def sinh_cosh(x):
"""
sinh_cosh(x) -> (number, number)
Return a tuple containing the hyperbolic sine and cosine of x.
"""
if isinstance(x, mpfr):
res1 = _new_mpfr(gmp.mpfr_get_prec(x._mpfr))
res2 = _new_mpfr(gmp.mpfr_get_prec(x._mpfr))
mpfr_x = x._mpfr
elif isinstance(x, float):
res1 = _new_mpfr()
res2 = _new_mpfr()
mpfr_x = res1
gmp.mpfr_set_d(mpfr_x, x, gmp.MPFR_RNDN)
elif isinstance(x, (int, long)):
res1 = _new_mpfr()
res2 = _new_mpfr()
mpfr_x = res1
_pyint_to_mpfr(x, mpfr_x)
elif isinstance(x, mpz):
res1 = _new_mpfr()
res2 = _new_mpfr()
mpfr_x = res1
gmp.mpfr_set_z(mpfr_x, x._mpz, gmp.MPFR_RNDN)
elif isinstance(x, mpq):
res1 = _new_mpfr()
res2 = _new_mpfr()
mpfr_x = res1
gmp.mpfr_set_q(mpfr_x, x._mpq, gmp.MPFR_RNDN)
else:
raise TypeError
gmp.mpfr_sinh_cosh(res1, res2, mpfr_x, gmp.MPFR_RNDN)
return (mpfr._from_c_mpfr(res1), mpfr._from_c_mpfr(res2))
def _init_check_mpfr(x):
"""
Returns a new mpfr and a pointer to a c mpfr storing the value of x
"""
if isinstance(x, mpfr):
res = _new_mpfr(gmp.mpfr_get_prec(x._mpfr))
mpfr_x = x._mpfr
elif isinstance(x, float):
res = _new_mpfr()
mpfr_x = res # avoid initialising another c mpfr
gmp.mpfr_set_d(mpfr_x, x, gmp.MPFR_RNDN)
elif isinstance(x, (int, long)):
res = _new_mpfr()
mpfr_x = res # avoid initialising another c mpfr
_pyint_to_mpfr(x, mpfr_x)
elif isinstance(x, mpz):
res = _new_mpfr()
mpfr_x = res # avoid initialising another c mpfr
gmp.mpfr_set_z(mpfr_x, x._mpz, gmp.MPFR_RNDN)
elif isinstance(x, mpq):
res = _new_mpfr()
mpfr_x = res # avoid initialising another c mpfr
gmp.mpfr_set_q(mpfr_x, x._mpq, gmp.MPFR_RNDN)
else:
raise TypeError
return res, mpfr_x
def __init__(self, *args):
nargs = len(args)
if nargs == 1 and isinstance(args[0], self.__class__):
self._mpfr = args[0]._mpfr
return
if nargs > 3:
raise TypeError("mpfr() requires 0 to 3 arguments")
if nargs >= 2:
a = self._mpfr = ffi.gc(_new_mpfr(prec=args[1]), _del_mpfr)
else:
a = self._mpfr = ffi.gc(_new_mpfr(), _del_mpfr)
if nargs == 0:
gmp.mpfr_set_zero(a, 1)
elif nargs == 3:
if isinstance(args[0], str):
_str_to_mpfr(args[0], args[2], a)
else:
raise TypeError('function takes at most 2 arguments (%i given)' % nargs)
else:
if isinstance(args[0], str):
_str_to_mpfr(args[0], 10, a)
elif isinstance(args[0], float):
gmp.mpfr_set_d(a, args[0], gmp.MPFR_RNDN)
elif isinstance(args[0], (int, long)):
_pyint_to_mpfr(args[0], a)
elif isinstance(args[0], mpz):
gmp.mpfr_set_z(a, args[0]._mpz, gmp.MPFR_RNDN)
elif isinstance(args[0], mpq):
gmp.mpfr_set_q(a, args[0]._mpq, gmp.MPFR_RNDN)
else:
raise TypeError('cannot construct mpfr from %s.' % args[0])
def __pow__(self, other):
res = _new_mpfr()
if isinstance(other, mpfr):
