# dahlquist_bjorck --
#
#	Copyright 2023 Nantes University, France.
#
#	This file is part of the QuadraticEquation library.
#
#	The QuadraticEquation library is free software; you can redistribute it and/or
# modify it under the terms of the GNU Lesser General Public License as published
# by the Free Software Foundation; either version 3 of the License, or (at your
#	option) any later version.
#	
#	The QuadraticEquation library is distributed in the hope that it will be useful,
# but	WITHOUT ANY WARRANTY; without even the implied warranty of MERCHANTABILITY
#	or FITNESS FOR A PARTICULAR PURPOSE.  See the GNU General Public License
#	for more details.
#	
#	You should have received copies of the GNU General Public License and the
#	GNU Lesser General Public License along with the QuadraticEquation Library.
# If not,	see https://www.gnu.org/licenses/.

export dahlquist_bjorck

"""
    Source: Numerical methods in scientific computing, Dahlquist & BjÃ¶rck, 
    SIAM, 2008
    
    Adapted from Algorithm 2.3.2, Page 35 in the reference
"""
function dahlquist_bjorck(a,b,c)
    a=Float64(a);b=Float64(b);c=Float64(c)
    delta = b^2-4*a*c
    if delta >= 0
        x1 = -(sign1(b)*(abs(b)+sqrt(delta)))/(2*a)
        x2 = c/(a*x1)
        if x1 > x2
            return (x2,x1)
        else
            return (x1, x2)
        end
    else
        return (NaN64,NaN64)
    end
end
