Precisely sum up floats while avoiding rising precision loss

precisesum.cpp

#include <algorithm>
using std::for_each;
using std::reverse;

#include <cmath>
using std::modf;

#include <iomanip>
using std::left;
using std::setprecision;
using std::setw;

#include <iostream>
using std::cout;

#include <numeric>
using std::accumulate;

#include <vector>
using std::begin;
using std::end;
using std::vector;


float sumNaive(vector<float> const & floats)
{
    return accumulate(begin(floats), end(floats), 0.0f);
}

double sumDouble(vector<float> const & floats)
{
    double result = 0;
    
    for (auto f : floats)
        result += f;

    return result;
}

float sumNormalized(vector<float> const & floats)
{
    int integerSum = 0;
    float floatSum = 0.0f;

    for_each(begin(floats), end(floats), [&integerSum, &floatSum] (float num) {
        float integer;
        floatSum += modf(num, &integer);
        integerSum += static_cast<int>(integer);
    });

    return integerSum + floatSum;
}

float sumStrictlyNormalized(vector<float> const & floats)
{
    int integerSum = 0;
    float floatSum = 0.0f;

    for_each(begin(floats), end(floats), [&integerSum, &floatSum] (float num) {
        float integer;
        
        if (floatSum > 1) {
            floatSum = modf(floatSum, &integer);
            integerSum += static_cast<int>(integer);
        }

        floatSum += modf(num, &integer);
        integerSum += static_cast<int>(integer);
    });

    return integerSum + floatSum;
}

template<class SORTED_VECTOR_ITERATOR>
float recursiveSum(SORTED_VECTOR_ITERATOR itBegin, SORTED_VECTOR_ITERATOR itEnd) {
	auto d = std::distance(itBegin, itEnd);
	if (d == 1)
		return *itBegin;
	return recursiveSum(itBegin, itBegin + d / 2) + recursiveSum(itBegin + d / 2, itEnd);
}

float preciseSum(vector<float> const & floats)
{
        return recursiveSum(begin(floats), end(floats));
}

float getRandomFloat()
{
    return static_cast<float>(rand()) / static_cast<float>(RAND_MAX);
}

vector<float> getRandomFloats(unsigned int amount)
{
    vector<float> result;

    for (unsigned int i = 0; i < amount; ++i)
        result.push_back(getRandomFloat());

    return result;
}

int main()
{
    auto floats = getRandomFloats(10'000'000);
    cout << setprecision(10) << left;

    cout << "### Unsorted ###\n";
    cout << setw(21) << "Double: " << sumDouble(floats) << "\n";
    cout << setw(21) << "Naive: " << sumNaive(floats) << "\n";
    cout << setw(21) << "Normalized: " << sumNormalized(floats) << "\n";
    cout << setw(21) << "Strictly normalized: " << sumStrictlyNormalized(floats) << "\n";
    cout << setw(21) << "Precise sum: " << preciseSum(floats) << "\n";

    sort(begin(floats), end(floats));
    cout << "### Sorted ###\n";
    cout << setw(21) << "Double: " << sumDouble(floats) << "\n";
    cout << setw(21) << "Naive: " << sumNaive(floats) << "\n";
    cout << setw(21) << "Normalized: " << sumNormalized(floats) << "\n";
    cout << setw(21) << "Strictly normalized: " << sumStrictlyNormalized(floats) << "\n";
    cout << setw(21) << "Precise sum: " << preciseSum(floats) << "\n";

    reverse(begin(floats), end(floats));
    cout << "### Revese sorted ###\n";
    cout << setw(21) << "Double: " << sumDouble(floats) << "\n";
    cout << setw(21) << "Naive: " << sumNaive(floats) << "\n";
    cout << setw(21) << "Normalized: " << sumNormalized(floats) << "\n";
    cout << setw(21) << "Strictly normalized: " << sumStrictlyNormalized(floats) << "\n";
    cout << setw(21) << "Precise sum: " << preciseSum(floats) << "\n";
    return 0;
}