// codesnip-guard: StaticRectangleAddRectangleSum
#[cfg_attr(any(),rustfmt::skip)]pub use self::static_rectangle_add_rectangle_sum::StaticRectangleAddRectangleSum;#[cfg_attr(any(),rustfmt::skip)]mod static_rectangle_add_rectangle_sum{use super::{ArrayOperation,BinaryIndexedTree,Invertible,Ring,SemiRing,SliceSortExt,StaticSearch};pub struct StaticRectangleAddRectangleSum<R>where R:SemiRing{rectangles:Vec<(u32,u32,u32,u32,R::T)>,queries:Vec<(u32,u32,u32,u32)>}impl<R>StaticRectangleAddRectangleSum<R>where R:SemiRing{#[doc=" Rectangles are `(left, bottom, right, top, weight)`."]pub fn new(rectangles:impl IntoIterator<Item=(u32,u32,u32,u32,R::T)>)->Self{Self{rectangles:rectangles.into_iter().collect(),queries:Vec::new()}}#[doc=" Returns its index in `execute`'s results."]pub fn query(&mut self,l:u32,d:u32,r:u32,u:u32)->usize{let index=self.queries.len();self.queries.push((l,d,r,u));index}#[doc=" Results in query order."]pub fn execute(self)->Vec<R::T>where R:Ring<Additive:Invertible>,R::T:From<u32>{let n=self.rectangles.len();let mut ys:Vec<_>=self.rectangles.iter().flat_map(|&(_,d,_,u,_)|[d,u]).collect();ys.radix_sort_by_key(|&y|y);ys.dedup();let search=StaticSearch::from_sorted(&ys);let endpoints:Vec<_>=self.rectangles.iter().flat_map(|&(_,d,_,u,_)|[d,u]).chain(self.queries.iter().flat_map(|&(_,d,_,u)|[d,u])).collect();let mut positions=vec![0;endpoints.len()];search.lower_bound_batch(&endpoints,&mut positions);let mut points:Vec<_>=self.rectangles.into_iter().zip(positions[..2*n].as_chunks().0).flat_map(|((l,_,r,_,w),&[d,u])|{let d=d as u32;let u=u as u32;let negative=R::neg(&w);[(l,d,w.clone()),(l,u,negative.clone()),(r,d,negative),(r,u,w)]}).collect();points.radix_sort_by_key(|&(x,..)|x);let mut events:Vec<_>=self.queries.into_iter().zip(positions[2*n..].as_chunks().0).enumerate().flat_map(|(i,((l,d,r,u),&[di,ui]))|{let di=di as u32;let ui=ui as u32;[(l,d,u,di,ui,i as u32,false),(r,d,u,di,ui,i as u32,true)]}).collect();events.radix_sort_by_key(|&(x,..)|x);let mut bit=BinaryIndexedTree::<ArrayOperation<R::Additive,4>>::new(ys.len());let mut points=points.into_iter().peekable();let mut answers=vec![R::zero();events.len()/2];for(x,d,u,di,ui,i,add)in events{while points.peek().is_some_and(|&(px,..)|px<x){let(px,py,w)=points.next().unwrap();let wx=R::mul(&w,&px.into());let wy=R::mul(&w,&ys[py as usize].into());let wxy=R::mul(&wx,&ys[py as usize].into());bit.update(py as usize,[w,wx,wy,wxy]);}for(y,yi,add)in[(d,di,!add),(u,ui,add)]{let[w,wx,wy,wxy]=bit.accumulate0(yi as usize);let value=R::add(&R::sub(&R::mul(&R::sub(&R::mul(&w,&x.into()),&wx),&y.into()),&R::mul(&wy,&x.into())),&wxy);if add{R::add_assign(&mut answers[i as usize],&value);}else{R::sub_assign(&mut answers[i as usize],&value);}}}answers}}}
// codesnip-guard: AdditiveOperation
#[cfg_attr(any(),rustfmt::skip)]pub use self::additive_operation_impl::AdditiveOperation;#[cfg_attr(any(),rustfmt::skip)]mod additive_operation_impl{use super::*;use std::{marker::PhantomData,ops::{Add,Neg,Sub}};#[doc=" $+$"]pub struct AdditiveOperation<T>where T:Clone+Zero+Add<Output=T>{_marker:PhantomData<fn()->T>}impl<T>Magma for AdditiveOperation<T>where T:Clone+Zero+Add<Output=T>{type T=T;#[inline]fn operate(x:&Self::T,y:&Self::T)->Self::T{x.clone()+y.clone()}}impl<T>Unital for AdditiveOperation<T>where T:Clone+Zero+Add<Output=T>{#[inline]fn unit()->Self::T{Zero::zero()}}impl<T>Associative for AdditiveOperation<T>where T:Clone+Zero+Add<Output=T>{}impl<T>Commutative for AdditiveOperation<T>where T:Clone+Zero+Add<Output=T>{}impl<T>Invertible for AdditiveOperation<T>where T:Clone+Zero+Add<Output=T>+Sub<Output=T>+Neg<Output=T>{#[inline]fn inverse(x:&Self::T)->Self::T{-x.clone()}#[inline]fn rinv_operate(x:&Self::T,y:&Self::T)->Self::T{x.clone()-y.clone()}}}
// codesnip-guard: ArrayOperation
#[cfg_attr(any(),rustfmt::skip)]pub use self::array_operation_impl::ArrayOperation;#[cfg_attr(any(),rustfmt::skip)]mod array_operation_impl{use super::*;use crate::array;use std::marker::PhantomData;pub struct ArrayOperation<M,const N:usize>{_marker:PhantomData<fn()->M>}impl<M,const N:usize>Magma for ArrayOperation<M,N>where M:Magma{type T=[M::T;N];#[inline]fn operate(x:&Self::T,y:&Self::T)->Self::T{array!(|i|M::operate(&x[i],&y[i]);N)}}impl<M,const N:usize>Unital for ArrayOperation<M,N>where M:Unital{#[inline]fn unit()->Self::T{array!(||M::unit();N)}}impl<M,const N:usize>Associative for ArrayOperation<M,N>where M:Associative{}impl<M,const N:usize>Commutative for ArrayOperation<M,N>where M:Commutative{}impl<M,const N:usize>Idempotent for ArrayOperation<M,N>where M:Idempotent{}impl<M,const N:usize>Invertible for ArrayOperation<M,N>where M:Invertible{#[inline]fn inverse(x:&Self::T)->Self::T{array!(|i|M::inverse(&x[i]);N)}}}
// codesnip-guard: BinaryIndexedTree
#[cfg_attr(any(),rustfmt::skip)]pub use self::binary_indexed_tree::BinaryIndexedTree;#[cfg_attr(any(),rustfmt::skip)]mod binary_indexed_tree{use super::{AbelianGroup,Group,Monoid};use std::fmt::{self,Debug,Formatter};pub struct BinaryIndexedTree<M>where M:Monoid{n:usize,bit:Vec<M::T>}impl<M>Clone for BinaryIndexedTree<M>where M:Monoid{fn clone(&self)->Self{Self{n:self.n,bit:self.bit.clone()}}}impl<M>Debug for BinaryIndexedTree<M>where M:Monoid<T:Debug>{fn fmt(&self,f:&mut Formatter<'_>)->fmt::Result{f.debug_struct("BinaryIndexedTree").field("n",&self.n).field("bit",&self.bit).finish()}}impl<M>BinaryIndexedTree<M>where M:Monoid{#[inline]pub fn new(n:usize)->Self{let bit=vec![M::unit();n+1];Self{n,bit}}#[inline]pub fn from_slice(slice:&[M::T])->Self{let n=slice.len();let mut bit=vec![M::unit();n+1];for(i,x)in slice.iter().enumerate(){let k=i+1;M::operate_assign(&mut bit[k],x);let j=k+(k&(!k+1));if j<=n{bit[j]=M::operate(&bit[j],&bit[k]);}}Self{n,bit}}#[inline]#[doc=" fold [0, k)"]pub fn accumulate0(&self,mut k:usize)->M::T{debug_assert!(k<=self.n);let mut res=M::unit();while k>0{res=M::operate(&self.bit[k],&res);k-=k&(!k+1);}res}#[inline]#[doc=" fold [0, k]"]pub fn accumulate(&self,k:usize)->M::T{self.accumulate0(k+1)}#[inline]pub fn update(&mut self,k:usize,x:M::T){debug_assert!(k<self.n);let mut k=k+1;while k<=self.n{self.bit[k]=M::operate(&self.bit[k],&x);k+=k&(!k+1);}}#[inline]pub fn partition_point_acc<P>(&self,mut pred:P)->usize where P:FnMut(&M::T)->bool{let n=self.n;let mut acc=M::unit();let mut pos=0;let mut k=n.next_power_of_two();while k>0{if k+pos<=n{let nacc=M::operate(&acc,&self.bit[k+pos]);if pred(&nacc){pos+=k;acc=nacc;}}k>>=1;}pos}}impl<G:Group>BinaryIndexedTree<G>{#[inline]pub fn fold(&self,l:usize,r:usize)->G::T{debug_assert!(l<=self.n&&r<=self.n);G::operate(&G::inverse(&self.accumulate0(l)),&self.accumulate0(r))}#[inline]pub fn fold_abelian(&self,mut l:usize,mut r:usize)->G::T where G:AbelianGroup{debug_assert!(l<=self.n&&r<=self.n);if l==r{return G::unit();}let common=l&!(usize::MAX>>(l^r).leading_zeros());let mut left=G::unit();let mut right=G::unit();while l!=common{G::operate_assign(&mut left,&self.bit[l]);l&=l-1;}while r!=common{G::operate_assign(&mut right,&self.bit[r]);r&=r-1;}G::rinv_operate(&right,&left)}#[inline]pub fn get(&self,k:usize)->G::T{self.fold(k,k+1)}#[inline]pub fn set(&mut self,k:usize,x:G::T){self.update(k,G::operate(&G::inverse(&self.get(k)),&x));}}}
// codesnip-guard: MultiplicativeOperation
#[cfg_attr(any(),rustfmt::skip)]pub use self::multiplicative_operation_impl::MultiplicativeOperation;#[cfg_attr(any(),rustfmt::skip)]mod multiplicative_operation_impl{use super::*;use std::{marker::PhantomData,ops::{Div,Mul}};#[doc=" $\\times$"]pub struct MultiplicativeOperation<T>where T:Clone+One+Mul<Output=T>{_marker:PhantomData<fn()->T>}impl<T>Magma for MultiplicativeOperation<T>where T:Clone+One+Mul<Output=T>{type T=T;#[inline]fn operate(x:&Self::T,y:&Self::T)->Self::T{x.clone()*y.clone()}}impl<T>Unital for MultiplicativeOperation<T>where T:Clone+One+Mul<Output=T>{#[inline]fn unit()->Self::T{One::one()}}impl<T>Associative for MultiplicativeOperation<T>where T:Clone+One+Mul<Output=T>{}impl<T>Commutative for MultiplicativeOperation<T>where T:Clone+One+Mul<Output=T>{}impl<T>Invertible for MultiplicativeOperation<T>where T:Clone+One+Mul<Output=T>+Div<Output=T>{#[inline]fn inverse(x:&Self::T)->Self::T{Self::unit().div(x.clone())}#[inline]fn rinv_operate(x:&Self::T,y:&Self::T)->Self::T{(x.clone()).div(y.clone())}}}
// codesnip-guard: StaticSearch
