342 lines
9.5 KiB
Python
342 lines
9.5 KiB
Python
import os
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from ctypes import c_long, sizeof
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from functools import reduce
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from typing import Tuple as tTuple, Type
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from warnings import warn
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from sympy.external import import_module
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from .pythonmpq import PythonMPQ
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from .ntheory import (
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bit_scan1 as python_bit_scan1,
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bit_scan0 as python_bit_scan0,
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remove as python_remove,
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factorial as python_factorial,
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sqrt as python_sqrt,
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sqrtrem as python_sqrtrem,
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gcd as python_gcd,
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lcm as python_lcm,
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gcdext as python_gcdext,
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is_square as python_is_square,
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invert as python_invert,
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legendre as python_legendre,
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jacobi as python_jacobi,
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kronecker as python_kronecker,
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iroot as python_iroot,
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is_fermat_prp as python_is_fermat_prp,
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is_euler_prp as python_is_euler_prp,
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is_strong_prp as python_is_strong_prp,
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is_fibonacci_prp as python_is_fibonacci_prp,
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is_lucas_prp as python_is_lucas_prp,
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is_selfridge_prp as python_is_selfridge_prp,
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is_strong_lucas_prp as python_is_strong_lucas_prp,
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is_strong_selfridge_prp as python_is_strong_selfridge_prp,
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is_bpsw_prp as python_is_bpsw_prp,
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is_strong_bpsw_prp as python_is_strong_bpsw_prp,
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)
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__all__ = [
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# GROUND_TYPES is either 'gmpy' or 'python' depending on which is used. If
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# gmpy is installed then it will be used unless the environment variable
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# SYMPY_GROUND_TYPES is set to something other than 'auto', 'gmpy', or
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# 'gmpy2'.
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'GROUND_TYPES',
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# If HAS_GMPY is 0, no supported version of gmpy is available. Otherwise,
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# HAS_GMPY will be 2 for gmpy2 if GROUND_TYPES is 'gmpy'. It used to be
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# possible for HAS_GMPY to be 1 for gmpy but gmpy is no longer supported.
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'HAS_GMPY',
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# SYMPY_INTS is a tuple containing the base types for valid integer types.
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# This is either (int,) or (int, type(mpz(0))) depending on GROUND_TYPES.
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'SYMPY_INTS',
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# MPQ is either gmpy.mpq or the Python equivalent from
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# sympy.external.pythonmpq
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'MPQ',
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# MPZ is either gmpy.mpz or int.
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'MPZ',
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'bit_scan1',
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'bit_scan0',
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'remove',
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'factorial',
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'sqrt',
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'is_square',
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'sqrtrem',
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'gcd',
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'lcm',
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'gcdext',
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'invert',
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'legendre',
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'jacobi',
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'kronecker',
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'iroot',
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'is_fermat_prp',
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'is_euler_prp',
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'is_strong_prp',
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'is_fibonacci_prp',
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'is_lucas_prp',
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'is_selfridge_prp',
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'is_strong_lucas_prp',
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'is_strong_selfridge_prp',
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'is_bpsw_prp',
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'is_strong_bpsw_prp',
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]
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#
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# Tested python-flint version. Future versions might work but we will only use
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# them if explicitly requested by SYMPY_GROUND_TYPES=flint.
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#
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_PYTHON_FLINT_VERSION_NEEDED = ["0.6", "0.7", "0.8", "0.9"]
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def _flint_version_okay(flint_version):
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major, minor = flint_version.split('.')[:2]
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flint_ver = f'{major}.{minor}'
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return flint_ver in _PYTHON_FLINT_VERSION_NEEDED
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#
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# We will only use gmpy2 >= 2.0.0
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#
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_GMPY2_MIN_VERSION = '2.0.0'
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def _get_flint(sympy_ground_types):
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if sympy_ground_types not in ('auto', 'flint'):
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return None
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try:
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import flint
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# Earlier versions of python-flint may not have __version__.
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from flint import __version__ as _flint_version
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except ImportError:
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if sympy_ground_types == 'flint':
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warn("SYMPY_GROUND_TYPES was set to flint but python-flint is not "
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"installed. Falling back to other ground types.")
