No Such Thing as a Dumb Question (Unless You're On Stack Overflow)

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

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.)

A: You are a victim of branch prediction fail.

What is Branch Prediction?

Consider a railroad junction:

Image showing a railroad junction Image by Mecanismo, via Wikimedia Commons. Used under the CC-By-SA 3.0 license.

Now for the sake of argument, suppose this is back in the 1800s - before long-distance or radio communication.

You are a blind operator of a junction and you hear a train coming. You have no idea which way it is supposed to go. You stop the train to ask the driver which direction they want. And then you set the switch appropriately.

Trains are heavy and have a lot of inertia, so they take forever to start up and slow down.

Is there a better way? You guess which direction the train will go!

If you guessed right, it continues on.
If you guessed wrong, the driver will stop, back up, and yell at you to flip the switch. Then it can restart down the other path.
If you guess right every time, the train will never have to stop.
If you guess wrong too often, the train will spend a lot of time stopping, backing up, and restarting.

Consider an if-statement: At the processor level, it is a branch instruction:

if(x >= 128) compiles into a jump-if-less-than processor instruction.

You are a processor and you see a branch. You have no idea which way it will go. What do you do? You halt execution and wait until the previous instructions are complete. Then you continue down the correct path.

Modern processors are complicated and have long pipelines. This means they take forever to "warm up" and "slow down".

Is there a better way? You guess which direction the branch will go!

If you guessed right, you continue executing.
If you guessed wrong, you need to flush the pipeline and roll back to the branch. Then you can restart down the other path.
If you guess right every time, the execution will never have to stop.
If you guess wrong too often, you spend a lot of time stalling, rolling back, and restarting.

This is branch prediction. I admit it's not the best analogy since the train could just signal the direction with a flag. But in computers, the processor doesn't know which direction a branch will go until the last moment.

How would you strategically guess to minimize the number of times that the train must back up and go down the other path? You look at the past history! If the train goes left 99% of the time, then you guess left. If it alternates, then you alternate your guesses. If it goes one way every three times, you guess the same...

In other words, you try to identify a pattern and follow it. This is more or less how branch predictors work.

Most applications have well-behaved branches. Therefore, modern branch predictors will typically achieve >90% hit rates. But when faced with unpredictable branches with no recognizable patterns, branch predictors are virtually useless.

Further reading: "Branch predictor" article on Wikipedia.

Loop makes only a single iteration. It gives me 105.0 every single time, and it's supposed to do more iterations than just a single one. Also, I need to write more details because "my post is mostly code", but I can't say anything else because there's anything else to say, I guess.

import java.util.Scanner;

public class Esercizio {

    public static void main(String[] args) {

        int giorniDieciAnni, mesiDieciAnni, anniDieciAnni;
        giorniDieciAnni = 365*10;
        mesiDieciAnni = 12*10;
        anniDieciAnni = 10;

        System.out.println("");
        System.out.println("Interessatoio!");
        System.out.println("");
        System.out.println("Scrivi un saldo, un interesse, e calcolero':");
        System.out.println("");
        System.out.println("Interesse annuale: una volta l'anno, per 10 anni.");
        System.out.println("Interesse mensile: una volta al mese, per 10 anni.");
        System.out.println("Interesse giornaliero: una volta al giorno per 10 anni.");
        System.out.println("");
        System.out.println("Scrivi un importo per il saldo: massimo due cifre decimali.");
        System.out.println("");

        Scanner tastiera = new Scanner(System.in);
        double saldo, interesse, saldoAnnuale = 0, valoreInteresse = 0;
        saldo = tastiera.nextDouble();

        System.out.println("");
        System.out.println("Inserire ora un tasso di interesse: massimo due cifre decimali.");
        System.out.println("");

        interesse = tastiera.nextDouble();
        valoreInteresse = ((saldo/100)*interesse);
        int conteggio = 1;

        do {
            saldoAnnuale = (saldo + valoreInteresse); 
            conteggio++;
            } while (conteggio <= 10);

        System.out.println("Saldo Annuale Prova: " + saldoAnnuale);


    }
}