#[cfg_attr(any(),rustfmt::skip)]pub use self::static_search::{SimdKey,StaticSearch};#[cfg_attr(any(),rustfmt::skip)]mod static_search{use super::SimdBackend;#[cfg(target_arch="x86_64")]use super::{avx512_enabled,simd};use std::{marker::PhantomData,ops::Range};#[inline]fn static_search_backend(bits:u32)->SimdBackend{#[cfg(target_arch="x86_64")]{if avx512_enabled()&&is_x86_feature_detected!("avx512f")&&(bits!=16||is_x86_feature_detected!("avx512bw")){return SimdBackend::Avx512;}if is_x86_feature_detected!("avx2"){return SimdBackend::Avx2;}}let _=bits;SimdBackend::Scalar}#[doc=" Maps a key to an unsigned integer with exactly the same ordering."]#[doc=""]#[doc=" `BITS` must be 8, 16, 32, 64, or 128. `encode` must be deterministic, fit in"]#[doc=" `BITS`, and satisfy `a.cmp(&b) == a.encode().cmp(&b.encode())`."]pub trait SimdKey:Copy+Ord{const BITS:u32;fn encode(self)->u128;}macro_rules!impl_unsigned_simd_key{($($value:ty),*$(,)?)=>{$(impl SimdKey for$value{const BITS:u32=<$value>::BITS;#[inline(always)]fn encode(self)->u128{self as u128}})*};}macro_rules!impl_signed_simd_key{($(($signed:ty,$unsigned:ty)),*$(,)?)=>{$(impl SimdKey for$signed{const BITS:u32=<$signed>::BITS;#[inline(always)]fn encode(self)->u128{((self as$unsigned)^((1 as$unsigned)<<(<$signed>::BITS-1)))as u128}})*};}impl_unsigned_simd_key!(u8,u16,u32,u64,u128,usize);impl_signed_simd_key!((i8,u8),(i16,u16),(i32,u32),(i64,u64),(i128,u128),(isize,usize),);#[derive(Clone,Debug)]enum DirectStaticSearch{U16(Vec<u16>),U32(Vec<u32>)}impl DirectStaticSearch{fn build<K:SimdKey>(values:&[K],bits:u32)->Self{assert!(values.len()<=u32::MAX as usize);if values.len()<=u16::MAX as usize{Self::U16(build_direct_positions(values,bits,|position|{position as u16}))}else{Self::U32(build_direct_positions(values,bits,|position|{position as u32}))}}#[inline(always)]fn lower_bound(&self,value:u128)->usize{let value=usize::try_from(value).expect("SimdKey::encode exceeds usize");match self{Self::U16(positions)=>positions[value]as usize,Self::U32(positions)=>positions[value]as usize,}}#[inline(always)]fn upper_bound(&self,value:u128)->usize{let value=usize::try_from(value).ok().and_then(|value|value.checked_add(1)).expect("SimdKey::encode exceeds usize");match self{Self::U16(positions)=>positions[value]as usize,Self::U32(positions)=>positions[value]as usize,}}#[inline(always)]fn contains(&self,value:u128)->bool{let value=usize::try_from(value).ok().and_then(|value|value.checked_add(1).map(|next|(value,next))).expect("SimdKey::encode exceeds usize");match self{Self::U16(positions)=>positions[value.0]!=positions[value.1],Self::U32(positions)=>positions[value.0]!=positions[value.1],}}}fn build_direct_positions<K,P>(values:&[K],bits:u32,position:impl Fn(usize)->P)->Vec<P>where K:SimdKey,P:Copy{let len=(1<<bits)+1;let mut positions=Vec::with_capacity(len);let maximum=(1u128<<bits)-1;let mut previous:Option<(K,u128)>=None;for(index,&value)in values.iter().enumerate(){let encoded=value.encode();assert!(encoded<=maximum,"SimdKey::encode exceeds its declared width");if let Some((previous_value,previous_encoded))=previous{assert_eq!(previous_value.cmp(&value),previous_encoded.cmp(&encoded),"SimdKey::encode does not preserve order");}if previous.is_none_or(|(_,previous)|previous!=encoded){positions.resize(encoded as usize+1,position(index));}previous=Some((value,encoded));}positions.resize(len,position(values.len()));positions}macro_rules!bound_batch{(lower,$this:ident,$values:ident,$search:expr)=>{{if$this.len==0{return[0;16];}let mut$values=*$values;let mut beyond=[false;16];for index in 0..16{beyond[index]=$values[index]>$this.maximum;$values[index]=$values[index].min($this.maximum);}let mut result=$search;for index in 0..16{if beyond[index]{result[index]=$this.len;}}result}};(upper,$this:ident,$values:ident,$search:expr)=>{{if$this.len==0{return[0;16];}let mut$values=*$values;let mut beyond=[false;16];for index in 0..16{beyond[index]=$values[index]>=$this.maximum;}let Some(value)=$values.iter().copied().find(|&value|value<$this.maximum)else{return[$this.len;16];};for index in 0..16{if beyond[index]{$values[index]=value;}}let mut result=$search;for index in 0..16{if beyond[index]{result[index]=$this.len;}}result}};}#[repr(C,align(64))]#[derive(Clone,Debug)]struct SearchBlock<T,const B:usize>([T;B]);#[derive(Clone,Debug)]struct StaticSearchTree<T,const B:usize>{values:Vec<SearchBlock<T,B>>,len:usize,maximum:T,levels:Vec<Vec<SearchBlock<T,B>>>,#[cfg(target_arch="x86_64")]backend:SimdBackend}impl<T:Copy+Ord,const B:usize>StaticSearchTree<T,B>{fn build<K>(values:&[K],sentinel:T,maximum_encoded:u128,convert:impl Fn(u128)->T,backend:SimdBackend)->Self where K:SimdKey{let _=&backend;let len=values.len();let mut previous:Option<(K,T)>=None;let mut separators=Vec::with_capacity(values.len().div_ceil(B));let mut blocks=Vec::with_capacity(separators.capacity());for chunk in values.chunks(B){let mut block=[sentinel;B];for(index,&value)in chunk.iter().enumerate(){let encoded=value.encode();assert!(encoded<=maximum_encoded,"SimdKey::encode exceeds its declared width");let encoded=convert(encoded);if let Some((previous_value,previous_encoded))=previous{assert!(previous_value.cmp(&value)==previous_encoded.cmp(&encoded),"SimdKey::encode does not preserve order");}previous=Some((value,encoded));block[index]=encoded;}separators.push(block[chunk.len()-1]);blocks.push(SearchBlock(block));}let maximum=separators.last().copied().unwrap_or(sentinel);let mut levels=Vec::new();while separators.len()>1{let mut blocks=Vec::with_capacity(separators.len().div_ceil(B));let mut next=Vec::with_capacity(blocks.capacity());for chunk in separators.chunks(B){let mut block=[sentinel;B];block[..chunk.len()].copy_from_slice(chunk);blocks.push(SearchBlock(block));next.push(chunk[chunk.len()-1]);}levels.push(blocks);separators=next;}Self{values:blocks,len,maximum,levels,#[cfg(target_arch="x86_64")]backend}}#[inline(always)]fn descend<F>(&self,value:T,mut position:F)->usize where F:FnMut(&[T;B],T)->usize{let mut block=0;for level in self.levels.iter().rev(){let values=&unsafe{level.get_unchecked(block)}.0;block=block*B+position(values,value);}let values=&unsafe{self.values.get_unchecked(block)}.0;(block*B+position(values,value)).min(self.len)}#[inline(always)]fn get(&self,index:usize)->T{unsafe{*self.values.get_unchecked(index/B).0 .get_unchecked(index%B)}}#[inline(always)]fn descend_batch<F>(&self,values:&[T;16],mut position:F)->[usize;16]where F:FnMut(&[T;B],T)->usize{let mut blocks=[0;16];for level in self.levels.iter().rev(){for index in 0..16{let block_values=&unsafe{level.get_unchecked(blocks[index])}.0;blocks[index]=blocks[index]*B+position(block_values,values[index]);}}for index in 0..16{let block=blocks[index];let block_values=&unsafe{self.values.get_unchecked(block)}.0;blocks[index]=(block*B+position(block_values,values[index])).min(self.len);}blocks}#[inline(always)]fn lower_bound_scalar(&self,value:T)->usize{self.descend(value,|values,value|{values.partition_point(|&current|current<value)})}#[inline(always)]fn upper_bound_scalar(&self,value:T)->usize{self.descend(value,|values,value|{values.partition_point(|&current|current<=value)})}#[inline(always)]fn lower_bound_batch_scalar(&self,values:&[T;16])->[usize;16]{self.descend_batch(values,|values,value|{values.partition_point(|&current|current<value)})}#[inline(always)]fn upper_bound_batch_scalar(&self,values:&[T;16])->[usize;16]{self.descend_batch(values,|values,value|{values.partition_point(|&current|current<=value)})}}macro_rules!impl_static_search_tree{($value:ty,$branch:expr,$first_ge_avx2:ident,$first_gt_avx2:ident,$first_ge_avx512:ident,$first_gt_avx512:ident,$avx512_features:literal)=>{impl StaticSearchTree<$value,$branch>{#[inline]fn lower_bound(&self,value:$value)->usize{if self.len==0||value>self.maximum{return self.len;}#[cfg(target_arch="x86_64")]return match self.backend{SimdBackend::Scalar=>self.lower_bound_scalar(value),SimdBackend::Avx2=>unsafe{self.lower_bound_avx2(value)},SimdBackend::Avx512=>unsafe{self.lower_bound_avx512(value)},};#[cfg(not(target_arch="x86_64"))]self.lower_bound_scalar(value)}#[inline]fn upper_bound(&self,value:$value)->usize{if self.len==0{return 0;}if value>=self.maximum{return self.len;}#[cfg(target_arch="x86_64")]return match self.backend{SimdBackend::Scalar=>self.upper_bound_scalar(value),SimdBackend::Avx2=>unsafe{self.upper_bound_avx2(value)},SimdBackend::Avx512=>unsafe{self.upper_bound_avx512(value)},};#[cfg(not(target_arch="x86_64"))]self.upper_bound_scalar(value)}#[inline]fn contains(&self,value:$value)->bool{let index=self.lower_bound(value);index<self.len&&self.get(index)==value}#[inline]fn lower_bound_batch(&self,values:&[$value;16])->[usize;16]{#[cfg(target_arch="x86_64")]if self.backend==SimdBackend::Avx512{return unsafe{self.lower_bound_batch_avx512(values)};}bound_batch!(lower,self,values,{#[cfg(target_arch="x86_64")]let result=if self.backend==SimdBackend::Avx2{unsafe{self.lower_bound_batch_avx2(&values)}}else{self.lower_bound_batch_scalar(&values)};#[cfg(not(target_arch="x86_64"))]let result=self.lower_bound_batch_scalar(&values);result})}#[inline]fn upper_bound_batch(&self,values:&[$value;16])->[usize;16]{#[cfg(target_arch="x86_64")]if self.backend==SimdBackend::Avx512{return unsafe{self.upper_bound_batch_avx512(values)};}bound_batch!