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return None
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if _flint_version_okay(_flint_version):
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return flint
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elif sympy_ground_types == 'auto':
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return None
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else:
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warn(f"Using python-flint {_flint_version} because SYMPY_GROUND_TYPES "
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f"is set to flint but this version of SymPy is only tested "
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f"with python-flint versions {_PYTHON_FLINT_VERSION_NEEDED}.")
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return flint
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def _get_gmpy2(sympy_ground_types):
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if sympy_ground_types not in ('auto', 'gmpy', 'gmpy2'):
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return None
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gmpy = import_module('gmpy2', min_module_version=_GMPY2_MIN_VERSION,
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module_version_attr='version', module_version_attr_call_args=())
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if sympy_ground_types != 'auto' and gmpy is None:
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warn("gmpy2 library is not installed, switching to 'python' ground types")
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return gmpy
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#
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# SYMPY_GROUND_TYPES can be flint, gmpy, gmpy2, python or auto (default)
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#
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_SYMPY_GROUND_TYPES = os.environ.get('SYMPY_GROUND_TYPES', 'auto').lower()
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_flint = None
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_gmpy = None
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#
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# First handle auto-detection of flint/gmpy2. We will prefer flint if available
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# or otherwise gmpy2 if available and then lastly the python types.
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#
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if _SYMPY_GROUND_TYPES in ('auto', 'flint'):
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_flint = _get_flint(_SYMPY_GROUND_TYPES)
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if _flint is not None:
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_SYMPY_GROUND_TYPES = 'flint'
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else:
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_SYMPY_GROUND_TYPES = 'auto'
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if _SYMPY_GROUND_TYPES in ('auto', 'gmpy', 'gmpy2'):
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_gmpy = _get_gmpy2(_SYMPY_GROUND_TYPES)
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if _gmpy is not None:
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_SYMPY_GROUND_TYPES = 'gmpy'
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else:
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_SYMPY_GROUND_TYPES = 'python'
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if _SYMPY_GROUND_TYPES not in ('flint', 'gmpy', 'python'):
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warn("SYMPY_GROUND_TYPES environment variable unrecognised. "
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"Should be 'auto', 'flint', 'gmpy', 'gmpy2' or 'python'.")
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_SYMPY_GROUND_TYPES = 'python'
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#
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# At this point _SYMPY_GROUND_TYPES is either flint, gmpy or python. The blocks
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# below define the values exported by this module in each case.
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#
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#
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# In gmpy2 and flint, there are functions that take a long (or unsigned long)
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# argument. That is, it is not possible to input a value larger than that.
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#
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LONG_MAX = (1 << (8*sizeof(c_long) - 1)) - 1
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#
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# Type checkers are confused by what SYMPY_INTS is. There may be a better type
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# hint for this like Type[Integral] or something.
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#
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SYMPY_INTS: tTuple[Type, ...]
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if _SYMPY_GROUND_TYPES == 'gmpy':
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assert _gmpy is not None
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flint = None
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gmpy = _gmpy
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HAS_GMPY = 2
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GROUND_TYPES = 'gmpy'
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SYMPY_INTS = (int, type(gmpy.mpz(0)))
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MPZ = gmpy.mpz
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MPQ = gmpy.mpq
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bit_scan1 = gmpy.bit_scan1
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bit_scan0 = gmpy.bit_scan0
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remove = gmpy.remove
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factorial = gmpy.fac
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sqrt = gmpy.isqrt
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is_square = gmpy.is_square
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sqrtrem = gmpy.isqrt_rem
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gcd = gmpy.gcd
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lcm = gmpy.lcm
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gcdext = gmpy.gcdext
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invert = gmpy.invert
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legendre = gmpy.legendre
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jacobi = gmpy.jacobi
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kronecker = gmpy.kronecker
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def iroot(x, n):
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# In the latest gmpy2, the threshold for n is ULONG_MAX,
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# but adjust to the older one.
