big_int ackermann(unsigned m, unsigned n) {
static big_int (*ack)(unsigned, big_int) =
[](unsigned m, big_int n)->big_int {
switch (m) {
case 0:
return n + 1;
case 1:
return n + 2;
case 2:
return 3 + 2 * n;
case 3:
return 5 + 8 * (ipow(big_int(2), n) - 1);
default:
return n == 0 ? ack(m - 1, big_int(1)) : ack(m - 1, ack(m, n - 1));
}
};
return ack(m, big_int(n));
}
//TODO move extra operations, eg: add leading zeros, extra copy constructors
big_int big_int::operator*(const big_int&rhs){
if(*this == 0|| rhs == 0){
return big_int(0);
}
auto max_len = std::max(val_.size(), rhs.val_.size());
if(max_len == 1){
return big_int(static_cast<unsigned>(val_[0]) * static_cast<unsigned>(rhs.val_[0]));
}
auto val = val_, rhs_val = rhs.val_;
val.insert(val.end(), max_len - val.size(), 0);
rhs_val.insert(rhs_val.end(), max_len - rhs_val.size(), 0);
auto mid = max_len >> 1;
big_int x[2], y[2];
x[0].val_.insert(x[0].val_.end(), val.begin(), val.begin()+mid);
x[1].val_.insert(x[1].val_.end(), val.begin()+mid, val.end());
y[0].val_.insert(y[0].val_.end(), rhs_val.begin(), rhs_val.begin()+mid);
y[1].val_.insert(y[1].val_.end(), rhs_val.begin()+mid, rhs_val.end());
x[0].positive_ = x[1].positive_ = y[0].positive_ = y[1].positive_ = 1;
big_int z2 = x[1]*y[1];
big_int z1 = x[1]*y[0] + x[0]*y[1];
big_int ans = big_int(x[0]*y[0]);
if(ans.val_.size() < mid){
ans.val_.insert(ans.val_.end(), mid-ans.val_.size(), 0);
}
std::vector<int>::size_type pos_ans, pos_z;
int carry = 0;
for(pos_ans = mid, pos_z = 0; pos_ans < ans.val_.size() && pos_z < z1.val_.size(); ++pos_ans,++pos_z){
auto tmp = ans.val_[pos_ans] + z1.val_[pos_z] + carry;
ans.val_[pos_ans] = tmp & lowbits_;
if(tmp > lowbits_){
carry = 1;
}else{
carry = 0;
}
}
if(pos_ans < ans.val_.size()){
for(;pos_ans < ans.val_.size(); ++pos_ans){
auto tmp = ans.val_[pos_ans] + carry;
ans.val_[pos_ans] = tmp & lowbits_;
if(tmp > lowbits_){
carry = 1;
}else{
carry = 0;
}
}
}else if(pos_z < z1.val_.size()){
for(;pos_z < z1.val_.size(); ++pos_z){
auto tmp = z1.val_[pos_z] + carry;
ans.val_.push_back(tmp & lowbits_);
if(tmp > lowbits_){
carry = 1;
}else{
carry = 0;
}
}
}
if(carry){
ans.val_.push_back(carry);
}
//ans.val_.insert(ans.val_.end(), z1.val_.begin(), z1.val_.end());
if(ans.val_.size() < (mid<<1) ){
ans.val_.insert(ans.val_.end(), (mid<<1)-ans.val_.size(), 0);
}
carry = 0;
for(pos_ans = mid<<1, pos_z = 0; pos_ans < ans.val_.size() && pos_z < z2.val_.size(); ++pos_ans,++pos_z){
auto tmp = ans.val_[pos_ans] + z2.val_[pos_z] + carry;
ans.val_[pos_ans] = tmp & lowbits_;
if(tmp > lowbits_){
carry = 1;
}else{
carry = 0;
}
}
if(pos_ans < ans.val_.size()){
for(;pos_ans < ans.val_.size(); ++pos_ans){
auto tmp = ans.val_[pos_ans] + carry;
ans.val_[pos_ans] = tmp & lowbits_;
if(tmp > lowbits_){
carry = 1;
}else{
carry = 0;
}
}
}else if(pos_z < z2.val_.size()){
for(;pos_z < z2.val_.size(); ++pos_z){
auto tmp = z2.val_[pos_z] + carry;
ans.val_.push_back(tmp & lowbits_);
if(tmp > lowbits_){
carry = 1;
}else{
carry = 0;
}
}
}
if(carry){
ans.val_.push_back(carry);
}
//ans.val_.insert(ans.val_.end(), z2.val_.begin(), z2.val_.end());
ans.positive_ = positive_ * rhs.positive_;
ans.fix_pre_zeros_();
return ans;
}