(upper,self,values,{#[cfg(target_arch="x86_64")]let result=if self.backend==SimdBackend::Avx2{unsafe{self.upper_bound_batch_avx2(&values)}}else{self.upper_bound_batch_scalar(&values)};#[cfg(not(target_arch="x86_64"))]let result=self.upper_bound_batch_scalar(&values);result})}#[cfg(target_arch="x86_64")]#[target_feature(enable="avx2")]unsafe fn lower_bound_avx2(&self,value:$value)->usize{self.descend(value,|values,value|unsafe{simd::$first_ge_avx2(values,value)})}#[cfg(target_arch="x86_64")]#[target_feature(enable="avx2")]unsafe fn upper_bound_avx2(&self,value:$value)->usize{self.descend(value,|values,value|unsafe{simd::$first_gt_avx2(values,value)})}#[cfg(target_arch="x86_64")]#[target_feature(enable="avx2")]unsafe fn lower_bound_batch_avx2(&self,values:&[$value;16])->[usize;16]{self.descend_batch(values,|values,value|unsafe{simd::$first_ge_avx2(values,value)})}#[cfg(target_arch="x86_64")]#[target_feature(enable="avx2")]unsafe fn upper_bound_batch_avx2(&self,values:&[$value;16])->[usize;16]{self.descend_batch(values,|values,value|unsafe{simd::$first_gt_avx2(values,value)})}#[cfg(target_arch="x86_64")]#[target_feature(enable=$avx512_features)]unsafe fn lower_bound_avx512(&self,value:$value)->usize{self.descend(value,|values,value|unsafe{simd::$first_ge_avx512(values,value)})}#[cfg(target_arch="x86_64")]#[target_feature(enable=$avx512_features)]unsafe fn upper_bound_avx512(&self,value:$value)->usize{self.descend(value,|values,value|unsafe{simd::$first_gt_avx512(values,value)})}#[cfg(target_arch="x86_64")]#[target_feature(enable=$avx512_features)]unsafe fn lower_bound_batch_avx512(&self,values:&[$value;16])->[usize;16]{bound_batch!(lower,self,values,self.descend_batch(&values,|values,value|unsafe{simd::$first_ge_avx512(values,value)}))}#[cfg(target_arch="x86_64")]#[target_feature(enable=$avx512_features)]unsafe fn upper_bound_batch_avx512(&self,values:&[$value;16])->[usize;16]{bound_batch!(upper,self,values,self.descend_batch(&values,|values,value|unsafe{simd::$first_gt_avx512(values,value)}))}}};}impl_static_search_tree!(u16,32,first_ge_u16x32_avx2,first_gt_u16x32_avx2,first_ge_u16x32_avx512,first_gt_u16x32_avx512,"avx512f,avx512bw");impl_static_search_tree!(u32,16,first_ge_u32x16_avx2,first_gt_u32x16_avx2,first_ge_u32x16_avx512,first_gt_u32x16_avx512,"avx512f");impl_static_search_tree!(u64,8,first_ge_u64x8_avx2,first_gt_u64x8_avx2,first_ge_u64x8_avx512,first_gt_u64x8_avx512,"avx512f");impl StaticSearchTree<u128,4>{#[inline]fn lower_bound(&self,value:u128)->usize{if self.len==0||value>self.maximum{self.len}else{self.descend(value,|values,value|{(values[0]<value)as usize+(values[1]<value)as usize+(values[2]<value)as usize+(values[3]<value)as usize})}}#[inline]fn upper_bound(&self,value:u128)->usize{if self.len==0||value>=self.maximum{self.len}else{self.descend(value,|values,value|{(values[0]<=value)as usize+(values[1]<=value)as usize+(values[2]<=value)as usize+(values[3]<=value)as usize})}}#[inline]fn contains(&self,value:u128)->bool{let index=self.lower_bound(value);index<self.len&&self.get(index)==value}#[inline]fn lower_bound_batch(&self,values:&[u128;16])->[usize;16]{bound_batch!(lower,self,values,self.descend_batch(&values,|values,value|{(values[0]<value)as usize+(values[1]<value)as usize+(values[2]<value)as usize+(values[3]<value)as usize}))}#[inline]fn upper_bound_batch(&self,values:&[u128;16])->[usize;16]{bound_batch!(upper,self,values,self.descend_batch(&values,|values,value|{(values[0]<=value)as usize+(values[1]<=value)as usize+(values[2]<=value)as usize+(values[3]<=value)as usize}))}}fn search_batch<K,T>(values:&[K],output:&mut[usize],convert:impl Fn(u128)->T,single:impl Fn(T)->usize,batch:impl Fn(&[T;16])->[usize;16])where K:SimdKey,T:Copy{let mut offset=0;while offset+16<=values.len(){let values=std::array::from_fn(|index|convert(values[offset+index].encode()));output[offset..offset+16].copy_from_slice(&batch(&values));offset+=16;}let remaining=values.len()-offset;if remaining>=8{let mut encoded=[convert(values[offset].encode());16];for index in 1..remaining{encoded[index]=convert(values[offset+index].encode());}let positions=batch(&encoded);output[offset..].copy_from_slice(&positions[..remaining]);}else{for(&value,position)in values[offset..].iter().zip(&mut output[offset..]){*position=single(convert(value.encode()));}}}#[derive(Clone,Debug)]enum StaticSearchStorage{Direct(DirectStaticSearch),U16(StaticSearchTree<u16,32>),U32(StaticSearchTree<u32,16>),U64(StaticSearchTree<u64,8>),U128(StaticSearchTree<u128,4>)}impl StaticSearchStorage{#[inline(always)]fn lower_bound(&self,value:u128)->usize{match self{Self::Direct(search)=>search.lower_bound(value),Self::U16(search)=>search.lower_bound(u16::try_from(value).expect("SimdKey::encode exceeds its declared width")),Self::U32(search)=>search.lower_bound(u32::try_from(value).expect("SimdKey::encode exceeds its declared width")),Self::U64(search)=>search.lower_bound(u64::try_from(value).expect("SimdKey::encode exceeds its declared width")),Self::U128(search)=>search.lower_bound(value),}}#[inline(always)]fn upper_bound(&self,value:u128)->usize{match self{Self::Direct(search)=>search.upper_bound(value),Self::U16(search)=>search.upper_bound(u16::try_from(value).expect("SimdKey::encode exceeds its declared width")),Self::U32(search)=>search.upper_bound(u32::try_from(value).expect("SimdKey::encode exceeds its declared width")),Self::U64(search)=>search.upper_bound(u64::try_from(value).expect("SimdKey::encode exceeds its declared width")),Self::U128(search)=>search.upper_bound(value),}}#[inline(always)]fn contains(&self,value:u128)->bool{match self{Self::Direct(search)=>search.contains(value),Self::U16(search)=>search.contains(u16::try_from(value).expect("SimdKey::encode exceeds its declared width")),Self::U32(search)=>search.contains(u32::try_from(value).expect("SimdKey::encode exceeds its declared width")),Self::U64(search)=>search.contains(u64::try_from(value).expect("SimdKey::encode exceeds its declared width")),Self::U128(search)=>search.contains(value),}}fn lower_bound_batch<K:SimdKey>(&self,values:&[K],output:&mut[usize]){match self{Self::Direct(search)=>{for(&value,position)in values.iter().zip(output){*position=search.lower_bound(value.encode());}}Self::U16(search)=>search_batch(values,output,|value|u16::try_from(value).expect("SimdKey::encode exceeds its declared width"),|value|search.lower_bound(value),|values|search.lower_bound_batch(values)),Self::U32(search)=>search_batch(values,output,|value|u32::try_from(value).expect("SimdKey::encode exceeds its declared width"),|value|search.lower_bound(value),|values|search.lower_bound_batch(values)),Self::U64(search)=>search_batch(values,output,|value|u64::try_from(value).expect("SimdKey::encode exceeds its declared width"),|value|search.lower_bound(value),|values|search.lower_bound_batch(values)),Self::U128(search)=>search_batch(values,output,|value|value,|value|search.lower_bound(value),|values|search.lower_bound_batch(values)),}}fn upper_bound_batch<K:SimdKey>(&self,values:&[K],output:&mut[usize]){match self{Self::Direct(search)=>{for(&value,position)in values.iter().zip(output){*position=search.upper_bound(value.encode());}}Self::U16(search)=>search_batch(values,output,|value|u16::try_from(value).expect("SimdKey::encode exceeds its declared width"),|value|search.upper_bound(value),|values|search.upper_bound_batch(values)),Self::U32(search)=>search_batch(values,output,|value|u32::try_from(value).expect("SimdKey::encode exceeds its declared width"),|value|search.upper_bound(value),|values|search.upper_bound_batch(values)),Self::U64(search)=>search_batch(values,output,|value|u64::try_from(value).expect("SimdKey::encode exceeds its declared width"),|value|search.upper_bound(value),|values|search.upper_bound_batch(values)),Self::U128(search)=>search_batch(values,output,|value|value,|value|search.upper_bound(value),|values|search.upper_bound_batch(values)),}}}#[doc=" A static search index over sorted integer or integer-encoded keys."]#[doc=""]#[doc=" The index adds build time and storage. For a small number of searches, search the sorted slice"]#[doc=" directly instead."]#[derive(Clone,Debug)]pub struct StaticSearch<K>{storage:StaticSearchStorage,len:usize,marker:PhantomData<fn()->K>}impl<K:SimdKey>StaticSearch<K>{#[doc=" Builds an index over sorted `values`."]#[doc=""]#[doc=" # Panics"]#[doc=""]#[doc=" Panics if `values` is not sorted or `SimdKey` does not satisfy its contract."]pub fn from_sorted(values:&[K])->Self{Self::build(values,static_search_backend(K::BITS),false)}#[doc=" Builds a direct lookup table over sorted 8-bit or 16-bit `values`."]