Alex Groce added the comment:

AND, right shift >> does not allocate memory, so there is a lack of symmetry 
that indicates the optimization might be desired.

see 

https://github.com/agroce/tstl/tree/master/examples/gmpy2/leftshiftalloc.py
vs.
https://github.com/agroce/tstl/tree/master/examples/gmpy2/rightshiftalloc.py

to compare behaviors, but these are depending on memory size, this was 
generated on MacBook Pro OS X Yosemite machine with 16GB)

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<https://bugs.python.org/issue27870>
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