std::exclusive_scan(3)

💅 std::exclusive_scan(3) 💅

okay bestie, welcome to the C++ Standard Library page for std::exclusive_scan — she's a <numeric> girlie, she's iconic, and she's about to hand you every prefix sum except the one you're standing on. periodt. 🎀

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✨ SYNOPSIS ✨

Defined in header <numeric>:

template< class InputIt, class OutputIt, class T >
OutputIt exclusive_scan( InputIt first, InputIt last,          (1)  (since C++17)
                         OutputIt d_first, T init );                (constexpr since C++20)

template< class ExecutionPolicy, class ForwardIt1, class ForwardIt2, class T >
ForwardIt2 exclusive_scan( ExecutionPolicy&& policy,            (2)  (since C++17)
                           ForwardIt1 first, ForwardIt1 last,
                           ForwardIt2 d_first, T init );

template< class InputIt, class OutputIt, class T, class BinaryOp >
OutputIt exclusive_scan( InputIt first, InputIt last,           (3)  (since C++17)
                         OutputIt d_first, T init,                   (constexpr since C++20)
                         BinaryOp op );

template< class ExecutionPolicy, class ForwardIt1, class ForwardIt2, class T, class BinaryOp >
ForwardIt2 exclusive_scan( ExecutionPolicy&& policy,             (4)  (since C++17)
                           ForwardIt1 first, ForwardIt1 last,
                           ForwardIt2 d_first, T init,
                           BinaryOp op );

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🦋 DESCRIPTION 🦋

so here's the tea, sip by sip 🍓

• (1) is literally equivalent to exclusive_scan(first, last, d_first, init, std::plus<>()).
• (3) computes the exclusive prefix sum using op. For each integer i in [0, std::distance(first, last)), it performs the following operations in order:
  1. Creates a sequence which is formed by init followed by the elements of [first, iter) in order, where iter is the next i-th iterator of first.
  2. Computes the generalized noncommutative sum of the sequence over op.
  3. Assigns the result to *dest, where dest is the next i-th iterator of d_first.
• (2,4) Same as (1,3), 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) — and since C++20 it's std::is_execution_policy_v<std::remove_cvref_t<ExecutionPolicy>> is true. no cap, that's the whole gatekeeping clause 🚪

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🌈 the generalized noncommutative sum, explained (iykyk)

The generalized noncommutative sum of a sequence of elements over a binary operation binary_op is defined as follows:

• If the sequence only has one element, the sum is the value of the element. that's it, that's the whole element 💀
• Otherwise, performs the following operations in order:
  1. Selects any two adjacent elements elem1 and elem2 from the sequence.
  2. Calculates binary_op(elem1, elem2) and replaces the two elements in the sequence with the result.
  3. Repeats steps 1 and 2 until there is only one element in the sequence.

Given binary_op as the actual binary operation:

• The result is non-deterministic if the binary_op is not associative (such as floating-point addition). 😭 yes girl, the order is genuinely chaos — don't come for me, come for the float.
• If any of the following values is not convertible to T, the program is ill-formed:
  • binary_op(init, *first)
  • binary_op(init, init)
  • binary_op(*first, *first)
• If any of the following conditions is satisfied, the behavior is undefined — say it with me, U-B, undefined 🫶:
  • T is not MoveConstructible.
  • binary_op modifies any element of [first, last).
  • binary_op invalidates any iterator or subrange of [first, last).

🚨 bestie listen: that undefined-behavior list is not a vibe, it's a warning. Don't let your binary_op touch the input range. Just don't.

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💖 PARAMETERS 💖

• first, last — the range of elements to sum ✨
• d_first — the beginning of the destination range; may be equal to first 👀 (yes, in-place is allowed, slay)
• policy — the execution policy to use. See execution policy for details.
• init — the initial value 🌱
• op — binary FunctionObject that will be applied in to the result of dereferencing the input iterators, the results of other op, and init

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🌸 TYPE REQUIREMENTS 🌸

• InputIt must meet the requirements of LegacyInputIterator.
• OutputIt must meet the requirements of LegacyOutputIterator.
• ForwardIt1, ForwardIt2 must meet the requirements of LegacyForwardIterator.

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⭐ RETURN VALUE ⭐

Iterator to the element past the last element written. she points one past the end, main character energy 👑

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🔥 COMPLEXITY 🔥

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

• 1,2) O(N) applications of std::plus<>().
• 3,4) O(N) applications of op.

linear, bestie. she ate and left no crumbs 🍽️

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🙈 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.

💀 yeah, standard policy + exception = std::terminate. no rescue mission. plan accordingly.

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🧚 EXAMPLE 🧚

// Run this code

#include <functional>
#include <iostream>
#include <iterator>
#include <numeric>
#include <vector>

int main()
{
    std::vector data{3, 1, 4, 1, 5, 9, 2, 6};

    std::cout << "Exclusive sum: ";
    std::exclusive_scan(data.begin(), data.end(),
                        std::ostream_iterator<int>(std::cout, " "),
                        0);

    std::cout << "\nInclusive sum: ";
    std::inclusive_scan(data.begin(), data.end(),
                        std::ostream_iterator<int>(std::cout, " "));

    std::cout << "\n\nExclusive product: ";
    std::exclusive_scan(data.begin(), data.end(),
                        std::ostream_iterator<int>(std::cout, " "),
                        1, std::multiplies<>{});

    std::cout << "\nInclusive product: ";
    std::inclusive_scan(data.begin(), data.end(),
                        std::ostream_iterator<int>(std::cout, " "),
                        std::multiplies<>{});
}

Output:

Exclusive sum: 0 3 4 8 9 14 23 25
Inclusive sum: 3 4 8 9 14 23 25 31

Exclusive product: 1 3 3 12 12 60 540 1080
Inclusive product: 3 3 12 12 60 540 1080 6480

see how the exclusive one starts with your init and then lags one behind? that's the whole bit. she's the ex-clusive scan for a reason 💔✨

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👑 SEE ALSO 👑

• adjacent_difference — computes the differences between adjacent elements in a range (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)
• transform_exclusive_scan (C++17) — applies an invocable, then calculates exclusive scan (function template)
• inclusive_scan (C++17) — similar to std::partial_sum, includes the i^th input element in the i^th sum (function template)

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okay that's the whole page, go forth and scan exclusively 🦋💜

this vibey lil rewrite comes to you from http://cppreference.com, dated 2024.06.10 — original page std::exclusive_scan(3) in the C++ Standard Library. mwah, bye bestie 💅🎀