"""
mpmath floating-point numbers

Implements mpf and mpc types, with binary operations and support
for interaction with other types. Also implements the main
context class, and related utilities.
"""

#*****************************************************************************
# This program is free software: you can redistribute it and/or modify
# it under the terms of the GNU General Public License as published by
# the Free Software Foundation, either version 2 of the License, or
# (at your option) any later version.
#                  http://www.gnu.org/licenses/
#*****************************************************************************

from cpython.long cimport *
from cpython.float cimport *
from cpython.complex cimport *
from cpython.number cimport *

from cysignals.signals cimport sig_on, sig_off

from sage.ext.stdsage cimport PY_NEW

from sage.libs.gmp.all cimport *
from sage.rings.integer cimport Integer

DEF ROUND_N = 0
DEF ROUND_F = 1
DEF ROUND_C = 2
DEF ROUND_D = 3
DEF ROUND_U = 4
DEF S_NORMAL = 0
DEF S_ZERO = 1
DEF S_NZERO = 2
DEF S_INF = 3
DEF S_NINF = 4
DEF S_NAN = 5

from .ext_impl cimport *

import mpmath.rational as rationallib
import mpmath.libmp as libmp
import mpmath.function_docs as function_docs
from mpmath.libmp import to_str
from mpmath.libmp import repr_dps, prec_to_dps, dps_to_prec

DEF OP_ADD = 0
DEF OP_SUB = 1
DEF OP_MUL = 2
DEF OP_DIV = 3
DEF OP_POW = 4
DEF OP_MOD = 5
DEF OP_RICHCMP = 6
DEF OP_EQ = (OP_RICHCMP + 2)
DEF OP_NE = (OP_RICHCMP + 3)
DEF OP_LT = (OP_RICHCMP + 0)
DEF OP_GT = (OP_RICHCMP + 4)
DEF OP_LE = (OP_RICHCMP + 1)
DEF OP_GE = (OP_RICHCMP + 5)

cdef MPopts opts_exact
cdef MPopts opts_double_precision
cdef MPopts opts_mini_prec

opts_exact.prec = 0
opts_exact.rounding = ROUND_N
opts_double_precision.prec = 53
opts_double_precision.rounding = ROUND_N
opts_mini_prec.prec = 5
opts_mini_prec.rounding = ROUND_D

cdef MPF MPF_C_0
cdef MPF MPF_C_1
cdef MPF MPF_C_2

MPF_init(&MPF_C_0)
MPF_set_zero(&MPF_C_0)
MPF_init(&MPF_C_1)
MPF_set_si(&MPF_C_1, 1)
MPF_init(&MPF_C_2)
MPF_set_si(&MPF_C_2, 2)

# Temporaries used for operands in binary operations
cdef mpz_t tmp_mpz
mpz_init(tmp_mpz)

cdef MPF tmp1
cdef MPF tmp2
cdef MPF tmp_opx_re
cdef MPF tmp_opx_im
cdef MPF tmp_opy_re
cdef MPF tmp_opy_im

MPF_init(&tmp1)
MPF_init(&tmp2)
MPF_init(&tmp_opx_re)
MPF_init(&tmp_opx_im)
MPF_init(&tmp_opy_re)
MPF_init(&tmp_opy_im)

cdef class Context
cdef class mpnumber
cdef class mpf_base
cdef class mpf
cdef class mpc
cdef class constant
cdef class wrapped_libmp_function
cdef class wrapped_specfun

cdef __isint(MPF *v):
    return v.special == S_ZERO or (v.special == S_NORMAL and mpz_sgn(v.exp) >= 0)

cdef int MPF_set_any(MPF *re, MPF *im, x, MPopts opts, bint str_tuple_ok) except -1:
    """
    Sets re + im*i = x, where x is any Python number.

    Returns 0 if unable to coerce x; 1 if x is real and re was set;
    2 if x is complex and both re and im were set.

    If str_tuple_ok=True, strings and tuples are accepted and converted
    (useful for parsing arguments, but not for arithmetic operands).
    """
    if isinstance(x, mpf):
        MPF_set(re, &(<mpf>x).value)
        return 1
    if isinstance(x, mpc):
        MPF_set(re, &(<mpc>x).re)
        MPF_set(im, &(<mpc>x).im)
        return 2
    if isinstance(x, (int, Integer)):
        MPF_set_int(re, x)
        return 1
    if isinstance(x, float):
        MPF_set_double(re, x)
        return 1
    if isinstance(x, complex):
        MPF_set_double(re, x.real)
        MPF_set_double(im, x.imag)
        return 2
    if isinstance(x, constant):
        MPF_set_tuple(re, x.func(opts.prec, rndmode_to_python(opts.rounding)))
        return 1
    if hasattr(x, "_mpf_"):
        MPF_set_tuple(re, x._mpf_)
        return 1
    if hasattr(x, "_mpc_"):
        r, i = x._mpc_
        MPF_set_tuple(re, r)
        MPF_set_tuple(im, i)
        return 2
    if hasattr(x, "_mpmath_"):
        return MPF_set_any(re, im, x._mpmath_(opts.prec,
            rndmode_to_python(opts.rounding)), opts, False)
    if isinstance(x, rationallib.mpq):
        p, q = x._mpq_
        MPF_set_int(re, p)
        MPF_set_int(im, q)
        MPF_div(re, re, im, opts)
        #MPF_set_tuple(re, libmp.from_rational(p, q, opts.prec,
        #    rndmode_to_python(opts.rounding)))
        return 1
    if hasattr(x, '_mpi_'):
        a, b = x._mpi_
        if a == b:
            MPF_set_tuple(re, a)
            return 1
        raise ValueError("can only create mpf from zero-width interval")
    if str_tuple_ok:
        if isinstance(x, tuple):
            if len(x) == 2:
                MPF_set_man_exp(re, x[0], x[1])
                return 1
            elif len(x) == 4:
                MPF_set_tuple(re, x)
                return 1
        if isinstance(x, str):
            try:
                st = libmp.from_str(x, opts.prec,
                    rndmode_to_python(opts.rounding))
            except ValueError:
                return 0
            MPF_set_tuple(re, st)
            return 1
    return 0

cdef binop(int op, x, y, MPopts opts):
    cdef int typx
    cdef int typy
    cdef MPF xre, xim, yre, yim
    cdef mpf rr
    cdef mpc rc
    cdef MPopts altopts

    if isinstance(x, mpf):
        xre = (<mpf>x).value
        typx = 1
    elif isinstance(x, mpc):
        xre = (<mpc>x).re
        xim = (<mpc>x).im
        typx = 2
    else:
        typx = MPF_set_any(&tmp_opx_re, &tmp_opx_im, x, opts, False)
        if typx == 0:
            return NotImplemented
        xre = tmp_opx_re
        xim = tmp_opx_im

    if isinstance(y, mpf):
        yre = (<mpf>y).value
        typy = 1
    elif isinstance(y, mpc):
        yre = (<mpc>y).re
        yim = (<mpc>y).im
        typy = 2
    else:
        typy = MPF_set_any(&tmp_opy_re, &tmp_opy_im, y, opts, False)
        if typy == 0:
            return NotImplemented
        yre = tmp_opy_re
        yim = tmp_opy_im

    if op == OP_ADD:
        if typx == 1 and typy == 1:
            # Real result
            rr = mpf.__new__(mpf)
            MPF_add(&rr.value, &xre, &yre, opts)
            return rr
        else:
            # Complex result
            rc = mpc.__new__(mpc)
            MPF_add(&rc.re, &xre, &yre, opts)
            if typx == 1:
                MPF_set(&rc.im, &yim)
                #MPF_normalize(&rc.im, opts)
            elif typy == 1:
                MPF_set(&rc.im, &xim)
                #MPF_normalize(&rc.im, opts)
            else:
                MPF_add(&rc.im, &xim, &yim, opts)
            return rc

    elif op == OP_SUB:
        if typx == 1 and typy == 1:
            # Real result
            rr = mpf.__new__(mpf)
            MPF_sub(&rr.value, &xre, &yre, opts)
            return rr
        else:
            # Complex result
            rc = mpc.__new__(mpc)
            MPF_sub(&rc.re, &xre, &yre, opts)
            if typx == 1:
                MPF_neg(&rc.im, &yim)
                MPF_normalize(&rc.im, opts)
            elif typy == 1:
                MPF_set(&rc.im, &xim)
                MPF_normalize(&rc.im, opts)
            else:
                MPF_sub(&rc.im, &xim, &yim, opts)
            return rc

    elif op == OP_MUL:
        if typx == 1 and typy == 1:
            # Real result
            rr = mpf.__new__(mpf)
            MPF_mul(&rr.value, &xre, &yre, opts)
            return rr
        else:
            # Complex result
            rc = mpc.__new__(mpc)
            if typx == 1:
                MPF_mul(&rc.re, &yre, &xre, opts)
                MPF_mul(&rc.im, &yim, &xre, opts)
            elif typy == 1:
                MPF_mul(&rc.re, &xre, &yre, opts)
                MPF_mul(&rc.im, &xim, &yre, opts)
            else:
                # a*c - b*d
                MPF_mul(&rc.re, &xre,   &yre,  opts_exact)
                MPF_mul(&tmp1,  &xim,   &yim,  opts_exact)
                MPF_sub(&rc.re, &rc.re, &tmp1, opts)
                # a*d + b*c
                MPF_mul(&rc.im, &xre,   &yim,  opts_exact)
                MPF_mul(&tmp1,  &xim,   &yre,  opts_exact)
                MPF_add(&rc.im, &rc.im, &tmp1, opts)
            return rc


