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// Roots.
import TestLib;
real x;
real[] r;
StartTest("quadratic roots");
r=quadraticroots(1,0,-8);
assert(r.length == 2);
r=sort(r);
x=2sqrt(2);
assert(close(r[0],-x));
assert(close(r[1],x));
r=quadraticroots(1,2,1);
assert(r.length == 2);
assert(close(r[0],-1));
assert(close(r[1],-1));
r=quadraticroots(1,0,8);
assert(r.length == 0);
r=quadraticroots(0,2,3);
assert(r.length == 1);
assert(close(r[0],-3/2));
EndTest();
StartTest("cubic roots");
r=cubicroots(1,0,0,-8);
assert(r.length == 1);
assert(close(r[0],2));
real[] r=cubicroots(1,3,3,1);
assert(r.length == 3);
assert(close(r[0],-1));
assert(close(r[1],-1));
assert(close(r[2],-1));
real[] r=cubicroots(1,-3,3,-1);
assert(r.length == 3);
assert(close(r[0],1));
assert(close(r[1],1));
assert(close(r[2],1));
r=cubicroots(1,0,0,0);
assert(r.length == 3);
assert(r[0] == 0);
assert(r[1] == 0);
assert(r[2] == 0);
r=cubicroots(1,0,-15,-4);
assert(r.length == 3);
r=sort(r);
assert(close(r[0],-2-sqrt(3)));
assert(close(r[1],-2+sqrt(3)));
assert(close(r[2],4));
r=cubicroots(1,0,-15,4);
assert(r.length == 3);
r=sort(r);
assert(close(r[0],-4));
assert(close(r[1],2-sqrt(3)));
assert(close(r[2],2+sqrt(3)));
r=cubicroots(1,0,-15,0);
assert(r.length == 3);
r=sort(r);
x=sqrt(15);
assert(close(r[0],-x));
assert(r[1] == 0);
assert(close(r[2],x));
r=cubicroots(1,1,1,0);
assert(r.length == 1);
assert(r[0] == 0);
r=cubicroots(1,0,20,-4);
assert(r.length == 1);
x=cbrt(54+6sqrt(6081));
assert(close(r[0],x/3-20/x));
EndTest();
StartTest("newton");
real f(real x) {return cos(x);}
real dfdx(real x) {return -sin(x);}
assert(close(newton(f,dfdx,1),pi/2));
assert(newton(f,dfdx,0) == realMax);
assert(newton(f,dfdx,0,2) == pi/2);
EndTest();
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