1150 lines
37 KiB
Python
1150 lines
37 KiB
Python
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#from ctx_base import StandardBaseContext
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from .libmp.backend import basestring, exec_
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from .libmp import (MPZ, MPZ_ZERO, MPZ_ONE, int_types, repr_dps,
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round_floor, round_ceiling, dps_to_prec, round_nearest, prec_to_dps,
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ComplexResult, to_pickable, from_pickable, normalize,
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from_int, from_float, from_npfloat, from_Decimal, from_str, to_int, to_float, to_str,
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from_rational, from_man_exp,
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fone, fzero, finf, fninf, fnan,
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mpf_abs, mpf_pos, mpf_neg, mpf_add, mpf_sub, mpf_mul, mpf_mul_int,
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mpf_div, mpf_rdiv_int, mpf_pow_int, mpf_mod,
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mpf_eq, mpf_cmp, mpf_lt, mpf_gt, mpf_le, mpf_ge,
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mpf_hash, mpf_rand,
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mpf_sum,
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bitcount, to_fixed,
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mpc_to_str,
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mpc_to_complex, mpc_hash, mpc_pos, mpc_is_nonzero, mpc_neg, mpc_conjugate,
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mpc_abs, mpc_add, mpc_add_mpf, mpc_sub, mpc_sub_mpf, mpc_mul, mpc_mul_mpf,
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mpc_mul_int, mpc_div, mpc_div_mpf, mpc_pow, mpc_pow_mpf, mpc_pow_int,
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mpc_mpf_div,
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mpf_pow,
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mpf_pi, mpf_degree, mpf_e, mpf_phi, mpf_ln2, mpf_ln10,
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mpf_euler, mpf_catalan, mpf_apery, mpf_khinchin,
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mpf_glaisher, mpf_twinprime, mpf_mertens,
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int_types)
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from . import rational
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from . import function_docs
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new = object.__new__
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class mpnumeric(object):
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"""Base class for mpf and mpc."""
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__slots__ = []
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def __new__(cls, val):
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raise NotImplementedError
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class _mpf(mpnumeric):
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"""
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An mpf instance holds a real-valued floating-point number. mpf:s
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work analogously to Python floats, but support arbitrary-precision
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arithmetic.
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"""
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__slots__ = ['_mpf_']
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def __new__(cls, val=fzero, **kwargs):
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"""A new mpf can be created from a Python float, an int, a
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or a decimal string representing a number in floating-point
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format."""
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prec, rounding = cls.context._prec_rounding
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if kwargs:
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prec = kwargs.get('prec', prec)
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if 'dps' in kwargs:
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prec = dps_to_prec(kwargs['dps'])
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rounding = kwargs.get('rounding', rounding)
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if type(val) is cls:
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sign, man, exp, bc = val._mpf_
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if (not man) and exp:
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return val
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v = new(cls)
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v._mpf_ = normalize(sign, man, exp, bc, prec, rounding)
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return v
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elif type(val) is tuple:
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if len(val) == 2:
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v = new(cls)
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v._mpf_ = from_man_exp(val[0], val[1], prec, rounding)
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return v
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if len(val) == 4:
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if val not in (finf, fninf, fnan):
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sign, man, exp, bc = val
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val = normalize(sign, MPZ(man), exp, bc, prec, rounding)
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v = new(cls)
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v._mpf_ = val
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return v
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raise ValueError
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else:
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v = new(cls)
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v._mpf_ = mpf_pos(cls.mpf_convert_arg(val, prec, rounding), prec, rounding)
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return v
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@classmethod
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def mpf_convert_arg(cls, x, prec, rounding):
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if isinstance(x, int_types): return from_int(x)
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if isinstance(x, float): return from_float(x)
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if isinstance(x, basestring): return from_str(x, prec, rounding)
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if isinstance(x, cls.context.constant): return x.func(prec, rounding)
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if hasattr(x, '_mpf_'): return x._mpf_
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if hasattr(x, '_mpmath_'):
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t = cls.context.convert(x._mpmath_(prec, rounding))
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if hasattr(t, '_mpf_'):
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return t._mpf_
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if hasattr(x, '_mpi_'):
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a, b = x._mpi_
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if a == b:
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return a
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raise ValueError("can only create mpf from zero-width interval")
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raise TypeError("cannot create mpf from " + repr(x))
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@classmethod
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def mpf_convert_rhs(cls, x):
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if isinstance(x, int_types): return from_int(x)
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if isinstance(x, float): return from_float(x)
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if isinstance(x, complex_types): return cls.context.mpc(x)
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if isinstance(x, rational.mpq):
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p, q = x._mpq_
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return from_rational(p, q, cls.context.prec)
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if hasattr(x, '_mpf_'): return x._mpf_
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if hasattr(x, '_mpmath_'):
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t = cls.context.convert(x._mpmath_(*cls.context._prec_rounding))
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if hasattr(t, '_mpf_'):
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return t._mpf_
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return t
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return NotImplemented
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@classmethod
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def mpf_convert_lhs(cls, x):
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x = cls.mpf_convert_rhs(x)
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if type(x) is tuple:
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return cls.context.make_mpf(x)
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return x
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man_exp = property(lambda self: self._mpf_[1:3])
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man = property(lambda self: self._mpf_[1])
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exp = property(lambda self: self._mpf_[2])
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bc = property(lambda self: self._mpf_[3])
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real = property(lambda self: self)
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imag = property(lambda self: self.context.zero)
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conjugate = lambda self: self
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def __getstate__(self): return to_pickable(self._mpf_)
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def __setstate__(self, val): self._mpf_ = from_pickable(val)
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def __repr__(s):
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if s.context.pretty:
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return str(s)
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return "mpf('%s')" % to_str(s._mpf_, s.context._repr_digits)
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def __str__(s): return to_str(s._mpf_, s.context._str_digits)
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def __hash__(s): return mpf_hash(s._mpf_)
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def __int__(s): return int(to_int(s._mpf_))
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def __long__(s): return long(to_int(s._mpf_))
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def __float__(s): return to_float(s._mpf_, rnd=s.context._prec_rounding[1])
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def __complex__(s): return complex(float(s))
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def __nonzero__(s): return s._mpf_ != fzero
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__bool__ = __nonzero__
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def __abs__(s):
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cls, new, (prec, rounding) = s._ctxdata
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v = new(cls)
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v._mpf_ = mpf_abs(s._mpf_, prec, rounding)
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return v
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def __pos__(s):
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cls, new, (prec, rounding) = s._ctxdata
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v = new(cls)
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v._mpf_ = mpf_pos(s._mpf_, prec, rounding)
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return v
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def __neg__(s):
