#! /usr/bin/env python
#
def r8_diff ( x, y, n ):

#*****************************************************************************80
#
## R8_DIFF computes (X-Y) to a specified accuracy.
#
#  Discussion:
#
#    The user controls how many binary digits of accuracy
#    are to be used.
#
#    N determines the accuracy of the value of the result.  If N = 10,
#    for example, only 11 binary places will be used in the arithmetic.
#    In general, only N+1 binary places will be used.
#
#    N may be zero.  However, a negative value of N should
#    not be used, since this will cause both X and Y to look like 0.
#
#  Licensing:
#
#    This code is distributed under the GNU LGPL license. 
#
#  Modified:
#
#    24 July 2014
#
#  Author:
#
#    John Burkardt
#
#  Parameters:
#
#    Input, real X, Y, the two values whose difference is desired.
#
#    Input, integer N, the number of binary digits to use.
#
#    Output, real VALUE, the value of X-Y.
#
  from r8_sign import r8_sign

  if ( x == y ):
    value = 0.0
    return value

  pow2 = 2.0 ** n
#
#  Compute the magnitude of X and Y, and take the larger of the
#  two.  At least one of the two values is not zero!
#
  size = max ( abs ( x ), abs ( y ) )
#
#  Make normalized copies of X and Y.  One of the two values will
#  actually be equal to 1.
#
  x = x / size
  y = y / size
#
#  Here's where rounding comes in.  We know that the larger of the
#  the two values equals 1.  We multiply both values by 2^N,
#  where N+1 is the number of binary digits of accuracy we want
#  to use, truncate the values, and divide back by 2^N.
#
  x = ( int ( x * pow2 + 0.5 * r8_sign ( x ) ) ) / pow2
  y = ( int ( y * pow2 + 0.5 * r8_sign ( y ) ) ) / pow2
#
#  Take the difference now.
#
  value = x - y
#
#  Undo the scaling.
#
  value = value * size

  return value

def r8_diff_test ( ):

#*****************************************************************************80
#
## R8_DIFF_TEST tests R8_DIFF.
#
#  Licensing:
#
#    This code is distributed under the GNU LGPL license.
#
#  Modified:
#
#    25 July 2014
#
#  Author:
#
#    John Burkardt
#
  import numpy as np
  import platform

  test_num = 15

  y_test = np.array ( [ \
    0.0625, 0.125, 0.25, 0.50,  0.874, \
    0.876,  0.90,  0.95, 0.99,  1.0, \
    1.01,   1.05,  1.10, 3.0,  10.0 ] )

  ndig = 3
  x = 1.0

  print ( '' )
  print ( 'R8_DIFF_TEST' )
  print ( '  Python version: %s' % ( platform.python_version ( ) ) )
  print ( '  R8_DIFF computes a difference X-Y to a given' )
  print ( '  number of binary places.' )
  print ( '' )
  print ( '  For this test, we use %d binary places.' % ( ndig ) )
  print ( '' )
  print ( '       X       Y       X-Y    R8_DIFF(X,Y)' )
  print ( '' )

  for test in range ( 0, test_num ):
    y = y_test[test]
    print ( '  %10f  %10f  %10f  %10f' % ( x, y, x - y, r8_diff ( x, y, ndig ) ) )
#
#  Terminate.
#
  print ( '' )
  print ( 'R8_DIFF_TEST' )
  print ( '  Normal end of execution.' )
  return

if ( __name__ == '__main__' ):
  from timestamp import timestamp
  timestamp ( ) 
  r8_diff_test ( )
  timestamp ( )