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if n <= LONG_MAX:
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return gmpy.iroot(x, n)
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return python_iroot(x, n)
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is_fermat_prp = gmpy.is_fermat_prp
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is_euler_prp = gmpy.is_euler_prp
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is_strong_prp = gmpy.is_strong_prp
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is_fibonacci_prp = gmpy.is_fibonacci_prp
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is_lucas_prp = gmpy.is_lucas_prp
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is_selfridge_prp = gmpy.is_selfridge_prp
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is_strong_lucas_prp = gmpy.is_strong_lucas_prp
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is_strong_selfridge_prp = gmpy.is_strong_selfridge_prp
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is_bpsw_prp = gmpy.is_bpsw_prp
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is_strong_bpsw_prp = gmpy.is_strong_bpsw_prp
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elif _SYMPY_GROUND_TYPES == 'flint':
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assert _flint is not None
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flint = _flint
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gmpy = None
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HAS_GMPY = 0
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GROUND_TYPES = 'flint'
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SYMPY_INTS = (int, flint.fmpz) # type: ignore
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MPZ = flint.fmpz # type: ignore
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MPQ = flint.fmpq # type: ignore
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bit_scan1 = python_bit_scan1
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bit_scan0 = python_bit_scan0
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remove = python_remove
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factorial = python_factorial
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def sqrt(x):
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return flint.fmpz(x).isqrt()
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def is_square(x):
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if x < 0:
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return False
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return flint.fmpz(x).sqrtrem()[1] == 0
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def sqrtrem(x):
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return flint.fmpz(x).sqrtrem()
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def gcd(*args):
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return reduce(flint.fmpz.gcd, args, flint.fmpz(0))
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def lcm(*args):
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return reduce(flint.fmpz.lcm, args, flint.fmpz(1))
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gcdext = python_gcdext
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invert = python_invert
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legendre = python_legendre
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def jacobi(x, y):
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if y <= 0 or not y % 2:
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raise ValueError("y should be an odd positive integer")
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return flint.fmpz(x).jacobi(y)
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kronecker = python_kronecker
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def iroot(x, n):
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if n <= LONG_MAX:
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y = flint.fmpz(x).root(n)
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return y, y**n == x
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return python_iroot(x, n)
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is_fermat_prp = python_is_fermat_prp
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is_euler_prp = python_is_euler_prp
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is_strong_prp = python_is_strong_prp
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is_fibonacci_prp = python_is_fibonacci_prp
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is_lucas_prp = python_is_lucas_prp
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is_selfridge_prp = python_is_selfridge_prp
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is_strong_lucas_prp = python_is_strong_lucas_prp
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is_strong_selfridge_prp = python_is_strong_selfridge_prp
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is_bpsw_prp = python_is_bpsw_prp
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is_strong_bpsw_prp = python_is_strong_bpsw_prp
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elif _SYMPY_GROUND_TYPES == 'python':
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flint = None
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gmpy = None
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HAS_GMPY = 0
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GROUND_TYPES = 'python'
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SYMPY_INTS = (int,)
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MPZ = int
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MPQ = PythonMPQ
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bit_scan1 = python_bit_scan1
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bit_scan0 = python_bit_scan0
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remove = python_remove
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factorial = python_factorial
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sqrt = python_sqrt
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is_square = python_is_square
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sqrtrem = python_sqrtrem
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gcd = python_gcd
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lcm = python_lcm
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gcdext = python_gcdext
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invert = python_invert
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legendre = python_legendre
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jacobi = python_jacobi
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kronecker = python_kronecker
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iroot = python_iroot
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is_fermat_prp = python_is_fermat_prp
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is_euler_prp = python_is_euler_prp
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is_strong_prp = python_is_strong_prp
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is_fibonacci_prp = python_is_fibonacci_prp
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is_lucas_prp = python_is_lucas_prp
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is_selfridge_prp = python_is_selfridge_prp
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is_strong_lucas_prp = python_is_strong_lucas_prp
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is_strong_selfridge_prp = python_is_strong_selfridge_prp
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is_bpsw_prp = python_is_bpsw_prp
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is_strong_bpsw_prp = python_is_strong_bpsw_prp
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else:
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assert False
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