namespace std {
template <class InputIterator, class T>
T accumulate(InputIterator first, InputIterator last, T init);
template <class InputIterator, class T, class BinaryOperation>
T accumulate(InputIterator first, InputIterator last, T init,
BinaryOperation binary_op);
template<class InputIterator>
typename iterator_traits<InputIterator>::value_type
reduce(InputIterator first, InputIterator last);
template<class InputIterator, class T>
T reduce(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 ForwardIterator>
typename iterator_traits<ForwardIterator>::value_type
reduce(ExecutionPolicy&& exec, ForwardIterator first, ForwardIterator last);
template<class ExecutionPolicy, class ForwardIterator, class T>
T reduce(ExecutionPolicy&& exec, ForwardIterator first, ForwardIterator last, T init);
template<class ExecutionPolicy, class ForwardIterator, class T, class BinaryOperation>
T reduce(ExecutionPolicy&& exec, ForwardIterator first, ForwardIterator last, T init,
BinaryOperation binary_op);
template <class InputIterator1, class InputIterator2, class T>
T inner_product(InputIterator1 first1, InputIterator1 last1,
InputIterator2 first2, T init);
template <class InputIterator1, class InputIterator2, class T,
class BinaryOperation1, class BinaryOperation2>
T inner_product(InputIterator1 first1, InputIterator1 last1,
InputIterator2 first2, T init,
BinaryOperation1 binary_op1,
BinaryOperation2 binary_op2);
template<class InputIterator1, class InputIterator2, class T>
T transform_reduce(InputIterator1 first1, InputIterator1 last1,
InputIterator2 first2,
T init);
template<class InputIterator1, class InputIterator2, class T,
class BinaryOperation1, class BinaryOperation2>
T transform_reduce(InputIterator1 first1, InputIterator1 last1,
InputIterator2 first2,
T init,
BinaryOperation1 binary_op1,
BinaryOperation2 binary_op2);
template<class InputIterator, class T,
class BinaryOperation, class UnaryOperation>
T transform_reduce(InputIterator first, InputIterator last,
T init,
BinaryOperation binary_op, UnaryOperation unary_op);
template<class ExecutionPolicy,
class ForwardIterator1, class ForwardIterator2, class T>
T transform_reduce(ExecutionPolicy&& exec, ForwardIterator1 first1, ForwardIterator1 last1,
ForwardIterator2 first2,
T init);
template<class ExecutionPolicy,
class ForwardIterator1, class ForwardIterator2, class T,
class BinaryOperation1, class BinaryOperation2>
T transform_reduce(ExecutionPolicy&& exec, ForwardIterator1 first1, ForwardIterator1 last1,
ForwardIterator2 first2,
T init,
BinaryOperation1 binary_op1,
BinaryOperation2 binary_op2);
template<class ExecutionPolicy,
class ForwardIterator, class T,
class BinaryOperation, class UnaryOperation>
T transform_reduce(ExecutionPolicy&& exec, ForwardIterator first, ForwardIterator last,
T init,
BinaryOperation binary_op, UnaryOperation unary_op);
template <class InputIterator, class OutputIterator>
OutputIterator partial_sum(InputIterator first,
InputIterator last,
OutputIterator result);
template <class InputIterator, class OutputIterator, class BinaryOperation>
OutputIterator partial_sum(InputIterator first,
InputIterator last,
OutputIterator result,
BinaryOperation binary_op);
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, class BinaryOperation>
OutputIterator exclusive_scan(InputIterator first, InputIterator last,
OutputIterator result,
T init, BinaryOperation binary_op);
template<class ExecutionPolicy, class ForwardIterator1, class ForwardIterator2, class T>
ForwardIterator2 exclusive_scan(ExecutionPolicy&& exec, ForwardIterator1 first, ForwardIterator1 last,
ForwardIterator2 result,
T init);
template<class ExecutionPolicy, class ForwardIterator1, class ForwardIterator2, class T,
class BinaryOperation>
ForwardIterator2 exclusive_scan(ExecutionPolicy&& exec, ForwardIterator1 first, ForwardIterator1 last,
ForwardIterator2 result,
T init, BinaryOperation binary_op);
template<class InputIterator, class OutputIterator>
OutputIterator inclusive_scan(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 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 ForwardIterator1, class ForwardIterator2>
ForwardIterator2 inclusive_scan(ExecutionPolicy&& exec, ForwardIterator1 first, ForwardIterator1 last,
ForwardIterator2 result);
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 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);
template<class InputIterator, class OutputIterator, class T,
class BinaryOperation, class UnaryOperation>
OutputIterator transform_exclusive_scan(InputIterator first, InputIterator last,
OutputIterator result,
T init,
BinaryOperation binary_op,
UnaryOperation unary_op);
template<class ExecutionPolicy,