    elif op == OP_DIV:
        if typx == 1 and typy == 1:
            # Real result
            rr = mpf.__new__(mpf)
            MPF_div(&rr.value, &xre, &yre, opts)
            return rr
        else:
            rc = mpc.__new__(mpc)
            if typy == 1:
                MPF_div(&rc.re, &xre, &yre, opts)
                MPF_div(&rc.im, &xim, &yre, opts)
            else:
                if typx == 1:
                    xim = MPF_C_0
                altopts = opts
                altopts.prec += 10
                # m = c*c + d*d
                MPF_mul(&tmp1, &yre,  &yre, opts_exact)
                MPF_mul(&tmp2, &yim,  &yim, opts_exact)
                MPF_add(&tmp1, &tmp1, &tmp2, altopts)
                # (a*c+b*d)/m
                MPF_mul(&rc.re, &xre,   &yre, opts_exact)
                MPF_mul(&tmp2,  &xim,   &yim, opts_exact)
                MPF_add(&rc.re, &rc.re, &tmp2, altopts)
                MPF_div(&rc.re, &rc.re, &tmp1, opts)
                # (b*c-a*d)/m
                MPF_mul(&rc.im, &xim,   &yre, opts_exact)
                MPF_mul(&tmp2,  &xre,   &yim, opts_exact)
                MPF_sub(&rc.im, &rc.im, &tmp2, altopts)
                MPF_div(&rc.im, &rc.im, &tmp1, opts)
            return rc

    elif op == OP_POW:
        if typx == 1 and typy == 1:
            rr = mpf.__new__(mpf)
            if not MPF_pow(&rr.value, &xre, &yre, opts):
                return rr
        if typx == 1: xim = MPF_C_0
        if typy == 1: yim = MPF_C_0
        rc = mpc.__new__(mpc)
        MPF_complex_pow(&rc.re, &rc.im, &xre, &xim, &yre, &yim, opts)
        return rc

    elif op == OP_MOD:
        if typx != 1 or typx != 1:
            raise TypeError("mod for complex numbers")
        xret = MPF_to_tuple(&xre)
        yret = MPF_to_tuple(&yre)
        v = libmp.mpf_mod(xret, yret, opts.prec, rndmode_to_python(opts.rounding))
        rr = mpf.__new__(mpf)
        MPF_set_tuple(&rr.value, v)
        return rr

    elif op == OP_EQ:
        if typx == 1 and typy == 1:
            return MPF_eq(&xre, &yre)
        if typx == 1:
            return MPF_eq(&xre, &yre) and MPF_eq(&yim, &MPF_C_0)
        if typy == 1:
            return MPF_eq(&xre, &yre) and MPF_eq(&xim, &MPF_C_0)
        return MPF_eq(&xre, &yre) and MPF_eq(&xim, &yim)

    elif op == OP_NE:
        if typx == 1 and typy == 1:
            return MPF_ne(&xre, &yre)
        if typx == 1:
            return MPF_ne(&xre, &yre) or MPF_ne(&yim, &MPF_C_0)
        if typy == 1:
            return MPF_ne(&xre, &yre) or MPF_ne(&xim, &MPF_C_0)
        return MPF_ne(&xre, &yre) or MPF_ne(&xim, &yim)

    elif op == OP_LT:
        if typx != 1 or typy != 1:
            raise ValueError("cannot compare complex numbers")
        return MPF_lt(&xre, &yre)

    elif op == OP_GT:
        if typx != 1 or typy != 1:
            raise ValueError("cannot compare complex numbers")
        return MPF_gt(&xre, &yre)

    elif op == OP_LE:
        if typx != 1 or typy != 1:
            raise ValueError("cannot compare complex numbers")
        return MPF_le(&xre, &yre)

    elif op == OP_GE:
        if typx != 1 or typy != 1:
            raise ValueError("cannot compare complex numbers")
        return MPF_ge(&xre, &yre)

    return NotImplemented


cdef MPopts global_opts

global_context = None

cdef class Context:
    cdef public mpf, mpc, constant #, def_mp_function
    cdef public trap_complex
    cdef public pretty

    def __cinit__(ctx):
        """
        At present, only a single global context should exist ::

            sage: from mpmath import mp
            sage: type(mp)
            <class 'mpmath.ctx_mp.MPContext'>
        """
        global global_opts, global_context
        global_opts = opts_double_precision
        global_context = ctx
        ctx.mpf = mpf
        ctx.mpc = mpc
        ctx.constant = constant
        #ctx.def_mp_function = def_mp_function
        ctx._mpq = rationallib.mpq

    def default(ctx):
        """
        Sets defaults.

        TESTS ::

            sage: import mpmath
            sage: mpmath.mp.prec = 100
            sage: mpmath.mp.default()
            sage: mpmath.mp.prec
            53
        """
        global global_opts
        global_opts = opts_double_precision
        ctx.trap_complex = False
        ctx.pretty = False

    def _get_prec(ctx):
        """
        Controls the working precision in bits ::

            sage: from mpmath import mp
            sage: mp.prec = 100
            sage: mp.prec
            100
            sage: mp.dps
            29
            sage: mp.prec = 53
        """
        return global_opts.prec

    def _set_prec(ctx, prec):
        """
        Controls the working precision in bits ::

            sage: from mpmath import mp
            sage: mp.prec = 100
            sage: mp.prec
            100
            sage: mp.dps
            29
            sage: mp.prec = 53
        """
        global_opts.prec = prec

    def _set_dps(ctx, n):
        """
        Controls the working precision in decimal digits ::

            sage: from mpmath import mp
            sage: mp.dps = 100
            sage: mp.prec
            336
            sage: mp.dps
            100
            sage: mp.prec = 53
        """
        global_opts.prec = dps_to_prec(int(n))

    def _get_dps(ctx):
        """
        Controls the working precision in decimal digits ::

            sage: from mpmath import mp
            sage: mp.dps = 100
            sage: mp.prec
            336
            sage: mp.dps
            100
            sage: mp.prec = 53
        """
        return prec_to_dps(global_opts.prec)

    dps = property(_get_dps, _set_dps, doc=_get_dps.__doc__)
    prec = property(_get_prec, _set_prec, doc=_get_dps.__doc__)
    _dps = property(_get_dps, _set_dps, doc=_get_dps.__doc__)
    _prec = property(_get_prec, _set_prec, doc=_get_dps.__doc__)

    def _get_prec_rounding(ctx):
        """
        Returns the precision and rounding mode ::

            sage: from mpmath import mp
            sage: mp._get_prec_rounding()
            (53, 'n')
        """
        return global_opts.prec, rndmode_to_python(global_opts.rounding)

    _prec_rounding = property(_get_prec_rounding)

    cpdef mpf make_mpf(ctx, tuple v):
        """
        Creates an mpf from tuple data ::

            sage: import mpmath
            sage: float(mpmath.mp.make_mpf((0,1,-1,1)))
            0.5
        """
        cdef mpf x
        x = mpf.__new__(mpf)
        MPF_set_tuple(&x.value, v)
        return x

    cpdef mpc make_mpc(ctx, tuple v):
        """
        Creates an mpc from tuple data ::

            sage: import mpmath
            sage: complex(mpmath.mp.make_mpc(((0,1,-1,1), (1,1,-2,1))))
            (0.5-0.25j)
        """
        cdef mpc x
        x = mpc.__new__(mpc)
        MPF_set_tuple(&x.re, v[0])
        MPF_set_tuple(&x.im, v[1])
        return x

    def convert(ctx, x, strings=True):
        """
        Converts *x* to an ``mpf``, ``mpc`` or ``mpi``. 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.

        TESTS ::

            sage: from mpmath import mp, convert
            sage: mp.dps = 15; mp.pretty = False
            sage: convert(3.5)
            mpf('3.5')
            sage: convert('2.1')
            mpf('2.1000000000000001')
            sage: convert('3/4')
            mpf('0.75')
            sage: convert('2+3j')
            mpc(real='2.0', imag='3.0')

        """
        cdef mpf rr
        cdef mpc rc
        if isinstance(x, mpnumber):
            return x
        typx = MPF_set_any(&tmp_opx_re, &tmp_opx_im, x, global_opts, strings)
        if typx == 1:
            rr = mpf.__new__(mpf)
            MPF_set(&rr.value, &tmp_opx_re)
            return rr
        if typx == 2:
            rc = mpc.__new__(mpc)
            MPF_set(&rc.re, &tmp_opx_re)
            MPF_set(&rc.im, &tmp_opx_im)
            return rc
        return ctx._convert_fallback(x, strings)

    def isnan(ctx, x):
        """
        For an ``mpf`` *x*, determines whether *x* is not-a-number (nan).

        TESTS::

            sage: from mpmath import isnan, nan
            sage: isnan(nan), isnan(3)
            (True, False)
        """
        cdef int s, t, typ
        if isinstance(x, mpf):
            return (<mpf>x).value.special == S_NAN
        if isinstance(x, mpc):
            s = (<mpc>x).re.special
            t = (<mpc>x).im.special
            return s == S_NAN or t == S_NAN
        if type(x) is int or type(x) is long or isinstance(x, Integer) \
            or isinstance(x, rationallib.mpq):
            return False
        typ = MPF_set_any(&tmp_opx_re, &tmp_opx_im, x, global_opts, 0)
        if typ == 1:
            s = tmp_opx_re.special
            return s == S_NAN
        if typ == 2:
            s = tmp_opx_re.special
            t = tmp_opx_im.special
            return s == S_NAN or t == S_NAN
        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*.

        TESTS::

            sage: from mpmath import isinf, inf, mpc
            sage: isinf(inf)
            True
            sage: isinf(-inf)
            True
            sage: isinf(3)
            False
            sage: isinf(3+4j)
            False
            sage: isinf(mpc(3,inf))
            True
            sage: isinf(mpc(inf,3))
            True

        """
        cdef int s, t, typ
        if isinstance(x, mpf):
            s = (<mpf>x).value.special
            return s == S_INF or s == S_NINF
        if isinstance(x, mpc):
            s = (<mpc>x).re.special
            t = (<mpc>x).im.special
            return s == S_INF or s == S_NINF or t == S_INF or t == S_NINF
        if type(x) is int or type(x) is long or isinstance(x, Integer) \
            or isinstance(x, rationallib.mpq):
            return False
        typ = MPF_set_any(&tmp_opx_re, &tmp_opx_im, x, global_opts, 0)
        if typ == 1:
            s = tmp_opx_re.special
            return s == S_INF or s == S_NINF
        if typ == 2:
            s = tmp_opx_re.special
            t = tmp_opx_im.special
            return s == S_INF or s == S_NINF or t == S_INF or t == S_NINF
        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.

