/C++

# std::remainder, std::remainderf, std::remainderl

Defined in header `<cmath>`
```float       remainder ( float x, float y );
float       remainderf( float x, float y );```
(1) (since C++11)
`double      remainder ( double x, double y );`
(2) (since C++11)
```long double remainder ( long double x, long double y );
long double remainderl( long double x, long double y );```
(3) (since C++11)
`Promoted    remainder ( Arithmetic1 x, Arithmetic2 y );`
(4) (since C++11)
1-3) Computes the IEEE remainder of the floating point division operation `x/y`.
4) A set of overloads or a function template for all combinations of arguments of arithmetic type not covered by (1-3). If any argument has integral type, it is cast to `double`. If any other argument is `long double`, then the return type is `long double`, otherwise it is `double`.

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

In contrast to `std::fmod()`, the returned value is not guaranteed to have the same sign as `x`.

If the returned value is `0`, it will have the same sign as `x`.

### Parameters

 x, y - values of floating-point or integral types

### Return value

If successful, returns the IEEE floating-point remainder of the division `x/y` as defined above.

If a domain error occurs, an implementation-defined value is returned (NaN where supported).

If a range error occurs due to underflow, the correct result is returned.

If `y` is zero, but the domain error does not occur, zero is returned.

### Error handling

Errors are reported as specified in `math_errhandling`.

Domain error may occur if `y` is zero.

If the implementation supports IEEE floating-point arithmetic (IEC 60559),

• The current rounding mode has no effect.
• `FE_INEXACT` is never raised, the result is always exact.
• If `x` is ±∞ and `y` is not NaN, NaN is returned and `FE_INVALID` is raised
• If `y` is ±0 and `x` is not NaN, NaN is returned and `FE_INVALID` is raised
• If either argument is NaN, NaN is returned

POSIX requires that a domain error occurs if `x` is infinite or `y` is zero.

`std::fmod`, but not `std::remainder` is useful for doing silent wrapping of floating-point types to unsigned integer types: `(0.0 <= (y = std::fmod( std::rint(x), 65536.0 )) ? y : 65536.0 + y)` is in the range `[-0.0 .. 65535.0]`, which corresponds to `unsigned short`, but `std::remainder(std::rint(x), 65536.0)` is in the range `[-32767.0, +32768.0]`, which is outside of the range of `signed short`.

### Example

```#include <iostream>
#include <cmath>
#include <cfenv>

#pragma STDC FENV_ACCESS ON
int main()
{
std::cout << "remainder(+5.1, +3.0) = " << std::remainder(5.1,3) << '\n'
<< "remainder(-5.1, +3.0) = " << std::remainder(-5.1,3) << '\n'
<< "remainder(+5.1, -3.0) = " << std::remainder(5.1,-3) << '\n'
<< "remainder(-5.1, -3.0) = " << std::remainder(-5.1,-3) << '\n';

// special values
std::cout << "remainder(-0.0, 1.0) = " << std::remainder(-0.0, 1) << '\n'
<< "remainder(5.1, Inf) = " << std::remainder(5.1, INFINITY) << '\n';

// error handling
std::feclearexcept(FE_ALL_EXCEPT);
std::cout << "remainder(+5.1, 0) = " << std::remainder(5.1, 0) << '\n';
if(fetestexcept(FE_INVALID))
std::cout << "    FE_INVALID raised\n";
}```

Possible output:

```remainder(+5.1, +3.0) = -0.9
remainder(-5.1, +3.0) = 0.9
remainder(+5.1, -3.0) = -0.9
remainder(-5.1, -3.0) = 0.9
remainder(-0.0, 1.0) = -0
remainder(5.1, Inf) = 5.1
remainder(+5.1, 0) = -nan
FE_INVALID raised```