[SOLVED] why lua bit.lshift(1, 40) is 256, not 1099511627776

why lua bit.lshift(1, 40) is 256, not 1099511627776

I tried left-shift in python and lua, but get different result

lua

print(bit.lshift(1, 40))  --> 256

python

1 << 40   --> 1099511627776

Solution

That's because bit.lshift uses 32 bits (assuming this is the bitop library running under PUC Lua 5.1 / LuaJIT):

It's desirable to define semantics that work the same across all platforms. This dictates that all operations are based on the common denominator of 32 bit integers. (https://bitop.luajit.org/semantics.html#range)

so it wraps around at 2^32 thus making the result 2^(40-32) = 2^8 = 256.

whereas Python uses bigints:

$ python3
Python 3.8.10 (default, Mar 15 2022, 12:22:08) 
[GCC 9.4.0] on linux
Type "help", "copyright", "credits" or "license" for more information.
>>> 1 << 128
340282366920938463463374607431768211456
>>> 1 << 256
115792089237316195423570985008687907853269984665640564039457584007913129639936

(these numbers well exceed 64-bit ints)

In Lua versions since 5.3, which have a 64 bit signed integer type, you'll get the same result:

$ lua
Lua 5.3.4  Copyright (C) 1994-2017 Lua.org, PUC-Rio
> 1 << 40
1099511627776

workaround in 5.1: Simply multiply by 2^40 instead of shifting:

$ lua5.1
> =2^40
1099511627776