def mpc_besseljn(n, z, prec, rounding=round_fast):
negate = n < 0 and n & 1
n = abs(n)
origprec = prec
prec += 20 + bitcount(abs(n))
zre, zim = z
zre = to_fixed(zre, prec)
zim = to_fixed(zim, prec)
z2re = (zre**2 - zim**2) >> prec
z2im = (zre * zim) >> (prec - 1)
if not n:
sre = tre = MP_ONE << prec
sim = tim = MP_ZERO
else:
re, im = complex_int_pow(zre, zim, n)
sre = tre = (re // int_fac(n)) >> ((n - 1) * prec + n)
sim = tim = (im // int_fac(n)) >> ((n - 1) * prec + n)
k = 1
while abs(tre) + abs(tim) > 3:
p = -4 * k * (k + n)
tre, tim = tre * z2re - tim * z2im, tim * z2re + tre * z2im
tre = (tre // p) >> prec
tim = (tim // p) >> prec
sre += tre
sim += tim
k += 1
if negate:
sre = -sre
sim = -sim
re = from_man_exp(sre, -prec, origprec, rounding)
im = from_man_exp(sim, -prec, origprec, rounding)
return (re, im)
def mpc_besseljn(n, z, prec, rounding=round_fast):
negate = n < 0 and n & 1
n = abs(n)
origprec = prec
zre, zim = z
mag = max(zre[2]+zre[3], zim[2]+zim[3])
prec += 20 + n*bitcount(n) + abs(mag)
if mag < 0:
prec -= n * mag
zre = to_fixed(zre, prec)
zim = to_fixed(zim, prec)
z2re = (zre**2 - zim**2) >> prec
z2im = (zre*zim) >> (prec-1)
if not n:
sre = tre = MPZ_ONE << prec
sim = tim = MPZ_ZERO
else:
re, im = complex_int_pow(zre, zim, n)
sre = tre = (re // ifac(n)) >> ((n-1)*prec + n)
sim = tim = (im // ifac(n)) >> ((n-1)*prec + n)
k = 1
while abs(tre) + abs(tim) > 3:
p = -4*k*(k+n)
tre, tim = tre*z2re - tim*z2im, tim*z2re + tre*z2im
tre = (tre // p) >> prec
tim = (tim // p) >> prec
sre += tre
sim += tim
k += 1
if negate:
sre = -sre
sim = -sim
re = from_man_exp(sre, -prec, origprec, rounding)
im = from_man_exp(sim, -prec, origprec, rounding)
return (re, im)
def mpc_besseljn(n, z, prec):
negate = n < 0 and n & 1
n = abs(n)
origprec = prec
prec += 20 + bitcount(abs(n))
zre, zim = z
zre = to_fixed(zre, prec)
zim = to_fixed(zim, prec)
z2re = (zre**2 - zim**2) >> prec
z2im = (zre*zim) >> (prec-1)
if not n:
sre = tre = MP_ONE << prec
sim = tim = MP_ZERO
else:
re, im = complex_int_pow(zre, zim, n)
sre = tre = (re // int_fac(n)) >> ((n-1)*prec + n)
sim = tim = (im // int_fac(n)) >> ((n-1)*prec + n)
k = 1
while abs(tre) + abs(tim) > 3:
p = -4*k*(k+n)
tre, tim = tre*z2re - tim*z2im, tim*z2re + tre*z2im
tre = (tre // p) >> prec
tim = (tim // p) >> prec
sre += tre
sim += tim
k += 1
if negate:
sre = -sre
sim = -sim
re = from_man_exp(sre, -prec, origprec, round_nearest)
im = from_man_exp(sim, -prec, origprec, round_nearest)
return (re, im)