#[doc=""]#[doc=" This layout uses a fixed table of 257 or 65,537 positions and is intended"]#[doc=" for query-heavy workloads."]#[doc=""]#[doc=" # Panics"]#[doc=""]#[doc=" Panics if `K::BITS` is neither 8 nor 16, or if `values` is not sorted."]pub fn from_sorted_direct(values:&[K])->Self{assert!(matches!(K::BITS,8|16));Self::build(values,static_search_backend(K::BITS),true)}#[inline]pub fn len(&self)->usize{self.len}#[inline]pub fn is_empty(&self)->bool{self.len==0}#[doc=" Returns the first index whose value is greater than or equal to `value`."]#[inline]pub fn lower_bound(&self,value:K)->usize{self.storage.lower_bound(value.encode())}#[doc=" Returns one past the last index whose value is less than or equal to `value`."]#[inline]pub fn upper_bound(&self,value:K)->usize{self.storage.upper_bound(value.encode())}#[doc=" Writes the first index greater than or equal to each value into `output`."]#[doc=""]#[doc=" # Panics"]#[doc=""]#[doc=" Panics if `values` and `output` have different lengths."]pub fn lower_bound_batch(&self,values:&[K],output:&mut[usize]){assert_eq!(values.len(),output.len());self.storage.lower_bound_batch(values,output);}#[doc=" Writes one past the last index less than or equal to each value into `output`."]#[doc=""]#[doc=" # Panics"]#[doc=""]#[doc=" Panics if `values` and `output` have different lengths."]pub fn upper_bound_batch(&self,values:&[K],output:&mut[usize]){assert_eq!(values.len(),output.len());self.storage.upper_bound_batch(values,output);}#[inline]pub fn range(&self,value:K)->Range<usize>{let value=value.encode();self.storage.lower_bound(value)..self.storage.upper_bound(value)}#[inline]pub fn contains(&self,value:K)->bool{self.storage.contains(value.encode())}fn build(values:&[K],backend:SimdBackend,direct:bool)->Self{assert!(matches!(K::BITS,8|16|32|64|128));assert!(values.windows(2).all(|pair|pair[0]<=pair[1]));let len=values.len();let storage=match K::BITS{8=>StaticSearchStorage::Direct(DirectStaticSearch::build(values,K::BITS)),16=>{if direct{StaticSearchStorage::Direct(DirectStaticSearch::build(values,K::BITS))}else{StaticSearchStorage::U16(StaticSearchTree::build(values,u16::MAX,u16::MAX as u128,|value|value as u16,backend))}}32=>StaticSearchStorage::U32(StaticSearchTree::build(values,u32::MAX,u32::MAX as u128,|value|value as u32,backend)),64=>StaticSearchStorage::U64(StaticSearchTree::build(values,u64::MAX,u64::MAX as u128,|value|value as u64,backend)),128=>StaticSearchStorage::U128(StaticSearchTree::build(values,u128::MAX,u128::MAX,|value|value,backend)),_=>unreachable!(),};Self{storage,len,marker:PhantomData}}}}
// codesnip-guard: _simd
#[cfg_attr(any(),rustfmt::skip)]pub mod simd{#![allow(unsafe_op_in_unsafe_fn)]#[cfg(target_arch="x86_64")]use std::arch::x86_64::*;#[cfg(target_arch="x86_64")]#[target_feature(enable="avx2")]#[inline]pub unsafe fn first_ge_u16x32_avx2(values:&[u16;32],key:u16)->usize{let sign=_mm256_set1_epi16(i16::MIN);let key=_mm256_xor_si256(_mm256_set1_epi16(key as i16),sign);let low=_mm256_xor_si256(_mm256_loadu_si256(values.as_ptr().cast()),sign);let high=_mm256_xor_si256(_mm256_loadu_si256(values.as_ptr().add(16).cast()),sign);let low=_mm256_movemask_epi8(_mm256_cmpgt_epi16(key,low))as u32 as u64;let high=_mm256_movemask_epi8(_mm256_cmpgt_epi16(key,high))as u32 as u64;(!(low|high<<32)).trailing_zeros()as usize/2}#[cfg(target_arch="x86_64")]#[target_feature(enable="avx2")]#[inline]pub unsafe fn first_gt_u16x32_avx2(values:&[u16;32],key:u16)->usize{let sign=_mm256_set1_epi16(i16::MIN);let key=_mm256_xor_si256(_mm256_set1_epi16(key as i16),sign);let low=_mm256_xor_si256(_mm256_loadu_si256(values.as_ptr().cast()),sign);let high=_mm256_xor_si256(_mm256_loadu_si256(values.as_ptr().add(16).cast()),sign);let low=_mm256_movemask_epi8(_mm256_cmpgt_epi16(low,key))as u32 as u64;let high=_mm256_movemask_epi8(_mm256_cmpgt_epi16(high,key))as u32 as u64;(low|high<<32).trailing_zeros()as usize/2}#[cfg(target_arch="x86_64")]#[target_feature(enable="avx2")]#[inline]pub unsafe fn first_ge_u32x16_avx2(values:&[u32;16],key:u32)->usize{let sign=_mm256_set1_epi32(i32::MIN);let key=_mm256_xor_si256(_mm256_set1_epi32(key as i32),sign);let low=_mm256_xor_si256(_mm256_loadu_si256(values.as_ptr().cast()),sign);let high=_mm256_xor_si256(_mm256_loadu_si256(values.as_ptr().add(8).cast()),sign);let low=_mm256_movemask_ps(_mm256_castsi256_ps(_mm256_cmpgt_epi32(key,low)));let high=_mm256_movemask_ps(_mm256_castsi256_ps(_mm256_cmpgt_epi32(key,high)));let mask=((!low as u32)&0xff)|(((!high as u32)&0xff)<<8);(mask as u16).trailing_zeros()as usize}#[cfg(target_arch="x86_64")]#[target_feature(enable="avx2")]#[inline]pub unsafe fn first_gt_u32x16_avx2(values:&[u32;16],key:u32)->usize{let sign=_mm256_set1_epi32(i32::MIN);let key=_mm256_xor_si256(_mm256_set1_epi32(key as i32),sign);let low=_mm256_xor_si256(_mm256_loadu_si256(values.as_ptr().cast()),sign);let high=_mm256_xor_si256(_mm256_loadu_si256(values.as_ptr().add(8).cast()),sign);let low=_mm256_movemask_ps(_mm256_castsi256_ps(_mm256_cmpgt_epi32(low,key)));let high=_mm256_movemask_ps(_mm256_castsi256_ps(_mm256_cmpgt_epi32(high,key)));let mask=low as u32|((high as u32)<<8);(mask as u16).trailing_zeros()as usize}#[cfg(target_arch="x86_64")]#[target_feature(enable="avx2")]#[inline]pub unsafe fn first_ge_u64x8_avx2(values:&[u64;8],key:u64)->usize{let sign=_mm256_set1_epi64x(i64::MIN);let key=_mm256_xor_si256(_mm256_set1_epi64x(key as i64),sign);let low=_mm256_xor_si256(_mm256_loadu_si256(values.as_ptr().cast()),sign);let high=_mm256_xor_si256(_mm256_loadu_si256(values.as_ptr().add(4).cast()),sign);let low=_mm256_movemask_pd(_mm256_castsi256_pd(_mm256_cmpgt_epi64(key,low)));let high=_mm256_movemask_pd(_mm256_castsi256_pd(_mm256_cmpgt_epi64(key,high)));let mask=((!low as u32)&0x0f)|(((!high as u32)&0x0f)<<4);(mask as u8).trailing_zeros()as usize}#[cfg(target_arch="x86_64")]#[target_feature(enable="avx2")]#[inline]pub unsafe fn first_gt_u64x8_avx2(values:&[u64;8],key:u64)->usize{let sign=_mm256_set1_epi64x(i64::MIN);let key=_mm256_xor_si256(_mm256_set1_epi64x(key as i64),sign);let low=_mm256_xor_si256(_mm256_loadu_si256(values.as_ptr().cast()),sign);let high=_mm256_xor_si256(_mm256_loadu_si256(values.as_ptr().add(4).cast()),sign);let low=_mm256_movemask_pd(_mm256_castsi256_pd(_mm256_cmpgt_epi64(low,key)));let high=_mm256_movemask_pd(_mm256_castsi256_pd(_mm256_cmpgt_epi64(high,key)));let mask=low as u32|((high as u32)<<4);(mask as u8).trailing_zeros()as usize}#[cfg(target_arch="x86_64")]#[target_feature(enable="avx512f,avx512bw")]#[inline]pub unsafe fn first_ge_u16x32_avx512(values:&[u16;32],key:u16)->usize{let values=_mm512_loadu_si512(values.as_ptr().cast());let key=_mm512_set1_epi16(key as i16);(!_mm512_cmplt_epu16_mask(values,key)).trailing_zeros()as usize}#[cfg(target_arch="x86_64")]#[target_feature(enable="avx512f,avx512bw")]#[inline]pub unsafe fn first_gt_u16x32_avx512(values:&[u16;32],key:u16)->usize{let values=_mm512_loadu_si512(values.as_ptr().cast());let key=_mm512_set1_epi16(key as i16);_mm512_cmpgt_epu16_mask(values,key).trailing_zeros()as usize}#[cfg(target_arch="x86_64")]#[target_feature(enable="avx512f")]#[inline]pub unsafe fn first_ge_u32x16_avx512(values:&[u32;16],key:u32)->usize{let values=_mm512_loadu_si512(values.as_ptr().cast());let key=_mm512_set1_epi32(key as i32);(!_mm512_cmplt_epu32_mask(values,key)).trailing_zeros()as usize}#[cfg(target_arch="x86_64")]#[target_feature(enable="avx512f")]#[inline]pub unsafe fn first_gt_u32x16_avx512(values:&[u32;16],key:u32)->usize{let values=_mm512_loadu_si512(values.as_ptr().cast());let key=_mm512_set1_epi32(key as i32);_mm512_cmpgt_epu32_mask(values,key).trailing_zeros()as usize}#[cfg(target_arch="x86_64")]#[target_feature(enable="avx512f")]#[inline]pub unsafe fn first_ge_u64x8_avx512(values:&[u64;8],key:u64)->usize{let values=_mm512_loadu_si512(values.as_ptr().cast());let key=_mm512_set1_epi64(key as i64);(!