std:: transform_reduce

From cppreference.com

Defined in header `<numeric>`
template < class InputIt1, class InputIt2, class T > T transform_reduce ( InputIt1 first1, InputIt1 last1, InputIt2 first2, T init ) ;	(1)	(since C++17) (constexpr since C++20)
template < class ExecutionPolicy, class ForwardIt1, class ForwardIt2, class T > T transform_reduce ( ExecutionPolicy && policy, ForwardIt1 first1, ForwardIt1 last1, ForwardIt2 first2, T init ) ;	(2)	(since C++17)
template < class InputIt1, class InputIt2, class T, class BinaryOp1, class BinaryOp2 > T transform_reduce ( InputIt1 first1, InputIt1 last1, InputIt2 first2, T init, BinaryOp1 reduce, BinaryOp2 transform ) ;	(3)	(since C++17) (constexpr since C++20)
template < class ExecutionPolicy, class ForwardIt1, class ForwardIt2, class T, class BinaryOp1, class BinaryOp2 > T transform_reduce ( ExecutionPolicy && policy, ForwardIt1 first1, ForwardIt1 last1, ForwardIt2 first2, T init, BinaryOp1 reduce, BinaryOp2 transform ) ;	(4)	(since C++17)
template < class InputIt, class T, class BinaryOp, class UnaryOp > T transform_reduce ( InputIt first, InputIt last, T init, BinaryOp reduce, UnaryOp transform ) ;	(5)	(since C++17) (constexpr since C++20)
template < class ExecutionPolicy, class ForwardIt, class T, class BinaryOp, class UnaryOp > T transform_reduce ( ExecutionPolicy && policy, ForwardIt first, ForwardIt last, T init, BinaryOp reduce, UnaryOp transform ) ;	(6)	(since C++17)

1) Equivalent to transform_reduce ( first1, last1, first2, init,
std:: plus <> ( ) , std:: multiplies <> ( ) ) , effectively parallelized version of the default std::inner_product .

3) Applies transform to each pair of elements from the ranges

first1

last1

and the range of std:: distance ( first1, last1 ) elements starting from first2 and reduces the results (possibly permuted and aggregated in unspecified manner) along with the initial value init over reduce .

The result is non-deterministic if the reduce is not associative or not commutative (such as floating-point addition).

If any of the following values is not convertible to

, the program is ill-formed:

reduce ( init, init )
reduce ( init, transform ( * first1, * first2 ) )
reduce ( transform ( * first1, * first2 ) , init )
reduce ( transform ( * first1, * first2 ) , transform ( * first1, * first2 ) )

Given last2 as the std:: distance ( first1, last1 ) th next iterator of first2 , if any of the following conditions is satisfied, the behavior is undefined:

T is not MoveConstructible .
transform or reduce modifies any element of [ first1 , last1 ) or [ first2 , last2 ) .
transform or reduce invalidates any iterator or subrange of [ first1 , last1 ] or [ first2 , last2 ] .

5) Applies transform to each element in the range

first

last

and reduces the results (possibly permuted and aggregated in unspecified manner) along with the initial value init over reduce .

The result is non-deterministic if the reduce is not associative or not commutative (such as floating-point addition).

If any of the following values is not convertible to

, the program is ill-formed:

reduce ( init, init )
reduce ( init, transform ( * first ) )
reduce ( transform ( * first ) , init )
reduce ( transform ( * first ) , transform ( * first ) )

If any of the following conditions is satisfied, the behavior is undefined:

T is not MoveConstructible .
transform or reduce modifies any element of [ first , last ) .
transform or reduce invalidates any iterator or subrange of [ first , last ] .

2,4,6) Same as (1,3,5) , but executed according to policy .

These overloads participate in overload resolution only if

std:: is_execution_policy_v < std:: decay_t < ExecutionPolicy >> is true .	(until C++20)
std:: is_execution_policy_v < std:: remove_cvref_t < ExecutionPolicy >> is true .	(since C++20)

Parameters

first1, last1	-	the range of elements to be taken as the left operand of transform
first2	-	the start of range of elements to be taken as the right operand of transform
first, last	-	the range of elements to be taken as the operand of transform
init	-	the initial value of the generalized sum
policy	-	the execution policy to use. See execution policy for details.
reduce	-	binary FunctionObject that will be applied in unspecified order to the results of transform , the results of other reduce and init .
transform	-	unary or binary FunctionObject that will be applied to each element of the input range(s). The return type must be acceptable as input to reduce .
Type requirements
- `InputIt1, InputIt2, InputIt` must meet the requirements of LegacyInputIterator .
- `ForwardIt1, ForwardIt2, ForwardIt` must meet the requirements of LegacyForwardIterator .

