标准库标头 <numeric>

 

C++

编译器支持

自立实现与有宿主实现

语言

标准库

标准库标头

具名要求

功能特性测试宏 (C++20)

语言支持库

概念库 (C++20)

元编程库 (C++11)

诊断库

通用工具库

字符串库

容器库

迭代器库

范围库 (C++20)

算法库

数值库

本地化库

输入/输出库

文件系统库 (C++17)

正则表达式库 (C++11)

并发支持库 (C++11)

技术规范

符号索引

外部库

 

标准库标头

语言支持
<cstddef> <cstdlib> <version> (C++20) <limits> <climits>	<cfloat> <cstdint> (C++11) <stdfloat> (C++23) <new> <typeinfo>	<source_location> (C++20) <exception> <initializer_list> (C++11) <compare> (C++20)	<coroutine> (C++20) <csignal> <csetjmp> <cstdarg>
概念
<concepts> (C++20)
诊断
<stdexcept> <stacktrace> (C++23)	<cassert>	<cerrno>	<system_error> (C++11)
内存管理
<memory>	<memory_resource> (C++17)	<scoped_allocator> (C++11)
元编程
<type_traits> (C++11)	<ratio> (C++11)
通用工具
<utility> <tuple> (C++11) <optional> (C++17) <variant> (C++17)	<any> (C++17) <debugging> (C++26) <expected> (C++23) <bitset>	<functional> <typeindex> (C++11) <execution> (C++17)	<charconv> (C++17) <format> (C++20) <bit> (C++20)
字符串
<string_view> (C++17) <string>	<cctype> <cwctype>	<cstring> <cwchar>	<cuchar> (C++11)
容器
<array> (C++11) <deque> <forward_list> (C++11) <list>	<vector> <map> <set> <unordered_map> (C++11)	<unordered_set> (C++11) <queue> <stack> <flat_map> (C++23)	<flat_set> (C++23) <span> (C++20) <mdspan> (C++23) <inplace_vector> (C++26)
迭代器
<iterator>
范围
<ranges> (C++20)	<generator> (C++23)
算法
<algorithm>	<numeric>
数值
<cfenv> (C++11) <complex>	<random> (C++11) <valarray>	<cmath> <linalg> (C++26)	<numbers> (C++20)
日期时间
<chrono> (C++11)	<ctime>
本地化
<locale>	<clocale>	<codecvt> (C++11/17/26*)	<text_encoding> (C++26)
输入/输出
<iosfwd> <iostream> <ios> <streambuf>	<istream> <ostream> <iomanip> <print> (C++23)	<sstream> <spanstream> (C++23) <fstream> <syncstream> (C++20)	<filesystem> (C++17) <cstdio> <cinttypes> (C++11) <strstream> (C++98/26*)
正则表达式
<regex> (C++11)
并发支持
<stop_token> (C++20) <thread> (C++11) <atomic> (C++11) <rcu> (C++26)	<stdatomic.h> (C++23) <mutex> (C++11) <shared_mutex> (C++14)	<condition_variable> (C++11)   <semaphore> (C++20) <latch> (C++20)	<barrier> (C++20) <future> (C++11) <hazard_pointer> (C++26)
C 兼容
<cstdbool> (C++11/17/20*)   <ccomplex> (C++11/17/20*)	<ctgmath> (C++11/17/20*)	<cstdalign> (C++11/17/20*)	<ciso646> (C++20 前)

 

