function xround = r8_roundx ( nplace, x )

%*****************************************************************************80
%
%% r8_roundx() rounds an R8.
%
%  Discussion:
%
%    Assume that the input quantity X has the form
%
%      X = S * J * 10^L
%
%    where S is plus or minus 1, L is an integer, and J is a decimal
%    mantissa which is either exactly zero, or greater than or equal
%    to 0.1 and less than 1.0.
%
%    Then on return, XROUND will satisfy
%
%      XROUND = S * K * 10^L
%
%    where S and L are unchanged, and K is a decimal mantissa which
%    agrees with J in the first NPLACE decimal digits and is zero
%    thereafter.
%
%    Note that because of rounding, most decimal fraction quantities
%    cannot be stored exactly in the computer, and hence will have
%    trailing "bogus" digits.
%
%    If NPLACE is 0, XROUND will always be zero.
%
%    If NPLACE is 1, the mantissa of XROUND will be 0, 0.1,
%    0.2, ..., or 0.9.
%
%    If NPLACE is 2, the mantissa of XROUND will be 0, 0.01, 0.02,
%    0.03, ..., 0.98, 0.99.
%
%  Licensing:
%
%    This code is distributed under the MIT license. 
%
%  Modified:
%
%    22 October 2005
%
%  Author:
%
%    John Burkardt
%
%  Input:
%
%    integer NPLACE, the number of decimal digits to
%    preserve.  NPLACE should be 0 or positive.
%
%    real X, the number to be decomposed.
%
%  Output:
%
%    real XROUND, the rounded value of X.
%
  xround = 0.0;
%
%  1: Handle the special case of 0.
%
  if ( x == 0.0 )
    return
  end

  if ( nplace <= 0 )
    return
  end
%
%  2: Determine the sign IS.
%
  if ( 0.0 < x )
    is = 1;
    xtemp = x;
  else
    is = -1;
    xtemp = -x;
  end
%
%  3: Force XTEMP to lie between 1 and 10, and compute the
%  logarithm L.
%
  l = 0;

  while ( 10.0 <= x )
    xtemp = xtemp / 10.0;
    l = l + 1;
  end

  while ( xtemp < 1.0 )
    xtemp = xtemp * 10.0;
    l = l - 1;
  end
%
%  4: Now strip out the digits of the mantissa as XMANT, and
%  decrease L.
%
  xmant = 0.0;
  iplace = 0;

  while ( true )

    xmant = 10.0 * xmant;

    if ( 1.0 <= xtemp )
      xmant = xmant + floor ( xtemp );
      xtemp = xtemp - floor ( xtemp );
    end

    iplace = iplace + 1;

    if ( xtemp == 0.0 || nplace <= iplace )
      xround = is * xmant * 10.0 ^ l;
      break
    end

    l = l - 1;
    xtemp = xtemp * 10.0;

  end

  return
end
