CP-Algorithms Library
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cp-algo/util/sort.hpp
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- Last update: 2026-10-10 16:26:24+02:00
- Include:
#include "cp-algo/util/sort.hpp"
Depends on
Required by
Verified with
- Minimum Spanning Tree (verify/graph/mst.test.cpp)
- Longest Increasing Subsequence (verify/structures/fenwick/lis.test.cpp)
- Ordered Set (verify/structures/fenwick/ordered_set.test.cpp)
Code
#ifndef CP_ALGO_UTIL_SORT_HPP
#define CP_ALGO_UTIL_SORT_HPP
#include "bit.hpp"
#include <algorithm>
#include <numeric>
#include <ranges>
#include <vector>
namespace cp_algo {
template<size_t maxc>
void count_sort(auto &a, auto &&proj) {
std::array<int, maxc> cnt = {};
for(auto &x: a) {
cnt[proj(x)]++;
}
std::partial_sum(begin(cnt), end(cnt), begin(cnt));
auto res = a;
for(auto const& it: a | std::views::reverse) {
res[--cnt[proj(it)]] = it;
}
a = std::move(res);
}
template<size_t maxc>
void count_sort(auto &a) {
count_sort<maxc>(a, std::identity{});
}
void radix_sort(auto &a, auto &&proj) {
if(empty(a)) {
return;
}
auto [mn, mx] = std::ranges::minmax(a, {}, proj);
with_bit_floor<1>(size(a), [&]<size_t floor>() {
constexpr int base = std::min<size_t>(floor, 1 << 16);
for(int64_t i = 1; i <= std::invoke(proj, mx) - std::invoke(proj, mn); i *= base) {
count_sort<base>(a, [&](auto const& x) {
return (std::invoke(proj, x) - std::invoke(proj, mn)) / i % base;
});
}
});
}
void radix_sort(auto &a) {
radix_sort(a, std::identity{});
}
}
#endif // CP_ALGO_UTIL_SORT_HPP
#line 1 "cp-algo/util/sort.hpp"
#line 1 "cp-algo/util/bit.hpp"
#line 1 "cp-algo/util/simd.hpp"
#include <experimental/simd>
#include <cstdint>
#include <cstddef>
#include <memory>
#if defined(__x86_64__) && !defined(CP_ALGO_DISABLE_AVX2)
#define CP_ALGO_SIMD_AVX2_TARGET _Pragma("GCC target(\"avx2,fma\")")
#else
#define CP_ALGO_SIMD_AVX2_TARGET
#endif
#define CP_ALGO_SIMD_PRAGMA_PUSH \
_Pragma("GCC push_options") \
CP_ALGO_SIMD_AVX2_TARGET
CP_ALGO_SIMD_PRAGMA_PUSH
namespace cp_algo {
template<typename T, size_t len>
using simd [[gnu::vector_size(len * sizeof(T))]] = T;
using u64x8 = simd<uint64_t, 8>;
using u32x16 = simd<uint32_t, 16>;
using i64x4 = simd<int64_t, 4>;
using u64x4 = simd<uint64_t, 4>;
using u32x8 = simd<uint32_t, 8>;
using u16x16 = simd<uint16_t, 16>;
using i32x4 = simd<int32_t, 4>;
using u32x4 = simd<uint32_t, 4>;
using u16x8 = simd<uint16_t, 8>;
using u16x4 = simd<uint16_t, 4>;
using i16x4 = simd<int16_t, 4>;
using u8x32 = simd<uint8_t, 32>;
using u8x16 = simd<uint8_t, 16>;
using u8x8 = simd<uint8_t, 8>;
using u8x4 = simd<uint8_t, 4>;
using dx4 = simd<double, 4>;
inline dx4 abs(dx4 a) {
return dx4{
std::abs(a[0]),
std::abs(a[1]),
std::abs(a[2]),
std::abs(a[3])
};
}
// https://stackoverflow.com/a/77376595
// works for ints in (-2^51, 2^51)
static constexpr dx4 magic = dx4() + (3ULL << 51);
inline i64x4 lround(dx4 x) {
return i64x4(x + magic) - i64x4(magic);
}
inline dx4 to_double(i64x4 x) {
return dx4(x + i64x4(magic)) - magic;
}
inline dx4 round(dx4 a) {
return dx4{
std::nearbyint(a[0]),
std::nearbyint(a[1]),
std::nearbyint(a[2]),
std::nearbyint(a[3])
};
}
inline u64x4 low32(u64x4 x) {
return x & uint32_t(-1);
}
inline auto swap_bytes(auto x) {
return decltype(x)(__builtin_shufflevector(u32x8(x), u32x8(x), 1, 0, 3, 2, 5, 4, 7, 6));
}
inline u64x4 montgomery_reduce(u64x4 x, uint32_t mod, uint32_t imod) {
#ifdef __AVX2__
auto x_ninv = u64x4(_mm256_mul_epu32(__m256i(x), __m256i() + imod));
x += u64x4(_mm256_mul_epu32(__m256i(x_ninv), __m256i() + mod));
#else
auto x_ninv = u64x4(u32x8(low32(x)) * imod);
x += x_ninv * uint64_t(mod);
#endif
return swap_bytes(x);
}
// x - mod where x >= mod, for x in [0, 2 mod). Unsigned, so it holds up to mod < 2^31;
// zero upper halves of 64-bit lanes stay zero.