此头文件是数值库的一部分。

函数
iota (C++11)	用从起始值开始连续递增的值填充一个范围 (函数模板)
ranges::iota (C++23)	用从起始值开始连续递增的值填充一个范围 (niebloid)
accumulate	对一个范围内的元素求和或折叠 (函数模板)
reduce (C++17)	类似 std::accumulate，但不依序执行 (函数模板)
transform_reduce (C++17)	应用一个可调用物，然后以乱序规约 (函数模板)
inner_product	计算两个范围的元素的内积 (函数模板)
adjacent_difference	计算范围内各相邻元素之间的差 (函数模板)
partial_sum	计算范围内元素的部分和 (函数模板)
inclusive_scan (C++17)	类似 std::partial_sum，第 i 个和中包含第 i 个输入 (函数模板)
exclusive_scan (C++17)	类似 std::partial_sum，第 i 个和中排除第 i 个输入 (函数模板)
transform_inclusive_scan (C++17)	应用一个可调用物，然后进行包含扫描 (函数模板)
transform_exclusive_scan (C++17)	应用一个可调用物，然后进行排除扫描 (函数模板)
gcd (C++17)	计算两个整数的最大公约数 (函数模板)
lcm (C++17)	计算两个整数的最小公倍数 (函数模板)
midpoint (C++20)	两个数值或指针间的中点 (函数模板)
add_sat (C++26)	两个整数的饱和加法运算 (函数模板)
sub_sat (C++26)	两个整数的饱和减法运算 (函数模板)
mul_sat (C++26)	两个整数的饱和乘法运算 (函数模板)
div_sat (C++26)	两个整数的饱和除法运算 (函数模板)
saturate_cast (C++26)	返回在另一个整数类型范围内的整数值 (函数模板)

概要

namespace std {
  // 累加
  template<class InputIt, class T>
    constexpr T accumulate(InputIt first, InputIt last, T init);
  template<class InputIt, class T, class BinaryOperation>
    constexpr T accumulate(InputIt first, InputIt last, T init, BinaryOperation binary_op);
 
  // 规约
  template<class InputIt>
    constexpr typename iterator_traits<InputIt>::value_type
      reduce(InputIt first, InputIt last);
  template<class InputIt, class T>
    constexpr T reduce(InputIt first, InputIt last, T init);
  template<class InputIt, class T, class BinaryOperation>
    constexpr T reduce(InputIt first, InputIt last, T init, BinaryOperation binary_op);
  template<class ExecutionPolicy, class ForwardIt>
    typename iterator_traits<ForwardIt>::value_type
      reduce(ExecutionPolicy&& exec,
             ForwardIt first, ForwardIt last);
  template<class ExecutionPolicy, class ForwardIt, class T>
    T reduce(ExecutionPolicy&& exec,
             ForwardIt first, ForwardIt last, T init);
  template<class ExecutionPolicy, class ForwardIt, class T, class BinaryOperation>
    T reduce(ExecutionPolicy&& exec,
             ForwardIt first, ForwardIt last, T init, BinaryOperation binary_op);
 
  // 内积
  template<class InputIt1, class InputIt2, class T>
    constexpr T inner_product(InputIt1 first1, InputIt1 last1,
                              InputIt2 first2, T init);
  template<class InputIt1, class InputIt2, class T,
           class BinaryOperation1, class BinaryOperation2>
    constexpr T inner_product(InputIt1 first1, InputIt1 last1,
                              InputIt2 first2, T init,
                              BinaryOperation1 binary_op1,
                              BinaryOperation2 binary_op2);
 
  // 变换规约
  template<class InputIt1, class InputIt2, class T>
    constexpr T transform_reduce(InputIt1 first1, InputIt1 last1,
                                 InputIt2 first2,
                                 T init);
  template<class InputIt1, class InputIt2, class T,
           class BinaryOperation1, class BinaryOperation2>
    constexpr T transform_reduce(InputIt1 first1, InputIt1 last1,
                                 InputIt2 first2,
                                 T init,
                                 BinaryOperation1 binary_op1,
                                 BinaryOperation2 binary_op2);
  template<class InputIt, class T,
           class BinaryOperation, class UnaryOperation>
    constexpr T transform_reduce(InputIt first, InputIt last,
                                 T init,
                                 BinaryOperation binary_op, UnaryOperation unary_op);
  template<class ExecutionPolicy,
           class ForwardIt1, class ForwardIt2, class T>
    T transform_reduce(ExecutionPolicy&& exec,
                       ForwardIt1 first1, ForwardIt1 last1,
                       ForwardIt2 first2,
                       T init);
  template<class ExecutionPolicy,
           class ForwardIt1, class ForwardIt2, class T,
           class BinaryOperation1, class BinaryOperation2>
    T transform_reduce(ExecutionPolicy&& exec,
                       ForwardIt1 first1, ForwardIt1 last1,
                       ForwardIt2 first2,
                       T init,
                       BinaryOperation1 binary_op1,
                       BinaryOperation2 binary_op2);
  template<class ExecutionPolicy,
           class ForwardIt, class T,
           class BinaryOperation, class UnaryOperation>
    T transform_reduce(ExecutionPolicy&& exec,
                       ForwardIt first, ForwardIt last,
                       T init,
                       BinaryOperation binary_op, UnaryOperation unary_op);
 
