Function math.log10 fails on large Sage integers while ok on Python ints

[ismail]

Using SageMath version 9.0.beta10 via docker image.

sage: x=4**10000                                                                                                                                                             
sage: from math import log10                                                                                                                                                 
sage: type(x)                                                                                                                                                                
<class 'sage.rings.integer.Integer'>                                                                                                                                         
sage: log10(x)                                                                                                                                                               
inf                                                                                                                                                                          
sage: log10(int(x))                                                                                                                                                          
6020.599913279624

Related:

• Meta-ticket: improve compatibility with the Python library and Python packages #29728: Meta-ticket: improve compatibility with the Python library

CC: @slel

Component: numerical

Issue created by migration from https://trac.sagemath.org/ticket/28912

[slel]

comment:1

Confirmed in Sage 9.0.beta10.

Smallest Sage integers where this fails:

sage: a = (2^54-1)*2^(1024-54)
sage: aa = int(a)

Import log10 from the math module:

sage: from math import log10
sage: [log10(x) for x in [0.01, 0.1, 1, 10, 100]]
[-2.0, -1.0, 0.0, 1.0, 2.0]

Computing log10(aa) works, but not log10(a):

sage: log10(aa)
308.25471555991675
sage: log10(a)
inf

No problem with a - 1 as a Sage integer:

sage: type(a-1)
<class 'sage.rings.integer.Integer'>
sage: log10(a-1)
308.25471555991675

Workaround:

sage: RR(a).log()/(10.0).log()
308.254715559917

Note that Sage has a built-in method for the "number of digits"
of an integer (a common reason for taking the base ten logarithm):

sage: a.ndigits()
309
sage: a.ndigits(base=2)
1024

[slel]

comment:2

More descriptive ticket title.

[ismail]

comment:3

More of the same problem:

sage: math.log2(a)                                                                                                                                                           
inf                                                                                                                                                                          
sage: math.log(a)                                                                                                                                                            
inf                                                                                                                                                                          
sage: math.isinf(a)                                                                                                                                                          
True 

[embray]

comment:4

Ticket retargeted after milestone closed

[mkoeppe]

comment:5

Moving tickets to milestone sage-9.2 based on a review of last modification date, branch status, and severity.

[mkoeppe]

comment:8

Moving to 9.4, as 9.3 has been released.

[DaveWitteMorris]

I'm certainly not an expert, but I don't think we can fix this without making Integer a subclass of int (or patching python).

I say this because it seems from line 2349 of cpython/Modules/mathmodule.c that math.log10 calls loghelper, and the code for loghelper that handles a pythonint is conditional on a specific verification ("if (PyLong_Check(arg))" in line 2252) that the argument is an int.

So perhaps this issue should go on the wishlist.

PS. On the other hand, I think it would make a lot of sense to have Integer be a subclass of int, but I'm assuming there are good reasons why it's not.