Difference between revisions of "cpp/algorithm/reduce"

Latest revision as of 00:21, 18 April 2024

Given binary_op as the actual binary operation:

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

• If any of the following values is not convertible to T, the program is ill-formed:

• binary_op(init, *first)
• binary_op(*first, init)
• binary_op(init, init)
• binary_op(*first, *first)

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

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

[edit] Parameters

[edit] Return value

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:

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

[edit] Complexity

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

[edit] 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.

[edit] Notes

std::reduce behaves like std::accumulate except the elements of the range may be grouped and rearranged in arbitrary order.

[edit] Example

#if PARALLEL
#include <execution>
#define SEQ std::execution::seq,
#define PAR std::execution::par,
#else
#define SEQ
#define PAR
#endif
 
#include <chrono>
#include <iomanip>
#include <iostream>
#include <numeric>
#include <utility>
#include <vector>
 
int main()
{
    std::cout.imbue(std::locale("en_US.UTF-8"));
    std::cout << std::fixed << std::setprecision(1);
 
    auto eval = [](auto fun)
    {
        const auto t1 = std::chrono::high_resolution_clock::now();
        const auto [name, result] = fun();
        const auto t2 = std::chrono::high_resolution_clock::now();
        const std::chrono::duration<double, std::milli> ms = t2 - t1;
        std::cout << std::setw(28) << std::left << name << "sum: "
                  << result << '\t' << "time: " << ms.count() << " ms\n";
    };
 
    {
        const std::vector<double> v(100'000'007, 0.1);
 
        eval([&v]{ return std::pair{"std::accumulate (double)",
            std::accumulate(v.cbegin(), v.cend(), 0.0)}; });
        eval([&v]{ return std::pair{"std::reduce (seq, double)",
            std::reduce(SEQ v.cbegin(), v.cend())}; });
        eval([&v]{ return std::pair{"std::reduce (par, double)",
            std::reduce(PAR v.cbegin(), v.cend())}; });
    }
 
    {
        const std::vector<long> v(100'000'007, 1);
 
        eval([&v]{ return std::pair{"std::accumulate (long)",
            std::accumulate(v.cbegin(), v.cend(), 0l)}; });
        eval([&v]{ return std::pair{"std::reduce (seq, long)",
            std::reduce(SEQ v.cbegin(), v.cend())}; });
        eval([&v]{ return std::pair{"std::reduce (par, long)",
            std::reduce(PAR v.cbegin(), v.cend())}; });
    }
}

// POSIX: g++ -std=c++23 ./example.cpp -ltbb -O3; ./a.out
std::accumulate (double)    sum: 10,000,000.7	time: 356.9 ms
std::reduce (seq, double)   sum: 10,000,000.7	time: 140.1 ms
std::reduce (par, double)   sum: 10,000,000.7	time: 140.1 ms
std::accumulate (long)      sum: 100,000,007	time: 46.0 ms
std::reduce (seq, long)     sum: 100,000,007	time: 67.3 ms
std::reduce (par, long)     sum: 100,000,007	time: 63.3 ms
 
// POSIX: g++ -std=c++23 ./example.cpp -ltbb -O3 -DPARALLEL; ./a.out
std::accumulate (double)    sum: 10,000,000.7	time: 353.4 ms
std::reduce (seq, double)   sum: 10,000,000.7	time: 140.7 ms
std::reduce (par, double)   sum: 10,000,000.7	time: 24.7 ms
std::accumulate (long)      sum: 100,000,007	time: 42.4 ms
std::reduce (seq, long)     sum: 100,000,007	time: 52.0 ms
std::reduce (par, long)     sum: 100,000,007	time: 23.1 ms

[edit] See also