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Difference between revisions of "cpp/header/numeric"

From cppreference.com
< cpp‎ | header
(Added C++17 functions, source: cpp/numeric)
(move <numeric> synopsis to template)
 
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{{cpp/header/navbar}}
 
{{cpp/header/navbar}}
  
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This header is part of the [[cpp/numeric|numeric]] library.
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This header is part of the {{lt|cpp/numeric}} library.
  
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===Functions===
 
 
{{dsc begin}}
 
{{dsc begin}}
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{{dsc inc | cpp/algorithm/dsc iota}}
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{{dsc h1|Functions}}
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{{dsc inc | cpp/algorithm/dsc accumulate}}
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{{dsc inc|cpp/algorithm/dsc iota}}
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{{dsc inc | cpp/algorithm/dsc reduce}}
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{{dsc inc|cpp/algorithm/ranges/dsc iota}}
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{{dsc inc | cpp/algorithm/dsc transform_reduce}}
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{{dsc inc|cpp/algorithm/dsc accumulate}}
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{{dsc inc | cpp/algorithm/dsc inner_product}}
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{{dsc inc|cpp/algorithm/dsc reduce}}
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{{dsc inc | cpp/algorithm/dsc adjacent_difference}}
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{{dsc inc|cpp/algorithm/dsc transform_reduce}}
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{{dsc inc | cpp/algorithm/dsc partial_sum}}
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{{dsc inc|cpp/algorithm/dsc inner_product}}
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{{dsc inc | cpp/algorithm/dsc inclusive_scan}}
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{{dsc inc|cpp/algorithm/dsc adjacent_difference}}
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{{dsc inc | cpp/algorithm/dsc exclusive_scan}}
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{{dsc inc|cpp/algorithm/dsc partial_sum}}
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{{dsc inc | cpp/algorithm/dsc transform_inclusive_scan}}
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{{dsc inc|cpp/algorithm/dsc inclusive_scan}}
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{{dsc inc | cpp/algorithm/dsc transform_exclusive_scan}}
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{{dsc inc|cpp/algorithm/dsc exclusive_scan}}
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{{dsc inc | cpp/numeric/dsc gcd}}
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{{dsc inc|cpp/algorithm/dsc transform_inclusive_scan}}
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{{dsc inc | cpp/numeric/dsc lcm}}
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{{dsc inc|cpp/algorithm/dsc transform_exclusive_scan}}
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{{dsc inc|cpp/numeric/dsc gcd}}
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{{dsc inc|cpp/numeric/dsc lcm}}
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{{dsc inc|cpp/numeric/dsc midpoint}}
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{{dsc inc|cpp/numeric/dsc add_sat}}
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{{dsc inc|cpp/numeric/dsc sub_sat}}
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{{dsc inc|cpp/numeric/dsc mul_sat}}
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{{dsc inc|cpp/numeric/dsc div_sat}}
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{{dsc inc|cpp/numeric/dsc saturate_cast}}
 
{{dsc end}}
 
{{dsc end}}
  
 
===Synopsis===
 
===Synopsis===
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{{source|
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{{cpp/synopsis/numeric}}
  
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namespace std {
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{{langlinks|ja|zh}}
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    template <class InputIterator, class T>
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        T accumulate(InputIterator first, InputIterator last, T init);
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    template <class InputIterator, class T, class BinaryOperation>
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        T accumulate(InputIterator first, InputIterator last, T init,
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            BinaryOperation binary_op);
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    template <class InputIterator1, class InputIterator2, class T>
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        T inner_product(InputIterator1 first1, InputIterator1 last1,
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            InputIterator2 first2, T init);
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    template <class InputIterator1, class InputIterator2, class T,
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            class BinaryOperation1, class BinaryOperation2>
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        T inner_product(InputIterator1 first1, InputIterator1 last1,
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            InputIterator2 first2, T init,
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            BinaryOperation1 binary_op1,
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            BinaryOperation2 binary_op2);
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    template <class InputIterator, class OutputIterator>
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        OutputIterator partial_sum(InputIterator first,
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            InputIterator last,
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            OutputIterator result);
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    template <class InputIterator, class OutputIterator,
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            class BinaryOperation>
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        OutputIterator partial_sum(InputIterator first,
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            InputIterator last,
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            OutputIterator result,
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            BinaryOperation binary_op);
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    template <class InputIterator, class OutputIterator>
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        OutputIterator adjacent_difference(InputIterator first,
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            InputIterator last,
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            OutputIterator result);
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    template <class InputIterator, class OutputIterator,
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            class BinaryOperation>
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        OutputIterator adjacent_difference(InputIterator first,
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            InputIterator last,
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            OutputIterator result,
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            BinaryOperation binary_op);
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    template <class ForwardIterator, class T>
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        void iota(ForwardIterator first, ForwardIterator last, T value);
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}
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}}
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Latest revision as of 06:16, 27 November 2023

 
C++
 
Standard library headers
Algorithms
<algorithm>
<numeric>
Strings
<cctype>
<cstring>
<cuchar> (C++11)
<cwchar>
<cwctype>
<string_view> (C++17)
<string>
Text processing
<clocale>
<codecvt> (C++11/17/26*)
<locale>
<regex> (C++11)
<text_encoding> (C++26)   
Numerics
<cfenv> (C++11)
<cmath>
<complex>
<linalg> (C++26)
<numbers> (C++20)
<random> (C++11)
<valarray>
Time
<chrono> (C++11)
<ctime>
C compatibility
<ccomplex> (C++11/17/20*)
<ciso646> (until C++20)
<cstdalign> (C++11/17/20*)
<cstdbool> (C++11/17/20*)
<ctgmath> (C++11/17/20*)
 

This header is part of the numeric library.

Functions

(C++11)
 fills a range with successive increments of the starting value
(function template) [edit]
(C++23)
 fills a range with successive increments of the starting value
(niebloid)[edit]
sums up or folds a range of elements
(function template) [edit]
(C++17)
 similar to std::accumulate, except out of order
(function template) [edit]
(C++17)
 applies an invocable, then reduces out of order
(function template) [edit]
computes the inner product of two ranges of elements
(function template) [edit]
computes the differences between adjacent elements in a range
(function template) [edit]
computes the partial sum of a range of elements
(function template) [edit]
(C++17)
 similar to std::partial_sum, includes the ith input element in the ith sum
(function template) [edit]
(C++17)
 similar to std::partial_sum, excludes the ith input element from the ith sum
(function template) [edit]
(C++17)
 applies an invocable, then calculates inclusive scan
(function template) [edit]
(C++17)
 applies an invocable, then calculates exclusive scan
(function template) [edit]
(C++17)
 computes the greatest common divisor of two integers
(function template) [edit]
(C++17)
 computes the least common multiple of two integers
(function template) [edit]
(C++20)
 midpoint between two numbers or pointers
(function template) [edit]
(C++26)
 saturating addition operation on two integers
(function template) [edit]
(C++26)
 saturating subtraction operation on two integers
(function template) [edit]
(C++26)
 saturating multiplication operation on two integers
(function template) [edit]
(C++26)
 saturating division operation on two integers
(function template) [edit]
(C++26)
 returns an integer value clamped to the range of a another integer type
(function template) [edit]

[edit] Synopsis

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);
 
  // inner product
  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);
 
  // partial sum
  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);
 
  // transform exclusive scan
  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);
 
  // transform inclusive scan
  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);
 
  // 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);
 
  // saturation arithmetic
  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
}
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