Standard library header <numeric>

 

C++

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Standard Library Headers

Freestanding and hosted implementations

Named requirements

Language support library

Concepts library (C++20)

Diagnostics library

Utilities library

Strings library

Containers library

Iterators library

Ranges library (C++20)

Algorithms library

Numerics library

Input/output library

Localizations library

Regular expressions library (C++11)

Atomic operations library (C++11)

Thread support library (C++11)

Filesystem library (C++17)

Technical Specifications

 

Standard Library headers

Language Support
<cstddef> <limits> <climits> <contract>	<cfloat> <cstdint> <new> <coroutine>	<typeinfo> <exception> <initializer_list> <version>	<csignal> <csetjmp> <cstdarg>
Concepts
<concepts>
Diagnostics
<stdexcept>	<cassert>	<cerrno>	<system_error>
General utilities
<utility> <memory> <memory_resource> <scoped_allocator>     <compare>	<bitset> <tuple> <optional> <any> <variant>	<type_traits> <ratio> <chrono> <typeindex> <functional>	<ctime> <cstdlib>
Strings
<string> <string_view>	<cctype> <cwctype>	<cwchar> <cuchar>	<cstring> <charconv>
Localization
<locale>	<codecvt>	<clocale>
Containers
<span> <array> <vector>	<deque> <forward_list> <list>	<map> <set> <queue>	<unordered_map> <unordered_set> <stack>
Iterators
<iterator>
Ranges
<ranges>
Algorithms
<algorithm>	<execution>
Numerics
<complex> <random>	<valarray> <numeric>	<cfenv> <cmath>	<bit>
Input/Output
<iosfwd> <ios> <iomanip> <streambuf>	<istream> <ostream> <iostream>	<sstream> <fstream> <syncstream>	<cstdio> <cinttypes> <strstream>
Regular expressions
<regex>
Filesystem support
<filesystem>
Thread support
<thread> <atomic>	<mutex> <shared_mutex>	<condition_variable> <future>
C compatibility
<ciso646> <cstdalign>	<cstdbool> <ccomplex>	<ctgmath>

 

This header is part of the numeric library.

Functions

iota (C++11)	fills a range with successive increments of the starting value (function template)
accumulate	sums up a range of elements (function template)
reduce (C++17)	similar to std::accumulate, except out of order (function template)
transform_reduce (C++17)	applies a functor, then reduces out of order (function template)
inner_product	computes the inner product of two ranges of elements (function template)
adjacent_difference	computes the differences between adjacent elements in a range (function template)
partial_sum	computes the partial sum of a range of elements (function template)
inclusive_scan (C++17)	similar to std::partial_sum, includes the ith input element in the ith sum (function template)
exclusive_scan (C++17)	similar to std::partial_sum, excludes the ith input element from the ith sum (function template)
transform_inclusive_scan (C++17)	applies a functor, then calculates inclusive scan (function template)
transform_exclusive_scan (C++17)	applies a functor, then calculates exclusive scan (function template)
gcd (C++17)	constexpr function template returning the greatest common divisor of two integers (function template)
lcm (C++17)	constexpr function template returning the least common multiple of two integers (function template)
midpoint (C++20)	midpoint between two numbers or pointers (function template)

Synopsis

namespace std {
  // 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);
 
  // 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);
 
  // 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);
 
  // transform reduce
  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);
 
  // partial sum
  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);
 
  // exclusive scan
  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);
 
  // inclusive scan
  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);
 
  // transform exclusive scan
  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);
 
  // transform inclusive scan
  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);
 
  // 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);
 
  // greatest common divisor
  template<class M, class N>
    constexpr common_type_t<M, N> gcd(M m, N n);
 
  // least common multiple
  template<class M, class N>
    constexpr common_type_t<M, N> lcm(M m, N n);
 
  // midpoint
  template<class T>
    constexpr T midpoint(T a, T b) noexcept;
  template<class T>
    constexpr T* midpoint(T* a, T* b);
}