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cppdraft/transform/inclusive/scan.md

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+[transform.inclusive.scan]
+
+# 26 Algorithms library [[algorithms]](./#algorithms)
+
+## 26.10 Generalized numeric operations [[numeric.ops]](numeric.ops#transform.inclusive.scan)
+
+### 26.10.11 Transform inclusive scan [transform.inclusive.scan]
+
+[🔗](#lib:transform_inclusive_scan)
+
+`template<class InputIterator, class OutputIterator,
+         class BinaryOperation, class UnaryOperation>
+  constexpr OutputIterator
+    transform_inclusive_scan(InputIterator first, InputIterator last,
+                             OutputIterator result,
+                             BinaryOperation binary_op, UnaryOperation unary_op);
+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 InputIterator, class OutputIterator,
+         class BinaryOperation, class UnaryOperation, class T>
+  constexpr 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, class T>
+  ForwardIterator2
+    transform_inclusive_scan(ExecutionPolicy&& exec,
+                             ForwardIterator1 first, ForwardIterator1 last,
+                             ForwardIterator2 result,
+                             BinaryOperation binary_op, UnaryOperation unary_op,
+                             T init);
+`
+
+[1](#1)
+
+[#](http://github.com/Eelis/draft/tree/9adde4bc1c62ec234483e63ea3b70a59724c745a/source/algorithms.tex#L13046)
+
+Let U be the value type of decltype(first)[.](#1.sentence-1)
+
+[2](#2)
+
+[#](http://github.com/Eelis/draft/tree/9adde4bc1c62ec234483e63ea3b70a59724c745a/source/algorithms.tex#L13049)
+
+*Mandates*: If init is provided, all of
+
+- [(2.1)](#2.1)
+
+binary_op(init, init),
+
+- [(2.2)](#2.2)
+
+binary_op(init, unary_op(*first)), and
+
+- [(2.3)](#2.3)
+
+binary_op(unary_op(*first), unary_op(*first))
+
+are convertible to T;
+otherwise, binary_op(unary_op(*first), unary_op(*first)) is convertible to U[.](#2.sentence-1)
+
+[3](#3)
+
+[#](http://github.com/Eelis/draft/tree/9adde4bc1c62ec234483e63ea3b70a59724c745a/source/algorithms.tex#L13061)
+
+*Preconditions*: 
+
+- [(3.1)](#3.1)
+
+  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[.](#3.1.sentence-1)
+
+- [(3.2)](#3.2)
+
+  Neither unary_op nor binary_op invalidates
+ iterators or subranges, nor modifies elements in
+ the ranges [first, last] or [result, result + (last - first)][.](#3.2.sentence-1)
+
+[4](#4)
+
+[#](http://github.com/Eelis/draft/tree/9adde4bc1c62ec234483e63ea3b70a59724c745a/source/algorithms.tex#L13075)
+
+*Effects*: For each integer K in [0, last - first)
+assigns through result + K the value of
+
+- [(4.1)](#4.1)
+
+  *GENERALIZED_NONCOMMUTATIVE_SUM*(  
+ binary_op, init,  
+ unary_op(*(first + 0)), unary_op(*(first + 1)), …, unary_op(*(first + K)))  
+   if init is provided, or
+
+- [(4.2)](#4.2)
+
+  *GENERALIZED_NONCOMMUTATIVE_SUM*(  
+ binary_op,  
+ unary_op(*(first + 0)), unary_op(*(first + 1)), …, unary_op(*(first + K)))  
+   otherwise[.](#4.2.sentence-2)
+
+[5](#5)
+
+[#](http://github.com/Eelis/draft/tree/9adde4bc1c62ec234483e63ea3b70a59724c745a/source/algorithms.tex#L13088)
+
+*Returns*: The end of the resulting range beginning at result[.](#5.sentence-1)
+
+[6](#6)
+
+[#](http://github.com/Eelis/draft/tree/9adde4bc1c62ec234483e63ea3b70a59724c745a/source/algorithms.tex#L13092)
+
+*Complexity*: O(last - first) applications each
+of unary_op and binary_op[.](#6.sentence-1)
+
+[7](#7)
+
+[#](http://github.com/Eelis/draft/tree/9adde4bc1c62ec234483e63ea3b70a59724c745a/source/algorithms.tex#L13097)
+
+*Remarks*: result may be equal to first[.](#7.sentence-1)
+
+[8](#8)
+
+[#](http://github.com/Eelis/draft/tree/9adde4bc1c62ec234483e63ea3b70a59724c745a/source/algorithms.tex#L13101)
+
+[*Note [1](#note-1)*:
+
+The difference between transform_exclusive_scan andtransform_inclusive_scan is that transform_inclusive_scan includes the ith input element in the ith sum[.](#8.sentence-1)
+
+If binary_op is not mathematically associative,
+the behavior of transform_inclusive_scan can be nondeterministic[.](#8.sentence-2)
+
+transform_inclusive_scan does not
+apply unary_op to init[.](#8.sentence-3)
+
+— *end note*]