346 lines
10 KiB
Python
346 lines
10 KiB
Python
import os
|
|
from ctypes import c_long, sizeof
|
|
from functools import reduce
|
|
from typing import Tuple as tTuple, Type
|
|
from warnings import warn
|
|
|
|
from .importtools import import_module
|
|
|
|
from .pythonmpq import PythonMPQ
|
|
|
|
from .ntheory import (
|
|
# bit_scan1 as python_bit_scan1,
|
|
# bit_scan0 as python_bit_scan0,
|
|
# remove as python_remove,
|
|
# factorial as python_factorial,
|
|
# sqrt as python_sqrt,
|
|
# sqrtrem as python_sqrtrem,
|
|
# gcd as python_gcd,
|
|
# lcm as python_lcm,
|
|
gcdext as python_gcdext,
|
|
# is_square as python_is_square,
|
|
# invert as python_invert,
|
|
# legendre as python_legendre,
|
|
# jacobi as python_jacobi,
|
|
# kronecker as python_kronecker,
|
|
# iroot as python_iroot,
|
|
# is_fermat_prp as python_is_fermat_prp,
|
|
# is_euler_prp as python_is_euler_prp,
|
|
# is_strong_prp as python_is_strong_prp,
|
|
# is_fibonacci_prp as python_is_fibonacci_prp,
|
|
# is_lucas_prp as python_is_lucas_prp,
|
|
# is_selfridge_prp as python_is_selfridge_prp,
|
|
# is_strong_lucas_prp as python_is_strong_lucas_prp,
|
|
# is_strong_selfridge_prp as python_is_strong_selfridge_prp,
|
|
# is_bpsw_prp as python_is_bpsw_prp,
|
|
# is_strong_bpsw_prp as python_is_strong_bpsw_prp,
|
|
)
|
|
|
|
|
|
__all__ = [
|
|
# GROUND_TYPES is either 'gmpy' or 'python' depending on which is used. If
|
|
# gmpy is installed then it will be used unless the environment variable
|
|
# SYMPY_GROUND_TYPES is set to something other than 'auto', 'gmpy', or
|
|
# 'gmpy2'.
|
|
'GROUND_TYPES',
|
|
|
|
# If HAS_GMPY is 0, no supported version of gmpy is available. Otherwise,
|
|
# HAS_GMPY will be 2 for gmpy2 if GROUND_TYPES is 'gmpy'. It used to be
|
|
# possible for HAS_GMPY to be 1 for gmpy but gmpy is no longer supported.
|
|
'HAS_GMPY',
|
|
|
|
# SYMPY_INTS is a tuple containing the base types for valid integer types.
|
|
# This is either (int,) or (int, type(mpz(0))) depending on GROUND_TYPES.
|
|
'SYMPY_INTS',
|
|
|
|
# MPQ is either gmpy.mpq or the Python equivalent from
|
|
# sympy.external.pythonmpq
|
|
'MPQ',
|
|
|
|
# MPZ is either gmpy.mpz or int.
|
|
'MPZ',
|
|
|
|
# 'bit_scan1',
|
|
# 'bit_scan0',
|
|
# 'remove',
|
|
# 'factorial',
|
|
# 'sqrt',
|
|
# 'is_square',
|
|
# 'sqrtrem',
|
|
# 'gcd',
|
|
# 'lcm',
|
|
'gcdext',
|
|
# 'invert',
|
|
# 'legendre',
|
|
# 'jacobi',
|
|
# 'kronecker',
|
|
# 'iroot',
|
|
# 'is_fermat_prp',
|
|
# 'is_euler_prp',
|
|
# 'is_strong_prp',
|
|
# 'is_fibonacci_prp',
|
|
# 'is_lucas_prp',
|
|
# 'is_selfridge_prp',
|
|
# 'is_strong_lucas_prp',
|
|
# 'is_strong_selfridge_prp',
|
|
# 'is_bpsw_prp',
|
|
# 'is_strong_bpsw_prp',
|
|
]