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cls, new, (prec, rounding) = s._ctxdata
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v = new(cls)
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v._mpf_ = mpf_neg(s._mpf_, prec, rounding)
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return v
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def _cmp(s, t, func):
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if hasattr(t, '_mpf_'):
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t = t._mpf_
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else:
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t = s.mpf_convert_rhs(t)
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if t is NotImplemented:
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return t
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return func(s._mpf_, t)
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def __cmp__(s, t): return s._cmp(t, mpf_cmp)
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def __lt__(s, t): return s._cmp(t, mpf_lt)
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def __gt__(s, t): return s._cmp(t, mpf_gt)
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def __le__(s, t): return s._cmp(t, mpf_le)
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def __ge__(s, t): return s._cmp(t, mpf_ge)
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def __ne__(s, t):
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v = s.__eq__(t)
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if v is NotImplemented:
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return v
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return not v
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def __rsub__(s, t):
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cls, new, (prec, rounding) = s._ctxdata
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if type(t) in int_types:
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v = new(cls)
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v._mpf_ = mpf_sub(from_int(t), s._mpf_, prec, rounding)
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return v
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t = s.mpf_convert_lhs(t)
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if t is NotImplemented:
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return t
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return t - s
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def __rdiv__(s, t):
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cls, new, (prec, rounding) = s._ctxdata
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if isinstance(t, int_types):
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v = new(cls)
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v._mpf_ = mpf_rdiv_int(t, s._mpf_, prec, rounding)
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return v
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t = s.mpf_convert_lhs(t)
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if t is NotImplemented:
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return t
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return t / s
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def __rpow__(s, t):
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t = s.mpf_convert_lhs(t)
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if t is NotImplemented:
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return t
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return t ** s
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def __rmod__(s, t):
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t = s.mpf_convert_lhs(t)
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if t is NotImplemented:
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return t
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return t % s
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def sqrt(s):
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return s.context.sqrt(s)
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def ae(s, t, rel_eps=None, abs_eps=None):
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return s.context.almosteq(s, t, rel_eps, abs_eps)
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def to_fixed(self, prec):
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return to_fixed(self._mpf_, prec)
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def __round__(self, *args):
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return round(float(self), *args)
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mpf_binary_op = """
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def %NAME%(self, other):
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mpf, new, (prec, rounding) = self._ctxdata
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sval = self._mpf_
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if hasattr(other, '_mpf_'):
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tval = other._mpf_
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%WITH_MPF%
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ttype = type(other)
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if ttype in int_types:
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%WITH_INT%
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elif ttype is float:
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tval = from_float(other)
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%WITH_MPF%
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elif hasattr(other, '_mpc_'):
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tval = other._mpc_
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mpc = type(other)
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%WITH_MPC%
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elif ttype is complex:
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tval = from_float(other.real), from_float(other.imag)
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mpc = self.context.mpc
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%WITH_MPC%
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if isinstance(other, mpnumeric):
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return NotImplemented
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try:
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other = mpf.context.convert(other, strings=False)
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except TypeError:
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return NotImplemented
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return self.%NAME%(other)
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"""
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return_mpf = "; obj = new(mpf); obj._mpf_ = val; return obj"
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return_mpc = "; obj = new(mpc); obj._mpc_ = val; return obj"
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mpf_pow_same = """
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try:
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val = mpf_pow(sval, tval, prec, rounding) %s
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except ComplexResult:
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if mpf.context.trap_complex:
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raise
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mpc = mpf.context.mpc
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val = mpc_pow((sval, fzero), (tval, fzero), prec, rounding) %s
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""" % (return_mpf, return_mpc)
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def binary_op(name, with_mpf='', with_int='', with_mpc=''):
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code = mpf_binary_op
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code = code.replace("%WITH_INT%", with_int)
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code = code.replace("%WITH_MPC%", with_mpc)
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code = code.replace("%WITH_MPF%", with_mpf)
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code = code.replace("%NAME%", name)
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np = {}
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exec_(code, globals(), np)
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return np[name]
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_mpf.__eq__ = binary_op('__eq__',
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'return mpf_eq(sval, tval)',
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'return mpf_eq(sval, from_int(other))',
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'return (tval[1] == fzero) and mpf_eq(tval[0], sval)')
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_mpf.__add__ = binary_op('__add__',
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'val = mpf_add(sval, tval, prec, rounding)' + return_mpf,
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'val = mpf_add(sval, from_int(other), prec, rounding)' + return_mpf,
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'val = mpc_add_mpf(tval, sval, prec, rounding)' + return_mpc)
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_mpf.__sub__ = binary_op('__sub__',
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'val = mpf_sub(sval, tval, prec, rounding)' + return_mpf,
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'val = mpf_sub(sval, from_int(other), prec, rounding)' + return_mpf,
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'val = mpc_sub((sval, fzero), tval, prec, rounding)' + return_mpc)
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_mpf.__mul__ = binary_op('__mul__',
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'val = mpf_mul(sval, tval, prec, rounding)' + return_mpf,
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'val = mpf_mul_int(sval, other, prec, rounding)' + return_mpf,
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'val = mpc_mul_mpf(tval, sval, prec, rounding)' + return_mpc)
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_mpf.__div__ = binary_op('__div__',
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'val = mpf_div(sval, tval, prec, rounding)' + return_mpf,
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'val = mpf_div(sval, from_int(other), prec, rounding)' + return_mpf,
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'val = mpc_mpf_div(sval, tval, prec, rounding)' + return_mpc)
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_mpf.__mod__ = binary_op('__mod__',
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'val = mpf_mod(sval, tval, prec, rounding)' + return_mpf,
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'val = mpf_mod(sval, from_int(other), prec, rounding)' + return_mpf,
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'raise NotImplementedError("complex modulo")')
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_mpf.__pow__ = binary_op('__pow__',
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mpf_pow_same,
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'val = mpf_pow_int(sval, other, prec, rounding)' + return_mpf,
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'val = mpc_pow((sval, fzero), tval, prec, rounding)' + return_mpc)
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_mpf.__radd__ = _mpf.__add__
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_mpf.__rmul__ = _mpf.__mul__
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_mpf.__truediv__ = _mpf.__div__
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_mpf.__rtruediv__ = _mpf.__rdiv__
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class _constant(_mpf):
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"""Represents a mathematical constant with dynamic precision.
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When printed or used in an arithmetic operation, a constant
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is converted to a regular mpf at the working precision. A
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regular mpf can also be obtained using the operation +x."""