_mm512_cmplt_epu64_mask(values,key)).trailing_zeros()as usize}#[cfg(target_arch="x86_64")]#[target_feature(enable="avx512f")]#[inline]pub unsafe fn first_gt_u64x8_avx512(values:&[u64;8],key:u64)->usize{let values=_mm512_loadu_si512(values.as_ptr().cast());let key=_mm512_set1_epi64(key as i64);_mm512_cmpgt_epu64_mask(values,key).trailing_zeros()as usize}#[cfg(target_arch="x86_64")]#[target_feature(enable="avx2")]#[inline]pub unsafe fn add_suffix_u32x16_avx2(values:&mut[u32;16],index:usize,delta:u32){let index=_mm256_set1_epi32(index as i32-1);let delta=_mm256_set1_epi32(delta as i32);let low_mask=_mm256_cmpgt_epi32(_mm256_setr_epi32(0,1,2,3,4,5,6,7),index);let high_mask=_mm256_cmpgt_epi32(_mm256_setr_epi32(8,9,10,11,12,13,14,15),index);let low=_mm256_add_epi32(_mm256_loadu_si256(values.as_ptr().cast()),_mm256_and_si256(delta,low_mask));let high=_mm256_add_epi32(_mm256_loadu_si256(values.as_ptr().add(8).cast()),_mm256_and_si256(delta,high_mask));_mm256_storeu_si256(values.as_mut_ptr().cast(),low);_mm256_storeu_si256(values.as_mut_ptr().add(8).cast(),high);}#[cfg(target_arch="x86_64")]#[target_feature(enable="avx2")]#[inline]pub unsafe fn add_suffix_u64x8_avx2(values:&mut[u64;8],index:usize,delta:u64){let index=_mm256_set1_epi64x(index as i64-1);let delta=_mm256_set1_epi64x(delta as i64);let low_mask=_mm256_cmpgt_epi64(_mm256_setr_epi64x(0,1,2,3),index);let high_mask=_mm256_cmpgt_epi64(_mm256_setr_epi64x(4,5,6,7),index);let low=_mm256_add_epi64(_mm256_loadu_si256(values.as_ptr().cast()),_mm256_and_si256(delta,low_mask));let high=_mm256_add_epi64(_mm256_loadu_si256(values.as_ptr().add(4).cast()),_mm256_and_si256(delta,high_mask));_mm256_storeu_si256(values.as_mut_ptr().cast(),low);_mm256_storeu_si256(values.as_mut_ptr().add(4).cast(),high);}#[cfg(target_arch="x86_64")]#[target_feature(enable="avx512f")]#[inline]pub unsafe fn add_suffix_u32x16_avx512(values:&mut[u32;16],index:usize,delta:u32){let values_vector=_mm512_loadu_si512(values.as_ptr().cast());let values_vector=_mm512_mask_add_epi32(values_vector,u16::MAX<<index,values_vector,_mm512_set1_epi32(delta as i32));_mm512_storeu_si512(values.as_mut_ptr().cast(),values_vector);}#[cfg(target_arch="x86_64")]#[target_feature(enable="avx512f")]#[inline]pub unsafe fn add_suffix_u64x8_avx512(values:&mut[u64;8],index:usize,delta:u64){let values_vector=_mm512_loadu_si512(values.as_ptr().cast());let values_vector=_mm512_mask_add_epi64(values_vector,u8::MAX<<index,values_vector,_mm512_set1_epi64(delta as i64));_mm512_storeu_si512(values.as_mut_ptr().cast(),values_vector);}#[cfg(target_arch="x86_64")]#[target_feature(enable="avx2")]#[inline]pub unsafe fn max_index_u32x16_avx2(values:&[u32;16])->usize{let low=_mm256_loadu_si256(values.as_ptr().cast());let high=_mm256_loadu_si256(values.as_ptr().add(8).cast());let mut maximum=_mm256_max_epu32(low,high);maximum=_mm256_max_epu32(maximum,_mm256_permute2x128_si256::<0x01>(maximum,maximum));maximum=_mm256_max_epu32(maximum,_mm256_shuffle_epi32::<0x4e>(maximum));maximum=_mm256_max_epu32(maximum,_mm256_shuffle_epi32::<0xb1>(maximum));let maximum=_mm256_set1_epi32(_mm256_extract_epi32::<0>(maximum));let low=_mm256_movemask_ps(_mm256_castsi256_ps(_mm256_cmpeq_epi32(low,maximum)));let high=_mm256_movemask_ps(_mm256_castsi256_ps(_mm256_cmpeq_epi32(high,maximum)));((low as u32|((high as u32)<<8))as u16).trailing_zeros()as usize}#[cfg(target_arch="x86_64")]#[target_feature(enable="avx512f")]#[inline]pub unsafe fn max_index_u32x16_avx512(values:&[u32;16])->usize{let values=_mm512_loadu_si512(values.as_ptr().cast());let maximum=_mm512_set1_epi32(_mm512_reduce_max_epu32(values)as i32);_mm512_cmpeq_epi32_mask(values,maximum).trailing_zeros()as usize}#[cfg(target_arch="x86_64")]#[target_feature(enable="avx2")]#[inline]unsafe fn max_epu64(left:__m256i,right:__m256i)->__m256i{let sign=_mm256_set1_epi64x(i64::MIN);let greater=_mm256_cmpgt_epi64(_mm256_xor_si256(left,sign),_mm256_xor_si256(right,sign));_mm256_blendv_epi8(right,left,greater)}#[cfg(target_arch="x86_64")]#[target_feature(enable="avx2")]#[inline]pub unsafe fn max_index_u64x8_avx2(values:&[u64;8])->usize{let sign=_mm256_set1_epi64x(i64::MIN);let low=_mm256_xor_si256(_mm256_loadu_si256(values.as_ptr().cast()),sign);let high=_mm256_xor_si256(_mm256_loadu_si256(values.as_ptr().add(4).cast()),sign);let mut maximum=max_i64x4(low,high);maximum=max_i64x4(maximum,_mm256_permute4x64_epi64::<0x4e>(maximum));maximum=max_i64x4(maximum,_mm256_permute4x64_epi64::<0xb1>(maximum));let low=_mm256_movemask_pd(_mm256_castsi256_pd(_mm256_cmpeq_epi64(low,maximum)));let high=_mm256_movemask_pd(_mm256_castsi256_pd(_mm256_cmpeq_epi64(high,maximum)));((low as u32|((high as u32)<<4))as u8).trailing_zeros()as usize}#[cfg(target_arch="x86_64")]#[target_feature(enable="avx512f")]#[inline]pub unsafe fn max_index_u64x8_avx512(values:&[u64;8])->usize{let values=_mm512_loadu_si512(values.as_ptr().cast());let maximum=_mm512_set1_epi64(_mm512_reduce_max_epu64(values)as i64);_mm512_cmpeq_epi64_mask(values,maximum).trailing_zeros()as usize}#[cfg(target_arch="x86_64")]#[target_feature(enable="avx2")]#[inline]pub unsafe fn max_index_u128x4_avx2(low:&[u64;4],high:&[u64;4])->usize{let low=_mm256_loadu_si256(low.as_ptr().cast());let high=_mm256_loadu_si256(high.as_ptr().cast());let mut maximum_high=high;maximum_high=max_epu64(maximum_high,_mm256_permute4x64_epi64::<0x4e>(maximum_high));maximum_high=max_epu64(maximum_high,_mm256_permute4x64_epi64::<0xb1>(maximum_high));let high_equal=_mm256_cmpeq_epi64(high,maximum_high);let high_mask=_mm256_movemask_pd(_mm256_castsi256_pd(high_equal))as u32&15;if high_mask.is_power_of_two(){return high_mask.trailing_zeros()as usize;}let mut maximum_low=_mm256_and_si256(low,high_equal);maximum_low=max_epu64(maximum_low,_mm256_permute4x64_epi64::<0x4e>(maximum_low));maximum_low=max_epu64(maximum_low,_mm256_permute4x64_epi64::<0xb1>(maximum_low));let both=_mm256_and_si256(high_equal,_mm256_cmpeq_epi64(low,maximum_low));(_mm256_movemask_pd(_mm256_castsi256_pd(both))as u32&15).trailing_zeros()as usize}#[cfg(target_arch="x86_64")]#[target_feature(enable="avx2,avx512f,avx512vl")]#[inline]pub unsafe fn max_index_u128x4_avx512(low:&[u64;4],high:&[u64;4])->usize{let low=_mm256_loadu_si256(low.as_ptr().cast());let high=_mm256_loadu_si256(high.as_ptr().cast());let mut maximum_high=high;maximum_high=_mm256_max_epu64(maximum_high,_mm256_permute4x64_epi64::<0x4e>(maximum_high));maximum_high=_mm256_max_epu64(maximum_high,_mm256_permute4x64_epi64::<0xb1>(maximum_high));let high_equal=_mm256_cmpeq_epi64(high,maximum_high);let high_mask=_mm256_movemask_pd(_mm256_castsi256_pd(high_equal))as u32&15;if high_mask.is_power_of_two(){return high_mask.trailing_zeros()as usize;}let mut maximum_low=_mm256_and_si256(low,high_equal);maximum_low=_mm256_max_epu64(maximum_low,_mm256_permute4x64_epi64::<0x4e>(maximum_low));maximum_low=_mm256_max_epu64(maximum_low,_mm256_permute4x64_epi64::<0xb1>(maximum_low));let both=_mm256_and_si256(high_equal,_mm256_cmpeq_epi64(low,maximum_low));(_mm256_movemask_pd(_mm256_castsi256_pd(both))as u32&15).trailing_zeros()as usize}#[cfg(target_arch="x86_64")]#[target_feature(enable="avx2")]#[inline]unsafe fn reduce_min_i32x8(mut values:__m256i)->i32{values=_mm256_min_epi32(values,_mm256_permute2x128_si256::<0x01>(values,values));values=_mm256_min_epi32(values,_mm256_shuffle_epi32::<0x4e>(values));values=_mm256_min_epi32(values,_mm256_shuffle_epi32::<0xb1>(values));_mm256_extract_epi32::<0>(values)}#[cfg(target_arch="x86_64")]#[target_feature(enable="avx2")]#[inline]unsafe fn reduce_max_i32x8(mut values:__m256i)->i32{values=_mm256_max_epi32(values,_mm256_permute2x128_si256::<0x01>(values,values));values=_mm256_max_epi32(values,_mm256_shuffle_epi32::<0x4e>(values));values=_mm256_max_epi32(values,_mm256_shuffle_epi32::<0xb1>(values));_mm256_extract_epi32::<0>(values)}#[cfg(target_arch="x86_64")]#[target_feature(enable="avx2")]#[inline]unsafe fn reduce_sum_i32x8(mut values:__m256i)->i32{values=_mm256_add_epi32(values,_mm256_permute2x128_si256::<0x01>(values,values));values=_mm256_add_epi32(values,_mm256_shuffle_epi32::<0x4e>(values));values=_mm256_add_epi32(values,_mm256_shuffle_epi32::<0xb1>(values));_mm256_extract_epi32::<0>(values)}#[cfg(target_arch="x86_64")]#[target_feature(enable="avx2")]#[inline]pub unsafe fn minimum_i32x16_avx2(values:&[i32;16])->i32{let low=_mm256_loadu_si256(values.as_ptr().cast());let high=_mm256_loadu_si256(values.as_ptr().add(8).cast());reduce_min_i32x8(_mm256_min_epi32(low,high))}#[cfg(target_arch="x86_64")]#[target_feature(enable="avx2")]#[inline]pub unsafe fn maximum_i32x16_avx2(values:&[i32;16])->i32{let low=_mm256_loadu_si256(values.as_ptr().cast());let high=_mm256_loadu_si256(values.as_ptr().add(8).cast());reduce_max_i32x8(_mm256_max_epi32(low,high))}#[cfg(target_arch="x86_64")]#[target_feature(enable="avx2")]#[inline]pub unsafe fn sum_i32x16_avx2(values:&[i32;16])->i32{let low=_mm256_loadu_si256(values.as_ptr().cast());let high=_mm256_loadu_si256(values.as_ptr().add(8).cast());reduce_sum_i32x8(_mm256_add_epi32(low,high))}#[cfg(target_arch="x86_64")]#[target_feature(enable="avx2")]#[inline]unsafe fn range_mask_i32x8(start:usize,end:usize,offset:i32)->__m256i{let lanes=_mm256_setr_epi32(offset,offset+1,offset+2,offset+3,offset+4,offset+5,offset+6,offset+7);_mm256_and_si256(_mm256_cmpgt_epi32(lanes,_mm256_set1_epi32(start as i32-1)),_mm256_cmpgt_epi32(_mm256_set1_epi32(end as i32),lanes))}#[cfg(target_arch="x86_64")]#[target_feature(enable="avx2")]#[inline]pub unsafe fn minimum_range_i32x16_avx2(values:&[i32;16],start:usize,end:usize)->i32{let unit=_mm256_set1_epi32(i32::MAX);let