def mpf_asin(x, prec, rnd=round_fast):
sign, man, exp, bc = x
if bc+exp > 0 and x not in (fone, fnone):
raise ComplexResult("asin(x) is real only for -1 <= x <= 1")
flag_nr = True
if prec < 1000 or exp+bc < -13:
flag_nr = False
else:
ebc = exp + bc
if ebc < -13:
flag_nr = False
elif ebc < -3:
if prec < 3000:
flag_nr = False
if not flag_nr:
# asin(x) = 2*atan(x/(1+sqrt(1-x**2)))
wp = prec + 15
a = mpf_mul(x, x)
b = mpf_add(fone, mpf_sqrt(mpf_sub(fone, a, wp), wp), wp)
c = mpf_div(x, b, wp)
return mpf_shift(mpf_atan(c, prec, rnd), 1)
# use Newton's method
extra = 10
extra_p = 10
prec2 = prec + extra
r = math.asin(to_float(x))
r = from_float(r, 50, rnd)
for p in giant_steps(50, prec2):
wp = p + extra_p
c, s = cos_sin(r, wp, rnd)
tmp = mpf_sub(x, s, wp, rnd)
tmp = mpf_div(tmp, c, wp, rnd)
r = mpf_add(r, tmp, wp, rnd)
sign, man, exp, bc = r
return normalize(sign, man, exp, bc, prec, rnd)
def mpc_to_complex(z, strict=False):
re, im = z
return complex(to_float(re, strict), to_float(im, strict))
def __float__(s): return to_float(s._mpf_) def __complex__(s): return complex(float(s))
def mpc_to_complex(z, strict=False):
re, im = z
return complex(to_float(re, strict), to_float(im, strict))
def __float__(s): return to_float(s._mpf_) def __complex__(s): return complex(float(s))