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|
def __new__(cls, func, name, docname=''):
|
||
|
|
a = object.__new__(cls)
|
||
|
|
a.name = name
|
||
|
|
a.func = func
|
||
|
|
a.__doc__ = getattr(function_docs, docname, '')
|
||
|
|
return a
|
||
|
|
|
||
|
|
def __call__(self, prec=None, dps=None, rounding=None):
|
||
|
|
prec2, rounding2 = self.context._prec_rounding
|
||
|
|
if not prec: prec = prec2
|
||
|
|
if not rounding: rounding = rounding2
|
||
|
|
if dps: prec = dps_to_prec(dps)
|
||
|
|
return self.context.make_mpf(self.func(prec, rounding))
|
||
|
|
|
||
|
|
@property
|
||
|
|
def _mpf_(self):
|
||
|
|
prec, rounding = self.context._prec_rounding
|
||
|
|
return self.func(prec, rounding)
|
||
|
|
|
||
|
|
def __repr__(self):
|
||
|
|
return "<%s: %s~>" % (self.name, self.context.nstr(self(dps=15)))
|
||
|
|
|
||
|
|
|
||
|
|
class _mpc(mpnumeric):
|
||
|
|
"""
|
||
|
|
An mpc represents a complex number using a pair of mpf:s (one
|
||
|
|
for the real part and another for the imaginary part.) The mpc
|
||
|
|
class behaves fairly similarly to Python's complex type.
|
||
|
|
"""
|
||
|
|
|
||
|
|
__slots__ = ['_mpc_']
|
||
|
|
|
||
|
|
def __new__(cls, real=0, imag=0):
|
||
|
|
s = object.__new__(cls)
|
||
|
|
if isinstance(real, complex_types):
|
||
|
|
real, imag = real.real, real.imag
|
||
|
|
elif hasattr(real, '_mpc_'):
|
||
|
|
s._mpc_ = real._mpc_
|
||
|
|
return s
|
||
|
|
real = cls.context.mpf(real)
|
||
|
|
imag = cls.context.mpf(imag)
|
||
|
|
s._mpc_ = (real._mpf_, imag._mpf_)
|
||
|
|
return s
|
||
|
|
|
||
|
|
real = property(lambda self: self.context.make_mpf(self._mpc_[0]))
|
||
|
|
imag = property(lambda self: self.context.make_mpf(self._mpc_[1]))
|
||
|
|
|
||
|
|
def __getstate__(self):
|
||
|
|
return to_pickable(self._mpc_[0]), to_pickable(self._mpc_[1])
|
||
|
|
|
||
|
|
def __setstate__(self, val):
|
||
|
|
self._mpc_ = from_pickable(val[0]), from_pickable(val[1])
|
||
|
|
|
||
|
|
def __repr__(s):
|
||
|
|
if s.context.pretty:
|
||
|
|
return str(s)
|
||
|
|
r = repr(s.real)[4:-1]
|
||
|
|
i = repr(s.imag)[4:-1]
|
||
|
|
return "%s(real=%s, imag=%s)" % (type(s).__name__, r, i)
|
||
|
|
|
||
|
|
def __str__(s):
|
||
|
|
return "(%s)" % mpc_to_str(s._mpc_, s.context._str_digits)
|
||
|
|
|
||
|
|
def __complex__(s):
|
||
|
|
return mpc_to_complex(s._mpc_, rnd=s.context._prec_rounding[1])
|
||
|
|
|
||
|
|
def __pos__(s):
|
||
|
|
cls, new, (prec, rounding) = s._ctxdata
|
||
|
|
v = new(cls)
|
||
|
|
v._mpc_ = mpc_pos(s._mpc_, prec, rounding)
|
||
|
|
return v
|
||
|
|
|
||
|
|
def __abs__(s):
|
||
|
|
prec, rounding = s.context._prec_rounding
|
||
|
|
v = new(s.context.mpf)
|
||
|
|
v._mpf_ = mpc_abs(s._mpc_, prec, rounding)
|
||
|
|
return v
|
||
|
|
|
||
|
|
def __neg__(s):
|
||
|
|
cls, new, (prec, rounding) = s._ctxdata
|
||
|
|
v = new(cls)
|
||
|
|
v._mpc_ = mpc_neg(s._mpc_, prec, rounding)
|
||
|
|
return v
|
||
|
|
|
||
|
|
def conjugate(s):
|
||
|
|
cls, new, (prec, rounding) = s._ctxdata
|
||
|
|
v = new(cls)
|
||
|
|
v._mpc_ = mpc_conjugate(s._mpc_, prec, rounding)
|
||
|
|
return v
|
||
|
|
|
||
|
|
def __nonzero__(s):
|
||
|
|
return mpc_is_nonzero(s._mpc_)
|
||
|
|
|
||
|
|
__bool__ = __nonzero__
|
||
|
|
|
||
|
|
def __hash__(s):
|
||
|
|
return mpc_hash(s._mpc_)
|
||
|
|
|
||
|
|
@classmethod
|
||
|
|
def mpc_convert_lhs(cls, x):
|
||
|
|
try:
|
||
|
|
y = cls.context.convert(x)
|
||
|
|
return y
|
||
|
|
except TypeError:
|
||
|
|
return NotImplemented
|
||
|
|
|
||
|
|
def __eq__(s, t):
|
||
|
|
if not hasattr(t, '_mpc_'):
|
||
|
|
if isinstance(t, str):
|
||
|
|
return False
|
||
|
|
t = s.mpc_convert_lhs(t)
|
||
|
|
if t is NotImplemented:
|
||
|
|
return t
|
||
|
|
return s.real == t.real and s.imag == t.imag
|
||
|
|
|
||
|
|
def __ne__(s, t):
|
||
|
|
b = s.__eq__(t)
|
||
|
|
if b is NotImplemented:
|
||
|
|
return b
|
||
|
|
return not b
|
||
|
|
|
||
|
|
def _compare(*args):
|
||
|
|
raise TypeError("no ordering relation is defined for complex numbers")
|
||
|
|
|
||
|
|
__gt__ = _compare
|
||
|
|
__le__ = _compare
|
||
|
|
__gt__ = _compare
|
||
|
|
__ge__ = _compare
|
||
|
|
|
||
|
|
def __add__(s, t):
|
||
|
|
cls, new, (prec, rounding) = s._ctxdata
|
||
|
|
if not hasattr(t, '_mpc_'):
|
||
|
|
t = s.mpc_convert_lhs(t)
|
||
|
|
if t is NotImplemented:
|
||
|
|
return t
|
||
|
|
if hasattr(t, '_mpf_'):
|
||
|
|
v = new(cls)
|
||
|
|
v._mpc_ = mpc_add_mpf(s._mpc_, t._mpf_, prec, rounding)
|
||
|
|
return v
|
||
|
|
v = new(cls)
|
||
|
|
v._mpc_ = mpc_add(s._mpc_, t._mpc_, prec, rounding)
|
||
|
|
return v
|
||
|
|
|
||
|
|
def __sub__(s, t):
|
||
|
|