class ForwardIterator1, class ForwardIterator2, class T,
class BinaryOperation, class UnaryOperation>
ForwardIterator2 transform_exclusive_scan(ExecutionPolicy&& exec, ForwardIterator1 first, ForwardIterator1 last,
ForwardIterator2 result,
T init,
BinaryOperation binary_op,
UnaryOperation unary_op);
template<class InputIterator, class OutputIterator,
class BinaryOperation, class UnaryOperation>
OutputIterator transform_inclusive_scan(InputIterator first, InputIterator last,
OutputIterator result,
BinaryOperation binary_op,
UnaryOperation unary_op);
template<class InputIterator, class OutputIterator,
class BinaryOperation, class UnaryOperation, class T>
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>
ForwardIterator2 transform_inclusive_scan(ExecutionPolicy&& exec, ForwardIterator1 first, ForwardIterator1 last,
ForwardIterator2 result,
BinaryOperation binary_op,
UnaryOperation unary_op);
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);
template <class InputIterator, class OutputIterator>
OutputIterator adjacent_difference(InputIterator first,
InputIterator last,
OutputIterator result);
template <class InputIterator, class OutputIterator, class BinaryOperation>
OutputIterator adjacent_difference(InputIterator first,
InputIterator last,
OutputIterator result,
BinaryOperation binary_op);
template <class ExecutionPolicy, class ForwardIterator1, class ForwardIterator2>
ForwardIterator2 adjacent_difference(ExecutionPolicy&& exec, ForwardIterator1 first,
ForwardIterator1 last,
ForwardIterator2 result);
template <class ExecutionPolicy, class ForwardIterator1, class ForwardIterator2,
class BinaryOperation>
ForwardIterator2 adjacent_difference(ExecutionPolicy&& exec, ForwardIterator1 first,
ForwardIterator1 last,
ForwardIterator2 result,
BinaryOperation binary_op);
template <class ForwardIterator, class T>
void iota(ForwardIterator first, ForwardIterator last, T value);
template <class M, class N>
constexpr common_type_t<M,N> gcd(M m, N n);
template <class M, class N>
constexpr common_type_t<M,N> lcm(M m, N n);
}
The requirements on the types of algorithms' arguments that are described in the introduction to Clause [algorithms] also apply to the following algorithms.
Throughout this subclause, the parameters UnaryOperation, BinaryOperation, BinaryOperation1, and BinaryOperation2 are used whenever an algorithm expects a function object ([function.objects]).
[ Note: The use of closed ranges as well as semi-open ranges to specify requirements throughout this subclause is intentional. — end note ]
29.8.2 Accumulate [accumulate]template <class InputIterator, class T> T accumulate(InputIterator first, InputIterator last, T init); template <class InputIterator, class T, class BinaryOperation> T accumulate(InputIterator first, InputIterator last, T init, BinaryOperation binary_op);
Requires: T shall meet the requirements of CopyConstructible and CopyAssignable types. In the range [first, last], binary_op shall neither modify elements nor invalidate iterators or subranges.281
Effects: Computes its result by initializing the accumulator acc with the initial value init and then modifies it with acc = acc + *i or acc = binary_op(acc, *i) for every iterator i in the range [first, last) in order.282
29.8.3 Reduce [reduce]template<class InputIterator> typename iterator_traits<InputIterator>::value_type reduce(InputIterator first, InputIterator last);
Effects: Equivalent to:
return reduce(first, last,
typename iterator_traits<InputIterator>::value_type{});
template<class ExecutionPolicy, class ForwardIterator> typename iterator_traits<ForwardIterator>::value_type reduce(ExecutionPolicy&& exec, ForwardIterator first, ForwardIterator last);
Effects: Equivalent to:
return reduce(std::forward<ExecutionPolicy>(exec), first, last,
typename iterator_traits<ForwardIterator>::value_type{});
template<class InputIterator, class T> T reduce(InputIterator first, InputIterator last, T init);
Effects: Equivalent to:
return reduce(first, last, init, plus<>());
template<class ExecutionPolicy, class ForwardIterator, class T> T reduce(ExecutionPolicy&& exec, ForwardIterator first, ForwardIterator last, T init);
Effects: Equivalent to:
return reduce(std::forward<ExecutionPolicy>(exec), first, last, init, plus<>());
template<class InputIterator, class T, class BinaryOperation> T reduce(InputIterator first, InputIterator last, T init, BinaryOperation binary_op); template<class ExecutionPolicy, class ForwardIterator, class T, class BinaryOperation> T reduce(ExecutionPolicy&& exec, ForwardIterator first, ForwardIterator last, T init, BinaryOperation binary_op);
Requires:
T shall be MoveConstructible (Table 23).
