Blame for research/native_build/discovered_kernel.cpp

#include <vector>
#include <array>
#include <map>
#include <tuple>
#include <algorithm>
#include <cstdint>
using I=long long;
static const I P=65537;
static const int A[3][2]={{0,1},{1,0},{1,-1}};
static const int B[3][2]={{0,1},{1,0},{1,-1}};
static const int C[3][3]={{0,1,0},{1,1,-1},{1,0,0}};
static const int IA=2, OA=2;
static I mod(I x){x%=P;return x<0?x+P:x;}
struct Plan{I mul,add;int split;};
static std::map<std::tuple<int,int,int>,Plan> cache;
static Plan plan(int n,int m,int d){
 auto key=std::make_tuple(n,m,d);auto it=cache.find(key);
 if(it!=cache.end())return it->second;
 Plan r{I(n)*m,I(n)*m-(n+m-1),0};
 if(d>0 && std::min(n,m)>1){
  int h=(std::max(n,m)+1)/2;auto q=plan(h,h,d-1);
  Plan c{3*q.mul,3*q.add+I(IA)*h+I(OA+2)*(2*h-1),1};
  if(c.mul+c.add<r.mul+r.add)r=c;
  if(std::max(n,m)>=2*std::min(n,m)){
   int half=std::max(n,m)/2;Plan x,y;int extra;
   if(n>=m){x=plan(half,m,d);y=plan(n-half,m,d);extra=n-half+m-1;}
   else{x=plan(n,half,d);y=plan(n,m-half,d);extra=n+m-half-1;}
   Plan rect{x.mul+y.mul,x.add+y.add+extra,2};
   if(rect.mul+rect.add<r.mul+r.add)r=rect;
  }
 }
 cache[key]=r;return r;
}
static void base(const I*a,int n,const I*b,int m,I*z){
 for(int t=0;t<n+m-1;++t){
  int lo=std::max(0,t-m+1),hi=std::min(n-1,t);
  I s=a[lo]*b[t-lo];for(int j=lo+1;j<=hi;++j)s+=a[j]*b[t-j];z[t]=mod(s);
 }
}
static void recurse(const I*a,int n,const I*b,int m,I*z,I*work,int depth){
 auto q=plan(n,m,depth);
 if(!q.split){base(a,n,b,m,z);return;}
 if(q.split==2){
  int h=std::max(n,m)/2;
  int l1=(n>=m?h+m-1:n+h-1),l2=(n>=m?n-h+m-1:n+m-h-1);
  I*left=work;I*right=left+l1;I*next=right+l2;
  if(n>=m){recurse(a,h,b,m,left,next,depth);recurse(a+h,n-h,b,m,right,next,depth);}
  else{recurse(a,n,b,h,left,next,depth);recurse(a,n,b+h,m-h,right,next,depth);}
  std::fill(z,z+n+m-1,0);std::copy(left,left+l1,z);
  for(int j=0;j<l2;++j)z[h+j]=mod(z[h+j]+right[j]);return;
 }
 int h=(std::max(n,m)+1)/2,l=2*h-1;
 I*aa=work;I*bb=aa+2*h;I*left=bb+2*h;I*right=left+h;
 I*q0=right+h;I*q1=q0+l;I*q2=q1+l;I*next=q2+l;
 std::fill(aa,aa+2*h,0);std::fill(bb,bb+2*h,0);
 std::copy(a,a+n,aa);std::copy(b,b+m,bb);
 I*products[3]={q0,q1,q2};
 for(int t=0;t<3;++t){
  for(int i=0;i<h;++i){left[i]=mod(A[t][0]*aa[i]+A[t][1]*aa[h+i]);
                          right[i]=mod(B[t][0]*bb[i]+B[t][1]*bb[h+i]);}
  recurse(left,h,right,h,products[t],next,depth-1);
 }
 std::fill(z,z+n+m-1,0);
 for(int t=0;t<3;++t)for(int j=0;j<l && t*h+j<n+m-1;++j){
  I v=mod(C[t][0]*q0[j]+C[t][1]*q1[j]+C[t][2]*q2[j]);
  z[t*h+j]=mod(z[t*h+j]+v);
 }
}
extern "C" int sorilun_mul(const I*a,int n,const I*b,int m,int d,I*out){
 try{
  if(n<1||m<1||n>8192||m>8192||d<0||d>20)return 1;
  if(!plan(n,m,d).split){base(a,n,b,m,out);return 0;}
  // Geometrically shrinking operands bound the arena by 32*n+128.
  std::vector<I> workspace(32*std::max(n,m)+128);
  recurse(a,n,b,m,out,workspace.data(),d);return 0;
 }catch(...){return 2;}
}

static std::map<std::pair<int,bool>,std::vector<I>> rootcache;
static I fpow(I a,I k,I*counter){I r=1;while(k){if(k&1){r=r*a%P;++counter[1];}
 k>>=1;if(k){a=a*a%P;++counter[1];}}return r;}
static const std::vector<I>& roots(int n,bool inv,I*counter){
 auto key=std::make_pair(n,inv);auto it=rootcache.find(key);if(it!=rootcache.end())return it->second;
 I w=fpow(3,(P-1)/n,counter);if(inv)w=fpow(w,P-2,counter);
 std::vector<I> r(n/2,1);for(int i=1;i<n/2;++i){r[i]=r[i-1]*w%P;++counter[1];}
 rootcache[key]=r;return rootcache[key];
}
static void transform(std::vector<I>&a,bool inv,I*counter){
 int n=a.size();for(int i=1,j=0;i<n;++i){int bit=n>>1;for(;j&bit;bit>>=1)j^=bit;j^=bit;if(i<j)std::swap(a[i],a[j]);}
 for(int size=2;size<=n;size<<=1){const auto&r=roots(size,inv,counter);
  for(int i=0;i<n;i+=size)for(int j=0;j<size/2;++j){I u=a[i+j],v=a[i+j+size/2]*r[j]%P;
   a[i+j]=(u+v)%P;a[i+j+size/2]=mod(u-v);}
  counter[0]+=n;counter[1]+=n/2;
 }
 if(inv){I c=fpow(n,P-2,counter);for(auto&x:a)x=x*c%P;counter[1]+=n;}
}
extern "C" int sorilun_ntt(const I*a,int n,const I*b,int m,I*out,I*counts){
 try{
  if(n<1||m<1||n>8192||m>8192)return 1;
  counts[0]=counts[1]=0;counts[2]=1;
  int len=1,lg=0;while(len<n+m-1){len<<=1;++lg;}
  I estimate=9LL*len*lg/2+2*len,bmul=I(n)*m,badd=I(n)*m-(n+m-1);
  if(bmul+badd<=estimate){base(a,n,b,m,out);counts[0]=badd;counts[1]=bmul;return 0;}
  std::vector<I> aa(len),bb(len);std::copy(a,a+n,aa.begin());std::copy(b,b+m,bb.begin());
  transform(aa,false,counts);transform(bb,false,counts);
  for(int i=0;i<len;++i)aa[i]=aa[i]*bb[i]%P;counts[1]+=len;
  transform(aa,true,counts);std::copy(aa.begin(),aa.begin()+n+m-1,out);return 0;
 }catch(...){return 2;}
}
extern "C" void sorilun_clear_cache(){cache.clear();rootcache.clear();}