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Editor: | NVIDIA Corporation |
Note: this is an early draft. It’s known to be incomplet and incorrekt, and it has lots of bad formatting.
This Technical Specification describes requirements for implementations of an interface that computer programs written in the C++ programming language may use to invoke algorithms with parallel execution. The algorithms described by this Technical Specification are realizable across a broad class of computer architectures.
This Technical Specification is non-normative. Some of the functionality described by this Technical Specification may be considered for standardization in a future version of C++, but it is not currently part of any C++ standard. Some of the functionality in this Technical Specification may never be standardized, and other functionality may be standardized in a substantially changed form.
The goal of this Technical Specification is to build widespread existing practice for parallelism in the C++ standard algorithms library. It gives advice on extensions to those vendors who wish to provide them.
The following referenced document is indispensable for the application of this document. For dated references, only the edition cited applies. For undated references, the latest edition of the referenced document (including any amendments) applies.
ISO/IEC 14882:— is herein called the C++ Standard. The library described in ISO/IEC 14882:— clauses 17-30 is herein called the C++ Standard Library. The C++ Standard Library components described in ISO/IEC 14882:— clauses 25, 26.7 and 20.7.2 are herein called the C++ Standard Algorithms Library.
Unless otherwise specified, the whole of the C++ Standard's Library
introduction (
Since the extensions described in this Technical Specification are
experimental and not part of the C++ Standard Library, they should not be
declared directly within namespace std
. Unless otherwise specified, all
components described in this Technical Specification are declared in namespace
std::experimental::parallel::v1
.
std
.
— end note ]
Unless otherwise specified, references to such entities described in this
Technical Specification are assumed to be qualified with
std::experimental::parallel::v1
, and references to entities described in the C++
Standard Library are assumed to be qualified with std::
.
Extensions that are expected to eventually be added to an existing header
<meow>
are provided inside the <experimental/meow>
header,
which shall include the standard contents of <meow>
as if by
#include <meow>
For the purposes of this document, the terms and definitions given in the C++ Standard and the following apply.
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:
sort
function may invoke the following element access functions:
RandomAccessIterator
.
swap
function on the elements of the sequence (as per 25.4.1.1 [sort]/2).
Compare
function object.
This clause describes classes that are execution policy types. An object of an execution policy type indicates the kinds of parallelism allowed in the execution of an algorithm and expresses the consequent requirements on the element access functions.
std::vector<int> v = ... // standard sequential sort std::sort(v.begin(), v.end()); using namespace std::experimental::parallel; // explicitly sequential sort sort(seq, v.begin(), v.end()); // permitting parallel execution sort(par, v.begin(), v.end()); // permitting vectorization as well sort(par_vec, v.begin(), v.end()); // sort with dynamically-selected execution size_t threshold = ... execution_policy exec = seq; if (v.size() > threshold) { exec = par; } sort(exec, v.begin(), v.end());— end example ]
<experimental/execution_policy>
synopsisnamespace std { namespace experimental { namespace parallel { inline namespace v1 {// 2.3, Execution policy type trait template<class T> struct is_execution_policy; template<class T> constexpr bool is_execution_policy_v = is_execution_policy<T>::value;// 2.4, Sequential execution policy class sequential_execution_policy;// 2.5, Parallel execution policy class parallel_execution_policy;// 2.6, Parallel+Vector execution policy class parallel_vector_execution_policy;// 2.7, Dynamic execution policy class execution_policy; } } } }
template<class T> struct is_execution_policy { see below };
is_execution_policy
can be used to detect parallel execution policies for the purpose of
excluding function signatures from otherwise ambiguous overload
resolution participation.
is_execution_policy<T>
shall be a UnaryTypeTrait with a BaseCharacteristic of true_type
if T
is the type of a standard or implementation-defined execution policy, otherwise false_type
.
The behavior of a program that adds specializations for is_execution_policy
is undefined.
class sequential_execution_policy{ unspecified };
The class sequential_execution_policy
is an execution policy type used as a unique type to disambiguate
parallel algorithm overloading and require that a parallel algorithm's
execution may not be parallelized.
class parallel_execution_policy{ unspecified };
The class parallel_execution_policy
is an execution policy type used as a unique type to disambiguate
parallel algorithm overloading and indicate that a parallel algorithm's
execution may be parallelized.
class parallel_vector_execution_policy{ unspecified };
The class class parallel_vector_execution_policy
is an execution policy type used as a unique type to disambiguate
parallel algorithm overloading and indicate that a parallel algorithm's
execution may be vectorized and parallelized.
