Sorting 32 bit ints is as fast as sorting 64 bit ints

Question

Here are things I believe are facts:

• Quick sort should be fairly cache friendly.
• A cache line of 64 bytes can contain 16 32-bit ints, or 8 64-bit ints.

Hypothesis:

• Sorting a vector of 32-bit integers should be faster than sorting a vector of 64-bit integers.

But when I run the code below I get the result:

i16 = 7.5168 
i32 = 7.3762 
i64 = 7.5758

Why am I not getting the results I want?

C++:

#include <iostream> 
#include <vector>
#include <cstdint>
#include <algorithm>
#include <chrono>


int main() {
  const int vlength = 100'000'000;
  const int maxI = 50'000;

  std::vector<int16_t> v16;
  for (int i = 0; i < vlength; ++i) {
    v16.push_back(int16_t(i%maxI));
  }
  std::random_shuffle(std::begin(v16), std::end(v16));
  std::vector<int32_t> v32;
  std::vector<int64_t> v64;
  for (int i = 0; i < vlength; ++i) {
    v32.push_back(int32_t(v16[i]));
    v64.push_back(int64_t(v16[i]));
  }

  auto t1 = std::chrono::high_resolution_clock::now();
  std::sort(std::begin(v16), std::end(v16));
  auto t2 = std::chrono::high_resolution_clock::now();
  std :: cout << "i16 = " << (std::chrono::duration_cast<std::chrono::duration<double>>(t2 - t1)).count() << std :: endl;

  t1 = std::chrono::high_resolution_clock::now();
  std::sort(std::begin(v32), std::end(v32));
  t2 = std::chrono::high_resolution_clock::now();
  std :: cout << "i32 = " << (std::chrono::duration_cast<std::chrono::duration<double>>(t2 - t1)).count() << std :: endl;

  t1 = std::chrono::high_resolution_clock::now();
  std::sort(std::begin(v64), std::end(v64));
  t2 = std::chrono::high_resolution_clock::now();
  std :: cout << "i64 = " << (std::chrono::duration_cast<std::chrono::duration<double>>(t2 - t1)).count() << std :: endl;

}

EDIT: In order to avoid the question of how cache friendly sort is, I've also tried the following code:

template <typename T>
inline void function_speed(T& vec) {
  for (auto& i : vec) {
    ++i;
  }
}

int main() {
  const int nIter = 1000;

  std::vector<int16_t> v16(1000000);
  std::vector<int32_t> v32(1000000);
  std::vector<int64_t> v64(1000000);



  auto t1 = std::chrono::high_resolution_clock::now();
  for (int i = 0; i < nIter; ++i) {
    function_speed(v16);
  }
  auto t2 = std::chrono::high_resolution_clock::now();
  std :: cout << "i16 = " << (std::chrono::duration_cast<std::chrono::duration<double>>(t2 - t1)).count()/double(nIter) << std :: endl;

  t1 = std::chrono::high_resolution_clock::now();
  for (int i = 0; i < nIter; ++i) {
    function_speed(v32);
  }
  t2 = std::chrono::high_resolution_clock::now();
  std :: cout << "i32 = " << (std::chrono::duration_cast<std::chrono::duration<double>>(t2 - t1)).count()/double(nIter) << std :: endl;

  t1 = std::chrono::high_resolution_clock::now();
  for (int i = 0; i < nIter; ++i) {
    function_speed(v64);
  }
  t2 = std::chrono::high_resolution_clock::now();
  std :: cout << "i64 = " << (std::chrono::duration_cast<std::chrono::duration<double>>(t2 - t1)).count()/double(nIter) << std :: endl;

}

Typical result:

i16 = 0.00618648
i32 = 0.00617911
i64 = 0.00606275

I know that proper benchmarking is a science of itself, perhaps I am doing to wrong.

EDIT2: By avoiding overflowing I am now starting to get more interesting results:

template <typename T>
inline void function_speed(T& vec) {
  for (auto& i : vec) {
    ++i;
    i %= 1000;
  }
}

Gives results such as:

i16 = 0.0143789
i32 = 0.00958941
i64 = 0.019691

If I instead do:

template <typename T>
inline void function_speed(T& vec) {
  for (auto& i : vec) {
    i = (i+1)%1000;
  }
}

I get:

i16 = 0.00939448
i32 = 0.00913768
i64 = 0.019615

Answer 1

Mistaken assumption; all O(N log N) sorting algorithms have to be cache-unfriendly for the vast majority of the N! possible inputs.

Furtehrmore, I think an optimizing compiler can remove the sorts outright, and an unoptimized build will of course be pointless to benchmark.