function alogam ( x, ifault )

!*****************************************************************************80
!
!! alogam() computes the logarithm of the Gamma function.
!
!  Licensing:
!
!    This code is distributed under the MIT license.
!
!  Modified:
!
!    28 March 1999
!
!  Author:
!
!    Malcolm Pike, David Hill
!    FORTRAN90 version by John Burkardt
!
!  Reference:
!
!    Malcolm Pike, David Hill,
!    Algorithm 291: 
!    Logarithm of Gamma Function,
!    Communications of the ACM,
!    Volume 9, Number 9, September 1966, page 684.
!
!  Parameters:
!
!    Input, real ( kind = rk ) X, the argument of the Gamma function.
!    X should be greater than 0.
!
!    Output, integer IFAULT, error flag.
!    0, no error.
!    1, X <= 0.
!
!    Output, real ( kind = rk ) ALOGAM, the logarithm of the Gamma 
!    function of X.
!
  implicit none

  integer, parameter :: rk = kind ( 1.0D+00 )

  real ( kind = rk ) alogam
  real ( kind = rk ) f
  integer ifault
  real ( kind = rk ) x
  real ( kind = rk ) y
  real ( kind = rk ) z

  if ( x <= 0.0D+00 ) then
    ifault = 1
    alogam = 0.0D+00
    return
  end if

  ifault = 0
  y = x

  if ( x < 7.0D+00 ) then

    f = 1.0D+00
    z = y

    do while ( z < 7.0D+00 )
      f = f * z
      z = z + 1.0D+00
    end do

    y = z
    f = - log ( f )

  else

    f = 0.0D+00

  end if

  z = 1.0D+00 / y / y
    
  alogam = f + ( y - 0.5D+00 ) * log ( y ) - y &
    + 0.918938533204673D+00 + &
    ((( &
    - 0.000595238095238D+00   * z &
    + 0.000793650793651D+00 ) * z &
    - 0.002777777777778D+00 ) * z &
    + 0.083333333333333D+00 ) / y

  return
end
subroutine gamma_log_values ( n_data, x, fx )

!*****************************************************************************80
!
!! GAMMA_LOG_VALUES returns some values of the Log Gamma function.
!
!  Discussion:
!
!    In Mathematica, the function can be evaluated by:
!
!      Log[Gamma[x]]
!
!  Modified:
!
!    14 August 2004
!
!  Author:
!
!    John Burkardt
!
!  Reference:
!
!    Milton Abramowitz, Irene Stegun,
!    Handbook of Mathematical Functions,
!    National Bureau of Standards, 1964,
!    ISBN: 0-486-61272-4,
!    LC: QA47.A34.
!
!    Stephen Wolfram,
!    The Mathematica Book,
!    Fourth Edition,
!    Cambridge University Press, 1999,
!    ISBN: 0-521-64314-7,
!    LC: QA76.95.W65.
!
!  Parameters:
!
!    Input/output, integer N_DATA.  The user sets N_DATA to 0 
!    before the first call.  On each call, the routine increments N_DATA by 1,
!    and returns the corresponding data; when there is no more data, the
!    output value of N_DATA will be 0 again.
!
!    Output, real ( kind = rk ) X, the argument of the function.
!
!    Output, real ( kind = rk ) FX, the value of the function.
!
  implicit none

  integer, parameter :: rk = kind ( 1.0D+00 )

  integer, parameter :: n_max = 20

  real ( kind = rk ) fx
  real ( kind = rk ), save, dimension ( n_max ) :: fx_vec = (/ &
     0.1524063822430784D+01, &
     0.7966778177017837D+00, &
     0.3982338580692348D+00, &
     0.1520596783998375D+00, &
     0.0000000000000000D+00, &
    -0.4987244125983972D-01, &
    -0.8537409000331584D-01, &
    -0.1081748095078604D+00, &
    -0.1196129141723712D+00, &
    -0.1207822376352452D+00, &
    -0.1125917656967557D+00, &
    -0.9580769740706586D-01, &
    -0.7108387291437216D-01, &
    -0.3898427592308333D-01, &
    0.00000000000000000D+00, &
    0.69314718055994530D+00, &
    0.17917594692280550D+01, &
    0.12801827480081469D+02, &
    0.39339884187199494D+02, &
    0.71257038967168009D+02 /) 
  integer n_data
  real ( kind = rk ) x
  real ( kind = rk ), save, dimension ( n_max ) :: x_vec = (/ &
     0.20D+00, &
     0.40D+00, &
     0.60D+00, &
     0.80D+00, &
     1.00D+00, &
     1.10D+00, &
     1.20D+00, &
     1.30D+00, &
     1.40D+00, &
     1.50D+00, &
     1.60D+00, &
     1.70D+00, &
     1.80D+00, &
     1.90D+00, &
     2.00D+00, &
     3.00D+00, &
     4.00D+00, &
    10.00D+00, &
    20.00D+00, &
    30.00D+00 /) 

  if ( n_data < 0 ) then
    n_data = 0
  end if

  n_data = n_data + 1

  if ( n_max < n_data ) then
    n_data = 0
    x = 0.0D+00
    fx = 0.0D+00
  else
    x = x_vec(n_data)
    fx = fx_vec(n_data)
  end if

  return
end
subroutine timestamp ( )

!*****************************************************************************80
!
!! TIMESTAMP prints the current YMDHMS date as a time stamp.
!
!  Example:
!
!    31 May 2001   9:45:54.872 AM
!
!  Licensing:
!
!    This code is distributed under the MIT license.
!
!  Modified:
!
!    18 May 2013
!
!  Author:
!
!    John Burkardt
!
  implicit none

  character ( len = 8 ) ampm
  integer d
  integer h
  integer m
  integer mm
  character ( len = 9 ), parameter, dimension(12) :: month = (/ &
    'January  ', 'February ', 'March    ', 'April    ', &
    'May      ', 'June     ', 'July     ', 'August   ', &
    'September', 'October  ', 'November ', 'December ' /)
  integer n
  integer s
  integer values(8)
  integer y

  call date_and_time ( values = values )

  y = values(1)
  m = values(2)
  d = values(3)
  h = values(5)
  n = values(6)
  s = values(7)
  mm = values(8)

  if ( h < 12 ) then
    ampm = 'AM'
  else if ( h == 12 ) then
    if ( n == 0 .and. s == 0 ) then
      ampm = 'Noon'
    else
      ampm = 'PM'
    end if
  else
    h = h - 12
    if ( h < 12 ) then
      ampm = 'PM'
    else if ( h == 12 ) then
      if ( n == 0 .and. s == 0 ) then
        ampm = 'Midnight'
      else
        ampm = 'AM'
      end if
    end if
  end if

  write ( *, '(i2,1x,a,1x,i4,2x,i2,a1,i2.2,a1,i2.2,a1,i3.3,1x,a)' ) &
    d, trim ( month(m) ), y, h, ':', n, ':', s, '.', mm, trim ( ampm )

  return
end