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ctx_iv.py

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+import operator
+
+from . import libmp
+
+from .libmp.backend import basestring
+
+from .libmp import (
+    int_types, MPZ_ONE,
+    prec_to_dps, dps_to_prec, repr_dps,
+    round_floor, round_ceiling,
+    fzero, finf, fninf, fnan,
+    mpf_le, mpf_neg,
+    from_int, from_float, from_str, from_rational,
+    mpi_mid, mpi_delta, mpi_str,
+    mpi_abs, mpi_pos, mpi_neg, mpi_add, mpi_sub,
+    mpi_mul, mpi_div, mpi_pow_int, mpi_pow,
+    mpi_from_str,
+    mpci_pos, mpci_neg, mpci_add, mpci_sub, mpci_mul, mpci_div, mpci_pow,
+    mpci_abs, mpci_pow, mpci_exp, mpci_log,
+    ComplexResult,
+    mpf_hash, mpc_hash)
+from .matrices.matrices import _matrix
+
+mpi_zero = (fzero, fzero)
+
+from .ctx_base import StandardBaseContext
+
+new = object.__new__
+
+def convert_mpf_(x, prec, rounding):
+    if hasattr(x, "_mpf_"): return x._mpf_
+    if isinstance(x, int_types): return from_int(x, prec, rounding)
+    if isinstance(x, float): return from_float(x, prec, rounding)
+    if isinstance(x, basestring): return from_str(x, prec, rounding)
+    raise NotImplementedError
+
+
+class ivmpf(object):
+    """
+    Interval arithmetic class. Precision is controlled by iv.prec.
+    """
+
+    def __new__(cls, x=0):
+        return cls.ctx.convert(x)
+
+    def cast(self, cls, f_convert):
+        a, b = self._mpi_
+        if a == b:
+            return cls(f_convert(a))
+        raise ValueError
+
+    def __int__(self):
+        return self.cast(int, libmp.to_int)
+
+    def __float__(self):
+        return self.cast(float, libmp.to_float)
+
+    def __complex__(self):
+        return self.cast(complex, libmp.to_float)
+
+    def __hash__(self):
+        a, b = self._mpi_
+        if a == b:
+            return mpf_hash(a)
+        else:
+            return hash(self._mpi_)
+
+    @property
+    def real(self): return self
+
+    @property
+    def imag(self): return self.ctx.zero
+
+    def conjugate(self): return self
+
+    @property
+    def a(self):
+        a, b = self._mpi_
+        return self.ctx.make_mpf((a, a))
+
+    @property
+    def b(self):
+        a, b = self._mpi_
+        return self.ctx.make_mpf((b, b))
+
+    @property
+    def mid(self):
+        ctx = self.ctx
+        v = mpi_mid(self._mpi_, ctx.prec)
+        return ctx.make_mpf((v, v))
+
+    @property
+    def delta(self):
+        ctx = self.ctx
+        v = mpi_delta(self._mpi_, ctx.prec)
+        return ctx.make_mpf((v,v))
+
+    @property
+    def _mpci_(self):
+        return self._mpi_, mpi_zero
+
+    def _compare(*args):
+        raise TypeError("no ordering relation is defined for intervals")
+
+    __gt__ = _compare
+    __le__ = _compare
+    __gt__ = _compare
+    __ge__ = _compare
+
+    def __contains__(self, t):
+        t = self.ctx.mpf(t)
+        return (self.a <= t.a) and (t.b <= self.b)
+
+    def __str__(self):
+        return mpi_str(self._mpi_, self.ctx.prec)
+
+    def __repr__(self):
+        if self.ctx.pretty:
+            return str(self)
+        a, b = self._mpi_
+        n = repr_dps(self.ctx.prec)
+        a = libmp.to_str(a, n)
+        b = libmp.to_str(b, n)
+        return "mpi(%r, %r)" % (a, b)
+
+    def _compare(s, t, cmpfun):
+        if not hasattr(t, "_mpi_"):
+            try:
+                t = s.ctx.convert(t)
+            except:
+                return NotImplemented
+        return cmpfun(s._mpi_, t._mpi_)
+
+    def __eq__(s, t): return s._compare(t, libmp.mpi_eq)
+    def __ne__(s, t): return s._compare(t, libmp.mpi_ne)
+    def __lt__(s, t): return s._compare(t, libmp.mpi_lt)
+    def __le__(s, t): return s._compare(t, libmp.mpi_le)
+    def __gt__(s, t): return s._compare(t, libmp.mpi_gt)
+    def __ge__(s, t): return s._compare(t, libmp.mpi_ge)
+
+    def __abs__(self):
+        return self.ctx.make_mpf(mpi_abs(self._mpi_, self.ctx.prec))
+    def __pos__(self):
+        return self.ctx.make_mpf(mpi_pos(self._mpi_, self.ctx.prec))
+    def __neg__(self):
+        return self.ctx.make_mpf(mpi_neg(self._mpi_, self.ctx.prec))
+
+    def ae(s, t, rel_eps=None, abs_eps=None):
+        return s.ctx.almosteq(s, t, rel_eps, abs_eps)
+
+class ivmpc(object):
+
+    def __new__(cls, re=0, im=0):
+        re = cls.ctx.convert(re)
+        im = cls.ctx.convert(im)
+        y = new(cls)
+        y._mpci_ = re._mpi_, im._mpi_
+        return y
+
+    def __hash__(self):
+        (a, b), (c,d) = self._mpci_
+        if a == b and c == d:
+            return mpc_hash((a, c))
+        else:
+            return hash(self._mpci_)
+
+    def __repr__(s):
+        if s.ctx.pretty:
+            return str(s)
+        return "iv.mpc(%s, %s)" % (repr(s.real), repr(s.imag))
+
+    def __str__(s):
+        return "(%s + %s*j)" % (str(s.real), str(s.imag))
+
+    @property
+    def a(self):
+        (a, b), (c,d) = self._mpci_
+        return self.ctx.make_mpf((a, a))
+
+    @property
+    def b(self):
+        (a, b), (c,d) = self._mpci_
+        return self.ctx.make_mpf((b, b))
+
+    @property
+    def c(self):
+        (a, b), (c,d) = self._mpci_
+        return self.ctx.make_mpf((c, c))
+
+    @property
+    def d(self):
+        (a, b), (c,d) = self._mpci_
+        return self.ctx.make_mpf((d, d))
+
+    @property
+    def real(s):
+        return s.ctx.make_mpf(s._mpci_[0])
+
+    @property
+    def imag(s):
+        return s.ctx.make_mpf(s._mpci_[1])
+
+    def conjugate(s):
+        a, b = s._mpci_
+        return s.ctx.make_mpc((a, mpf_neg(b)))
+
+    def overlap(s, t):
+        t = s.ctx.convert(t)
+        real_overlap = (s.a <= t.a <= s.b) or (s.a <= t.b <= s.b) or (t.a <= s.a <= t.b) or (t.a <= s.b <= t.b)
+        imag_overlap = (s.c <= t.c <= s.d) or (s.c <= t.d <= s.d) or (t.c <= s.c <= t.d) or (t.c <= s.d <= t.d)
+        return real_overlap and imag_overlap
+
+    def __contains__(s, t):
+        t = s.ctx.convert(t)
+        return t.real in s.real and t.imag in s.imag
+
+    def _compare(s, t, ne=False):
+        if not isinstance(t, s.ctx._types):
+            try:
+                t = s.ctx.convert(t)
+            except:
+                return NotImplemented
+        if hasattr(t, '_mpi_'):
+            tval = t._mpi_, mpi_zero
+        elif hasattr(t, '_mpci_'):
+            tval = t._mpci_
+        if ne:
+            return s._mpci_ != tval
+        return s._mpci_ == tval
+
+    def __eq__(s, t): return s._compare(t)
+    def __ne__(s, t): return s._compare(t, True)
+
+    def __lt__(s, t): raise TypeError("complex intervals cannot be ordered")
+    __le__ = __gt__ = __ge__ = __lt__
+
+    def __neg__(s): return s.ctx.make_mpc(mpci_neg(s._mpci_, s.ctx.prec))
+    def __pos__(s): return s.ctx.make_mpc(mpci_pos(s._mpci_, s.ctx.prec))
+    def __abs__(s): return s.ctx.make_mpf(mpci_abs(s._mpci_, s.ctx.prec))
