std::adjacent_difference

Defined in header `<numeric>`
	(1)
template< class InputIt, class OutputIt > OutputIt adjacent_difference( InputIt first, InputIt last, OutputIt d_first );			(until C++20)
template< class InputIt, class OutputIt > constexpr OutputIt adjacent_difference( InputIt first, InputIt last, OutputIt d_first );			(since C++20)
template< class ExecutionPolicy, class ForwardIt1, class ForwardIt2 > ForwardIt2 adjacent_difference( ExecutionPolicy&& policy, ForwardIt1 first, ForwardIt1 last, ForwardIt2 d_first );		(2)	(since C++17)
		(3)
template< class InputIt, class OutputIt, class BinaryOperation > OutputIt adjacent_difference( InputIt first, InputIt last, OutputIt d_first, BinaryOperation op );				(until C++20)
template< class InputIt, class OutputIt, class BinaryOperation > constexpr OutputIt adjacent_difference( InputIt first, InputIt last, OutputIt d_first, BinaryOperation op );				(since C++20)
template< class ExecutionPolicy, class ForwardIt1, class ForwardIt2, class BinaryOperation > ForwardIt2 adjacent_difference( ExecutionPolicy&& policy, ForwardIt1 first, ForwardIt1 last, ForwardIt2 d_first, BinaryOperation op );			(4)	(since C++17)

If [first, last) is not empty, computes the differences between the second and the first of each adjacent pair of its elements and writes the differences to the range beginning at d_first + 1. An unmodified copy of *first is written to *d_first. Overloads (1,2) use operator- to calculate the differences, overloads (3,4) use the given binary function op, all applying std::move to their operands on the right hand side (since C++11).

Equivalent operation for overload (1), if [first, last) is not empty, uses the accumulator acc to store the value to be subtracted:

std::iterator_traits<InputIt>::value_type acc = *first;
*d_first = acc;
 
std::iterator_traits<InputIt>::value_type val1 = *(first + 1);
*(d_first + 1) = val1 - std::move(acc);
// or *(d_first + 1) = op(val1, std::move(acc)); for overload (2)
acc = std::move(val1);
 
std::iterator_traits<InputIt>::value_type val2 = *(first + 2);
*(d_first + 2) = val2 - std::move(acc);
acc = std::move(val2);
 
std::iterator_traits<InputIt>::value_type val3 = *(first + 3);
*(d_first + 3) = val3 - std::move(acc);
acc = std::move(val3);
// ...

Equivalent operation for overload (3), if [first, last) is not empty:

// performed first
*d_first = *first;
 
// performed after the initial assignment, might not be sequenced
*(d_first + 1) = *(first + 1) - *(first);
// or *(d_first + 1) = op(*(first + 1), *(first)); for overload (4)
*(d_first + 2) = *(first + 2) - *(first + 1);
*(d_first + 3) = *(first + 3) - *(first + 2);
...

If op invalidates any iterator (including any of the end iterators) or modify any elements of the ranges involved, the behavior is undefined.

For overloads (1,3), if std::iterator_traits<InputIt>::value_type is not CopyAssignable (until C++11)MoveAssignable (since C++11), the behavior is undefined.

Parameters

first, last	-	the range of elements
d_first	-	the beginning of the destination range
policy	-	the execution policy to use. See execution policy for details.
op	-	binary operation function object that will be applied. 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 an object of type iterator_traits<InputIt>::value_type can be implicitly converted to both of them. The type Ret must be such that an object of type OutputIt can be dereferenced and assigned a value of type Ret.
Type requirements
- `InputIt` must meet the requirements of LegacyInputIterator. For overloads (1,3), its value type must be constructible from *first.
- `OutputIt` must meet the requirements of LegacyOutputIterator. acc (defined above) and the result of val - acc (for (1)) or op(val, acc) (for (3)) (until C++11)val - std::move(acc) (for (1)) or op(val, std::move(acc)) (for (3)) (since C++11) must be writable to d_first.
- `ForwardIt1, ForwardIt2` must meet the requirements of LegacyForwardIterator. The result of first and the result of first - first (for (2)) or op(first, *first) (for (4)) must be writable to d_first.

