Bignum implementation that has efficient addition of small integers

Question

I have been using python's native bignums for an algorithm and decided to try and speed it up by converting it to C++. When I used long longs, the C++ was about 100x faster than the python, but when I used GMP bindings in C++, it was only 10x faster than the python (for the same cases that fit in long longs).

Is there a better bignum implementation for doing a large number of small additions? For example, we have a big number N we'll be adding a lot of little +1, +21, +1, etc. and every once and a while adds another big number M?

Answer 1

The GMP library itself has a fast short integer add to MPZ routine

void mpz_add_ui (mpz_t rop, mpz_t op1, unsigned long int op2)

I don't know whether gmpy uses that, but if it does try adding a normal python int to an mpz vs adding an mpz to mpz and see if it is quicker.

Edit

I tried a bit of benchmarking and found it doesn't make any difference

$ python -m timeit -c 'from gmpy import mpz
> a=mpz(10**1000)' 'a+1'
100000 loops, best of 3: 5.4 usec per loop

$ python -m timeit -c 'from gmpy import mpz
a=mpz(10**1000); b=mpz(1)' 'a+b'
100000 loops, best of 3: 5.5 usec per loop

So I guess gmpy doesn't use mpz_add_ui as I really would expect that to be a lot quicker.

Answer 2

Did you do profiling ? Of Python and C++ whole applications. So that you know that you really need that additional speed.

Try Python 3k it now have any-length integers implemented!

Answer 3

(Note: I help maintain GMPY and I've implemented quite a few optimizations in the most recent release.)

GMPY v1.11 does use mpz_add_ui when adding a small number to an mpz. The newest version of GMPY is also about 25% faster than prior versions when working with small numbers.

With GMPY 1.04
$ py26 -mtimeit -s "import gmpy;a=gmpy.mpz(10**1000)" "a+1"
10000000 loops, best of 3: 0.18 usec per loop
$ py26 -mtimeit -s "import gmpy;a=gmpy.mpz(10**1000);b=gmpy.mpz(1)" "a+b"
10000000 loops, best of 3: 0.153 usec per loop

With GMPY 1.11
$ py26 -mtimeit -s "import gmpy;a=gmpy.mpz(10**1000)" "a+1"
10000000 loops, best of 3: 0.127 usec per loop
$ py26 -mtimeit -s "import gmpy;a=gmpy.mpz(10**1000);b=gmpy.mpz(1)" "a+b"
10000000 loops, best of 3: 0.148 usec per loop

Since it is quicker to convert a Python int to a long and call mpz_add_ui than to convert a Python int to an mpz, there is a moderate performance advantage. I wouldn't be surprised if there is a 10x performance penalty for calling the GMP functions vs. native operations on a long long.

Can you accumulate several of the small numbers into one long long and add them at one time to your large number?