From 037f5dae06a963611739cddf4cd5c63074bc526f Mon Sep 17 00:00:00 2001 From: Jared Hoberock Date: Tue, 7 Apr 2015 14:18:55 -0700 Subject: [PATCH 1/2] Add N4407 with cleaned up formatting --- README.md | 24 ++--- algorithms.html | 169 +++++++++++++-------------------- exceptions.html | 16 +--- execution_policies.html | 10 +- front_matter.html | 6 +- general.html | 5 +- parallelism-ts.html | 201 +++++++++++++++------------------------- parallelism-ts.pdf | Bin 141908 -> 141155 bytes 8 files changed, 157 insertions(+), 274 deletions(-) diff --git a/README.md b/README.md index d41d3ce..9ca0c39 100644 --- a/README.md +++ b/README.md @@ -1,5 +1,5 @@ - Document Number: N4353 - Date: 2015-01-08 + Document Number: N4408 + Date: 2015-04-10 Revises: Project: Programming Language C++ Project Number: TS 19570 @@ -7,25 +7,15 @@ NVIDIA Corporation jhoberock@nvidia.com -# Parallelism TS Editor's Report, pre-DTS ballot +# Parallelism TS Editor's Report, pre-Lenexa mailing -N4352 is the latest Parallelism TS Working Draft. It contains editorial changes to the Parallelism TS as directed by an editing committee appointed during the Urbana meeting to approve the correctness of the Parallelism TS working paper. +N4407 is the latest Parallelism TS Working Draft. It contains editorial changes to the Parallelism TS to address whitespace and other formatting issues. -N4352 updates the previous draft, N4310, published in the post-Urbana mailing. +N4407 updates the previous draft, N4352, published in the midterm mailing. -N4354 is document N4352 reformatted as a DTS ballot document. It updates N4312, which was published in the post-Urbana mailing. +N4409 is document N4407 reformatted as a TS document. It updates N4354, which was published in the midterm mailing. ## Editorial Changes -1. A missing signature for `execution_policy::type` was added to the synopsis in Section 2.7. -2. A missing `ExecutionPolicy` overload signature for `for_each_n` was added to the synopsis in Section 4.3.1. -3. Missing `ExecutionPolicy` overload signatures for `reduce`, `exclusive_scan`, `inclusive_scan`, `transform_reduce`, `transform_exclusive_scan`, and `transform_inclusive_scan` were added to the synopsis in Section 4.4.1. - -## Acknowledgements - -Thanks to the review committee, who identified these issues. - -* Hans Boehm -* Lawrence Crowl -* Alisdair Meredith +Eliminated spurious whitespace and superfluous paragraph numbers. diff --git a/algorithms.html b/algorithms.html index c957c48..90fed62 100644 --- a/algorithms.html +++ b/algorithms.html @@ -389,13 +389,11 @@

Header <experimental/algorithm> synopsis

For each

- - template<class ExecutionPolicy, - class InputIterator, class Function> - void for_each(ExecutionPolicy&& exec, - InputIterator first, InputIterator last, - Function f); - + template<class ExecutionPolicy, + class InputIterator, class Function> +void for_each(ExecutionPolicy&& exec, + InputIterator first, InputIterator last, + Function f); Applies f to the result of dereferencing every iterator in the range [first,last). @@ -426,11 +424,9 @@

For each

 - - template<class InputIterator, class Size, class Function> - InputIterator for_each_n(InputIterator first, Size n, - Function f); - + template<class InputIterator, class Size, class Function> +InputIterator for_each_n(InputIterator first, Size n, + Function f); Function shall meet the requirements of MoveConstructible @@ -460,13 +456,11 @@