+
+    def ae(s, t, rel_eps=None, abs_eps=None):
+        return s.ctx.almosteq(s, t, rel_eps, abs_eps)
+
+def _binary_op(f_real, f_complex):
+    def g_complex(ctx, sval, tval):
+        return ctx.make_mpc(f_complex(sval, tval, ctx.prec))
+    def g_real(ctx, sval, tval):
+        try:
+            return ctx.make_mpf(f_real(sval, tval, ctx.prec))
+        except ComplexResult:
+            sval = (sval, mpi_zero)
+            tval = (tval, mpi_zero)
+            return g_complex(ctx, sval, tval)
+    def lop_real(s, t):
+        if isinstance(t, _matrix): return NotImplemented
+        ctx = s.ctx
+        if not isinstance(t, ctx._types): t = ctx.convert(t)
+        if hasattr(t, "_mpi_"): return g_real(ctx, s._mpi_, t._mpi_)
+        if hasattr(t, "_mpci_"): return g_complex(ctx, (s._mpi_, mpi_zero), t._mpci_)
+        return NotImplemented
+    def rop_real(s, t):
+        ctx = s.ctx
+        if not isinstance(t, ctx._types): t = ctx.convert(t)
+        if hasattr(t, "_mpi_"): return g_real(ctx, t._mpi_, s._mpi_)
+        if hasattr(t, "_mpci_"): return g_complex(ctx, t._mpci_, (s._mpi_, mpi_zero))
+        return NotImplemented
+    def lop_complex(s, t):
+        if isinstance(t, _matrix): return NotImplemented
+        ctx = s.ctx
+        if not isinstance(t, s.ctx._types):
+            try:
+                t = s.ctx.convert(t)
+            except (ValueError, TypeError):
+                return NotImplemented
+        return g_complex(ctx, s._mpci_, t._mpci_)
+    def rop_complex(s, t):
+        ctx = s.ctx
+        if not isinstance(t, s.ctx._types):
+            t = s.ctx.convert(t)
+        return g_complex(ctx, t._mpci_, s._mpci_)
+    return lop_real, rop_real, lop_complex, rop_complex
+
+ivmpf.__add__, ivmpf.__radd__, ivmpc.__add__, ivmpc.__radd__ = _binary_op(mpi_add, mpci_add)
+ivmpf.__sub__, ivmpf.__rsub__, ivmpc.__sub__, ivmpc.__rsub__ = _binary_op(mpi_sub, mpci_sub)
+ivmpf.__mul__, ivmpf.__rmul__, ivmpc.__mul__, ivmpc.__rmul__ = _binary_op(mpi_mul, mpci_mul)
+ivmpf.__div__, ivmpf.__rdiv__, ivmpc.__div__, ivmpc.__rdiv__ = _binary_op(mpi_div, mpci_div)
+ivmpf.__pow__, ivmpf.__rpow__, ivmpc.__pow__, ivmpc.__rpow__ = _binary_op(mpi_pow, mpci_pow)
+
+ivmpf.__truediv__ = ivmpf.__div__; ivmpf.__rtruediv__ = ivmpf.__rdiv__
+ivmpc.__truediv__ = ivmpc.__div__; ivmpc.__rtruediv__ = ivmpc.__rdiv__
+
+class ivmpf_constant(ivmpf):
+    def __new__(cls, f):
+        self = new(cls)
+        self._f = f
+        return self
+    def _get_mpi_(self):
+        prec = self.ctx._prec[0]
+        a = self._f(prec, round_floor)
+        b = self._f(prec, round_ceiling)
+        return a, b
+    _mpi_ = property(_get_mpi_)
+
+class MPIntervalContext(StandardBaseContext):
+
+    def __init__(ctx):
+        ctx.mpf = type('ivmpf', (ivmpf,), {})
+        ctx.mpc = type('ivmpc', (ivmpc,), {})
+        ctx._types = (ctx.mpf, ctx.mpc)
+        ctx._constant = type('ivmpf_constant', (ivmpf_constant,), {})
+        ctx._prec = [53]
+        ctx._set_prec(53)
+        ctx._constant._ctxdata = ctx.mpf._ctxdata = ctx.mpc._ctxdata = [ctx.mpf, new, ctx._prec]
+        ctx._constant.ctx = ctx.mpf.ctx = ctx.mpc.ctx = ctx
+        ctx.pretty = False
+        StandardBaseContext.__init__(ctx)
+        ctx._init_builtins()
+
+    def _mpi(ctx, a, b=None):
+        if b is None:
+            return ctx.mpf(a)
+        return ctx.mpf((a,b))
+
