Why "is_modulo" is false for double and float?

Question

I wrote some code to check if a type has a modulo representation:

#include <iostream>
#include <limits>

using namespace std;

int main( )
{
    cout << "Whether float objects have a modulo representation: "
         << numeric_limits<float>::is_modulo << endl;
    cout << "Whether double objects have a modulo representation: "
         << numeric_limits<double>::is_modulo << endl;
}

Output:

Whether float objects have a modulo representation: 0
Whether double objects have a modulo representation: 0

But we can use fmod() (from <math.h>) to find modulo of float or double. So, why is is_modulo false if it is possible to find a modulo of a float or double?

score 6 · Accepted Answer · answered Aug 26 '15 at 15:16

From cppreference

The value of std::numeric_limits<T>::is_modulo is true for all arithmetic types T that handle overflows with modulo arithmetic, that is, if the result of addition, subtraction, multiplication, or division of this type would fall outside the range [min(), max()], the value returned by such operation differs from the expected value by a multiple of max()-min()+1.

Overflow of floating point numbers is undefined behavior, therefore std::numeric_limits::is_modulo for float and double is false.

score 3 · Answer 2 · answered Aug 26 '15 at 15:22

This has nothing to do with fmod. Arbitrary operations on a floating-point value are irrelevant.

Whether one has "a modulo representation" is like how unsigned ints automatically wrap-around.

Neither floats nor doubles do that, and is_modulo is false accordingly.

score 2 · Answer 3 · answered Aug 26 '15 at 15:16

As described here:

The value of std::numeric_limits<T>::is_modulo is true for all arithmetic types T that handle overflows with modulo arithmetic, that is, if the result of addition, subtraction, multiplication, or division of this type would fall outside the range [min(), max()], the value returned by such operation differs from the expected value by a multiple of max()-min()+1.

so it does not say about 'finding modulo' but how a + b will behave. Floating point arithmetics do not overflows as integer arithmetics can.

Why "is_modulo" is false for double and float?

3 Answers3