', '233595', '233596', '233598', '233601', '233602', '233607', '233630', '233674', '233692', '233720', '233737', '233842', '233843', '233894', '233912', '233917', '233920']
nosy_count = 11.0
nosy_names = ['lemburg', 'gvanrossum', 'rhettinger', 'mark.dickinson', 'pitrou', 'vstinner', 'eric.smith', 'stutzbach', 'ethan.furman', 'python-dev', 'serhiy.storchaka']
pr_nums = []
priority = 'normal'
resolution = 'fixed'
stage = 'resolved'
status = 'closed'
superseder = None
type = 'enhancement'
url = 'https://bugs.python.org/issue23185'
versions = ['Python 3.5']

ethanfurman · 2015-01-07T16:33:44Z

Proposal:

  math.nan = float('nan')
  math.inf = float('inf')

Guido's approval:

https://mail.python.org/pipermail/python-ideas/2015-January/030775.html

Followup question:

Do we add a math.neginf, or somesuch, for float('-inf')? Or just use -math.inf?

vstinner · 2015-01-07T16:42:16Z

Do we add a math.neginf, or somesuch, for float('-inf')? Or just use -math.inf?

I would prefer to only add inf.

It looks like float("-inf") and -float("inf") have exactly the same IEEE 754 representation (at least on my x86_64 CPU):

>>> struct.pack("d", float("-inf")) == struct.pack("d", -float("inf"))
True

mdickinson · 2015-01-07T16:57:53Z

Sounds good to me.

Do we add a math.neginf

IMO no: -inf should be fine.

mdickinson · 2015-01-07T16:58:50Z

float("-inf") and -float("inf") have exactly the same IEEE 754 representation

Indeed: there's only one negative infinity (and only one positive infinity) in IEEE 754 binary64 format.

mdickinson · 2015-01-07T17:07:00Z

Implementation suggestion: if possible, use the _Py_dg_stdnan and _Py_dg_infinity functions from Python/dtoa.c. These are a little safer than the Py_NAN and Py_HUGE_VAL macros, and will give results consistent with the float("inf") and float("nan") constructions.

vstinner · 2015-01-07T17:25:58Z

Oh, NaN can be signed?

>>> struct.pack("d", float("nan"))
b'\x00\x00\x00\x00\x00\x00\xf8\x7f'
>>> struct.pack("d", float("-nan"))
b'\x00\x00\x00\x00\x00\x00\xf8\xff'
>>> struct.pack("d", -float("nan"))
b'\x00\x00\x00\x00\x00\x00\xf8\xff'
>>> struct.pack("d", -float("-nan"))
b'\x00\x00\x00\x00\x00\x00\xf8\x7f'

Why does Python return the same representation for positive and negative NaN?

>>> float("nan")
nan
>>> float("-nan")
nan

mdickinson · 2015-01-07T18:18:08Z

Why does Python return the same representation for positive and negative NaN?

History, perhaps? In any case, the sign of a NaN isn't useful information in the same way that the sign of an infinity is. The IEEE 754 standard explicitly refuses to attach any meaning to the sign bit of a NaN. And if we were aiming for a full and faithful representation of NaNs, we'd want to output the payload, too (which is just about as meaningless / meaningful as the sign bit).

serhiy-storchaka · 2015-01-07T18:25:28Z

There are several different NaNs.

>>> x = struct.unpack('d', b'\x00\x00\x00\x00\x00\x00\xf8\x7f')[0]
>>> x
nan
>>> x == x
False
>>> struct.pack('d', x)
b'\x00\x00\x00\x00\x00\x00\xf8\x7f'
>>> x = struct.unpack('d', b'\x00\x00\x00\x00\x00\x00\xf9\x7f')[0]
>>> x
nan
>>> x == x
False
>>> struct.pack('d', x)
b'\x00\x00\x00\x00\x00\x00\xf9\x7f'

Interesting, but 0*inf and inf-inf return values with the same representation as float('-nan'), not float('nan').

>>> inf = float("inf")
>>> struct.pack('d', 0*inf)
b'\x00\x00\x00\x00\x00\x00\xf8\xff'
>>> struct.pack('d', inf-inf)
b'\x00\x00\x00\x00\x00\x00\xf8\xff'
>>> struct.pack('d', float('nan'))
b'\x00\x00\x00\x00\x00\x00\xf8\x7f'
>>> struct.pack('d', float('-nan'))
b'\x00\x00\x00\x00\x00\x00\xf8\xff'

pitrou · 2015-01-07T18:27:07Z

By tweaking the grammar we can have math.-inf.

mdickinson · 2015-01-07T18:27:27Z

but 0*inf and inf-inf return values with the same representation as float('-nan'), not float('nan')

Right: that's because Intel's "default" NaN (i.e., the float it produces as a result of any invalid operation) has its sign bit set.

mdickinson · 2015-01-07T18:27:46Z

By tweaking the grammar we can have math.-inf.

AAAARRGH!

mdickinson · 2015-01-07T18:42:47Z

Here's a patch.

mdickinson · 2015-01-07T19:27:27Z

Thanks for the review comments. Here's an updated patch taking the review comments into account (and fixing the spelling of PY_NAN, which should have been Py_NAN).

mdickinson · 2015-01-07T20:02:37Z

One more patch, fixing a misplaced period.

vstinner · 2015-01-07T22:09:05Z

"History, perhaps? In any case, the sign of a NaN isn't useful information in the same way that the sign of an infinity is. The IEEE 754 standard explicitly refuses to attach any meaning to the sign bit of a NaN. And if we were aiming for a full and faithful representation of NaNs, we'd want to output the payload, too (which is just about as meaningless / meaningful as the sign bit)."