|
|
|
|
|
|
#
|
|
# Tested python-flint version. Future versions might work but we will only use
|
|
# them if explicitly requested by SYMPY_GROUND_TYPES=flint.
|
|
#
|
|
_PYTHON_FLINT_VERSION_NEEDED = "0.6.*"
|
|
|
|
|
|
def _flint_version_okay(flint_version):
|
|
flint_ver = flint_version.split('.')[:2]
|
|
needed_ver = _PYTHON_FLINT_VERSION_NEEDED.split('.')[:2]
|
|
return flint_ver == needed_ver
|
|
|
|
#
|
|
# We will only use gmpy2 >= 2.0.0
|
|
#
|
|
_GMPY2_MIN_VERSION = '2.0.0'
|
|
|
|
|
|
def _get_flint(sympy_ground_types):
|
|
if sympy_ground_types not in ('auto', 'flint'):
|
|
return None
|
|
|
|
try:
|
|
import flint
|
|
# Earlier versions of python-flint may not have __version__.
|
|
from flint import __version__ as _flint_version
|
|
except ImportError:
|
|
if sympy_ground_types == 'flint':
|
|
warn("SYMPY_GROUND_TYPES was set to flint but python-flint is not "
|
|
"installed. Falling back to other ground types.")
|
|
return None
|
|
|
|
if _flint_version_okay(_flint_version):
|
|
return flint
|
|
elif sympy_ground_types == 'auto':
|
|
warn(f"python-flint {_flint_version} is installed but only version "
|
|
f"{_PYTHON_FLINT_VERSION_NEEDED} will be used by default. "
|
|
f"Falling back to other ground types. Use "
|
|
f"SYMPY_GROUND_TYPES=flint to force the use of python-flint.")
|
|
return None
|
|
else:
|
|
warn(f"Using python-flint {_flint_version} because SYMPY_GROUND_TYPES "
|
|
f"is set to flint but this version of SymPy has only been tested "
|
|
f"with python-flint {_PYTHON_FLINT_VERSION_NEEDED}.")
|
|
return flint
|
|
|
|
|
|
def _get_gmpy2(sympy_ground_types):
|
|
if sympy_ground_types not in ('auto', 'gmpy', 'gmpy2'):
|
|
return None
|
|
|
|
gmpy = import_module('gmpy2', min_module_version=_GMPY2_MIN_VERSION,
|
|
module_version_attr='version', module_version_attr_call_args=())
|
|
|
|
if sympy_ground_types != 'auto' and gmpy is None:
|
|
warn("gmpy2 library is not installed, switching to 'python' ground types")
|
|
|
|
return gmpy
|
|
|
|
|
|
#
|
|
# SYMPY_GROUND_TYPES can be flint, gmpy, gmpy2, python or auto (default)
|
|
#
|
|
_SYMPY_GROUND_TYPES = os.environ.get('SYMPY_GROUND_TYPES', 'auto').lower()
|
|
_flint = None
|
|
_gmpy = None
|
|
|
|
#
|
|
# First handle auto-detection of flint/gmpy2. We will prefer flint if available
|
|
# or otherwise gmpy2 if available and then lastly the python types.
|
|
#
|
|
if _SYMPY_GROUND_TYPES in ('auto', 'flint'):
|
|
_flint = _get_flint(_SYMPY_GROUND_TYPES)
|
|
if _flint is not None:
|
|
_SYMPY_GROUND_TYPES = 'flint'
|
|
else:
|
|
_SYMPY_GROUND_TYPES = 'auto'
|
|
|
|
if _SYMPY_GROUND_TYPES in ('auto', 'gmpy', 'gmpy2'):
|
|
_gmpy = _get_gmpy2(_SYMPY_GROUND_TYPES)
|
|
if _gmpy is not None:
|
|
_SYMPY_GROUND_TYPES = 'gmpy'
|
|
else:
|
|
_SYMPY_GROUND_TYPES = 'python'
|
|
|
|
if _SYMPY_GROUND_TYPES not in ('flint', 'gmpy', 'python'):
|
|
warn("SYMPY_GROUND_TYPES environment variable unrecognised. "
|
|
"Should be 'auto', 'flint', 'gmpy', 'gmpy2' or 'python'.")
