Why is the remainder function giving me the wrong remainder in some cases?

Question

This might be a very long-winded question, and I'm new to this site, so my formatting will probably be incorrect but please, bear with me.

I am currently experimenting with the remainder() function. In the case of this exercise program, I am writing code that will tell you how long it will take you to travel 1 mile at a given speed in miles per hour. This is the code I have written (please excuse my use of "using namespace std;" and other suboptimal if not downright appalling practices, I'm only doing as my textbook says until I get more comfortable):

#include <iostream>
#include <conio.h>
#include <cmath> 

using namespace std;

int main(int argc, char *argv[])
{
    char ans1, ans2;
    double mph, pace, pace_secs;
    int pace_mins;

    do
    {
        do
        {
            cout << "Please input a speed (in miles per hour) to be converted to a standard pace\n";
            cin >> mph;

            cout << "You have entered " << mph << " miles per hour, is this correct?\n";
            cin >> ans1;
        } while (ans1 != 'y' && ans1 != 'Y');

        pace = (3600 / mph);
        pace_mins = (pace / 60);
        pace_secs = remainder(pace, 60); 

        cout << "If you are running at " << mph << " miles per hour it will take you ";

        if (pace_mins == 1)
            cout << pace_mins << " minute and ";
        else
            cout << pace_mins << " minutes and ";

        cout << pace_secs << " seconds to run one mile\n";
        cout << "Would you like to run the program again?\n";
        cin >> ans2;
    } while (ans2 != 'n' && ans2 != 'N');

    return 0;
}

What has me confused is that this code works fine for my purposes but only up to a certain point.

For instance, if I input "6.5" as the 'mph' the program delivers the correct answer of 9 minutes and 13.84 seconds to cover a single mile (the program delivers the correct answer for several other values as well).

However, if I instead input "15.1" as the 'mph' the program delivers the time it will take as 3 minutes and -1.5894 seconds to cover a mile. Upon initial glance it is clear to me that the program is delivering the "opposite" of the remainder so to speak. The remainder should be about 58.41 seconds, but instead it is subtracting 60 from 58.41 and is giving me the result in its place.

I am still very new to c++ so I really can't figure out why this is the case. Any help would be much appreciated.

Answer 1

Instead of making assumptions based on a function name, always read the documentation or a reference for the library function before using it.

std::remainder is specified exactly in the way you see it behave:

The IEEE floating-point remainder of the division operation x / y calculated by this function is exactly the value x - quo * y, where the value quo is the integral value nearest the exact value x / y. When |quo - x / y| = ½, the value quo is chosen to be even.

However, from your description it seems like you actually want std::fmod:

The floating-point remainder of the division operation x / y calculated by this function is exactly the value x - rem * y, where rem is x / y with its fractional part truncated.