cls, new, (prec, rounding) = s._ctxdata
|
||
|
|
if not hasattr(t, '_mpc_'):
|
||
|
|
t = s.mpc_convert_lhs(t)
|
||
|
|
if t is NotImplemented:
|
||
|
|
return t
|
||
|
|
if hasattr(t, '_mpf_'):
|
||
|
|
v = new(cls)
|
||
|
|
v._mpc_ = mpc_sub_mpf(s._mpc_, t._mpf_, prec, rounding)
|
||
|
|
return v
|
||
|
|
v = new(cls)
|
||
|
|
v._mpc_ = mpc_sub(s._mpc_, t._mpc_, prec, rounding)
|
||
|
|
return v
|
||
|
|
|
||
|
|
def __mul__(s, t):
|
||
|
|
cls, new, (prec, rounding) = s._ctxdata
|
||
|
|
if not hasattr(t, '_mpc_'):
|
||
|
|
if isinstance(t, int_types):
|
||
|
|
v = new(cls)
|
||
|
|
v._mpc_ = mpc_mul_int(s._mpc_, t, prec, rounding)
|
||
|
|
return v
|
||
|
|
t = s.mpc_convert_lhs(t)
|
||
|
|
if t is NotImplemented:
|
||
|
|
return t
|
||
|
|
if hasattr(t, '_mpf_'):
|
||
|
|
v = new(cls)
|
||
|
|
v._mpc_ = mpc_mul_mpf(s._mpc_, t._mpf_, prec, rounding)
|
||
|
|
return v
|
||
|
|
t = s.mpc_convert_lhs(t)
|
||
|
|
v = new(cls)
|
||
|
|
v._mpc_ = mpc_mul(s._mpc_, t._mpc_, prec, rounding)
|
||
|
|
return v
|
||
|
|
|
||
|
|
def __div__(s, t):
|
||
|
|
cls, new, (prec, rounding) = s._ctxdata
|
||
|
|
if not hasattr(t, '_mpc_'):
|
||
|
|
t = s.mpc_convert_lhs(t)
|
||
|
|
if t is NotImplemented:
|
||
|
|
return t
|
||
|
|
if hasattr(t, '_mpf_'):
|
||
|
|
v = new(cls)
|
||
|
|
v._mpc_ = mpc_div_mpf(s._mpc_, t._mpf_, prec, rounding)
|
||
|
|
return v
|
||
|
|
v = new(cls)
|
||
|
|
v._mpc_ = mpc_div(s._mpc_, t._mpc_, prec, rounding)
|
||
|
|
return v
|
||
|
|
|
||
|
|
def __pow__(s, t):
|
||
|
|
cls, new, (prec, rounding) = s._ctxdata
|
||
|
|
if isinstance(t, int_types):
|
||
|
|
v = new(cls)
|
||
|
|
v._mpc_ = mpc_pow_int(s._mpc_, t, prec, rounding)
|
||
|
|
return v
|
||
|
|
t = s.mpc_convert_lhs(t)
|
||
|
|
if t is NotImplemented:
|
||
|
|
return t
|
||
|
|
v = new(cls)
|
||
|
|
if hasattr(t, '_mpf_'):
|
||
|
|
v._mpc_ = mpc_pow_mpf(s._mpc_, t._mpf_, prec, rounding)
|
||
|
|
else:
|
||
|
|
v._mpc_ = mpc_pow(s._mpc_, t._mpc_, prec, rounding)
|
||
|
|
return v
|
||
|
|
|
||
|
|
__radd__ = __add__
|
||
|
|
|
||
|
|
def __rsub__(s, t):
|
||
|
|
t = s.mpc_convert_lhs(t)
|
||
|
|
if t is NotImplemented:
|
||
|
|
return t
|
||
|
|
return t - s
|
||
|
|
|
||
|
|
def __rmul__(s, t):
|
||
|
|
cls, new, (prec, rounding) = s._ctxdata
|
||
|
|
if isinstance(t, int_types):
|
||
|
|
v = new(cls)
|
||
|
|
v._mpc_ = mpc_mul_int(s._mpc_, t, prec, rounding)
|
||
|
|
return v
|
||
|
|
t = s.mpc_convert_lhs(t)
|
||
|
|
if t is NotImplemented:
|
||
|
|
return t
|
||
|
|
return t * s
|
||
|
|
|
||
|
|
def __rdiv__(s, t):
|
||
|
|
t = s.mpc_convert_lhs(t)
|
||
|
|
if t is NotImplemented:
|
||
|
|
return t
|
||
|
|
return t / s
|
||
|
|
|
||
|
|
def __rpow__(s, t):
|
||
|
|
t = s.mpc_convert_lhs(t)
|
||
|
|
if t is NotImplemented:
|
||
|
|
return t
|
||
|
|
return t ** s
|
||
|
|
|
||
|
|
__truediv__ = __div__
|
||
|
|
__rtruediv__ = __rdiv__
|
||
|
|
|
||
|
|
def ae(s, t, rel_eps=None, abs_eps=None):
|
||
|
|
return s.context.almosteq(s, t, rel_eps, abs_eps)
|
||
|
|
|
||
|
|
|
||
|
|
complex_types = (complex, _mpc)
|
||
|
|
|
||
|
|
|
||
|
|
class PythonMPContext(object):
|
||
|
|
|
||
|
|
def __init__(ctx):
|
||
|
|
ctx._prec_rounding = [53, round_nearest]
|
||
|
|
ctx.mpf = type('mpf', (_mpf,), {})
|
||
|
|
ctx.mpc = type('mpc', (_mpc,), {})
|
||
|
|
ctx.mpf._ctxdata = [ctx.mpf, new, ctx._prec_rounding]
|
||
|
|
ctx.mpc._ctxdata = [ctx.mpc, new, ctx._prec_rounding]
|
||
|
|
ctx.mpf.context = ctx
|
||
|
|
ctx.mpc.context = ctx
|
||
|
|
ctx.constant = type('constant', (_constant,), {})
|
||
|
|
ctx.constant._ctxdata = [ctx.mpf, new, ctx._prec_rounding]
|
||
|
|
ctx.constant.context = ctx
|
||
|
|
|
||
|
|
def make_mpf(ctx, v):
|
||
|
|
a = new(ctx.mpf)
|
||
|
|
a._mpf_ = v
|
||
|
|
return a
|
||
|
|
|
||
|
|
def make_mpc(ctx, v):
|
||
|
|
a = new(ctx.mpc)
|
||
|
|
a._mpc_ = v
|
||
|
|
return a
|
||
|
|
|
||
|
|
def default(ctx):
|
||
|
|
ctx._prec = ctx._prec_rounding[0] = 53
|
||
|
|
ctx._dps = 15
|
||
|
|
ctx.trap_complex = False
|
||
|
|
|
||
|
|
def _set_prec(ctx, n):
|
||
|
|
ctx._prec = ctx._prec_rounding[0] = max(1, int(n))
|
||
|
|
ctx._dps = prec_to_dps(n)
|
||
|
|
|
||
|
|
def _set_dps(ctx, n):
|
||
|
|
ctx._prec = ctx._prec_rounding[0] = dps_to_prec(n)
|
||
|
|
ctx._dps = max(1, int(n))
|
||
|
|
|
||
|
|
prec = property(lambda ctx: ctx._prec, _set_prec)
|
||
|
|
dps = property(lambda ctx: ctx._dps, _set_dps)
|
||
|
|
|
||
|
|
def convert(ctx, x, strings=True):
|
||
|
|
"""
|
||
|
|
Converts *x* to an ``mpf`` or ``mpc``. If *x* is of type ``mpf``,
|
||
|
|
``mpc``, ``int``, ``float``, ``complex``, the conversion
|
||
|
|
will be performed losslessly.