|
|
_SYMPY_GROUND_TYPES = 'python'
|
|
|
|
#
|
|
# At this point _SYMPY_GROUND_TYPES is either flint, gmpy or python. The blocks
|
|
# below define the values exported by this module in each case.
|
|
#
|
|
|
|
#
|
|
# In gmpy2 and flint, there are functions that take a long (or unsigned long)
|
|
# argument. That is, it is not possible to input a value larger than that.
|
|
#
|
|
LONG_MAX = (1 << (8*sizeof(c_long) - 1)) - 1
|
|
|
|
#
|
|
# Type checkers are confused by what SYMPY_INTS is. There may be a better type
|
|
# hint for this like Type[Integral] or something.
|
|
#
|
|
SYMPY_INTS: tTuple[Type, ...]
|
|
|
|
if _SYMPY_GROUND_TYPES == 'gmpy':
|
|
|
|
assert _gmpy is not None
|
|
|
|
flint = None
|
|
gmpy = _gmpy
|
|
|
|
HAS_GMPY = 2
|
|
GROUND_TYPES = 'gmpy'
|
|
SYMPY_INTS = (int, type(gmpy.mpz(0)))
|
|
MPZ = gmpy.mpz
|
|
MPQ = gmpy.mpq
|
|
|
|
# bit_scan1 = gmpy.bit_scan1
|
|
# bit_scan0 = gmpy.bit_scan0
|
|
# remove = gmpy.remove
|
|
# factorial = gmpy.fac
|
|
# sqrt = gmpy.isqrt
|
|
# is_square = gmpy.is_square
|
|
# sqrtrem = gmpy.isqrt_rem
|
|
# gcd = gmpy.gcd
|
|
# lcm = gmpy.lcm
|
|
gcdext = gmpy.gcdext
|
|
# invert = gmpy.invert
|
|
# legendre = gmpy.legendre
|
|
# jacobi = gmpy.jacobi
|
|
# kronecker = gmpy.kronecker
|
|
|
|
# def iroot(x, n):
|
|
# # In the latest gmpy2, the threshold for n is ULONG_MAX,
|
|
# # but adjust to the older one.
|
|
# if n <= LONG_MAX:
|
|
# return gmpy.iroot(x, n)
|
|
# return python_iroot(x, n)
|
|
|
|
# is_fermat_prp = gmpy.is_fermat_prp
|
|
# is_euler_prp = gmpy.is_euler_prp
|
|
# is_strong_prp = gmpy.is_strong_prp
|
|
# is_fibonacci_prp = gmpy.is_fibonacci_prp
|
|
# is_lucas_prp = gmpy.is_lucas_prp
|
|
# is_selfridge_prp = gmpy.is_selfridge_prp
|
|
# is_strong_lucas_prp = gmpy.is_strong_lucas_prp
|
|
# is_strong_selfridge_prp = gmpy.is_strong_selfridge_prp
|
|
# is_bpsw_prp = gmpy.is_bpsw_prp
|
|
# is_strong_bpsw_prp = gmpy.is_strong_bpsw_prp
|
|
|
|
elif _SYMPY_GROUND_TYPES == 'flint':
|
|
|
|
assert _flint is not None
|
|
|
|
flint = _flint
|
|
gmpy = None
|
|
|
|
HAS_GMPY = 0
|
|
GROUND_TYPES = 'flint'
|
|
SYMPY_INTS = (int, flint.fmpz) # type: ignore
|
|
MPZ = flint.fmpz # type: ignore
|
|
MPQ = flint.fmpq # type: ignore
|
|
|
|
# bit_scan1 = python_bit_scan1
|
|
# bit_scan0 = python_bit_scan0
|
|
# remove = python_remove
|
|
# factorial = python_factorial
|
|
|
|
# def sqrt(x):
|
|
# return flint.fmpz(x).isqrt()
|
