标准库头文件 <numeric>

 

C++

语言

标准库头文件

自立与有宿主实现

具名要求

语言支持库

概念库 (C++20)

诊断库

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

输入/输出库

本地化库

正则表达式库 (C++11)

原子操作库 (C++11)

线程支持库 (C++11)

文件系统库 (C++17)

技术规范

 

标准库头文件

语言支持
<cstddef> <limits> <climits> <coroutine>	<cfloat> <cstdint> <new> <source_location>	<typeinfo> <exception> <initializer_list> <version>	<csignal> <csetjmp> <cstdarg>
概念
<concepts>
诊断
<stdexcept>	<cassert>	<cerrno>	<system_error>
通用工具
<utility> <memory> <memory_resource> <scoped_allocator>     <compare>	<bitset> <tuple> <optional> <any> <variant>	<type_traits> <ratio> <chrono> <typeindex> <functional>	<ctime> <cstdlib>
字符串
<string> <string_view> <cstring>	<charconv> <format>	<cctype> <cwctype>	<cwchar> <cuchar>
本地化
<locale>	<codecvt>	<clocale>
容器
<span> <array> <vector>	<deque> <forward_list> <list>	<map> <set> <queue>	<unordered_map> <unordered_set> <stack>
迭代器
<iterator>
范围
<ranges>
算法
<algorithm>	<execution>
数值
<complex> <random>	<valarray> <numeric>	<bit> <numbers>	<cfenv> <cmath>
输入/输出
<iosfwd> <ios> <iomanip> <streambuf>	<istream> <ostream> <iostream>	<sstream> <fstream> <syncstream>	<cstdio> <cinttypes> <strstream>
正则表达式
<regex>
文件系统
<filesystem>
线程支持
<thread> <atomic> <mutex>	<shared_mutex> <condition_variable> <future>	<stop_token> <semaphore>	<latch> <barrier>
C 兼容
<ciso646> <cstdalign>	<cstdbool> <ccomplex>	<ctgmath>

 

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)
accumulate	对一个范围内的元素求和 (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)	应用一个函数对象，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)	应用一个函数对象，然后进行包含扫描 (函数模板)
transform_exclusive_scan (C++17)	应用一个函数对象，然后进行排除扫描 (函数模板)
gcd (C++17)	返回二个整数最大公约数的 constexpr 函数模板 (函数模板)
lcm (C++17)	返回二个整数最小公倍数的 constexpr 函数模板 (函数模板)
midpoint (C++20)	两个数值或指针间的中点 (函数模板)

概要

namespace std {
  // 累加（accumulate）
  template<class InputIt, class T>
    T accumulate(InputIt first, InputIt last, T init);
  template<class InputIt, class T, class BinaryOperation>
    T accumulate(InputIt first, InputIt last, T init, BinaryOperation binary_op);
 
  // 规约（reduce）
  template<class InputIt>
    typename iterator_traits<InputIt>::value_type
      reduce(InputIt first, InputIt last);
  template<class InputIt, class T>
    T reduce(InputIt first, InputIt last, T init);
  template<class InputIt, class T, class BinaryOperation>
    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（inner product）
  template<class InputIt1, class InputIt2, class T>
    T inner_product(InputIt1 first1, InputIt1 last1,
                    InputIt2 first2, T init);
  template<class InputIt1, class InputIt2, class T,
           class BinaryOperation1, class BinaryOperation2>
    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>
    T transform_reduce(InputIt1 first1, InputIt1 last1,
                       InputIt2 first2,
                       T init);
  template<class InputIt1, class InputIt2, class T,
           class BinaryOperation1, class BinaryOperation2>
    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>
    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>
    OutputIt partial_sum(InputIt first,
                         InputIt last,
                         OutputIt result);
  template<class InputIt, class OutputIt, class BinaryOperation>
    OutputIt partial_sum(InputIt first,
                         InputIt last,
                         OutputIt result,
                         BinaryOperation binary_op);
 
  // 不包含扫描
  template<class InputIt, class OutputIt, class T>
    OutputIt exclusive_scan(InputIt first, InputIt last,
                            OutputIt result,
                            T init);
  template<class InputIt, class OutputIt, class T, class BinaryOperation>
    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>
    OutputIt inclusive_scan(InputIt first, InputIt last, OutputIt result);
  template<class InputIt, class OutputIt, class BinaryOperation>
    OutputIt inclusive_scan(InputIt first, InputIt last,
                            OutputIt result,
                            BinaryOperation binary_op);
  template<class InputIt, class OutputIt, class BinaryOperation, class T>
    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);
 
  // 变换不包含扫描
  template<class InputIt, class OutputIt, class T,
           class BinaryOperation, class UnaryOperation>
    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>
    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>
    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);
 
  // 临差（adjacent difference）
  template<class InputIt, class OutputIt>
    OutputIt adjacent_difference(InputIt first, InputIt last,
                                 OutputIt result);
  template<class InputIt, class OutputIt, class BinaryOperation>
    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>
    void iota(ForwardIt first, ForwardIt last, 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);
}