+    def _init_builtins(ctx):
+        ctx.one = ctx.mpf(1)
+        ctx.zero = ctx.mpf(0)
+        ctx.inf = ctx.mpf('inf')
+        ctx.ninf = -ctx.inf
+        ctx.nan = ctx.mpf('nan')
+        ctx.j = ctx.mpc(0,1)
+        ctx.exp = ctx._wrap_mpi_function(libmp.mpi_exp, libmp.mpci_exp)
+        ctx.sqrt = ctx._wrap_mpi_function(libmp.mpi_sqrt)
+        ctx.ln = ctx._wrap_mpi_function(libmp.mpi_log, libmp.mpci_log)
+        ctx.cos = ctx._wrap_mpi_function(libmp.mpi_cos, libmp.mpci_cos)
+        ctx.sin = ctx._wrap_mpi_function(libmp.mpi_sin, libmp.mpci_sin)
+        ctx.tan = ctx._wrap_mpi_function(libmp.mpi_tan)
+        ctx.gamma = ctx._wrap_mpi_function(libmp.mpi_gamma, libmp.mpci_gamma)
+        ctx.loggamma = ctx._wrap_mpi_function(libmp.mpi_loggamma, libmp.mpci_loggamma)
+        ctx.rgamma = ctx._wrap_mpi_function(libmp.mpi_rgamma, libmp.mpci_rgamma)
+        ctx.factorial = ctx._wrap_mpi_function(libmp.mpi_factorial, libmp.mpci_factorial)
+        ctx.fac = ctx.factorial
+
+        ctx.eps = ctx._constant(lambda prec, rnd: (0, MPZ_ONE, 1-prec, 1))
+        ctx.pi = ctx._constant(libmp.mpf_pi)
+        ctx.e = ctx._constant(libmp.mpf_e)
+        ctx.ln2 = ctx._constant(libmp.mpf_ln2)
+        ctx.ln10 = ctx._constant(libmp.mpf_ln10)
+        ctx.phi = ctx._constant(libmp.mpf_phi)
+        ctx.euler = ctx._constant(libmp.mpf_euler)
+        ctx.catalan = ctx._constant(libmp.mpf_catalan)
+        ctx.glaisher = ctx._constant(libmp.mpf_glaisher)
+        ctx.khinchin = ctx._constant(libmp.mpf_khinchin)
+        ctx.twinprime = ctx._constant(libmp.mpf_twinprime)
+
+    def _wrap_mpi_function(ctx, f_real, f_complex=None):
+        def g(x, **kwargs):
+            if kwargs:
+                prec = kwargs.get('prec', ctx._prec[0])
+            else:
+                prec = ctx._prec[0]
+            x = ctx.convert(x)
+            if hasattr(x, "_mpi_"):
+                return ctx.make_mpf(f_real(x._mpi_, prec))
+            if hasattr(x, "_mpci_"):
+                return ctx.make_mpc(f_complex(x._mpci_, prec))
+            raise ValueError
+        return g
+
+    @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
+        setattr(cls, name, f_wrapped)
+
+    def _set_prec(ctx, n):
+        ctx._prec[0] = max(1, int(n))
+        ctx._dps = prec_to_dps(n)
+
+    def _set_dps(ctx, n):
+        ctx._prec[0] = dps_to_prec(n)
+        ctx._dps = max(1, int(n))
+
+    prec = property(lambda ctx: ctx._prec[0], _set_prec)
+    dps = property(lambda ctx: ctx._dps, _set_dps)
+
+    def make_mpf(ctx, v):
+        a = new(ctx.mpf)
+        a._mpi_ = v
+        return a
+
+    def make_mpc(ctx, v):
+        a = new(ctx.mpc)
+        a._mpci_ = v
+        return a
+
+    def _mpq(ctx, pq):
+        p, q = pq
+        a = libmp.from_rational(p, q, ctx.prec, round_floor)
+        b = libmp.from_rational(p, q, ctx.prec, round_ceiling)
+        return ctx.make_mpf((a, b))
+
+    def convert(ctx, x):
+        if isinstance(x, (ctx.mpf, ctx.mpc)):
+            return x
+        if isinstance(x, ctx._constant):
+            return +x
+        if isinstance(x, complex) or hasattr(x, "_mpc_"):
+            re = ctx.convert(x.real)
+            im = ctx.convert(x.imag)
+            return ctx.mpc(re,im)
+        if isinstance(x, basestring):
+            v = mpi_from_str(x, ctx.prec)
+            return ctx.make_mpf(v)
+        if hasattr(x, "_mpi_"):
+            a, b = x._mpi_
