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

Rythm · Jan 13, 2024

In this C++ code, sorting the data (before the timed region) makes the primary loop ~6x 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.

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

Rythm

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