All of binary_op(init, *first), binary_op(*first, init), binary_op(init, init), and binary_op(*first, *first) shall be convertible to T.
binary_op shall neither invalidate iterators or subranges, nor modify elements in the range [first, last].
Returns: GENERALIZED_SUM(binary_op, init, *i, ...) for every i in [first, last).
Complexity: O(last - first) applications of binary_op.
[ Note: The difference between reduce and accumulate is that reduce applies binary_op in an unspecified order, which yields a nondeterministic result for non-associative or non-commutative binary_op such as floating-point addition. — end note ]
29.8.4 Inner product [inner.product]template <class InputIterator1, class InputIterator2, class T> T inner_product(InputIterator1 first1, InputIterator1 last1, InputIterator2 first2, T init); template <class InputIterator1, class InputIterator2, class T, class BinaryOperation1, class BinaryOperation2> T inner_product(InputIterator1 first1, InputIterator1 last1, InputIterator2 first2, T init, BinaryOperation1 binary_op1, BinaryOperation2 binary_op2);
Requires: T shall meet the requirements of CopyConstructible and CopyAssignable types. In the ranges [first1, last1] and [first2, first2 + (last1 - first1)] binary_op1 and binary_op2 shall neither modify elements nor invalidate iterators or subranges.283
Effects: Computes its result by initializing the accumulator acc with the initial value init and then modifying it with acc = acc + (*i1) * (*i2) or acc = binary_op1(acc, binary_op2(*i1, *i2)) for every iterator i1 in the range [first1, last1) and iterator i2 in the range [first2, first2 + (last1 - first1)) in order.
29.8.5 Transform reduce [transform.reduce]template <class InputIterator1, class InputIterator2, class T> T transform_reduce(InputIterator1 first1, InputIterator1 last1, InputIterator2 first2, T init); template <class ExecutionPolicy, class ForwardIterator1, class ForwardIterator2, class T> T transform_reduce(ExecutionPolicy&& exec, ForwardIterator1 first1, ForwardIterator1 last1, ForwardIterator2 first2, T init);
Effects: Equivalent to:
return transform_reduce(first1, last1, first2, init, plus<>(), multiplies<>());
template <class InputIterator1, class InputIterator2, class T, class BinaryOperation1, class BinaryOperation2> T transform_reduce(InputIterator1 first1, InputIterator1 last1, InputIterator2 first2, T init, BinaryOperation1 binary_op1, BinaryOperation2 binary_op2); template <class ExecutionPolicy, class ForwardIterator1, class ForwardIterator2, class T, class BinaryOperation1, class BinaryOperation2> T transform_reduce(ExecutionPolicy&& exec, ForwardIterator1 first1, ForwardIterator1 last1, ForwardIterator2 first2, T init, BinaryOperation1 binary_op1, BinaryOperation2 binary_op2);
Requires:
T shall be MoveConstructible (Table 23).
All of
binary_op1(init, init),
binary_op1(init, binary_op2(*first1, *first2)),
binary_op1(binary_op2(*first1, *first2), init), and
binary_op1(binary_op2(*first1, *first2), binary_op2(*first1, *first2))
shall be convertible to T.
Neither binary_op1 nor binary_op2 shall invalidate subranges, or modify elements in the ranges [first1, last1] and [first2, first2 + (last1 - first1)].
Returns:
GENERALIZED_SUM(binary_op1, init, binary_op2(*i, *(first2 + (i - first1))), ...)
for every iterator i in [first1, last1).