        TESTS ::

            sage: from mpmath import isnormal, inf, nan, mpc
            sage: isnormal(3)
            True
            sage: isnormal(0)
            False
            sage: isnormal(inf); isnormal(-inf); isnormal(nan)
            False
            False
            False
            sage: isnormal(0+0j)
            False
            sage: isnormal(0+3j)
            True
            sage: isnormal(mpc(2,nan))
            False
        """
        # TODO: optimize this
        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 == libmp.fzero: return im_normal
            if im == libmp.fzero: return re_normal
            return re_normal and im_normal
        if type(x) is int or type(x) is long or isinstance(x, Integer) \
            or isinstance(x, rationallib.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*.

        TESTS ::

            sage: from mpmath import isint, mpf, inf
            sage: isint(3)
            True
            sage: isint(mpf(3))
            True
            sage: isint(3.2)
            False
            sage: isint(inf)
            False

        Optionally, Gaussian integers can be checked for::

            sage: isint(3+0j)
            True
            sage: isint(3+2j)
            False
            sage: isint(3+2j, gaussian=True)
            True

        """
        cdef MPF v
        cdef MPF w
        cdef int typ
        if type(x) is int or type(x) is long or isinstance(x, Integer):
            return True
        if isinstance(x, mpf):
            v = (<mpf>x).value
            return __isint(&v)
        if isinstance(x, mpc):
            v = (<mpc>x).re
            w = (<mpc>x).im
            if gaussian:
                return __isint(&v) and __isint(&w)
            return (w.special == S_ZERO) and __isint(&v)
        if isinstance(x, rationallib.mpq):
            p, q = x._mpq_
            return not (p % q)
        typ = MPF_set_any(&tmp_opx_re, &tmp_opx_im, x, global_opts, 0)
        if typ == 1:
            return __isint(&tmp_opx_re)
        if typ == 2:
            v = tmp_opx_re
            w = tmp_opx_im
            if gaussian:
                return __isint(&v) and __isint(&w)
            return (w.special == S_ZERO) and __isint(&v)
        raise TypeError("isint() needs a number as input")

    def fsum(ctx, terms, bint absolute=False, bint squared=False):
        """
        Calculates a sum containing a finite number of terms (for infinite
        series, see :func:`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`.

        TESTS ::

            sage: from mpmath import mp, fsum
            sage: mp.dps = 15; mp.pretty = False
            sage: 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.
        """
        cdef MPF sre, sim, tre, tim, tmp
        cdef mpf rr
        cdef mpc rc
        cdef MPopts workopts
        cdef int styp, ttyp
        workopts = global_opts
        workopts.prec = workopts.prec * 2 + 50
        workopts.rounding = ROUND_D
        unknown = global_context.zero
        sig_on()
        try:  # Way down, there is a ``finally`` with sig_off()
            MPF_init(&sre)
            MPF_init(&sim)
            MPF_init(&tre)
            MPF_init(&tim)
            MPF_init(&tmp)
            styp = 1
            for term in terms:
                ttyp = MPF_set_any(&tre, &tim, term, workopts, 0)
                if ttyp == 0:
                    if absolute: term = ctx.absmax(term)
                    if squared: term = term**2
                    unknown += term
                    continue
                if absolute:
                    if squared:
                        if ttyp == 1:
                            MPF_mul(&tre, &tre, &tre, opts_exact)
                            MPF_add(&sre, &sre, &tre, workopts)
                        elif ttyp == 2:
                            # |(a+bi)^2| = a^2+b^2
                            MPF_mul(&tre, &tre, &tre, opts_exact)
                            MPF_add(&sre, &sre, &tre, workopts)
                            MPF_mul(&tim, &tim, &tim, opts_exact)
                            MPF_add(&sre, &sre, &tim, workopts)
                    else:
                        if ttyp == 1:
                            MPF_abs(&tre, &tre)
                            MPF_add(&sre, &sre, &tre, workopts)
                        elif ttyp == 2:
                            # |a+bi| = sqrt(a^2+b^2)
                            MPF_mul(&tre, &tre, &tre, opts_exact)
                            MPF_mul(&tim, &tim, &tim, opts_exact)
                            MPF_add(&tre, &tre, &tim, workopts)
                            MPF_sqrt(&tre, &tre, workopts)
                            MPF_add(&sre, &sre, &tre, workopts)
                elif squared:
                    if ttyp == 1:
                        MPF_mul(&tre, &tre, &tre, opts_exact)
                        MPF_add(&sre, &sre, &tre, workopts)
                    elif ttyp == 2:
                        # (a+bi)^2 = a^2-b^2 + 2i*ab
                        MPF_mul(&tmp, &tre, &tim, opts_exact)
                        MPF_mul(&tmp, &tmp, &MPF_C_2, opts_exact)
                        MPF_add(&sim, &sim, &tmp, workopts)
                        MPF_mul(&tre, &tre, &tre, opts_exact)
                        MPF_add(&sre, &sre, &tre, workopts)
                        MPF_mul(&tim, &tim, &tim, opts_exact)
                        MPF_sub(&sre, &sre, &tim, workopts)
                        styp = 2
                else:
                    if ttyp == 1:
                        MPF_add(&sre, &sre, &tre, workopts)
                    elif ttyp == 2:
                        MPF_add(&sre, &sre, &tre, workopts)
                        MPF_add(&sim, &sim, &tim, workopts)
                        styp = 2
            MPF_clear(&tre)
            MPF_clear(&tim)
            if styp == 1:
                rr = mpf.__new__(mpf)
                MPF_set(&rr.value, &sre)
                MPF_clear(&sre)
                MPF_clear(&sim)
                MPF_normalize(&rr.value, global_opts)
                if unknown is not global_context.zero:
                    return ctx._stupid_add(rr, unknown)
                return rr
            elif styp == 2:
                rc = mpc.__new__(mpc)
                MPF_set(&rc.re, &sre)
                MPF_set(&rc.im, &sim)
                MPF_clear(&sre)
                MPF_clear(&sim)
                MPF_normalize(&rc.re, global_opts)
                MPF_normalize(&rc.im, global_opts)
                if unknown is not global_context.zero:
                    return ctx._stupid_add(rc, unknown)
                return rc
            else:
                MPF_clear(&sre)
                MPF_clear(&sim)
                return +unknown
        finally:
            sig_off()

    def fdot(ctx, A, B=None, bint conjugate=False):
        r"""
        Compute the dot product of the iterables `A` and `B`,

        .. MATH::

            \sum_{k=0} A_k B_k.

        Alternatively, :func:`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.

        TESTS::

            sage: from mpmath import mp, fdot
            sage: mp.dps = 15; mp.pretty = False
            sage: A = [2, 1.5r, 3]
            sage: B = [1, -1, 2]
            sage: fdot(A, B)
            mpf('6.5')
            sage: list(zip(A, B))
            [(2, 1), (1.5, -1), (3, 2)]
            sage: fdot(_)
            mpf('6.5')
        """
        if B:
            A = zip(A, B)
        cdef MPF sre, sim, tre, tim, ure, uim, tmp
        cdef mpf rr
        cdef mpc rc
        cdef MPopts workopts
        cdef int styp, ttyp, utyp
        MPF_init(&sre)
        MPF_init(&sim)
        MPF_init(&tre)
        MPF_init(&tim)
        MPF_init(&ure)
        MPF_init(&uim)
        MPF_init(&tmp)
        workopts = global_opts
        workopts.prec = workopts.prec * 2 + 50
        workopts.rounding = ROUND_D
        unknown = global_context.zero
        styp = 1
        for a, b in A:
            ttyp = MPF_set_any(&tre, &tim, a, workopts, 0)
            utyp = MPF_set_any(&ure, &uim, b, workopts, 0)
            if utyp == 2 and conjugate:
                MPF_neg(&uim, &uim)
            if ttyp == 0 or utyp == 0:
                if conjugate:
                    b = b.conj()
                unknown += a * b
                continue
            styp = max(styp, ttyp)
            styp = max(styp, utyp)
            if ttyp == 1:
                if utyp == 1:
                    MPF_mul(&tre, &tre, &ure, opts_exact)
                    MPF_add(&sre, &sre, &tre, workopts)
                elif utyp == 2:
                    MPF_mul(&ure, &ure, &tre, opts_exact)
                    MPF_mul(&uim, &uim, &tre, opts_exact)
                    MPF_add(&sre, &sre, &ure, workopts)
                    MPF_add(&sim, &sim, &uim, workopts)
                    styp = 2
            elif ttyp == 2:
                styp = 2
                if utyp == 1:
                    MPF_mul(&tre, &tre, &ure, opts_exact)
                    MPF_mul(&tim, &tim, &ure, opts_exact)
                    MPF_add(&sre, &sre, &tre, workopts)
                    MPF_add(&sim, &sim, &tim, workopts)
                elif utyp == 2:
                    MPF_mul(&tmp, &tre, &ure, opts_exact)
                    MPF_add(&sre, &sre, &tmp, workopts)
                    MPF_mul(&tmp, &tim, &uim, opts_exact)
                    MPF_sub(&sre, &sre, &tmp, workopts)
                    MPF_mul(&tmp, &tim, &ure, opts_exact)
                    MPF_add(&sim, &sim, &tmp, workopts)
                    MPF_mul(&tmp, &tre, &uim, opts_exact)
                    MPF_add(&sim, &sim, &tmp, workopts)
        MPF_clear(&tre)
        MPF_clear(&tim)
        MPF_clear(&ure)
        MPF_clear(&uim)
        MPF_clear(&tmp)
        if styp == 1:
            rr = mpf.__new__(mpf)
            MPF_set(&rr.value, &sre)
            MPF_clear(&sre)
            MPF_clear(&sim)
            MPF_normalize(&rr.value, global_opts)
            if unknown is not global_context.zero:
                return ctx._stupid_add(rr, unknown)
            return rr
        elif styp == 2:
            rc = mpc.__new__(mpc)
            MPF_set(&rc.re, &sre)
            MPF_set(&rc.im, &sim)
            MPF_clear(&sre)
            MPF_clear(&sim)
            MPF_normalize(&rc.re, global_opts)
            MPF_normalize(&rc.im, global_opts)
            if unknown is not global_context.zero:
                return ctx._stupid_add(rc, unknown)
            return rc
        else:
            MPF_clear(&sre)
            MPF_clear(&sim)
            return +unknown

    # Doing a+b directly doesn't work with mpi, presumably due to
    # Cython trying to be clever with the operation resolution
    cdef _stupid_add(ctx, a, b):
        return a + b

    def _convert_param(ctx, x):
        """
        Internal function for parsing a hypergeometric function parameter.
        Retrurns (T, x) where T = 'Z', 'Q', 'R', 'C' depending on the
        type of the parameter, and with x converted to the canonical
        mpmath type.

