Calculate Big Number

[Nac Temha]

Hello,
How to *quickly* calculate large numbers. For example11258999068426240000000000000000000000000L




Regards.

 

[Steven D'Aprano]

Hello,
How to *quickly* calculate large numbers. For example
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

 

[Gisle Vanem]

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.

That's pretty fast. So is there still a need for a GMP python-binding like
gmpy? http://code.google.com/p/gmpy/wiki/IntroductionToGmpy

GMP can include optimized assembler for the CPU you're using. But
I guess it needs more memory. Hence disk-swapping could be an issue
on performance.

--gv

 

[casevh]

That's pretty fast. So is there still a need for a GMP python-binding like
gmpy? http://code.google.com/p/gmpy/wiki/IntroductionToGmpy

GMP can include optimized assembler for the CPU you're using. But
I guess it needs more memory. Hence disk-swapping could be an issue
on performance.

gmpy will be faster than Python as the numbers get larger. The cutover varies depending on the platform, but usually occurs between 50 and 100 digits.

casevh

 

[casevh]

That's pretty fast. So is there still a need for a GMP python-binding like
gmpy? http://code.google.com/p/gmpy/wiki/IntroductionToGmpy

GMP can include optimized assembler for the CPU you're using. But
I guess it needs more memory. Hence disk-swapping could be an issue
on performance.

gmpy will be faster than Python as the numbers get larger. The cutover varies depending on the platform, but usually occurs between 50 and 100 digits.

casevh