Calculate Big Number

[Steven D'Aprano]

On Tue, 08 Jan 2013 02:44:04 +0200, Nac Temha wrote:

> Hello,
> How to *quickly* calculate large numbers. For example
>>>> (10**25) * (2**50)
> 11258999068426240000000000000000000000000L


Timing how long that takes is trickier than it seems, because modern 
versions of Python include a keyhole optimizer that will optimize some, 
or all, of that calculation to constant(s). In Python 2.7:


py> import dis
py> code = compile("(10**25) * (2**50)", "", "single")
py> dis.dis(code)
  1           0 LOAD_CONST               5 (10000000000000000000000000L)
              3 LOAD_CONST               6 (1125899906842624L)
              6 BINARY_MULTIPLY
              7 PRINT_EXPR
              8 LOAD_CONST               4 (None)
             11 RETURN_VALUE


So, here's the best of five attempts to calculate the above in full, with 
no optimizations, one hundred thousand times:

py> from timeit import Timer
py> t1 = Timer("(a**b)*(c**d)", setup="a,b,c,d = 10, 25, 2, 50")
py> min(t1.repeat(repeat=5, number=100000))
0.5256571769714355

So that's about 5 microseconds on my (slow) computer.


You can find the source code here:

http://hg.python.org/cpython/file/944e86223d1f/Objects/longobject.c



-- 
Steven