Language: C++

#include<cstdio>
#include<complex>
#include<utility>
#include<vector>
#include<cmath>
#include<cassert>

using namespace std;

double eps=1e-9;

typedef complex<double> Point;
typedef complex<double> Vector;

template<class T> bool eq(T a,T b){
	return abs(a-b)<eps;
}

template<class T> int sgn(T r){
	return eq(r,0.0)?0:(r>0?1:-1);
}

struct Circle{
	Point center;
	double r;
	Circle(Point c,double r):center(c),r(r){}
	Circle(){}
};

struct Line{
	double a,b,c;//ax+by=c
	Line(){}
	Line(double a,double b,double c):a(a),b(b),c(c){}
	Line(Point p1,Point p2){//not verified
		if(eq(abs(p1-p2),0.0)){
			fprintf(stderr,"called Line for same points\n");
			assert(0);
		}
		double x1=p1.real(),y1=p1.imag();
		double x2=p2.real(),y2=p2.imag();
		a=y2-y1;
		b=-(x2-x1);
		c=x1*y2-x2*y1;
	}
};

void print(Point p){
	if(isnan(p.real())||isnan(p.imag())){
		printf("NaN Point\n");
		return;
	}
	printf("(%f,%f)\n",p.real(),p.imag());
}

double pointsDistance(Point p1,Point p2){/*abs(p1-p2)と書いてよい*/
	double dx=p1.real()-p2.real();
	double dy=p1.imag()-p2.imag();
	return sqrt(dx*dx+dy*dy);
}

double linePointDistance(Line l,Point p){
	double a=l.a,b=l.b,c=l.c;
	double x=p.real(),y=p.imag();
	double num=abs(a*x+b*y-c);
	double den=sqrt(a*a+b*b);
	return num/den;
}

Vector basisVector(Vector v){
	if(eq(v.real(),0.0)&&eq(v.imag(),0.0)) return v;
	return v/sqrt(norm(v));
}

Point linePointProjection(Line l,Point p){
	double dx=l.a,dy=l.b;
	double a=l.a,b=l.b,c=l.c;
	double x=p.real(),y=p.imag();
	Vector ba=basisVector(Vector(dx,dy));
	double num=a*x+b*y-c;
	double den=sqrt(a*a+b*b);
	Vector v=ba*(-num/den);
	return p+v;
}

vector<Point> circleLineIntersection(Circle c,Line l){
	vector<Point> res;
	Point p=linePointProjection(l,c.center);
	double d=linePointDistance(l,c.center);
	int s=sgn(d-c.r);
	if(s==1){
		return res;//empty
	}else if(s==0){
		res.push_back(p);
		return res;
	}else{
		double r=c.r;
		double t=sqrt(r*r-d*d);
		Vector e=basisVector(Vector(l.b,-l.a));
		res.push_back(p+t*e);
		res.push_back(p-t*e);
		return res;
	}
}

vector<Point> circlesIntersection(Circle c1,Circle c2){/*一致するとき処理できない*/
	if(eq(c1.center.real(),c2.center.real())&&eq(c1.center.imag(),c2.center.imag())&&
		eq(c1.r,c2.r)){
				Point p=Point(NAN,NAN);
				vector<Point> v;
				v.push_back(p);
				return v;
	}
	double d=pointsDistance(c1.center,c2.center);
	double r1=c1.r,r2=c2.r;
	double dif=max(r1,r2)-min(r1,r2);
	double sum=r1+r2;
	if(sgn(d-sum)==1||sgn(dif-d)==1){//d>sum||dif>d
		vector<Point> v;
		return v;
	}
	double x1=c1.center.real(),y1=c1.center.imag();
	double x2=c2.center.real(),y2=c2.center.imag();
	Line l=Line(-x1*2+x2*2,-y1*2+y2*2,r1*r1-r2*r2-(x1*x1-x2*x2)-(y1*y1-y2*y2));
	return circleLineIntersection(c1,l);
}

double det(double a,double b,double c,double d){
	return a*d-b*c;
}

Point linesIntersection(Line l1,Line l2){/*平行の時は常にNAN*/
	double a=l1.a,b=l1.b,c=l1.c;
	double d=l2.a,e=l2.b,f=l2.c;
	double den=det(a,b,d,e);
	double numx=det(c,b,f,e);
	double numy=det(a,c,d,f);
	if(eq(den,0.0)){
		return Point(NAN,NAN);
	}
	return Point(numx/den,numy/den);
}

//circlesIntersection verify AOJ1190 ICPC Domestic 2013 Balloon

double crossProduct(Vector a,Vector b){
	return (conj(a)*b).imag();
}

double dotProduct(Vector a,Vector b){
	return (conj(a)*b).real();
}

int ccw(Point p1,Point p2,Point p3){
	/*p1,p2,p3はすべて異なると仮定
	そうでない場合の戻り値は不定
	ではなく
	p1!=p2と仮定*/
	Vector b=p2-p1;
	Vector c=p3-p1;
	int s=sgn(crossProduct(b,c));
	if(s==1) return 1;//counterclockwise
	if(s==-1) return -1;//clockwise
	int t=sgn(dotProduct(b,c));
	if(t==-1) return 2;//3--1--2
	int u=sgn(norm(b)-norm(c));
	if(eq(norm(c),0.0)) return 0;//1==3
	if(u==-1) return -2;//1--2--3
	return 0;//1--3--2 or 2==3
}

