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cppdraft/inclusive/scan.md

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+[inclusive.scan]
+
+# 26 Algorithms library [[algorithms]](./#algorithms)
+
+## 26.10 Generalized numeric operations [[numeric.ops]](numeric.ops#inclusive.scan)
+
+### 26.10.9 Inclusive scan [inclusive.scan]
+
+[🔗](#lib:inclusive_scan)
+
+`template<class InputIterator, class OutputIterator>
+  constexpr OutputIterator
+    inclusive_scan(InputIterator first, InputIterator last,
+                   OutputIterator result);
+`
+
+[1](#1)
+
+[#](http://github.com/Eelis/draft/tree/9adde4bc1c62ec234483e63ea3b70a59724c745a/source/algorithms.tex#L12816)
+
+*Effects*: Equivalent to:return inclusive_scan(first, last, result, plus<>());
+
+[🔗](#lib:inclusive_scan_)
+
+`template<class ExecutionPolicy, class ForwardIterator1, class ForwardIterator2>
+  ForwardIterator2
+    inclusive_scan(ExecutionPolicy&& exec,
+                   ForwardIterator1 first, ForwardIterator1 last,
+                   ForwardIterator2 result);
+`
+
+[2](#2)
+
+[#](http://github.com/Eelis/draft/tree/9adde4bc1c62ec234483e63ea3b70a59724c745a/source/algorithms.tex#L12834)
+
+*Effects*: Equivalent to:return inclusive_scan(std::forward<ExecutionPolicy>(exec), first, last, result, plus<>());
+
+[🔗](#lib:inclusive_scan__)
+
+`template<class InputIterator, class OutputIterator, class BinaryOperation>
+  constexpr OutputIterator
+    inclusive_scan(InputIterator first, InputIterator last,
+                   OutputIterator result, BinaryOperation binary_op);
+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 InputIterator, class OutputIterator, class BinaryOperation, class T>
+  constexpr OutputIterator
+    inclusive_scan(InputIterator first, InputIterator last,
+                   OutputIterator result, BinaryOperation binary_op, T init);
+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);
+`
+
+[3](#3)
+
+[#](http://github.com/Eelis/draft/tree/9adde4bc1c62ec234483e63ea3b70a59724c745a/source/algorithms.tex#L12868)
+
+Let U be the value type of decltype(first)[.](#3.sentence-1)
+
+[4](#4)
+
+[#](http://github.com/Eelis/draft/tree/9adde4bc1c62ec234483e63ea3b70a59724c745a/source/algorithms.tex#L12871)
+
+*Mandates*: If init is provided, all of
+
+- [(4.1)](#4.1)
+
+binary_op(init, init),
+
+- [(4.2)](#4.2)
+
+binary_op(init, *first), and
+
+- [(4.3)](#4.3)
+
+binary_op(*first, *first)
+
+are convertible to T;
+otherwise, binary_op(*first, *first) is convertible to U[.](#4.sentence-1)
+
+[5](#5)
+
+[#](http://github.com/Eelis/draft/tree/9adde4bc1c62ec234483e63ea3b70a59724c745a/source/algorithms.tex#L12883)
+
+*Preconditions*: 
+
+- [(5.1)](#5.1)
+
+  If init is provided, T meets the [*Cpp17MoveConstructible*](utility.arg.requirements#:Cpp17MoveConstructible "16.4.4.2 Template argument requirements [utility.arg.requirements]") (Table [31](utility.arg.requirements#tab:cpp17.moveconstructible "Table 31: Cpp17MoveConstructible requirements")) requirements;
+ otherwise, U meets the [*Cpp17MoveConstructible*](utility.arg.requirements#:Cpp17MoveConstructible "16.4.4.2 Template argument requirements [utility.arg.requirements]") requirements[.](#5.1.sentence-1)
+
+- [(5.2)](#5.2)
+
+  binary_op neither invalidates iterators or subranges,
+ nor modifies elements in
+ the ranges [first, last] or [result, result + (last - first)][.](#5.2.sentence-1)
+
+[6](#6)
+
+[#](http://github.com/Eelis/draft/tree/9adde4bc1c62ec234483e63ea3b70a59724c745a/source/algorithms.tex#L12897)
+
+*Effects*: For each integer K in [0, last - first)
+assigns through result + K the value of
+
+- [(6.1)](#6.1)
+
+  *GENERALIZED_NONCOMMUTATIVE_SUM*(  
+ binary_op,
+ init, *(first + 0), *(first + 1), …, *(first + K))  
+  if init is provided, or
+
+- [(6.2)](#6.2)
+
+  *GENERALIZED_NONCOMMUTATIVE_SUM*(  
+ binary_op, *(first + 0), *(first + 1), …, *(first + K))  
+  otherwise[.](#6.2.sentence-2)
+
+[7](#7)
+
+[#](http://github.com/Eelis/draft/tree/9adde4bc1c62ec234483e63ea3b70a59724c745a/source/algorithms.tex#L12910)
+
+*Returns*: The end of the resulting range beginning at result[.](#7.sentence-1)
+
+[8](#8)
+
+[#](http://github.com/Eelis/draft/tree/9adde4bc1c62ec234483e63ea3b70a59724c745a/source/algorithms.tex#L12914)
+
+*Complexity*: O(last - first) applications of binary_op[.](#8.sentence-1)
+
+[9](#9)
+
+[#](http://github.com/Eelis/draft/tree/9adde4bc1c62ec234483e63ea3b70a59724c745a/source/algorithms.tex#L12918)
+
+*Remarks*: result may be equal to first[.](#9.sentence-1)
+
+[10](#10)
+
+[#](http://github.com/Eelis/draft/tree/9adde4bc1c62ec234483e63ea3b70a59724c745a/source/algorithms.tex#L12922)
+
+[*Note [1](#note-1)*:
+
+The difference between exclusive_scan and inclusive_scan is
+that inclusive_scan includes the ith input element
+in the ith sum[.](#10.sentence-1)
+
+If binary_op is not mathematically associative,
+the behavior of inclusive_scan can be nondeterministic[.](#10.sentence-2)
+
+— *end note*]