[issue44339] Discrepancy between math.pow(0.0, -inf) and 0.0**-inf

[Mark Dickinson]

Change by Mark Dickinson :


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resolution:  -> fixed
stage: patch review -> resolved
status: open -> closed

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[issue44339] Discrepancy between math.pow(0.0, -inf) and 0.0**-inf

[Mark Dickinson]

Mark Dickinson  added the comment:


New changeset 4a42cebf6dd769e2fa4e234a9e91093b3ad1cb63 by Mark Dickinson in 
branch 'main':
bpo-44339: Fix math.pow corner case to comply with IEEE 754 (GH-26606)
https://github.com/python/cpython/commit/4a42cebf6dd769e2fa4e234a9e91093b3ad1cb63


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[issue44339] Discrepancy between math.pow(0.0, -inf) and 0.0**-inf

[Steven D'Aprano]

Change by Steven D'Aprano :


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nosy: +steven.daprano

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[issue44339] Discrepancy between math.pow(0.0, -inf) and 0.0**-inf

[Mark Dickinson]

Change by Mark Dickinson :


--
keywords: +patch
pull_requests: +25189
stage:  -> patch review
pull_request: https://github.com/python/cpython/pull/26606

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[issue44339] Discrepancy between math.pow(0.0, -inf) and 0.0**-inf

[Mark Dickinson]

Mark Dickinson  added the comment:

> What about math.pow(0.0, -1.0)? Should it return -inf or raise 
> ZeroDivisionError?

Neither: it should raise ValueError, as it does now. This matches IEEE 754 
along with the math module's mapping of IEEE 754 floating-point exceptions to 
Python exceptions.

> And what about math.pow(-0.0, -inf)?

This should return inf, the same as math.pow(0.0, -inf). The relevant clauses 
of the C standard and IEEE 754 cover both these cases; I should have written 
`math.pow(±0.0, -inf)` throughout my previous message.

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[issue44339] Discrepancy between math.pow(0.0, -inf) and 0.0**-inf

[Serhiy Storchaka]

Serhiy Storchaka  added the comment:

What about math.pow(0.0, -1.0)? Should it return -inf or raise 
ZeroDivisionError?

And what about math.pow(-0.0, -inf)? Should it return inf, -inf or nan or raise 
an exception?

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nosy: +serhiy.storchaka

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[issue44339] Discrepancy between math.pow(0.0, -inf) and 0.0**-inf

[Raymond Hettinger]

Raymond Hettinger  added the comment:

+1 from me as well.

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nosy: +rhettinger

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[issue44339] Discrepancy between math.pow(0.0, -inf) and 0.0**-inf

[Tim Peters]

Tim Peters  added the comment:

+1. Although, to be fair, I'd personally be happy if (+-0)**inf returned, say, 
1.375 instead ;-)

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[issue44339] Discrepancy between math.pow(0.0, -inf) and 0.0**-inf

[Mark Dickinson]

Change by Mark Dickinson :


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components: +Library (Lib)
type:  -> enhancement

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[issue44339] Discrepancy between math.pow(0.0, -inf) and 0.0**-inf

[Mark Dickinson]

New submission from Mark Dickinson :

For floats x and y, x ** y and math.pow(x, y) mostly agree. There are three 
points of difference:

1. if x is finite and negative and y is finite and non-integral, then x ** y 
returns a complex number, while math.pow(x, y) raises ValueError
2. for cases where x ** y raises ZeroDivisionError (for example, 0.0 ** -1.0), 
math.pow(x, y) raises ValueError instead
3. the special cases 0.0 ** -inf and (-0.0) ** -inf return inf, but the 
equivalent math.pow calls raise ValueError

That third discrepancy is a surprising one: in particular, it's the only case 
where math.pow does not follow IEEE 754 rules.

Note that the math.pow behaviour is not accidental. The special cases were 
based on C99 Annex F (and are documented to do so), but the standards 
themselves have evolved here. In chronological order:

- IEEE 754-1985 did not cover transcendental functions, so has nothing to say 
on the topic of special values for pow.
- C99 §F.9.4.4 implies that pow(0, -inf) should raise the "divide-by-zero" 
exception; the relevant clause covers pow(0, y) for any y satisfying y < 0 and 
y not an odd integer
- IEEE 754-2008 §9.2.1 has an explicit clause specifying that pow(0, -inf) 
should be inf and that the operation does not raise any exception.
- C11 §F.10.4.4 mentions the case pow(0, -inf) explicitly and now says "may 
raise the divide-by-zero floating-point exception". The "may" is significant: 
other clauses simply say "raises the "divide-by-zero" floating-point exception".
- IEEE 754-2019 §9.2.1 is unchanged from IEEE 754-2008 for this particular 
special case.
- Similarly, C17 is unchanged from C11 in this respect.

For Python 3.11, I propose changing the behaviour of math.pow in this corner 
case so that it returns inf instead of raising. This would make math.pow 
conformant with IEEE 754, consistent with C11 and later, and consistent with 
the built-in pow function.

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messages: 395277
nosy: mark.dickinson
priority: normal
severity: normal
status: open
title: Discrepancy between math.pow(0.0, -inf) and 0.0**-inf
versions: Python 3.11

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