inline u32x8 reduce_once(u32x8 x, uint32_t mod) {
auto y = x - mod;
return x < y ? x : y;
}
inline u64x4 reduce_once(u64x4 x, uint32_t mod) {
return u64x4(reduce_once(u32x8(x), mod));
}
inline u64x4 montgomery_mul(u64x4 x, u64x4 y, uint32_t mod, uint32_t imod) {
#ifdef __AVX2__
return montgomery_reduce(u64x4(_mm256_mul_epu32(__m256i(x), __m256i(y))), mod, imod);
#else
return montgomery_reduce(x * y, mod, imod);
#endif
}
inline u32x8 montgomery_mul(u32x8 x, u32x8 y, uint32_t mod, uint32_t imod) {
return u32x8(montgomery_mul(u64x4(x), u64x4(y), mod, imod)) |
u32x8(swap_bytes(montgomery_mul(u64x4(swap_bytes(x)), u64x4(swap_bytes(y)), mod, imod)));
}
inline dx4 rotate_right(dx4 x) {
static constexpr u64x4 shuffler = {3, 0, 1, 2};
return __builtin_shuffle(x, shuffler);
}
template<std::size_t Align = 32>
inline bool is_aligned(const auto *p) noexcept {
return (reinterpret_cast<std::uintptr_t>(p) % Align) == 0;
}
template<class Target>
inline Target& vector_cast(auto &&p) {
return *reinterpret_cast<Target*>(std::assume_aligned<alignof(Target)>(&p));
}
}
#pragma GCC pop_options
#line 6 "cp-algo/util/bit.hpp"
#include <array>
#include <bit>
#if defined(__x86_64__) && !defined(CP_ALGO_DISABLE_AVX2)
#define CP_ALGO_BIT_OPS_TARGET _Pragma("GCC target(\"avx2,bmi,bmi2,lzcnt,popcnt\")")
#else
#define CP_ALGO_BIT_OPS_TARGET _Pragma("GCC target(\"bmi,bmi2,lzcnt,popcnt\")")
#endif
#define CP_ALGO_BIT_PRAGMA_PUSH \
_Pragma("GCC push_options") \
CP_ALGO_BIT_OPS_TARGET
CP_ALGO_BIT_PRAGMA_PUSH
namespace cp_algo {
template<typename Uint>
constexpr size_t bit_width = sizeof(Uint) * 8;
// n < 64
uint64_t mask(size_t n) {
return (1ULL << n) - 1;
}
size_t order_of_bit(auto x, size_t k) {
return k ? std::popcount(x << (bit_width<decltype(x)> - k)) : 0;
}
inline size_t kth_set_bit(uint64_t x, size_t k) {
return std::countr_zero(_pdep_u64(1ULL << k, x));
}
template<int fl = 0>
void with_bit_floor(size_t n, auto &&callback) {
if constexpr (fl >= 63) {
return;
} else if (n >> (fl + 1)) {
with_bit_floor<fl + 1>(n, callback);
} else {
callback.template operator()<1ULL << fl>();
}
}
void with_bit_ceil(size_t n, auto &&callback) {
with_bit_floor(n, [&]<size_t N>() {
if(N == n) {
callback.template operator()<N>();
} else {
callback.template operator()<N << 1>();
}
});
}
inline uint32_t read_bits(char const* p) {
return _mm256_movemask_epi8(__m256i(vector_cast<u8x32 const>(p[0]) + (127 - '0')));
}
inline uint64_t read_bits64(char const* p) {
return read_bits(p) | (uint64_t(read_bits(p + 32)) << 32);
}
inline void write_bits(char *p, uint32_t bits) {
static constexpr u8x32 shuffler = {
0, 0, 0, 0, 0, 0, 0, 0,
1, 1, 1, 1, 1, 1, 1, 1,
2, 2, 2, 2, 2, 2, 2, 2,
3, 3, 3, 3, 3, 3, 3, 3
};
