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Why is processing a sorted array faster than processing an unsorted array?

Here is a piece of C++ code that shows some very peculiar behavior.

For some reason, sorting the data (before the timed region) miraculously makes the primary loop almost six times faster:

#include <algorithm>
#include <ctime>
#include <iostream>

int main()
{
    // Generate data
    const unsigned arraySize = 32768;
    int data[arraySize];

    for (unsigned c = 0; c < arraySize; ++c)
        data[c] = std::rand() % 256;

    // !!! With this, the next loop runs faster.
    std::sort(data, data + arraySize);

    // Test
    clock_t start = clock();
    long long sum = 0;
    for (unsigned i = 0; i < 100000; ++i)
    {
        for (unsigned c = 0; c < arraySize; ++c)
        {   // Primary loop.
            if (data[c] >= 128)
                sum += data[c];
        }
    }

    double elapsedTime = static_cast<double>(clock()-start) / CLOCKS_PER_SEC;

    std::cout << elapsedTime << '\n';
    std::cout << "sum = " << sum << '\n';
}
  • Without std::sort(data, data + arraySize);, the code runs in 11.54 seconds.
  • With the sorted data, the code runs in 1.93 seconds.

(Sorting itself takes more time than this one pass over the array, so it's not actually worth doing if we needed to calculate this for an unknown array.)


Initially, I thought this might be just a language or compiler anomaly, so I tried Java:

import java.util.Arrays;
import java.util.Random;

public class Main
{
    public static void main(String[] args)
    {
        // Generate data
        int arraySize = 32768;
        int data[] = new int[arraySize];

        Random rnd = new Random(0);
        for (int c = 0; c < arraySize; ++c)
            data[c] = rnd.nextInt() % 256;

        // !!! With this, the next loop runs faster
        Arrays.sort(data);

        // Test
        long start = System.nanoTime();
        long sum = 0;
        for (int i = 0; i < 100000; ++i)
        {
            for (int c = 0; c < arraySize; ++c)
            {   // Primary loop.
                if (data[c] >= 128)
                    sum += data[c];
            }
        }

        System.out.println((System.nanoTime() - start) / 1000000000.0);
        System.out.println("sum = " + sum);
    }
}

With a similar but less extreme result.


My first thought was that sorting brings the data into the cache, but that's silly because the array was just generated.

  • What is going on?
  • Why is processing a sorted array faster than processing an unsorted array?

The code is summing up some independent terms, so the order should not matter.


Related / follow-up Q&As about the same effect with different/later compilers and options:

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2
  • 7
    That is a very interesting article (in fact, I have just read all of it), but how does it answer the question? Mar 16, 2018 at 12:47
  • 5
    @PeterMortensen I am a bit flummoxed by your question. For example here is one relevant line from that piece: When the input is unsorted, all the rest of the loop takes substantial time. But with sorted input, the processor is somehow able to spend not just less time in the body of the loop, meaning the buckets at offsets 0x18 and 0x1C, but vanishingly little time on the mechanism of looping. Author is trying to discuss profiling in the context of code posted here and in the process trying to explain why the sorted case is so much more faster. Mar 16, 2018 at 15:37