So I understand that adding a math.neg_nan would be useless. As adding one constant per possible "NaN" value :-) If I recall correctly the IEEE 754 standard, there is not single NaN value, but a range of NaN.

"Two kinds of NaN: a quiet NaN (qNaN) and a signaling NaN (sNaN). A NaN may carry a payload that is intended for diagnostic information indicating the source of the NaN. The sign of a NaN has no meaning, but it may be predictable in some circumstances." says Wikipedia.

Well, the current definition of math.nan makes sense, it's the same value than float("nan").

Note: On python-ideas, I asked if math.nan and math.inf should be singleton (as it was requested for float("0.0") in issue bpo-4024). The answer is no.

mdickinson · 2015-01-08T08:58:49Z

I have an updated patch taking into account the most recent review comments (for which thanks!), but it's at home; I'll upload it this evening (UTC+00:00).

mdickinson · 2015-01-08T17:40:19Z

New patch, addressing review comments.

vstinner · 2015-01-08T22:41:09Z

Except of my small suggestion on the doc (see the review), math_inf_nan4.patch looks good to me.

serhiy-storchaka · 2015-01-09T07:16:12Z

May be make math.inf and math.nan special objects so that for all x (except inf and nan):

x < math.inf
x > -math.inf
not (x < math.nan)
not (x > math.nan)

vstinner · 2015-01-09T08:57:16Z

2015-01-09 8:16 GMT+01:00 Serhiy Storchaka <report@bugs.python.org>:

May be make math.inf and math.nan special objects so that for all x (except inf and nan):

What do you mean? Implement a subtype of float and override some methods?

x < math.inf
x > -math.inf

It's already the case for int, float and decimal.Decimal.

not (x < math.nan)
not (x > math.nan)

Comparison to nan always return False.

I would be better to raise an error when nan is compared to other numbers (I mean operations like a>b, not a==b), but Python was not designed like that (nor the IEEE 754?).

>>> sorted((nan, 1, nan, 2))
[nan, 1, nan, 2]

Sorting with NaN is a common issue :-/ See for example:
https://stackoverflow.com/questions/4240050/python-sort-function-breaks-in-the-presence-of-nan

Anyway, changing NaN behaviour is out of the scope of this issue!

python-dev · 2015-01-11T11:55:41Z

New changeset cf4bf577749c by Mark Dickinson in branch 'default':
Issue bpo-23185: add math.inf and math.nan constants.
https://hg.python.org/cpython/rev/cf4bf577749c

mdickinson · 2015-01-11T11:56:31Z

Committed. Thanks for all the helpful review comments!

gvanrossum · 2015-01-12T22:41:31Z

Should inf and nan be added to cmath too? It has e and pi and isnan() and isinf()...

Also complex(0, math.nan) a value that is printed as "nanj" and complex("nanj") parses and returns such a value, so the point could be made that there should be a constant named complex.nanj.

vstinner · 2015-01-13T09:07:12Z

Guido van Rossum added the comment:

Should inf and nan be added to cmath too? It has e and pi and isnan() and isinf()...

Also complex(0, math.nan) a value that is printed as "nanj" and complex("nanj") parses and returns such a value, so the point could be made that there should be a constant named complex.nanj.

Since it's a different module and we are talking about more and
different constants, I suggest to open a new issue.

mdickinson · 2015-01-13T09:35:45Z

Should inf and nan be added to cmath too?

Hmm; probably, yes. I'll open an issue.

so the point could be made that there should be a constant named complex.nanj

Yes, I suppose it could (along with infj, of course). I don't like it much, and I suspect it would get almost no uses. complex(0, inf) and complex(0, nan) seem like good enough spellings.

mdickinson · 2015-01-13T09:37:34Z

Opened issue bpo-23229.

ethanfurman added easy type-feature A feature request or enhancement labels Jan 7, 2015

berkerpeksag added the stdlib Python modules in the Lib dir label Jan 7, 2015

mdickinson self-assigned this Jan 7, 2015

mdickinson closed this as completed Jan 11, 2015

ezio-melotti transferred this issue from another repository Apr 10, 2022

add inf and nan to math module #67374

add inf and nan to math module #67374

ethanfurman commented Jan 7, 2015

ethanfurman commented Jan 7, 2015

vstinner commented Jan 7, 2015

mdickinson commented Jan 7, 2015

mdickinson commented Jan 7, 2015

mdickinson commented Jan 7, 2015

vstinner commented Jan 7, 2015

mdickinson commented Jan 7, 2015

serhiy-storchaka commented Jan 7, 2015

pitrou commented Jan 7, 2015

mdickinson commented Jan 7, 2015

mdickinson commented Jan 7, 2015

mdickinson commented Jan 7, 2015

mdickinson commented Jan 7, 2015

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vstinner commented Jan 7, 2015

mdickinson commented Jan 8, 2015

mdickinson commented Jan 8, 2015

vstinner commented Jan 8, 2015

serhiy-storchaka commented Jan 9, 2015

vstinner commented Jan 9, 2015

python-dev mannequin commented Jan 11, 2015

mdickinson commented Jan 11, 2015

gvanrossum commented Jan 12, 2015

vstinner commented Jan 13, 2015

mdickinson commented Jan 13, 2015

mdickinson commented Jan 13, 2015

add inf and nan to math module #67374

add inf and nan to math module #67374

Comments

ethanfurman commented Jan 7, 2015

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vstinner commented Jan 7, 2015

mdickinson commented Jan 7, 2015

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