高精度乘法（FFT）

#include 

using namespace std;
const double PI = acos(-1.0);
struct Complex  {
    double x, y;
    Complex(double _x=0.0,double _y = 0.0) {
        x = _x;
        y = _y;
    }
    Complex operator -(const Complex &b) const {
        return Complex(x-b.x, y-b.y);
    }
    Complex operator +(const Complex &b) const {
        return Complex(x+b.x, y+b.y);
    }
    Complex operator *(const Complex &b) const {
        return Complex(x*b.x-y*b.y, x*b.y+y*b.x);
    }
};
void change(Complex y[], int len) {
    int i,j,k;
    for(i = 1, j = len/2; i < len-1; i++) {
        if(i < j) swap(y[i],y[j]);
        k = len/2;
        while(j >= k) {
            j -= k;
            k /= 2;
        }
        if(j < k) j += k;
    }
}
void fft(Complex y[], int len, int on) {
    change(y, len);
    for(int h = 2; h <= len; h <<= 1) {
        Complex wn(cos(-on*2*PI/h),sin(-on*2*PI/h));
        for(int j = 0; j <= len; j+= h) {
            Complex w(1,0);
            for(int k = j; k < j+h/2; k++) {
                Complex u = y[k];
                Complex t = w*y[k+h/2];
                y[k] = u+t;
                y[k+h/2] = u-t;
                w = w*wn;
            }
        }
    }
    if(on == -1)
        for(int i = 0; i < len; i++)
            y[i].x /= len;
}
const int N = 3e6+100;
Complex x1[N],x2[N];
int sum[N];
int main() {
    //freopen("a.txt","r",stdin);
    ios::sync_with_stdio(0);
    int T;
    cin>>T;
    string a,b;
    while(T--){
        cin>>a>>b;
        int flag = 1;
        int len1 = a.length();
        int len2 = b.length();
        reverse(a.begin(),a.end());  //方便之后进位
        reverse(b.begin(),b.end());

        int len = 1;
        while(len < len1*2 || len < len2*2) len <<= 1;
        for(int i = 0; i < len1; i++) x1[i] = Complex(a[i]-'0',0);
        for(int i = len1; i < len; i++) x1[i] = Complex(0,0);
        for(int i = 0; i < len2; i++) x2[i] = Complex(b[i]-'0',0);
        for(int i = len2; i < len; i++) x2[i] = Complex(0,0);
        fft(x1,len,1);
        fft(x2,len,1);
        for(int i = 0; i < len; i++) x1[i] = x1[i]*x2[i];
        fft(x1,len,-1);

        for(int i = 0; i < len; i++)
            sum[i] = (int)(x1[i].x+0.5);
        for(int i = 0; i < len; i++) {
            sum[i+1] += sum[i]/10;
            sum[i] %= 10;
        }
        int top = len1+len2-1;
        while(top>0&&sum[top]<=0) top--;

        for(int i = top; i >= 0; i--)
            cout<