|
||
|
|
|
||
|
|
If *x* is a string, the result will be rounded to the present
|
||
|
|
working precision. Strings representing fractions or complex
|
||
|
|
numbers are permitted.
|
||
|
|
|
||
|
|
>>> from mpmath import *
|
||
|
|
>>> mp.dps = 15; mp.pretty = False
|
||
|
|
>>> mpmathify(3.5)
|
||
|
|
mpf('3.5')
|
||
|
|
>>> mpmathify('2.1')
|
||
|
|
mpf('2.1000000000000001')
|
||
|
|
>>> mpmathify('3/4')
|
||
|
|
mpf('0.75')
|
||
|
|
>>> mpmathify('2+3j')
|
||
|
|
mpc(real='2.0', imag='3.0')
|
||
|
|
|
||
|
|
"""
|
||
|
|
if type(x) in ctx.types: return x
|
||
|
|
if isinstance(x, int_types): return ctx.make_mpf(from_int(x))
|
||
|
|
if isinstance(x, float): return ctx.make_mpf(from_float(x))
|
||
|
|
if isinstance(x, complex):
|
||
|
|
return ctx.make_mpc((from_float(x.real), from_float(x.imag)))
|
||
|
|
if type(x).__module__ == 'numpy': return ctx.npconvert(x)
|
||
|
|
if isinstance(x, numbers.Rational): # e.g. Fraction
|
||
|
|
try: x = rational.mpq(int(x.numerator), int(x.denominator))
|
||
|
|
except: pass
|
||
|
|
prec, rounding = ctx._prec_rounding
|
||
|
|
if isinstance(x, rational.mpq):
|
||
|
|
p, q = x._mpq_
|
||
|
|
return ctx.make_mpf(from_rational(p, q, prec))
|
||
|
|
if strings and isinstance(x, basestring):
|
||
|
|
try:
|
||
|
|
_mpf_ = from_str(x, prec, rounding)
|
||
|
|
return ctx.make_mpf(_mpf_)
|
||
|
|
except ValueError:
|
||
|
|
pass
|
||
|
|
if hasattr(x, '_mpf_'): return ctx.make_mpf(x._mpf_)
|
||
|
|
if hasattr(x, '_mpc_'): return ctx.make_mpc(x._mpc_)
|
||
|
|
if hasattr(x, '_mpmath_'):
|
||
|
|
return ctx.convert(x._mpmath_(prec, rounding))
|
||
|
|
if type(x).__module__ == 'decimal':
|
||
|
|
try: return ctx.make_mpf(from_Decimal(x, prec, rounding))
|
||
|
|
except: pass
|
||
|
|
return ctx._convert_fallback(x, strings)
|
||
|
|
|
||
|
|
def npconvert(ctx, x):
|
||
|
|
"""
|
||
|
|
Converts *x* to an ``mpf`` or ``mpc``. *x* should be a numpy
|
||
|
|
scalar.
|
||
|
|
"""
|
||
|
|
import numpy as np
|
||
|
|
if isinstance(x, np.integer): return ctx.make_mpf(from_int(int(x)))
|
||
|
|
if isinstance(x, np.floating): return ctx.make_mpf(from_npfloat(x))
|
||
|
|
if isinstance(x, np.complexfloating):
|
||
|
|
return ctx.make_mpc((from_npfloat(x.real), from_npfloat(x.imag)))
|
||
|
|
raise TypeError("cannot create mpf from " + repr(x))
|
||
|
|
|
||
|
|
def isnan(ctx, x):
|
||
|
|
"""
|
||
|
|
Return *True* if *x* is a NaN (not-a-number), or for a complex
|
||
|
|
number, whether either the real or complex part is NaN;
|
||
|
|
otherwise return *False*::
|
||
|
|
|
||
|
|
>>> from mpmath import *
|
||
|
|
>>> isnan(3.14)
|
||
|
|
False
|
||
|
|
>>> isnan(nan)
|
||
|
|
True
|
||
|
|
>>> isnan(mpc(3.14,2.72))
|
||
|
|
False
|
||
|
|
>>> isnan(mpc(3.14,nan))
|
||
|
|
True
|
||
|
|
|
||
|
|
"""
|
||
|
|
if hasattr(x, "_mpf_"):
|
||
|
|
return x._mpf_ == fnan
|
||
|
|
if hasattr(x, "_mpc_"):
|
||
|
|
return fnan in x._mpc_
|
||
|
|
if isinstance(x, int_types) or isinstance(x, rational.mpq):
|
||
|
|
return False
|
||
|
|
x = ctx.convert(x)
|
||
|
|
if hasattr(x, '_mpf_') or hasattr(x, '_mpc_'):
|
||
|
|
return ctx.isnan(x)
|
||
|
|
raise TypeError("isnan() needs a number as input")
|
||
|
|
|
||
|
|
def isinf(ctx, x):
|
||
|
|
"""
|
||
|
|
Return *True* if the absolute value of *x* is infinite;
|
||
|
|
otherwise return *False*::
|
||
|
|
|
||
|
|
>>> from mpmath import *
|
||
|
|
>>> isinf(inf)
|
||
|
|
True
|
||
|
|
>>> isinf(-inf)
|
||
|
|
True
|
||
|
|
>>> isinf(3)
|
||
|
|
False
|
||
|
|
>>> isinf(3+4j)
|
||
|
|
False
|
||
|
|
>>> isinf(mpc(3,inf))
|
||
|
|
True
|
||
|
|
>>> isinf(mpc(inf,3))
|
||
|
|
True
|
||
|
|
|
||
|
|
"""
|
||
|
|
if hasattr(x, "_mpf_"):
|
||
|
|
return x._mpf_ in (finf, fninf)
|
||
|
|
if hasattr(x, "_mpc_"):
|
||
|
|
re, im = x._mpc_
|
||
|
|
return re in (finf, fninf) or im in (finf, fninf)
|
||
|
|
if isinstance(x, int_types) or isinstance(x, rational.mpq):
|
||
|
|
return False
|
||
|
|
x = ctx.convert(x)
|
||
|
|
if hasattr(x, '_mpf_') or hasattr(x, '_mpc_'):
|
||
|
|
return ctx.isinf(x)
|
||
|
|
raise TypeError("isinf() needs a number as input")
|
||
|
|
|
||
|
|
def isnormal(ctx, x):
|
||
|
|
"""
|
||
|
|
Determine whether *x* is "normal" in the sense of floating-point
|
||
|
|
representation; that is, return *False* if *x* is zero, an
|
||
|
|
infinity or NaN; otherwise return *True*. By extension, a
|
||
|
|
complex number *x* is considered "normal" if its magnitude is
|
||
|
|
normal::
|
||
|
|
|
||
|
|
>>> from mpmath import *
|
||
|
|
