def mpf_ei(x, prec, rnd=round_fast, e1=False):
if e1:
x = mpf_neg(x)
sign, man, exp, bc = x
if e1 and not sign:
if x == fzero:
return finf
raise ComplexResult("E1(x) for x < 0")
if man:
xabs = 0, man, exp, bc
xmag = exp+bc
wp = prec + 20
can_use_asymp = xmag > wp
if not can_use_asymp:
if exp >= 0:
xabsint = man << exp
else:
xabsint = man >> (-exp)
can_use_asymp = xabsint > int(wp*0.693) + 10
if can_use_asymp:
if xmag > wp:
v = fone
else:
v = from_man_exp(ei_asymptotic(to_fixed(x, wp), wp), -wp)
v = mpf_mul(v, mpf_exp(x, wp), wp)
v = mpf_div(v, x, prec, rnd)
else:
wp += 2*int(to_int(xabs))
u = to_fixed(x, wp)
v = ei_taylor(u, wp) + euler_fixed(wp)
t1 = from_man_exp(v,-wp)
t2 = mpf_log(xabs,wp)
v = mpf_add(t1, t2, prec, rnd)
else:
if x == fzero: v = fninf
elif x == finf: v = finf
elif x == fninf: v = fzero
else: v = fnan
if e1:
v = mpf_neg(v)
return v
def mpf_ei(x, prec, rnd=round_fast, e1=False):
if e1:
x = mpf_neg(x)
sign, man, exp, bc = x
if e1 and not sign:
if x == fzero:
return finf
raise ComplexResult("E1(x) for x < 0")
if man:
xabs = 0, man, exp, bc
xmag = exp + bc
wp = prec + 20
can_use_asymp = xmag > wp
if not can_use_asymp:
if exp >= 0:
xabsint = man << exp
else:
xabsint = man >> (-exp)
can_use_asymp = xabsint > int(wp * 0.693) + 10
if can_use_asymp:
if xmag > wp:
v = fone
else:
v = from_man_exp(ei_asymptotic(to_fixed(x, wp), wp), -wp)
v = mpf_mul(v, mpf_exp(x, wp), wp)
v = mpf_div(v, x, prec, rnd)
else:
wp += 2 * int(to_int(xabs))
u = to_fixed(x, wp)
v = ei_taylor(u, wp) + euler_fixed(wp)
t1 = from_man_exp(v, -wp)
t2 = mpf_log(xabs, wp)
v = mpf_add(t1, t2, prec, rnd)
else:
if x == fzero: v = fninf
elif x == finf: v = finf
elif x == fninf: v = fzero
else: v = fnan
if e1:
v = mpf_neg(v)
return v
def mpc_ei(z, prec, rnd=round_fast, e1=False):
if e1:
z = mpc_neg(z)
a, b = z
asign, aman, aexp, abc = a
bsign, bman, bexp, bbc = b
if b == fzero:
if e1:
x = mpf_neg(mpf_ei(a, prec, rnd))
if not asign:
y = mpf_neg(mpf_pi(prec, rnd))
else:
y = fzero
return x, y
else:
return mpf_ei(a, prec, rnd), fzero
if a != fzero:
if not aman or not bman:
return (fnan, fnan)
wp = prec + 40
amag = aexp+abc
bmag = bexp+bbc
zmag = max(amag, bmag)
can_use_asymp = zmag > wp
if not can_use_asymp:
zabsint = abs(to_int(a)) + abs(to_int(b))
can_use_asymp = zabsint > int(wp*0.693) + 20
try:
if can_use_asymp:
if zmag > wp:
v = fone, fzero
else:
zre = to_fixed(a, wp)
zim = to_fixed(b, wp)
vre, vim = complex_ei_asymptotic(zre, zim, wp)
v = from_man_exp(vre, -wp), from_man_exp(vim, -wp)
v = mpc_mul(v, mpc_exp(z, wp), wp)
v = mpc_div(v, z, wp)
if e1:
v = mpc_neg(v, prec, rnd)
else:
x, y = v
if bsign:
v = mpf_pos(x, prec, rnd), mpf_sub(y, mpf_pi(wp), prec, rnd)
else:
v = mpf_pos(x, prec, rnd), mpf_add(y, mpf_pi(wp), prec, rnd)
return v
except NoConvergence:
pass
#wp += 2*max(0,zmag)
wp += 2*int(to_int(mpc_abs(z, 5)))
zre = to_fixed(a, wp)
zim = to_fixed(b, wp)
vre, vim = complex_ei_taylor(zre, zim, wp)
vre += euler_fixed(wp)
v = from_man_exp(vre,-wp), from_man_exp(vim,-wp)
if e1:
u = mpc_log(mpc_neg(z),wp)
else:
u = mpc_log(z,wp)
v = mpc_add(v, u, prec, rnd)
if e1:
v = mpc_neg(v)
return v
def mpc_ei(z, prec, rnd=round_fast, e1=False):
if e1:
z = mpc_neg(z)
a, b = z
asign, aman, aexp, abc = a
bsign, bman, bexp, bbc = b
if b == fzero:
if e1:
x = mpf_neg(mpf_ei(a, prec, rnd))
if not asign:
y = mpf_neg(mpf_pi(prec, rnd))
else:
y = fzero
return x, y
else:
return mpf_ei(a, prec, rnd), fzero
if a != fzero:
if not aman or not bman:
return (fnan, fnan)
wp = prec + 40
amag = aexp + abc
bmag = bexp + bbc
zmag = max(amag, bmag)
can_use_asymp = zmag > wp
if not can_use_asymp:
zabsint = abs(to_int(a)) + abs(to_int(b))
can_use_asymp = zabsint > int(wp * 0.693) + 20
try:
if can_use_asymp:
if zmag > wp:
v = fone, fzero
else:
zre = to_fixed(a, wp)
zim = to_fixed(b, wp)
vre, vim = complex_ei_asymptotic(zre, zim, wp)
v = from_man_exp(vre, -wp), from_man_exp(vim, -wp)
v = mpc_mul(v, mpc_exp(z, wp), wp)
v = mpc_div(v, z, wp)
if e1:
v = mpc_neg(v, prec, rnd)
else:
x, y = v
if bsign:
v = mpf_pos(x, prec, rnd), mpf_sub(y, mpf_pi(wp), prec,
rnd)
else:
v = mpf_pos(x, prec, rnd), mpf_add(y, mpf_pi(wp), prec,
rnd)
return v
except NoConvergence:
pass
#wp += 2*max(0,zmag)
wp += 2 * int(to_int(mpc_abs(z, 5)))
zre = to_fixed(a, wp)
zim = to_fixed(b, wp)
vre, vim = complex_ei_taylor(zre, zim, wp)
vre += euler_fixed(wp)
v = from_man_exp(vre, -wp), from_man_exp(vim, -wp)
if e1:
u = mpc_log(mpc_neg(z), wp)
else:
u = mpc_log(z, wp)
v = mpc_add(v, u, prec, rnd)
if e1:
v = mpc_neg(v)
return v