def nthroot(ctx, x, n):
x = ctx.convert(x)
n = int(n)
if hasattr(x, '_mpf_'):
try:
return ctx.make_mpf(libelefun.mpf_nthroot(x._mpf_, n, *ctx._prec_rounding))
except ComplexResult:
if ctx.trap_complex:
raise
x = (x._mpf_, libmpf.fzero)
else:
x = x._mpc_
return ctx.make_mpc(libmpc.mpc_nthroot(x, n, *ctx._prec_rounding))
def nthroot(x, n):
"""principal n-th root"""
n = int(n)
if isinstance(x, mpf):
try:
return make_mpf(libelefun.mpf_nthroot(x._mpf_, n, *prec_rounding))
except ComplexResult:
if mp.trap_complex:
raise
x = (x._mpf_, libmpf.fzero)
else:
x = x._mpc_
return make_mpc(libmpc.mpc_nthroot(x, n, *prec_rounding))
def nthroot(x, n):
"""principal n-th root"""
n = int(n)
if isinstance(x, mpf):
try:
return make_mpf(libelefun.mpf_nthroot(x._mpf_, n, *prec_rounding))
except ComplexResult:
if mp.trap_complex:
raise
x = (x._mpf_, libmpf.fzero)
else:
x = x._mpc_
return make_mpc(libmpc.mpc_nthroot(x, n, *prec_rounding))
def nthroot(ctx, x, n):
x = ctx.convert(x)
n = int(n)
if hasattr(x, '_mpf_'):
try:
return ctx.make_mpf(
libelefun.mpf_nthroot(x._mpf_, n, *ctx._prec_rounding))
except ComplexResult:
if ctx.trap_complex:
raise
x = (x._mpf_, libmpf.fzero)
else:
x = x._mpc_
return ctx.make_mpc(libmpc.mpc_nthroot(x, n, *ctx._prec_rounding))
def mpc_nthroot(z, n, prec, rnd=round_fast):
"""
Complex n-th root.
Use Newton method as in the real case when it is faster,
otherwise use z**(1/n)
"""
a, b = z
if a[0] == 0 and b == fzero:
re = mpf_nthroot(a, n, prec, rnd)
return (re, fzero)
if n < 2:
if n == 0:
return mpc_one
if n == 1:
return mpc_pos((a, b), prec, rnd)
if n == -1:
return mpc_div(mpc_one, (a, b), prec, rnd)
inverse = mpc_nthroot((a, b), -n, prec + 5, reciprocal_rnd[rnd])
return mpc_div(mpc_one, inverse, prec, rnd)
if n <= 20:
prec2 = int(1.2 * (prec + 10))
asign, aman, aexp, abc = a
bsign, bman, bexp, bbc = b
pf = mpc_abs((a, b), prec)
if pf[-2] + pf[-1] > -10 and pf[-2] + pf[-1] < prec:
af = to_fixed(a, prec2)
bf = to_fixed(b, prec2)
re, im = mpc_nthroot_fixed(af, bf, n, prec2)
extra = 10
re = from_man_exp(re, -prec2 - extra, prec2, rnd)
im = from_man_exp(im, -prec2 - extra, prec2, rnd)
return re, im
fn = from_int(n)
prec2 = prec + 10 + 10
nth = mpf_rdiv_int(1, fn, prec2)
re, im = mpc_pow((a, b), (nth, fzero), prec2, rnd)
re = normalize(re[0], re[1], re[2], re[3], prec, rnd)
im = normalize(im[0], im[1], im[2], im[3], prec, rnd)
return re, im
def mpc_nthroot(z, n, prec, rnd=round_fast):
"""
Complex n-th root.
Use Newton method as in the real case when it is faster,
otherwise use z**(1/n)
"""
a, b = z
if a[0] == 0 and b == fzero:
re = mpf_nthroot(a, n, prec, rnd)
return (re, fzero)
if n < 2:
if n == 0:
return mpc_one
if n == 1:
return mpc_pos((a, b), prec, rnd)
if n == -1:
return mpc_div(mpc_one, (a, b), prec, rnd)
inverse = mpc_nthroot((a, b), -n, prec+5, reciprocal_rnd[rnd])
return mpc_div(mpc_one, inverse, prec, rnd)
if n <= 20:
prec2 = int(1.2 * (prec + 10))
asign, aman, aexp, abc = a
bsign, bman, bexp, bbc = b
pf = mpc_abs((a,b), prec)
if pf[-2] + pf[-1] > -10 and pf[-2] + pf[-1] < prec:
af = to_fixed(a, prec2)
bf = to_fixed(b, prec2)
re, im = mpc_nthroot_fixed(af, bf, n, prec2)
extra = 10
re = from_man_exp(re, -prec2-extra, prec2, rnd)
im = from_man_exp(im, -prec2-extra, prec2, rnd)
return re, im
fn = from_int(n)
prec2 = prec+10 + 10
nth = mpf_rdiv_int(1, fn, prec2)
re, im = mpc_pow((a, b), (nth, fzero), prec2, rnd)
re = normalize(re[0], re[1], re[2], re[3], prec, rnd)
im = normalize(im[0], im[1], im[2], im[3], prec, rnd)
return re, im
imb = (imc << p) // r4
re = (reb + (n-1)*lshift(re, p-prevp))//n
im = (imb + (n-1)*lshift(im, p-prevp))//n
prevp = p
return re, im
def mpc_nthroot((a, b), n, prec, rnd=round_fast):
"""
Complex n-th root.
Use Newton method as in the real case when it is faster,
otherwise use z**(1/n)
"""
if a[0] == 0 and b == fzero:
re = mpf_nthroot(a, n, prec, rnd)
return (re, fzero)
if n < 2:
if n == 0:
return mpc_one
if n == 1:
return mpc_pos((a, b), prec, rnd)
if n == -1:
return mpc_div(mpc_one, (a, b), prec, rnd)
inverse = mpc_nthroot((a, b), -n, prec+5, reciprocal_rnd[rnd])
return mpc_div(mpc_one, inverse, prec, rnd)
if n <= 20:
prec2 = int(1.2 * (prec + 10))
asign, aman, aexp, abc = a
bsign, bman, bexp, bbc = b
pf = mpc_abs((a,b), prec)