class execution_policy { public:// 2.7.1, execution_policy construct/assign template<class T> execution_policy(const T& exec); template<class T> execution_policy& operator=(const T& exec);// 2.7.2, execution_policy object access const type_info& type() const noexcept; template<class T> T* get() noexcept; template<class T> const T* get() const noexcept; };
The class execution_policy
is a container for execution policy objects.
execution_policy
allows dynamic control over standard algorithm execution.
std::vector<float> sort_me = ... using namespace std::experimental::parallel; execution_policy exec = seq; if(sort_me.size() > threshold) { exec = std::par; } std::sort(exec, std::begin(sort_me), std::end(sort_me));— end example ]
Objects of type execution_policy
shall be constructible and assignable from objects of
type T
for which is_execution_policy<T>::value
is true
.
execution_policy
construct/assigntemplate<class T> execution_policy(const T& exec);
execution_policy
object with a copy of exec
's state.is_execution_policy<T>::value
is true
.
template<class T> execution_policy& operator=(const T& exec);
exec
's state to *this
.*this
.
execution_policy
object access
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;
target_type() == typeid(T)
, a pointer to the stored execution policy object; otherwise a null pointer.is_execution_policy<T>::value
is true
.
constexpr sequential_execution_policy seq{}; constexpr parallel_execution_policy par{}; constexpr parallel_vector_execution_policy par_vec{};
The header <experimental/execution_policy>
declares a global object associated with each type of execution policy defined by this Technical Specification.
During the execution of a standard parallel algorithm,
if temporary memory resources are required and none are available,
the algorithm throws a std::bad_alloc
exception.
During the execution of a standard parallel algorithm, if the invocation of an element access function terminates with an uncaught exception, the behavior of the program is determined by the type of execution policy used to invoke the algorithm:
class parallel_vector_execution_policy
,
std::terminate
shall be called.
sequential_execution_policy
or
parallel_execution_policy
, the execution of the algorithm terminates with an
exception_list
exception. All uncaught exceptions thrown during
the invocations of element access functions shall be contained in the
exception_list
.
for_each
is unspecified. When for_each
is executed sequentially,
only one exception will be contained in the exception_list
object.
— end note ]
std::bad_alloc
, all
exceptions thrown during the execution of
the algorithm are communicated to the caller. It is
unspecified whether an algorithm implementation will "forge ahead" after
encountering and capturing a user exception.
— end note ]
std::bad_alloc
exception even if one or more
user-provided function objects have terminated with an
exception. For example, this can happen when an algorithm fails to
allocate memory while
creating or adding elements to the exception_list
object.
— end note ]
<experimental/exception_list>
synopsisnamespace std { namespace experimental { namespace parallel { inline namespace v1 { class exception_list : public exception { public: typedef unspecified iterator; size_t size() const noexcept; iterator begin() const noexcept; iterator end() const noexcept; const char* what() const noexcept override; }; } } } }
The class exception_list
owns a sequence of exception_ptr
objects. The parallel
algorithms may use the exception_list
to communicate uncaught exceptions encountered during parallel execution to the
caller of the algorithm.
The type exception_list::iterator
shall fulfill the requirements of
ForwardIterator
.
size_t size() const noexcept;
exception_ptr
objects contained within the exception_list
.
iterator begin() const noexcept;
exception_ptr
object contained within the exception_list
.
iterator end() const noexcept;
const char* what() const noexcept override;
Function objects passed into parallel algorithms as objects of type BinaryPredicate
,
Compare
, and BinaryOperation
shall not directly or indirectly modify
objects via their arguments.
Parallel algorithms have template parameters named ExecutionPolicy
which describe
the manner in which the execution of these algorithms may be parallelized and the manner in
which they apply the element access functions.
The invocations of element access functions in parallel algorithms invoked with an execution
policy object of type sequential_execution_policy
execute in sequential order in
the calling thread.
The invocations of element access functions in parallel algorithms invoked with an execution
policy object of type parallel_execution_policy
are permitted to execute in an
unordered fashion in either the invoking thread or in a thread implicitly created by the library
to support parallel algorithm execution. Any such invocations executing in the same thread are
indeterminately sequenced with respect to each other.
using namespace std::experimental::parallel; int a[] = {0,1}; std::vector<int> v; for_each(par, std::begin(a), std::end(a), [&](int i) { v.push_back(i*2+1); });The program above has a data race because of the unsynchronized access to the container
v
.