gmp.mpfr_pow(res, self._mpfr, other._mpfr, gmp.MPFR_RNDN)
elif isinstance(other, mpq):
# There is no mpfr_pow_q
gmp.mpfr_set_q(res, other._mpq, gmp.MPFR_RNDN)
gmp.mpfr_pow(res, self._mpfr, res, gmp.MPFR_RNDN)
elif isinstance(other, mpz):
gmp.mpfr_pow_z(res, self._mpfr, other._mpz, gmp.MPFR_RNDN)
elif isinstance(other, float):
# There is no mpfr_pow_d
gmp.mpfr_set_d(res, other, gmp.MPFR_RNDN)
gmp.mpfr_pow(res, self._mpfr, res, gmp.MPFR_RNDN)
elif isinstance(other, (int, long)):
if -sys.maxsize - 1 <= other <= sys.maxsize:
gmp.mpfr_pow_si(res, self._mpfr, other, gmp.MPFR_RNDN)
elif 0 <= other <= MAX_UI:
gmp.mpfr_pow_ui(res, self._mpfr, other, gmp.MPFR_RNDN)
else:
tmp_mpz = _new_mpz()
_pylong_to_mpz(other, tmp_mpz)
gmp.mpfr_pow_z(res, self._mpfr, tmp_mpz, gmp.MPFR_RNDN)
_del_mpz(tmp_mpz)
else:
return NotImplemented
return mpfr._from_c_mpfr(res)
def atan2(y, x):
"""
atan2(y, x) -> number
Return the arc-tangent of (y/x).
"""
# X
if isinstance(x, mpfr):
mpfr_x = x._mpfr
elif isinstance(x, float):
mpfr_x = _new_mpfr()
gmp.mpfr_set_d(mpfr_x, x, gmp.MPFR_RNDN)
elif isinstance(x, (int, long)):
mpfr_x = _new_mpfr()
_pyint_to_mpfr(x, mpfr_x)
elif isinstance(x, mpz):
mpfr_x = _new_mpfr()
gmp.mpfr_set_z(mpfr_x, x._mpz, gmp.MPFR_RNDN)
elif isinstance(x, mpq):
mpfr_x = _new_mpfr()
gmp.mpfr_set_q(mpfr_x, x._mpq, gmp.MPFR_RNDN)
else:
raise TypeError
# Y
if isinstance(y, mpfr):
mpfr_y = y._mpfr
elif isinstance(y, float):
mpfr_y = _new_mpfr()
gmp.mpfr_set_d(mpfr_y, y, gmp.MPFR_RNDN)
elif isinstance(y, (int, long)):
mpfr_y = _new_mpfr()
_pyint_to_mpfr(y, mpfr_y)
elif isinstance(y, mpz):
mpfr_y = _new_mpfr()
gmp.mpfr_set_z(mpfr_y, y._mpz, gmp.MPFR_RNDN)
elif isinstance(y, mpq):
mpfr_y = _new_mpfr()
gmp.mpfr_set_q(mpfr_y, y._mpq, gmp.MPFR_RNDN)
else:
raise TypeError
res = _new_mpfr(min(gmp.mpfr_get_prec(mpfr_x), gmp.mpfr_get_prec(mpfr_x)))
gmp.mpfr_atan2(res, mpfr_y, mpfr_x, gmp.MPFR_RNDN)
return mpfr._from_c_mpfr(res)
def __rpow__(self, other):
res = _new_mpfr()
if isinstance(other, mpq):
# There is no mpfr_pow_q
gmp.mpfr_set_q(res, other._mpq, gmp.MPFR_RNDN)
gmp.mpfr_pow(res, res, self._mpfr, gmp.MPFR_RNDN)
elif isinstance(other, mpz):
# There is no mpfr_pow_z
gmp.mpfr_set_z(res, other._mpz, gmp.MPFR_RNDN)
gmp.mpfr_pow(res, res, self._mpfr, gmp.MPFR_RNDN)
elif isinstance(other, float):
# There is no mpfr_pow_d
gmp.mpfr_set_d(res, other, gmp.MPFR_RNDN)
gmp.mpfr_pow(res, res, self._mpfr, gmp.MPFR_RNDN)
elif isinstance(other, (int, long)):
# There is no mpfr_si_pow
_pyint_to_mpfr(other, res)
gmp.mpfr_pow(res, res, self._mpfr, gmp.MPFR_RNDN)
else:
return NotImplemented
return mpfr._from_c_mpfr(res)
def __init__(self, *args):
nargs = len(args)