        TESTS ::

            sage: from mpmath import mp
            sage: mp.pretty = True
            sage: (x, T) = mp._convert_param(3)
            sage: (x, type(x).__name__, T)
            (3, 'int', 'Z')
            sage: (x, T) = mp._convert_param(2.5)
            sage: (x, type(x).__name__, T)
            (mpq(5,2), 'mpq', 'Q')
            sage: (x, T) = mp._convert_param(2.3)
            sage: (x, type(x).__name__, T)
            (2.3, 'mpf', 'R')
            sage: (x, T) = mp._convert_param(2+3j)
            sage: (x, type(x).__name__, T)
            ((2.0 + 3.0j), 'mpc', 'C')
            sage: mp.pretty = False

        """
        cdef MPF v
        cdef bint ismpf, ismpc
        if isinstance(x, (int, Integer)):
            return int(x), 'Z'
        if isinstance(x, tuple):
            p, q = x
            p = int(p)
            q = int(q)
            if not p % q:
                return p // q, 'Z'
            return rationallib.mpq((p,q)), 'Q'
        if isinstance(x, str) and '/' in x:
            p, q = x.split('/')
            p = int(p)
            q = int(q)
            if not p % q:
                return p // q, 'Z'
            return rationallib.mpq((p,q)), 'Q'
        if isinstance(x, constant):
            return x, 'R'
        ismpf = isinstance(x, mpf)
        ismpc = isinstance(x, mpc)
        if not (ismpf or ismpc):
            x = global_context.convert(x)
            ismpf = isinstance(x, mpf)
            ismpc = isinstance(x, mpc)
            if not (ismpf or ismpc):
                return x, 'U'
        if ismpf:
            v = (<mpf>x).value
        elif ismpc:
            if (<mpc>x).im.special != S_ZERO:
                return x, 'C'
            x = (<mpc>x).real
            v = (<mpc>x).re
        # A real number
        if v.special == S_ZERO:
            return 0, 'Z'
        if v.special != S_NORMAL:
            return x, 'U'
        if mpz_sgn(v.exp) >= 0:
            return (mpzi(v.man) << mpzi(v.exp)), 'Z'
        if mpz_cmp_si(v.exp, -4) > 0:
            p = mpzi(v.man)
            q = 1 << (-mpzi(v.exp))
            return rationallib.mpq((p,q)), 'Q'
        return x, 'R'

    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).

        TESTS::

            sage: from mpmath import *
            sage: mp.pretty = True
            sage: mag(10), mag(10.0), mag(mpf(10)), int(ceil(log(10,2)))
            (4, 4, 4, 4)
            sage: mag(10j), mag(10+10j)
            (4, 5)
            sage: mag(0.01), int(ceil(log(0.01,2)))
            (-6, -6)
            sage: mag(0), mag(inf), mag(-inf), mag(nan)
            (-inf, +inf, +inf, nan)

        ::

            sage: class MyInt(int):
            ....:     pass
            sage: class MyFloat(float):
            ....:     pass
            sage: mag(MyInt(10))
            4

        """
        cdef int typ
        if isinstance(x, (int, Integer)):
            mpz_set_integer(tmp_opx_re.man, x)
            if mpz_sgn(tmp_opx_re.man) == 0:
                return global_context.ninf
            else:
                return mpz_sizeinbase(tmp_opx_re.man,2)
        if isinstance(x, rationallib.mpq):
            p, q = x._mpq_
            mpz_set_integer(tmp_opx_re.man, int(p))
            if mpz_sgn(tmp_opx_re.man) == 0:
                return global_context.ninf
            mpz_set_integer(tmp_opx_re.exp, int(q))
            return 1 + mpz_sizeinbase(tmp_opx_re.man,2) + mpz_sizeinbase(tmp_opx_re.exp,2)
        typ = MPF_set_any(&tmp_opx_re, &tmp_opx_im, x, global_opts, False)
        if typ == 1:
            if tmp_opx_re.special == S_ZERO:
                return global_context.ninf
            if tmp_opx_re.special == S_INF or tmp_opx_re.special == S_NINF:
                return global_context.inf
            if tmp_opx_re.special != S_NORMAL:
                return global_context.nan
            mpz_add_ui(tmp_opx_re.exp, tmp_opx_re.exp, mpz_sizeinbase(tmp_opx_re.man, 2))
            return mpzi(tmp_opx_re.exp)
        if typ == 2:
            if tmp_opx_re.special == S_NAN or tmp_opx_im.special == S_NAN:
                return global_context.nan
            if tmp_opx_re.special == S_INF or tmp_opx_im.special == S_NINF or \
               tmp_opx_im.special == S_INF or tmp_opx_im.special == S_NINF:
                return global_context.inf
            if tmp_opx_re.special == S_ZERO:
                if tmp_opx_im.special == S_ZERO:
                    return global_context.ninf
                else:
                    mpz_add_ui(tmp_opx_im.exp, tmp_opx_im.exp, mpz_sizeinbase(tmp_opx_im.man, 2))
                    return mpzi(tmp_opx_im.exp)
            elif tmp_opx_im.special == S_ZERO:
                mpz_add_ui(tmp_opx_re.exp, tmp_opx_re.exp, mpz_sizeinbase(tmp_opx_re.man, 2))
                return mpzi(tmp_opx_re.exp)
            mpz_add_ui(tmp_opx_im.exp, tmp_opx_im.exp, mpz_sizeinbase(tmp_opx_im.man, 2))
            mpz_add_ui(tmp_opx_re.exp, tmp_opx_re.exp, mpz_sizeinbase(tmp_opx_re.man, 2))
            if mpz_cmp(tmp_opx_re.exp, tmp_opx_im.exp) >= 0:
                mpz_add_ui(tmp_opx_re.exp, tmp_opx_re.exp, 1)
                return mpzi(tmp_opx_re.exp)
            else:
                mpz_add_ui(tmp_opx_im.exp, tmp_opx_im.exp, 1)
                return mpzi(tmp_opx_im.exp)
        raise TypeError("requires an mpf/mpc")

    def _wrap_libmp_function(ctx, mpf_f, mpc_f=None, mpi_f=None, doc="<no doc>"):
        """
        Create a high-level mpmath function from base functions working
        on mpf, mpc and mpi tuple data.

        TESTS ::

            sage: from mpmath import mp
            sage: mp.pretty = False
            sage: f = lambda x, prec, rnd: x
            sage: g = mp._wrap_libmp_function(f)
            sage: g(mp.mpf(2))
            mpf('2.0')

        """
        name = mpf_f.__name__[4:]
        doc = function_docs.__dict__.get(name, "Computes the %s of x" % doc)
        # workaround lack of closures in Cython
        f_cls = type(name, (wrapped_libmp_function,), {'__doc__':doc})
        f = f_cls(mpf_f, mpc_f, mpi_f, doc)
        return f

    @classmethod
    def _wrap_specfun(cls, name, f, wrap):
        """
        Adds the given function as a method to the context object,
        optionally wrapping it to do automatic conversions and
        allocating a small number of guard bits to suppress
        typical roundoff error.

        TESTS ::

            sage: from mpmath import mp
            sage: mp._wrap_specfun("foo", lambda ctx, x: ctx.prec + x, True)
            sage: mp.pretty = False; mp.prec = 53
            sage: mp.foo(5)       # 53 + 10 guard bits + 5
            mpf('68.0')

        """
        doc = function_docs.__dict__.get(name, getattr(f, '__doc__', '<no doc>'))
        if wrap:
            # workaround lack of closures in Cython
            f_wrapped_cls = type(name, (wrapped_specfun,), {'__doc__':doc})
            f_wrapped = f_wrapped_cls(name, f)
        else:
            f_wrapped = f
        f_wrapped.__doc__ = doc
        setattr(cls, name, f_wrapped)

    cdef MPopts _fun_get_opts(ctx, kwargs):
        """
        Helper function that extracts precision and rounding information
        from kwargs, or returns the global working precision and rounding
        if no options are specified.
        """
        cdef MPopts opts
        opts.prec = global_opts.prec
        opts.rounding = global_opts.rounding
        if kwargs:
            if 'prec' in kwargs:
                opts.prec = int(kwargs['prec'])
            if 'dps'  in kwargs:
                opts.prec = libmp.dps_to_prec(int(kwargs['dps']))
            if 'rounding' in kwargs:
                opts.rounding = rndmode_from_python(kwargs['rounding'])
        return opts

    def _sage_sqrt(ctx, x, **kwargs):
        """
        Square root of an mpmath number x, using the Sage mpmath backend.

        TESTS ::

            sage: from mpmath import mp
            sage: mp.dps = 15
            sage: print(mp.sqrt(2))   # indirect doctest
            1.4142135623731
            sage: print(mp.sqrt(-2))
            (0.0 + 1.4142135623731j)
            sage: print(mp.sqrt(2+2j))
            (1.55377397403004 + 0.643594252905583j)

        """
        cdef MPopts opts
        cdef int typx
        cdef mpf rr
        cdef mpc rc
        cdef tuple rev, imv
        opts = ctx._fun_get_opts(kwargs)
        typx = MPF_set_any(&tmp_opx_re, &tmp_opx_im, x, opts, 1)
        if typx == 1:
            rr = mpf.__new__(mpf)
            if MPF_sqrt(&rr.value, &tmp_opx_re, opts):
                rc = mpc.__new__(mpc)
                MPF_complex_sqrt(&rc.re, &rc.im, &tmp_opx_re, &MPF_C_0, opts)
                return rc
            return rr
        elif typx == 2:
            rc = mpc.__new__(mpc)
            MPF_complex_sqrt(&rc.re, &rc.im, &tmp_opx_re, &tmp_opx_im, opts)
            return rc
        else:
            raise NotImplementedError("unknown argument")

    def _sage_exp(ctx, x, **kwargs):
        """
        Exponential function of an mpmath number x, using the Sage
        mpmath backend.