— end example ]
using namespace std::experimental::parallel; std::atomic<int> x = 0; int a[] = {1,2}; for_each(par, std::begin(a), std::end(a), [&](int n) { x.fetch_add(1, std::memory_order_relaxed); // spin wait for another iteration to change the value of x while (x.load(std::memory_order_relaxed) == 1) { } });The above example depends on the order of execution of the iterations, and is therefore undefined (may deadlock). — end example ]
using namespace std::experimental::parallel; int x=0; std::mutex m; int a[] = {1,2}; for_each(par, std::begin(a), std::end(a), [&](int) { m.lock(); ++x; m.unlock(); });The above example synchronizes access to object
x
ensuring that it is
incremented correctly.
— end example ]
The invocations of element access functions in parallel algorithms invoked with an execution
policy of type parallel_vector_execution_policy
are permitted to execute in an unordered fashion in unspecified threads, and unsequenced
with respect to one another within each thread.
parallel_vector_execution_policy
allows the execution of element access functions to be
interleaved on a single thread, synchronization, including the use of mutexes, risks deadlock. Thus the
synchronization with parallel_vector_execution_policy
is restricted as follows:
A standard library function is vectorization-unsafe if it is specified to synchronize with
another function invocation, or another function invocation is specified to synchronize with it, and if
it is not a memory allocation or deallocation function. Vectorization-unsafe standard library functions
may not be invoked by user code called from parallel_vector_execution_policy
algorithms.
using namespace std::experimental::parallel; int x=0; std::mutex m; int a[] = {1,2}; for_each(par_vec, std::begin(a), std::end(a), [&](int) { m.lock(); ++x; m.unlock(); });The above program is invalid because the applications of the function object are not guaranteed to run on different threads. — end example ]
m.lock
on the same thread, which may deadlock.
— end note ]
parallel_execution_policy
or the
parallel_vector_execution_policy
invocation allow the implementation to fall back to
sequential execution if the system cannot parallelize an algorithm invocation due to lack of
resources.
— end note ]
Algorithms invoked with an execution policy object of type execution_policy
execute internally as if invoked with the contained execution policy object.
The semantics of parallel algorithms invoked with an execution policy object of implementation-defined type are implementation-defined.
ExecutionPolicy
algorithm overloads
The Parallel Algorithms Library provides overloads for each of the algorithms named in
Table 1, corresponding to the algorithms with the same name in the C++ Standard Algorithms Library.
For each algorithm in ExecutionPolicy
, which shall be the first template parameter.
In addition, each such overload shall have the new function parameter as the
first function parameter of type ExecutionPolicy&&
.
Unless otherwise specified, the semantics of ExecutionPolicy
algorithm overloads
are identical to their overloads without.
Parallel algorithms shall not participate in overload resolution unless
is_execution_policy<decay_t<ExecutionPolicy>>::value
is true
.
adjacent_difference |
adjacent_find |
all_of |
any_of |
copy |
copy_if |
copy_n |
count |
count_if |
equal |
exclusive_scan |
fill |
fill_n |
find |
find_end |
find_first_of |
find_if |
find_if_not |
for_each |
for_each_n |
generate |
generate_n |
includes |
inclusive_scan |
inner_product |
inplace_merge |
is_heap |
is_heap_until |
is_partitioned |
is_sorted |
is_sorted_until |
lexicographical_compare |
max_element |
merge |
min_element |
minmax_element |
mismatch |
move |
none_of |
nth_element |
partial_sort |
partial_sort_copy |
partition |
partition_copy |
reduce |
remove |
remove_copy |
remove_copy_if |
remove_if |
replace |
replace_copy |
replace_copy_if |
replace_if |
reverse |
reverse_copy |
rotate |
rotate_copy |
search |
search_n |
set_difference |
set_intersection |
set_symmetric_difference |
set_union |
sort |
stable_partition |
stable_sort |
swap_ranges |
transform |
transform_exclusive_scan |
transform_inclusive_scan |
transform_reduce |
uninitialized_copy |
uninitialized_copy_n |
uninitialized_fill |
uninitialized_fill_n |
unique |
unique_copy |
Define GENERALIZED_SUM(op, a1, ..., aN)
as follows:
a1
when N
is 1
op(GENERALIZED_SUM(op, b1, ..., bK)
, GENERALIZED_SUM(op, bM, ..., bN))
where
b1, ..., bN
may be any permutation of a1, ..., aN
and1 < K+1 = M ≤ N
.
Define GENERALIZED_NONCOMMUTATIVE_SUM(op, a1, ..., aN)
as follows:
a1
when N
is 1
op(GENERALIZED_NONCOMMUTATIVE_SUM(op, a1, ..., aK), GENERALIZED_NONCOMMUTATIVE_SUM(op, aM, ..., aN)
where 1 < K+1 = M ≤ N
.
