#from ctx_base import StandardBaseContext
from .libmp.backend import basestring, exec_
from .libmp import (MPZ, MPZ_ZERO, MPZ_ONE, int_types, repr_dps,
round_floor, round_ceiling, dps_to_prec, round_nearest, prec_to_dps,
ComplexResult, to_pickable, from_pickable, normalize,
from_int, from_float, from_npfloat, from_Decimal, from_str, to_int, to_float, to_str,
from_rational, from_man_exp,
fone, fzero, finf, fninf, fnan,
mpf_abs, mpf_pos, mpf_neg, mpf_add, mpf_sub, mpf_mul, mpf_mul_int,
mpf_div, mpf_rdiv_int, mpf_pow_int, mpf_mod,
mpf_eq, mpf_cmp, mpf_lt, mpf_gt, mpf_le, mpf_ge,
mpf_hash, mpf_rand,
mpf_sum,
bitcount, to_fixed,
mpc_to_str,
mpc_to_complex, mpc_hash, mpc_pos, mpc_is_nonzero, mpc_neg, mpc_conjugate,
mpc_abs, mpc_add, mpc_add_mpf, mpc_sub, mpc_sub_mpf, mpc_mul, mpc_mul_mpf,
mpc_mul_int, mpc_div, mpc_div_mpf, mpc_pow, mpc_pow_mpf, mpc_pow_int,
mpc_mpf_div,
mpf_pow,
mpf_pi, mpf_degree, mpf_e, mpf_phi, mpf_ln2, mpf_ln10,
mpf_euler, mpf_catalan, mpf_apery, mpf_khinchin,
mpf_glaisher, mpf_twinprime, mpf_mertens,
int_types)
from . import rational
from . import function_docs
new = object.__new__
class mpnumeric(object):
"""Base class for mpf and mpc."""
__slots__ = []
def __new__(cls, val):
raise NotImplementedError
class _mpf(mpnumeric):
"""
An mpf instance holds a real-valued floating-point number. mpf:s
work analogously to Python floats, but support arbitrary-precision
arithmetic.
"""
__slots__ = ['_mpf_']
def __new__(cls, val=fzero, **kwargs):
"""A new mpf can be created from a Python float, an int, a
or a decimal string representing a number in floating-point
format."""
prec, rounding = cls.context._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 type(val) is cls:
sign, man, exp, bc = val._mpf_
if (not man) and exp:
return val
v = new(cls)
v._mpf_ = normalize(sign, man, exp, bc, prec, rounding)
return v
elif type(val) is tuple:
if len(val) == 2:
v = new(cls)
v._mpf_ = from_man_exp(val[0], val[1], prec, rounding)
return v
if len(val) == 4:
if val not in (finf, fninf, fnan):
sign, man, exp, bc = val
val = normalize(sign, MPZ(man), exp, bc, prec, rounding)
v = new(cls)
v._mpf_ = val
return v
raise ValueError
else:
v = new(cls)
v._mpf_ = mpf_pos(cls.mpf_convert_arg(val, prec, rounding), prec, rounding)
return v
@classmethod
def mpf_convert_arg(cls, x, prec, rounding):
if isinstance(x, int_types): return from_int(x)
if isinstance(x, float): return from_float(x)
if isinstance(x, basestring): return from_str(x, prec, rounding)
if isinstance(x, cls.context.constant): return x.func(prec, rounding)
if hasattr(x, '_mpf_'): return x._mpf_
if hasattr(x, '_mpmath_'):
t = cls.context.convert(x._mpmath_(prec, rounding))
if hasattr(t, '_mpf_'):
return t._mpf_
if hasattr(x, '_mpi_'):
a, b = x._mpi_
if a == b:
return a
raise ValueError("can only create mpf from zero-width interval")
raise TypeError("cannot create mpf from " + repr(x))
@classmethod
def mpf_convert_rhs(cls, x):
if isinstance(x, int_types): return from_int(x)
if isinstance(x, float): return from_float(x)
if isinstance(x, complex_types): return cls.context.mpc(x)
if isinstance(x, rational.mpq):
