#! /usr/bin/env python
#
def rat_add ( top1, bot1, top2, bot2 ):

#*****************************************************************************80
#
## RAT_ADD adds two rational values.
#
#  Discussion:
#
#    The routine computes
#
#      TOP/BOT = TOP1/BOT1 + TOP2/BOT2
#
#    while trying to avoid integer overflow.
#
#  Licensing:
#
#    This code is distributed under the GNU LGPL license.
#
#  Modified:
#
#    02 June 2015
#
#  Author:
#
#    John Burkardt
#
#  Parameters:
#
#    Input, integer TOP1, BOT1, the first value to add.
#
#    Input, integer TOP2, BOT2, the second value to add.
#
#    Output, integer TOP, BOT, the sum.
#
#    Output, integer IERROR.
#    0, no error occurred.
#    1, an error occurred.  The addition of the two values
#    requires a numerator or denominator larger than the
#    maximum legal integer.
#
  from i4_gcd import i4_gcd
  from i4_huge import i4_huge

  i_max = i4_huge ( )

  ierror = 0

  if ( top1 == 0 ):
    top = top2
    bot = bot2
    return top, bot, ierror
  elif ( top2 == 0 ):
    top = top1
    bot = bot1
    return top, bot, ierror
#
#  Compute the greatest common factor of the two denominators,
#  and factor it out.
#
  bot3 = i4_gcd ( bot1, bot2 )
  bot1 = bot1 // bot3
  bot2 = bot2 // bot3
#
#  The fraction may now be formally written as:
#
#    (top1*bot2 + top2*bot1) / (bot1*bot2*bot3)
#
#  Check the tops for overflow.
#
  if ( i_max < abs ( top1 * bot2 ) ):
    print ( '' )
    print ( 'RAT_ADD - Warning!' )
    print ( '  Overflow of top of rational sum.' )
    top = 0
    bot = 1
    ierror = 1
    return top, bot, ierror

  top1 = top1 * bot2

  if ( i_max < abs ( top2 * bot1 ) ):
    ierror = 1
    print ( '' )
    print ( 'RAT_ADD - Fatal error!' )
    print ( '  Overflow of top of rational sum.' )
    top = 0
    bot = 1
    ierror = 1
    return top, bot, ierror

  top2 = top2 * bot1

  if ( i_max < abs ( top1 + top2 ) ):
    print ( '' )
    print ( 'RAT_ADD - Fatal error!' )
    print ( '  Overflow of top of rational sum.' )
    top = 0
    bot = 1
    return top, bot, ierror

  top = top1 + top2
#
#  Check the bottom for overflow.
#
  if ( i_max < abs ( bot1 * bot2 * bot3 ) ):
    print ( '' )
    print ( 'RAT_ADD - Fatal error!' )
    print ( '  Overflow of bottom of rational sum.' )
    top = 0
    bot = 1
    ierror = 1
    return top, bot, ierror

  bot = bot1 * bot2 * bot3
#
#  Put the fraction in lowest terms.
#
  itemp = i4_gcd ( top, bot )
  top = top // itemp
  bot = bot // itemp
#
#  The bottom should be positive.
#
  if ( bot < 0 ):
    bot = -bot
    top = -top

  return top, bot, ierror

def rat_add_test ( ):

#*****************************************************************************80
#
#% RAT_ADD_TEST tests RAT_ADD.
#
#  Licensing:
#
#    This code is distributed under the GNU LGPL license.
#
#  Modified:
#
#    02 June 2015
#
#  Author:
#
#    John Burkardt
#
  import platform
  from rat_to_s import rat_to_s

  print ( '' )
  print ( 'RAT_ADD_TEST' )
  print ( '  Python version: %s' % ( platform.python_version ( ) ) )
  print ( '  RAT_ADD adds two rationals.' )

  atop = 3
  abot = 4
  btop = 10
  bbot = 7

  ctop, cbot, ierror = rat_add ( atop, abot, btop, bbot )

  print ( '' )
  s = rat_to_s ( atop, abot )
  print ( '  A = %s' % ( s ) )
  s = rat_to_s ( btop, bbot )
  print ( '  B = %s' % ( s ) )
  s = rat_to_s ( ctop, cbot )
  print ( '  C = A + B = %s' % ( s ) )
#
#  Terminate.
#
  print ( '' )
  print ( 'RAT_ADD_TEST' )
  print ( '  Normal end of execution.' )
  return

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