# if nargs == 1 and isinstance(args[0], self.__class__):
# self._mpc = args[0]._mpc
# return
if nargs == 0:
self._mpc = ffi.gc(_new_mpc(), _del_mpc)
gmp.mpc_set_ui(self._mpc, 0, gmp.MPC_RNDNN)
elif isinstance(args[0], str): # unicode?
# First argument is a string
if nargs == 1:
prec, base = 0, 10
elif nargs == 2:
prec, base = args[1], 10
elif nargs == 3:
prec, base = args[1], args[2]
else:
raise TypeError("function takes at most 3 arguments (4 given)")
prec = _check_prec(prec)
self._mpc = ffi.gc(_new_mpc(prec), _del_mpc)
_str_to_mpc(args[0], base, self._mpc)
elif isinstance(args[0], (mpc, complex)):
# First argument is complex
if nargs == 1:
prec = (0, 0)
elif nargs == 2:
prec = _check_prec(args[1])
else:
raise TypeError("function takes at most 2 arguments (3 given)")
self._mpc = ffi.gc(_new_mpc(prec), _del_mpc)
if isinstance(args[0], mpc):
gmp.mpc_set(self._mpc, args[0]._mpc, gmp.MPC_RNDNN)
elif isinstance(args[0], complex):
gmp.mpc_set_d_d(self._mpc, args[0].real, args[0].imag,
gmp.MPC_RNDNN)
elif isinstance(args[0], (mpfr, mpq, mpz, float, int, long)):
# First argument is real
if nargs <= 2:
prec = (0, 0)
elif nargs == 3:
prec = _check_prec(args[2])
else:
raise TypeError("function takes at most 3 arguments (4 given)")
self._mpc = ffi.gc(_new_mpc(prec), _del_mpc)
realref = gmp.mpc_realref(self._mpc)
imagref = gmp.mpc_imagref(self._mpc)
if isinstance(args[0], mpfr):
gmp.mpfr_set(realref, args[0]._mpfr, gmp.MPFR_RNDN)
elif isinstance(args[0], mpz):
gmp.mpfr_set_z(realref, args[0]._mpz, gmp.MPFR_RNDN)
elif isinstance(args[0], mpq):
gmp.mpfr_set_q(realref, args[0]._mpq, gmp.MPFR_RNDN)
elif isinstance(args[0], float):
gmp.mpfr_set_d(realref, args[0], gmp.MPFR_RNDN)
elif isinstance(args[0], (int, long)):
_pyint_to_mpfr(args[0], realref)
if nargs >= 2:
# Check if second argument is real
if isinstance(args[1], mpfr):
gmp.mpfr_set(imagref, args[1]._mpfr, gmp.MPFR_RNDN)
elif isinstance(args[1], mpz):
gmp.mpfr_set_z(imagref, args[1]._mpz, gmp.MPFR_RNDN)
elif isinstance(args[1], mpq):
gmp.mpfr_set_q(imagref, args[1]._mpq, gmp.MPFR_RNDN)
elif isinstance(args[1], float):
gmp.mpfr_set_d(imagref, args[1], gmp.MPFR_RNDN)
elif isinstance(args[1], (int, long)):
_pyint_to_mpfr(args[1], imagref)
else:
raise TypeError(
"invalid type for imaginary component in mpc()")
else:
gmp.mpfr_set_ui(imagref, 0, gmp.MPFR_RNDN)
else:
raise TypeError("mpc() requires numeric or string argument")
def __init__(self, *args):
nargs = len(args)
# if nargs == 1 and isinstance(args[0], self.__class__):
# self._mpc = args[0]._mpc
# return
if nargs == 0:
self._mpc = ffi.gc(_new_mpc(), _del_mpc)
gmp.mpc_set_ui(self._mpc, 0, gmp.MPC_RNDNN)
elif isinstance(args[0], str): # unicode?