Complexity: O(last1 - first1) applications each of binary_op1 and binary_op2.
template<class InputIterator, class T, class BinaryOperation, class UnaryOperation> T transform_reduce(InputIterator first, InputIterator last, T init, BinaryOperation binary_op, UnaryOperation unary_op); template<class ExecutionPolicy, class ForwardIterator, class T, class BinaryOperation, class UnaryOperation> T transform_reduce(ExecutionPolicy&& exec, ForwardIterator first, ForwardIterator last, T init, BinaryOperation binary_op, UnaryOperation unary_op);
Requires:
T shall be MoveConstructible (Table 23).
All of
binary_op(init, init),
binary_op(init, unary_op(*first)),
binary_op(unary_op(*first), init), and
binary_op(unary_op(*first), unary_op(*first))
shall be convertible to T.
Neither unary_op nor binary_op shall invalidate subranges, or modify elements in the range [first, last].
Returns:
GENERALIZED_SUM(binary_op, init, unary_op(*i), ...)
for every iterator i in [first, last).
Complexity: O(last - first) applications each of unary_op and binary_op.
[ Note: transform_reduce does not apply unary_op to init. — end note ]
29.8.6 Partial sum [partial.sum]template <class InputIterator, class OutputIterator> OutputIterator partial_sum( InputIterator first, InputIterator last, OutputIterator result); template <class InputIterator, class OutputIterator, class BinaryOperation> OutputIterator partial_sum( InputIterator first, InputIterator last, OutputIterator result, BinaryOperation binary_op);
Requires: InputIterator's value type shall be constructible from the type of *first. The result of the expression acc + *i or binary_op(acc, *i) shall be implicitly convertible to InputIterator's value type. acc shall be writable to the result output iterator. In the ranges [first, last] and [result, result + (last - first)] binary_op shall neither modify elements nor invalidate iterators or subranges.284
Effects: For a non-empty range, the function creates an accumulator acc whose type is InputIterator's value type, initializes it with *first, and assigns the result to *result. For every iterator i in [first + 1, last) in order, acc is then modified by acc = acc + *i or acc = binary_op(acc, *i) and the result is assigned to *(result + (i - first)).
Returns: result + (last - first).
Complexity: Exactly (last - first) - 1 applications of the binary operation.
Remarks: result may be equal to first.
29.8.7 Exclusive scan [exclusive.scan]template<class InputIterator, class OutputIterator, class T> OutputIterator exclusive_scan(InputIterator first, InputIterator last, OutputIterator result, T init);
Effects: Equivalent to:
return exclusive_scan(first, last, result, init, plus<>());
template<class ExecutionPolicy, class ForwardIterator1, class ForwardIterator2, class T> ForwardIterator2 exclusive_scan(ExecutionPolicy&& exec, ForwardIterator1 first, ForwardIterator1 last, ForwardIterator2 result, T init);
Effects: Equivalent to:
return exclusive_scan(std::forward<ExecutionPolicy>(exec),
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); template<class ExecutionPolicy, class ForwardIterator1, class ForwardIterator2, class T, class BinaryOperation> ForwardIterator2 exclusive_scan(ExecutionPolicy&& exec, ForwardIterator1 first, ForwardIterator1 last, ForwardIterator2 result, T init, BinaryOperation binary_op);
Requires:
T shall be MoveConstructible (Table 23).
All of binary_op(init, init), binary_op(init, *first), and binary_op(*first, *first) shall be convertible to T.
binary_op shall neither invalidate iterators or subranges, nor modify elements in the ranges [first, last] or [result, result + (last - first)].
Effects: For each integer K in [0, last - first) assigns through result + K the value of:
GENERALIZED_NONCOMMUTATIVE_SUM(
binary_op, init, *(first + 0), *(first + 1), ..., *(first + K - 1))
Returns: The end of the resulting range beginning at result.
Complexity: O(last - first) applications of binary_op.
Remarks: result may be equal to first.
[ Note: The difference between exclusive_scan and inclusive_scan is that exclusive_scan excludes the ith input element from the ith sum. If binary_op is not mathematically associative, the behavior of exclusive_scan may be nondeterministic. — end note ]
29.8.8 Inclusive scan [inclusive.scan]template<class InputIterator, class OutputIterator> OutputIterator inclusive_scan(InputIterator first, InputIterator last, OutputIterator result);
Effects: Equivalent to:
return inclusive_scan(first, last, result, plus<>());
template<class ExecutionPolicy, class ForwardIterator1, class ForwardIterator2> ForwardIterator2 inclusive_scan(ExecutionPolicy&& exec, ForwardIterator1 first, ForwardIterator1 last, ForwardIterator2 result);
Effects: Equivalent to:
return inclusive_scan(std::forward<ExecutionPolicy>(exec), 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 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> 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);
Requires:
If init is provided, T shall be MoveConstructible (Table 23); otherwise, ForwardIterator1's value type shall be MoveConstructible.
