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json
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Tags:
recursive-self-improvement
autonomous-learning
formal-power-series
exact-arithmetic
certified-compilation
reproducible-research
| using I=long long; | |
| using V=std::vector<I>; | |
| 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;bool 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),false}; | |
| 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),true}; | |
| if(c.mul+c.add<r.mul+r.add)r=c; | |
| } | |
| cache[key]=r;return r; | |
| } | |
| static V lin2(const V&a,const V&b,const int*r){ | |
| V z(a.size());for(size_t i=0;i<a.size();++i)z[i]=mod(r[0]*a[i]+r[1]*b[i]);return z; | |
| } | |
| static V lin3(const std::array<V,3>&a,const int*r){ | |
| V z(a[0].size());for(size_t i=0;i<z.size();++i) | |
| z[i]=mod(r[0]*a[0][i]+r[1]*a[1][i]+r[2]*a[2][i]);return z; | |
| } | |
| static V mul(const V&a,const V&b,int d){ | |
| int n=a.size(),m=b.size();auto q=plan(n,m,d); | |
| if(!q.split){ | |
| V z(n+m-1);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); | |
| }return z; | |
| } | |
| int h=(std::max(n,m)+1)/2;V a0(h),a1(h),b0(h),b1(h); | |
| for(int i=0;i<n;++i)(i<h?a0[i]:a1[i-h])=a[i]; | |
| for(int i=0;i<m;++i)(i<h?b0[i]:b1[i-h])=b[i]; | |
| std::array<V,3> p; | |
| for(int t=0;t<3;++t)p[t]=mul(lin2(a0,a1,A[t]),lin2(b0,b1,B[t]),d-1); | |
| std::array<V,3> c;for(int t=0;t<3;++t)c[t]=lin3(p,C[t]); | |
| V z(4*h-1);std::copy(c[0].begin(),c[0].end(),z.begin()); | |
| for(int t=1;t<3;++t)for(int j=0;j<2*h-1;++j)z[t*h+j]=mod(z[t*h+j]+c[t][j]); | |
| z.resize(n+m-1);return z; | |
| } | |
| 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; | |
| V av(a,a+n),bv(b,b+m);auto z=mul(av,bv,d);std::copy(z.begin(),z.end(),out);return 0; | |
| }catch(...){return 2;} | |
| } | |
| extern "C" void sorilun_clear_cache(){cache.clear();} | |