std::inner_product

Defined in header `<numeric>`
	(1)
`template< class InputIt1, class InputIt2, class T > T inner_product( InputIt1 first1, InputIt1 last1, InputIt2 first2, T init );`		(until C++20)
`template< class InputIt1, class InputIt2, class T > constexpr T inner_product( InputIt1 first1, InputIt1 last1, InputIt2 first2, T init );`		(since C++20)
	(2)
`template< class InputIt1, class InputIt2, class T, class BinaryOperation1, class BinaryOperation2 > T inner_product( InputIt1 first1, InputIt1 last1, InputIt2 first2, T init, BinaryOperation1 op1, BinaryOperation2 op2 );`		(until C++20)
`template< class InputIt1, class InputIt2, class T, class BinaryOperation1, class BinaryOperation2 > constexpr T inner_product( InputIt1 first1, InputIt1 last1, InputIt2 first2, T init, BinaryOperation1 op1, BinaryOperation2 op2 );`		(since C++20)

Computes inner product (i.e. sum of products) or performs ordered map/reduce operation on the range [first1, last1) and the range beginning at first2.

1) Initializes the accumulator acc (of type T) with the initial value init and then modifies it with the expression acc = acc + (*i1) * (*i2)(until C++11)acc = std::move(acc) + (*i1) * (*i2)(since C++11) for every iterator i1 in the range [first1, last1) in order and its corresponding iterator i2 in the range beginning at first2. For built-in meaning of + and *, this computes inner product of the two ranges.

2) Initializes the accumulator acc (of type T) with the initial value init and then modifies it with the expression acc = op1(acc, op2(*i1, *i2))(until C++11)acc = op1(std::move(acc), op2(*i1, *i2))(since C++11) for every iterator i1 in the range [first1, last1) in order and its corresponding iterator i2 in the range beginning at first2.

If op1 or op2 invalidates any iterators (including the end iterators) or modify any elements of the range involved, the behavior is undefined.

Parameters

first1, last1	-	the first range of elements
first2	-	the beginning of the second range of elements
init	-	initial value of the sum of the products
op1	-	binary operation function object that will be applied. This "sum" function takes a value returned by `op2` and the current value of the accumulator and produces a new value to be stored in the accumulator. The signature of the function should be equivalent to the following: `Ret fun(const Type1 &a, const Type2 &b);` The signature does not need to have `const &`. The types Type1 and Type2 must be such that objects of types T and Type3 can be implicitly converted to Type1 and Type2 respectively. The type `Ret` must be such that an object of type `T` can be assigned a value of type `Ret`.
op2	-	binary operation function object that will be applied. This "product" function takes one value from each range and produces a new value. The signature of the function should be equivalent to the following: `Ret fun(const Type1 &a, const Type2 &b);` The signature does not need to have `const &`. The types Type1 and Type2 must be such that objects of types InputIt1 and InputIt2 can be dereferenced and then implicitly converted to Type1 and Type2 respectively. The type `Ret` must be such that an object of type `Type3` can be assigned a value of type `Ret`.
Type requirements
-`InputIt1, InputIt2` must meet the requirements of LegacyInputIterator.
-`ForwardIt1, ForwardIt2` must meet the requirements of LegacyForwardIterator.
-`T` must meet the requirements of CopyAssignable and CopyConstructible.

Return value

acc after all modifications.

Possible implementation

inner_product (1)
`template<class InputIt1, class InputIt2, class T> constexpr // since C++20 T inner_product(InputIt1 first1, InputIt1 last1, InputIt2 first2, T init) { while (first1 != last1) { init = std::move(init) + (first1) (*first2); // std::move since C++11 ++first1; ++first2; } return init; }`
inner_product (2)
`template<class InputIt1, class InputIt2, class T, class BinaryOperation1, class BinaryOperation2> constexpr // since C++20 T inner_product(InputIt1 first1, InputIt1 last1, InputIt2 first2, T init, BinaryOperation1 op1 BinaryOperation2 op2) { while (first1 != last1) { init = op1(std::move(init), op2(first1, first2)); // std::move since C++11 ++first1; ++first2; } return init; }`

inner_product (1)

template<class InputIt1, class InputIt2, class T>
constexpr // since C++20
T inner_product(InputIt1 first1, InputIt1 last1, InputIt2 first2, T init)
{
    while (first1 != last1)
    {
        init = std::move(init) + (*first1) * (*first2); // std::move since C++11
        ++first1;
        ++first2;
    }
 
    return init;
}

inner_product (2)

template<class InputIt1, class InputIt2, class T,
         class BinaryOperation1, class BinaryOperation2>
constexpr // since C++20
T inner_product(InputIt1 first1, InputIt1 last1,
                InputIt2 first2, T init,
                BinaryOperation1 op1
                BinaryOperation2 op2)
{
    while (first1 != last1)
    {
        init = op1(std::move(init), op2(*first1, *first2)); // std::move since C++11
        ++first1;
        ++first2;
    }
 
    return init;
}

Notes

The parallelizable version of this algorithm, std::transform_reduce, requires op1 and op2 to be commutative and associative, but std::inner_product makes no such requirement, and always performs the operations in the order given.

Example

#include <functional>
#include <iostream>
#include <numeric>
#include <vector>
 
int main()
{
    std::vector<int> a {0, 1, 2, 3, 4};
    std::vector<int> b {5, 4, 2, 3, 1};
 
    int r1 = std::inner_product(a.begin(), a.end(), b.begin(), 0);
    std::cout << "Inner product of a and b: " << r1 << '\n';
 
    int r2 = std::inner_product(a.begin(), a.end(), b.begin(), 0,
                                std::plus<>(), std::equal_to<>());
    std::cout << "Number of pairwise matches between a and b: " <<  r2 << '\n';
}

Output:

Inner product of a and b: 21
Number of pairwise matches between a and b: 2

Defect reports

The following behavior-changing defect reports were applied retroactively to previously published C++ standards.

DR	Applied to	Behavior as published	Correct behavior
LWG 242	C++98	`op1` and `op2` could not have side effects	they cannot modify the ranges involved
LWG 2055 (P0616R0)	C++11	`acc` was not moved while being accumulated	it is moved

transform_reduce (C++17)	applies an invocable, then reduces out of order (function template)
accumulate	sums up or folds a range of elements (function template)
partial_sum	computes the partial sum of a range of elements (function template)

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