//  Discussion:
//
//    Examine the math functions:
//
//      abs
//      acos
//      acosh
//      asin
//      asinh
//      atan
//      atan2
//      atanh
//      ceil
//      cos
//      cosh
//      erf
//      erfc
//      exp
//      floor
//      imag
//      j0
//      j1
//      jn
//      lgamma
//      log
//      log10
//      max
//      min
//      pow
//      rint
//      sin
//      sinh
//      sqrt
//      tan
//      tanh
//      tgamma
//      y0
//      y1
//      yn
//
//  Location:
//
//    http://people.sc.fsu.edu/~jburkardt/freefem_src/math_test/math_test.edp
//
//  Licensing:
//
//    This code is distributed under the MIT license.
//
//  Modified:
//
//    15 February 2015
//
//  Reference:
//
//    Frederic Hecht,
//    Freefem++,
//    Third Edition, version 3.22
//
cout << "\n";
cout << "math_test:\n";
cout << "  FreeFem++ version\n";
cout << "  Try out the FreeFem++ Math Library Functions.\n";
//
//  Initialize the random number generator.
//
int seed;
//
//  Y = ABS ( X );
//
seed = 123456789;
randinit ( seed );
cout << "\n";
cout << "  Y = ABS ( X ):\n";
cout << "\n";
for ( int i = 0; i < 10; i++ )
{
  x = 10.0 * randreal1 ( ) - 5.0;
  y = abs ( x );
  cout << "  " << x << "  " << y << "\n";
}
//
//  Y = ACOS ( X );
//  X <= 1.0 required.
//
seed = 123456789;
randinit ( seed );
cout << "\n";
cout << "  Y = ACOS ( X ):\n";
cout << "\n";
for ( int i = 0; i < 10; i++ )
{
  x = 2.0 * randreal1 ( ) - 1.0;
  y = acos ( x );
  cout << "  " << x << "  " << y << "\n";
}
//
//  Y = ACOSH ( X );
//  1 <= |X| required.
//
seed = 123456789;
randinit ( seed );
cout << "\n";
cout << "  Y = ACOSH ( X ):\n";
cout << "\n";
for ( int i = 0; i < 10; i++ )
{
  x = randreal1 ( );
  if ( x < 0.0 )
  {
    x = 10.0 * x - 1.0;
  }
  else
  {
    x = 10.0 * x + 1.0;
  }
  y = acosh ( x );
  cout << "  " << x << "  " << y << "\n";
}
//
//  Y = ASIN ( X );
//  |X| <= 1.
//
seed = 123456789;
randinit ( seed );
cout << "\n";
cout << "  Y = ASIN ( X ):\n";
cout << "\n";
for ( int i = 0; i < 10; i++ )
{
  x = 2.0 * randreal1 ( ) - 1.0;
  y = asin ( x );
  cout << "  " << x << "  " << y << "\n";
}
//
//  Y = ASINH ( X );
//
seed = 123456789;
randinit ( seed );
cout << "\n";
cout << "  Y = ASINH ( X ):\n";
cout << "\n";
for ( int i = 0; i < 10; i++ )
{
  x = 10.0 * randreal1 ( ) - 5.0;
  y = asinh ( x );
  cout << "  " << x << "  " << y << "\n";
}
//
//  Z = ATAN ( Y / X );
//
seed = 123456789;
randinit ( seed );
cout << "\n";
cout << "  Z = ATAN ( Y / X ):\n";
cout << "\n";
for ( int i = 0; i < 10; i++ )
{
  x = 10.0 * randreal1 ( ) - 5.0;
  y = 10.0 * randreal1 ( ) - 5.0;
  z = atan ( y / x );
  cout << "  " << x << "  " << y << "  " << z << "\n";
}
//
//  Z = ATAN2 ( Y, X );
//
seed = 123456789;
randinit ( seed );
cout << "\n";
cout << "  Z = ATAN2 ( Y, X ):\n";
cout << "\n";
for ( int i = 0; i < 10; i++ )
{
  x = 10.0 * randreal1 ( ) - 5.0;
  y = 10.0 * randreal1 ( ) - 5.0;
  z = atan2 ( y, x );
  cout << "  " << x << "  " << y << "  " << z << "\n";
}
//
//  Y = ATANH ( X );
//  |X| < 1 required.
