#! /usr/bin/env python
#
def fresnel_sin_values ( n_data ):

#*****************************************************************************80
#
## FRESNEL_SIN_VALUES returns some values of the Fresnel sine integral function.
#
#  Discussion:
#
#    The Fresnel sine integral is defined by
#
#      S(X) = integral ( 0 <= T <= X ) sin ( pi * T^2 / 2 ) dT
#
#    In Mathematica, the function can be evaluated by:
#
#      FresnelS[x]
#
#  Licensing:
#
#    This code is distributed under the GNU LGPL license.
#
#  Modified:
#
#    16 November 2015
#
#  Author:
#
#    John Burkardt
#
#  Reference:
#
#    Milton Abramowitz and Irene Stegun,
#    Handbook of Mathematical Functions,
#    US Department of Commerce, 1964.
#
#    Stephen Wolfram,
#    The Mathematica Book,
#    Fourth Edition,
#    Wolfram Media / Cambridge University Press, 1999.
#
#  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 X, the argument of the function.
#
#    Output, real F, the value of the function.
#
  import numpy as np

  n_max = 16

  f_vec = np.array ( ( \
     0.0000000000000000E+00, \
     0.4187609161656762E-02, \
     0.3335943266061318E-01, \
     0.1105402073593870E+00, \
     0.2493413930539178E+00, \
     0.4382591473903548E+00, \
     0.6234009185462497E+00, \
     0.7135250773634121E+00, \
     0.6388876835093809E+00, \
     0.4509387692675831E+00, \
     0.3434156783636982E+00, \
     0.4557046121246569E+00, \
     0.6196899649456836E+00, \
     0.5499893231527195E+00, \
     0.3915284435431718E+00, \
     0.4963129989673750E+00 ) )

  x_vec = np.array ( ( \
     0.0E+00, \
     0.2E+00, \
     0.4E+00, \
     0.6E+00, \
     0.8E+00, \
     1.0E+00, \
     1.2E+00, \
     1.4E+00, \
     1.6E+00, \
     1.8E+00, \
     2.0E+00, \
     2.2E+00, \
     2.4E+00, \
     2.6E+00, \
     2.8E+00, \
     3.0E+00 ) )

  if ( n_data < 0 ):
    n_data = 0

  if ( n_max <= n_data ):
    n_data = 0
    x = 0.0
    f = 0.0
  else:
    x = x_vec[n_data]
    f = f_vec[n_data]
    n_data = n_data + 1

  return n_data, x, f

def fresnel_sin_values_test ( ):

#*****************************************************************************80
#
## FRESNEL_SIN_VALUES_TEST demonstrates the use of FRESNEL_SIN_VALUES.
#
#  Licensing:
#
#    This code is distributed under the GNU LGPL license.
#
#  Modified:
#
#    09 February 2015
#
#  Author:
#
#    John Burkardt
#
  import platform

  print ( '' )
  print ( 'FRESNEL_SIN_VALUES_TEST:' )
  print ( '  Python version: %s' % ( platform.python_version ( ) ) )
  print ( '  FRESNEL_SIN_VALUES stores values of the Fresnel sine integral.' )
  print ( '' )
  print ( '        X              F' )
  print ( '' )

  n_data = 0

  while ( True ):

    n_data, x, fx = fresnel_sin_values ( n_data )

    if ( n_data == 0 ):
      break

    print ( '  %12f  %24.16f' % ( x, fx ) )
#
#  Terminate.
#
  print ( '' )
  print ( 'FRESNEL_SIN_VALUES_TEST:' )
  print ( '  Normal end of execution.' )
  return

if ( __name__ == '__main__' ):
  from timestamp import timestamp
  timestamp ( )
  fresnel_sin_values_test ( )
  timestamp ( )