def __rmul__(s, t):
prec, rounding = prec_rounding
if isinstance(t, int_types):
return make_mpc(mpc_mul_int(s._mpc_, t, prec, rounding))
t = mpc_convert_lhs(t)
if t is NotImplemented:
return t
return t * s
def __rmul__(s, t):
prec, rounding = prec_rounding
if isinstance(t, int_types):
return make_mpc(mpc_mul_int(s._mpc_, t, prec, rounding))
t = mpc_convert_lhs(t)
if t is NotImplemented:
return t
return t * s
def __mul__(s, t):
prec, rounding = prec_rounding
if not isinstance(t, mpc):
if isinstance(t, int_types):
return make_mpc(mpc_mul_int(s._mpc_, t, prec, rounding))
t = mpc_convert_lhs(t)
if t is NotImplemented:
return t
if isinstance(t, mpf):
return make_mpc(mpc_mul_mpf(s._mpc_, t._mpf_, prec, rounding))
t = mpc(t)
return make_mpc(mpc_mul(s._mpc_, t._mpc_, prec, rounding))
def __mul__(s, t):
prec, rounding = prec_rounding
if not isinstance(t, mpc):
if isinstance(t, int_types):
return make_mpc(mpc_mul_int(s._mpc_, t, prec, rounding))
t = mpc_convert_lhs(t)
if t is NotImplemented:
return t
if isinstance(t, mpf):
return make_mpc(mpc_mul_mpf(s._mpc_, t._mpf_, prec, rounding))
t = mpc(t)
return make_mpc(mpc_mul(s._mpc_, t._mpc_, prec, rounding))
def mpc_psi0(z, prec, rnd=round_fast):
"""
Computation of the digamma function (psi function of order 0)
of a complex argument.
"""
re, im = z
# Fall back to the real case
if im == fzero:
return (mpf_psi0(re, prec, rnd), fzero)
wp = prec + 20
sign, man, exp, bc = re
# Reflection formula
if sign and exp+bc > 3:
c = mpc_cos_pi(z, wp)
s = mpc_sin_pi(z, wp)
q = mpc_mul_mpf(mpc_div(c, s, wp), mpf_pi(wp), wp)
p = mpc_psi0(mpc_sub(mpc_one, z, wp), wp)
return mpc_sub(p, q, prec, rnd)
# Just the logarithmic term
if (not sign) and bc + exp > wp:
return mpc_log(mpc_sub(z, mpc_one, wp), prec, rnd)
# Initial recurrence to obtain a large enough z
w = to_int(re)
n = int(0.11*wp) + 2
s = mpc_zero
if w < n:
for k in xrange(w, n):
s = mpc_sub(s, mpc_reciprocal(z, wp), wp)
z = mpc_add_mpf(z, fone, wp)
z = mpc_sub(z, mpc_one, wp)
# Logarithmic and endpoint term
s = mpc_add(s, mpc_log(z, wp), wp)
s = mpc_add(s, mpc_div(mpc_half, z, wp), wp)
# Euler-Maclaurin remainder sum
z2 = mpc_square(z, wp)
t = mpc_one
prev = mpc_zero
k = 1
eps = mpf_shift(fone, -wp+2)
while 1:
t = mpc_mul(t, z2, wp)
bern = mpf_bernoulli(2*k, wp)
term = mpc_mpf_div(bern, mpc_mul_int(t, 2*k, wp), wp)
s = mpc_sub(s, term, wp)
szterm = mpc_abs(term, 10)
if k > 2 and mpf_le(szterm, eps):
break
prev = term
k += 1
return s
def mpc_psi0(z, prec, rnd=round_fast):
"""
Computation of the digamma function (psi function of order 0)
of a complex argument.
"""
re, im = z
# Fall back to the real case
if im == fzero:
return (mpf_psi0(re, prec, rnd), fzero)
wp = prec + 20
sign, man, exp, bc = re
# Reflection formula
if sign and exp + bc > 3:
c = mpc_cos_pi(z, wp)
s = mpc_sin_pi(z, wp)
q = mpc_mul(mpc_div(c, s, wp), (mpf_pi(wp), fzero), wp)
p = mpc_psi0(mpc_sub(mpc_one, z, wp), wp)
return mpc_sub(p, q, prec, rnd)
# Just the logarithmic term
if (not sign) and bc + exp > wp:
return mpc_log(mpc_sub(z, mpc_one, wp), prec, rnd)
# Initial recurrence to obtain a large enough z
w = to_int(re)
n = int(0.11 * wp) + 2
s = mpc_zero
if w < n:
for k in xrange(w, n):
s = mpc_sub(s, mpc_div(mpc_one, z, wp), wp)
z = mpc_add_mpf(z, fone, wp)
z = mpc_sub(z, mpc_one, wp)
# Logarithmic and endpoint term
s = mpc_add(s, mpc_log(z, wp), wp)
s = mpc_add(s, mpc_div(mpc_half, z, wp), wp)
# Euler-Maclaurin remainder sum
z2 = mpc_mul(z, z, wp)
t = mpc_one
prev = mpc_zero
k = 1
eps = mpf_shift(fone, -wp + 2)
while 1:
t = mpc_mul(t, z2, wp)
bern = mpf_bernoulli(2 * k, wp)
term = mpc_div((bern, fzero), mpc_mul_int(t, 2 * k, wp), wp)
s = mpc_sub(s, term, wp)
szterm = mpc_abs(term, 10)
if k > 2 and mpf_le(szterm, eps):
break
prev = term
k += 1
return s