auto shuffled = u8x32(_mm256_shuffle_epi8(__m256i() + bits, __m256i(shuffler)));
static constexpr u8x32 mask = {
1, 2, 4, 8, 16, 32, 64, 128,
1, 2, 4, 8, 16, 32, 64, 128,
1, 2, 4, 8, 16, 32, 64, 128,
1, 2, 4, 8, 16, 32, 64, 128
};
for(int z = 0; z < 32; z++) {
p[z] = shuffled[z] & mask[z] ? '1' : '0';
}
}
inline void write_bits64(char *p, uint64_t bits) {
write_bits(p, uint32_t(bits));
write_bits(p + 32, uint32_t(bits >> 32));
}
}
#pragma GCC pop_options
#line 4 "cp-algo/util/sort.hpp"
#include <algorithm>
#include <numeric>
#include <ranges>
#include <vector>
namespace cp_algo {
template<size_t maxc>
void count_sort(auto &a, auto &&proj) {
std::array<int, maxc> cnt = {};
for(auto &x: a) {
cnt[proj(x)]++;
}
std::partial_sum(begin(cnt), end(cnt), begin(cnt));
auto res = a;
for(auto const& it: a | std::views::reverse) {
res[--cnt[proj(it)]] = it;
}
a = std::move(res);
}
template<size_t maxc>
void count_sort(auto &a) {
count_sort<maxc>(a, std::identity{});
}
void radix_sort(auto &a, auto &&proj) {
if(empty(a)) {
return;
}
auto [mn, mx] = std::ranges::minmax(a, {}, proj);
with_bit_floor<1>(size(a), [&]<size_t floor>() {
constexpr int base = std::min<size_t>(floor, 1 << 16);
for(int64_t i = 1; i <= std::invoke(proj, mx) - std::invoke(proj, mn); i *= base) {
count_sort<base>(a, [&](auto const& x) {
return (std::invoke(proj, x) - std::invoke(proj, mn)) / i % base;
});
}
});
}
void radix_sort(auto &a) {
radix_sort(a, std::identity{});
}
}
#ifndef CP_ALGO_UTIL_SORT_HPP
#define CP_ALGO_UTIL_SORT_HPP
#include "bit.hpp"
#include <algorithm>
#include <numeric>
#include <ranges>
#include <vector>
namespace cp_algo{ template<size_t maxc> void count_sort(auto&a,auto&&proj){ std::array<int,maxc>cnt={}; for(auto&x:a){ cnt[proj(x)]++; } std::partial_sum(begin(cnt),end(cnt),begin(cnt)); auto res=a; for(auto const&it:a|std::views::reverse){ res[--cnt[proj(it)]] =it; } a=std::move(res); } template<size_t maxc> void count_sort(auto&a){ count_sort<maxc>(a,std::identity{}); } void radix_sort(auto&a,auto&&proj){ if(empty(a)){ return; } auto[mn,mx] =std::ranges::minmax(a,{},proj); with_bit_floor<1>(size(a),[&]<size_t floor>(){ constexpr int base=std::min<size_t>(floor,1<<16); for(int64_t i=1;i<=std::invoke(proj,mx)-std::invoke(proj,mn);i*=base){ count_sort<base>(a,[&](auto const&x){ return(std::invoke(proj,x)-std::invoke(proj,mn))/i%base; }); } }); } void radix_sort(auto&a){ radix_sort(a,std::identity{}); } }
#endif
#line 1 "cp-algo/util/sort.hpp"
#line 1 "cp-algo/util/bit.hpp"
#line 1 "cp-algo/util/simd.hpp"
#include <experimental/simd>
#include <cstdint>
#include <cstddef>
#include <memory>
#if defined(__x86_64__) && !defined(CP_ALGO_DISABLE_AVX2)
#define CP_ALGO_SIMD_AVX2_TARGET _Pragma("GCC target(\"avx2,fma\")")
#else