//
seed = 123456789;
randinit ( seed );
cout << "\n";
cout << "  Y = ATANH ( X ):\n";
cout << "\n";
for ( int i = 0; i < 10; i++ )
{
  x = 2.0 * randreal1 ( ) - 1.0;
  y = atanh ( x );
  cout << "  " << x << "  " << y << "\n";
}
//
//  Y = CEIL ( X );
//
seed = 123456789;
randinit ( seed );
cout << "\n";
cout << "  Y = CEIL ( X ):\n";
cout << "\n";
for ( int i = 0; i < 10; i++ )
{
  x = 10.0 * randreal1 ( ) - 5.0;
  y = ceil ( x );
  cout << "  " << x << "  " << y << "\n";
}
//
//  Y = COS ( X );
//
seed = 123456789;
randinit ( seed );
cout << "\n";
cout << "  Y = COS ( X ):\n";
cout << "\n";
for ( int i = 0; i < 10; i++ )
{
  x = 10.0 * randreal1 ( ) - 5.0;
  y = cos ( x );
  cout << "  " << x << "  " << y << "\n";
}
//
//  Y = COSH ( X );
//
seed = 123456789;
randinit ( seed );
cout << "\n";
cout << "  Y = COSH ( X ):\n";
cout << "\n";
for ( int i = 0; i < 10; i++ )
{
  x = 10.0 * randreal1 ( ) - 5.0;
  y = cosh ( x );
  cout << "  " << x << "  " << y << "\n";
}
//
//  Y = ERF ( X );
//
seed = 123456789;
randinit ( seed );
cout << "\n";
cout << "  Y = ERF ( X ):\n";
cout << "\n";
for ( int i = 0; i < 10; i++ )
{
  x = 10.0 * randreal1 ( ) - 5.0;
  y = erf ( x );
  cout << "  " << x << "  " << y << "\n";
}
//
//  Y = ERFC ( X );
//
seed = 123456789;
randinit ( seed );
cout << "\n";
cout << "  Y = ERFC ( X ):\n";
cout << "\n";
for ( int i = 0; i < 10; i++ )
{
  x = 10.0 * randreal1 ( ) - 5.0;
  y = erfc ( x );
  cout << "  " << x << "  " << y << "\n";
}
//
//  Y = EXP ( X );
//
seed = 123456789;
randinit ( seed );
cout << "\n";
cout << "  Y = EXP ( X ):\n";
cout << "\n";
for ( int i = 0; i < 10; i++ )
{
  x = 10.0 * randreal1 ( ) - 5.0;
  y = exp ( x );
  cout << "  " << x << "  " << y << "\n";
}
//
//  Y = FLOOR ( X );
//
seed = 123456789;
randinit ( seed );
cout << "\n";
cout << "  Y = FLOOR ( X ):\n";
cout << "\n";
for ( int i = 0; i < 10; i++ )
{
  x = 10.0 * randreal1 ( ) - 5.0;
  y = floor ( x );
  cout << "  " << x << "  " << y << "\n";
}
//
//  Y = J0 ( X );
//
seed = 123456789;
randinit ( seed );
cout << "\n";
cout << "  Y = J0 ( X ):\n";
cout << "\n";
for ( int i = 0; i < 10; i++ )
{
  x = 10.0 * randreal1 ( ) - 5.0;
  y = j0 ( x );
  cout << "  " << x << "  " << y << "\n";
}
//
//  Y = J1 ( X );
//
seed = 123456789;
randinit ( seed );
cout << "\n";
cout << "  Y = J1 ( X ):\n";
cout << "\n";
for ( int i = 0; i < 10; i++ )
{
  x = 10.0 * randreal1 ( ) - 5.0;
  y = j1 ( x );
  cout << "  " << x << "  " << y << "\n";
}
//
//  Y = JN ( 2, X );
//
seed = 123456789;
randinit ( seed );
cout << "\n";
cout << "  Y = JN ( 2, X ):\n";
cout << "\n";
for ( int i = 0; i < 10; i++ )
{
  x = 10.0 * randreal1 ( ) - 5.0;
  y = jn ( 2, x );
  cout << "  " << x << "  " << y << "\n";
}
//
//  Y = LGAMMA ( X );
//  X must not be 0 or a negative integer.
//
seed = 123456789;
randinit ( seed );
cout << "\n";
cout << "  Y = LGAMMA ( X ):\n";
cout << "\n";
for ( int i = 0; i < 10; i++ )
{
  x = 10.0 * randreal1 ( );
  y = lgamma ( x );
  cout << "  " << x << "  " << y << "\n";
}
//
//  Y = LOG ( X );
//  0 < X required.
//
seed = 123456789;
randinit ( seed );
cout << "\n";
cout << "  Y = LOG ( X ):\n";
cout << "\n";
for ( int i = 0; i < 10; i++ )
{
  x = 10.0 * randreal1 ( );
  y = log ( x );
  cout << "  " << x << "  " << y << "\n";
}
//
//  Y = LOG10 ( X );
//  0 < X required.
//
seed = 123456789;
randinit ( seed );
cout << "\n";
cout << "  Y = LOG10 ( X ):\n";
cout << "\n";
for ( int i = 0; i < 10; i++ )
{
  x = 10.0 * randreal1 ( );
  y = log10 ( x );
  cout << "  " << x << "  " << y << "\n";
}
//
//  Z = MAX ( X, Y );
//
seed = 123456789;
randinit ( seed );
cout << "\n";
cout << "  Z = MAX ( X, Y ):\n";
cout << "\n";
for ( int i = 0; i < 10; i++ )
{
  x = 10.0 * randreal1 ( ) - 5.0;
  y = 10.0 * randreal1 ( ) - 5.0;
  z = max ( x, y );
  cout << "  " << x << "  " << y << "  " << z << "\n";
}
//
//  Z = MIN ( X, Y );
//
seed = 123456789;
randinit ( seed );
cout << "\n";
cout << "  Z = MIN ( X, Y ):\n";
cout << "\n";
for ( int i = 0; i < 10; i++ )
{
  x = 10.0 * randreal1 ( ) - 5.0;
  y = 10.0 * randreal1 ( ) - 5.0;
  z = min ( x, y );
  cout << "  " << x << "  " << y << "  " << z << "\n";
}
//
//  Z = POW ( X, Y );
//  If X negative, Y must be an integer.