>>> isnormal(3)
|
||
|
|
True
|
||
|
|
>>> isnormal(0)
|
||
|
|
False
|
||
|
|
>>> isnormal(inf); isnormal(-inf); isnormal(nan)
|
||
|
|
False
|
||
|
|
False
|
||
|
|
False
|
||
|
|
>>> isnormal(0+0j)
|
||
|
|
False
|
||
|
|
>>> isnormal(0+3j)
|
||
|
|
True
|
||
|
|
>>> isnormal(mpc(2,nan))
|
||
|
|
False
|
||
|
|
"""
|
||
|
|
if hasattr(x, "_mpf_"):
|
||
|
|
return bool(x._mpf_[1])
|
||
|
|
if hasattr(x, "_mpc_"):
|
||
|
|
re, im = x._mpc_
|
||
|
|
re_normal = bool(re[1])
|
||
|
|
im_normal = bool(im[1])
|
||
|
|
if re == fzero: return im_normal
|
||
|
|
if im == fzero: return re_normal
|
||
|
|
return re_normal and im_normal
|
||
|
|
if isinstance(x, int_types) or isinstance(x, rational.mpq):
|
||
|
|
return bool(x)
|
||
|
|
x = ctx.convert(x)
|
||
|
|
if hasattr(x, '_mpf_') or hasattr(x, '_mpc_'):
|
||
|
|
return ctx.isnormal(x)
|
||
|
|
raise TypeError("isnormal() needs a number as input")
|
||
|
|
|
||
|
|
def isint(ctx, x, gaussian=False):
|
||
|
|
"""
|
||
|
|
Return *True* if *x* is integer-valued; otherwise return
|
||
|
|
*False*::
|
||
|
|
|
||
|
|
>>> from mpmath import *
|
||
|
|
>>> isint(3)
|
||
|
|
True
|
||
|
|
>>> isint(mpf(3))
|
||
|
|
True
|
||
|
|
>>> isint(3.2)
|
||
|
|
False
|
||
|
|
>>> isint(inf)
|
||
|
|
False
|
||
|
|
|
||
|
|
Optionally, Gaussian integers can be checked for::
|
||
|
|
|
||
|
|
>>> isint(3+0j)
|
||
|
|
True
|
||
|
|
>>> isint(3+2j)
|
||
|
|
False
|
||
|
|
>>> isint(3+2j, gaussian=True)
|
||
|
|
True
|
||
|
|
|
||
|
|
"""
|
||
|
|
if isinstance(x, int_types):
|
||
|
|
return True
|
||
|
|
if hasattr(x, "_mpf_"):
|
||
|
|
sign, man, exp, bc = xval = x._mpf_
|
||
|
|
return bool((man and exp >= 0) or xval == fzero)
|
||
|
|
if hasattr(x, "_mpc_"):
|
||
|
|
re, im = x._mpc_
|
||
|
|
rsign, rman, rexp, rbc = re
|
||
|
|
isign, iman, iexp, ibc = im
|
||
|
|
re_isint = (rman and rexp >= 0) or re == fzero
|
||
|
|
if gaussian:
|
||
|
|
im_isint = (iman and iexp >= 0) or im == fzero
|
||
|
|
return re_isint and im_isint
|
||
|
|
return re_isint and im == fzero
|
||
|
|
if isinstance(x, rational.mpq):
|
||
|
|
p, q = x._mpq_
|
||
|
|
return p % q == 0
|
||
|
|
x = ctx.convert(x)
|
||
|
|
if hasattr(x, '_mpf_') or hasattr(x, '_mpc_'):
|
||
|
|
return ctx.isint(x, gaussian)
|
||
|
|
raise TypeError("isint() needs a number as input")
|
||
|
|
|
||
|
|
def fsum(ctx, terms, absolute=False, squared=False):
|
||
|
|
"""
|
||
|
|
Calculates a sum containing a finite number of terms (for infinite
|
||
|
|
series, see :func:`~mpmath.nsum`). The terms will be converted to
|
||
|
|
mpmath numbers. For len(terms) > 2, this function is generally
|
||
|
|
faster and produces more accurate results than the builtin
|
||
|
|
Python function :func:`sum`.
|
||
|
|
|
||
|
|
>>> from mpmath import *
|
||
|
|
>>> mp.dps = 15; mp.pretty = False
|
||
|
|
>>> fsum([1, 2, 0.5, 7])
|
||
|
|
mpf('10.5')
|
||
|
|
|
||
|
|
With squared=True each term is squared, and with absolute=True
|
||
|
|
the absolute value of each term is used.
|
||
|
|
"""
|
||
|
|
prec, rnd = ctx._prec_rounding
|
||
|
|
real = []
|
||
|
|
imag = []
|
||
|
|
for term in terms:
|
||
|
|
reval = imval = 0
|
||
|
|
if hasattr(term, "_mpf_"):
|
||
|
|
reval = term._mpf_
|
||
|
|
elif hasattr(term, "_mpc_"):
|
||
|
|
reval, imval = term._mpc_
|
||
|
|
else:
|
||
|
|
term = ctx.convert(term)
|
||
|
|
if hasattr(term, "_mpf_"):
|
||
|
|
reval = term._mpf_
|
||
|
|
elif hasattr(term, "_mpc_"):
|
||
|
|
reval, imval = term._mpc_
|
||
|
|
else:
|
||
|
|
raise NotImplementedError
|
||
|
|
if imval:
|
||
|
|
if squared:
|
||
|
|
if absolute:
|
||
|
|
real.append(mpf_mul(reval,reval))
|
||
|
|
real.append(mpf_mul(imval,imval))
|
||
|
|
else:
|
||
|
|
reval, imval = mpc_pow_int((reval,imval),2,prec+10)
|
||
|
|
real.append(reval)
|
||
|
|
imag.append(imval)
|
||
|
|
elif absolute:
|
||
|
|
real.append(mpc_abs((reval,imval), prec))
|
||
|
|
else:
|
||
|
|
real.append(reval)
|
||
|
|
imag.append(imval)
|
||
|
|
else:
|
||
|
|
if squared:
|
||
|
|
reval = mpf_mul(reval, reval)
|
||
|
|
elif absolute:
|
||
|
|
reval = mpf_abs(reval)
|
||
|
|
real.append(reval)
|
||
|
|
s = mpf_sum(real, prec, rnd, absolute)
|
||
|
|
if imag:
|
||
|
|
s = ctx.make_mpc((s, mpf_sum(imag, prec, rnd)))
|
||
|
|
else:
|
||
|
|
s = ctx.make_mpf(s)
|
||
|
|
return s
|
||
|
|
|
||
|
|
def fdot(ctx, A, B=None, conjugate=False):
|
||
|
|
r"""
|
||
|
|
Computes the dot product of the iterables `A` and `B`,
|
||
|
|
|
||
|
|
.. math ::
|
||
|
|
|
||
|
|
\sum_{k=0} A_k B_k.