  // 部分和
  template<class InputIt, class OutputIt>
    constexpr OutputIt partial_sum(InputIt first,
                                   InputIt last,
                                   OutputIt result);
  template<class InputIt, class OutputIt, class BinaryOperation>
    constexpr OutputIt partial_sum(InputIt first,
                                   InputIt last,
                                   OutputIt result,
                                   BinaryOperation binary_op);
 
  // 排除扫描
  template<class InputIt, class OutputIt, class T>
    constexpr OutputIt exclusive_scan(InputIt first, InputIt last,
                                      OutputIt result,
                                      T init);
  template<class InputIt, class OutputIt, class T, class BinaryOperation>
    constexpr OutputIt exclusive_scan(InputIt first, InputIt last,
                                      OutputIt result,
                                      T init, BinaryOperation binary_op);
  template<class ExecutionPolicy, class ForwardIt1, class ForwardIt2, class T>
    ForwardIt2 exclusive_scan(ExecutionPolicy&& exec,
                              ForwardIt1 first, ForwardIt1 last,
                              ForwardIt2 result,
                              T init);
  template<class ExecutionPolicy, class ForwardIt1, class ForwardIt2, class T,
           class BinaryOperation>
    ForwardIt2 exclusive_scan(ExecutionPolicy&& exec,
                              ForwardIt1 first, ForwardIt1 last,
                              ForwardIt2 result,
                              T init, BinaryOperation binary_op);
 
  // 包含扫描
  template<class InputIt, class OutputIt>
    constexpr OutputIt inclusive_scan(InputIt first, InputIt last, OutputIt result);
  template<class InputIt, class OutputIt, class BinaryOperation>
    constexpr OutputIt inclusive_scan(InputIt first, InputIt last,
                                      OutputIt result,
                                      BinaryOperation binary_op);
  template<class InputIt, class OutputIt, class BinaryOperation, class T>
    constexpr OutputIt inclusive_scan(InputIt first, InputIt last,
                                      OutputIt result,
                                      BinaryOperation binary_op, T init);
  template<class ExecutionPolicy, class ForwardIt1, class ForwardIt2>
    ForwardIt2 inclusive_scan(ExecutionPolicy&& exec,
                              ForwardIt1 first, ForwardIt1 last,
                              ForwardIt2 result);
  template<class ExecutionPolicy, class ForwardIt1, class ForwardIt2,
           class BinaryOperation>
    ForwardIt2 inclusive_scan(ExecutionPolicy&& exec,
                              ForwardIt1 first, ForwardIt1 last,
                              ForwardIt2 result,
                              BinaryOperation binary_op);
  template<class ExecutionPolicy, class ForwardIt1, class ForwardIt2,
           class BinaryOperation, class T>
    ForwardIt2 inclusive_scan(ExecutionPolicy&& exec,
                              ForwardIt1 first, ForwardIt1 last,
                              ForwardIt2 result,
                              BinaryOperation binary_op, T init);
 
  // 变换排除扫描
  template<class InputIt, class OutputIt, class T,
           class BinaryOperation, class UnaryOperation>
    constexpr OutputIt transform_exclusive_scan(InputIt first, InputIt last,
                                                OutputIt result,
                                                T init,
                                                BinaryOperation binary_op,
                                                UnaryOperation unary_op);
  template<class ExecutionPolicy,
           class ForwardIt1, class ForwardIt2, class T,
           class BinaryOperation, class UnaryOperation>
    ForwardIt2 transform_exclusive_scan(ExecutionPolicy&& exec,
                                        ForwardIt1 first, ForwardIt1 last,
                                        ForwardIt2 result,
                                        T init,
                                        BinaryOperation binary_op,
                                        UnaryOperation unary_op);
 