#define CP_ALGO_SIMD_AVX2_TARGET
#endif
#define CP_ALGO_SIMD_PRAGMA_PUSH _Pragma("GCC push_options") CP_ALGO_SIMD_AVX2_TARGET
CP_ALGO_SIMD_PRAGMA_PUSH
namespace cp_algo{ template<typename T,size_t len> using simd[[gnu::vector_size(len*sizeof(T))]] =T; using u64x8=simd<uint64_t,8>; using u32x16=simd<uint32_t,16>; using i64x4=simd<int64_t,4>; using u64x4=simd<uint64_t,4>; using u32x8=simd<uint32_t,8>; using u16x16=simd<uint16_t,16>; using i32x4=simd<int32_t,4>; using u32x4=simd<uint32_t,4>; using u16x8=simd<uint16_t,8>; using u16x4=simd<uint16_t,4>; using i16x4=simd<int16_t,4>; using u8x32=simd<uint8_t,32>; using u8x16=simd<uint8_t,16>; using u8x8=simd<uint8_t,8>; using u8x4=simd<uint8_t,4>; using dx4=simd<double,4>; inline dx4 abs(dx4 a){ return dx4{ std::abs(a[0]), std::abs(a[1]), std::abs(a[2]), std::abs(a[3]) }; } static constexpr dx4 magic=dx4()+(3ULL<<51); inline i64x4 lround(dx4 x){ return i64x4(x+magic)-i64x4(magic); } inline dx4 to_double(i64x4 x){ return dx4(x+i64x4(magic))-magic; } inline dx4 round(dx4 a){ return dx4{ std::nearbyint(a[0]), std::nearbyint(a[1]), std::nearbyint(a[2]), std::nearbyint(a[3]) }; } inline u64x4 low32(u64x4 x){ return x&uint32_t(-1); } inline auto swap_bytes(auto x){ return decltype(x)(__builtin_shufflevector(u32x8(x),u32x8(x),1,0,3,2,5,4,7,6)); } inline u64x4 montgomery_reduce(u64x4 x,uint32_t mod,uint32_t imod){
#ifdef __AVX2__
auto x_ninv=u64x4(_mm256_mul_epu32(__m256i(x),__m256i()+imod)); x+=u64x4(_mm256_mul_epu32(__m256i(x_ninv),__m256i()+mod));
#else
auto x_ninv=u64x4(u32x8(low32(x))*imod); x+=x_ninv*uint64_t(mod);
#endif
return swap_bytes(x); } inline u32x8 reduce_once(u32x8 x,uint32_t mod){ auto y=x-mod; return x<y?x:y; } inline u64x4 reduce_once(u64x4 x,uint32_t mod){ return u64x4(reduce_once(u32x8(x),mod)); } inline u64x4 montgomery_mul(u64x4 x,u64x4 y,uint32_t mod,uint32_t imod){
#ifdef __AVX2__
return montgomery_reduce(u64x4(_mm256_mul_epu32(__m256i(x),__m256i(y))),mod,imod);
#else
return montgomery_reduce(x*y,mod,imod);
#endif
} inline u32x8 montgomery_mul(u32x8 x,u32x8 y,uint32_t mod,uint32_t imod){ return u32x8(montgomery_mul(u64x4(x),u64x4(y),mod,imod))| u32x8(swap_bytes(montgomery_mul(u64x4(swap_bytes(x)),u64x4(swap_bytes(y)),mod,imod))); } inline dx4 rotate_right(dx4 x){ static constexpr u64x4 shuffler={3,0,1,2}; return __builtin_shuffle(x,shuffler); } template<std::size_t Align=32> inline bool is_aligned(const auto*p)noexcept{ return(reinterpret_cast<std::uintptr_t>(p)%Align)==0; } template<class Target> inline Target&vector_cast(auto&&p){ return*reinterpret_cast<Target*>(std::assume_aligned<alignof(Target)>(&p)); } }
#pragma GCC pop_options
#line 6 "cp-algo/util/bit.hpp"
#include <array>
#include <bit>
