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Standard library header <numeric>

From cppreference.net
C++
Standard library headers

此头文件是 numeric 库的组成部分。

函数

(C++11)
以起始值的连续递增填充范围
(函数模板)
(C++23)
用起始值的连续递增填充范围
(算法函数对象)
对范围内的元素进行求和或折叠操作
(函数模板)
(C++17)
类似于 std::accumulate ，但允许无序计算
(函数模板)
(C++17)
应用可调用对象，然后进行无序规约
(函数模板)
计算两个元素范围的内积
(函数模板)
计算范围内相邻元素之间的差值
(函数模板)
计算范围内元素的部分和
(函数模板)
(C++17)
与 std::partial_sum 类似，但在第 i 次 求和时包含第 i 个 输入元素
(函数模板)
(C++17)
类似于 std::partial_sum ，但从第 i 个 累加结果中排除第 i 个 输入元素
(函数模板)
(C++17)
应用可调用对象后计算包含性扫描
(函数模板)
(C++17)
应用可调用对象后计算排除性扫描
(函数模板)
(C++17)
计算两个整数的最大公约数
(函数模板)
(C++17)
计算两个整数的最小公倍数
(函数模板)
(C++20)
两个数值或指针之间的中点
(函数模板)
(C++26)
对两个整数进行饱和加法运算
(函数模板)
(C++26)
对两个整数进行饱和减法运算
(函数模板)
(C++26)
对两个整数进行饱和乘法运算
(函数模板)
(C++26)
对两个整数进行饱和除法运算
(函数模板)
(C++26)
返回限制在另一整数类型范围内的整数值
(函数模板)

概要 

namespace std {
  // accumulate
  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);
  // reduce
  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);
  // transform reduce
  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);
  // exclusive scan
  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);
  // inclusive scan
  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);
  // 变换独占扫描
  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);
  // adjacent difference
  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);
  }
  // greatest common divisor
  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;           // freestanding
  template<class T>
    constexpr T sub_sat(T x, T y) noexcept;           // freestanding
  template<class T>
    constexpr T mul_sat(T x, T y) noexcept;           // freestanding
  template<class T>
    constexpr T div_sat(T x, T y) noexcept;           // freestanding
  template<class T, class U>
    constexpr T saturate_cast(U x) noexcept;          // freestanding
}