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