Standard library header <numeric>

C++

Language

Headers

Freestanding and hosted implementations

Named requirements

Language support library

Concepts library (C++20)

Diagnostics library

Utilities library

Strings library

Containers library

Algorithms library

Iterators 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 header files

Language Support
<cstddef> <limits> <climits> <contract>	<cfloat> <cstdint> <new> <version>	<typeinfo> <exception> <initializer_list>	<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>
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)

Synopsis

namespace std {
  // accumulate:
  template<class InputIterator, class T>
    T accumulate(InputIterator first, InputIterator last, T init);
  template<class InputIterator, class T, class BinaryOperation>
    T accumulate(InputIterator first, InputIterator last, T init,
                 BinaryOperation binary_op);

  // reduce:
  template<class InputIterator>
    typename iterator_traits<InputIterator>::value_type
      reduce(InputIterator first, InputIterator last);
  template<class InputIterator, class T>
    T reduce(InputIterator first, InputIterator last, T init);
  template<class InputIterator, class T, class BinaryOperation>
    T reduce(InputIterator first, InputIterator last, T init, BinaryOperation binary_op);
  template<class ExecutionPolicy, class ForwardIterator>
    typename iterator_traits<ForwardIterator>::value_type
      reduce(ExecutionPolicy&& exec,
             ForwardIterator first, ForwardIterator last);
  template<class ExecutionPolicy, class ForwardIterator, class T>
    T reduce(ExecutionPolicy&& exec,
             ForwardIterator first, ForwardIterator last, T init);
  template<class ExecutionPolicy, class ForwardIterator, class T, class BinaryOperation>
    T reduce(ExecutionPolicy&& exec,
             ForwardIterator first, ForwardIterator last, T init,
             BinaryOperation binary_op);

  // inner product:
  template<class InputIterator1, class InputIterator2, class T>
    T inner_product(InputIterator1 first1, InputIterator1 last1,
                    InputIterator2 first2, T init);
  template<class InputIterator1, class InputIterator2, class T,
           class BinaryOperation1, class BinaryOperation2>
    T inner_product(InputIterator1 first1, InputIterator1 last1,
                    InputIterator2 first2, T init,
                    BinaryOperation1 binary_op1,
                    BinaryOperation2 binary_op2);

  // transform reduce:
  template<class InputIterator1, class InputIterator2, class T>
    T transform_reduce(InputIterator1 first1, InputIterator1 last1,
                       InputIterator2 first2,
                       T init);
  template<class InputIterator1, class InputIterator2, class T,
           class BinaryOperation1, class BinaryOperation2>
    T transform_reduce(InputIterator1 first1, InputIterator1 last1,
                       InputIterator2 first2,
                       T init,
                       BinaryOperation1 binary_op1,
                       BinaryOperation2 binary_op2);
  template<class InputIterator, class T,
           class BinaryOperation, class UnaryOperation>
    T transform_reduce(InputIterator first, InputIterator last,
                       T init,
                       BinaryOperation binary_op, UnaryOperation unary_op);
  template<class ExecutionPolicy,
           class ForwardIterator1, class ForwardIterator2, class T>
    T transform_reduce(ExecutionPolicy&& exec,
                       ForwardIterator1 first1, ForwardIterator1 last1,
                       ForwardIterator2 first2,
                       T init);
  template<class ExecutionPolicy,
           class ForwardIterator1, class ForwardIterator2, class T,
           class BinaryOperation1, class BinaryOperation2>
    T transform_reduce(ExecutionPolicy&& exec, 
                       ForwardIterator1 first1, ForwardIterator1 last1,
                       ForwardIterator2 first2,
                       T init,
                       BinaryOperation1 binary_op1,
                       BinaryOperation2 binary_op2);

  template<class ExecutionPolicy,
           class ForwardIterator, class T,
           class BinaryOperation, class UnaryOperation>
    T transform_reduce(ExecutionPolicy&& exec,
                       ForwardIterator first, ForwardIterator last,
                       T init,
                       BinaryOperation binary_op, UnaryOperation unary_op);

  // partial sum:
  template<class InputIterator, class OutputIterator>
    OutputIterator partial_sum(InputIterator first,
                               InputIterator last,
                               OutputIterator result);
  template<class InputIterator, class OutputIterator, class BinaryOperation>
    OutputIterator partial_sum(InputIterator first,
                               InputIterator last,
                               OutputIterator result,
                               BinaryOperation binary_op);

  // exclusive scan:
  template<class InputIterator, class OutputIterator, class T>
    OutputIterator exclusive_scan(InputIterator first, InputIterator last,
                                  OutputIterator result,
                                  T init);
  template<class InputIterator, class OutputIterator, class T, class BinaryOperation>
    OutputIterator exclusive_scan(InputIterator first, InputIterator last,
                                  OutputIterator result,
                                  T init, BinaryOperation binary_op);
  template<class ExecutionPolicy, class ForwardIterator1, class ForwardIterator2, class T>
    ForwardIterator2 exclusive_scan(ExecutionPolicy&& exec,
                                    ForwardIterator1 first, ForwardIterator1 last,
                                    ForwardIterator2 result,
                                    T init);
  template<class ExecutionPolicy, class ForwardIterator1, class ForwardIterator2, class T,
           class BinaryOperation>
    ForwardIterator2 exclusive_scan(ExecutionPolicy&& exec,
                                    ForwardIterator1 first, ForwardIterator1 last,
                                    ForwardIterator2 result,
                                    T init, BinaryOperation binary_op);