Return value

Iterator to the element past the last element written, or d_first if [first, last) is empty.

Complexity

Given N as std::distance(first, last) - 1:

1,2) exactly N applications of operator-

3,4) exactly N applications of the binary function op

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.

Possible implementation

adjacent_difference (1)

template<class InputIt, class OutputIt>
constexpr // since C++20
OutputIt adjacent_difference(InputIt first, InputIt last, OutputIt d_first)
{
    if (first == last)
        return d_first;
 
    typedef typename std::iterator_traits<InputIt>::value_type value_t;
    value_t acc = *first;
    *d_first = acc;
 
    while (++first != last)
    {
        value_t val = *first;
        *++d_first = val - std::move(acc); // std::move since C++11
        acc = std::move(val);
    }
 
    return ++d_first;
}

adjacent_difference (3)

template<class InputIt, class OutputIt, class BinaryOperation>
constexpr // since C++20
OutputIt adjacent_difference(InputIt first, InputIt last, 
                             OutputIt d_first, BinaryOperation op)
{
    if (first == last)
        return d_first;
 
    typedef typename std::iterator_traits<InputIt>::value_type value_t;
    value_t acc = *first;
    *d_first = acc;
 
    while (++first != last)
    {
        value_t val = *first;
        *++d_first = op(val, std::move(acc)); // std::move since C++11
        acc = std::move(val);
    }
 
    return ++d_first;
}

Notes

acc was introduced because of the resolution of LWG issue 539. The reason of using acc rather than directly calculating the differences is because the semantic of the latter is confusing if the following types mismatch:

the value type of InputIt
the writable type(s) of OutputIt
the types of the parameters of operator- or op
the return type of operator- or op

acc serves as the intermediate object to cache values of the iterated elements:

its type is the value type of InputIt
the value written to d_first (which is the return value of operator- or op) is assigned to it
its value is passed to operator- or op

char i_array[4] = {100, 100, 100, 100};
int  o_array[4];
 
// OK: performs conversions when needed
// 1. creates `acc` of type char (the value type)
// 2. `acc` is assigned to the first element of `o_array`
// 3. the char arguments are used for long multiplication (char -> long)
// 4. the long product is assigned to the output range (long -> int)
// 5. the next value of `i_array` is assigned to `acc`
// 6. go back to step 3 to process the remaining elements in the input range
std::adjacent_difference(i_array, i_array + 4, o_array, std::multiplies<long>{});

Example

Run this code

#include <array>
#include <functional>
#include <iostream>
#include <iterator>
#include <numeric>
#include <vector>
 
auto print = [](auto comment, auto const& sequence)
{
    std::cout << comment;
    for (const auto& n : sequence)
        std::cout << n << ' ';
    std::cout << '\n';
};
 
int main()
{
    // Default implementation - the difference b/w two adjacent items
    std::vector v {4, 6, 9, 13, 18, 19, 19, 15, 10};
    print("Initially, v = ", v);
    std::adjacent_difference(v.begin(), v.end(), v.begin());
    print("Modified v = ", v);
 
    // Fibonacci
    std::array<int, 10> a {1};
    std::adjacent_difference(std::begin(a), std::prev(std::end(a)),
                             std::next(std::begin(a)), std::plus<>{});
    print("Fibonacci, a = ", a);
}

Output:

Initially, v = 4 6 9 13 18 19 19 15 10 
Modified v = 4 2 3 4 5 1 0 -4 -5 
Fibonacci, a = 1 1 2 3 5 8 13 21 34 55

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	op could not have side effects	it cannot modify the ranges involved
LWG 539	C++98	the type requirements needed for the result evaluations and assignments to be valid were missing	added
LWG 2055 (P0616R0)	C++11	acc was not moved while being accumulated	it is moved
LWG 3058	C++17	for overloads (2,4), the result of each invocation of operator- or op was assigned to a temporary object, and that object is assigned to the output range	assign the results to the output range directly

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External libraries

partial_sum	computes the partial sum of a range of elements (function template)
accumulate	sums up or folds a range of elements (function template)