low=_mm256_blendv_epi8(unit,_mm256_loadu_si256(values.as_ptr().cast()),range_mask_i32x8(start,end,0));let high=_mm256_blendv_epi8(unit,_mm256_loadu_si256(values.as_ptr().add(8).cast()),range_mask_i32x8(start,end,8));reduce_min_i32x8(_mm256_min_epi32(low,high))}#[cfg(target_arch="x86_64")]#[target_feature(enable="avx2")]#[inline]pub unsafe fn maximum_range_i32x16_avx2(values:&[i32;16],start:usize,end:usize)->i32{let unit=_mm256_set1_epi32(i32::MIN);let low=_mm256_blendv_epi8(unit,_mm256_loadu_si256(values.as_ptr().cast()),range_mask_i32x8(start,end,0));let high=_mm256_blendv_epi8(unit,_mm256_loadu_si256(values.as_ptr().add(8).cast()),range_mask_i32x8(start,end,8));reduce_max_i32x8(_mm256_max_epi32(low,high))}#[cfg(target_arch="x86_64")]#[target_feature(enable="avx2")]#[inline]pub unsafe fn sum_range_i32x16_avx2(values:&[i32;16],start:usize,end:usize)->i32{let low=_mm256_and_si256(_mm256_loadu_si256(values.as_ptr().cast()),range_mask_i32x8(start,end,0));let high=_mm256_and_si256(_mm256_loadu_si256(values.as_ptr().add(8).cast()),range_mask_i32x8(start,end,8));reduce_sum_i32x8(_mm256_add_epi32(low,high))}#[cfg(target_arch="x86_64")]#[target_feature(enable="avx512f")]#[inline]pub unsafe fn minimum_i32x16_avx512(values:&[i32;16])->i32{_mm512_reduce_min_epi32(_mm512_loadu_si512(values.as_ptr().cast()))}#[cfg(target_arch="x86_64")]#[target_feature(enable="avx512f")]#[inline]pub unsafe fn maximum_i32x16_avx512(values:&[i32;16])->i32{_mm512_reduce_max_epi32(_mm512_loadu_si512(values.as_ptr().cast()))}#[cfg(target_arch="x86_64")]#[target_feature(enable="avx512f")]#[inline]pub unsafe fn sum_i32x16_avx512(values:&[i32;16])->i32{_mm512_reduce_add_epi32(_mm512_loadu_si512(values.as_ptr().cast()))}#[cfg(target_arch="x86_64")]#[target_feature(enable="avx512f")]#[inline]pub unsafe fn minimum_range_i32x16_avx512(values:&[i32;16],start:usize,end:usize)->i32{let mask=(u16::MAX<<start)&(u16::MAX>>(16-end));_mm512_mask_reduce_min_epi32(mask,_mm512_loadu_si512(values.as_ptr().cast()))}#[cfg(target_arch="x86_64")]#[target_feature(enable="avx512f")]#[inline]pub unsafe fn maximum_range_i32x16_avx512(values:&[i32;16],start:usize,end:usize)->i32{let mask=(u16::MAX<<start)&(u16::MAX>>(16-end));_mm512_mask_reduce_max_epi32(mask,_mm512_loadu_si512(values.as_ptr().cast()))}#[cfg(target_arch="x86_64")]#[target_feature(enable="avx512f")]#[inline]pub unsafe fn sum_range_i32x16_avx512(values:&[i32;16],start:usize,end:usize)->i32{let mask=(u16::MAX<<start)&(u16::MAX>>(16-end));_mm512_mask_reduce_add_epi32(mask,_mm512_loadu_si512(values.as_ptr().cast()))}#[cfg(target_arch="x86_64")]#[target_feature(enable="avx2")]#[inline]unsafe fn min_i64x4(left:__m256i,right:__m256i)->__m256i{_mm256_blendv_epi8(left,right,_mm256_cmpgt_epi64(left,right))}#[cfg(target_arch="x86_64")]#[target_feature(enable="avx2")]#[inline]unsafe fn max_i64x4(left:__m256i,right:__m256i)->__m256i{_mm256_blendv_epi8(right,left,_mm256_cmpgt_epi64(left,right))}#[cfg(target_arch="x86_64")]#[target_feature(enable="avx2")]#[inline]unsafe fn reduce_min_i64x4(mut values:__m256i)->i64{values=min_i64x4(values,_mm256_permute4x64_epi64::<0x4e>(values));values=min_i64x4(values,_mm256_permute4x64_epi64::<0xb1>(values));_mm256_extract_epi64::<0>(values)}#[cfg(target_arch="x86_64")]#[target_feature(enable="avx2")]#[inline]unsafe fn reduce_max_i64x4(mut values:__m256i)->i64{values=max_i64x4(values,_mm256_permute4x64_epi64::<0x4e>(values));values=max_i64x4(values,_mm256_permute4x64_epi64::<0xb1>(values));_mm256_extract_epi64::<0>(values)}#[cfg(target_arch="x86_64")]#[target_feature(enable="avx2")]#[inline]unsafe fn reduce_sum_i64x4(mut values:__m256i)->i64{values=_mm256_add_epi64(values,_mm256_permute4x64_epi64::<0x4e>(values));values=_mm256_add_epi64(values,_mm256_permute4x64_epi64::<0xb1>(values));_mm256_extract_epi64::<0>(values)}#[cfg(target_arch="x86_64")]#[target_feature(enable="avx2")]#[inline]pub unsafe fn minimum_i64x8_avx2(values:&[i64;8])->i64{let low=_mm256_loadu_si256(values.as_ptr().cast());let high=_mm256_loadu_si256(values.as_ptr().add(4).cast());reduce_min_i64x4(min_i64x4(low,high))}#[cfg(target_arch="x86_64")]#[target_feature(enable="avx2")]#[inline]pub unsafe fn maximum_i64x8_avx2(values:&[i64;8])->i64{let low=_mm256_loadu_si256(values.as_ptr().cast());let high=_mm256_loadu_si256(values.as_ptr().add(4).cast());reduce_max_i64x4(max_i64x4(low,high))}#[cfg(target_arch="x86_64")]#[target_feature(enable="avx2")]#[inline]pub unsafe fn sum_i64x8_avx2(values:&[i64;8])->i64{let low=_mm256_loadu_si256(values.as_ptr().cast());let high=_mm256_loadu_si256(values.as_ptr().add(4).cast());reduce_sum_i64x4(_mm256_add_epi64(low,high))}#[cfg(target_arch="x86_64")]#[target_feature(enable="avx2")]#[inline]unsafe fn range_mask_i64x4(start:usize,end:usize,offset:i64)->__m256i{let lanes=_mm256_setr_epi64x(offset,offset+1,offset+2,offset+3);_mm256_and_si256(_mm256_cmpgt_epi64(lanes,_mm256_set1_epi64x(start as i64-1)),_mm256_cmpgt_epi64(_mm256_set1_epi64x(end as i64),lanes))}#[cfg(target_arch="x86_64")]#[target_feature(enable="avx2")]#[inline]pub unsafe fn minimum_range_i64x8_avx2(values:&[i64;8],start:usize,end:usize)->i64{let unit=_mm256_set1_epi64x(i64::MAX);let low=_mm256_blendv_epi8(unit,_mm256_loadu_si256(values.as_ptr().cast()),range_mask_i64x4(start,end,0));let high=_mm256_blendv_epi8(unit,_mm256_loadu_si256(values.as_ptr().add(4).cast()),range_mask_i64x4(start,end,4));reduce_min_i64x4(min_i64x4(low,high))}#[cfg(target_arch="x86_64")]#[target_feature(enable="avx2")]#[inline]pub unsafe fn maximum_range_i64x8_avx2(values:&[i64;8],start:usize,end:usize)->i64{let unit=_mm256_set1_epi64x(i64::MIN);let low=_mm256_blendv_epi8(unit,_mm256_loadu_si256(values.as_ptr().cast()),range_mask_i64x4(start,end,0));let high=_mm256_blendv_epi8(unit,_mm256_loadu_si256(values.as_ptr().add(4).cast()),range_mask_i64x4(start,end,4));reduce_max_i64x4(max_i64x4(low,high))}#[cfg(target_arch="x86_64")]#[target_feature(enable="avx2")]#[inline]pub unsafe fn sum_range_i64x8_avx2(values:&[i64;8],start:usize,end:usize)->i64{let low=_mm256_and_si256(_mm256_loadu_si256(values.as_ptr().cast()),range_mask_i64x4(start,end,0));let high=_mm256_and_si256(_mm256_loadu_si256(values.as_ptr().add(4).cast()),range_mask_i64x4(start,end,4));reduce_sum_i64x4(_mm256_add_epi64(low,high))}#[cfg(target_arch="x86_64")]#[target_feature(enable="avx512f")]#[inline]pub unsafe fn minimum_i64x8_avx512(values:&[i64;8])->i64{_mm512_reduce_min_epi64(_mm512_loadu_si512(values.as_ptr().cast()))}#[cfg(target_arch="x86_64")]#[target_feature(enable="avx512f")]#[inline]pub unsafe fn maximum_i64x8_avx512(values:&[i64;8])->i64{_mm512_reduce_max_epi64(_mm512_loadu_si512(values.as_ptr().cast()))}#[cfg(target_arch="x86_64")]#[target_feature(enable="avx512f")]#[inline]pub unsafe fn sum_i64x8_avx512(values:&[i64;8])->i64{_mm512_reduce_add_epi64(_mm512_loadu_si512(values.as_ptr().cast()))}#[cfg(target_arch="x86_64")]#[target_feature(enable="avx512f")]#[inline]pub unsafe fn minimum_range_i64x8_avx512(values:&[i64;8],start:usize,end:usize)->i64{let mask=(u8::MAX<<start)&(u8::MAX>>(8-end));_mm512_mask_reduce_min_epi64(mask,_mm512_loadu_si512(values.as_ptr().cast()))}#[cfg(target_arch="x86_64")]#[target_feature(enable="avx512f")]#[inline]pub unsafe fn maximum_range_i64x8_avx512(values:&[i64;8],start:usize,end:usize)->i64{let mask=(u8::MAX<<start)&(u8::MAX>>(8-end));_mm512_mask_reduce_max_epi64(mask,_mm512_loadu_si512(values.as_ptr().cast()))}#[cfg(target_arch="x86_64")]#[target_feature(enable="avx512f")]#[inline]pub unsafe fn sum_range_i64x8_avx512(values:&[i64;8],start:usize,end:usize)->i64{let mask=(u8::MAX<<start)&(u8::MAX>>(8-end));_mm512_mask_reduce_add_epi64(mask,_mm512_loadu_si512(values.as_ptr().cast()))}}
// codesnip-guard: algebra