struct Segment{
	Point p1,p2;
	Line l;
	Segment(){}
	Segment(Point p1,Point p2):p1(p1),p2(p2){
		l=Line(p1,p2);
	}
};

int oneLineCCW(Point p1,Point p2,Point p3){
	/*p1!=p2かつp1,p2,p3は一直線上と仮定*/
	/*それ以外の時の戻り値は不定*/
	Vector b=p2-p1,c=p3-p1;
	if(sgn(dotProduct(b,c))==-1) return 2;//p3--p1--p2
	if(eq(abs(p1-p3),0.0)) return 1;//p1==p3--p2
	int s=sgn(norm(b)-norm(c));
	if(s==1) return 0;//p1--p3--p2
	if(s==0) return -1;//p1--p3==p2
	else return -2;//p1--p2--p3
}

double pointSegmentDistance(Point p,Segment s){
	Line l=s.l;
	double d=linePointDistance(l,p);
	Point pr=linePointProjection(l,p);
//	int x=oneLineCCW(s.p1,s.p2,pr);
	int x=ccw(s.p1,s.p2,pr);
//	if(x>=-1&&x<=1) return d;
	if(x==0)
	double a=abs(s.p1-p);
	double b=abs(s.p2-p);
	return min(a,b);
}

bool segmentsIntersect(Segment s1,Segment s2){
	Point p[2],q[2];
	p[0]=s1.p1,p[1]=s1.p2;
	q[0]=s2.p1,q[1]=s2.p2;
	return ccw(p[0],p[1],q[0])*ccw(p[0],p[1],q[1])<=0&&
		ccw(q[0],q[1],p[0])*ccw(q[0],q[1],p[1])<=0;
}

double segmentsDistance(Segment s1,Segment s2){
	bool flg=segmentsIntersect(s1,s2);
	if(flg) return 0;
	Point p[2],q[2];
	p[0]=s1.p1,p[1]=s1.p2;
	q[0]=s2.p1,q[1]=s2.p2;
	double res=-1;
	for(int k=0;k<2;k++){
		Point r=linePointProjection(s2.l,p[k]);
	//	if(abs(oneLineCCW(q[0],q[1],r))<=1){
		if(ccw(q[0],q[1],r)==0)
			double tmp=abs(r-p[k]);
			if(res<0||tmp<res) res=tmp;
		}
		r=linePointProjection(s1.l,q[k]);
	//	if(abs(oneLineCCW(p[0],p[1],r))<=1){
		if(ccw(p[0],p[1],r)==0){
			double tmp=abs(r-q[k]);
			if(res<0||tmp<res) res=tmp;
		}
	}
	for(int i=0;i<2;i++) for(int j=0;j<2;j++){
		double tmp=abs(p[i]-q[j]);
		if(res<0||tmp<res) res=tmp;
	}
	return res;
}

Point inputPoint(){
	double x,y;
	scanf("%lf%lf",&x,&y);
	return Point(x,y);
}

int main(){
	int Q;
	scanf("%d",&Q);
	for(int datano=0;datano<Q;datano++){
		Point p1,p2;
		Point q1,q2;
		p1=inputPoint();
		p2=inputPoint();
		q1=inputPoint();
		q2=inputPoint();
		if(abs(p1-p2)<eps) break;
		Segment s1=Segment(p1,p2);
		Segment s2=Segment(q1,q2);
		double ans=segmentsDistance(s1,s2);
		printf("%.9f\n",ans);
	}
	return 0;
}

Compiler output:
a.cc: In function 'double pointSegmentDistance(Point, Segment)':
a.cc:202:20: error: 'a' was not declared in this scope
  202 |         return min(a,b);
      |                    ^
a.cc: In function 'double segmentsDistance(Segment, Segment)':
a.cc:225:35: error: 'tmp' was not declared in this scope; did you mean 'tm'?
  225 |                         if(res<0||tmp<res) res=tmp;
      |                                   ^~~
      |                                   tm
a.cc:227:17: error: 'r' was not declared in this scope
  227 |                 r=linePointProjection(s1.l,q[k]);
      |                 ^
a.cc:227:46: error: 'k' was not declared in this scope
  227 |                 r=linePointProjection(s1.l,q[k]);
      |                                              ^
a.cc: At global scope:
a.cc:234:9: error: expected unqualified-id before 'for'
  234 |         for(int i=0;i<2;i++) for(int j=0;j<2;j++){
      |         ^~~
a.cc:234:21: error: 'i' does not name a type
  234 |         for(int i=0;i<2;i++) for(int j=0;j<2;j++){
      |                     ^
a.cc:234:25: error: 'i' does not name a type
  234 |         for(int i=0;i<2;i++) for(int j=0;j<2;j++){
      |                         ^
a.cc:234:42: error: 'j' does not name a type
  234 |         for(int i=0;i<2;i++) for(int j=0;j<2;j++){
      |                                          ^
a.cc:234:46: error: 'j' does not name a type
  234 |         for(int i=0;i<2;i++) for(int j=0;j<2;j++){
      |                                              ^
a.cc:238:9: error: expected unqualified-id before 'return'
  238 |         return res;
      |         ^~~~~~
a.cc:239:1: error: expected declaration before '}' token
  239 | }
      | ^
a.cc: In function 'double segmentsDistance(Segment, Segment)':
a.cc:233:9: warning: control reaches end of non-void function [-Wreturn-type]
  233 |         }
      |         ^