def _eval_expint_k(A, B, x):
# helper function for all subsequent intervals
A, B = [jnp.array(U, dtype=x.dtype) for U in [A, B]]
one = _constant_like(x, 1.0)
w = one / x
f = jnp.polyval(A, w) / jnp.polyval(B, w)
f = w * f + one
return jnp.exp(x) * w * f
def _expint1(x):
# 0 < x <= 2
A = [
-5.350447357812542947283e0,
2.185049168816613393830e2,
-4.176572384826693777058e3,
5.541176756393557601232e4,
-3.313381331178144034309e5,
1.592627163384945414220e6,
]
B = [
1.0,
-5.250547959112862969197e1,
1.259616186786790571525e3,
-1.756549581973534652631e4,
1.493062117002725991967e5,
-7.294949239640527645655e5,
1.592627163384945429726e6,
]
A, B = [jnp.array(U, dtype=x.dtype) for U in [A, B]]
f = jnp.polyval(A, x) / jnp.polyval(B, x)
return x * f + jnp.euler_gamma + jnp.log(x)