program main

!*****************************************************************************80
!
!! sine_integral_test() tests sine_integral().
!
!  Licensing:
!
!    This code is distributed under the MIT license.
!
!  Modified:
!
!    19 November 2024
!
!  Author:
!
!    John Burkardt
!
  implicit none

  integer, parameter :: rk8 = kind ( 1.0D+00 )

  call timestamp ( )
  write ( *, '(a)' ) ' '
  write ( *, '(a)' ) 'sine_integral_test():'
  write ( *, '(a)' ) '  Fortran90 version'
  write ( *, '(a)' ) '  Test sine_integral().'

  call ci_test ( )
  call si_test ( )
!
!  Terminate.
!
  write ( *, '(a)' ) ' '
  write ( *, '(a)' ) 'sine_integral_test():'
  write ( *, '(a)' ) '  Normal end of execution.'
  write ( *, '(a)' ) ' '
  call timestamp ( )

  stop 0
end
subroutine ci_test ( )

!*****************************************************************************80
!
!! ci_test() tests ci().
!
!  Licensing:
!
!    This code is distributed under the MIT license.
!
!  Modified:
!
!    26 March 2025
!
!  Author:
!
!    John Burkardt
!
  implicit none

  integer, parameter :: rk8 = kind ( 1.0D+00 )

  real ( kind = rk8 ) fx1
  real ( kind = rk8 ) fx2
  integer n_data
  real ( kind = rk8 ) si
  real ( kind = rk8 ) x

  write ( *, '(a)' ) ' '
  write ( *, '(a)' ) 'ci_test():'
  write ( *, '(a)' ) '  ci() evaluates the Cosine Integral function CI(X).'
  write ( *, '(a)' ) ' '
  write ( *, '(a)' ) '          X           CI(X)'
  write ( *, '(a)' ) ' '

  n_data = 0

  do

    call ci_values ( n_data, x, fx1 )

    if ( n_data == 0 ) then
      exit
    end if

    call cisi ( x, fx2, si )

    write ( *, '(2x,g14.6,2x,g24.16,g24.16)' ) x, fx1, fx2

  end do

  return
end
subroutine ci_values ( n_data, x, fx )

!*****************************************************************************80
!
!! ci_values() returns some values of the cosine integral function.
!
!  Discussion:
!
!    The cosine integral is defined by
!
!      ci ( x ) = - integral ( x <= t < +oo ) ( cos ( t ) ) / t  dt
!
!    In Mathematica, the function can be evaluated by:
!
!      CosIntegral[x]
!
!  Licensing:
!
!    This code is distributed under the MIT license.
!
!  Modified:
!
!    12 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.
!
!  Input:
!
!    integer N_DATA: The user sets N_DATA to 0 before the first call.
!
!  Output:
!
!    integer N_DATA: 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.
!
!    real ( kind = rk8 ) X, the argument of the function.
!
!    real ( kind = rk8 ) FX, the value of the function.
!
  implicit none

  integer, parameter :: rk8 = kind ( 1.0D+00 )

  integer, parameter :: n_max = 16

  real ( kind = rk8 ) fx
  real ( kind = rk8 ), save, dimension ( n_max ) :: fx_vec = (/ &
    -0.1777840788066129D+00, &
    -0.2227070695927976D-01, &
     0.1005147070088978D+00, &
     0.1982786159524672D+00, &
     0.2760678304677729D+00, &
     0.3374039229009681D+00, &
     0.4204591828942405D+00, &
     0.4620065850946773D+00, &
     0.4717325169318778D+00, &
     0.4568111294183369D+00, &
     0.4229808287748650D+00, &
     0.2858711963653835D+00, &
     0.1196297860080003D+00, &
    -0.3212854851248112D-01, &
    -0.1409816978869304D+00, &
    -0.1934911221017388D+00 /)
  integer n_data
  real ( kind = rk8 ) x
  real ( kind = rk8 ), save, dimension ( n_max ) :: x_vec = (/ &
     0.5D+00, &
     0.6D+00, &
     0.7D+00, &
     0.8D+00, &
     0.9D+00, &
     1.0D+00, &
     1.2D+00, &
     1.4D+00, &
     1.6D+00, &
     1.8D+00, &
     2.0D+00, &
     2.5D+00, &
     3.0D+00, &
     3.5D+00, &
     4.0D+00, &
     4.5D+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 si_test ( )

!*****************************************************************************80
!
!! si_test() tests si().
!
!  Licensing:
!
!    This code is distributed under the MIT license.
!
!  Modified:
!
!    26 March 2025
!
!  Author:
!
!    John Burkardt
!
  implicit none

  integer, parameter :: rk8 = kind ( 1.0D+00 )

  real ( kind = rk8 ) ci
  real ( kind = rk8 ) fx1
  real ( kind = rk8 ) fx2
  integer n_data
  real ( kind = rk8 ) x

  write ( *, '(a)' ) ' '
  write ( *, '(a)' ) 'si_test():'
  write ( *, '(a)' ) '  si() evalues the sine integral function.'
  write ( *, '(a)' ) ' '
  write ( *, '(a)' ) '      X            SI(X)'
  write ( *, '(a)' ) ' '

  n_data = 0

  do

    call si_values ( n_data, x, fx1 )

    if ( n_data == 0 ) then
      exit
    end if

    call cisi ( x, ci, fx2 )

    write ( *, '(2x,g14.6,2x,g24.16,g24.16)' ) x, fx1, fx2

  end do

  return
end
subroutine si_values ( n_data, x, fx )

!*****************************************************************************80
!
!! si_values() returns some values of the sine integral function.
!
!  Discussion:
!
!    SI(X) = integral ( 0 <= T <= X ) sin ( T ) / T dt
!
!    In Mathematica, the function can be evaluated by:
!
!      SinIntegral[x]
!
!  Licensing:
!
!    This code is distributed under the MIT license.
!
!  Modified:
!
!    12 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.
!
!  Input:
!
!    integer N_DATA: The user sets N_DATA to 0 before the first call.
!
!  Output:
!
!    integer N_DATA: 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.
!
!    real ( kind = rk8 ) X, the argument of the function.
!
!    real ( kind = rk8 ) FX, the value of the function.
!
  implicit none

  integer, parameter :: rk8 = kind ( 1.0D+00 )

  integer, parameter :: n_max = 16

  real ( kind = rk8 ) fx
  real ( kind = rk8 ), save, dimension ( n_max ) :: fx_vec = (/ &
    0.4931074180430667D+00, &
    0.5881288096080801D+00, &
    0.6812222391166113D+00, &
    0.7720957854819966D+00, &
    0.8604707107452929D+00, &
    0.9460830703671830D+00, &
    0.1108047199013719D+01, &
    0.1256226732779218D+01, &
    0.1389180485870438D+01, &
    0.1505816780255579D+01, &
    0.1605412976802695D+01, &
    0.1778520173443827D+01, &
    0.1848652527999468D+01, &
    0.1833125398665997D+01, &
    0.1758203138949053D+01, &
    0.1654140414379244D+01 /)
  integer n_data
  real ( kind = rk8 ) x
  real ( kind = rk8 ), save, dimension ( n_max ) :: x_vec = (/ &
     0.5D+00, &
     0.6D+00, &
     0.7D+00, &
     0.8D+00, &
     0.9D+00, &
     1.0D+00, &
     1.2D+00, &
     1.4D+00, &
     1.6D+00, &
     1.8D+00, &
     2.0D+00, &
     2.5D+00, &
     3.0D+00, &
     3.5D+00, &
     4.0D+00, &
     4.5D+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

  integer, parameter :: rk8 = kind ( 1.0D+00 )

  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