<experimental/algorithm>
synopsisnamespace std { namespace experimental { namespace parallel { inline namespace v1 { template<class ExecutionPolicy, class InputIterator, class Function> void for_each(ExecutionPolicy&& exec, InputIterator first, InputIterator last, Function f); template<class InputIterator, class Size, class Function> InputIterator for_each_n(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); } } } }
template<class ExecutionPolicy,
class InputIterator, class Function>
void for_each(ExecutionPolicy&& exec,
InputIterator first, InputIterator last,
Function f);
f
to the result of dereferencing every iterator in the range [first,last)
.
first
satisfies the requirements of a mutable iterator, f
may
apply nonconstant functions through the dereferenced iterator.
— end note ]
f
exactly last - first
times.
f
returns a result, the result is ignored.
for_each
does not return a copy of
its Function
parameter, since parallelization may not permit efficient state
accumulation.
for_each
requires
Function
to meet the requirements of CopyConstructible
.
template<class InputIterator, class Size, class Function>
InputIterator for_each_n(InputIterator first, Size n,
Function f);
Function
shall meet the requirements of MoveConstructible
Function
need not meet the requirements of CopyConstructible
.
— end note ]
f
to the result of dereferencing every iterator in the range
[first,first + n)
, starting from first
and proceeding to first + n - 1
.
first
satisfies the requirements of a mutable iterator,
f
may apply nonconstant functions through the dereferenced iterator.
— end note ]
first + n
for non-negative values of n
and first
for negative values.
f
returns a result, the result is ignored.
template<class ExecutionPolicy,
class InputIterator, class Size, class Function>
InputIterator for_each_n(ExecutionPolicy && exec,
InputIterator first, Size n,
Function f);
f
to the result of dereferencing every iterator in the range
[first,first + n)
, starting from first
and proceeding to first + n - 1
.
first
satisfies the requirements of a mutable iterator,
f
may apply nonconstant functions through the dereferenced iterator.
— end note ]
first + n
for non-negative values of n
and first
for negative values.
f
returns a result, the result is ignored.
for_each_n
requires
Function
to meet the requirements of CopyConstructible
.
<experimental/numeric>
synopsisnamespace std { namespace experimental { namespace parallel { inline namespace v1 { template<class InputIterator> typename iterator_traits<InputIterator>::value_type reduce(InputIterator first, InputIterator last); template<class ExecutionPolicy, class InputIterator> typename iterator_traits<InputIterator>::value_type reduce(ExecutionPolicy&& exec, InputIterator first, InputIterator last); template<class InputIterator, class T> T reduce(InputIterator first, InputIterator last, T init); template<class ExecutionPolicy, class InputIterator, class T> T reduce(ExecutionPolicy&& exec, 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 InputIterator, class T, class BinaryOperation> T reduce(ExecutionPolicy&& exec, InputIterator first, InputIterator last, T init, BinaryOperation binary_op); template<class InputIterator, class OutputIterator, class T> OutputIterator exclusive_scan(InputIterator first, InputIterator last, OutputIterator result, T init); template<class ExecutionPolicy, class InputIterator, class OutputIterator, class T> OutputIterator exclusive_scan(ExecutionPolicy&& exec, 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 InputIterator, class OutputIterator, class T, class BinaryOperation> OutputIterator exclusive_scan(ExecutionPolicy&& exec, InputIterator first, InputIterator last, OutputIterator result, T init, BinaryOperation binary_op); template<class InputIterator, class OutputIterator> OutputIterator inclusive_scan(InputIterator first, InputIterator last, OutputIterator result); template<class ExecutionPolicy, class InputIterator, class OutputIterator> OutputIterator inclusive_scan(ExecutionPolicy&& exec, 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 ExecutionPolicy, class InputIterator, class OutputIterator, class BinaryOperation> OutputIterator inclusive_scan(ExecutionPolicy&& exec, 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 InputIterator, class OutputIterator, class BinaryOperation, class T> OutputIterator inclusive_scan(ExecutionPolicy&& exec, InputIterator first, InputIterator last, OutputIterator result, BinaryOperation binary_op, T init); template<class InputIterator, class UnaryOperation, class T, class BinaryOperation> T transform_reduce(InputIterator first, InputIterator last, UnaryOperation unary_op, T init, BinaryOperation binary_op); template<class ExecutionPolicy, class InputIterator, class UnaryOperation, class T, class BinaryOperation> T transform_reduce(ExecutionPolicy&& exec, InputIterator first, InputIterator last, 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); template<class ExecutionPolicy, class InputIterator, class OutputIterator, class UnaryOperation, class T, class BinaryOperation> OutputIterator transform_exclusive_scan(ExecutionPolicy&& exec, InputIterator first, InputIterator last, OutputIterator result, UnaryOperation unary_op, T init, BinaryOperation binary_op); 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 ExecutionPolicy, class InputIterator, class OutputIterator, class UnaryOperation, class BinaryOperation> OutputIterator transform_inclusive_scan(ExecutionPolicy&& exec, 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 ExecutionPolicy, class InputIterator, class OutputIterator, class UnaryOperation, class BinaryOperation, class T> OutputIterator transform_inclusive_scan(ExecutionPolicy&& exec, InputIterator first, InputIterator last, OutputIterator result, UnaryOperation unary_op, BinaryOperation binary_op, T init); } } } }
template<class InputIterator>
typename iterator_traits<InputIterator>::value_type
reduce(InputIterator first, InputIterator last);
reduce(first, last, typename iterator_traits<InputIterator>::value_type{})
.