# First argument is a string
if nargs == 1:
prec, base = 0, 10
elif nargs == 2:
prec, base = args[1], 10
elif nargs == 3:
prec, base = args[1], args[2]
else:
raise TypeError("function takes at most 3 arguments (4 given)")
prec = _check_prec(prec)
self._mpc = ffi.gc(_new_mpc(prec), _del_mpc)
_str_to_mpc(args[0], base, self._mpc)
elif isinstance(args[0], (mpc, complex)):
# First argument is complex
if nargs == 1:
prec = (0, 0)
elif nargs == 2:
prec = _check_prec(args[1])
else:
raise TypeError("function takes at most 2 arguments (3 given)")
self._mpc = ffi.gc(_new_mpc(prec), _del_mpc)
if isinstance(args[0], mpc):
gmp.mpc_set(self._mpc, args[0]._mpc, gmp.MPC_RNDNN)
elif isinstance(args[0], complex):
gmp.mpc_set_d_d(self._mpc, args[0].real, args[0].imag, gmp.MPC_RNDNN)
elif isinstance(args[0], (mpfr, mpq, mpz, float, int, long)):
# First argument is real
if nargs <= 2:
prec = (0, 0)
elif nargs == 3:
prec = _check_prec(args[2])
else:
raise TypeError("function takes at most 3 arguments (4 given)")
self._mpc = ffi.gc(_new_mpc(prec), _del_mpc)
realref = gmp.mpc_realref(self._mpc)
imagref = gmp.mpc_imagref(self._mpc)
if isinstance(args[0], mpfr):
gmp.mpfr_set(realref, args[0]._mpfr, gmp.MPFR_RNDN)
elif isinstance(args[0], mpz):
gmp.mpfr_set_z(realref, args[0]._mpz, gmp.MPFR_RNDN)
elif isinstance(args[0], mpq):
gmp.mpfr_set_q(realref, args[0]._mpq, gmp.MPFR_RNDN)
elif isinstance(args[0], float):
gmp.mpfr_set_d(realref, args[0], gmp.MPFR_RNDN)
elif isinstance(args[0], (int, long)):
_pyint_to_mpfr(args[0], realref)
if nargs >= 2:
# Check if second argument is real
if isinstance(args[1], mpfr):
gmp.mpfr_set(imagref, args[1]._mpfr, gmp.MPFR_RNDN)
elif isinstance(args[1], mpz):
gmp.mpfr_set_z(imagref, args[1]._mpz, gmp.MPFR_RNDN)
elif isinstance(args[1], mpq):
gmp.mpfr_set_q(imagref, args[1]._mpq, gmp.MPFR_RNDN)
elif isinstance(args[1], float):
gmp.mpfr_set_d(imagref, args[1], gmp.MPFR_RNDN)
elif isinstance(args[1], (int, long)):
_pyint_to_mpfr(args[1], imagref)
else:
raise TypeError("invalid type for imaginary component in mpc()")
else:
gmp.mpfr_set_ui(imagref, 0, gmp.MPFR_RNDN)
else:
raise TypeError("mpc() requires numeric or string argument")