|
|
|
# def is_square(x):
|
|
# if x < 0:
|
|
# return False
|
|
# return flint.fmpz(x).sqrtrem()[1] == 0
|
|
|
|
# def sqrtrem(x):
|
|
# return flint.fmpz(x).sqrtrem()
|
|
|
|
# def gcd(*args):
|
|
# return reduce(flint.fmpz.gcd, args, flint.fmpz(0))
|
|
|
|
# def lcm(*args):
|
|
# return reduce(flint.fmpz.lcm, args, flint.fmpz(1))
|
|
|
|
gcdext = python_gcdext
|
|
# invert = python_invert
|
|
# legendre = python_legendre
|
|
|
|
# def jacobi(x, y):
|
|
# if y <= 0 or not y % 2:
|
|
# raise ValueError("y should be an odd positive integer")
|
|
# return flint.fmpz(x).jacobi(y)
|
|
|
|
# kronecker = python_kronecker
|
|
|
|
# def iroot(x, n):
|
|
# if n <= LONG_MAX:
|
|
# y = flint.fmpz(x).root(n)
|
|
# return y, y**n == x
|
|
# return python_iroot(x, n)
|
|
|
|
# is_fermat_prp = python_is_fermat_prp
|
|
# is_euler_prp = python_is_euler_prp
|
|
# is_strong_prp = python_is_strong_prp
|
|
# is_fibonacci_prp = python_is_fibonacci_prp
|
|
# is_lucas_prp = python_is_lucas_prp
|
|
# is_selfridge_prp = python_is_selfridge_prp
|
|
# is_strong_lucas_prp = python_is_strong_lucas_prp
|
|
# is_strong_selfridge_prp = python_is_strong_selfridge_prp
|
|
# is_bpsw_prp = python_is_bpsw_prp
|
|
# is_strong_bpsw_prp = python_is_strong_bpsw_prp
|
|
|
|
elif _SYMPY_GROUND_TYPES == 'python':
|
|
|
|
flint = None
|
|
gmpy = None
|
|
|
|
HAS_GMPY = 0
|
|
GROUND_TYPES = 'python'
|
|
SYMPY_INTS = (int,)
|
|
MPZ = int
|
|
MPQ = PythonMPQ
|
|
|
|
# bit_scan1 = python_bit_scan1
|
|
# bit_scan0 = python_bit_scan0
|
|
# remove = python_remove
|
|
# factorial = python_factorial
|
|
# sqrt = python_sqrt
|
|
# is_square = python_is_square
|
|
# sqrtrem = python_sqrtrem
|
|
# gcd = python_gcd
|
|
# lcm = python_lcm
|
|
gcdext = python_gcdext
|
|
# invert = python_invert
|
|
# legendre = python_legendre
|
|
# jacobi = python_jacobi
|
|
# kronecker = python_kronecker
|
|
# iroot = python_iroot
|
|
# is_fermat_prp = python_is_fermat_prp
|
|
# is_euler_prp = python_is_euler_prp
|
|
# is_strong_prp = python_is_strong_prp
|
|
# is_fibonacci_prp = python_is_fibonacci_prp
|
|
# is_lucas_prp = python_is_lucas_prp
|
|
# is_selfridge_prp = python_is_selfridge_prp
|
|
# is_strong_lucas_prp = python_is_strong_lucas_prp
|
|
# is_strong_selfridge_prp = python_is_strong_selfridge_prp
|
|
# is_bpsw_prp = python_is_bpsw_prp
|
|
# is_strong_bpsw_prp = python_is_strong_bpsw_prp
|
|
|
|
else:
|
|
assert False
|