        EXAMPLES::

            sage: from mpmath import mp
            sage: mp.dps = 15
            sage: print(mp.exp(2))   # indirect doctest
            7.38905609893065
            sage: print(mp.exp(2+2j))
            (-3.07493232063936 + 6.71884969742825j)

        """
        cdef MPopts opts
        cdef int typx
        cdef mpf rr
        cdef mpc rc
        cdef tuple rev, imv
        opts = ctx._fun_get_opts(kwargs)
        typx = MPF_set_any(&tmp_opx_re, &tmp_opx_im, x, opts, 1)
        if typx == 1:
            rr = mpf.__new__(mpf)
            MPF_exp(&rr.value, &tmp_opx_re, opts)
            return rr
        elif typx == 2:
            rc = mpc.__new__(mpc)
            MPF_complex_exp(&rc.re, &rc.im, &tmp_opx_re, &tmp_opx_im, opts)
            return rc
        else:
            raise NotImplementedError("unknown argument")

    def _sage_cos(ctx, x, **kwargs):
        """
        Cosine of an mpmath number x, using the Sage mpmath backend.

        EXAMPLES::

            sage: from mpmath import mp
            sage: mp.dps = 15
            sage: print(mp.cos(2))   # indirect doctest
            -0.416146836547142
            sage: print(mp.cos(2+2j))
            (-1.56562583531574 - 3.29789483631124j)

        """
        cdef MPopts opts
        cdef int typx
        cdef mpf rr
        cdef mpc rc
        cdef tuple rev, imv
        opts = ctx._fun_get_opts(kwargs)
        typx = MPF_set_any(&tmp_opx_re, &tmp_opx_im, x, global_opts, 1)
        if typx == 1:
            rr = mpf.__new__(mpf)
            MPF_cos(&rr.value, &tmp_opx_re, opts)
            return rr
        elif typx == 2:
            rev = MPF_to_tuple(&tmp_opx_re)
            imv = MPF_to_tuple(&tmp_opx_im)
            cxu = libmp.mpc_cos((rev, imv), opts.prec,
                rndmode_to_python(opts.rounding))
            rc = mpc.__new__(mpc)
            MPF_set_tuple(&rc.re, cxu[0])
            MPF_set_tuple(&rc.im, cxu[1])
            return rc
        else:
            raise NotImplementedError("unknown argument")

    def _sage_sin(ctx, x, **kwargs):
        """
        Sine of an mpmath number x, using the Sage mpmath backend.

        EXAMPLES::

            sage: from mpmath import mp
            sage: mp.dps = 15
            sage: print(mp.sin(2))   # indirect doctest
            0.909297426825682
            sage: print(mp.sin(2+2j))
            (3.42095486111701 - 1.50930648532362j)

        """
        cdef MPopts opts
        cdef int typx
        cdef mpf rr
        cdef mpc rc
        cdef tuple rev, imv
        opts = ctx._fun_get_opts(kwargs)
        typx = MPF_set_any(&tmp_opx_re, &tmp_opx_im, x, global_opts, 1)
        if typx == 1:
            rr = mpf.__new__(mpf)
            MPF_sin(&rr.value, &tmp_opx_re, opts)
            return rr
        elif typx == 2:
            rev = MPF_to_tuple(&tmp_opx_re)
            imv = MPF_to_tuple(&tmp_opx_im)
            cxu = libmp.mpc_sin((rev, imv), opts.prec,
                rndmode_to_python(opts.rounding))
            rc = mpc.__new__(mpc)
            MPF_set_tuple(&rc.re, cxu[0])
            MPF_set_tuple(&rc.im, cxu[1])
            return rc
        else:
            raise NotImplementedError("unknown argument")

    def _sage_ln(ctx, x, **kwargs):
        """
        Natural logarithm of an mpmath number x, using the Sage mpmath backend.

        EXAMPLES::

            sage: from mpmath import mp
            sage: print(mp.ln(2))   # indirect doctest
            0.693147180559945
            sage: print(mp.ln(-2))
            (0.693147180559945 + 3.14159265358979j)
            sage: print(mp.ln(2+2j))
            (1.03972077083992 + 0.785398163397448j)

        """
        cdef MPopts opts
        cdef int typx
        cdef mpf rr
        cdef mpc rc
        cdef tuple rev, imv
        typx = MPF_set_any(&tmp_opx_re, &tmp_opx_im, x, global_opts, 1)
        prec = global_opts.prec
        rounding = rndmode_to_python(global_opts.rounding)
        opts.prec = global_opts.prec
        opts.rounding = global_opts.rounding
        if kwargs:
            if 'prec' in kwargs: opts.prec = int(kwargs['prec'])
            if 'dps'  in kwargs: opts.prec = libmp.dps_to_prec(int(kwargs['dps']))
            if 'rounding' in kwargs: opts.rounding = rndmode_from_python(kwargs['rounding'])
        if typx == 1:
            if MPF_sgn(&tmp_opx_re) < 0:
                rc = mpc.__new__(mpc)
                MPF_log(&rc.re, &tmp_opx_re, opts)
                MPF_set_pi(&rc.im, opts)
                return rc
            else:
                rr = mpf.__new__(mpf)
                MPF_log(&rr.value, &tmp_opx_re, opts)
                return rr
        elif typx == 2:
            rev = MPF_to_tuple(&tmp_opx_re)
            imv = MPF_to_tuple(&tmp_opx_im)
            cxu = libmp.mpc_log((rev, imv), opts.prec, rndmode_to_python(opts.rounding))
            rc = mpc.__new__(mpc)
            MPF_set_tuple(&rc.re, cxu[0])
            MPF_set_tuple(&rc.im, cxu[1])
            return rc

            #rc = mpc.__new__(mpc)
            #MPF_complex_log(&rc.re, &rc.im, &tmp_opx_re, &tmp_opx_im, opts)
            #return rc
        else:
            raise NotImplementedError("unknown argument")


cdef class wrapped_libmp_function:

    cdef public mpf_f, mpc_f, mpi_f, name, __name__, __doc__

    def __init__(self, mpf_f, mpc_f=None, mpi_f=None, doc="<no doc>"):
        """
        Create a high-level mpmath function from base functions working
        on mpf, mpc and mpi tuple data.

        TESTS ::

            sage: from sage.libs.mpmath.ext_main import wrapped_libmp_function
            sage: from mpmath import mp
            sage: from mpmath.libmp import mpf_exp, mpf_sqrt
            sage: f = lambda x, prec, rnd: mpf_exp(mpf_sqrt(x, prec, rnd), prec, rnd)
            sage: g = wrapped_libmp_function(f)
            sage: g(mp.mpf(3))
            mpf('5.6522336740340915')
            sage: mp.exp(mp.sqrt(3))
            mpf('5.6522336740340915')
            sage: g(mp.mpf(3), prec=10)
            mpf('5.65625')
            sage: g(mp.mpf(3), prec=10, rounding='u')
            mpf('5.65625')
            sage: g(mp.mpf(3), prec=10, rounding='d')
            mpf('5.640625')
        """
        self.mpf_f = mpf_f
        self.mpc_f = mpc_f
        self.mpi_f = mpi_f
        self.name = self.__name__ = mpf_f.__name__[4:]
        self.__doc__ = function_docs.__dict__.get(self.name, "Computes the %s of x" % doc)

    def __call__(self, x, **kwargs):
        """
        A wrapped mpmath library function performs automatic
        conversions and uses the default working precision
        unless overridden ::

            sage: from mpmath import mp
            sage: mp.sinh(2)
            mpf('3.6268604078470186')
            sage: mp.sinh(2, prec=10)
            mpf('3.625')
            sage: mp.sinh(2, prec=10, rounding='d')
            mpf('3.625')
            sage: mp.sinh(2, prec=10, rounding='u')
            mpf('3.62890625')
        """
        cdef int typx
        cdef tuple rev, imv, reu, cxu
        cdef mpf rr
        cdef mpc rc
        prec = global_opts.prec
        rounding = rndmode_to_python(global_opts.rounding)
        if kwargs:
            if 'prec' in kwargs: prec = int(kwargs['prec'])
            if 'dps'  in kwargs: prec = libmp.dps_to_prec(int(kwargs['dps']))
            if 'rounding' in kwargs: rounding = kwargs['rounding']
        typx = MPF_set_any(&tmp_opx_re, &tmp_opx_im, x, global_opts, 1)
        if typx == 1:
            rev = MPF_to_tuple(&tmp_opx_re)
            try:
                reu = self.mpf_f(rev, prec, rounding)
                rr = mpf.__new__(mpf)
                MPF_set_tuple(&rr.value, reu)
                return rr
            except libmp.ComplexResult:
                if global_context.trap_complex:
                    raise
                cxu = self.mpc_f((rev, libmp.fzero), prec, rounding)
                rc = mpc.__new__(mpc)
                MPF_set_tuple(&rc.re, cxu[0])
                MPF_set_tuple(&rc.im, cxu[1])
                return rc
        if typx == 2:
            rev = MPF_to_tuple(&tmp_opx_re)
            imv = MPF_to_tuple(&tmp_opx_im)
            cxu = self.mpc_f((rev, imv), prec, rounding)
            rc = mpc.__new__(mpc)
            MPF_set_tuple(&rc.re, cxu[0])
            MPF_set_tuple(&rc.im, cxu[1])
            return rc
        x = global_context.convert(x)
        if hasattr(x, "_mpf_") or hasattr(x, "_mpc_"):
            return self(x, **kwargs)
        #if hasattr(x, "_mpi_"):
        #    if self.mpi_f:
        #        return global_context.make_mpi(self.mpi_f(x._mpi_, prec))
        raise NotImplementedError("%s of a %s" % (self.name, type(x)))



cdef class wrapped_specfun:
    cdef public f, name, __name__, __doc__

    def __init__(self, name, f):
        """
        Creates an object holding a wrapped mpmath function
        along with metadata (name and documentation).