p, q = x._mpq_
return from_rational(p, q, cls.context.prec)
if hasattr(x, '_mpf_'): return x._mpf_
if hasattr(x, '_mpmath_'):
t = cls.context.convert(x._mpmath_(*cls.context._prec_rounding))
if hasattr(t, '_mpf_'):
return t._mpf_
return t
return NotImplemented
@classmethod
def mpf_convert_lhs(cls, x):
x = cls.mpf_convert_rhs(x)
if type(x) is tuple:
return cls.context.make_mpf(x)
return x
man_exp = property(lambda self: self._mpf_[1:3])
man = property(lambda self: self._mpf_[1])
exp = property(lambda self: self._mpf_[2])
bc = property(lambda self: self._mpf_[3])
real = property(lambda self: self)
imag = property(lambda self: self.context.zero)
conjugate = lambda self: self
def __getstate__(self): return to_pickable(self._mpf_)
def __setstate__(self, val): self._mpf_ = from_pickable(val)
def __repr__(s):
if s.context.pretty:
return str(s)
return "mpf('%s')" % to_str(s._mpf_, s.context._repr_digits)
def __str__(s): return to_str(s._mpf_, s.context._str_digits)
def __hash__(s): return mpf_hash(s._mpf_)
def __int__(s): return int(to_int(s._mpf_))
def __long__(s): return long(to_int(s._mpf_))
def __float__(s): return to_float(s._mpf_, rnd=s.context._prec_rounding[1])
def __complex__(s): return complex(float(s))
def __nonzero__(s): return s._mpf_ != fzero
__bool__ = __nonzero__
def __abs__(s):
cls, new, (prec, rounding) = s._ctxdata
v = new(cls)
v._mpf_ = mpf_abs(s._mpf_, prec, rounding)
return v
def __pos__(s):
cls, new, (prec, rounding) = s._ctxdata
v = new(cls)
v._mpf_ = mpf_pos(s._mpf_, prec, rounding)
return v
def __neg__(s):
cls, new, (prec, rounding) = s._ctxdata
v = new(cls)
v._mpf_ = mpf_neg(s._mpf_, prec, rounding)
return v
def _cmp(s, t, func):
if hasattr(t, '_mpf_'):
t = t._mpf_
else:
t = s.mpf_convert_rhs(t)
if t is NotImplemented:
return t
return func(s._mpf_, t)
def __cmp__(s, t): return s._cmp(t, mpf_cmp)
def __lt__(s, t): return s._cmp(t, mpf_lt)
def __gt__(s, t): return s._cmp(t, mpf_gt)
def __le__(s, t): return s._cmp(t, mpf_le)
def __ge__(s, t): return s._cmp(t, mpf_ge)
def __ne__(s, t):
v = s.__eq__(t)
if v is NotImplemented:
return v
return not v
def __rsub__(s, t):
cls, new, (prec, rounding) = s._ctxdata
if type(t) in int_types:
v = new(cls)
v._mpf_ = mpf_sub(from_int(t), s._mpf_, prec, rounding)
return v
t = s.mpf_convert_lhs(t)
if t is NotImplemented:
return t
return t - s
def __rdiv__(s, t):
cls, new, (prec, rounding) = s._ctxdata
if isinstance(t, int_types):
v = new(cls)
v._mpf_ = mpf_rdiv_int(t, s._mpf_, prec, rounding)
return v
t = s.mpf_convert_lhs(t)
if t is NotImplemented:
return t
return t / s
def __rpow__(s, t):
t = s.mpf_convert_lhs(t)
if t is NotImplemented:
return t
return t ** s
def __rmod__(s, t):
t = s.mpf_convert_lhs(t)
if t is NotImplemented:
return t
return t % s
def sqrt(s):
return s.context.sqrt(s)
def ae(s, t, rel_eps=None, abs_eps=None):
return s.context.almosteq(s, t, rel_eps, abs_eps)
def to_fixed(self, prec):
return to_fixed(self._mpf_, prec)
def __round__(self, *args):
return round(float(self), *args)
mpf_binary_op = """
def %NAME%(self, other):
mpf, new, (prec, rounding) = self._ctxdata