#[cfg_attr(any(),rustfmt::skip)]pub use self::magma::*;#[cfg_attr(any(),rustfmt::skip)]mod magma{#![doc=" algebraic traits"]#[doc=" binary operaion: $T \\circ T \\to T$"]pub trait Magma{#[doc=" type of operands: $T$"]type T:Clone;#[doc=" binary operaion: $\\circ$"]fn operate(x:&Self::T,y:&Self::T)->Self::T;fn reverse_operate(x:&Self::T,y:&Self::T)->Self::T{Self::operate(y,x)}fn operate_assign(x:&mut Self::T,y:&Self::T){*x=Self::operate(x,y);}}#[doc=" $\\forall a,\\forall b,\\forall c \\in T, (a \\circ b) \\circ c = a \\circ (b \\circ c)$"]pub trait Associative:Magma{}#[doc=" associative binary operation"]pub trait SemiGroup:Magma+Associative{}impl<S>SemiGroup for S where S:Magma+Associative{}#[doc=" $\\exists e \\in T, \\forall a \\in T, e \\circ a = a \\circ e = a$"]pub trait Unital:Magma{#[doc=" identity element: $e$"]fn unit()->Self::T;fn is_unit(x:&Self::T)->bool where Self::T:PartialEq{x==&Self::unit()}fn set_unit(x:&mut Self::T){*x=Self::unit();}}pub trait ExpBits{type Iter:Iterator<Item=bool>;fn bits(self)->Self::Iter;}pub trait SignedExpBits{type T:ExpBits;fn neg_and_bits(self)->(bool,Self::T);}pub struct Bits<T>{n:T}macro_rules!impl_exp_bits_for_uint{($($t:ty)*)=>{$(impl Iterator for Bits<$t>{type Item=bool;fn next(&mut self)->Option<bool>{if self.n==0{None}else{let bit=(self.n&1)==1;self.n>>=1;Some(bit)}}}impl ExpBits for$t{type Iter=Bits<$t>;fn bits(self)->Self::Iter{Bits{n:self}}}impl SignedExpBits for$t{type T=$t;fn neg_and_bits(self)->(bool,Self::T){(false,self)}})*};}impl_exp_bits_for_uint!(u8 u16 u32 u64 u128 usize);macro_rules!impl_signed_exp_bits_for_sint{($($s:ty,$u:ty;)*)=>{$(impl SignedExpBits for$s{type T=$u;fn neg_and_bits(self)->(bool,Self::T){(self<0,self.unsigned_abs())}})*};}impl_signed_exp_bits_for_sint!(i8,u8;i16,u16;i32,u32;i64,u64;i128,u128;isize,usize;);#[doc=" associative binary operation and an identity element"]pub trait Monoid:SemiGroup+Unital{#[doc=" binary exponentiation: $x^n = x\\circ\\ddots\\circ x$"]fn pow<E>(mut x:Self::T,exp:E)->Self::T where E:ExpBits{let mut bits=exp.bits();let Some(first)=bits.next()else{return Self::unit();};let mut res=if first{x.clone()}else{Self::unit()};for bit in bits{x=Self::operate(&x,&x);if bit{res=Self::operate(&res,&x);}}res}fn fold<I>(iter:I)->Self::T where I:IntoIterator<Item=Self::T>{let mut iter=iter.into_iter();if let Some(item)=iter.next(){iter.fold(item,|acc,x|Self::operate(&acc,&x))}else{Self::unit()}}}impl<M>Monoid for M where M:SemiGroup+Unital{}#[doc=" $\\exists e \\in T, \\forall a \\in T, \\exists b,c \\in T, b \\circ a = a \\circ c = e$"]pub trait Invertible:Magma+Unital{#[doc=" $a$ where $a \\circ x = e$"]fn inverse(x:&Self::T)->Self::T;fn rinv_operate(x:&Self::T,y:&Self::T)->Self::T{Self::operate(x,&Self::inverse(y))}fn rinv_operate_assign(x:&mut Self::T,y:&Self::T){*x=Self::rinv_operate(x,y);}}#[doc=" associative binary operation and an identity element and inverse elements"]pub trait Group:Monoid+Invertible{fn signed_pow<E>(x:Self::T,exp:E)->Self::T where E:SignedExpBits{let(neg,exp)=E::neg_and_bits(exp);let res=Self::pow(x,exp);if neg{Self::inverse(&res)}else{res}}}impl<G>Group for G where G:Monoid+Invertible{}#[doc=" $\\forall a,\\forall b \\in T, a \\circ b = b \\circ a$"]pub trait Commutative:Magma{}#[doc=" commutative monoid"]pub trait AbelianMonoid:Monoid+Commutative{}impl<M>AbelianMonoid for M where M:Monoid+Commutative{}#[doc=" commutative group"]pub trait AbelianGroup:Group+Commutative{}impl<G>AbelianGroup for G where G:Group+Commutative{}#[doc=" $\\forall a \\in T, a \\circ a = a$"]pub trait Idempotent:Magma{}#[doc=" idempotent monoid"]pub trait IdempotentMonoid:Monoid+Idempotent{}impl<M>IdempotentMonoid for M where M:Monoid+Idempotent{}#[macro_export]macro_rules!monoid_fold{($m:ty)=>{<$m as Unital>::unit()};($m:ty,)=>{<$m as Unital>::unit()};($m:ty,$f:expr)=>{$f};($m:ty,$f:expr,$($ff:expr),*)=>{<$m as Magma>::operate(&($f),&monoid_fold!($m,$($ff),*))};}#[macro_export]macro_rules!define_monoid{($Name:ident,$t:ty,|$x:ident,$y:ident|$op:expr,$unit:expr)=>{struct$Name;impl Magma for$Name{type T=$t;fn operate($x:&Self::T,$y:&Self::T)->Self::T{$op}}impl Unital for$Name{fn unit()->Self::T{$unit}}impl Associative for$Name{}};}}
// codesnip-guard: array
#[cfg_attr(any(),rustfmt::skip)]mod array{#[macro_export]macro_rules!array{[@inner$data:ident=[$init:expr;$len:expr]]=>{{use::std::mem::{ManuallyDrop,MaybeUninit};let mut$data:[MaybeUninit<_>;$len]=unsafe{MaybeUninit::uninit().assume_init()};$init;#[repr(C)]union __Transmuter<const N:usize,T:Clone>{src:ManuallyDrop<[MaybeUninit<T>;N]>,dst:ManuallyDrop<[T;N]>,}ManuallyDrop::into_inner(unsafe{__Transmuter{src:ManuallyDrop::new($data)}.dst})}};[||$e:expr;$len:expr]=>{$crate::array![@inner data=[data.iter_mut().for_each(|item|*item=MaybeUninit::new($e));$len]]};[|$i:pat_param|$e:expr;$len:expr]=>{$crate::array![@inner data=[data.iter_mut().enumerate().for_each(|($i,item)|*item=MaybeUninit::new($e));$len]]};[$e:expr;$len:expr]=>{{let e=$e;$crate::array![||Clone::clone(&e);$len]}};}}
// codesnip-guard: avx_helper
#[cfg_attr(any(),rustfmt::skip)]pub use self::avx_helper::{SimdBackend,avx512_enabled,avx512_supported,disable_avx512,enable_avx512,simd_backend};#[cfg_attr(any(),rustfmt::skip)]mod avx_helper{use std::sync::atomic::{AtomicBool,Ordering};#[derive(Copy,Clone,Debug,Eq,PartialEq)]pub enum SimdBackend{Scalar,Avx2,Avx512}static AVX512_ENABLED:AtomicBool=AtomicBool::new(true);#[inline]pub fn disable_avx512(){AVX512_ENABLED.store(false,Ordering::Relaxed);}#[inline]pub fn enable_avx512(){AVX512_ENABLED.store(true,Ordering::Relaxed);}#[inline]pub fn avx512_enabled()->bool{AVX512_ENABLED.load(Ordering::Relaxed)}#[inline]pub fn avx512_supported()->bool{#[cfg(any(target_arch="x86",target_arch="x86_64"))]return is_x86_feature_detected!("avx512f")&&is_x86_feature_detected!("avx512dq")&&is_x86_feature_detected!("avx512cd")&&is_x86_feature_detected!("avx512bw")&&is_x86_feature_detected!("avx512vl");#[cfg(not(any(target_arch="x86",target_arch="x86_64")))]false}#[inline]pub fn simd_backend()->SimdBackend{#[cfg(any(target_arch="x86",target_arch="x86_64"))]{if avx512_enabled()&&avx512_supported(){return SimdBackend::Avx512;}if is_x86_feature_detected!("avx2"){return SimdBackend::Avx2;}}SimdBackend::Scalar}#[macro_export]macro_rules!avx_helper{(@dispatch$backend:path,$kind:ident;$avx512:expr,$avx2:expr,$scalar:expr)=>{{#[cfg(target_arch="x86_64")]{match$backend(){$kind::Avx512=>$avx512,$kind::Avx2=>$avx2,$kind::Scalar=>$scalar,}}#[cfg(not(target_arch="x86_64"))]$scalar}};(@dispatch_avx2_fma$avx2:expr,$scalar:expr)=>{{#[cfg(target_arch="x86_64")]{if is_x86_feature_detected!("avx2")&&is_x86_feature_detected!("fma"){$avx2}else{$scalar}}#[cfg(not(target_arch="x86_64"))]$scalar}};(@avx512$(#[$meta:meta])*$vis:vis fn$name:ident$(<$($T:ident),+>)?($($i:ident:$t:ty),*)->$ret:ty where[$($clauses:tt)*]$body:block)=>{$(#[$meta])*$vis fn$name$(<$($T)*>)?($($i:$t),*)->$ret where$($clauses)*{if$crate::avx512_supported(){$crate::avx_helper!(@def_avx512 fn avx512$(<$($T)*>)?($($i:$t),*)->$ret where[$($clauses)*]$body);unsafe{avx512$(::<$($T),*>)?($($i),*)}}else if is_x86_feature_detected!("avx2"){$crate::avx_helper!(@def_avx2 fn avx2$(<$($T)*>)?($($i:$t),*)->$ret where[$($clauses)*]$body);unsafe{avx2$(::<$($T),*>)?($($i),*)}}else{$body}}};(@avx2$(#[$meta:meta])*$vis:vis fn$name:ident$(<$($T:ident),+>)?($($i:ident:$t:ty),*)->$ret:ty where[$($clauses:tt)*]$body:block)=>{$(#[$meta])*$vis fn$name$(<$($T)*>)?($($i:$t),*)->$ret where$($clauses)*{if is_x86_feature_detected!("avx2"){$crate::avx_helper!(@def_avx2 fn avx2$(<$($T)*>)?($($i:$t),*)->$ret where[$($clauses)*]$body);unsafe{avx2$(::<$($T),*>)?($($i),*)}}else{$body}}};(@def_avx512 fn$name:ident$(<$($T:ident),+>)?($($args:tt)*)->$ret:ty where[$($clauses:tt)*]$body:block)=>{#[target_feature(enable="avx512f,avx512dq,avx512cd,avx512bw,avx512vl")]unsafe fn$name$(<$($T)*>)?($($args)*)->$ret where$($clauses)*$body};(@def_avx2 fn$name:ident$(<$($T:ident),+>)?($($args:tt)*)->$ret:ty where[$($clauses:tt)*]$body:block)=>{#[target_feature(enable="avx2")]unsafe fn$name$(<$($T)*>)?($($args)*)->$ret where$($clauses)*$body};(@$tag:ident$(#[$meta:meta])*$vis:vis fn$name:ident$(<$($T:ident),+>)?($($args:tt)*)->$ret:ty$body:block)=>{$crate::avx_helper!(@$tag$(#[$meta])*$vis fn$name$(<$($T)*>)?($($args)*)->$ret where[]$body);};(@$tag:ident$(#[$meta:meta])*$vis:vis fn$name:ident$(<$($T:ident),+>)?($($args:tt)*)$($t:tt)*)=>{$crate::avx_helper!(@$tag$(#[$meta])*$vis fn$name$(<$($T)*>)?($($args)*)->()$($t)*);};($($t:tt)*)=>{::std::compile_error!($($t)*);}}}
// codesnip-guard: ring