  // 变换包含扫描
  template<class InputIt, class OutputIt,
           class BinaryOperation, class UnaryOperation>
    constexpr OutputIt transform_inclusive_scan(InputIt first, InputIt last,
                                                OutputIt result,
                                                BinaryOperation binary_op,
                                                UnaryOperation unary_op);
  template<class InputIt, class OutputIt,
           class BinaryOperation, class UnaryOperation, class T>
    constexpr OutputIt transform_inclusive_scan(InputIt first, InputIt last,
                                                OutputIt result,
                                                BinaryOperation binary_op,
                                                UnaryOperation unary_op,
                                                T init);
  template<class ExecutionPolicy,
           class ForwardIt1, class ForwardIt2,
           class BinaryOperation, class UnaryOperation>
    ForwardIt2 transform_inclusive_scan(ExecutionPolicy&& exec,
                                        ForwardIt1 first, ForwardIt1 last,
                                        ForwardIt2 result,
                                        BinaryOperation binary_op,
                                        UnaryOperation unary_op);
  template<class ExecutionPolicy,
           class ForwardIt1, class ForwardIt2,
           class BinaryOperation, class UnaryOperation, class T>
    ForwardIt2 transform_inclusive_scan(ExecutionPolicy&& exec,
                                        ForwardIt1 first, ForwardIt1 last,
                                        ForwardIt2 result,
                                        BinaryOperation binary_op,
                                        UnaryOperation unary_op,
                                        T init);
 
  // 相邻差
  template<class InputIt, class OutputIt>
    constexpr OutputIt adjacent_difference(InputIt first, InputIt last,
                                           OutputIt result);
  template<class InputIt, class OutputIt, class BinaryOperation>
    constexpr OutputIt adjacent_difference(InputIt first, InputIt last,
                                           OutputIt result,
                                           BinaryOperation binary_op);
  template<class ExecutionPolicy, class ForwardIt1, class ForwardIt2>
    ForwardIt2 adjacent_difference(ExecutionPolicy&& exec,
                                   ForwardIt1 first, ForwardIt1 last,
                                   ForwardIt2 result);
  template<class ExecutionPolicy, class ForwardIt1, class ForwardIt2,
           class BinaryOperation>
    ForwardIt2 adjacent_difference(ExecutionPolicy&& exec,
                                   ForwardIt1 first, ForwardIt1 last,
                                   ForwardIt2 result,
                                   BinaryOperation binary_op);
 
  // iota
  template<class ForwardIt, class T>
    constexpr void iota(ForwardIt first, ForwardIt last, T value);
 
  namespace ranges {
    template<class O, class T>
      using iota_result = out_value_result<O, T>;
 
    template<input_or_output_iterator O, sentinel_for<O> S, weakly_incrementable T>
      requires indirectly_writable<O, const T&>
      constexpr iota_result<O, T> iota(O first, S last, T value);
 
    template<weakly_incrementable T, output_range<const T&> R>
      constexpr iota_result<borrowed_iterator_t<R>, T> iota(R&& r, T value);
  }
 
  // 最大公约数
  template<class M, class N>
    constexpr common_type_t<M, N> gcd(M m, N n);
 
  // 最小公倍数
  template<class M, class N>
    constexpr common_type_t<M, N> lcm(M m, N n);
 
  // 中点
  template<class T>
    constexpr T midpoint(T a, T b) noexcept;
  template<class T>
    constexpr T* midpoint(T* a, T* b);
 
  // 饱和算术
  template<class T>
    constexpr T add_sat(T x, T y) noexcept;           // 独立
  template<class T>
    constexpr T sub_sat(T x, T y) noexcept;           // 独立
  template<class T>
    constexpr T mul_sat(T x, T y) noexcept;           // 独立
  template<class T>
    constexpr T div_sat(T x, T y) noexcept;           // 独立
  template<class T, class U>
    constexpr T saturate_cast(U x) noexcept;          // 独立
}