tifa
Fast factorization of integers of up to about 220 bits (66 digits), with the TIFA C library: its quadratic sieve, elliptic curves and smaller methods, chosen by the size of the number.
>>> import tifa
>>> tifa.factor(360)
{2: 3, 3: 2, 5: 1}
>>> tifa.factor(2**64 + 1)
{274177: 1, 67280421310721: 1}
>>> tifa.factor(1)
{}
factor(n) returns the prime factorization of a positive integer as
{prime: exponent}, primes in increasing order, like SymPy's factorint.
n can be an int or any integer type with __index__ (NumPy's, gmpy2's).
Speed
One thread, balanced semiprimes (the hardest numbers of a size), on an AMD EPYC 9V45:
| bits | 100 | 140 | 180 | 220 |
|---|---|---|---|---|
tifa.factor |
0.7 ms | 9.6 ms | 0.18 s | 3.0 s |
PARI/GP 2.15 factorint |
1.9 ms | 39 ms | 0.55 s | 9.0 s |
Numbers with small factors take much less. From 180 to 220 bits the time doubles about every 10 bits, and keeps growing beyond.
Hints
When something is known of n, a hint saves time:
tifa.factor(n, hint="balanced") # two primes of about the same size
tifa.factor(n, hint="unbalanced") # a prime factor under a third of its size
A hint never changes the result, but a wrong one can cost much more time than none.
Threads
factor releases the GIL, so that threads factor in parallel:
from concurrent.futures import ThreadPoolExecutor
with ThreadPoolExecutor() as pool:
results = list(pool.map(tifa.factor, numbers))
Errors
TypeError if n is not an integer, ValueError if it is not positive
or the hint is unknown. In the rare event that n can not be factored
completely, tifa.FactorizationError is raised, its factors attribute
holding what was found (factors that multiply to n, some of them not
prime).
Installing
From PyPI:
pip install tifa-factor
Wheels exist for Linux (x86-64 and arm64, glibc and musl) and macOS (arm64 and x86-64, 11.0 and later), for Python 3.10 and later; GMP comes in them. Elsewhere, pip builds the package from source.
From a checkout of TIFA, at the top of the tree:
pip install ".[test]" # or "pip install ." without pytest
python -m pytest # the tests
A build from source needs a C compiler, CMake 3.26 or later (pip fetches it
if the system's is older) and GMP with its headers (libgmp-dev on
Debian and Ubuntu, gmp-devel on Fedora, brew install gmp on macOS). A
GMP installed elsewhere than in the usual places is found through
GMP_ROOT, the directory holding its include and lib:
GMP_ROOT=/opt/gmp pip install .
Licence
LGPL 2.1 or later, as TIFA. The wheels contain GMP 6.3.0
(gmplib.org), under the LGPL 3 (readme/license_v3.txt),
linked statically: pip install --no-binary tifa-factor tifa-factor builds
the package against the GMP of the system instead.
1 maintainer
Metadata
1 maintainer
Release files for tifa-factor 0.4.6
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