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 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 cot(x):
"""
cot(x) -> number
Return the cotangent of x; x in radians.
"""
res, x = _init_check_mpfr(x)
gmp.mpfr_cot(res, x, gmp.MPFR_RNDN)
return mpfr._from_c_mpfr(res)
def sec(x):
"""
sec(x) -> number
Return the secant of x; x in radians.
"""
res, x = _init_check_mpfr(x)
gmp.mpfr_sec(res, x, gmp.MPFR_RNDN)
return mpfr._from_c_mpfr(res)
def lngamma(x):
"""
lngamma(x) -> number
Return logarithm of gamma(x).
"""
res, x = _init_check_mpfr(x)
gmp.mpfr_lngamma(res, x, gmp.MPFR_RNDN)
return mpfr._from_c_mpfr(res)
def log2(x):
"""
log2(x) -> number
Return the base-2 logarithm of x.
"""
res, x = _init_check_mpfr(x)
gmp.mpfr_log2(res, x, gmp.MPFR_RNDN)
return mpfr._from_c_mpfr(res)
def coth(x):
"""
coth(x) -> number
Return the hyperbolic cotangent of x.
"""
res, x = _init_check_mpfr(x)
gmp.mpfr_coth(res, x, gmp.MPFR_RNDN)
return mpfr._from_c_mpfr(res)
def sech(x):
"""
sech(x) -> number
Return the hyperbolic secant of x.
"""
res, x = _init_check_mpfr(x)
gmp.mpfr_sech(res, x, gmp.MPFR_RNDN)
return mpfr._from_c_mpfr(res)
def ai(x):
"""
ai(x) -> number
Return the Airy function of x.
"""
res, mpfr_x = _init_check_mpfr(x)
gmp.mpfr_ai(res, mpfr_x, gmp.MPFR_RNDN)
return mpfr._from_c_mpfr(res)
def exp10(x):
"""
exp10(x) -> number
Return 10**x.
"""
res, x = _init_check_mpfr(x)
gmp.mpfr_exp10(res, x, gmp.MPFR_RNDN)
return mpfr._from_c_mpfr(res)
def y1(x):
"""
y1(x) -> number
Return the second kind Bessel function of order 1 of x.
"""
res, x = _init_check_mpfr(x)
gmp.mpfr_y1(res, x, gmp.MPFR_RNDN)
return mpfr._from_c_mpfr(res)
def erfc(x):
"""
zeta(x) -> number
Return complementary error function of x.
"""
res, x = _init_check_mpfr(x)
gmp.mpfr_erfc(res, x, gmp.MPFR_RNDN)
return mpfr._from_c_mpfr(res)
def j0(x):
"""
j0(x) -> number
Return the first kind Bessel function of order 0 of x.
"""
res, x = _init_check_mpfr(x)
gmp.mpfr_j0(res, x, gmp.MPFR_RNDN)
return mpfr._from_c_mpfr(res)
def digamma(x):
"""
digamma(x) -> number
Return digamma of x.
"""
res, x = _init_check_mpfr(x)
gmp.mpfr_digamma(res, x, gmp.MPFR_RNDN)
return mpfr._from_c_mpfr(res)
def li2(x):
"""
li2(x) -> number
Return the real part of dilogarithm of x.
"""
res, x = _init_check_mpfr(x)
gmp.mpfr_li2(res, x, gmp.MPFR_RNDN)
return mpfr._from_c_mpfr(res)
def eint(x):
"""
eint(x) -> number
Return the exponential integral of x.
"""
res, x = _init_check_mpfr(x)
gmp.mpfr_eint(res, x, gmp.MPFR_RNDN)
return mpfr._from_c_mpfr(res)
def expm1(x):
"""
expm1(x) -> number
Return exponential(x) - 1.
"""
res, x = _init_check_mpfr(x)
gmp.mpfr_expm1(res, x, gmp.MPFR_RNDN)
return mpfr._from_c_mpfr(res)
def log1p(x):
"""
log1p(x) -> number
Return the logarithm of (1+x).
"""
res, x = _init_check_mpfr(x)
gmp.mpfr_log1p(res, x, gmp.MPFR_RNDN)
return mpfr._from_c_mpfr(res)
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 yn(x, n):
"""
yn(x, n) -> number
Return the second kind Bessel function of order n of x.
