def expn(n, x):
n, x = _promote_args_inexact("expn", n, x)
_c = _constant_like
zero = _c(x, 0)
one = _c(x, 1)
conds = [
(n < _c(n, 0)) | (x < zero),
(x == zero) & (n < _c(n, 2)),
(x == zero) & (n >= _c(n, 2)),
(n == _c(n, 0)) & (x >= zero),
(n >= _c(n, 5000)),
(x > one),
]
n1 = jnp.where(n == _c(n, 1), n + n, n)
vals = [
jnp.nan,
jnp.inf,
one / n1, # prevent div by zero
jnp.exp(-x) / x,
partial(_expn3, n),
partial(_expn2, n),
partial(_expn1, n),
]
ret = jnp.piecewise(x, conds, vals)
return ret
def _expi_pos(x):
# x > 0
_c = _constant_like
conds = [(_c(x, 0) < x) & (x <= _c(x, 2))] + [(_c(x, 2**i) < x) &
(x <= _c(x, 2**(i + 1)))
for i in range(1, 6)]
return jnp.piecewise(
x,
conds,
[_expint1, _expint2, _expint3, _expint4, _expint5, _expint6, _expint7],
)
def expi(x):
(x, ) = _promote_args_inexact("expi", x)
ret = jnp.piecewise(x, [x < 0], [lambda x: -exp1(-x), _expi_pos])
return ret
