python - Integer caching for numbers greater than 256 and less than -5

Question

I know that python has a concept of small integers which are numbers from -5 to 256, and if two variables assign to same numbers between this range, they both will use the same underlying object.

From Python documentation,

#ifndef NSMALLPOSINTS
#define NSMALLPOSINTS           257
#endif
#ifndef NSMALLNEGINTS
#define NSMALLNEGINTS           5
#endif

/* Small integers are preallocated in this array so that they can be shared. The integers that are preallocated are those in the range -NSMALLNEGINTS (inclusive) to NSMALLPOSINTS (not inclusive). */

Also explained here,

The current implementation keeps an array of integer objects for all integers between -5 and 256, when you create an int in that range you actually just get back a reference to the existing object. So it should be possible to change the value of 1. I suspect the behaviour of Python in this case is undefined. :-)

Example,

a = 255
b = 255
print(id(a))
print(id(b))

gives the same id,

1561854394096
1561854394096

Which makes sense and also explained on this answer, "is" operator behaves unexpectedly with integers

If two numbers are less than -5, they should also have different IDs as follows,

a = -6
b = -6
print(id(a))
print(id(b))

gives,

2827426032208
2827426032272

this makes sense so far,

But any number greater than 256 should have different id,

This should return different IDs,

a = 257
b = 257
print(id(a))
print(id(b))

But it doesn't

2177675280112
2177675280112

Even when I am using very large integer, the IDs are same,

a = 2571299123876321621378
b = 2571299123876321621378
print(id(a))
print(id(b))

gives me,

1956826139184
1956826139184

Can someone tell me why number greater than 256 have same IDs even though in the Python code the range is -5 to 257 (not inclusive)

EDIT:

I have tried using PyCharm with both Python 2.7 and 3.6. Also tried on PythonTutor.com

Answer 1

On mint Python 3.6.3 (2 as well) I cannot reproduce. My guess is PyCharm or pythontutor are wrapping the run in something before interpreting - since those are not open code we cannot see the internals so I cannot verify. The reason I think this is true, is while (everything below is mint Python 3):

>>> x=2571299123876321621378
>>> y=2571299123876321621378
>>> print(id(x),id(y))
140671727739528 140671727739808

You can have this:

>>> def bla():
...  x=2571299123876321621378
...  y=2571299123876321621378
...  id(x)
...  print(id(x),id(y))
...
>>> bla()
140671727742528 140671727742528

so wrapping the two integers in something the interpreter can compile allows for these extra optimizations - like using the same constant for both definitions. Note this is limited as well:

>>> def bla():
...  x=2571299123876321621378
...  y=2571299123876321621378
...  print(id(x),id(y))
...  x+=1
...  y+=1
...  print(id(x),id(y))
...
>>> bla()
140671727755592 140671727755592
140671728111088 140671728108808

I would not have code that depends on this on any way - the guarantee is only on -5 to 256.