//  If X 0, Y must be positive.
//
seed = 123456789;
randinit ( seed );
cout << "\n";
cout << "  Z = POW ( X, Y ):\n";
cout << "\n";
for ( int i = 0; i < 10; i++ )
{
  x = 10.0 * randreal1 ( );
  y = 10.0 * randreal1 ( ) - 5.0;
  z = pow ( x, y );
  cout << "  " << x << "  " << y << "  " << z << "\n";
}
//
//  Y = RINT ( X );
//
seed = 123456789;
randinit ( seed );
cout << "\n";
cout << "  Y = RINT ( X ):\n";
cout << "\n";
for ( int i = 0; i < 10; i++ )
{
  x = 10.0 * randreal1 ( ) - 5.0;
  y = rint ( x );
  cout << "  " << x << "  " << y << "\n";
}
//
//  Y = SIN ( X );
//
seed = 123456789;
randinit ( seed );
cout << "\n";
cout << "  Y = SIN ( X ):\n";
cout << "\n";
for ( int i = 0; i < 10; i++ )
{
  x = 10.0 * randreal1 ( ) - 5.0;
  y = sin ( x );
  cout << "  " << x << "  " << y << "\n";
}
//
//  Y = SINH ( X );
//
seed = 123456789;
randinit ( seed );
cout << "\n";
cout << "  Y = SINH ( X ):\n";
cout << "\n";
for ( int i = 0; i < 10; i++ )
{
  x = 10.0 * randreal1 ( ) - 5.0;
  y = sinh ( x );
  cout << "  " << x << "  " << y << "\n";
}
//
//  Y = SQRT ( X );
//  0 <= X required.
//
seed = 123456789;
randinit ( seed );
cout << "\n";
cout << "  Y = SQRT ( X ):\n";
cout << "\n";
for ( int i = 0; i < 10; i++ )
{
  x = 10.0 * randreal1 ( );
  y = sqrt ( x );
  cout << "  " << x << "  " << y << "\n";
}
//
//  Y = TAN ( X );
//
seed = 123456789;
randinit ( seed );
cout << "\n";
cout << "  Y = TAN ( X ):\n";
cout << "\n";
for ( int i = 0; i < 10; i++ )
{
  x = 10.0 * randreal1 ( ) - 5.0;
  y = tan ( x );
  cout << "  " << x << "  " << y << "\n";
}
//
//  Y = TANH ( X );
//
seed = 123456789;
randinit ( seed );
cout << "\n";
cout << "  Y = TANH ( X ):\n";
cout << "\n";
for ( int i = 0; i < 10; i++ )
{
  x = 10.0 * randreal1 ( ) - 5.0;
  y = tanh ( x );
  cout << "  " << x << "  " << y << "\n";
}
//
//  Y = TGAMMA ( X );
//  X must not be 0 or a negative integer.
//
seed = 123456789;
randinit ( seed );
cout << "\n";
cout << "  Y = TGAMMA ( X ):\n";
cout << "\n";
for ( int i = 0; i < 10; i++ )
{
  x = 10.0 * randreal1 ( ) - 5.0;
  y = tgamma ( x );
  cout << "  " << x << "  " << y << "\n";
}
//
//  Y = Y0 ( X );
//
seed = 123456789;
randinit ( seed );
cout << "\n";
cout << "  Y = Y0 ( X ):\n";
cout << "\n";
for ( int i = 0; i < 10; i++ )
{
  x = 10.0 * randreal1 ( ) - 5.0;
  y = y0 ( x );
  cout << "  " << x << "  " << y << "\n";
}
//
//  Y = Y1 ( X );
//
seed = 123456789;
randinit ( seed );
cout << "\n";
cout << "  Y = Y1 ( X ):\n";
cout << "\n";
for ( int i = 0; i < 10; i++ )
{
  x = 10.0 * randreal1 ( ) - 5.0;
  y = y1 ( x );
  cout << "  " << x << "  " << y << "\n";
}
//
//  Y = YN ( 2, X );
//
seed = 123456789;
randinit ( seed );
cout << "\n";
cout << "  Y = YN ( 2, X ):\n";
cout << "\n";
for ( int i = 0; i < 10; i++ )
{
  x = 10.0 * randreal1 ( ) - 5.0;
  y = yn ( 2, x );
  cout << "  " << x << "  " << y << "\n";
}
//
//  Terminate.
//
cout << "\n";
cout << "math_test:\n";
cout << "  Normal end of execution.\n";

exit ( 0 );