#if defined(__x86_64__) && !defined(CP_ALGO_DISABLE_AVX2)
#define CP_ALGO_BIT_OPS_TARGET _Pragma("GCC target(\"avx2,bmi,bmi2,lzcnt,popcnt\")")
#else
#define CP_ALGO_BIT_OPS_TARGET _Pragma("GCC target(\"bmi,bmi2,lzcnt,popcnt\")")
#endif
#define CP_ALGO_BIT_PRAGMA_PUSH _Pragma("GCC push_options") CP_ALGO_BIT_OPS_TARGET
CP_ALGO_BIT_PRAGMA_PUSH
namespace cp_algo{ template<typename Uint> constexpr size_t bit_width=sizeof(Uint)*8; uint64_t mask(size_t n){ return(1ULL<<n)-1; } size_t order_of_bit(auto x,size_t k){ return k?std::popcount(x<<(bit_width<decltype(x)> -k)):0; } inline size_t kth_set_bit(uint64_t x,size_t k){ return std::countr_zero(_pdep_u64(1ULL<<k,x)); } template<int fl=0> void with_bit_floor(size_t n,auto&&callback){ if constexpr(fl>=63){ return; }else if(n>>(fl+1)){ with_bit_floor<fl+1>(n,callback); }else{ callback.template operator()<1ULL<<fl>(); } } void with_bit_ceil(size_t n,auto&&callback){ with_bit_floor(n,[&]<size_t N>(){ if(N==n){ callback.template operator()<N>(); }else{ callback.template operator()<N<<1>(); } }); } inline uint32_t read_bits(char const*p){ return _mm256_movemask_epi8(__m256i(vector_cast<u8x32 const>(p[0])+(127-'0'))); } inline uint64_t read_bits64(char const*p){ return read_bits(p)|(uint64_t(read_bits(p+32))<<32); } inline void write_bits(char*p,uint32_t bits){ static constexpr u8x32 shuffler={ 0,0,0,0,0,0,0,0, 1,1,1,1,1,1,1,1, 2,2,2,2,2,2,2,2, 3,3,3,3,3,3,3,3 }; auto shuffled=u8x32(_mm256_shuffle_epi8(__m256i()+bits,__m256i(shuffler))); static constexpr u8x32 mask={ 1,2,4,8,16,32,64,128, 1,2,4,8,16,32,64,128, 1,2,4,8,16,32,64,128, 1,2,4,8,16,32,64,128 }; for(int z=0;z<32;z++){ p[z] =shuffled[z] &mask[z]?'1':'0'; } } inline void write_bits64(char*p,uint64_t bits){ write_bits(p,uint32_t(bits)); write_bits(p+32,uint32_t(bits>>32)); } }
#pragma GCC pop_options
#line 4 "cp-algo/util/sort.hpp"
#include <algorithm>
#include <numeric>
#include <ranges>
#include <vector>
namespace cp_algo{ template<size_t maxc> void count_sort(auto&a,auto&&proj){ std::array<int,maxc>cnt={}; for(auto&x:a){ cnt[proj(x)]++; } std::partial_sum(begin(cnt),end(cnt),begin(cnt)); auto res=a; for(auto const&it:a|std::views::reverse){ res[--cnt[proj(it)]] =it; } a=std::move(res); } template<size_t maxc> void count_sort(auto&a){ count_sort<maxc>(a,std::identity{}); } void radix_sort(auto&a,auto&&proj){ if(empty(a)){ return; } auto[mn,mx] =std::ranges::minmax(a,{},proj); with_bit_floor<1>(size(a),[&]<size_t floor>(){ constexpr int base=std::min<size_t>(floor,1<<16); for(int64_t i=1;i<=std::invoke(proj,mx)-std::invoke(proj,mn);i*=base){ count_sort<base>(a,[&](auto const&x){ return(std::invoke(proj,x)-std::invoke(proj,mn))/i%base; }); } }); } void radix_sort(auto&a){ radix_sort(a,std::identity{}); } }