For each

 - - template<class ExecutionPolicy, - class InputIterator, class Size, class Function> - InputIterator for_each_n(ExecutionPolicy && exec, - InputIterator first, Size n, - Function f); - + template<class ExecutionPolicy, + class InputIterator, class Size, class Function> +InputIterator for_each_n(ExecutionPolicy && exec, + InputIterator first, Size n, + Function f); Applies f to the result of dereferencing every iterator in the range @@ -669,11 +663,9 @@

Header <experimental/numeric> synopsis

Reduce

- - template<class InputIterator> - typename iterator_traits<InputIterator>::value_type - reduce(InputIterator first, InputIterator last); - + template<class InputIterator> +typename iterator_traits<InputIterator>::value_type + reduce(InputIterator first, InputIterator last); Same as reduce(first, last, typename iterator_traits<InputIterator>::value_type{}). @@ -681,10 +673,8 @@

Reduce

 - - template<class InputIterator, class T> - T reduce(InputIterator first, InputIterator last, T init); - + template<class InputIterator, class T> +T reduce(InputIterator first, InputIterator last, T init); Same as reduce(first, last, init, plus<>()). @@ -692,11 +682,9 @@

Reduce

 - - template<class InputIterator, class T, class BinaryOperation> - T reduce(InputIterator first, InputIterator last, T init, - BinaryOperation binary_op); - + template<class InputIterator, class T, class BinaryOperation> +T reduce(InputIterator first, InputIterator last, T init, + BinaryOperation binary_op); GENERALIZED_SUM(binary_op, init, *first, ..., *(first + (last - first) - 1)). @@ -722,14 +710,10 @@

Reduce

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> +OutputIterator exclusive_scan(InputIterator first, InputIterator last, + OutputIterator result, + T init); Same as exclusive_scan(first, last, result, init, plus<>()). @@ -737,14 +721,10 @@

Exclusive scan

 - - 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 InputIterator, class OutputIterator, class T, class BinaryOperation> +OutputIterator exclusive_scan(InputIterator first, InputIterator last, + OutputIterator result, + T init, BinaryOperation binary_op); Assigns through each iterator i in [result,result + (last - first)) the @@ -777,12 +757,9 @@

Exclusive scan

Inclusive scan

- - template<class InputIterator, class OutputIterator> - OutputIterator - inclusive_scan(InputIterator first, InputIterator last, - OutputIterator result); - + template<class InputIterator, class OutputIterator> +OutputIterator inclusive_scan(InputIterator first, InputIterator last, + OutputIterator result); Same as inclusive_scan(first, last, result, plus<>()). @@ -790,21 +767,14 @@

Inclusive scan

 - - 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> - OutputIterator - inclusive_scan(InputIterator first, InputIterator last, - OutputIterator result, - BinaryOperation binary_op, T init); - + 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> +OutputIterator inclusive_scan(InputIterator first, InputIterator last, + OutputIterator result, + BinaryOperation binary_op, T init); Assigns through each iterator i in [result,result + (last - first)) the value of @@ -839,11 +809,9 @@

Inclusive scan

Transform reduce

- - template<class InputIterator, class UnaryFunction, class T, class BinaryOperation> - T transform_reduce(InputIterator first, InputIterator last, - UnaryOperation unary_op, T init, BinaryOperation binary_op); - + template<class InputIterator, class UnaryFunction, class T, class BinaryOperation> +T transform_reduce(InputIterator first, InputIterator last, + UnaryOperation unary_op, T init, BinaryOperation binary_op); GENERALIZED_SUM(binary_op, init, unary_op(*first), ..., unary_op(*(first + (last - first) - 1))). @@ -867,16 +835,13 @@

Transform reduce

Transform exclusive scan

- - template<class InputIterator, class OutputIterator, - class UnaryOperation, - class T, class BinaryOperation> - OutputIterator - transform_exclusive_scan(InputIterator first, InputIterator last, - OutputIterator result, - UnaryOperation unary_op, - T init, BinaryOperation binary_op); - + template<class InputIterator, class OutputIterator, + class UnaryOperation, + class T, class BinaryOperation> +OutputIterator transform_exclusive_scan(InputIterator first, InputIterator last, + OutputIterator result, + UnaryOperation unary_op, + T init, BinaryOperation binary_op); Assigns through each iterator i in [result,result + (last - first)) the value of @@ -908,25 +873,21 @@