If init is provided, all of binary_op(init, init), binary_op(init, *first), and binary_op(*first, *first) shall be convertible to T; otherwise, binary_op(*first, *first) shall be convertible to ForwardIterator1's value type.
binary_op shall neither invalidate iterators or subranges, nor modify elements in the ranges [first, last] or [result, result + (last - first)].
Effects: For each integer K in [0, last - first) assigns through result + K the value of
GENERALIZED_NONCOMMUTATIVE_SUM(
binary_op, init, *(first + 0), *(first + 1), ..., *(first + K))
if init is provided, or
GENERALIZED_NONCOMMUTATIVE_SUM(
binary_op, *(first + 0), *(first + 1), ..., *(first + K))
otherwise.
Returns: The end of the resulting range beginning at result.
Complexity: O(last - first) applications of binary_op.
Remarks: result may be equal to first.
[ Note: The difference between exclusive_scan and inclusive_scan is that inclusive_scan includes the ith input element in the ith sum. If binary_op is not mathematically associative, the behavior of inclusive_scan may be nondeterministic. — end note ]
29.8.9 Transform exclusive scan [transform.exclusive.scan]template<class InputIterator, class OutputIterator, class T, class BinaryOperation, class UnaryOperation> OutputIterator transform_exclusive_scan(InputIterator first, InputIterator last, OutputIterator result, T init, BinaryOperation binary_op, UnaryOperation unary_op); template<class ExecutionPolicy, class ForwardIterator1, class ForwardIterator2, class T, class BinaryOperation, class UnaryOperation> ForwardIterator2 transform_exclusive_scan(ExecutionPolicy&& exec, ForwardIterator1 first, ForwardIterator1 last, ForwardIterator2 result, T init, BinaryOperation binary_op, UnaryOperation unary_op);
Requires:
T shall be MoveConstructible (Table 23).
All of
binary_op(init, init),
binary_op(init, unary_op(*first)), and
binary_op(unary_op(*first), unary_op(*first))
shall be convertible to T.
Neither unary_op nor binary_op shall invalidate iterators or subranges, or modify elements in the ranges [first, last] or [result, result + (last - first)].
Effects: For each integer K in [0, last - first) assigns through result + K the value of:
GENERALIZED_NONCOMMUTATIVE_SUM(
binary_op, init,
unary_op(*(first + 0)), unary_op(*(first + 1)), ..., unary_op(*(first + K - 1)))
Returns: The end of the resulting range beginning at result.
Complexity: O(last - first) applications each of unary_op and binary_op.
Remarks: result may be equal to first.
[ Note: The difference between 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 nondeterministic. transform_exclusive_scan does not apply unary_op to init. — end note ]
29.8.10 Transform inclusive scan [transform.inclusive.scan]template<class InputIterator, class OutputIterator, class BinaryOperation, class UnaryOperation> 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> 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);
Requires:
If init is provided, T shall be MoveConstructible (Table 23); otherwise, ForwardIterator1's value type shall be MoveConstructible.
If init is provided, all of
binary_op(init, init),
binary_op(init, unary_op(*first)), and
binary_op(unary_op(*first), unary_op(*first))
shall be convertible to T; otherwise, binary_op(unary_op(*first), unary_op(*first)) shall be convertible to ForwardIterator1's value type.
Neither unary_op nor binary_op shall invalidate iterators or subranges, nor modify elements in the ranges [first, last] or [result, result + (last - first)].
Effects: For each integer K in [0, last - first) assigns through result + K the value of
GENERALIZED_NONCOMMUTATIVE_SUM(
binary_op, init,
unary_op(*(first + 0)), unary_op(*(first + 1)), ..., unary_op(*(first + K)))
if init is provided, or
GENERALIZED_NONCOMMUTATIVE_SUM(
binary_op,
unary_op(*(first + 0)), unary_op(*(first + 1)), ..., unary_op(*(first + K)))
otherwise.
Returns: The end of the resulting range beginning at result.
Complexity: O(last - first) applications each of unary_op and binary_op.
Remarks: result may be equal to first.