Return value

1,2) The generalized sum of init and values over std:: plus <> ( ) , where values are the values transformed by std:: multiplies <> ( ) , each value is transformed from a pair of elements from the two input ranges.

3,4) The generalized sum of init and values over reduce , where values are the values transformed by transform , each value is transformed from a pair of elements from the two input ranges.

5,6) The generalized sum of init and values over reduce , where values are the values transformed by transform , each value is transformed from an element from the input range.

The generalized sum of a group of elements over an binary operation binary_op is defined as follows:

If the group only has one element, the sum is the value of the element.
Otherwise, performs the following operations in order:

Takes any two elements elem1 and elem2 from the group.
Calculates binary_op ( elem1, elem2 ) and puts the result back to the group.
Repeats steps 1 and 2 until there is only one element in the group.

Complexity

Given $\scriptsize N$ $N$ as std:: distance ( first1, last1 ) (or std:: distance ( first, last ) for overloads (5,6) ):

1,2)

O(N)

applications of std:: plus <> ( ) and std:: multiplies <> ( ) respectively.

3-6)

O(N)

applications of reduce and transform respectively.

Exceptions

The overloads with a template parameter named ExecutionPolicy report errors as follows:

If execution of a function invoked as part of the algorithm throws an exception and ExecutionPolicy is one of the standard policies , std::terminate is called. For any other ExecutionPolicy , the behavior is implementation-defined.
If the algorithm fails to allocate memory, std::bad_alloc is thrown.

Notes

transform is never applied to init .

If first == last or first1 == last1 , init is returned, unmodified.

Example

transform_reduce can be used to parallelize std::inner_product . Some systems may need additional support to get advantages of parallel execution. E.g., on GNU/Linux, the Intel TBB be installed and - ltbb option be provided to gcc/clang compiler.

Run this code

#if PARALLEL
#include <execution>
#define PAR std::execution::par,
#else
#define PAR
#endif
 
#include <algorithm>
#include <functional>
#include <iostream>
#include <iterator>
#include <locale>
#include <numeric>
#include <vector>
 
// to parallelize non-associate accumulative operation, you'd better choose
// transform_reduce instead of reduce; e.g., a + b * b != b + a * a
void print_sum_squared(long const num)
{
    std::cout.imbue(std::locale{"en_US.UTF8"});
    std::cout << "num = " << num << '\n';
 
    // create an immutable vector filled with pattern: 1,2,3,4, 1,2,3,4 ...
    const std::vector<long> v{[n = num * 4] {
        std::vector<long> v;
        v.reserve(n);
        std::generate_n(std::back_inserter(v), n,
            [i = 0]() mutable { return 1 + i++ % 4; });
        return v;
    }()};
 
    auto squared_sum = [](auto sum, auto val) { return sum + val * val; };
 
    auto sum1 = std::accumulate(v.cbegin(), v.cend(), 0L, squared_sum);
    std::cout << "accumulate(): " << sum1 << '\n';
 
    auto sum2 = std::reduce(PAR v.cbegin(), v.cend(), 0L, squared_sum);
    std::cout << "reduce(): " << sum2 << '\n';
 
    auto sum3 = std::transform_reduce(PAR v.cbegin(), v.cend(), 0L, std::plus{},
                                      [](auto val) { return val * val; });
    std::cout << "transform_reduce(): " << sum3 << "\n\n";
}
 
int main()
{
    print_sum_squared(1);
    print_sum_squared(1'000);
    print_sum_squared(1'000'000);
}

Possible output:

num = 1
accumulate(): 30
reduce(): 30
transform_reduce(): 30
 
num = 1,000
accumulate(): 30,000
reduce(): -7,025,681,278,312,630,348
transform_reduce(): 30,000
 
num = 1,000,000
accumulate(): 30,000,000
reduce(): -5,314,886,882,370,003,032
transform_reduce(): 30,000,000
 
// Compile-options for parallel execution on POSIX:
// g++ -O2 -std=c++17 -Wall -Wextra -pedantic -DPARALLEL ./example.cpp -ltbb -o tr; ./tr

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accumulate	sums up or folds a range of elements (function template)
transform	applies a function to a range of elements, storing results in a destination range (function template)
reduce (C++17)	similar to std::accumulate , except out of order (function template)