"""
if not (isinstance(n, (int, long)) and -sys.maxsize-1 <= n <= sys.maxsize):
raise TypeError("yn() requires 'mpfr', 'int' arguments")
res, x = _init_check_mpfr(x)
gmp.mpfr_yn(res, n, x, gmp.MPFR_RNDN)
return mpfr._from_c_mpfr(res)
def hypot(x, y):
"""
hypot(y, x) -> number
Return the square root of (x**2 + y**2).
"""
# XXX Optimise
res, mpfr_x = _init_check_mpfr(x)
res, mpfr_y = _init_check_mpfr(y)
gmp.mpfr_hypot(res, mpfr_x, mpfr_y, gmp.MPFR_RNDN)
return mpfr._from_c_mpfr(res)
def lgamma(x):
"""
lgamma(x) -> (number, int)
Return a tuple containing the logarithm of the absolute value of
gamma(x) and the sign of gamma(x)
"""
res, x = _init_check_mpfr(x)
sgn = ffi.new('int *')
gmp.mpfr_lgamma(res, sgn, x, gmp.MPFR_RNDN)
return (mpfr._from_c_mpfr(res), int(sgn[0]))
def agm(x, y):
"""
agm(x, y) -> number
Return the arithmetic-geometric mean of x and y.
"""
# XXX Optimise
res, mpfr_x = _init_check_mpfr(x)
res, mpfr_y = _init_check_mpfr(y)
gmp.mpfr_agm(res, mpfr_x, mpfr_y, gmp.MPFR_RNDN)
return mpfr._from_c_mpfr(res)
def fms(x, y, z):
"""
fms(x, y, z) -> number
Return the correctly rounded result of (x * y) - z.
"""
# XXX Optimise
res, mpfr_x = _init_check_mpfr(x)
res, mpfr_y = _init_check_mpfr(y)
res, mpfr_z = _init_check_mpfr(z)
gmp.mpfr_fms(res, mpfr_x, mpfr_y, mpfr_z, gmp.MPFR_RNDN)
return mpfr._from_c_mpfr(res)
def zeta(x):
"""
zeta(x) -> number
Return Riemann zeta of x.
"""
# if isinstance(x, (int, long)) and 0 <= x <= MAX_UI:
# res = _new_mpfr()
# gmp.mpfr_zeta_ui(res, x, gmp.MPFR_RNDN)
res, x = _init_check_mpfr(x)
gmp.mpfr_zeta(res, x, gmp.MPFR_RNDN)
return mpfr._from_c_mpfr(res)
def sinh(x):
"""
sinh(x) -> number
Return the hyperbolic sine of x.
"""
try:
res, x = _init_check_mpfr(x)
gmp.mpfr_sinh(res, x, gmp.MPFR_RNDN)
return mpfr._from_c_mpfr(res)
except TypeError:
res, x = _init_check_mpc(x)
gmp.mpc_sinh(res, x, gmp.MPC_RNDNN)
return mpc._from_c_mpc(res)
def atanh(x):
"""
atanh(x) -> number
Return the inverse hyperbolic tangent of x.
"""
try:
res, x = _init_check_mpfr(x)
gmp.mpfr_atanh(res, x, gmp.MPFR_RNDN)
return mpfr._from_c_mpfr(res)
except TypeError:
res, x = _init_check_mpc(x)
gmp.mpc_atanh(res, x, gmp.MPC_RNDNN)
return mpc._from_c_mpc(res)
def atan(x):
"""
atan(x) -> number
Return the arc-tangent of x; x in radians.
"""
try:
res, x = _init_check_mpfr(x)
gmp.mpfr_atan(res, x, gmp.MPFR_RNDN)
return mpfr._from_c_mpfr(res)
except TypeError:
res, x = _init_check_mpc(x)
gmp.mpc_atan(res, x, gmp.MPC_RNDNN)
return mpc._from_c_mpc(res)
def sin(x):
"""
sin(x) -> number
Return the sine of x; x in radians.
"""
try:
res, x = _init_check_mpfr(x)
gmp.mpfr_sin(res, x, gmp.MPFR_RNDN)
return mpfr._from_c_mpfr(res)
except TypeError:
res, x = _init_check_mpc(x)
gmp.mpc_sin(res, x, gmp.MPC_RNDNN)
return mpc._from_c_mpc(res)
def log(x):
"""
log(x) -> number
Return the natural logarithm of x.
"""
try:
res, x = _init_check_mpfr(x)
gmp.mpfr_log(res, x, gmp.MPFR_RNDN)
return mpfr._from_c_mpfr(res)
except TypeError:
res, x = _init_check_mpc(x)
gmp.mpc_log(res, x, gmp.MPC_RNDNN)
return mpc._from_c_mpc(res)