Transform exclusive scan

Transform inclusive scan

- - template<class InputIterator, class OutputIterator, - class UnaryOperation, - class BinaryOperation> - OutputIterator - transform_inclusive_scan(InputIterator first, InputIterator last, - OutputIterator result, - UnaryOperation unary_op, - BinaryOperation binary_op); - - template<class InputIterator, class OutputIterator, - class UnaryOperation, - class BinaryOperation, class T> - OutputIterator - transform_inclusive_scan(InputIterator first, InputIterator last, - OutputIterator result, - UnaryOperation unary_op, - BinaryOperation binary_op, T init); - + template<class InputIterator, class OutputIterator, + class UnaryOperation, + class BinaryOperation> +OutputIterator transform_inclusive_scan(InputIterator first, InputIterator last, + OutputIterator result, + UnaryOperation unary_op, + BinaryOperation binary_op); + + template<class InputIterator, class OutputIterator, + class UnaryOperation, + class BinaryOperation, class T> +OutputIterator transform_inclusive_scan(InputIterator first, InputIterator last, + OutputIterator result, + UnaryOperation unary_op, + BinaryOperation binary_op, T init); Assigns through each iterator i in [result,result + (last - first)) the value of diff --git a/exceptions.html b/exceptions.html index 5a85255..7dd96cd 100644 --- a/exceptions.html +++ b/exceptions.html @@ -90,9 +90,7 @@

Header <experimental/exception_list> synopsis

- - size_t size() const noexcept; - + size_t size() const noexcept; The number of exception_ptr objects contained within the exception_list. @@ -104,9 +102,7 @@

Header <experimental/exception_list> synopsis

 - - iterator begin() const noexcept; - + iterator begin() const noexcept; An iterator referring to the first exception_ptr object contained within the exception_list. @@ -114,9 +110,7 @@

Header <experimental/exception_list> synopsis

 - - iterator end() const noexcept; - + iterator end() const noexcept; An iterator that is past the end of the owned sequence. @@ -124,9 +118,7 @@

Header <experimental/exception_list> synopsis

 - - const char* what() const noexcept override; - + const char* what() const noexcept override; An implementation-defined NTBS. diff --git a/execution_policies.html b/execution_policies.html index aa1fcd9..5e6be39 100644 --- a/execution_policies.html +++ b/execution_policies.html @@ -191,18 +191,14 @@

execution_policy construct/assign

execution_policy object access

- - const type_info& type() const noexcept; - + const type_info& type() const noexcept; typeid(T), such that T is the type of the execution policy object contained by *this. - - template<class T> T* get() noexcept; - template<class T> const T* get() const noexcept; - + template<class T> T* get() noexcept; + template<class T> const T* get() const noexcept; If target_type() == typeid(T), a pointer to the stored execution policy object; otherwise a null pointer. diff --git a/front_matter.html b/front_matter.html index 505e4f8..ad32aad 100644 --- a/front_matter.html +++ b/front_matter.html @@ -1,8 +1,8 @@ -N4352 +N4407 19570 - - N4310 + + N4352 Jared Hoberock
NVIDIA Corporation
diff --git a/general.html b/general.html index 725cc1a..c99c435 100644 --- a/general.html +++ b/general.html @@ -78,7 +78,6 @@

Terms and definitions

A parallel algorithm is a function template described by this Technical Specification declared in namespace std::experimental::parallel::v1 with a formal template parameter named ExecutionPolicy.