+        else:
+            try:
+                a, b = x
+            except (TypeError, ValueError):
+                a = b = x
+            if hasattr(a, "_mpi_"):
+                a = a._mpi_[0]
+            else:
+                a = convert_mpf_(a, ctx.prec, round_floor)
+            if hasattr(b, "_mpi_"):
+                b = b._mpi_[1]
+            else:
+                b = convert_mpf_(b, ctx.prec, round_ceiling)
+        if a == fnan or b == fnan:
+            a = fninf
+            b = finf
+        assert mpf_le(a, b), "endpoints must be properly ordered"
+        return ctx.make_mpf((a, b))
+
+    def nstr(ctx, x, n=5, **kwargs):
+        x = ctx.convert(x)
+        if hasattr(x, "_mpi_"):
+            return libmp.mpi_to_str(x._mpi_, n, **kwargs)
+        if hasattr(x, "_mpci_"):
+            re = libmp.mpi_to_str(x._mpci_[0], n, **kwargs)
+            im = libmp.mpi_to_str(x._mpci_[1], n, **kwargs)
+            return "(%s + %s*j)" % (re, im)
+
+    def mag(ctx, x):
+        x = ctx.convert(x)
+        if isinstance(x, ctx.mpc):
+            return max(ctx.mag(x.real), ctx.mag(x.imag)) + 1
+        a, b = libmp.mpi_abs(x._mpi_)
+        sign, man, exp, bc = b
+        if man:
+            return exp+bc
+        if b == fzero:
+            return ctx.ninf
+        if b == fnan:
+            return ctx.nan
+        return ctx.inf
+
+    def isnan(ctx, x):
+        return False
+
+    def isinf(ctx, x):
+        return x == ctx.inf
+
+    def isint(ctx, x):
+        x = ctx.convert(x)
+        a, b = x._mpi_
+        if a == b:
+            sign, man, exp, bc = a
+            if man:
+                return exp >= 0
+            return a == fzero
+        return None
+
+    def ldexp(ctx, x, n):
+        a, b = ctx.convert(x)._mpi_
+        a = libmp.mpf_shift(a, n)
+        b = libmp.mpf_shift(b, n)
+        return ctx.make_mpf((a,b))
+
+    def absmin(ctx, x):
+        return abs(ctx.convert(x)).a
+
+    def absmax(ctx, x):
+        return abs(ctx.convert(x)).b
+
+    def atan2(ctx, y, x):
+        y = ctx.convert(y)._mpi_
+        x = ctx.convert(x)._mpi_
+        return ctx.make_mpf(libmp.mpi_atan2(y,x,ctx.prec))
+
+    def _convert_param(ctx, x):
+        if isinstance(x, libmp.int_types):
+            return x, 'Z'
+        if isinstance(x, tuple):
+            p, q = x
+            return (ctx.mpf(p) / ctx.mpf(q), 'R')
+        x = ctx.convert(x)
+        if isinstance(x, ctx.mpf):
+            return x, 'R'
+        if isinstance(x, ctx.mpc):
+            return x, 'C'
+        raise ValueError
+
+    def _is_real_type(ctx, z):
+        return isinstance(z, ctx.mpf) or isinstance(z, int_types)
+
+    def _is_complex_type(ctx, z):
+        return isinstance(z, ctx.mpc)
+
+    def hypsum(ctx, p, q, types, coeffs, z, maxterms=6000, **kwargs):
+        coeffs = list(coeffs)
+        num = range(p)
+        den = range(p,p+q)
+        #tol = ctx.eps
+        s = t = ctx.one
+        k = 0
+        while 1:
+            for i in num: t *= (coeffs[i]+k)
+            for i in den: t /= (coeffs[i]+k)
+            k += 1; t /= k; t *= z; s += t
+            if t == 0:
+                return s
+            #if abs(t) < tol:
+            #    return s
+            if k > maxterms:
+                raise ctx.NoConvergence
+
+
+# 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(ivmpc)
+    numbers.Real.register(ivmpf)
+except ImportError:
+    pass