[ Note: The difference between transform_exclusive_scan and transform_inclusive_scan is that transform_inclusive_scan includes the ith input element in the ith sum. If binary_op is not mathematically associative, the behavior of transform_inclusive_scan may be nondeterministic. transform_inclusive_scan does not apply unary_op to init. — end note ]
29.8.11 Adjacent difference [adjacent.difference]template <class InputIterator, class OutputIterator> OutputIterator adjacent_difference(InputIterator first, InputIterator last, OutputIterator result); template <class ExecutionPolicy, class ForwardIterator1, class ForwardIterator2> ForwardIterator2 adjacent_difference(ExecutionPolicy&& exec, ForwardIterator1 first, ForwardIterator1 last, ForwardIterator2 result); template <class InputIterator, class OutputIterator, class BinaryOperation> OutputIterator adjacent_difference(InputIterator first, InputIterator last, OutputIterator result, BinaryOperation binary_op); template <class ExecutionPolicy, class ForwardIterator1, class ForwardIterator2, class BinaryOperation> ForwardIterator2 adjacent_difference(ExecutionPolicy&& exec, ForwardIterator1 first, ForwardIterator1 last, ForwardIterator2 result, BinaryOperation binary_op);
Requires:
For the overloads with no ExecutionPolicy, InputIterator's value type shall be MoveAssignable (Table 25) and shall be constructible from the type of *first. acc (defined below) shall be writable ([iterator.requirements.general]) to the result output iterator. The result of the expression val - acc or binary_op(val, acc) shall be writable to the result output iterator.
For the overloads with an ExecutionPolicy, the value type of ForwardIterator1 shall be CopyConstructible (Table 24), constructible from the expression *first - *first or binary_op(*first, *first), and assignable to the value type of ForwardIterator2.
For all overloads, in the ranges [first, last] and [result, result + (last - first)], binary_op shall neither modify elements nor invalidate iterators or subranges.285
Effects: For the overloads with no ExecutionPolicy and a non-empty range, the function creates an accumulator acc whose type is InputIterator's value type, initializes it with *first, and assigns the result to *result. For every iterator i in [first + 1, last) in order, creates an object val whose type is InputIterator's value type, initializes it with *i, computes val - acc or binary_op(val, acc), assigns the result to *(result + (i - first)), and move assigns from val to acc.
For the overloads with an ExecutionPolicy and a non-empty range, first the function creates an object whose type is ForwardIterator1's value type, initializes it with *first, and assigns the result to *result. Then for every d in [1, last - first - 1], creates an object val whose type is ForwardIterator1's value type, initializes it with *(first + d) - *(first + d - 1) or binary_op(*(first + d), *(first + d - 1)), and assigns the result to *(result + d).
Returns: result + (last - first).
Complexity: Exactly (last - first) - 1 applications of the binary operation.
Remarks: For the overloads with no ExecutionPolicy, result may be equal to first. For the overloads with an ExecutionPolicy, the ranges [first, last) and [result, result + (last - first)) shall not overlap.
29.8.12 Iota [numeric.iota]template <class ForwardIterator, class T> void iota(ForwardIterator first, ForwardIterator last, T value);
Requires: T shall be convertible to ForwardIterator's value type. The expression ++val, where val has type T, shall be well formed.
Effects: For each element referred to by the iterator i in the range [first, last), assigns *i = value and increments value as if by ++value.
Complexity: Exactly last - first increments and assignments.
29.8.13 Greatest common divisor [numeric.ops.gcd]template <class M, class N> constexpr common_type_t<M,N> gcd(M m, N n);
Requires: |m| and |n| shall be representable as a value of common_type_t<M, N>. [ Note: These requirements ensure, for example, that gcd(m, m) = |m| is representable as a value of type M. — end note ]
Remarks: If either M or N is not an integer type, or if either is cv bool, the program is ill-formed.
Returns: Zero when m and n are both zero. Otherwise, returns the greatest common divisor of |m| and |n|.
29.8.14 Least common multiple [numeric.ops.lcm]template <class M, class N> constexpr common_type_t<M,N> lcm(M m, N n);
Requires: |m| and |n| shall be representable as a value of common_type_t<M, N>. The least common multiple of |m| and |n| shall be representable as a value of type common_type_t<M,N>.
Remarks: If either M or N is not an integer type, or if either is cv bool the program is ill-formed.
Returns: Zero when either m or n is zero. Otherwise, returns the least common multiple of |m| and |n|.
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