        TESTS ::

            sage: import mpmath
            sage: from sage.libs.mpmath.ext_main import wrapped_specfun
            sage: f = wrapped_specfun("f", lambda ctx, x: x)
            sage: f.name
            'f'
        """
        self.name = self.__name__ = name
        self.f = f
        self.__doc__ = function_docs.__dict__.get(name, "<no doc>")

    def __call__(self, *args, **kwargs):
        """
        Call wrapped mpmath function. Arguments are automatically converted
        to mpmath number, and the internal working precision is increased
        by a few bits to suppress typical rounding errors ::

            sage: from mpmath import mp
            sage: from sage.libs.mpmath.ext_main import wrapped_specfun
            sage: f = wrapped_specfun("f", lambda ctx, x: x + ctx.prec)
            sage: f("1")     # 53 + 10 guard bits + 1
            mpf('64.0')

        """
        cdef int origprec
        args = [global_context.convert(a) for a in args]
        origprec = global_opts.prec
        global_opts.prec += 10
        try:
            retval = self.f(global_context, *args, **kwargs)
        finally:
            global_opts.prec = origprec
        return +retval


cdef class mpnumber:

    def __richcmp__(self, other, int op):
        """
        Comparison of mpmath numbers. Compatible numerical types
        are automatically converted to mpmath numbers ::

            sage: from mpmath import mpf, mpc
            sage: mpf(3) == mpc(3)
            True
            sage: mpf(3) == mpc(4)
            False
            sage: mpf(3) == float(3)
            True
            sage: mpf(3) < float(2.5)
            False
            sage: mpc(3) < mpc(4)
            Traceback (most recent call last):
                ...
            ValueError: cannot compare complex numbers

        """
        return binop(OP_RICHCMP+op, self, other, global_opts)

    def __add__(self, other):
        """
        Addition of mpmath numbers. Compatible numerical types
        are automatically converted to mpmath numbers ::

            sage: from mpmath import mpf, mpc
            sage: mpf(3) + mpc(3)
            mpc(real='6.0', imag='0.0')
            sage: float(4) + mpf(3)
            mpf('7.0')
        """
        return binop(OP_ADD, self, other, global_opts)

    def __sub__(self, other):
        """
        Subtraction of mpmath numbers. Compatible numerical types
        are automatically converted to mpmath numbers ::

            sage: from mpmath import mpf, mpc
            sage: mpf(5) - mpc(3)
            mpc(real='2.0', imag='0.0')
            sage: float(4) - mpf(3)
            mpf('1.0')
        """
        return binop(OP_SUB, self, other, global_opts)

    def __mul__(self, other):
        """
        Multiplication of mpmath numbers. Compatible numerical types
        are automatically converted to mpmath numbers ::

            sage: from mpmath import mpf, mpc
            sage: mpf(5) * mpc(3)
            mpc(real='15.0', imag='0.0')
            sage: float(4) * mpf(3)
            mpf('12.0')
        """
        return binop(OP_MUL, self, other, global_opts)

    def __truediv__(self, other):
        """
        Division of mpmath numbers. Compatible numerical types
        are automatically converted to mpmath numbers ::

            sage: from mpmath import mpf, mpc
            sage: mpf(10) / mpc(5)
            mpc(real='2.0', imag='0.0')
            sage: float(9) / mpf(3)
            mpf('3.0')
        """
        return binop(OP_DIV, self, other, global_opts)

    def __mod__(self, other):
        """
        Remainder of mpmath numbers. Compatible numerical types
        are automatically converted to mpmath numbers ::

            sage: from mpmath import mpf
            sage: mpf(12) % float(7)
            mpf('5.0')
        """
        return binop(OP_MOD, self, other, global_opts)

    def __pow__(self, other, mod):
        """
        Exponentiation of mpmath numbers. Compatible numerical types
        are automatically converted to mpmath numbers ::

            sage: from mpmath import mpf, mpc
            sage: mpf(10) ** mpc(3)
            mpc(real='1000.0', imag='0.0')
            sage: mpf(3) ** float(2)
            mpf('9.0')
        """
        if mod is not None:
            raise ValueError("three-argument pow not supported")
        return binop(OP_POW, self, other, global_opts)

    def ae(s, t, rel_eps=None, abs_eps=None):
        """
        Check if two numbers are approximately equal to within the specified
        tolerance (see mp.almosteq for documentation) ::

            sage: from mpmath import mpf, mpc
            sage: mpf(3).ae(mpc(3,1e-10))
            False
            sage: mpf(3).ae(mpc(3,1e-10), rel_eps=1e-5)
            True
        """
        return global_context.almosteq(s, t, rel_eps, abs_eps)


cdef class mpf_base(mpnumber):

    # Shared methods for mpf, constant. However, somehow some methods
    # (hash?, __richcmp__?) are not inherited, so they have to
    # be defined multiple times. TODO: fix this.

    def __hash__(self):
        """
        Support hashing of derived classes ::

            sage: from mpmath import mpf
            sage: from sage.libs.mpmath.ext_main import mpf_base
            sage: class X(mpf_base): _mpf_ = mpf(3.25)._mpf_
            sage: hash(X()) == hash(float(X()))
            True
        """
        return libmp.mpf_hash(self._mpf_)

    def __repr__(self):
        """
        Support repr() of derived classes ::

            sage: from mpmath import mpf
            sage: from sage.libs.mpmath.ext_main import mpf_base
            sage: class X(mpf_base): _mpf_ = mpf(3.25)._mpf_
            sage: repr(X())
            "mpf('3.25')"
        """
        if global_context.pretty:
            return str(self)
        n = repr_dps(global_opts.prec)
        return "mpf('%s')" % to_str(self._mpf_, n)

    def __str__(self):
        """
        Support str() of derived classes ::

            sage: from mpmath import mpf
            sage: from sage.libs.mpmath.ext_main import mpf_base
            sage: class X(mpf_base): _mpf_ = mpf(3.25)._mpf_
            sage: str(X())
            '3.25'
        """
        return to_str(self._mpf_, global_context._str_digits)

    @property
    def real(self):
        """
        Support real part of derived classes ::

            sage: from mpmath import mpf
            sage: from sage.libs.mpmath.ext_main import mpf_base
            sage: class X(mpf_base): _mpf_ = mpf(3.25)._mpf_
            sage: X().real
            mpf('3.25')
        """
        return self

    @property
    def imag(self):
        """
        Support imaginary part of derived classes ::

            sage: from mpmath import mpf
            sage: from sage.libs.mpmath.ext_main import mpf_base
            sage: class X(mpf_base): _mpf_ = mpf(3.25)._mpf_
            sage: X().imag
            mpf('0.0')
        """
        return global_context.zero

    def conjugate(self):
        """
        Support complex conjugate of derived classes ::

            sage: from mpmath import mpf
            sage: from sage.libs.mpmath.ext_main import mpf_base
            sage: class X(mpf_base): _mpf_ = mpf(3.25)._mpf_
            sage: X().conjugate()
            mpf('3.25')
        """
        return self

    @property
    def man(self):
        """
        Support mantissa extraction of derived classes ::

            sage: from mpmath import mpf
            sage: from sage.libs.mpmath.ext_main import mpf_base
            sage: class X(mpf_base): _mpf_ = mpf(3.25)._mpf_
            sage: X().man
            13
        """
        return self._mpf_[1]

    @property
    def exp(self):
        """
        Support exponent extraction of derived classes ::

            sage: from mpmath import mpf
            sage: from sage.libs.mpmath.ext_main import mpf_base
            sage: class X(mpf_base): _mpf_ = mpf(3.25)._mpf_
            sage: X().exp
            -2
        """
        return self._mpf_[2]

    @property
    def bc(self):
        """
        Support bitcount extraction of derived classes ::

            sage: from mpmath import mpf
            sage: from sage.libs.mpmath.ext_main import mpf_base
            sage: class X(mpf_base): _mpf_ = mpf(3.25)._mpf_
            sage: X().bc
            4
        """
        return self._mpf_[3]

    # XXX: optimize
    def __int__(self):
        """
        Support integer conversion for derived classes ::

            sage: from mpmath import mpf
            sage: from sage.libs.mpmath.ext_main import mpf_base
            sage: class X(mpf_base): _mpf_ = mpf(3.25)._mpf_
            sage: int(X())
            3
        """
        return int(libmp.to_int(self._mpf_))

    def __float__(self):
        """
        Support float conversion for derived classes ::

            sage: from mpmath import mpf
            sage: from sage.libs.mpmath.ext_main import mpf_base
            sage: class X(mpf_base): _mpf_ = mpf(3.25)._mpf_
            sage: float(X())
            3.25
        """
        return libmp.to_float(self._mpf_)

    def __complex__(self):
        """
        Support complex conversion for derived classes ::

            sage: from mpmath import mpf
            sage: from sage.libs.mpmath.ext_main import mpf_base
            sage: class X(mpf_base): _mpf_ = mpf(3.25)._mpf_
            sage: complex(X())
            (3.25+0j)
        """
        return complex(float(self))

    def to_fixed(self, prec):
        """
        Support conversion to a fixed-point integer for derived classes ::

            sage: from mpmath import mpf
            sage: from sage.libs.mpmath.ext_main import mpf_base
            sage: class X(mpf_base): _mpf_ = mpf(3.25)._mpf_
            sage: X().to_fixed(30)
            3489660928
        """
        return libmp.to_fixed(self._mpf_, prec)

    def __getstate__(self):
        return libmp.to_pickable(self._mpf_)

    def __setstate__(self, val):
        self._mpf_ = libmp.from_pickable(val)


cdef class mpf(mpf_base):
    """
    An mpf instance holds a real-valued floating-point number. mpf:s
    work analogously to Python floats, but support arbitrary-precision
    arithmetic.
    """

    cdef MPF value

    def __init__(self, x=0, **kwargs):
        """
        Create an mpf from a recognized type, optionally rounding
        to a precision and in a direction different from the default.