-

Parallel algorithms access objects indirectly accessible via their arguments by invoking the following functions: @@ -96,8 +95,7 @@

Terms and definitions

- These functions are herein called element access functions.
-
+ These functions are herein called element access functions. The sort function may invoke the following element access functions: @@ -117,7 +115,6 @@

Terms and definitions

 -

diff --git a/parallelism-ts.html b/parallelism-ts.html index e935232..1d8c84e 100644 --- a/parallelism-ts.html +++ b/parallelism-ts.html @@ -1047,7 +1047,6 @@

Contents

A parallel algorithm is a function template described by this Technical Specification declared in namespace std::experimental::parallel::v1 with a formal template parameter named ExecutionPolicy.

-

Parallel algorithms access objects indirectly accessible via their arguments by invoking the following functions: @@ -1066,7 +1065,7 @@

Contents

- These functions are herein called element access functions.

+        These functions are herein called element access functions.
   
         
     
@@ -1092,7 +1091,6 @@ 
Contents

         
     — end example ]
   
-      

     
     
   
@@ -1407,9 +1405,7 @@ 
Contents

 
       
     
-    

-          const type_info& type() const noexcept;
-        

+    
const type_info& type() const noexcept;

 
     

       
@@ -1425,14 +1421,12 @@ 
Contents

 
       
     
-    

-          template<class T> T* get() noexcept;
-          template<class T> const T* get() const noexcept;
-        

+    
template<class T> T* get() noexcept;template<class T> const T* get() const noexcept;

 
     

       
-        
+      
+      
 
         
     
@@ -1597,9 +1591,7 @@ 
Contents

 
       
     
-    

-          size_t size() const noexcept;
-        

+    
size_t size() const noexcept;

 
     

       
@@ -1624,9 +1616,7 @@ 
Contents

 
       
     
-    

-          iterator begin() const noexcept;
-        

+    
iterator begin() const noexcept;

 
     

       
@@ -1644,9 +1634,7 @@ 
Contents

 
       
     
-    

-          iterator end() const noexcept;
-        

+    
iterator end() const noexcept;

 
     

       
@@ -1664,9 +1652,7 @@ 
Contents

 
       
     
-    

-          const char* what() const noexcept override;
-        

+    
const char* what() const noexcept override;

 
     

       
@@ -2171,13 +2157,11 @@ 
Contents

 
       
     
-    

-          template<class ExecutionPolicy,
-                   class InputIterator, class Function>
-            void for_each(ExecutionPolicy&& exec,
-                          InputIterator first, InputIterator last,
-                          Function f);
-        

+    
template<class ExecutionPolicy,
+      class InputIterator, class Function>
+void for_each(ExecutionPolicy&& exec,
+              InputIterator first, InputIterator last,
+              Function f);

 
     

       
@@ -2233,11 +2217,9 @@ 
Contents

 
       
     
-    

-          template<class InputIterator, class Size, class Function>
-            InputIterator for_each_n(InputIterator first, Size n,
-                                     Function f);
-        

+    
template<class InputIterator, class Size, class Function>
+InputIterator for_each_n(InputIterator first, Size n,
+                         Function f);

 
     

       
@@ -2292,13 +2274,11 @@ 
Contents

 
       
     
-    

-        template<class ExecutionPolicy,
-                 class InputIterator, class Size, class Function>
-                 InputIterator for_each_n(ExecutionPolicy && exec,
-                                          InputIterator first, Size n,
-                                          Function f);
-        

+    
template<class ExecutionPolicy,
+      class InputIterator, class Size, class Function>
+InputIterator for_each_n(ExecutionPolicy && exec,
+                         InputIterator first, Size n,
+                         Function f);

 
     

       
@@ -2543,11 +2523,9 @@ 
Contents

 
       
     
-    

-          template<class InputIterator>
-            typename iterator_traits<InputIterator>::value_type
-              reduce(InputIterator first, InputIterator last);
-        

+    
template<class InputIterator>
+typename iterator_traits<InputIterator>::value_type
+    reduce(InputIterator first, InputIterator last);

