#!/usr/bin/env python
#
def r8_cas ( x ):

#*****************************************************************************80
#
## R8_CAS returns the "casine" of a number.
#
#  Definition:
#
#    The "casine", used in the discrete Hartley transform, is abbreviated
#    CAS(X), and defined by:
#
#      CAS(X) = cos ( X ) + sin( X )
#             = sqrt ( 2 ) * sin ( X + pi/4 )
#             = sqrt ( 2 ) * cos ( X - pi/4 )
#
#  Licensing:
#
#    This code is distributed under the GNU LGPL license. 
#
#  Modified:
#
#    03 June 2013
#
#  Author:
#
#    John Burkardt
#
#  Parameters:
#
#    Input, real X, the number whose casine is desired.
#
#    Output, real VALUE, the casine of X, which will be between
#    plus or minus the square root of 2.
#
  from math import cos
  from math import sin

  value = cos ( x ) + sin ( x )

  return value

def r8_cas_test ( ):

#*****************************************************************************80
#
## R8_CAS_TEST tests R8_CAS.
#
#  Licensing:
#
#    This code is distributed under the GNU LGPL license.
#
#  Modified:
#
#    07 June 2013
#
#  Author:
#
#    John Burkardt
#
  from r8_pi import r8_pi

  test_num = 12

  print ''
  print 'R8_CAS_TEST'
  print '  R8_CAS evaluates the casine of a number.'
  print ''
  print '	X	   R8_CAS ( X )'
  print ''
  for test in range ( 0, test_num + 1 ):
    x = r8_pi ( ) * test / test_num
    print '  %14f  %14f' % ( x, r8_cas ( x ) )
#
#  Terminate.
#
  print ''
  print 'R8_CAS_TEST'
  print '  Normal end of execution.'

  return

if ( __name__ == '__main__' ):
  from timestamp import timestamp
  timestamp ( ) 
  r8_cas_test ( )
  timestamp ( )