        TESTS ::

            sage: from mpmath import mpf
            sage: mpf()
            mpf('0.0')
            sage: mpf(5)
            mpf('5.0')
            sage: mpf('inf')
            mpf('+inf')
            sage: mpf('nan')
            mpf('nan')
            sage: mpf(float(2.5))
            mpf('2.5')
            sage: mpf("2.5")
            mpf('2.5')
            sage: mpf("0.3")
            mpf('0.29999999999999999')
            sage: mpf("0.3", prec=10)
            mpf('0.2998046875')
            sage: mpf("0.3", prec=10, rounding='u')
            mpf('0.30029296875')

        """
        cdef MPopts opts
        opts = global_opts
        if kwargs:
            if 'prec' in kwargs: opts.prec = int(kwargs['prec'])
            if 'dps'  in kwargs: opts.prec = libmp.dps_to_prec(int(kwargs['dps']))
            if 'rounding' in kwargs: opts.rounding = rndmode_from_python(kwargs['rounding'])
        if MPF_set_any(&self.value, &self.value, x, opts, 1) != 1:
            raise TypeError

    def __reduce__(self):
        """
        Support pickling ::

            sage: from mpmath import mpf
            sage: loads(dumps(mpf(0.5))) == mpf(0.5)
            True
        """
        return (mpf, (), self._mpf_)

    def _get_mpf(self):
        """
        Returns internal representation of self as a tuple
        of (sign bit, mantissa, exponent, bitcount) ::

            sage: from mpmath import mp
            sage: mp.mpf(-3)._mpf_
            (1, 3, 0, 2)
        """
        return MPF_to_tuple(&self.value)

    def _set_mpf(self, v):
        """
        Sets tuple value of self (warning: unsafe) ::

            sage: from mpmath import mp
            sage: x = mp.mpf(-3)
            sage: x._mpf_ = (1, 3, -1, 2)
            sage: x
            mpf('-1.5')
        """
        MPF_set_tuple(&self.value, v)

    _mpf_ = property(_get_mpf, _set_mpf, doc=_get_mpf.__doc__)

    def __bool__(self):
        """
        Returns whether the number is nonzero ::

            sage: from mpmath import mpf
            sage: bool(mpf(3.5))
            True
            sage: bool(mpf(0.0))
            False
        """
        return self.value.special != S_ZERO

    def __hash__(self):
        """
        Hash values are compatible with builtin Python floats
        when the precision is small enough ::

            sage: from mpmath import mpf
            sage: hash(mpf(2.5)) == hash(float(2.5))
            True
            sage: hash(mpf('inf')) == hash(float(Infinity))
            True
        """
        return libmp.mpf_hash(self._mpf_)

    @property
    def real(self):
        """
        Real part, leaves self unchanged ::

            sage: from mpmath import mpf
            sage: mpf(2.5).real
            mpf('2.5')
        """
        return self

    @property
    def imag(self):
        """
        Imaginary part, equal to zero ::

            sage: from mpmath import mpf
            sage: mpf(2.5).imag
            mpf('0.0')
        """
        return global_context.zero

    def conjugate(self):
        """
        Complex conjugate, leaves self unchanged ::

            sage: from mpmath import mpf
            sage: mpf(2.5).conjugate()
            mpf('2.5')
        """
        return self

    @property
    def man(self):
        """
        Returns the binary mantissa of self. The result is a Sage
        integer ::

            sage: from mpmath import mpf
            sage: mpf(-500.5).man
            1001
            sage: type(_)
            <class 'sage.rings.integer.Integer'>
        """
        return self._mpf_[1]

    @property
    def exp(self):
        """
        Returns the binary exponent of self ::

            sage: from mpmath import mpf
            sage: mpf(1/64.).exp
            -6
        """
        return self._mpf_[2]

    @property
    def bc(self):
        """
        Returns the number of bits in the mantissa of self ::

            sage: from mpmath import mpf
            sage: mpf(-256).bc
            1
            sage: mpf(-255).bc
            8
        """
        return self._mpf_[3]

    def to_fixed(self, long prec):
        """
        Convert to a fixed-point integer of the given precision ::

            sage: from mpmath import mpf
            sage: mpf(7.25).to_fixed(30)
            7784628224
            sage: ZZ(7.25 * 2**30)
            7784628224
        """
        # return libmp.to_fixed(self._mpf_, prec)
        MPF_to_fixed(tmp_mpz, &self.value, prec, False)
        cdef Integer r
        r = PY_NEW(Integer)
        mpz_set(r.value, tmp_mpz)
        return r

    def __int__(self):
        """
        Convert to a Python integer (truncating if necessary) ::

            sage: from mpmath import mpf
            sage: int(mpf(2.5))
            2
            sage: type(_)
            <... 'int'>
        """
        MPF_to_fixed(tmp_mpz, &self.value, 0, True)
        return mpzi(tmp_mpz)

    def __float__(self):
        """
        Convert to a double-precision Python float ::

            sage: from mpmath import mpf
            sage: float(mpf(2.5))
            2.5
            sage: type(_)
            <... 'float'>
        """
        return MPF_to_double(&self.value, False)

    def __getstate__(self):
        """
        Support pickling ::

            sage: from mpmath import mpf
            sage: loads(dumps(mpf(3))) == mpf(3)
            True
        """
        return libmp.to_pickable(self._mpf_)

    def __setstate__(self, val):
        """
        Support pickling ::

            sage: from mpmath import mpf
            sage: loads(dumps(mpf(3))) == mpf(3)
            True
        """
        self._mpf_ = libmp.from_pickable(val)

    def __cinit__(self):
        """
        Create a new mpf ::

            sage: from mpmath import mpf
            sage: x = mpf()

        """
        MPF_init(&self.value)

    def __dealloc__(self):
        MPF_clear(&self.value)

    def __neg__(s):
        """
        Negates self, rounded to the current working precision ::

            sage: from mpmath import mpf
            sage: -mpf(2)
            mpf('-2.0')
        """
        cdef mpf r = mpf.__new__(mpf)
        MPF_neg(&r.value, &s.value)
        MPF_normalize(&r.value, global_opts)
        return r

    def __pos__(s):
        """
        Rounds the number to the current working precision ::

            sage: from mpmath import mp, mpf
            sage: mp.prec = 200
            sage: x = mpf(1) / 3
            sage: x.man
            1071292029505993517027974728227441735014801995855195223534251
            sage: mp.prec = 53
            sage: (+x).man
            6004799503160661
            sage: print(+x)
            0.333333333333333
        """
        cdef mpf r = mpf.__new__(mpf)
        MPF_set(&r.value, &s.value)
        MPF_normalize(&r.value, global_opts)
        return r

    def __abs__(s):
        """
        Computes the absolute value, rounded to the current
        working precision ::

            sage: from mpmath import mpf
            sage: abs(mpf(-2))
            mpf('2.0')
        """
        cdef mpf r = mpf.__new__(mpf)
        MPF_abs(&r.value, &s.value)
        MPF_normalize(&r.value, global_opts)
        return r

    def sqrt(s):
        """
        Computes the square root, rounded to the current
        working precision ::

            sage: from mpmath import mpf
            sage: mpf(2).sqrt()
            mpf('1.4142135623730951')
        """
        cdef mpf r = mpf.__new__(mpf)
        MPF_sqrt(&r.value, &s.value, global_opts)
        return r

    def __richcmp__(self, other, int op):
        """
        Compares numbers ::

            sage: from mpmath import mpf
            sage: mpf(3) > 2
            True
            sage: mpf(3) == 3
            True
            sage: mpf(3) == 4
            False
        """
        return binop(OP_RICHCMP+op, self, other, global_opts)



cdef class constant(mpf_base):
    """
    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.
    """

    cdef public name, func, __doc__

    def __init__(self, func, name, docname=''):
        """
        Creates a constant from a function computing an mpf
        tuple value ::

            sage: from mpmath import mp, mpf
            sage: q = mp.constant(lambda prec, rnd: mpf(0.25)._mpf_, "quarter", "q")
            sage: q
            <quarter: 0.25~>
            sage: q + 1
            mpf('1.25')

        """
        self.name = name
        self.func = func
        self.__doc__ = getattr(function_docs, docname, '')

    def __call__(self, prec=None, dps=None, rounding=None):
        """
        Calling a constant is equivalent to rounding it. A
        custom precision and rounding direction can also be passed ::

            sage: from mpmath import pi
            sage: print(pi(dps=5, rounding='d'))
            3.1415901184082
            sage: print(pi(dps=5, rounding='u'))
            3.14159393310547

        """
        prec2 = global_opts.prec
        rounding2 = rndmode_to_python(global_opts.rounding)
        if not prec: prec = prec2
        if not rounding: rounding = rounding2
        if dps: prec = dps_to_prec(dps)
        return global_context.make_mpf(self.func(prec, rounding))

    @property
    def _mpf_(self):
        """
        Returns the tuple value of the constant as if rounded
        to an mpf at the present working precision ::

            sage: from mpmath import pi
            sage: pi._mpf_
            (0, 884279719003555, -48, 50)
            sage: 884279719003555 / 2.0**48
            3.14159265358979
        """
        prec = global_opts.prec
        rounding = rndmode_to_python(global_opts.rounding)
        return self.func(prec, rounding)

    def __repr__(self):
        """
        Represents self as a string. With mp.pretty=False, the
        representation differs from that of an ordinary mpf ::

            sage: from mpmath import mp, pi
            sage: mp.pretty = True
            sage: repr(pi)
            '3.14159265358979'
            sage: mp.pretty = False
            sage: repr(pi)
            '<pi: 3.14159~>'

