#! /usr/bin/env python
#
def r8_tanh ( x ):

#*****************************************************************************80
#
## R8_TANH evaluates the hyperbolic tangent of an R8 argument.
#
#  Licensing:
#
#    This code is distributed under the GNU LGPL license.
#
#  Modified:
#
#    24 April 2016
#
#  Author:
#
#    Original FORTRAN77 version by Wayne Fullerton.
#    Python version by John Burkardt.
#
#  Reference:
#
#    Wayne Fullerton,
#    Portable Special Function Routines,
#    in Portability of Numerical Software,
#    edited by Wayne Cowell,
#    Lecture Notes in Computer Science, Volume 57,
#    Springer 1977,
#    ISBN: 978-3-540-08446-4,
#    LC: QA297.W65.
#
#  Parameters:
#
#    Input, real X, the argument.
#
#    Output, real VALUE, the hyperbolic tangent of X.
#
  import numpy as np
  from r8_csevl import r8_csevl
  from r8_inits import r8_inits
  from machine import r8_mach

  tanhcs = np.array ( [ \
      -0.25828756643634710438338151450605, \
      -0.11836106330053496535383671940204, \
      +0.98694426480063988762827307999681E-02, \
      -0.83579866234458257836163690398638E-03, \
      +0.70904321198943582626778034363413E-04, \
      -0.60164243181207040390743479001010E-05, \
      +0.51052419080064402965136297723411E-06, \
      -0.43320729077584087216545467387192E-07, \
      +0.36759990553445306144930076233714E-08, \
      -0.31192849612492011117215651480953E-09, \
      +0.26468828199718962579377758445381E-10, \
      -0.22460239307504140621870997006196E-11, \
      +0.19058733768288196054319468396139E-12, \
      -0.16172371446432292391330769279701E-13, \
      +0.13723136142294289632897761289386E-14, \
      -0.11644826870554194634439647293781E-15, \
      +0.98812684971669738285540514338133E-17, \
      -0.83847933677744865122269229055999E-18, \
      +0.71149528869124351310723506176000E-19, \
      -0.60374242229442045413288837119999E-20, \
      +0.51230825877768084883404663466666E-21, \
      -0.43472140157782110106047829333333E-22, \
      +0.36888473639031328479423146666666E-23, \
      -0.31301874774939399883325439999999E-24, \
      +0.26561342006551994468488533333333E-25, \
      -0.22538742304145029883494399999999E-26, \
      +0.19125347827973995102208000000000E-27, \
      -0.16228897096543663117653333333333E-28, \
      +0.13771101229854738786986666666666E-29, \
      -0.11685527840188950118399999999999E-30, \
      +0.99158055384640389120000000000000E-32 ] )

  nterms = r8_inits ( tanhcs, 31, 0.1 * r8_mach ( 3 ) )
  sqeps = np.sqrt ( 3.0 * r8_mach ( 3 ) )
  xmax = - 0.5 * np.log ( r8_mach ( 3 ) )

  y = abs ( x )

  if ( y <= sqeps ):

    value = x

  elif ( y <= 1.0 ):

    value = x * ( 1.0 + r8_csevl ( 2.0 * x * x - 1.0, tanhcs, nterms ) )

  elif ( y <= xmax ):

    y = np.exp ( y )
    yrec = 1.0 / y
    value = ( y - yrec ) / ( y + yrec )

    if ( x < 0.0 ):
      value = - value

  else:

    if ( x < 0.0 ):
      value = - 1.0
    else:
      value = + 1.0

  return value

def r8_tanh_test ( ):

#*****************************************************************************80
#
## R8_TANH_TEST tests R8_TANH.
#
#  Licensing:
#
#    This code is distributed under the GNU LGPL license.
#
#  Modified:
#
#    24 April 2016
#
#  Author:
#
#    John Burkardt
#
  import platform
  from tanh_values import tanh_values

  print ( '' )
  print ( 'R8_TANH_TEST:' )
  print ( '  Python version: %s' % ( platform.python_version ( ) ) )
  print ( '  R8_TANH evaluates the hyperbolic tangent function.' )
  print ( '  TANH_VALUES returns some exact values.' )
  print ( '' )
  print ( '             X         TANH(X)  R8_TANH(X)         Diff' )
  print ( '' )

  n_data = 0

  while ( True ):

    n_data, x, fx1 = tanh_values ( n_data )

    if ( n_data == 0 ):
      break

    fx2 = r8_tanh ( x )

    print ( '  %14.4g  %14.6g  %14.6g  %14.6g' % ( x, fx1, fx2, abs ( fx1 - fx2 ) ) )
#
#  Terminate.
#
  print ( '' )
  print ( 'R8_TANH_TEST:' )
  print ( '  Normal end of execution.' )
  return

if ( __name__ == '__main__' ):
  from timestamp import timestamp
  timestamp ( )
  r8_tanh_test ( )
  timestamp ( )