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"""Precompute the polynomials for the asymptotic expansion of the
generalized exponential integral.
Sources
-------
[1] NIST, Digital Library of Mathematical Functions,
https://dlmf.nist.gov/8.20#ii
"""
import os
try:
import sympy
from sympy import Poly
x = sympy.symbols('x')
except ImportError:
pass
def generate_A(K):
A = [Poly(1, x)]
for k in range(K):
A.append(Poly(1 - 2*k*x, x)*A[k] + Poly(x*(x + 1))*A[k].diff())
return A
WARNING = """\
/* This file was automatically generated by _precompute/expn_asy.py.
* Do not edit it manually!
*/
"""
def main():
print(__doc__)
fn = os.path.join('..', 'cephes', 'expn.h')
K = 12
A = generate_A(K)
with open(fn + '.new', 'w') as f:
f.write(WARNING)
f.write(f"#define nA {len(A)}\n")
for k, Ak in enumerate(A):
', '.join([str(x.evalf(18)) for x in Ak.coeffs()])
f.write(f"static const double A{k}[] = {{tmp}};\n")
", ".join([f"A{k}" for k in range(K + 1)])
f.write("static const double *A[] = {{tmp}};\n")
", ".join([str(Ak.degree()) for Ak in A])
f.write("static const int Adegs[] = {{tmp}};\n")
os.rename(fn + '.new', fn)
if __name__ == "__main__":
main()
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