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// Copyright (c) 2003 INRIA Sophia-Antipolis (France). // All rights reserved. // // This file is part of CGAL (www.cgal.org). // // $URL: https://github.com/CGAL/cgal/blob/v6.1/Apollonius_graph_2/include/CGAL/functions_on_signs.h $ // $Id: include/CGAL/functions_on_signs.h b26b07a1242 $ // SPDX-License-Identifier: GPL-3.0-or-later OR LicenseRef-Commercial // // // Author(s) : Menelaos Karavelas #ifndef CGAL_FUNCTIONS_ON_SIGNS_H #define CGAL_FUNCTIONS_ON_SIGNS_H #include #include #include namespace CGAL { #if 0 inline Sign operator*(const Sign &s1, const Sign &s2) { if ( s1 == ZERO || s2 == ZERO ) return ZERO; if ( s1 == s2 ) return POSITIVE; return NEGATIVE; } #endif template < class RT > Sign sign_a_plus_b_x_sqrt_c(const RT &a, const RT &b, const RT &c) { // computes the sign of quantity: a + b * sqrt(c) CGAL_assertion( !(CGAL::is_negative(c)) ); Sign sa = CGAL::sign(a); if ( CGAL::sign(c) == ZERO ) return sa; Sign sb = CGAL::sign(b); if ( sa == sb ) return sa; if ( sa == ZERO ) return sb; return sa * CGAL::compare( CGAL::square(a), c * CGAL::square(b) ); } template < class RT > Sign sign_a_x_sqrt_c_plus_b_x_sqrt_d(const RT &a, const RT &b, const RT &c, const RT &d) { // computes the sign of quantity: a * sqrt(c) + b * sqrt(d) CGAL_assertion( !(CGAL::is_negative(c)) ); CGAL_assertion( !(CGAL::is_negative(d)) ); Sign sb = CGAL::sign(b); if ( CGAL::sign(d) == ZERO ) return CGAL::sign(a * c); if ( CGAL::sign(c) == ZERO ) return sb; Sign sa = CGAL::sign(a); if ( sa == sb ) return sa; if ( sa == ZERO ) return sb; return sa * CGAL::compare( CGAL::square(a) * c, CGAL::square(b) * d ); } template < class RT > Sign sign_a_plus_b_x_sqrt_e_plus_c_x_sqrt_f(const RT &a, const RT &b, const RT &c, const RT &e, const RT &f) { // computes the sign of quantity: a + b * sqrt(e) + c * sqrt(f) CGAL_assertion( !(CGAL::is_negative(e)) ); CGAL_assertion( !(CGAL::is_negative(f)) ); Sign s_a_plus_b_x_sqrt_e = sign_a_plus_b_x_sqrt_c(a, b, e); if ( CGAL::sign(f) == ZERO ) return s_a_plus_b_x_sqrt_e; Sign sc = CGAL::sign(c); if ( s_a_plus_b_x_sqrt_e == sc ) return sc; if ( s_a_plus_b_x_sqrt_e == ZERO ) return sc; return s_a_plus_b_x_sqrt_e * sign_a_plus_b_x_sqrt_c(CGAL::square(a) + CGAL::square(b) * e - CGAL::square(c) * f, RT(2) * a * b, e); } template < class RT > Sign sign_a_plus_b_x_sqrt_e_plus_c_x_sqrt_f_plus_d_sqrt_e_x_f(const RT &a, const RT &b, const RT &c, const RT &d, const RT &e, const RT &f) { // computes the sign of quantity: // a + b * sqrt(e) + c * sqrt(f) + d * sqrt(e * f) CGAL_assertion( !(CGAL::is_negative(e)) ); CGAL_assertion( !(CGAL::is_negative(f)) ); Sign s_a_plus_b_sqrt_e = sign_a_plus_b_x_sqrt_c(a, b, e); Sign s_c_plus_d_sqrt_e = sign_a_plus_b_x_sqrt_c(c, d, e); if ( s_a_plus_b_sqrt_e == s_c_plus_d_sqrt_e ) return s_a_plus_b_sqrt_e; if ( s_a_plus_b_sqrt_e == ZERO ) return s_a_plus_b_sqrt_e; return s_a_plus_b_sqrt_e * sign_a_plus_b_x_sqrt_c(CGAL::square(a) + CGAL::square(b) * e - CGAL::square(c) * f - CGAL::square(d) * e * f, RT(2) * (a * b - c * d * f), e); } } //namespace CGAL #include #endif // CGAL_FUNCTIONS_ON_SIGNS_H