#[cfg_attr(any(),rustfmt::skip)]pub use self::ring::*;#[cfg_attr(any(),rustfmt::skip)]mod ring{use super::*;use std::{marker::PhantomData,num::Wrapping,ops::{Add,Mul}};pub trait SemiRing{type T:Clone;type Additive:AbelianMonoid<T=Self::T>;type Multiplicative:Monoid<T=Self::T>;#[doc=" additive identity: $0$"]fn zero()->Self::T{<Self::Additive as Unital>::unit()}fn is_zero(x:&Self::T)->bool where Self::T:PartialEq{*x==Self::zero()}#[doc=" multiplicative identity: $1$"]fn one()->Self::T{<Self::Multiplicative as Unital>::unit()}fn is_one(x:&Self::T)->bool where Self::T:PartialEq{*x==Self::one()}#[doc=" additive operaion: $+$"]fn add(x:&Self::T,y:&Self::T)->Self::T{<Self::Additive as Magma>::operate(x,y)}#[doc=" multiplicative operaion: $+$"]fn mul(x:&Self::T,y:&Self::T)->Self::T{<Self::Multiplicative as Magma>::operate(x,y)}fn try_matrix_product(_a:&[Vec<Self::T>],_b:&[Vec<Self::T>])->Option<Vec<Vec<Self::T>>>{None}fn dot_product(x:&[Self::T],y:&[Self::T])->Self::T{assert_eq!(x.len(),y.len());x.iter().zip(y).fold(Self::zero(),|mut sum,(x,y)|{Self::add_assign(&mut sum,&Self::mul(x,y));sum})}fn add_scaled_assign(x:&mut[Self::T],y:&[Self::T],a:&Self::T){assert_eq!(x.len(),y.len());for(x,y)in x.iter_mut().zip(y){Self::add_assign(x,&Self::mul(a,y));}}fn add_assign(x:&mut Self::T,y:&Self::T){<Self::Additive as Magma>::operate_assign(x,y);}fn mul_assign(x:&mut Self::T,y:&Self::T){<Self::Multiplicative as Magma>::operate_assign(x,y);}}pub trait Ring:SemiRing<Additive:Invertible>{#[doc=" additive inverse: $-$"]fn neg(x:&Self::T)->Self::T{<Self::Additive as Invertible>::inverse(x)}#[doc=" additive right inversed operaion: $-$"]fn sub(x:&Self::T,y:&Self::T)->Self::T{<Self::Additive as Invertible>::rinv_operate(x,y)}fn sub_assign(x:&mut Self::T,y:&Self::T){<Self::Additive as Invertible>::rinv_operate_assign(x,y);}}impl<R>Ring for R where R:SemiRing<Additive:Invertible>{}pub trait Field:Ring<Multiplicative:Invertible>{#[doc=" multiplicative inverse: $-$"]fn inv(x:&Self::T)->Self::T{<Self::Multiplicative as Invertible>::inverse(x)}#[doc=" multiplicative right inversed operaion: $-$"]fn div(x:&Self::T,y:&Self::T)->Self::T{<Self::Multiplicative as Invertible>::rinv_operate(x,y)}fn div_assign(x:&mut Self::T,y:&Self::T){<Self::Multiplicative as Invertible>::rinv_operate_assign(x,y);}}impl<F>Field for F where F:Ring<Multiplicative:Invertible>{}pub trait DotProduct:Sized+Clone+Zero+Add<Output=Self>+Mul<Output=Self>{fn try_matrix_product(_a:&[Vec<Self>],_b:&[Vec<Self>])->Option<Vec<Vec<Self>>>{None}fn add_scaled_assign(x:&mut[Self],y:&[Self],a:&Self){assert_eq!(x.len(),y.len());for(x,y)in x.iter_mut().zip(y){*x=x.clone()+a.clone()*y.clone();}}fn dot_product(x:&[Self],y:&[Self])->Self{assert_eq!(x.len(),y.len());x.iter().zip(y).fold(Self::zero(),|sum,(x,y)|sum+x.clone()*y.clone())}}macro_rules!impl_dot_product{($($t:ty)*)=>{$(impl DotProduct for$t{})*};}impl_dot_product!(u8 u16 u32 u64 usize u128 i8 i16 i32 i64 isize i128 f32 f64);impl<T>DotProduct for Wrapping<T>where Wrapping<T>:Clone+Zero+Add<Output=Wrapping<T>>+Mul<Output=Wrapping<T>>{}#[doc=" $+,\\times$"]pub struct AddMulOperation<T>where T:DotProduct+One{_marker:PhantomData<fn()->T>}impl<T>SemiRing for AddMulOperation<T>where T:DotProduct+One{type T=T;type Additive=AdditiveOperation<T>;type Multiplicative=MultiplicativeOperation<T>;#[inline]fn try_matrix_product(a:&[Vec<T>],b:&[Vec<T>])->Option<Vec<Vec<T>>>{T::try_matrix_product(a,b)}#[inline]fn dot_product(x:&[Self::T],y:&[Self::T])->Self::T{T::dot_product(x,y)}#[inline]fn add_scaled_assign(x:&mut[Self::T],y:&[Self::T],a:&Self::T){T::add_scaled_assign(x,y,a);}}}
// codesnip-guard: sort
#[cfg_attr(any(),rustfmt::skip)]pub use self::sort::{RadixSortKey,SliceSortExt};#[cfg_attr(any(),rustfmt::skip)]mod sort{use std::{cmp::Ordering,ptr::copy_nonoverlapping};pub trait RadixSortKey:Copy{const BYTES:usize;fn radix_byte(self,byte:usize)->usize;}macro_rules!unsigned_radix_sort_key{($($t:ty),*$(,)?)=>{$(impl RadixSortKey for$t{const BYTES:usize=(<$t>::BITS/8)as usize;fn radix_byte(self,byte:usize)->usize{((self>>(byte*8))&0xff)as usize}})*};}macro_rules!signed_radix_sort_key{($($t:ty=>$u:ty),*$(,)?)=>{$(impl RadixSortKey for$t{const BYTES:usize=(<$t>::BITS/8)as usize;fn radix_byte(self,byte:usize)->usize{let key=self as$u^(1<<(<$t>::BITS-1));((key>>(byte*8))&0xff)as usize}})*};}unsigned_radix_sort_key!(u8,u16,u32,u64,u128,usize);signed_radix_sort_key!(i8=>u8,i16=>u16,i32=>u32,i64=>u64,i128=>u128,isize=>usize,);pub trait SliceSortExt<T>{fn bubble_sort(&mut self)where T:Ord;fn bubble_sort_by<F>(&mut self,compare:F)where F:FnMut(&T,&T)->Ordering;fn merge_sort(&mut self)where T:Ord;fn merge_sort_by<F>(&mut self,compare:F)where F:FnMut(&T,&T)->Ordering;fn insertion_sort(&mut self)where T:Ord;fn insertion_sort_by<F>(&mut self,compare:F)where F:FnMut(&T,&T)->Ordering;fn radix_sort_by_key<K>(&mut self,key:impl FnMut(&T)->K)where T:Clone,K:RadixSortKey;}impl<T>SliceSortExt<T>for[T]{fn bubble_sort(&mut self)where T:Ord{bubble_sort(self,|a,b|a.lt(b));}fn bubble_sort_by<F>(&mut self,mut compare:F)where F:FnMut(&T,&T)->Ordering{bubble_sort(self,|a,b|compare(a,b)==Ordering::Less);}fn merge_sort(&mut self)where T:Ord{merge_sort(self,|a,b|a.lt(b));}fn merge_sort_by<F>(&mut self,mut compare:F)where F:FnMut(&T,&T)->Ordering{merge_sort(self,|a,b|compare(a,b)==Ordering::Less);}fn insertion_sort(&mut self)where T:Ord{insertion_sort(self,|a,b|a.lt(b));}fn insertion_sort_by<F>(&mut self,mut compare:F)where F:FnMut(&T,&T)->Ordering{insertion_sort(self,|a,b|compare(a,b)==Ordering::Less);}fn radix_sort_by_key<K>(&mut self,key:impl FnMut(&T)->K)where T:Clone,K:RadixSortKey{radix_sort_by_key(self,key);}}fn radix_sort_by_key<T,K>(values:&mut[T],mut key:impl FnMut(&T)->K)where T:Clone,K:RadixSortKey{if values.len()<=1{return;}let mut histograms=vec![[0usize;256];K::BYTES];for value in values.iter(){let key=key(value);for(byte,histogram)in histograms.iter_mut().enumerate(){histogram[key.radix_byte(byte)]+=1;}}for histogram in histograms.iter_mut(){let mut position=0;for count in histogram.iter_mut(){let next=position+*count;*count=position;position=next;}}let mut ends=[values.len();256];ends[..255].copy_from_slice(&histograms[0][1..]);let mut buffer=Vec::with_capacity(values.len());{let spare=buffer.spare_capacity_mut();let positions=&mut histograms[0];for value in values.iter(){let bucket=key(value).radix_byte(0);let position=&mut positions[bucket];assert!(*position<ends[bucket]);spare[*position].write(value.clone());*position+=1;}}unsafe{buffer.set_len(values.len())};for(byte,positions)in histograms.iter_mut().enumerate().skip(1){macro_rules!distribute{($source:expr,$destination:expr)=>{{let source=$source;let destination=$destination;for value in source{let bucket=key(value).radix_byte(byte);let position=&mut positions[bucket];destination[*position].clone_from(value);*position+=1;}}};}if byte%2==0{distribute!(&*values,&mut buffer);}else{distribute!(&buffer,&mut*values);}}if K::BYTES%2==1{values.clone_from_slice(&buffer);}}fn bubble_sort<T,F>(v:&mut[T],mut is_less:F)where F:FnMut(&T,&T)->bool{let len=v.len();if len<=1{return;}for i in 0..len-1{for j in 0..len-i-1{unsafe{if is_less(v.get_unchecked(j+1),v.get_unchecked(j)){v.swap(j,j+1);}}}}}unsafe fn merge<T,F>(v:&mut[T],mid:usize,buf:*mut T,is_less:&mut F)where F:FnMut(&T,&T)->bool{unsafe{let len=v.len();let v=v.as_mut_ptr();let(v_mid,v_end)=(v.add(mid),v.add(len));copy_nonoverlapping(v,buf,mid);let mut guard=MergeGuard{start:buf,dest:v,len:mid};let mut right=v_mid;while guard.len!=0&&right<v_end{let to_copy=if is_less(&*right,&*guard.start){get_and_increment(&mut right)}else{guard.len-=1;get_and_increment(&mut guard.start)};copy_nonoverlapping(to_copy,get_and_increment(&mut guard.dest),1);}}struct MergeGuard<T>{start:*mut T,dest:*mut T,len:usize}impl<T>Drop for MergeGuard<T>{fn drop(&mut self){unsafe{copy_nonoverlapping(self.start,self.dest,self.len)};}}unsafe fn get_and_increment<T>(ptr:&mut*mut T)->*mut T{let old=*ptr;*ptr=unsafe{ptr.offset(1)};old}}fn merge_sort<T,F>(v:&mut[T],mut is_less:F)where F:FnMut(&T,&T)->bool{let len=v.len();if len<=1{return;}let mut buf=Vec::with_capacity(len/2);let mut runs:Vec<Run>=vec![];let mut end=len;while end>0{let start=end-1;let mut left=Run{start,len:end-start};end=start;while let Some(right)=runs.pop_if(|right|left.start==0||right.len<=left.len){unsafe{merge(&mut v[left.start..right.start+right.len],left.len,buf.as_mut_ptr(),&mut is_less);}left=Run{start:left.start,len:left.len+right.len};}runs.push(left);}debug_assert!(runs.len()==1&&runs[0].start==0&&runs[0].len==len);#[derive(Clone,Copy)]struct Run{start:usize,len:usize}}fn insertion_sort<T,F>(v:&mut[T],mut is_less:F)where F:FnMut(&T,&T)->bool{for i in 1..v.len(){let x=&v[i];let p=v[..i].partition_point(|y|is_less(y,x));v[p..=i].rotate_right(1);}}}
// codesnip-guard: zero_one
#[cfg_attr(any(),rustfmt::skip)]pub use self::zero_one::{One,Zero};#[cfg_attr(any(),rustfmt::skip)]mod zero_one{pub trait Zero:Sized{fn zero()->Self;#[inline]fn is_zero(&self)->bool where Self:PartialEq{self==&Self::zero()}#[inline]fn set_zero(&mut self){*self=Self::zero();}}pub trait One:Sized{fn one()->Self;#[inline]fn is_one(&self)->bool where Self:PartialEq{self==&Self::one()}#[inline]fn set_one(&mut self){*self=Self::one();}}macro_rules!impl_zero_one{($({$(<$T:ident:$Bound:ident>)?$Trait:ident$method:ident$($t:ty)*,$e:expr})*)=>{$(impl_zero_one!(@impl[$(<$T:$Bound>)?]$Trait$method[$($t)*],$e);)*};(@impl[<$T:ident:$Bound:ident>]$Trait:ident$method:ident[$($t:ty)*],$e:expr)=>{$(impl<$T:$Bound>$Trait for$t{fn$method()->Self{$e}})*};(@impl[]$Trait:ident$method:ident[$($t:ty)*],$e:expr)=>{$(impl$Trait for$t{fn$method()->Self{$e}})*};}impl_zero_one!({Zero zero u8 u16 u32 u64 usize i8 i16 i32 i64 isize u128 i128,0}{Zero zero f32 f64,0.}{One one u8 u16 u32 u64 usize i8 i16 i32 i64 isize u128 i128,1}{One one f32 f64,1.}{<T:Zero>Zero zero std::num::Wrapping<T>,Self(T::zero())}{<T:One>One one std::num::Wrapping<T>,Self(T::one())});}