!****************************************************
!*    Program to demonstrate Log(X!) Subroutine     *
!* ------------------------------------------------ *
!* Reference: BASIC Scientific Subroutines, Vol. II *
!* By F.R. Ruckdeschel, BYTE/McGRAWW-HILL, 1981 [1].*
!*                                                  *
!*              F90 Version by J.-P. Moreau, Paris. *
!*                      (www.jpmoreau.fr)           *
!* ------------------------------------------------ *
!* SAMPLE RUN:                                      *
!*                                                  *
!*    X     LN(X!)        EXP(LN(X!))               *
!*  ----------------------------------              *
!*    1    -0.000307                1               *
!*    2     0.693146                2               *
!*    3     1.791759                6               *
!*    4     3.178054               24               *
!*    5     4.787492              120               *
!*    6     6.579251              720               *
!*    7     8.525161             5040               *
!*    8    10.604603            40320               *
!*    9    12.801827           362880               *
!*   10    15.104413          3628800               *
!*   11    17.502308         39916800               *
!*   12    19.987214        479001600               *
!*   13    22.552164       6227020800               *
!*   14    25.191221      87178291200               *
!*   15    27.899271    1307674368000               *
!*                                                  *
!****************************************************
!See file chi-sq.txt, equation (2.3.9)

PROGRAM LNFACTX

integer i
real*8  x,y

  print *, ' '
  print *,'  X     LN(X!)        EXP(LN(X!))'
  print *,'---------------------------------'
  do i = 1, 15
    x = dfloat(i)

    call LN_FactX(x,y)

    write(*,100) i,y,dexp(y)
  end do
  print *,'---------------------------------'
  print *, ' '
  
stop
100 format(' ',i2,'    ',f9.6,'    ',f14.0)
end


!**************************************************
!* Series approximation subroutine for LN(X!)     *
!* Accuracy better then 6 places for x>=3         * 
!* Accuracy better than 12 places for x>10        *
!* Advantage is that very large values of the     *
!* argument can be used without fear of over flow *.
!*! Reference: CRC Math Tables.                   *
!* x is the input, y is the output.               *
!**************************************************
Subroutine LN_FactX(x,y)
  real*8 x,y,x1
  x1 = 1.d0 / (x * x)
  y = (x + 0.5d0) * dlog(x) - x * (1.d0 - x1 / 12.d0 + x1 * x1 / 360.d0 - x1 * x1 * x1 / 1260 + x1 * x1 * x1 * x1 / 1680.d0)
  y = y + 0.918938533205d0
  return
end

!End of file logn!.f90