  // inclusive scan:
  template<class InputIterator, class OutputIterator>
    OutputIterator inclusive_scan(InputIterator first, InputIterator last,
                                  OutputIterator result);
  template<class InputIterator, class OutputIterator, class BinaryOperation>
    OutputIterator inclusive_scan(InputIterator first, InputIterator last,
                                  OutputIterator result,
                                  BinaryOperation binary_op);
  template<class InputIterator, class OutputIterator, class BinaryOperation, class T>
    OutputIterator inclusive_scan(InputIterator first, InputIterator last,
                                  OutputIterator result,
                                  BinaryOperation binary_op, T init);
  template<class ExecutionPolicy, class ForwardIterator1, class ForwardIterator2>
    ForwardIterator2 inclusive_scan(ExecutionPolicy&& exec,
                                    ForwardIterator1 first, ForwardIterator1 last,
                                    ForwardIterator2 result);
  template<class ExecutionPolicy, class ForwardIterator1, class ForwardIterator2,
           class BinaryOperation>
    ForwardIterator2 inclusive_scan(ExecutionPolicy&& exec,
                                    ForwardIterator1 first, ForwardIterator1 last,
                                    ForwardIterator2 result,
                                    BinaryOperation binary_op);
  template<class ExecutionPolicy, class ForwardIterator1, class ForwardIterator2,
           class BinaryOperation, class T>
    ForwardIterator2 inclusive_scan(ExecutionPolicy&& exec,
                                    ForwardIterator1 first, ForwardIterator1 last,
                                    ForwardIterator2 result,
                                    BinaryOperation binary_op, T init);

  // transform exclusive scan:
  template<class InputIterator, class OutputIterator, class T,
           class BinaryOperation, class UnaryOperation>
    OutputIterator transform_exclusive_scan(InputIterator first, InputIterator last,
                                            OutputIterator result,
                                            T init,
                                            BinaryOperation binary_op,
                                            UnaryOperation unary_op);
  template<class ExecutionPolicy,
           class ForwardIterator1, class ForwardIterator2, class T,
           class BinaryOperation, class UnaryOperation>
    ForwardIterator2 transform_exclusive_scan(ExecutionPolicy&& exec,
                                              ForwardIterator1 first,
                                              ForwardIterator1 last,
                                              ForwardIterator2 result,
                                              T init,
                                              BinaryOperation binary_op,
                                              UnaryOperation unary_op);

  // transform inclusive scan:
  template<class InputIterator, class OutputIterator,
           class BinaryOperation, class UnaryOperation>
    OutputIterator transform_inclusive_scan(InputIterator first, InputIterator last,
                                            OutputIterator result,
                                            BinaryOperation binary_op,
                                            UnaryOperation unary_op);
  template<class InputIterator, class OutputIterator,
           class BinaryOperation, class UnaryOperation, class T>
    OutputIterator transform_inclusive_scan(InputIterator first, InputIterator last,
                                            OutputIterator result,
                                            BinaryOperation binary_op,
                                            UnaryOperation unary_op,
                                            T init);
  template<class ExecutionPolicy,
           class ForwardIterator1, class ForwardIterator2,
           class BinaryOperation, class UnaryOperation>
    ForwardIterator2 transform_inclusive_scan(ExecutionPolicy&& exec,
                                              ForwardIterator1 first,
                                              ForwardIterator1 last,
                                              ForwardIterator2 result,
                                              BinaryOperation binary_op,
                                              UnaryOperation unary_op);
  template<class ExecutionPolicy,
           class ForwardIterator1, class ForwardIterator2,
           class BinaryOperation, class UnaryOperation, class T>
    ForwardIterator2 transform_inclusive_scan(ExecutionPolicy&& exec,
                                              ForwardIterator1 first,
                                              ForwardIterator1 last,
                                              ForwardIterator2 result,
                                              BinaryOperation binary_op,
                                              UnaryOperation unary_op,
                                              T init);

  // adjacent difference:
  template<class InputIterator, class OutputIterator>
    OutputIterator adjacent_difference(InputIterator first,
                                       InputIterator last,
                                       OutputIterator result);
  template<class InputIterator, class OutputIterator, class BinaryOperation>
    OutputIterator adjacent_difference(InputIterator first,
                                       InputIterator last,
                                       OutputIterator result,
                                       BinaryOperation binary_op);
  template<class ExecutionPolicy, class ForwardIterator1, class ForwardIterator2>
    ForwardIterator2 adjacent_difference(ExecutionPolicy&& exec,
                                         ForwardIterator1 first,
                                         ForwardIterator1 last,
                                         ForwardIterator2 result);
  template<class ExecutionPolicy, class ForwardIterator1, class ForwardIterator2,
           class BinaryOperation>
    ForwardIterator2 adjacent_difference(ExecutionPolicy&& exec,
                                         ForwardIterator1 first,
                                         ForwardIterator1 last,
                                         ForwardIterator2 result,
                                         BinaryOperation binary_op);

  // iota:
  template<class ForwardIterator, class T>
    void iota(ForwardIterator first, ForwardIterator 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);
}