https://gcc.gnu.org/bugzilla/show_bug.cgi?id=86655
Bug ID: 86655
Summary: std::assoc_legendre should not constrain the value of
m
Product: gcc
Version: 9.0
Status: UNCONFIRMED
Severity: normal
Priority: P3
Component: libstdc++
Assignee: unassigned at gcc dot gnu.org
Reporter: kretz at kde dot org
Target Milestone: ---
https://wg21.link/c.math#sf.cmath.assoc_legendre leaves m unconstrained.
__detail::__assoc_legendre_p documents "@param m The order of the associated
Legendre function. @f$ m <= l @f$." and throws a domain error if m > l.
IIUC correctly, m > l simply implies that the result of std::assoc_legendre is
0. Which is why Wikipedia documents "This equation has nonzero solutions that
are nonsingular on [−1, 1] only if ℓ and m are integers with 0 ≤ m ≤ ℓ".
If this is correct, then the m <= l restriction should be removed. Otherwise,
we'd need to file a defect report to the C++ standard to constrain m.