|
||
|
|
|
||
|
|
Alternatively, :func:`~mpmath.fdot` accepts a single iterable of pairs.
|
||
|
|
In other words, ``fdot(A,B)`` and ``fdot(zip(A,B))`` are equivalent.
|
||
|
|
The elements are automatically converted to mpmath numbers.
|
||
|
|
|
||
|
|
With ``conjugate=True``, the elements in the second vector
|
||
|
|
will be conjugated:
|
||
|
|
|
||
|
|
.. math ::
|
||
|
|
|
||
|
|
\sum_{k=0} A_k \overline{B_k}
|
||
|
|
|
||
|
|
**Examples**
|
||
|
|
|
||
|
|
>>> from mpmath import *
|
||
|
|
>>> mp.dps = 15; mp.pretty = False
|
||
|
|
>>> A = [2, 1.5, 3]
|
||
|
|
>>> B = [1, -1, 2]
|
||
|
|
>>> fdot(A, B)
|
||
|
|
mpf('6.5')
|
||
|
|
>>> list(zip(A, B))
|
||
|
|
[(2, 1), (1.5, -1), (3, 2)]
|
||
|
|
>>> fdot(_)
|
||
|
|
mpf('6.5')
|
||
|
|
>>> A = [2, 1.5, 3j]
|
||
|
|
>>> B = [1+j, 3, -1-j]
|
||
|
|
>>> fdot(A, B)
|
||
|
|
mpc(real='9.5', imag='-1.0')
|
||
|
|
>>> fdot(A, B, conjugate=True)
|
||
|
|
mpc(real='3.5', imag='-5.0')
|
||
|
|
|
||
|
|
"""
|
||
|
|
if B is not None:
|
||
|
|
A = zip(A, B)
|
||
|
|
prec, rnd = ctx._prec_rounding
|
||
|
|
real = []
|
||
|
|
imag = []
|
||
|
|
hasattr_ = hasattr
|
||
|
|
types = (ctx.mpf, ctx.mpc)
|
||
|
|
for a, b in A:
|
||
|
|
if type(a) not in types: a = ctx.convert(a)
|
||
|
|
if type(b) not in types: b = ctx.convert(b)
|
||
|
|
a_real = hasattr_(a, "_mpf_")
|
||
|
|
b_real = hasattr_(b, "_mpf_")
|
||
|
|
if a_real and b_real:
|
||
|
|
real.append(mpf_mul(a._mpf_, b._mpf_))
|
||
|
|
continue
|
||
|
|
a_complex = hasattr_(a, "_mpc_")
|
||
|
|
b_complex = hasattr_(b, "_mpc_")
|
||
|
|
if a_real and b_complex:
|
||
|
|
aval = a._mpf_
|
||
|
|
bre, bim = b._mpc_
|
||
|
|
if conjugate:
|
||
|
|
bim = mpf_neg(bim)
|
||
|
|
real.append(mpf_mul(aval, bre))
|
||
|
|
imag.append(mpf_mul(aval, bim))
|
||
|
|
elif b_real and a_complex:
|
||
|
|
are, aim = a._mpc_
|
||
|
|
bval = b._mpf_
|
||
|
|
real.append(mpf_mul(are, bval))
|
||
|
|
imag.append(mpf_mul(aim, bval))
|
||
|
|
elif a_complex and b_complex:
|
||
|
|
#re, im = mpc_mul(a._mpc_, b._mpc_, prec+20)
|
||
|
|
are, aim = a._mpc_
|
||
|
|
bre, bim = b._mpc_
|
||
|
|
if conjugate:
|
||
|
|
bim = mpf_neg(bim)
|
||
|
|
real.append(mpf_mul(are, bre))
|
||
|
|
real.append(mpf_neg(mpf_mul(aim, bim)))
|
||
|
|
imag.append(mpf_mul(are, bim))
|
||
|
|
imag.append(mpf_mul(aim, bre))
|
||
|
|
else:
|
||
|
|
raise NotImplementedError
|
||
|
|
s = mpf_sum(real, prec, rnd)
|
||
|
|
if imag:
|
||
|
|
s = ctx.make_mpc((s, mpf_sum(imag, prec, rnd)))
|
||
|
|
else:
|
||
|
|
s = ctx.make_mpf(s)
|
||
|
|
return s
|
||
|
|
|
||
|
|
def _wrap_libmp_function(ctx, mpf_f, mpc_f=None, mpi_f=None, doc="<no doc>"):
|
||
|
|
"""
|
||
|
|
Given a low-level mpf_ function, and optionally similar functions
|
||
|
|
for mpc_ and mpi_, defines the function as a context method.
|
||
|
|
|
||
|
|
It is assumed that the return type is the same as that of
|
||
|
|
the input; the exception is that propagation from mpf to mpc is possible
|
||
|
|
by raising ComplexResult.
