Tarun Prabhu bef2bb34bf [flang] Lowering and runtime support for F08 transformational intrinsics: BESSEL_JN and BESSEL_YN ...

The runtime implementation uses the recurrence relations

`J(n-1, x) = (2.0 / x) * n * J(n, x) - J(n+1, x)`
`Y(n+1, x) = (2.0 / x) * n * Y(n, x) - Y(n-1, x)`

(see https://dlmf.nist.gov/10.74.iv and https://dlmf.nist.gov/10.6.E1).

Although the standard requires that `N1` and `N2` in `BESSEL_JN(N1, N2, x)`
and `BESSEL_YN(N1, N2, x)` be non-negative, this is not checked in the
runtime functions. This is in keeping with some other compilers which also
return some results when `N1` and/or `N2` are negative.

The special case for `x == 0` is  handled in different runtime functions
for each of `BESSEL_JN` and `BESSEL_YN`. The lowering code checks for this
case and inserts the checks and the appropriate runtime calls in FIR.

The existing tests for the two intrinsics was modified to keep the style
consistent with the additional lowering tests that were added.

2022-12-19 07:59:38 -07:00

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