        """
        if global_context.pretty:
            return str(self)
        return "<%s: %s~>" % (self.name, global_context.nstr(self))

    def __bool__(self):
        """
        Returns whether the constant is nonzero ::

            sage: from mpmath import pi
            sage: bool(pi)
            True
        """
        return self._mpf_ != libmp.fzero

    def __neg__(self):
        """
        Negates the constant ::

            sage: from mpmath import pi
            sage: -pi
            mpf('-3.1415926535897931')
        """
        return -mpf(self)

    def __pos__(self):
        """
        Instantiates the constant as an mpf ::

            sage: from mpmath import pi
            sage: +pi
            mpf('3.1415926535897931')
        """
        return mpf(self)

    def __abs__(self):
        """
        Computes the absolute value of the constant ::

            sage: from mpmath import pi
            sage: abs(pi)
            mpf('3.1415926535897931')
        """
        return abs(mpf(self))

    def sqrt(self):
        """
        Computes the square root of the constant ::

            sage: from mpmath import pi
            sage: print(pi.sqrt())
            1.77245385090552
        """
        return mpf(self).sqrt()

    # XXX: optimize
    def to_fixed(self, prec):
        """
        Convert to a fixed-point integer ::

            sage: from mpmath import pi
            sage: float(pi.to_fixed(10) / 2.0**10)
            3.140625
        """
        return libmp.to_fixed(self._mpf_, prec)

    def __getstate__(self):
        return libmp.to_pickable(self._mpf_)

    def __setstate__(self, val):
        self._mpf_ = libmp.from_pickable(val)

    # WHY is this method not inherited from the base class by Cython?
    def __hash__(self):
        """
        A constant hashes as if instantiated to a number ::

            sage: from mpmath import pi
            sage: hash(pi) == hash(+pi)
            True
        """
        return libmp.mpf_hash(self._mpf_)

    def __richcmp__(self, other, int op):
        """
        A constant hashes as if instantiated to a number ::

            sage: from mpmath import pi
            sage: pi == pi
            True
            sage: pi > 3.14
            True
            sage: pi < 3.14
            False
        """
        return binop(OP_RICHCMP+op, self, other, global_opts)


cdef class mpc(mpnumber):
    """
    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.
    """

    cdef MPF re
    cdef MPF im

    def __init__(self, real=0, imag=0):
        """
        Creates a new mpc::

            sage: from mpmath import mpc
            sage: mpc() == mpc(0,0) == mpc(1,0)-1 == 0
            True

        """
        cdef int typx, typy
        typx = MPF_set_any(&self.re, &self.im, real, global_opts, 1)
        if typx == 2:
            typy = 1
        else:
            typy = MPF_set_any(&self.im, &self.im, imag, global_opts, 1)
        if typx == 0 or typy != 1:
            raise TypeError

    def __cinit__(self):
        """
        Create a new mpc ::

            sage: from mpmath import mpc
            sage: x = mpc()

        """
        MPF_init(&self.re)
        MPF_init(&self.im)

    def __dealloc__(self):
        MPF_clear(&self.re)
        MPF_clear(&self.im)

    def __reduce__(self):
        """
        Support pickling ::

            sage: from mpmath import mpc
            sage: loads(dumps(mpc(1,3))) == mpc(1,3)
            True
        """
        return (mpc, (), self._mpc_)

    def __setstate__(self, val):
        """
        Support pickling ::

            sage: from mpmath import mpc
            sage: loads(dumps(mpc(1,3))) == mpc(1,3)
            True
        """
        self._mpc_ = val[0], val[1]

    def __repr__(self):
        """
        TESTS ::

            sage: from mpmath import mp
            sage: mp.pretty = True
            sage: repr(mp.mpc(2,3))
            '(2.0 + 3.0j)'
            sage: mp.pretty = False
            sage: repr(mp.mpc(2,3))
            "mpc(real='2.0', imag='3.0')"
        """
        if global_context.pretty:
            return str(self)
        re, im = self._mpc_
        n = repr_dps(global_opts.prec)
        return "mpc(real='%s', imag='%s')" % (to_str(re, n), to_str(im, n))

    def __str__(s):
        """
        TESTS ::

            sage: from mpmath import mp
            sage: str(mp.mpc(2,3))
            '(2.0 + 3.0j)'
        """
        return "(%s)" % libmp.mpc_to_str(s._mpc_, global_context._str_digits)

    def __bool__(self):
        """
        TESTS ::

            sage: from mpmath import mp
            sage: bool(mp.mpc(0,1))
            True
            sage: bool(mp.mpc(1,0))
            True
            sage: bool(mp.mpc(0,0))
            False
        """
        return self.re.special != S_ZERO or self.im.special != S_ZERO

    #def __complex__(self):
    #    a, b = self._mpc_
    #    return complex(libmp.to_float(a), libmp.to_float(b))

    def __complex__(self):
        """
        TESTS ::

            sage: from mpmath import mp
            sage: complex(mp.mpc(1,2)) == complex(1,2)
            True
        """
        return complex(MPF_to_double(&self.re, False), MPF_to_double(&self.im, False))

    def _get_mpc(self):
        """
        Returns tuple value of self ::

            sage: from mpmath import mp
            sage: mp.mpc(2,3)._mpc_
            ((0, 1, 1, 1), (0, 3, 0, 2))
        """
        return MPF_to_tuple(&self.re), MPF_to_tuple(&self.im)

    def _set_mpc(self, tuple v):
        """
        Sets tuple value of self (warning: unsafe) ::

            sage: from mpmath import mp
            sage: x = mp.mpc(2,3)
            sage: x._mpc_ = (x._mpc_[1], x._mpc_[0])
            sage: x
            mpc(real='3.0', imag='2.0')
        """
        MPF_set_tuple(&self.re, v[0])
        MPF_set_tuple(&self.im, v[1])

    _mpc_ = property(_get_mpc, _set_mpc, doc=_get_mpc.__doc__)

    @property
    def real(self):
        """
        Returns the real part of self as an mpf ::

            sage: from mpmath import mp
            sage: mp.mpc(1,2).real
            mpf('1.0')
        """
        cdef mpf r = mpf.__new__(mpf)
        MPF_set(&r.value, &self.re)
        return r

    @property
    def imag(self):
        """
        Returns the imaginary part of self as an mpf ::

            sage: from mpmath import mp
            sage: mp.mpc(1,2).imag
            mpf('2.0')
        """
        cdef mpf r = mpf.__new__(mpf)
        MPF_set(&r.value, &self.im)
        return r

    def __hash__(self):
        """
        Returns the hash value of self ::

        EXAMPLES::

            sage: from mpmath import mp
            sage: hash(mp.mpc(2,3)) == hash(complex(2,3))
            True

        TESTS:

        Check that :trac:`31676` is fixed::

            sage: from mpmath import mpc
            sage: hash(mpc(1, -1)) == hash(mpc(-1, -1))  # should not return OverflowError: Python int too large to convert to C ssize_t
            False
        """
        return hash(libmp.mpc_hash(self._mpc_))

    def __neg__(s):
        """
        Negates the number ::

            sage: from mpmath import mpc
            sage: -mpc(1,2)
            mpc(real='-1.0', imag='-2.0')
        """
        cdef mpc r = mpc.__new__(mpc)
        MPF_neg(&r.re, &s.re)
        MPF_neg(&r.im, &s.im)
        MPF_normalize(&r.re, global_opts)
        MPF_normalize(&r.im, global_opts)
        return r

    def conjugate(s):
        """
        Returns the complex conjugate ::

            sage: from mpmath import mpc
            sage: mpc(1,2).conjugate()
            mpc(real='1.0', imag='-2.0')
        """
        cdef mpc r = mpc.__new__(mpc)
        MPF_set(&r.re, &s.re)
        MPF_neg(&r.im, &s.im)
        MPF_normalize(&r.re, global_opts)
        MPF_normalize(&r.im, global_opts)
        return r

    def __pos__(s):
        """
        Rounds the number to the current working precision ::

            sage: from mpmath import mp
            sage: mp.prec = 200
            sage: x = mp.mpc(1) / 3
            sage: x.real.man
            1071292029505993517027974728227441735014801995855195223534251
            sage: mp.prec = 53
            sage: +x
            mpc(real='0.33333333333333331', imag='0.0')
            sage: (+x).real.man
            6004799503160661
        """
        cdef mpc r = mpc.__new__(mpc)
        MPF_set(&r.re, &s.re)
        MPF_set(&r.im, &s.im)
        MPF_normalize(&r.re, global_opts)
        MPF_normalize(&r.im, global_opts)
        return r

    def __abs__(s):
        """
        Returns the absolute value of self ::

            sage: from mpmath import mpc
            sage: abs(mpc(3,4))
            mpf('5.0')
        """
        cdef mpf r = mpf.__new__(mpf)
        MPF_hypot(&r.value, &s.re, &s.im, global_opts)
        return r

    def __richcmp__(self, other, int op):
        """
        Complex numbers can be compared for equality ::

            sage: from mpmath import mpc
            sage: mpc(2,3) == complex(2,3)
            True
            sage: mpc(-2,3) == complex(2,3)
            False
            sage: mpc(-2,3) != complex(2,3)
            True
        """
        return binop(OP_RICHCMP+op, self, other, global_opts)


def hypsum_internal(int p, int q, param_types, str ztype, coeffs, z,
    long prec, long wp, long epsshift, dict magnitude_check, kwargs):
    """
    Internal summation routine for hypergeometric series (wraps
    extension function MPF_hypsum to handle mpf/mpc types).

    EXAMPLES::

        sage: from mpmath import mp  # indirect doctest
        sage: mp.dps = 15
        sage: print(mp.hyp1f1(1,2,3))
        6.36184564106256

    .. TODO::

        convert mpf/mpc parameters to fixed-point numbers here
        instead of converting to tuples within MPF_hypsum.
    """
    cdef mpf f
    cdef mpc c
    c = mpc.__new__(mpc)
    have_complex, magn = MPF_hypsum(&c.re, &c.im, p, q, param_types,
        ztype, coeffs, z, prec, wp, epsshift, magnitude_check, kwargs)
    if have_complex:
        v = c
    else:
        f = mpf.__new__(mpf)
        MPF_set(&f.value, &c.re)
        v = f
    return v, have_complex, magn
