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 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 sin_cos(x):
"""
sin_cos(x) -> (number, number)
Return a tuple containing the sine and cosine of x; x in radians.
"""
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
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:
if isinstance(x, mpc):
res1 = _new_mpc()
res2 = _new_mpc()
mpc_x = x._mpc
elif isinstance(x, complex):
res1 = _new_mpc()
res2 = _new_mpc()
mpc_x = res1
gmp.mpc_set_d_d(mpc_x, x.real, x.imag, gmp.MPC_RNDNN)
else:
raise TypeError
gmp.mpc_sin_cos(res1, res2, mpc_x, gmp.MPC_RNDNN, gmp.MPC_RNDNN)
return (mpc._from_c_mpc(res1), mpc._from_c_mpc(res2))
gmp.mpfr_sin_cos(res1, res2, mpfr_x, gmp.MPFR_RNDN)
return (mpfr._from_c_mpfr(res1), mpfr._from_c_mpfr(res2))
def _mpfr_to_str(a):
precision = int(log10(2) * gmp.mpfr_get_prec(a) + 2)
buf = ffi.new('char []', precision + 10)
fmtstr = "%.{0}Rg".format(precision)
buflen = gmp.mpfr_sprintf(buf, fmtstr.encode('UTF-8'), a)
if PY3:
pybuf = ffi.string(buf).decode('UTF-8')
else:
pybuf = ffi.string(buf)
if gmp.mpfr_number_p(a) and '.' not in pybuf:
pybuf = pybuf + '.0'
return pybuf
def _mpfr_to_str(a):
precision = int(log10(2) * gmp.mpfr_get_prec(a) + 2)
buf = ffi.new('char []', precision + 10)
fmtstr = "%.{0}Rg".format(precision)
buflen = gmp.mpfr_sprintf(buf, fmtstr.encode('UTF-8'), a)
if PY3:
pybuf = ffi.string(buf).decode('UTF-8')
else:
pybuf = ffi.string(buf)
if gmp.mpfr_number_p(a) and '.' not in pybuf:
pybuf = pybuf + '.0'
return pybuf
def precision(self):
return gmp.mpfr_get_prec(self._mpfr)