|
||
|
|
|
||
|
|
"""
|
||
|
|
def f(x, **kwargs):
|
||
|
|
if type(x) not in ctx.types:
|
||
|
|
x = ctx.convert(x)
|
||
|
|
prec, rounding = ctx._prec_rounding
|
||
|
|
if kwargs:
|
||
|
|
prec = kwargs.get('prec', prec)
|
||
|
|
if 'dps' in kwargs:
|
||
|
|
prec = dps_to_prec(kwargs['dps'])
|
||
|
|
rounding = kwargs.get('rounding', rounding)
|
||
|
|
if hasattr(x, '_mpf_'):
|
||
|
|
try:
|
||
|
|
return ctx.make_mpf(mpf_f(x._mpf_, prec, rounding))
|
||
|
|
except ComplexResult:
|
||
|
|
# Handle propagation to complex
|
||
|
|
if ctx.trap_complex:
|
||
|
|
raise
|
||
|
|
return ctx.make_mpc(mpc_f((x._mpf_, fzero), prec, rounding))
|
||
|
|
elif hasattr(x, '_mpc_'):
|
||
|
|
return ctx.make_mpc(mpc_f(x._mpc_, prec, rounding))
|
||
|
|
raise NotImplementedError("%s of a %s" % (name, type(x)))
|
||
|
|
name = mpf_f.__name__[4:]
|
||
|
|
f.__doc__ = function_docs.__dict__.get(name, "Computes the %s of x" % doc)
|
||
|
|
return f
|
||
|
|
|
||
|
|
# Called by SpecialFunctions.__init__()
|
||
|
|
@classmethod
|
||
|
|
def _wrap_specfun(cls, name, f, wrap):
|
||
|
|
if wrap:
|
||
|
|
def f_wrapped(ctx, *args, **kwargs):
|
||
|
|
convert = ctx.convert
|
||
|
|
args = [convert(a) for a in args]
|
||
|
|
prec = ctx.prec
|
||
|
|
try:
|
||
|
|
ctx.prec += 10
|
||
|
|
retval = f(ctx, *args, **kwargs)
|
||
|
|
finally:
|
||
|
|
ctx.prec = prec
|
||
|
|
return +retval
|
||
|
|
else:
|
||
|
|
f_wrapped = f
|
||
|
|
f_wrapped.__doc__ = function_docs.__dict__.get(name, f.__doc__)
|
||
|
|
setattr(cls, name, f_wrapped)
|
||
|
|
|
||
|
|
def _convert_param(ctx, x):
|
||
|
|
if hasattr(x, "_mpc_"):
|
||
|
|
v, im = x._mpc_
|
||
|
|
if im != fzero:
|
||
|
|
return x, 'C'
|
||
|
|
elif hasattr(x, "_mpf_"):
|
||
|
|
v = x._mpf_
|
||
|
|
else:
|
||
|
|
if type(x) in int_types:
|
||
|
|
return int(x), 'Z'
|
||
|
|
p = None
|
||
|
|
if isinstance(x, tuple):
|
||
|
|
p, q = x
|
||
|
|
elif hasattr(x, '_mpq_'):
|
||
|
|
p, q = x._mpq_
|
||
|
|
elif isinstance(x, basestring) and '/' in x:
|
||
|
|
p, q = x.split('/')
|
||
|
|
p = int(p)
|
||
|
|
q = int(q)
|
||
|
|
if p is not None:
|
||
|
|
if not p % q:
|
||
|
|
return p // q, 'Z'
|
||
|
|
return ctx.mpq(p,q), 'Q'
|
||
|
|
x = ctx.convert(x)
|
||
|
|
if hasattr(x, "_mpc_"):
|
||
|
|
v, im = x._mpc_
|
||
|
|
if im != fzero:
|
||
|
|
return x, 'C'
|
||
|
|
elif hasattr(x, "_mpf_"):
|
||
|
|
v = x._mpf_
|
||
|
|
else:
|
||
|
|
return x, 'U'
|
||
|
|
sign, man, exp, bc = v
|
||
|
|
if man:
|
||
|
|
if exp >= -4:
|
||
|
|
if sign:
|
||
|
|
man = -man
|
||
|
|
if exp >= 0:
|
||
|
|
return int(man) << exp, 'Z'
|
||
|
|
if exp >= -4:
|
||
|
|
p, q = int(man), (1<<(-exp))
|
||
|
|
return ctx.mpq(p,q), 'Q'
|
||
|
|
x = ctx.make_mpf(v)
|
||
|
|
return x, 'R'
|
||
|
|
elif not exp:
|
||
|
|
return 0, 'Z'
|
||
|
|
else:
|
||
|
|
return x, 'U'
|
||
|
|
|
||
|
|
def _mpf_mag(ctx, x):
|
||
|
|
sign, man, exp, bc = x
|
||
|
|
if man:
|
||
|
|
return exp+bc
|
||
|
|
if x == fzero:
|
||
|
|
return ctx.ninf
|
||
|
|
if x == finf or x == fninf:
|
||
|
|
return ctx.inf
|
||
|
|
return ctx.nan
|
||
|
|
|
||
|
|
def mag(ctx, x):
|
||
|
|
"""
|
||
|
|
Quick logarithmic magnitude estimate of a number. Returns an
|
||
|
|
integer or infinity `m` such that `|x| <= 2^m`. It is not
|
||
|
|
guaranteed that `m` is an optimal bound, but it will never
|
||
|
|
be too large by more than 2 (and probably not more than 1).
|
||
|
|
|
||
|
|
**Examples**
|
||
|
|
|
||
|
|
>>> from mpmath import *
|
||
|
|
>>> mp.pretty = True
|
||
|
|
>>> mag(10), mag(10.0), mag(mpf(10)), int(ceil(log(10,2)))
|
||
|
|
(4, 4, 4, 4)
|
||
|
|
>>> mag(10j), mag(10+10j)
|
||
|
|
(4, 5)
|
||
|
|
>>> mag(0.01), int(ceil(log(0.01,2)))
|
||
|
|
(-6, -6)
|
||
|
|
>>> mag(0), mag(inf), mag(-inf), mag(nan)
|
||
|
|
(-inf, +inf, +inf, nan)
|
||
|
|
|
||
|
|
"""
|
||
|
|
if hasattr(x, "_mpf_"):
|
||
|
|
return ctx._mpf_mag(x._mpf_)
|
||
|
|
elif hasattr(x, "_mpc_"):
|
||
|
|
r, i = x._mpc_
|
||
|
|
if r == fzero:
|
||
|
|
return ctx._mpf_mag(i)
|
||
|
|
if i == fzero:
|
||
|
|
return ctx._mpf_mag(r)
|
||
|
|
return 1+max(ctx._mpf_mag(r), ctx._mpf_mag(i))
|
||
|
|
elif isinstance(x, int_types):
|
||
|
|
if x:
|
||
|
|
return bitcount(abs(x))
|
||
|
|
return ctx.ninf
|
||
|
|
elif isinstance(x, rational.mpq):
|
||
|
|
p, q = x._mpq_
|
||
|
|
if p:
|
||
|
|
return 1 + bitcount(abs(p)) - bitcount(q)
|
||
|
|
return ctx.ninf
|
||
|
|
else:
|
||
|
|
x = ctx.convert(x)
|
||
|
|
if hasattr(x, "_mpf_") or hasattr(x, "_mpc_"):
|
||
|
|
return ctx.mag(x)
|
||
|
|
else:
|
||
|
|
raise TypeError("requires an mpf/mpc")
|
||
|
|
|
||
|
|
|
||
|
|
# Register with "numbers" ABC
|
||
|
|
# We do not subclass, hence we do not use the @abstractmethod checks. While
|
||
|
|
# this is less invasive it may turn out that we do not actually support
|
||
|
|
# parts of the expected interfaces. See
|
||
|
|
# http://docs.python.org/2/library/numbers.html for list of abstract
|
||
|
|
# methods.
|
||
|
|
try:
|
||
|
|
import numbers
|
||
|
|
numbers.Complex.register(_mpc)
|
||
|
|
numbers.Real.register(_mpf)
|
||
|
|
except ImportError:
|
||
|
|
pass
|