 
     

       
@@ -2565,10 +2543,8 @@ 
Contents

 
       
     
-    

-          template<class InputIterator, class T>
-            T reduce(InputIterator first, InputIterator last, T init);
-        

+    
template<class InputIterator, class T>
+T reduce(InputIterator first, InputIterator last, T init);

 
     

       
@@ -2586,11 +2562,9 @@ 
Contents

 
       
     
-    

-          template<class InputIterator, class T, class BinaryOperation>
-            T reduce(InputIterator first, InputIterator last, T init,
-                     BinaryOperation binary_op);
-        

+    
template<class InputIterator, class T, class BinaryOperation>
+T reduce(InputIterator first, InputIterator last, T init,
+         BinaryOperation binary_op);

 
     

       
@@ -2642,14 +2616,10 @@ 
Contents

 
       
     
-    

-          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>
+OutputIterator exclusive_scan(InputIterator first, InputIterator last,
+                              OutputIterator result,
+                              T init);

 
     

       
@@ -2667,14 +2637,10 @@ 
Contents

 
       
     
-    

-          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 InputIterator, class OutputIterator, class T, class BinaryOperation>
+OutputIterator exclusive_scan(InputIterator first, InputIterator last,
+                              OutputIterator result,
+                              T init, BinaryOperation binary_op);

 
     

       
@@ -2736,12 +2702,9 @@ 
Contents

 
       
     
-    

-          template<class InputIterator, class OutputIterator>
-            OutputIterator
-              inclusive_scan(InputIterator first, InputIterator last,
-                             OutputIterator result);
-        

+    
template<class InputIterator, class OutputIterator>
+OutputIterator inclusive_scan(InputIterator first, InputIterator last,
+                              OutputIterator result);

 
     

       
@@ -2759,25 +2722,18 @@ 
Contents

 
       
     
-    

-          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>
-            OutputIterator
-              inclusive_scan(InputIterator first, InputIterator last,
-                             OutputIterator result,
-                             BinaryOperation binary_op, T init);
-        

+    
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>
+OutputIterator inclusive_scan(InputIterator first, InputIterator last,
+                              OutputIterator result,
+                              BinaryOperation binary_op, T init);

 
     

       
         
+        
 
         
     
@@ -2837,11 +2793,9 @@ 
Contents

 
       
     
-    

-          template<class InputIterator, class UnaryFunction, class T, class BinaryOperation>
-          T transform_reduce(InputIterator first, InputIterator last,
-                             UnaryOperation unary_op, T init, BinaryOperation binary_op);
-        

+    
template<class InputIterator, class UnaryFunction, class T, class BinaryOperation>
+T transform_reduce(InputIterator first, InputIterator last,
+                   UnaryOperation unary_op, T init, BinaryOperation binary_op);

 
     

       
@@ -2891,16 +2845,13 @@ 
Contents

 
       
     
-    

-          template<class InputIterator, class OutputIterator,
-                   class UnaryOperation,
-                   class T, class BinaryOperation>
-            OutputIterator
-              transform_exclusive_scan(InputIterator first, InputIterator last,
-                                       OutputIterator result,
-                                       UnaryOperation unary_op,
-                                       T init, BinaryOperation binary_op);
-        

+    
template<class InputIterator, class OutputIterator,
+      class UnaryOperation,
+      class T, class BinaryOperation>
+OutputIterator transform_exclusive_scan(InputIterator first, InputIterator last,
+                                        OutputIterator result,
+                                        UnaryOperation unary_op,
+                                        T init, BinaryOperation binary_op);

 
     

       
@@ -2961,30 +2912,26 @@ 
Contents

 
       
