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 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 const_catalan(precision=0):
"""
const_catalan([precision=0]) -> mpfr
Return the catalan constant using the specified precision. If no
precision is specified, the default precision is used.
"""
res = _new_mpfr(precision)
gmp.mpfr_const_catalan(res, gmp.MPFR_RNDN)
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 factorial(n):
"""
factorial(n) -> number
Return the floating-point approximation to the factorial of n.
See fac(n) to get the exact integer result.
"""
if isinstance(n, (int, long)):
if 0 <= n <= MAX_UI:
res = _new_mpfr()
gmp.mpfr_fac_ui(res, n, gmp.MPFR_RNDN)
return mpfr._from_c_mpfr(res)
elif n < 0:
raise ValueError("factorial() of negative number")
raise TypeError("factorial() requires 'int' argument")
