5  *  Utility functions to find cubic and quartic roots,
10  *  The functions return the number of non-complex roots and
24  *                  correct but multiple roots might be reported more
34         const double t0, const bool oneHint, double roots[4]) {  in reducedQuarticRoots()
85             return quadraticRootsReal(t2, t1, t0, roots);  in reducedQuarticRoots()
88             return cubicRootsReal(t3, t2, t1, t0, roots);  in reducedQuarticRoots()
95         int num = cubicRootsReal(t4, t3, t2, t1, roots);  in reducedQuarticRoots()
97             if (approximately_zero(roots[i])) {  in reducedQuarticRoots()
101         roots[num++] = 0;  in reducedQuarticRoots()
106         int num = cubicRootsReal(t4, t4 + t3, -(t1 + t0), -t0, roots); // note that -C==A+B+D+E  in reducedQuarticRoots()
108             if (approximately_equal(roots[i], 1)) {  in reducedQuarticRoots()
112         roots[num++] = 1;  in reducedQuarticRoots()
141         int roots = cubicRootsReal(1, -p / 2, -r, r * p / 2 - q * q / 8, cubicRoots);  in quarticRootsReal()  local
146         for (index = 0; index < roots; ++index) {  in quarticRootsReal()
176         for (index = 0; index < roots; ++index) {  in quarticRootsReal()
188         for (index = firstCubicRoot; index < roots; ++index) {  in quarticRootsReal()
210                 break; // prefer solutions without single quad roots  in quarticRootsReal()