     
-    

-          template<class InputIterator, class OutputIterator,
-                   class UnaryOperation,
-                   class BinaryOperation>
-            OutputIterator
-              transform_inclusive_scan(InputIterator first, InputIterator last,
-                                       OutputIterator result,
-                                       UnaryOperation unary_op,
-                                       BinaryOperation binary_op);
-
-          template<class InputIterator, class OutputIterator,
-                   class UnaryOperation,
-                   class BinaryOperation, class T>
-            OutputIterator
-              transform_inclusive_scan(InputIterator first, InputIterator last,
-                                       OutputIterator result,
-                                       UnaryOperation unary_op,
-                                       BinaryOperation binary_op, T init);
-        

+    
template<class InputIterator, class OutputIterator,
+      class UnaryOperation,
+      class BinaryOperation>
+OutputIterator transform_inclusive_scan(InputIterator first, InputIterator last,
+                                        OutputIterator result,
+                                        UnaryOperation unary_op,
+                                        BinaryOperation binary_op);template<class InputIterator, class OutputIterator,
+      class UnaryOperation,
+      class BinaryOperation, class T>
+OutputIterator transform_inclusive_scan(InputIterator first, InputIterator last,
+                                        OutputIterator result,
+                                        UnaryOperation unary_op,
+                                        BinaryOperation binary_op, T init);

 
     

       
         
 
+        
+
         
     
     
Effects:

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L*3d9AU&{U;;g#hl


From 329cc2458780f5b79a83261399cd7965f3c11305 Mon Sep 17 00:00:00 2001
From: Jared Hoberock 
Date: Tue, 7 Apr 2015 14:45:51 -0700
Subject: [PATCH 2/2] Manually break code lines which were spilling into the
 margin.

---
 README.md           |   2 +-
 algorithms.html     |  15 ++++++++++-----
 parallelism-ts.html |  21 +++++++++++++--------
 parallelism-ts.pdf  | Bin 141155 -> 141295 bytes
 4 files changed, 24 insertions(+), 14 deletions(-)

diff --git a/README.md b/README.md
index 9ca0c39..ed2dfe1 100644
--- a/README.md
+++ b/README.md
@@ -17,5 +17,5 @@ N4409 is document N4407 reformatted as a TS document. It updates N4354, which wa
 
 ## Editorial Changes
 
-Eliminated spurious whitespace and superfluous paragraph numbers.
+Eliminated spurious whitespace and paragraph numbers and manually broke code lines which were spilling into the margin.
 
diff --git a/algorithms.html b/algorithms.html
index 90fed62..0a62818 100644
--- a/algorithms.html
+++ b/algorithms.html
@@ -348,7 +348,8 @@ 
Definitions

         
  • a1 when N is 1
    • 
 
         
  • 
-          op(GENERALIZED_NONCOMMUTATIVE_SUM(op, a1, ..., aK), GENERALIZED_NONCOMMUTATIVE_SUM(op, aM, ..., aN) where 1 < K+1 = M ≤ N.
+          op(GENERALIZED_NONCOMMUTATIVE_SUM(op, a1, ..., aK), GENERALIZED_NONCOMMUTATIVE_SUM(op, aM, 
    
+          ..., aN) where 1 < K+1 = M ≤ N.
         
    • 
       
     
    
@@ -814,7 +815,8 @@ 
    Transform reduce
    
                    UnaryOperation unary_op, T init, BinaryOperation binary_op);
 
         
-          GENERALIZED_SUM(binary_op, init, unary_op(*first), ..., unary_op(*(first + (last - first) - 1))).
+          GENERALIZED_SUM(binary_op, init, unary_op(*first), ..., unary_op(*(first + (last - first) -
    
+          1))).
             
 
         
@@ -845,7 +847,8 @@ 
    Transform exclusive scan
    
 
         
           Assigns through each iterator i in [result,result + (last - first)) the value of
-          GENERALIZED_NONCOMMUTATIVE_SUM(binary_op, init, unary_op(*first), ..., unary_op(*(first + (i - result) - 1))).
+          GENERALIZED_NONCOMMUTATIVE_SUM(binary_op, init, unary_op(*first), ..., unary_op(*(first + (i
    
+          - result) - 1))).
             