sval = self._mpf_
if hasattr(other, '_mpf_'):
tval = other._mpf_
%WITH_MPF%
ttype = type(other)
if ttype in int_types:
%WITH_INT%
elif ttype is float:
tval = from_float(other)
%WITH_MPF%
elif hasattr(other, '_mpc_'):
tval = other._mpc_
mpc = type(other)
%WITH_MPC%
elif ttype is complex:
tval = from_float(other.real), from_float(other.imag)
mpc = self.context.mpc
%WITH_MPC%
if isinstance(other, mpnumeric):
return NotImplemented
try:
other = mpf.context.convert(other, strings=False)
except TypeError:
return NotImplemented
return self.%NAME%(other)
"""
return_mpf = "; obj = new(mpf); obj._mpf_ = val; return obj"
return_mpc = "; obj = new(mpc); obj._mpc_ = val; return obj"
mpf_pow_same = """
try:
val = mpf_pow(sval, tval, prec, rounding) %s
except ComplexResult:
if mpf.context.trap_complex:
raise
mpc = mpf.context.mpc
val = mpc_pow((sval, fzero), (tval, fzero), prec, rounding) %s
""" % (return_mpf, return_mpc)
def binary_op(name, with_mpf='', with_int='', with_mpc=''):
code = mpf_binary_op
code = code.replace("%WITH_INT%", with_int)
code = code.replace("%WITH_MPC%", with_mpc)
code = code.replace("%WITH_MPF%", with_mpf)
code = code.replace("%NAME%", name)
np = {}
exec_(code, globals(), np)
return np[name]
_mpf.__eq__ = binary_op('__eq__',
'return mpf_eq(sval, tval)',
'return mpf_eq(sval, from_int(other))',
'return (tval[1] == fzero) and mpf_eq(tval[0], sval)')
_mpf.__add__ = binary_op('__add__',
'val = mpf_add(sval, tval, prec, rounding)' + return_mpf,
'val = mpf_add(sval, from_int(other), prec, rounding)' + return_mpf,
'val = mpc_add_mpf(tval, sval, prec, rounding)' + return_mpc)
_mpf.__sub__ = binary_op('__sub__',
'val = mpf_sub(sval, tval, prec, rounding)' + return_mpf,
'val = mpf_sub(sval, from_int(other), prec, rounding)' + return_mpf,
'val = mpc_sub((sval, fzero), tval, prec, rounding)' + return_mpc)
_mpf.__mul__ = binary_op('__mul__',
'val = mpf_mul(sval, tval, prec, rounding)' + return_mpf,
'val = mpf_mul_int(sval, other, prec, rounding)' + return_mpf,
'val = mpc_mul_mpf(tval, sval, prec, rounding)' + return_mpc)
_mpf.__div__ = binary_op('__div__',
'val = mpf_div(sval, tval, prec, rounding)' + return_mpf,
'val = mpf_div(sval, from_int(other), prec, rounding)' + return_mpf,
'val = mpc_mpf_div(sval, tval, prec, rounding)' + return_mpc)
_mpf.__mod__ = binary_op('__mod__',
'val = mpf_mod(sval, tval, prec, rounding)' + return_mpf,
'val = mpf_mod(sval, from_int(other), prec, rounding)' + return_mpf,
'raise NotImplementedError("complex modulo")')
_mpf.__pow__ = binary_op('__pow__',
mpf_pow_same,
'val = mpf_pow_int(sval, other, prec, rounding)' + return_mpf,
'val = mpc_pow((sval, fzero), tval, prec, rounding)' + return_mpc)
_mpf.__radd__ = _mpf.__add__
_mpf.__rmul__ = _mpf.__mul__
_mpf.__truediv__ = _mpf.__div__
_mpf.__rtruediv__ = _mpf.__rdiv__
class _constant(_mpf):
"""Represents a mathematical constant with dynamic precision.
When printed or used in an arithmetic operation, a constant
is converted to a regular mpf at the working precision. A
regular mpf can also be obtained using the operation +x."""
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