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#include "equation-solver.h"
#define _USE_MATH_DEFINES
#include <cmath>
#define TOO_LARGE_RATIO 1e12
namespace msdfgen {
int solveQuadratic(double x[2], double a, double b, double c) {
// a = 0 -> linear equation
if (a == 0 || fabs(b)+fabs(c) > TOO_LARGE_RATIO*fabs(a)) {
// a, b = 0 -> no solution
if (b == 0 || fabs(c) > TOO_LARGE_RATIO*fabs(b)) {
if (c == 0)
return -1; // 0 = 0
return 0;
}
x[0] = -c/b;
return 1;
}
double dscr = b*b-4*a*c;
if (dscr > 0) {
dscr = sqrt(dscr);
x[0] = (-b+dscr)/(2*a);
x[1] = (-b-dscr)/(2*a);
return 2;
} else if (dscr == 0) {
x[0] = -b/(2*a);
return 1;
} else
return 0;
}
static int solveCubicNormed(double x[3], double a, double b, double c) {
double a2 = a*a;
double q = (a2 - 3*b)/9;
double r = (a*(2*a2-9*b) + 27*c)/54;
double r2 = r*r;
double q3 = q*q*q;
double A, B;
if (r2 < q3) {
double t = r/sqrt(q3);
if (t < -1) t = -1;
if (t > 1) t = 1;
t = acos(t);
a /= 3; q = -2*sqrt(q);
x[0] = q*cos(t/3)-a;
x[1] = q*cos((t+2*M_PI)/3)-a;
x[2] = q*cos((t-2*M_PI)/3)-a;
return 3;
} else {
A = -pow(fabs(r)+sqrt(r2-q3), 1/3.);
if (r < 0) A = -A;
B = A == 0 ? 0 : q/A;
a /= 3;
x[0] = (A+B)-a;
x[1] = -0.5*(A+B)-a;
x[2] = 0.5*sqrt(3.)*(A-B);
if (fabs(x[2]) < 1e-14)
return 2;
return 1;
}
}
int solveCubic(double x[3], double a, double b, double c, double d) {
if (a != 0) {
double bn = b/a, cn = c/a, dn = d/a;
// Check that a isn't "almost zero"
if (fabs(bn) < TOO_LARGE_RATIO && fabs(cn) < TOO_LARGE_RATIO && fabs(dn) < TOO_LARGE_RATIO)
return solveCubicNormed(x, bn, cn, dn);
}
return solveQuadratic(x, b, c, d);
}
}
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