template<class InputIterator, class T>
T reduce(InputIterator first, InputIterator last, T init);
reduce(first, last, init, plus<>())
.
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))
.
binary_op
shall not invalidate iterators or subranges, nor modify elements in the
range [first,last)
.
last - first
) applications of binary_op
.
reduce
and accumulate
is that the behavior
of reduce
may be non-deterministic for non-associative or non-commutative binary_op
.
template<class InputIterator, class OutputIterator,
class T>
OutputIterator
exclusive_scan(InputIterator first, InputIterator last,
OutputIterator result,
T init);
exclusive_scan(first, last, result, init, plus<>())
.
template<class InputIterator, class OutputIterator,
class T, class BinaryOperation>
OutputIterator
exclusive_scan(InputIterator first, InputIterator last,
OutputIterator result,
T init, BinaryOperation binary_op);
i
in [result,result + (last - first))
the
value of GENERALIZED_NONCOMMUTATIVE_SUM(binary_op, init, *first, ..., *(first + (i - result) - 1))
.
result
.
binary_op
shall not invalidate iterators or subranges, nor modify elements in the
ranges [first,last)
or [result,result + (last - first))
.
last - first
) applications of binary_op
.
exclusive_scan
and inclusive_scan
is that
exclusive_scan
excludes the i
th input element from the i
th
sum. If binary_op
is not mathematically associative, the behavior of
exclusive_scan
may be non-deterministic.
template<class InputIterator, class OutputIterator>
OutputIterator
inclusive_scan(InputIterator first, InputIterator last,
OutputIterator result);
inclusive_scan(first, last, result, plus<>())
.
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);
i
in [result,result + (last - first))
the value of
GENERALIZED_NONCOMMUTATIVE_SUM(binary_op, *first, ..., *(first + (i - result)))
or
GENERALIZED_NONCOMMUTATIVE_SUM(binary_op, init, *first, ..., *(first + (i - result)))
if init
is provided.
result
.
binary_op
shall not invalidate iterators or subranges, nor modify elements in the
ranges [first,last)
or [result,result + (last - first))
.
last - first
) applications of binary_op
.
exclusive_scan
and inclusive_scan
is that
inclusive_scan
includes the i
th input element in the i
th sum.
If binary_op
is not mathematically associative, the behavior of
inclusive_scan
may be non-deterministic.
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)))
.
unary_op
nor binary_op
shall invalidate subranges, or modify elements in the range [first,last)
last - first
) applications each of unary_op
and binary_op
.
transform_reduce
does not apply unary_op
to init
.
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);
i
in [result,result + (last - first))
the value of
GENERALIZED_NONCOMMUTATIVE_SUM(binary_op, init, unary_op(*first), ..., unary_op(*(first + (i - result) - 1)))
.
result
.
unary_op
nor binary_op
shall invalidate iterators or subranges, or modify elements in the
ranges [first,last)
or [result,result + (last - first))
.
last - first
) applications each of unary_op
and binary_op
.
transform_exclusive_scan
and transform_inclusive_scan
is that transform_exclusive_scan
excludes the ith input element from the ith sum. If binary_op
is not mathematically associative, the behavior of
transform_exclusive_scan
may be non-deterministic. transform_exclusive_scan
does not apply unary_op
to 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);
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))))
if init
is provided.
result
.
unary_op
nor binary_op
shall invalidate iterators or subranges, or modify elements in the ranges [first,last)
or [result,result + (last - first))
.
last - first
) applications each of unary_op
and binary_op
.
transform_exclusive_scan
and transform_inclusive_scan
is that transform_inclusive_scan
includes the ith input element from the ith sum. If binary_op
is not mathematically associative, the behavior of
transform_inclusive_scan
may be non-deterministic. transform_inclusive_scan
does not apply unary_op
to init
.