LOG_FACT_DP Function

private function LOG_FACT_DP(N) result(LOG_FACT)

$\ln(n!)$, via $\ln(n!) = \ln\Gamma(n{+}1)$ (the intrinsic LOG_GAMMA). Used throughout CGCOEFF, SSH, and ASSOC_LEGENDRE to evaluate factorial ratios like $\sqrt{(\ell-k)!/(\ell+k)!}$ as $\exp(\tfrac12[\texttt{LOG\_FACT}(\ell{-}k)-\texttt{LOG\_FACT}(\ell{+}k)])$ without overflowing the individual factorials for large $\ell$.

Returns: $\ln(n!)$.

Arguments

Return Value real(kind=dp)

  FUNCTION LOG_FACT_DP(N) RESULT(LOG_FACT)
  IMPLICIT NONE
  INTEGER(KIND=i4), INTENT(IN) :: N
  REAL(KIND=dp) :: LOG_FACT
  IF (N <= 1) THEN
    LOG_FACT = 0.0_dp
  ELSE
    ! ln(n!) = ln(Gamma(n+1))
    LOG_FACT = LOG_GAMMA(REAL(N + 1, KIND=dp))
  END IF
  END FUNCTION LOG_FACT_DP