 
         
@@ -891,8 +894,10 @@ 
    Transform inclusive scan
    
 
         
           Assigns through each iterator i in [result,result + (last - first)) the value of
-          GENERALIZED_NONCOMMUTATIVE_SUM(binary_op, unary_op(*first), ..., unary_op(*(first + (i - result)))) or
-          GENERALIZED_NONCOMMUTATIVE_SUM(binary_op, init, unary_op(*first), ..., unary_op(*(first + (i - result))))
+          GENERALIZED_NONCOMMUTATIVE_SUM(binary_op, unary_op(*first), ..., unary_op(*(first + (i -
    
+          result)))) or
+          GENERALIZED_NONCOMMUTATIVE_SUM(binary_op, init, unary_op(*first), ..., unary_op(*(first + (i
    
+          - result))))
           if init is provided.
             
 
diff --git a/parallelism-ts.html b/parallelism-ts.html
index 1d8c84e..cf00674 100644
--- a/parallelism-ts.html
+++ b/parallelism-ts.html
@@ -712,13 +712,13 @@
       
    
         
           
-            
+            
           
           
-            
+            
           
           
-            
+            
    Document Number:N4352
    Document Number:N4407
    Date:
    Date:
    Revises:N4310
    Revises:N4352
    
           
           
             
    Editor:
@@ -2097,7 +2097,8 @@ 
    Contents
    
         
  • a1 when N is 1
    • 
 
         
  • 
-          op(GENERALIZED_NONCOMMUTATIVE_SUM(op, a1, ..., aK), GENERALIZED_NONCOMMUTATIVE_SUM(op, aM, ..., aN) where 1 < K+1 = M ≤ N.
+          op(GENERALIZED_NONCOMMUTATIVE_SUM(op, a1, ..., aK), GENERALIZED_NONCOMMUTATIVE_SUM(op, aM, 
    
+          ..., aN) where 1 < K+1 = M ≤ N.
         
    • 
       
     
    
@@ -2804,7 +2805,8 @@ 
    Contents
    
         
     
     
    Returns:
    
-          GENERALIZED_SUM(binary_op, init, unary_op(*first), ..., unary_op(*(first + (last - first) - 1))).
+          GENERALIZED_SUM(binary_op, init, unary_op(*first), ..., unary_op(*(first + (last - first) -
    
+          1))).
         
    
       
 
@@ -2861,7 +2863,8 @@ 
    Contents
    
     
     
    Effects:
    
           Assigns through each iterator i in [result,result + (last - first)) the value of
-          GENERALIZED_NONCOMMUTATIVE_SUM(binary_op, init, unary_op(*first), ..., unary_op(*(first + (i - result) - 1))).
+          GENERALIZED_NONCOMMUTATIVE_SUM(binary_op, init, unary_op(*first), ..., unary_op(*(first + (i
    
+          - result) - 1))).
         
    
   
 
@@ -2936,8 +2939,10 @@ 
    Contents
    
     
     
    Effects:
    
           Assigns through each iterator i in [result,result + (last - first)) the value of
-          GENERALIZED_NONCOMMUTATIVE_SUM(binary_op, unary_op(*first), ..., unary_op(*(first + (i - result)))) or
-          GENERALIZED_NONCOMMUTATIVE_SUM(binary_op, init, unary_op(*first), ..., unary_op(*(first + (i - result))))
+          GENERALIZED_NONCOMMUTATIVE_SUM(binary_op, unary_op(*first), ..., unary_op(*(first + (i -
    
+          result)))) or
+          GENERALIZED_NONCOMMUTATIVE_SUM(binary_op, init, unary_op(*first), ..., unary_op(*(first + (i
    
+          - result))))
           if init is provided.
         
    
   
diff --git a/parallelism-ts.pdf b/parallelism-ts.pdf
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